| // Copyright John Maddock 2006, 2007 |
| // Copyright Paul A. Bristow 2007 |
| |
| // Use, modification and distribution are subject to the |
| // Boost Software License, Version 1.0. (See accompanying file |
| // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) |
| |
| #include <pch.hpp> |
| |
| #ifdef _MSC_VER |
| # pragma warning(disable : 4127) // conditional expression is constant |
| # pragma warning(disable : 4512) // assignment operator could not be generated |
| # pragma warning(disable : 4756) // overflow in constant arithmetic |
| // Constants are too big for float case, but this doesn't matter for test. |
| #endif |
| |
| #include <boost/math/concepts/real_concept.hpp> |
| #include <boost/test/test_exec_monitor.hpp> |
| #include <boost/test/floating_point_comparison.hpp> |
| #include <boost/math/special_functions/hermite.hpp> |
| #include <boost/math/constants/constants.hpp> |
| #include <boost/array.hpp> |
| #include "functor.hpp" |
| |
| #include "handle_test_result.hpp" |
| #include "test_legendre_hooks.hpp" |
| |
| // |
| // DESCRIPTION: |
| // ~~~~~~~~~~~~ |
| // |
| // This file tests the Hermite polynomials. |
| // There are two sets of tests, spot |
| // tests which compare our results with selected values computed |
| // using the online special function calculator at |
| // functions.wolfram.com, while the bulk of the accuracy tests |
| // use values generated with NTL::RR at 1000-bit precision |
| // and our generic versions of these functions. |
| // |
| // Note that when this file is first run on a new platform many of |
| // these tests will fail: the default accuracy is 1 epsilon which |
| // is too tight for most platforms. In this situation you will |
| // need to cast a human eye over the error rates reported and make |
| // a judgement as to whether they are acceptable. Either way please |
| // report the results to the Boost mailing list. Acceptable rates of |
| // error are marked up below as a series of regular expressions that |
| // identify the compiler/stdlib/platform/data-type/test-data/test-function |
| // along with the maximum expected peek and RMS mean errors for that |
| // test. |
| // |
| |
| void expected_results() |
| { |
| // |
| // Define the max and mean errors expected for |
| // various compilers and platforms. |
| // |
| const char* largest_type; |
| #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS |
| if(boost::math::policies::digits<double, boost::math::policies::policy<> >() == boost::math::policies::digits<long double, boost::math::policies::policy<> >()) |
| { |
| largest_type = "(long\\s+)?double"; |
| } |
| else |
| { |
| largest_type = "long double"; |
| } |
| #else |
| largest_type = "(long\\s+)?double"; |
| #endif |
| |
| // |
| // Catch all cases come last: |
| // |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| ".*", // test data group |
| "boost::math::hermite", 10, 5); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "real_concept", // test type(s) |
| ".*", // test data group |
| "boost::math::hermite", 10, 5); // test function |
| // |
| // Finish off by printing out the compiler/stdlib/platform names, |
| // we do this to make it easier to mark up expected error rates. |
| // |
| std::cout << "Tests run with " << BOOST_COMPILER << ", " |
| << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; |
| } |
| |
| template <class T> |
| void do_test_hermite(const T& data, const char* type_name, const char* test_name) |
| { |
| typedef typename T::value_type row_type; |
| typedef typename row_type::value_type value_type; |
| |
| typedef value_type (*pg)(unsigned, value_type); |
| #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) |
| pg funcp = boost::math::hermite<value_type>; |
| #else |
| pg funcp = boost::math::hermite; |
| #endif |
| |
| typedef unsigned (*cast_t)(value_type); |
| |
| boost::math::tools::test_result<value_type> result; |
| |
| std::cout << "Testing " << test_name << " with type " << type_name |
| << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n"; |
| |
| // |
| // test hermite against data: |
| // |
| result = boost::math::tools::test( |
| data, |
| bind_func_int1(funcp, 0, 1), |
| extract_result(2)); |
| handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::hermite", test_name); |
| |
| std::cout << std::endl; |
| } |
| |
| template <class T> |
| void test_hermite(T, const char* name) |
| { |
| // |
| // The actual test data is rather verbose, so it's in a separate file |
| // |
| // The contents are as follows, each row of data contains |
| // three items, input value a, input value b and erf(a, b): |
| // |
| # include "hermite.ipp" |
| |
| do_test_hermite(hermite, name, "Hermite Polynomials"); |
| } |
| |
| template <class T> |
| void test_spots(T, const char* t) |
| { |
| std::cout << "Testing basic sanity checks for type " << t << std::endl; |
| // |
| // basic sanity checks, tolerance is 100 epsilon: |
| // These spots were generated by MathCAD, precision is |
| // 14-16 digits. |
| // |
| T tolerance = (std::max)(boost::math::tools::epsilon<T>() * 100, static_cast<T>(1e-14)); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::hermite(0, static_cast<T>(1)), static_cast<T>(1.L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::hermite(1, static_cast<T>(1)), static_cast<T>(2.L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::hermite(1, static_cast<T>(2)), static_cast<T>(4.L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::hermite(1, static_cast<T>(10)), static_cast<T>(20), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::hermite(1, static_cast<T>(100)), static_cast<T>(200), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::hermite(1, static_cast<T>(1e6)), static_cast<T>(2e6), tolerance); |
| if(std::numeric_limits<T>::max_exponent >= std::numeric_limits<double>::max_exponent) |
| { |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::hermite(1, static_cast<T>(1e307)), static_cast<T>(2e307), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::hermite(99, static_cast<T>(100)), static_cast<T>(4.967223743011310E+227L), tolerance); |
| } |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::hermite(10, static_cast<T>(30)), static_cast<T>(5.896624628001300E+17L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::hermite(10, static_cast<T>(1000)), static_cast<T>(1.023976960161280E+33L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::hermite(10, static_cast<T>(10)), static_cast<T>(8.093278209760000E+12L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::hermite(10, static_cast<T>(-10)), static_cast<T>(8.093278209760000E+12L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::hermite(3, static_cast<T>(-10)), static_cast<T>(-7.880000000000000E+3L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::hermite(3, static_cast<T>(-1000)), static_cast<T>(-7.999988000000000E+9L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::hermite(3, static_cast<T>(-1000000)), static_cast<T>(-7.999999999988000E+18L), tolerance); |
| } |
| |
| int test_main(int, char* []) |
| { |
| BOOST_MATH_CONTROL_FP; |
| |
| boost::math::hermite(51, 915.0); |
| |
| #ifndef BOOST_MATH_BUGGY_LARGE_FLOAT_CONSTANTS |
| test_spots(0.0F, "float"); |
| #endif |
| test_spots(0.0, "double"); |
| #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS |
| test_spots(0.0L, "long double"); |
| test_spots(boost::math::concepts::real_concept(0.1), "real_concept"); |
| #endif |
| |
| expected_results(); |
| |
| #ifndef BOOST_MATH_BUGGY_LARGE_FLOAT_CONSTANTS |
| test_hermite(0.1F, "float"); |
| #endif |
| test_hermite(0.1, "double"); |
| #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS |
| test_hermite(0.1L, "long double"); |
| #ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS |
| test_hermite(boost::math::concepts::real_concept(0.1), "real_concept"); |
| #endif |
| #else |
| std::cout << "<note>The long double tests have been disabled on this platform " |
| "either because the long double overloads of the usual math functions are " |
| "not available at all, or because they are too inaccurate for these tests " |
| "to pass.</note>" << std::cout; |
| #endif |
| return 0; |
| } |
| |
| |
| |