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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
// Copyright (C) 2008-2014 Gael Guennebaud <>
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at
#include "./InternalHeaderCheck.h"
namespace Eigen {
/** \ingroup SparseCore_Module
* \class SparseMatrixBase
* \brief Base class of any sparse matrices or sparse expressions
* \tparam Derived is the derived type, e.g. a sparse matrix type, or an expression, etc.
* This class can be extended with the help of the plugin mechanism described on the page
* \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_SPARSEMATRIXBASE_PLUGIN.
template<typename Derived> class SparseMatrixBase
: public EigenBase<Derived>
typedef typename internal::traits<Derived>::Scalar Scalar;
/** The numeric type of the expression' coefficients, e.g. float, double, int or std::complex<float>, etc.
* It is an alias for the Scalar type */
typedef Scalar value_type;
typedef typename internal::packet_traits<Scalar>::type PacketScalar;
typedef typename internal::traits<Derived>::StorageKind StorageKind;
/** The integer type used to \b store indices within a SparseMatrix.
* For a \c SparseMatrix<Scalar,Options,IndexType> it an alias of the third template parameter \c IndexType. */
typedef typename internal::traits<Derived>::StorageIndex StorageIndex;
typedef typename internal::add_const_on_value_type_if_arithmetic<
typename internal::packet_traits<Scalar>::type
>::type PacketReturnType;
typedef SparseMatrixBase StorageBaseType;
typedef Matrix<StorageIndex,Dynamic,1> IndexVector;
typedef Matrix<Scalar,Dynamic,1> ScalarVector;
template<typename OtherDerived>
Derived& operator=(const EigenBase<OtherDerived> &other);
enum {
RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
/**< The number of rows at compile-time. This is just a copy of the value provided
* by the \a Derived type. If a value is not known at compile-time,
* it is set to the \a Dynamic constant.
* \sa MatrixBase::rows(), MatrixBase::cols(), ColsAtCompileTime, SizeAtCompileTime */
ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
/**< The number of columns at compile-time. This is just a copy of the value provided
* by the \a Derived type. If a value is not known at compile-time,
* it is set to the \a Dynamic constant.
* \sa MatrixBase::rows(), MatrixBase::cols(), RowsAtCompileTime, SizeAtCompileTime */
SizeAtCompileTime = (internal::size_of_xpr_at_compile_time<Derived>::ret),
/**< This is equal to the number of coefficients, i.e. the number of
* rows times the number of columns, or to \a Dynamic if this is not
* known at compile-time. \sa RowsAtCompileTime, ColsAtCompileTime */
MaxRowsAtCompileTime = RowsAtCompileTime,
MaxColsAtCompileTime = ColsAtCompileTime,
MaxSizeAtCompileTime = internal::size_at_compile_time(MaxRowsAtCompileTime, MaxColsAtCompileTime),
IsVectorAtCompileTime = RowsAtCompileTime == 1 || ColsAtCompileTime == 1,
/**< This is set to true if either the number of rows or the number of
* columns is known at compile-time to be equal to 1. Indeed, in that case,
* we are dealing with a column-vector (if there is only one column) or with
* a row-vector (if there is only one row). */
NumDimensions = int(MaxSizeAtCompileTime) == 1 ? 0 : bool(IsVectorAtCompileTime) ? 1 : 2,
/**< This value is equal to Tensor::NumDimensions, i.e. 0 for scalars, 1 for vectors,
* and 2 for matrices.
Flags = internal::traits<Derived>::Flags,
/**< This stores expression \ref flags flags which may or may not be inherited by new expressions
* constructed from this one. See the \ref flags "list of flags".
IsRowMajor = Flags&RowMajorBit ? 1 : 0,
InnerSizeAtCompileTime = int(IsVectorAtCompileTime) ? int(SizeAtCompileTime)
: int(IsRowMajor) ? int(ColsAtCompileTime) : int(RowsAtCompileTime),
HasDirectAccess_ = (int(Flags)&DirectAccessBit) ? 1 : 0 // workaround sunCC
/** \internal the return type of MatrixBase::adjoint() */
typedef std::conditional_t<NumTraits<Scalar>::IsComplex,
CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, Eigen::Transpose<const Derived> >,
Transpose<const Derived>
> AdjointReturnType;
typedef Transpose<Derived> TransposeReturnType;
typedef Transpose<const Derived> ConstTransposeReturnType;
// FIXME storage order do not match evaluator storage order
typedef SparseMatrix<Scalar, Flags&RowMajorBit ? RowMajor : ColMajor, StorageIndex> PlainObject;
/** This is the "real scalar" type; if the \a Scalar type is already real numbers
* (e.g. int, float or double) then \a RealScalar is just the same as \a Scalar. If
* \a Scalar is \a std::complex<T> then RealScalar is \a T.
* \sa class NumTraits
typedef typename NumTraits<Scalar>::Real RealScalar;
/** \internal the return type of coeff()
typedef std::conditional_t<HasDirectAccess_, const Scalar&, Scalar> CoeffReturnType;
/** \internal Represents a matrix with all coefficients equal to one another*/
typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>,Matrix<Scalar,Dynamic,Dynamic> > ConstantReturnType;
/** type of the equivalent dense matrix */
typedef Matrix<Scalar,RowsAtCompileTime,ColsAtCompileTime> DenseMatrixType;
/** type of the equivalent square matrix */
typedef Matrix<Scalar, internal::max_size_prefer_dynamic(RowsAtCompileTime, ColsAtCompileTime),
internal::max_size_prefer_dynamic(RowsAtCompileTime, ColsAtCompileTime)> SquareMatrixType;
inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
inline Derived& derived() { return *static_cast<Derived*>(this); }
inline Derived& const_cast_derived() const
{ return *static_cast<Derived*>(const_cast<SparseMatrixBase*>(this)); }
typedef EigenBase<Derived> Base;
#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::SparseMatrixBase
#define EIGEN_DOC_UNARY_ADDONS(METHOD,OP) /** <p>This method does not change the sparsity of \c *this: the OP is applied to explicitly stored coefficients only. \sa SparseCompressedBase::coeffs() </p> */
#define EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL /** <p> \warning This method returns a read-only expression for any sparse matrices. \sa \ref TutorialSparse_SubMatrices "Sparse block operations" </p> */
#define EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(COND) /** <p> \warning This method returns a read-write expression for COND sparse matrices only. Otherwise, the returned expression is read-only. \sa \ref TutorialSparse_SubMatrices "Sparse block operations" </p> */
# include "../plugins/CommonCwiseUnaryOps.h"
# include "../plugins/CommonCwiseBinaryOps.h"
# include "../plugins/MatrixCwiseUnaryOps.h"
# include "../plugins/MatrixCwiseBinaryOps.h"
# include "../plugins/BlockMethods.h"
# endif
/** \returns the number of rows. \sa cols() */
inline Index rows() const { return derived().rows(); }
/** \returns the number of columns. \sa rows() */
inline Index cols() const { return derived().cols(); }
/** \returns the number of coefficients, which is \a rows()*cols().
* \sa rows(), cols(). */
inline Index size() const { return rows() * cols(); }
/** \returns true if either the number of rows or the number of columns is equal to 1.
* In other words, this function returns
* \code rows()==1 || cols()==1 \endcode
* \sa rows(), cols(), IsVectorAtCompileTime. */
inline bool isVector() const { return rows()==1 || cols()==1; }
/** \returns the size of the storage major dimension,
* i.e., the number of columns for a columns major matrix, and the number of rows otherwise */
Index outerSize() const { return (int(Flags)&RowMajorBit) ? this->rows() : this->cols(); }
/** \returns the size of the inner dimension according to the storage order,
* i.e., the number of rows for a columns major matrix, and the number of cols otherwise */
Index innerSize() const { return (int(Flags)&RowMajorBit) ? this->cols() : this->rows(); }
bool isRValue() const { return m_isRValue; }
Derived& markAsRValue() { m_isRValue = true; return derived(); }
SparseMatrixBase() : m_isRValue(false) { /* TODO check flags */ }
template<typename OtherDerived>
Derived& operator=(const ReturnByValue<OtherDerived>& other);
template<typename OtherDerived>
inline Derived& operator=(const SparseMatrixBase<OtherDerived>& other);
inline Derived& operator=(const Derived& other);
template<typename OtherDerived>
inline Derived& assign(const OtherDerived& other);
template<typename OtherDerived>
inline void assignGeneric(const OtherDerived& other);
#ifndef EIGEN_NO_IO
friend std::ostream & operator << (std::ostream & s, const SparseMatrixBase& m)
typedef typename Derived::Nested Nested;
typedef internal::remove_all_t<Nested> NestedCleaned;
if (Flags&RowMajorBit)
Nested nm(m.derived());
internal::evaluator<NestedCleaned> thisEval(nm);
for (Index row=0; row<nm.outerSize(); ++row)
Index col = 0;
for (typename internal::evaluator<NestedCleaned>::InnerIterator it(thisEval, row); it; ++it)
for ( ; col<it.index(); ++col)
s << "0 ";
s << it.value() << " ";
for ( ; col<m.cols(); ++col)
s << "0 ";
s << std::endl;
Nested nm(m.derived());
internal::evaluator<NestedCleaned> thisEval(nm);
if (m.cols() == 1) {
Index row = 0;
for (typename internal::evaluator<NestedCleaned>::InnerIterator it(thisEval, 0); it; ++it)
for ( ; row<it.index(); ++row)
s << "0" << std::endl;
s << it.value() << std::endl;
for ( ; row<m.rows(); ++row)
s << "0" << std::endl;
SparseMatrix<Scalar, RowMajorBit, StorageIndex> trans = m;
s << static_cast<const SparseMatrixBase<SparseMatrix<Scalar, RowMajorBit, StorageIndex> >&>(trans);
return s;
template<typename OtherDerived>
Derived& operator+=(const SparseMatrixBase<OtherDerived>& other);
template<typename OtherDerived>
Derived& operator-=(const SparseMatrixBase<OtherDerived>& other);
template<typename OtherDerived>
Derived& operator+=(const DiagonalBase<OtherDerived>& other);
template<typename OtherDerived>
Derived& operator-=(const DiagonalBase<OtherDerived>& other);
template<typename OtherDerived>
Derived& operator+=(const EigenBase<OtherDerived> &other);
template<typename OtherDerived>
Derived& operator-=(const EigenBase<OtherDerived> &other);
Derived& operator*=(const Scalar& other);
Derived& operator/=(const Scalar& other);
template<typename OtherDerived> struct CwiseProductDenseReturnType {
typedef CwiseBinaryOp<internal::scalar_product_op<typename ScalarBinaryOpTraits<
typename internal::traits<Derived>::Scalar,
typename internal::traits<OtherDerived>::Scalar
const Derived,
const OtherDerived
> Type;
template<typename OtherDerived>
EIGEN_STRONG_INLINE const typename CwiseProductDenseReturnType<OtherDerived>::Type
cwiseProduct(const MatrixBase<OtherDerived> &other) const;
// sparse * diagonal
template<typename OtherDerived>
const Product<Derived,OtherDerived>
operator*(const DiagonalBase<OtherDerived> &other) const
{ return Product<Derived,OtherDerived>(derived(), other.derived()); }
// diagonal * sparse
template<typename OtherDerived> friend
const Product<OtherDerived,Derived>
operator*(const DiagonalBase<OtherDerived> &lhs, const SparseMatrixBase& rhs)
{ return Product<OtherDerived,Derived>(lhs.derived(), rhs.derived()); }
// sparse * sparse
template<typename OtherDerived>
const Product<Derived,OtherDerived,AliasFreeProduct>
operator*(const SparseMatrixBase<OtherDerived> &other) const;
// sparse * dense
template<typename OtherDerived>
const Product<Derived,OtherDerived>
operator*(const MatrixBase<OtherDerived> &other) const
{ return Product<Derived,OtherDerived>(derived(), other.derived()); }
// dense * sparse
template<typename OtherDerived> friend
const Product<OtherDerived,Derived>
operator*(const MatrixBase<OtherDerived> &lhs, const SparseMatrixBase& rhs)
{ return Product<OtherDerived,Derived>(lhs.derived(), rhs.derived()); }
/** \returns an expression of P H P^-1 where H is the matrix represented by \c *this */
SparseSymmetricPermutationProduct<Derived,Upper|Lower> twistedBy(const PermutationMatrix<Dynamic,Dynamic,StorageIndex>& perm) const
return SparseSymmetricPermutationProduct<Derived,Upper|Lower>(derived(), perm);
template<typename OtherDerived>
Derived& operator*=(const SparseMatrixBase<OtherDerived>& other);
template<int Mode>
inline const TriangularView<const Derived, Mode> triangularView() const;
template<unsigned int UpLo> struct SelfAdjointViewReturnType { typedef SparseSelfAdjointView<Derived, UpLo> Type; };
template<unsigned int UpLo> struct ConstSelfAdjointViewReturnType { typedef const SparseSelfAdjointView<const Derived, UpLo> Type; };
template<unsigned int UpLo> inline
typename ConstSelfAdjointViewReturnType<UpLo>::Type selfadjointView() const;
template<unsigned int UpLo> inline
typename SelfAdjointViewReturnType<UpLo>::Type selfadjointView();
template<typename OtherDerived> Scalar dot(const MatrixBase<OtherDerived>& other) const;
template<typename OtherDerived> Scalar dot(const SparseMatrixBase<OtherDerived>& other) const;
RealScalar squaredNorm() const;
RealScalar norm() const;
RealScalar blueNorm() const;
TransposeReturnType transpose() { return TransposeReturnType(derived()); }
const ConstTransposeReturnType transpose() const { return ConstTransposeReturnType(derived()); }
const AdjointReturnType adjoint() const { return AdjointReturnType(transpose()); }
DenseMatrixType toDense() const
return DenseMatrixType(derived());
template<typename OtherDerived>
bool isApprox(const SparseMatrixBase<OtherDerived>& other,
const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
template<typename OtherDerived>
bool isApprox(const MatrixBase<OtherDerived>& other,
const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const
{ return toDense().isApprox(other,prec); }
/** \returns the matrix or vector obtained by evaluating this expression.
* Notice that in the case of a plain matrix or vector (not an expression) this function just returns
* a const reference, in order to avoid a useless copy.
inline const typename internal::eval<Derived>::type eval() const
{ return typename internal::eval<Derived>::type(derived()); }
Scalar sum() const;
inline const SparseView<Derived>
pruned(const Scalar& reference = Scalar(0), const RealScalar& epsilon = NumTraits<Scalar>::dummy_precision()) const;
bool m_isRValue;
static inline StorageIndex convert_index(const Index idx) {
return internal::convert_index<StorageIndex>(idx);
template<typename Dest> void evalTo(Dest &) const;
} // end namespace Eigen