#include <SymShiftInvert.h>

Public Types
using	Scalar = Scalar_

Public Member Functions
Index	cols () const

void	perform_op (const Scalar x_in, Scalar y_out) const

Index	rows () const

void	set_shift (const Scalar &sigma)

template<typename DerivedA , typename DerivedB >
	SymShiftInvert (const Eigen::EigenBase< DerivedA > &A, const Eigen::EigenBase< DerivedB > &B)

Private Types
using	ASparse = std::is_same< TypeA, Eigen::Sparse >

using	BSparse = std::is_same< TypeB, Eigen::Sparse >

using	ConstGenericMatrixA = const Eigen::Ref< const MatrixA >

using	ConstGenericMatrixB = const Eigen::Ref< const MatrixB >

using	DenseType = typename std::conditional< ASparse::value, MatrixB, MatrixA >::type

using	DenseTypeA = Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic, FlagsA >

using	DenseTypeB = Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic, FlagsB >

using	FacType = typename std::conditional< ASparse::value &&BSparse::value, Eigen::SparseLU< ResType >, BKLDLT< Scalar > >::type

using	Index = Eigen::Index

using	MapConstVec = Eigen::Map< const Vector >

using	MapVec = Eigen::Map< Vector >

using	MatrixA = typename std::conditional< ASparse::value, SparseTypeA, DenseTypeA >::type

using	MatrixB = typename std::conditional< BSparse::value, SparseTypeB, DenseTypeB >::type

using	ResType = typename std::conditional< ASparse::value &&BSparse::value, MatrixA, DenseType >::type

using	SparseTypeA = Eigen::SparseMatrix< Scalar, FlagsA, StorageIndexA >

using	SparseTypeB = Eigen::SparseMatrix< Scalar, FlagsB, StorageIndexB >

using	Vector = Eigen::Matrix< Scalar, Eigen::Dynamic, 1 >

Private Attributes
ConstGenericMatrixA	m_matA

ConstGenericMatrixB	m_matB

const Index	m_n

FacType	m_solver

Detailed Description

template<typename Scalar_, typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse, int UploA = Eigen::Lower, int UploB = Eigen::Lower, int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor, typename StorageIndexA = int, typename StorageIndexB = int>
class Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB >

This class defines matrix operations required by the generalized eigen solver in the shift-and-invert mode. Given two symmetric matrices $A$ and $B$ , it solves the linear equation $y=(A-\sigma B)^{-1}x$ , where $\sigma$ is a real shift. Each of $A$ and $B$ can be a dense or sparse matrix.

This class is intended to be used with the SymGEigsShiftSolver generalized eigen solver.

Template Parameters

Scalar_	The element type of the matrices. Currently supported types are `float`, `double`, and `long double`.
TypeA	The type of the matrix, indicating whether is dense or sparse. Possible values are `Eigen::Dense` and `Eigen::Sparse`.
TypeB	The type of the matrix, indicating whether is dense or sparse. Possible values are `Eigen::Dense` and `Eigen::Sparse`.
UploA	Whether the lower or upper triangular part of should be used. Possible values are `Eigen::Lower` and `Eigen::Upper`.
UploB	Whether the lower or upper triangular part of should be used. Possible values are `Eigen::Lower` and `Eigen::Upper`.
FlagsA	Additional flags for the matrix class of . Possible values are `Eigen::ColMajor` and `Eigen::RowMajor`.
FlagsB	Additional flags for the matrix class of . Possible values are `Eigen::ColMajor` and `Eigen::RowMajor`.
StorageIndexA	The storage index type of the matrix, only used when is a sparse matrix.
StorageIndexB	The storage index type of the matrix, only used when is a sparse matrix.

Definition at line 127 of file SymShiftInvert.h.

Member Typedef Documentation

◆ ASparse

template<typename Scalar_ , typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse, int UploA = Eigen::Lower, int UploB = Eigen::Lower, int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor, typename StorageIndexA = int, typename StorageIndexB = int>

using Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB >::ASparse = std::is_same<TypeA, Eigen::Sparse>

private

Definition at line 142 of file SymShiftInvert.h.

◆ BSparse

template<typename Scalar_ , typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse, int UploA = Eigen::Lower, int UploB = Eigen::Lower, int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor, typename StorageIndexA = int, typename StorageIndexB = int>

using Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB >::BSparse = std::is_same<TypeB, Eigen::Sparse>

private

Definition at line 150 of file SymShiftInvert.h.

◆ ConstGenericMatrixA

template<typename Scalar_ , typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse, int UploA = Eigen::Lower, int UploB = Eigen::Lower, int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor, typename StorageIndexA = int, typename StorageIndexB = int>

using Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB >::ConstGenericMatrixA = const Eigen::Ref<const MatrixA>

private

Definition at line 172 of file SymShiftInvert.h.

◆ ConstGenericMatrixB

template<typename Scalar_ , typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse, int UploA = Eigen::Lower, int UploB = Eigen::Lower, int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor, typename StorageIndexA = int, typename StorageIndexB = int>

using Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB >::ConstGenericMatrixB = const Eigen::Ref<const MatrixB>

private

Definition at line 173 of file SymShiftInvert.h.

◆ DenseType

template<typename Scalar_ , typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse, int UploA = Eigen::Lower, int UploB = Eigen::Lower, int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor, typename StorageIndexA = int, typename StorageIndexB = int>

using Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB >::DenseType = typename std::conditional<ASparse::value, MatrixB, MatrixA>::type

private

Definition at line 160 of file SymShiftInvert.h.

◆ DenseTypeA

template<typename Scalar_ , typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse, int UploA = Eigen::Lower, int UploB = Eigen::Lower, int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor, typename StorageIndexA = int, typename StorageIndexB = int>

using Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB >::DenseTypeA = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, FlagsA>

private

Definition at line 139 of file SymShiftInvert.h.

◆ DenseTypeB

template<typename Scalar_ , typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse, int UploA = Eigen::Lower, int UploB = Eigen::Lower, int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor, typename StorageIndexA = int, typename StorageIndexB = int>

using Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB >::DenseTypeB = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, FlagsB>

private

Definition at line 147 of file SymShiftInvert.h.

◆ FacType

template<typename Scalar_ , typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse, int UploA = Eigen::Lower, int UploB = Eigen::Lower, int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor, typename StorageIndexA = int, typename StorageIndexB = int>

using Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB >::FacType = typename std::conditional< ASparse::value && BSparse::value, Eigen::SparseLU<ResType>, BKLDLT<Scalar> >::type

private

Definition at line 170 of file SymShiftInvert.h.

◆ Index

template<typename Scalar_ , typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse, int UploA = Eigen::Lower, int UploB = Eigen::Lower, int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor, typename StorageIndexA = int, typename StorageIndexB = int>

using Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB >::Index = Eigen::Index

private

Definition at line 136 of file SymShiftInvert.h.

◆ MapConstVec

template<typename Scalar_ , typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse, int UploA = Eigen::Lower, int UploB = Eigen::Lower, int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor, typename StorageIndexA = int, typename StorageIndexB = int>

using Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB >::MapConstVec = Eigen::Map<const Vector>

private

Definition at line 155 of file SymShiftInvert.h.

◆ MapVec

template<typename Scalar_ , typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse, int UploA = Eigen::Lower, int UploB = Eigen::Lower, int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor, typename StorageIndexA = int, typename StorageIndexB = int>

using Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB >::MapVec = Eigen::Map<Vector>

private

Definition at line 156 of file SymShiftInvert.h.

◆ MatrixA

template<typename Scalar_ , typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse, int UploA = Eigen::Lower, int UploB = Eigen::Lower, int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor, typename StorageIndexA = int, typename StorageIndexB = int>

using Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB >::MatrixA = typename std::conditional<ASparse::value, SparseTypeA, DenseTypeA>::type

private

Definition at line 144 of file SymShiftInvert.h.

◆ MatrixB

template<typename Scalar_ , typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse, int UploA = Eigen::Lower, int UploB = Eigen::Lower, int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor, typename StorageIndexA = int, typename StorageIndexB = int>

using Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB >::MatrixB = typename std::conditional<BSparse::value, SparseTypeB, DenseTypeB>::type

private

Definition at line 152 of file SymShiftInvert.h.

◆ ResType

template<typename Scalar_ , typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse, int UploA = Eigen::Lower, int UploB = Eigen::Lower, int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor, typename StorageIndexA = int, typename StorageIndexB = int>

using Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB >::ResType = typename std::conditional<ASparse::value && BSparse::value, MatrixA, DenseType>::type

private

Definition at line 163 of file SymShiftInvert.h.

◆ Scalar

template<typename Scalar_ , typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse, int UploA = Eigen::Lower, int UploB = Eigen::Lower, int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor, typename StorageIndexA = int, typename StorageIndexB = int>

using Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB >::Scalar = Scalar_

Element type of the matrix.

Definition at line 133 of file SymShiftInvert.h.

◆ SparseTypeA

template<typename Scalar_ , typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse, int UploA = Eigen::Lower, int UploB = Eigen::Lower, int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor, typename StorageIndexA = int, typename StorageIndexB = int>

using Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB >::SparseTypeA = Eigen::SparseMatrix<Scalar, FlagsA, StorageIndexA>

private

Definition at line 140 of file SymShiftInvert.h.

◆ SparseTypeB

template<typename Scalar_ , typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse, int UploA = Eigen::Lower, int UploB = Eigen::Lower, int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor, typename StorageIndexA = int, typename StorageIndexB = int>

using Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB >::SparseTypeB = Eigen::SparseMatrix<Scalar, FlagsB, StorageIndexB>

private

Definition at line 148 of file SymShiftInvert.h.

◆ Vector

template<typename Scalar_ , typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse, int UploA = Eigen::Lower, int UploB = Eigen::Lower, int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor, typename StorageIndexA = int, typename StorageIndexB = int>

using Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB >::Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>

private

Definition at line 154 of file SymShiftInvert.h.

Constructor & Destructor Documentation

◆ SymShiftInvert()

template<typename Scalar_ , typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse, int UploA = Eigen::Lower, int UploB = Eigen::Lower, int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor, typename StorageIndexA = int, typename StorageIndexB = int>

template<typename DerivedA , typename DerivedB >

Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB >::SymShiftInvert	(	const Eigen::EigenBase< DerivedA > &	A,
		const Eigen::EigenBase< DerivedB > &	B
	)

inline

Constructor to create the matrix operation object.

Parameters

A	A dense or sparse matrix object, whose type can be `Eigen::Matrix<...>`, `Eigen::SparseMatrix<...>`, `Eigen::Map<Eigen::Matrix<...>>`, `Eigen::Map<Eigen::SparseMatrix<...>>`, `Eigen::Ref<Eigen::Matrix<...>>`, `Eigen::Ref<Eigen::SparseMatrix<...>>`, etc.
B	A dense or sparse matrix object.

Definition at line 191 of file SymShiftInvert.h.

Member Function Documentation

◆ cols()

template<typename Scalar_ , typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse, int UploA = Eigen::Lower, int UploB = Eigen::Lower, int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor, typename StorageIndexA = int, typename StorageIndexB = int>

Index Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB >::cols ( ) const

inline

Return the number of columns of the underlying matrix.

Definition at line 213 of file SymShiftInvert.h.

◆ perform_op()

template<typename Scalar_ , typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse, int UploA = Eigen::Lower, int UploB = Eigen::Lower, int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor, typename StorageIndexA = int, typename StorageIndexB = int>

void Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB >::perform_op	(	const Scalar *	x_in,
		Scalar *	y_out
	)		const

inline

Perform the shift-invert operation $y=(A-\sigma B)^{-1}x$ .

Parameters

x_in	Pointer to the vector.
y_out	Pointer to the vector.

Definition at line 235 of file SymShiftInvert.h.

◆ rows()

template<typename Scalar_ , typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse, int UploA = Eigen::Lower, int UploB = Eigen::Lower, int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor, typename StorageIndexA = int, typename StorageIndexB = int>

Index Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB >::rows ( ) const

inline

Return the number of rows of the underlying matrix.

Definition at line 209 of file SymShiftInvert.h.

◆ set_shift()

template<typename Scalar_ , typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse, int UploA = Eigen::Lower, int UploB = Eigen::Lower, int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor, typename StorageIndexA = int, typename StorageIndexB = int>

void Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB >::set_shift ( const Scalar & sigma )

inline

Set the real shift $\sigma$ .

Definition at line 218 of file SymShiftInvert.h.

Member Data Documentation

◆ m_matA

template<typename Scalar_ , typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse, int UploA = Eigen::Lower, int UploB = Eigen::Lower, int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor, typename StorageIndexA = int, typename StorageIndexB = int>

ConstGenericMatrixA Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB >::m_matA

private

Definition at line 175 of file SymShiftInvert.h.

◆ m_matB

template<typename Scalar_ , typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse, int UploA = Eigen::Lower, int UploB = Eigen::Lower, int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor, typename StorageIndexA = int, typename StorageIndexB = int>

ConstGenericMatrixB Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB >::m_matB

private

Definition at line 176 of file SymShiftInvert.h.

◆ m_n

template<typename Scalar_ , typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse, int UploA = Eigen::Lower, int UploB = Eigen::Lower, int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor, typename StorageIndexA = int, typename StorageIndexB = int>

const Index Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB >::m_n

private

Definition at line 177 of file SymShiftInvert.h.

◆ m_solver

template<typename Scalar_ , typename TypeA = Eigen::Sparse, typename TypeB = Eigen::Sparse, int UploA = Eigen::Lower, int UploB = Eigen::Lower, int FlagsA = Eigen::ColMajor, int FlagsB = Eigen::ColMajor, typename StorageIndexA = int, typename StorageIndexB = int>

FacType Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB >::m_solver

private

Definition at line 178 of file SymShiftInvert.h.

The documentation for this class was generated from the following file:

SymShiftInvert.h

Public Types

Public Member Functions

Private Types

Private Attributes

Detailed Description

Member Typedef Documentation

◆ ASparse

◆ BSparse

◆ ConstGenericMatrixA

◆ ConstGenericMatrixB

◆ DenseType

◆ DenseTypeA

◆ DenseTypeB

◆ FacType

◆ Index

◆ MapConstVec

◆ MapVec

◆ MatrixA

◆ MatrixB

◆ ResType

◆ Scalar

◆ SparseTypeA

◆ SparseTypeB

◆ Vector

Constructor & Destructor Documentation

◆ SymShiftInvert()

Member Function Documentation

◆ cols()

◆ perform_op()

◆ rows()

◆ set_shift()

Member Data Documentation

◆ m_matA

◆ m_matB

◆ m_n

◆ m_solver