Spectra::SymShiftInvert< Scalar_, TypeA, TypeB, UploA, UploB, FlagsA, FlagsB, StorageIndexA, StorageIndexB > Class Template Reference

#include <Spectra/MatOp/SymShiftInvert.h>

Public Types
using	Scalar = Scalar_

Public Member Functions
template<typename DerivedA , typename DerivedB >
	SymShiftInvert (const Eigen::EigenBase< DerivedA > &A, const Eigen::EigenBase< DerivedB > &B)
Index	rows () const
Index	cols () const
void	set_shift (const Scalar &sigma)
void	perform_op (const Scalar *x_in, Scalar *y_out) const

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 \(A\) matrix, indicating whether \(A\) is dense or sparse. Possible values are Eigen::Dense and Eigen::Sparse.
TypeB	The type of the \(B\) matrix, indicating whether \(B\) is dense or sparse. Possible values are Eigen::Dense and Eigen::Sparse.
UploA	Whether the lower or upper triangular part of \(A\) should be used. Possible values are Eigen::Lower and Eigen::Upper.
UploB	Whether the lower or upper triangular part of \(B\) should be used. Possible values are Eigen::Lower and Eigen::Upper.
FlagsA	Additional flags for the matrix class of \(A\). Possible values are Eigen::ColMajor and Eigen::RowMajor.
FlagsB	Additional flags for the matrix class of \(B\). Possible values are Eigen::ColMajor and Eigen::RowMajor.
StorageIndexA	The storage index type of the \(A\) matrix, only used when \(A\) is a sparse matrix.
StorageIndexB	The storage index type of the \(B\) matrix, only used when \(B\) is a sparse matrix.

Definition at line 127 of file SymShiftInvert.h.

Member Typedef Documentation

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.

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

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.

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.

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.

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 \(x\) vector.
y_out	Pointer to the \(y\) vector.

Definition at line 235 of file SymShiftInvert.h.

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

• Spectra/MatOp/SymShiftInvert.h