Classes
class	Arnoldi

class	ArnoldiOp

class	ArnoldiOp< Scalar, OpType, IdentityBOp >

class	BKLDLT

class	DavidsonSymEigsSolver

class	DenseCholesky

class	DenseGenComplexShiftSolve

class	DenseGenMatProd

class	DenseGenRealShiftSolve

class	DenseHermMatProd

class	DenseSymMatProd

class	DenseSymShiftSolve

class	DoubleShiftQR

class	GenEigsBase

class	GenEigsComplexShiftSolver

class	GenEigsRealShiftSolver

class	GenEigsSolver

class	HermEigsBase

class	HermEigsSolver

class	IdentityBOp

class	JDSymEigsBase

class	Lanczos

class	LOBPCGSolver

class	PartialSVDSolver

class	RitzPairs

struct	ScalarOp

struct	ScalarOp< std::complex< RealScalar > >

class	SearchSpace

class	SparseCholesky

class	SparseGenComplexShiftSolve

class	SparseGenMatProd

class	SparseGenRealShiftSolve

class	SparseHermMatProd

class	SparseRegularInverse

class	SparseSymMatProd

class	SparseSymShiftSolve

class	SVDMatOp

class	SVDTallMatOp

class	SVDWideMatOp

class	SymEigsShiftSolver

class	SymEigsSolver

class	SymGEigsBucklingOp

class	SymGEigsCayleyOp

class	SymGEigsCholeskyOp

class	SymGEigsRegInvOp

class	SymGEigsShiftInvertOp

class	SymGEigsShiftSolver

class	SymGEigsShiftSolver< OpType, BOpType, GEigsMode::Buckling >

class	SymGEigsShiftSolver< OpType, BOpType, GEigsMode::Cayley >

class	SymGEigsShiftSolver< OpType, BOpType, GEigsMode::ShiftInvert >

class	SymGEigsSolver

class	SymGEigsSolver< OpType, BOpType, GEigsMode::Cholesky >

class	SymGEigsSolver< OpType, BOpType, GEigsMode::RegularInverse >

class	SymShiftInvert

class	TridiagEigen

class	TridiagQR

class	UpperHessenbergEigen

class	UpperHessenbergQR

class	UpperHessenbergSchur

Functions
template<typename Matrix >
void	assert_left_cols_to_skip (Matrix &in_output, Eigen::Index left_cols_to_skip)

template<typename Matrix >
void	GS_orthogonalisation (Matrix &in_output, Eigen::Index left_cols_to_skip=0)

template<typename Matrix >
void	JensWehner_orthogonalisation (Matrix &in_output, Eigen::Index left_cols_to_skip=0)

template<typename Matrix >
void	MGS_orthogonalisation (Matrix &in_output, Eigen::Index left_cols_to_skip=0)

template<typename Matrix >
void	QR_orthogonalisation (Matrix &in_output)

template<typename Matrix >
void	subspace_orthogonalisation (Matrix &in_output, Eigen::Index left_cols_to_skip)

template<typename Matrix >
Eigen::Index	treat_first_col (Matrix &in_output, Eigen::Index left_cols_to_skip)

template<typename Matrix >
void	twice_is_enough_orthogonalisation (Matrix &in_output, Eigen::Index left_cols_to_skip=0)

Function Documentation

◆ assert_left_cols_to_skip()

template<typename Matrix >

void Spectra::assert_left_cols_to_skip	(	Matrix &	in_output,
		Eigen::Index	left_cols_to_skip
	)

Check if the number of columns to skip is larger than 0 but smaller than the total number of columns of the matrix

Parameters

in_output	Matrix to be orthogonalized
left_cols_to_skip	Number of left columns to be left untouched

Definition at line 21 of file Orthogonalization.h.

◆ GS_orthogonalisation()

template<typename Matrix >

void Spectra::GS_orthogonalisation	(	Matrix &	in_output,
		Eigen::Index	left_cols_to_skip = `0`
	)

Orthogonalize the in_output matrix using a Gram Schmidt process

Parameters

in_output	matrix to be orthogonalized
left_cols_to_skip	Number of left columns to be left untouched

Definition at line 80 of file Orthogonalization.h.

◆ JensWehner_orthogonalisation()

template<typename Matrix >

void Spectra::JensWehner_orthogonalisation	(	Matrix &	in_output,
		Eigen::Index	left_cols_to_skip = `0`
	)

Orthogonalize the in_output matrix using a Jens process The subspace spanned by right columns are first orthogonalized agains the left columns, and then a QR decomposition is applied on the right columns to make them orthogonalized agains each other

Parameters

in_output	Matrix to be orthogonalized
left_cols_to_skip	Number of left columns to be left untouched

Definition at line 119 of file Orthogonalization.h.

◆ MGS_orthogonalisation()

template<typename Matrix >

void Spectra::MGS_orthogonalisation	(	Matrix &	in_output,
		Eigen::Index	left_cols_to_skip = `0`
	)

Orthogonalize the in_output matrix using a modified Gram Schmidt process

Parameters

in_output	matrix to be orthogonalized
left_cols_to_skip	Number of left columns to be left untouched

Definition at line 61 of file Orthogonalization.h.

◆ QR_orthogonalisation()

template<typename Matrix >

void Spectra::QR_orthogonalisation ( Matrix & in_output )

Orthogonalize the in_output matrix using a QR decomposition

Parameters

in_output Matrix to be orthogonalized

Definition at line 46 of file Orthogonalization.h.

◆ subspace_orthogonalisation()

template<typename Matrix >

void Spectra::subspace_orthogonalisation	(	Matrix &	in_output,
		Eigen::Index	left_cols_to_skip
	)

Orthogonalize the subspace spanned by right columns of in_output against the subspace spanned by left columns It assumes that the left columns are already orthogonal and normalized, and it does not orthogonalize the left columns against each other

Parameters

in_output	Matrix to be orthogonalized
left_cols_to_skip	Number of left columns to be left untouched

Definition at line 99 of file Orthogonalization.h.

◆ treat_first_col()

template<typename Matrix >

Eigen::Index Spectra::treat_first_col	(	Matrix &	in_output,
		Eigen::Index	left_cols_to_skip
	)

If the the number of columns to skip is null, normalize the first column and set left_cols_to_skip=1

Parameters

in_output	Matrix to be orthogonalized
left_cols_to_skip	Number of left columns to be left untouched

Returns: Actual number of left columns to skip

Definition at line 33 of file Orthogonalization.h.

◆ twice_is_enough_orthogonalisation()

template<typename Matrix >

void Spectra::twice_is_enough_orthogonalisation	(	Matrix &	in_output,
		Eigen::Index	left_cols_to_skip = `0`
	)

Orthogonalize the in_output matrix using a twice-is-enough Jens process

Parameters

in_output	Matrix to be orthogonalized
left_cols_to_skip	Number of left columns to be left untouched

Definition at line 133 of file Orthogonalization.h.

Enumerations
enum	CompInfo { CompInfo::Successful, CompInfo::NotComputed, CompInfo::NotConverging, CompInfo::NumericalIssue }

enum	GEigsMode { GEigsMode::Cholesky, GEigsMode::RegularInverse, GEigsMode::ShiftInvert, GEigsMode::Buckling, GEigsMode::Cayley }

enum	SortRule { SortRule::LargestMagn, SortRule::LargestReal, SortRule::LargestImag, SortRule::LargestAlge, SortRule::SmallestMagn, SortRule::SmallestReal, SortRule::SmallestImag, SortRule::SmallestAlge, SortRule::BothEnds }

Classes

Enumerations

Functions

Function Documentation

◆ assert_left_cols_to_skip()

◆ GS_orthogonalisation()

◆ JensWehner_orthogonalisation()

◆ MGS_orthogonalisation()

◆ QR_orthogonalisation()

◆ subspace_orthogonalisation()

◆ treat_first_col()

◆ twice_is_enough_orthogonalisation()