#include <UpperHessenbergQR.h>

Inheritance diagram for Spectra::TridiagQR< Scalar >:

Public Member Functions
void	compute (ConstGenericMatrix &mat, const Scalar &shift=Scalar(0)) override

void	matrix_QtHQ (ComplexMatrix &dest) const

void	matrix_QtHQ (Matrix &dest) const override

Matrix	matrix_R () const override

	TridiagQR (ConstGenericMatrix &mat, const Scalar &shift=Scalar(0))

	TridiagQR (Index size)

Public Member Functions inherited from Spectra::UpperHessenbergQR< double >
void	apply_QtY (GenericMatrix Y) const

void	apply_QtY (Vector &Y) const

void	apply_QY (GenericMatrix Y) const

void	apply_QY (Vector &Y) const

void	apply_YQ (GenericMatrix Y) const

void	apply_YQt (GenericMatrix Y) const

virtual void	compute (ConstGenericMatrix &mat, const double &shift=double(0))

virtual void	matrix_QtHQ (Matrix &dest) const

virtual Matrix	matrix_R () const

	UpperHessenbergQR (ConstGenericMatrix &mat, const double &shift=double(0))

	UpperHessenbergQR (Index size)

virtual	~UpperHessenbergQR ()

Private Types
using	ComplexMatrix = Eigen::Matrix< std::complex< Scalar >, Eigen::Dynamic, Eigen::Dynamic >

using	ConstGenericMatrix = const Eigen::Ref< const Matrix >

using	Index = Eigen::Index

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

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

Private Attributes
Vector	m_R_diag

Vector	m_R_supd

Vector	m_R_supd2

Vector	m_T_diag

Vector	m_T_subd

Additional Inherited Members
Static Protected Member Functions inherited from Spectra::UpperHessenbergQR< double >
static void	compute_rotation (const double &x, const double &y, double &r, double &c, double &s)

static void	stable_scaling (const double &a, const double &b, double &r, double &c, double &s)

Protected Attributes inherited from Spectra::UpperHessenbergQR< double >
bool	m_computed

Index	m_n

Array	m_rot_cos

Array	m_rot_sin

double	m_shift

Detailed Description

template<typename Scalar = double>
class Spectra::TridiagQR< Scalar >

Perform the QR decomposition of a tridiagonal matrix, a special case of upper Hessenberg matrices.

Template Parameters

Scalar The element type of the matrix. Currently supported types are float, double and long double.

Definition at line 545 of file UpperHessenbergQR.h.

Member Typedef Documentation

◆ ComplexMatrix

template<typename Scalar = double>

using Spectra::TridiagQR< Scalar >::ComplexMatrix = Eigen::Matrix<std::complex<Scalar>, Eigen::Dynamic, Eigen::Dynamic>

private

Definition at line 552 of file UpperHessenbergQR.h.

◆ ConstGenericMatrix

template<typename Scalar = double>

using Spectra::TridiagQR< Scalar >::ConstGenericMatrix = const Eigen::Ref<const Matrix>

private

Definition at line 551 of file UpperHessenbergQR.h.

◆ Index

template<typename Scalar = double>

using Spectra::TridiagQR< Scalar >::Index = Eigen::Index

private

Definition at line 548 of file UpperHessenbergQR.h.

◆ Matrix

template<typename Scalar = double>

using Spectra::TridiagQR< Scalar >::Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>

private

Definition at line 549 of file UpperHessenbergQR.h.

◆ Vector

template<typename Scalar = double>

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

private

Definition at line 550 of file UpperHessenbergQR.h.

Constructor & Destructor Documentation

◆ TridiagQR() [1/2]

template<typename Scalar = double>

Spectra::TridiagQR< Scalar >::TridiagQR ( Index size )

inline

Constructor to preallocate memory. Computation can be performed later by calling the compute() method.

Definition at line 571 of file UpperHessenbergQR.h.

◆ TridiagQR() [2/2]

template<typename Scalar = double>

Spectra::TridiagQR< Scalar >::TridiagQR	(	ConstGenericMatrix &	mat,
		const Scalar &	shift = `Scalar(0)`
	)

inline

Constructor to create an object that performs and stores the QR decomposition of a tridiagonal matrix mat, with an optional shift: $T-sI=QR$ . Here $T$ stands for the matrix mat, and $s$ is the shift.

Parameters

mat	Matrix type can be `Eigen::Matrix<Scalar, ...>` (e.g. `Eigen::MatrixXd` and `Eigen::MatrixXf`), or its mapped version (e.g. `Eigen::Map<Eigen::MatrixXd>`). Only the diagonal and subdiagonal elements of the matrix are used.

Definition at line 586 of file UpperHessenbergQR.h.

Member Function Documentation

◆ compute()

template<typename Scalar = double>

void Spectra::TridiagQR< Scalar >::compute	(	ConstGenericMatrix &	mat,
		const Scalar &	shift = `Scalar(0)`
	)

inlineoverride

Compute the QR decomposition of a tridiagonal matrix with an optional shift.

Parameters

mat	Matrix type can be `Eigen::Matrix<Scalar, ...>` (e.g. `Eigen::MatrixXd` and `Eigen::MatrixXf`), or its mapped version (e.g. `Eigen::Map<Eigen::MatrixXd>`). Only the diagonal and subdiagonal elements of the matrix are used.

Definition at line 601 of file UpperHessenbergQR.h.

◆ matrix_QtHQ() [1/2]

template<typename Scalar = double>

void Spectra::TridiagQR< Scalar >::matrix_QtHQ ( ComplexMatrix & dest ) const

inline

The version of matrix_QtHQ() when dest has a complex value type.

This is used in Hermitian eigen solvers where the result is stored as a complex matrix.

Definition at line 787 of file UpperHessenbergQR.h.

◆ matrix_QtHQ() [2/2]

template<typename Scalar = double>

void Spectra::TridiagQR< Scalar >::matrix_QtHQ ( Matrix & dest ) const

inlineoverride

Overwrite dest with $Q'TQ = RQ + sI$ , where $T$ is the input matrix mat, and $s$ is the shift. The result is a tridiagonal matrix.

Parameters

mat	The matrix to be overwritten, whose type should be `Eigen::Matrix<Scalar, ...>`, depending on the template parameter `Scalar` defined.

Definition at line 713 of file UpperHessenbergQR.h.

◆ matrix_R()

template<typename Scalar = double>

Matrix Spectra::TridiagQR< Scalar >::matrix_R ( ) const

inlineoverride

Return the $R$ matrix in the QR decomposition, which is an upper triangular matrix.

Returns: Returned matrix type will be Eigen::Matrix<Scalar, ...>, depending on the template parameter Scalar defined.

Definition at line 693 of file UpperHessenbergQR.h.

Member Data Documentation

◆ m_R_diag

template<typename Scalar = double>

Vector Spectra::TridiagQR< Scalar >::m_R_diag

private

Definition at line 562 of file UpperHessenbergQR.h.

◆ m_R_supd

template<typename Scalar = double>

Vector Spectra::TridiagQR< Scalar >::m_R_supd

private

Definition at line 563 of file UpperHessenbergQR.h.

◆ m_R_supd2

template<typename Scalar = double>

Vector Spectra::TridiagQR< Scalar >::m_R_supd2

private

Definition at line 564 of file UpperHessenbergQR.h.

◆ m_T_diag

template<typename Scalar = double>

Vector Spectra::TridiagQR< Scalar >::m_T_diag

private

Definition at line 560 of file UpperHessenbergQR.h.

◆ m_T_subd

template<typename Scalar = double>

Vector Spectra::TridiagQR< Scalar >::m_T_subd

private

Definition at line 561 of file UpperHessenbergQR.h.

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

UpperHessenbergQR.h

Public Member Functions

Private Types

Private Attributes

Additional Inherited Members

Detailed Description

template<typename Scalar = double> class Spectra::TridiagQR< Scalar >

Member Typedef Documentation

◆ ComplexMatrix

◆ ConstGenericMatrix

◆ Index

◆ Matrix

◆ Vector

Constructor & Destructor Documentation

◆ TridiagQR() [1/2]

◆ TridiagQR() [2/2]

Member Function Documentation

◆ compute()

◆ matrix_QtHQ() [1/2]

◆ matrix_QtHQ() [2/2]

◆ matrix_R()

Member Data Documentation

◆ m_R_diag

◆ m_R_supd

◆ m_R_supd2

◆ m_T_diag

◆ m_T_subd

template<typename Scalar = double>
class Spectra::TridiagQR< Scalar >