#include <UpperHessenbergQR.h>

Inheritance diagram for Spectra::TridiagQR< Scalar >:

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

void	matrix_QtHQ (Matrix &dest) const

Matrix	matrix_R () const

	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
typedef Matrix::Index	Index

typedef Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic >	Matrix

typedef Eigen::Matrix< Scalar, Eigen::Dynamic, 1 >	Vector

Private Attributes
const typedef Eigen::Ref< const Matrix >	ConstGenericMatrix

Vector	m_T_diag

Vector	m_T_lsub

Vector	m_T_usub

Vector	m_T_usub2

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)

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 475 of file UpperHessenbergQR.h.

Member Typedef Documentation

◆ Index

template<typename Scalar = double>

typedef Matrix::Index Spectra::TridiagQR< Scalar >::Index

private

Definition at line 482 of file UpperHessenbergQR.h.

◆ Matrix

template<typename Scalar = double>

typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> Spectra::TridiagQR< Scalar >::Matrix

private

Definition at line 478 of file UpperHessenbergQR.h.

◆ Vector

template<typename Scalar = double>

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

private

Definition at line 479 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 494 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 an upper Hessenberg matrix mat, with an optional shift: $H-sI=QR$ . Here $H$ 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 major- and sub- diagonal parts of the matrix are used.

Definition at line 510 of file UpperHessenbergQR.h.

Member Function Documentation

◆ compute()

template<typename Scalar = double>

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

inline

Conduct the QR factorization 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 major- and sub- diagonal parts of the matrix are used.

Definition at line 526 of file UpperHessenbergQR.h.

◆ matrix_QtHQ()

template<typename Scalar = double>

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

inline

Overwrite dest with $Q'HQ = RQ + sI$ , where $H$ 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 623 of file UpperHessenbergQR.h.

◆ matrix_R()

template<typename Scalar = double>

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

inline

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 603 of file UpperHessenbergQR.h.

Member Data Documentation

◆ ConstGenericMatrix

template<typename Scalar = double>

const typedef Eigen::Ref<const Matrix> Spectra::TridiagQR< Scalar >::ConstGenericMatrix

private

Definition at line 480 of file UpperHessenbergQR.h.

◆ m_T_diag

template<typename Scalar = double>

Vector Spectra::TridiagQR< Scalar >::m_T_diag

private

Definition at line 484 of file UpperHessenbergQR.h.

◆ m_T_lsub

template<typename Scalar = double>

Vector Spectra::TridiagQR< Scalar >::m_T_lsub

private

Definition at line 485 of file UpperHessenbergQR.h.

◆ m_T_usub

template<typename Scalar = double>

Vector Spectra::TridiagQR< Scalar >::m_T_usub

private

Definition at line 486 of file UpperHessenbergQR.h.

◆ m_T_usub2

template<typename Scalar = double>

Vector Spectra::TridiagQR< Scalar >::m_T_usub2

private

Definition at line 487 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

◆ Index

◆ Matrix

◆ Vector

Constructor & Destructor Documentation

◆ TridiagQR() [1/2]

◆ TridiagQR() [2/2]

Member Function Documentation

◆ compute()

◆ matrix_QtHQ()

◆ matrix_R()

Member Data Documentation

◆ ConstGenericMatrix

◆ m_T_diag

◆ m_T_lsub

◆ m_T_usub

◆ m_T_usub2

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