#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 (Index size)

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

Public Member Functions inherited from Spectra::UpperHessenbergQR< Scalar >
void	apply_QtY (Vector &Y) const

void	apply_QtY (GenericMatrix Y) const

void	apply_QY (Vector &Y) const

void	apply_QY (GenericMatrix Y) const

void	apply_YQ (GenericMatrix Y) const

void	apply_YQt (GenericMatrix Y) const

	UpperHessenbergQR (Index size)

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

virtual	~UpperHessenbergQR ()

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

typedef Matrix::Index	Index

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

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

Private Attributes
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< Scalar >
static void	compute_rotation (const Scalar &x, const Scalar &y, Scalar &r, Scalar &c, Scalar &s)

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

Index	m_n

Array	m_rot_cos

Array	m_rot_sin

Scalar	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

template<typename Scalar = double>

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

private

Definition at line 480 of file UpperHessenbergQR.h.

template<typename Scalar = double>

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

private

Definition at line 482 of file UpperHessenbergQR.h.

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.

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

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.

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

template<typename Scalar = double>

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

inlinevirtual

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.

Reimplemented from Spectra::UpperHessenbergQR< Scalar >.

Definition at line 526 of file UpperHessenbergQR.h.

template<typename Scalar = double>

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