#include <UpperHessenbergQR.h>

Public Member Functions
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 Scalar &shift=Scalar(0))

virtual void	matrix_QtHQ (Matrix &dest) const

virtual Matrix	matrix_R () const

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

	UpperHessenbergQR (Index size)

virtual	~UpperHessenbergQR ()

Static Protected Member Functions
static void	compute_rotation (const Scalar &x, const Scalar &y, Scalar &r, Scalar &c, Scalar &s)

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

Protected Attributes
bool	m_computed

Index	m_n

Array	m_rot_cos

Array	m_rot_sin

Scalar	m_shift

Private Types
using	Array = Eigen::Array< Scalar, Eigen::Dynamic, 1 >

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

using	GenericMatrix = Eigen::Ref< Matrix >

using	Index = Eigen::Index

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

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

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

Private Attributes
Matrix	m_mat_R

Detailed Description

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

Perform the QR decomposition of an upper Hessenberg matrix.

Template Parameters

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

Definition at line 45 of file UpperHessenbergQR.h.

Member Typedef Documentation

◆ Array

template<typename Scalar = double>

using Spectra::UpperHessenbergQR< Scalar >::Array = Eigen::Array<Scalar, Eigen::Dynamic, 1>

private

Definition at line 52 of file UpperHessenbergQR.h.

◆ ConstGenericMatrix

template<typename Scalar = double>

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

private

Definition at line 55 of file UpperHessenbergQR.h.

◆ GenericMatrix

template<typename Scalar = double>

using Spectra::UpperHessenbergQR< Scalar >::GenericMatrix = Eigen::Ref<Matrix>

private

Definition at line 54 of file UpperHessenbergQR.h.

◆ Index

template<typename Scalar = double>

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

private

Definition at line 48 of file UpperHessenbergQR.h.

◆ Matrix

template<typename Scalar = double>

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

private

Definition at line 49 of file UpperHessenbergQR.h.

◆ RowVector

template<typename Scalar = double>

using Spectra::UpperHessenbergQR< Scalar >::RowVector = Eigen::Matrix<Scalar, 1, Eigen::Dynamic>

private

Definition at line 51 of file UpperHessenbergQR.h.

◆ Vector

template<typename Scalar = double>

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

private

Definition at line 50 of file UpperHessenbergQR.h.

Constructor & Destructor Documentation

◆ UpperHessenbergQR() [1/2]

template<typename Scalar = double>

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

inline

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

Definition at line 178 of file UpperHessenbergQR.h.

◆ UpperHessenbergQR() [2/2]

template<typename Scalar = double>

Spectra::UpperHessenbergQR< Scalar >::UpperHessenbergQR	(	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 upper triangular and the subdiagonal elements of the matrix are used.

Definition at line 198 of file UpperHessenbergQR.h.

◆ ~UpperHessenbergQR()

template<typename Scalar = double>

virtual Spectra::UpperHessenbergQR< Scalar >::~UpperHessenbergQR ( )

inlinevirtual

Virtual destructor.

Definition at line 211 of file UpperHessenbergQR.h.

Member Function Documentation

◆ apply_QtY() [1/2]

template<typename Scalar = double>

void Spectra::UpperHessenbergQR< Scalar >::apply_QtY ( GenericMatrix Y ) const

inline

Apply the $Q$ matrix to another matrix $Y$ .

Parameters

Y	A matrix that will be overwritten by the matrix product .

Matrix type can be Eigen::Matrix<Scalar, ...> (e.g. Eigen::MatrixXd and Eigen::MatrixXf), or its mapped version (e.g. Eigen::Map<Eigen::MatrixXd>).

Definition at line 438 of file UpperHessenbergQR.h.

◆ apply_QtY() [2/2]

template<typename Scalar = double>

void Spectra::UpperHessenbergQR< Scalar >::apply_QtY ( Vector & Y ) const

inline

Apply the $Q$ matrix to a vector $y$ .

Parameters

Y	A vector that will be overwritten by the matrix product .

Vector type can be Eigen::Vector<Scalar, ...>, depending on the template parameter Scalar defined.

Definition at line 379 of file UpperHessenbergQR.h.

◆ apply_QY() [1/2]

template<typename Scalar = double>

void Spectra::UpperHessenbergQR< Scalar >::apply_QY ( GenericMatrix Y ) const

inline

Apply the $Q$ matrix to another matrix $Y$ .

Parameters

Y	A matrix that will be overwritten by the matrix product .

Matrix type can be Eigen::Matrix<Scalar, ...> (e.g. Eigen::MatrixXd and Eigen::MatrixXf), or its mapped version (e.g. Eigen::Map<Eigen::MatrixXd>).

Definition at line 408 of file UpperHessenbergQR.h.

◆ apply_QY() [2/2]

template<typename Scalar = double>

void Spectra::UpperHessenbergQR< Scalar >::apply_QY ( Vector & Y ) const

inline

Apply the $Q$ matrix to a vector $y$ .

Parameters

Y	A vector that will be overwritten by the matrix product .

Vector type can be Eigen::Vector<Scalar, ...>, depending on the template parameter Scalar defined.

Definition at line 352 of file UpperHessenbergQR.h.

◆ apply_YQ()

template<typename Scalar = double>

void Spectra::UpperHessenbergQR< Scalar >::apply_YQ ( GenericMatrix Y ) const

inline

Apply the $Q$ matrix to another matrix $Y$ .

Parameters

Y	A matrix that will be overwritten by the matrix product .

Matrix type can be Eigen::Matrix<Scalar, ...> (e.g. Eigen::MatrixXd and Eigen::MatrixXf), or its mapped version (e.g. Eigen::Map<Eigen::MatrixXd>).

Definition at line 469 of file UpperHessenbergQR.h.

◆ apply_YQt()

template<typename Scalar = double>

void Spectra::UpperHessenbergQR< Scalar >::apply_YQt ( GenericMatrix Y ) const

inline

Apply the $Q$ matrix to another matrix $Y$ .

Parameters

Y	A matrix that will be overwritten by the matrix product .

Matrix type can be Eigen::Matrix<Scalar, ...> (e.g. Eigen::MatrixXd and Eigen::MatrixXf), or its mapped version (e.g. Eigen::Map<Eigen::MatrixXd>).

Definition at line 515 of file UpperHessenbergQR.h.

◆ compute()

template<typename Scalar = double>

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

inlinevirtual

Compute the QR decomposition of an upper Hessenberg 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 upper triangular and the subdiagonal elements of the matrix are used.

Definition at line 223 of file UpperHessenbergQR.h.

◆ compute_rotation()

template<typename Scalar = double>

static void Spectra::UpperHessenbergQR< Scalar >::compute_rotation	(	const Scalar &	x,
		const Scalar &	y,
		Scalar &	r,
		Scalar &	c,
		Scalar &	s
	)

inlinestaticprotected

Definition at line 132 of file UpperHessenbergQR.h.

◆ matrix_QtHQ()

template<typename Scalar = double>

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

inlinevirtual

Overwrite dest with $Q'HQ = RQ + sI$ , where $H$ is the input matrix mat, and $s$ is the shift. The result is an upper Hessenberg 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 305 of file UpperHessenbergQR.h.

◆ matrix_R()

template<typename Scalar = double>

virtual Matrix Spectra::UpperHessenbergQR< Scalar >::matrix_R ( ) const

inlinevirtual

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 290 of file UpperHessenbergQR.h.

◆ stable_scaling()

template<typename Scalar = double>

static void Spectra::UpperHessenbergQR< Scalar >::stable_scaling	(	const Scalar &	a,
		const Scalar &	b,
		Scalar &	r,
		Scalar &	c,
		Scalar &	s
	)

inlinestaticprotected

Definition at line 70 of file UpperHessenbergQR.h.

Member Data Documentation

◆ m_computed

template<typename Scalar = double>

bool Spectra::UpperHessenbergQR< Scalar >::m_computed

protected

Definition at line 67 of file UpperHessenbergQR.h.

◆ m_mat_R

template<typename Scalar = double>

Matrix Spectra::UpperHessenbergQR< Scalar >::m_mat_R

private

Definition at line 57 of file UpperHessenbergQR.h.

◆ m_n

template<typename Scalar = double>

Index Spectra::UpperHessenbergQR< Scalar >::m_n

protected

Definition at line 60 of file UpperHessenbergQR.h.

◆ m_rot_cos

template<typename Scalar = double>

Array Spectra::UpperHessenbergQR< Scalar >::m_rot_cos

protected

Definition at line 65 of file UpperHessenbergQR.h.

◆ m_rot_sin

template<typename Scalar = double>

Array Spectra::UpperHessenbergQR< Scalar >::m_rot_sin

protected

Definition at line 66 of file UpperHessenbergQR.h.

◆ m_shift

template<typename Scalar = double>

Scalar Spectra::UpperHessenbergQR< Scalar >::m_shift

protected

Definition at line 64 of file UpperHessenbergQR.h.

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

UpperHessenbergQR.h

Public Member Functions

Static Protected Member Functions

Protected Attributes

Private Types

Private Attributes

Detailed Description

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

Member Typedef Documentation

◆ Array

◆ ConstGenericMatrix

◆ GenericMatrix

◆ Index

◆ Matrix

◆ RowVector

◆ Vector

Constructor & Destructor Documentation

◆ UpperHessenbergQR() [1/2]

◆ UpperHessenbergQR() [2/2]

◆ ~UpperHessenbergQR()

Member Function Documentation

◆ apply_QtY() [1/2]

◆ apply_QtY() [2/2]

◆ apply_QY() [1/2]

◆ apply_QY() [2/2]

◆ apply_YQ()

◆ apply_YQt()

◆ compute()

◆ compute_rotation()

◆ matrix_QtHQ()

◆ matrix_R()

◆ stable_scaling()

Member Data Documentation

◆ m_computed

◆ m_mat_R

◆ m_n

◆ m_rot_cos

◆ m_rot_sin

◆ m_shift

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