LSMR solves Ax = b or min ||Ax - b|| with or without damping, using the iterative algorithm of David Fong and Michael Saunders: http://www.stanford.edu/group/SOL/software/lsmr.html. More...

Public Member Functions
	LSMRSolver (double damp=0., double atol=1.e-6, double btol=1.e-6, double conlim=1.e8, size_t maxiter=0, ElemUtils::Formatter *output=0)
	Constructor. More...

virtual	~LSMRSolver ()
	Default destructor. More...

VectorD	solve (const MatrixD &A, const VectorD &B)
	Solves the linear system \( A X = B \) and returns \( X \) in the least-squares sense. More...

double	getToleranceA () const
	Stopping tolerance. LSMR continues iterations until a certain backward error estimate is smaller than some quantity depending on atol and btol. More...

void	setToleranceA (double atol)
	Stopping tolerance. LSMR continues iterations until a certain backward error estimate is smaller than some quantity depending on atol and btol. More...

double	getToleranceB () const
	Stopping tolerance. LSMR continues iterations until a certain backward error estimate is smaller than some quantity depending on atol and btol. More...

void	setToleranceB (double btol)
	Stopping tolerance. LSMR continues iterations until a certain backward error estimate is smaller than some quantity depending on atol and btol. More...

double	getConditionNumberLimit () const
	LSMR terminates if an estimate of `cond(A)` exceeds conlim. More...

void	setConditionNumberLimit (double conlim)
	LSMR terminates if an estimate of `cond(A)` exceeds conlim. More...

double	getDamping () const
	Damping factor for regularized least-squares. More...

void	setDamping (double damp)
	Damping factor for regularized least-squares. More...

size_t	getMaximumIerations () const
	LSMR terminates if the number of iterations reaches maxiter. More...

void	setMaximumIerations (size_t maxiter)
	LSMR terminates if the number of iterations reaches maxiter. More...

ElemUtils::Formatter &	getOutput () const

void	setOutput (ElemUtils::Formatter &output)

double	getConditionNumber () const

unsigned int	getStoppingCase () const
	Reason for stopping the iterations. More...

size_t	getNumberIterations () const
	Number of iterations. More...

double	getNormA () const

double	getNormAr () const

double	getNormr () const

double	getNormX () const

const std::string &	getStoppingMessage () const
	Reason for stopping the iterations. More...

Private Member Functions
void	_sym_ortho (double a, double b, double &c, double &s, double &r) const
	Routine of rotation from scipy. More...

Private Attributes
double	m_damp
	Damping factor for regularized least-squares. More...

double	m_atol
	Stopping tolerance. LSMR continues iterations until a certain backward error estimate is smaller than some quantity depending on atol and btol. More...

double	m_btol
	Stopping tolerance. LSMR continues iterations until a certain backward error estimate is smaller than some quantity depending on atol and btol. More...

double	m_conlim
	LSMR terminates if an estimate of `cond(A)` exceeds conlim. More...

size_t	m_maxiter
	LSMR terminates if the number of iterations reaches maxiter. More...

ElemUtils::Formatter *	m_output
	Pointer to the stream where to write the output. More...

unsigned int	m_istop
	Reason for stopping the iterations. More...

size_t	m_itn
	Number of iterations. More...

double	m_normr

double	m_normar

double	m_normA

double	m_condA

double	m_normx

std::string	m_stopMessage
	Reason for stopping the iterations. More...

std::vector< std::string >	m_msg

std::string	m_hdg1

std::string	m_hdg2

unsigned int	m_pfreq

Detailed Description

LSMR solves Ax = b or min ||Ax - b|| with or without damping, using the iterative algorithm of David Fong and Michael Saunders: http://www.stanford.edu/group/SOL/software/lsmr.html.

Adapted for C++ from the scipy implementation: https://github.com/scipy/scipy/blob/v0.18.1/scipy/sparse/linalg/isolve/lsmr.py

Constructor & Destructor Documentation

◆ LSMRSolver()

NumA::LSMRSolver::LSMRSolver	(	double	damp = `0.`,
		double	atol = `1.e-6`,
		double	btol = `1.e-6`,
		double	conlim = `1.e8`,
		size_t	maxiter = `0`,
		ElemUtils::Formatter *	output = `0`
	)

Constructor.

Parameters

damp	Damping factor for regularized least-squares.
atol	Stopping tolerance.
btol	Stopping tolerance.
conlim	LSMR terminates if an estimate of `cond(A)` exceeds conlim.
maxiter	LSMR terminates if the number of iterations reaches maxiter.
output	Pointer to the stream where to write the output.

◆ ~LSMRSolver()

NumA::LSMRSolver::~LSMRSolver ( )

virtual

Default destructor.

Member Function Documentation

◆ _sym_ortho()

void NumA::LSMRSolver::_sym_ortho	(	double	a,
		double	b,
		double &	c,
		double &	s,
		double &	r
	)		const

private

Routine of rotation from scipy.

Parameters

a
b
c
s
r

◆ getConditionNumber()

double NumA::LSMRSolver::getConditionNumber ( ) const

◆ getConditionNumberLimit()

double NumA::LSMRSolver::getConditionNumberLimit ( ) const

LSMR terminates if an estimate of cond(A) exceeds conlim.

◆ getDamping()

double NumA::LSMRSolver::getDamping ( ) const

Damping factor for regularized least-squares.

◆ getMaximumIerations()

size_t NumA::LSMRSolver::getMaximumIerations ( ) const

LSMR terminates if the number of iterations reaches maxiter.

◆ getNormA()

double NumA::LSMRSolver::getNormA ( ) const

◆ getNormAr()

double NumA::LSMRSolver::getNormAr ( ) const

◆ getNormr()

double NumA::LSMRSolver::getNormr ( ) const

◆ getNormX()

double NumA::LSMRSolver::getNormX ( ) const

◆ getNumberIterations()

size_t NumA::LSMRSolver::getNumberIterations ( ) const

Number of iterations.

◆ getOutput()

ElemUtils::Formatter & NumA::LSMRSolver::getOutput ( ) const

Returns: Reference to the stream where the output is written.

◆ getStoppingCase()

unsigned int NumA::LSMRSolver::getStoppingCase ( ) const

Reason for stopping the iterations.

◆ getStoppingMessage()

const std::string & NumA::LSMRSolver::getStoppingMessage ( ) const

Reason for stopping the iterations.

◆ getToleranceA()

double NumA::LSMRSolver::getToleranceA ( ) const

Stopping tolerance. LSMR continues iterations until a certain backward error estimate is smaller than some quantity depending on atol and btol.

◆ getToleranceB()

double NumA::LSMRSolver::getToleranceB ( ) const

Stopping tolerance. LSMR continues iterations until a certain backward error estimate is smaller than some quantity depending on atol and btol.

◆ setConditionNumberLimit()

void NumA::LSMRSolver::setConditionNumberLimit ( double conlim )

LSMR terminates if an estimate of cond(A) exceeds conlim.

◆ setDamping()

void NumA::LSMRSolver::setDamping ( double damp )

Damping factor for regularized least-squares.

◆ setMaximumIerations()

void NumA::LSMRSolver::setMaximumIerations ( size_t maxiter )

LSMR terminates if the number of iterations reaches maxiter.

◆ setOutput()

void NumA::LSMRSolver::setOutput ( ElemUtils::Formatter & output )

Parameters

output Reference to the stream where the output is written.

◆ setToleranceA()

void NumA::LSMRSolver::setToleranceA ( double atol )

Stopping tolerance. LSMR continues iterations until a certain backward error estimate is smaller than some quantity depending on atol and btol.

◆ setToleranceB()

void NumA::LSMRSolver::setToleranceB ( double btol )

Stopping tolerance. LSMR continues iterations until a certain backward error estimate is smaller than some quantity depending on atol and btol.

◆ solve()

VectorD NumA::LSMRSolver::solve	(	const MatrixD &	A,
		const VectorD &	B
	)

Solves the linear system \( A X = B \) and returns \( X \) in the least-squares sense.

Iterative method for large sparse matrices.

Parameters

A	MatrixD.
B	VectorD.

Returns: VectorD Solution X.

Member Data Documentation

◆ m_atol

double NumA::LSMRSolver::m_atol

private

Stopping tolerance. LSMR continues iterations until a certain backward error estimate is smaller than some quantity depending on atol and btol.

◆ m_btol

double NumA::LSMRSolver::m_btol

private

Stopping tolerance. LSMR continues iterations until a certain backward error estimate is smaller than some quantity depending on atol and btol.

◆ m_condA

double NumA::LSMRSolver::m_condA

private

◆ m_conlim

double NumA::LSMRSolver::m_conlim

private

LSMR terminates if an estimate of cond(A) exceeds conlim.

◆ m_damp

double NumA::LSMRSolver::m_damp

private

Damping factor for regularized least-squares.

◆ m_hdg1

std::string NumA::LSMRSolver::m_hdg1

private

◆ m_hdg2

std::string NumA::LSMRSolver::m_hdg2

private

◆ m_istop

unsigned int NumA::LSMRSolver::m_istop

private

Reason for stopping the iterations.

◆ m_itn

size_t NumA::LSMRSolver::m_itn

private

Number of iterations.

◆ m_maxiter

size_t NumA::LSMRSolver::m_maxiter

private

LSMR terminates if the number of iterations reaches maxiter.

◆ m_msg

std::vector<std::string> NumA::LSMRSolver::m_msg

private

◆ m_normA

double NumA::LSMRSolver::m_normA

private

◆ m_normar

double NumA::LSMRSolver::m_normar

private

◆ m_normr

double NumA::LSMRSolver::m_normr

private

◆ m_normx

double NumA::LSMRSolver::m_normx

private

◆ m_output

ElemUtils::Formatter* NumA::LSMRSolver::m_output

private

Pointer to the stream where to write the output.

◆ m_pfreq

unsigned int NumA::LSMRSolver::m_pfreq

private

◆ m_stopMessage

std::string NumA::LSMRSolver::m_stopMessage

private

Reason for stopping the iterations.

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

include/NumA/linear_algebra/least_squares/LSMRSolver.h
src/NumA/linear_algebra/least_squares/LSMRSolver.cpp

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ LSMRSolver()

◆ ~LSMRSolver()

Member Function Documentation

◆ _sym_ortho()

◆ getConditionNumber()

◆ getConditionNumberLimit()

◆ getDamping()

◆ getMaximumIerations()

◆ getNormA()

◆ getNormAr()

◆ getNormr()

◆ getNormX()

◆ getNumberIterations()

◆ getOutput()

◆ getStoppingCase()

◆ getStoppingMessage()

◆ getToleranceA()

◆ getToleranceB()

◆ setConditionNumberLimit()

◆ setDamping()

◆ setMaximumIerations()

◆ setOutput()

◆ setToleranceA()

◆ setToleranceB()

◆ solve()

Member Data Documentation

◆ m_atol

◆ m_btol

◆ m_condA

◆ m_conlim

◆ m_damp

◆ m_hdg1

◆ m_hdg2

◆ m_istop

◆ m_itn

◆ m_maxiter

◆ m_msg

◆ m_normA

◆ m_normar

◆ m_normr

◆ m_normx

◆ m_output

◆ m_pfreq

◆ m_stopMessage