Template Numerical Library: TNL::Solvers::Linear::GMRES< Matrix

Iterative solver of linear systems based on the Generalized minimal residual (GMRES) method. More...

#include <TNL/Solvers/Linear/GMRES.h>

Inheritance diagram for TNL::Solvers::Linear::GMRES< Matrix >:

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Collaboration diagram for TNL::Solvers::Linear::GMRES< Matrix >:

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Public Types
using	ConstVectorViewType = typename Base::ConstVectorViewType
	Type for constant vector view.

using	DeviceType = typename Base::DeviceType
	Device where the solver will run on and auxillary data will alloacted on.

using	IndexType = typename Base::IndexType
	Type for indexing.

using	RealType = typename Base::RealType
	Floating point type used for computations.

using	VectorViewType = typename Base::VectorViewType
	Type for vector view.

Public Types inherited from TNL::Solvers::Linear::LinearSolver< Matrix >
using	ConstVectorViewType = typename Traits< Matrix >::ConstVectorViewType
	Type for constant vector view.

using	DeviceType = typename Matrix::DeviceType
	Device where the solver will run on and auxillary data will alloacted on.

using	IndexType = typename Matrix::IndexType
	Type for indexing.

using	MatrixPointer = std::shared_ptr< std::add_const_t< MatrixType > >
	Type of shared pointer to the matrix.

using	MatrixType = Matrix
	Type of the matrix representing the linear system.

using	PreconditionerPointer = std::shared_ptr< std::add_const_t< PreconditionerType > >
	Type of shared pointer to the preconditioner.

using	PreconditionerType = Preconditioners::Preconditioner< MatrixType >
	Type of preconditioner.

using	RealType = typename Matrix::RealType
	Floating point type used for computations.

using	VectorViewType = typename Traits< Matrix >::VectorViewType
	Type for vector view.

Public Types inherited from TNL::Solvers::IterativeSolver< Matrix::RealType, Matrix::IndexType >
using	SolverMonitorType
	Type of an object used for monitoring of the convergence.

Public Member Functions
bool	setup (const Config::ParameterContainer &parameters, const String &prefix="") override
	Method for setup of the linear iterative solver based on configuration parameters.

bool	solve (ConstVectorViewType b, VectorViewType x) override
	Method for solving of a linear system.

Public Member Functions inherited from TNL::Solvers::Linear::LinearSolver< Matrix >
virtual	~LinearSolver ()
	Default destructor.

void	setMatrix (const MatrixPointer &matrix)
	Set the matrix of the linear system.

void	setPreconditioner (const PreconditionerPointer &preconditioner)
	Set the preconditioner.

Public Member Functions inherited from TNL::Solvers::IterativeSolver< Matrix::RealType, Matrix::IndexType >
	IterativeSolver ()=default
	Default constructor.

bool	checkConvergence ()
	Checks whether the convergence occurred already.

bool	checkNextIteration ()
	Checks if the solver is allowed to do the next iteration.

const Matrix::RealType &	getConvergenceResidue () const
	Gets the the convergence threshold.

const Matrix::RealType &	getDivergenceResidue () const
	Gets the limit for the divergence criterion.

const Matrix::IndexType &	getIterations () const
	Gets the number of iterations performed by the solver so far.

const Matrix::IndexType &	getMaxIterations () const
	Gets the maximal number of iterations the solver is allowed to perform.

const Matrix::IndexType &	getMinIterations () const
	Gets the minimal number of iterations the solver is supposed to do.

const Matrix::RealType &	getResidue () const
	Gets the residue reached at the current iteration.

bool	nextIteration ()
	Proceeds to the next iteration.

void	resetIterations ()
	Sets the the number of the current iterations to zero.

void	setConvergenceResidue (const Matrix::RealType &convergenceResidue)
	Sets the threshold for the convergence.

void	setDivergenceResidue (const Matrix::RealType &divergenceResidue)
	Sets the residue limit for the divergence criterion.

void	setMaxIterations (const Matrix::IndexType &maxIterations)
	Sets the maximal number of iterations the solver is allowed to perform.

void	setMinIterations (const Matrix::IndexType &minIterations)
	Sets the minimal number of iterations the solver is supposed to do.

void	setRefreshRate (const Matrix::IndexType &refreshRate)
	Sets the refresh rate (in milliseconds) for the solver monitor.

void	setResidue (const Matrix::RealType &residue)
	Sets the residue reached at the current iteration.

void	setSolverMonitor (SolverMonitorType &solverMonitor)
	Sets the solver monitor object.

bool	setup (const Config::ParameterContainer &parameters, const std::string &prefix="")
	Method for setup of the iterative solver based on configuration parameters.

Static Public Member Functions
static void	configSetup (Config::ConfigDescription &config, const String &prefix="")
	This is method defines configuration entries for setup of the linear iterative solver.

Static Public Member Functions inherited from TNL::Solvers::Linear::LinearSolver< Matrix >
static void	configSetup (Config::ConfigDescription &config, const String &prefix="")
	This method defines configuration entries for setup of the linear iterative solver.

Static Public Member Functions inherited from TNL::Solvers::IterativeSolver< Matrix::RealType, Matrix::IndexType >
static void	configSetup (Config::ConfigDescription &config, const std::string &prefix="")
	This method defines configuration entries for setup of the iterative solver.

Protected Types
using	ConstDeviceView = typename Traits::ConstLocalViewType

using	DeviceVector = typename Traits::LocalVectorType

using	DeviceView = typename Traits::LocalViewType

using	HostVector = typename DeviceVector::template Self< RealType, Devices::Host >

using	HostView = typename DeviceView::template Self< RealType, Devices::Host >

enum class	Variant { CGS , CGSR , MGS , MGSR , CWY }

using	VectorType = typename Traits::VectorType

Protected Member Functions
void	apply_givens_rotations (int i, int m)

void	applyPlaneRotation (RealType &dx, RealType &dy, RealType &cs, RealType &sn)

void	compute_residue (VectorViewType r, ConstVectorViewType x, ConstVectorViewType b)

void	generatePlaneRotation (RealType &dx, RealType &dy, RealType &cs, RealType &sn)

void	hauseholder_apply_trunc (HostView out, int i, VectorViewType y_i, ConstVectorViewType z)

void	hauseholder_cwy (VectorViewType v, int i)

void	hauseholder_cwy_transposed (VectorViewType z, int i, ConstVectorViewType w)

void	hauseholder_generate (int i, VectorViewType y_i, ConstVectorViewType z)

int	orthogonalize_CGS (int m, RealType normb, RealType beta)

int	orthogonalize_CWY (int m, RealType normb, RealType beta)

int	orthogonalize_MGS (int m, RealType normb, RealType beta)

void	preconditioned_matvec (VectorViewType w, ConstVectorViewType v)

void	setSize (const VectorViewType &x)

template<typename Vector >
void	update (int k, int m, const HostVector &H, const HostVector &s, DeviceVector &V, Vector &x)

Static Protected Member Functions
template<typename M >
static IndexType	getLocalOffset (const M &m)

template<typename M >
static IndexType	getLocalOffset (const Matrices::DistributedMatrix< M > &m)

Protected Attributes
VectorType	_M_tmp

HostVector	cs

HostVector	H

IndexType	ldSize = 0

IndexType	localOffset = 0

VectorType	r

int	restarting_max = 10

int	restarting_min = 10

int	restarting_step_max = 3

int	restarting_step_min = 3

HostVector	s

IndexType	size = 0

HostVector	sn

HostVector	T

DeviceVector	V

Variant	variant = Variant::CWY

VectorType	w

DeviceVector	Y

HostVector	YL

VectorType	z

Protected Attributes inherited from TNL::Solvers::Linear::LinearSolver< Matrix >
MatrixPointer	matrix = nullptr

PreconditionerPointer	preconditioner = nullptr

Protected Attributes inherited from TNL::Solvers::IterativeSolver< Matrix::RealType, Matrix::IndexType >
Matrix::RealType	convergenceResidue

Matrix::IndexType	currentIteration

Matrix::RealType	currentResidue

Matrix::RealType	divergenceResidue

Matrix::IndexType	maxIterations

Matrix::IndexType	minIterations

Matrix::IndexType	refreshRate

std::ofstream	residualHistoryFile

std::string	residualHistoryFileName

IterativeSolverMonitor< Matrix::RealType, Matrix::IndexType > *	solverMonitor

Detailed Description

template<typename Matrix>
class TNL::Solvers::Linear::GMRES< Matrix >

Iterative solver of linear systems based on the Generalized minimal residual (GMRES) method.

This method can be used for solving of non-semmetric linear systems. This implementation offers various methods for the orthogonalization of vectors generated by the Arnoldi algorithm. The user may choose one of the following:

CGS - Classical Gramm-Schmidt,

CGSR - Classical Gramm-Schmidt with reorthogonalization,

MGS - Modified Gramm-Schmidt,

MGSR - Modified Gramm-Schmidt with reorthogonalization (the default one),

CWY - Compact WY form of the Householder reflections).

See Wikipedia for more details.

See TNL::Solvers::Linear::LinearSolver for example of showing how to use the linear solvers.

Template Parameters

Matrix is type of matrix describing the linear system.

Member Function Documentation

◆ configSetup()

template<typename Matrix >

void TNL::Solvers::Linear::GMRES< Matrix >::configSetup	(	Config::ConfigDescription &	config,
		const String &	prefix = "" )

static

This is method defines configuration entries for setup of the linear iterative solver.

In addition to config entries defined by IterativeSolver::configSetup, this method defines the following:

gmres-variant - Algorithm used for the orthogonalization - CGS (Classical Gramm-Schmidt), CGSR(Classical Gramm-Schmidt with reorthogonalization), MGS(Modified Gramm-Schmidt), MGSR(Modified Gramm-Schmidt with reorthogonalization), CWY(Compact WY form of the Householder reflections).

gmres-restarting-min - minimal number of iterations after which the GMRES restarts.

gmres-restarting-max - maximal number of iterations after which the GMRES restarts.

gmres-restarting-step-min - minimal adjusting step for the adaptivity of the GMRES restarting parameter.

gmres-restarting-step-max - maximal adjusting step for the adaptivity of the GMRES restarting parameter.

Parameters

config	contains description of configuration parameters.
prefix	is a prefix of particular configuration entries.

◆ setup()

template<typename Matrix >

bool TNL::Solvers::Linear::GMRES< Matrix >::setup	(	const Config::ParameterContainer &	parameters,
		const String &	prefix = "" )

overridevirtual

Method for setup of the linear iterative solver based on configuration parameters.

Parameters

parameters	contains values of the define configuration entries.
prefix	is a prefix of particular configuration entries.

Reimplemented from TNL::Solvers::Linear::LinearSolver< Matrix >.

◆ solve()

template<typename Matrix >

bool TNL::Solvers::Linear::GMRES< Matrix >::solve	(	ConstVectorViewType	b,
		VectorViewType	x )

overridevirtual

Method for solving of a linear system.

See LinearSolver::solve for more details.

Parameters

b	vector with the right-hand side of the linear system.
x	vector for the solution of the linear system.

Returns: true if the solver converged.; false if the solver did not converge.

Implements TNL::Solvers::Linear::LinearSolver< Matrix >.

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

src/TNL/Solvers/Linear/GMRES.h
src/TNL/Solvers/Linear/GMRES.hpp

Public Types

Public Member Functions

Static Public Member Functions

Protected Types

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Detailed Description

Member Function Documentation

◆ configSetup()

◆ setup()

◆ solve()