TNL::Solvers::Linear::GEM< Matrix, Real, SolverMonitor > Struct Template Reference

Gaussian Elimination Method (GEM) direct solver for dense linear systems. More...

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

Inheritance diagram for TNL::Solvers::Linear::GEM< Matrix, Real, SolverMonitor >:

Collaboration diagram for TNL::Solvers::Linear::GEM< Matrix, Real, SolverMonitor >:

Public Types
using	ConstVectorViewType = typename Base::ConstVectorViewType
using	DeviceType = typename Base::DeviceType
using	IndexType = typename Base::IndexType
using	MatrixPointer = typename Base::MatrixPointer
using	MatrixType = typename Base::MatrixType
using	RealType = typename Base::RealType
using	VectorViewType = typename Base::VectorViewType
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 auxiliary 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
	GEM ()=default
	Default constructor.
bool	getPivoting () const
	Checks if pivoting is enabled.
void	setPivoting (bool pivoting)
	Enables or disables pivoting in the GEM algorithm.
bool	solve (ConstVectorViewType b, VectorViewType x) override
	Solves the linear system Ax = b.
bool	solve (MatrixType &A, ConstVectorViewType b, VectorViewType x)
	Solves the linear system Ax = b.
Public Member Functions inherited from TNL::Solvers::Linear::LinearSolver< Matrix >
virtual	~LinearSolver ()=default
	Default destructor.
virtual void	setMatrix (const MatrixPointer &matrix)
	Set the matrix of the linear system.
void	setPreconditioner (const PreconditionerPointer &preconditioner)
	Set the preconditioner.
virtual bool	setup (const Config::ParameterContainer &parameters, const String &prefix="")
	Method for setup of the linear iterative solver based on configuration parameters.
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.

Protected Attributes
bool	pivoting = true
	Indicates whether pivoting is enabled.
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< double > *	solverMonitor

Additional Inherited Members
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.

Detailed Description

template<typename Matrix, typename Real = typename Matrix::RealType, typename SolverMonitor = IterativeSolverMonitor< double >>
struct TNL::Solvers::Linear::GEM< Matrix, Real, SolverMonitor >

Gaussian Elimination Method (GEM) direct solver for dense linear systems.

This class implements the GEM algorithm for solving linear systems with dense matrices. It supports optional pivoting.

Template Parameters

Matrix	Type of the matrix representing the linear system. Must be a dense matrix.
Real	Floating point type used for computations.
SolverMonitor	Type of the solver monitor.

Member Function Documentation

getPivoting()

template<typename Matrix, typename Real, typename SolverMonitor>

bool TNL::Solvers::Linear::GEM< Matrix, Real, SolverMonitor >::getPivoting ( ) const

nodiscard

Checks if pivoting is enabled.

Returns

True if pivoting is enabled, false otherwise.

setPivoting()

template<typename Matrix, typename Real, typename SolverMonitor>

void TNL::Solvers::Linear::GEM< Matrix, Real, SolverMonitor >::setPivoting

(

bool

pivoting

)

Enables or disables pivoting in the GEM algorithm.

Parameters

pivoting

If true, pivoting is enabled; otherwise, it is disabled.

solve() [1/2]

template<typename Matrix, typename Real, typename SolverMonitor>

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

overridevirtual

Solves the linear system Ax = b.

This method makes a copy of the matrix A. In case that it is consuming too much memory use method solve taking matrix as input parameter.

Parameters

b	Right-hand side vector.
x	Solution vector (output).

Returns

True if the solver succeeded, false otherwise.

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

solve() [2/2]

template<typename Matrix, typename Real, typename SolverMonitor>

bool TNL::Solvers::Linear::GEM< Matrix, Real, SolverMonitor >::solve	(	MatrixType &	A,
		ConstVectorViewType	b,
		VectorViewType	x )

Solves the linear system Ax = b.

Parameters

A	Matrix representing the linear system. This matrix is modified during the execution of this method.
b	Right-hand side vector.
x	Solution vector (output).

Returns

True if the solver succeeded, false otherwise.

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

• src/TNL/Solvers/Linear/GEM.h
• src/TNL/Solvers/Linear/GEM.hpp