A GMRES solver for sparse square problems. More...

#include <GMRES.h>

Inheritance diagram for Eigen::GMRES< _MatrixType, _Preconditioner >:

Public Types
typedef _MatrixType	MatrixType

typedef _Preconditioner	Preconditioner

typedef MatrixType::RealScalar	RealScalar

typedef MatrixType::Scalar	Scalar

Public Types inherited from Eigen::IterativeSolverBase< GMRES< _MatrixType, _Preconditioner > >
enum

typedef internal::traits< GMRES< _MatrixType, _Preconditioner > >::MatrixType	MatrixType

typedef internal::traits< GMRES< _MatrixType, _Preconditioner > >::Preconditioner	Preconditioner

typedef MatrixType::RealScalar	RealScalar

typedef MatrixType::Scalar	Scalar

typedef MatrixType::StorageIndex	StorageIndex

Public Member Functions
template<typename Rhs , typename Dest >
void	_solve_impl (const Rhs &b, MatrixBase< Dest > &x) const

template<typename Rhs , typename Dest >
void	_solve_with_guess_impl (const Rhs &b, Dest &x) const

Index	get_restart ()

	GMRES ()

template<typename MatrixDerived >
	GMRES (const EigenBase< MatrixDerived > &A)

void	set_restart (const Index restart)

	~GMRES ()

Public Member Functions inherited from Eigen::IterativeSolverBase< GMRES< _MatrixType, _Preconditioner > >
void	_solve_impl (const Rhs &b, SparseMatrixBase< DestDerived > &aDest) const

GMRES< _MatrixType, _Preconditioner > &	analyzePattern (const EigenBase< MatrixDerived > &A)

Index	cols () const

GMRES< _MatrixType, _Preconditioner > &	compute (const EigenBase< MatrixDerived > &A)

RealScalar	error () const

GMRES< _MatrixType, _Preconditioner > &	factorize (const EigenBase< MatrixDerived > &A)

ComputationInfo	info () const

Index	iterations () const

	IterativeSolverBase ()

	IterativeSolverBase (const EigenBase< MatrixDerived > &A)

Index	maxIterations () const

Preconditioner &	preconditioner ()

const Preconditioner &	preconditioner () const

Index	rows () const

GMRES< _MatrixType, _Preconditioner > &	setMaxIterations (Index maxIters)

GMRES< _MatrixType, _Preconditioner > &	setTolerance (const RealScalar &tolerance)

const SolveWithGuess< GMRES< _MatrixType, _Preconditioner >, Rhs, Guess >	solveWithGuess (const MatrixBase< Rhs > &b, const Guess &x0) const

RealScalar	tolerance () const

	~IterativeSolverBase ()

Public Member Functions inherited from Eigen::SparseSolverBase< GMRES< _MatrixType, _Preconditioner > >
void	_solve_impl (const SparseMatrixBase< Rhs > &b, SparseMatrixBase< Dest > &dest) const

GMRES< _MatrixType, _Preconditioner > &	derived ()

const GMRES< _MatrixType, _Preconditioner > &	derived () const

const Solve< GMRES< _MatrixType, _Preconditioner >, Rhs >	solve (const MatrixBase< Rhs > &b) const

const Solve< GMRES< _MatrixType, _Preconditioner >, Rhs >	solve (const SparseMatrixBase< Rhs > &b) const

	SparseSolverBase ()

	~SparseSolverBase ()

Private Types
typedef IterativeSolverBase< GMRES >	Base

Private Attributes
Index	m_restart

Additional Inherited Members
Protected Types inherited from Eigen::IterativeSolverBase< GMRES< _MatrixType, _Preconditioner > >
typedef MatrixWrapper::ActualMatrixType	ActualMatrixType

typedef SparseSolverBase< GMRES< _MatrixType, _Preconditioner > >	Base

typedef internal::generic_matrix_wrapper< MatrixType >	MatrixWrapper

Protected Member Functions inherited from Eigen::IterativeSolverBase< GMRES< _MatrixType, _Preconditioner > >
void	grab (const InputType &A)

void	init ()

const ActualMatrixType &	matrix () const

Protected Attributes inherited from Eigen::IterativeSolverBase< GMRES< _MatrixType, _Preconditioner > >
bool	m_analysisIsOk

RealScalar	m_error

bool	m_factorizationIsOk

ComputationInfo	m_info

Index	m_iterations

MatrixWrapper	m_matrixWrapper

Index	m_maxIterations

Preconditioner	m_preconditioner

RealScalar	m_tolerance

Protected Attributes inherited from Eigen::SparseSolverBase< GMRES< _MatrixType, _Preconditioner > >
bool	m_isInitialized

Detailed Description

template<typename _MatrixType, typename _Preconditioner>
class Eigen::GMRES< _MatrixType, _Preconditioner >

A GMRES solver for sparse square problems.

This class allows to solve for A.x = b sparse linear problems using a generalized minimal residual method. The vectors x and b can be either dense or sparse.

Template Parameters

_MatrixType	the type of the sparse matrix A, can be a dense or a sparse matrix.
_Preconditioner	the type of the preconditioner. Default is DiagonalPreconditioner

The maximal number of iterations and tolerance value can be controlled via the setMaxIterations() and setTolerance() methods. The defaults are the size of the problem for the maximal number of iterations and NumTraits<Scalar>::epsilon() for the tolerance.

This class can be used as the direct solver classes. Here is a typical usage example:

int n = 10000;
VectorXd x(n), b(n);
SparseMatrix<double> A(n,n);
// fill A and b
GMRES<SparseMatrix<double> > solver(A);
x = solver.solve(b);
std::cout << "#iterations:     " << solver.iterations() << std::endl;
std::cout << "estimated error: " << solver.error()      << std::endl;
// update b, and solve again
x = solver.solve(b);

By default the iterations start with x=0 as an initial guess of the solution. One can control the start using the solveWithGuess() method.

GMRES can also be used in a matrix-free context, see the following example .

See also: class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner

Definition at line 212 of file GMRES.h.

Member Typedef Documentation

◆ Base

template<typename _MatrixType , typename _Preconditioner >

typedef IterativeSolverBase<GMRES> Eigen::GMRES< _MatrixType, _Preconditioner >::Base

private

Definition at line 262 of file GMRES.h.

◆ MatrixType

template<typename _MatrixType , typename _Preconditioner >

typedef _MatrixType Eigen::GMRES< _MatrixType, _Preconditioner >::MatrixType

Definition at line 274 of file GMRES.h.

◆ Preconditioner

template<typename _MatrixType , typename _Preconditioner >

typedef _Preconditioner Eigen::GMRES< _MatrixType, _Preconditioner >::Preconditioner

Definition at line 277 of file GMRES.h.

◆ RealScalar

template<typename _MatrixType , typename _Preconditioner >

typedef MatrixType::RealScalar Eigen::GMRES< _MatrixType, _Preconditioner >::RealScalar

Definition at line 276 of file GMRES.h.

◆ Scalar

template<typename _MatrixType , typename _Preconditioner >

typedef MatrixType::Scalar Eigen::GMRES< _MatrixType, _Preconditioner >::Scalar

Definition at line 275 of file GMRES.h.

Constructor & Destructor Documentation

◆ GMRES() [1/2]

template<typename _MatrixType , typename _Preconditioner >

Eigen::GMRES< _MatrixType, _Preconditioner >::GMRES ( )

inline

Default constructor.

Definition at line 282 of file GMRES.h.

◆ GMRES() [2/2]

template<typename _MatrixType , typename _Preconditioner >

template<typename MatrixDerived >

Eigen::GMRES< _MatrixType, _Preconditioner >::GMRES ( const EigenBase< MatrixDerived > & A )

inlineexplicit

Initialize the solver with matrix A for further Ax=b solving.

This constructor is a shortcut for the default constructor followed by a call to compute().

Warning: this class stores a reference to the matrix A as well as some precomputed values that depend on it. Therefore, if A is changed this class becomes invalid. Call compute() to update it with the new matrix A, or modify a copy of A.

Definition at line 295 of file GMRES.h.

◆ ~GMRES()

template<typename _MatrixType , typename _Preconditioner >

Eigen::GMRES< _MatrixType, _Preconditioner >::~GMRES ( )

inline

Definition at line 297 of file GMRES.h.

Member Function Documentation

◆ _solve_impl()

template<typename _MatrixType , typename _Preconditioner >

template<typename Rhs , typename Dest >

void Eigen::GMRES< _MatrixType, _Preconditioner >::_solve_impl	(	const Rhs &	b,
		MatrixBase< Dest > &	x
	)		const

inline

Definition at line 330 of file GMRES.h.

◆ _solve_with_guess_impl()

template<typename _MatrixType , typename _Preconditioner >

template<typename Rhs , typename Dest >

void Eigen::GMRES< _MatrixType, _Preconditioner >::_solve_with_guess_impl	(	const Rhs &	b,
		Dest &	x
	)		const

inline

Definition at line 310 of file GMRES.h.

◆ get_restart()

template<typename _MatrixType , typename _Preconditioner >

Index Eigen::GMRES< _MatrixType, _Preconditioner >::get_restart ( )

inline

Get the number of iterations after that a restart is performed.

Definition at line 301 of file GMRES.h.

◆ set_restart()

template<typename _MatrixType , typename _Preconditioner >

void Eigen::GMRES< _MatrixType, _Preconditioner >::set_restart ( const Index restart )

inline

Set the number of iterations after that a restart is performed.

Parameters

restart number of iterations for a restarti, default is 30.

Definition at line 306 of file GMRES.h.

Member Data Documentation

◆ m_restart

template<typename _MatrixType , typename _Preconditioner >

Index Eigen::GMRES< _MatrixType, _Preconditioner >::m_restart

private

Definition at line 270 of file GMRES.h.

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

GMRES.h

Public Types

Public Member Functions

Private Types

Private Attributes

Additional Inherited Members

Detailed Description

template<typename _MatrixType, typename _Preconditioner> class Eigen::GMRES< _MatrixType, _Preconditioner >

Member Typedef Documentation

◆ Base

◆ MatrixType

◆ Preconditioner

◆ RealScalar

◆ Scalar

Constructor & Destructor Documentation

◆ GMRES() [1/2]

◆ GMRES() [2/2]

◆ ~GMRES()

Member Function Documentation

◆ _solve_impl()

◆ _solve_with_guess_impl()

◆ get_restart()

◆ set_restart()

Member Data Documentation

◆ m_restart

template<typename _MatrixType, typename _Preconditioner>
class Eigen::GMRES< _MatrixType, _Preconditioner >