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

#include <GMRES.h>

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

Public Types
typedef _MatrixType	MatrixType

typedef MatrixType::Scalar	Scalar

typedef MatrixType::Index	Index

typedef MatrixType::RealScalar	RealScalar

typedef _Preconditioner	Preconditioner

Public Types inherited from Eigen::IterativeSolverBase< GMRES< _MatrixType, _Preconditioner > >
typedef internal::traits< GMRES< _MatrixType, _Preconditioner > >::MatrixType	MatrixType

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

typedef MatrixType::Scalar	Scalar

typedef MatrixType::Index	Index

typedef MatrixType::RealScalar	RealScalar

Public Member Functions
	GMRES ()
	Default constructor. More...

template<typename MatrixDerived >
	GMRES (const EigenBase< MatrixDerived > &A)
	Initialize the solver with matrix A for further `Ax=b` solving. More...

int	get_restart ()
	Get the number of iterations after that a restart is performed.

void	set_restart (const int restart)
	Set the number of iterations after that a restart is performed. More...

template<typename Rhs , typename Guess >
const internal::solve_retval_with_guess< GMRES, Rhs, Guess >	solveWithGuess (const MatrixBase< Rhs > &b, const Guess &x0) const

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

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

Public Member Functions inherited from Eigen::IterativeSolverBase< GMRES< _MatrixType, _Preconditioner > >
GMRES< _MatrixType, _Preconditioner > &	derived ()

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

	IterativeSolverBase ()
	Default constructor. More...

	IterativeSolverBase (const EigenBase< InputDerived > &A)
	Initialize the solver with matrix A for further `Ax=b` solving. More...

GMRES< _MatrixType, _Preconditioner > &	analyzePattern (const EigenBase< InputDerived > &A)
	Initializes the iterative solver for the sparcity pattern of the matrix A for further solving `Ax=b` problems. More...

GMRES< _MatrixType, _Preconditioner > &	factorize (const EigenBase< InputDerived > &A)
	Initializes the iterative solver with the numerical values of the matrix A for further solving `Ax=b` problems. More...

GMRES< _MatrixType, _Preconditioner > &	compute (const EigenBase< InputDerived > &A)
	Initializes the iterative solver with the matrix A for further solving `Ax=b` problems. More...

Index	rows () const

Index	cols () const

RealScalar	tolerance () const

GMRES< _MatrixType, _Preconditioner > &	setTolerance (const RealScalar &tolerance)
	Sets the tolerance threshold used by the stopping criteria.

Preconditioner &	preconditioner ()

const Preconditioner &	preconditioner () const

int	maxIterations () const

GMRES< _MatrixType, _Preconditioner > &	setMaxIterations (int maxIters)
	Sets the max number of iterations.

int	iterations () const

RealScalar	error () const

const internal::solve_retval< GMRES< _MatrixType, _Preconditioner >, Rhs >	solve (const MatrixBase< Rhs > &b) const

const internal::sparse_solve_retval< IterativeSolverBase, Rhs >	solve (const SparseMatrixBase< Rhs > &b) const

ComputationInfo	info () const

void	_solve_sparse (const Rhs &b, SparseMatrix< DestScalar, DestOptions, DestIndex > &dest) const

Additional Inherited Members
Protected Member Functions inherited from Eigen::IterativeSolverBase< GMRES< _MatrixType, _Preconditioner > >
void	grabInput (const EigenBase< InputDerived > &A)

void	grabInput_impl (const EigenBase< InputDerived > &A)

void	grabInput_impl (MatrixType &A)

void	init ()

Protected Attributes inherited from Eigen::IterativeSolverBase< GMRES< _MatrixType, _Preconditioner > >
MatrixType	m_copyMatrix

const MatrixType *	mp_matrix

Preconditioner	m_preconditioner

int	m_maxIterations

RealScalar	m_tolerance

RealScalar	m_error

int	m_iterations

ComputationInfo	m_info

bool	m_isInitialized

bool	m_analysisIsOk

bool	m_factorizationIsOk

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.

See also: class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner

Constructor & Destructor Documentation

§ GMRES() [1/2]

template<typename _MatrixType, typename _Preconditioner>

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

inline

Default constructor.

§ 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.

Member Function Documentation

§ set_restart()

template<typename _MatrixType, typename _Preconditioner>

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

inline

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

Parameters

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

§ solveWithGuess()

template<typename _MatrixType, typename _Preconditioner>

template<typename Rhs , typename Guess >

const internal::solve_retval_with_guess<GMRES, Rhs, Guess> Eigen::GMRES< _MatrixType, _Preconditioner >::solveWithGuess	(	const MatrixBase< Rhs > &	b,
		const Guess &	x0
	)		const

inline

Returns: the solution x of \( A x = b \) using the current decomposition of A x0 as an initial solution.

See also: compute()

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

vendor/eigen/unsupported/Eigen/src/IterativeSolvers/GMRES.h

Public Types

Public Member Functions

Additional Inherited Members

Detailed Description

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

Constructor & Destructor Documentation

§ GMRES() [1/2]

§ GMRES() [2/2]

Member Function Documentation

§ set_restart()

§ solveWithGuess()

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