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

#include <GMRES.h>

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

Public Types
typedef MatrixType::Index	Index

typedef _MatrixType	MatrixType

typedef _Preconditioner	Preconditioner

typedef MatrixType::RealScalar	RealScalar

typedef MatrixType::Scalar	Scalar

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

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

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

typedef MatrixType::RealScalar	RealScalar

typedef MatrixType::Scalar	Scalar

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

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

int	get_restart ()

	GMRES ()

	GMRES (const MatrixType &A)

void	set_restart (const int restart)

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

	~GMRES ()

Public Member Functions inherited from Eigen::IterativeSolverBase< GMRES< _MatrixType, _Preconditioner > >
void	_solve_sparse (const Rhs &b, SparseMatrix< DestScalar, DestOptions, DestIndex > &dest) const

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

Index	cols () const

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

GMRES< _MatrixType, _Preconditioner > &	derived ()

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

RealScalar	error () const

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

ComputationInfo	info () const

int	iterations () const

	IterativeSolverBase ()

	IterativeSolverBase (const MatrixType &A)

int	maxIterations () const

Preconditioner &	preconditioner ()

const Preconditioner &	preconditioner () const

Index	rows () const

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

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

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

RealScalar	tolerance () const

	~IterativeSolverBase ()

Private Types
typedef IterativeSolverBase< GMRES >	Base

Private Attributes
int	m_restart

Additional Inherited Members
Protected Member Functions inherited from Eigen::IterativeSolverBase< GMRES< _MatrixType, _Preconditioner > >
void	init ()

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

RealScalar	m_error

bool	m_factorizationIsOk

ComputationInfo	m_info

bool	m_isInitialized

int	m_iterations

int	m_maxIterations

Preconditioner	m_preconditioner

RealScalar	m_tolerance

const MatrixType *	mp_matrix

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. Here is a step by step execution example starting with a random guess and printing the evolution of the estimated error:

x = VectorXd::Random(n);
solver.setMaxIterations(1);
int i = 0;
do {
x = solver.solveWithGuess(b,x);
std::cout << i << " : " << solver.error() << std::endl;
++i;
} while (solver.info()!=Success && i<100);
Note that such a step by step excution is slightly slower.

See also: class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner

Definition at line 204 of file GMRES.h.

Member Typedef Documentation

template<typename _MatrixType , typename _Preconditioner >

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

private

Definition at line 265 of file GMRES.h.

template<typename _MatrixType , typename _Preconditioner >

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

Definition at line 278 of file GMRES.h.

template<typename _MatrixType , typename _Preconditioner >

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

Definition at line 276 of file GMRES.h.

template<typename _MatrixType , typename _Preconditioner >

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

Definition at line 280 of file GMRES.h.

template<typename _MatrixType , typename _Preconditioner >

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

Definition at line 279 of file GMRES.h.

template<typename _MatrixType , typename _Preconditioner >

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

Definition at line 277 of file GMRES.h.

Constructor & Destructor Documentation

template<typename _MatrixType , typename _Preconditioner >

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

inline

Default constructor.

Definition at line 285 of file GMRES.h.

template<typename _MatrixType , typename _Preconditioner >

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

inline

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 297 of file GMRES.h.

template<typename _MatrixType , typename _Preconditioner >

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

inline

Definition at line 299 of file GMRES.h.

Member Function Documentation

template<typename _MatrixType , typename _Preconditioner >

template<typename Rhs , typename Dest >

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

inline

Definition at line 348 of file GMRES.h.

template<typename _MatrixType , typename _Preconditioner >

template<typename Rhs , typename Dest >

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

inline

Definition at line 328 of file GMRES.h.

template<typename _MatrixType , typename _Preconditioner >

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

inline

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

Definition at line 303 of file GMRES.h.

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.

Definition at line 308 of file GMRES.h.

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 using the current decomposition of A x0 as an initial solution.

See also: compute()

Definition at line 317 of file GMRES.h.

Member Data Documentation

template<typename _MatrixType , typename _Preconditioner >

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

private

Definition at line 273 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

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

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