Eigen::GMRES< _MatrixType, _Preconditioner > Class Template Reference

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

#include <GMRES.h>

Public Types
typedef _MatrixType	MatrixType
typedef MatrixType::Scalar	Scalar
typedef MatrixType::RealScalar	RealScalar
typedef _Preconditioner	Preconditioner

Public Member Functions
	GMRES ()
template<typename MatrixDerived >
	GMRES (const EigenBase< MatrixDerived > &A)
Index	get_restart ()
void	set_restart (const Index restart)
template<typename Rhs , typename Dest >
void	_solve_with_guess_impl (const Rhs &b, Dest &x) const
template<typename Rhs , typename Dest >
void	_solve_impl (const Rhs &b, MatrixBase< Dest > &x) const

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 217 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 287 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 300 of file GMRES.h.

Member Function Documentation

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 306 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 311 of file GMRES.h.

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

• src/fmm/GMRES.h