Eigen::GMRES< MatrixType_, Preconditioner_ > Class Template Reference

#include <Eigen/src/IterativeLinearSolvers/GMRES.h>

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 twice the number of columns of the matrix for the maximal number of iterations and NumTraits<Scalar>::epsilon() for the tolerance.

When a left preconditioner M is used, GMRES applies the stopping criterion to the preconditioned system M^{-1} A x = M^{-1} b. The reported error is therefore \(\|M^{-1}(b-Ax)\| / \|M^{-1}b\|\).

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

Inheritance diagram for Eigen::GMRES< MatrixType_, Preconditioner_ >:

Public Member Functions
Index	get_restart () const
	GMRES ()
template<typename MatrixDerived>
	GMRES (const EigenBase< MatrixDerived > &A)
void	set_restart (const Index restart)
Public Member Functions inherited from Eigen::IterativeSolverBase< GMRES< MatrixType_, Preconditioner_ > >
GMRES< MatrixType_, Preconditioner_ > &	analyzePattern (const EigenBase< MatrixDerived > &A)
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
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
void	solveWithGuessInPlace (const Rhs &b, Dest &x) const
RealScalar	tolerance () const
Public Member Functions inherited from Eigen::SparseSolverBase< GMRES< MatrixType_, Preconditioner_ > >
Solve< GMRES< MatrixType_, Preconditioner_ >, Rhs >	solve (const MatrixBase< Rhs > &b) const
Solve< GMRES< MatrixType_, Preconditioner_ >, Rhs >	solve (const SparseMatrixBase< Rhs > &b) const
	SparseSolverBase ()=default

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

get_restart()

template<typename MatrixType_, typename Preconditioner_>

Index Eigen::GMRES< MatrixType_, Preconditioner_ >::get_restart ( ) const

inline

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

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 restart, default is 30.

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

• /builds/libeigen/eigen/Eigen/src/IterativeLinearSolvers/GMRES.h