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

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
_MatrixTypethe type of the sparse matrix A, can be a dense or a sparse matrix.
_Preconditionerthe 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

Public Member Functions

Index get_restart ()
template<typename MatrixDerived >
 GMRES (const EigenBase< MatrixDerived > &A)
void set_restart (const Index restart)

Constructor & Destructor Documentation

◆ GMRES() [1/2]

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

Default constructor.

◆ GMRES() [2/2]

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

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().

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 ( )

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)

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

restartnumber of iterations for a restarti, default is 30.

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