 Eigen-unsupported  3.4.90 (git rev 67eeba6e720c5745abc77ae6c92ce0a44aa7b7ae) 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
 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);
Matrix< double, Dynamic, 1 > VectorXd

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 .

class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner Inheritance diagram for Eigen::GMRES< MatrixType_, Preconditioner_ >:

## Public Member Functions

Index get_restart ()

GMRES ()

template<typename MatrixDerived >
GMRES (const EigenBase< MatrixDerived > &A)

void set_restart (const Index restart)

## ◆ 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.

## ◆ 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.

## ◆ 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.

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