GMRES< _MatrixType, _Preconditioner > Class Template Reference

Detailed Description

template<typename _MatrixType, typename _Preconditioner = DiagonalPreconditioner<typename _MatrixType::Scalar>>
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.

See Also

class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner

Inherits IterativeSolverBase< GMRES< _MatrixType, _Preconditioner > >.

Public Member Functions
int	get_restart ()
	GMRES ()
template<typename MatrixDerived >
	GMRES (const EigenBase< MatrixDerived > &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

Constructor & Destructor Documentation

GMRES ( )

inline

Default constructor.

Referenced by GMRES< _MatrixType, _Preconditioner >::solveWithGuess().

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

int get_restart ( )

inline

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

void 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.

const internal::solve_retval_with_guess<GMRES, Rhs, Guess> 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()

References GMRES< _MatrixType, _Preconditioner >::GMRES().

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

• GMRES.h