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Eigen::GMRES< _MatrixType, _Preconditioner > Class Template Reference
Sparse linear algebra » Reference » IterativeLinearSolvers_Module

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

#include <GMRES.h>

Inheritance diagram for Eigen::GMRES< _MatrixType, _Preconditioner >:
Eigen::IterativeSolverBase< GMRES< _MatrixType, _Preconditioner > > Eigen::SparseSolverBase< Derived > Eigen::internal::noncopyable

Public Types

typedef _MatrixType MatrixType
 
typedef MatrixType::Scalar Scalar
 
typedef MatrixType::RealScalar RealScalar
 
typedef _Preconditioner Preconditioner
 
- Public Types inherited from Eigen::IterativeSolverBase< GMRES< _MatrixType, _Preconditioner > >
enum  
 
typedef internal::traits< GMRES< _MatrixType, _Preconditioner > >::MatrixType MatrixType
 
typedef internal::traits< GMRES< _MatrixType, _Preconditioner > >::Preconditioner Preconditioner
 
typedef MatrixType::Scalar Scalar
 
typedef MatrixType::StorageIndex StorageIndex
 
typedef MatrixType::RealScalar RealScalar
 

Public Member Functions

 GMRES ()
 
template<typename MatrixDerived >
 GMRES (const EigenBase< MatrixDerived > &A)
 
 ~GMRES ()
 
Index get_restart ()
 
void set_restart (const Index restart)
 
template<typename Rhs , typename Dest >
void _solve_vector_with_guess_impl (const Rhs &b, Dest &x) const
 
template<typename Rhs , typename Dest >
void _solve_impl (const Rhs &b, Dest &x) const
 
- Public Member Functions inherited from Eigen::IterativeSolverBase< GMRES< _MatrixType, _Preconditioner > >
 IterativeSolverBase ()
 
 IterativeSolverBase (const EigenBase< MatrixDerived > &A)
 
 ~IterativeSolverBase ()
 
GMRES< _MatrixType, _Preconditioner > & analyzePattern (const EigenBase< MatrixDerived > &A)
 
GMRES< _MatrixType, _Preconditioner > & factorize (const EigenBase< MatrixDerived > &A)
 
GMRES< _MatrixType, _Preconditioner > & compute (const EigenBase< MatrixDerived > &A)
 
EIGEN_CONSTEXPR Index rows () const EIGEN_NOEXCEPT
 
EIGEN_CONSTEXPR Index cols () const EIGEN_NOEXCEPT
 
RealScalar tolerance () const
 
GMRES< _MatrixType, _Preconditioner > & setTolerance (const RealScalar &tolerance)
 
Preconditioner & preconditioner ()
 
const Preconditioner & preconditioner () const
 
Index maxIterations () const
 
GMRES< _MatrixType, _Preconditioner > & setMaxIterations (Index maxIters)
 
Index iterations () const
 
RealScalar error () const
 
const SolveWithGuess< GMRES< _MatrixType, _Preconditioner >, Rhs, Guess > solveWithGuess (const MatrixBase< Rhs > &b, const Guess &x0) const
 
ComputationInfo info () const
 
void _solve_with_guess_impl (const Rhs &b, SparseMatrixBase< DestDerived > &aDest) const
 
internal::enable_if< Rhs::ColsAtCompileTime!=1 &&DestDerived::ColsAtCompileTime!=1 >::type _solve_with_guess_impl (const Rhs &b, MatrixBase< DestDerived > &aDest) const
 
internal::enable_if< Rhs::ColsAtCompileTime==1||DestDerived::ColsAtCompileTime==1 >::type _solve_with_guess_impl (const Rhs &b, MatrixBase< DestDerived > &dest) const
 
void _solve_impl (const Rhs &b, Dest &x) const
 
GMRES< _MatrixType, _Preconditioner > & derived ()
 
const GMRES< _MatrixType, _Preconditioner > & derived () const
 
- Public Member Functions inherited from Eigen::SparseSolverBase< Derived >
 SparseSolverBase ()
 
 ~SparseSolverBase ()
 
Derived & derived ()
 
const Derived & derived () const
 
template<typename Rhs >
const Solve< Derived, Rhs > solve (const MatrixBase< Rhs > &b) const
 
template<typename Rhs >
const Solve< Derived, Rhs > solve (const SparseMatrixBase< Rhs > &b) const
 
template<typename Rhs , typename Dest >
void _solve_impl (const SparseMatrixBase< Rhs > &b, SparseMatrixBase< Dest > &dest) const
 

Additional Inherited Members

- Protected Types inherited from Eigen::IterativeSolverBase< GMRES< _MatrixType, _Preconditioner > >
typedef SparseSolverBase< GMRES< _MatrixType, _Preconditioner > > Base
 
typedef internal::generic_matrix_wrapper< MatrixType > MatrixWrapper
 
typedef MatrixWrapper::ActualMatrixType ActualMatrixType
 
- Protected Member Functions inherited from Eigen::IterativeSolverBase< GMRES< _MatrixType, _Preconditioner > >
void init ()
 
const ActualMatrixType & matrix () const
 
void grab (const InputType &A)
 
- Protected Attributes inherited from Eigen::IterativeSolverBase< GMRES< _MatrixType, _Preconditioner > >
MatrixWrapper m_matrixWrapper
 
Preconditioner m_preconditioner
 
Index m_maxIterations
 
RealScalar m_tolerance
 
RealScalar m_error
 
Index m_iterations
 
ComputationInfo m_info
 
bool m_analysisIsOk
 
bool m_factorizationIsOk
 
bool m_isInitialized
 
- Protected Attributes inherited from Eigen::SparseSolverBase< Derived >
bool m_isInitialized
 

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);
solver
BiCGSTAB< SparseMatrix< double > > solver
Definition BiCGSTAB_simple.cpp:5
n
int n
Definition BiCGSTAB_simple.cpp:1
b
Scalar * b
Definition benchVecAdd.cpp:17
A
Matrix< SCALARA, Dynamic, Dynamic, opt_A > A
Definition bench_gemm.cpp:48
Eigen::GMRES
A GMRES solver for sparse square problems.
Definition GMRES.h:270
Eigen::Matrix
The matrix class, also used for vectors and row-vectors.
Definition Matrix.h:180
Eigen::SparseMatrix
A versatible sparse matrix representation.
Definition SparseMatrix.h:98
x
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Definition gnuplot_common_settings.hh:12

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

Member Typedef Documentation

◆ MatrixType

template<typename _MatrixType , typename _Preconditioner >
typedef _MatrixType Eigen::GMRES< _MatrixType, _Preconditioner >::MatrixType

◆ Preconditioner

template<typename _MatrixType , typename _Preconditioner >
typedef _Preconditioner Eigen::GMRES< _MatrixType, _Preconditioner >::Preconditioner

◆ RealScalar

template<typename _MatrixType , typename _Preconditioner >
typedef MatrixType::RealScalar Eigen::GMRES< _MatrixType, _Preconditioner >::RealScalar

◆ Scalar

template<typename _MatrixType , typename _Preconditioner >
typedef MatrixType::Scalar Eigen::GMRES< _MatrixType, _Preconditioner >::Scalar

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.

◆ ~GMRES()

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

Member Function Documentation

◆ _solve_impl()

template<typename _MatrixType , typename _Preconditioner >
template<typename Rhs , typename Dest >
void Eigen::IterativeSolverBase< Derived >::_solve_impl ( const Rhs &  b,
Dest &  x 
) const
inline

◆ _solve_vector_with_guess_impl()

template<typename _MatrixType , typename _Preconditioner >
template<typename Rhs , typename Dest >
void Eigen::GMRES< _MatrixType, _Preconditioner >::_solve_vector_with_guess_impl ( const Rhs &  b,
Dest &  x 
) const
inline

◆ 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
restartnumber of iterations for a restarti, default is 30.
The documentation for this class was generated from the following file:
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