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

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

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

Public Types
typedef MatrixType_	MatrixType
typedef Preconditioner_	Preconditioner
typedef MatrixType::RealScalar	RealScalar
typedef MatrixType::Scalar	Scalar
Public Types inherited from Eigen::IterativeSolverBase< GMRES< MatrixType_, Preconditioner_ > >
typedef internal::traits< Derived >::MatrixType	MatrixType
typedef internal::traits< Derived >::Preconditioner	Preconditioner
typedef MatrixType::RealScalar	RealScalar
typedef MatrixType::Scalar	Scalar
typedef MatrixType::StorageIndex	StorageIndex

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

Private Types
typedef IterativeSolverBase< GMRES >	Base

Private Member Functions
const ActualMatrixType &	matrix () const

Private Attributes
RealScalar	m_error
ComputationInfo	m_info
bool	m_isInitialized
Index	m_iterations
Index	m_restart

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

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);

Code

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

Definition at line 271 of file GMRES.h.

Member Typedef Documentation

Base

template<typename MatrixType_ , typename Preconditioner_ >

typedef IterativeSolverBase<GMRES> Eigen::GMRES< MatrixType_, Preconditioner_ >::Base

private

Definition at line 273 of file GMRES.h.

MatrixType

template<typename MatrixType_ , typename Preconditioner_ >

typedef MatrixType_ Eigen::GMRES< MatrixType_, Preconditioner_ >::MatrixType

Definition at line 285 of file GMRES.h.

Preconditioner

template<typename MatrixType_ , typename Preconditioner_ >

typedef Preconditioner_ Eigen::GMRES< MatrixType_, Preconditioner_ >::Preconditioner

Definition at line 288 of file GMRES.h.

RealScalar

template<typename MatrixType_ , typename Preconditioner_ >

typedef MatrixType::RealScalar Eigen::GMRES< MatrixType_, Preconditioner_ >::RealScalar

Definition at line 287 of file GMRES.h.

Scalar

template<typename MatrixType_ , typename Preconditioner_ >

typedef MatrixType::Scalar Eigen::GMRES< MatrixType_, Preconditioner_ >::Scalar

Definition at line 286 of file GMRES.h.

Constructor & Destructor Documentation

GMRES() [1/2]

template<typename MatrixType_ , typename Preconditioner_ >

Eigen::GMRES< MatrixType_, Preconditioner_ >::GMRES ( )

inline

Default constructor.

Definition at line 293 of file GMRES.h.

: Base(), m_restart(30) {}

Code

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.

Definition at line 306 of file GMRES.h.

: Base(A.derived()), m_restart(30) {}

Code

~GMRES()

template<typename MatrixType_ , typename Preconditioner_ >

Eigen::GMRES< MatrixType_, Preconditioner_ >::~GMRES ( )

inline

Definition at line 308 of file GMRES.h.

{}

Code

Member Function Documentation

_solve_impl()

template<typename MatrixType_ , typename Preconditioner_ >

void Eigen::IterativeSolverBase< class >::_solve_impl

_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

Definition at line 321 of file GMRES.h.

  {
    m_iterations = Base::maxIterations();
    m_error = Base::m_tolerance;
    bool ret = internal::gmres(matrix(), b, x, Base::m_preconditioner, m_iterations, m_restart, m_error);
    m_info = (!ret) ? NumericalIssue
          : m_error <= Base::m_tolerance ? Success
          : NoConvergence;
  }

Code

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.

Definition at line 312 of file GMRES.h.

{ return m_restart; }

Code

matrix()

template<typename MatrixType_ , typename Preconditioner_ >

const ActualMatrixType & Eigen::IterativeSolverBase< class >::matrix

private

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.

Definition at line 317 of file GMRES.h.

{ m_restart=restart; }

Code

Member Data Documentation

m_error

template<typename MatrixType_ , typename Preconditioner_ >

RealScalar Eigen::IterativeSolverBase< class >::m_error

private

m_info

template<typename MatrixType_ , typename Preconditioner_ >

ComputationInfo Eigen::IterativeSolverBase< class >::m_info

private

m_isInitialized

template<typename MatrixType_ , typename Preconditioner_ >

bool Eigen::IterativeSolverBase< class >::m_isInitialized

private

m_iterations

template<typename MatrixType_ , typename Preconditioner_ >

Index Eigen::IterativeSolverBase< class >::m_iterations

private

m_restart

template<typename MatrixType_ , typename Preconditioner_ >

Index Eigen::GMRES< MatrixType_, Preconditioner_ >::m_restart

private

Definition at line 281 of file GMRES.h.

---

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

• GMRES.h