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);

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.

293 : Base(), m_restart(30) {}

Eigen::GMRES::Base

IterativeSolverBase< GMRES > Base

Definition: GMRES.h:273

Eigen::GMRES::m_restart

Index m_restart

Definition: GMRES.h:281

◆ 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.

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

EigenBase< SparseMatrix< double, Options_, StorageIndex_ > >::derived

SparseMatrix< double, Options_, StorageIndex_ > & derived()

◆ ~GMRES()

template<typename MatrixType_ , typename Preconditioner_ >

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

inline

Definition at line 308 of file GMRES.h.

308 {}

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;
   }

◆ 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.

312 { return m_restart; }

◆ 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.

317 { m_restart=restart; }

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

Public Types

Public Member Functions

Private Types

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

template<typename MatrixType_, typename Preconditioner_> class Eigen::GMRES< MatrixType_, Preconditioner_ >

Member Typedef Documentation

◆ Base

◆ MatrixType

◆ Preconditioner

◆ RealScalar

◆ Scalar

Constructor & Destructor Documentation

◆ GMRES() [1/2]

◆ GMRES() [2/2]

◆ ~GMRES()

Member Function Documentation

◆ _solve_impl()

◆ _solve_vector_with_guess_impl()

◆ get_restart()

◆ matrix()

◆ set_restart()

Member Data Documentation

◆ m_error

◆ m_info

◆ m_isInitialized

◆ m_iterations

◆ m_restart

template<typename MatrixType_, typename Preconditioner_>
class Eigen::GMRES< MatrixType_, Preconditioner_ >