The IDR(s)STAB(l) is a combination of IDR(s) and BiCGSTAB(l). It is a short-recurrences Krylov method for sparse square problems. It can outperform both IDR(s) and BiCGSTAB(l). IDR(s)STAB(l) generally closely follows the optimal GMRES convergence in terms of the number of Matrix-Vector products. However, without the increasing cost per iteration of GMRES. IDR(s)STAB(l) is suitable for both indefinite systems and systems with complex eigenvalues. More...

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

Public Types
typedef MatrixType_	MatrixType

typedef Preconditioner_	Preconditioner

typedef MatrixType::RealScalar	RealScalar

typedef MatrixType::Scalar	Scalar

Public Types inherited from Eigen::IterativeSolverBase< IDRSTABL< 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
template<typename Rhs , typename Dest >
void	_solve_vector_with_guess_impl (const Rhs &b, Dest &x) const

	IDRSTABL ()

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

void	setL (Index L)

void	setS (Index S)

Public Member Functions inherited from Eigen::IterativeSolverBase< IDRSTABL< 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< IDRSTABL >	Base

Private Member Functions
const ActualMatrixType &	matrix () const

Private Attributes
RealScalar	m_error

ComputationInfo	m_info

bool	m_isInitialized

Index	m_iterations

Index	m_L

Index	m_S

Additional Inherited Members
Public Attributes inherited from Eigen::IterativeSolverBase< IDRSTABL< MatrixType_, Preconditioner_ > >
	ColsAtCompileTime

	MaxColsAtCompileTime

Protected Types inherited from Eigen::IterativeSolverBase< IDRSTABL< MatrixType_, Preconditioner_ > >
typedef MatrixWrapper::ActualMatrixType	ActualMatrixType

typedef SparseSolverBase< Derived >	Base

typedef internal::generic_matrix_wrapper< MatrixType >	MatrixWrapper

Protected Member Functions inherited from Eigen::IterativeSolverBase< IDRSTABL< MatrixType_, Preconditioner_ > >
void	grab (const InputType &A)

void	init ()

const ActualMatrixType &	matrix () const

Protected Attributes inherited from Eigen::IterativeSolverBase< IDRSTABL< 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::IDRSTABL< MatrixType_, Preconditioner_ >

The IDR(s)STAB(l) is a combination of IDR(s) and BiCGSTAB(l). It is a short-recurrences Krylov method for sparse square problems. It can outperform both IDR(s) and BiCGSTAB(l). IDR(s)STAB(l) generally closely follows the optimal GMRES convergence in terms of the number of Matrix-Vector products. However, without the increasing cost per iteration of GMRES. IDR(s)STAB(l) is suitable for both indefinite systems and systems with complex eigenvalues.

This class allows solving for A.x = b sparse linear problems. 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

This class follows the sparse solver concept .

The maximum 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 maximum number of iterations and NumTraits<Scalar>::epsilon() for the tolerance.

The tolerance is the maximum relative residual error: |Ax-b|/|b| for which the linear system is considered solved.

Performance: When using sparse matrices, best performance is achieved for a row-major sparse matrix format. Moreover, in this case multi-threading can be exploited if the user code is compiled with OpenMP enabled. See Eigen and multi-threading for details.

By default the iterations start with x=0 as an initial guess of the solution. One can control the start using the solveWithGuess() method.

IDR(s)STAB(l) can also be used in a matrix-free context, see the following example .

See also: class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner

Definition at line 412 of file IDRSTABL.h.

Member Typedef Documentation

◆ Base

template<typename MatrixType_ , typename Preconditioner_ >

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

private

Definition at line 413 of file IDRSTABL.h.

◆ MatrixType

template<typename MatrixType_ , typename Preconditioner_ >

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

Definition at line 423 of file IDRSTABL.h.

◆ Preconditioner

template<typename MatrixType_ , typename Preconditioner_ >

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

Definition at line 426 of file IDRSTABL.h.

◆ RealScalar

template<typename MatrixType_ , typename Preconditioner_ >

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

Definition at line 425 of file IDRSTABL.h.

◆ Scalar

template<typename MatrixType_ , typename Preconditioner_ >

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

Definition at line 424 of file IDRSTABL.h.

Constructor & Destructor Documentation

◆ IDRSTABL() [1/2]

template<typename MatrixType_ , typename Preconditioner_ >

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

inline

Default constructor.

Definition at line 430 of file IDRSTABL.h.

430 : m_L(2), m_S(4) {}

Eigen::IDRSTABL::m_S

Index m_S

Definition: IDRSTABL.h:420

Eigen::IDRSTABL::m_L

Index m_L

Definition: IDRSTABL.h:419

Code

◆ IDRSTABL() [2/2]

template<typename MatrixType_ , typename Preconditioner_ >

template<typename MatrixDerived >

Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::IDRSTABL ( 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 443 of file IDRSTABL.h.

443 : Base(A.derived()), m_L(2), m_S(4) {}

A

SparseMatrix< double > A(n, n)

Eigen::IDRSTABL::Base

IterativeSolverBase< IDRSTABL > Base

Definition: IDRSTABL.h:413

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

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

Code

Member Function Documentation

◆ _solve_vector_with_guess_impl()

template<typename MatrixType_ , typename Preconditioner_ >

template<typename Rhs , typename Dest >

void Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::_solve_vector_with_guess_impl	(	const Rhs &	b,
		Dest &	x
	)		const

inline

Loops over the number of columns of b and does the following:

sets the tolerance and maxIterations
Calls the function that has the core solver routine

Definition at line 452 of file IDRSTABL.h.

                                                                   {
     m_iterations = Base::maxIterations();
     m_error = Base::m_tolerance;
     bool ret = internal::idrstabl(matrix(), b, x, Base::m_preconditioner, m_iterations, m_error, m_L, m_S);
  
     m_info = (!ret) ? NumericalIssue : m_error <= 10 * Base::m_tolerance ? Success : NoConvergence;
   }

Code

◆ matrix()

template<typename MatrixType_ , typename Preconditioner_ >

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

private

◆ setL()

template<typename MatrixType_ , typename Preconditioner_ >

void Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::setL ( Index L )

inline

Sets the parameter L, indicating the amount of minimize residual steps are used.

Definition at line 462 of file IDRSTABL.h.

                      {
     eigen_assert(L >= 1 && "L needs to be positive");
     m_L = L;
   }

Code

◆ setS()

template<typename MatrixType_ , typename Preconditioner_ >

void Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::setS ( Index S )

inline

Sets the parameter S, indicating the dimension of the shadow residual space..

Definition at line 468 of file IDRSTABL.h.

                      {
     eigen_assert(S >= 1 && "S needs to be positive");
     m_S = S;
   }

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_L

template<typename MatrixType_ , typename Preconditioner_ >

Index Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::m_L

private

Definition at line 419 of file IDRSTABL.h.

◆ m_S

template<typename MatrixType_ , typename Preconditioner_ >

Index Eigen::IDRSTABL< MatrixType_, Preconditioner_ >::m_S

private

Definition at line 420 of file IDRSTABL.h.

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

IDRSTABL.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::IDRSTABL< MatrixType_, Preconditioner_ >

Member Typedef Documentation

◆ Base

◆ MatrixType

◆ Preconditioner

◆ RealScalar

◆ Scalar

Constructor & Destructor Documentation

◆ IDRSTABL() [1/2]

◆ IDRSTABL() [2/2]

Member Function Documentation

◆ _solve_vector_with_guess_impl()

◆ matrix()

◆ setL()

◆ setS()

Member Data Documentation

◆ m_error

◆ m_info

◆ m_isInitialized

◆ m_iterations

◆ m_L

◆ m_S

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