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

#include <Eigen/src/IterativeLinearSolvers/IDRSTABL.h>

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

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

Public Member Functions
template<typename Rhs, typename Dest>
void	_solve_vector_with_guess_impl (const Rhs &b, Dest &x) const
	IDRSTABL ()=default
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_ > >
IDRSTABL< MatrixType_, Preconditioner_ > &	analyzePattern (const EigenBase< MatrixDerived > &A)
IDRSTABL< MatrixType_, Preconditioner_ > &	compute (const EigenBase< MatrixDerived > &A)
RealScalar	error () const
IDRSTABL< MatrixType_, Preconditioner_ > &	factorize (const EigenBase< MatrixDerived > &A)
ComputationInfo	info () const
Index	iterations () const
	IterativeSolverBase ()
	IterativeSolverBase (const EigenBase< MatrixDerived > &A)
Index	maxIterations () const
Preconditioner &	preconditioner ()
const Preconditioner &	preconditioner () const
IDRSTABL< MatrixType_, Preconditioner_ > &	setMaxIterations (Index maxIters)
IDRSTABL< MatrixType_, Preconditioner_ > &	setTolerance (const RealScalar &tolerance)
const SolveWithGuess< IDRSTABL< MatrixType_, Preconditioner_ >, Rhs, Guess >	solveWithGuess (const MatrixBase< Rhs > &b, const Guess &x0) const
void	solveWithGuessInPlace (const Rhs &b, Dest &x) const
RealScalar	tolerance () const
Public Member Functions inherited from Eigen::SparseSolverBase< IDRSTABL< MatrixType_, Preconditioner_ > >
Solve< IDRSTABL< MatrixType_, Preconditioner_ >, Rhs >	solve (const MatrixBase< Rhs > &b) const
Solve< IDRSTABL< MatrixType_, Preconditioner_ >, Rhs >	solve (const SparseMatrixBase< Rhs > &b) const
	SparseSolverBase ()=default

Constructor & Destructor Documentation

IDRSTABL() [1/2]

template<typename MatrixType_, typename Preconditioner_>

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

default

Default constructor.

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.

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:

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

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.

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.

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

• /builds/libeigen/eigen/Eigen/src/IterativeLinearSolvers/IDRSTABL.h