Eigen::BiCGSTAB< _MatrixType, _Preconditioner > Class Template Reference

A bi conjugate gradient stabilized solver for sparse square problems. More...

#include <BiCGSTAB.h>

Public Types
typedef _MatrixType	MatrixType
typedef MatrixType::Scalar	Scalar
typedef MatrixType::RealScalar	RealScalar
typedef _Preconditioner	Preconditioner

Public Member Functions
	BiCGSTAB ()
template<typename MatrixDerived >
	BiCGSTAB (const EigenBase< MatrixDerived > &A)
template<typename Rhs , typename Dest >
void	_solve_vector_with_guess_impl (const Rhs &b, Dest &x) const

Detailed Description

template<typename _MatrixType, typename _Preconditioner>
class Eigen::BiCGSTAB< _MatrixType, _Preconditioner >

A bi conjugate gradient stabilized solver for sparse square problems.

This class allows to solve for A.x = b sparse linear problems using a bi conjugate gradient stabilized algorithm. 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

\implsparsesolverconcept

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.

The tolerance corresponds to the relative residual error: |Ax-b|/|b|

Performance: when using sparse matrices, best performance is achied 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 TopicMultiThreading for details.

This class can be used as the direct solver classes. Here is a typical usage example:

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

BiCGSTAB can also be used in a matrix-free context, see the following example .

See also

class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner

Constructor & Destructor Documentation

BiCGSTAB() [1/2]

template<typename _MatrixType , typename _Preconditioner >

Eigen::BiCGSTAB< _MatrixType, _Preconditioner >::BiCGSTAB ( )

inline

Default constructor.

BiCGSTAB() [2/2]

template<typename _MatrixType , typename _Preconditioner >

template<typename MatrixDerived >

Eigen::BiCGSTAB< _MatrixType, _Preconditioner >::BiCGSTAB ( 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.

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

• BiCGSTAB.h