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 _Preconditioner	Preconditioner
typedef MatrixType::RealScalar	RealScalar
typedef MatrixType::Scalar	Scalar

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

Private Types
typedef IterativeSolverBase< BiCGSTAB >	Base

Private Member Functions
const ActualMatrixType &	matrix () const

Private Attributes
RealScalar	m_error
ComputationInfo	m_info
Index	m_iterations

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 Eigen and multi-threading for details.

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 ... */ 
  BiCGSTAB<SparseMatrix<double> > solver;
  solver.compute(A);
  x = solver.solve(b);
  std::cout << "#iterations:     " << solver.iterations() << std::endl;
  std::cout << "estimated error: " << solver.error()      << std::endl;
  /* ... update b ... */
  x = solver.solve(b); // solve again

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

Definition at line 113 of file BiCGSTAB.h.

Member Typedef Documentation

Base

template<typename _MatrixType , typename _Preconditioner >

typedef IterativeSolverBase<BiCGSTAB> Eigen::BiCGSTAB< _MatrixType, _Preconditioner >::Base

private

Definition at line 160 of file BiCGSTAB.h.

MatrixType

template<typename _MatrixType , typename _Preconditioner >

typedef _MatrixType Eigen::BiCGSTAB< _MatrixType, _Preconditioner >::MatrixType

Definition at line 167 of file BiCGSTAB.h.

Preconditioner

template<typename _MatrixType , typename _Preconditioner >

typedef _Preconditioner Eigen::BiCGSTAB< _MatrixType, _Preconditioner >::Preconditioner

Definition at line 170 of file BiCGSTAB.h.

RealScalar

template<typename _MatrixType , typename _Preconditioner >

typedef MatrixType::RealScalar Eigen::BiCGSTAB< _MatrixType, _Preconditioner >::RealScalar

Definition at line 169 of file BiCGSTAB.h.

Scalar

template<typename _MatrixType , typename _Preconditioner >

typedef MatrixType::Scalar Eigen::BiCGSTAB< _MatrixType, _Preconditioner >::Scalar

Definition at line 168 of file BiCGSTAB.h.

Constructor & Destructor Documentation

BiCGSTAB() [1/2]

template<typename _MatrixType , typename _Preconditioner >

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

inline

Default constructor.

Definition at line 175 of file BiCGSTAB.h.

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.

Definition at line 188 of file BiCGSTAB.h.

~BiCGSTAB()

template<typename _MatrixType , typename _Preconditioner >

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

inline

Definition at line 190 of file BiCGSTAB.h.

Member Function Documentation

_solve_vector_with_guess_impl()

template<typename _MatrixType , typename _Preconditioner >

template<typename Rhs , typename Dest >

void Eigen::BiCGSTAB< _MatrixType, _Preconditioner >::_solve_vector_with_guess_impl ( const Rhs &  b, Dest &  x  ) const

inline

Definition at line 194 of file BiCGSTAB.h.

matrix()

template<typename _MatrixType , typename _Preconditioner >

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

inlineprivate

Definition at line 419 of file IterativeSolverBase.h.

Member Data Documentation

m_error

template<typename _MatrixType , typename _Preconditioner >

RealScalar Eigen::IterativeSolverBase< Derived >::m_error

mutableprivate

Definition at line 436 of file IterativeSolverBase.h.

m_info

template<typename _MatrixType , typename _Preconditioner >

ComputationInfo Eigen::IterativeSolverBase< Derived >::m_info

mutableprivate

Definition at line 438 of file IterativeSolverBase.h.

m_iterations

template<typename _MatrixType , typename _Preconditioner >

Index Eigen::IterativeSolverBase< Derived >::m_iterations

mutableprivate

Definition at line 437 of file IterativeSolverBase.h.

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

• BiCGSTAB.h