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

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

#include <BiCGSTAB.h>

Inheritance diagram for Eigen::BiCGSTAB< _MatrixType, _Preconditioner >:

List of all members.

Public Types
typedef MatrixType::Index	Index
typedef _MatrixType	MatrixType
typedef _Preconditioner	Preconditioner
typedef MatrixType::RealScalar	RealScalar
typedef MatrixType::Scalar	Scalar
Public Member Functions
template<typename Rhs , typename Dest >
void	_solve (const Rhs &b, Dest &x) const
template<typename Rhs , typename Dest >
void	_solveWithGuess (const Rhs &b, Dest &x) const
	BiCGSTAB ()
	BiCGSTAB (const MatrixType &A)
template<typename Rhs , typename Guess >
const internal::solve_retval_with_guess < BiCGSTAB, Rhs, Guess >	solveWithGuess (const MatrixBase< Rhs > &b, const Guess &x0) const
	~BiCGSTAB ()
Private Types
typedef IterativeSolverBase < BiCGSTAB >	Base

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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

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
 BiCGSTAB<SparseMatrix<double> > solver;
 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. Here is a step by step execution example starting with a random guess and printing the evolution of the estimated error: *

 x = VectorXd::Random(n);
 solver.setMaxIterations(1);
 int i = 0;
 do {
   x = solver.solveWithGuess(b,x);
   std::cout << i << " : " << solver.error() << std::endl;
   ++i;
 } while (solver.info()!=Success && i<100);

Note that such a step by step excution is slightly slower.

See also:

class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner

Definition at line 172 of file BiCGSTAB.h.

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Member Typedef Documentation

template<typename _MatrixType , typename _Preconditioner >

typedef IterativeSolverBase<BiCGSTAB> Eigen::BiCGSTAB< _MatrixType, _Preconditioner >::Base [private]

Definition at line 174 of file BiCGSTAB.h.

template<typename _MatrixType , typename _Preconditioner >

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

Reimplemented from Eigen::IterativeSolverBase< BiCGSTAB< _MatrixType, _Preconditioner > >.

Definition at line 183 of file BiCGSTAB.h.

template<typename _MatrixType , typename _Preconditioner >

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

Reimplemented from Eigen::IterativeSolverBase< BiCGSTAB< _MatrixType, _Preconditioner > >.

Definition at line 181 of file BiCGSTAB.h.

template<typename _MatrixType , typename _Preconditioner >

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

Reimplemented from Eigen::IterativeSolverBase< BiCGSTAB< _MatrixType, _Preconditioner > >.

Definition at line 185 of file BiCGSTAB.h.

template<typename _MatrixType , typename _Preconditioner >

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

Reimplemented from Eigen::IterativeSolverBase< BiCGSTAB< _MatrixType, _Preconditioner > >.

Definition at line 184 of file BiCGSTAB.h.

template<typename _MatrixType , typename _Preconditioner >

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

Reimplemented from Eigen::IterativeSolverBase< BiCGSTAB< _MatrixType, _Preconditioner > >.

Definition at line 182 of file BiCGSTAB.h.

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Constructor & Destructor Documentation

template<typename _MatrixType , typename _Preconditioner >

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

(

)

[inline]

Default constructor.

Definition at line 190 of file BiCGSTAB.h.

template<typename _MatrixType , typename _Preconditioner >

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

(

const MatrixType &

A

)

[inline]

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 202 of file BiCGSTAB.h.

template<typename _MatrixType , typename _Preconditioner >

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

(

)

[inline]

Definition at line 204 of file BiCGSTAB.h.

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Member Function Documentation

template<typename _MatrixType , typename _Preconditioner >

template<typename Rhs , typename Dest >

void Eigen::BiCGSTAB< _MatrixType, _Preconditioner >::_solve	(	const Rhs &	b,
		Dest &	x
	)		const [inline]

Definition at line 244 of file BiCGSTAB.h.

template<typename _MatrixType , typename _Preconditioner >

template<typename Rhs , typename Dest >

void Eigen::BiCGSTAB< _MatrixType, _Preconditioner >::_solveWithGuess	(	const Rhs &	b,
		Dest &	x
	)		const [inline]

Definition at line 224 of file BiCGSTAB.h.

template<typename _MatrixType , typename _Preconditioner >

template<typename Rhs , typename Guess >

const internal::solve_retval_with_guess<BiCGSTAB, Rhs, Guess> Eigen::BiCGSTAB< _MatrixType, _Preconditioner >::solveWithGuess	(	const MatrixBase< Rhs > &	b,
		const Guess &	x0
	)		const [inline]

Returns:

the solution x of using the current decomposition of A x0 as an initial solution.

See also:

compute()

Definition at line 213 of file BiCGSTAB.h.

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

• BiCGSTAB.h