bicgstab.h File Reference

Implements the TBCI::BiCGSTAB solver. More...

#include "tbci/vector.h"
#include "tbci/solver/precond.h"

Include dependency graph for bicgstab.h:

Go to the source code of this file.

Macros
#define	BICGSTAB_RESTART

Functions
NAMESPACE_TBCI	INST3 (template< typename T, Matrix< T >, double > class NN friend int BiCGSTAB(const Matrix< T > &, Vector< T > &, const Vector< T > &, const Preconditioner_Sig< T, Matrix< T > > &, unsigned int &, double &, const unsigned);) INST3(template< typename T
NAMESPACE_TBCI double class NN friend int	BiCGSTAB (const BdMatrix< T > &, Vector< T > &, const Vector< T > &, const Preconditioner_Sig< T, BdMatrix< T > > &, unsigned int &, double &, const unsigned)
	INST3 (template< typename T, Symm_BdMatrix< T >, double > class NN friend int BiCGSTAB(const Symm_BdMatrix< T > &, Vector< T > &, const Vector< T > &, const Preconditioner_Sig< T, Symm_BdMatrix< T > > &, unsigned int &, double &, const unsigned);) template< typename T
	BiCGSTAB solves the unsymmetric linear system Ax = b using the Preconditioned BiConjugate Gradient Stabilized method. More...
T_tol int	BiCGSTAB (const SysMatrix &A, Vector< T > &x, const Vector< T > &b, const Preconditioner_Sig< T, SysMatrix > &M, unsigned int &max_iter, T_tol &tol, const unsigned off=0)

Variables
NAMESPACE_TBCI	BdMatrix< T >
	SysMatrix

Detailed Description

Implements the TBCI::BiCGSTAB solver.

Definition in file bicgstab.h.

Macro Definition Documentation

#define BICGSTAB_RESTART

Definition at line 18 of file bicgstab.h.

Function Documentation

NAMESPACE_TBCI double class NN friend int BiCGSTAB	(	const BdMatrix< T > &	,
		Vector< T > &	,
		const Vector< T > &	,
		const Preconditioner_Sig< T, BdMatrix< T > > &	,
		unsigned int &	,
		double &	,
		const unsigned
	)

T_tol int BiCGSTAB	(	const SysMatrix &	A,
		Vector< T > &	x,
		const Vector< T > &	b,
		const Preconditioner_Sig< T, SysMatrix > &	M,
		unsigned int &	max_iter,
		T_tol &	tol,
		const unsigned	off = 0
	)

Definition at line 91 of file bicgstab.h.

References TBCI::dot(), std::fabs(), TBCI::fabssqr(), Vector< T >::fabssqr(), i, LIKELY, MATH__, p, Preconditioner_Sig< T, MatrixType >::solve(), sqr(), std::sqrt(), STD__, TBCI__, UNLIKELY, v, and x.

NAMESPACE_TBCI INST3

(

template< typename T, Matrix< T >, double > class NN friend int BiCGSTAB(const Matrix< T > &, Vector< T > &, const Vector< T > &, const Preconditioner_Sig< T, Matrix< T > > &, unsigned int &, double &, const unsigned);

)

INST3

(

template< typename T, Symm_BdMatrix< T >, double > class NN friend int BiCGSTAB(const Symm_BdMatrix< T > &, Vector< T > &, const Vector< T > &, const Preconditioner_Sig< T, Symm_BdMatrix< T > > &, unsigned int &, double &, const unsigned);

)

BiCGSTAB solves the unsymmetric linear system Ax = b using the Preconditioned BiConjugate Gradient Stabilized method.

BiCGSTAB follows the algorithm described on p. 27 of the SIAM Templates book.

Returns

The return value indicates convergence within max_iter (input) iterations (0), or no convergence within max_iter iterations (1). If the solver breaks down prematurely, it will return a value > 1.

Parameters

A	– System Matrix with coeffs of linear system to be solved
x	– input: initial guess value; output: approximate solution to Ax = b
b	– Vector (inhomogeneity)
M	– Preconditioner
max_iter	– input: max number of iterations allowed; output: the number of iterations performed before the tolerance was reached
tol	– input: desired accuracy (residual is a measure for the relative error); output: residual after the final iteration
off	– only used when debug output is generated: offset

If you use a preconditioner, don't forget to initialize it with the sys matrix (via constructor or update() member fct.)

BiCGstab is a good general purpose iterative solver; it's convergence is not as fast as CGS, when CGS finally gets on the right path, but it works a bit more reliably and makes progress right from the start.

Variable Documentation

NAMESPACE_TBCI BdMatrix< T >

Definition at line 49 of file bicgstab.h.

SysMatrix

Definition at line 90 of file bicgstab.h.