qmr.h File Reference

#include "tbci/basics.h"

Include dependency graph for qmr.h:

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Macros
#define	QMR_OUT(r)

Functions
NAMESPACE_TBCI	INST3 (template< typename T, Matrix< T >, Vector< T > > class NN friend int QMR(const Matrix< T > &, Vector< T > &, const Vector< T > &, const Preconditioner_Sig< T, Matrix< T > > &, const Preconditioner_Sig< T, Matrix< T > > &, unsigned int &, double &);) INST3(template< typename T
NAMESPACE_TBCI Vector< T > class NN friend int	QMR (const BdMatrix< T > &, Vector< T > &, const Vector< T > &, const Preconditioner_Sig< T, BdMatrix< T > > &, const Preconditioner_Sig< T, BdMatrix< T > > &, unsigned int &, double &)
template<typename T, typename SysMatrix, typename SysVector>
int	QMR (const SysMatrix &A, SysVector &x, const SysVector &b, const Preconditioner_Sig< T, SysMatrix > &M1, const Preconditioner_Sig< T, SysMatrix > &M2, unsigned int &max_iter, double &tol)

Variables
NAMESPACE_TBCI	BdMatrix< T >

Detailed Description

TBCI::QMR solver

Version

Id

qmr.h,v 1.8.2.27 2019/05/28 11:13:02 garloff Exp

Definition in file qmr.h.

Macro Definition Documentation

QMR_OUT

#define QMR_OUT

(

r

)

Value:

do { err = r; goto qmr_out; } while(0)

Referenced by QMR().

Function Documentation

INST3()

NAMESPACE_TBCI INST3

(

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

)

QMR() [1/2]

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

References QMR(), and T.

Referenced by QMR().

QMR() [2/2]

template<typename T, typename SysMatrix, typename SysVector>

int QMR	(	const SysMatrix &	A,
		SysVector &	x,
		const SysVector &	b,
		const Preconditioner_Sig< T, SysMatrix > &	M1,
		const Preconditioner_Sig< T, SysMatrix > &	M2,
		unsigned int &	max_iter,
		double &	tol )

Iterative template routine – QMR

QMR solves the unsymmetric linear system Ax = b using the Quasi-Minimal Residual method following the algorithm as described on p. 24 in the SIAM Templates book.

Returns

-------------------------------------------------------—
return value indicates
---------— ------------------—
0 convergence within max_iter iterations
1 no convergence after max_iter iterations
breakdown in:
2 rho
3 beta
4 gamma
5 delta
6 ep

7 xi

Upon successful return, output arguments have the following values:

Parameters

x	– approximate solution to Ax=b
max_iter	– the number of iterations performed before the tolerance was reached
tol	– the residual after the final iteration

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

Definition at line 59 of file qmr.h.

References b, c, err, fabssqr(), gamma(), i, MATH__, p, QMR_OUT, Preconditioner_Sig< T, MatrixType >::solve(), sqr(), sqrt(), std::sqrt(), STD__, SysMatrix, Preconditioner_Sig< T, MatrixType >::transSolve(), x, and y.

Variable Documentation

BdMatrix< T >

NAMESPACE_TBCI BdMatrix< T >

Definition at line 15 of file qmr.h.