cg.h File Reference

The iterative Vector equation solver TBCI::CG. More...

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

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Functions
NAMESPACE_TBCI	INST3 (template< typename T, Matrix< T >, Vector< T > > class NN friend int CG(const Matrix< T > &, Vector< T > &, const Vector< T > &, const Preconditioner_Sig< T, Matrix< T > > &, unsigned int &, double &);) INST3(template< typename T
NAMESPACE_TBCI Vector< T > class NN friend int	CG (const BdMatrix< T > &, Vector< T > &, const Vector< T > &, const Preconditioner_Sig< T, BdMatrix< T > > &, unsigned int &, double &)
template<typename T , typename SysMatrix , typename SysVector >
int	CG (const SysMatrix &A, SysVector &x, const SysVector &b, const Preconditioner_Sig< T, SysMatrix > &M, unsigned int &max_iter, double &tol)
	Iterative template solver routine – CG. More...
	INST3 (template< typename T, Matrix< T >, Vector< T > > class NN friend int CG2(const Matrix< T > &, Vector< T > &, const Vector< T > &, const Preconditioner_Sig< T, Matrix< T > > &, unsigned int &, double &);) INST3(template< typename T
Vector< T > class NN friend int	CG2 (const BdMatrix< T > &, Vector< T > &, const Vector< T > &, const Preconditioner_Sig< T, BdMatrix< T > > &, unsigned int &, double &)
template<typename T , typename SysMatrix , typename SysVector >
int	CG2 (const SysMatrix &A, SysVector &x, const SysVector &b, const Preconditioner_Sig< T, SysMatrix > &M, unsigned int &max_iter, double &tol)
	CG2 solves the symmetric complex (positive definite?) linear system Ax=b using the Conjugate Gradient method. More...

Variables
NAMESPACE_TBCI	BdMatrix< T >

Detailed Description

The iterative Vector equation solver TBCI::CG.

Definition in file cg.h.

Function Documentation

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

template<typename T , typename SysMatrix , typename SysVector >

int CG	(	const SysMatrix &	A,
		SysVector &	x,
		const SysVector &	b,
		const Preconditioner_Sig< T, SysMatrix > &	M,
		unsigned int &	max_iter,
		double &	tol
	)

Iterative template solver routine – CG.

CG solves the symmetric positive definite linear system Ax=b using the Conjugate Gradient method.

CG follows the algorithm described on p. 15 in the SIAM Templates book.

Returns

The return value indicates convergence within max_iter (input) iterations (0), or no convergence within max_iter iterations (1).

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

Definition at line 45 of file cg.h.

References BVector< T >::dim, TBCI::dot(), i, p, Preconditioner_Sig< T, MatrixType >::solve(), and z.

Vector<T> class NN friend int CG2	(	const BdMatrix< T > &	,
		Vector< T > &	,
		const Vector< T > &	,
		const Preconditioner_Sig< T, BdMatrix< T > > &	,
		unsigned int &	,
		double &
	)

template<typename T , typename SysMatrix , typename SysVector >

int CG2	(	const SysMatrix &	A,
		SysVector &	x,
		const SysVector &	b,
		const Preconditioner_Sig< T, SysMatrix > &	M,
		unsigned int &	max_iter,
		double &	tol
	)

CG2 solves the symmetric complex (positive definite?) linear system Ax=b using the Conjugate Gradient method.

Definition at line 112 of file cg.h.

References BVector< T >::dim, i, p, Preconditioner_Sig< T, MatrixType >::solve(), and z.

NAMESPACE_TBCI INST3

(

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

)

INST3

(

template< typename T, Matrix< T >, Vector< T > > class NN friend int CG2(const Matrix< T > &, Vector< T > &, const Vector< T > &, const Preconditioner_Sig< T, Matrix< T > > &, unsigned int &, double &);

)

Variable Documentation

BdMatrix< T >

Definition at line 19 of file cg.h.