KryPcg.c File Reference

Krylov subspace methods – Preconditioned CG. More...

#include <math.h>
#include "fasp.h"
#include "fasp_functs.h"
#include "KryUtil.inl"

Go to the source code of this file.

Functions
INT	fasp_solver_dcsr_pcg (dCSRmat *A, dvector *b, dvector *u, precond *pc, const REAL tol, const REAL abstol, const INT MaxIt, const SHORT StopType, const SHORT PrtLvl)
	Preconditioned conjugate gradient method for solving Au=b. More...
INT	fasp_solver_dbsr_pcg (dBSRmat *A, dvector *b, dvector *u, precond *pc, const REAL tol, const REAL abstol, const INT MaxIt, const SHORT StopType, const SHORT PrtLvl)
	Preconditioned conjugate gradient method for solving Au=b. More...
INT	fasp_solver_dblc_pcg (dBLCmat *A, dvector *b, dvector *u, precond *pc, const REAL tol, const REAL abstol, const INT MaxIt, const SHORT StopType, const SHORT PrtLvl)
	Preconditioned conjugate gradient method for solving Au=b. More...
INT	fasp_solver_dstr_pcg (dSTRmat *A, dvector *b, dvector *u, precond *pc, const REAL tol, const REAL abstol, const INT MaxIt, const SHORT StopType, const SHORT PrtLvl)
	Preconditioned conjugate gradient method for solving Au=b. More...
INT	fasp_solver_pcg (mxv_matfree *mf, dvector *b, dvector *u, precond *pc, const REAL tol, const REAL abstol, const INT MaxIt, const SHORT StopType, const SHORT PrtLvl)

Detailed Description

Krylov subspace methods – Preconditioned CG.

Note

This file contains Level-3 (Kry) functions. It requires: AuxArray.c, AuxMemory.c, AuxMessage.c, BlaArray.c, BlaSpmvBLC.c, BlaSpmvBSR.c, BlaSpmvCSR.c, and BlaSpmvSTR.c

See KrySPcg.c for a safer version

Reference: Y. Saad 2003 Iterative methods for sparse linear systems (2nd Edition), SIAM

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Copyright (C) 2009–Present by the FASP team. All rights reserved.

Released under the terms of the GNU Lesser General Public License 3.0 or later.

Abstract algorithm

PCG method to solve A*x=b is to generate {x_k} to approximate x

Step 0. Given A, b, x_0, M

Step 1. Compute residual r_0 = b-A*x_0 and convergence check;

Step 2. Initialization z_0 = M^{-1}*r_0, p_0=z_0;

Step 3. Main loop ...

FOR k = 0:MaxIt

• get step size alpha = f(r_k,z_k,p_k);
• update solution: x_{k+1} = x_k + alpha*p_k;
• perform stagnation check;
• update residual: r_{k+1} = r_k - alpha*(A*p_k);
• perform residual check;
• obtain p_{k+1} using {p_0, p_1, ... , p_k};
• prepare for next iteration;
• print the result of k-th iteration; END FOR

Convergence check: norm(r)/norm(b) < tol

Stagnation check:

• IF norm(alpha*p_k)/norm(x_{k+1}) < tol_stag
  1. compute r=b-A*x_{k+1};
  2. convergence check;
  3. IF ( not converged & restart_number < Max_Stag_Check ) restart;
• END IF

Residual check:

• IF norm(r_{k+1})/norm(b) < tol
  1. compute the real residual r = b-A*x_{k+1};
  2. convergence check;
  3. IF ( not converged & restart_number < Max_Res_Check ) restart;
• END IF

Definition in file KryPcg.c.

Function Documentation

fasp_solver_dblc_pcg()

INT fasp_solver_dblc_pcg	(	dBLCmat *	A,
		dvector *	b,
		dvector *	u,
		precond *	pc,
		const REAL	tol,
		const REAL	abstol,
		const INT	MaxIt,
		const SHORT	StopType,
		const SHORT	PrtLvl
	)

Preconditioned conjugate gradient method for solving Au=b.

Parameters

A	Pointer to dBLCmat: coefficient matrix
b	Pointer to dvector: right hand side
u	Pointer to dvector: unknowns
pc	Pointer to precond: structure of precondition
tol	Tolerance for relative residual
abstol	Tolerance for absolute residual
MaxIt	Maximal number of iterations
StopType	Stopping criteria type
PrtLvl	How much information to print out

Returns

Iteration number if converges; ERROR otherwise.

Author

Xiaozhe Hu

Date

05/24/2010

Modified by Chensong Zhang on 03/28/2013

Definition at line 678 of file KryPcg.c.

fasp_solver_dbsr_pcg()

INT fasp_solver_dbsr_pcg	(	dBSRmat *	A,
		dvector *	b,
		dvector *	u,
		precond *	pc,
		const REAL	tol,
		const REAL	abstol,
		const INT	MaxIt,
		const SHORT	StopType,
		const SHORT	PrtLvl
	)

Preconditioned conjugate gradient method for solving Au=b.

Parameters

A	Pointer to dBSRmat: coefficient matrix
b	Pointer to dvector: right hand side
u	Pointer to dvector: unknowns
pc	Pointer to precond: structure of precondition
tol	Tolerance for relative residual
abstol	Tolerance for absolute residual
MaxIt	Maximal number of iterations
StopType	Stopping criteria type
PrtLvl	How much information to print out

Returns

Iteration number if converges; ERROR otherwise.

Author

Xiaozhe Hu

Date

05/26/2014

Definition at line 386 of file KryPcg.c.

fasp_solver_dcsr_pcg()

INT fasp_solver_dcsr_pcg	(	dCSRmat *	A,
		dvector *	b,
		dvector *	u,
		precond *	pc,
		const REAL	tol,
		const REAL	abstol,
		const INT	MaxIt,
		const SHORT	StopType,
		const SHORT	PrtLvl
	)

Preconditioned conjugate gradient method for solving Au=b.

Parameters

A	Pointer to dCSRmat: coefficient matrix
b	Pointer to dvector: right hand side
u	Pointer to dvector: unknowns
pc	Pointer to precond: structure of precondition
tol	Tolerance for relative residual
abstol	Tolerance for absolute residual
MaxIt	Maximal number of iterations
StopType	Stopping criteria type
PrtLvl	How much information to print out

Returns

Iteration number if converges; ERROR otherwise.

Author

Chensong Zhang, Xiaozhe Hu, Shiquan Zhang

Date

05/06/2010

Definition at line 96 of file KryPcg.c.

fasp_solver_dstr_pcg()

INT fasp_solver_dstr_pcg	(	dSTRmat *	A,
		dvector *	b,
		dvector *	u,
		precond *	pc,
		const REAL	tol,
		const REAL	abstol,
		const INT	MaxIt,
		const SHORT	StopType,
		const SHORT	PrtLvl
	)

Preconditioned conjugate gradient method for solving Au=b.

Parameters

A	Pointer to dSTRmat: coefficient matrix
b	Pointer to dvector: right hand side
u	Pointer to dvector: unknowns
pc	Pointer to precond: structure of precondition
tol	Tolerance for relative residual
abstol	Tolerance for absolute residual
MaxIt	Maximal number of iterations
StopType	Stopping criteria type
PrtLvl	How much information to print out

Returns

Iteration number if converges; ERROR otherwise.

Author

Zhiyang Zhou

Date

04/25/2010

Modified by Chensong Zhang on 03/28/2013

Definition at line 970 of file KryPcg.c.

fasp_solver_pcg()

INT fasp_solver_pcg	(	mxv_matfree *	mf,
		dvector *	b,
		dvector *	u,
		precond *	pc,
		const REAL	tol,
		const REAL	abstol,
		const INT	MaxIt,
		const SHORT	StopType,
		const SHORT	PrtLvl
	)

Definition at line 1260 of file KryPcg.c.