/[escript]/trunk/paso/src/BiCGStab.c
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Annotation of /trunk/paso/src/BiCGStab.c

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Revision 1312 - (hide annotations)
Mon Sep 24 06:18:44 2007 UTC (12 years, 1 month ago) by ksteube
File MIME type: text/plain
File size: 7597 byte(s)
The MPI branch is hereby closed. All future work should be in trunk.

Previously in revision 1295 I merged the latest changes to trunk into trunk-mpi-branch.
In this revision I copied all files from trunk-mpi-branch over the corresponding
trunk files. I did not use 'svn merge', it was a copy.

1 ksteube 1312
2 jgs 150 /* $Id$ */
3    
4 ksteube 1312 /*******************************************************
5     *
6     * Copyright 2003-2007 by ACceSS MNRF
7     * Copyright 2007 by University of Queensland
8     *
9     * http://esscc.uq.edu.au
10     * Primary Business: Queensland, Australia
11     * Licensed under the Open Software License version 3.0
12     * http://www.opensource.org/licenses/osl-3.0.php
13     *
14     *******************************************************/
15 dhawcroft 631
16     /*
17 jgs 150 Crude modifications and translations for Paso by Matt Davies and Lutz Gross
18     */
19    
20 gross 700 #include "Paso.h"
21     #include "SystemMatrix.h"
22 jgs 150 #include "Solver.h"
23     #ifdef _OPENMP
24     #include <omp.h>
25     #endif
26    
27     /* -- Iterative template routine --
28     * Univ. of Tennessee and Oak Ridge National Laboratory
29     * October 1, 1993
30     * Details of this algorithm are described in "Templates for the
31     * Solution of Linear Systems: Building Blocks for Iterative
32     * Methods", Barrett, Berry, Chan, Demmel, Donato, Dongarra,
33     * Eijkhout, Pozo, Romine, and van der Vorst, SIAM Publications,
34     * 1993. (ftp netlib2.cs.utk.edu; cd linalg; get templates.ps).
35     *
36     * Purpose
37     * =======
38     *
39     * BICGSTAB solves the linear system A*x = b using the
40     * BiConjugate Gradient Stabilized iterative method with
41     * preconditioning.
42     *
43     * Convergence test: norm( b - A*x )< TOL.
44     * For other measures, see the above reference.
45     *
46     * Arguments
47     * =========
48     *
49     * A (input)
50     *
51     * R (input) DOUBLE PRECISION array, dimension N.
52     * On entry, residual of inital guess X
53     *
54     * X (input/output) DOUBLE PRECISION array, dimension N.
55     * On input, the initial guess.
56     *
57     * ITER (input/output) INT
58     * On input, the maximum iterations to be performed.
59     * On output, actual number of iterations performed.
60     *
61     * RESID (input/output) DOUBLE PRECISION
62     * On input, the allowable convergence measure for
63     * norm( b - A*x )
64     * On output, the final value of this measure.
65     *
66     * return value
67     *
68     * = SOLVER_NO_ERROR: Successful exit. Iterated approximate solution returned.
69     * = SOLVER_MAXITER_REACHED
70     * = SOLVER_INPUT_ERROR Illegal parameter:
71     * = SOLVER_BREAKDOWN: If parameters RHO or OMEGA become smaller
72     * = SOLVER_MEMORY_ERROR : If parameters RHO or OMEGA become smaller
73     *
74     * ==============================================================
75     */
76    
77     err_t Paso_Solver_BiCGStab(
78     Paso_SystemMatrix * A,
79     double * r,
80     double * x,
81     dim_t *iter,
82 gross 584 double * tolerance,
83     Paso_Performance* pp) {
84 jgs 150
85    
86     /* Local variables */
87 ksteube 1312 double *rtld=NULL,*p=NULL,*v=NULL,*t=NULL,*phat=NULL,*shat=NULL,*s=NULL, *buf1=NULL, *buf0=NULL;
88 jgs 150 double beta,norm_of_residual,sum_1,sum_2,sum_3,sum_4,norm_of_residual_global;
89     double alpha, omega, omegaNumtr, omegaDenumtr, rho, tol, rho1;
90     dim_t num_iter=0,maxit,num_iter_global;
91 ksteube 1312 dim_t i0;
92 jgs 150 bool_t breakFlag=FALSE, maxIterFlag=FALSE, convergeFlag=FALSE;
93     dim_t status = SOLVER_NO_ERROR;
94 gross 1028 double *resid = tolerance;
95 ksteube 1312 dim_t n = Paso_SystemMatrix_getTotalNumRows(A);
96 jgs 150
97     /* Executable Statements */
98    
99     /* allocate memory: */
100     rtld=TMPMEMALLOC(n,double);
101     p=TMPMEMALLOC(n,double);
102     v=TMPMEMALLOC(n,double);
103     t=TMPMEMALLOC(n,double);
104     phat=TMPMEMALLOC(n,double);
105     shat=TMPMEMALLOC(n,double);
106     s=TMPMEMALLOC(n,double);
107     /* Test the input parameters. */
108    
109     if (n < 0) {
110     status = SOLVER_INPUT_ERROR;
111     } else if (rtld==NULL || p==NULL || v==NULL || t==NULL || phat==NULL || shat==NULL || s==NULL) {
112     status = SOLVER_MEMORY_ERROR;
113     } else {
114    
115     /* now bicgstab starts : */
116     maxit = *iter;
117     tol = *resid;
118    
119 gross 929 #pragma omp parallel firstprivate(maxit,tol) \
120     private(rho,omega,num_iter,norm_of_residual,beta,alpha,rho1, convergeFlag,maxIterFlag,breakFlag)
121 jgs 150 {
122     num_iter =0;
123 gross 929 convergeFlag=FALSE;
124     maxIterFlag=FALSE;
125     breakFlag=FALSE;
126 jgs 150
127     /* initialize arrays */
128    
129     #pragma omp for private(i0) schedule(static)
130     for (i0 = 0; i0 < n; i0++) {
131     rtld[i0]=0;
132     p[i0]=0;
133     v[i0]=0;
134     t[i0]=0;
135     phat[i0]=0;
136     shat[i0]=0;
137     }
138     #pragma omp for private(i0) schedule(static)
139     for (i0 = 0; i0 < n; i0++) rtld[i0] = r[i0];
140    
141     /* Perform BiConjugate Gradient Stabilized iteration. */
142    
143     L10:
144     ++(num_iter);
145     #pragma omp barrier
146     #pragma omp master
147     {
148     sum_1 = 0;
149     sum_2 = 0;
150     sum_3 = 0;
151     sum_4 = 0;
152     omegaNumtr = 0.0;
153     omegaDenumtr = 0.0;
154     }
155     #pragma omp barrier
156     #pragma omp for private(i0) reduction(+:sum_1) schedule(static)
157     for (i0 = 0; i0 < n; i0++) sum_1 += rtld[i0] * r[i0];
158     rho = sum_1;
159    
160     if (! (breakFlag = (ABS(rho) <= TOLERANCE_FOR_SCALARS))) {
161     /* Compute vector P. */
162    
163     if (num_iter > 1) {
164     beta = rho / rho1 * (alpha / omega);
165     #pragma omp for private(i0) schedule(static)
166     for (i0 = 0; i0 < n; i0++) p[i0] = r[i0] + beta * (p[i0] - omega * v[i0]);
167     } else {
168     #pragma omp for private(i0) schedule(static)
169     for (i0 = 0; i0 < n; i0++) p[i0] = r[i0];
170     }
171    
172     /* Compute direction adjusting vector PHAT and scalar ALPHA. */
173    
174     Paso_Solver_solvePreconditioner(A,&phat[0], &p[0]);
175 gross 415 Paso_SystemMatrix_MatrixVector_CSR_OFFSET0(ONE, A, &phat[0],ZERO, &v[0]);
176 jgs 150
177     #pragma omp for private(i0) reduction(+:sum_2) schedule(static)
178     for (i0 = 0; i0 < n; i0++) sum_2 += rtld[i0] * v[i0];
179     if (! (breakFlag = (ABS(sum_2) <= TOLERANCE_FOR_SCALARS))) {
180     alpha = rho / sum_2;
181    
182     #pragma omp for private(i0) reduction(+:sum_3) schedule(static)
183     for (i0 = 0; i0 < n; i0++) {
184     r[i0] -= alpha * v[i0];
185     s[i0] = r[i0];
186     sum_3 += s[i0] * s[i0];
187     }
188     norm_of_residual = sqrt(sum_3);
189    
190     /* Early check for tolerance. */
191     if ( (convergeFlag = (norm_of_residual <= tol)) ) {
192     #pragma omp for private(i0) schedule(static)
193     for (i0 = 0; i0 < n; i0++) x[i0] += alpha * phat[i0];
194     maxIterFlag = FALSE;
195     breakFlag = FALSE;
196     } else {
197     /* Compute stabilizer vector SHAT and scalar OMEGA. */
198     Paso_Solver_solvePreconditioner(A,&shat[0], &s[0]);
199 gross 415 Paso_SystemMatrix_MatrixVector_CSR_OFFSET0(ONE, A, &shat[0],ZERO,&t[0]);
200 jgs 150
201     #pragma omp for private(i0) reduction(+:omegaNumtr,omegaDenumtr) schedule(static)
202     for (i0 = 0; i0 < n; i0++) {
203     omegaNumtr +=t[i0] * s[i0];
204     omegaDenumtr += t[i0] * t[i0];
205     }
206     if (! (breakFlag = (ABS(omegaDenumtr) <= TOLERANCE_FOR_SCALARS))) {
207     omega = omegaNumtr / omegaDenumtr;
208    
209     #pragma omp for private(i0) reduction(+:sum_4) schedule(static)
210     for (i0 = 0; i0 < n; i0++) {
211     x[i0] += alpha * phat[i0] + omega * shat[i0];
212     r[i0] -= omega * t[i0];
213     sum_4 += r[i0] * r[i0];
214     }
215     norm_of_residual = sqrt(sum_4);
216     convergeFlag = norm_of_residual <= tol;
217     maxIterFlag = num_iter == maxit;
218     breakFlag = (ABS(omega) <= TOLERANCE_FOR_SCALARS);
219     }
220     }
221     }
222     if (!(convergeFlag || maxIterFlag || breakFlag)) {
223     rho1 = rho;
224     goto L10;
225     }
226     }
227     /* end of iteration */
228     #pragma omp master
229     {
230     num_iter_global=num_iter;
231     norm_of_residual_global=norm_of_residual;
232     if (maxIterFlag) {
233     status = SOLVER_MAXITER_REACHED;
234     } else if (breakFlag) {
235     status = SOLVER_BREAKDOWN;
236     }
237     }
238     } /* end of parallel region */
239     }
240     TMPMEMFREE(rtld);
241     TMPMEMFREE(p);
242     TMPMEMFREE(v);
243     TMPMEMFREE(t);
244     TMPMEMFREE(phat);
245     TMPMEMFREE(shat);
246     TMPMEMFREE(s);
247     *iter=num_iter_global;
248     *resid=norm_of_residual_global;
249    
250     /* End of BICGSTAB */
251     return status;
252     }

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