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

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Revision 155 - (hide annotations)
Wed Nov 9 02:02:19 2005 UTC (13 years, 10 months ago) by jgs
Original Path: trunk/paso/src/Solvers/BiCGStab.c
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File size: 7453 byte(s)
move all directories from trunk/esys2 into trunk and remove esys2

1 jgs 150 /* $Id$ */
2    
3     /*
4     Crude modifications and translations for Paso by Matt Davies and Lutz Gross
5     */
6    
7     #include "Paso.h"
8     #include "SystemMatrix.h"
9     #include "Solver.h"
10     #ifdef _OPENMP
11     #include <omp.h>
12     #endif
13    
14     /* -- Iterative template routine --
15     * Univ. of Tennessee and Oak Ridge National Laboratory
16     * October 1, 1993
17     * Details of this algorithm are described in "Templates for the
18     * Solution of Linear Systems: Building Blocks for Iterative
19     * Methods", Barrett, Berry, Chan, Demmel, Donato, Dongarra,
20     * Eijkhout, Pozo, Romine, and van der Vorst, SIAM Publications,
21     * 1993. (ftp netlib2.cs.utk.edu; cd linalg; get templates.ps).
22     *
23     * Purpose
24     * =======
25     *
26     * BICGSTAB solves the linear system A*x = b using the
27     * BiConjugate Gradient Stabilized iterative method with
28     * preconditioning.
29     *
30     * Convergence test: norm( b - A*x )< TOL.
31     * For other measures, see the above reference.
32     *
33     * Arguments
34     * =========
35     *
36     * A (input)
37     *
38     * R (input) DOUBLE PRECISION array, dimension N.
39     * On entry, residual of inital guess X
40     *
41     * X (input/output) DOUBLE PRECISION array, dimension N.
42     * On input, the initial guess.
43     *
44     * ITER (input/output) INT
45     * On input, the maximum iterations to be performed.
46     * On output, actual number of iterations performed.
47     *
48     * RESID (input/output) DOUBLE PRECISION
49     * On input, the allowable convergence measure for
50     * norm( b - A*x )
51     * On output, the final value of this measure.
52     *
53     * return value
54     *
55     * = SOLVER_NO_ERROR: Successful exit. Iterated approximate solution returned.
56     * = SOLVER_MAXITER_REACHED
57     * = SOLVER_INPUT_ERROR Illegal parameter:
58     * = SOLVER_BREAKDOWN: If parameters RHO or OMEGA become smaller
59     * = SOLVER_MEMORY_ERROR : If parameters RHO or OMEGA become smaller
60     *
61     * ==============================================================
62     */
63    
64     err_t Paso_Solver_BiCGStab(
65     Paso_SystemMatrix * A,
66     double * r,
67     double * x,
68     dim_t *iter,
69     double * tolerance) {
70    
71    
72     /* Local variables */
73     double *rtld=NULL,*p=NULL,*v=NULL,*t=NULL,*phat=NULL,*shat=NULL,*s=NULL;
74     double beta,norm_of_residual,sum_1,sum_2,sum_3,sum_4,norm_of_residual_global;
75     double alpha, omega, omegaNumtr, omegaDenumtr, rho, tol, rho1;
76     dim_t num_iter=0,maxit,num_iter_global;
77     dim_t i0;
78     bool_t breakFlag=FALSE, maxIterFlag=FALSE, convergeFlag=FALSE;
79     dim_t status = SOLVER_NO_ERROR;
80    
81     /* adapt original routine parameters */
82     dim_t n = A->num_cols * A-> col_block_size;;
83     double * resid = tolerance;
84    
85     /* Executable Statements */
86    
87     /* allocate memory: */
88     rtld=TMPMEMALLOC(n,double);
89     p=TMPMEMALLOC(n,double);
90     v=TMPMEMALLOC(n,double);
91     t=TMPMEMALLOC(n,double);
92     phat=TMPMEMALLOC(n,double);
93     shat=TMPMEMALLOC(n,double);
94     s=TMPMEMALLOC(n,double);
95    
96     /* Test the input parameters. */
97    
98     if (n < 0) {
99     status = SOLVER_INPUT_ERROR;
100     } else if (rtld==NULL || p==NULL || v==NULL || t==NULL || phat==NULL || shat==NULL || s==NULL) {
101     status = SOLVER_MEMORY_ERROR;
102     } else {
103    
104     /* now bicgstab starts : */
105     maxit = *iter;
106     tol = *resid;
107    
108     #pragma omp parallel firstprivate(maxit,tol,convergeFlag,maxIterFlag,breakFlag) \
109     private(rho,omega,num_iter,norm_of_residual,beta,alpha,rho1)
110     {
111     num_iter =0;
112    
113     /* initialize arrays */
114    
115     #pragma omp for private(i0) schedule(static)
116     for (i0 = 0; i0 < n; i0++) {
117     rtld[i0]=0;
118     p[i0]=0;
119     v[i0]=0;
120     t[i0]=0;
121     phat[i0]=0;
122     shat[i0]=0;
123     }
124     #pragma omp for private(i0) schedule(static)
125     for (i0 = 0; i0 < n; i0++) rtld[i0] = r[i0];
126    
127     /* Perform BiConjugate Gradient Stabilized iteration. */
128    
129     L10:
130     ++(num_iter);
131     #pragma omp barrier
132     #pragma omp master
133     {
134     sum_1 = 0;
135     sum_2 = 0;
136     sum_3 = 0;
137     sum_4 = 0;
138     omegaNumtr = 0.0;
139     omegaDenumtr = 0.0;
140     }
141     #pragma omp barrier
142     #pragma omp for private(i0) reduction(+:sum_1) schedule(static)
143     for (i0 = 0; i0 < n; i0++) sum_1 += rtld[i0] * r[i0];
144     rho = sum_1;
145    
146     if (! (breakFlag = (ABS(rho) <= TOLERANCE_FOR_SCALARS))) {
147     /* Compute vector P. */
148    
149     if (num_iter > 1) {
150     beta = rho / rho1 * (alpha / omega);
151     #pragma omp for private(i0) schedule(static)
152     for (i0 = 0; i0 < n; i0++) p[i0] = r[i0] + beta * (p[i0] - omega * v[i0]);
153     } else {
154     #pragma omp for private(i0) schedule(static)
155     for (i0 = 0; i0 < n; i0++) p[i0] = r[i0];
156     }
157    
158     /* Compute direction adjusting vector PHAT and scalar ALPHA. */
159    
160     Paso_Solver_solvePreconditioner(A,&phat[0], &p[0]);
161     Paso_SystemMatrix_MatrixVector(ONE, A, &phat[0],ZERO, &v[0]);
162    
163     #pragma omp for private(i0) reduction(+:sum_2) schedule(static)
164     for (i0 = 0; i0 < n; i0++) sum_2 += rtld[i0] * v[i0];
165     if (! (breakFlag = (ABS(sum_2) <= TOLERANCE_FOR_SCALARS))) {
166     alpha = rho / sum_2;
167    
168     #pragma omp for private(i0) reduction(+:sum_3) schedule(static)
169     for (i0 = 0; i0 < n; i0++) {
170     r[i0] -= alpha * v[i0];
171     s[i0] = r[i0];
172     sum_3 += s[i0] * s[i0];
173     }
174     norm_of_residual = sqrt(sum_3);
175    
176     /* Early check for tolerance. */
177     if ( (convergeFlag = (norm_of_residual <= tol)) ) {
178     #pragma omp for private(i0) schedule(static)
179     for (i0 = 0; i0 < n; i0++) x[i0] += alpha * phat[i0];
180     maxIterFlag = FALSE;
181     breakFlag = FALSE;
182     } else {
183     /* Compute stabilizer vector SHAT and scalar OMEGA. */
184     Paso_Solver_solvePreconditioner(A,&shat[0], &s[0]);
185     Paso_SystemMatrix_MatrixVector(ONE, A, &shat[0],ZERO,&t[0]);
186    
187     #pragma omp for private(i0) reduction(+:omegaNumtr,omegaDenumtr) schedule(static)
188     for (i0 = 0; i0 < n; i0++) {
189     omegaNumtr +=t[i0] * s[i0];
190     omegaDenumtr += t[i0] * t[i0];
191     }
192     if (! (breakFlag = (ABS(omegaDenumtr) <= TOLERANCE_FOR_SCALARS))) {
193     omega = omegaNumtr / omegaDenumtr;
194    
195     #pragma omp for private(i0) reduction(+:sum_4) schedule(static)
196     for (i0 = 0; i0 < n; i0++) {
197     x[i0] += alpha * phat[i0] + omega * shat[i0];
198     r[i0] -= omega * t[i0];
199     sum_4 += r[i0] * r[i0];
200     }
201     norm_of_residual = sqrt(sum_4);
202     convergeFlag = norm_of_residual <= tol;
203     maxIterFlag = num_iter == maxit;
204     breakFlag = (ABS(omega) <= TOLERANCE_FOR_SCALARS);
205     }
206     }
207     }
208     if (!(convergeFlag || maxIterFlag || breakFlag)) {
209     rho1 = rho;
210     goto L10;
211     }
212     }
213     /* end of iteration */
214     #pragma omp master
215     {
216     num_iter_global=num_iter;
217     norm_of_residual_global=norm_of_residual;
218     if (maxIterFlag) {
219     status = SOLVER_MAXITER_REACHED;
220     } else if (breakFlag) {
221     status = SOLVER_BREAKDOWN;
222     }
223     }
224     } /* end of parallel region */
225     }
226     TMPMEMFREE(rtld);
227     TMPMEMFREE(p);
228     TMPMEMFREE(v);
229     TMPMEMFREE(t);
230     TMPMEMFREE(phat);
231     TMPMEMFREE(shat);
232     TMPMEMFREE(s);
233     *iter=num_iter_global;
234     *resid=norm_of_residual_global;
235    
236     /* End of BICGSTAB */
237     return status;
238     }
239     /*
240     * $Log$
241     * Revision 1.2 2005/09/15 03:44:40 jgs
242     * Merge of development branch dev-02 back to main trunk on 2005-09-15
243     *
244     * Revision 1.1.2.1 2005/09/05 06:29:49 gross
245     * These files have been extracted from finley to define a stand alone libray for iterative
246     * linear solvers on the ALTIX. main entry through Paso_solve. this version compiles but
247     * has not been tested yet.
248     *
249     *
250     */

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