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

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Revision 1476 - (hide annotations)
Mon Apr 7 23:38:50 2008 UTC (13 years, 3 months ago) by gross
File MIME type: text/plain
File size: 6204 byte(s)
Jacobian-free Newton method added to Paso
1 gross 1476 /* $Id:$ */
2    
3     /*******************************************************
4     *
5     * Copyright 2008 by University of Queensland
6     *
7     * http://esscc.uq.edu.au
8     * Primary Business: Queensland, Australia
9     * Licensed under the Open Software License version 3.0
10     * http://www.opensource.org/licenses/osl-3.0.php
11     *
12     *******************************************************/
13     /*
14     * Purpose
15     * =======
16     *
17     * FGMRES solves the non-linear system f0+J_0*d=0
18     * where f0=F(x0), J_0 is the jacobian of F at x0.
19     *
20     * Convergence test: norm(f0+J_0*d)<=tolerance*norm(f0)
21     *
22     * Arguments
23     * =========
24     *
25     * Paso_Function * F evaluation of F (including any preconditioner)
26     *
27     * x0 (input) current point
28     *
29     * f0 (input) function F at current point x0
30     *
31     * d (output) solution of f0+J0*d=0 with accuracy tolerance
32     *
33     * iter (input/output)
34     * On input, the maximum num_iterations to be performed.
35     * On output, actual number of num_iterations performed.
36     * tolerance (input/output)
37     * On input, the allowable convergence measure for norm(f0+J0*d)/norm(f0)
38     * On output, the final value for norm(f0+J0*d)
39     * return value
40     *
41     * =SOLVER_NO_ERROR: Successful exit. approximate solution returned.
42     * =SOLVER_MAXNUM_ITER_REACHED
43     * =SOLVER_INPUT_ERROR Illegal parameter:
44     * =SOLVER_BREAKDOWN: bad luck!
45     * =SOLVER_MEMORY_ERROR : no memory available
46     *
47     * ==============================================================
48     */
49    
50     #include "Common.h"
51     #include "Solver.h"
52     #ifdef _OPENMP
53     #include <omp.h>
54     #endif
55    
56     err_t Paso_Solver_NLGMRES(
57     Paso_Function * F,
58     const double* f0,
59     const double* x0,
60     double * x,
61     dim_t *iter,
62     double* tolerance,
63     Paso_Performance* pp)
64     {
65     double static RENORMALIZATION_CONST=0.001;
66     dim_t l=(*iter)+1, iter_max=*iter,k=0,n=F->local_n,i,j;
67     double rel_tol=*tolerance, abs_tol, normf0, normv, normv2, hh, hr, nu, norm_of_residual=0.;
68     bool_t breakFlag=FALSE, maxIterFlag=FALSE, convergeFlag=FALSE;
69     double *h=NULL, **v=NULL, *c=NULL,*s=NULL,*g=NULL, *work=NULL;
70     err_t Status=SOLVER_NO_ERROR;
71    
72     /* Test the input parameters. */
73     if (n < 0 || iter_max<=0 || l<1 || rel_tol<0) {
74     return SOLVER_INPUT_ERROR;
75     }
76     Paso_zeroes(n,x);
77     /*
78     * allocate memory:
79     */
80     h=TMPMEMALLOC(l*l,double);
81     v=TMPMEMALLOC(iter_max,double*);
82     c=TMPMEMALLOC(l,double);
83     s=TMPMEMALLOC(l,double);
84     g=TMPMEMALLOC(l,double);
85     work=TMPMEMALLOC(n,double);
86    
87     if (h==NULL || v ==NULL || c== NULL || s == NULL || g== NULL || work==NULL) {
88     Status=SOLVER_MEMORY_ERROR;
89     } else {
90     for (i=0;i<iter_max;i++) v[i]=NULL;
91     for (i=0;i<iter_max;i++) {
92     v[i]=TMPMEMALLOC(n,double);
93     if (v[i]==NULL) {
94     Status=SOLVER_MEMORY_ERROR;
95     break;
96     }
97     }
98     }
99     if ( Status ==SOLVER_NO_ERROR ) {
100     /*
101     * the show begins:
102     */
103     normf0=Paso_l2(n,f0,F->mpi_info);
104     k=0;
105     convergeFlag=(ABS(normf0)<=0);
106     if (! convergeFlag) {
107     abs_tol=rel_tol*normf0;
108     Paso_zeroes(n,v[0]);
109     Paso_Update(n,1.,v[0],-1./normf0,f0);
110     g[0]=normf0;
111     while(! (breakFlag || maxIterFlag || convergeFlag)) {
112     k++;
113     /*
114     * call directional derivative function
115     */
116     Paso_FunctionDerivative(v[k],v[k-1],F,f0,x0,work);
117     normv=Paso_l2(n,v[k],F->mpi_info);
118     /*
119     * Modified Gram-Schmidt
120     */
121     for (j=0;j<k;j++){
122     hh=Paso_InnerProduct(n,v[j],v[k],F->mpi_info);
123     Paso_Update(n,1.,v[k],(-hh),v[j]);
124     h[INDEX2(j,k-1,l)]=hh;
125     }
126     normv2=Paso_l2(n,v[k],F->mpi_info);
127     h[INDEX2(k,k-1,l)]=normv2;
128     /*
129     * reorthogonalize
130     */
131     if (! (normv + RENORMALIZATION_CONST*normv2 > normv)) {
132     for (j=0;j<k;j++){
133     hr=Paso_InnerProduct(n,v[j],v[k],F->mpi_info);
134     h[INDEX2(j,k-1,l)]+=hr;
135     Paso_Update(n,1.,v[k],(-hr),v[j]);
136     }
137     normv2=Paso_l2(n,v[k],F->mpi_info);
138     h[INDEX2(k,k-1,l)]=normv2;
139     }
140     /*
141     * watch out for happy breakdown
142     */
143     if(normv2 > 0.) {
144     Paso_update(n,1./normv2,v[k],0.,v[k]);
145     }
146     /*
147     * Form and store the information for the new Givens rotation
148     */
149     ApplyGivensRotations(iter,&h[INDEX2(0,k-1,l)],c,s);
150     /*
151     * Don't divide by zero if solution has been found
152     */
153     g[k]=0;
154     nu=sqrt(h[INDEX2(k-1,k-1,l)]*h[INDEX2(k-1,k-1,l)]+h[INDEX2(k,k-1,l)]*h[INDEX2(k,k-1,l)]);
155     if (nu>0) {
156     c[k-1]=h[INDEX2(k-1,k-1,l)]/nu;
157     s[k-1]=-h[k,k-1]/nu;
158     h[INDEX2(k-1,k-1,l)]=c[k-1]*h[INDEX2(k-1,k-1,l)]-s[k-1]*h[k,k-1];
159     h[INDEX2(k,k-1,l)]=0;
160     ApplyGivensRotations(2,&(g[k-1]),&(c[k-1]),&(s[k-1]));
161     }
162     norm_of_residual=abs(g[k]);
163     maxIterFlag = (k>=iter_max);
164     convergeFlag = (abs(g[k]) <= abs_tol);
165     printf("FGMRES step %d: error %e (tol=%d)\n",k,abs(g[k]),abs_tol);
166     }
167     }
168     /*
169     * all done and ready for the forward substitution:
170     */
171    
172     for (i=0;i<k;i++) {
173     for (j=0;j<i;j++) {
174     g[i]-=h[INDEX2(j,i,l)]*g[j];
175     }
176     g[i]/=h[INDEX2(i,i,l)];
177     Paso_Update(n,x[k],g[i],v[i]);
178     }
179     }
180     /*
181     * clean up:
182     */
183     if ( v !=NULL) {
184     for (i=0;i<iter_max;i++) TMPMEMFREE(v);
185     }
186     TMPMEMFREE(h);
187     TMPMEMFREE(v);
188     TMPMEMFREE(c);
189     TMPMEMFREE(s);
190     TMPMEMFREE(g);
191     TMPMEMFREE(work);
192     *iter=k;
193     *tolerance=norm_of_residual;
194     return Status;
195     }
196    

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