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

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Revision 1954 - (hide annotations)
Fri Oct 31 03:22:34 2008 UTC (11 years, 3 months ago) by artak
File MIME type: text/plain
File size: 18165 byte(s)
condition is added to check wheter row sum is ZERO and some new coarsening algorithm is also added
1 jfenwick 1851
2     /*******************************************************
3     *
4     * Copyright (c) 2003-2008 by University of Queensland
5     * Earth Systems Science Computational Center (ESSCC)
6     * http://www.uq.edu.au/esscc
7     *
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    
15     /**************************************************************/
16    
17     /* Paso: AMG preconditioner with reordering */
18    
19     /**************************************************************/
20    
21     /* Author: artak@access.edu.au */
22    
23     /**************************************************************/
24    
25     #include "Paso.h"
26     #include "Solver.h"
27     #include "PasoUtil.h"
28 artak 1931 #include "UMFPACK.h"
29 phornby 1917 #include "Pattern_coupling.h"
30 jfenwick 1851
31     /**************************************************************/
32    
33     /* free all memory used by AMG */
34    
35     void Paso_Solver_AMG_free(Paso_Solver_AMG * in) {
36     if (in!=NULL) {
37     Paso_Solver_AMG_free(in->AMG_of_Schur);
38 artak 1939 Paso_Solver_GS_free(in->GS);
39 jfenwick 1851 MEMFREE(in->inv_A_FF);
40     MEMFREE(in->A_FF_pivot);
41     Paso_SparseMatrix_free(in->A_FC);
42     Paso_SparseMatrix_free(in->A_CF);
43     MEMFREE(in->rows_in_F);
44     MEMFREE(in->rows_in_C);
45     MEMFREE(in->mask_F);
46     MEMFREE(in->mask_C);
47     MEMFREE(in->x_F);
48     MEMFREE(in->b_F);
49     MEMFREE(in->x_C);
50     MEMFREE(in->b_C);
51     MEMFREE(in);
52     }
53     }
54    
55     /**************************************************************/
56    
57     /* constructs the block-block factorization of
58    
59     [ A_FF A_FC ]
60     A_p=
61     [ A_CF A_FF ]
62    
63     to
64    
65     [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ]
66     [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ]
67    
68    
69     where S=A_FF-ACF*invA_FF*A_FC within the shape of S
70    
71     then AMG is applied to S again until S becomes empty
72    
73     */
74 artak 1890 Paso_Solver_AMG* Paso_Solver_getAMG(Paso_SparseMatrix *A_p,bool_t verbose,dim_t level) {
75 jfenwick 1851 Paso_Solver_AMG* out=NULL;
76     dim_t n=A_p->numRows;
77     dim_t n_block=A_p->row_block_size;
78     index_t* mis_marker=NULL;
79 artak 1881 index_t* counter=NULL;
80     index_t iPtr,*index, *where_p, iPtr_s;
81     dim_t i,k,j,j0;
82 jfenwick 1851 Paso_SparseMatrix * schur=NULL;
83 artak 1881 Paso_SparseMatrix * schur_withFillIn=NULL;
84 phornby 1917 double time0,time1,time2,S;
85 artak 1890
86 jfenwick 1851 /* identify independend set of rows/columns */
87     mis_marker=TMPMEMALLOC(n,index_t);
88     counter=TMPMEMALLOC(n,index_t);
89     out=MEMALLOC(1,Paso_Solver_AMG);
90     out->AMG_of_Schur=NULL;
91     out->inv_A_FF=NULL;
92     out->A_FF_pivot=NULL;
93     out->A_FC=NULL;
94     out->A_CF=NULL;
95     out->rows_in_F=NULL;
96     out->rows_in_C=NULL;
97     out->mask_F=NULL;
98     out->mask_C=NULL;
99     out->x_F=NULL;
100     out->b_F=NULL;
101     out->x_C=NULL;
102     out->b_C=NULL;
103 artak 1890 out->A=Paso_SparseMatrix_getReference(A_p);
104 artak 1939 out->GS=Paso_Solver_getGS(A_p,verbose);
105 artak 1954 out->GS->sweeps=4;
106 artak 1890 out->level=level;
107 artak 1881
108 jfenwick 1851 if ( !(Paso_checkPtr(mis_marker) || Paso_checkPtr(out) || Paso_checkPtr(counter) ) ) {
109     /* identify independend set of rows/columns */
110     time0=Paso_timer();
111     #pragma omp parallel for private(i) schedule(static)
112     for (i=0;i<n;++i) mis_marker[i]=-1;
113 artak 1954 /*Paso_Pattern_RS(A_p,mis_marker,0.25);*/
114     /*Paso_Pattern_Aggregiation(A_p,mis_marker,0.5);*/
115     Paso_Pattern_coup(A_p,mis_marker,0.05);
116 jfenwick 1851 time2=Paso_timer()-time0;
117     if (Paso_noError()) {
118     #pragma omp parallel for private(i) schedule(static)
119     for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
120     out->n=n;
121     out->n_block=n_block;
122     out->n_F=Paso_Util_cumsum(n,counter);
123     out->mask_F=MEMALLOC(n,index_t);
124     out->rows_in_F=MEMALLOC(out->n_F,index_t);
125     out->inv_A_FF=MEMALLOC(n_block*n_block*out->n_F,double);
126     out->A_FF_pivot=NULL; /* later use for block size>3 */
127     if (! (Paso_checkPtr(out->mask_F) || Paso_checkPtr(out->inv_A_FF) || Paso_checkPtr(out->rows_in_F) ) ) {
128     #pragma omp parallel
129     {
130     /* creates an index for F from mask */
131     #pragma omp for private(i) schedule(static)
132     for (i = 0; i < out->n_F; ++i) out->rows_in_F[i]=-1;
133     #pragma omp for private(i) schedule(static)
134     for (i = 0; i < n; ++i) {
135     if (mis_marker[i]) {
136     out->rows_in_F[counter[i]]=i;
137     out->mask_F[i]=counter[i];
138     } else {
139     out->mask_F[i]=-1;
140     }
141     }
142 artak 1881 /* Compute row-sum for getting rs(A_FF)*/
143     #pragma omp for private(i,iPtr) schedule(static)
144     for (i = 0; i < out->n_F; ++i) {
145 artak 1902 out->inv_A_FF[i]=0;
146 artak 1881 for (iPtr=A_p->pattern->ptr[out->rows_in_F[i]];iPtr<A_p->pattern->ptr[out->rows_in_F[i] + 1]; ++iPtr) {
147 artak 1902 out->inv_A_FF[i]+=A_p->val[iPtr];
148 artak 1881 }
149     }
150 artak 1954
151     /* for (i=0;i<out->n_F;++i) {
152     fprintf(stderr,"GET INV_A_FF %g %d of %d (%d)\n",out->inv_A_FF[i],i,out->rows_in_F[i],(out->inv_A_FF[i]==0));
153     }
154     fprintf(stderr,"END\n");
155     */
156 phornby 1917 #pragma omp for private(i, where_p,iPtr,index) schedule(static)
157 jfenwick 1851 for (i = 0; i < out->n_F; i++) {
158     /* find main diagonal */
159     iPtr=A_p->pattern->ptr[out->rows_in_F[i]];
160     index=&(A_p->pattern->index[iPtr]);
161     where_p=(index_t*)bsearch(&out->rows_in_F[i],
162     index,
163     A_p->pattern->ptr[out->rows_in_F[i] + 1]-A_p->pattern->ptr[out->rows_in_F[i]],
164     sizeof(index_t),
165     Paso_comparIndex);
166     if (where_p==NULL) {
167     Paso_setError(VALUE_ERROR, "Paso_Solver_getAMG: main diagonal element missing.");
168     } else {
169     iPtr+=(index_t)(where_p-index);
170     /* get inverse of A_FF block: */
171 artak 1902 S=out->inv_A_FF[i];
172     if (ABS(A_p->val[iPtr])>0.) {
173     if(ABS(S)>0.)
174     out->inv_A_FF[i]=1./S;
175 artak 1954 else
176 artak 1931 {
177 artak 1954 fprintf(stderr,"ROWSUM OF ROW %d->%d is 0\n",i,out->rows_in_F[i]);
178 artak 1931 S=0;
179     for (iPtr=A_p->pattern->ptr[out->rows_in_F[i]];iPtr<A_p->pattern->ptr[out->rows_in_F[i] + 1]; ++iPtr) {
180     if(A_p->val[iPtr]!=0) {
181     fprintf(stderr,"A_p[%d,%d]=%f ",out->rows_in_F[i],A_p->pattern->index[iPtr],A_p->val[iPtr]);
182     S+=A_p->val[iPtr];
183     }
184     }
185     fprintf(stderr,"\n SUMMMMMMM %f\n",S);
186     }
187 artak 1954 } else {
188 artak 1902 Paso_setError(ZERO_DIVISION_ERROR, "Paso_Solver_getAMG: Break-down in AMG decomposition: non-regular main diagonal block.");
189 artak 1890 }
190 artak 1881 }
191 jfenwick 1851 }
192     } /* end parallel region */
193    
194     if( Paso_noError()) {
195     /* if there are no nodes in the coarse level there is no more work to do */
196     out->n_C=n-out->n_F;
197 artak 1954 if (level<2) {
198     /*if (out->n_C>10) {*/
199 jfenwick 1851 out->rows_in_C=MEMALLOC(out->n_C,index_t);
200     out->mask_C=MEMALLOC(n,index_t);
201     if (! (Paso_checkPtr(out->mask_C) || Paso_checkPtr(out->rows_in_C) ) ) {
202     /* creates an index for C from mask */
203     #pragma omp parallel for private(i) schedule(static)
204     for (i = 0; i < n; ++i) counter[i]=! mis_marker[i];
205     Paso_Util_cumsum(n,counter);
206     #pragma omp parallel
207     {
208     #pragma omp for private(i) schedule(static)
209     for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
210     #pragma omp for private(i) schedule(static)
211     for (i = 0; i < n; ++i) {
212     if (! mis_marker[i]) {
213     out->rows_in_C[counter[i]]=i;
214     out->mask_C[i]=counter[i];
215     } else {
216     out->mask_C[i]=-1;
217     }
218     }
219     } /* end parallel region */
220     /* get A_CF block: */
221     out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
222     if (Paso_noError()) {
223     /* get A_FC block: */
224     out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
225 artak 1881 /* get A_CC block: */
226 jfenwick 1851 if (Paso_noError()) {
227     schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
228 artak 1881
229     /*find the pattern of the schur complement with fill in*/
230     schur_withFillIn=Paso_SparseMatrix_alloc(A_p->type,Paso_Pattern_binop(PATTERN_FORMAT_DEFAULT, schur->pattern, Paso_Pattern_multiply(PATTERN_FORMAT_DEFAULT,out->A_CF->pattern,out->A_FC->pattern)),1,1);
231 artak 1902
232 artak 1881 /* copy values over*/
233     #pragma omp for private(i,iPtr,iPtr_s,j,j0) schedule(static)
234     for (i = 0; i < schur_withFillIn->numRows; ++i) {
235     for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
236     j=schur_withFillIn->pattern->index[iPtr];
237     schur_withFillIn->val[iPtr]=0.;
238     for (iPtr_s=schur->pattern->ptr[i];iPtr_s<schur->pattern->ptr[i + 1]; ++iPtr_s){
239     j0=schur->pattern->index[iPtr_s];
240     if (j==j0) {
241     schur_withFillIn->val[iPtr]=schur->val[iPtr_s];
242     break;
243     }
244     }
245     }
246     }
247 artak 1902 time0=Paso_timer()-time0;
248 artak 1931
249 jfenwick 1851 if (Paso_noError()) {
250     time1=Paso_timer();
251     /* update A_CC block to get Schur complement and then apply AMG to it */
252 artak 1881 Paso_Solver_updateIncompleteSchurComplement(schur_withFillIn,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC);
253 jfenwick 1851 time1=Paso_timer()-time1;
254 artak 1939 out->AMG_of_Schur=Paso_Solver_getAMG(schur_withFillIn,verbose,level+1);
255 artak 1881
256 artak 1931 /*Paso_SparseMatrix_free(schur);*/
257 artak 1890 /* Paso_SparseMatrix_free(schur_withFillIn);*/
258 jfenwick 1851 }
259     /* allocate work arrays for AMG application */
260     if (Paso_noError()) {
261     out->x_F=MEMALLOC(n_block*out->n_F,double);
262     out->b_F=MEMALLOC(n_block*out->n_F,double);
263     out->x_C=MEMALLOC(n_block*out->n_C,double);
264     out->b_C=MEMALLOC(n_block*out->n_C,double);
265 artak 1890
266 jfenwick 1851 if (! (Paso_checkPtr(out->x_F) || Paso_checkPtr(out->b_F) || Paso_checkPtr(out->x_C) || Paso_checkPtr(out->b_C) ) ) {
267     #pragma omp parallel
268     {
269     #pragma omp for private(i,k) schedule(static)
270     for (i = 0; i < out->n_F; ++i) {
271     for (k=0; k<n_block;++k) {
272     out->x_F[i*n_block+k]=0.;
273     out->b_F[i*n_block+k]=0.;
274     }
275     }
276     #pragma omp for private(i,k) schedule(static)
277     for (i = 0; i < out->n_C; ++i) {
278     for (k=0; k<n_block;++k) {
279     out->x_C[i*n_block+k]=0.;
280     out->b_C[i*n_block+k]=0.;
281     }
282     }
283     } /* end parallel region */
284     }
285     }
286     }
287     }
288     }
289     }
290     }
291     }
292     }
293     }
294     TMPMEMFREE(mis_marker);
295     TMPMEMFREE(counter);
296     if (Paso_noError()) {
297     if (verbose) {
298     printf("AMG: %d unknowns eliminated. %d left.\n",out->n_F,n-out->n_F);
299 artak 1954 if (out->n_C>10) {
300 jfenwick 1851 printf("timing: AMG: MIS/reordering/elemination : %e/%e/%e\n",time2,time0,time1);
301     } else {
302     printf("timing: AMG: MIS: %e\n",time2);
303     }
304     }
305     return out;
306     } else {
307     Paso_Solver_AMG_free(out);
308     return NULL;
309     }
310     }
311    
312     /**************************************************************/
313    
314     /* apply AMG precondition b-> x
315    
316     in fact it solves
317    
318     [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ] [ x_F ] = [b_F]
319     [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] [ x_C ] = [b_C]
320    
321     in the form
322    
323     b->[b_F,b_C]
324     x_F=invA_FF*b_F
325     b_C=b_C-A_CF*x_F
326     x_C=AMG(b_C)
327     b_F=b_F-A_FC*x_C
328     x_F=invA_FF*b_F
329     x<-[x_F,x_C]
330    
331     should be called within a parallel region
332     barrier synconization should be performed to make sure that the input vector available
333    
334     */
335    
336     void Paso_Solver_solveAMG(Paso_Solver_AMG * amg, double * x, double * b) {
337 artak 1954 dim_t i,k,oldsweeps,j;
338 artak 1890 double *r=MEMALLOC(amg->n,double);
339 artak 1939 /*Paso_Solver_GS* GS=NULL;*/
340 artak 1954 double *bold=MEMALLOC(amg->n,double);
341     double *bnew=MEMALLOC(amg->n,double);
342     double *x0=MEMALLOC(amg->n,double);
343     index_t iPtr;
344 artak 1939
345 artak 1954 if (amg->level==2) {
346     /*if (amg->n_C<=10) {*/
347 artak 1939 Paso_UMFPACK1(amg->A,x,b,0);
348 jfenwick 1851 } else {
349 artak 1954
350 artak 1902 /* presmoothing */
351 artak 1939 Paso_Solver_solveGS(amg->GS,x,b);
352     oldsweeps=amg->GS->sweeps;
353     if (amg->GS->sweeps>1) {
354 artak 1931
355     #pragma omp parallel for private(i) schedule(static)
356 artak 1954 for (i=0;i<amg->GS->n;++i) bold[i]=b[i];
357 artak 1931
358 artak 1939 while(amg->GS->sweeps>1) {
359 artak 1931 #pragma omp parallel for private(i) schedule(static)
360 artak 1954 for (i=0;i<amg->GS->n;++i) bnew[i]=bold[i]+b[i];
361 artak 1931 /* Compute the residual b=b-Ax*/
362     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(DBLE(-1), amg->A, x, DBLE(1), bnew);
363     /* Go round again*/
364 artak 1939 Paso_Solver_solveGS(amg->GS,x,bnew);
365 artak 1931 #pragma omp parallel for private(i) schedule(static)
366 artak 1954 for (i=0;i<amg->GS->n;++i) bold[i]=bnew[i];
367 artak 1939 amg->GS->sweeps=amg->GS->sweeps-1;
368 artak 1931 }
369     }
370 artak 1939 amg->GS->sweeps=oldsweeps;
371 artak 1931 /* end of presmoothing */
372 artak 1939
373 artak 1890 #pragma omp parallel for private(i) schedule(static)
374     for (i=0;i<amg->n;++i) r[i]=b[i];
375    
376     /*r=b-Ax*/
377     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
378 artak 1954
379 jfenwick 1851 /* b->[b_F,b_C] */
380 artak 1954 #pragma omp parallel for private(i) schedule(static)
381     for (i=0;i<amg->n_F;++i) amg->b_F[i]=r[amg->rows_in_F[i]];
382    
383     #pragma omp parallel for private(i) schedule(static)
384     for (i=0;i<amg->n_C;++i) amg->b_C[i]=r[amg->rows_in_C[i]];
385 artak 1890
386 jfenwick 1851 /* x_F=invA_FF*b_F */
387 artak 1954 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
388 artak 1890
389 jfenwick 1851 /* b_C=b_C-A_CF*x_F */
390     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->x_F,1.,amg->b_C);
391 artak 1890
392 jfenwick 1851 /* x_C=AMG(b_C) */
393     Paso_Solver_solveAMG(amg->AMG_of_Schur,amg->x_C,amg->b_C);
394 artak 1890
395 jfenwick 1851 /* b_F=b_F-A_FC*x_C */
396     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_FC,amg->x_C,1.,amg->b_F);
397     /* x_F=invA_FF*b_F */
398 artak 1954 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
399 jfenwick 1851 /* x<-[x_F,x_C] */
400 artak 1890
401 artak 1954 #pragma omp parallel for private(i) schedule(static)
402     for (i=0;i<amg->n;++i) {
403     if (amg->mask_C[i]>-1) {
404     x[i]+=amg->x_C[amg->mask_C[i]];
405     } else {
406     x[i]+=amg->x_F[amg->mask_F[i]];
407     }
408 jfenwick 1851 }
409 artak 1954
410 artak 1931
411     /*postsmoothing*/
412 artak 1954 #pragma omp parallel for private(i) schedule(static)
413     for (i=0;i<amg->n;++i) r[i]=b[i];
414    
415     /*for (i=0;i<amg->n;++i) fprintf(stderr,"%lf %lf %d %d %d BBB\n",r[i],x[i],amg->n,amg->A->numCols, amg->level);*/
416    
417     /*
418     for (i = 0; i < amg->A->numRows; ++i) {
419     for (iPtr=amg->A->pattern->ptr[i];iPtr<amg->A->pattern->ptr[i + 1]; ++iPtr) {
420     j=amg->A->pattern->index[iPtr];
421     fprintf(stderr,"A[%d,%d]=%lf ",i,j,amg->A->val[iPtr]);
422     }
423     fprintf(stderr,"\n");
424     }*/
425    
426     /*r=b-Ax*/
427     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
428     Paso_Solver_solveGS(amg->GS,x0,r);
429    
430     #pragma omp parallel for private(i) schedule(static)
431     for (i=0;i<amg->n;++i) {
432     /*fprintf(stderr,"%lf %lf %lf\n",x[i],x0[i],x[i]+x0[i]);*/
433     x[i]+=x0[i];
434     }
435    
436 artak 1931 /*end of postsmoothing*/
437    
438 artak 1954 /*Paso_Solver_GS_free(amg->GS);*/
439 jfenwick 1851 }
440 artak 1890 MEMFREE(r);
441 artak 1931 MEMFREE(bold);
442 artak 1954 MEMFREE(bnew);
443     MEMFREE(x0);
444 artak 1931 return;
445 jfenwick 1851 }
446    
447     /*
448     * $Log$
449     *
450     */

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