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

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Revision 1890 - (hide annotations)
Fri Oct 17 00:14:22 2008 UTC (11 years, 4 months ago) by artak
File MIME type: text/plain
File size: 18331 byte(s)
Current version of AMG. check levels for stoping applies presmoothing, but not ready yet
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    
29     /**************************************************************/
30    
31     /* free all memory used by AMG */
32    
33     void Paso_Solver_AMG_free(Paso_Solver_AMG * in) {
34     if (in!=NULL) {
35     Paso_Solver_AMG_free(in->AMG_of_Schur);
36     MEMFREE(in->inv_A_FF);
37     MEMFREE(in->A_FF_pivot);
38     Paso_SparseMatrix_free(in->A_FC);
39     Paso_SparseMatrix_free(in->A_CF);
40     MEMFREE(in->rows_in_F);
41     MEMFREE(in->rows_in_C);
42     MEMFREE(in->mask_F);
43     MEMFREE(in->mask_C);
44     MEMFREE(in->x_F);
45     MEMFREE(in->b_F);
46     MEMFREE(in->x_C);
47     MEMFREE(in->b_C);
48     MEMFREE(in);
49     }
50     }
51    
52     /**************************************************************/
53    
54     /* constructs the block-block factorization of
55    
56     [ A_FF A_FC ]
57     A_p=
58     [ A_CF A_FF ]
59    
60     to
61    
62     [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ]
63     [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ]
64    
65    
66     where S=A_FF-ACF*invA_FF*A_FC within the shape of S
67    
68     then AMG is applied to S again until S becomes empty
69    
70     */
71 artak 1890 Paso_Solver_AMG* Paso_Solver_getAMG(Paso_SparseMatrix *A_p,bool_t verbose,dim_t level) {
72 jfenwick 1851 Paso_Solver_AMG* out=NULL;
73     dim_t n=A_p->numRows;
74     dim_t n_block=A_p->row_block_size;
75     index_t* mis_marker=NULL;
76 artak 1881 index_t* counter=NULL;
77     double *rs=NULL;
78     index_t iPtr,*index, *where_p, iPtr_s;
79     dim_t i,k,j,j0;
80 jfenwick 1851 Paso_SparseMatrix * schur=NULL;
81 artak 1881 Paso_SparseMatrix * schur_withFillIn=NULL;
82 artak 1890 schur_withFillIn=MEMALLOC(1,Paso_SparseMatrix);
83    
84    
85 ksteube 1887 double A11,A12,A13,A21,A22,A23,A31,A32,A33,D,time0,time1,time2;
86 jfenwick 1851
87    
88     /* identify independend set of rows/columns */
89     mis_marker=TMPMEMALLOC(n,index_t);
90     counter=TMPMEMALLOC(n,index_t);
91 artak 1881 rs=TMPMEMALLOC(n,double);
92 jfenwick 1851 out=MEMALLOC(1,Paso_Solver_AMG);
93     out->AMG_of_Schur=NULL;
94     out->inv_A_FF=NULL;
95     out->A_FF_pivot=NULL;
96     out->A_FC=NULL;
97     out->A_CF=NULL;
98     out->rows_in_F=NULL;
99     out->rows_in_C=NULL;
100     out->mask_F=NULL;
101     out->mask_C=NULL;
102     out->x_F=NULL;
103     out->b_F=NULL;
104     out->x_C=NULL;
105     out->b_C=NULL;
106 artak 1890 out->A=Paso_SparseMatrix_getReference(A_p);
107     out->level=level;
108 artak 1881
109     /* fprintf(stderr,"START OF MATRIX \n\n");
110     for (i = 0; i < A_p->numRows; ++i) {
111     for (iPtr=A_p->pattern->ptr[i];iPtr<A_p->pattern->ptr[i + 1]; ++iPtr) {
112     j=A_p->pattern->index[iPtr];
113     fprintf(stderr,"A[%d,%d]=%.2f ",i,j,A_p->val[iPtr]);
114     }
115     fprintf(stderr,"\n");
116     }
117     fprintf(stderr,"END OF MATRIX \n\n");
118     */
119 jfenwick 1851 if ( !(Paso_checkPtr(mis_marker) || Paso_checkPtr(out) || Paso_checkPtr(counter) ) ) {
120     /* identify independend set of rows/columns */
121     time0=Paso_timer();
122     #pragma omp parallel for private(i) schedule(static)
123     for (i=0;i<n;++i) mis_marker[i]=-1;
124 artak 1890 Paso_Pattern_RS(A_p,mis_marker,0.25);
125     /*
126     for (i=0;i<n;++i) fprintf(stderr," i=%d mis[i]=%d \n",i,mis_marker[i]);
127     */
128 jfenwick 1851 time2=Paso_timer()-time0;
129     if (Paso_noError()) {
130     #pragma omp parallel for private(i) schedule(static)
131     for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
132     out->n=n;
133     out->n_block=n_block;
134     out->n_F=Paso_Util_cumsum(n,counter);
135     out->mask_F=MEMALLOC(n,index_t);
136     out->rows_in_F=MEMALLOC(out->n_F,index_t);
137     out->inv_A_FF=MEMALLOC(n_block*n_block*out->n_F,double);
138     out->A_FF_pivot=NULL; /* later use for block size>3 */
139     if (! (Paso_checkPtr(out->mask_F) || Paso_checkPtr(out->inv_A_FF) || Paso_checkPtr(out->rows_in_F) ) ) {
140     #pragma omp parallel
141     {
142     /* creates an index for F from mask */
143     #pragma omp for private(i) schedule(static)
144     for (i = 0; i < out->n_F; ++i) out->rows_in_F[i]=-1;
145     #pragma omp for private(i) schedule(static)
146     for (i = 0; i < n; ++i) {
147     if (mis_marker[i]) {
148     out->rows_in_F[counter[i]]=i;
149     out->mask_F[i]=counter[i];
150     } else {
151     out->mask_F[i]=-1;
152     }
153     }
154 artak 1881 /* Compute row-sum for getting rs(A_FF)*/
155     #pragma omp for private(i,iPtr) schedule(static)
156     for (i = 0; i < out->n_F; ++i) {
157     rs[i]=0;
158     for (iPtr=A_p->pattern->ptr[out->rows_in_F[i]];iPtr<A_p->pattern->ptr[out->rows_in_F[i] + 1]; ++iPtr) {
159     rs[i]+=A_p->val[iPtr];
160     }
161     }
162    
163 jfenwick 1851 #pragma omp for private(i, where_p,iPtr,A11,A12,A13,A21,A22,A23,A31,A32,A33,D,index) schedule(static)
164     for (i = 0; i < out->n_F; i++) {
165     /* find main diagonal */
166     iPtr=A_p->pattern->ptr[out->rows_in_F[i]];
167     index=&(A_p->pattern->index[iPtr]);
168     where_p=(index_t*)bsearch(&out->rows_in_F[i],
169     index,
170     A_p->pattern->ptr[out->rows_in_F[i] + 1]-A_p->pattern->ptr[out->rows_in_F[i]],
171     sizeof(index_t),
172     Paso_comparIndex);
173     if (where_p==NULL) {
174     Paso_setError(VALUE_ERROR, "Paso_Solver_getAMG: main diagonal element missing.");
175     } else {
176     iPtr+=(index_t)(where_p-index);
177     /* get inverse of A_FF block: */
178 artak 1881 if (ABS(rs[i])>0.) {
179     out->inv_A_FF[i]=1./rs[i];
180     } else {
181 artak 1890 out->inv_A_FF[i]=0;
182     }
183    
184     /* } else {
185 jfenwick 1851 Paso_setError(ZERO_DIVISION_ERROR, "Paso_Solver_getAMG: Break-down in AMG decomposition: non-regular main diagonal block.");
186 artak 1890 }*/
187 artak 1881 }
188 jfenwick 1851 }
189     } /* end parallel region */
190    
191     if( Paso_noError()) {
192     /* if there are no nodes in the coarse level there is no more work to do */
193     out->n_C=n-out->n_F;
194 artak 1890 /*if (out->n_C>11) {*/
195     if (level>0) {
196 jfenwick 1851 out->rows_in_C=MEMALLOC(out->n_C,index_t);
197     out->mask_C=MEMALLOC(n,index_t);
198     if (! (Paso_checkPtr(out->mask_C) || Paso_checkPtr(out->rows_in_C) ) ) {
199     /* creates an index for C from mask */
200     #pragma omp parallel for private(i) schedule(static)
201     for (i = 0; i < n; ++i) counter[i]=! mis_marker[i];
202     Paso_Util_cumsum(n,counter);
203     #pragma omp parallel
204     {
205     #pragma omp for private(i) schedule(static)
206     for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
207     #pragma omp for private(i) schedule(static)
208     for (i = 0; i < n; ++i) {
209     if (! mis_marker[i]) {
210     out->rows_in_C[counter[i]]=i;
211     out->mask_C[i]=counter[i];
212     } else {
213     out->mask_C[i]=-1;
214     }
215     }
216     } /* end parallel region */
217     /* get A_CF block: */
218     out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
219     if (Paso_noError()) {
220     /* get A_FC block: */
221     out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
222 artak 1881 /* get A_CC block: */
223 jfenwick 1851 if (Paso_noError()) {
224     schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
225 artak 1881
226     /*find the pattern of the schur complement with fill in*/
227     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);
228    
229     /* copy values over*/
230     #pragma omp for private(i,iPtr,iPtr_s,j,j0) schedule(static)
231     for (i = 0; i < schur_withFillIn->numRows; ++i) {
232     for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
233     j=schur_withFillIn->pattern->index[iPtr];
234     schur_withFillIn->val[iPtr]=0.;
235     for (iPtr_s=schur->pattern->ptr[i];iPtr_s<schur->pattern->ptr[i + 1]; ++iPtr_s){
236     j0=schur->pattern->index[iPtr_s];
237     if (j==j0) {
238     schur_withFillIn->val[iPtr]=schur->val[iPtr_s];
239     break;
240     }
241     }
242     }
243     }
244    
245     /* for (i = 0; i < schur_withFillIn->numRows; ++i) {
246     for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
247     j=schur_withFillIn->pattern->index[iPtr];
248     fprintf(stderr,"A_CC[%d,%d]=%.2f ",i,j,schur_withFillIn->val[iPtr]);
249     }
250     fprintf(stderr,"\n");
251     }*/
252 jfenwick 1851 time0=Paso_timer()-time0;
253     if (Paso_noError()) {
254     time1=Paso_timer();
255     /* update A_CC block to get Schur complement and then apply AMG to it */
256 artak 1881 Paso_Solver_updateIncompleteSchurComplement(schur_withFillIn,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC);
257 jfenwick 1851 time1=Paso_timer()-time1;
258 artak 1890 out->AMG_of_Schur=Paso_Solver_getAMG(schur_withFillIn,verbose,level-1);
259 artak 1881
260 jfenwick 1851 Paso_SparseMatrix_free(schur);
261 artak 1890 /* Paso_SparseMatrix_free(schur_withFillIn);*/
262 jfenwick 1851 }
263     /* allocate work arrays for AMG application */
264     if (Paso_noError()) {
265     out->x_F=MEMALLOC(n_block*out->n_F,double);
266     out->b_F=MEMALLOC(n_block*out->n_F,double);
267     out->x_C=MEMALLOC(n_block*out->n_C,double);
268     out->b_C=MEMALLOC(n_block*out->n_C,double);
269 artak 1890
270 jfenwick 1851 if (! (Paso_checkPtr(out->x_F) || Paso_checkPtr(out->b_F) || Paso_checkPtr(out->x_C) || Paso_checkPtr(out->b_C) ) ) {
271     #pragma omp parallel
272     {
273     #pragma omp for private(i,k) schedule(static)
274     for (i = 0; i < out->n_F; ++i) {
275     for (k=0; k<n_block;++k) {
276     out->x_F[i*n_block+k]=0.;
277     out->b_F[i*n_block+k]=0.;
278     }
279     }
280     #pragma omp for private(i,k) schedule(static)
281     for (i = 0; i < out->n_C; ++i) {
282     for (k=0; k<n_block;++k) {
283     out->x_C[i*n_block+k]=0.;
284     out->b_C[i*n_block+k]=0.;
285     }
286     }
287     } /* end parallel region */
288     }
289     }
290     }
291     }
292     }
293     }
294     }
295     }
296     }
297     }
298     TMPMEMFREE(mis_marker);
299     TMPMEMFREE(counter);
300 artak 1881 TMPMEMFREE(rs);
301 jfenwick 1851 if (Paso_noError()) {
302     if (verbose) {
303     printf("AMG: %d unknowns eliminated. %d left.\n",out->n_F,n-out->n_F);
304     if (out->n_C>0) {
305     printf("timing: AMG: MIS/reordering/elemination : %e/%e/%e\n",time2,time0,time1);
306     } else {
307     printf("timing: AMG: MIS: %e\n",time2);
308     }
309     }
310     return out;
311     } else {
312     Paso_Solver_AMG_free(out);
313     return NULL;
314     }
315     }
316    
317     /**************************************************************/
318    
319     /* apply AMG precondition b-> x
320    
321     in fact it solves
322    
323     [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ] [ x_F ] = [b_F]
324     [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] [ x_C ] = [b_C]
325    
326     in the form
327    
328     b->[b_F,b_C]
329     x_F=invA_FF*b_F
330     b_C=b_C-A_CF*x_F
331     x_C=AMG(b_C)
332     b_F=b_F-A_FC*x_C
333     x_F=invA_FF*b_F
334     x<-[x_F,x_C]
335    
336     should be called within a parallel region
337     barrier synconization should be performed to make sure that the input vector available
338    
339     */
340    
341     void Paso_Solver_solveAMG(Paso_Solver_AMG * amg, double * x, double * b) {
342     dim_t i,k;
343     dim_t n_block=amg->n_block;
344 artak 1890 double *r=MEMALLOC(amg->n,double);
345     double *x0=MEMALLOC(amg->n,double);
346    
347     if (amg->level==0) {
348 jfenwick 1851 /* x=invA_FF*b */
349     Paso_Solver_applyBlockDiagonalMatrix(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,x,b);
350     } else {
351 artak 1890 fprintf(stdout,"LEVEL %d \n",amg->level);
352 artak 1881 /* presmoothing on (Shure, x, b, r) */
353 artak 1890 /****************/
354     Paso_Solver_GS* GS=MEMALLOC(1,Paso_Solver_GS);
355     GS=Paso_Solver_getGS(amg->A,-1);
356     Paso_Solver_solveGS(GS,x,b);
357    
358     #pragma omp parallel for private(i) schedule(static)
359     for (i=0;i<amg->n;++i) r[i]=b[i];
360    
361     /*r=b-Ax*/
362     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
363     /****************/
364 jfenwick 1851 /* b->[b_F,b_C] */
365     if (n_block==1) {
366     #pragma omp parallel for private(i) schedule(static)
367 artak 1890 for (i=0;i<amg->n_F;++i) amg->b_F[i]=r[amg->rows_in_F[i]]; /* was b istead of r */
368     #pragma omp parallel for private(i) schedule(static)
369     for (i=0;i<amg->n_C;++i) amg->b_C[i]=r[amg->rows_in_C[i]];
370 jfenwick 1851 } else {
371     #pragma omp parallel for private(i,k) schedule(static)
372     for (i=0;i<amg->n_F;++i)
373 artak 1890 for (k=0;k<n_block;k++) amg->b_F[amg->n_block*i+k]=r[n_block*amg->rows_in_F[i]+k];
374 jfenwick 1851 #pragma omp parallel for private(i,k) schedule(static)
375     for (i=0;i<amg->n_C;++i)
376 artak 1890 for (k=0;k<n_block;k++) amg->b_C[amg->n_block*i+k]=r[n_block*amg->rows_in_C[i]+k];
377 jfenwick 1851 }
378 artak 1890
379     /****************/
380     /* Coursening part */
381    
382     /* r_F=A_FF^-1*r_F */
383     /*Paso_Solver_applyBlockDiagonalMatrix(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->b_F,amg->b_F);
384     fprintf(stderr,"2\n");
385     */
386     /* r_C=r_C-A_CF*r_F */
387     /*Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->b_F,1.,amg->b_C);
388     fprintf(stderr,"3\n");
389     */
390     /****************/
391    
392    
393 jfenwick 1851 /* x_F=invA_FF*b_F */
394     Paso_Solver_applyBlockDiagonalMatrix(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
395 artak 1890
396 jfenwick 1851 /* b_C=b_C-A_CF*x_F */
397     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->x_F,1.,amg->b_C);
398 artak 1890
399 jfenwick 1851 /* x_C=AMG(b_C) */
400     Paso_Solver_solveAMG(amg->AMG_of_Schur,amg->x_C,amg->b_C);
401 artak 1890
402 jfenwick 1851 /* b_F=b_F-A_FC*x_C */
403     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_FC,amg->x_C,1.,amg->b_F);
404     /* x_F=invA_FF*b_F */
405     Paso_Solver_applyBlockDiagonalMatrix(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
406     /* x<-[x_F,x_C] */
407 artak 1890
408     /* */
409    
410    
411 jfenwick 1851 if (n_block==1) {
412     #pragma omp parallel for private(i) schedule(static)
413     for (i=0;i<amg->n;++i) {
414     if (amg->mask_C[i]>-1) {
415 artak 1890 x[i]+=amg->x_C[amg->mask_C[i]];
416 jfenwick 1851 } else {
417 artak 1890 x[i]+=amg->x_F[amg->mask_F[i]];
418 jfenwick 1851 }
419     }
420     } else {
421     #pragma omp parallel for private(i,k) schedule(static)
422     for (i=0;i<amg->n;++i) {
423     if (amg->mask_C[i]>-1) {
424 artak 1890 for (k=0;k<n_block;k++) x[n_block*i+k]+=amg->x_C[n_block*amg->mask_C[i]+k];
425 jfenwick 1851 } else {
426 artak 1890 for (k=0;k<n_block;k++) x[n_block*i+k]+=amg->x_F[n_block*amg->mask_F[i]+k];
427 jfenwick 1851 }
428     }
429     }
430     /* all done */
431 artak 1890 /*post smoothing*/
432     /* Paso_Solver_solveGS(GS,x0,b);
433     if (n_block==1) {
434     #pragma omp parallel for private(i) schedule(static)
435     for (i=0;i<amg->n;++i) x[i]+=x0[i];
436     } else {
437     #pragma omp parallel for private(i,k) schedule(static)
438     for (i=0;i<amg->n;++i) {
439     for (k=0;k<n_block;k++) x[n_block*i+k]+=x0[n_block*i+k];
440     }
441     }
442     */
443     Paso_Solver_GS_free(GS);
444 jfenwick 1851 }
445 artak 1890 MEMFREE(x0);
446     MEMFREE(r);
447 jfenwick 1851 return;
448     }
449    
450     /*
451     * $Log$
452     *
453     */

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