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

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Revision 2686 - (hide annotations)
Tue Sep 29 03:39:36 2009 UTC (10 years, 1 month ago) by artak
File MIME type: text/plain
File size: 18111 byte(s)
 changes the default thresold, bug fixes in RS coupling and extra checks added in Solver 
1 jfenwick 1851
2     /*******************************************************
3     *
4 jfenwick 2548 * Copyright (c) 2003-2009 by University of Queensland
5 jfenwick 1851 * 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 artak 2475 /* Paso: AMG preconditioner */
18 jfenwick 1851
19     /**************************************************************/
20    
21 jfenwick 2625 /* Author: artak@uq.edu.au */
22 jfenwick 1851
23     /**************************************************************/
24    
25     #include "Paso.h"
26     #include "Solver.h"
27 artak 2475 #include "Options.h"
28 jfenwick 1851 #include "PasoUtil.h"
29 artak 1931 #include "UMFPACK.h"
30 artak 2507 #include "MKL.h"
31     #include "SystemMatrix.h"
32 phornby 1917 #include "Pattern_coupling.h"
33 jfenwick 1851
34     /**************************************************************/
35    
36     /* free all memory used by AMG */
37    
38 artak 2659 void Paso_Solver_AMG_System_free(Paso_Solver_AMG_System * in) {
39 artak 2662 dim_t i;
40 artak 2659 if (in!=NULL) {
41 artak 2662 for (i=0;i<in->block_size;++i) {
42     Paso_Solver_AMG_free(in->amgblock[i]);
43 artak 2670 Paso_SparseMatrix_free(in->block[i]);
44 artak 2662 }
45 artak 2659 MEMFREE(in);
46     }
47     }
48    
49    
50     /* free all memory used by AMG */
51    
52 jfenwick 1851 void Paso_Solver_AMG_free(Paso_Solver_AMG * in) {
53     if (in!=NULL) {
54     Paso_Solver_AMG_free(in->AMG_of_Schur);
55 artak 2112 Paso_Solver_Jacobi_free(in->GS);
56 jfenwick 1851 MEMFREE(in->inv_A_FF);
57     MEMFREE(in->A_FF_pivot);
58     Paso_SparseMatrix_free(in->A_FC);
59     Paso_SparseMatrix_free(in->A_CF);
60 artak 2556 Paso_SparseMatrix_free(in->A);
61 jfenwick 1851 MEMFREE(in->rows_in_F);
62     MEMFREE(in->rows_in_C);
63     MEMFREE(in->mask_F);
64     MEMFREE(in->mask_C);
65     MEMFREE(in->x_F);
66     MEMFREE(in->b_F);
67     MEMFREE(in->x_C);
68     MEMFREE(in->b_C);
69 gross 2551 #ifdef MKL
70     #else
71     #ifdef UMFPACK
72     Paso_UMFPACK1_free((Paso_UMFPACK_Handler*)(in->solver));
73     #endif
74     #endif
75     in->solver=NULL;
76     MEMFREE(in->b_C);
77 jfenwick 1851 MEMFREE(in);
78     }
79     }
80    
81     /**************************************************************/
82    
83     /* constructs the block-block factorization of
84    
85     [ A_FF A_FC ]
86     A_p=
87     [ A_CF A_FF ]
88    
89     to
90    
91     [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ]
92     [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ]
93    
94    
95     where S=A_FF-ACF*invA_FF*A_FC within the shape of S
96    
97     then AMG is applied to S again until S becomes empty
98    
99     */
100 artak 2520 Paso_Solver_AMG* Paso_Solver_getAMG(Paso_SparseMatrix *A_p,dim_t level,Paso_Options* options) {
101 jfenwick 1851 Paso_Solver_AMG* out=NULL;
102 artak 2556 Paso_Pattern* temp1=NULL;
103     Paso_Pattern* temp2=NULL;
104 artak 2520 bool_t verbose=options->verbose;
105 jfenwick 1851 dim_t n=A_p->numRows;
106     dim_t n_block=A_p->row_block_size;
107     index_t* mis_marker=NULL;
108 artak 1881 index_t* counter=NULL;
109     index_t iPtr,*index, *where_p, iPtr_s;
110 artak 2686 dim_t i,j;
111 jfenwick 1851 Paso_SparseMatrix * schur=NULL;
112 artak 1881 Paso_SparseMatrix * schur_withFillIn=NULL;
113 artak 2381 double S=0;
114 artak 2475
115 artak 2439 /*Make sure we have block sizes 1*/
116 gross 2550 if (A_p->col_block_size>1) {
117     Paso_setError(TYPE_ERROR,"Paso_Solver_getAMG: AMG requires column block size 1.");
118     return NULL;
119     }
120     if (A_p->row_block_size>1) {
121     Paso_setError(TYPE_ERROR,"Paso_Solver_getAMG: AMG requires row block size 1.");
122     return NULL;
123     }
124 gross 2551 out=MEMALLOC(1,Paso_Solver_AMG);
125 jfenwick 1851 /* identify independend set of rows/columns */
126     mis_marker=TMPMEMALLOC(n,index_t);
127     counter=TMPMEMALLOC(n,index_t);
128 gross 2551 if ( !( Paso_checkPtr(mis_marker) || Paso_checkPtr(counter) || Paso_checkPtr(out)) ) {
129     out->AMG_of_Schur=NULL;
130     out->inv_A_FF=NULL;
131     out->A_FF_pivot=NULL;
132     out->A_FC=NULL;
133     out->A_CF=NULL;
134     out->rows_in_F=NULL;
135     out->rows_in_C=NULL;
136     out->mask_F=NULL;
137     out->mask_C=NULL;
138     out->x_F=NULL;
139     out->b_F=NULL;
140     out->x_C=NULL;
141     out->b_C=NULL;
142     out->GS=NULL;
143     out->A=Paso_SparseMatrix_getReference(A_p);
144     out->GS=NULL;
145     out->solver=NULL;
146     /*out->GS=Paso_Solver_getGS(A_p,verbose);*/
147     out->level=level;
148 artak 2661 out->n=n;
149     out->n_block=n_block;
150 artak 2556
151 gross 2551 if (level==0 || n<=options->min_coarse_matrix_size) {
152     out->coarsest_level=TRUE;
153     #ifdef MKL
154     #else
155     #ifdef UMFPACK
156     #else
157     out->GS=Paso_Solver_getJacobi(A_p);
158     #endif
159     #endif
160     } else {
161     out->coarsest_level=FALSE;
162     out->GS=Paso_Solver_getJacobi(A_p);
163 artak 2442
164 gross 2551 /* identify independend set of rows/columns */
165     #pragma omp parallel for private(i) schedule(static)
166     for (i=0;i<n;++i) mis_marker[i]=-1;
167    
168     if (options->coarsening_method == PASO_YAIR_SHAPIRA_COARSENING) {
169 artak 2652 Paso_Pattern_YS(A_p,mis_marker,options->coarsening_threshold);
170 gross 2551 }
171     else if (options->coarsening_method == PASO_RUGE_STUEBEN_COARSENING) {
172     Paso_Pattern_RS(A_p,mis_marker,options->coarsening_threshold);
173     }
174     else if (options->coarsening_method == PASO_AGGREGATION_COARSENING) {
175     Paso_Pattern_Aggregiation(A_p,mis_marker,options->coarsening_threshold);
176     }
177     else {
178     /*Default coarseneing*/
179 artak 2686 Paso_Pattern_RS(A_p,mis_marker,options->coarsening_threshold);
180 artak 2659 /*Paso_Pattern_YS(A_p,mis_marker,options->coarsening_threshold);*/
181 artak 2556 /*Paso_Pattern_Aggregiation(A_p,mis_marker,options->coarsening_threshold);*/
182 gross 2551 }
183 artak 2686
184     #pragma omp parallel for private(i) schedule(static)
185     for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
186     out->n_F=Paso_Util_cumsum(n,counter);
187    
188     if (out->n_F==n) {
189     out->coarsest_level=TRUE;
190     if (verbose) {
191     printf("AMG coarsening eliminates all unknowns, switching to direct solver.\n");
192     }
193     } else {
194 artak 2475
195 artak 2686 if (Paso_noError()) {
196    
197     /*#pragma omp parallel for private(i) schedule(static)
198     for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
199     out->n_F=Paso_Util_cumsum(n,counter);
200     */
201     out->mask_F=MEMALLOC(n,index_t);
202     out->rows_in_F=MEMALLOC(out->n_F,index_t);
203     out->inv_A_FF=MEMALLOC(n_block*n_block*out->n_F,double);
204     out->A_FF_pivot=NULL; /* later use for block size>3 */
205     if (! (Paso_checkPtr(out->mask_F) || Paso_checkPtr(out->inv_A_FF) || Paso_checkPtr(out->rows_in_F) ) ) {
206     /* creates an index for F from mask */
207     #pragma omp parallel for private(i) schedule(static)
208     for (i = 0; i < out->n_F; ++i) out->rows_in_F[i]=-1;
209     #pragma omp parallel for private(i) schedule(static)
210     for (i = 0; i < n; ++i) {
211     if (mis_marker[i]) {
212     out->rows_in_F[counter[i]]=i;
213     out->mask_F[i]=counter[i];
214     } else {
215     out->mask_F[i]=-1;
216     }
217     }
218    
219     /* Compute row-sum for getting rs(A_FF)^-1*/
220     #pragma omp parallel for private(i,iPtr,j,S) schedule(static)
221     for (i = 0; i < out->n_F; ++i) {
222     S=0;
223     /*printf("[%d ]: [%d] -> ",i, out->rows_in_F[i]);*/
224     for (iPtr=A_p->pattern->ptr[out->rows_in_F[i]];iPtr<A_p->pattern->ptr[out->rows_in_F[i] + 1]; ++iPtr) {
225     j=A_p->pattern->index[iPtr];
226     /*if (j==out->rows_in_F[i]) printf("diagonal %e",A_p->val[iPtr]);*/
227     if (mis_marker[j])
228     S+=A_p->val[iPtr];
229     }
230     /*printf("-> %e \n",S);*/
231     out->inv_A_FF[i]=1./S;
232     }
233 jfenwick 1851 }
234     }
235 artak 2686
236     /*check whether coarsening process actually makes sense to continue.
237     if coarse matrix at least smaller by 30% then continue, otherwise we stop.*/
238     if ((out->n_F*100/n)<30) {
239     level=1;
240 artak 1881 }
241 gross 2551
242 artak 2686 if ( Paso_noError()) {
243     /* if there are no nodes in the coarse level there is no more work to do */
244     out->n_C=n-out->n_F;
245    
246     /*if (out->n_F>500) */
247     out->rows_in_C=MEMALLOC(out->n_C,index_t);
248     out->mask_C=MEMALLOC(n,index_t);
249     if (! (Paso_checkPtr(out->mask_C) || Paso_checkPtr(out->rows_in_C) ) ) {
250     /* creates an index for C from mask */
251     #pragma omp parallel for private(i) schedule(static)
252     for (i = 0; i < n; ++i) counter[i]=! mis_marker[i];
253     Paso_Util_cumsum(n,counter);
254     #pragma omp parallel for private(i) schedule(static)
255     for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
256     #pragma omp parallel for private(i) schedule(static)
257     for (i = 0; i < n; ++i) {
258     if (! mis_marker[i]) {
259     out->rows_in_C[counter[i]]=i;
260     out->mask_C[i]=counter[i];
261     } else {
262     out->mask_C[i]=-1;
263     }
264     }
265     }
266     }
267     if ( Paso_noError()) {
268     /* get A_CF block: */
269     out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
270     /* get A_FC block: */
271     out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
272     /* get A_CC block: */
273     schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
274    
275 gross 2551 }
276 artak 2686 if ( Paso_noError()) {
277     /*find the pattern of the schur complement with fill in*/
278     temp1=Paso_Pattern_multiply(PATTERN_FORMAT_DEFAULT,out->A_CF->pattern,out->A_FC->pattern);
279     temp2=Paso_Pattern_binop(PATTERN_FORMAT_DEFAULT, schur->pattern, temp1);
280     schur_withFillIn=Paso_SparseMatrix_alloc(A_p->type,temp2,1,1, TRUE);
281     Paso_Pattern_free(temp1);
282     Paso_Pattern_free(temp2);
283 gross 2551 }
284 artak 2686 if ( Paso_noError()) {
285     /* copy values over*/
286     #pragma omp parallel for private(i,iPtr,j,iPtr_s,index,where_p) schedule(static)
287     for (i = 0; i < schur_withFillIn->numRows; ++i) {
288     for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
289     j=schur_withFillIn->pattern->index[iPtr];
290     iPtr_s=schur->pattern->ptr[i];
291     index=&(schur->pattern->index[iPtr_s]);
292     where_p=(index_t*)bsearch(&j,
293     index,
294     schur->pattern->ptr[i + 1]-schur->pattern->ptr[i],
295     sizeof(index_t),
296     Paso_comparIndex);
297     if (where_p!=NULL) {
298     schur_withFillIn->val[iPtr]=schur->val[iPtr_s+(index_t)(where_p-index)];
299     }
300     }
301     }
302     Paso_Solver_updateIncompleteSchurComplement(schur_withFillIn,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC);
303     out->AMG_of_Schur=Paso_Solver_getAMG(schur_withFillIn,level-1,options);
304     }
305     /* allocate work arrays for AMG application */
306     if (Paso_noError()) {
307     out->x_F=MEMALLOC(n_block*out->n_F,double);
308     out->b_F=MEMALLOC(n_block*out->n_F,double);
309     out->x_C=MEMALLOC(n_block*out->n_C,double);
310     out->b_C=MEMALLOC(n_block*out->n_C,double);
311    
312     if (! (Paso_checkPtr(out->x_F) || Paso_checkPtr(out->b_F) || Paso_checkPtr(out->x_C) || Paso_checkPtr(out->b_C) ) ) {
313     #pragma omp parallel for private(i) schedule(static)
314     for (i = 0; i < out->n_F; ++i) {
315     out->x_F[i]=0.;
316     out->b_F[i]=0.;
317     }
318     #pragma omp parallel for private(i) schedule(static)
319     for (i = 0; i < out->n_C; ++i) {
320     out->x_C[i]=0.;
321     out->b_C[i]=0.;
322     }
323     }
324     }
325     Paso_SparseMatrix_free(schur);
326     Paso_SparseMatrix_free(schur_withFillIn);
327     }
328 jfenwick 1851 }
329     }
330     TMPMEMFREE(mis_marker);
331     TMPMEMFREE(counter);
332 artak 2686
333 jfenwick 1851 if (Paso_noError()) {
334 artak 2524 if (verbose && level>0 && !out->coarsest_level) {
335 gross 2551 printf("AMG: level: %d: %d unknowns eliminated. %d left.\n",level, out->n_F,out->n_C);
336 jfenwick 1851 }
337     return out;
338     } else {
339     Paso_Solver_AMG_free(out);
340     return NULL;
341     }
342     }
343    
344     /**************************************************************/
345    
346     /* apply AMG precondition b-> x
347    
348     in fact it solves
349    
350 artak 2381 [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FC ] [ x_F ] = [b_F]
351 jfenwick 1851 [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] [ x_C ] = [b_C]
352    
353     in the form
354    
355     b->[b_F,b_C]
356     x_F=invA_FF*b_F
357     b_C=b_C-A_CF*x_F
358     x_C=AMG(b_C)
359     b_F=b_F-A_FC*x_C
360     x_F=invA_FF*b_F
361     x<-[x_F,x_C]
362    
363     should be called within a parallel region
364     barrier synconization should be performed to make sure that the input vector available
365    
366     */
367    
368     void Paso_Solver_solveAMG(Paso_Solver_AMG * amg, double * x, double * b) {
369 artak 2107 dim_t i;
370 artak 2507 double time0=0;
371 gross 2551 double *r=NULL, *x0=NULL;
372 artak 2509 bool_t verbose=0;
373 artak 2507 #ifdef MKL
374 gross 2551 Paso_SparseMatrix *temp=NULL;
375     #else
376     #ifdef UMFPACK
377     Paso_UMFPACK_Handler * ptr=NULL;
378     #endif
379 artak 2507 #endif
380 gross 2551 r=MEMALLOC(amg->n,double);
381     x0=MEMALLOC(amg->n,double);
382 artak 2507
383 artak 2524 if (amg->coarsest_level) {
384 artak 2507
385     time0=Paso_timer();
386     #ifdef MKL
387 gross 2551 temp=Paso_SparseMatrix_alloc(MATRIX_FORMAT_BLK1 + MATRIX_FORMAT_OFFSET1, amg->A->pattern,1,1, FALSE);
388 artak 2507 #pragma omp parallel for private(i) schedule(static)
389     for (i=0;i<amg->A->len;++i) {
390     temp->val[i]=amg->A->val[i];
391     }
392     Paso_MKL1(temp,x,b,0);
393     Paso_SparseMatrix_free(temp);
394     #else
395 gross 2551 #ifdef UMFPACK
396     ptr=(Paso_UMFPACK_Handler *)(amg->solver);
397 artak 2652 Paso_UMFPACK1(&ptr,amg->A,x,b,verbose);
398 gross 2551 amg->solver=(void*) ptr;
399     #else
400     Paso_Solver_solveJacobi(amg->GS,x,b);
401     #endif
402 artak 2507 #endif
403 artak 2475 time0=Paso_timer()-time0;
404 artak 2652 if (verbose) fprintf(stderr,"timing: DIRECT SOLVER: %e\n",time0);
405 artak 2507
406 jfenwick 1851 } else {
407 artak 1902 /* presmoothing */
408 artak 2507 time0=Paso_timer();
409 artak 2112 Paso_Solver_solveJacobi(amg->GS,x,b);
410 artak 2507 time0=Paso_timer()-time0;
411     if (verbose) fprintf(stderr,"timing: Presmooting: %e\n",time0);
412 artak 1931 /* end of presmoothing */
413 artak 1939
414 artak 2507
415     time0=Paso_timer();
416 artak 1890 #pragma omp parallel for private(i) schedule(static)
417     for (i=0;i<amg->n;++i) r[i]=b[i];
418    
419     /*r=b-Ax*/
420     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
421 artak 1954
422 jfenwick 1851 /* b->[b_F,b_C] */
423 artak 1954 #pragma omp parallel for private(i) schedule(static)
424     for (i=0;i<amg->n_F;++i) amg->b_F[i]=r[amg->rows_in_F[i]];
425    
426     #pragma omp parallel for private(i) schedule(static)
427     for (i=0;i<amg->n_C;++i) amg->b_C[i]=r[amg->rows_in_C[i]];
428 artak 1890
429 jfenwick 1851 /* x_F=invA_FF*b_F */
430 artak 1954 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
431 artak 1890
432 jfenwick 1851 /* b_C=b_C-A_CF*x_F */
433     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->x_F,1.,amg->b_C);
434 artak 1890
435 artak 2507 time0=Paso_timer()-time0;
436     if (verbose) fprintf(stderr,"timing: Before next level: %e\n",time0);
437    
438 jfenwick 1851 /* x_C=AMG(b_C) */
439     Paso_Solver_solveAMG(amg->AMG_of_Schur,amg->x_C,amg->b_C);
440 artak 1890
441 artak 2507 time0=Paso_timer();
442 jfenwick 1851 /* b_F=b_F-A_FC*x_C */
443     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_FC,amg->x_C,1.,amg->b_F);
444     /* x_F=invA_FF*b_F */
445 artak 1954 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
446 jfenwick 1851 /* x<-[x_F,x_C] */
447 artak 2113
448 artak 1954 #pragma omp parallel for private(i) schedule(static)
449     for (i=0;i<amg->n;++i) {
450     if (amg->mask_C[i]>-1) {
451 artak 2107 x[i]=amg->x_C[amg->mask_C[i]];
452 artak 1954 } else {
453 artak 2107 x[i]=amg->x_F[amg->mask_F[i]];
454 artak 1954 }
455 jfenwick 1851 }
456 artak 1954
457 artak 2507 time0=Paso_timer()-time0;
458     if (verbose) fprintf(stderr,"timing: After next level: %e\n",time0);
459    
460 artak 1931 /*postsmoothing*/
461 artak 2507 time0=Paso_timer();
462 artak 1954 #pragma omp parallel for private(i) schedule(static)
463     for (i=0;i<amg->n;++i) r[i]=b[i];
464 artak 2107
465 artak 2442 /*r=b-Ax */
466 artak 1954 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
467 artak 2112 Paso_Solver_solveJacobi(amg->GS,x0,r);
468 artak 2107
469     #pragma omp parallel for private(i) schedule(static)
470     for (i=0;i<amg->n;++i) x[i]+=x0[i];
471    
472 artak 2507 time0=Paso_timer()-time0;
473     if (verbose) fprintf(stderr,"timing: Postsmoothing: %e\n",time0);
474 artak 2509
475 artak 1931 /*end of postsmoothing*/
476    
477 jfenwick 1851 }
478 artak 1890 MEMFREE(r);
479 artak 1954 MEMFREE(x0);
480 gross 2551 return;
481 jfenwick 1851 }

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