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

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Revision 2765 - (hide annotations)
Fri Nov 20 01:49:19 2009 UTC (10 years, 3 months ago) by artak
File MIME type: text/plain
File size: 18693 byte(s)
First steps toward efficiency. Coarsening process is improved. Some profiling tools are added.
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 artak 2112 Paso_Solver_Jacobi_free(in->GS);
55 jfenwick 1851 Paso_SparseMatrix_free(in->A_FC);
56 artak 2760 Paso_SparseMatrix_free(in->A_FF);
57     Paso_SparseMatrix_free(in->W_FC);
58 jfenwick 1851 Paso_SparseMatrix_free(in->A_CF);
59 artak 2760 Paso_SparseMatrix_free(in->P);
60     Paso_SparseMatrix_free(in->R);
61    
62 artak 2556 Paso_SparseMatrix_free(in->A);
63 artak 2711 if(in->coarsest_level==TRUE) {
64     #ifdef MKL
65     Paso_MKL_free1(in->AOffset1);
66     Paso_SparseMatrix_free(in->AOffset1);
67     #else
68     #ifdef UMFPACK
69     Paso_UMFPACK1_free((Paso_UMFPACK_Handler*)(in->solver));
70     #endif
71     #endif
72     }
73 jfenwick 1851 MEMFREE(in->rows_in_F);
74     MEMFREE(in->rows_in_C);
75     MEMFREE(in->mask_F);
76     MEMFREE(in->mask_C);
77     MEMFREE(in->x_F);
78     MEMFREE(in->b_F);
79     MEMFREE(in->x_C);
80     MEMFREE(in->b_C);
81 gross 2551 in->solver=NULL;
82 artak 2760 Paso_Solver_AMG_free(in->AMG_of_Coarse);
83 gross 2551 MEMFREE(in->b_C);
84 jfenwick 1851 MEMFREE(in);
85     }
86     }
87    
88     /**************************************************************/
89    
90     /* constructs the block-block factorization of
91    
92     [ A_FF A_FC ]
93     A_p=
94     [ A_CF A_FF ]
95    
96     to
97    
98     [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ]
99     [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ]
100    
101    
102     where S=A_FF-ACF*invA_FF*A_FC within the shape of S
103    
104     then AMG is applied to S again until S becomes empty
105    
106     */
107 artak 2520 Paso_Solver_AMG* Paso_Solver_getAMG(Paso_SparseMatrix *A_p,dim_t level,Paso_Options* options) {
108 jfenwick 1851 Paso_Solver_AMG* out=NULL;
109 artak 2760 /*
110     Paso_Pattern* temp1=NULL;
111 artak 2556 Paso_Pattern* temp2=NULL;
112 artak 2760 */
113 artak 2520 bool_t verbose=options->verbose;
114 jfenwick 1851 dim_t n=A_p->numRows;
115     dim_t n_block=A_p->row_block_size;
116     index_t* mis_marker=NULL;
117 artak 1881 index_t* counter=NULL;
118 artak 2760 /*index_t iPtr,*index, *where_p;*/
119     dim_t i;
120     Paso_SparseMatrix * A_c=NULL;
121 artak 2765 double time0=0;
122 artak 2475
123 artak 2760 /*
124     double *temp,*temp_1;
125     double S;
126     index_t iptr;
127     */
128 artak 2726
129 artak 2760 /*char filename[8];*/
130     /*sprintf(filename,"AMGLevel%d",level);
131 artak 2726
132 artak 2760 Paso_SparseMatrix_saveMM(A_p,filename);
133 artak 2726 */
134    
135 artak 2439 /*Make sure we have block sizes 1*/
136 gross 2550 if (A_p->col_block_size>1) {
137     Paso_setError(TYPE_ERROR,"Paso_Solver_getAMG: AMG requires column block size 1.");
138     return NULL;
139     }
140     if (A_p->row_block_size>1) {
141     Paso_setError(TYPE_ERROR,"Paso_Solver_getAMG: AMG requires row block size 1.");
142     return NULL;
143     }
144 gross 2551 out=MEMALLOC(1,Paso_Solver_AMG);
145 jfenwick 1851 /* identify independend set of rows/columns */
146     mis_marker=TMPMEMALLOC(n,index_t);
147     counter=TMPMEMALLOC(n,index_t);
148 gross 2551 if ( !( Paso_checkPtr(mis_marker) || Paso_checkPtr(counter) || Paso_checkPtr(out)) ) {
149 artak 2760 out->AMG_of_Coarse=NULL;
150     out->A_FF=NULL;
151 gross 2551 out->A_FC=NULL;
152     out->A_CF=NULL;
153 artak 2760 out->W_FC=NULL;
154     out->P=NULL;
155     out->R=NULL;
156 gross 2551 out->rows_in_F=NULL;
157     out->rows_in_C=NULL;
158     out->mask_F=NULL;
159     out->mask_C=NULL;
160     out->x_F=NULL;
161     out->b_F=NULL;
162     out->x_C=NULL;
163     out->b_C=NULL;
164     out->GS=NULL;
165     out->A=Paso_SparseMatrix_getReference(A_p);
166     out->GS=NULL;
167     out->solver=NULL;
168     /*out->GS=Paso_Solver_getGS(A_p,verbose);*/
169     out->level=level;
170 artak 2661 out->n=n;
171 artak 2726 out->n_F=n+1;
172 artak 2661 out->n_block=n_block;
173 artak 2556
174 gross 2551 if (level==0 || n<=options->min_coarse_matrix_size) {
175     out->coarsest_level=TRUE;
176 artak 2712 #ifdef MKL
177 artak 2711 out->AOffset1=Paso_SparseMatrix_alloc(MATRIX_FORMAT_BLK1 + MATRIX_FORMAT_OFFSET1, out->A->pattern,1,1, FALSE);
178     #pragma omp parallel for private(i) schedule(static)
179     for (i=0;i<out->A->len;++i) {
180     out->AOffset1->val[i]=out->A->val[i];
181     }
182 artak 2712 #else
183     #ifdef UMFPACK
184     #else
185 gross 2551 out->GS=Paso_Solver_getJacobi(A_p);
186     #endif
187     #endif
188     } else {
189     out->coarsest_level=FALSE;
190     out->GS=Paso_Solver_getJacobi(A_p);
191 artak 2442
192 gross 2551 /* identify independend set of rows/columns */
193     #pragma omp parallel for private(i) schedule(static)
194     for (i=0;i<n;++i) mis_marker[i]=-1;
195    
196 artak 2765 /*mesuring coarsening time */
197     time0=Paso_timer();
198    
199 gross 2551 if (options->coarsening_method == PASO_YAIR_SHAPIRA_COARSENING) {
200 artak 2652 Paso_Pattern_YS(A_p,mis_marker,options->coarsening_threshold);
201 gross 2551 }
202     else if (options->coarsening_method == PASO_RUGE_STUEBEN_COARSENING) {
203     Paso_Pattern_RS(A_p,mis_marker,options->coarsening_threshold);
204     }
205     else if (options->coarsening_method == PASO_AGGREGATION_COARSENING) {
206     Paso_Pattern_Aggregiation(A_p,mis_marker,options->coarsening_threshold);
207     }
208     else {
209     /*Default coarseneing*/
210 artak 2760 Paso_Pattern_RS_MI(A_p,mis_marker,options->coarsening_threshold);
211 artak 2659 /*Paso_Pattern_YS(A_p,mis_marker,options->coarsening_threshold);*/
212 artak 2760 /*Paso_Pattern_RS(A_p,mis_marker,options->coarsening_threshold);*/
213 artak 2726 /*Paso_Pattern_Aggregiation(A_p,mis_marker,options->coarsening_threshold);*/
214 artak 2760
215 gross 2551 }
216 artak 2765
217     time0=Paso_timer()-time0;
218     if (verbose) fprintf(stderr,"timing: Coarsening: %e\n",time0);
219 artak 2760
220 artak 2686 #pragma omp parallel for private(i) schedule(static)
221     for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
222 artak 2726
223 artak 2686 out->n_F=Paso_Util_cumsum(n,counter);
224    
225 artak 2726 if (out->n_F==0) {
226 artak 2686 out->coarsest_level=TRUE;
227 artak 2726 level=0;
228 artak 2686 if (verbose) {
229 artak 2726 /*printf("AMG coarsening eliminates all unknowns, switching to Jacobi preconditioner.\n");*/
230     printf("AMG coarsening does not eliminate any of the unknowns, switching to Jacobi preconditioner.\n");
231 artak 2686 }
232 artak 2726 }
233     else if (out->n_F==n) {
234     out->coarsest_level=TRUE;
235     level=0;
236     if (verbose) {
237     /*printf("AMG coarsening eliminates all unknowns, switching to Jacobi preconditioner.\n");*/
238     printf("AMG coarsening eliminates all of the unknowns, switching to Jacobi preconditioner.\n");
239    
240     }
241 artak 2686 } else {
242 artak 2475
243 artak 2686 if (Paso_noError()) {
244    
245     /*#pragma omp parallel for private(i) schedule(static)
246     for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
247     out->n_F=Paso_Util_cumsum(n,counter);
248     */
249 artak 2760
250 artak 2686 out->mask_F=MEMALLOC(n,index_t);
251     out->rows_in_F=MEMALLOC(out->n_F,index_t);
252 artak 2760 if (! (Paso_checkPtr(out->mask_F) || Paso_checkPtr(out->rows_in_F) ) ) {
253 artak 2686 /* creates an index for F from mask */
254     #pragma omp parallel for private(i) schedule(static)
255     for (i = 0; i < out->n_F; ++i) out->rows_in_F[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_F[counter[i]]=i;
260     out->mask_F[i]=counter[i];
261     } else {
262     out->mask_F[i]=-1;
263     }
264     }
265    
266 jfenwick 1851 }
267     }
268 artak 2686
269     /*check whether coarsening process actually makes sense to continue.
270     if coarse matrix at least smaller by 30% then continue, otherwise we stop.*/
271     if ((out->n_F*100/n)<30) {
272     level=1;
273 artak 1881 }
274 gross 2551
275 artak 2686 if ( Paso_noError()) {
276     /* if there are no nodes in the coarse level there is no more work to do */
277     out->n_C=n-out->n_F;
278    
279     /*if (out->n_F>500) */
280     out->rows_in_C=MEMALLOC(out->n_C,index_t);
281     out->mask_C=MEMALLOC(n,index_t);
282     if (! (Paso_checkPtr(out->mask_C) || Paso_checkPtr(out->rows_in_C) ) ) {
283     /* creates an index for C from mask */
284     #pragma omp parallel for private(i) schedule(static)
285     for (i = 0; i < n; ++i) counter[i]=! mis_marker[i];
286     Paso_Util_cumsum(n,counter);
287     #pragma omp parallel for private(i) schedule(static)
288     for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
289     #pragma omp parallel for private(i) schedule(static)
290     for (i = 0; i < n; ++i) {
291     if (! mis_marker[i]) {
292     out->rows_in_C[counter[i]]=i;
293     out->mask_C[i]=counter[i];
294     } else {
295     out->mask_C[i]=-1;
296     }
297     }
298     }
299     }
300     if ( Paso_noError()) {
301 artak 2760 /* get A_FF block: */
302     /*
303     out->A_FF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_F,out->rows_in_F,out->mask_F);
304 artak 2686 out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
305     out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
306 artak 2760 */
307    
308     /*Compute W_FC*/
309     /*initialy W_FC=A_FC*/
310     out->W_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
311    
312     /*sprintf(filename,"W_FCbefore_%d",level);
313     Paso_SparseMatrix_saveMM(out->W_FC,filename);
314     */
315 artak 2765
316     time0=Paso_timer();
317 artak 2760 Paso_SparseMatrix_updateWeights(A_p,out->W_FC,mis_marker);
318 artak 2765 time0=Paso_timer()-time0;
319     if (verbose) fprintf(stderr,"timing: updateWeights: %e\n",time0);
320    
321 artak 2760 /*
322     printf("GOT W_FC, but n=%d,n_F=%d,n_C=%d\n",out->n,out->n_F,out->n_C);
323     sprintf(filename,"W_FCafter_%d",level);
324     Paso_SparseMatrix_saveMM(out->W_FC,filename);
325     */
326     /* get Prolongation and Restriction */
327 artak 2765
328     time0=Paso_timer();
329 artak 2760 out->P=Paso_SparseMatrix_getProlongation(out->W_FC,mis_marker);
330 artak 2765 time0=Paso_timer()-time0;
331     if (verbose) fprintf(stderr,"timing: getProlongation: %e\n",time0);
332 artak 2760
333     /*
334     printf("GOT Prolongation P->nxc %dx%d\n",out->P->numRows,out->P->numCols);
335     sprintf(filename,"P_%d",level);
336     Paso_SparseMatrix_saveMM(out->P,filename);
337     */
338    
339 artak 2765 time0=Paso_timer();
340 artak 2760 out->R=Paso_SparseMatrix_getRestriction(out->P);
341 artak 2765 time0=Paso_timer()-time0;
342     if (verbose) fprintf(stderr,"timing: getRestriction: %e\n",time0);
343    
344 artak 2760 /*
345     printf("GOT Restriction->cxn %dx%d\n",out->R->numRows,out->R->numCols);
346     sprintf(filename,"R_%d",level);
347     Paso_SparseMatrix_saveMM(out->R,filename);
348     */
349    
350 gross 2551 }
351 artak 2686 if ( Paso_noError()) {
352 artak 2765
353     time0=Paso_timer();
354 artak 2760 A_c=Paso_Solver_getCoarseMatrix(A_p,out->R,out->P);
355 artak 2765 time0=Paso_timer()-time0;
356     if (verbose) fprintf(stderr,"timing: getCoarseMatrix: %e\n",time0);
357    
358 artak 2760 /*Paso_Solver_getCoarseMatrix(A_c, A_p,out->R,out->P);*/
359     /*
360     sprintf(filename,"A_C_%d",level);
361     Paso_SparseMatrix_saveMM(A_c,filename);
362     */
363     out->AMG_of_Coarse=Paso_Solver_getAMG(A_c,level-1,options);
364 gross 2551 }
365 artak 2760
366 artak 2686 /* allocate work arrays for AMG application */
367     if (Paso_noError()) {
368     out->x_F=MEMALLOC(n_block*out->n_F,double);
369     out->b_F=MEMALLOC(n_block*out->n_F,double);
370     out->x_C=MEMALLOC(n_block*out->n_C,double);
371     out->b_C=MEMALLOC(n_block*out->n_C,double);
372    
373     if (! (Paso_checkPtr(out->x_F) || Paso_checkPtr(out->b_F) || Paso_checkPtr(out->x_C) || Paso_checkPtr(out->b_C) ) ) {
374     #pragma omp parallel for private(i) schedule(static)
375     for (i = 0; i < out->n_F; ++i) {
376     out->x_F[i]=0.;
377     out->b_F[i]=0.;
378     }
379     #pragma omp parallel for private(i) schedule(static)
380     for (i = 0; i < out->n_C; ++i) {
381     out->x_C[i]=0.;
382     out->b_C[i]=0.;
383     }
384     }
385     }
386 artak 2760 Paso_SparseMatrix_free(A_c);
387 artak 2686 }
388 jfenwick 1851 }
389     }
390     TMPMEMFREE(mis_marker);
391     TMPMEMFREE(counter);
392 artak 2686
393 jfenwick 1851 if (Paso_noError()) {
394 artak 2524 if (verbose && level>0 && !out->coarsest_level) {
395 gross 2551 printf("AMG: level: %d: %d unknowns eliminated. %d left.\n",level, out->n_F,out->n_C);
396 jfenwick 1851 }
397     return out;
398     } else {
399     Paso_Solver_AMG_free(out);
400     return NULL;
401     }
402     }
403    
404     /**************************************************************/
405    
406     /* apply AMG precondition b-> x
407    
408     in fact it solves
409    
410 artak 2381 [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FC ] [ x_F ] = [b_F]
411 jfenwick 1851 [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] [ x_C ] = [b_C]
412    
413     in the form
414    
415     b->[b_F,b_C]
416     x_F=invA_FF*b_F
417     b_C=b_C-A_CF*x_F
418     x_C=AMG(b_C)
419     b_F=b_F-A_FC*x_C
420     x_F=invA_FF*b_F
421     x<-[x_F,x_C]
422    
423     should be called within a parallel region
424     barrier synconization should be performed to make sure that the input vector available
425    
426     */
427    
428     void Paso_Solver_solveAMG(Paso_Solver_AMG * amg, double * x, double * b) {
429 artak 2107 dim_t i;
430 artak 2507 double time0=0;
431 gross 2551 double *r=NULL, *x0=NULL;
432 artak 2509 bool_t verbose=0;
433 artak 2699 #ifdef UMFPACK
434     Paso_UMFPACK_Handler * ptr=NULL;
435 artak 2507 #endif
436 artak 2760
437 gross 2551 r=MEMALLOC(amg->n,double);
438     x0=MEMALLOC(amg->n,double);
439 artak 2507
440 artak 2524 if (amg->coarsest_level) {
441 artak 2507
442     time0=Paso_timer();
443 artak 2699 /*If all unknown are eliminated then Jacobi is the best preconditioner*/
444 artak 2726 if (amg->n_F==0 || amg->n_F==amg->n) {
445 artak 2699 Paso_Solver_solveJacobi(amg->GS,x,b);
446     }
447     else {
448 artak 2712 #ifdef MKL
449     Paso_MKL1(amg->AOffset1,x,b,verbose);
450     #else
451     #ifdef UMFPACK
452 gross 2551 ptr=(Paso_UMFPACK_Handler *)(amg->solver);
453 artak 2652 Paso_UMFPACK1(&ptr,amg->A,x,b,verbose);
454 gross 2551 amg->solver=(void*) ptr;
455 artak 2712 #else
456     Paso_Solver_solveJacobi(amg->GS,x,b);
457 artak 2699 #endif
458 artak 2507 #endif
459 artak 2699 }
460 artak 2475 time0=Paso_timer()-time0;
461 artak 2652 if (verbose) fprintf(stderr,"timing: DIRECT SOLVER: %e\n",time0);
462 artak 2507
463 jfenwick 1851 } else {
464 artak 1902 /* presmoothing */
465 artak 2507 time0=Paso_timer();
466 artak 2112 Paso_Solver_solveJacobi(amg->GS,x,b);
467 artak 2507 time0=Paso_timer()-time0;
468     if (verbose) fprintf(stderr,"timing: Presmooting: %e\n",time0);
469 artak 1931 /* end of presmoothing */
470 artak 1939
471 artak 2507
472     time0=Paso_timer();
473 artak 1890 #pragma omp parallel for private(i) schedule(static)
474     for (i=0;i<amg->n;++i) r[i]=b[i];
475    
476     /*r=b-Ax*/
477     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
478 artak 2760
479    
480     /* b_c <- R*r */
481     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(1.,amg->R,r,0.,amg->b_C);
482 artak 1954
483 artak 2507 time0=Paso_timer()-time0;
484     if (verbose) fprintf(stderr,"timing: Before next level: %e\n",time0);
485    
486 jfenwick 1851 /* x_C=AMG(b_C) */
487 artak 2760 Paso_Solver_solveAMG(amg->AMG_of_Coarse,amg->x_C,amg->b_C);
488 artak 1890
489 artak 2507 time0=Paso_timer();
490 artak 2726
491 artak 2760 /* x_0 <- P*x_c */
492     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(1.,amg->P,amg->x_C,0.,x0);
493    
494     /* x=x+x0 */
495 artak 1954 #pragma omp parallel for private(i) schedule(static)
496 artak 2760 for (i=0;i<amg->n;++i) x[i]+=x0[i];
497 artak 1954
498 artak 1931 /*postsmoothing*/
499 artak 2507 time0=Paso_timer();
500 artak 1954 #pragma omp parallel for private(i) schedule(static)
501     for (i=0;i<amg->n;++i) r[i]=b[i];
502 artak 2107
503 artak 2442 /*r=b-Ax */
504 artak 1954 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
505 artak 2112 Paso_Solver_solveJacobi(amg->GS,x0,r);
506 artak 2107
507 artak 2760
508 artak 2107 #pragma omp parallel for private(i) schedule(static)
509 artak 2760 for (i=0;i<amg->n;++i) {
510     x[i]+=x0[i];
511     /*printf("x[%d]=%e \n",i,x[i]);*/
512     }
513 artak 2107
514 artak 2507 time0=Paso_timer()-time0;
515     if (verbose) fprintf(stderr,"timing: Postsmoothing: %e\n",time0);
516 artak 2509
517 artak 1931 /*end of postsmoothing*/
518    
519 jfenwick 1851 }
520 artak 1890 MEMFREE(r);
521 artak 1954 MEMFREE(x0);
522 artak 2760
523 gross 2551 return;
524 jfenwick 1851 }

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