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

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Revision 2699 - (hide annotations)
Wed Sep 30 05:43:20 2009 UTC (10 years, 5 months ago) by artak
File MIME type: text/plain
File size: 18362 byte(s)
Direct solver switched to UMFPACK, till problem with MKL solved. When all unknows are eliminated then we switch to Jacobi preconditiner.
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 MEMFREE(in->inv_A_FF);
56     MEMFREE(in->A_FF_pivot);
57     Paso_SparseMatrix_free(in->A_FC);
58     Paso_SparseMatrix_free(in->A_CF);
59 artak 2556 Paso_SparseMatrix_free(in->A);
60 jfenwick 1851 MEMFREE(in->rows_in_F);
61     MEMFREE(in->rows_in_C);
62     MEMFREE(in->mask_F);
63     MEMFREE(in->mask_C);
64     MEMFREE(in->x_F);
65     MEMFREE(in->b_F);
66     MEMFREE(in->x_C);
67     MEMFREE(in->b_C);
68 artak 2699 #ifdef UMFPACK
69     Paso_UMFPACK1_free((Paso_UMFPACK_Handler*)(in->solver));
70 gross 2551 #endif
71     in->solver=NULL;
72 artak 2699 Paso_Solver_AMG_free(in->AMG_of_Schur);
73 gross 2551 MEMFREE(in->b_C);
74 jfenwick 1851 MEMFREE(in);
75     }
76     }
77    
78     /**************************************************************/
79    
80     /* constructs the block-block factorization of
81    
82     [ A_FF A_FC ]
83     A_p=
84     [ A_CF A_FF ]
85    
86     to
87    
88     [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ]
89     [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ]
90    
91    
92     where S=A_FF-ACF*invA_FF*A_FC within the shape of S
93    
94     then AMG is applied to S again until S becomes empty
95    
96     */
97 artak 2520 Paso_Solver_AMG* Paso_Solver_getAMG(Paso_SparseMatrix *A_p,dim_t level,Paso_Options* options) {
98 jfenwick 1851 Paso_Solver_AMG* out=NULL;
99 artak 2556 Paso_Pattern* temp1=NULL;
100     Paso_Pattern* temp2=NULL;
101 artak 2520 bool_t verbose=options->verbose;
102 jfenwick 1851 dim_t n=A_p->numRows;
103     dim_t n_block=A_p->row_block_size;
104     index_t* mis_marker=NULL;
105 artak 1881 index_t* counter=NULL;
106     index_t iPtr,*index, *where_p, iPtr_s;
107 artak 2686 dim_t i,j;
108 jfenwick 1851 Paso_SparseMatrix * schur=NULL;
109 artak 1881 Paso_SparseMatrix * schur_withFillIn=NULL;
110 artak 2381 double S=0;
111 artak 2475
112 artak 2439 /*Make sure we have block sizes 1*/
113 gross 2550 if (A_p->col_block_size>1) {
114     Paso_setError(TYPE_ERROR,"Paso_Solver_getAMG: AMG requires column block size 1.");
115     return NULL;
116     }
117     if (A_p->row_block_size>1) {
118     Paso_setError(TYPE_ERROR,"Paso_Solver_getAMG: AMG requires row block size 1.");
119     return NULL;
120     }
121 gross 2551 out=MEMALLOC(1,Paso_Solver_AMG);
122 jfenwick 1851 /* identify independend set of rows/columns */
123     mis_marker=TMPMEMALLOC(n,index_t);
124     counter=TMPMEMALLOC(n,index_t);
125 gross 2551 if ( !( Paso_checkPtr(mis_marker) || Paso_checkPtr(counter) || Paso_checkPtr(out)) ) {
126     out->AMG_of_Schur=NULL;
127     out->inv_A_FF=NULL;
128     out->A_FF_pivot=NULL;
129     out->A_FC=NULL;
130     out->A_CF=NULL;
131     out->rows_in_F=NULL;
132     out->rows_in_C=NULL;
133     out->mask_F=NULL;
134     out->mask_C=NULL;
135     out->x_F=NULL;
136     out->b_F=NULL;
137     out->x_C=NULL;
138     out->b_C=NULL;
139     out->GS=NULL;
140     out->A=Paso_SparseMatrix_getReference(A_p);
141     out->GS=NULL;
142     out->solver=NULL;
143     /*out->GS=Paso_Solver_getGS(A_p,verbose);*/
144     out->level=level;
145 artak 2661 out->n=n;
146     out->n_block=n_block;
147 artak 2556
148 gross 2551 if (level==0 || n<=options->min_coarse_matrix_size) {
149     out->coarsest_level=TRUE;
150 artak 2699 #ifdef UMFPACK
151 gross 2551 #else
152 artak 2699 #ifdef MKL
153 gross 2551 #else
154     out->GS=Paso_Solver_getJacobi(A_p);
155     #endif
156     #endif
157     } else {
158     out->coarsest_level=FALSE;
159     out->GS=Paso_Solver_getJacobi(A_p);
160 artak 2442
161 gross 2551 /* identify independend set of rows/columns */
162     #pragma omp parallel for private(i) schedule(static)
163     for (i=0;i<n;++i) mis_marker[i]=-1;
164    
165     if (options->coarsening_method == PASO_YAIR_SHAPIRA_COARSENING) {
166 artak 2652 Paso_Pattern_YS(A_p,mis_marker,options->coarsening_threshold);
167 gross 2551 }
168     else if (options->coarsening_method == PASO_RUGE_STUEBEN_COARSENING) {
169     Paso_Pattern_RS(A_p,mis_marker,options->coarsening_threshold);
170     }
171     else if (options->coarsening_method == PASO_AGGREGATION_COARSENING) {
172     Paso_Pattern_Aggregiation(A_p,mis_marker,options->coarsening_threshold);
173     }
174     else {
175     /*Default coarseneing*/
176 artak 2686 Paso_Pattern_RS(A_p,mis_marker,options->coarsening_threshold);
177 artak 2659 /*Paso_Pattern_YS(A_p,mis_marker,options->coarsening_threshold);*/
178 artak 2556 /*Paso_Pattern_Aggregiation(A_p,mis_marker,options->coarsening_threshold);*/
179 gross 2551 }
180 artak 2686
181     #pragma omp parallel for private(i) schedule(static)
182     for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
183     out->n_F=Paso_Util_cumsum(n,counter);
184    
185     if (out->n_F==n) {
186     out->coarsest_level=TRUE;
187     if (verbose) {
188 artak 2699 printf("AMG coarsening eliminates all unknowns, switching to Jacobi preconditioner.\n");
189 artak 2686 }
190     } else {
191 artak 2475
192 artak 2686 if (Paso_noError()) {
193    
194     /*#pragma omp parallel for private(i) schedule(static)
195     for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
196     out->n_F=Paso_Util_cumsum(n,counter);
197     */
198     out->mask_F=MEMALLOC(n,index_t);
199     out->rows_in_F=MEMALLOC(out->n_F,index_t);
200     out->inv_A_FF=MEMALLOC(n_block*n_block*out->n_F,double);
201     out->A_FF_pivot=NULL; /* later use for block size>3 */
202     if (! (Paso_checkPtr(out->mask_F) || Paso_checkPtr(out->inv_A_FF) || Paso_checkPtr(out->rows_in_F) ) ) {
203     /* creates an index for F from mask */
204     #pragma omp parallel for private(i) schedule(static)
205     for (i = 0; i < out->n_F; ++i) out->rows_in_F[i]=-1;
206     #pragma omp parallel for private(i) schedule(static)
207     for (i = 0; i < n; ++i) {
208     if (mis_marker[i]) {
209     out->rows_in_F[counter[i]]=i;
210     out->mask_F[i]=counter[i];
211     } else {
212     out->mask_F[i]=-1;
213     }
214     }
215    
216     /* Compute row-sum for getting rs(A_FF)^-1*/
217     #pragma omp parallel for private(i,iPtr,j,S) schedule(static)
218     for (i = 0; i < out->n_F; ++i) {
219     S=0;
220     /*printf("[%d ]: [%d] -> ",i, out->rows_in_F[i]);*/
221     for (iPtr=A_p->pattern->ptr[out->rows_in_F[i]];iPtr<A_p->pattern->ptr[out->rows_in_F[i] + 1]; ++iPtr) {
222     j=A_p->pattern->index[iPtr];
223     /*if (j==out->rows_in_F[i]) printf("diagonal %e",A_p->val[iPtr]);*/
224     if (mis_marker[j])
225     S+=A_p->val[iPtr];
226     }
227     /*printf("-> %e \n",S);*/
228     out->inv_A_FF[i]=1./S;
229     }
230 jfenwick 1851 }
231     }
232 artak 2686
233     /*check whether coarsening process actually makes sense to continue.
234     if coarse matrix at least smaller by 30% then continue, otherwise we stop.*/
235     if ((out->n_F*100/n)<30) {
236     level=1;
237 artak 1881 }
238 gross 2551
239 artak 2686 if ( Paso_noError()) {
240     /* if there are no nodes in the coarse level there is no more work to do */
241     out->n_C=n-out->n_F;
242    
243     /*if (out->n_F>500) */
244     out->rows_in_C=MEMALLOC(out->n_C,index_t);
245     out->mask_C=MEMALLOC(n,index_t);
246     if (! (Paso_checkPtr(out->mask_C) || Paso_checkPtr(out->rows_in_C) ) ) {
247     /* creates an index for C from mask */
248     #pragma omp parallel for private(i) schedule(static)
249     for (i = 0; i < n; ++i) counter[i]=! mis_marker[i];
250     Paso_Util_cumsum(n,counter);
251     #pragma omp parallel for private(i) schedule(static)
252     for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
253     #pragma omp parallel for private(i) schedule(static)
254     for (i = 0; i < n; ++i) {
255     if (! mis_marker[i]) {
256     out->rows_in_C[counter[i]]=i;
257     out->mask_C[i]=counter[i];
258     } else {
259     out->mask_C[i]=-1;
260     }
261     }
262     }
263     }
264     if ( Paso_noError()) {
265     /* get A_CF block: */
266     out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
267     /* get A_FC block: */
268     out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
269     /* get A_CC block: */
270     schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
271    
272 gross 2551 }
273 artak 2686 if ( Paso_noError()) {
274     /*find the pattern of the schur complement with fill in*/
275     temp1=Paso_Pattern_multiply(PATTERN_FORMAT_DEFAULT,out->A_CF->pattern,out->A_FC->pattern);
276     temp2=Paso_Pattern_binop(PATTERN_FORMAT_DEFAULT, schur->pattern, temp1);
277     schur_withFillIn=Paso_SparseMatrix_alloc(A_p->type,temp2,1,1, TRUE);
278     Paso_Pattern_free(temp1);
279     Paso_Pattern_free(temp2);
280 gross 2551 }
281 artak 2686 if ( Paso_noError()) {
282     /* copy values over*/
283     #pragma omp parallel for private(i,iPtr,j,iPtr_s,index,where_p) schedule(static)
284     for (i = 0; i < schur_withFillIn->numRows; ++i) {
285     for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
286     j=schur_withFillIn->pattern->index[iPtr];
287     iPtr_s=schur->pattern->ptr[i];
288     index=&(schur->pattern->index[iPtr_s]);
289     where_p=(index_t*)bsearch(&j,
290     index,
291     schur->pattern->ptr[i + 1]-schur->pattern->ptr[i],
292     sizeof(index_t),
293     Paso_comparIndex);
294     if (where_p!=NULL) {
295     schur_withFillIn->val[iPtr]=schur->val[iPtr_s+(index_t)(where_p-index)];
296     }
297     }
298     }
299     Paso_Solver_updateIncompleteSchurComplement(schur_withFillIn,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC);
300     out->AMG_of_Schur=Paso_Solver_getAMG(schur_withFillIn,level-1,options);
301     }
302     /* allocate work arrays for AMG application */
303     if (Paso_noError()) {
304     out->x_F=MEMALLOC(n_block*out->n_F,double);
305     out->b_F=MEMALLOC(n_block*out->n_F,double);
306     out->x_C=MEMALLOC(n_block*out->n_C,double);
307     out->b_C=MEMALLOC(n_block*out->n_C,double);
308    
309     if (! (Paso_checkPtr(out->x_F) || Paso_checkPtr(out->b_F) || Paso_checkPtr(out->x_C) || Paso_checkPtr(out->b_C) ) ) {
310     #pragma omp parallel for private(i) schedule(static)
311     for (i = 0; i < out->n_F; ++i) {
312     out->x_F[i]=0.;
313     out->b_F[i]=0.;
314     }
315     #pragma omp parallel for private(i) schedule(static)
316     for (i = 0; i < out->n_C; ++i) {
317     out->x_C[i]=0.;
318     out->b_C[i]=0.;
319     }
320     }
321     }
322     Paso_SparseMatrix_free(schur);
323     Paso_SparseMatrix_free(schur_withFillIn);
324     }
325 jfenwick 1851 }
326     }
327     TMPMEMFREE(mis_marker);
328     TMPMEMFREE(counter);
329 artak 2686
330 jfenwick 1851 if (Paso_noError()) {
331 artak 2524 if (verbose && level>0 && !out->coarsest_level) {
332 gross 2551 printf("AMG: level: %d: %d unknowns eliminated. %d left.\n",level, out->n_F,out->n_C);
333 jfenwick 1851 }
334     return out;
335     } else {
336     Paso_Solver_AMG_free(out);
337     return NULL;
338     }
339     }
340    
341     /**************************************************************/
342    
343     /* apply AMG precondition b-> x
344    
345     in fact it solves
346    
347 artak 2381 [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FC ] [ x_F ] = [b_F]
348 jfenwick 1851 [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] [ x_C ] = [b_C]
349    
350     in the form
351    
352     b->[b_F,b_C]
353     x_F=invA_FF*b_F
354     b_C=b_C-A_CF*x_F
355     x_C=AMG(b_C)
356     b_F=b_F-A_FC*x_C
357     x_F=invA_FF*b_F
358     x<-[x_F,x_C]
359    
360     should be called within a parallel region
361     barrier synconization should be performed to make sure that the input vector available
362    
363     */
364    
365     void Paso_Solver_solveAMG(Paso_Solver_AMG * amg, double * x, double * b) {
366 artak 2107 dim_t i;
367 artak 2507 double time0=0;
368 gross 2551 double *r=NULL, *x0=NULL;
369 artak 2509 bool_t verbose=0;
370 artak 2699 #ifdef UMFPACK
371     Paso_UMFPACK_Handler * ptr=NULL;
372     #else
373     #ifdef MKL
374     Paso_SparseMatrix *temp=NULL;
375 gross 2551 #endif
376 artak 2507 #endif
377 gross 2551 r=MEMALLOC(amg->n,double);
378     x0=MEMALLOC(amg->n,double);
379 artak 2507
380 artak 2524 if (amg->coarsest_level) {
381 artak 2507
382     time0=Paso_timer();
383 artak 2699 /*If all unknown are eliminated then Jacobi is the best preconditioner*/
384     if (amg->n_F==amg->n) {
385     Paso_Solver_solveJacobi(amg->GS,x,b);
386     }
387     else {
388     #ifdef UMFPACK
389 gross 2551 ptr=(Paso_UMFPACK_Handler *)(amg->solver);
390 artak 2652 Paso_UMFPACK1(&ptr,amg->A,x,b,verbose);
391 gross 2551 amg->solver=(void*) ptr;
392 artak 2699 #else
393     #ifdef MKL
394     ptr=(Paso_MKL_Handler *)(amg->solver);
395     temp=Paso_SparseMatrix_alloc(MATRIX_FORMAT_BLK1 + MATRIX_FORMAT_OFFSET1, amg->A->pattern,1,1, FALSE);
396     #pragma omp parallel for private(i) schedule(static)
397     for (i=0;i<amg->A->len;++i) {
398     temp->val[i]=amg->A->val[i];
399     }
400     Paso_MKL1(ptr,temp,x,b,verbose);
401     amg->solver=(void*) ptr;
402     Paso_SparseMatrix_free(temp);
403     #else
404     Paso_Solver_solveJacobi(amg->GS,x,b);
405     #endif
406 artak 2507 #endif
407 artak 2699 }
408 artak 2475 time0=Paso_timer()-time0;
409 artak 2652 if (verbose) fprintf(stderr,"timing: DIRECT SOLVER: %e\n",time0);
410 artak 2507
411 jfenwick 1851 } else {
412 artak 1902 /* presmoothing */
413 artak 2507 time0=Paso_timer();
414 artak 2112 Paso_Solver_solveJacobi(amg->GS,x,b);
415 artak 2507 time0=Paso_timer()-time0;
416     if (verbose) fprintf(stderr,"timing: Presmooting: %e\n",time0);
417 artak 1931 /* end of presmoothing */
418 artak 1939
419 artak 2507
420     time0=Paso_timer();
421 artak 1890 #pragma omp parallel for private(i) schedule(static)
422     for (i=0;i<amg->n;++i) r[i]=b[i];
423    
424     /*r=b-Ax*/
425     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
426 artak 1954
427 jfenwick 1851 /* b->[b_F,b_C] */
428 artak 1954 #pragma omp parallel for private(i) schedule(static)
429     for (i=0;i<amg->n_F;++i) amg->b_F[i]=r[amg->rows_in_F[i]];
430    
431     #pragma omp parallel for private(i) schedule(static)
432     for (i=0;i<amg->n_C;++i) amg->b_C[i]=r[amg->rows_in_C[i]];
433 artak 1890
434 jfenwick 1851 /* x_F=invA_FF*b_F */
435 artak 1954 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
436 artak 1890
437 jfenwick 1851 /* b_C=b_C-A_CF*x_F */
438     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->x_F,1.,amg->b_C);
439 artak 1890
440 artak 2507 time0=Paso_timer()-time0;
441     if (verbose) fprintf(stderr,"timing: Before next level: %e\n",time0);
442    
443 jfenwick 1851 /* x_C=AMG(b_C) */
444     Paso_Solver_solveAMG(amg->AMG_of_Schur,amg->x_C,amg->b_C);
445 artak 1890
446 artak 2507 time0=Paso_timer();
447 jfenwick 1851 /* b_F=b_F-A_FC*x_C */
448     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_FC,amg->x_C,1.,amg->b_F);
449     /* x_F=invA_FF*b_F */
450 artak 1954 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
451 jfenwick 1851 /* x<-[x_F,x_C] */
452 artak 2113
453 artak 1954 #pragma omp parallel for private(i) schedule(static)
454     for (i=0;i<amg->n;++i) {
455     if (amg->mask_C[i]>-1) {
456 artak 2107 x[i]=amg->x_C[amg->mask_C[i]];
457 artak 1954 } else {
458 artak 2107 x[i]=amg->x_F[amg->mask_F[i]];
459 artak 1954 }
460 jfenwick 1851 }
461 artak 1954
462 artak 2507 time0=Paso_timer()-time0;
463     if (verbose) fprintf(stderr,"timing: After next level: %e\n",time0);
464    
465 artak 1931 /*postsmoothing*/
466 artak 2507 time0=Paso_timer();
467 artak 1954 #pragma omp parallel for private(i) schedule(static)
468     for (i=0;i<amg->n;++i) r[i]=b[i];
469 artak 2107
470 artak 2442 /*r=b-Ax */
471 artak 1954 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
472 artak 2112 Paso_Solver_solveJacobi(amg->GS,x0,r);
473 artak 2107
474     #pragma omp parallel for private(i) schedule(static)
475     for (i=0;i<amg->n;++i) x[i]+=x0[i];
476    
477 artak 2507 time0=Paso_timer()-time0;
478     if (verbose) fprintf(stderr,"timing: Postsmoothing: %e\n",time0);
479 artak 2509
480 artak 1931 /*end of postsmoothing*/
481    
482 jfenwick 1851 }
483 artak 1890 MEMFREE(r);
484 artak 1954 MEMFREE(x0);
485 gross 2551 return;
486 jfenwick 1851 }

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