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

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Revision 2726 - (show annotations)
Wed Oct 21 23:50:05 2009 UTC (10 years, 4 months ago) by artak
File MIME type: text/plain
File size: 19172 byte(s)
New diagonal dominancy based algorithm is added. The coarseneng strategy is changed.
1
2 /*******************************************************
3 *
4 * Copyright (c) 2003-2009 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 */
18
19 /**************************************************************/
20
21 /* Author: artak@uq.edu.au */
22
23 /**************************************************************/
24
25 #include "Paso.h"
26 #include "Solver.h"
27 #include "Options.h"
28 #include "PasoUtil.h"
29 #include "UMFPACK.h"
30 #include "MKL.h"
31 #include "SystemMatrix.h"
32 #include "Pattern_coupling.h"
33
34 /**************************************************************/
35
36 /* free all memory used by AMG */
37
38 void Paso_Solver_AMG_System_free(Paso_Solver_AMG_System * in) {
39 dim_t i;
40 if (in!=NULL) {
41 for (i=0;i<in->block_size;++i) {
42 Paso_Solver_AMG_free(in->amgblock[i]);
43 Paso_SparseMatrix_free(in->block[i]);
44 }
45 MEMFREE(in);
46 }
47 }
48
49
50 /* free all memory used by AMG */
51
52 void Paso_Solver_AMG_free(Paso_Solver_AMG * in) {
53 if (in!=NULL) {
54 Paso_Solver_Jacobi_free(in->GS);
55 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 Paso_SparseMatrix_free(in->A);
60 if(in->coarsest_level==TRUE) {
61 #ifdef MKL
62 Paso_MKL_free1(in->AOffset1);
63 Paso_SparseMatrix_free(in->AOffset1);
64 #else
65 #ifdef UMFPACK
66 Paso_UMFPACK1_free((Paso_UMFPACK_Handler*)(in->solver));
67 #endif
68 #endif
69 }
70 MEMFREE(in->rows_in_F);
71 MEMFREE(in->rows_in_C);
72 MEMFREE(in->mask_F);
73 MEMFREE(in->mask_C);
74 MEMFREE(in->x_F);
75 MEMFREE(in->b_F);
76 MEMFREE(in->x_C);
77 MEMFREE(in->b_C);
78 in->solver=NULL;
79 Paso_Solver_AMG_free(in->AMG_of_Schur);
80 MEMFREE(in->b_C);
81 MEMFREE(in);
82 }
83 }
84
85 /**************************************************************/
86
87 /* constructs the block-block factorization of
88
89 [ A_FF A_FC ]
90 A_p=
91 [ A_CF A_FF ]
92
93 to
94
95 [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ]
96 [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ]
97
98
99 where S=A_FF-ACF*invA_FF*A_FC within the shape of S
100
101 then AMG is applied to S again until S becomes empty
102
103 */
104 Paso_Solver_AMG* Paso_Solver_getAMG(Paso_SparseMatrix *A_p,dim_t level,Paso_Options* options) {
105 Paso_Solver_AMG* out=NULL;
106 Paso_Pattern* temp1=NULL;
107 Paso_Pattern* temp2=NULL;
108 bool_t verbose=options->verbose;
109 dim_t n=A_p->numRows;
110 dim_t n_block=A_p->row_block_size;
111 index_t* mis_marker=NULL;
112 index_t* counter=NULL;
113 index_t iPtr,*index, *where_p, iPtr_s;
114 dim_t i,j;
115 Paso_SparseMatrix * schur=NULL;
116 Paso_SparseMatrix * schur_withFillIn=NULL;
117 double S=0;
118
119
120 /* char filename[8];
121 sprintf(filename,"AMGLevel%d",level);
122
123 Paso_SparseMatrix_saveMM(A_p,filename);
124 */
125
126 /*Make sure we have block sizes 1*/
127 if (A_p->col_block_size>1) {
128 Paso_setError(TYPE_ERROR,"Paso_Solver_getAMG: AMG requires column block size 1.");
129 return NULL;
130 }
131 if (A_p->row_block_size>1) {
132 Paso_setError(TYPE_ERROR,"Paso_Solver_getAMG: AMG requires row block size 1.");
133 return NULL;
134 }
135 out=MEMALLOC(1,Paso_Solver_AMG);
136 /* identify independend set of rows/columns */
137 mis_marker=TMPMEMALLOC(n,index_t);
138 counter=TMPMEMALLOC(n,index_t);
139 if ( !( Paso_checkPtr(mis_marker) || Paso_checkPtr(counter) || Paso_checkPtr(out)) ) {
140 out->AMG_of_Schur=NULL;
141 out->inv_A_FF=NULL;
142 out->A_FF_pivot=NULL;
143 out->A_FC=NULL;
144 out->A_CF=NULL;
145 out->rows_in_F=NULL;
146 out->rows_in_C=NULL;
147 out->mask_F=NULL;
148 out->mask_C=NULL;
149 out->x_F=NULL;
150 out->b_F=NULL;
151 out->x_C=NULL;
152 out->b_C=NULL;
153 out->GS=NULL;
154 out->A=Paso_SparseMatrix_getReference(A_p);
155 out->GS=NULL;
156 out->solver=NULL;
157 /*out->GS=Paso_Solver_getGS(A_p,verbose);*/
158 out->level=level;
159 out->n=n;
160 out->n_F=n+1;
161 out->n_block=n_block;
162
163 if (level==0 || n<=options->min_coarse_matrix_size) {
164 out->coarsest_level=TRUE;
165 #ifdef MKL
166 out->AOffset1=Paso_SparseMatrix_alloc(MATRIX_FORMAT_BLK1 + MATRIX_FORMAT_OFFSET1, out->A->pattern,1,1, FALSE);
167 #pragma omp parallel for private(i) schedule(static)
168 for (i=0;i<out->A->len;++i) {
169 out->AOffset1->val[i]=out->A->val[i];
170 }
171 #else
172 #ifdef UMFPACK
173 #else
174 out->GS=Paso_Solver_getJacobi(A_p);
175 #endif
176 #endif
177 } else {
178 out->coarsest_level=FALSE;
179 out->GS=Paso_Solver_getJacobi(A_p);
180
181 /* identify independend set of rows/columns */
182 #pragma omp parallel for private(i) schedule(static)
183 for (i=0;i<n;++i) mis_marker[i]=-1;
184
185 if (options->coarsening_method == PASO_YAIR_SHAPIRA_COARSENING) {
186 Paso_Pattern_YS(A_p,mis_marker,options->coarsening_threshold);
187 }
188 else if (options->coarsening_method == PASO_RUGE_STUEBEN_COARSENING) {
189 Paso_Pattern_RS(A_p,mis_marker,options->coarsening_threshold);
190 }
191 else if (options->coarsening_method == PASO_AGGREGATION_COARSENING) {
192 Paso_Pattern_Aggregiation(A_p,mis_marker,options->coarsening_threshold);
193 }
194 else {
195 /*Default coarseneing*/
196 Paso_Pattern_RS(A_p,mis_marker,options->coarsening_threshold);
197 /*Paso_Pattern_YS(A_p,mis_marker,options->coarsening_threshold);*/
198 /*Paso_Pattern_greedy_diag(A_p,mis_marker,options->coarsening_threshold);*/
199 /*Paso_Pattern_Aggregiation(A_p,mis_marker,options->coarsening_threshold);*/
200 }
201
202 #pragma omp parallel for private(i) schedule(static)
203 for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
204
205 out->n_F=Paso_Util_cumsum(n,counter);
206
207 if (out->n_F==0) {
208 out->coarsest_level=TRUE;
209 level=0;
210 if (verbose) {
211 /*printf("AMG coarsening eliminates all unknowns, switching to Jacobi preconditioner.\n");*/
212 printf("AMG coarsening does not eliminate any of the unknowns, switching to Jacobi preconditioner.\n");
213 }
214 }
215 else if (out->n_F==n) {
216 out->coarsest_level=TRUE;
217 level=0;
218 if (verbose) {
219 /*printf("AMG coarsening eliminates all unknowns, switching to Jacobi preconditioner.\n");*/
220 printf("AMG coarsening eliminates all of the unknowns, switching to Jacobi preconditioner.\n");
221
222 }
223 } else {
224
225 if (Paso_noError()) {
226
227 /*#pragma omp parallel for private(i) schedule(static)
228 for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
229 out->n_F=Paso_Util_cumsum(n,counter);
230 */
231 out->mask_F=MEMALLOC(n,index_t);
232 out->rows_in_F=MEMALLOC(out->n_F,index_t);
233 out->inv_A_FF=MEMALLOC(n_block*n_block*out->n_F,double);
234 out->A_FF_pivot=NULL; /* later use for block size>3 */
235 if (! (Paso_checkPtr(out->mask_F) || Paso_checkPtr(out->inv_A_FF) || Paso_checkPtr(out->rows_in_F) ) ) {
236 /* creates an index for F from mask */
237 #pragma omp parallel for private(i) schedule(static)
238 for (i = 0; i < out->n_F; ++i) out->rows_in_F[i]=-1;
239 #pragma omp parallel for private(i) schedule(static)
240 for (i = 0; i < n; ++i) {
241 if (mis_marker[i]) {
242 out->rows_in_F[counter[i]]=i;
243 out->mask_F[i]=counter[i];
244 } else {
245 out->mask_F[i]=-1;
246 }
247 }
248
249 /* Compute row-sum for getting rs(A_FF)^-1*/
250 #pragma omp parallel for private(i,iPtr,j,S) schedule(static)
251 for (i = 0; i < out->n_F; ++i) {
252 S=0;
253 /*printf("[%d ]: [%d] -> ",i, out->rows_in_F[i]);*/
254 for (iPtr=A_p->pattern->ptr[out->rows_in_F[i]];iPtr<A_p->pattern->ptr[out->rows_in_F[i] + 1]; ++iPtr) {
255 j=A_p->pattern->index[iPtr];
256 /*if (j==out->rows_in_F[i]) printf("diagonal %e",A_p->val[iPtr]);*/
257 if (mis_marker[j])
258 S+=A_p->val[iPtr];
259 }
260 /*printf("-> %e \n",S);*/
261 out->inv_A_FF[i]=1./S;
262 }
263 }
264 }
265
266 /*check whether coarsening process actually makes sense to continue.
267 if coarse matrix at least smaller by 30% then continue, otherwise we stop.*/
268 if ((out->n_F*100/n)<30) {
269 level=1;
270 }
271
272 if ( Paso_noError()) {
273 /* if there are no nodes in the coarse level there is no more work to do */
274 out->n_C=n-out->n_F;
275
276 /*if (out->n_F>500) */
277 out->rows_in_C=MEMALLOC(out->n_C,index_t);
278 out->mask_C=MEMALLOC(n,index_t);
279 if (! (Paso_checkPtr(out->mask_C) || Paso_checkPtr(out->rows_in_C) ) ) {
280 /* creates an index for C from mask */
281 #pragma omp parallel for private(i) schedule(static)
282 for (i = 0; i < n; ++i) counter[i]=! mis_marker[i];
283 Paso_Util_cumsum(n,counter);
284 #pragma omp parallel for private(i) schedule(static)
285 for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
286 #pragma omp parallel for private(i) schedule(static)
287 for (i = 0; i < n; ++i) {
288 if (! mis_marker[i]) {
289 out->rows_in_C[counter[i]]=i;
290 out->mask_C[i]=counter[i];
291 } else {
292 out->mask_C[i]=-1;
293 }
294 }
295 }
296 }
297 if ( Paso_noError()) {
298 /* get A_CF block: */
299 out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
300 /* get A_FC block: */
301 out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
302 /* get A_CC block: */
303 schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
304
305 }
306 if ( Paso_noError()) {
307 /*find the pattern of the schur complement with fill in*/
308 temp1=Paso_Pattern_multiply(PATTERN_FORMAT_DEFAULT,out->A_CF->pattern,out->A_FC->pattern);
309 temp2=Paso_Pattern_binop(PATTERN_FORMAT_DEFAULT, schur->pattern, temp1);
310 schur_withFillIn=Paso_SparseMatrix_alloc(A_p->type,temp2,1,1, TRUE);
311 Paso_Pattern_free(temp1);
312 Paso_Pattern_free(temp2);
313 }
314 if ( Paso_noError()) {
315 /* copy values over*/
316 #pragma omp parallel for private(i,iPtr,j,iPtr_s,index,where_p) schedule(static)
317 for (i = 0; i < schur_withFillIn->numRows; ++i) {
318 for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
319 j=schur_withFillIn->pattern->index[iPtr];
320 iPtr_s=schur->pattern->ptr[i];
321 index=&(schur->pattern->index[iPtr_s]);
322 where_p=(index_t*)bsearch(&j,
323 index,
324 schur->pattern->ptr[i + 1]-schur->pattern->ptr[i],
325 sizeof(index_t),
326 Paso_comparIndex);
327 if (where_p!=NULL) {
328 schur_withFillIn->val[iPtr]=schur->val[iPtr_s+(index_t)(where_p-index)];
329 }
330 }
331 }
332 Paso_Solver_updateIncompleteSchurComplement(schur_withFillIn,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC);
333 out->AMG_of_Schur=Paso_Solver_getAMG(schur_withFillIn,level-1,options);
334 }
335 /* allocate work arrays for AMG application */
336 if (Paso_noError()) {
337 out->x_F=MEMALLOC(n_block*out->n_F,double);
338 out->b_F=MEMALLOC(n_block*out->n_F,double);
339 out->x_C=MEMALLOC(n_block*out->n_C,double);
340 out->b_C=MEMALLOC(n_block*out->n_C,double);
341
342 if (! (Paso_checkPtr(out->x_F) || Paso_checkPtr(out->b_F) || Paso_checkPtr(out->x_C) || Paso_checkPtr(out->b_C) ) ) {
343 #pragma omp parallel for private(i) schedule(static)
344 for (i = 0; i < out->n_F; ++i) {
345 out->x_F[i]=0.;
346 out->b_F[i]=0.;
347 }
348 #pragma omp parallel for private(i) schedule(static)
349 for (i = 0; i < out->n_C; ++i) {
350 out->x_C[i]=0.;
351 out->b_C[i]=0.;
352 }
353 }
354 }
355 Paso_SparseMatrix_free(schur);
356 Paso_SparseMatrix_free(schur_withFillIn);
357 }
358 }
359 }
360 TMPMEMFREE(mis_marker);
361 TMPMEMFREE(counter);
362
363 if (Paso_noError()) {
364 if (verbose && level>0 && !out->coarsest_level) {
365 printf("AMG: level: %d: %d unknowns eliminated. %d left.\n",level, out->n_F,out->n_C);
366 }
367 return out;
368 } else {
369 Paso_Solver_AMG_free(out);
370 return NULL;
371 }
372 }
373
374 /**************************************************************/
375
376 /* apply AMG precondition b-> x
377
378 in fact it solves
379
380 [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FC ] [ x_F ] = [b_F]
381 [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] [ x_C ] = [b_C]
382
383 in the form
384
385 b->[b_F,b_C]
386 x_F=invA_FF*b_F
387 b_C=b_C-A_CF*x_F
388 x_C=AMG(b_C)
389 b_F=b_F-A_FC*x_C
390 x_F=invA_FF*b_F
391 x<-[x_F,x_C]
392
393 should be called within a parallel region
394 barrier synconization should be performed to make sure that the input vector available
395
396 */
397
398 void Paso_Solver_solveAMG(Paso_Solver_AMG * amg, double * x, double * b) {
399 dim_t i;
400 double time0=0;
401 double *r=NULL, *x0=NULL;
402 bool_t verbose=0;
403 #ifdef UMFPACK
404 Paso_UMFPACK_Handler * ptr=NULL;
405 #endif
406 r=MEMALLOC(amg->n,double);
407 x0=MEMALLOC(amg->n,double);
408
409 if (amg->coarsest_level) {
410
411 time0=Paso_timer();
412 /*If all unknown are eliminated then Jacobi is the best preconditioner*/
413 if (amg->n_F==0 || amg->n_F==amg->n) {
414 Paso_Solver_solveJacobi(amg->GS,x,b);
415 }
416 else {
417 #ifdef MKL
418 Paso_MKL1(amg->AOffset1,x,b,verbose);
419 #else
420 #ifdef UMFPACK
421 ptr=(Paso_UMFPACK_Handler *)(amg->solver);
422 Paso_UMFPACK1(&ptr,amg->A,x,b,verbose);
423 amg->solver=(void*) ptr;
424 #else
425 Paso_Solver_solveJacobi(amg->GS,x,b);
426 #endif
427 #endif
428 }
429 time0=Paso_timer()-time0;
430 if (verbose) fprintf(stderr,"timing: DIRECT SOLVER: %e\n",time0);
431
432 } else {
433 /* presmoothing */
434 time0=Paso_timer();
435 Paso_Solver_solveJacobi(amg->GS,x,b);
436 time0=Paso_timer()-time0;
437 if (verbose) fprintf(stderr,"timing: Presmooting: %e\n",time0);
438 /* end of presmoothing */
439
440
441 time0=Paso_timer();
442 #pragma omp parallel for private(i) schedule(static)
443 for (i=0;i<amg->n;++i) r[i]=b[i];
444
445 /*r=b-Ax*/
446 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
447
448 /* r->[b_F,b_C] */
449 #pragma omp parallel for private(i) schedule(static)
450 for (i=0;i<amg->n_F;++i) amg->b_F[i]=r[amg->rows_in_F[i]];
451
452 #pragma omp parallel for private(i) schedule(static)
453 for (i=0;i<amg->n_C;++i) amg->b_C[i]=r[amg->rows_in_C[i]];
454
455 /* x_F=invA_FF*b_F */
456 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
457
458 /* b_C=b_C-A_CF*x_F */
459 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->x_F,1.,amg->b_C);
460
461 time0=Paso_timer()-time0;
462 if (verbose) fprintf(stderr,"timing: Before next level: %e\n",time0);
463
464 /* x_C=AMG(b_C) */
465 Paso_Solver_solveAMG(amg->AMG_of_Schur,amg->x_C,amg->b_C);
466
467 time0=Paso_timer();
468 /* b_F=b_F-A_FC*x_C */
469 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_FC,amg->x_C,1.,amg->b_F);
470 /* x_F=invA_FF*b_F */
471 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
472
473 /* x<-[x_F,x_C] */
474 #pragma omp parallel for private(i) schedule(static)
475 for (i=0;i<amg->n;++i) {
476 if (amg->mask_C[i]>-1) {
477 x[i]=amg->x_C[amg->mask_C[i]];
478 } else {
479 x[i]=amg->x_F[amg->mask_F[i]];
480 }
481 }
482
483 time0=Paso_timer()-time0;
484 if (verbose) fprintf(stderr,"timing: After next level: %e\n",time0);
485
486 /*postsmoothing*/
487 time0=Paso_timer();
488 #pragma omp parallel for private(i) schedule(static)
489 for (i=0;i<amg->n;++i) r[i]=b[i];
490
491 /*r=b-Ax */
492 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
493 Paso_Solver_solveJacobi(amg->GS,x0,r);
494
495 #pragma omp parallel for private(i) schedule(static)
496 for (i=0;i<amg->n;++i) x[i]+=x0[i];
497
498 time0=Paso_timer()-time0;
499 if (verbose) fprintf(stderr,"timing: Postsmoothing: %e\n",time0);
500
501 /*end of postsmoothing*/
502
503 }
504 MEMFREE(r);
505 MEMFREE(x0);
506 return;
507 }

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