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

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Revision 1902 - (show annotations)
Wed Oct 22 03:54:14 2008 UTC (11 years, 4 months ago) by artak
File MIME type: text/plain
File size: 19991 byte(s)
some bugs fixed in coresening methods
1
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 Paso_Solver_AMG* Paso_Solver_getAMG(Paso_SparseMatrix *A_p,bool_t verbose,dim_t level) {
72 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 index_t* counter=NULL;
77 index_t iPtr,*index, *where_p, iPtr_s;
78 dim_t i,k,j,j0;
79 Paso_SparseMatrix * schur=NULL;
80 Paso_SparseMatrix * schur_withFillIn=NULL;
81 Paso_Pattern* mult=NULL;
82 double A11,A12,A13,A21,A22,A23,A31,A32,A33,D,time0,time1,time2,S;
83
84 /* identify independend set of rows/columns */
85 mis_marker=TMPMEMALLOC(n,index_t);
86 counter=TMPMEMALLOC(n,index_t);
87 out=MEMALLOC(1,Paso_Solver_AMG);
88 out->AMG_of_Schur=NULL;
89 out->inv_A_FF=NULL;
90 out->A_FF_pivot=NULL;
91 out->A_FC=NULL;
92 out->A_CF=NULL;
93 out->rows_in_F=NULL;
94 out->rows_in_C=NULL;
95 out->mask_F=NULL;
96 out->mask_C=NULL;
97 out->x_F=NULL;
98 out->b_F=NULL;
99 out->x_C=NULL;
100 out->b_C=NULL;
101 out->A=Paso_SparseMatrix_getReference(A_p);
102 out->level=level;
103
104 if ( !(Paso_checkPtr(mis_marker) || Paso_checkPtr(out) || Paso_checkPtr(counter) ) ) {
105 /* identify independend set of rows/columns */
106 time0=Paso_timer();
107 #pragma omp parallel for private(i) schedule(static)
108 for (i=0;i<n;++i) mis_marker[i]=-1;
109 /*Paso_Pattern_RS(A_p,mis_marker,0.25);*/
110 Paso_Pattern_coup(A_p,mis_marker);
111 time2=Paso_timer()-time0;
112 if (Paso_noError()) {
113 #pragma omp parallel for private(i) schedule(static)
114 for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
115 out->n=n;
116 out->n_block=n_block;
117 out->n_F=Paso_Util_cumsum(n,counter);
118 out->mask_F=MEMALLOC(n,index_t);
119 out->rows_in_F=MEMALLOC(out->n_F,index_t);
120 out->inv_A_FF=MEMALLOC(n_block*n_block*out->n_F,double);
121 out->A_FF_pivot=NULL; /* later use for block size>3 */
122 if (! (Paso_checkPtr(out->mask_F) || Paso_checkPtr(out->inv_A_FF) || Paso_checkPtr(out->rows_in_F) ) ) {
123 #pragma omp parallel
124 {
125 /* creates an index for F from mask */
126 #pragma omp for private(i) schedule(static)
127 for (i = 0; i < out->n_F; ++i) out->rows_in_F[i]=-1;
128 #pragma omp for private(i) schedule(static)
129 for (i = 0; i < n; ++i) {
130 if (mis_marker[i]) {
131 out->rows_in_F[counter[i]]=i;
132 out->mask_F[i]=counter[i];
133 } else {
134 out->mask_F[i]=-1;
135 }
136 }
137 /* Compute row-sum for getting rs(A_FF)*/
138 #pragma omp for private(i,iPtr) schedule(static)
139 for (i = 0; i < out->n_F; ++i) {
140 out->inv_A_FF[i]=0;
141 for (iPtr=A_p->pattern->ptr[out->rows_in_F[i]];iPtr<A_p->pattern->ptr[out->rows_in_F[i] + 1]; ++iPtr) {
142 out->inv_A_FF[i]+=A_p->val[iPtr];
143 }
144 }
145
146 /* fprintf(stderr,"\n MATRIX START\n");
147 j=0;
148 for (i = 0; i < n; ++i) {
149 for (iPtr=A_p->pattern->ptr[i];iPtr<A_p->pattern->ptr[i + 1]; ++iPtr) {
150 fprintf(stderr,"A[%d,%d]=%.2f ",i,A_p->pattern->index[iPtr],A_p->val[iPtr]);
151 }
152 if (mis_marker[i]) {
153 fprintf(stderr,"ROW SUM %.2f\n ",out->inv_A_FF[j]);
154 j++;
155 }
156 else {
157 fprintf(stderr,"\n ");
158 }
159 }
160 fprintf(stderr,"\n MATRIX END\n");
161 */
162 #pragma omp for private(i, where_p,iPtr,A11,A12,A13,A21,A22,A23,A31,A32,A33,D,index) schedule(static)
163 for (i = 0; i < out->n_F; i++) {
164 /* find main diagonal */
165 iPtr=A_p->pattern->ptr[out->rows_in_F[i]];
166 index=&(A_p->pattern->index[iPtr]);
167 where_p=(index_t*)bsearch(&out->rows_in_F[i],
168 index,
169 A_p->pattern->ptr[out->rows_in_F[i] + 1]-A_p->pattern->ptr[out->rows_in_F[i]],
170 sizeof(index_t),
171 Paso_comparIndex);
172 if (where_p==NULL) {
173 Paso_setError(VALUE_ERROR, "Paso_Solver_getAMG: main diagonal element missing.");
174 } else {
175 iPtr+=(index_t)(where_p-index);
176 /* get inverse of A_FF block: */
177 S=out->inv_A_FF[i];
178 if (ABS(A_p->val[iPtr])>0.) {
179 if(ABS(S)>0.)
180 out->inv_A_FF[i]=1./S;
181 } else {
182 Paso_setError(ZERO_DIVISION_ERROR, "Paso_Solver_getAMG: Break-down in AMG decomposition: non-regular main diagonal block.");
183 }
184 }
185 }
186 } /* end parallel region */
187
188 if( Paso_noError()) {
189 /* if there are no nodes in the coarse level there is no more work to do */
190 out->n_C=n-out->n_F;
191 /*if (out->n_C>11) {*/
192 /*fprintf(stderr,"SPARSITY in level %d \n", level);*/
193 if (level>0) {
194 out->rows_in_C=MEMALLOC(out->n_C,index_t);
195 out->mask_C=MEMALLOC(n,index_t);
196 if (! (Paso_checkPtr(out->mask_C) || Paso_checkPtr(out->rows_in_C) ) ) {
197 /* creates an index for C from mask */
198 #pragma omp parallel for private(i) schedule(static)
199 for (i = 0; i < n; ++i) counter[i]=! mis_marker[i];
200 Paso_Util_cumsum(n,counter);
201 #pragma omp parallel
202 {
203 #pragma omp for private(i) schedule(static)
204 for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
205 #pragma omp for private(i) schedule(static)
206 for (i = 0; i < n; ++i) {
207 if (! mis_marker[i]) {
208 out->rows_in_C[counter[i]]=i;
209 out->mask_C[i]=counter[i];
210 } else {
211 out->mask_C[i]=-1;
212 }
213 }
214 } /* end parallel region */
215 /* get A_CF block: */
216 out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
217 if (Paso_noError()) {
218 /* get A_FC block: */
219 out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
220 /* get A_CC block: */
221 if (Paso_noError()) {
222 schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
223
224 /*find the pattern of the schur complement with fill in*/
225 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);
226 /* fprintf(stderr,"\nSHURE MATRIX START\n");
227
228 for (i = 0; i < schur->numRows; ++i) {
229 for (iPtr=schur->pattern->ptr[i];iPtr<schur->pattern->ptr[i + 1]; ++iPtr) {
230 fprintf(stderr,"A[%d,%d]=%.2f ",i,schur->pattern->index[iPtr],schur->val[iPtr]);
231 }
232 fprintf(stderr,"\n");
233 }
234 fprintf(stderr,"MATRIX END\n");
235
236 fprintf(stderr,"\nA_CF MATRIX START\n");
237 for (i = 0; i < out->n_C; ++i) {
238 for (iPtr=out->A_CF->pattern->ptr[i];iPtr<out->A_CF->pattern->ptr[i + 1]; ++iPtr) {
239 fprintf(stderr,"A_CF[%d,%d]=%.2f ",i,out->A_CF->pattern->index[iPtr],out->A_CF->val[iPtr]);
240 }
241 fprintf(stderr,"\n");
242 }
243 fprintf(stderr,"MATRIX END\n");
244
245 fprintf(stderr,"\nA_FC MATRIX START\n");
246 for (i = 0; i < out->n_F; ++i) {
247 for (iPtr=out->A_FC->pattern->ptr[i];iPtr<out->A_FC->pattern->ptr[i + 1]; ++iPtr) {
248 fprintf(stderr,"A_FC[%d,%d]=%.2f ",i,out->A_FC->pattern->index[iPtr],out->A_FC->val[iPtr]);
249 }
250 fprintf(stderr,"\n");
251 }
252 fprintf(stderr,"MATRIX END\n");
253
254 mult=Paso_Pattern_multiply(PATTERN_FORMAT_DEFAULT,out->A_CF->pattern,out->A_FC->pattern);
255 fprintf(stderr,"\nPATTERN MATRIX START\n");
256 for (i = 0; i < mult->numOutput; ++i) {
257 for (iPtr=mult->ptr[i];iPtr<mult->ptr[i + 1]; ++iPtr) {
258 fprintf(stderr," P[%d,%d]=X ",i,mult->index[iPtr]);
259 }
260 fprintf(stderr,"\n");
261 }
262 fprintf(stderr,"MATRIX END\n");
263 */
264 /* copy values over*/
265 #pragma omp for private(i,iPtr,iPtr_s,j,j0) schedule(static)
266 for (i = 0; i < schur_withFillIn->numRows; ++i) {
267 for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
268 j=schur_withFillIn->pattern->index[iPtr];
269 schur_withFillIn->val[iPtr]=0.;
270 for (iPtr_s=schur->pattern->ptr[i];iPtr_s<schur->pattern->ptr[i + 1]; ++iPtr_s){
271 j0=schur->pattern->index[iPtr_s];
272 if (j==j0) {
273 schur_withFillIn->val[iPtr]=schur->val[iPtr_s];
274 break;
275 }
276 }
277 }
278 }
279 time0=Paso_timer()-time0;
280 if (Paso_noError()) {
281 time1=Paso_timer();
282 /* update A_CC block to get Schur complement and then apply AMG to it */
283 Paso_Solver_updateIncompleteSchurComplement(schur_withFillIn,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC);
284
285 /*
286 fprintf(stderr,"\n SHURE WITH FILL IN MATRIX START\n");
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 fprintf(stderr,"A[%d,%d]=%.2f ",i,schur_withFillIn->pattern->index[iPtr],schur_withFillIn->val[iPtr]);
290 }
291 fprintf(stderr,"\n");
292 }
293 fprintf(stderr,"MATRIX END\n");
294 */
295 time1=Paso_timer()-time1;
296 out->AMG_of_Schur=Paso_Solver_getAMG(schur_withFillIn,verbose,level-1);
297
298 Paso_SparseMatrix_free(schur);
299 /* Paso_SparseMatrix_free(schur_withFillIn);*/
300 }
301 /* allocate work arrays for AMG application */
302 if (Paso_noError()) {
303 out->x_F=MEMALLOC(n_block*out->n_F,double);
304 out->b_F=MEMALLOC(n_block*out->n_F,double);
305 out->x_C=MEMALLOC(n_block*out->n_C,double);
306 out->b_C=MEMALLOC(n_block*out->n_C,double);
307
308 if (! (Paso_checkPtr(out->x_F) || Paso_checkPtr(out->b_F) || Paso_checkPtr(out->x_C) || Paso_checkPtr(out->b_C) ) ) {
309 #pragma omp parallel
310 {
311 #pragma omp for private(i,k) schedule(static)
312 for (i = 0; i < out->n_F; ++i) {
313 for (k=0; k<n_block;++k) {
314 out->x_F[i*n_block+k]=0.;
315 out->b_F[i*n_block+k]=0.;
316 }
317 }
318 #pragma omp for private(i,k) schedule(static)
319 for (i = 0; i < out->n_C; ++i) {
320 for (k=0; k<n_block;++k) {
321 out->x_C[i*n_block+k]=0.;
322 out->b_C[i*n_block+k]=0.;
323 }
324 }
325 } /* end parallel region */
326 }
327 }
328 }
329 }
330 }
331 }
332 }
333 }
334 }
335 }
336 TMPMEMFREE(mis_marker);
337 TMPMEMFREE(counter);
338 if (Paso_noError()) {
339 if (verbose) {
340 printf("AMG: %d unknowns eliminated. %d left.\n",out->n_F,n-out->n_F);
341 if (out->n_C>0) {
342 printf("timing: AMG: MIS/reordering/elemination : %e/%e/%e\n",time2,time0,time1);
343 } else {
344 printf("timing: AMG: MIS: %e\n",time2);
345 }
346 }
347 return out;
348 } else {
349 Paso_Solver_AMG_free(out);
350 return NULL;
351 }
352 }
353
354 /**************************************************************/
355
356 /* apply AMG precondition b-> x
357
358 in fact it solves
359
360 [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ] [ x_F ] = [b_F]
361 [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] [ x_C ] = [b_C]
362
363 in the form
364
365 b->[b_F,b_C]
366 x_F=invA_FF*b_F
367 b_C=b_C-A_CF*x_F
368 x_C=AMG(b_C)
369 b_F=b_F-A_FC*x_C
370 x_F=invA_FF*b_F
371 x<-[x_F,x_C]
372
373 should be called within a parallel region
374 barrier synconization should be performed to make sure that the input vector available
375
376 */
377
378 void Paso_Solver_solveAMG(Paso_Solver_AMG * amg, double * x, double * b) {
379 dim_t i,k;
380 dim_t n_block=amg->n_block;
381 double *r=MEMALLOC(amg->n,double);
382 Paso_Solver_GS* GS=NULL;
383
384 if (amg->level==0) {
385 /* x=invA_FF*b */
386 /*Paso_Solver_applyBlockDiagonalMatrix(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,x,b);*/
387 GS=Paso_Solver_getGS(amg->A,-1);
388 Paso_Solver_solveGS(GS,x,b);
389 Paso_Solver_GS_free(GS);
390 } else {
391
392 /* presmoothing */
393 GS=Paso_Solver_getGS(amg->A,-1);
394 Paso_Solver_solveGS(GS,x,b);
395
396 #pragma omp parallel for private(i) schedule(static)
397 for (i=0;i<amg->n;++i) r[i]=b[i];
398
399 /*r=b-Ax*/
400 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
401 /****************/
402 /* b->[b_F,b_C] */
403 if (n_block==1) {
404 #pragma omp parallel for private(i) schedule(static)
405 for (i=0;i<amg->n_F;++i) amg->b_F[i]=r[amg->rows_in_F[i]];
406 #pragma omp parallel for private(i) schedule(static)
407 for (i=0;i<amg->n_C;++i) amg->b_C[i]=r[amg->rows_in_C[i]];
408 } else {
409 #pragma omp parallel for private(i,k) schedule(static)
410 for (i=0;i<amg->n_F;++i)
411 for (k=0;k<n_block;k++) amg->b_F[amg->n_block*i+k]=r[n_block*amg->rows_in_F[i]+k];
412 #pragma omp parallel for private(i,k) schedule(static)
413 for (i=0;i<amg->n_C;++i)
414 for (k=0;k<n_block;k++) amg->b_C[amg->n_block*i+k]=r[n_block*amg->rows_in_C[i]+k];
415 }
416
417 /* x_F=invA_FF*b_F */
418 Paso_Solver_applyBlockDiagonalMatrix(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
419
420 /* b_C=b_C-A_CF*x_F */
421 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->x_F,1.,amg->b_C);
422
423 /* x_C=AMG(b_C) */
424 Paso_Solver_solveAMG(amg->AMG_of_Schur,amg->x_C,amg->b_C);
425
426 /* b_F=b_F-A_FC*x_C */
427 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_FC,amg->x_C,1.,amg->b_F);
428 /* x_F=invA_FF*b_F */
429 Paso_Solver_applyBlockDiagonalMatrix(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
430 /* x<-[x_F,x_C] */
431
432 if (n_block==1) {
433 #pragma omp parallel for private(i) schedule(static)
434 for (i=0;i<amg->n;++i) {
435 if (amg->mask_C[i]>-1) {
436 x[i]+=amg->x_C[amg->mask_C[i]];
437 } else {
438 x[i]+=amg->x_F[amg->mask_F[i]];
439 }
440 }
441 } else {
442 #pragma omp parallel for private(i,k) schedule(static)
443 for (i=0;i<amg->n;++i) {
444 if (amg->mask_C[i]>-1) {
445 for (k=0;k<n_block;k++) x[n_block*i+k]+=amg->x_C[n_block*amg->mask_C[i]+k];
446 } else {
447 for (k=0;k<n_block;k++) x[n_block*i+k]+=amg->x_F[n_block*amg->mask_F[i]+k];
448 }
449 }
450 }
451 /* all done */
452 /*post smoothing*/
453 Paso_Solver_solveGS1(GS,x,b);
454
455 Paso_Solver_GS_free(GS);
456 }
457 MEMFREE(r);
458 return;
459 }
460
461 /*
462 * $Log$
463 *
464 */

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