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Contents of /trunk/paso/src/Solver_AMG.c

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Revision 1917 - (show annotations)
Thu Oct 23 09:09:31 2008 UTC (10 years, 11 months ago) by phornby
File MIME type: text/plain
File size: 19945 byte(s)
Remove unused vars, do a bit of standardising of indentation, and use the new Pattern_coupling.h to eliminate some implicit function declarations in Solver_AMG.c
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 #include "Pattern_coupling.h"
29
30 /**************************************************************/
31
32 /* free all memory used by AMG */
33
34 void Paso_Solver_AMG_free(Paso_Solver_AMG * in) {
35 if (in!=NULL) {
36 Paso_Solver_AMG_free(in->AMG_of_Schur);
37 MEMFREE(in->inv_A_FF);
38 MEMFREE(in->A_FF_pivot);
39 Paso_SparseMatrix_free(in->A_FC);
40 Paso_SparseMatrix_free(in->A_CF);
41 MEMFREE(in->rows_in_F);
42 MEMFREE(in->rows_in_C);
43 MEMFREE(in->mask_F);
44 MEMFREE(in->mask_C);
45 MEMFREE(in->x_F);
46 MEMFREE(in->b_F);
47 MEMFREE(in->x_C);
48 MEMFREE(in->b_C);
49 MEMFREE(in);
50 }
51 }
52
53 /**************************************************************/
54
55 /* constructs the block-block factorization of
56
57 [ A_FF A_FC ]
58 A_p=
59 [ A_CF A_FF ]
60
61 to
62
63 [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ]
64 [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ]
65
66
67 where S=A_FF-ACF*invA_FF*A_FC within the shape of S
68
69 then AMG is applied to S again until S becomes empty
70
71 */
72 Paso_Solver_AMG* Paso_Solver_getAMG(Paso_SparseMatrix *A_p,bool_t verbose,dim_t level) {
73 Paso_Solver_AMG* out=NULL;
74 dim_t n=A_p->numRows;
75 dim_t n_block=A_p->row_block_size;
76 index_t* mis_marker=NULL;
77 index_t* counter=NULL;
78 index_t iPtr,*index, *where_p, iPtr_s;
79 dim_t i,k,j,j0;
80 Paso_SparseMatrix * schur=NULL;
81 Paso_SparseMatrix * schur_withFillIn=NULL;
82 Paso_Pattern* mult=NULL;
83 double time0,time1,time2,S;
84
85 /* identify independend set of rows/columns */
86 mis_marker=TMPMEMALLOC(n,index_t);
87 counter=TMPMEMALLOC(n,index_t);
88 out=MEMALLOC(1,Paso_Solver_AMG);
89 out->AMG_of_Schur=NULL;
90 out->inv_A_FF=NULL;
91 out->A_FF_pivot=NULL;
92 out->A_FC=NULL;
93 out->A_CF=NULL;
94 out->rows_in_F=NULL;
95 out->rows_in_C=NULL;
96 out->mask_F=NULL;
97 out->mask_C=NULL;
98 out->x_F=NULL;
99 out->b_F=NULL;
100 out->x_C=NULL;
101 out->b_C=NULL;
102 out->A=Paso_SparseMatrix_getReference(A_p);
103 out->level=level;
104
105 if ( !(Paso_checkPtr(mis_marker) || Paso_checkPtr(out) || Paso_checkPtr(counter) ) ) {
106 /* identify independend set of rows/columns */
107 time0=Paso_timer();
108 #pragma omp parallel for private(i) schedule(static)
109 for (i=0;i<n;++i) mis_marker[i]=-1;
110 /*Paso_Pattern_RS(A_p,mis_marker,0.25);*/
111 Paso_Pattern_coup(A_p,mis_marker);
112 time2=Paso_timer()-time0;
113 if (Paso_noError()) {
114 #pragma omp parallel for private(i) schedule(static)
115 for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
116 out->n=n;
117 out->n_block=n_block;
118 out->n_F=Paso_Util_cumsum(n,counter);
119 out->mask_F=MEMALLOC(n,index_t);
120 out->rows_in_F=MEMALLOC(out->n_F,index_t);
121 out->inv_A_FF=MEMALLOC(n_block*n_block*out->n_F,double);
122 out->A_FF_pivot=NULL; /* later use for block size>3 */
123 if (! (Paso_checkPtr(out->mask_F) || Paso_checkPtr(out->inv_A_FF) || Paso_checkPtr(out->rows_in_F) ) ) {
124 #pragma omp parallel
125 {
126 /* creates an index for F from mask */
127 #pragma omp for private(i) schedule(static)
128 for (i = 0; i < out->n_F; ++i) out->rows_in_F[i]=-1;
129 #pragma omp for private(i) schedule(static)
130 for (i = 0; i < n; ++i) {
131 if (mis_marker[i]) {
132 out->rows_in_F[counter[i]]=i;
133 out->mask_F[i]=counter[i];
134 } else {
135 out->mask_F[i]=-1;
136 }
137 }
138 /* Compute row-sum for getting rs(A_FF)*/
139 #pragma omp for private(i,iPtr) schedule(static)
140 for (i = 0; i < out->n_F; ++i) {
141 out->inv_A_FF[i]=0;
142 for (iPtr=A_p->pattern->ptr[out->rows_in_F[i]];iPtr<A_p->pattern->ptr[out->rows_in_F[i] + 1]; ++iPtr) {
143 out->inv_A_FF[i]+=A_p->val[iPtr];
144 }
145 }
146
147 /* fprintf(stderr,"\n MATRIX START\n");
148 j=0;
149 for (i = 0; i < n; ++i) {
150 for (iPtr=A_p->pattern->ptr[i];iPtr<A_p->pattern->ptr[i + 1]; ++iPtr) {
151 fprintf(stderr,"A[%d,%d]=%.2f ",i,A_p->pattern->index[iPtr],A_p->val[iPtr]);
152 }
153 if (mis_marker[i]) {
154 fprintf(stderr,"ROW SUM %.2f\n ",out->inv_A_FF[j]);
155 j++;
156 }
157 else {
158 fprintf(stderr,"\n ");
159 }
160 }
161 fprintf(stderr,"\n MATRIX END\n");
162 */
163 #pragma omp for private(i, where_p,iPtr,index) schedule(static)
164 for (i = 0; i < out->n_F; i++) {
165 /* find main diagonal */
166 iPtr=A_p->pattern->ptr[out->rows_in_F[i]];
167 index=&(A_p->pattern->index[iPtr]);
168 where_p=(index_t*)bsearch(&out->rows_in_F[i],
169 index,
170 A_p->pattern->ptr[out->rows_in_F[i] + 1]-A_p->pattern->ptr[out->rows_in_F[i]],
171 sizeof(index_t),
172 Paso_comparIndex);
173 if (where_p==NULL) {
174 Paso_setError(VALUE_ERROR, "Paso_Solver_getAMG: main diagonal element missing.");
175 } else {
176 iPtr+=(index_t)(where_p-index);
177 /* get inverse of A_FF block: */
178 S=out->inv_A_FF[i];
179 if (ABS(A_p->val[iPtr])>0.) {
180 if(ABS(S)>0.)
181 out->inv_A_FF[i]=1./S;
182 } else {
183 Paso_setError(ZERO_DIVISION_ERROR, "Paso_Solver_getAMG: Break-down in AMG decomposition: non-regular main diagonal block.");
184 }
185 }
186 }
187 } /* end parallel region */
188
189 if( Paso_noError()) {
190 /* if there are no nodes in the coarse level there is no more work to do */
191 out->n_C=n-out->n_F;
192 /*if (out->n_C>11) {*/
193 /*fprintf(stderr,"SPARSITY in level %d \n", level);*/
194 if (level>0) {
195 out->rows_in_C=MEMALLOC(out->n_C,index_t);
196 out->mask_C=MEMALLOC(n,index_t);
197 if (! (Paso_checkPtr(out->mask_C) || Paso_checkPtr(out->rows_in_C) ) ) {
198 /* creates an index for C from mask */
199 #pragma omp parallel for private(i) schedule(static)
200 for (i = 0; i < n; ++i) counter[i]=! mis_marker[i];
201 Paso_Util_cumsum(n,counter);
202 #pragma omp parallel
203 {
204 #pragma omp for private(i) schedule(static)
205 for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
206 #pragma omp for private(i) schedule(static)
207 for (i = 0; i < n; ++i) {
208 if (! mis_marker[i]) {
209 out->rows_in_C[counter[i]]=i;
210 out->mask_C[i]=counter[i];
211 } else {
212 out->mask_C[i]=-1;
213 }
214 }
215 } /* end parallel region */
216 /* get A_CF block: */
217 out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
218 if (Paso_noError()) {
219 /* get A_FC block: */
220 out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
221 /* get A_CC block: */
222 if (Paso_noError()) {
223 schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
224
225 /*find the pattern of the schur complement with fill in*/
226 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);
227 /* fprintf(stderr,"\nSHURE MATRIX START\n");
228
229 for (i = 0; i < schur->numRows; ++i) {
230 for (iPtr=schur->pattern->ptr[i];iPtr<schur->pattern->ptr[i + 1]; ++iPtr) {
231 fprintf(stderr,"A[%d,%d]=%.2f ",i,schur->pattern->index[iPtr],schur->val[iPtr]);
232 }
233 fprintf(stderr,"\n");
234 }
235 fprintf(stderr,"MATRIX END\n");
236
237 fprintf(stderr,"\nA_CF MATRIX START\n");
238 for (i = 0; i < out->n_C; ++i) {
239 for (iPtr=out->A_CF->pattern->ptr[i];iPtr<out->A_CF->pattern->ptr[i + 1]; ++iPtr) {
240 fprintf(stderr,"A_CF[%d,%d]=%.2f ",i,out->A_CF->pattern->index[iPtr],out->A_CF->val[iPtr]);
241 }
242 fprintf(stderr,"\n");
243 }
244 fprintf(stderr,"MATRIX END\n");
245
246 fprintf(stderr,"\nA_FC MATRIX START\n");
247 for (i = 0; i < out->n_F; ++i) {
248 for (iPtr=out->A_FC->pattern->ptr[i];iPtr<out->A_FC->pattern->ptr[i + 1]; ++iPtr) {
249 fprintf(stderr,"A_FC[%d,%d]=%.2f ",i,out->A_FC->pattern->index[iPtr],out->A_FC->val[iPtr]);
250 }
251 fprintf(stderr,"\n");
252 }
253 fprintf(stderr,"MATRIX END\n");
254
255 mult=Paso_Pattern_multiply(PATTERN_FORMAT_DEFAULT,out->A_CF->pattern,out->A_FC->pattern);
256 fprintf(stderr,"\nPATTERN MATRIX START\n");
257 for (i = 0; i < mult->numOutput; ++i) {
258 for (iPtr=mult->ptr[i];iPtr<mult->ptr[i + 1]; ++iPtr) {
259 fprintf(stderr," P[%d,%d]=X ",i,mult->index[iPtr]);
260 }
261 fprintf(stderr,"\n");
262 }
263 fprintf(stderr,"MATRIX END\n");
264 */
265 /* copy values over*/
266 #pragma omp for private(i,iPtr,iPtr_s,j,j0) schedule(static)
267 for (i = 0; i < schur_withFillIn->numRows; ++i) {
268 for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
269 j=schur_withFillIn->pattern->index[iPtr];
270 schur_withFillIn->val[iPtr]=0.;
271 for (iPtr_s=schur->pattern->ptr[i];iPtr_s<schur->pattern->ptr[i + 1]; ++iPtr_s){
272 j0=schur->pattern->index[iPtr_s];
273 if (j==j0) {
274 schur_withFillIn->val[iPtr]=schur->val[iPtr_s];
275 break;
276 }
277 }
278 }
279 }
280 time0=Paso_timer()-time0;
281 if (Paso_noError()) {
282 time1=Paso_timer();
283 /* update A_CC block to get Schur complement and then apply AMG to it */
284 Paso_Solver_updateIncompleteSchurComplement(schur_withFillIn,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC);
285
286 /*
287 fprintf(stderr,"\n SHURE WITH FILL IN MATRIX START\n");
288 for (i = 0; i < schur_withFillIn->numRows; ++i) {
289 for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
290 fprintf(stderr,"A[%d,%d]=%.2f ",i,schur_withFillIn->pattern->index[iPtr],schur_withFillIn->val[iPtr]);
291 }
292 fprintf(stderr,"\n");
293 }
294 fprintf(stderr,"MATRIX END\n");
295 */
296 time1=Paso_timer()-time1;
297 out->AMG_of_Schur=Paso_Solver_getAMG(schur_withFillIn,verbose,level-1);
298
299 Paso_SparseMatrix_free(schur);
300 /* Paso_SparseMatrix_free(schur_withFillIn);*/
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
311 {
312 #pragma omp for private(i,k) schedule(static)
313 for (i = 0; i < out->n_F; ++i) {
314 for (k=0; k<n_block;++k) {
315 out->x_F[i*n_block+k]=0.;
316 out->b_F[i*n_block+k]=0.;
317 }
318 }
319 #pragma omp for private(i,k) schedule(static)
320 for (i = 0; i < out->n_C; ++i) {
321 for (k=0; k<n_block;++k) {
322 out->x_C[i*n_block+k]=0.;
323 out->b_C[i*n_block+k]=0.;
324 }
325 }
326 } /* end parallel region */
327 }
328 }
329 }
330 }
331 }
332 }
333 }
334 }
335 }
336 }
337 TMPMEMFREE(mis_marker);
338 TMPMEMFREE(counter);
339 if (Paso_noError()) {
340 if (verbose) {
341 printf("AMG: %d unknowns eliminated. %d left.\n",out->n_F,n-out->n_F);
342 if (out->n_C>0) {
343 printf("timing: AMG: MIS/reordering/elemination : %e/%e/%e\n",time2,time0,time1);
344 } else {
345 printf("timing: AMG: MIS: %e\n",time2);
346 }
347 }
348 return out;
349 } else {
350 Paso_Solver_AMG_free(out);
351 return NULL;
352 }
353 }
354
355 /**************************************************************/
356
357 /* apply AMG precondition b-> x
358
359 in fact it solves
360
361 [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ] [ x_F ] = [b_F]
362 [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] [ x_C ] = [b_C]
363
364 in the form
365
366 b->[b_F,b_C]
367 x_F=invA_FF*b_F
368 b_C=b_C-A_CF*x_F
369 x_C=AMG(b_C)
370 b_F=b_F-A_FC*x_C
371 x_F=invA_FF*b_F
372 x<-[x_F,x_C]
373
374 should be called within a parallel region
375 barrier synconization should be performed to make sure that the input vector available
376
377 */
378
379 void Paso_Solver_solveAMG(Paso_Solver_AMG * amg, double * x, double * b) {
380 dim_t i,k;
381 dim_t n_block=amg->n_block;
382 double *r=MEMALLOC(amg->n,double);
383 Paso_Solver_GS* GS=NULL;
384
385 if (amg->level==0) {
386 /* x=invA_FF*b */
387 /*Paso_Solver_applyBlockDiagonalMatrix(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,x,b);*/
388 GS=Paso_Solver_getGS(amg->A,-1);
389 Paso_Solver_solveGS(GS,x,b);
390 Paso_Solver_GS_free(GS);
391 } else {
392
393 /* presmoothing */
394 GS=Paso_Solver_getGS(amg->A,-1);
395 Paso_Solver_solveGS(GS,x,b);
396
397 #pragma omp parallel for private(i) schedule(static)
398 for (i=0;i<amg->n;++i) r[i]=b[i];
399
400 /*r=b-Ax*/
401 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
402 /****************/
403 /* b->[b_F,b_C] */
404 if (n_block==1) {
405 #pragma omp parallel for private(i) schedule(static)
406 for (i=0;i<amg->n_F;++i) amg->b_F[i]=r[amg->rows_in_F[i]];
407 #pragma omp parallel for private(i) schedule(static)
408 for (i=0;i<amg->n_C;++i) amg->b_C[i]=r[amg->rows_in_C[i]];
409 } else {
410 #pragma omp parallel for private(i,k) schedule(static)
411 for (i=0;i<amg->n_F;++i)
412 for (k=0;k<n_block;k++) amg->b_F[amg->n_block*i+k]=r[n_block*amg->rows_in_F[i]+k];
413 #pragma omp parallel for private(i,k) schedule(static)
414 for (i=0;i<amg->n_C;++i)
415 for (k=0;k<n_block;k++) amg->b_C[amg->n_block*i+k]=r[n_block*amg->rows_in_C[i]+k];
416 }
417
418 /* x_F=invA_FF*b_F */
419 Paso_Solver_applyBlockDiagonalMatrix(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
420
421 /* b_C=b_C-A_CF*x_F */
422 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->x_F,1.,amg->b_C);
423
424 /* x_C=AMG(b_C) */
425 Paso_Solver_solveAMG(amg->AMG_of_Schur,amg->x_C,amg->b_C);
426
427 /* b_F=b_F-A_FC*x_C */
428 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_FC,amg->x_C,1.,amg->b_F);
429 /* x_F=invA_FF*b_F */
430 Paso_Solver_applyBlockDiagonalMatrix(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
431 /* x<-[x_F,x_C] */
432
433 if (n_block==1) {
434 #pragma omp parallel for private(i) schedule(static)
435 for (i=0;i<amg->n;++i) {
436 if (amg->mask_C[i]>-1) {
437 x[i]+=amg->x_C[amg->mask_C[i]];
438 } else {
439 x[i]+=amg->x_F[amg->mask_F[i]];
440 }
441 }
442 } else {
443 #pragma omp parallel for private(i,k) schedule(static)
444 for (i=0;i<amg->n;++i) {
445 if (amg->mask_C[i]>-1) {
446 for (k=0;k<n_block;k++) x[n_block*i+k]+=amg->x_C[n_block*amg->mask_C[i]+k];
447 } else {
448 for (k=0;k<n_block;k++) x[n_block*i+k]+=amg->x_F[n_block*amg->mask_F[i]+k];
449 }
450 }
451 }
452 /* all done */
453 /*post smoothing*/
454 Paso_Solver_solveGS1(GS,x,b);
455
456 Paso_Solver_GS_free(GS);
457 }
458 MEMFREE(r);
459 return;
460 }
461
462 /*
463 * $Log$
464 *
465 */

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