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

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Revision 1931 - (show annotations)
Mon Oct 27 01:31:28 2008 UTC (10 years, 9 months ago) by artak
File MIME type: text/plain
File size: 18557 byte(s)
Direct solver is added to solve_AMG. It is now working but I guess need optimization.
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 "UMFPACK.h"
29 #include "Pattern_coupling.h"
30
31 /**************************************************************/
32
33 /* free all memory used by AMG */
34
35 void Paso_Solver_AMG_free(Paso_Solver_AMG * in) {
36 if (in!=NULL) {
37 Paso_Solver_AMG_free(in->AMG_of_Schur);
38 MEMFREE(in->inv_A_FF);
39 MEMFREE(in->A_FF_pivot);
40 Paso_SparseMatrix_free(in->A_FC);
41 Paso_SparseMatrix_free(in->A_CF);
42 MEMFREE(in->rows_in_F);
43 MEMFREE(in->rows_in_C);
44 MEMFREE(in->mask_F);
45 MEMFREE(in->mask_C);
46 MEMFREE(in->x_F);
47 MEMFREE(in->b_F);
48 MEMFREE(in->x_C);
49 MEMFREE(in->b_C);
50 MEMFREE(in);
51 }
52 }
53
54 /**************************************************************/
55
56 /* constructs the block-block factorization of
57
58 [ A_FF A_FC ]
59 A_p=
60 [ A_CF A_FF ]
61
62 to
63
64 [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ]
65 [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ]
66
67
68 where S=A_FF-ACF*invA_FF*A_FC within the shape of S
69
70 then AMG is applied to S again until S becomes empty
71
72 */
73 Paso_Solver_AMG* Paso_Solver_getAMG(Paso_SparseMatrix *A_p,bool_t verbose,dim_t level) {
74 Paso_Solver_AMG* out=NULL;
75 dim_t n=A_p->numRows;
76 dim_t n_block=A_p->row_block_size;
77 index_t* mis_marker=NULL;
78 index_t* counter=NULL;
79 index_t iPtr,*index, *where_p, iPtr_s;
80 dim_t i,k,j,j0;
81 Paso_SparseMatrix * schur=NULL;
82 Paso_SparseMatrix * schur_withFillIn=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,0.05);*/
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 #pragma omp for private(i, where_p,iPtr,index) schedule(static)
148 for (i = 0; i < out->n_F; i++) {
149 /* find main diagonal */
150 iPtr=A_p->pattern->ptr[out->rows_in_F[i]];
151 index=&(A_p->pattern->index[iPtr]);
152 where_p=(index_t*)bsearch(&out->rows_in_F[i],
153 index,
154 A_p->pattern->ptr[out->rows_in_F[i] + 1]-A_p->pattern->ptr[out->rows_in_F[i]],
155 sizeof(index_t),
156 Paso_comparIndex);
157 if (where_p==NULL) {
158 Paso_setError(VALUE_ERROR, "Paso_Solver_getAMG: main diagonal element missing.");
159 } else {
160 iPtr+=(index_t)(where_p-index);
161 /* get inverse of A_FF block: */
162 S=out->inv_A_FF[i];
163 if (ABS(A_p->val[iPtr])>0.) {
164 if(ABS(S)>0.)
165 out->inv_A_FF[i]=1./S;
166 /* else
167 {
168 fprintf(stderr,"ROWSUM OF ROW %d is 0\n",out->rows_in_F[i]);
169 S=0;
170 for (iPtr=A_p->pattern->ptr[out->rows_in_F[i]];iPtr<A_p->pattern->ptr[out->rows_in_F[i] + 1]; ++iPtr) {
171 if(A_p->val[iPtr]!=0) {
172 fprintf(stderr,"A_p[%d,%d]=%f ",out->rows_in_F[i],A_p->pattern->index[iPtr],A_p->val[iPtr]);
173 S+=A_p->val[iPtr];
174 }
175 }
176 fprintf(stderr,"\n SUMMMMMMM %f\n",S);
177 }
178 */ } else {
179 Paso_setError(ZERO_DIVISION_ERROR, "Paso_Solver_getAMG: Break-down in AMG decomposition: non-regular main diagonal block.");
180 }
181 }
182 }
183 } /* end parallel region */
184
185 if( Paso_noError()) {
186 /* if there are no nodes in the coarse level there is no more work to do */
187 out->n_C=n-out->n_F;
188 if (level>0) {
189 out->rows_in_C=MEMALLOC(out->n_C,index_t);
190 out->mask_C=MEMALLOC(n,index_t);
191 if (! (Paso_checkPtr(out->mask_C) || Paso_checkPtr(out->rows_in_C) ) ) {
192 /* creates an index for C from mask */
193 #pragma omp parallel for private(i) schedule(static)
194 for (i = 0; i < n; ++i) counter[i]=! mis_marker[i];
195 Paso_Util_cumsum(n,counter);
196 #pragma omp parallel
197 {
198 #pragma omp for private(i) schedule(static)
199 for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
200 #pragma omp for private(i) schedule(static)
201 for (i = 0; i < n; ++i) {
202 if (! mis_marker[i]) {
203 out->rows_in_C[counter[i]]=i;
204 out->mask_C[i]=counter[i];
205 } else {
206 out->mask_C[i]=-1;
207 }
208 }
209 } /* end parallel region */
210 /* get A_CF block: */
211 out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
212 if (Paso_noError()) {
213 /* get A_FC block: */
214 out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
215 /* get A_CC block: */
216 if (Paso_noError()) {
217 schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
218
219 /*find the pattern of the schur complement with fill in*/
220 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);
221
222 /* copy values over*/
223 #pragma omp for private(i,iPtr,iPtr_s,j,j0) schedule(static)
224 for (i = 0; i < schur_withFillIn->numRows; ++i) {
225 for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
226 j=schur_withFillIn->pattern->index[iPtr];
227 schur_withFillIn->val[iPtr]=0.;
228 for (iPtr_s=schur->pattern->ptr[i];iPtr_s<schur->pattern->ptr[i + 1]; ++iPtr_s){
229 j0=schur->pattern->index[iPtr_s];
230 if (j==j0) {
231 schur_withFillIn->val[iPtr]=schur->val[iPtr_s];
232 break;
233 }
234 }
235 }
236 }
237 time0=Paso_timer()-time0;
238
239 if (Paso_noError()) {
240 time1=Paso_timer();
241 /* update A_CC block to get Schur complement and then apply AMG to it */
242 Paso_Solver_updateIncompleteSchurComplement(schur_withFillIn,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC);
243 time1=Paso_timer()-time1;
244 out->AMG_of_Schur=Paso_Solver_getAMG(schur_withFillIn,verbose,level-1);
245
246 /*Paso_SparseMatrix_free(schur);*/
247 /* Paso_SparseMatrix_free(schur_withFillIn);*/
248 }
249 /* allocate work arrays for AMG application */
250 if (Paso_noError()) {
251 out->x_F=MEMALLOC(n_block*out->n_F,double);
252 out->b_F=MEMALLOC(n_block*out->n_F,double);
253 out->x_C=MEMALLOC(n_block*out->n_C,double);
254 out->b_C=MEMALLOC(n_block*out->n_C,double);
255
256 if (! (Paso_checkPtr(out->x_F) || Paso_checkPtr(out->b_F) || Paso_checkPtr(out->x_C) || Paso_checkPtr(out->b_C) ) ) {
257 #pragma omp parallel
258 {
259 #pragma omp for private(i,k) schedule(static)
260 for (i = 0; i < out->n_F; ++i) {
261 for (k=0; k<n_block;++k) {
262 out->x_F[i*n_block+k]=0.;
263 out->b_F[i*n_block+k]=0.;
264 }
265 }
266 #pragma omp for private(i,k) schedule(static)
267 for (i = 0; i < out->n_C; ++i) {
268 for (k=0; k<n_block;++k) {
269 out->x_C[i*n_block+k]=0.;
270 out->b_C[i*n_block+k]=0.;
271 }
272 }
273 } /* end parallel region */
274 }
275 }
276 }
277 }
278 }
279 }
280 }
281 }
282 }
283 }
284 TMPMEMFREE(mis_marker);
285 TMPMEMFREE(counter);
286 if (Paso_noError()) {
287 if (verbose) {
288 printf("AMG: %d unknowns eliminated. %d left.\n",out->n_F,n-out->n_F);
289 if (out->n_C>0) {
290 printf("timing: AMG: MIS/reordering/elemination : %e/%e/%e\n",time2,time0,time1);
291 } else {
292 printf("timing: AMG: MIS: %e\n",time2);
293 }
294 }
295 return out;
296 } else {
297 Paso_Solver_AMG_free(out);
298 return NULL;
299 }
300 }
301
302 /**************************************************************/
303
304 /* apply AMG precondition b-> x
305
306 in fact it solves
307
308 [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ] [ x_F ] = [b_F]
309 [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] [ x_C ] = [b_C]
310
311 in the form
312
313 b->[b_F,b_C]
314 x_F=invA_FF*b_F
315 b_C=b_C-A_CF*x_F
316 x_C=AMG(b_C)
317 b_F=b_F-A_FC*x_C
318 x_F=invA_FF*b_F
319 x<-[x_F,x_C]
320
321 should be called within a parallel region
322 barrier synconization should be performed to make sure that the input vector available
323
324 */
325
326 void Paso_Solver_solveAMG(Paso_Solver_AMG * amg, double * x, double * b) {
327 dim_t i,k,oldsweeps;
328 dim_t n_block=amg->n_block;
329 double *r=MEMALLOC(amg->n,double);
330 Paso_Solver_GS* GS=NULL;
331 double *bold=MEMALLOC(amg->n*amg->n_block,double);
332 double *bnew=MEMALLOC(amg->n*amg->n_block,double);
333
334 if (amg->level==0) {
335 Paso_UMFPACK1(amg->A,x,b,1);
336 } else {
337
338 /* presmoothing */
339 GS=Paso_Solver_getGS(amg->A,-1);
340 Paso_Solver_solveGS(GS,x,b);
341 oldsweeps=GS->sweeps;
342 if (GS->sweeps>1) {
343
344 #pragma omp parallel for private(i) schedule(static)
345 for (i=0;i<GS->n*GS->n_block;++i) bold[i]=b[i];
346
347 while(GS->sweeps>1) {
348 #pragma omp parallel for private(i) schedule(static)
349 for (i=0;i<GS->n*GS->n_block;++i) bnew[i]=bold[i]+b[i];
350 /* Compute the residual b=b-Ax*/
351 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(DBLE(-1), amg->A, x, DBLE(1), bnew);
352 /* Go round again*/
353 Paso_Solver_solveGS(GS,x,bnew);
354 #pragma omp parallel for private(i) schedule(static)
355 for (i=0;i<GS->n*GS->n_block;++i) bold[i]=bnew[i];
356 GS->sweeps=GS->sweeps-1;
357 }
358 }
359 GS->sweeps=oldsweeps;
360 /* end of presmoothing */
361
362 #pragma omp parallel for private(i) schedule(static)
363 for (i=0;i<amg->n;++i) r[i]=b[i];
364
365 /*r=b-Ax*/
366 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
367
368 /* b->[b_F,b_C] */
369 if (n_block==1) {
370 #pragma omp parallel for private(i) schedule(static)
371 for (i=0;i<amg->n_F;++i) amg->b_F[i]=r[amg->rows_in_F[i]];
372 #pragma omp parallel for private(i) schedule(static)
373 for (i=0;i<amg->n_C;++i) amg->b_C[i]=r[amg->rows_in_C[i]];
374 } else {
375 #pragma omp parallel for private(i,k) schedule(static)
376 for (i=0;i<amg->n_F;++i)
377 for (k=0;k<n_block;k++) amg->b_F[amg->n_block*i+k]=r[n_block*amg->rows_in_F[i]+k];
378 #pragma omp parallel for private(i,k) schedule(static)
379 for (i=0;i<amg->n_C;++i)
380 for (k=0;k<n_block;k++) amg->b_C[amg->n_block*i+k]=r[n_block*amg->rows_in_C[i]+k];
381 }
382
383 /* x_F=invA_FF*b_F */
384 Paso_Solver_applyBlockDiagonalMatrix(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
385
386 /* b_C=b_C-A_CF*x_F */
387 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->x_F,1.,amg->b_C);
388
389 /* x_C=AMG(b_C) */
390 Paso_Solver_solveAMG(amg->AMG_of_Schur,amg->x_C,amg->b_C);
391
392 /* b_F=b_F-A_FC*x_C */
393 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_FC,amg->x_C,1.,amg->b_F);
394 /* x_F=invA_FF*b_F */
395 Paso_Solver_applyBlockDiagonalMatrix(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
396 /* x<-[x_F,x_C] */
397
398 if (n_block==1) {
399 #pragma omp parallel for private(i) schedule(static)
400 for (i=0;i<amg->n;++i) {
401 if (amg->mask_C[i]>-1) {
402 x[i]+=amg->x_C[amg->mask_C[i]];
403 } else {
404 x[i]+=amg->x_F[amg->mask_F[i]];
405 }
406 }
407 } else {
408 #pragma omp parallel for private(i,k) schedule(static)
409 for (i=0;i<amg->n;++i) {
410 if (amg->mask_C[i]>-1) {
411 for (k=0;k<n_block;k++) x[n_block*i+k]+=amg->x_C[n_block*amg->mask_C[i]+k];
412 } else {
413 for (k=0;k<n_block;k++) x[n_block*i+k]+=amg->x_F[n_block*amg->mask_F[i]+k];
414 }
415 }
416 }
417
418 /*postsmoothing*/
419 Paso_Solver_solveGS1(GS,x,b);
420 if (GS->sweeps>1) {
421 #pragma omp parallel for private(i) schedule(static)
422 for (i=0;i<GS->n*GS->n_block;++i) bold[i]=b[i];
423
424 while(GS->sweeps>1) {
425 #pragma omp parallel for private(i) schedule(static)
426 for (i=0;i<GS->n*GS->n_block;++i) bnew[i]=bold[i]+b[i];
427 /* Compute the residual b=b-Ax*/
428 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(DBLE(-1), amg->A, x, DBLE(1), bnew);
429 /* Go round again*/
430 Paso_Solver_solveGS(GS,x,bnew);
431 #pragma omp parallel for private(i) schedule(static)
432 for (i=0;i<GS->n*GS->n_block;++i) bold[i]=bnew[i];
433 GS->sweeps=GS->sweeps-1;
434 }
435 }
436 /*end of postsmoothing*/
437
438 Paso_Solver_GS_free(GS);
439 }
440 MEMFREE(r);
441 MEMFREE(bold);
442 MEMFREE(bnew);
443 return;
444 }
445
446 /*
447 * $Log$
448 *
449 */

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