/[escript]/trunk/paso/src/Solver_AMG.c
ViewVC logotype

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

Parent Directory Parent Directory | Revision Log Revision Log


Revision 1892 - (show annotations)
Fri Oct 17 00:55:59 2008 UTC (11 years, 4 months ago) by artak
File MIME type: text/plain
File size: 18246 byte(s)
memory leak is fixed
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 double *rs=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 double A11,A12,A13,A21,A22,A23,A31,A32,A33,D,time0,time1,time2;
83
84 /* identify independend set of rows/columns */
85 mis_marker=TMPMEMALLOC(n,index_t);
86 counter=TMPMEMALLOC(n,index_t);
87 rs=TMPMEMALLOC(n,double);
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 /* fprintf(stderr,"START OF MATRIX \n\n");
106 for (i = 0; i < A_p->numRows; ++i) {
107 for (iPtr=A_p->pattern->ptr[i];iPtr<A_p->pattern->ptr[i + 1]; ++iPtr) {
108 j=A_p->pattern->index[iPtr];
109 fprintf(stderr,"A[%d,%d]=%.2f ",i,j,A_p->val[iPtr]);
110 }
111 fprintf(stderr,"\n");
112 }
113 fprintf(stderr,"END OF MATRIX \n\n");
114 */
115 if ( !(Paso_checkPtr(mis_marker) || Paso_checkPtr(out) || Paso_checkPtr(counter) ) ) {
116 /* identify independend set of rows/columns */
117 time0=Paso_timer();
118 #pragma omp parallel for private(i) schedule(static)
119 for (i=0;i<n;++i) mis_marker[i]=-1;
120 Paso_Pattern_RS(A_p,mis_marker,0.25);
121 /*
122 for (i=0;i<n;++i) fprintf(stderr," i=%d mis[i]=%d \n",i,mis_marker[i]);
123 */
124 time2=Paso_timer()-time0;
125 if (Paso_noError()) {
126 #pragma omp parallel for private(i) schedule(static)
127 for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
128 out->n=n;
129 out->n_block=n_block;
130 out->n_F=Paso_Util_cumsum(n,counter);
131 out->mask_F=MEMALLOC(n,index_t);
132 out->rows_in_F=MEMALLOC(out->n_F,index_t);
133 out->inv_A_FF=MEMALLOC(n_block*n_block*out->n_F,double);
134 out->A_FF_pivot=NULL; /* later use for block size>3 */
135 if (! (Paso_checkPtr(out->mask_F) || Paso_checkPtr(out->inv_A_FF) || Paso_checkPtr(out->rows_in_F) ) ) {
136 #pragma omp parallel
137 {
138 /* creates an index for F from mask */
139 #pragma omp for private(i) schedule(static)
140 for (i = 0; i < out->n_F; ++i) out->rows_in_F[i]=-1;
141 #pragma omp for private(i) schedule(static)
142 for (i = 0; i < n; ++i) {
143 if (mis_marker[i]) {
144 out->rows_in_F[counter[i]]=i;
145 out->mask_F[i]=counter[i];
146 } else {
147 out->mask_F[i]=-1;
148 }
149 }
150 /* Compute row-sum for getting rs(A_FF)*/
151 #pragma omp for private(i,iPtr) schedule(static)
152 for (i = 0; i < out->n_F; ++i) {
153 rs[i]=0;
154 for (iPtr=A_p->pattern->ptr[out->rows_in_F[i]];iPtr<A_p->pattern->ptr[out->rows_in_F[i] + 1]; ++iPtr) {
155 rs[i]+=A_p->val[iPtr];
156 }
157 }
158
159 #pragma omp for private(i, where_p,iPtr,A11,A12,A13,A21,A22,A23,A31,A32,A33,D,index) schedule(static)
160 for (i = 0; i < out->n_F; i++) {
161 /* find main diagonal */
162 iPtr=A_p->pattern->ptr[out->rows_in_F[i]];
163 index=&(A_p->pattern->index[iPtr]);
164 where_p=(index_t*)bsearch(&out->rows_in_F[i],
165 index,
166 A_p->pattern->ptr[out->rows_in_F[i] + 1]-A_p->pattern->ptr[out->rows_in_F[i]],
167 sizeof(index_t),
168 Paso_comparIndex);
169 if (where_p==NULL) {
170 Paso_setError(VALUE_ERROR, "Paso_Solver_getAMG: main diagonal element missing.");
171 } else {
172 iPtr+=(index_t)(where_p-index);
173 /* get inverse of A_FF block: */
174 if (ABS(rs[i])>0.) {
175 out->inv_A_FF[i]=1./rs[i];
176 } else {
177 out->inv_A_FF[i]=0;
178 }
179
180 /* } else {
181 Paso_setError(ZERO_DIVISION_ERROR, "Paso_Solver_getAMG: Break-down in AMG decomposition: non-regular main diagonal block.");
182 }*/
183 }
184 }
185 } /* end parallel region */
186
187 if( Paso_noError()) {
188 /* if there are no nodes in the coarse level there is no more work to do */
189 out->n_C=n-out->n_F;
190 /*if (out->n_C>11) {*/
191 if (level>0) {
192 out->rows_in_C=MEMALLOC(out->n_C,index_t);
193 out->mask_C=MEMALLOC(n,index_t);
194 if (! (Paso_checkPtr(out->mask_C) || Paso_checkPtr(out->rows_in_C) ) ) {
195 /* creates an index for C from mask */
196 #pragma omp parallel for private(i) schedule(static)
197 for (i = 0; i < n; ++i) counter[i]=! mis_marker[i];
198 Paso_Util_cumsum(n,counter);
199 #pragma omp parallel
200 {
201 #pragma omp for private(i) schedule(static)
202 for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
203 #pragma omp for private(i) schedule(static)
204 for (i = 0; i < n; ++i) {
205 if (! mis_marker[i]) {
206 out->rows_in_C[counter[i]]=i;
207 out->mask_C[i]=counter[i];
208 } else {
209 out->mask_C[i]=-1;
210 }
211 }
212 } /* end parallel region */
213 /* get A_CF block: */
214 out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
215 if (Paso_noError()) {
216 /* get A_FC block: */
217 out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
218 /* get A_CC block: */
219 if (Paso_noError()) {
220 schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
221
222 /*find the pattern of the schur complement with fill in*/
223 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);
224
225 /* copy values over*/
226 #pragma omp for private(i,iPtr,iPtr_s,j,j0) schedule(static)
227 for (i = 0; i < schur_withFillIn->numRows; ++i) {
228 for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
229 j=schur_withFillIn->pattern->index[iPtr];
230 schur_withFillIn->val[iPtr]=0.;
231 for (iPtr_s=schur->pattern->ptr[i];iPtr_s<schur->pattern->ptr[i + 1]; ++iPtr_s){
232 j0=schur->pattern->index[iPtr_s];
233 if (j==j0) {
234 schur_withFillIn->val[iPtr]=schur->val[iPtr_s];
235 break;
236 }
237 }
238 }
239 }
240
241 /* for (i = 0; i < schur_withFillIn->numRows; ++i) {
242 for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
243 j=schur_withFillIn->pattern->index[iPtr];
244 fprintf(stderr,"A_CC[%d,%d]=%.2f ",i,j,schur_withFillIn->val[iPtr]);
245 }
246 fprintf(stderr,"\n");
247 }*/
248 time0=Paso_timer()-time0;
249 if (Paso_noError()) {
250 time1=Paso_timer();
251 /* update A_CC block to get Schur complement and then apply AMG to it */
252 Paso_Solver_updateIncompleteSchurComplement(schur_withFillIn,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC);
253 time1=Paso_timer()-time1;
254 out->AMG_of_Schur=Paso_Solver_getAMG(schur_withFillIn,verbose,level-1);
255
256 Paso_SparseMatrix_free(schur);
257 /* Paso_SparseMatrix_free(schur_withFillIn);*/
258 }
259 /* allocate work arrays for AMG application */
260 if (Paso_noError()) {
261 out->x_F=MEMALLOC(n_block*out->n_F,double);
262 out->b_F=MEMALLOC(n_block*out->n_F,double);
263 out->x_C=MEMALLOC(n_block*out->n_C,double);
264 out->b_C=MEMALLOC(n_block*out->n_C,double);
265
266 if (! (Paso_checkPtr(out->x_F) || Paso_checkPtr(out->b_F) || Paso_checkPtr(out->x_C) || Paso_checkPtr(out->b_C) ) ) {
267 #pragma omp parallel
268 {
269 #pragma omp for private(i,k) schedule(static)
270 for (i = 0; i < out->n_F; ++i) {
271 for (k=0; k<n_block;++k) {
272 out->x_F[i*n_block+k]=0.;
273 out->b_F[i*n_block+k]=0.;
274 }
275 }
276 #pragma omp for private(i,k) schedule(static)
277 for (i = 0; i < out->n_C; ++i) {
278 for (k=0; k<n_block;++k) {
279 out->x_C[i*n_block+k]=0.;
280 out->b_C[i*n_block+k]=0.;
281 }
282 }
283 } /* end parallel region */
284 }
285 }
286 }
287 }
288 }
289 }
290 }
291 }
292 }
293 }
294 TMPMEMFREE(mis_marker);
295 TMPMEMFREE(counter);
296 TMPMEMFREE(rs);
297 if (Paso_noError()) {
298 if (verbose) {
299 printf("AMG: %d unknowns eliminated. %d left.\n",out->n_F,n-out->n_F);
300 if (out->n_C>0) {
301 printf("timing: AMG: MIS/reordering/elemination : %e/%e/%e\n",time2,time0,time1);
302 } else {
303 printf("timing: AMG: MIS: %e\n",time2);
304 }
305 }
306 return out;
307 } else {
308 Paso_Solver_AMG_free(out);
309 return NULL;
310 }
311 }
312
313 /**************************************************************/
314
315 /* apply AMG precondition b-> x
316
317 in fact it solves
318
319 [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ] [ x_F ] = [b_F]
320 [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] [ x_C ] = [b_C]
321
322 in the form
323
324 b->[b_F,b_C]
325 x_F=invA_FF*b_F
326 b_C=b_C-A_CF*x_F
327 x_C=AMG(b_C)
328 b_F=b_F-A_FC*x_C
329 x_F=invA_FF*b_F
330 x<-[x_F,x_C]
331
332 should be called within a parallel region
333 barrier synconization should be performed to make sure that the input vector available
334
335 */
336
337 void Paso_Solver_solveAMG(Paso_Solver_AMG * amg, double * x, double * b) {
338 dim_t i,k;
339 dim_t n_block=amg->n_block;
340 double *r=MEMALLOC(amg->n,double);
341 double *x0=MEMALLOC(amg->n,double);
342 Paso_Solver_GS* GS=NULL;
343
344 if (amg->level==0) {
345 /* x=invA_FF*b */
346 Paso_Solver_applyBlockDiagonalMatrix(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,x,b);
347 } else {
348 fprintf(stdout,"LEVEL %d \n",amg->level);
349 /* presmoothing on (Shure, x, b, r) */
350 /****************/
351 GS=Paso_Solver_getGS(amg->A,-1);
352 Paso_Solver_solveGS(GS,x,b);
353
354 #pragma omp parallel for private(i) schedule(static)
355 for (i=0;i<amg->n;++i) r[i]=b[i];
356
357 /*r=b-Ax*/
358 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
359 /****************/
360 /* b->[b_F,b_C] */
361 if (n_block==1) {
362 #pragma omp parallel for private(i) schedule(static)
363 for (i=0;i<amg->n_F;++i) amg->b_F[i]=r[amg->rows_in_F[i]]; /* was b istead of r */
364 #pragma omp parallel for private(i) schedule(static)
365 for (i=0;i<amg->n_C;++i) amg->b_C[i]=r[amg->rows_in_C[i]];
366 } else {
367 #pragma omp parallel for private(i,k) schedule(static)
368 for (i=0;i<amg->n_F;++i)
369 for (k=0;k<n_block;k++) amg->b_F[amg->n_block*i+k]=r[n_block*amg->rows_in_F[i]+k];
370 #pragma omp parallel for private(i,k) schedule(static)
371 for (i=0;i<amg->n_C;++i)
372 for (k=0;k<n_block;k++) amg->b_C[amg->n_block*i+k]=r[n_block*amg->rows_in_C[i]+k];
373 }
374
375 /****************/
376 /* Corsening part */
377
378 /* r_F=A_FF^-1*r_F */
379 /*Paso_Solver_applyBlockDiagonalMatrix(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->b_F,amg->b_F);
380 fprintf(stderr,"2\n");
381 */
382 /* r_C=r_C-A_CF*r_F */
383 /*Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->b_F,1.,amg->b_C);
384 fprintf(stderr,"3\n");
385 */
386 /****************/
387
388
389 /* x_F=invA_FF*b_F */
390 Paso_Solver_applyBlockDiagonalMatrix(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
391
392 /* b_C=b_C-A_CF*x_F */
393 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->x_F,1.,amg->b_C);
394
395 /* x_C=AMG(b_C) */
396 Paso_Solver_solveAMG(amg->AMG_of_Schur,amg->x_C,amg->b_C);
397
398 /* b_F=b_F-A_FC*x_C */
399 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_FC,amg->x_C,1.,amg->b_F);
400 /* x_F=invA_FF*b_F */
401 Paso_Solver_applyBlockDiagonalMatrix(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
402 /* x<-[x_F,x_C] */
403
404 /* */
405
406
407 if (n_block==1) {
408 #pragma omp parallel for private(i) schedule(static)
409 for (i=0;i<amg->n;++i) {
410 if (amg->mask_C[i]>-1) {
411 x[i]+=amg->x_C[amg->mask_C[i]];
412 } else {
413 x[i]+=amg->x_F[amg->mask_F[i]];
414 }
415 }
416 } else {
417 #pragma omp parallel for private(i,k) schedule(static)
418 for (i=0;i<amg->n;++i) {
419 if (amg->mask_C[i]>-1) {
420 for (k=0;k<n_block;k++) x[n_block*i+k]+=amg->x_C[n_block*amg->mask_C[i]+k];
421 } else {
422 for (k=0;k<n_block;k++) x[n_block*i+k]+=amg->x_F[n_block*amg->mask_F[i]+k];
423 }
424 }
425 }
426 /* all done */
427 /*post smoothing*/
428 /* Paso_Solver_solveGS(GS,x0,b);
429 if (n_block==1) {
430 #pragma omp parallel for private(i) schedule(static)
431 for (i=0;i<amg->n;++i) x[i]+=x0[i];
432 } else {
433 #pragma omp parallel for private(i,k) schedule(static)
434 for (i=0;i<amg->n;++i) {
435 for (k=0;k<n_block;k++) x[n_block*i+k]+=x0[n_block*i+k];
436 }
437 }
438 */
439 Paso_Solver_GS_free(GS);
440 }
441 MEMFREE(x0);
442 MEMFREE(r);
443 return;
444 }
445
446 /*
447 * $Log$
448 *
449 */

  ViewVC Help
Powered by ViewVC 1.1.26