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

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Revision 1891 - (show annotations)
Fri Oct 17 00:15:17 2008 UTC (12 years, 8 months ago) by artak
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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 schur_withFillIn=MEMALLOC(1,Paso_SparseMatrix);
84
85 /* identify independend set of rows/columns */
86 mis_marker=TMPMEMALLOC(n,index_t);
87 counter=TMPMEMALLOC(n,index_t);
88 rs=TMPMEMALLOC(n,double);
89 out=MEMALLOC(1,Paso_Solver_AMG);
90 out->AMG_of_Schur=NULL;
91 out->inv_A_FF=NULL;
92 out->A_FF_pivot=NULL;
93 out->A_FC=NULL;
94 out->A_CF=NULL;
95 out->rows_in_F=NULL;
96 out->rows_in_C=NULL;
97 out->mask_F=NULL;
98 out->mask_C=NULL;
99 out->x_F=NULL;
100 out->b_F=NULL;
101 out->x_C=NULL;
102 out->b_C=NULL;
103 out->A=Paso_SparseMatrix_getReference(A_p);
104 out->level=level;
105
106 /* fprintf(stderr,"START OF MATRIX \n\n");
107 for (i = 0; i < A_p->numRows; ++i) {
108 for (iPtr=A_p->pattern->ptr[i];iPtr<A_p->pattern->ptr[i + 1]; ++iPtr) {
109 j=A_p->pattern->index[iPtr];
110 fprintf(stderr,"A[%d,%d]=%.2f ",i,j,A_p->val[iPtr]);
111 }
112 fprintf(stderr,"\n");
113 }
114 fprintf(stderr,"END OF MATRIX \n\n");
115 */
116 if ( !(Paso_checkPtr(mis_marker) || Paso_checkPtr(out) || Paso_checkPtr(counter) ) ) {
117 /* identify independend set of rows/columns */
118 time0=Paso_timer();
119 #pragma omp parallel for private(i) schedule(static)
120 for (i=0;i<n;++i) mis_marker[i]=-1;
121 Paso_Pattern_RS(A_p,mis_marker,0.25);
122 /*
123 for (i=0;i<n;++i) fprintf(stderr," i=%d mis[i]=%d \n",i,mis_marker[i]);
124 */
125 time2=Paso_timer()-time0;
126 if (Paso_noError()) {
127 #pragma omp parallel for private(i) schedule(static)
128 for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
129 out->n=n;
130 out->n_block=n_block;
131 out->n_F=Paso_Util_cumsum(n,counter);
132 out->mask_F=MEMALLOC(n,index_t);
133 out->rows_in_F=MEMALLOC(out->n_F,index_t);
134 out->inv_A_FF=MEMALLOC(n_block*n_block*out->n_F,double);
135 out->A_FF_pivot=NULL; /* later use for block size>3 */
136 if (! (Paso_checkPtr(out->mask_F) || Paso_checkPtr(out->inv_A_FF) || Paso_checkPtr(out->rows_in_F) ) ) {
137 #pragma omp parallel
138 {
139 /* creates an index for F from mask */
140 #pragma omp for private(i) schedule(static)
141 for (i = 0; i < out->n_F; ++i) out->rows_in_F[i]=-1;
142 #pragma omp for private(i) schedule(static)
143 for (i = 0; i < n; ++i) {
144 if (mis_marker[i]) {
145 out->rows_in_F[counter[i]]=i;
146 out->mask_F[i]=counter[i];
147 } else {
148 out->mask_F[i]=-1;
149 }
150 }
151 /* Compute row-sum for getting rs(A_FF)*/
152 #pragma omp for private(i,iPtr) schedule(static)
153 for (i = 0; i < out->n_F; ++i) {
154 rs[i]=0;
155 for (iPtr=A_p->pattern->ptr[out->rows_in_F[i]];iPtr<A_p->pattern->ptr[out->rows_in_F[i] + 1]; ++iPtr) {
156 rs[i]+=A_p->val[iPtr];
157 }
158 }
159
160 #pragma omp for private(i, where_p,iPtr,A11,A12,A13,A21,A22,A23,A31,A32,A33,D,index) schedule(static)
161 for (i = 0; i < out->n_F; i++) {
162 /* find main diagonal */
163 iPtr=A_p->pattern->ptr[out->rows_in_F[i]];
164 index=&(A_p->pattern->index[iPtr]);
165 where_p=(index_t*)bsearch(&out->rows_in_F[i],
166 index,
167 A_p->pattern->ptr[out->rows_in_F[i] + 1]-A_p->pattern->ptr[out->rows_in_F[i]],
168 sizeof(index_t),
169 Paso_comparIndex);
170 if (where_p==NULL) {
171 Paso_setError(VALUE_ERROR, "Paso_Solver_getAMG: main diagonal element missing.");
172 } else {
173 iPtr+=(index_t)(where_p-index);
174 /* get inverse of A_FF block: */
175 if (ABS(rs[i])>0.) {
176 out->inv_A_FF[i]=1./rs[i];
177 } else {
178 out->inv_A_FF[i]=0;
179 }
180
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 if (level>0) {
193 out->rows_in_C=MEMALLOC(out->n_C,index_t);
194 out->mask_C=MEMALLOC(n,index_t);
195 if (! (Paso_checkPtr(out->mask_C) || Paso_checkPtr(out->rows_in_C) ) ) {
196 /* creates an index for C from mask */
197 #pragma omp parallel for private(i) schedule(static)
198 for (i = 0; i < n; ++i) counter[i]=! mis_marker[i];
199 Paso_Util_cumsum(n,counter);
200 #pragma omp parallel
201 {
202 #pragma omp for private(i) schedule(static)
203 for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
204 #pragma omp for private(i) schedule(static)
205 for (i = 0; i < n; ++i) {
206 if (! mis_marker[i]) {
207 out->rows_in_C[counter[i]]=i;
208 out->mask_C[i]=counter[i];
209 } else {
210 out->mask_C[i]=-1;
211 }
212 }
213 } /* end parallel region */
214 /* get A_CF block: */
215 out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
216 if (Paso_noError()) {
217 /* get A_FC block: */
218 out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
219 /* get A_CC block: */
220 if (Paso_noError()) {
221 schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
222
223 /*find the pattern of the schur complement with fill in*/
224 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);
225
226 /* copy values over*/
227 #pragma omp for private(i,iPtr,iPtr_s,j,j0) schedule(static)
228 for (i = 0; i < schur_withFillIn->numRows; ++i) {
229 for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
230 j=schur_withFillIn->pattern->index[iPtr];
231 schur_withFillIn->val[iPtr]=0.;
232 for (iPtr_s=schur->pattern->ptr[i];iPtr_s<schur->pattern->ptr[i + 1]; ++iPtr_s){
233 j0=schur->pattern->index[iPtr_s];
234 if (j==j0) {
235 schur_withFillIn->val[iPtr]=schur->val[iPtr_s];
236 break;
237 }
238 }
239 }
240 }
241
242 /* for (i = 0; i < schur_withFillIn->numRows; ++i) {
243 for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
244 j=schur_withFillIn->pattern->index[iPtr];
245 fprintf(stderr,"A_CC[%d,%d]=%.2f ",i,j,schur_withFillIn->val[iPtr]);
246 }
247 fprintf(stderr,"\n");
248 }*/
249 time0=Paso_timer()-time0;
250 if (Paso_noError()) {
251 time1=Paso_timer();
252 /* update A_CC block to get Schur complement and then apply AMG to it */
253 Paso_Solver_updateIncompleteSchurComplement(schur_withFillIn,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC);
254 time1=Paso_timer()-time1;
255 out->AMG_of_Schur=Paso_Solver_getAMG(schur_withFillIn,verbose,level-1);
256
257 Paso_SparseMatrix_free(schur);
258 /* Paso_SparseMatrix_free(schur_withFillIn);*/
259 }
260 /* allocate work arrays for AMG application */
261 if (Paso_noError()) {
262 out->x_F=MEMALLOC(n_block*out->n_F,double);
263 out->b_F=MEMALLOC(n_block*out->n_F,double);
264 out->x_C=MEMALLOC(n_block*out->n_C,double);
265 out->b_C=MEMALLOC(n_block*out->n_C,double);
266
267 if (! (Paso_checkPtr(out->x_F) || Paso_checkPtr(out->b_F) || Paso_checkPtr(out->x_C) || Paso_checkPtr(out->b_C) ) ) {
268 #pragma omp parallel
269 {
270 #pragma omp for private(i,k) schedule(static)
271 for (i = 0; i < out->n_F; ++i) {
272 for (k=0; k<n_block;++k) {
273 out->x_F[i*n_block+k]=0.;
274 out->b_F[i*n_block+k]=0.;
275 }
276 }
277 #pragma omp for private(i,k) schedule(static)
278 for (i = 0; i < out->n_C; ++i) {
279 for (k=0; k<n_block;++k) {
280 out->x_C[i*n_block+k]=0.;
281 out->b_C[i*n_block+k]=0.;
282 }
283 }
284 } /* end parallel region */
285 }
286 }
287 }
288 }
289 }
290 }
291 }
292 }
293 }
294 }
295 TMPMEMFREE(mis_marker);
296 TMPMEMFREE(counter);
297 TMPMEMFREE(rs);
298 if (Paso_noError()) {
299 if (verbose) {
300 printf("AMG: %d unknowns eliminated. %d left.\n",out->n_F,n-out->n_F);
301 if (out->n_C>0) {
302 printf("timing: AMG: MIS/reordering/elemination : %e/%e/%e\n",time2,time0,time1);
303 } else {
304 printf("timing: AMG: MIS: %e\n",time2);
305 }
306 }
307 return out;
308 } else {
309 Paso_Solver_AMG_free(out);
310 return NULL;
311 }
312 }
313
314 /**************************************************************/
315
316 /* apply AMG precondition b-> x
317
318 in fact it solves
319
320 [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ] [ x_F ] = [b_F]
321 [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] [ x_C ] = [b_C]
322
323 in the form
324
325 b->[b_F,b_C]
326 x_F=invA_FF*b_F
327 b_C=b_C-A_CF*x_F
328 x_C=AMG(b_C)
329 b_F=b_F-A_FC*x_C
330 x_F=invA_FF*b_F
331 x<-[x_F,x_C]
332
333 should be called within a parallel region
334 barrier synconization should be performed to make sure that the input vector available
335
336 */
337
338 void Paso_Solver_solveAMG(Paso_Solver_AMG * amg, double * x, double * b) {
339 dim_t i,k;
340 dim_t n_block=amg->n_block;
341 double *r=MEMALLOC(amg->n,double);
342 double *x0=MEMALLOC(amg->n,double);
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 Paso_Solver_GS* GS=MEMALLOC(1,Paso_Solver_GS);
352 GS=Paso_Solver_getGS(amg->A,-1);
353 Paso_Solver_solveGS(GS,x,b);
354
355 #pragma omp parallel for private(i) schedule(static)
356 for (i=0;i<amg->n;++i) r[i]=b[i];
357
358 /*r=b-Ax*/
359 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
360 /****************/
361 /* b->[b_F,b_C] */
362 if (n_block==1) {
363 #pragma omp parallel for private(i) schedule(static)
364 for (i=0;i<amg->n_F;++i) amg->b_F[i]=r[amg->rows_in_F[i]]; /* was b istead of r */
365 #pragma omp parallel for private(i) schedule(static)
366 for (i=0;i<amg->n_C;++i) amg->b_C[i]=r[amg->rows_in_C[i]];
367 } else {
368 #pragma omp parallel for private(i,k) schedule(static)
369 for (i=0;i<amg->n_F;++i)
370 for (k=0;k<n_block;k++) amg->b_F[amg->n_block*i+k]=r[n_block*amg->rows_in_F[i]+k];
371 #pragma omp parallel for private(i,k) schedule(static)
372 for (i=0;i<amg->n_C;++i)
373 for (k=0;k<n_block;k++) amg->b_C[amg->n_block*i+k]=r[n_block*amg->rows_in_C[i]+k];
374 }
375
376 /****************/
377 /* Coursening part */
378
379 /* r_F=A_FF^-1*r_F */
380 /*Paso_Solver_applyBlockDiagonalMatrix(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->b_F,amg->b_F);
381 fprintf(stderr,"2\n");
382 */
383 /* r_C=r_C-A_CF*r_F */
384 /*Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->b_F,1.,amg->b_C);
385 fprintf(stderr,"3\n");
386 */
387 /****************/
388
389
390 /* x_F=invA_FF*b_F */
391 Paso_Solver_applyBlockDiagonalMatrix(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
392
393 /* b_C=b_C-A_CF*x_F */
394 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->x_F,1.,amg->b_C);
395
396 /* x_C=AMG(b_C) */
397 Paso_Solver_solveAMG(amg->AMG_of_Schur,amg->x_C,amg->b_C);
398
399 /* b_F=b_F-A_FC*x_C */
400 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_FC,amg->x_C,1.,amg->b_F);
401 /* x_F=invA_FF*b_F */
402 Paso_Solver_applyBlockDiagonalMatrix(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
403 /* x<-[x_F,x_C] */
404
405 /* */
406
407
408 if (n_block==1) {
409 #pragma omp parallel for private(i) schedule(static)
410 for (i=0;i<amg->n;++i) {
411 if (amg->mask_C[i]>-1) {
412 x[i]+=amg->x_C[amg->mask_C[i]];
413 } else {
414 x[i]+=amg->x_F[amg->mask_F[i]];
415 }
416 }
417 } else {
418 #pragma omp parallel for private(i,k) schedule(static)
419 for (i=0;i<amg->n;++i) {
420 if (amg->mask_C[i]>-1) {
421 for (k=0;k<n_block;k++) x[n_block*i+k]+=amg->x_C[n_block*amg->mask_C[i]+k];
422 } else {
423 for (k=0;k<n_block;k++) x[n_block*i+k]+=amg->x_F[n_block*amg->mask_F[i]+k];
424 }
425 }
426 }
427 /* all done */
428 /*post smoothing*/
429 /* Paso_Solver_solveGS(GS,x0,b);
430 if (n_block==1) {
431 #pragma omp parallel for private(i) schedule(static)
432 for (i=0;i<amg->n;++i) x[i]+=x0[i];
433 } else {
434 #pragma omp parallel for private(i,k) schedule(static)
435 for (i=0;i<amg->n;++i) {
436 for (k=0;k<n_block;k++) x[n_block*i+k]+=x0[n_block*i+k];
437 }
438 }
439 */
440 Paso_Solver_GS_free(GS);
441 }
442 MEMFREE(x0);
443 MEMFREE(r);
444 return;
445 }
446
447 /*
448 * $Log$
449 *
450 */

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