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

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Revision 2550 - (show annotations)
Tue Jul 21 03:36:13 2009 UTC (10 years, 2 months ago) by gross
File MIME type: text/plain
File size: 16037 byte(s)
AMG throws an error now if block size not 1
1
2 /*******************************************************
3 *
4 * Copyright (c) 2003-2009 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 */
18
19 /**************************************************************/
20
21 /* Author: artak@access.edu.au */
22
23 /**************************************************************/
24
25 #include "Paso.h"
26 #include "Solver.h"
27 #include "Options.h"
28 #include "PasoUtil.h"
29 #include "UMFPACK.h"
30 #include "MKL.h"
31 #include "SystemMatrix.h"
32 #include "Pattern_coupling.h"
33
34 /**************************************************************/
35
36 /* free all memory used by AMG */
37
38 void Paso_Solver_AMG_free(Paso_Solver_AMG * in) {
39 if (in!=NULL) {
40 Paso_Solver_AMG_free(in->AMG_of_Schur);
41 Paso_Solver_Jacobi_free(in->GS);
42 MEMFREE(in->inv_A_FF);
43 MEMFREE(in->A_FF_pivot);
44 Paso_SparseMatrix_free(in->A_FC);
45 Paso_SparseMatrix_free(in->A_CF);
46 MEMFREE(in->rows_in_F);
47 MEMFREE(in->rows_in_C);
48 MEMFREE(in->mask_F);
49 MEMFREE(in->mask_C);
50 MEMFREE(in->x_F);
51 MEMFREE(in->b_F);
52 MEMFREE(in->x_C);
53 MEMFREE(in->b_C);
54 MEMFREE(in);
55 }
56 }
57
58 /**************************************************************/
59
60 /* constructs the block-block factorization of
61
62 [ A_FF A_FC ]
63 A_p=
64 [ A_CF A_FF ]
65
66 to
67
68 [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ]
69 [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ]
70
71
72 where S=A_FF-ACF*invA_FF*A_FC within the shape of S
73
74 then AMG is applied to S again until S becomes empty
75
76 */
77 Paso_Solver_AMG* Paso_Solver_getAMG(Paso_SparseMatrix *A_p,dim_t level,Paso_Options* options) {
78 Paso_Solver_AMG* out=NULL;
79 bool_t verbose=options->verbose;
80 dim_t n=A_p->numRows;
81 dim_t n_block=A_p->row_block_size;
82 index_t* mis_marker=NULL;
83 index_t* counter=NULL;
84 index_t iPtr,*index, *where_p, iPtr_s;
85 dim_t i,k,j;
86 Paso_SparseMatrix * schur=NULL;
87 Paso_SparseMatrix * schur_withFillIn=NULL;
88 double S=0;
89
90 /*Make sure we have block sizes 1*/
91 if (A_p->col_block_size>1) {
92 Paso_setError(TYPE_ERROR,"Paso_Solver_getAMG: AMG requires column block size 1.");
93 return NULL;
94 }
95 if (A_p->row_block_size>1) {
96 Paso_setError(TYPE_ERROR,"Paso_Solver_getAMG: AMG requires row block size 1.");
97 return NULL;
98 }
99
100 /* identify independend set of rows/columns */
101 mis_marker=TMPMEMALLOC(n,index_t);
102 counter=TMPMEMALLOC(n,index_t);
103 out=MEMALLOC(1,Paso_Solver_AMG);
104 out->AMG_of_Schur=NULL;
105 out->inv_A_FF=NULL;
106 out->A_FF_pivot=NULL;
107 out->A_FC=NULL;
108 out->A_CF=NULL;
109 out->rows_in_F=NULL;
110 out->rows_in_C=NULL;
111 out->mask_F=NULL;
112 out->mask_C=NULL;
113 out->x_F=NULL;
114 out->b_F=NULL;
115 out->x_C=NULL;
116 out->b_C=NULL;
117 out->GS=NULL;
118 out->A=Paso_SparseMatrix_getReference(A_p);
119 /*out->GS=Paso_Solver_getGS(A_p,verbose);*/
120 out->GS=Paso_Solver_getJacobi(A_p);
121 out->level=level;
122
123 if (level==0 || n<=options->min_coarse_matrix_size)
124 out->coarsest_level=TRUE;
125 else
126 out->coarsest_level=FALSE;
127
128 if ( !(Paso_checkPtr(mis_marker) || Paso_checkPtr(out) || Paso_checkPtr(counter) || level==0 || n<=options->min_coarse_matrix_size) ) {
129 /* identify independend set of rows/columns */
130 #pragma omp parallel for private(i) schedule(static)
131 for (i=0;i<n;++i) mis_marker[i]=-1;
132
133 if (options->coarsening_method == PASO_YAIR_SHAPIRA_COARSENING) {
134 Paso_Pattern_coup(A_p,mis_marker,options->coarsening_threshold);
135 }
136 else if (options->coarsening_method == PASO_RUGE_STUEBEN_COARSENING) {
137 Paso_Pattern_RS(A_p,mis_marker,options->coarsening_threshold);
138 }
139 else if (options->coarsening_method == PASO_AGGREGATION_COARSENING) {
140 Paso_Pattern_Aggregiation(A_p,mis_marker,options->coarsening_threshold);
141 }
142 else {
143 /*Default coarseneing*/
144 Paso_Pattern_RS(A_p,mis_marker,options->coarsening_threshold);
145 }
146
147 if (Paso_noError()) {
148 #pragma omp parallel for private(i) schedule(static)
149 for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
150 out->n=n;
151 out->n_block=n_block;
152 out->n_F=Paso_Util_cumsum(n,counter);
153 out->mask_F=MEMALLOC(n,index_t);
154 out->rows_in_F=MEMALLOC(out->n_F,index_t);
155 out->inv_A_FF=MEMALLOC(n_block*n_block*out->n_F,double);
156 out->A_FF_pivot=NULL; /* later use for block size>3 */
157 if (! (Paso_checkPtr(out->mask_F) || Paso_checkPtr(out->inv_A_FF) || Paso_checkPtr(out->rows_in_F) ) ) {
158 /* creates an index for F from mask */
159 #pragma omp parallel for private(i) schedule(static)
160 for (i = 0; i < out->n_F; ++i) out->rows_in_F[i]=-1;
161 #pragma omp parallel for private(i) schedule(static)
162 for (i = 0; i < n; ++i) {
163 if (mis_marker[i]) {
164 out->rows_in_F[counter[i]]=i;
165 out->mask_F[i]=counter[i];
166 } else {
167 out->mask_F[i]=-1;
168 }
169 }
170
171 /* Compute row-sum for getting rs(A_FF)^-1*/
172 #pragma omp parallel for private(i,iPtr,j,S) schedule(static)
173 for (i = 0; i < out->n_F; ++i) {
174 S=0;
175 for (iPtr=A_p->pattern->ptr[out->rows_in_F[i]];iPtr<A_p->pattern->ptr[out->rows_in_F[i] + 1]; ++iPtr) {
176 j=A_p->pattern->index[iPtr];
177 if (mis_marker[j])
178 S+=A_p->val[iPtr];
179 }
180 out->inv_A_FF[i]=1./S;
181 }
182
183 if( Paso_noError()) {
184 /* if there are no nodes in the coarse level there is no more work to do */
185 out->n_C=n-out->n_F;
186
187 /*if (out->n_F>500) {*/
188 out->rows_in_C=MEMALLOC(out->n_C,index_t);
189 out->mask_C=MEMALLOC(n,index_t);
190 if (! (Paso_checkPtr(out->mask_C) || Paso_checkPtr(out->rows_in_C) ) ) {
191 /* creates an index for C from mask */
192 #pragma omp parallel for private(i) schedule(static)
193 for (i = 0; i < n; ++i) counter[i]=! mis_marker[i];
194 Paso_Util_cumsum(n,counter);
195 #pragma omp parallel for private(i) schedule(static)
196 for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
197 #pragma omp parallel for private(i) schedule(static)
198 for (i = 0; i < n; ++i) {
199 if (! mis_marker[i]) {
200 out->rows_in_C[counter[i]]=i;
201 out->mask_C[i]=counter[i];
202 } else {
203 out->mask_C[i]=-1;
204 }
205 }
206 /* get A_CF block: */
207 out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
208 if (Paso_noError()) {
209 /* get A_FC block: */
210 out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
211 /* get A_CC block: */
212 if (Paso_noError()) {
213 schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
214 /*find the pattern of the schur complement with fill in*/
215
216 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);
217 /* copy values over*/
218 #pragma omp parallel for private(i,iPtr,j,iPtr_s,index,where_p) schedule(static)
219 for (i = 0; i < schur_withFillIn->numRows; ++i) {
220 for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
221 j=schur_withFillIn->pattern->index[iPtr];
222 iPtr_s=schur->pattern->ptr[i];
223 schur_withFillIn->val[iPtr]=0.;
224 index=&(schur->pattern->index[iPtr_s]);
225 where_p=(index_t*)bsearch(&j,
226 index,
227 schur->pattern->ptr[i + 1]-schur->pattern->ptr[i],
228 sizeof(index_t),
229 Paso_comparIndex);
230 if (where_p!=NULL) {
231 schur_withFillIn->val[iPtr]=schur->val[iPtr_s+(index_t)(where_p-index)];
232 }
233 }
234 }
235 if (Paso_noError()) {
236 Paso_Solver_updateIncompleteSchurComplement(schur_withFillIn,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC);
237 out->AMG_of_Schur=Paso_Solver_getAMG(schur_withFillIn,level-1,options);
238 Paso_SparseMatrix_free(schur);
239 }
240 /* allocate work arrays for AMG application */
241 if (Paso_noError()) {
242 out->x_F=MEMALLOC(n_block*out->n_F,double);
243 out->b_F=MEMALLOC(n_block*out->n_F,double);
244 out->x_C=MEMALLOC(n_block*out->n_C,double);
245 out->b_C=MEMALLOC(n_block*out->n_C,double);
246
247 if (! (Paso_checkPtr(out->x_F) || Paso_checkPtr(out->b_F) || Paso_checkPtr(out->x_C) || Paso_checkPtr(out->b_C) ) ) {
248 #pragma omp parallel for private(i,k) schedule(static)
249 for (i = 0; i < out->n_F; ++i) {
250 for (k=0; k<n_block;++k) {
251 out->x_F[i*n_block+k]=0.;
252 out->b_F[i*n_block+k]=0.;
253 }
254 }
255 #pragma omp parallel for private(i,k) schedule(static)
256 for (i = 0; i < out->n_C; ++i) {
257 for (k=0; k<n_block;++k) {
258 out->x_C[i*n_block+k]=0.;
259 out->b_C[i*n_block+k]=0.;
260 }
261 }
262 }
263 }
264 }
265 }
266 }
267
268 }
269 }
270 }
271 }
272 TMPMEMFREE(mis_marker);
273 TMPMEMFREE(counter);
274 if (Paso_noError()) {
275 if (verbose && level>0 && !out->coarsest_level) {
276 printf("AMG: %d unknowns eliminated. %d left.\n",out->n_F,out->n_C);
277 }
278 return out;
279 } else {
280 Paso_Solver_AMG_free(out);
281 return NULL;
282 }
283 }
284
285 /**************************************************************/
286
287 /* apply AMG precondition b-> x
288
289 in fact it solves
290
291 [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FC ] [ x_F ] = [b_F]
292 [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] [ x_C ] = [b_C]
293
294 in the form
295
296 b->[b_F,b_C]
297 x_F=invA_FF*b_F
298 b_C=b_C-A_CF*x_F
299 x_C=AMG(b_C)
300 b_F=b_F-A_FC*x_C
301 x_F=invA_FF*b_F
302 x<-[x_F,x_C]
303
304 should be called within a parallel region
305 barrier synconization should be performed to make sure that the input vector available
306
307 */
308
309 void Paso_Solver_solveAMG(Paso_Solver_AMG * amg, double * x, double * b) {
310 dim_t i;
311 double *r=MEMALLOC(amg->n,double);
312 double *x0=MEMALLOC(amg->n,double);
313 double time0=0;
314 bool_t verbose=0;
315
316 #ifdef MKL
317 Paso_SparseMatrix *temp=NULL;
318 #endif
319
320
321 if (amg->coarsest_level) {
322
323 time0=Paso_timer();
324 #ifdef MKL
325 temp=Paso_SparseMatrix_alloc(MATRIX_FORMAT_BLK1 + MATRIX_FORMAT_OFFSET1, amg->A->pattern,1,1);
326 #pragma omp parallel for private(i) schedule(static)
327 for (i=0;i<amg->A->len;++i) {
328 temp->val[i]=amg->A->val[i];
329 }
330 Paso_MKL1(temp,x,b,0);
331 Paso_SparseMatrix_free(temp);
332 #else
333 #ifdef UMFPACK
334 Paso_UMFPACK1(amg->A,x,b,0);
335 #else
336 Paso_Solver_solveJacobi(amg->GS,x,b);
337 #endif
338 #endif
339
340 time0=Paso_timer()-time0;
341 if (verbose) fprintf(stderr,"timing: DIRECT SOLVER: %e\n\n\n",time0);
342
343 } else {
344 /* presmoothing */
345 time0=Paso_timer();
346 Paso_Solver_solveJacobi(amg->GS,x,b);
347 time0=Paso_timer()-time0;
348 if (verbose) fprintf(stderr,"timing: Presmooting: %e\n",time0);
349 /* end of presmoothing */
350
351
352 time0=Paso_timer();
353 #pragma omp parallel for private(i) schedule(static)
354 for (i=0;i<amg->n;++i) r[i]=b[i];
355
356 /*r=b-Ax*/
357 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
358
359 /* b->[b_F,b_C] */
360 #pragma omp parallel for private(i) schedule(static)
361 for (i=0;i<amg->n_F;++i) amg->b_F[i]=r[amg->rows_in_F[i]];
362
363 #pragma omp parallel for private(i) schedule(static)
364 for (i=0;i<amg->n_C;++i) amg->b_C[i]=r[amg->rows_in_C[i]];
365
366 /* x_F=invA_FF*b_F */
367 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
368
369 /* b_C=b_C-A_CF*x_F */
370 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->x_F,1.,amg->b_C);
371
372 time0=Paso_timer()-time0;
373 if (verbose) fprintf(stderr,"timing: Before next level: %e\n",time0);
374
375 /* x_C=AMG(b_C) */
376 Paso_Solver_solveAMG(amg->AMG_of_Schur,amg->x_C,amg->b_C);
377
378 time0=Paso_timer();
379 /* b_F=b_F-A_FC*x_C */
380 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_FC,amg->x_C,1.,amg->b_F);
381 /* x_F=invA_FF*b_F */
382 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
383 /* x<-[x_F,x_C] */
384
385 #pragma omp parallel for private(i) schedule(static)
386 for (i=0;i<amg->n;++i) {
387 if (amg->mask_C[i]>-1) {
388 x[i]=amg->x_C[amg->mask_C[i]];
389 } else {
390 x[i]=amg->x_F[amg->mask_F[i]];
391 }
392 }
393
394 time0=Paso_timer()-time0;
395 if (verbose) fprintf(stderr,"timing: After next level: %e\n",time0);
396
397 /*postsmoothing*/
398 time0=Paso_timer();
399 #pragma omp parallel for private(i) schedule(static)
400 for (i=0;i<amg->n;++i) r[i]=b[i];
401
402 /*r=b-Ax */
403 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
404 Paso_Solver_solveJacobi(amg->GS,x0,r);
405
406 #pragma omp parallel for private(i) schedule(static)
407 for (i=0;i<amg->n;++i) x[i]+=x0[i];
408
409 time0=Paso_timer()-time0;
410 if (verbose) fprintf(stderr,"timing: Postsmoothing: %e\n",time0);
411
412 /*end of postsmoothing*/
413
414 }
415 MEMFREE(r);
416 MEMFREE(x0);
417 return;
418 }
419
420 /*
421 * $Log$
422 *
423 */

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