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

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Revision 2524 - (show annotations)
Wed Jul 8 00:39:26 2009 UTC (10 years, 7 months ago) by artak
File MIME type: text/plain
File size: 15911 byte(s)
Minimum size of the coarsest level matrix option added to solver options
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 */
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 A_p->pattern->input_block_size=A_p->col_block_size;
92 A_p->pattern->output_block_size=A_p->row_block_size;
93 A_p->pattern->block_size=A_p->block_size;
94
95 /* identify independend set of rows/columns */
96 mis_marker=TMPMEMALLOC(n,index_t);
97 counter=TMPMEMALLOC(n,index_t);
98 out=MEMALLOC(1,Paso_Solver_AMG);
99 out->AMG_of_Schur=NULL;
100 out->inv_A_FF=NULL;
101 out->A_FF_pivot=NULL;
102 out->A_FC=NULL;
103 out->A_CF=NULL;
104 out->rows_in_F=NULL;
105 out->rows_in_C=NULL;
106 out->mask_F=NULL;
107 out->mask_C=NULL;
108 out->x_F=NULL;
109 out->b_F=NULL;
110 out->x_C=NULL;
111 out->b_C=NULL;
112 out->GS=NULL;
113 out->A=Paso_SparseMatrix_getReference(A_p);
114 /*out->GS=Paso_Solver_getGS(A_p,verbose);*/
115 out->GS=Paso_Solver_getJacobi(A_p);
116 out->level=level;
117
118 if (level==0 || n<=options->min_coarse_matrix_size)
119 out->coarsest_level=TRUE;
120 else
121 out->coarsest_level=FALSE;
122
123 if ( !(Paso_checkPtr(mis_marker) || Paso_checkPtr(out) || Paso_checkPtr(counter) || level==0 || n<=options->min_coarse_matrix_size) ) {
124 /* identify independend set of rows/columns */
125 #pragma omp parallel for private(i) schedule(static)
126 for (i=0;i<n;++i) mis_marker[i]=-1;
127
128 if (options->coarsening_method == PASO_YAIR_SHAPIRA_COARSENING) {
129 Paso_Pattern_coup(A_p,mis_marker,options->coarsening_threshold);
130 }
131 else if (options->coarsening_method == PASO_RUGE_STUEBEN_COARSENING) {
132 Paso_Pattern_RS(A_p,mis_marker,options->coarsening_threshold);
133 }
134 else if (options->coarsening_method == PASO_AGGREGATION_COARSENING) {
135 Paso_Pattern_Aggregiation(A_p,mis_marker,options->coarsening_threshold);
136 }
137 else {
138 /*Default coarseneing*/
139 Paso_Pattern_RS(A_p,mis_marker,options->coarsening_threshold);
140 }
141
142 if (Paso_noError()) {
143 #pragma omp parallel for private(i) schedule(static)
144 for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
145 out->n=n;
146 out->n_block=n_block;
147 out->n_F=Paso_Util_cumsum(n,counter);
148 out->mask_F=MEMALLOC(n,index_t);
149 out->rows_in_F=MEMALLOC(out->n_F,index_t);
150 out->inv_A_FF=MEMALLOC(n_block*n_block*out->n_F,double);
151 out->A_FF_pivot=NULL; /* later use for block size>3 */
152 if (! (Paso_checkPtr(out->mask_F) || Paso_checkPtr(out->inv_A_FF) || Paso_checkPtr(out->rows_in_F) ) ) {
153 /* creates an index for F from mask */
154 #pragma omp parallel for private(i) schedule(static)
155 for (i = 0; i < out->n_F; ++i) out->rows_in_F[i]=-1;
156 #pragma omp parallel for private(i) schedule(static)
157 for (i = 0; i < n; ++i) {
158 if (mis_marker[i]) {
159 out->rows_in_F[counter[i]]=i;
160 out->mask_F[i]=counter[i];
161 } else {
162 out->mask_F[i]=-1;
163 }
164 }
165
166 /* Compute row-sum for getting rs(A_FF)^-1*/
167 #pragma omp parallel for private(i,iPtr,j,S) schedule(static)
168 for (i = 0; i < out->n_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 j=A_p->pattern->index[iPtr];
172 if (mis_marker[j])
173 S+=A_p->val[iPtr];
174 }
175 out->inv_A_FF[i]=1./S;
176 }
177
178 if( Paso_noError()) {
179 /* if there are no nodes in the coarse level there is no more work to do */
180 out->n_C=n-out->n_F;
181
182 /*if (out->n_F>500) {*/
183 out->rows_in_C=MEMALLOC(out->n_C,index_t);
184 out->mask_C=MEMALLOC(n,index_t);
185 if (! (Paso_checkPtr(out->mask_C) || Paso_checkPtr(out->rows_in_C) ) ) {
186 /* creates an index for C from mask */
187 #pragma omp parallel for private(i) schedule(static)
188 for (i = 0; i < n; ++i) counter[i]=! mis_marker[i];
189 Paso_Util_cumsum(n,counter);
190 #pragma omp parallel for private(i) schedule(static)
191 for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
192 #pragma omp parallel for private(i) schedule(static)
193 for (i = 0; i < n; ++i) {
194 if (! mis_marker[i]) {
195 out->rows_in_C[counter[i]]=i;
196 out->mask_C[i]=counter[i];
197 } else {
198 out->mask_C[i]=-1;
199 }
200 }
201 /* get A_CF block: */
202 out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
203 if (Paso_noError()) {
204 /* get A_FC block: */
205 out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
206 /* get A_CC block: */
207 if (Paso_noError()) {
208 schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
209 /*find the pattern of the schur complement with fill in*/
210
211 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);
212 /* copy values over*/
213 #pragma omp parallel for private(i,iPtr,j,iPtr_s,index,where_p) schedule(static)
214 for (i = 0; i < schur_withFillIn->numRows; ++i) {
215 for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
216 j=schur_withFillIn->pattern->index[iPtr];
217 iPtr_s=schur->pattern->ptr[i];
218 schur_withFillIn->val[iPtr]=0.;
219 index=&(schur->pattern->index[iPtr_s]);
220 where_p=(index_t*)bsearch(&j,
221 index,
222 schur->pattern->ptr[i + 1]-schur->pattern->ptr[i],
223 sizeof(index_t),
224 Paso_comparIndex);
225 if (where_p!=NULL) {
226 schur_withFillIn->val[iPtr]=schur->val[iPtr_s+(index_t)(where_p-index)];
227 }
228 }
229 }
230 if (Paso_noError()) {
231 Paso_Solver_updateIncompleteSchurComplement(schur_withFillIn,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC);
232 out->AMG_of_Schur=Paso_Solver_getAMG(schur_withFillIn,level-1,options);
233 Paso_SparseMatrix_free(schur);
234 }
235 /* allocate work arrays for AMG application */
236 if (Paso_noError()) {
237 out->x_F=MEMALLOC(n_block*out->n_F,double);
238 out->b_F=MEMALLOC(n_block*out->n_F,double);
239 out->x_C=MEMALLOC(n_block*out->n_C,double);
240 out->b_C=MEMALLOC(n_block*out->n_C,double);
241
242 if (! (Paso_checkPtr(out->x_F) || Paso_checkPtr(out->b_F) || Paso_checkPtr(out->x_C) || Paso_checkPtr(out->b_C) ) ) {
243 #pragma omp parallel for private(i,k) schedule(static)
244 for (i = 0; i < out->n_F; ++i) {
245 for (k=0; k<n_block;++k) {
246 out->x_F[i*n_block+k]=0.;
247 out->b_F[i*n_block+k]=0.;
248 }
249 }
250 #pragma omp parallel for private(i,k) schedule(static)
251 for (i = 0; i < out->n_C; ++i) {
252 for (k=0; k<n_block;++k) {
253 out->x_C[i*n_block+k]=0.;
254 out->b_C[i*n_block+k]=0.;
255 }
256 }
257 }
258 }
259 }
260 }
261 }
262
263 }
264 }
265 }
266 }
267 TMPMEMFREE(mis_marker);
268 TMPMEMFREE(counter);
269 if (Paso_noError()) {
270 if (verbose && level>0 && !out->coarsest_level) {
271 printf("AMG: %d unknowns eliminated. %d left.\n",out->n_F,out->n_C);
272 }
273 return out;
274 } else {
275 Paso_Solver_AMG_free(out);
276 return NULL;
277 }
278 }
279
280 /**************************************************************/
281
282 /* apply AMG precondition b-> x
283
284 in fact it solves
285
286 [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FC ] [ x_F ] = [b_F]
287 [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] [ x_C ] = [b_C]
288
289 in the form
290
291 b->[b_F,b_C]
292 x_F=invA_FF*b_F
293 b_C=b_C-A_CF*x_F
294 x_C=AMG(b_C)
295 b_F=b_F-A_FC*x_C
296 x_F=invA_FF*b_F
297 x<-[x_F,x_C]
298
299 should be called within a parallel region
300 barrier synconization should be performed to make sure that the input vector available
301
302 */
303
304 void Paso_Solver_solveAMG(Paso_Solver_AMG * amg, double * x, double * b) {
305 dim_t i;
306 double *r=MEMALLOC(amg->n,double);
307 double *x0=MEMALLOC(amg->n,double);
308 double time0=0;
309 bool_t verbose=0;
310
311 #ifdef MKL
312 Paso_SparseMatrix *temp=NULL;
313 #endif
314
315
316 if (amg->coarsest_level) {
317
318 time0=Paso_timer();
319 #ifdef MKL
320 temp=Paso_SparseMatrix_alloc(MATRIX_FORMAT_BLK1 + MATRIX_FORMAT_OFFSET1, amg->A->pattern,1,1);
321 #pragma omp parallel for private(i) schedule(static)
322 for (i=0;i<amg->A->len;++i) {
323 temp->val[i]=amg->A->val[i];
324 }
325 Paso_MKL1(temp,x,b,0);
326 Paso_SparseMatrix_free(temp);
327 #else
328 #ifdef UMFPACK
329 Paso_UMFPACK1(amg->A,x,b,0);
330 #else
331 Paso_Solver_solveJacobi(amg->GS,x,b);
332 #endif
333 #endif
334
335 time0=Paso_timer()-time0;
336 if (verbose) fprintf(stderr,"timing: DIRECT SOLVER: %e\n\n\n",time0);
337
338 } else {
339 /* presmoothing */
340 time0=Paso_timer();
341 Paso_Solver_solveJacobi(amg->GS,x,b);
342 time0=Paso_timer()-time0;
343 if (verbose) fprintf(stderr,"timing: Presmooting: %e\n",time0);
344 /* end of presmoothing */
345
346
347 time0=Paso_timer();
348 #pragma omp parallel for private(i) schedule(static)
349 for (i=0;i<amg->n;++i) r[i]=b[i];
350
351 /*r=b-Ax*/
352 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
353
354 /* b->[b_F,b_C] */
355 #pragma omp parallel for private(i) schedule(static)
356 for (i=0;i<amg->n_F;++i) amg->b_F[i]=r[amg->rows_in_F[i]];
357
358 #pragma omp parallel for private(i) schedule(static)
359 for (i=0;i<amg->n_C;++i) amg->b_C[i]=r[amg->rows_in_C[i]];
360
361 /* x_F=invA_FF*b_F */
362 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
363
364 /* b_C=b_C-A_CF*x_F */
365 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->x_F,1.,amg->b_C);
366
367 time0=Paso_timer()-time0;
368 if (verbose) fprintf(stderr,"timing: Before next level: %e\n",time0);
369
370 /* x_C=AMG(b_C) */
371 Paso_Solver_solveAMG(amg->AMG_of_Schur,amg->x_C,amg->b_C);
372
373 time0=Paso_timer();
374 /* b_F=b_F-A_FC*x_C */
375 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_FC,amg->x_C,1.,amg->b_F);
376 /* x_F=invA_FF*b_F */
377 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
378 /* x<-[x_F,x_C] */
379
380 #pragma omp parallel for private(i) schedule(static)
381 for (i=0;i<amg->n;++i) {
382 if (amg->mask_C[i]>-1) {
383 x[i]=amg->x_C[amg->mask_C[i]];
384 } else {
385 x[i]=amg->x_F[amg->mask_F[i]];
386 }
387 }
388
389 time0=Paso_timer()-time0;
390 if (verbose) fprintf(stderr,"timing: After next level: %e\n",time0);
391
392 /*postsmoothing*/
393 time0=Paso_timer();
394 #pragma omp parallel for private(i) schedule(static)
395 for (i=0;i<amg->n;++i) r[i]=b[i];
396
397 /*r=b-Ax */
398 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
399 Paso_Solver_solveJacobi(amg->GS,x0,r);
400
401 #pragma omp parallel for private(i) schedule(static)
402 for (i=0;i<amg->n;++i) x[i]+=x0[i];
403
404 time0=Paso_timer()-time0;
405 if (verbose) fprintf(stderr,"timing: Postsmoothing: %e\n",time0);
406
407 /*end of postsmoothing*/
408
409 }
410 MEMFREE(r);
411 MEMFREE(x0);
412 return;
413 }
414
415 /*
416 * $Log$
417 *
418 */

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