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

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Revision 2439 - (show annotations)
Tue May 26 04:34:21 2009 UTC (10 years, 3 months ago) by artak
File MIME type: text/plain
File size: 15935 byte(s)
AMG now works with blocksize 3. Logical block sizes replaced with real block size before starting AMG. But this happens only when we use AMG as a preconditioner.
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 Paso_Solver_Jacobi_free(in->GS);
39 MEMFREE(in->inv_A_FF);
40 MEMFREE(in->A_FF_pivot);
41 Paso_SparseMatrix_free(in->A_FC);
42 Paso_SparseMatrix_free(in->A_CF);
43 MEMFREE(in->rows_in_F);
44 MEMFREE(in->rows_in_C);
45 MEMFREE(in->mask_F);
46 MEMFREE(in->mask_C);
47 MEMFREE(in->x_F);
48 MEMFREE(in->b_F);
49 MEMFREE(in->x_C);
50 MEMFREE(in->b_C);
51 MEMFREE(in);
52 }
53 }
54
55 /**************************************************************/
56
57 /* constructs the block-block factorization of
58
59 [ A_FF A_FC ]
60 A_p=
61 [ A_CF A_FF ]
62
63 to
64
65 [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ]
66 [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ]
67
68
69 where S=A_FF-ACF*invA_FF*A_FC within the shape of S
70
71 then AMG is applied to S again until S becomes empty
72
73 */
74 Paso_Solver_AMG* Paso_Solver_getAMG(Paso_SparseMatrix *A_p,bool_t verbose,dim_t level, double couplingParam) {
75 Paso_Solver_AMG* out=NULL;
76 dim_t n=A_p->numRows;
77 dim_t n_block=A_p->row_block_size;
78 index_t* mis_marker=NULL;
79 index_t* counter=NULL;
80 index_t iPtr,*index, *where_p, iPtr_s;
81 dim_t i,k,j;
82 Paso_SparseMatrix * schur=NULL;
83 Paso_SparseMatrix * schur_withFillIn=NULL;
84 double S=0;
85
86 /*Make sure we have block sizes 1*/
87 A_p->pattern->input_block_size=A_p->col_block_size;
88 A_p->pattern->output_block_size=A_p->row_block_size;
89 A_p->pattern->block_size=A_p->block_size;
90
91 /* identify independend set of rows/columns */
92 mis_marker=TMPMEMALLOC(n,index_t);
93 counter=TMPMEMALLOC(n,index_t);
94 out=MEMALLOC(1,Paso_Solver_AMG);
95 out->AMG_of_Schur=NULL;
96 out->inv_A_FF=NULL;
97 out->A_FF_pivot=NULL;
98 out->A_FC=NULL;
99 out->A_CF=NULL;
100 out->rows_in_F=NULL;
101 out->rows_in_C=NULL;
102 out->mask_F=NULL;
103 out->mask_C=NULL;
104 out->x_F=NULL;
105 out->b_F=NULL;
106 out->x_C=NULL;
107 out->b_C=NULL;
108 out->GS=NULL;
109 out->A=Paso_SparseMatrix_getReference(A_p);
110 /*out->GS=Paso_Solver_getGS(A_p,verbose);*/
111 out->GS=Paso_Solver_getJacobi(A_p);
112 /*out->GS->sweeps=2;*/
113 out->level=level;
114
115 if ( !(Paso_checkPtr(mis_marker) || Paso_checkPtr(out) || Paso_checkPtr(counter) ) ) {
116 /* identify independend set of rows/columns */
117 #pragma omp parallel for private(i) schedule(static)
118 for (i=0;i<n;++i) mis_marker[i]=-1;
119 Paso_Pattern_coup(A_p,mis_marker,couplingParam);
120 /*Paso_Pattern_RS(A_p,mis_marker,couplingParam);*/
121 /*Paso_Pattern_Aggregiation(A_p,mis_marker,couplingParam);*/
122 if (Paso_noError()) {
123 #pragma omp parallel for private(i) schedule(static)
124 for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
125 out->n=n;
126 out->n_block=n_block;
127 out->n_F=Paso_Util_cumsum(n,counter);
128 out->mask_F=MEMALLOC(n,index_t);
129 out->rows_in_F=MEMALLOC(out->n_F,index_t);
130 out->inv_A_FF=MEMALLOC(n_block*n_block*out->n_F,double);
131 out->A_FF_pivot=NULL; /* later use for block size>3 */
132 if (! (Paso_checkPtr(out->mask_F) || Paso_checkPtr(out->inv_A_FF) || Paso_checkPtr(out->rows_in_F) ) ) {
133 /* creates an index for F from mask */
134 #pragma omp parallel for private(i) schedule(static)
135 for (i = 0; i < out->n_F; ++i) out->rows_in_F[i]=-1;
136 #pragma omp parallel for private(i) schedule(static)
137 for (i = 0; i < n; ++i) {
138 if (mis_marker[i]) {
139 out->rows_in_F[counter[i]]=i;
140 out->mask_F[i]=counter[i];
141 } else {
142 out->mask_F[i]=-1;
143 }
144 }
145
146 /* Compute row-sum for getting rs(A_FF)^-1*/
147 #pragma omp parallel for private(i,iPtr,j,S) schedule(static)
148 for (i = 0; i < out->n_F; ++i) {
149 S=0;
150 for (iPtr=A_p->pattern->ptr[out->rows_in_F[i]];iPtr<A_p->pattern->ptr[out->rows_in_F[i] + 1]; ++iPtr) {
151 j=A_p->pattern->index[iPtr];
152 if (mis_marker[j])
153 S+=A_p->val[iPtr];
154 }
155 out->inv_A_FF[i]=1./S;
156 }
157
158 if( Paso_noError()) {
159 /* if there are no nodes in the coarse level there is no more work to do */
160 out->n_C=n-out->n_F;
161 if (level>0 && out->n_C>500) {
162 /*if (out->n_F>500) {*/
163 out->rows_in_C=MEMALLOC(out->n_C,index_t);
164 out->mask_C=MEMALLOC(n,index_t);
165 if (! (Paso_checkPtr(out->mask_C) || Paso_checkPtr(out->rows_in_C) ) ) {
166 /* creates an index for C from mask */
167 #pragma omp parallel for private(i) schedule(static)
168 for (i = 0; i < n; ++i) counter[i]=! mis_marker[i];
169 Paso_Util_cumsum(n,counter);
170 #pragma omp parallel for private(i) schedule(static)
171 for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
172 #pragma omp parallel for private(i) schedule(static)
173 for (i = 0; i < n; ++i) {
174 if (! mis_marker[i]) {
175 out->rows_in_C[counter[i]]=i;
176 out->mask_C[i]=counter[i];
177 } else {
178 out->mask_C[i]=-1;
179 }
180 }
181 /* get A_CF block: */
182 out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
183 if (Paso_noError()) {
184 /* get A_FC block: */
185 out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
186 /* get A_CC block: */
187 if (Paso_noError()) {
188 schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
189 /*find the pattern of the schur complement with fill in*/
190
191 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);
192
193 /*fprintf(stderr,"Sparsity of Schure: %dx%d LEN %d Percentage %f\n",schur_withFillIn->pattern->numOutput,schur_withFillIn->pattern->numInput,schur_withFillIn->len,schur_withFillIn->len/(1.*schur_withFillIn->pattern->numOutput*schur_withFillIn->pattern->numInput));*/
194
195 /* copy values over*/
196 #pragma omp parallel for private(i,iPtr,j,iPtr_s,index,where_p) schedule(static)
197 for (i = 0; i < schur_withFillIn->numRows; ++i) {
198 for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
199 j=schur_withFillIn->pattern->index[iPtr];
200 iPtr_s=schur->pattern->ptr[i];
201 schur_withFillIn->val[iPtr]=0.;
202 index=&(schur->pattern->index[iPtr_s]);
203 where_p=(index_t*)bsearch(&j,
204 index,
205 schur->pattern->ptr[i + 1]-schur->pattern->ptr[i],
206 sizeof(index_t),
207 Paso_comparIndex);
208 if (where_p!=NULL) {
209 schur_withFillIn->val[iPtr]=schur->val[iPtr_s+(index_t)(where_p-index)];
210 }
211 }
212 }
213
214 if (Paso_noError()) {
215 Paso_Solver_updateIncompleteSchurComplement(schur_withFillIn,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC);
216 out->AMG_of_Schur=Paso_Solver_getAMG(schur_withFillIn,verbose,level-1,couplingParam);
217 Paso_SparseMatrix_free(schur);
218 }
219 /* allocate work arrays for AMG application */
220 if (Paso_noError()) {
221 out->x_F=MEMALLOC(n_block*out->n_F,double);
222 out->b_F=MEMALLOC(n_block*out->n_F,double);
223 out->x_C=MEMALLOC(n_block*out->n_C,double);
224 out->b_C=MEMALLOC(n_block*out->n_C,double);
225
226 if (! (Paso_checkPtr(out->x_F) || Paso_checkPtr(out->b_F) || Paso_checkPtr(out->x_C) || Paso_checkPtr(out->b_C) ) ) {
227 #pragma omp parallel for private(i,k) schedule(static)
228 for (i = 0; i < out->n_F; ++i) {
229 for (k=0; k<n_block;++k) {
230 out->x_F[i*n_block+k]=0.;
231 out->b_F[i*n_block+k]=0.;
232 }
233 }
234 #pragma omp parallel for private(i,k) schedule(static)
235 for (i = 0; i < out->n_C; ++i) {
236 for (k=0; k<n_block;++k) {
237 out->x_C[i*n_block+k]=0.;
238 out->b_C[i*n_block+k]=0.;
239 }
240 }
241 }
242 }
243 }
244 }
245 }
246 }
247 }
248 }
249 }
250 }
251 TMPMEMFREE(mis_marker);
252 TMPMEMFREE(counter);
253 if (Paso_noError()) {
254 if (verbose) {
255 printf("AMG: %d unknowns eliminated. %d left.\n",out->n_F,n-out->n_F);
256 /*if (level>0 && out->n_F>500) {*/
257 /* if (out->n_F<500) {*/
258 /* printf("timing: AMG: MIS/reordering/elemination : %e/%e\n",time0,time1);
259 } else {
260 printf("timing: AMG: MIS: %e\n",time2);
261 }*/
262 }
263 return out;
264 } else {
265 Paso_Solver_AMG_free(out);
266 return NULL;
267 }
268 }
269
270 /**************************************************************/
271
272 /* apply AMG precondition b-> x
273
274 in fact it solves
275
276 [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FC ] [ x_F ] = [b_F]
277 [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] [ x_C ] = [b_C]
278
279 in the form
280
281 b->[b_F,b_C]
282 x_F=invA_FF*b_F
283 b_C=b_C-A_CF*x_F
284 x_C=AMG(b_C)
285 b_F=b_F-A_FC*x_C
286 x_F=invA_FF*b_F
287 x<-[x_F,x_C]
288
289 should be called within a parallel region
290 barrier synconization should be performed to make sure that the input vector available
291
292 */
293
294 void Paso_Solver_solveAMG(Paso_Solver_AMG * amg, double * x, double * b) {
295 dim_t i;
296 double *r=MEMALLOC(amg->n,double);
297 double *x0=MEMALLOC(amg->n,double);
298 /*double time0=0;*/
299
300 if (amg->level==0 || amg->n_C<=500) {
301 /*if (amg->n_F<=500) {*/
302 /*time0=Paso_timer();*/
303
304 Paso_Solver_solveJacobi(amg->GS,x,b);
305
306 /* #pragma omp parallel for private(i) schedule(static)
307 for (i=0;i<amg->n;++i) r[i]=b[i];
308 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
309 Paso_Solver_solveGS(amg->GS,x0,r);
310 #pragma omp parallel for private(i) schedule(static)
311 for (i=0;i<amg->n;++i) {
312 x[i]+=x0[i];
313 }
314 */
315 /*Paso_UMFPACK1(amg->A,x,b,0);*/
316
317 /*time0=Paso_timer()-time0;
318 fprintf(stderr,"timing: DIRECT SOLVER: %e/\n",time0);*/
319 } else {
320 /* presmoothing */
321 Paso_Solver_solveJacobi(amg->GS,x,b);
322 /*
323 #pragma omp parallel for private(i) schedule(static)
324 for (i=0;i<amg->n;++i) r[i]=b[i];
325
326 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
327 Paso_Solver_solveGS(amg->GS,x0,r);
328
329 #pragma omp parallel for private(i) schedule(static)
330 for (i=0;i<amg->n;++i) {
331 x[i]+=x0[i];
332 }
333 */
334 /* end of presmoothing */
335
336 #pragma omp parallel for private(i) schedule(static)
337 for (i=0;i<amg->n;++i) r[i]=b[i];
338
339 /*r=b-Ax*/
340 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
341
342 /* b->[b_F,b_C] */
343 #pragma omp parallel for private(i) schedule(static)
344 for (i=0;i<amg->n_F;++i) amg->b_F[i]=r[amg->rows_in_F[i]];
345
346 #pragma omp parallel for private(i) schedule(static)
347 for (i=0;i<amg->n_C;++i) amg->b_C[i]=r[amg->rows_in_C[i]];
348
349 /* x_F=invA_FF*b_F */
350 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
351
352 /* b_C=b_C-A_CF*x_F */
353 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->x_F,1.,amg->b_C);
354
355 /* x_C=AMG(b_C) */
356 Paso_Solver_solveAMG(amg->AMG_of_Schur,amg->x_C,amg->b_C);
357
358 /* b_F=b_F-A_FC*x_C */
359 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_FC,amg->x_C,1.,amg->b_F);
360 /* x_F=invA_FF*b_F */
361 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
362 /* x<-[x_F,x_C] */
363
364 #pragma omp parallel for private(i) schedule(static)
365 for (i=0;i<amg->n;++i) {
366 if (amg->mask_C[i]>-1) {
367 x[i]=amg->x_C[amg->mask_C[i]];
368 } else {
369 x[i]=amg->x_F[amg->mask_F[i]];
370 }
371 }
372
373 /*postsmoothing*/
374
375 #pragma omp parallel for private(i) schedule(static)
376 for (i=0;i<amg->n;++i) r[i]=b[i];
377
378 /*r=b-Ax*/
379 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
380 Paso_Solver_solveJacobi(amg->GS,x0,r);
381
382 #pragma omp parallel for private(i) schedule(static)
383 for (i=0;i<amg->n;++i) x[i]+=x0[i];
384
385
386 /*#pragma omp parallel for private(i) schedule(static)
387 for (i=0;i<amg->n;++i) r[i]=b[i];
388
389 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
390 Paso_Solver_solveGS(amg->GS,x0,r);
391
392 #pragma omp parallel for private(i) schedule(static)
393 for (i=0;i<amg->n;++i) {
394 x[i]+=x0[i];
395 }
396 */
397 /*end of postsmoothing*/
398
399 }
400 MEMFREE(r);
401 MEMFREE(x0);
402 return;
403 }
404
405 /*
406 * $Log$
407 *
408 */

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