/[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 2113 - (show annotations)
Mon Dec 1 06:27:14 2008 UTC (12 years, 9 months ago) by artak
File MIME type: text/plain
File size: 16031 byte(s)
Temporary solution for nusty rows: a condition added 
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) {
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 time0=0,time1=0,time2=0,S=0;
85 /*Paso_Pattern* test;*/
86
87 /* identify independend set of rows/columns */
88 mis_marker=TMPMEMALLOC(n,index_t);
89 counter=TMPMEMALLOC(n,index_t);
90 out=MEMALLOC(1,Paso_Solver_AMG);
91 out->AMG_of_Schur=NULL;
92 out->inv_A_FF=NULL;
93 out->A_FF_pivot=NULL;
94 out->A_FC=NULL;
95 out->A_CF=NULL;
96 out->rows_in_F=NULL;
97 out->rows_in_C=NULL;
98 out->mask_F=NULL;
99 out->mask_C=NULL;
100 out->x_F=NULL;
101 out->b_F=NULL;
102 out->x_C=NULL;
103 out->b_C=NULL;
104 out->GS=NULL;
105 out->A=Paso_SparseMatrix_getReference(A_p);
106 /*out->GS=Paso_Solver_getGS(A_p,verbose);*/
107 out->GS=Paso_Solver_getJacobi(A_p);
108 /*out->GS->sweeps=2;*/
109 out->level=level;
110
111 if ( !(Paso_checkPtr(mis_marker) || Paso_checkPtr(out) || Paso_checkPtr(counter) ) ) {
112 /* identify independend set of rows/columns */
113 #pragma omp parallel for private(i) schedule(static)
114 for (i=0;i<n;++i) mis_marker[i]=-1;
115 /*Paso_Pattern_RS(A_p,mis_marker,0.25);*/
116 /*Paso_Pattern_Aggregiation(A_p,mis_marker,0.5);*/
117 Paso_Pattern_coup(A_p,mis_marker,0.05);
118 if (Paso_noError()) {
119 #pragma omp parallel for private(i) schedule(static)
120 for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
121 out->n=n;
122 out->n_block=n_block;
123 out->n_F=Paso_Util_cumsum(n,counter);
124 out->mask_F=MEMALLOC(n,index_t);
125 out->rows_in_F=MEMALLOC(out->n_F,index_t);
126 out->inv_A_FF=MEMALLOC(n_block*n_block*out->n_F,double);
127 out->A_FF_pivot=NULL; /* later use for block size>3 */
128 if (! (Paso_checkPtr(out->mask_F) || Paso_checkPtr(out->inv_A_FF) || Paso_checkPtr(out->rows_in_F) ) ) {
129 /* creates an index for F from mask */
130 #pragma omp parallel for private(i) schedule(static)
131 for (i = 0; i < out->n_F; ++i) out->rows_in_F[i]=-1;
132 #pragma omp parallel for private(i) schedule(static)
133 for (i = 0; i < n; ++i) {
134 if (mis_marker[i]) {
135 out->rows_in_F[counter[i]]=i;
136 out->mask_F[i]=counter[i];
137 } else {
138 out->mask_F[i]=-1;
139 }
140 }
141
142 /* Compute row-sum for getting rs(A_FF)^-1*/
143 #pragma omp parallel for private(i,iPtr,j) schedule(static)
144 for (i = 0; i < out->n_F; ++i) {
145 S=0;
146 for (iPtr=A_p->pattern->ptr[out->rows_in_F[i]];iPtr<A_p->pattern->ptr[out->rows_in_F[i] + 1]; ++iPtr) {
147 j=A_p->pattern->index[iPtr];
148 if (mis_marker[j])
149 S+=A_p->val[iPtr];
150 }
151 /* This check is to make sure we dont get some nusty rows which were not removed durring coarsing process.*/
152 /* TODO: we have to mechanism that this does not happend at all, and get rid of this 'If'. */
153 if (ABS(S)>1.e-10)
154 out->inv_A_FF[i]=1./S;
155 else
156 out->inv_A_FF[i]=1.;
157 }
158
159 if( Paso_noError()) {
160 /* if there are no nodes in the coarse level there is no more work to do */
161 out->n_C=n-out->n_F;
162 if (level<3) {
163 /*if (out->n_F>500) {*/
164 out->rows_in_C=MEMALLOC(out->n_C,index_t);
165 out->mask_C=MEMALLOC(n,index_t);
166 if (! (Paso_checkPtr(out->mask_C) || Paso_checkPtr(out->rows_in_C) ) ) {
167 /* creates an index for C from mask */
168 #pragma omp parallel for private(i) schedule(static)
169 for (i = 0; i < n; ++i) counter[i]=! mis_marker[i];
170 Paso_Util_cumsum(n,counter);
171 #pragma omp parallel for private(i) schedule(static)
172 for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
173 #pragma omp parallel for private(i) schedule(static)
174 for (i = 0; i < n; ++i) {
175 if (! mis_marker[i]) {
176 out->rows_in_C[counter[i]]=i;
177 out->mask_C[i]=counter[i];
178 } else {
179 out->mask_C[i]=-1;
180 }
181 }
182 /* get A_CF block: */
183 out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
184 if (Paso_noError()) {
185 /* get A_FC block: */
186 out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
187 /* get A_CC block: */
188 if (Paso_noError()) {
189 schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
190 /*find the pattern of the schur complement with fill in*/
191
192 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);
193
194 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));
195
196 /* copy values over*/
197 #pragma omp parallel for private(i,iPtr,j,iPtr_s,index,where_p) schedule(static)
198 for (i = 0; i < schur_withFillIn->numRows; ++i) {
199 for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
200 j=schur_withFillIn->pattern->index[iPtr];
201 iPtr_s=schur->pattern->ptr[i];
202 schur_withFillIn->val[iPtr]=0.;
203 index=&(schur->pattern->index[iPtr_s]);
204 where_p=(index_t*)bsearch(&j,
205 index,
206 schur->pattern->ptr[i + 1]-schur->pattern->ptr[i],
207 sizeof(index_t),
208 Paso_comparIndex);
209 if (where_p!=NULL) {
210 schur_withFillIn->val[iPtr]=schur->val[iPtr_s+(index_t)(where_p-index)];
211 }
212 }
213 }
214
215 if (Paso_noError()) {
216 Paso_Solver_updateIncompleteSchurComplement(schur_withFillIn,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC);
217 out->AMG_of_Schur=Paso_Solver_getAMG(schur_withFillIn,verbose,level+1);
218 Paso_SparseMatrix_free(schur);
219 }
220 /* allocate work arrays for AMG application */
221 if (Paso_noError()) {
222 out->x_F=MEMALLOC(n_block*out->n_F,double);
223 out->b_F=MEMALLOC(n_block*out->n_F,double);
224 out->x_C=MEMALLOC(n_block*out->n_C,double);
225 out->b_C=MEMALLOC(n_block*out->n_C,double);
226
227 if (! (Paso_checkPtr(out->x_F) || Paso_checkPtr(out->b_F) || Paso_checkPtr(out->x_C) || Paso_checkPtr(out->b_C) ) ) {
228 #pragma omp parallel for private(i,k) schedule(static)
229 for (i = 0; i < out->n_F; ++i) {
230 for (k=0; k<n_block;++k) {
231 out->x_F[i*n_block+k]=0.;
232 out->b_F[i*n_block+k]=0.;
233 }
234 }
235 #pragma omp parallel for private(i,k) schedule(static)
236 for (i = 0; i < out->n_C; ++i) {
237 for (k=0; k<n_block;++k) {
238 out->x_C[i*n_block+k]=0.;
239 out->b_C[i*n_block+k]=0.;
240 }
241 }
242 }
243 }
244 }
245 }
246 }
247 }
248 }
249 }
250 }
251 }
252 TMPMEMFREE(mis_marker);
253 TMPMEMFREE(counter);
254 if (Paso_noError()) {
255 if (verbose) {
256 printf("AMG: %d unknowns eliminated. %d left.\n",out->n_F,n-out->n_F);
257 if (level<3) {
258 /*if (out->n_F<500) {*/
259 printf("timing: AMG: MIS/reordering/elemination : %e/%e/%e\n",time2,time0,time1);
260 } else {
261 printf("timing: AMG: MIS: %e\n",time2);
262 }
263 }
264 return out;
265 } else {
266 Paso_Solver_AMG_free(out);
267 return NULL;
268 }
269 }
270
271 /**************************************************************/
272
273 /* apply AMG precondition b-> x
274
275 in fact it solves
276
277 [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ] [ x_F ] = [b_F]
278 [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] [ x_C ] = [b_C]
279
280 in the form
281
282 b->[b_F,b_C]
283 x_F=invA_FF*b_F
284 b_C=b_C-A_CF*x_F
285 x_C=AMG(b_C)
286 b_F=b_F-A_FC*x_C
287 x_F=invA_FF*b_F
288 x<-[x_F,x_C]
289
290 should be called within a parallel region
291 barrier synconization should be performed to make sure that the input vector available
292
293 */
294
295 void Paso_Solver_solveAMG(Paso_Solver_AMG * amg, double * x, double * b) {
296 dim_t i;
297 double *r=MEMALLOC(amg->n,double);
298 /*Paso_Solver_GS* GS=NULL;*/
299 double *x0=MEMALLOC(amg->n,double);
300 double time0=0;
301
302 if (amg->level==3) {
303 /*if (amg->n_F<=500) {*/
304 time0=Paso_timer();
305
306 Paso_Solver_solveJacobi(amg->GS,x,b);
307
308 /* #pragma omp parallel for private(i) schedule(static)
309 for (i=0;i<amg->n;++i) r[i]=b[i];
310 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
311 Paso_Solver_solveGS(amg->GS,x0,r);
312 #pragma omp parallel for private(i) schedule(static)
313 for (i=0;i<amg->n;++i) {
314 x[i]+=x0[i];
315 }
316 */
317 /*Paso_UMFPACK1(amg->A,x,b,0);*/
318
319 time0=Paso_timer()-time0;
320 /*fprintf(stderr,"timing: DIRECT SOLVER: %e/\n",time0);*/
321 } else {
322
323 /* presmoothing */
324 Paso_Solver_solveJacobi(amg->GS,x,b);
325 /*
326 #pragma omp parallel for private(i) schedule(static)
327 for (i=0;i<amg->n;++i) r[i]=b[i];
328
329 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
330 Paso_Solver_solveGS(amg->GS,x0,r);
331
332 #pragma omp parallel for private(i) schedule(static)
333 for (i=0;i<amg->n;++i) {
334 x[i]+=x0[i];
335 }
336 */
337 /* end of presmoothing */
338
339 #pragma omp parallel for private(i) schedule(static)
340 for (i=0;i<amg->n;++i) r[i]=b[i];
341
342 /*r=b-Ax*/
343 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
344
345 /* b->[b_F,b_C] */
346 #pragma omp parallel for private(i) schedule(static)
347 for (i=0;i<amg->n_F;++i) amg->b_F[i]=r[amg->rows_in_F[i]];
348
349 #pragma omp parallel for private(i) schedule(static)
350 for (i=0;i<amg->n_C;++i) amg->b_C[i]=r[amg->rows_in_C[i]];
351
352 /* x_F=invA_FF*b_F */
353 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
354
355 /* b_C=b_C-A_CF*x_F */
356 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->x_F,1.,amg->b_C);
357
358 /* x_C=AMG(b_C) */
359 Paso_Solver_solveAMG(amg->AMG_of_Schur,amg->x_C,amg->b_C);
360
361 /* b_F=b_F-A_FC*x_C */
362 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_FC,amg->x_C,1.,amg->b_F);
363 /* x_F=invA_FF*b_F */
364 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
365 /* x<-[x_F,x_C] */
366
367 #pragma omp parallel for private(i) schedule(static)
368 for (i=0;i<amg->n;++i) {
369 if (amg->mask_C[i]>-1) {
370 x[i]=amg->x_C[amg->mask_C[i]];
371 } else {
372 x[i]=amg->x_F[amg->mask_F[i]];
373 }
374 }
375
376 /*postsmoothing*/
377
378 #pragma omp parallel for private(i) schedule(static)
379 for (i=0;i<amg->n;++i) r[i]=b[i];
380
381 /*r=b-Ax*/
382 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
383 Paso_Solver_solveJacobi(amg->GS,x0,r);
384
385 #pragma omp parallel for private(i) schedule(static)
386 for (i=0;i<amg->n;++i) x[i]+=x0[i];
387
388
389 /*#pragma omp parallel for private(i) schedule(static)
390 for (i=0;i<amg->n;++i) r[i]=b[i];
391
392 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
393 Paso_Solver_solveGS(amg->GS,x0,r);
394
395 #pragma omp parallel for private(i) schedule(static)
396 for (i=0;i<amg->n;++i) {
397 x[i]+=x0[i];
398 }
399 */
400 /*end of postsmoothing*/
401
402 }
403 MEMFREE(r);
404 MEMFREE(x0);
405 return;
406 }
407
408 /*
409 * $Log$
410 *
411 */

  ViewVC Help
Powered by ViewVC 1.1.26