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

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Revision 2381 - (show annotations)
Tue Apr 14 03:46:59 2009 UTC (10 years, 6 months ago) by artak
File MIME type: text/plain
File size: 15783 byte(s)
Ruge Stuben and Aggregiation is added for testing performance of AMG solver.
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 /*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_coup(A_p,mis_marker,couplingParam);*/
116 Paso_Pattern_RS(A_p,mis_marker,couplingParam);
117 /*Paso_Pattern_Aggregiation(A_p,mis_marker,couplingParam);*/
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,S) 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 out->inv_A_FF[i]=1./S;
152 }
153
154 if( Paso_noError()) {
155 /* if there are no nodes in the coarse level there is no more work to do */
156 out->n_C=n-out->n_F;
157 if (level>0 && out->n_C>500) {
158 /*if (out->n_F>500) {*/
159 out->rows_in_C=MEMALLOC(out->n_C,index_t);
160 out->mask_C=MEMALLOC(n,index_t);
161 if (! (Paso_checkPtr(out->mask_C) || Paso_checkPtr(out->rows_in_C) ) ) {
162 /* creates an index for C from mask */
163 #pragma omp parallel for private(i) schedule(static)
164 for (i = 0; i < n; ++i) counter[i]=! mis_marker[i];
165 Paso_Util_cumsum(n,counter);
166 #pragma omp parallel for private(i) schedule(static)
167 for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
168 #pragma omp parallel for private(i) schedule(static)
169 for (i = 0; i < n; ++i) {
170 if (! mis_marker[i]) {
171 out->rows_in_C[counter[i]]=i;
172 out->mask_C[i]=counter[i];
173 } else {
174 out->mask_C[i]=-1;
175 }
176 }
177 /* get A_CF block: */
178 out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
179 if (Paso_noError()) {
180 /* get A_FC block: */
181 out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
182 /* get A_CC block: */
183 if (Paso_noError()) {
184 schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
185 /*find the pattern of the schur complement with fill in*/
186
187 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);
188
189 /*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));*/
190
191 /* copy values over*/
192 #pragma omp parallel for private(i,iPtr,j,iPtr_s,index,where_p) schedule(static)
193 for (i = 0; i < schur_withFillIn->numRows; ++i) {
194 for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
195 j=schur_withFillIn->pattern->index[iPtr];
196 iPtr_s=schur->pattern->ptr[i];
197 schur_withFillIn->val[iPtr]=0.;
198 index=&(schur->pattern->index[iPtr_s]);
199 where_p=(index_t*)bsearch(&j,
200 index,
201 schur->pattern->ptr[i + 1]-schur->pattern->ptr[i],
202 sizeof(index_t),
203 Paso_comparIndex);
204 if (where_p!=NULL) {
205 schur_withFillIn->val[iPtr]=schur->val[iPtr_s+(index_t)(where_p-index)];
206 }
207 }
208 }
209
210 if (Paso_noError()) {
211 Paso_Solver_updateIncompleteSchurComplement(schur_withFillIn,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC);
212 out->AMG_of_Schur=Paso_Solver_getAMG(schur_withFillIn,verbose,level-1,couplingParam);
213 Paso_SparseMatrix_free(schur);
214 }
215 /* allocate work arrays for AMG application */
216 if (Paso_noError()) {
217 out->x_F=MEMALLOC(n_block*out->n_F,double);
218 out->b_F=MEMALLOC(n_block*out->n_F,double);
219 out->x_C=MEMALLOC(n_block*out->n_C,double);
220 out->b_C=MEMALLOC(n_block*out->n_C,double);
221
222 if (! (Paso_checkPtr(out->x_F) || Paso_checkPtr(out->b_F) || Paso_checkPtr(out->x_C) || Paso_checkPtr(out->b_C) ) ) {
223 #pragma omp parallel for private(i,k) schedule(static)
224 for (i = 0; i < out->n_F; ++i) {
225 for (k=0; k<n_block;++k) {
226 out->x_F[i*n_block+k]=0.;
227 out->b_F[i*n_block+k]=0.;
228 }
229 }
230 #pragma omp parallel for private(i,k) schedule(static)
231 for (i = 0; i < out->n_C; ++i) {
232 for (k=0; k<n_block;++k) {
233 out->x_C[i*n_block+k]=0.;
234 out->b_C[i*n_block+k]=0.;
235 }
236 }
237 }
238 }
239 }
240 }
241 }
242 }
243 }
244 }
245 }
246 }
247 TMPMEMFREE(mis_marker);
248 TMPMEMFREE(counter);
249 if (Paso_noError()) {
250 if (verbose) {
251 printf("AMG: %d unknowns eliminated. %d left.\n",out->n_F,n-out->n_F);
252 /*if (level>0 && out->n_F>500) {*/
253 /* if (out->n_F<500) {*/
254 /* printf("timing: AMG: MIS/reordering/elemination : %e/%e\n",time0,time1);
255 } else {
256 printf("timing: AMG: MIS: %e\n",time2);
257 }*/
258 }
259 return out;
260 } else {
261 Paso_Solver_AMG_free(out);
262 return NULL;
263 }
264 }
265
266 /**************************************************************/
267
268 /* apply AMG precondition b-> x
269
270 in fact it solves
271
272 [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FC ] [ x_F ] = [b_F]
273 [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] [ x_C ] = [b_C]
274
275 in the form
276
277 b->[b_F,b_C]
278 x_F=invA_FF*b_F
279 b_C=b_C-A_CF*x_F
280 x_C=AMG(b_C)
281 b_F=b_F-A_FC*x_C
282 x_F=invA_FF*b_F
283 x<-[x_F,x_C]
284
285 should be called within a parallel region
286 barrier synconization should be performed to make sure that the input vector available
287
288 */
289
290 void Paso_Solver_solveAMG(Paso_Solver_AMG * amg, double * x, double * b) {
291 dim_t i;
292 double *r=MEMALLOC(amg->n,double);
293 double *x0=MEMALLOC(amg->n,double);
294 /*double time0=0;*/
295
296 if (amg->level==0 || amg->n_C<=500) {
297 /*if (amg->n_F<=500) {*/
298 /*time0=Paso_timer();*/
299
300 Paso_Solver_solveJacobi(amg->GS,x,b);
301
302 /* #pragma omp parallel for private(i) schedule(static)
303 for (i=0;i<amg->n;++i) r[i]=b[i];
304 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
305 Paso_Solver_solveGS(amg->GS,x0,r);
306 #pragma omp parallel for private(i) schedule(static)
307 for (i=0;i<amg->n;++i) {
308 x[i]+=x0[i];
309 }
310 */
311
312 /*Paso_UMFPACK1(amg->A,x,b,0);*/
313
314 /*time0=Paso_timer()-time0;
315 fprintf(stderr,"timing: DIRECT SOLVER: %e/\n",time0);*/
316 } else {
317
318 /* presmoothing */
319 Paso_Solver_solveJacobi(amg->GS,x,b);
320 /*
321 #pragma omp parallel for private(i) schedule(static)
322 for (i=0;i<amg->n;++i) r[i]=b[i];
323
324 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
325 Paso_Solver_solveGS(amg->GS,x0,r);
326
327 #pragma omp parallel for private(i) schedule(static)
328 for (i=0;i<amg->n;++i) {
329 x[i]+=x0[i];
330 }
331 */
332 /* end of presmoothing */
333
334 #pragma omp parallel for private(i) schedule(static)
335 for (i=0;i<amg->n;++i) r[i]=b[i];
336
337 /*r=b-Ax*/
338 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
339
340 /* b->[b_F,b_C] */
341 #pragma omp parallel for private(i) schedule(static)
342 for (i=0;i<amg->n_F;++i) amg->b_F[i]=r[amg->rows_in_F[i]];
343
344 #pragma omp parallel for private(i) schedule(static)
345 for (i=0;i<amg->n_C;++i) amg->b_C[i]=r[amg->rows_in_C[i]];
346
347 /* x_F=invA_FF*b_F */
348 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
349
350 /* b_C=b_C-A_CF*x_F */
351 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->x_F,1.,amg->b_C);
352
353 /* x_C=AMG(b_C) */
354 Paso_Solver_solveAMG(amg->AMG_of_Schur,amg->x_C,amg->b_C);
355
356 /* b_F=b_F-A_FC*x_C */
357 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_FC,amg->x_C,1.,amg->b_F);
358 /* x_F=invA_FF*b_F */
359 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
360 /* x<-[x_F,x_C] */
361
362 #pragma omp parallel for private(i) schedule(static)
363 for (i=0;i<amg->n;++i) {
364 if (amg->mask_C[i]>-1) {
365 x[i]=amg->x_C[amg->mask_C[i]];
366 } else {
367 x[i]=amg->x_F[amg->mask_F[i]];
368 }
369 }
370
371 /*postsmoothing*/
372
373 #pragma omp parallel for private(i) schedule(static)
374 for (i=0;i<amg->n;++i) r[i]=b[i];
375
376 /*r=b-Ax*/
377 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
378 Paso_Solver_solveJacobi(amg->GS,x0,r);
379
380 #pragma omp parallel for private(i) schedule(static)
381 for (i=0;i<amg->n;++i) x[i]+=x0[i];
382
383
384 /*#pragma omp parallel for private(i) schedule(static)
385 for (i=0;i<amg->n;++i) r[i]=b[i];
386
387 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
388 Paso_Solver_solveGS(amg->GS,x0,r);
389
390 #pragma omp parallel for private(i) schedule(static)
391 for (i=0;i<amg->n;++i) {
392 x[i]+=x0[i];
393 }
394 */
395 /*end of postsmoothing*/
396
397 }
398 MEMFREE(r);
399 MEMFREE(x0);
400 return;
401 }
402
403 /*
404 * $Log$
405 *
406 */

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