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

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Revision 2662 - (hide annotations)
Tue Sep 15 03:05:23 2009 UTC (10 years, 5 months ago) by artak
File MIME type: text/plain
File size: 16898 byte(s)
Migrating to block_sizes greather than 3 made easy.
1 jfenwick 1851
2     /*******************************************************
3     *
4 jfenwick 2548 * Copyright (c) 2003-2009 by University of Queensland
5 jfenwick 1851 * 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 artak 2475 /* Paso: AMG preconditioner */
18 jfenwick 1851
19     /**************************************************************/
20    
21 jfenwick 2625 /* Author: artak@uq.edu.au */
22 jfenwick 1851
23     /**************************************************************/
24    
25     #include "Paso.h"
26     #include "Solver.h"
27 artak 2475 #include "Options.h"
28 jfenwick 1851 #include "PasoUtil.h"
29 artak 1931 #include "UMFPACK.h"
30 artak 2507 #include "MKL.h"
31     #include "SystemMatrix.h"
32 phornby 1917 #include "Pattern_coupling.h"
33 jfenwick 1851
34     /**************************************************************/
35    
36     /* free all memory used by AMG */
37    
38 artak 2659 void Paso_Solver_AMG_System_free(Paso_Solver_AMG_System * in) {
39 artak 2662 dim_t i;
40 artak 2659 if (in!=NULL) {
41 artak 2662 for (i=0;i<in->block_size;++i) {
42     Paso_Solver_AMG_free(in->amgblock[i]);
43     Paso_SparseMatrix_free(in->block[i]);
44     }
45 artak 2659 MEMFREE(in);
46     }
47     }
48    
49    
50     /* free all memory used by AMG */
51    
52 jfenwick 1851 void Paso_Solver_AMG_free(Paso_Solver_AMG * in) {
53     if (in!=NULL) {
54     Paso_Solver_AMG_free(in->AMG_of_Schur);
55 artak 2112 Paso_Solver_Jacobi_free(in->GS);
56 jfenwick 1851 MEMFREE(in->inv_A_FF);
57     MEMFREE(in->A_FF_pivot);
58     Paso_SparseMatrix_free(in->A_FC);
59     Paso_SparseMatrix_free(in->A_CF);
60 artak 2556 Paso_SparseMatrix_free(in->A);
61 jfenwick 1851 MEMFREE(in->rows_in_F);
62     MEMFREE(in->rows_in_C);
63     MEMFREE(in->mask_F);
64     MEMFREE(in->mask_C);
65     MEMFREE(in->x_F);
66     MEMFREE(in->b_F);
67     MEMFREE(in->x_C);
68     MEMFREE(in->b_C);
69 gross 2551 #ifdef MKL
70     #else
71     #ifdef UMFPACK
72     Paso_UMFPACK1_free((Paso_UMFPACK_Handler*)(in->solver));
73     #endif
74     #endif
75     in->solver=NULL;
76     MEMFREE(in->b_C);
77 jfenwick 1851 MEMFREE(in);
78     }
79     }
80    
81     /**************************************************************/
82    
83     /* constructs the block-block factorization of
84    
85     [ A_FF A_FC ]
86     A_p=
87     [ A_CF A_FF ]
88    
89     to
90    
91     [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ]
92     [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ]
93    
94    
95     where S=A_FF-ACF*invA_FF*A_FC within the shape of S
96    
97     then AMG is applied to S again until S becomes empty
98    
99     */
100 artak 2520 Paso_Solver_AMG* Paso_Solver_getAMG(Paso_SparseMatrix *A_p,dim_t level,Paso_Options* options) {
101 jfenwick 1851 Paso_Solver_AMG* out=NULL;
102 artak 2556 Paso_Pattern* temp1=NULL;
103     Paso_Pattern* temp2=NULL;
104 artak 2520 bool_t verbose=options->verbose;
105 jfenwick 1851 dim_t n=A_p->numRows;
106     dim_t n_block=A_p->row_block_size;
107     index_t* mis_marker=NULL;
108 artak 1881 index_t* counter=NULL;
109     index_t iPtr,*index, *where_p, iPtr_s;
110 artak 2107 dim_t i,k,j;
111 jfenwick 1851 Paso_SparseMatrix * schur=NULL;
112 artak 1881 Paso_SparseMatrix * schur_withFillIn=NULL;
113 artak 2381 double S=0;
114 artak 2475
115 artak 2439 /*Make sure we have block sizes 1*/
116 gross 2550 if (A_p->col_block_size>1) {
117     Paso_setError(TYPE_ERROR,"Paso_Solver_getAMG: AMG requires column block size 1.");
118     return NULL;
119     }
120     if (A_p->row_block_size>1) {
121     Paso_setError(TYPE_ERROR,"Paso_Solver_getAMG: AMG requires row block size 1.");
122     return NULL;
123     }
124 gross 2551 out=MEMALLOC(1,Paso_Solver_AMG);
125 jfenwick 1851 /* identify independend set of rows/columns */
126     mis_marker=TMPMEMALLOC(n,index_t);
127     counter=TMPMEMALLOC(n,index_t);
128 gross 2551 if ( !( Paso_checkPtr(mis_marker) || Paso_checkPtr(counter) || Paso_checkPtr(out)) ) {
129     out->AMG_of_Schur=NULL;
130     out->inv_A_FF=NULL;
131     out->A_FF_pivot=NULL;
132     out->A_FC=NULL;
133     out->A_CF=NULL;
134     out->rows_in_F=NULL;
135     out->rows_in_C=NULL;
136     out->mask_F=NULL;
137     out->mask_C=NULL;
138     out->x_F=NULL;
139     out->b_F=NULL;
140     out->x_C=NULL;
141     out->b_C=NULL;
142     out->GS=NULL;
143     out->A=Paso_SparseMatrix_getReference(A_p);
144     out->GS=NULL;
145     out->solver=NULL;
146     /*out->GS=Paso_Solver_getGS(A_p,verbose);*/
147     out->level=level;
148 artak 2661 out->n=n;
149     out->n_block=n_block;
150 artak 2556
151 gross 2551 if (level==0 || n<=options->min_coarse_matrix_size) {
152     out->coarsest_level=TRUE;
153     #ifdef MKL
154     #else
155     #ifdef UMFPACK
156     #else
157     out->GS=Paso_Solver_getJacobi(A_p);
158     #endif
159     #endif
160     } else {
161     out->coarsest_level=FALSE;
162     out->GS=Paso_Solver_getJacobi(A_p);
163 artak 2442
164 gross 2551 /* identify independend set of rows/columns */
165     #pragma omp parallel for private(i) schedule(static)
166     for (i=0;i<n;++i) mis_marker[i]=-1;
167    
168     if (options->coarsening_method == PASO_YAIR_SHAPIRA_COARSENING) {
169 artak 2652 Paso_Pattern_YS(A_p,mis_marker,options->coarsening_threshold);
170 gross 2551 }
171     else if (options->coarsening_method == PASO_RUGE_STUEBEN_COARSENING) {
172     Paso_Pattern_RS(A_p,mis_marker,options->coarsening_threshold);
173     }
174     else if (options->coarsening_method == PASO_AGGREGATION_COARSENING) {
175     Paso_Pattern_Aggregiation(A_p,mis_marker,options->coarsening_threshold);
176     }
177     else {
178     /*Default coarseneing*/
179 artak 2659 Paso_Pattern_RS(A_p,mis_marker,options->coarsening_threshold);
180     /*Paso_Pattern_YS(A_p,mis_marker,options->coarsening_threshold);*/
181 artak 2556 /*Paso_Pattern_Aggregiation(A_p,mis_marker,options->coarsening_threshold);*/
182 gross 2551 }
183 artak 2475
184 gross 2551 if (Paso_noError()) {
185     #pragma omp parallel for private(i) schedule(static)
186     for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
187     out->n_F=Paso_Util_cumsum(n,counter);
188     out->mask_F=MEMALLOC(n,index_t);
189     out->rows_in_F=MEMALLOC(out->n_F,index_t);
190     out->inv_A_FF=MEMALLOC(n_block*n_block*out->n_F,double);
191     out->A_FF_pivot=NULL; /* later use for block size>3 */
192     if (! (Paso_checkPtr(out->mask_F) || Paso_checkPtr(out->inv_A_FF) || Paso_checkPtr(out->rows_in_F) ) ) {
193 jfenwick 1851 /* creates an index for F from mask */
194 artak 2107 #pragma omp parallel for private(i) schedule(static)
195 jfenwick 1851 for (i = 0; i < out->n_F; ++i) out->rows_in_F[i]=-1;
196 artak 2107 #pragma omp parallel for private(i) schedule(static)
197 jfenwick 1851 for (i = 0; i < n; ++i) {
198     if (mis_marker[i]) {
199     out->rows_in_F[counter[i]]=i;
200     out->mask_F[i]=counter[i];
201     } else {
202     out->mask_F[i]=-1;
203     }
204     }
205 artak 2107
206     /* Compute row-sum for getting rs(A_FF)^-1*/
207 artak 2131 #pragma omp parallel for private(i,iPtr,j,S) schedule(static)
208 artak 1881 for (i = 0; i < out->n_F; ++i) {
209 artak 2107 S=0;
210 artak 2659 /*printf("[%d ]: [%d] -> ",i, out->rows_in_F[i]);*/
211 artak 1881 for (iPtr=A_p->pattern->ptr[out->rows_in_F[i]];iPtr<A_p->pattern->ptr[out->rows_in_F[i] + 1]; ++iPtr) {
212 artak 1975 j=A_p->pattern->index[iPtr];
213 artak 2556 /*if (j==out->rows_in_F[i]) printf("diagonal %e",A_p->val[iPtr]);*/
214 artak 2659 if (mis_marker[j])
215     S+=A_p->val[iPtr];
216 artak 1881 }
217 artak 2659 /*printf("-> %e \n",S);*/
218 artak 2442 out->inv_A_FF[i]=1./S;
219 artak 1881 }
220 gross 2551 }
221     }
222 jfenwick 1851
223 gross 2551 if ( Paso_noError()) {
224 jfenwick 1851 /* if there are no nodes in the coarse level there is no more work to do */
225     out->n_C=n-out->n_F;
226 gross 2551
227     /*if (out->n_F>500) */
228     out->rows_in_C=MEMALLOC(out->n_C,index_t);
229     out->mask_C=MEMALLOC(n,index_t);
230     if (! (Paso_checkPtr(out->mask_C) || Paso_checkPtr(out->rows_in_C) ) ) {
231     /* creates an index for C from mask */
232     #pragma omp parallel for private(i) schedule(static)
233     for (i = 0; i < n; ++i) counter[i]=! mis_marker[i];
234     Paso_Util_cumsum(n,counter);
235     #pragma omp parallel for private(i) schedule(static)
236     for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
237     #pragma omp parallel for private(i) schedule(static)
238     for (i = 0; i < n; ++i) {
239     if (! mis_marker[i]) {
240 jfenwick 1851 out->rows_in_C[counter[i]]=i;
241     out->mask_C[i]=counter[i];
242     } else {
243     out->mask_C[i]=-1;
244     }
245 gross 2551 }
246     }
247     }
248     if ( Paso_noError()) {
249     /* get A_CF block: */
250     out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
251     /* get A_FC block: */
252     out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
253     /* get A_CC block: */
254     schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
255    
256     }
257     if ( Paso_noError()) {
258     /*find the pattern of the schur complement with fill in*/
259 artak 2556 temp1=Paso_Pattern_multiply(PATTERN_FORMAT_DEFAULT,out->A_CF->pattern,out->A_FC->pattern);
260     temp2=Paso_Pattern_binop(PATTERN_FORMAT_DEFAULT, schur->pattern, temp1);
261     schur_withFillIn=Paso_SparseMatrix_alloc(A_p->type,temp2,1,1, TRUE);
262     Paso_Pattern_free(temp1);
263     Paso_Pattern_free(temp2);
264 gross 2551 }
265     if ( Paso_noError()) {
266     /* copy values over*/
267     #pragma omp parallel for private(i,iPtr,j,iPtr_s,index,where_p) schedule(static)
268     for (i = 0; i < schur_withFillIn->numRows; ++i) {
269     for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
270     j=schur_withFillIn->pattern->index[iPtr];
271     iPtr_s=schur->pattern->ptr[i];
272     schur_withFillIn->val[iPtr]=0.;
273     index=&(schur->pattern->index[iPtr_s]);
274     where_p=(index_t*)bsearch(&j,
275 artak 2107 index,
276     schur->pattern->ptr[i + 1]-schur->pattern->ptr[i],
277     sizeof(index_t),
278     Paso_comparIndex);
279 gross 2551 if (where_p!=NULL) {
280     schur_withFillIn->val[iPtr]=schur->val[iPtr_s+(index_t)(where_p-index)];
281     }
282     }
283     }
284     Paso_Solver_updateIncompleteSchurComplement(schur_withFillIn,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC);
285     out->AMG_of_Schur=Paso_Solver_getAMG(schur_withFillIn,level-1,options);
286     }
287     /* allocate work arrays for AMG application */
288     if (Paso_noError()) {
289     out->x_F=MEMALLOC(n_block*out->n_F,double);
290     out->b_F=MEMALLOC(n_block*out->n_F,double);
291     out->x_C=MEMALLOC(n_block*out->n_C,double);
292     out->b_C=MEMALLOC(n_block*out->n_C,double);
293 artak 1890
294 gross 2551 if (! (Paso_checkPtr(out->x_F) || Paso_checkPtr(out->b_F) || Paso_checkPtr(out->x_C) || Paso_checkPtr(out->b_C) ) ) {
295     #pragma omp parallel for private(i,k) schedule(static)
296     for (i = 0; i < out->n_F; ++i) {
297     for (k=0; k<n_block;++k) {
298     out->x_F[i*n_block+k]=0.;
299     out->b_F[i*n_block+k]=0.;
300 jfenwick 1851 }
301 gross 2551 }
302     #pragma omp parallel for private(i,k) schedule(static)
303     for (i = 0; i < out->n_C; ++i) {
304     for (k=0; k<n_block;++k) {
305     out->x_C[i*n_block+k]=0.;
306     out->b_C[i*n_block+k]=0.;
307     }
308     }
309     }
310 jfenwick 1851 }
311     }
312     }
313     TMPMEMFREE(mis_marker);
314     TMPMEMFREE(counter);
315 gross 2551 Paso_SparseMatrix_free(schur);
316     Paso_SparseMatrix_free(schur_withFillIn);
317 jfenwick 1851 if (Paso_noError()) {
318 artak 2524 if (verbose && level>0 && !out->coarsest_level) {
319 gross 2551 printf("AMG: level: %d: %d unknowns eliminated. %d left.\n",level, out->n_F,out->n_C);
320 jfenwick 1851 }
321     return out;
322     } else {
323     Paso_Solver_AMG_free(out);
324     return NULL;
325     }
326     }
327    
328     /**************************************************************/
329    
330     /* apply AMG precondition b-> x
331    
332     in fact it solves
333    
334 artak 2381 [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FC ] [ x_F ] = [b_F]
335 jfenwick 1851 [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] [ x_C ] = [b_C]
336    
337     in the form
338    
339     b->[b_F,b_C]
340     x_F=invA_FF*b_F
341     b_C=b_C-A_CF*x_F
342     x_C=AMG(b_C)
343     b_F=b_F-A_FC*x_C
344     x_F=invA_FF*b_F
345     x<-[x_F,x_C]
346    
347     should be called within a parallel region
348     barrier synconization should be performed to make sure that the input vector available
349    
350     */
351    
352     void Paso_Solver_solveAMG(Paso_Solver_AMG * amg, double * x, double * b) {
353 artak 2107 dim_t i;
354 artak 2507 double time0=0;
355 gross 2551 double *r=NULL, *x0=NULL;
356 artak 2509 bool_t verbose=0;
357 artak 2507 #ifdef MKL
358 gross 2551 Paso_SparseMatrix *temp=NULL;
359     #else
360     #ifdef UMFPACK
361     Paso_UMFPACK_Handler * ptr=NULL;
362     #endif
363 artak 2507 #endif
364 gross 2551 r=MEMALLOC(amg->n,double);
365     x0=MEMALLOC(amg->n,double);
366 artak 2507
367 artak 2524 if (amg->coarsest_level) {
368 artak 2507
369     time0=Paso_timer();
370     #ifdef MKL
371 gross 2551 temp=Paso_SparseMatrix_alloc(MATRIX_FORMAT_BLK1 + MATRIX_FORMAT_OFFSET1, amg->A->pattern,1,1, FALSE);
372 artak 2507 #pragma omp parallel for private(i) schedule(static)
373     for (i=0;i<amg->A->len;++i) {
374     temp->val[i]=amg->A->val[i];
375     }
376     Paso_MKL1(temp,x,b,0);
377     Paso_SparseMatrix_free(temp);
378     #else
379 gross 2551 #ifdef UMFPACK
380     ptr=(Paso_UMFPACK_Handler *)(amg->solver);
381 artak 2652 Paso_UMFPACK1(&ptr,amg->A,x,b,verbose);
382 gross 2551 amg->solver=(void*) ptr;
383     #else
384     Paso_Solver_solveJacobi(amg->GS,x,b);
385     #endif
386 artak 2507 #endif
387 artak 2475 time0=Paso_timer()-time0;
388 artak 2652 if (verbose) fprintf(stderr,"timing: DIRECT SOLVER: %e\n",time0);
389 artak 2507
390 jfenwick 1851 } else {
391 artak 1902 /* presmoothing */
392 artak 2507 time0=Paso_timer();
393 artak 2112 Paso_Solver_solveJacobi(amg->GS,x,b);
394 artak 2507 time0=Paso_timer()-time0;
395     if (verbose) fprintf(stderr,"timing: Presmooting: %e\n",time0);
396 artak 1931 /* end of presmoothing */
397 artak 1939
398 artak 2507
399     time0=Paso_timer();
400 artak 1890 #pragma omp parallel for private(i) schedule(static)
401     for (i=0;i<amg->n;++i) r[i]=b[i];
402    
403     /*r=b-Ax*/
404     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
405 artak 1954
406 jfenwick 1851 /* b->[b_F,b_C] */
407 artak 1954 #pragma omp parallel for private(i) schedule(static)
408     for (i=0;i<amg->n_F;++i) amg->b_F[i]=r[amg->rows_in_F[i]];
409    
410     #pragma omp parallel for private(i) schedule(static)
411     for (i=0;i<amg->n_C;++i) amg->b_C[i]=r[amg->rows_in_C[i]];
412 artak 1890
413 jfenwick 1851 /* x_F=invA_FF*b_F */
414 artak 1954 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
415 artak 1890
416 jfenwick 1851 /* b_C=b_C-A_CF*x_F */
417     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->x_F,1.,amg->b_C);
418 artak 1890
419 artak 2507 time0=Paso_timer()-time0;
420     if (verbose) fprintf(stderr,"timing: Before next level: %e\n",time0);
421    
422 jfenwick 1851 /* x_C=AMG(b_C) */
423     Paso_Solver_solveAMG(amg->AMG_of_Schur,amg->x_C,amg->b_C);
424 artak 1890
425 artak 2507 time0=Paso_timer();
426 jfenwick 1851 /* b_F=b_F-A_FC*x_C */
427     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_FC,amg->x_C,1.,amg->b_F);
428     /* x_F=invA_FF*b_F */
429 artak 1954 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
430 jfenwick 1851 /* x<-[x_F,x_C] */
431 artak 2113
432 artak 1954 #pragma omp parallel for private(i) schedule(static)
433     for (i=0;i<amg->n;++i) {
434     if (amg->mask_C[i]>-1) {
435 artak 2107 x[i]=amg->x_C[amg->mask_C[i]];
436 artak 1954 } else {
437 artak 2107 x[i]=amg->x_F[amg->mask_F[i]];
438 artak 1954 }
439 jfenwick 1851 }
440 artak 1954
441 artak 2507 time0=Paso_timer()-time0;
442     if (verbose) fprintf(stderr,"timing: After next level: %e\n",time0);
443    
444 artak 1931 /*postsmoothing*/
445 artak 2507 time0=Paso_timer();
446 artak 1954 #pragma omp parallel for private(i) schedule(static)
447     for (i=0;i<amg->n;++i) r[i]=b[i];
448 artak 2107
449 artak 2442 /*r=b-Ax */
450 artak 1954 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
451 artak 2112 Paso_Solver_solveJacobi(amg->GS,x0,r);
452 artak 2107
453     #pragma omp parallel for private(i) schedule(static)
454     for (i=0;i<amg->n;++i) x[i]+=x0[i];
455    
456 artak 2507 time0=Paso_timer()-time0;
457     if (verbose) fprintf(stderr,"timing: Postsmoothing: %e\n",time0);
458 artak 2509
459 artak 1931 /*end of postsmoothing*/
460    
461 jfenwick 1851 }
462 artak 1890 MEMFREE(r);
463 artak 1954 MEMFREE(x0);
464 gross 2551 return;
465 jfenwick 1851 }

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