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

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Revision 2652 - (hide annotations)
Mon Sep 7 05:04:45 2009 UTC (10 years, 5 months ago) by artak
File MIME type: text/plain
File size: 16583 byte(s)
Paso_Pattern_coup changed to Paso_Pattern_YS for making clear that it refers to YAIR-SHAPIRA coarsenenig.
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     void Paso_Solver_AMG_free(Paso_Solver_AMG * in) {
39     if (in!=NULL) {
40     Paso_Solver_AMG_free(in->AMG_of_Schur);
41 artak 2112 Paso_Solver_Jacobi_free(in->GS);
42 jfenwick 1851 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 artak 2556 Paso_SparseMatrix_free(in->A);
47 jfenwick 1851 MEMFREE(in->rows_in_F);
48     MEMFREE(in->rows_in_C);
49     MEMFREE(in->mask_F);
50     MEMFREE(in->mask_C);
51     MEMFREE(in->x_F);
52     MEMFREE(in->b_F);
53     MEMFREE(in->x_C);
54     MEMFREE(in->b_C);
55 gross 2551 #ifdef MKL
56     #else
57     #ifdef UMFPACK
58     Paso_UMFPACK1_free((Paso_UMFPACK_Handler*)(in->solver));
59     #endif
60     #endif
61     in->solver=NULL;
62     MEMFREE(in->b_C);
63 jfenwick 1851 MEMFREE(in);
64     }
65     }
66    
67     /**************************************************************/
68    
69     /* constructs the block-block factorization of
70    
71     [ A_FF A_FC ]
72     A_p=
73     [ A_CF A_FF ]
74    
75     to
76    
77     [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ]
78     [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ]
79    
80    
81     where S=A_FF-ACF*invA_FF*A_FC within the shape of S
82    
83     then AMG is applied to S again until S becomes empty
84    
85     */
86 artak 2520 Paso_Solver_AMG* Paso_Solver_getAMG(Paso_SparseMatrix *A_p,dim_t level,Paso_Options* options) {
87 jfenwick 1851 Paso_Solver_AMG* out=NULL;
88 artak 2556 Paso_Pattern* temp1=NULL;
89     Paso_Pattern* temp2=NULL;
90 artak 2520 bool_t verbose=options->verbose;
91 jfenwick 1851 dim_t n=A_p->numRows;
92     dim_t n_block=A_p->row_block_size;
93     index_t* mis_marker=NULL;
94 artak 1881 index_t* counter=NULL;
95     index_t iPtr,*index, *where_p, iPtr_s;
96 artak 2107 dim_t i,k,j;
97 jfenwick 1851 Paso_SparseMatrix * schur=NULL;
98 artak 1881 Paso_SparseMatrix * schur_withFillIn=NULL;
99 artak 2381 double S=0;
100 artak 2475
101 artak 2439 /*Make sure we have block sizes 1*/
102 gross 2550 if (A_p->col_block_size>1) {
103     Paso_setError(TYPE_ERROR,"Paso_Solver_getAMG: AMG requires column block size 1.");
104     return NULL;
105     }
106     if (A_p->row_block_size>1) {
107     Paso_setError(TYPE_ERROR,"Paso_Solver_getAMG: AMG requires row block size 1.");
108     return NULL;
109     }
110 gross 2551 out=MEMALLOC(1,Paso_Solver_AMG);
111 jfenwick 1851 /* identify independend set of rows/columns */
112     mis_marker=TMPMEMALLOC(n,index_t);
113     counter=TMPMEMALLOC(n,index_t);
114 gross 2551 if ( !( Paso_checkPtr(mis_marker) || Paso_checkPtr(counter) || Paso_checkPtr(out)) ) {
115     out->AMG_of_Schur=NULL;
116     out->inv_A_FF=NULL;
117     out->A_FF_pivot=NULL;
118     out->A_FC=NULL;
119     out->A_CF=NULL;
120     out->rows_in_F=NULL;
121     out->rows_in_C=NULL;
122     out->mask_F=NULL;
123     out->mask_C=NULL;
124     out->x_F=NULL;
125     out->b_F=NULL;
126     out->x_C=NULL;
127     out->b_C=NULL;
128     out->GS=NULL;
129     out->A=Paso_SparseMatrix_getReference(A_p);
130     out->GS=NULL;
131     out->solver=NULL;
132     /*out->GS=Paso_Solver_getGS(A_p,verbose);*/
133     out->level=level;
134 artak 2556
135 gross 2551 if (level==0 || n<=options->min_coarse_matrix_size) {
136     out->coarsest_level=TRUE;
137     #ifdef MKL
138     #else
139     #ifdef UMFPACK
140     #else
141     out->GS=Paso_Solver_getJacobi(A_p);
142     #endif
143     #endif
144     } else {
145     out->coarsest_level=FALSE;
146     out->GS=Paso_Solver_getJacobi(A_p);
147 artak 2442
148 gross 2551 /* identify independend set of rows/columns */
149     #pragma omp parallel for private(i) schedule(static)
150     for (i=0;i<n;++i) mis_marker[i]=-1;
151    
152     if (options->coarsening_method == PASO_YAIR_SHAPIRA_COARSENING) {
153 artak 2652 Paso_Pattern_YS(A_p,mis_marker,options->coarsening_threshold);
154 gross 2551 }
155     else if (options->coarsening_method == PASO_RUGE_STUEBEN_COARSENING) {
156     Paso_Pattern_RS(A_p,mis_marker,options->coarsening_threshold);
157     }
158     else if (options->coarsening_method == PASO_AGGREGATION_COARSENING) {
159     Paso_Pattern_Aggregiation(A_p,mis_marker,options->coarsening_threshold);
160     }
161     else {
162     /*Default coarseneing*/
163 artak 2652 /*Paso_Pattern_RS(A_p,mis_marker,options->coarsening_threshold);*/
164     Paso_Pattern_YS(A_p,mis_marker,options->coarsening_threshold);
165 artak 2556 /*Paso_Pattern_Aggregiation(A_p,mis_marker,options->coarsening_threshold);*/
166 gross 2551 }
167 artak 2475
168 gross 2551 if (Paso_noError()) {
169     #pragma omp parallel for private(i) schedule(static)
170     for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
171 artak 2509
172 gross 2551 out->n=n;
173     out->n_block=n_block;
174     out->n_F=Paso_Util_cumsum(n,counter);
175     out->mask_F=MEMALLOC(n,index_t);
176     out->rows_in_F=MEMALLOC(out->n_F,index_t);
177     out->inv_A_FF=MEMALLOC(n_block*n_block*out->n_F,double);
178     out->A_FF_pivot=NULL; /* later use for block size>3 */
179     if (! (Paso_checkPtr(out->mask_F) || Paso_checkPtr(out->inv_A_FF) || Paso_checkPtr(out->rows_in_F) ) ) {
180 jfenwick 1851 /* creates an index for F from mask */
181 artak 2107 #pragma omp parallel for private(i) schedule(static)
182 jfenwick 1851 for (i = 0; i < out->n_F; ++i) out->rows_in_F[i]=-1;
183 artak 2107 #pragma omp parallel for private(i) schedule(static)
184 jfenwick 1851 for (i = 0; i < n; ++i) {
185     if (mis_marker[i]) {
186     out->rows_in_F[counter[i]]=i;
187     out->mask_F[i]=counter[i];
188     } else {
189     out->mask_F[i]=-1;
190     }
191     }
192 artak 2107
193     /* Compute row-sum for getting rs(A_FF)^-1*/
194 artak 2131 #pragma omp parallel for private(i,iPtr,j,S) schedule(static)
195 artak 1881 for (i = 0; i < out->n_F; ++i) {
196 artak 2107 S=0;
197 artak 2556 /*printf("%d : %d -> ",i, out->rows_in_F[i]);*/
198 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) {
199 artak 1975 j=A_p->pattern->index[iPtr];
200 artak 2556 /*if (j==out->rows_in_F[i]) printf("diagonal %e",A_p->val[iPtr]);*/
201     if (mis_marker[j] && j==out->rows_in_F[i])
202     S=A_p->val[iPtr];
203 artak 1881 }
204 artak 2556 /*printf("-> %e\n",S);*/
205 artak 2442 out->inv_A_FF[i]=1./S;
206 artak 1881 }
207 gross 2551 }
208     }
209 jfenwick 1851
210 gross 2551 if ( Paso_noError()) {
211 jfenwick 1851 /* if there are no nodes in the coarse level there is no more work to do */
212     out->n_C=n-out->n_F;
213 gross 2551
214     /*if (out->n_F>500) */
215     out->rows_in_C=MEMALLOC(out->n_C,index_t);
216     out->mask_C=MEMALLOC(n,index_t);
217     if (! (Paso_checkPtr(out->mask_C) || Paso_checkPtr(out->rows_in_C) ) ) {
218     /* creates an index for C from mask */
219     #pragma omp parallel for private(i) schedule(static)
220     for (i = 0; i < n; ++i) counter[i]=! mis_marker[i];
221     Paso_Util_cumsum(n,counter);
222     #pragma omp parallel for private(i) schedule(static)
223     for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
224     #pragma omp parallel for private(i) schedule(static)
225     for (i = 0; i < n; ++i) {
226     if (! mis_marker[i]) {
227 jfenwick 1851 out->rows_in_C[counter[i]]=i;
228     out->mask_C[i]=counter[i];
229     } else {
230     out->mask_C[i]=-1;
231     }
232 gross 2551 }
233     }
234     }
235     if ( Paso_noError()) {
236     /* get A_CF block: */
237     out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
238     /* get A_FC block: */
239     out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
240     /* get A_CC block: */
241     schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
242    
243     }
244     if ( Paso_noError()) {
245     /*find the pattern of the schur complement with fill in*/
246 artak 2556 temp1=Paso_Pattern_multiply(PATTERN_FORMAT_DEFAULT,out->A_CF->pattern,out->A_FC->pattern);
247     temp2=Paso_Pattern_binop(PATTERN_FORMAT_DEFAULT, schur->pattern, temp1);
248     schur_withFillIn=Paso_SparseMatrix_alloc(A_p->type,temp2,1,1, TRUE);
249     Paso_Pattern_free(temp1);
250     Paso_Pattern_free(temp2);
251 gross 2551 }
252     if ( Paso_noError()) {
253     /* copy values over*/
254     #pragma omp parallel for private(i,iPtr,j,iPtr_s,index,where_p) schedule(static)
255     for (i = 0; i < schur_withFillIn->numRows; ++i) {
256     for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
257     j=schur_withFillIn->pattern->index[iPtr];
258     iPtr_s=schur->pattern->ptr[i];
259     schur_withFillIn->val[iPtr]=0.;
260     index=&(schur->pattern->index[iPtr_s]);
261     where_p=(index_t*)bsearch(&j,
262 artak 2107 index,
263     schur->pattern->ptr[i + 1]-schur->pattern->ptr[i],
264     sizeof(index_t),
265     Paso_comparIndex);
266 gross 2551 if (where_p!=NULL) {
267     schur_withFillIn->val[iPtr]=schur->val[iPtr_s+(index_t)(where_p-index)];
268     }
269     }
270     }
271     Paso_Solver_updateIncompleteSchurComplement(schur_withFillIn,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC);
272     out->AMG_of_Schur=Paso_Solver_getAMG(schur_withFillIn,level-1,options);
273     }
274     /* allocate work arrays for AMG application */
275     if (Paso_noError()) {
276     out->x_F=MEMALLOC(n_block*out->n_F,double);
277     out->b_F=MEMALLOC(n_block*out->n_F,double);
278     out->x_C=MEMALLOC(n_block*out->n_C,double);
279     out->b_C=MEMALLOC(n_block*out->n_C,double);
280 artak 1890
281 gross 2551 if (! (Paso_checkPtr(out->x_F) || Paso_checkPtr(out->b_F) || Paso_checkPtr(out->x_C) || Paso_checkPtr(out->b_C) ) ) {
282     #pragma omp parallel for private(i,k) schedule(static)
283     for (i = 0; i < out->n_F; ++i) {
284     for (k=0; k<n_block;++k) {
285     out->x_F[i*n_block+k]=0.;
286     out->b_F[i*n_block+k]=0.;
287 jfenwick 1851 }
288 gross 2551 }
289     #pragma omp parallel for private(i,k) schedule(static)
290     for (i = 0; i < out->n_C; ++i) {
291     for (k=0; k<n_block;++k) {
292     out->x_C[i*n_block+k]=0.;
293     out->b_C[i*n_block+k]=0.;
294     }
295     }
296     }
297 jfenwick 1851 }
298     }
299     }
300     TMPMEMFREE(mis_marker);
301     TMPMEMFREE(counter);
302 gross 2551 Paso_SparseMatrix_free(schur);
303     Paso_SparseMatrix_free(schur_withFillIn);
304 jfenwick 1851 if (Paso_noError()) {
305 artak 2524 if (verbose && level>0 && !out->coarsest_level) {
306 gross 2551 printf("AMG: level: %d: %d unknowns eliminated. %d left.\n",level, out->n_F,out->n_C);
307 jfenwick 1851 }
308     return out;
309     } else {
310     Paso_Solver_AMG_free(out);
311     return NULL;
312     }
313     }
314    
315     /**************************************************************/
316    
317     /* apply AMG precondition b-> x
318    
319     in fact it solves
320    
321 artak 2381 [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FC ] [ x_F ] = [b_F]
322 jfenwick 1851 [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] [ x_C ] = [b_C]
323    
324     in the form
325    
326     b->[b_F,b_C]
327     x_F=invA_FF*b_F
328     b_C=b_C-A_CF*x_F
329     x_C=AMG(b_C)
330     b_F=b_F-A_FC*x_C
331     x_F=invA_FF*b_F
332     x<-[x_F,x_C]
333    
334     should be called within a parallel region
335     barrier synconization should be performed to make sure that the input vector available
336    
337     */
338    
339     void Paso_Solver_solveAMG(Paso_Solver_AMG * amg, double * x, double * b) {
340 artak 2107 dim_t i;
341 artak 2507 double time0=0;
342 gross 2551 double *r=NULL, *x0=NULL;
343 artak 2509 bool_t verbose=0;
344 artak 2507 #ifdef MKL
345 gross 2551 Paso_SparseMatrix *temp=NULL;
346     #else
347     #ifdef UMFPACK
348     Paso_UMFPACK_Handler * ptr=NULL;
349     #endif
350 artak 2507 #endif
351 gross 2551 r=MEMALLOC(amg->n,double);
352     x0=MEMALLOC(amg->n,double);
353 artak 2507
354 artak 2524 if (amg->coarsest_level) {
355 artak 2507
356     time0=Paso_timer();
357     #ifdef MKL
358 gross 2551 temp=Paso_SparseMatrix_alloc(MATRIX_FORMAT_BLK1 + MATRIX_FORMAT_OFFSET1, amg->A->pattern,1,1, FALSE);
359 artak 2507 #pragma omp parallel for private(i) schedule(static)
360     for (i=0;i<amg->A->len;++i) {
361     temp->val[i]=amg->A->val[i];
362     }
363     Paso_MKL1(temp,x,b,0);
364     Paso_SparseMatrix_free(temp);
365     #else
366 gross 2551 #ifdef UMFPACK
367     ptr=(Paso_UMFPACK_Handler *)(amg->solver);
368 artak 2652 Paso_UMFPACK1(&ptr,amg->A,x,b,verbose);
369 gross 2551 amg->solver=(void*) ptr;
370     #else
371     Paso_Solver_solveJacobi(amg->GS,x,b);
372     #endif
373 artak 2507 #endif
374 artak 2475 time0=Paso_timer()-time0;
375 artak 2652 if (verbose) fprintf(stderr,"timing: DIRECT SOLVER: %e\n",time0);
376 artak 2507
377 jfenwick 1851 } else {
378 artak 1902 /* presmoothing */
379 artak 2507 time0=Paso_timer();
380 artak 2112 Paso_Solver_solveJacobi(amg->GS,x,b);
381 artak 2507 time0=Paso_timer()-time0;
382     if (verbose) fprintf(stderr,"timing: Presmooting: %e\n",time0);
383 artak 1931 /* end of presmoothing */
384 artak 1939
385 artak 2507
386     time0=Paso_timer();
387 artak 1890 #pragma omp parallel for private(i) schedule(static)
388     for (i=0;i<amg->n;++i) r[i]=b[i];
389    
390     /*r=b-Ax*/
391     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
392 artak 1954
393 jfenwick 1851 /* b->[b_F,b_C] */
394 artak 1954 #pragma omp parallel for private(i) schedule(static)
395     for (i=0;i<amg->n_F;++i) amg->b_F[i]=r[amg->rows_in_F[i]];
396    
397     #pragma omp parallel for private(i) schedule(static)
398     for (i=0;i<amg->n_C;++i) amg->b_C[i]=r[amg->rows_in_C[i]];
399 artak 1890
400 jfenwick 1851 /* x_F=invA_FF*b_F */
401 artak 1954 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
402 artak 1890
403 jfenwick 1851 /* b_C=b_C-A_CF*x_F */
404     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->x_F,1.,amg->b_C);
405 artak 1890
406 artak 2507 time0=Paso_timer()-time0;
407     if (verbose) fprintf(stderr,"timing: Before next level: %e\n",time0);
408    
409 jfenwick 1851 /* x_C=AMG(b_C) */
410     Paso_Solver_solveAMG(amg->AMG_of_Schur,amg->x_C,amg->b_C);
411 artak 1890
412 artak 2507 time0=Paso_timer();
413 jfenwick 1851 /* b_F=b_F-A_FC*x_C */
414     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_FC,amg->x_C,1.,amg->b_F);
415     /* x_F=invA_FF*b_F */
416 artak 1954 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
417 jfenwick 1851 /* x<-[x_F,x_C] */
418 artak 2113
419 artak 1954 #pragma omp parallel for private(i) schedule(static)
420     for (i=0;i<amg->n;++i) {
421     if (amg->mask_C[i]>-1) {
422 artak 2107 x[i]=amg->x_C[amg->mask_C[i]];
423 artak 1954 } else {
424 artak 2107 x[i]=amg->x_F[amg->mask_F[i]];
425 artak 1954 }
426 jfenwick 1851 }
427 artak 1954
428 artak 2507 time0=Paso_timer()-time0;
429     if (verbose) fprintf(stderr,"timing: After next level: %e\n",time0);
430    
431 artak 1931 /*postsmoothing*/
432 artak 2507 time0=Paso_timer();
433 artak 1954 #pragma omp parallel for private(i) schedule(static)
434     for (i=0;i<amg->n;++i) r[i]=b[i];
435 artak 2107
436 artak 2442 /*r=b-Ax */
437 artak 1954 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
438 artak 2112 Paso_Solver_solveJacobi(amg->GS,x0,r);
439 artak 2107
440     #pragma omp parallel for private(i) schedule(static)
441     for (i=0;i<amg->n;++i) x[i]+=x0[i];
442    
443 artak 2507 time0=Paso_timer()-time0;
444     if (verbose) fprintf(stderr,"timing: Postsmoothing: %e\n",time0);
445 artak 2509
446 artak 1931 /*end of postsmoothing*/
447    
448 jfenwick 1851 }
449 artak 1890 MEMFREE(r);
450 artak 1954 MEMFREE(x0);
451 gross 2551 return;
452 jfenwick 1851 }

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