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

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Revision 1891 - (hide annotations)
Fri Oct 17 00:15:17 2008 UTC (11 years, 4 months ago) by artak
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1 jfenwick 1851
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    
29     /**************************************************************/
30    
31     /* free all memory used by AMG */
32    
33     void Paso_Solver_AMG_free(Paso_Solver_AMG * in) {
34     if (in!=NULL) {
35     Paso_Solver_AMG_free(in->AMG_of_Schur);
36     MEMFREE(in->inv_A_FF);
37     MEMFREE(in->A_FF_pivot);
38     Paso_SparseMatrix_free(in->A_FC);
39     Paso_SparseMatrix_free(in->A_CF);
40     MEMFREE(in->rows_in_F);
41     MEMFREE(in->rows_in_C);
42     MEMFREE(in->mask_F);
43     MEMFREE(in->mask_C);
44     MEMFREE(in->x_F);
45     MEMFREE(in->b_F);
46     MEMFREE(in->x_C);
47     MEMFREE(in->b_C);
48     MEMFREE(in);
49     }
50     }
51    
52     /**************************************************************/
53    
54     /* constructs the block-block factorization of
55    
56     [ A_FF A_FC ]
57     A_p=
58     [ A_CF A_FF ]
59    
60     to
61    
62     [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ]
63     [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ]
64    
65    
66     where S=A_FF-ACF*invA_FF*A_FC within the shape of S
67    
68     then AMG is applied to S again until S becomes empty
69    
70     */
71 artak 1890 Paso_Solver_AMG* Paso_Solver_getAMG(Paso_SparseMatrix *A_p,bool_t verbose,dim_t level) {
72 jfenwick 1851 Paso_Solver_AMG* out=NULL;
73     dim_t n=A_p->numRows;
74     dim_t n_block=A_p->row_block_size;
75     index_t* mis_marker=NULL;
76 artak 1881 index_t* counter=NULL;
77     double *rs=NULL;
78     index_t iPtr,*index, *where_p, iPtr_s;
79     dim_t i,k,j,j0;
80 jfenwick 1851 Paso_SparseMatrix * schur=NULL;
81 artak 1881 Paso_SparseMatrix * schur_withFillIn=NULL;
82 artak 1891 double A11,A12,A13,A21,A22,A23,A31,A32,A33,D,time0,time1,time2;
83 artak 1890 schur_withFillIn=MEMALLOC(1,Paso_SparseMatrix);
84    
85 jfenwick 1851 /* identify independend set of rows/columns */
86     mis_marker=TMPMEMALLOC(n,index_t);
87     counter=TMPMEMALLOC(n,index_t);
88 artak 1881 rs=TMPMEMALLOC(n,double);
89 jfenwick 1851 out=MEMALLOC(1,Paso_Solver_AMG);
90     out->AMG_of_Schur=NULL;
91     out->inv_A_FF=NULL;
92     out->A_FF_pivot=NULL;
93     out->A_FC=NULL;
94     out->A_CF=NULL;
95     out->rows_in_F=NULL;
96     out->rows_in_C=NULL;
97     out->mask_F=NULL;
98     out->mask_C=NULL;
99     out->x_F=NULL;
100     out->b_F=NULL;
101     out->x_C=NULL;
102     out->b_C=NULL;
103 artak 1890 out->A=Paso_SparseMatrix_getReference(A_p);
104     out->level=level;
105 artak 1881
106     /* fprintf(stderr,"START OF MATRIX \n\n");
107     for (i = 0; i < A_p->numRows; ++i) {
108     for (iPtr=A_p->pattern->ptr[i];iPtr<A_p->pattern->ptr[i + 1]; ++iPtr) {
109     j=A_p->pattern->index[iPtr];
110     fprintf(stderr,"A[%d,%d]=%.2f ",i,j,A_p->val[iPtr]);
111     }
112     fprintf(stderr,"\n");
113     }
114     fprintf(stderr,"END OF MATRIX \n\n");
115     */
116 jfenwick 1851 if ( !(Paso_checkPtr(mis_marker) || Paso_checkPtr(out) || Paso_checkPtr(counter) ) ) {
117     /* identify independend set of rows/columns */
118     time0=Paso_timer();
119     #pragma omp parallel for private(i) schedule(static)
120     for (i=0;i<n;++i) mis_marker[i]=-1;
121 artak 1890 Paso_Pattern_RS(A_p,mis_marker,0.25);
122     /*
123     for (i=0;i<n;++i) fprintf(stderr," i=%d mis[i]=%d \n",i,mis_marker[i]);
124     */
125 jfenwick 1851 time2=Paso_timer()-time0;
126     if (Paso_noError()) {
127     #pragma omp parallel for private(i) schedule(static)
128     for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
129     out->n=n;
130     out->n_block=n_block;
131     out->n_F=Paso_Util_cumsum(n,counter);
132     out->mask_F=MEMALLOC(n,index_t);
133     out->rows_in_F=MEMALLOC(out->n_F,index_t);
134     out->inv_A_FF=MEMALLOC(n_block*n_block*out->n_F,double);
135     out->A_FF_pivot=NULL; /* later use for block size>3 */
136     if (! (Paso_checkPtr(out->mask_F) || Paso_checkPtr(out->inv_A_FF) || Paso_checkPtr(out->rows_in_F) ) ) {
137     #pragma omp parallel
138     {
139     /* creates an index for F from mask */
140     #pragma omp for private(i) schedule(static)
141     for (i = 0; i < out->n_F; ++i) out->rows_in_F[i]=-1;
142     #pragma omp for private(i) schedule(static)
143     for (i = 0; i < n; ++i) {
144     if (mis_marker[i]) {
145     out->rows_in_F[counter[i]]=i;
146     out->mask_F[i]=counter[i];
147     } else {
148     out->mask_F[i]=-1;
149     }
150     }
151 artak 1881 /* Compute row-sum for getting rs(A_FF)*/
152     #pragma omp for private(i,iPtr) schedule(static)
153     for (i = 0; i < out->n_F; ++i) {
154     rs[i]=0;
155     for (iPtr=A_p->pattern->ptr[out->rows_in_F[i]];iPtr<A_p->pattern->ptr[out->rows_in_F[i] + 1]; ++iPtr) {
156     rs[i]+=A_p->val[iPtr];
157     }
158     }
159    
160 jfenwick 1851 #pragma omp for private(i, where_p,iPtr,A11,A12,A13,A21,A22,A23,A31,A32,A33,D,index) schedule(static)
161     for (i = 0; i < out->n_F; i++) {
162     /* find main diagonal */
163     iPtr=A_p->pattern->ptr[out->rows_in_F[i]];
164     index=&(A_p->pattern->index[iPtr]);
165     where_p=(index_t*)bsearch(&out->rows_in_F[i],
166     index,
167     A_p->pattern->ptr[out->rows_in_F[i] + 1]-A_p->pattern->ptr[out->rows_in_F[i]],
168     sizeof(index_t),
169     Paso_comparIndex);
170     if (where_p==NULL) {
171     Paso_setError(VALUE_ERROR, "Paso_Solver_getAMG: main diagonal element missing.");
172     } else {
173     iPtr+=(index_t)(where_p-index);
174     /* get inverse of A_FF block: */
175 artak 1881 if (ABS(rs[i])>0.) {
176     out->inv_A_FF[i]=1./rs[i];
177     } else {
178 artak 1890 out->inv_A_FF[i]=0;
179     }
180    
181     /* } else {
182 jfenwick 1851 Paso_setError(ZERO_DIVISION_ERROR, "Paso_Solver_getAMG: Break-down in AMG decomposition: non-regular main diagonal block.");
183 artak 1890 }*/
184 artak 1881 }
185 jfenwick 1851 }
186     } /* end parallel region */
187    
188     if( Paso_noError()) {
189     /* if there are no nodes in the coarse level there is no more work to do */
190     out->n_C=n-out->n_F;
191 artak 1890 /*if (out->n_C>11) {*/
192     if (level>0) {
193 jfenwick 1851 out->rows_in_C=MEMALLOC(out->n_C,index_t);
194     out->mask_C=MEMALLOC(n,index_t);
195     if (! (Paso_checkPtr(out->mask_C) || Paso_checkPtr(out->rows_in_C) ) ) {
196     /* creates an index for C from mask */
197     #pragma omp parallel for private(i) schedule(static)
198     for (i = 0; i < n; ++i) counter[i]=! mis_marker[i];
199     Paso_Util_cumsum(n,counter);
200     #pragma omp parallel
201     {
202     #pragma omp for private(i) schedule(static)
203     for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
204     #pragma omp for private(i) schedule(static)
205     for (i = 0; i < n; ++i) {
206     if (! mis_marker[i]) {
207     out->rows_in_C[counter[i]]=i;
208     out->mask_C[i]=counter[i];
209     } else {
210     out->mask_C[i]=-1;
211     }
212     }
213     } /* end parallel region */
214     /* get A_CF block: */
215     out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
216     if (Paso_noError()) {
217     /* get A_FC block: */
218     out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
219 artak 1881 /* get A_CC block: */
220 jfenwick 1851 if (Paso_noError()) {
221     schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
222 artak 1881
223     /*find the pattern of the schur complement with fill in*/
224     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);
225    
226     /* copy values over*/
227     #pragma omp for private(i,iPtr,iPtr_s,j,j0) schedule(static)
228     for (i = 0; i < schur_withFillIn->numRows; ++i) {
229     for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
230     j=schur_withFillIn->pattern->index[iPtr];
231     schur_withFillIn->val[iPtr]=0.;
232     for (iPtr_s=schur->pattern->ptr[i];iPtr_s<schur->pattern->ptr[i + 1]; ++iPtr_s){
233     j0=schur->pattern->index[iPtr_s];
234     if (j==j0) {
235     schur_withFillIn->val[iPtr]=schur->val[iPtr_s];
236     break;
237     }
238     }
239     }
240     }
241    
242     /* for (i = 0; i < schur_withFillIn->numRows; ++i) {
243     for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
244     j=schur_withFillIn->pattern->index[iPtr];
245     fprintf(stderr,"A_CC[%d,%d]=%.2f ",i,j,schur_withFillIn->val[iPtr]);
246     }
247     fprintf(stderr,"\n");
248     }*/
249 jfenwick 1851 time0=Paso_timer()-time0;
250     if (Paso_noError()) {
251     time1=Paso_timer();
252     /* update A_CC block to get Schur complement and then apply AMG to it */
253 artak 1881 Paso_Solver_updateIncompleteSchurComplement(schur_withFillIn,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC);
254 jfenwick 1851 time1=Paso_timer()-time1;
255 artak 1890 out->AMG_of_Schur=Paso_Solver_getAMG(schur_withFillIn,verbose,level-1);
256 artak 1881
257 jfenwick 1851 Paso_SparseMatrix_free(schur);
258 artak 1890 /* Paso_SparseMatrix_free(schur_withFillIn);*/
259 jfenwick 1851 }
260     /* allocate work arrays for AMG application */
261     if (Paso_noError()) {
262     out->x_F=MEMALLOC(n_block*out->n_F,double);
263     out->b_F=MEMALLOC(n_block*out->n_F,double);
264     out->x_C=MEMALLOC(n_block*out->n_C,double);
265     out->b_C=MEMALLOC(n_block*out->n_C,double);
266 artak 1890
267 jfenwick 1851 if (! (Paso_checkPtr(out->x_F) || Paso_checkPtr(out->b_F) || Paso_checkPtr(out->x_C) || Paso_checkPtr(out->b_C) ) ) {
268     #pragma omp parallel
269     {
270     #pragma omp for private(i,k) schedule(static)
271     for (i = 0; i < out->n_F; ++i) {
272     for (k=0; k<n_block;++k) {
273     out->x_F[i*n_block+k]=0.;
274     out->b_F[i*n_block+k]=0.;
275     }
276     }
277     #pragma omp for private(i,k) schedule(static)
278     for (i = 0; i < out->n_C; ++i) {
279     for (k=0; k<n_block;++k) {
280     out->x_C[i*n_block+k]=0.;
281     out->b_C[i*n_block+k]=0.;
282     }
283     }
284     } /* end parallel region */
285     }
286     }
287     }
288     }
289     }
290     }
291     }
292     }
293     }
294     }
295     TMPMEMFREE(mis_marker);
296     TMPMEMFREE(counter);
297 artak 1881 TMPMEMFREE(rs);
298 jfenwick 1851 if (Paso_noError()) {
299     if (verbose) {
300     printf("AMG: %d unknowns eliminated. %d left.\n",out->n_F,n-out->n_F);
301     if (out->n_C>0) {
302     printf("timing: AMG: MIS/reordering/elemination : %e/%e/%e\n",time2,time0,time1);
303     } else {
304     printf("timing: AMG: MIS: %e\n",time2);
305     }
306     }
307     return out;
308     } else {
309     Paso_Solver_AMG_free(out);
310     return NULL;
311     }
312     }
313    
314     /**************************************************************/
315    
316     /* apply AMG precondition b-> x
317    
318     in fact it solves
319    
320     [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ] [ x_F ] = [b_F]
321     [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] [ x_C ] = [b_C]
322    
323     in the form
324    
325     b->[b_F,b_C]
326     x_F=invA_FF*b_F
327     b_C=b_C-A_CF*x_F
328     x_C=AMG(b_C)
329     b_F=b_F-A_FC*x_C
330     x_F=invA_FF*b_F
331     x<-[x_F,x_C]
332    
333     should be called within a parallel region
334     barrier synconization should be performed to make sure that the input vector available
335    
336     */
337    
338     void Paso_Solver_solveAMG(Paso_Solver_AMG * amg, double * x, double * b) {
339     dim_t i,k;
340     dim_t n_block=amg->n_block;
341 artak 1890 double *r=MEMALLOC(amg->n,double);
342     double *x0=MEMALLOC(amg->n,double);
343    
344     if (amg->level==0) {
345 jfenwick 1851 /* x=invA_FF*b */
346     Paso_Solver_applyBlockDiagonalMatrix(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,x,b);
347     } else {
348 artak 1890 fprintf(stdout,"LEVEL %d \n",amg->level);
349 artak 1881 /* presmoothing on (Shure, x, b, r) */
350 artak 1890 /****************/
351     Paso_Solver_GS* GS=MEMALLOC(1,Paso_Solver_GS);
352     GS=Paso_Solver_getGS(amg->A,-1);
353     Paso_Solver_solveGS(GS,x,b);
354    
355     #pragma omp parallel for private(i) schedule(static)
356     for (i=0;i<amg->n;++i) r[i]=b[i];
357    
358     /*r=b-Ax*/
359     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
360     /****************/
361 jfenwick 1851 /* b->[b_F,b_C] */
362     if (n_block==1) {
363     #pragma omp parallel for private(i) schedule(static)
364 artak 1890 for (i=0;i<amg->n_F;++i) amg->b_F[i]=r[amg->rows_in_F[i]]; /* was b istead of r */
365     #pragma omp parallel for private(i) schedule(static)
366     for (i=0;i<amg->n_C;++i) amg->b_C[i]=r[amg->rows_in_C[i]];
367 jfenwick 1851 } else {
368     #pragma omp parallel for private(i,k) schedule(static)
369     for (i=0;i<amg->n_F;++i)
370 artak 1890 for (k=0;k<n_block;k++) amg->b_F[amg->n_block*i+k]=r[n_block*amg->rows_in_F[i]+k];
371 jfenwick 1851 #pragma omp parallel for private(i,k) schedule(static)
372     for (i=0;i<amg->n_C;++i)
373 artak 1890 for (k=0;k<n_block;k++) amg->b_C[amg->n_block*i+k]=r[n_block*amg->rows_in_C[i]+k];
374 jfenwick 1851 }
375 artak 1890
376     /****************/
377     /* Coursening part */
378    
379     /* r_F=A_FF^-1*r_F */
380     /*Paso_Solver_applyBlockDiagonalMatrix(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->b_F,amg->b_F);
381     fprintf(stderr,"2\n");
382     */
383     /* r_C=r_C-A_CF*r_F */
384     /*Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->b_F,1.,amg->b_C);
385     fprintf(stderr,"3\n");
386     */
387     /****************/
388    
389    
390 jfenwick 1851 /* x_F=invA_FF*b_F */
391     Paso_Solver_applyBlockDiagonalMatrix(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
392 artak 1890
393 jfenwick 1851 /* b_C=b_C-A_CF*x_F */
394     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->x_F,1.,amg->b_C);
395 artak 1890
396 jfenwick 1851 /* x_C=AMG(b_C) */
397     Paso_Solver_solveAMG(amg->AMG_of_Schur,amg->x_C,amg->b_C);
398 artak 1890
399 jfenwick 1851 /* b_F=b_F-A_FC*x_C */
400     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_FC,amg->x_C,1.,amg->b_F);
401     /* x_F=invA_FF*b_F */
402     Paso_Solver_applyBlockDiagonalMatrix(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
403     /* x<-[x_F,x_C] */
404 artak 1890
405     /* */
406    
407    
408 jfenwick 1851 if (n_block==1) {
409     #pragma omp parallel for private(i) schedule(static)
410     for (i=0;i<amg->n;++i) {
411     if (amg->mask_C[i]>-1) {
412 artak 1890 x[i]+=amg->x_C[amg->mask_C[i]];
413 jfenwick 1851 } else {
414 artak 1890 x[i]+=amg->x_F[amg->mask_F[i]];
415 jfenwick 1851 }
416     }
417     } else {
418     #pragma omp parallel for private(i,k) schedule(static)
419     for (i=0;i<amg->n;++i) {
420     if (amg->mask_C[i]>-1) {
421 artak 1890 for (k=0;k<n_block;k++) x[n_block*i+k]+=amg->x_C[n_block*amg->mask_C[i]+k];
422 jfenwick 1851 } else {
423 artak 1890 for (k=0;k<n_block;k++) x[n_block*i+k]+=amg->x_F[n_block*amg->mask_F[i]+k];
424 jfenwick 1851 }
425     }
426     }
427     /* all done */
428 artak 1890 /*post smoothing*/
429     /* Paso_Solver_solveGS(GS,x0,b);
430     if (n_block==1) {
431     #pragma omp parallel for private(i) schedule(static)
432     for (i=0;i<amg->n;++i) x[i]+=x0[i];
433     } else {
434     #pragma omp parallel for private(i,k) schedule(static)
435     for (i=0;i<amg->n;++i) {
436     for (k=0;k<n_block;k++) x[n_block*i+k]+=x0[n_block*i+k];
437     }
438     }
439     */
440     Paso_Solver_GS_free(GS);
441 jfenwick 1851 }
442 artak 1890 MEMFREE(x0);
443     MEMFREE(r);
444 jfenwick 1851 return;
445     }
446    
447     /*
448     * $Log$
449     *
450     */

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