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

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Revision 2509 - (hide annotations)
Thu Jul 2 04:51:51 2009 UTC (10 years, 7 months ago) by artak
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File size: 15781 byte(s)
Now one can choose coarsening method from python for AMG. Some commented lines are removed.
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 artak 2475 /* Paso: AMG preconditioner */
18 jfenwick 1851
19     /**************************************************************/
20    
21     /* Author: artak@access.edu.au */
22    
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     MEMFREE(in->rows_in_F);
47     MEMFREE(in->rows_in_C);
48     MEMFREE(in->mask_F);
49     MEMFREE(in->mask_C);
50     MEMFREE(in->x_F);
51     MEMFREE(in->b_F);
52     MEMFREE(in->x_C);
53     MEMFREE(in->b_C);
54     MEMFREE(in);
55     }
56     }
57    
58     /**************************************************************/
59    
60     /* constructs the block-block factorization of
61    
62     [ A_FF A_FC ]
63     A_p=
64     [ A_CF A_FF ]
65    
66     to
67    
68     [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ]
69     [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ]
70    
71    
72     where S=A_FF-ACF*invA_FF*A_FC within the shape of S
73    
74     then AMG is applied to S again until S becomes empty
75    
76     */
77 artak 2475 Paso_Solver_AMG* Paso_Solver_getAMG(Paso_SparseMatrix *A_p,bool_t verbose,dim_t level, double coarsening_threshold, dim_t coarsening_method) {
78 jfenwick 1851 Paso_Solver_AMG* out=NULL;
79     dim_t n=A_p->numRows;
80     dim_t n_block=A_p->row_block_size;
81     index_t* mis_marker=NULL;
82 artak 1881 index_t* counter=NULL;
83     index_t iPtr,*index, *where_p, iPtr_s;
84 artak 2107 dim_t i,k,j;
85 jfenwick 1851 Paso_SparseMatrix * schur=NULL;
86 artak 1881 Paso_SparseMatrix * schur_withFillIn=NULL;
87 artak 2381 double S=0;
88 artak 2475
89 artak 2439 /*Make sure we have block sizes 1*/
90     A_p->pattern->input_block_size=A_p->col_block_size;
91     A_p->pattern->output_block_size=A_p->row_block_size;
92     A_p->pattern->block_size=A_p->block_size;
93    
94 jfenwick 1851 /* identify independend set of rows/columns */
95     mis_marker=TMPMEMALLOC(n,index_t);
96     counter=TMPMEMALLOC(n,index_t);
97     out=MEMALLOC(1,Paso_Solver_AMG);
98     out->AMG_of_Schur=NULL;
99     out->inv_A_FF=NULL;
100     out->A_FF_pivot=NULL;
101     out->A_FC=NULL;
102     out->A_CF=NULL;
103     out->rows_in_F=NULL;
104     out->rows_in_C=NULL;
105     out->mask_F=NULL;
106     out->mask_C=NULL;
107     out->x_F=NULL;
108     out->b_F=NULL;
109     out->x_C=NULL;
110     out->b_C=NULL;
111 artak 2107 out->GS=NULL;
112 artak 1890 out->A=Paso_SparseMatrix_getReference(A_p);
113 artak 2112 /*out->GS=Paso_Solver_getGS(A_p,verbose);*/
114     out->GS=Paso_Solver_getJacobi(A_p);
115 artak 2107 /*out->GS->sweeps=2;*/
116 artak 1890 out->level=level;
117 artak 2442
118     if ( !(Paso_checkPtr(mis_marker) || Paso_checkPtr(out) || Paso_checkPtr(counter) || level==0 ) ) {
119 jfenwick 1851 /* identify independend set of rows/columns */
120     #pragma omp parallel for private(i) schedule(static)
121     for (i=0;i<n;++i) mis_marker[i]=-1;
122 artak 2475
123     if (coarsening_method == PASO_YAIR_SHAPIRA_COARSENING) {
124     Paso_Pattern_coup(A_p,mis_marker,coarsening_threshold);
125     }
126     else if (coarsening_method == PASO_RUGE_STUEBEN_COARSENING) {
127     Paso_Pattern_RS(A_p,mis_marker,coarsening_threshold);
128     }
129     else if (coarsening_method == PASO_AGGREGATION_COARSENING) {
130     Paso_Pattern_Aggregiation(A_p,mis_marker,coarsening_threshold);
131     }
132     else {
133     /*Default coarseneing*/
134     Paso_Pattern_RS(A_p,mis_marker,coarsening_threshold);
135     }
136 artak 2509
137 artak 2475 if (Paso_noError()) {
138 jfenwick 1851 #pragma omp parallel for private(i) schedule(static)
139     for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
140     out->n=n;
141     out->n_block=n_block;
142     out->n_F=Paso_Util_cumsum(n,counter);
143     out->mask_F=MEMALLOC(n,index_t);
144     out->rows_in_F=MEMALLOC(out->n_F,index_t);
145     out->inv_A_FF=MEMALLOC(n_block*n_block*out->n_F,double);
146     out->A_FF_pivot=NULL; /* later use for block size>3 */
147     if (! (Paso_checkPtr(out->mask_F) || Paso_checkPtr(out->inv_A_FF) || Paso_checkPtr(out->rows_in_F) ) ) {
148     /* creates an index for F from mask */
149 artak 2107 #pragma omp parallel for private(i) schedule(static)
150 jfenwick 1851 for (i = 0; i < out->n_F; ++i) out->rows_in_F[i]=-1;
151 artak 2107 #pragma omp parallel for private(i) schedule(static)
152 jfenwick 1851 for (i = 0; i < n; ++i) {
153     if (mis_marker[i]) {
154     out->rows_in_F[counter[i]]=i;
155     out->mask_F[i]=counter[i];
156     } else {
157     out->mask_F[i]=-1;
158     }
159     }
160 artak 2107
161     /* Compute row-sum for getting rs(A_FF)^-1*/
162 artak 2131 #pragma omp parallel for private(i,iPtr,j,S) schedule(static)
163 artak 1881 for (i = 0; i < out->n_F; ++i) {
164 artak 2107 S=0;
165 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) {
166 artak 1975 j=A_p->pattern->index[iPtr];
167     if (mis_marker[j])
168 artak 2107 S+=A_p->val[iPtr];
169 artak 1881 }
170 artak 2442 out->inv_A_FF[i]=1./S;
171 artak 1881 }
172 jfenwick 1851
173     if( Paso_noError()) {
174     /* if there are no nodes in the coarse level there is no more work to do */
175     out->n_C=n-out->n_F;
176 artak 2381 if (level>0 && out->n_C>500) {
177 artak 2280 /*if (out->n_F>500) {*/
178 jfenwick 1851 out->rows_in_C=MEMALLOC(out->n_C,index_t);
179     out->mask_C=MEMALLOC(n,index_t);
180     if (! (Paso_checkPtr(out->mask_C) || Paso_checkPtr(out->rows_in_C) ) ) {
181     /* creates an index for C from mask */
182     #pragma omp parallel for private(i) schedule(static)
183     for (i = 0; i < n; ++i) counter[i]=! mis_marker[i];
184     Paso_Util_cumsum(n,counter);
185 artak 2107 #pragma omp parallel for private(i) schedule(static)
186 jfenwick 1851 for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
187 artak 2107 #pragma omp parallel for private(i) schedule(static)
188 jfenwick 1851 for (i = 0; i < n; ++i) {
189     if (! mis_marker[i]) {
190     out->rows_in_C[counter[i]]=i;
191     out->mask_C[i]=counter[i];
192     } else {
193     out->mask_C[i]=-1;
194     }
195     }
196     /* get A_CF block: */
197     out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
198     if (Paso_noError()) {
199     /* get A_FC block: */
200     out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
201 artak 1881 /* get A_CC block: */
202 jfenwick 1851 if (Paso_noError()) {
203     schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
204 artak 2107 /*find the pattern of the schur complement with fill in*/
205 artak 2507
206 artak 1881 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);
207     /* copy values over*/
208 artak 2107 #pragma omp parallel for private(i,iPtr,j,iPtr_s,index,where_p) schedule(static)
209 artak 1881 for (i = 0; i < schur_withFillIn->numRows; ++i) {
210     for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
211     j=schur_withFillIn->pattern->index[iPtr];
212 artak 2107 iPtr_s=schur->pattern->ptr[i];
213 artak 2507 schur_withFillIn->val[iPtr]=0.;
214 artak 2107 index=&(schur->pattern->index[iPtr_s]);
215     where_p=(index_t*)bsearch(&j,
216     index,
217     schur->pattern->ptr[i + 1]-schur->pattern->ptr[i],
218     sizeof(index_t),
219     Paso_comparIndex);
220     if (where_p!=NULL) {
221     schur_withFillIn->val[iPtr]=schur->val[iPtr_s+(index_t)(where_p-index)];
222 artak 1881 }
223     }
224 artak 2509 }
225 jfenwick 1851 if (Paso_noError()) {
226 artak 1881 Paso_Solver_updateIncompleteSchurComplement(schur_withFillIn,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC);
227 artak 2475 out->AMG_of_Schur=Paso_Solver_getAMG(schur_withFillIn,verbose,level-1,coarsening_threshold,coarsening_method);
228 artak 2107 Paso_SparseMatrix_free(schur);
229 jfenwick 1851 }
230     /* allocate work arrays for AMG application */
231     if (Paso_noError()) {
232     out->x_F=MEMALLOC(n_block*out->n_F,double);
233     out->b_F=MEMALLOC(n_block*out->n_F,double);
234     out->x_C=MEMALLOC(n_block*out->n_C,double);
235     out->b_C=MEMALLOC(n_block*out->n_C,double);
236 artak 1890
237 jfenwick 1851 if (! (Paso_checkPtr(out->x_F) || Paso_checkPtr(out->b_F) || Paso_checkPtr(out->x_C) || Paso_checkPtr(out->b_C) ) ) {
238 artak 2107 #pragma omp parallel for private(i,k) schedule(static)
239     for (i = 0; i < out->n_F; ++i) {
240 jfenwick 1851 for (k=0; k<n_block;++k) {
241     out->x_F[i*n_block+k]=0.;
242     out->b_F[i*n_block+k]=0.;
243     }
244     }
245 artak 2107 #pragma omp parallel for private(i,k) schedule(static)
246 jfenwick 1851 for (i = 0; i < out->n_C; ++i) {
247     for (k=0; k<n_block;++k) {
248     out->x_C[i*n_block+k]=0.;
249     out->b_C[i*n_block+k]=0.;
250     }
251     }
252     }
253     }
254     }
255     }
256     }
257     }
258     }
259     }
260     }
261     }
262     TMPMEMFREE(mis_marker);
263     TMPMEMFREE(counter);
264     if (Paso_noError()) {
265 artak 2442 if (verbose && level>0) {
266     printf("AMG: %d unknowns eliminated. %d left.\n",out->n_F,out->n_C);
267 jfenwick 1851 }
268     return out;
269     } else {
270     Paso_Solver_AMG_free(out);
271     return NULL;
272     }
273     }
274    
275     /**************************************************************/
276    
277     /* apply AMG precondition b-> x
278    
279     in fact it solves
280    
281 artak 2381 [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FC ] [ x_F ] = [b_F]
282 jfenwick 1851 [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] [ x_C ] = [b_C]
283    
284     in the form
285    
286     b->[b_F,b_C]
287     x_F=invA_FF*b_F
288     b_C=b_C-A_CF*x_F
289     x_C=AMG(b_C)
290     b_F=b_F-A_FC*x_C
291     x_F=invA_FF*b_F
292     x<-[x_F,x_C]
293    
294     should be called within a parallel region
295     barrier synconization should be performed to make sure that the input vector available
296    
297     */
298    
299     void Paso_Solver_solveAMG(Paso_Solver_AMG * amg, double * x, double * b) {
300 artak 2107 dim_t i;
301 artak 1890 double *r=MEMALLOC(amg->n,double);
302 artak 1954 double *x0=MEMALLOC(amg->n,double);
303 artak 2507 double time0=0;
304 artak 2509 bool_t verbose=0;
305 artak 2107
306 artak 2507 #ifdef MKL
307     Paso_SparseMatrix *temp=NULL;
308     #endif
309    
310    
311 artak 2381 if (amg->level==0 || amg->n_C<=500) {
312 artak 2507
313     time0=Paso_timer();
314     #ifdef MKL
315     temp=Paso_SparseMatrix_alloc(MATRIX_FORMAT_BLK1 + MATRIX_FORMAT_OFFSET1, amg->A->pattern,1,1);
316     #pragma omp parallel for private(i) schedule(static)
317     for (i=0;i<amg->A->len;++i) {
318     temp->val[i]=amg->A->val[i];
319     }
320     Paso_MKL1(temp,x,b,0);
321     Paso_SparseMatrix_free(temp);
322     #else
323     #ifdef UMFPACK
324     Paso_UMFPACK1(amg->A,x,b,0);
325     #else
326     Paso_Solver_solveJacobi(amg->GS,x,b);
327     #endif
328     #endif
329    
330 artak 2475 time0=Paso_timer()-time0;
331 artak 2507 if (verbose) fprintf(stderr,"timing: DIRECT SOLVER: %e\n\n\n",time0);
332    
333 jfenwick 1851 } else {
334 artak 1902 /* presmoothing */
335 artak 2507 time0=Paso_timer();
336 artak 2112 Paso_Solver_solveJacobi(amg->GS,x,b);
337 artak 2507 time0=Paso_timer()-time0;
338     if (verbose) fprintf(stderr,"timing: Presmooting: %e\n",time0);
339 artak 1931 /* end of presmoothing */
340 artak 1939
341 artak 2507
342     time0=Paso_timer();
343 artak 1890 #pragma omp parallel for private(i) schedule(static)
344     for (i=0;i<amg->n;++i) r[i]=b[i];
345    
346     /*r=b-Ax*/
347     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
348 artak 1954
349 jfenwick 1851 /* b->[b_F,b_C] */
350 artak 1954 #pragma omp parallel for private(i) schedule(static)
351     for (i=0;i<amg->n_F;++i) amg->b_F[i]=r[amg->rows_in_F[i]];
352    
353     #pragma omp parallel for private(i) schedule(static)
354     for (i=0;i<amg->n_C;++i) amg->b_C[i]=r[amg->rows_in_C[i]];
355 artak 1890
356 jfenwick 1851 /* x_F=invA_FF*b_F */
357 artak 1954 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
358 artak 1890
359 jfenwick 1851 /* b_C=b_C-A_CF*x_F */
360     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->x_F,1.,amg->b_C);
361 artak 1890
362 artak 2507 time0=Paso_timer()-time0;
363     if (verbose) fprintf(stderr,"timing: Before next level: %e\n",time0);
364    
365 jfenwick 1851 /* x_C=AMG(b_C) */
366     Paso_Solver_solveAMG(amg->AMG_of_Schur,amg->x_C,amg->b_C);
367 artak 1890
368 artak 2507 time0=Paso_timer();
369 jfenwick 1851 /* b_F=b_F-A_FC*x_C */
370     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_FC,amg->x_C,1.,amg->b_F);
371     /* x_F=invA_FF*b_F */
372 artak 1954 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
373 jfenwick 1851 /* x<-[x_F,x_C] */
374 artak 2113
375 artak 1954 #pragma omp parallel for private(i) schedule(static)
376     for (i=0;i<amg->n;++i) {
377     if (amg->mask_C[i]>-1) {
378 artak 2107 x[i]=amg->x_C[amg->mask_C[i]];
379 artak 1954 } else {
380 artak 2107 x[i]=amg->x_F[amg->mask_F[i]];
381 artak 1954 }
382 jfenwick 1851 }
383 artak 1954
384 artak 2507 time0=Paso_timer()-time0;
385     if (verbose) fprintf(stderr,"timing: After next level: %e\n",time0);
386    
387 artak 1931 /*postsmoothing*/
388 artak 2507 time0=Paso_timer();
389 artak 1954 #pragma omp parallel for private(i) schedule(static)
390     for (i=0;i<amg->n;++i) r[i]=b[i];
391 artak 2107
392 artak 2442 /*r=b-Ax */
393 artak 1954 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
394 artak 2112 Paso_Solver_solveJacobi(amg->GS,x0,r);
395 artak 2107
396     #pragma omp parallel for private(i) schedule(static)
397     for (i=0;i<amg->n;++i) x[i]+=x0[i];
398    
399 artak 2507 time0=Paso_timer()-time0;
400     if (verbose) fprintf(stderr,"timing: Postsmoothing: %e\n",time0);
401 artak 2509
402 artak 1931 /*end of postsmoothing*/
403    
404 jfenwick 1851 }
405 artak 1890 MEMFREE(r);
406 artak 1954 MEMFREE(x0);
407 artak 1931 return;
408 jfenwick 1851 }
409    
410     /*
411     * $Log$
412     *
413     */

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