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

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Revision 2280 - (hide annotations)
Thu Feb 19 03:34:35 2009 UTC (11 years, 7 months ago) by artak
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File size: 15750 byte(s)
Some statistics changed in solver.c. In AMG stopping criteria now depend on levels specified. In loadMM conditions on pivot and lval reformulated to avoid numerical overflow.
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 artak 1931 #include "UMFPACK.h"
29 phornby 1917 #include "Pattern_coupling.h"
30 jfenwick 1851
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 artak 2112 Paso_Solver_Jacobi_free(in->GS);
39 jfenwick 1851 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 artak 2178 Paso_Solver_AMG* Paso_Solver_getAMG(Paso_SparseMatrix *A_p,bool_t verbose,dim_t level, double couplingParam) {
75 jfenwick 1851 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 artak 1881 index_t* counter=NULL;
80     index_t iPtr,*index, *where_p, iPtr_s;
81 artak 2107 dim_t i,k,j;
82 jfenwick 1851 Paso_SparseMatrix * schur=NULL;
83 artak 1881 Paso_SparseMatrix * schur_withFillIn=NULL;
84 artak 2107 double time0=0,time1=0,time2=0,S=0;
85     /*Paso_Pattern* test;*/
86 artak 1890
87 jfenwick 1851 /* 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 artak 2107 out->GS=NULL;
105 artak 1890 out->A=Paso_SparseMatrix_getReference(A_p);
106 artak 2112 /*out->GS=Paso_Solver_getGS(A_p,verbose);*/
107     out->GS=Paso_Solver_getJacobi(A_p);
108 artak 2107 /*out->GS->sweeps=2;*/
109 artak 1890 out->level=level;
110 artak 2107
111 jfenwick 1851 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 artak 1954 /*Paso_Pattern_RS(A_p,mis_marker,0.25);*/
116     /*Paso_Pattern_Aggregiation(A_p,mis_marker,0.5);*/
117 artak 2178 Paso_Pattern_coup(A_p,mis_marker,couplingParam);
118 jfenwick 1851 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 artak 2107 #pragma omp parallel for private(i) schedule(static)
131 jfenwick 1851 for (i = 0; i < out->n_F; ++i) out->rows_in_F[i]=-1;
132 artak 2107 #pragma omp parallel for private(i) schedule(static)
133 jfenwick 1851 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 artak 2107
142     /* Compute row-sum for getting rs(A_FF)^-1*/
143 artak 2131 #pragma omp parallel for private(i,iPtr,j,S) schedule(static)
144 artak 1881 for (i = 0; i < out->n_F; ++i) {
145 artak 2107 S=0;
146 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) {
147 artak 1975 j=A_p->pattern->index[iPtr];
148     if (mis_marker[j])
149 artak 2107 S+=A_p->val[iPtr];
150 artak 1881 }
151 artak 2107 out->inv_A_FF[i]=1./S;
152 artak 1881 }
153 jfenwick 1851
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 artak 2280 if (level<3) {
158     /*if (out->n_F>500) {*/
159 jfenwick 1851 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 artak 2107 #pragma omp parallel for private(i) schedule(static)
167 jfenwick 1851 for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
168 artak 2107 #pragma omp parallel for private(i) schedule(static)
169 jfenwick 1851 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 artak 1881 /* get A_CC block: */
183 jfenwick 1851 if (Paso_noError()) {
184     schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
185 artak 2107 /*find the pattern of the schur complement with fill in*/
186 artak 2112
187 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);
188 artak 2107
189 artak 2280 /*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 artak 2107
191 artak 1881 /* copy values over*/
192 artak 2107 #pragma omp parallel for private(i,iPtr,j,iPtr_s,index,where_p) schedule(static)
193 artak 1881 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 artak 2107 iPtr_s=schur->pattern->ptr[i];
197 artak 1881 schur_withFillIn->val[iPtr]=0.;
198 artak 2107 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 artak 1881 }
207     }
208     }
209 artak 2107
210 jfenwick 1851 if (Paso_noError()) {
211 artak 1881 Paso_Solver_updateIncompleteSchurComplement(schur_withFillIn,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC);
212 artak 2178 out->AMG_of_Schur=Paso_Solver_getAMG(schur_withFillIn,verbose,level+1,couplingParam);
213 artak 2107 Paso_SparseMatrix_free(schur);
214 jfenwick 1851 }
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 artak 1890
222 jfenwick 1851 if (! (Paso_checkPtr(out->x_F) || Paso_checkPtr(out->b_F) || Paso_checkPtr(out->x_C) || Paso_checkPtr(out->b_C) ) ) {
223 artak 2107 #pragma omp parallel for private(i,k) schedule(static)
224     for (i = 0; i < out->n_F; ++i) {
225 jfenwick 1851 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 artak 2107 #pragma omp parallel for private(i,k) schedule(static)
231 jfenwick 1851 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 artak 2280 if (level<3) {
253     /* if (out->n_F<500) {*/
254 jfenwick 1851 printf("timing: AMG: MIS/reordering/elemination : %e/%e/%e\n",time2,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_FF ] [ 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 artak 2107 dim_t i;
292 artak 1890 double *r=MEMALLOC(amg->n,double);
293 artak 1939 /*Paso_Solver_GS* GS=NULL;*/
294 artak 1954 double *x0=MEMALLOC(amg->n,double);
295 artak 2107 double time0=0;
296    
297 artak 2280 if (amg->level==3) {
298     /*if (amg->n_F<=500) {*/
299 artak 2107 time0=Paso_timer();
300    
301 artak 2112 Paso_Solver_solveJacobi(amg->GS,x,b);
302 artak 2107
303     /* #pragma omp parallel for private(i) schedule(static)
304     for (i=0;i<amg->n;++i) r[i]=b[i];
305     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
306     Paso_Solver_solveGS(amg->GS,x0,r);
307     #pragma omp parallel for private(i) schedule(static)
308     for (i=0;i<amg->n;++i) {
309     x[i]+=x0[i];
310     }
311     */
312 artak 2112 /*Paso_UMFPACK1(amg->A,x,b,0);*/
313 artak 1939
314 artak 2107 time0=Paso_timer()-time0;
315     /*fprintf(stderr,"timing: DIRECT SOLVER: %e/\n",time0);*/
316 jfenwick 1851 } else {
317 artak 1954
318 artak 1902 /* presmoothing */
319 artak 2112 Paso_Solver_solveJacobi(amg->GS,x,b);
320 artak 2107 /*
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 artak 1931 /* end of presmoothing */
333 artak 1939
334 artak 1890 #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 artak 1954
340 jfenwick 1851 /* b->[b_F,b_C] */
341 artak 1954 #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 artak 1890
347 jfenwick 1851 /* x_F=invA_FF*b_F */
348 artak 1954 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
349 artak 1890
350 jfenwick 1851 /* 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 artak 1890
353 jfenwick 1851 /* x_C=AMG(b_C) */
354     Paso_Solver_solveAMG(amg->AMG_of_Schur,amg->x_C,amg->b_C);
355 artak 1890
356 jfenwick 1851 /* 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 artak 1954 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
360 jfenwick 1851 /* x<-[x_F,x_C] */
361 artak 2113
362 artak 1954 #pragma omp parallel for private(i) schedule(static)
363     for (i=0;i<amg->n;++i) {
364     if (amg->mask_C[i]>-1) {
365 artak 2107 x[i]=amg->x_C[amg->mask_C[i]];
366 artak 1954 } else {
367 artak 2107 x[i]=amg->x_F[amg->mask_F[i]];
368 artak 1954 }
369 jfenwick 1851 }
370 artak 1954
371 artak 1931 /*postsmoothing*/
372 artak 2107
373 artak 1954 #pragma omp parallel for private(i) schedule(static)
374     for (i=0;i<amg->n;++i) r[i]=b[i];
375 artak 2107
376 artak 1954 /*r=b-Ax*/
377     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
378 artak 2112 Paso_Solver_solveJacobi(amg->GS,x0,r);
379 artak 2107
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 artak 1954 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 artak 2107 */
395 artak 1931 /*end of postsmoothing*/
396    
397 jfenwick 1851 }
398 artak 1890 MEMFREE(r);
399 artak 1954 MEMFREE(x0);
400 artak 1931 return;
401 jfenwick 1851 }
402    
403     /*
404     * $Log$
405     *
406     */

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