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

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Revision 1881 - (hide annotations)
Tue Oct 14 04:34:09 2008 UTC (10 years, 11 months ago) by artak
File MIME type: text/plain
File size: 16389 byte(s)
pattern multiply, binary operation are added
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     Paso_Solver_AMG* Paso_Solver_getAMG(Paso_SparseMatrix *A_p,bool_t verbose) {
72     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     schur_withFillIn=MEMALLOC(1,Paso_SparseMatrix);
83    
84    
85 jfenwick 1851 double A11,A12,A13,A21,A22,A23,A31,A32,A33,D,time0,time1,time2;
86    
87    
88     /* identify independend set of rows/columns */
89     mis_marker=TMPMEMALLOC(n,index_t);
90     counter=TMPMEMALLOC(n,index_t);
91 artak 1881 rs=TMPMEMALLOC(n,double);
92 jfenwick 1851 out=MEMALLOC(1,Paso_Solver_AMG);
93     out->AMG_of_Schur=NULL;
94     out->inv_A_FF=NULL;
95     out->A_FF_pivot=NULL;
96     out->A_FC=NULL;
97     out->A_CF=NULL;
98     out->rows_in_F=NULL;
99     out->rows_in_C=NULL;
100     out->mask_F=NULL;
101     out->mask_C=NULL;
102     out->x_F=NULL;
103     out->b_F=NULL;
104     out->x_C=NULL;
105     out->b_C=NULL;
106 artak 1881
107     /* fprintf(stderr,"START OF MATRIX \n\n");
108     for (i = 0; i < A_p->numRows; ++i) {
109     for (iPtr=A_p->pattern->ptr[i];iPtr<A_p->pattern->ptr[i + 1]; ++iPtr) {
110     j=A_p->pattern->index[iPtr];
111     fprintf(stderr,"A[%d,%d]=%.2f ",i,j,A_p->val[iPtr]);
112     }
113     fprintf(stderr,"\n");
114     }
115     fprintf(stderr,"END OF MATRIX \n\n");
116     */
117 jfenwick 1851 if ( !(Paso_checkPtr(mis_marker) || Paso_checkPtr(out) || Paso_checkPtr(counter) ) ) {
118     /* identify independend set of rows/columns */
119     time0=Paso_timer();
120     #pragma omp parallel for private(i) schedule(static)
121     for (i=0;i<n;++i) mis_marker[i]=-1;
122 artak 1881 Paso_Pattern_coup(A_p,mis_marker);
123 jfenwick 1851 time2=Paso_timer()-time0;
124     if (Paso_noError()) {
125     #pragma omp parallel for private(i) schedule(static)
126     for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
127     out->n=n;
128     out->n_block=n_block;
129     out->n_F=Paso_Util_cumsum(n,counter);
130     out->mask_F=MEMALLOC(n,index_t);
131     out->rows_in_F=MEMALLOC(out->n_F,index_t);
132     out->inv_A_FF=MEMALLOC(n_block*n_block*out->n_F,double);
133     out->A_FF_pivot=NULL; /* later use for block size>3 */
134     if (! (Paso_checkPtr(out->mask_F) || Paso_checkPtr(out->inv_A_FF) || Paso_checkPtr(out->rows_in_F) ) ) {
135     #pragma omp parallel
136     {
137     /* creates an index for F from mask */
138     #pragma omp for private(i) schedule(static)
139     for (i = 0; i < out->n_F; ++i) out->rows_in_F[i]=-1;
140     #pragma omp for private(i) schedule(static)
141     for (i = 0; i < n; ++i) {
142     if (mis_marker[i]) {
143     out->rows_in_F[counter[i]]=i;
144     out->mask_F[i]=counter[i];
145     } else {
146     out->mask_F[i]=-1;
147     }
148     }
149 artak 1881 /* Compute row-sum for getting rs(A_FF)*/
150     #pragma omp for private(i,iPtr) schedule(static)
151     for (i = 0; i < out->n_F; ++i) {
152     rs[i]=0;
153     for (iPtr=A_p->pattern->ptr[out->rows_in_F[i]];iPtr<A_p->pattern->ptr[out->rows_in_F[i] + 1]; ++iPtr) {
154     rs[i]+=A_p->val[iPtr];
155     }
156     }
157    
158 jfenwick 1851 #pragma omp for private(i, where_p,iPtr,A11,A12,A13,A21,A22,A23,A31,A32,A33,D,index) schedule(static)
159     for (i = 0; i < out->n_F; i++) {
160     /* find main diagonal */
161     iPtr=A_p->pattern->ptr[out->rows_in_F[i]];
162     index=&(A_p->pattern->index[iPtr]);
163     where_p=(index_t*)bsearch(&out->rows_in_F[i],
164     index,
165     A_p->pattern->ptr[out->rows_in_F[i] + 1]-A_p->pattern->ptr[out->rows_in_F[i]],
166     sizeof(index_t),
167     Paso_comparIndex);
168     if (where_p==NULL) {
169     Paso_setError(VALUE_ERROR, "Paso_Solver_getAMG: main diagonal element missing.");
170     } else {
171     iPtr+=(index_t)(where_p-index);
172     /* get inverse of A_FF block: */
173 artak 1881 if (ABS(rs[i])>0.) {
174     out->inv_A_FF[i]=1./rs[i];
175     } else {
176 jfenwick 1851 Paso_setError(ZERO_DIVISION_ERROR, "Paso_Solver_getAMG: Break-down in AMG decomposition: non-regular main diagonal block.");
177 artak 1881 }
178     }
179 jfenwick 1851 }
180     } /* end parallel region */
181    
182     if( Paso_noError()) {
183     /* if there are no nodes in the coarse level there is no more work to do */
184     out->n_C=n-out->n_F;
185     if (out->n_C>0) {
186     out->rows_in_C=MEMALLOC(out->n_C,index_t);
187     out->mask_C=MEMALLOC(n,index_t);
188     if (! (Paso_checkPtr(out->mask_C) || Paso_checkPtr(out->rows_in_C) ) ) {
189     /* creates an index for C from mask */
190     #pragma omp parallel for private(i) schedule(static)
191     for (i = 0; i < n; ++i) counter[i]=! mis_marker[i];
192     Paso_Util_cumsum(n,counter);
193     #pragma omp parallel
194     {
195     #pragma omp for private(i) schedule(static)
196     for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
197     #pragma omp for private(i) schedule(static)
198     for (i = 0; i < n; ++i) {
199     if (! mis_marker[i]) {
200     out->rows_in_C[counter[i]]=i;
201     out->mask_C[i]=counter[i];
202     } else {
203     out->mask_C[i]=-1;
204     }
205     }
206     } /* end parallel region */
207     /* get A_CF block: */
208     out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
209     if (Paso_noError()) {
210     /* get A_FC block: */
211     out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
212 artak 1881 /* get A_CC block: */
213 jfenwick 1851 if (Paso_noError()) {
214     schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
215 artak 1881
216     /*find the pattern of the schur complement with fill in*/
217     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);
218    
219     /* copy values over*/
220     #pragma omp for private(i,iPtr,iPtr_s,j,j0) schedule(static)
221     for (i = 0; i < schur_withFillIn->numRows; ++i) {
222     for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
223     j=schur_withFillIn->pattern->index[iPtr];
224     schur_withFillIn->val[iPtr]=0.;
225     for (iPtr_s=schur->pattern->ptr[i];iPtr_s<schur->pattern->ptr[i + 1]; ++iPtr_s){
226     j0=schur->pattern->index[iPtr_s];
227     if (j==j0) {
228     schur_withFillIn->val[iPtr]=schur->val[iPtr_s];
229     break;
230     }
231     }
232     }
233     }
234    
235     /* for (i = 0; i < schur_withFillIn->numRows; ++i) {
236     for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
237     j=schur_withFillIn->pattern->index[iPtr];
238     fprintf(stderr,"A_CC[%d,%d]=%.2f ",i,j,schur_withFillIn->val[iPtr]);
239     }
240     fprintf(stderr,"\n");
241     }*/
242 jfenwick 1851 time0=Paso_timer()-time0;
243     if (Paso_noError()) {
244     time1=Paso_timer();
245     /* update A_CC block to get Schur complement and then apply AMG to it */
246 artak 1881 Paso_Solver_updateIncompleteSchurComplement(schur_withFillIn,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC);
247 jfenwick 1851 time1=Paso_timer()-time1;
248 artak 1881 out->AMG_of_Schur=Paso_Solver_getAMG(schur_withFillIn,verbose);
249    
250 jfenwick 1851 Paso_SparseMatrix_free(schur);
251 artak 1881 Paso_SparseMatrix_free(schur_withFillIn);
252 jfenwick 1851 }
253     /* allocate work arrays for AMG application */
254     if (Paso_noError()) {
255     out->x_F=MEMALLOC(n_block*out->n_F,double);
256     out->b_F=MEMALLOC(n_block*out->n_F,double);
257     out->x_C=MEMALLOC(n_block*out->n_C,double);
258     out->b_C=MEMALLOC(n_block*out->n_C,double);
259     if (! (Paso_checkPtr(out->x_F) || Paso_checkPtr(out->b_F) || Paso_checkPtr(out->x_C) || Paso_checkPtr(out->b_C) ) ) {
260     #pragma omp parallel
261     {
262     #pragma omp for private(i,k) schedule(static)
263     for (i = 0; i < out->n_F; ++i) {
264     for (k=0; k<n_block;++k) {
265     out->x_F[i*n_block+k]=0.;
266     out->b_F[i*n_block+k]=0.;
267     }
268     }
269     #pragma omp for private(i,k) schedule(static)
270     for (i = 0; i < out->n_C; ++i) {
271     for (k=0; k<n_block;++k) {
272     out->x_C[i*n_block+k]=0.;
273     out->b_C[i*n_block+k]=0.;
274     }
275     }
276     } /* end parallel region */
277     }
278     }
279     }
280     }
281     }
282     }
283     }
284     }
285     }
286     }
287     TMPMEMFREE(mis_marker);
288     TMPMEMFREE(counter);
289 artak 1881 TMPMEMFREE(rs);
290 jfenwick 1851 if (Paso_noError()) {
291     if (verbose) {
292     printf("AMG: %d unknowns eliminated. %d left.\n",out->n_F,n-out->n_F);
293     if (out->n_C>0) {
294     printf("timing: AMG: MIS/reordering/elemination : %e/%e/%e\n",time2,time0,time1);
295     } else {
296     printf("timing: AMG: MIS: %e\n",time2);
297     }
298     }
299     return out;
300     } else {
301     Paso_Solver_AMG_free(out);
302     return NULL;
303     }
304     }
305    
306     /**************************************************************/
307    
308     /* apply AMG precondition b-> x
309    
310     in fact it solves
311    
312     [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ] [ x_F ] = [b_F]
313     [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] [ x_C ] = [b_C]
314    
315     in the form
316    
317     b->[b_F,b_C]
318     x_F=invA_FF*b_F
319     b_C=b_C-A_CF*x_F
320     x_C=AMG(b_C)
321     b_F=b_F-A_FC*x_C
322     x_F=invA_FF*b_F
323     x<-[x_F,x_C]
324    
325     should be called within a parallel region
326     barrier synconization should be performed to make sure that the input vector available
327    
328     */
329    
330     void Paso_Solver_solveAMG(Paso_Solver_AMG * amg, double * x, double * b) {
331     dim_t i,k;
332     dim_t n_block=amg->n_block;
333 artak 1881
334 jfenwick 1851 if (amg->n_C==0) {
335     /* x=invA_FF*b */
336     Paso_Solver_applyBlockDiagonalMatrix(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,x,b);
337     } else {
338 artak 1881 /* presmoothing on (Shure, x, b, r) */
339 jfenwick 1851 /* b->[b_F,b_C] */
340     if (n_block==1) {
341     #pragma omp parallel for private(i) schedule(static)
342     for (i=0;i<amg->n_F;++i) amg->b_F[i]=b[amg->rows_in_F[i]];
343     #pragma omp parallel for private(i) schedule(static)
344     for (i=0;i<amg->n_C;++i) amg->b_C[i]=b[amg->rows_in_C[i]];
345     } else {
346     #pragma omp parallel for private(i,k) schedule(static)
347     for (i=0;i<amg->n_F;++i)
348     for (k=0;k<n_block;k++) amg->b_F[amg->n_block*i+k]=b[n_block*amg->rows_in_F[i]+k];
349     #pragma omp parallel for private(i,k) schedule(static)
350     for (i=0;i<amg->n_C;++i)
351     for (k=0;k<n_block;k++) amg->b_C[amg->n_block*i+k]=b[n_block*amg->rows_in_C[i]+k];
352     }
353     /* x_F=invA_FF*b_F */
354     Paso_Solver_applyBlockDiagonalMatrix(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
355     /* b_C=b_C-A_CF*x_F */
356     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->x_F,1.,amg->b_C);
357     /* x_C=AMG(b_C) */
358     Paso_Solver_solveAMG(amg->AMG_of_Schur,amg->x_C,amg->b_C);
359     /* b_F=b_F-A_FC*x_C */
360     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_FC,amg->x_C,1.,amg->b_F);
361     /* x_F=invA_FF*b_F */
362     Paso_Solver_applyBlockDiagonalMatrix(n_block,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
363     /* x<-[x_F,x_C] */
364     if (n_block==1) {
365     #pragma omp parallel for private(i) schedule(static)
366     for (i=0;i<amg->n;++i) {
367     if (amg->mask_C[i]>-1) {
368     x[i]=amg->x_C[amg->mask_C[i]];
369     } else {
370     x[i]=amg->x_F[amg->mask_F[i]];
371     }
372     }
373     } else {
374     #pragma omp parallel for private(i,k) schedule(static)
375     for (i=0;i<amg->n;++i) {
376     if (amg->mask_C[i]>-1) {
377     for (k=0;k<n_block;k++) x[n_block*i+k]=amg->x_C[n_block*amg->mask_C[i]+k];
378     } else {
379     for (k=0;k<n_block;k++) x[n_block*i+k]=amg->x_F[n_block*amg->mask_F[i]+k];
380     }
381     }
382     }
383     /* all done */
384     }
385     return;
386     }
387    
388     /*
389     * $Log$
390     *
391     */

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