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

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Revision 3315 - (hide annotations)
Wed Oct 27 01:20:27 2010 UTC (9 years ago) by gross
File MIME type: text/plain
File size: 16563 byte(s)
bug in sparse matrixmatrix fixed.
1 gross 3193
2     /*******************************************************
3     *
4     * Copyright (c) 2003-2010 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 */
18    
19     /**************************************************************/
20    
21 gross 3303 /* Author: artak@uq.edu.au, l.gross@uq.edu.au */
22 gross 3193
23     /**************************************************************/
24    
25 gross 3283 #define SHOW_TIMING FALSE
26    
27 gross 3193 #include "Paso.h"
28     #include "Preconditioner.h"
29     #include "Options.h"
30     #include "PasoUtil.h"
31     #include "UMFPACK.h"
32     #include "MKL.h"
33    
34     /**************************************************************/
35    
36     /* free all memory used by AMG */
37    
38     void Paso_Preconditioner_LocalAMG_free(Paso_Preconditioner_LocalAMG * in) {
39     if (in!=NULL) {
40     Paso_Preconditioner_LocalSmoother_free(in->Smoother);
41 gross 3283 Paso_SparseMatrix_free(in->P);
42     Paso_SparseMatrix_free(in->R);
43     Paso_SparseMatrix_free(in->A_C);
44     Paso_Preconditioner_LocalAMG_free(in->AMG_C);
45     MEMFREE(in->r);
46     MEMFREE(in->x_C);
47     MEMFREE(in->b_C);
48 gross 3193
49 gross 3283
50     MEMFREE(in);
51 gross 3193 }
52     }
53    
54 gross 3283 /*****************************************************************
55 gross 3193
56 gross 3283 constructs AMG
57    
58     ******************************************************************/
59     Paso_Preconditioner_LocalAMG* Paso_Preconditioner_LocalAMG_alloc(Paso_SparseMatrix *A_p,dim_t level,Paso_Options* options) {
60 gross 3193
61     Paso_Preconditioner_LocalAMG* out=NULL;
62     bool_t verbose=options->verbose;
63    
64 gross 3303 Paso_SparseMatrix *Atemp=NULL, *A_C=NULL;
65 gross 3193 const dim_t n=A_p->numRows;
66     const dim_t n_block=A_p->row_block_size;
67 gross 3303 index_t* split_marker=NULL, *counter=NULL, *mask_C=NULL, *rows_in_F=NULL, *S=NULL, *degree=NULL;
68 gross 3283 dim_t n_F=0, n_C=0, i;
69     double time0=0;
70     const double theta = options->coarsening_threshold;
71     const double tau = options->diagonal_dominance_threshold;
72 gross 3193
73    
74     /*
75 gross 3283 is the input matrix A suitable for coarsening
76    
77 gross 3193 */
78 gross 3283 if ( (A_p->pattern->len >= options->min_coarse_sparsity * n * n ) || (n <= options->min_coarse_matrix_size) || (level > options->level_max) ) {
79     if (verbose) printf("Paso: AMG level %d (limit = %d) stopped. sparsity = %e (limit = %e), unknowns = %d (limit = %d)\n",
80     level, options->level_max, A_p->pattern->len/(1.*n * n), options->min_coarse_sparsity, n, options->min_coarse_matrix_size );
81 gross 3193 return NULL;
82 gross 3283 }
83     /* Start Coarsening : */
84 gross 3193
85 gross 3283 split_marker=TMPMEMALLOC(n,index_t);
86     counter=TMPMEMALLOC(n,index_t);
87 gross 3303 degree=TMPMEMALLOC(n, dim_t);
88     S=TMPMEMALLOC(A_p->pattern->len, index_t);
89     if ( !( Esys_checkPtr(split_marker) || Esys_checkPtr(counter) || Esys_checkPtr(degree) || Esys_checkPtr(S) ) ) {
90 gross 3283 /*
91     set splitting of unknows:
92    
93     */
94     time0=Esys_timer();
95     if (n_block>1) {
96 gross 3303 Paso_Preconditioner_AMG_setStrongConnections_Block(A_p, degree, S, theta,tau);
97 gross 3283 } else {
98 gross 3303 Paso_Preconditioner_AMG_setStrongConnections(A_p, degree, S, theta,tau);
99 gross 3283 }
100 gross 3303 Paso_Preconditioner_AMG_RungeStuebenSearch(n, A_p->pattern->ptr, degree, S, split_marker);
101 gross 3283 options->coarsening_selection_time=Esys_timer()-time0 + MAX(0, options->coarsening_selection_time);
102    
103     if (Esys_noError() ) {
104     #pragma omp parallel for private(i) schedule(static)
105     for (i = 0; i < n; ++i) split_marker[i]= (split_marker[i] == PASO_AMG_IN_F);
106    
107     /*
108     count number of unkowns to be eliminated:
109     */
110     n_F=Paso_Util_cumsum_maskedTrue(n,counter, split_marker);
111     n_C=n-n_F;
112 gross 3312 if (verbose) printf("Paso: AMG level %d: %d unknowns are flagged for elimination. %d left.\n",level,n_F,n-n_F);
113 gross 3283
114     if ( n_F == 0 ) { /* is a nasty case. a direct solver should be used, return NULL */
115     out = NULL;
116     } else {
117     out=MEMALLOC(1,Paso_Preconditioner_LocalAMG);
118     mask_C=TMPMEMALLOC(n,index_t);
119     rows_in_F=TMPMEMALLOC(n_F,index_t);
120     if ( !( Esys_checkPtr(mask_C) || Esys_checkPtr(rows_in_F) || Esys_checkPtr(out)) ) {
121     out->level = level;
122     out->n = n;
123     out->n_F = n_F;
124     out->n_block = n_block;
125     out->A_C = NULL;
126     out->P = NULL;
127     out->R = NULL;
128     out->post_sweeps = options->post_sweeps;
129     out->pre_sweeps = options->pre_sweeps;
130     out->r = NULL;
131     out->x_C = NULL;
132     out->b_C = NULL;
133     out->AMG_C = NULL;
134     out->Smoother = Paso_Preconditioner_LocalSmoother_alloc(A_p, (options->smoother == PASO_JACOBI), verbose);
135    
136     if ( n_F < n ) { /* if nothing is been removed we have a diagonal dominant matrix and we just run a few steps of the smoother */
137    
138 gross 3315 /* allocate helpers :*/
139     out->x_C=MEMALLOC(n_block*n_C,double);
140     out->b_C=MEMALLOC(n_block*n_C,double);
141     out->r=MEMALLOC(n_block*n,double);
142    
143     Esys_checkPtr(out->r);
144     Esys_checkPtr(out->Smoother);
145     Esys_checkPtr(out->x_C);
146     Esys_checkPtr(out->b_C);
147    
148     /* creates index for F:*/
149 gross 3283 #pragma omp parallel for private(i) schedule(static)
150     for (i = 0; i < n; ++i) {
151     if (split_marker[i]) rows_in_F[counter[i]]=i;
152     }
153     /* create mask of C nodes with value >-1 gives new id */
154     i=Paso_Util_cumsum_maskedFalse(n,counter, split_marker);
155 gross 3193
156 gross 3283 #pragma omp parallel for private(i) schedule(static)
157     for (i = 0; i < n; ++i) {
158     if (split_marker[i]) {
159     mask_C[i]=-1;
160     } else {
161     mask_C[i]=counter[i];;
162     }
163     }
164     /*
165 gross 3303 get Restriction :
166     */
167 gross 3283 time0=Esys_timer();
168 gross 3303 out->P=Paso_Preconditioner_AMG_getDirectProlongation(A_p,degree,S,n_C,mask_C);
169 gross 3283 if (SHOW_TIMING) printf("timing: level %d: getProlongation: %e\n",level, Esys_timer()-time0);
170 gross 3303 /*
171 gross 3283 construct Prolongation operator as transposed of restriction operator:
172     */
173 gross 3315 if ( Esys_noError()) {
174     time0=Esys_timer();
175     out->R=Paso_SparseMatrix_getTranspose(out->P);
176     if (SHOW_TIMING) printf("timing: level %d: Paso_SparseMatrix_getTranspose: %e\n",level,Esys_timer()-time0);
177     }
178 gross 3283 /*
179 gross 3312 construct coarse level matrix:
180 gross 3283 */
181 gross 3315 if ( Esys_noError()) {
182     time0=Esys_timer();
183     Atemp=Paso_SparseMatrix_MatrixMatrix(A_p,out->P);
184     A_C=Paso_SparseMatrix_MatrixMatrix(out->R,Atemp);
185     Paso_SparseMatrix_free(Atemp);
186     if (SHOW_TIMING) printf("timing: level %d : construct coarse matrix: %e\n",level,Esys_timer()-time0);
187     }
188    
189 gross 3283
190     /*
191     constructe courser level:
192    
193     */
194     if ( Esys_noError()) {
195 gross 3315 out->AMG_C=Paso_Preconditioner_LocalAMG_alloc(A_C,level+1,options);
196     }
197     if ( Esys_noError()) {
198 gross 3283 if ( out->AMG_C == NULL ) {
199     out->reordering = options->reordering;
200     out->refinements = options->coarse_matrix_refinements;
201     /* no coarse level matrix has been constructed. use direct solver */
202     #ifdef MKL
203 gross 3312 out->A_C=Paso_SparseMatrix_unroll(MATRIX_FORMAT_BLK1 + MATRIX_FORMAT_OFFSET1, A_C);
204 gross 3283 Paso_SparseMatrix_free(A_C);
205     out->A_C->solver_package = PASO_MKL;
206 gross 3314 if (verbose) printf("Paso: AMG: use MKL direct solver on the coarsest level (number of unknowns = %d).\n",n_C);
207 gross 3283 #else
208     #ifdef UMFPACK
209 gross 3312 out->A_C=Paso_SparseMatrix_unroll(MATRIX_FORMAT_BLK1 + MATRIX_FORMAT_CSC, A_C);
210 gross 3283 Paso_SparseMatrix_free(A_C);
211     out->A_C->solver_package = PASO_UMFPACK;
212 gross 3314 if (verbose) printf("Paso: AMG: use UMFPACK direct solver on the coarsest level (number of unknowns = %d).\n",n_C);
213 gross 3283 #else
214     out->A_C=A_C;
215     out->A_C->solver_p=Paso_Preconditioner_LocalSmoother_alloc(out->A_C, (options->smoother == PASO_JACOBI), verbose);
216     out->A_C->solver_package = PASO_SMOOTHER;
217 gross 3314 if (verbose) printf("Paso: AMG: use smoother on the coarsest level (number of unknowns = %d).\n",n_C);
218 gross 3283 #endif
219     #endif
220     } else {
221     /* finally we set some helpers for the solver step */
222     out->A_C=A_C;
223     }
224     }
225     }
226     }
227     TMPMEMFREE(mask_C);
228     TMPMEMFREE(rows_in_F);
229     }
230     }
231 gross 3193 }
232     TMPMEMFREE(counter);
233 gross 3283 TMPMEMFREE(split_marker);
234 gross 3303 TMPMEMFREE(degree);
235     TMPMEMFREE(S);
236 gross 3193
237 jfenwick 3259 if (Esys_noError()) {
238 gross 3193 return out;
239     } else {
240     Paso_Preconditioner_LocalAMG_free(out);
241     return NULL;
242     }
243     }
244    
245    
246 gross 3283 void Paso_Preconditioner_LocalAMG_solve(Paso_SparseMatrix* A, Paso_Preconditioner_LocalAMG * amg, double * x, double * b) {
247     const dim_t n = amg->n * amg->n_block;
248     double time0=0;
249     const dim_t post_sweeps=amg->post_sweeps;
250     const dim_t pre_sweeps=amg->pre_sweeps;
251 gross 3193
252 gross 3283 /* presmoothing */
253     time0=Esys_timer();
254     Paso_Preconditioner_LocalSmoother_solve(A, amg->Smoother, x, b, pre_sweeps, FALSE);
255     time0=Esys_timer()-time0;
256     if (SHOW_TIMING) printf("timing: level %d: Presmooting: %e\n",amg->level, time0);
257     /* end of presmoothing */
258    
259     if (amg->n_F < amg->n) { /* is there work on the coarse level? */
260     time0=Esys_timer();
261     Paso_Copy(n, amg->r, b); /* r <- b */
262 gross 3312 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,A,x,1.,amg->r); /*r=r-Ax*/
263     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0_DIAG(1.,amg->R,amg->r,0.,amg->b_C); /* b_c = R*r */
264 gross 3283 time0=Esys_timer()-time0;
265     /* coarse level solve */
266     if ( amg->AMG_C == NULL) {
267     time0=Esys_timer();
268     /* A_C is the coarsest level */
269     switch (amg->A_C->solver_package) {
270     case (PASO_MKL):
271     Paso_MKL(amg->A_C, amg->x_C,amg->b_C, amg->reordering, amg->refinements, SHOW_TIMING);
272     break;
273     case (PASO_UMFPACK):
274     Paso_UMFPACK(amg->A_C, amg->x_C,amg->b_C, amg->refinements, SHOW_TIMING);
275     break;
276     case (PASO_SMOOTHER):
277     Paso_Preconditioner_LocalSmoother_solve(amg->A_C, amg->Smoother,amg->x_C,amg->b_C,pre_sweeps, FALSE);
278     break;
279     }
280     if (SHOW_TIMING) printf("timing: level %d: DIRECT SOLVER: %e\n",amg->level,Esys_timer()-time0);
281     } else {
282     Paso_Preconditioner_LocalAMG_solve(amg->A_C, amg->AMG_C,amg->x_C,amg->b_C); /* x_C=AMG(b_C) */
283     }
284     time0=time0+Esys_timer();
285 gross 3303 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0_DIAG(1.,amg->P,amg->x_C,1.,x); /* x = x + P*x_c */
286 gross 3283
287     /*postsmoothing*/
288    
289     /*solve Ax=b with initial guess x */
290     time0=Esys_timer();
291     Paso_Preconditioner_LocalSmoother_solve(A, amg->Smoother, x, b, post_sweeps, TRUE);
292     time0=Esys_timer()-time0;
293     if (SHOW_TIMING) printf("timing: level %d: Postsmoothing: %e\n",amg->level,time0);
294     /*end of postsmoothing*/
295    
296     }
297     return;
298     }
299 gross 3193
300 gross 3283 /* theta = threshold for strong connections */
301     /* tau = threshold for diagonal dominance */
302 gross 3193
303 gross 3303 /*S_i={j \in N_i; i strongly coupled to j}
304    
305     in the sense that |A_{ij}| >= theta * max_k |A_{ik}|
306     */
307    
308     void Paso_Preconditioner_AMG_setStrongConnections(Paso_SparseMatrix* A,
309     dim_t *degree, index_t *S,
310     const double theta, const double tau)
311 gross 3283 {
312     const dim_t n=A->numRows;
313 gross 3303 index_t iptr, i,j;
314 gross 3283 dim_t kdeg;
315     double max_offdiagonal, threshold, sum_row, main_row, fnorm;
316 gross 3193
317 gross 3303
318 gross 3283 #pragma omp parallel for private(i,iptr,max_offdiagonal, threshold,j, kdeg, sum_row, main_row, fnorm) schedule(static)
319     for (i=0;i<n;++i) {
320 gross 3193
321 gross 3283 max_offdiagonal = 0.;
322     sum_row=0;
323     main_row=0;
324     #pragma ivdep
325     for (iptr=A->pattern->ptr[i];iptr<A->pattern->ptr[i+1]; ++iptr) {
326     j=A->pattern->index[iptr];
327     fnorm=ABS(A->val[iptr]);
328    
329     if( j != i) {
330     max_offdiagonal = MAX(max_offdiagonal,fnorm);
331     sum_row+=fnorm;
332     } else {
333     main_row=fnorm;
334     }
335     }
336     threshold = theta*max_offdiagonal;
337     kdeg=0;
338     if (tau*main_row < sum_row) { /* no diagonal domainance */
339     #pragma ivdep
340     for (iptr=A->pattern->ptr[i];iptr<A->pattern->ptr[i+1]; ++iptr) {
341     j=A->pattern->index[iptr];
342     if(ABS(A->val[iptr])>threshold && i!=j) {
343     S[A->pattern->ptr[i]+kdeg] = j;
344     kdeg++;
345     }
346     }
347     }
348     degree[i]=kdeg;
349     }
350 gross 3303
351 gross 3283 }
352 gross 3193
353 gross 3283 /* theta = threshold for strong connections */
354     /* tau = threshold for diagonal dominance */
355 gross 3303 /*S_i={j \in N_i; i strongly coupled to j}
356 gross 3283
357 gross 3303 in the sense that |A_{ij}|_F >= theta * max_k |A_{ik}|_F
358     */
359     void Paso_Preconditioner_AMG_setStrongConnections_Block(Paso_SparseMatrix* A,
360     dim_t *degree, index_t *S,
361     const double theta, const double tau)
362    
363 gross 3283 {
364     const dim_t n_block=A->row_block_size;
365     const dim_t n=A->numRows;
366 gross 3303 index_t iptr, i,j, bi;
367 gross 3283 dim_t kdeg, max_deg;
368     register double max_offdiagonal, threshold, fnorm, sum_row, main_row;
369     double *rtmp;
370    
371    
372     #pragma omp parallel private(i,iptr,max_offdiagonal, kdeg, threshold,j, max_deg, fnorm, sum_row, main_row, rtmp)
373     {
374     max_deg=0;
375     #pragma omp for schedule(static)
376     for (i=0;i<n;++i) max_deg=MAX(max_deg, A->pattern->ptr[i+1]-A->pattern->ptr[i]);
377 gross 3193
378 gross 3283 rtmp=TMPMEMALLOC(max_deg, double);
379    
380     #pragma omp for schedule(static)
381     for (i=0;i<n;++i) {
382 gross 3193
383 gross 3283 max_offdiagonal = 0.;
384     sum_row=0;
385     main_row=0;
386     for (iptr=A->pattern->ptr[i];iptr<A->pattern->ptr[i+1]; ++iptr) {
387     j=A->pattern->index[iptr];
388     fnorm=0;
389     #pragma ivdep
390     for(bi=0;bi<n_block*n_block;++bi) fnorm+=A->val[iptr*n_block*n_block+bi]*A->val[iptr*n_block*n_block+bi];
391     fnorm=sqrt(fnorm);
392 gross 3287 rtmp[iptr-A->pattern->ptr[i]]=fnorm;
393 gross 3283 if( j != i) {
394     max_offdiagonal = MAX(max_offdiagonal,fnorm);
395     sum_row+=fnorm;
396     } else {
397     main_row=fnorm;
398     }
399     }
400     threshold = theta*max_offdiagonal;
401 gross 3193
402 gross 3283 kdeg=0;
403     if (tau*main_row < sum_row) { /* no diagonal domainance */
404     #pragma ivdep
405     for (iptr=A->pattern->ptr[i];iptr<A->pattern->ptr[i+1]; ++iptr) {
406     j=A->pattern->index[iptr];
407     if(rtmp[iptr-A->pattern->ptr[i]] > threshold && i!=j) {
408     S[A->pattern->ptr[i]+kdeg] = j;
409     kdeg++;
410     }
411     }
412     }
413     degree[i]=kdeg;
414     }
415     TMPMEMFREE(rtmp);
416     } /* end of parallel region */
417 gross 3303
418 gross 3283 }
419    
420     /* the runge stueben coarsening algorithm: */
421 gross 3303 void Paso_Preconditioner_AMG_RungeStuebenSearch(const dim_t n, const index_t* offset,
422     const dim_t* degree, const index_t* S,
423 gross 3283 index_t*split_marker)
424     {
425     index_t *lambda=NULL, j, *ST=NULL;
426     dim_t i,k, p, q, *degreeT=NULL, itmp;
427    
428     if (n<=0) return; /* make sure that the return of Paso_Util_arg_max is not pointing to nirvana */
429    
430     lambda=TMPMEMALLOC(n, index_t);
431     degreeT=TMPMEMALLOC(n, dim_t);
432     ST=TMPMEMALLOC(offset[n], index_t);
433    
434     if (! ( Esys_checkPtr(lambda) || Esys_checkPtr(degreeT) || Esys_checkPtr(ST) ) ) {
435     /* initialize split_marker and split_marker :*/
436     /* those unknows which are not influenced go into F, the rest is available for F or C */
437     #pragma omp parallel for private(i) schedule(static)
438     for (i=0;i<n;++i) {
439     degreeT[i]=0;
440     if (degree[i]>0) {
441     lambda[i]=0;
442     split_marker[i]=PASO_AMG_UNDECIDED;
443     } else {
444     split_marker[i]=PASO_AMG_IN_F;
445     lambda[i]=-1;
446     }
447     }
448     /* create transpose :*/
449     for (i=0;i<n;++i) {
450     for (p=0; p<degree[i]; ++p) {
451     j=S[offset[i]+p];
452     ST[offset[j]+degreeT[j]]=i;
453     degreeT[j]++;
454     }
455     }
456     /* lambda[i] = |undecided k in ST[i]| + 2 * |F-unknown in ST[i]| */
457     #pragma omp parallel for private(i, j, itmp) schedule(static)
458     for (i=0;i<n;++i) {
459     if (split_marker[i]==PASO_AMG_UNDECIDED) {
460     itmp=lambda[i];
461     for (p=0; p<degreeT[i]; ++p) {
462     j=ST[offset[i]+p];
463     if (split_marker[j]==PASO_AMG_UNDECIDED) {
464     itmp++;
465     } else { /* at this point there are no C points */
466     itmp+=2;
467     }
468     }
469     lambda[i]=itmp;
470     }
471     }
472    
473     /* start search :*/
474     i=Paso_Util_arg_max(n,lambda);
475     while (lambda[i]>-1) { /* is there any undecided unknowns? */
476 gross 3193
477 gross 3283 /* the unknown i is moved to C */
478     split_marker[i]=PASO_AMG_IN_C;
479     lambda[i]=-1; /* lambda fro unavailable unknowns is set to -1 */
480    
481     /* all undecided unknown strongly coupled to i are moved to F */
482     for (p=0; p<degreeT[i]; ++p) {
483     j=ST[offset[i]+p];
484    
485     if (split_marker[j]==PASO_AMG_UNDECIDED) {
486    
487     split_marker[j]=PASO_AMG_IN_F;
488     lambda[j]=-1;
489    
490     for (q=0; q<degreeT[j]; ++q) {
491     k=ST[offset[j]+q];
492     if (split_marker[k]==PASO_AMG_UNDECIDED) lambda[k]++;
493     }
494 gross 3193
495 gross 3283 }
496     }
497     for (p=0; p<degree[i]; ++p) {
498     j=S[offset[i]+p];
499     if(split_marker[j]==PASO_AMG_UNDECIDED) lambda[j]--;
500     }
501    
502     i=Paso_Util_arg_max(n,lambda);
503     }
504     }
505     TMPMEMFREE(lambda);
506     TMPMEMFREE(ST);
507     TMPMEMFREE(degreeT);
508 gross 3193 }

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