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Contents of /trunk/paso/src/AMG.c

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Revision 3314 - (show annotations)
Tue Oct 26 22:22:20 2010 UTC (8 years, 11 months ago) by gross
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File size: 16443 byte(s)
output removed/leaned up
1
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 /* Author: artak@uq.edu.au, l.gross@uq.edu.au */
22
23 /**************************************************************/
24
25 #define SHOW_TIMING FALSE
26
27 #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 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
49
50 MEMFREE(in);
51 }
52 }
53
54 /*****************************************************************
55
56 constructs AMG
57
58 ******************************************************************/
59 Paso_Preconditioner_LocalAMG* Paso_Preconditioner_LocalAMG_alloc(Paso_SparseMatrix *A_p,dim_t level,Paso_Options* options) {
60
61 Paso_Preconditioner_LocalAMG* out=NULL;
62 bool_t verbose=options->verbose;
63
64 Paso_SparseMatrix *Atemp=NULL, *A_C=NULL;
65 const dim_t n=A_p->numRows;
66 const dim_t n_block=A_p->row_block_size;
67 index_t* split_marker=NULL, *counter=NULL, *mask_C=NULL, *rows_in_F=NULL, *S=NULL, *degree=NULL;
68 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
73
74 /*
75 is the input matrix A suitable for coarsening
76
77 */
78 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 return NULL;
82 }
83 /* Start Coarsening : */
84
85 split_marker=TMPMEMALLOC(n,index_t);
86 counter=TMPMEMALLOC(n,index_t);
87 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 /*
91 set splitting of unknows:
92
93 */
94 time0=Esys_timer();
95 if (n_block>1) {
96 Paso_Preconditioner_AMG_setStrongConnections_Block(A_p, degree, S, theta,tau);
97 } else {
98 Paso_Preconditioner_AMG_setStrongConnections(A_p, degree, S, theta,tau);
99 }
100 Paso_Preconditioner_AMG_RungeStuebenSearch(n, A_p->pattern->ptr, degree, S, split_marker);
101 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 if (verbose) printf("Paso: AMG level %d: %d unknowns are flagged for elimination. %d left.\n",level,n_F,n-n_F);
113
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 /* creates index for F:*/
139 #pragma omp parallel for private(i) schedule(static)
140 for (i = 0; i < n; ++i) {
141 if (split_marker[i]) rows_in_F[counter[i]]=i;
142 }
143 /* create mask of C nodes with value >-1 gives new id */
144 i=Paso_Util_cumsum_maskedFalse(n,counter, split_marker);
145
146 #pragma omp parallel for private(i) schedule(static)
147 for (i = 0; i < n; ++i) {
148 if (split_marker[i]) {
149 mask_C[i]=-1;
150 } else {
151 mask_C[i]=counter[i];;
152 }
153 }
154 /*
155 get Restriction :
156 */
157 time0=Esys_timer();
158 out->P=Paso_Preconditioner_AMG_getDirectProlongation(A_p,degree,S,n_C,mask_C);
159 if (SHOW_TIMING) printf("timing: level %d: getProlongation: %e\n",level, Esys_timer()-time0);
160 /*
161 construct Prolongation operator as transposed of restriction operator:
162 */
163 time0=Esys_timer();
164 out->R=Paso_SparseMatrix_getTranspose(out->P);
165 if (SHOW_TIMING) printf("timing: level %d: Paso_SparseMatrix_getTranspose: %e\n",level,Esys_timer()-time0);
166
167 /*
168 construct coarse level matrix:
169 */
170 time0=Esys_timer();
171 Atemp=Paso_SparseMatrix_MatrixMatrix(A_p,out->P);
172 A_C=Paso_SparseMatrix_MatrixMatrix(out->R,Atemp);
173 Paso_SparseMatrix_free(Atemp);
174 if (SHOW_TIMING) printf("timing: level %d : construct coarse matrix: %e\n",level,Esys_timer()-time0);
175
176 /* allocate helpers :*/
177 out->x_C=MEMALLOC(n_block*n_C,double);
178 out->b_C=MEMALLOC(n_block*n_C,double);
179 out->r=MEMALLOC(n_block*n,double);
180
181 Esys_checkPtr(out->r);
182 Esys_checkPtr(out->Smoother);
183 Esys_checkPtr(out->x_C);
184 Esys_checkPtr(out->b_C);
185
186 /*
187 constructe courser level:
188
189 */
190 out->AMG_C=Paso_Preconditioner_LocalAMG_alloc(A_C,level+1,options);
191
192 if ( Esys_noError()) {
193 if ( out->AMG_C == NULL ) {
194 out->reordering = options->reordering;
195 out->refinements = options->coarse_matrix_refinements;
196 /* no coarse level matrix has been constructed. use direct solver */
197 #ifdef MKL
198 out->A_C=Paso_SparseMatrix_unroll(MATRIX_FORMAT_BLK1 + MATRIX_FORMAT_OFFSET1, A_C);
199 Paso_SparseMatrix_free(A_C);
200 out->A_C->solver_package = PASO_MKL;
201 if (verbose) printf("Paso: AMG: use MKL direct solver on the coarsest level (number of unknowns = %d).\n",n_C);
202 #else
203 #ifdef UMFPACK
204 out->A_C=Paso_SparseMatrix_unroll(MATRIX_FORMAT_BLK1 + MATRIX_FORMAT_CSC, A_C);
205 Paso_SparseMatrix_free(A_C);
206 out->A_C->solver_package = PASO_UMFPACK;
207 if (verbose) printf("Paso: AMG: use UMFPACK direct solver on the coarsest level (number of unknowns = %d).\n",n_C);
208 #else
209 out->A_C=A_C;
210 out->A_C->solver_p=Paso_Preconditioner_LocalSmoother_alloc(out->A_C, (options->smoother == PASO_JACOBI), verbose);
211 out->A_C->solver_package = PASO_SMOOTHER;
212 if (verbose) printf("Paso: AMG: use smoother on the coarsest level (number of unknowns = %d).\n",n_C);
213 #endif
214 #endif
215 } else {
216 /* finally we set some helpers for the solver step */
217 out->A_C=A_C;
218 }
219 }
220 }
221 }
222 TMPMEMFREE(mask_C);
223 TMPMEMFREE(rows_in_F);
224 }
225 }
226 }
227 TMPMEMFREE(counter);
228 TMPMEMFREE(split_marker);
229 TMPMEMFREE(degree);
230 TMPMEMFREE(S);
231
232 if (Esys_noError()) {
233 return out;
234 } else {
235 Paso_Preconditioner_LocalAMG_free(out);
236 return NULL;
237 }
238 }
239
240
241 void Paso_Preconditioner_LocalAMG_solve(Paso_SparseMatrix* A, Paso_Preconditioner_LocalAMG * amg, double * x, double * b) {
242 const dim_t n = amg->n * amg->n_block;
243 double time0=0;
244 const dim_t post_sweeps=amg->post_sweeps;
245 const dim_t pre_sweeps=amg->pre_sweeps;
246
247 /* presmoothing */
248 time0=Esys_timer();
249 Paso_Preconditioner_LocalSmoother_solve(A, amg->Smoother, x, b, pre_sweeps, FALSE);
250 time0=Esys_timer()-time0;
251 if (SHOW_TIMING) printf("timing: level %d: Presmooting: %e\n",amg->level, time0);
252 /* end of presmoothing */
253
254 if (amg->n_F < amg->n) { /* is there work on the coarse level? */
255 time0=Esys_timer();
256 Paso_Copy(n, amg->r, b); /* r <- b */
257 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,A,x,1.,amg->r); /*r=r-Ax*/
258 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0_DIAG(1.,amg->R,amg->r,0.,amg->b_C); /* b_c = R*r */
259 time0=Esys_timer()-time0;
260 /* coarse level solve */
261 if ( amg->AMG_C == NULL) {
262 time0=Esys_timer();
263 /* A_C is the coarsest level */
264 switch (amg->A_C->solver_package) {
265 case (PASO_MKL):
266 Paso_MKL(amg->A_C, amg->x_C,amg->b_C, amg->reordering, amg->refinements, SHOW_TIMING);
267 break;
268 case (PASO_UMFPACK):
269 Paso_UMFPACK(amg->A_C, amg->x_C,amg->b_C, amg->refinements, SHOW_TIMING);
270 break;
271 case (PASO_SMOOTHER):
272 Paso_Preconditioner_LocalSmoother_solve(amg->A_C, amg->Smoother,amg->x_C,amg->b_C,pre_sweeps, FALSE);
273 break;
274 }
275 if (SHOW_TIMING) printf("timing: level %d: DIRECT SOLVER: %e\n",amg->level,Esys_timer()-time0);
276 } else {
277 Paso_Preconditioner_LocalAMG_solve(amg->A_C, amg->AMG_C,amg->x_C,amg->b_C); /* x_C=AMG(b_C) */
278 }
279 time0=time0+Esys_timer();
280 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0_DIAG(1.,amg->P,amg->x_C,1.,x); /* x = x + P*x_c */
281
282 /*postsmoothing*/
283
284 /*solve Ax=b with initial guess x */
285 time0=Esys_timer();
286 Paso_Preconditioner_LocalSmoother_solve(A, amg->Smoother, x, b, post_sweeps, TRUE);
287 time0=Esys_timer()-time0;
288 if (SHOW_TIMING) printf("timing: level %d: Postsmoothing: %e\n",amg->level,time0);
289 /*end of postsmoothing*/
290
291 }
292 return;
293 }
294
295 /* theta = threshold for strong connections */
296 /* tau = threshold for diagonal dominance */
297
298 /*S_i={j \in N_i; i strongly coupled to j}
299
300 in the sense that |A_{ij}| >= theta * max_k |A_{ik}|
301 */
302
303 void Paso_Preconditioner_AMG_setStrongConnections(Paso_SparseMatrix* A,
304 dim_t *degree, index_t *S,
305 const double theta, const double tau)
306 {
307 const dim_t n=A->numRows;
308 index_t iptr, i,j;
309 dim_t kdeg;
310 double max_offdiagonal, threshold, sum_row, main_row, fnorm;
311
312
313 #pragma omp parallel for private(i,iptr,max_offdiagonal, threshold,j, kdeg, sum_row, main_row, fnorm) schedule(static)
314 for (i=0;i<n;++i) {
315
316 max_offdiagonal = 0.;
317 sum_row=0;
318 main_row=0;
319 #pragma ivdep
320 for (iptr=A->pattern->ptr[i];iptr<A->pattern->ptr[i+1]; ++iptr) {
321 j=A->pattern->index[iptr];
322 fnorm=ABS(A->val[iptr]);
323
324 if( j != i) {
325 max_offdiagonal = MAX(max_offdiagonal,fnorm);
326 sum_row+=fnorm;
327 } else {
328 main_row=fnorm;
329 }
330 }
331 threshold = theta*max_offdiagonal;
332 kdeg=0;
333 if (tau*main_row < sum_row) { /* no diagonal domainance */
334 #pragma ivdep
335 for (iptr=A->pattern->ptr[i];iptr<A->pattern->ptr[i+1]; ++iptr) {
336 j=A->pattern->index[iptr];
337 if(ABS(A->val[iptr])>threshold && i!=j) {
338 S[A->pattern->ptr[i]+kdeg] = j;
339 kdeg++;
340 }
341 }
342 }
343 degree[i]=kdeg;
344 }
345
346 }
347
348 /* theta = threshold for strong connections */
349 /* tau = threshold for diagonal dominance */
350 /*S_i={j \in N_i; i strongly coupled to j}
351
352 in the sense that |A_{ij}|_F >= theta * max_k |A_{ik}|_F
353 */
354 void Paso_Preconditioner_AMG_setStrongConnections_Block(Paso_SparseMatrix* A,
355 dim_t *degree, index_t *S,
356 const double theta, const double tau)
357
358 {
359 const dim_t n_block=A->row_block_size;
360 const dim_t n=A->numRows;
361 index_t iptr, i,j, bi;
362 dim_t kdeg, max_deg;
363 register double max_offdiagonal, threshold, fnorm, sum_row, main_row;
364 double *rtmp;
365
366
367 #pragma omp parallel private(i,iptr,max_offdiagonal, kdeg, threshold,j, max_deg, fnorm, sum_row, main_row, rtmp)
368 {
369 max_deg=0;
370 #pragma omp for schedule(static)
371 for (i=0;i<n;++i) max_deg=MAX(max_deg, A->pattern->ptr[i+1]-A->pattern->ptr[i]);
372
373 rtmp=TMPMEMALLOC(max_deg, double);
374
375 #pragma omp for schedule(static)
376 for (i=0;i<n;++i) {
377
378 max_offdiagonal = 0.;
379 sum_row=0;
380 main_row=0;
381 for (iptr=A->pattern->ptr[i];iptr<A->pattern->ptr[i+1]; ++iptr) {
382 j=A->pattern->index[iptr];
383 fnorm=0;
384 #pragma ivdep
385 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];
386 fnorm=sqrt(fnorm);
387 rtmp[iptr-A->pattern->ptr[i]]=fnorm;
388 if( j != i) {
389 max_offdiagonal = MAX(max_offdiagonal,fnorm);
390 sum_row+=fnorm;
391 } else {
392 main_row=fnorm;
393 }
394 }
395 threshold = theta*max_offdiagonal;
396
397 kdeg=0;
398 if (tau*main_row < sum_row) { /* no diagonal domainance */
399 #pragma ivdep
400 for (iptr=A->pattern->ptr[i];iptr<A->pattern->ptr[i+1]; ++iptr) {
401 j=A->pattern->index[iptr];
402 if(rtmp[iptr-A->pattern->ptr[i]] > threshold && i!=j) {
403 S[A->pattern->ptr[i]+kdeg] = j;
404 kdeg++;
405 }
406 }
407 }
408 degree[i]=kdeg;
409 }
410 TMPMEMFREE(rtmp);
411 } /* end of parallel region */
412
413 }
414
415 /* the runge stueben coarsening algorithm: */
416 void Paso_Preconditioner_AMG_RungeStuebenSearch(const dim_t n, const index_t* offset,
417 const dim_t* degree, const index_t* S,
418 index_t*split_marker)
419 {
420 index_t *lambda=NULL, j, *ST=NULL;
421 dim_t i,k, p, q, *degreeT=NULL, itmp;
422
423 if (n<=0) return; /* make sure that the return of Paso_Util_arg_max is not pointing to nirvana */
424
425 lambda=TMPMEMALLOC(n, index_t);
426 degreeT=TMPMEMALLOC(n, dim_t);
427 ST=TMPMEMALLOC(offset[n], index_t);
428
429 if (! ( Esys_checkPtr(lambda) || Esys_checkPtr(degreeT) || Esys_checkPtr(ST) ) ) {
430 /* initialize split_marker and split_marker :*/
431 /* those unknows which are not influenced go into F, the rest is available for F or C */
432 #pragma omp parallel for private(i) schedule(static)
433 for (i=0;i<n;++i) {
434 degreeT[i]=0;
435 if (degree[i]>0) {
436 lambda[i]=0;
437 split_marker[i]=PASO_AMG_UNDECIDED;
438 } else {
439 split_marker[i]=PASO_AMG_IN_F;
440 lambda[i]=-1;
441 }
442 }
443 /* create transpose :*/
444 for (i=0;i<n;++i) {
445 for (p=0; p<degree[i]; ++p) {
446 j=S[offset[i]+p];
447 ST[offset[j]+degreeT[j]]=i;
448 degreeT[j]++;
449 }
450 }
451 /* lambda[i] = |undecided k in ST[i]| + 2 * |F-unknown in ST[i]| */
452 #pragma omp parallel for private(i, j, itmp) schedule(static)
453 for (i=0;i<n;++i) {
454 if (split_marker[i]==PASO_AMG_UNDECIDED) {
455 itmp=lambda[i];
456 for (p=0; p<degreeT[i]; ++p) {
457 j=ST[offset[i]+p];
458 if (split_marker[j]==PASO_AMG_UNDECIDED) {
459 itmp++;
460 } else { /* at this point there are no C points */
461 itmp+=2;
462 }
463 }
464 lambda[i]=itmp;
465 }
466 }
467
468 /* start search :*/
469 i=Paso_Util_arg_max(n,lambda);
470 while (lambda[i]>-1) { /* is there any undecided unknowns? */
471
472 /* the unknown i is moved to C */
473 split_marker[i]=PASO_AMG_IN_C;
474 lambda[i]=-1; /* lambda fro unavailable unknowns is set to -1 */
475
476 /* all undecided unknown strongly coupled to i are moved to F */
477 for (p=0; p<degreeT[i]; ++p) {
478 j=ST[offset[i]+p];
479
480 if (split_marker[j]==PASO_AMG_UNDECIDED) {
481
482 split_marker[j]=PASO_AMG_IN_F;
483 lambda[j]=-1;
484
485 for (q=0; q<degreeT[j]; ++q) {
486 k=ST[offset[j]+q];
487 if (split_marker[k]==PASO_AMG_UNDECIDED) lambda[k]++;
488 }
489
490 }
491 }
492 for (p=0; p<degree[i]; ++p) {
493 j=S[offset[i]+p];
494 if(split_marker[j]==PASO_AMG_UNDECIDED) lambda[j]--;
495 }
496
497 i=Paso_Util_arg_max(n,lambda);
498 }
499 }
500 TMPMEMFREE(lambda);
501 TMPMEMFREE(ST);
502 TMPMEMFREE(degreeT);
503 }

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