/[escript]/trunk/paso/src/Solver_RILU.c
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Contents of /trunk/paso/src/Solver_RILU.c

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Revision 1387 - (show annotations)
Fri Jan 11 07:45:26 2008 UTC (11 years, 10 months ago) by trankine
Original Path: temp/paso/src/Solver_RILU.c
File MIME type: text/plain
File size: 15902 byte(s)
Restore the trunk that existed before the windows changes were committed to the (now moved to branches) old trunk.
1
2 /* $Id$ */
3
4 /*******************************************************
5 *
6 * Copyright 2003-2007 by ACceSS MNRF
7 * Copyright 2007 by University of Queensland
8 *
9 * http://esscc.uq.edu.au
10 * Primary Business: Queensland, Australia
11 * Licensed under the Open Software License version 3.0
12 * http://www.opensource.org/licenses/osl-3.0.php
13 *
14 *******************************************************/
15
16 /**************************************************************/
17
18 /* Paso: RILU preconditioner with reordering */
19
20 /**************************************************************/
21
22 /* Copyrights by ACcESS Australia 2004,2004,2005, 2006, 2007 */
23 /* Author: gross@access.edu.au */
24
25 /**************************************************************/
26
27 #include "Paso.h"
28 #include "Solver.h"
29 #include "PasoUtil.h"
30
31 /**************************************************************/
32
33 /* free all memory used by RILU */
34
35 void Paso_Solver_RILU_free(Paso_Solver_RILU * in) {
36 if (in!=NULL) {
37 Paso_Solver_RILU_free(in->RILU_of_Schur);
38 MEMFREE(in->inv_A_FF);
39 MEMFREE(in->A_FF_pivot);
40 Paso_SparseMatrix_free(in->A_FC);
41 Paso_SparseMatrix_free(in->A_CF);
42 MEMFREE(in->rows_in_F);
43 MEMFREE(in->rows_in_C);
44 MEMFREE(in->mask_F);
45 MEMFREE(in->mask_C);
46 MEMFREE(in->x_F);
47 MEMFREE(in->b_F);
48 MEMFREE(in->x_C);
49 MEMFREE(in->b_C);
50 MEMFREE(in);
51 }
52 }
53
54 /**************************************************************/
55
56 /* constructs the block-block factorization of
57
58 [ A_FF A_FC ]
59 A_p=
60 [ A_CF A_FF ]
61
62 to
63
64 [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ]
65 [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ]
66
67
68 where S=A_FF-ACF*invA_FF*A_FC within the shape of S
69
70 then RILU is applied to S again until S becomes empty
71
72 */
73 Paso_Solver_RILU* Paso_Solver_getRILU(Paso_SparseMatrix *A_p,bool_t verbose) {
74 Paso_Solver_RILU* out=NULL;
75 dim_t n=A_p->numRows;
76 dim_t n_block=A_p->row_block_size;
77 index_t* mis_marker=NULL;
78 index_t* counter=NULL;
79 index_t iPtr,*index, *where_p;
80 dim_t i,k;
81 Paso_SparseMatrix * schur=NULL;
82 double A11,A12,A13,A21,A22,A23,A31,A32,A33,D,time0,time1,time2;
83
84
85 /* identify independend set of rows/columns */
86 mis_marker=TMPMEMALLOC(n,index_t);
87 counter=TMPMEMALLOC(n,index_t);
88 out=MEMALLOC(1,Paso_Solver_RILU);
89 out->RILU_of_Schur=NULL;
90 out->inv_A_FF=NULL;
91 out->A_FF_pivot=NULL;
92 out->A_FC=NULL;
93 out->A_CF=NULL;
94 out->rows_in_F=NULL;
95 out->rows_in_C=NULL;
96 out->mask_F=NULL;
97 out->mask_C=NULL;
98 out->x_F=NULL;
99 out->b_F=NULL;
100 out->x_C=NULL;
101 out->b_C=NULL;
102
103 if ( !(Paso_checkPtr(mis_marker) || Paso_checkPtr(out) || Paso_checkPtr(counter) ) ) {
104 /* identify independend set of rows/columns */
105 time0=Paso_timer();
106 #pragma omp parallel for private(i) schedule(static)
107 for (i=0;i<n;++i) mis_marker[i]=-1;
108 Paso_Pattern_mis(A_p->pattern,mis_marker);
109 time2=Paso_timer()-time0;
110 if (Paso_noError()) {
111 #pragma omp parallel for private(i) schedule(static)
112 for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
113 out->n=n;
114 out->n_block=n_block;
115 out->n_F=Paso_Util_cumsum(n,counter);
116 out->mask_F=MEMALLOC(n,index_t);
117 out->rows_in_F=MEMALLOC(out->n_F,index_t);
118 out->inv_A_FF=MEMALLOC(n_block*n_block*out->n_F,double);
119 out->A_FF_pivot=NULL; /* later use for block size>3 */
120 if (! (Paso_checkPtr(out->mask_F) || Paso_checkPtr(out->inv_A_FF) || Paso_checkPtr(out->rows_in_F) ) ) {
121 #pragma omp parallel
122 {
123 /* creates an index for F from mask */
124 #pragma omp for private(i) schedule(static)
125 for (i = 0; i < out->n_F; ++i) out->rows_in_F[i]=-1;
126 #pragma omp for private(i) schedule(static)
127 for (i = 0; i < n; ++i) {
128 if (mis_marker[i]) {
129 out->rows_in_F[counter[i]]=i;
130 out->mask_F[i]=counter[i];
131 } else {
132 out->mask_F[i]=-1;
133 }
134 }
135 #pragma omp for private(i, where_p,iPtr,A11,A12,A13,A21,A22,A23,A31,A32,A33,D,index) schedule(static)
136 for (i = 0; i < out->n_F; i++) {
137 /* find main diagonal */
138 iPtr=A_p->pattern->ptr[out->rows_in_F[i]];
139 index=&(A_p->pattern->index[iPtr]);
140 where_p=(index_t*)bsearch(&out->rows_in_F[i],
141 index,
142 A_p->pattern->ptr[out->rows_in_F[i] + 1]-A_p->pattern->ptr[out->rows_in_F[i]],
143 sizeof(index_t),
144 Paso_comparIndex);
145 if (where_p==NULL) {
146 Paso_setError(VALUE_ERROR, "Paso_Solver_getRILU: main diagonal element missing.");
147 } else {
148 iPtr+=(index_t)(where_p-index);
149 /* get inverse of A_FF block: */
150 if (n_block==1) {
151 if (ABS(A_p->val[iPtr])>0.) {
152 out->inv_A_FF[i]=1./A_p->val[iPtr];
153 } else {
154 Paso_setError(ZERO_DIVISION_ERROR, "Paso_Solver_getRILU: Break-down in RILU decomposition: non-regular main diagonal block.");
155 }
156 } else if (n_block==2) {
157 A11=A_p->val[iPtr*4];
158 A21=A_p->val[iPtr*4+1];
159 A12=A_p->val[iPtr*4+2];
160 A22=A_p->val[iPtr*4+3];
161 D = A11*A22-A12*A21;
162 if (ABS(D) > 0 ){
163 D=1./D;
164 out->inv_A_FF[i*4]= A22*D;
165 out->inv_A_FF[i*4+1]=-A21*D;
166 out->inv_A_FF[i*4+2]=-A12*D;
167 out->inv_A_FF[i*4+3]= A11*D;
168 } else {
169 Paso_setError(ZERO_DIVISION_ERROR, "Paso_Solver_getRILU:Break-down in RILU decomposition: non-regular main diagonal block.");
170 }
171 } else if (n_block==3) {
172 A11=A_p->val[iPtr*9 ];
173 A21=A_p->val[iPtr*9+1];
174 A31=A_p->val[iPtr*9+2];
175 A12=A_p->val[iPtr*9+3];
176 A22=A_p->val[iPtr*9+4];
177 A32=A_p->val[iPtr*9+5];
178 A13=A_p->val[iPtr*9+6];
179 A23=A_p->val[iPtr*9+7];
180 A33=A_p->val[iPtr*9+8];
181 D = A11*(A22*A33-A23*A32)+ A12*(A31*A23-A21*A33)+A13*(A21*A32-A31*A22);
182 if (ABS(D) > 0 ){
183 D=1./D;
184 out->inv_A_FF[i*9 ]=(A22*A33-A23*A32)*D;
185 out->inv_A_FF[i*9+1]=(A31*A23-A21*A33)*D;
186 out->inv_A_FF[i*9+2]=(A21*A32-A31*A22)*D;
187 out->inv_A_FF[i*9+3]=(A13*A32-A12*A33)*D;
188 out->inv_A_FF[i*9+4]=(A11*A33-A31*A13)*D;
189 out->inv_A_FF[i*9+5]=(A12*A31-A11*A32)*D;
190 out->inv_A_FF[i*9+6]=(A12*A23-A13*A22)*D;
191 out->inv_A_FF[i*9+7]=(A13*A21-A11*A23)*D;
192 out->inv_A_FF[i*9+8]=(A11*A22-A12*A21)*D;
193 } else {
194 Paso_setError(ZERO_DIVISION_ERROR, "Paso_Solver_getRILU:Break-down in RILU decomposition: non-regular main diagonal block.");
195 }
196 }
197 }
198 }
199 } /* end parallel region */
200
201 if( Paso_noError()) {
202 /* if there are no nodes in the coarse level there is no more work to do */
203 out->n_C=n-out->n_F;
204 if (out->n_C>0) {
205 out->rows_in_C=MEMALLOC(out->n_C,index_t);
206 out->mask_C=MEMALLOC(n,index_t);
207 if (! (Paso_checkPtr(out->mask_C) || Paso_checkPtr(out->rows_in_C) ) ) {
208 /* creates an index for C from mask */
209 #pragma omp parallel for private(i) schedule(static)
210 for (i = 0; i < n; ++i) counter[i]=! mis_marker[i];
211 Paso_Util_cumsum(n,counter);
212 #pragma omp parallel
213 {
214 #pragma omp for private(i) schedule(static)
215 for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
216 #pragma omp for private(i) schedule(static)
217 for (i = 0; i < n; ++i) {
218 if (! mis_marker[i]) {
219 out->rows_in_C[counter[i]]=i;
220 out->mask_C[i]=counter[i];
221 } else {
222 out->mask_C[i]=-1;
223 }
224 }
225 } /* end parallel region */
226 /* get A_CF block: */
227 out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
228 if (Paso_noError()) {
229 /* get A_FC block: */
230 out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
231 /* get A_FF block: */
232 if (Paso_noError()) {
233 schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
234 time0=Paso_timer()-time0;
235 if (Paso_noError()) {
236 time1=Paso_timer();
237 /* update A_CC block to get Schur complement and then apply RILU to it */
238 Paso_Solver_updateIncompleteSchurComplement(schur,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC);
239 time1=Paso_timer()-time1;
240 out->RILU_of_Schur=Paso_Solver_getRILU(schur,verbose);
241 Paso_SparseMatrix_free(schur);
242 }
243 /* allocate work arrays for RILU application */
244 if (Paso_noError()) {
245 out->x_F=MEMALLOC(n_block*out->n_F,double);
246 out->b_F=MEMALLOC(n_block*out->n_F,double);
247 out->x_C=MEMALLOC(n_block*out->n_C,double);
248 out->b_C=MEMALLOC(n_block*out->n_C,double);
249 if (! (Paso_checkPtr(out->x_F) || Paso_checkPtr(out->b_F) || Paso_checkPtr(out->x_C) || Paso_checkPtr(out->b_C) ) ) {
250 #pragma omp parallel
251 {
252 #pragma omp for private(i,k) schedule(static)
253 for (i = 0; i < out->n_F; ++i) {
254 for (k=0; k<n_block;++k) {
255 out->x_F[i*n_block+k]=0.;
256 out->b_F[i*n_block+k]=0.;
257 }
258 }
259 #pragma omp for private(i,k) schedule(static)
260 for (i = 0; i < out->n_C; ++i) {
261 for (k=0; k<n_block;++k) {
262 out->x_C[i*n_block+k]=0.;
263 out->b_C[i*n_block+k]=0.;
264 }
265 }
266 } /* end parallel region */
267 }
268 }
269 }
270 }
271 }
272 }
273 }
274 }
275 }
276 }
277 TMPMEMFREE(mis_marker);
278 TMPMEMFREE(counter);
279 if (Paso_noError()) {
280 if (verbose) {
281 printf("RILU: %d unknowns eliminated. %d left.\n",out->n_F,n-out->n_F);
282 if (out->n_C>0) {
283 printf("timing: RILU: MIS/reordering/elemination : %e/%e/%e\n",time2,time0,time1);
284 } else {
285 printf("timing: RILU: MIS: %e\n",time2);
286 }
287 }
288 return out;
289 } else {
290 Paso_Solver_RILU_free(out);
291 return NULL;
292 }
293 }
294
295 /**************************************************************/
296
297 /* apply RILU precondition b-> x
298
299 in fact it solves
300
301 [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ] [ x_F ] = [b_F]
302 [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] [ x_C ] = [b_C]
303
304 in the form
305
306 b->[b_F,b_C]
307 x_F=invA_FF*b_F
308 b_C=b_C-A_CF*x_F
309 x_C=RILU(b_C)
310 b_F=b_F-A_FC*x_C
311 x_F=invA_FF*b_F
312 x<-[x_F,x_C]
313
314 should be called within a parallel region
315 barrier synconization should be performed to make sure that the input vector available
316
317 */
318
319 void Paso_Solver_solveRILU(Paso_Solver_RILU * rilu, double * x, double * b) {
320 dim_t i,k;
321 dim_t n_block=rilu->n_block;
322
323 if (rilu->n_C==0) {
324 /* x=invA_FF*b */
325 Paso_Solver_applyBlockDiagonalMatrix(n_block,rilu->n_F,rilu->inv_A_FF,rilu->A_FF_pivot,x,b);
326 } else {
327 /* b->[b_F,b_C] */
328 if (n_block==1) {
329 #pragma omp for private(i) schedule(static)
330 for (i=0;i<rilu->n_F;++i) rilu->b_F[i]=b[rilu->rows_in_F[i]];
331 #pragma omp for private(i) schedule(static)
332 for (i=0;i<rilu->n_C;++i) rilu->b_C[i]=b[rilu->rows_in_C[i]];
333 } else {
334 #pragma omp for private(i,k) schedule(static)
335 for (i=0;i<rilu->n_F;++i)
336 for (k=0;k<n_block;k++) rilu->b_F[rilu->n_block*i+k]=b[n_block*rilu->rows_in_F[i]+k];
337 #pragma omp for private(i,k) schedule(static)
338 for (i=0;i<rilu->n_C;++i)
339 for (k=0;k<n_block;k++) rilu->b_C[rilu->n_block*i+k]=b[n_block*rilu->rows_in_C[i]+k];
340 }
341 /* x_F=invA_FF*b_F */
342 Paso_Solver_applyBlockDiagonalMatrix(n_block,rilu->n_F,rilu->inv_A_FF,rilu->A_FF_pivot,rilu->x_F,rilu->b_F);
343 /* b_C=b_C-A_CF*x_F */
344 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,rilu->A_CF,rilu->x_F,1.,rilu->b_C);
345 /* x_C=RILU(b_C) */
346 Paso_Solver_solveRILU(rilu->RILU_of_Schur,rilu->x_C,rilu->b_C);
347 /* b_F=b_F-A_FC*x_C */
348 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,rilu->A_FC,rilu->x_C,1.,rilu->b_F);
349 /* x_F=invA_FF*b_F */
350 Paso_Solver_applyBlockDiagonalMatrix(n_block,rilu->n_F,rilu->inv_A_FF,rilu->A_FF_pivot,rilu->x_F,rilu->b_F);
351 /* x<-[x_F,x_C] */
352 if (n_block==1) {
353 #pragma omp for private(i) schedule(static)
354 for (i=0;i<rilu->n;++i) {
355 if (rilu->mask_C[i]>-1) {
356 x[i]=rilu->x_C[rilu->mask_C[i]];
357 } else {
358 x[i]=rilu->x_F[rilu->mask_F[i]];
359 }
360 }
361 } else {
362 #pragma omp for private(i,k) schedule(static)
363 for (i=0;i<rilu->n;++i) {
364 if (rilu->mask_C[i]>-1) {
365 for (k=0;k<n_block;k++) x[n_block*i+k]=rilu->x_C[n_block*rilu->mask_C[i]+k];
366 } else {
367 for (k=0;k<n_block;k++) x[n_block*i+k]=rilu->x_F[n_block*rilu->mask_F[i]+k];
368 }
369 }
370 }
371 /* all done */
372 }
373 return;
374 }
375
376 /*
377 * $Log$
378 *
379 */

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