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

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Revision 1388 - (hide annotations)
Fri Jan 11 07:45:58 2008 UTC (11 years, 8 months ago) by trankine
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And get the *(&(*&(* name right
1 ksteube 1312
2 gross 430 /* $Id$ */
3    
4 ksteube 1312 /*******************************************************
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 dhawcroft 631
16 gross 430 /**************************************************************/
17    
18     /* Paso: RILU preconditioner with reordering */
19    
20     /**************************************************************/
21    
22 ksteube 1312 /* Copyrights by ACcESS Australia 2004,2004,2005, 2006, 2007 */
23 gross 430 /* Author: gross@access.edu.au */
24    
25     /**************************************************************/
26    
27 gross 700 #include "Paso.h"
28 gross 430 #include "Solver.h"
29 gross 700 #include "PasoUtil.h"
30 gross 430
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 ksteube 1312 Paso_SparseMatrix_free(in->A_FC);
41     Paso_SparseMatrix_free(in->A_CF);
42 gross 430 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 ksteube 1312 Paso_Solver_RILU* Paso_Solver_getRILU(Paso_SparseMatrix *A_p,bool_t verbose) {
74 gross 430 Paso_Solver_RILU* out=NULL;
75 ksteube 1312 dim_t n=A_p->numRows;
76 gross 430 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 ksteube 1312 Paso_SparseMatrix * schur=NULL;
82 gross 430 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 gross 431 #pragma omp parallel for private(i) schedule(static)
107     for (i=0;i<n;++i) mis_marker[i]=-1;
108 ksteube 1312 Paso_Pattern_mis(A_p->pattern,mis_marker);
109 gross 430 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 ksteube 1312 out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
228 gross 430 if (Paso_noError()) {
229     /* get A_FC block: */
230 ksteube 1312 out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
231 gross 430 /* get A_FF block: */
232     if (Paso_noError()) {
233 ksteube 1312 schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
234 gross 430 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 ksteube 1312 Paso_SparseMatrix_free(schur);
242 gross 430 }
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 ksteube 1312 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,rilu->A_CF,rilu->x_F,1.,rilu->b_C);
345 gross 430 /* 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 ksteube 1312 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,rilu->A_FC,rilu->x_C,1.,rilu->b_F);
349 gross 430 /* 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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