xref: /petsc/src/mat/impls/aij/seq/aijfact.c (revision 7a2efc394589b136789e5cec3f47c1a804ea8ac0)
1 #ifndef lint
2 static char vcid[] = "$Id: aijfact.c,v 1.39 1995/09/22 20:17:46 bsmith Exp bsmith $";
3 #endif
4 
5 
6 #include "aij.h"
7 #include "inline/spops.h"
8 /*
9     Factorization code for AIJ format.
10 */
11 
12 int MatLUFactorSymbolic_SeqAIJ(Mat A,IS isrow,IS iscol,double f,Mat *B)
13 {
14   Mat_SeqAIJ *a = (Mat_SeqAIJ *) A->data, *b;
15   IS         isicol;
16   int        *r,*ic, ierr, i, n = a->m, *ai = a->i, *aj = a->j;
17   int        *ainew,*ajnew, jmax,*fill, *ajtmp, nz,shift = a->indexshift;
18   int        *idnew, idx, row,m,fm, nnz, nzi,len, realloc = 0,nzbd,*im;
19 
20   if (n != a->n) SETERRQ(1,"MatLUFactorSymbolic_SeqAIJ:Must be square");
21   if (!isrow) SETERRQ(1,"MatLUFactorSymbolic_SeqAIJ:Must have row permutation");
22   if (!iscol) SETERRQ(1,"MatLUFactorSymbolic_SeqAIJ:Must have column permutation");
23 
24   ierr = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
25   ISGetIndices(isrow,&r); ISGetIndices(isicol,&ic);
26 
27   /* get new row pointers */
28   ainew = (int *) PETSCMALLOC( (n+1)*sizeof(int) ); CHKPTRQ(ainew);
29   ainew[0] = -shift;
30   /* don't know how many column pointers are needed so estimate */
31   jmax = (int) (f*ai[n]+(!shift));
32   ajnew = (int *) PETSCMALLOC( (jmax)*sizeof(int) ); CHKPTRQ(ajnew);
33   /* fill is a linked list of nonzeros in active row */
34   fill = (int *) PETSCMALLOC( (2*n+1)*sizeof(int)); CHKPTRQ(fill);
35   im = fill + n + 1;
36   /* idnew is location of diagonal in factor */
37   idnew = (int *) PETSCMALLOC( (n+1)*sizeof(int)); CHKPTRQ(idnew);
38   idnew[0] = -shift;
39 
40   for ( i=0; i<n; i++ ) {
41     /* first copy previous fill into linked list */
42     nnz     = nz    = ai[r[i]+1] - ai[r[i]];
43     ajtmp   = aj + ai[r[i]] + shift;
44     fill[n] = n;
45     while (nz--) {
46       fm  = n;
47       idx = ic[*ajtmp++ + shift];
48       do {
49         m  = fm;
50         fm = fill[m];
51       } while (fm < idx);
52       fill[m]   = idx;
53       fill[idx] = fm;
54     }
55     row = fill[n];
56     while ( row < i ) {
57       ajtmp = ajnew + idnew[row] + (!shift);
58       nzbd  = 1 + idnew[row] - ainew[row];
59       nz    = im[row] - nzbd;
60       fm    = row;
61       while (nz-- > 0) {
62         idx = *ajtmp++ + shift;
63         nzbd++;
64         if (idx == i) im[row] = nzbd;
65         do {
66           m  = fm;
67           fm = fill[m];
68         } while (fm < idx);
69         if (fm != idx) {
70           fill[m]   = idx;
71           fill[idx] = fm;
72           fm        = idx;
73           nnz++;
74         }
75       }
76       row = fill[row];
77     }
78     /* copy new filled row into permanent storage */
79     ainew[i+1] = ainew[i] + nnz;
80     if (ainew[i+1] > jmax+1) {
81       /* allocate a longer ajnew */
82       int maxadd;
83       maxadd = (int) ((f*(ai[n]+(!shift))*(n-i+5))/n);
84       if (maxadd < nnz) maxadd = (n-i)*(nnz+1);
85       jmax += maxadd;
86       ajtmp = (int *) PETSCMALLOC( jmax*sizeof(int) );CHKPTRQ(ajtmp);
87       PetscMemcpy(ajtmp,ajnew,(ainew[i]+shift)*sizeof(int));
88       PETSCFREE(ajnew);
89       ajnew = ajtmp;
90       realloc++; /* count how many times we realloc */
91     }
92     ajtmp = ajnew + ainew[i] + shift;
93     fm    = fill[n];
94     nzi   = 0;
95     im[i] = nnz;
96     while (nnz--) {
97       if (fm < i) nzi++;
98       *ajtmp++ = fm - shift;
99       fm       = fill[fm];
100     }
101     idnew[i] = ainew[i] + nzi;
102   }
103 
104   PLogInfo((PetscObject)A,
105     "Info:MatLUFactorSymbolic_SeqAIJ:Reallocs %d Fill ratio:given %g needed %g\n",
106                              realloc,f,((double)ainew[n])/((double)ai[i]));
107 
108   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
109   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
110   ierr = ISDestroy(isicol); CHKERRQ(ierr);
111   PETSCFREE(fill);
112 
113   /* put together the new matrix */
114   ierr = MatCreateSeqAIJ(A->comm,n, n, 0, 0, B); CHKERRQ(ierr);
115   b = (Mat_SeqAIJ *) (*B)->data;
116   PETSCFREE(b->imax);
117   b->singlemalloc = 0;
118   len             = (ainew[n] + shift)*sizeof(Scalar);
119   /* the next line frees the default space generated by the Create() */
120   PETSCFREE(b->a); PETSCFREE(b->ilen);
121   b->a          = (Scalar *) PETSCMALLOC( len ); CHKPTRQ(b->a);
122   b->j          = ajnew;
123   b->i          = ainew;
124   b->diag       = idnew;
125   b->ilen       = 0;
126   b->imax       = 0;
127   b->row        = isrow;
128   b->col        = iscol;
129   b->solve_work = (Scalar *) PETSCMALLOC( n*sizeof(Scalar));
130   CHKPTRQ(b->solve_work);
131   /* In b structure:  Free imax, ilen, old a, old j.
132      Allocate idnew, solve_work, new a, new j */
133   PLogObjectMemory(*B,(ainew[n]+shift-n)*(sizeof(int)+sizeof(Scalar)));
134   b->maxnz = b->nz = ainew[n] + shift;
135 
136   /* Cannot do this here because child is destroyed before parent created
137      PLogObjectParent(*B,isicol); */
138   return 0;
139 }
140 /* ----------------------------------------------------------- */
141 int MatLUFactorNumeric_SeqAIJ(Mat A,Mat *B)
142 {
143   Mat        C = *B;
144   Mat_SeqAIJ *a = (Mat_SeqAIJ *) A->data, *b = (Mat_SeqAIJ *)C->data;
145   IS         iscol = b->col, isrow = b->row, isicol;
146   int        *r,*ic, ierr, i, j, n = a->m, *ai = b->i, *aj = b->j;
147   int        *ajtmpold, *ajtmp, nz, row,*pj, *ics, shift = a->indexshift;
148   Scalar     *rtmp,*v, *pv, *pc, multiplier, *rtmps;
149 
150   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
151   PLogObjectParent(*B,isicol);
152   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
153   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
154   rtmp  = (Scalar *) PETSCMALLOC( (n+1)*sizeof(Scalar) ); CHKPTRQ(rtmp);
155   rtmps = rtmp + shift; ics = ic + shift;
156 
157   for ( i=0; i<n; i++ ) {
158     nz    = ai[i+1] - ai[i];
159     ajtmp = aj + ai[i] + shift;
160     for  ( j=0; j<nz; j++ ) rtmps[ajtmp[j]] = 0.0;
161 
162     /* load in initial (unfactored row) */
163     nz       = a->i[r[i]+1] - a->i[r[i]];
164     ajtmpold = a->j + a->i[r[i]] + shift;
165     v        = a->a + a->i[r[i]] + shift;
166     for ( j=0; j<nz; j++ ) rtmp[ics[ajtmpold[j]]] =  v[j];
167 
168     row = *ajtmp++ + shift;
169     while (row < i) {
170       pc = rtmp + row;
171       if (*pc != 0.0) {
172         pv         = b->a + b->diag[row] + shift;
173         pj         = b->j + b->diag[row] + (!shift);
174         multiplier = *pc * *pv++;
175         *pc        = multiplier;
176         nz         = ai[row+1] - b->diag[row] - 1;
177         PLogFlops(2*nz);
178         while (nz-->0) rtmps[*pj++] -= multiplier* *pv++;
179       }
180       row = *ajtmp++ + shift;
181     }
182     /* finished row so stick it into b->a */
183     pv = b->a + ai[i] + shift;
184     pj = b->j + ai[i] + shift;
185     nz = ai[i+1] - ai[i];
186     if (rtmp[i] == 0.0) {SETERRQ(1,"MatLUFactorNumeric_SeqAIJ:Zero pivot");}
187     rtmp[i] = 1.0/rtmp[i];
188     for ( j=0; j<nz; j++ ) {pv[j] = rtmps[pj[j]];}
189   }
190   PETSCFREE(rtmp);
191   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
192   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
193   ierr = ISDestroy(isicol); CHKERRQ(ierr);
194   C->factor      = FACTOR_LU;
195   b->assembled = 1;
196   PLogFlops(b->n);
197   return 0;
198 }
199 /* ----------------------------------------------------------- */
200 int MatLUFactor_SeqAIJ(Mat A,IS row,IS col,double f)
201 {
202   Mat_SeqAIJ *mat = (Mat_SeqAIJ *) A->data;
203   int        ierr;
204   Mat        C;
205 
206   ierr = MatLUFactorSymbolic_SeqAIJ(A,row,col,f,&C); CHKERRQ(ierr);
207   ierr = MatLUFactorNumeric_SeqAIJ(A,&C); CHKERRQ(ierr);
208 
209   /* free all the data structures from mat */
210   PETSCFREE(mat->a);
211   if (!mat->singlemalloc) {PETSCFREE(mat->i); PETSCFREE(mat->j);}
212   if (mat->diag) PETSCFREE(mat->diag);
213   if (mat->ilen) PETSCFREE(mat->ilen);
214   if (mat->imax) PETSCFREE(mat->imax);
215   if (mat->solve_work) PETSCFREE(mat->solve_work);
216   PETSCFREE(mat);
217 
218   PetscMemcpy(A,C,sizeof(struct _Mat));
219   PETSCHEADERDESTROY(C);
220   return 0;
221 }
222 /* ----------------------------------------------------------- */
223 int MatSolve_SeqAIJ(Mat A,Vec bb, Vec xx)
224 {
225   Mat_SeqAIJ *a = (Mat_SeqAIJ *) A->data;
226   IS         iscol = a->col, isrow = a->row;
227   int        *r,*c, ierr, i,  n = a->m, *vi, *ai = a->i, *aj = a->j;
228   int        nz,shift = a->indexshift;
229   Scalar     *x,*b,*tmp, *tmps, *aa = a->a, sum, *v;
230 
231   if (A->factor != FACTOR_LU) SETERRQ(1,"MatSolve_SeqAIJ:Not for unfactored matrix");
232 
233   ierr = VecGetArray(bb,&b); CHKERRQ(ierr);
234   ierr = VecGetArray(xx,&x); CHKERRQ(ierr);
235   tmp  = a->solve_work;
236 
237   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
238   ierr = ISGetIndices(iscol,&c);CHKERRQ(ierr); c = c + (n-1);
239 
240   /* forward solve the lower triangular */
241   tmp[0] = b[*r++];
242   tmps   = tmp + shift;
243   for ( i=1; i<n; i++ ) {
244     v   = aa + ai[i] + shift;
245     vi  = aj + ai[i] + shift;
246     nz  = a->diag[i] - ai[i];
247     sum = b[*r++];
248     while (nz--) sum -= *v++ * tmps[*vi++];
249     tmp[i] = sum;
250   }
251 
252   /* backward solve the upper triangular */
253   for ( i=n-1; i>=0; i-- ){
254     v   = aa + a->diag[i] + (!shift);
255     vi  = aj + a->diag[i] + (!shift);
256     nz  = ai[i+1] - a->diag[i] - 1;
257     sum = tmp[i];
258     while (nz--) sum -= *v++ * tmps[*vi++];
259     x[*c--] = tmp[i] = sum*aa[a->diag[i]+shift];
260   }
261 
262   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
263   ierr = ISRestoreIndices(iscol,&c); CHKERRQ(ierr);
264   PLogFlops(2*a->nz - a->n);
265   return 0;
266 }
267 int MatSolveAdd_SeqAIJ(Mat A,Vec bb, Vec yy, Vec xx)
268 {
269   Mat_SeqAIJ *a = (Mat_SeqAIJ *) A->data;
270   IS         iscol = a->col, isrow = a->row;
271   int        *r,*c, ierr, i,  n = a->m, *vi, *ai = a->i, *aj = a->j;
272   int        nz, shift = a->indexshift;
273   Scalar     *x,*b,*tmp, *aa = a->a, sum, *v;
274 
275   if (A->factor != FACTOR_LU) SETERRQ(1,"MatSolveAdd_SeqAIJ:Not for unfactored matrix");
276   if (yy != xx) {ierr = VecCopy(yy,xx); CHKERRQ(ierr);}
277 
278   ierr = VecGetArray(bb,&b); CHKERRQ(ierr);
279   ierr = VecGetArray(xx,&x); CHKERRQ(ierr);
280   tmp  = a->solve_work;
281 
282   ierr = ISGetIndices(isrow,&r); CHKERRQ(ierr);
283   ierr = ISGetIndices(iscol,&c); CHKERRQ(ierr); c = c + (n-1);
284 
285   /* forward solve the lower triangular */
286   tmp[0] = b[*r++];
287   for ( i=1; i<n; i++ ) {
288     v   = aa + ai[i] + shift;
289     vi  = aj + ai[i] + shift;
290     nz  = a->diag[i] - ai[i];
291     sum = b[*r++];
292     while (nz--) sum -= *v++ * tmp[*vi++ + shift];
293     tmp[i] = sum;
294   }
295 
296   /* backward solve the upper triangular */
297   for ( i=n-1; i>=0; i-- ){
298     v   = aa + a->diag[i] + (!shift);
299     vi  = aj + a->diag[i] + (!shift);
300     nz  = ai[i+1] - a->diag[i] - 1;
301     sum = tmp[i];
302     while (nz--) sum -= *v++ * tmp[*vi++ + shift];
303     tmp[i] = sum*aa[a->diag[i]+shift];
304     x[*c--] += tmp[i];
305   }
306 
307   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
308   ierr = ISRestoreIndices(iscol,&c); CHKERRQ(ierr);
309   PLogFlops(2*a->nz);
310 
311   return 0;
312 }
313 /* -------------------------------------------------------------------*/
314 int MatSolveTrans_SeqAIJ(Mat A,Vec bb, Vec xx)
315 {
316   Mat_SeqAIJ *a = (Mat_SeqAIJ *) A->data;
317   IS         iscol = a->col, isrow = a->row, invisrow,inviscol;
318   int        *r,*c, ierr, i, n = a->m, *vi, *ai = a->i, *aj = a->j;
319   int        nz,shift = a->indexshift;
320   Scalar     *x,*b,*tmp, *aa = a->a, *v;
321 
322   if (A->factor != FACTOR_LU)  SETERRQ(1,"MatSolveTrans_SeqAIJ:Not unfactored matrix");
323   ierr = VecGetArray(bb,&b); CHKERRQ(ierr);
324   ierr = VecGetArray(xx,&x); CHKERRQ(ierr);
325   tmp  = a->solve_work;
326 
327   /* invert the permutations */
328   ierr = ISInvertPermutation(isrow,&invisrow); CHKERRQ(ierr);
329   ierr = ISInvertPermutation(iscol,&inviscol); CHKERRQ(ierr);
330 
331   ierr = ISGetIndices(invisrow,&r); CHKERRQ(ierr);
332   ierr = ISGetIndices(inviscol,&c); CHKERRQ(ierr);
333 
334   /* copy the b into temp work space according to permutation */
335   for ( i=0; i<n; i++ ) tmp[c[i]] = b[i];
336 
337   /* forward solve the U^T */
338   for ( i=0; i<n; i++ ) {
339     v   = aa + a->diag[i] + shift;
340     vi  = aj + a->diag[i] + (!shift);
341     nz  = ai[i+1] - a->diag[i] - 1;
342     tmp[i] *= *v++;
343     while (nz--) {
344       tmp[*vi++ + shift] -= (*v++)*tmp[i];
345     }
346   }
347 
348   /* backward solve the L^T */
349   for ( i=n-1; i>=0; i-- ){
350     v   = aa + a->diag[i] - 1 + shift;
351     vi  = aj + a->diag[i] - 1 + shift;
352     nz  = a->diag[i] - ai[i];
353     while (nz--) {
354       tmp[*vi-- + shift] -= (*v--)*tmp[i];
355     }
356   }
357 
358   /* copy tmp into x according to permutation */
359   for ( i=0; i<n; i++ ) x[r[i]] = tmp[i];
360 
361   ierr = ISRestoreIndices(invisrow,&r); CHKERRQ(ierr);
362   ierr = ISRestoreIndices(inviscol,&c); CHKERRQ(ierr);
363   ierr = ISDestroy(invisrow); CHKERRQ(ierr);
364   ierr = ISDestroy(inviscol); CHKERRQ(ierr);
365 
366   PLogFlops(2*a->nz-a->n);
367   return 0;
368 }
369 
370 int MatSolveTransAdd_SeqAIJ(Mat A,Vec bb, Vec zz,Vec xx)
371 {
372   Mat_SeqAIJ *a = (Mat_SeqAIJ *) A->data;
373   IS         iscol = a->col, isrow = a->row, invisrow,inviscol;
374   int        *r,*c, ierr, i, n = a->m, *vi, *ai = a->i, *aj = a->j;
375   int        nz,shift = a->indexshift;
376   Scalar     *x,*b,*tmp, *aa = a->a, *v;
377 
378   if (A->factor != FACTOR_LU)SETERRQ(1,"MatSolveTransAdd_SeqAIJ:Not unfactored matrix");
379   if (zz != xx) VecCopy(zz,xx);
380 
381   ierr = VecGetArray(bb,&b); CHKERRQ(ierr);
382   ierr = VecGetArray(xx,&x); CHKERRQ(ierr);
383   tmp = a->solve_work;
384 
385   /* invert the permutations */
386   ierr = ISInvertPermutation(isrow,&invisrow); CHKERRQ(ierr);
387   ierr = ISInvertPermutation(iscol,&inviscol); CHKERRQ(ierr);
388   ierr = ISGetIndices(invisrow,&r); CHKERRQ(ierr);
389   ierr = ISGetIndices(inviscol,&c); CHKERRQ(ierr);
390 
391   /* copy the b into temp work space according to permutation */
392   for ( i=0; i<n; i++ ) tmp[c[i]] = b[i];
393 
394   /* forward solve the U^T */
395   for ( i=0; i<n; i++ ) {
396     v   = aa + a->diag[i] + shift;
397     vi  = aj + a->diag[i] + (!shift);
398     nz  = ai[i+1] - a->diag[i] - 1;
399     tmp[i] *= *v++;
400     while (nz--) {
401       tmp[*vi++ + shift] -= (*v++)*tmp[i];
402     }
403   }
404 
405   /* backward solve the L^T */
406   for ( i=n-1; i>=0; i-- ){
407     v   = aa + a->diag[i] - 1 + shift;
408     vi  = aj + a->diag[i] - 1 + shift;
409     nz  = a->diag[i] - ai[i];
410     while (nz--) {
411       tmp[*vi-- + shift] -= (*v--)*tmp[i];
412     }
413   }
414 
415   /* copy tmp into x according to permutation */
416   for ( i=0; i<n; i++ ) x[r[i]] += tmp[i];
417 
418   ierr = ISRestoreIndices(invisrow,&r); CHKERRQ(ierr);
419   ierr = ISRestoreIndices(inviscol,&c); CHKERRQ(ierr);
420   ierr = ISDestroy(invisrow); CHKERRQ(ierr);
421   ierr = ISDestroy(inviscol); CHKERRQ(ierr);
422 
423   PLogFlops(2*a->nz);
424   return 0;
425 }
426 /* ----------------------------------------------------------------*/
427 int MatILUFactorSymbolic_SeqAIJ(Mat A,IS isrow,IS iscol,double f,
428                              int levels,Mat *fact)
429 {
430   Mat_SeqAIJ *a = (Mat_SeqAIJ *) A->data, *b;
431   IS         isicol;
432   int        *r,*ic, ierr, prow, n = a->m, *ai = a->i, *aj = a->j;
433   int        *ainew,*ajnew, jmax,*fill, *xi, nz, *im,*ajfill,*flev;
434   int        *dloc, idx, row,m,fm, nzf, nzi,len,  realloc = 0;
435   int        incrlev,nnz,i,shift = a->indexshift;
436 
437   if (n != a->n) SETERRQ(1,"MatILUFactorSymbolic_SeqAIJ:Matrix must be square");
438   if (!isrow) SETERRQ(1,"MatILUFactorSymbolic_SeqAIJ:Must have row permutation");
439   if (!iscol) SETERRQ(1,"MatILUFactorSymbolic_SeqAIJ:Must have column permutation");
440 
441   ierr = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
442   ierr = ISGetIndices(isrow,&r); CHKERRQ(ierr);
443   ierr = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
444 
445   /* get new row pointers */
446   ainew = (int *) PETSCMALLOC( (n+1)*sizeof(int) ); CHKPTRQ(ainew);
447   ainew[0] = -shift;
448   /* don't know how many column pointers are needed so estimate */
449   jmax = (int) (f*(ai[n]+!shift));
450   ajnew = (int *) PETSCMALLOC( (jmax)*sizeof(int) ); CHKPTRQ(ajnew);
451   /* ajfill is level of fill for each fill entry */
452   ajfill = (int *) PETSCMALLOC( (jmax)*sizeof(int) ); CHKPTRQ(ajfill);
453   /* fill is a linked list of nonzeros in active row */
454   fill = (int *) PETSCMALLOC( (n+1)*sizeof(int)); CHKPTRQ(fill);
455   /* im is level for each filled value */
456   im = (int *) PETSCMALLOC( (n+1)*sizeof(int)); CHKPTRQ(im);
457   /* dloc is location of diagonal in factor */
458   dloc = (int *) PETSCMALLOC( (n+1)*sizeof(int)); CHKPTRQ(dloc);
459   dloc[0]  = 0;
460 
461   for ( prow=0; prow<n; prow++ ) {
462     /* first copy previous fill into linked list */
463     nzf     = nz  = ai[r[prow]+1] - ai[r[prow]];
464     xi      = aj + ai[r[prow]] + shift;
465     fill[n] = n;
466     while (nz--) {
467       fm  = n;
468       idx = ic[*xi++ + shift];
469       do {
470         m  = fm;
471         fm = fill[m];
472       } while (fm < idx);
473       fill[m]   = idx;
474       fill[idx] = fm;
475       im[idx]   = 0;
476     }
477     nzi = 0;
478     row = fill[n];
479     while ( row < prow ) {
480       incrlev = im[row] + 1;
481       nz      = dloc[row];
482       xi      = ajnew  + ainew[row] + shift + nz;
483       flev    = ajfill + ainew[row] + shift + nz + 1;
484       nnz     = ainew[row+1] - ainew[row] - nz - 1;
485       if (*xi++ + shift != row) {
486         SETERRQ(1,"MatILUFactorSymbolic_SeqAIJ:zero pivot");
487       }
488       fm      = row;
489       while (nnz-- > 0) {
490         idx = *xi++ + shift;
491         if (*flev + incrlev > levels) {
492           flev++;
493           continue;
494         }
495         do {
496           m  = fm;
497           fm = fill[m];
498         } while (fm < idx);
499         if (fm != idx) {
500           im[idx]   = *flev + incrlev;
501           fill[m]   = idx;
502           fill[idx] = fm;
503           fm        = idx;
504           nzf++;
505         }
506         else {
507           if (im[idx] > *flev + incrlev) im[idx] = *flev+incrlev;
508         }
509         flev++;
510       }
511       row = fill[row];
512       nzi++;
513     }
514     /* copy new filled row into permanent storage */
515     ainew[prow+1] = ainew[prow] + nzf;
516     if (ainew[prow+1] > jmax+1) {
517       /* allocate a longer ajnew */
518       int maxadd;
519       maxadd = (int) ((f*(ai[n]+!shift)*(n-prow+5))/n);
520       if (maxadd < nzf) maxadd = (n-prow)*(nzf+1);
521       jmax += maxadd;
522       xi = (int *) PETSCMALLOC( jmax*sizeof(int) );CHKPTRQ(xi);
523       PetscMemcpy(xi,ajnew,(ainew[prow]+shift)*sizeof(int));
524       PETSCFREE(ajnew);
525       ajnew = xi;
526       /* allocate a longer ajfill */
527       xi = (int *) PETSCMALLOC( jmax*sizeof(int) );CHKPTRQ(xi);
528       PetscMemcpy(xi,ajfill,(ainew[prow]+shift)*sizeof(int));
529       PETSCFREE(ajfill);
530       ajfill = xi;
531       realloc++;
532     }
533     xi          = ajnew + ainew[prow] + shift;
534     flev        = ajfill + ainew[prow] + shift;
535     dloc[prow]  = nzi;
536     fm          = fill[n];
537     while (nzf--) {
538       *xi++   = fm - shift;
539       *flev++ = im[fm];
540       fm      = fill[fm];
541     }
542   }
543   PETSCFREE(ajfill);
544   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
545   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
546   ierr = ISDestroy(isicol); CHKERRQ(ierr);
547   PETSCFREE(fill); PETSCFREE(im);
548 
549   PLogInfo((PetscObject)A,
550     "Info:MatILUFactorSymbolic_SeqAIJ:Realloc %d Fill ratio:given %g needed %g\n",
551                              realloc,f,((double)ainew[n])/((double)ai[prow]));
552 
553   /* put together the new matrix */
554   ierr = MatCreateSeqAIJ(A->comm,n, n, 0, 0, fact); CHKERRQ(ierr);
555   b = (Mat_SeqAIJ *) (*fact)->data;
556   PETSCFREE(b->imax);
557   b->singlemalloc = 0;
558   len = (ainew[n] + shift)*sizeof(Scalar);
559   /* the next line frees the default space generated by the Create() */
560   PETSCFREE(b->a); PETSCFREE(b->ilen);
561   b->a          = (Scalar *) PETSCMALLOC( len ); CHKPTRQ(b->a);
562   b->j          = ajnew;
563   b->i          = ainew;
564   for ( i=0; i<n; i++ ) dloc[i] += ainew[i];
565   b->diag       = dloc;
566   b->ilen       = 0;
567   b->imax       = 0;
568   b->row        = isrow;
569   b->col        = iscol;
570   b->solve_work = (Scalar *) PETSCMALLOC( (n+1)*sizeof(Scalar));
571   CHKPTRQ(b->solve_work);
572   /* In b structure:  Free imax, ilen, old a, old j.
573      Allocate dloc, solve_work, new a, new j */
574   PLogObjectMemory(*fact,(ainew[n]+shift-n) * (sizeof(int)+sizeof(Scalar)));
575   b->maxnz          = b->nz = ainew[n] + shift;
576   (*fact)->factor   = FACTOR_LU;
577   return 0;
578 }
579