xref: /petsc/src/mat/impls/aij/seq/aijfact.c (revision ce3d78c064643d93723ba32f90168623e06aefd5)
1 #define PETSCMAT_DLL
2 
3 
4 #include "../src/mat/impls/aij/seq/aij.h"
5 #include "petscbt.h"
6 #include "../src/mat/utils/freespace.h"
7 
8 EXTERN_C_BEGIN
9 #undef __FUNCT__
10 #define __FUNCT__ "MatOrdering_Flow_SeqAIJ"
11 /*
12       Computes an ordering to get most of the large numerical values in the lower triangular part of the matrix
13 */
14 PetscErrorCode MatOrdering_Flow_SeqAIJ(Mat mat,const MatOrderingType type,IS *irow,IS *icol)
15 {
16   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)mat->data;
17   PetscErrorCode    ierr;
18   PetscInt          i,j,jj,k, kk,n = mat->rmap->n, current = 0, newcurrent = 0,*order;
19   const PetscInt    *ai = a->i, *aj = a->j;
20   const PetscScalar *aa = a->a;
21   PetscTruth        *done;
22   PetscReal         best,past = 0,future;
23 
24   PetscFunctionBegin;
25   /* pick initial row */
26   best = -1;
27   for (i=0; i<n; i++) {
28     future = 0;
29     for (j=ai[i]; j<ai[i+1]; j++) {
30       if (aj[j] != i) future  += PetscAbsScalar(aa[j]); else past = PetscAbsScalar(aa[j]);
31     }
32     if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */
33     if (past/future > best) {
34       best = past/future;
35       current = i;
36     }
37   }
38 
39   ierr = PetscMalloc(n*sizeof(PetscTruth),&done);CHKERRQ(ierr);
40   ierr = PetscMalloc(n*sizeof(PetscInt),&order);CHKERRQ(ierr);
41   ierr = PetscMemzero(done,n*sizeof(PetscTruth));CHKERRQ(ierr);
42   order[0] = current;
43   for (i=0; i<n-1; i++) {
44     done[current] = PETSC_TRUE;
45     best          = -1;
46     /* loop over all neighbors of current pivot */
47     for (j=ai[current]; j<ai[current+1]; j++) {
48       jj = aj[j];
49       if (done[jj]) continue;
50       /* loop over columns of potential next row computing weights for below and above diagonal */
51       past = future = 0.0;
52       for (k=ai[jj]; k<ai[jj+1]; k++) {
53         kk = aj[k];
54         if (done[kk]) past += PetscAbsScalar(aa[k]);
55         else if (kk != jj) future  += PetscAbsScalar(aa[k]);
56       }
57       if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */
58       if (past/future > best) {
59         best = past/future;
60         newcurrent = jj;
61       }
62     }
63     if (best == -1) { /* no neighbors to select from so select best of all that remain */
64       best = -1;
65       for (k=0; k<n; k++) {
66         if (done[k]) continue;
67         future = 0;
68         past   = 0;
69         for (j=ai[k]; j<ai[k+1]; j++) {
70           kk = aj[j];
71           if (done[kk]) past += PetscAbsScalar(aa[j]);
72           else if (kk != k) future  += PetscAbsScalar(aa[j]);
73         }
74         if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */
75         if (past/future > best) {
76           best = past/future;
77           newcurrent = k;
78         }
79       }
80     }
81     if (current == newcurrent) SETERRQ(PETSC_ERR_PLIB,"newcurrent cannot be current");
82     current = newcurrent;
83     order[i+1] = current;
84   }
85   ierr = ISCreateGeneral(PETSC_COMM_SELF,n,order,irow);CHKERRQ(ierr);
86   *icol = *irow;
87   ierr = PetscObjectReference((PetscObject)*irow);CHKERRQ(ierr);
88   ierr = PetscFree(done);CHKERRQ(ierr);
89   ierr = PetscFree(order);CHKERRQ(ierr);
90   PetscFunctionReturn(0);
91 }
92 EXTERN_C_END
93 
94 EXTERN_C_BEGIN
95 #undef __FUNCT__
96 #define __FUNCT__ "MatGetFactorAvailable_seqaij_petsc"
97 PetscErrorCode MatGetFactorAvailable_seqaij_petsc(Mat A,MatFactorType ftype,PetscTruth *flg)
98 {
99   PetscFunctionBegin;
100   *flg = PETSC_TRUE;
101   PetscFunctionReturn(0);
102 }
103 EXTERN_C_END
104 
105 EXTERN_C_BEGIN
106 #undef __FUNCT__
107 #define __FUNCT__ "MatGetFactor_seqaij_petsc"
108 PetscErrorCode MatGetFactor_seqaij_petsc(Mat A,MatFactorType ftype,Mat *B)
109 {
110   PetscInt           n = A->rmap->n;
111   PetscErrorCode     ierr;
112 
113   PetscFunctionBegin;
114   ierr = MatCreate(((PetscObject)A)->comm,B);CHKERRQ(ierr);
115   ierr = MatSetSizes(*B,n,n,n,n);CHKERRQ(ierr);
116   if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT){
117     ierr = MatSetType(*B,MATSEQAIJ);CHKERRQ(ierr);
118     (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqAIJ;
119     (*B)->ops->lufactorsymbolic  = MatLUFactorSymbolic_SeqAIJ;
120     (*B)->ops->iludtfactor       = MatILUDTFactor_SeqAIJ;
121   } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) {
122     ierr = MatSetType(*B,MATSEQSBAIJ);CHKERRQ(ierr);
123     ierr = MatSeqSBAIJSetPreallocation(*B,1,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
124     (*B)->ops->iccfactorsymbolic      = MatICCFactorSymbolic_SeqAIJ;
125     (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJ;
126   } else SETERRQ(PETSC_ERR_SUP,"Factor type not supported");
127   (*B)->factor = ftype;
128   PetscFunctionReturn(0);
129 }
130 EXTERN_C_END
131 
132 #undef __FUNCT__
133 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ"
134 PetscErrorCode MatLUFactorSymbolic_SeqAIJ(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
135 {
136   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
137   IS                 isicol;
138   PetscErrorCode     ierr;
139   const PetscInt     *r,*ic;
140   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j;
141   PetscInt           *bi,*bj,*ajtmp;
142   PetscInt           *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im;
143   PetscReal          f;
144   PetscInt           nlnk,*lnk,k,**bi_ptr;
145   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
146   PetscBT            lnkbt;
147   PetscTruth         newdatastruct=PETSC_FALSE;
148 
149   PetscFunctionBegin;
150   ierr = PetscOptionsGetTruth(PETSC_NULL,"-lu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
151   if(newdatastruct){
152     ierr = MatLUFactorSymbolic_SeqAIJ_newdatastruct(B,A,isrow,iscol,info);CHKERRQ(ierr);
153     PetscFunctionReturn(0);
154   }
155 
156   if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square");
157   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
158   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
159   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
160 
161   /* get new row pointers */
162   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
163   bi[0] = 0;
164 
165   /* bdiag is location of diagonal in factor */
166   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
167   bdiag[0] = 0;
168 
169   /* linked list for storing column indices of the active row */
170   nlnk = n + 1;
171   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
172 
173   ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr);
174 
175   /* initial FreeSpace size is f*(ai[n]+1) */
176   f = info->fill;
177   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
178   current_space = free_space;
179 
180   for (i=0; i<n; i++) {
181     /* copy previous fill into linked list */
182     nzi = 0;
183     nnz = ai[r[i]+1] - ai[r[i]];
184     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
185     ajtmp = aj + ai[r[i]];
186     ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
187     nzi += nlnk;
188 
189     /* add pivot rows into linked list */
190     row = lnk[n];
191     while (row < i) {
192       nzbd    = bdiag[row] - bi[row] + 1; /* num of entries in the row with column index <= row */
193       ajtmp   = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */
194       ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr);
195       nzi += nlnk;
196       row  = lnk[row];
197     }
198     bi[i+1] = bi[i] + nzi;
199     im[i]   = nzi;
200 
201     /* mark bdiag */
202     nzbd = 0;
203     nnz  = nzi;
204     k    = lnk[n];
205     while (nnz-- && k < i){
206       nzbd++;
207       k = lnk[k];
208     }
209     bdiag[i] = bi[i] + nzbd;
210 
211     /* if free space is not available, make more free space */
212     if (current_space->local_remaining<nzi) {
213       nnz = (n - i)*nzi; /* estimated and max additional space needed */
214       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
215       reallocs++;
216     }
217 
218     /* copy data into free space, then initialize lnk */
219     ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
220     bi_ptr[i] = current_space->array;
221     current_space->array           += nzi;
222     current_space->local_used      += nzi;
223     current_space->local_remaining -= nzi;
224   }
225 #if defined(PETSC_USE_INFO)
226   if (ai[n] != 0) {
227     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
228     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
229     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
230     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr);
231     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
232   } else {
233     ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr);
234   }
235 #endif
236 
237   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
238   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
239 
240   /* destroy list of free space and other temporary array(s) */
241   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
242   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
243   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
244   ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr);
245 
246   /* put together the new matrix */
247   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
248   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
249   b    = (Mat_SeqAIJ*)(B)->data;
250   b->free_a       = PETSC_TRUE;
251   b->free_ij      = PETSC_TRUE;
252   b->singlemalloc = PETSC_FALSE;
253   ierr          = PetscMalloc((bi[n]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
254   b->j          = bj;
255   b->i          = bi;
256   b->diag       = bdiag;
257   b->ilen       = 0;
258   b->imax       = 0;
259   b->row        = isrow;
260   b->col        = iscol;
261   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
262   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
263   b->icol       = isicol;
264   ierr          = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
265 
266   /* In b structure:  Free imax, ilen, old a, old j.  Allocate solve_work, new a, new j */
267   ierr = PetscLogObjectMemory(B,(bi[n]-n)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
268   b->maxnz = b->nz = bi[n] ;
269 
270   (B)->factor                = MAT_FACTOR_LU;
271   (B)->info.factor_mallocs   = reallocs;
272   (B)->info.fill_ratio_given = f;
273 
274   if (ai[n]) {
275     (B)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
276   } else {
277     (B)->info.fill_ratio_needed = 0.0;
278   }
279   (B)->ops->lufactornumeric  = MatLUFactorNumeric_SeqAIJ;
280   (B)->ops->solve            = MatSolve_SeqAIJ;
281   (B)->ops->solvetranspose   = MatSolveTranspose_SeqAIJ;
282   /* switch to inodes if appropriate */
283   ierr = MatLUFactorSymbolic_Inode(B,A,isrow,iscol,info);CHKERRQ(ierr);
284   PetscFunctionReturn(0);
285 }
286 
287 #undef __FUNCT__
288 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ_newdatastruct"
289 PetscErrorCode MatLUFactorSymbolic_SeqAIJ_newdatastruct(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
290 {
291   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
292   IS                 isicol;
293   PetscErrorCode     ierr;
294   const PetscInt     *r,*ic;
295   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j;
296   PetscInt           *bi,*bj,*ajtmp;
297   PetscInt           *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im;
298   PetscReal          f;
299   PetscInt           nlnk,*lnk,k,**bi_ptr;
300   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
301   PetscBT            lnkbt;
302 
303   PetscFunctionBegin;
304   if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square");
305   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
306   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
307   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
308 
309   /* get new row pointers */
310   ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
311   bi[0] = 0;
312 
313   /* bdiag is location of diagonal in factor */
314   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
315   bdiag[0] = 0;
316 
317   /* linked list for storing column indices of the active row */
318   nlnk = n + 1;
319   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
320 
321   ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr);
322 
323   /* initial FreeSpace size is f*(ai[n]+1) */
324   f = info->fill;
325   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
326   current_space = free_space;
327 
328   for (i=0; i<n; i++) {
329     /* copy previous fill into linked list */
330     nzi = 0;
331     nnz = ai[r[i]+1] - ai[r[i]];
332     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
333     ajtmp = aj + ai[r[i]];
334     ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
335     nzi += nlnk;
336 
337     /* add pivot rows into linked list */
338     row = lnk[n];
339     while (row < i) {
340       nzbd    = bdiag[row] - bi[row] + 1; /* num of entries in the row with column index <= row */
341       ajtmp   = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */
342       ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr);
343       nzi += nlnk;
344       row  = lnk[row];
345     }
346     bi[i+1] = bi[i] + nzi;
347     im[i]   = nzi;
348 
349     /* mark bdiag */
350     nzbd = 0;
351     nnz  = nzi;
352     k    = lnk[n];
353     while (nnz-- && k < i){
354       nzbd++;
355       k = lnk[k];
356     }
357     bdiag[i] = bi[i] + nzbd;
358 
359     /* if free space is not available, make more free space */
360     if (current_space->local_remaining<nzi) {
361       nnz = 2*(n - i)*nzi; /* estimated and max additional space needed */
362       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
363       reallocs++;
364     }
365 
366     /* copy data into free space, then initialize lnk */
367     ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
368     bi_ptr[i] = current_space->array;
369     current_space->array           += nzi;
370     current_space->local_used      += nzi;
371     current_space->local_remaining -= nzi;
372   }
373 #if defined(PETSC_USE_INFO)
374   if (ai[n] != 0) {
375     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
376     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
377     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
378     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr);
379     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
380   } else {
381     ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr);
382   }
383 #endif
384 
385   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
386   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
387 
388   /* destroy list of free space and other temporary array(s) */
389   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
390   ierr = PetscFreeSpaceContiguous_newdatastruct(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr);
391   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
392   ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr);
393 
394   /* put together the new matrix */
395   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
396   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
397   b    = (Mat_SeqAIJ*)(B)->data;
398   b->free_a       = PETSC_TRUE;
399   b->free_ij      = PETSC_TRUE;
400   b->singlemalloc = PETSC_FALSE;
401   ierr          = PetscMalloc((bi[2*n+1])*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
402   b->j          = bj;
403   b->i          = bi;
404   b->diag       = bdiag;
405   b->ilen       = 0;
406   b->imax       = 0;
407   b->row        = isrow;
408   b->col        = iscol;
409   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
410   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
411   b->icol       = isicol;
412   ierr          = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
413 
414   /* In b structure:  Free imax, ilen, old a, old j.  Allocate solve_work, new a, new j */
415   ierr = PetscLogObjectMemory(B,bi[2*n+1]*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
416   b->maxnz = b->nz = bi[2*n+1] ;
417 
418   (B)->factor                = MAT_FACTOR_LU;
419   (B)->info.factor_mallocs   = reallocs;
420   (B)->info.fill_ratio_given = f;
421 
422   if (ai[n]) {
423     (B)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
424   } else {
425     (B)->info.fill_ratio_needed = 0.0;
426   }
427   (B)->ops->lufactornumeric  = MatLUFactorNumeric_SeqAIJ_newdatastruct;
428   (B)->ops->solve            = MatSolve_SeqAIJ;
429   (B)->ops->solvetranspose   = MatSolveTranspose_SeqAIJ;
430   /* switch to inodes if appropriate */
431 /*  ierr = MatLUFactorSymbolic_Inode(B,A,isrow,iscol,info);CHKERRQ(ierr); */
432   PetscFunctionReturn(0);
433 }
434 
435 
436 /*
437     Trouble in factorization, should we dump the original matrix?
438 */
439 #undef __FUNCT__
440 #define __FUNCT__ "MatFactorDumpMatrix"
441 PetscErrorCode MatFactorDumpMatrix(Mat A)
442 {
443   PetscErrorCode ierr;
444   PetscTruth     flg = PETSC_FALSE;
445 
446   PetscFunctionBegin;
447   ierr = PetscOptionsGetTruth(PETSC_NULL,"-mat_factor_dump_on_error",&flg,PETSC_NULL);CHKERRQ(ierr);
448   if (flg) {
449     PetscViewer viewer;
450     char        filename[PETSC_MAX_PATH_LEN];
451 
452     ierr = PetscSNPrintf(filename,PETSC_MAX_PATH_LEN,"matrix_factor_error.%d",PetscGlobalRank);CHKERRQ(ierr);
453     ierr = PetscViewerBinaryOpen(((PetscObject)A)->comm,filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr);
454     ierr = MatView(A,viewer);CHKERRQ(ierr);
455     ierr = PetscViewerDestroy(viewer);CHKERRQ(ierr);
456   }
457   PetscFunctionReturn(0);
458 }
459 
460 extern PetscErrorCode MatSolve_Inode(Mat,Vec,Vec);
461 
462 /* ----------------------------------------------------------- */
463 extern PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_iludt(Mat,Vec,Vec);
464 extern PetscErrorCode MatSolve_SeqAIJ_iludt(Mat,Vec,Vec);
465 
466 #undef __FUNCT__
467 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_newdatastruct"
468 PetscErrorCode MatLUFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info)
469 {
470   Mat            C=B;
471   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
472   IS             isrow = b->row,isicol = b->icol;
473   PetscErrorCode ierr;
474   const PetscInt *r,*ic,*ics;
475   PetscInt       i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
476   PetscInt       *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj;
477   MatScalar      *rtmp,*pc,multiplier,*v,*pv,*aa=a->a;
478   PetscReal      shift=info->shiftinblocks;
479   PetscTruth     row_identity, col_identity;
480 
481   PetscFunctionBegin;
482   /* printf("MatLUFactorNumeric_SeqAIJ_newdatastruct is called ...\n"); */
483   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
484   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
485   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
486   ics  = ic;
487 
488   for (i=0; i<n; i++){
489     /* zero rtmp */
490     /* L part */
491     nz    = bi[i+1] - bi[i];
492     bjtmp = bj + bi[i];
493     for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
494 
495     /* U part */
496     nz = bi[2*n-i+1] - bi[2*n-i];
497     bjtmp = bj + bi[2*n-i];
498     for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
499 
500     /* load in initial (unfactored row) */
501     nz    = ai[r[i]+1] - ai[r[i]];
502     ajtmp = aj + ai[r[i]];
503     v     = aa + ai[r[i]];
504     for (j=0; j<nz; j++) {
505       rtmp[ics[ajtmp[j]]] = v[j];
506     }
507     if (rtmp[ics[r[i]]] == 0.0){
508       rtmp[ics[r[i]]] += shift; /* shift the diagonal of the matrix */
509       /* printf("row %d, shift %g\n",i,shift); */
510     }
511 
512     /* elimination */
513     bjtmp = bj + bi[i];
514     row   = *bjtmp++;
515     nzL   = bi[i+1] - bi[i];
516     k   = 0;
517     while  (k < nzL) {
518       pc = rtmp + row;
519       if (*pc != 0.0) {
520         pv         = b->a + bdiag[row];
521         multiplier = *pc * (*pv);
522         *pc        = multiplier;
523         pj         = b->j + bi[2*n-row]; /* begining of U(row,:) */
524         pv         = b->a + bi[2*n-row];
525         nz         = bi[2*n-row+1] - bi[2*n-row] - 1; /* num of entries in U(row,:), excluding diag */
526         for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
527         ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
528       }
529       row = *bjtmp++; k++;
530     }
531 
532     /* finished row so stick it into b->a */
533     /* L part */
534     pv   = b->a + bi[i] ;
535     pj   = b->j + bi[i] ;
536     nz   = bi[i+1] - bi[i];
537     for (j=0; j<nz; j++) {
538       pv[j] = rtmp[pj[j]];
539     }
540 
541     /* Mark diagonal and invert diagonal for simplier triangular solves */
542     pv  = b->a + bdiag[i];
543     pj  = b->j + bdiag[i];
544     /* if (*pj != i)SETERRQ2(PETSC_ERR_SUP,"row %d != *pj %d",i,*pj) */
545     *pv = 1.0/rtmp[*pj];
546 
547     /* U part */
548     pv = b->a + bi[2*n-i];
549     pj = b->j + bi[2*n-i];
550     nz = bi[2*n-i+1] - bi[2*n-i] - 1;
551     for (j=0; j<nz; j++) pv[j] = rtmp[pj[j]];
552   }
553   ierr = PetscFree(rtmp);CHKERRQ(ierr);
554   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
555   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
556 
557   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
558   ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
559   if (row_identity && col_identity) {
560     C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_iludt;
561   } else {
562     C->ops->solve = MatSolve_SeqAIJ_iludt;
563   }
564 
565   C->ops->solveadd           = 0;
566   C->ops->solvetranspose     = 0;
567   C->ops->solvetransposeadd  = 0;
568   C->ops->matsolve           = 0;
569   C->assembled    = PETSC_TRUE;
570   C->preallocated = PETSC_TRUE;
571   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
572   PetscFunctionReturn(0);
573 }
574 
575 #undef __FUNCT__
576 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ"
577 PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info)
578 {
579   Mat             C=B;
580   Mat_SeqAIJ      *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
581   IS              isrow = b->row,isicol = b->icol;
582   PetscErrorCode  ierr;
583   const PetscInt   *r,*ic,*ics;
584   PetscInt        nz,row,i,j,n=A->rmap->n,diag;
585   const PetscInt  *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
586   const PetscInt  *ajtmp,*bjtmp,*diag_offset = b->diag,*pj;
587   MatScalar       *pv,*rtmp,*pc,multiplier,d;
588   const MatScalar *v,*aa=a->a;
589   PetscReal       rs=0.0;
590   LUShift_Ctx     sctx;
591   PetscInt        newshift,*ddiag;
592 
593   PetscFunctionBegin;
594   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
595   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
596   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
597   ics  = ic;
598 
599   sctx.shift_top      = 0;
600   sctx.nshift_max     = 0;
601   sctx.shift_lo       = 0;
602   sctx.shift_hi       = 0;
603   sctx.shift_fraction = 0;
604 
605   /* if both shift schemes are chosen by user, only use info->shiftpd */
606   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
607     ddiag          = a->diag;
608     sctx.shift_top = info->zeropivot;
609     for (i=0; i<n; i++) {
610       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
611       d  = (aa)[ddiag[i]];
612       rs = -PetscAbsScalar(d) - PetscRealPart(d);
613       v  = aa+ai[i];
614       nz = ai[i+1] - ai[i];
615       for (j=0; j<nz; j++)
616 	rs += PetscAbsScalar(v[j]);
617       if (rs>sctx.shift_top) sctx.shift_top = rs;
618     }
619     sctx.shift_top   *= 1.1;
620     sctx.nshift_max   = 5;
621     sctx.shift_lo     = 0.;
622     sctx.shift_hi     = 1.;
623   }
624 
625   sctx.shift_amount = 0.0;
626   sctx.nshift       = 0;
627   do {
628     sctx.lushift = PETSC_FALSE;
629     for (i=0; i<n; i++){
630       nz    = bi[i+1] - bi[i];
631       bjtmp = bj + bi[i];
632       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
633 
634       /* load in initial (unfactored row) */
635       nz    = ai[r[i]+1] - ai[r[i]];
636       ajtmp = aj + ai[r[i]];
637       v     = aa + ai[r[i]];
638       for (j=0; j<nz; j++) {
639         rtmp[ics[ajtmp[j]]] = v[j];
640       }
641       rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */
642       /* if (sctx.shift_amount > 0.0) printf("row %d, shift %g\n",i,sctx.shift_amount); */
643 
644       row = *bjtmp++;
645       while  (row < i) {
646         pc = rtmp + row;
647         if (*pc != 0.0) {
648           pv         = b->a + diag_offset[row];
649           pj         = b->j + diag_offset[row] + 1;
650           multiplier = *pc / *pv++;
651           *pc        = multiplier;
652           nz         = bi[row+1] - diag_offset[row] - 1;
653           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
654           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
655         }
656         row = *bjtmp++;
657       }
658       /* finished row so stick it into b->a */
659       pv   = b->a + bi[i] ;
660       pj   = b->j + bi[i] ;
661       nz   = bi[i+1] - bi[i];
662       diag = diag_offset[i] - bi[i];
663       rs   = 0.0;
664       for (j=0; j<nz; j++) {
665         pv[j] = rtmp[pj[j]];
666         rs   += PetscAbsScalar(pv[j]);
667       }
668       rs   -= PetscAbsScalar(pv[diag]);
669 
670       /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */
671       sctx.rs  = rs;
672       sctx.pv  = pv[diag];
673       ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr);
674       if (newshift == 1) break;
675     }
676 
677     if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
678       /*
679        * if no shift in this attempt & shifting & started shifting & can refine,
680        * then try lower shift
681        */
682       sctx.shift_hi       = sctx.shift_fraction;
683       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
684       sctx.shift_amount   = sctx.shift_fraction * sctx.shift_top;
685       sctx.lushift        = PETSC_TRUE;
686       sctx.nshift++;
687     }
688   } while (sctx.lushift);
689 
690   /* invert diagonal entries for simplier triangular solves */
691   for (i=0; i<n; i++) {
692     b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]];
693   }
694   ierr = PetscFree(rtmp);CHKERRQ(ierr);
695   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
696   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
697   if (b->inode.use) {
698     C->ops->solve   = MatSolve_Inode;
699   } else {
700     PetscTruth row_identity, col_identity;
701     ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
702     ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
703     if (row_identity && col_identity) {
704       C->ops->solve   = MatSolve_SeqAIJ_NaturalOrdering;
705     } else {
706       C->ops->solve   = MatSolve_SeqAIJ;
707     }
708   }
709   C->ops->solveadd           = MatSolveAdd_SeqAIJ;
710   C->ops->solvetranspose     = MatSolveTranspose_SeqAIJ;
711   C->ops->solvetransposeadd  = MatSolveTransposeAdd_SeqAIJ;
712   C->ops->matsolve           = MatMatSolve_SeqAIJ;
713   C->assembled    = PETSC_TRUE;
714   C->preallocated = PETSC_TRUE;
715   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
716   if (sctx.nshift){
717      if (info->shiftpd) {
718       ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %G, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,sctx.shift_amount,sctx.shift_fraction,sctx.shift_top);CHKERRQ(ierr);
719     } else if (info->shiftnz) {
720       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
721     }
722   }
723   PetscFunctionReturn(0);
724 }
725 
726 /*
727    This routine implements inplace ILU(0) with row or/and column permutations.
728    Input:
729      A - original matrix
730    Output;
731      A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i]
732          a->j (col index) is permuted by the inverse of colperm, then sorted
733          a->a reordered accordingly with a->j
734          a->diag (ptr to diagonal elements) is updated.
735 */
736 #undef __FUNCT__
737 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_InplaceWithPerm"
738 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info)
739 {
740   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
741   IS             isrow = a->row,isicol = a->icol;
742   PetscErrorCode ierr;
743   const PetscInt *r,*ic,*ics;
744   PetscInt       i,j,n=A->rmap->n,*ai=a->i,*aj=a->j;
745   PetscInt       *ajtmp,nz,row;
746   PetscInt       *diag = a->diag,nbdiag,*pj;
747   PetscScalar    *rtmp,*pc,multiplier,d;
748   MatScalar      *v,*pv;
749   PetscReal      rs;
750   LUShift_Ctx    sctx;
751   PetscInt       newshift;
752 
753   PetscFunctionBegin;
754   if (A != B) SETERRQ(PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address");
755   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
756   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
757   ierr  = PetscMalloc((n+1)*sizeof(PetscScalar),&rtmp);CHKERRQ(ierr);
758   ierr  = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr);
759   ics = ic;
760 
761   sctx.shift_top      = 0;
762   sctx.nshift_max     = 0;
763   sctx.shift_lo       = 0;
764   sctx.shift_hi       = 0;
765   sctx.shift_fraction = 0;
766 
767   /* if both shift schemes are chosen by user, only use info->shiftpd */
768   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
769     sctx.shift_top = 0;
770     for (i=0; i<n; i++) {
771       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
772       d  = (a->a)[diag[i]];
773       rs = -PetscAbsScalar(d) - PetscRealPart(d);
774       v  = a->a+ai[i];
775       nz = ai[i+1] - ai[i];
776       for (j=0; j<nz; j++)
777 	rs += PetscAbsScalar(v[j]);
778       if (rs>sctx.shift_top) sctx.shift_top = rs;
779     }
780     if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot;
781     sctx.shift_top    *= 1.1;
782     sctx.nshift_max   = 5;
783     sctx.shift_lo     = 0.;
784     sctx.shift_hi     = 1.;
785   }
786 
787   sctx.shift_amount = 0;
788   sctx.nshift       = 0;
789   do {
790     sctx.lushift = PETSC_FALSE;
791     for (i=0; i<n; i++){
792       /* load in initial unfactored row */
793       nz    = ai[r[i]+1] - ai[r[i]];
794       ajtmp = aj + ai[r[i]];
795       v     = a->a + ai[r[i]];
796       /* sort permuted ajtmp and values v accordingly */
797       for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]];
798       ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr);
799 
800       diag[r[i]] = ai[r[i]];
801       for (j=0; j<nz; j++) {
802         rtmp[ajtmp[j]] = v[j];
803         if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */
804       }
805       rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */
806 
807       row = *ajtmp++;
808       while  (row < i) {
809         pc = rtmp + row;
810         if (*pc != 0.0) {
811           pv         = a->a + diag[r[row]];
812           pj         = aj + diag[r[row]] + 1;
813 
814           multiplier = *pc / *pv++;
815           *pc        = multiplier;
816           nz         = ai[r[row]+1] - diag[r[row]] - 1;
817           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
818           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
819         }
820         row = *ajtmp++;
821       }
822       /* finished row so overwrite it onto a->a */
823       pv   = a->a + ai[r[i]] ;
824       pj   = aj + ai[r[i]] ;
825       nz   = ai[r[i]+1] - ai[r[i]];
826       nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */
827 
828       rs   = 0.0;
829       for (j=0; j<nz; j++) {
830         pv[j] = rtmp[pj[j]];
831         if (j != nbdiag) rs += PetscAbsScalar(pv[j]);
832       }
833 
834       /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */
835       sctx.rs  = rs;
836       sctx.pv  = pv[nbdiag];
837       ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr);
838       if (newshift == 1) break;
839     }
840 
841     if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
842       /*
843        * if no shift in this attempt & shifting & started shifting & can refine,
844        * then try lower shift
845        */
846       sctx.shift_hi        = sctx.shift_fraction;
847       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
848       sctx.shift_amount    = sctx.shift_fraction * sctx.shift_top;
849       sctx.lushift         = PETSC_TRUE;
850       sctx.nshift++;
851     }
852   } while (sctx.lushift);
853 
854   /* invert diagonal entries for simplier triangular solves */
855   for (i=0; i<n; i++) {
856     a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]];
857   }
858 
859   ierr = PetscFree(rtmp);CHKERRQ(ierr);
860   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
861   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
862   A->ops->solve             = MatSolve_SeqAIJ_InplaceWithPerm;
863   A->ops->solveadd          = MatSolveAdd_SeqAIJ;
864   A->ops->solvetranspose    = MatSolveTranspose_SeqAIJ;
865   A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ;
866   A->assembled = PETSC_TRUE;
867   A->preallocated = PETSC_TRUE;
868   ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr);
869   if (sctx.nshift){
870     if (info->shiftpd) {
871       ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %G, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,sctx.shift_amount,sctx.shift_fraction,sctx.shift_top);CHKERRQ(ierr);
872     } else if (info->shiftnz) {
873       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
874     }
875   }
876   PetscFunctionReturn(0);
877 }
878 
879 /* ----------------------------------------------------------- */
880 #undef __FUNCT__
881 #define __FUNCT__ "MatLUFactor_SeqAIJ"
882 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info)
883 {
884   PetscErrorCode ierr;
885   Mat            C;
886 
887   PetscFunctionBegin;
888   ierr = MatGetFactor(A,MAT_SOLVER_PETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr);
889   ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr);
890   ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr);
891   A->ops->solve            = C->ops->solve;
892   A->ops->solvetranspose   = C->ops->solvetranspose;
893   ierr = MatHeaderCopy(A,C);CHKERRQ(ierr);
894   ierr = PetscLogObjectParent(A,((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr);
895   PetscFunctionReturn(0);
896 }
897 /* ----------------------------------------------------------- */
898 
899 
900 #undef __FUNCT__
901 #define __FUNCT__ "MatSolve_SeqAIJ"
902 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx)
903 {
904   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
905   IS                iscol = a->col,isrow = a->row;
906   PetscErrorCode    ierr;
907   PetscInt          i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
908   PetscInt          nz;
909   const PetscInt    *rout,*cout,*r,*c;
910   PetscScalar       *x,*tmp,*tmps,sum;
911   const PetscScalar *b;
912   const MatScalar   *aa = a->a,*v;
913 
914   PetscFunctionBegin;
915   if (!n) PetscFunctionReturn(0);
916 
917   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
918   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
919   tmp  = a->solve_work;
920 
921   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
922   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
923 
924   /* forward solve the lower triangular */
925   tmp[0] = b[*r++];
926   tmps   = tmp;
927   for (i=1; i<n; i++) {
928     v   = aa + ai[i] ;
929     vi  = aj + ai[i] ;
930     nz  = a->diag[i] - ai[i];
931     sum = b[*r++];
932     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
933     tmp[i] = sum;
934   }
935 
936   /* backward solve the upper triangular */
937   for (i=n-1; i>=0; i--){
938     v   = aa + a->diag[i] + 1;
939     vi  = aj + a->diag[i] + 1;
940     nz  = ai[i+1] - a->diag[i] - 1;
941     sum = tmp[i];
942     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
943     x[*c--] = tmp[i] = sum*aa[a->diag[i]];
944   }
945 
946   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
947   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
948   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
949   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
950   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
951   PetscFunctionReturn(0);
952 }
953 
954 #undef __FUNCT__
955 #define __FUNCT__ "MatMatSolve_SeqAIJ"
956 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X)
957 {
958   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
959   IS              iscol = a->col,isrow = a->row;
960   PetscErrorCode  ierr;
961   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
962   PetscInt        nz,neq;
963   const PetscInt  *rout,*cout,*r,*c;
964   PetscScalar     *x,*b,*tmp,*tmps,sum;
965   const MatScalar *aa = a->a,*v;
966   PetscTruth      bisdense,xisdense;
967 
968   PetscFunctionBegin;
969   if (!n) PetscFunctionReturn(0);
970 
971   ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr);
972   if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix");
973   ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr);
974   if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix");
975 
976   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
977   ierr = MatGetArray(X,&x);CHKERRQ(ierr);
978 
979   tmp  = a->solve_work;
980   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
981   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
982 
983   for (neq=0; neq<B->cmap->n; neq++){
984     /* forward solve the lower triangular */
985     tmp[0] = b[r[0]];
986     tmps   = tmp;
987     for (i=1; i<n; i++) {
988       v   = aa + ai[i] ;
989       vi  = aj + ai[i] ;
990       nz  = a->diag[i] - ai[i];
991       sum = b[r[i]];
992       PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
993       tmp[i] = sum;
994     }
995     /* backward solve the upper triangular */
996     for (i=n-1; i>=0; i--){
997       v   = aa + a->diag[i] + 1;
998       vi  = aj + a->diag[i] + 1;
999       nz  = ai[i+1] - a->diag[i] - 1;
1000       sum = tmp[i];
1001       PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1002       x[c[i]] = tmp[i] = sum*aa[a->diag[i]];
1003     }
1004 
1005     b += n;
1006     x += n;
1007   }
1008   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1009   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1010   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
1011   ierr = MatRestoreArray(X,&x);CHKERRQ(ierr);
1012   ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr);
1013   PetscFunctionReturn(0);
1014 }
1015 
1016 #undef __FUNCT__
1017 #define __FUNCT__ "MatSolve_SeqAIJ_InplaceWithPerm"
1018 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx)
1019 {
1020   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1021   IS              iscol = a->col,isrow = a->row;
1022   PetscErrorCode  ierr;
1023   const PetscInt  *r,*c,*rout,*cout;
1024   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1025   PetscInt        nz,row;
1026   PetscScalar     *x,*b,*tmp,*tmps,sum;
1027   const MatScalar *aa = a->a,*v;
1028 
1029   PetscFunctionBegin;
1030   if (!n) PetscFunctionReturn(0);
1031 
1032   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
1033   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1034   tmp  = a->solve_work;
1035 
1036   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1037   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1038 
1039   /* forward solve the lower triangular */
1040   tmp[0] = b[*r++];
1041   tmps   = tmp;
1042   for (row=1; row<n; row++) {
1043     i   = rout[row]; /* permuted row */
1044     v   = aa + ai[i] ;
1045     vi  = aj + ai[i] ;
1046     nz  = a->diag[i] - ai[i];
1047     sum = b[*r++];
1048     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1049     tmp[row] = sum;
1050   }
1051 
1052   /* backward solve the upper triangular */
1053   for (row=n-1; row>=0; row--){
1054     i   = rout[row]; /* permuted row */
1055     v   = aa + a->diag[i] + 1;
1056     vi  = aj + a->diag[i] + 1;
1057     nz  = ai[i+1] - a->diag[i] - 1;
1058     sum = tmp[row];
1059     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1060     x[*c--] = tmp[row] = sum*aa[a->diag[i]];
1061   }
1062 
1063   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1064   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1065   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
1066   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1067   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1068   PetscFunctionReturn(0);
1069 }
1070 
1071 /* ----------------------------------------------------------- */
1072 #include "../src/mat/impls/aij/seq/ftn-kernels/fsolve.h"
1073 #undef __FUNCT__
1074 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering"
1075 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx)
1076 {
1077   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1078   PetscErrorCode    ierr;
1079   PetscInt          n = A->rmap->n;
1080   const PetscInt    *ai = a->i,*aj = a->j,*adiag = a->diag;
1081   PetscScalar       *x;
1082   const PetscScalar *b;
1083   const MatScalar   *aa = a->a;
1084 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ)
1085   PetscInt          adiag_i,i,nz,ai_i;
1086   const PetscInt    *vi;
1087   const MatScalar   *v;
1088   PetscScalar       sum;
1089 #endif
1090 
1091   PetscFunctionBegin;
1092   if (!n) PetscFunctionReturn(0);
1093 
1094   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1095   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1096 
1097 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ)
1098   fortransolveaij_(&n,x,ai,aj,adiag,aa,b);
1099 #else
1100   /* forward solve the lower triangular */
1101   x[0] = b[0];
1102   for (i=1; i<n; i++) {
1103     ai_i = ai[i];
1104     v    = aa + ai_i;
1105     vi   = aj + ai_i;
1106     nz   = adiag[i] - ai_i;
1107     sum  = b[i];
1108     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
1109     x[i] = sum;
1110   }
1111 
1112   /* backward solve the upper triangular */
1113   for (i=n-1; i>=0; i--){
1114     adiag_i = adiag[i];
1115     v       = aa + adiag_i + 1;
1116     vi      = aj + adiag_i + 1;
1117     nz      = ai[i+1] - adiag_i - 1;
1118     sum     = x[i];
1119     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
1120     x[i]    = sum*aa[adiag_i];
1121   }
1122 #endif
1123   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1124   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1125   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1126   PetscFunctionReturn(0);
1127 }
1128 
1129 #undef __FUNCT__
1130 #define __FUNCT__ "MatSolveAdd_SeqAIJ"
1131 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx)
1132 {
1133   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1134   IS              iscol = a->col,isrow = a->row;
1135   PetscErrorCode  ierr;
1136   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1137   PetscInt        nz;
1138   const PetscInt  *rout,*cout,*r,*c;
1139   PetscScalar     *x,*b,*tmp,sum;
1140   const MatScalar *aa = a->a,*v;
1141 
1142   PetscFunctionBegin;
1143   if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);}
1144 
1145   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
1146   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1147   tmp  = a->solve_work;
1148 
1149   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1150   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1151 
1152   /* forward solve the lower triangular */
1153   tmp[0] = b[*r++];
1154   for (i=1; i<n; i++) {
1155     v   = aa + ai[i] ;
1156     vi  = aj + ai[i] ;
1157     nz  = a->diag[i] - ai[i];
1158     sum = b[*r++];
1159     while (nz--) sum -= *v++ * tmp[*vi++ ];
1160     tmp[i] = sum;
1161   }
1162 
1163   /* backward solve the upper triangular */
1164   for (i=n-1; i>=0; i--){
1165     v   = aa + a->diag[i] + 1;
1166     vi  = aj + a->diag[i] + 1;
1167     nz  = ai[i+1] - a->diag[i] - 1;
1168     sum = tmp[i];
1169     while (nz--) sum -= *v++ * tmp[*vi++ ];
1170     tmp[i] = sum*aa[a->diag[i]];
1171     x[*c--] += tmp[i];
1172   }
1173 
1174   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1175   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1176   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
1177   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1178   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1179 
1180   PetscFunctionReturn(0);
1181 }
1182 /* -------------------------------------------------------------------*/
1183 #undef __FUNCT__
1184 #define __FUNCT__ "MatSolveTranspose_SeqAIJ"
1185 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx)
1186 {
1187   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1188   IS              iscol = a->col,isrow = a->row;
1189   PetscErrorCode  ierr;
1190   const PetscInt  *rout,*cout,*r,*c;
1191   PetscInt        i,n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1192   PetscInt        nz,*diag = a->diag;
1193   PetscScalar     *x,*b,*tmp,s1;
1194   const MatScalar *aa = a->a,*v;
1195 
1196   PetscFunctionBegin;
1197   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
1198   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1199   tmp  = a->solve_work;
1200 
1201   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1202   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1203 
1204   /* copy the b into temp work space according to permutation */
1205   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1206 
1207   /* forward solve the U^T */
1208   for (i=0; i<n; i++) {
1209     v   = aa + diag[i] ;
1210     vi  = aj + diag[i] + 1;
1211     nz  = ai[i+1] - diag[i] - 1;
1212     s1  = tmp[i];
1213     s1 *= (*v++);  /* multiply by inverse of diagonal entry */
1214     while (nz--) {
1215       tmp[*vi++ ] -= (*v++)*s1;
1216     }
1217     tmp[i] = s1;
1218   }
1219 
1220   /* backward solve the L^T */
1221   for (i=n-1; i>=0; i--){
1222     v   = aa + diag[i] - 1 ;
1223     vi  = aj + diag[i] - 1 ;
1224     nz  = diag[i] - ai[i];
1225     s1  = tmp[i];
1226     while (nz--) {
1227       tmp[*vi-- ] -= (*v--)*s1;
1228     }
1229   }
1230 
1231   /* copy tmp into x according to permutation */
1232   for (i=0; i<n; i++) x[r[i]] = tmp[i];
1233 
1234   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1235   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1236   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
1237   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1238 
1239   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1240   PetscFunctionReturn(0);
1241 }
1242 
1243 #undef __FUNCT__
1244 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ"
1245 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx)
1246 {
1247   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1248   IS              iscol = a->col,isrow = a->row;
1249   PetscErrorCode  ierr;
1250   const PetscInt  *r,*c,*rout,*cout;
1251   PetscInt        i,n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1252   PetscInt        nz,*diag = a->diag;
1253   PetscScalar     *x,*b,*tmp;
1254   const MatScalar *aa = a->a,*v;
1255 
1256   PetscFunctionBegin;
1257   if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);}
1258 
1259   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
1260   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1261   tmp = a->solve_work;
1262 
1263   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1264   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1265 
1266   /* copy the b into temp work space according to permutation */
1267   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1268 
1269   /* forward solve the U^T */
1270   for (i=0; i<n; i++) {
1271     v   = aa + diag[i] ;
1272     vi  = aj + diag[i] + 1;
1273     nz  = ai[i+1] - diag[i] - 1;
1274     tmp[i] *= *v++;
1275     while (nz--) {
1276       tmp[*vi++ ] -= (*v++)*tmp[i];
1277     }
1278   }
1279 
1280   /* backward solve the L^T */
1281   for (i=n-1; i>=0; i--){
1282     v   = aa + diag[i] - 1 ;
1283     vi  = aj + diag[i] - 1 ;
1284     nz  = diag[i] - ai[i];
1285     while (nz--) {
1286       tmp[*vi-- ] -= (*v--)*tmp[i];
1287     }
1288   }
1289 
1290   /* copy tmp into x according to permutation */
1291   for (i=0; i<n; i++) x[r[i]] += tmp[i];
1292 
1293   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1294   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1295   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
1296   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1297 
1298   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1299   PetscFunctionReturn(0);
1300 }
1301 /* ----------------------------------------------------------------*/
1302 EXTERN PetscErrorCode Mat_CheckInode(Mat,PetscTruth);
1303 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption,PetscTruth);
1304 
1305 /*
1306    ilu(0) with natural ordering under new data structure.
1307    Factored arrays bj and ba are stored as
1308      L(0,:), L(1,:), ...,L(n-1,:),  U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:)
1309 
1310    bi=fact->i is an array of size 2n+2, in which
1311    bi+
1312      bi[i]      ->  1st entry of L(i,:),i=0,...,i-1
1313      bi[n]      ->  points to L(n-1,:)+1
1314      bi[n+1]    ->  1st entry of U(n-1,:)
1315      bi[2n-i]   ->  1st entry of U(i,:)
1316      bi[2n-i+1] ->  end of U(i,:)+1, the 1st entry of U(i-1,:)
1317      bi[2n]     ->  1st entry of U(0,:)
1318      bi[2n+1]   ->  points to U(0,:)+1
1319 
1320    U(i,:) contains diag[i] as its last entry, i.e.,
1321     U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i])
1322 */
1323 #undef __FUNCT__
1324 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct"
1325 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1326 {
1327 
1328   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1329   PetscErrorCode     ierr;
1330   PetscInt           n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag;
1331   PetscInt           i,j,nz,*bi,*bj,*bdiag;
1332 
1333   PetscFunctionBegin;
1334   ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr);
1335   b    = (Mat_SeqAIJ*)(fact)->data;
1336 
1337   /* allocate matrix arrays for new data structure */
1338   ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,2*n+2,PetscInt,&b->i);CHKERRQ(ierr);
1339   ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(2*n+2)*sizeof(PetscInt));CHKERRQ(ierr);
1340   b->singlemalloc = PETSC_TRUE;
1341   if (!b->diag){
1342     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr);
1343   }
1344   bdiag = b->diag;
1345 
1346   if (n > 0) {
1347     ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr);
1348   }
1349 
1350   /* set bi and bj with new data structure */
1351   bi = b->i;
1352   bj = b->j;
1353 
1354   /* L part */
1355   bi[0] = 0;
1356   for (i=0; i<n; i++){
1357     nz = adiag[i] - ai[i];
1358     bi[i+1] = bi[i] + nz;
1359     aj = a->j + ai[i];
1360     for (j=0; j<nz; j++){
1361       *bj = aj[j]; bj++;
1362     }
1363   }
1364 
1365   /* U part */
1366   bi[n+1] = bi[n];
1367   for (i=n-1; i>=0; i--){
1368     nz = ai[i+1] - adiag[i] - 1;
1369     bi[2*n-i+1] = bi[2*n-i] + nz + 1;
1370     aj = a->j + adiag[i] + 1;
1371     for (j=0; j<nz; j++){
1372       *bj = aj[j]; bj++;
1373     }
1374     /* diag[i] */
1375     *bj = i; bj++;
1376     bdiag[i] = bi[2*n-i+1]-1;
1377   }
1378   PetscFunctionReturn(0);
1379 }
1380 
1381 #undef __FUNCT__
1382 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_newdatastruct"
1383 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1384 {
1385   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1386   IS                 isicol;
1387   PetscErrorCode     ierr;
1388   const PetscInt     *r,*ic;
1389   PetscInt           n=A->rmap->n,*ai=a->i,*aj=a->j,d;
1390   PetscInt           *bi,*cols,nnz,*cols_lvl;
1391   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1392   PetscInt           i,levels,diagonal_fill;
1393   PetscTruth         col_identity,row_identity;
1394   PetscReal          f;
1395   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
1396   PetscBT            lnkbt;
1397   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
1398   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1399   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1400   PetscTruth         missing;
1401 
1402   PetscFunctionBegin;
1403   //printf("MatILUFactorSymbolic_SeqAIJ_newdatastruct ...\n");
1404   if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n);
1405   f             = info->fill;
1406   levels        = (PetscInt)info->levels;
1407   diagonal_fill = (PetscInt)info->diagonal_fill;
1408   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1409 
1410   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1411   ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
1412 
1413   if (!levels && row_identity && col_identity) {
1414     /* special case: ilu(0) with natural ordering */
1415     ierr = MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1416     (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ_newdatastruct;
1417 
1418     fact->factor = MAT_FACTOR_ILU;
1419     (fact)->info.factor_mallocs    = 0;
1420     (fact)->info.fill_ratio_given  = info->fill;
1421     (fact)->info.fill_ratio_needed = 1.0;
1422     b               = (Mat_SeqAIJ*)(fact)->data;
1423     ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
1424     if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
1425     b->row              = isrow;
1426     b->col              = iscol;
1427     b->icol             = isicol;
1428     ierr                = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1429     ierr                = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1430     ierr                = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1431     /* ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */
1432     PetscFunctionReturn(0);
1433   }
1434 
1435   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1436   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1437 
1438   /* get new row pointers */
1439   ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1440   bi[0] = 0;
1441   /* bdiag is location of diagonal in factor */
1442   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
1443   bdiag[0]  = 0;
1444 
1445   ierr = PetscMalloc((2*n+1)*sizeof(PetscInt**),&bj_ptr);CHKERRQ(ierr);
1446   bjlvl_ptr = (PetscInt**)(bj_ptr + n);
1447 
1448   /* create a linked list for storing column indices of the active row */
1449   nlnk = n + 1;
1450   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1451 
1452   /* initial FreeSpace size is f*(ai[n]+1) */
1453   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
1454   current_space = free_space;
1455   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
1456   current_space_lvl = free_space_lvl;
1457 
1458   for (i=0; i<n; i++) {
1459     nzi = 0;
1460     /* copy current row into linked list */
1461     nnz  = ai[r[i]+1] - ai[r[i]];
1462     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1463     cols = aj + ai[r[i]];
1464     lnk[i] = -1; /* marker to indicate if diagonal exists */
1465     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1466     nzi += nlnk;
1467 
1468     /* make sure diagonal entry is included */
1469     if (diagonal_fill && lnk[i] == -1) {
1470       fm = n;
1471       while (lnk[fm] < i) fm = lnk[fm];
1472       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
1473       lnk[fm]    = i;
1474       lnk_lvl[i] = 0;
1475       nzi++; dcount++;
1476     }
1477 
1478     /* add pivot rows into the active row */
1479     nzbd = 0;
1480     prow = lnk[n];
1481     while (prow < i) {
1482       nnz      = bdiag[prow];
1483       cols     = bj_ptr[prow] + nnz + 1;
1484       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1485       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
1486       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
1487       nzi += nlnk;
1488       prow = lnk[prow];
1489       nzbd++;
1490     }
1491     bdiag[i] = nzbd;
1492     bi[i+1]  = bi[i] + nzi;
1493 
1494     /* if free space is not available, make more free space */
1495     if (current_space->local_remaining<nzi) {
1496       nnz = 2*nzi*(n - i); /* estimated and max additional space needed */
1497       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
1498       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
1499       reallocs++;
1500     }
1501 
1502     /* copy data into free_space and free_space_lvl, then initialize lnk */
1503     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1504     bj_ptr[i]    = current_space->array;
1505     bjlvl_ptr[i] = current_space_lvl->array;
1506 
1507     /* make sure the active row i has diagonal entry */
1508     if (*(bj_ptr[i]+bdiag[i]) != i) {
1509       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
1510     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
1511     }
1512 
1513     current_space->array           += nzi;
1514     current_space->local_used      += nzi;
1515     current_space->local_remaining -= nzi;
1516     current_space_lvl->array           += nzi;
1517     current_space_lvl->local_used      += nzi;
1518     current_space_lvl->local_remaining -= nzi;
1519   }
1520 
1521   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1522   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1523 
1524   /* destroy list of free space and other temporary arrays */
1525   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
1526 
1527   /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */
1528   ierr = PetscFreeSpaceContiguous_newdatastruct(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr);
1529 
1530   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1531   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
1532   ierr = PetscFree(bj_ptr);CHKERRQ(ierr);
1533 
1534 #if defined(PETSC_USE_INFO)
1535   {
1536     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1537     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
1538     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
1539     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
1540     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
1541     if (diagonal_fill) {
1542       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
1543     }
1544   }
1545 #endif
1546 
1547   /* put together the new matrix */
1548   ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
1549   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
1550   b = (Mat_SeqAIJ*)(fact)->data;
1551   b->free_a       = PETSC_TRUE;
1552   b->free_ij      = PETSC_TRUE;
1553   b->singlemalloc = PETSC_FALSE;
1554   ierr = PetscMalloc( (bi[2*n+1] )*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
1555   b->j          = bj;
1556   b->i          = bi;
1557   b->diag       = bdiag;
1558   b->ilen       = 0;
1559   b->imax       = 0;
1560   b->row        = isrow;
1561   b->col        = iscol;
1562   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1563   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1564   b->icol       = isicol;
1565   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1566   /* In b structure:  Free imax, ilen, old a, old j.
1567      Allocate bdiag, solve_work, new a, new j */
1568   ierr = PetscLogObjectMemory(fact,bi[2*n+1] * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
1569   b->maxnz = b->nz = bi[2*n+1] ;
1570   (fact)->info.factor_mallocs    = reallocs;
1571   (fact)->info.fill_ratio_given  = f;
1572   (fact)->info.fill_ratio_needed = ((PetscReal)bi[2*n+1])/((PetscReal)ai[n]);
1573   (fact)->ops->lufactornumeric   = MatLUFactorNumeric_SeqAIJ_newdatastruct;
1574   /* ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */
1575   PetscFunctionReturn(0);
1576 }
1577 
1578 #undef __FUNCT__
1579 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ"
1580 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1581 {
1582   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1583   IS                 isicol;
1584   PetscErrorCode     ierr;
1585   const PetscInt     *r,*ic;
1586   PetscInt           n=A->rmap->n,*ai=a->i,*aj=a->j,d;
1587   PetscInt           *bi,*cols,nnz,*cols_lvl;
1588   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1589   PetscInt           i,levels,diagonal_fill;
1590   PetscTruth         col_identity,row_identity;
1591   PetscReal          f;
1592   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
1593   PetscBT            lnkbt;
1594   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
1595   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1596   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1597   PetscTruth         missing;
1598   PetscTruth         newdatastruct=PETSC_FALSE;
1599 
1600   PetscFunctionBegin;
1601   ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
1602   if (newdatastruct){
1603     ierr = MatILUFactorSymbolic_SeqAIJ_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1604     PetscFunctionReturn(0);
1605   }
1606 
1607   if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n);
1608   f             = info->fill;
1609   levels        = (PetscInt)info->levels;
1610   diagonal_fill = (PetscInt)info->diagonal_fill;
1611   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1612 
1613   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1614   ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
1615   if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */
1616     ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr);
1617     (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ;
1618 
1619     fact->factor = MAT_FACTOR_ILU;
1620     (fact)->info.factor_mallocs    = 0;
1621     (fact)->info.fill_ratio_given  = info->fill;
1622     (fact)->info.fill_ratio_needed = 1.0;
1623     b               = (Mat_SeqAIJ*)(fact)->data;
1624     ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
1625     if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
1626     b->row              = isrow;
1627     b->col              = iscol;
1628     b->icol             = isicol;
1629     ierr                = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1630     ierr                = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1631     ierr                = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1632     ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1633     PetscFunctionReturn(0);
1634   }
1635 
1636   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1637   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1638 
1639   /* get new row pointers */
1640   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1641   bi[0] = 0;
1642   /* bdiag is location of diagonal in factor */
1643   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
1644   bdiag[0]  = 0;
1645 
1646   ierr = PetscMalloc((2*n+1)*sizeof(PetscInt**),&bj_ptr);CHKERRQ(ierr);
1647   bjlvl_ptr = (PetscInt**)(bj_ptr + n);
1648 
1649   /* create a linked list for storing column indices of the active row */
1650   nlnk = n + 1;
1651   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1652 
1653   /* initial FreeSpace size is f*(ai[n]+1) */
1654   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
1655   current_space = free_space;
1656   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
1657   current_space_lvl = free_space_lvl;
1658 
1659   for (i=0; i<n; i++) {
1660     nzi = 0;
1661     /* copy current row into linked list */
1662     nnz  = ai[r[i]+1] - ai[r[i]];
1663     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1664     cols = aj + ai[r[i]];
1665     lnk[i] = -1; /* marker to indicate if diagonal exists */
1666     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1667     nzi += nlnk;
1668 
1669     /* make sure diagonal entry is included */
1670     if (diagonal_fill && lnk[i] == -1) {
1671       fm = n;
1672       while (lnk[fm] < i) fm = lnk[fm];
1673       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
1674       lnk[fm]    = i;
1675       lnk_lvl[i] = 0;
1676       nzi++; dcount++;
1677     }
1678 
1679     /* add pivot rows into the active row */
1680     nzbd = 0;
1681     prow = lnk[n];
1682     while (prow < i) {
1683       nnz      = bdiag[prow];
1684       cols     = bj_ptr[prow] + nnz + 1;
1685       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1686       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
1687       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
1688       nzi += nlnk;
1689       prow = lnk[prow];
1690       nzbd++;
1691     }
1692     bdiag[i] = nzbd;
1693     bi[i+1]  = bi[i] + nzi;
1694 
1695     /* if free space is not available, make more free space */
1696     if (current_space->local_remaining<nzi) {
1697       nnz = nzi*(n - i); /* estimated and max additional space needed */
1698       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
1699       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
1700       reallocs++;
1701     }
1702 
1703     /* copy data into free_space and free_space_lvl, then initialize lnk */
1704     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1705     bj_ptr[i]    = current_space->array;
1706     bjlvl_ptr[i] = current_space_lvl->array;
1707 
1708     /* make sure the active row i has diagonal entry */
1709     if (*(bj_ptr[i]+bdiag[i]) != i) {
1710       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
1711     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
1712     }
1713 
1714     current_space->array           += nzi;
1715     current_space->local_used      += nzi;
1716     current_space->local_remaining -= nzi;
1717     current_space_lvl->array           += nzi;
1718     current_space_lvl->local_used      += nzi;
1719     current_space_lvl->local_remaining -= nzi;
1720   }
1721 
1722   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1723   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1724 
1725   /* destroy list of free space and other temporary arrays */
1726   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
1727   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */
1728   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1729   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
1730   ierr = PetscFree(bj_ptr);CHKERRQ(ierr);
1731 
1732 #if defined(PETSC_USE_INFO)
1733   {
1734     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1735     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
1736     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
1737     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
1738     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
1739     if (diagonal_fill) {
1740       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
1741     }
1742   }
1743 #endif
1744 
1745   /* put together the new matrix */
1746   ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
1747   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
1748   b = (Mat_SeqAIJ*)(fact)->data;
1749   b->free_a       = PETSC_TRUE;
1750   b->free_ij      = PETSC_TRUE;
1751   b->singlemalloc = PETSC_FALSE;
1752   ierr = PetscMalloc( (bi[n] )*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
1753   b->j          = bj;
1754   b->i          = bi;
1755   for (i=0; i<n; i++) bdiag[i] += bi[i];
1756   b->diag       = bdiag;
1757   b->ilen       = 0;
1758   b->imax       = 0;
1759   b->row        = isrow;
1760   b->col        = iscol;
1761   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1762   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1763   b->icol       = isicol;
1764   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1765   /* In b structure:  Free imax, ilen, old a, old j.
1766      Allocate bdiag, solve_work, new a, new j */
1767   ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
1768   b->maxnz             = b->nz = bi[n] ;
1769   (fact)->info.factor_mallocs    = reallocs;
1770   (fact)->info.fill_ratio_given  = f;
1771   (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1772   (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ;
1773   ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1774   PetscFunctionReturn(0);
1775 }
1776 
1777 #include "../src/mat/impls/sbaij/seq/sbaij.h"
1778 #undef __FUNCT__
1779 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ"
1780 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info)
1781 {
1782   Mat            C = B;
1783   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1784   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
1785   IS             ip=b->row,iip = b->icol;
1786   PetscErrorCode ierr;
1787   const PetscInt *rip,*riip;
1788   PetscInt       i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol;
1789   PetscInt       *ai=a->i,*aj=a->j;
1790   PetscInt       k,jmin,jmax,*jl,*il,col,nexti,ili,nz;
1791   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
1792   PetscReal      zeropivot,rs,shiftnz;
1793   PetscReal      shiftpd;
1794   ChShift_Ctx    sctx;
1795   PetscInt       newshift;
1796   PetscTruth     perm_identity;
1797 
1798   PetscFunctionBegin;
1799 
1800   shiftnz   = info->shiftnz;
1801   shiftpd   = info->shiftpd;
1802   zeropivot = info->zeropivot;
1803 
1804   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
1805   ierr  = ISGetIndices(iip,&riip);CHKERRQ(ierr);
1806 
1807   /* initialization */
1808   nz   = (2*mbs+1)*sizeof(PetscInt)+mbs*sizeof(MatScalar);
1809   ierr = PetscMalloc(nz,&il);CHKERRQ(ierr);
1810   jl   = il + mbs;
1811   rtmp = (MatScalar*)(jl + mbs);
1812 
1813   sctx.shift_amount = 0;
1814   sctx.nshift       = 0;
1815   do {
1816     sctx.chshift = PETSC_FALSE;
1817     for (i=0; i<mbs; i++) {
1818       rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0;
1819     }
1820 
1821     for (k = 0; k<mbs; k++){
1822       bval = ba + bi[k];
1823       /* initialize k-th row by the perm[k]-th row of A */
1824       jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
1825       for (j = jmin; j < jmax; j++){
1826         col = riip[aj[j]];
1827         if (col >= k){ /* only take upper triangular entry */
1828           rtmp[col] = aa[j];
1829           *bval++  = 0.0; /* for in-place factorization */
1830         }
1831       }
1832       /* shift the diagonal of the matrix */
1833       if (sctx.nshift) rtmp[k] += sctx.shift_amount;
1834 
1835       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
1836       dk = rtmp[k];
1837       i = jl[k]; /* first row to be added to k_th row  */
1838 
1839       while (i < k){
1840         nexti = jl[i]; /* next row to be added to k_th row */
1841 
1842         /* compute multiplier, update diag(k) and U(i,k) */
1843         ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
1844         uikdi = - ba[ili]*ba[bi[i]];  /* diagonal(k) */
1845         dk += uikdi*ba[ili];
1846         ba[ili] = uikdi; /* -U(i,k) */
1847 
1848         /* add multiple of row i to k-th row */
1849         jmin = ili + 1; jmax = bi[i+1];
1850         if (jmin < jmax){
1851           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
1852           /* update il and jl for row i */
1853           il[i] = jmin;
1854           j = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
1855         }
1856         i = nexti;
1857       }
1858 
1859       /* shift the diagonals when zero pivot is detected */
1860       /* compute rs=sum of abs(off-diagonal) */
1861       rs   = 0.0;
1862       jmin = bi[k]+1;
1863       nz   = bi[k+1] - jmin;
1864       bcol = bj + jmin;
1865       while (nz--){
1866         rs += PetscAbsScalar(rtmp[*bcol]);
1867         bcol++;
1868       }
1869 
1870       sctx.rs = rs;
1871       sctx.pv = dk;
1872       ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr);
1873 
1874       if (newshift == 1) {
1875         if (!sctx.shift_amount) {
1876           sctx.shift_amount = 1e-5;
1877         }
1878         break;
1879       }
1880 
1881       /* copy data into U(k,:) */
1882       ba[bi[k]] = 1.0/dk; /* U(k,k) */
1883       jmin = bi[k]+1; jmax = bi[k+1];
1884       if (jmin < jmax) {
1885         for (j=jmin; j<jmax; j++){
1886           col = bj[j]; ba[j] = rtmp[col]; rtmp[col] = 0.0;
1887         }
1888         /* add the k-th row into il and jl */
1889         il[k] = jmin;
1890         i = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
1891       }
1892     }
1893   } while (sctx.chshift);
1894   ierr = PetscFree(il);CHKERRQ(ierr);
1895 
1896   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
1897   ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr);
1898 
1899   ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
1900   if (perm_identity){
1901     (B)->ops->solve           = MatSolve_SeqSBAIJ_1_NaturalOrdering;
1902     (B)->ops->solvetranspose  = MatSolve_SeqSBAIJ_1_NaturalOrdering;
1903     (B)->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering;
1904     (B)->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering;
1905   } else {
1906     (B)->ops->solve           = MatSolve_SeqSBAIJ_1;
1907     (B)->ops->solvetranspose  = MatSolve_SeqSBAIJ_1;
1908     (B)->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1;
1909     (B)->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1;
1910   }
1911 
1912   C->assembled    = PETSC_TRUE;
1913   C->preallocated = PETSC_TRUE;
1914   ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr);
1915   if (sctx.nshift){
1916     if (shiftnz) {
1917       ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
1918     } else if (shiftpd) {
1919       ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
1920     }
1921   }
1922   PetscFunctionReturn(0);
1923 }
1924 
1925 #undef __FUNCT__
1926 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ"
1927 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
1928 {
1929   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
1930   Mat_SeqSBAIJ       *b;
1931   PetscErrorCode     ierr;
1932   PetscTruth         perm_identity,missing;
1933   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui;
1934   const PetscInt     *rip,*riip;
1935   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
1936   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL,d;
1937   PetscInt           ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
1938   PetscReal          fill=info->fill,levels=info->levels;
1939   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1940   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1941   PetscBT            lnkbt;
1942   IS                 iperm;
1943 
1944   PetscFunctionBegin;
1945   if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n);
1946   ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
1947   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
1948   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
1949   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
1950 
1951   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
1952   ui[0] = 0;
1953 
1954   /* ICC(0) without matrix ordering: simply copies fill pattern */
1955   if (!levels && perm_identity) {
1956 
1957     for (i=0; i<am; i++) {
1958       ui[i+1] = ui[i] + ai[i+1] - a->diag[i];
1959     }
1960     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
1961     cols = uj;
1962     for (i=0; i<am; i++) {
1963       aj    = a->j + a->diag[i];
1964       ncols = ui[i+1] - ui[i];
1965       for (j=0; j<ncols; j++) *cols++ = *aj++;
1966     }
1967   } else { /* case: levels>0 || (levels=0 && !perm_identity) */
1968     ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
1969     ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
1970 
1971     /* initialization */
1972     ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr);
1973 
1974     /* jl: linked list for storing indices of the pivot rows
1975        il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
1976     ierr = PetscMalloc((2*am+1)*sizeof(PetscInt)+2*am*sizeof(PetscInt**),&jl);CHKERRQ(ierr);
1977     il         = jl + am;
1978     uj_ptr     = (PetscInt**)(il + am);
1979     uj_lvl_ptr = (PetscInt**)(uj_ptr + am);
1980     for (i=0; i<am; i++){
1981       jl[i] = am; il[i] = 0;
1982     }
1983 
1984     /* create and initialize a linked list for storing column indices of the active row k */
1985     nlnk = am + 1;
1986     ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1987 
1988     /* initial FreeSpace size is fill*(ai[am]+1) */
1989     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
1990     current_space = free_space;
1991     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr);
1992     current_space_lvl = free_space_lvl;
1993 
1994     for (k=0; k<am; k++){  /* for each active row k */
1995       /* initialize lnk by the column indices of row rip[k] of A */
1996       nzk   = 0;
1997       ncols = ai[rip[k]+1] - ai[rip[k]];
1998       if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
1999       ncols_upper = 0;
2000       for (j=0; j<ncols; j++){
2001         i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2002         if (riip[i] >= k){ /* only take upper triangular entry */
2003           ajtmp[ncols_upper] = i;
2004           ncols_upper++;
2005         }
2006       }
2007       ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2008       nzk += nlnk;
2009 
2010       /* update lnk by computing fill-in for each pivot row to be merged in */
2011       prow = jl[k]; /* 1st pivot row */
2012 
2013       while (prow < k){
2014         nextprow = jl[prow];
2015 
2016         /* merge prow into k-th row */
2017         jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2018         jmax = ui[prow+1];
2019         ncols = jmax-jmin;
2020         i     = jmin - ui[prow];
2021         cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2022         uj    = uj_lvl_ptr[prow] + i; /* levels of cols */
2023         j     = *(uj - 1);
2024         ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr);
2025         nzk += nlnk;
2026 
2027         /* update il and jl for prow */
2028         if (jmin < jmax){
2029           il[prow] = jmin;
2030           j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2031         }
2032         prow = nextprow;
2033       }
2034 
2035       /* if free space is not available, make more free space */
2036       if (current_space->local_remaining<nzk) {
2037         i = am - k + 1; /* num of unfactored rows */
2038         i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2039         ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2040         ierr = PetscFreeSpaceGet(i,&current_space_lvl);CHKERRQ(ierr);
2041         reallocs++;
2042       }
2043 
2044       /* copy data into free_space and free_space_lvl, then initialize lnk */
2045       if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2046       ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
2047 
2048       /* add the k-th row into il and jl */
2049       if (nzk > 1){
2050         i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2051         jl[k] = jl[i]; jl[i] = k;
2052         il[k] = ui[k] + 1;
2053       }
2054       uj_ptr[k]     = current_space->array;
2055       uj_lvl_ptr[k] = current_space_lvl->array;
2056 
2057       current_space->array           += nzk;
2058       current_space->local_used      += nzk;
2059       current_space->local_remaining -= nzk;
2060 
2061       current_space_lvl->array           += nzk;
2062       current_space_lvl->local_used      += nzk;
2063       current_space_lvl->local_remaining -= nzk;
2064 
2065       ui[k+1] = ui[k] + nzk;
2066     }
2067 
2068 #if defined(PETSC_USE_INFO)
2069     if (ai[am] != 0) {
2070       PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]);
2071       ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2072       ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2073       ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2074     } else {
2075       ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2076     }
2077 #endif
2078 
2079     ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2080     ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2081     ierr = PetscFree(jl);CHKERRQ(ierr);
2082     ierr = PetscFree(ajtmp);CHKERRQ(ierr);
2083 
2084     /* destroy list of free space and other temporary array(s) */
2085     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2086     ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
2087     ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2088     ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2089 
2090   } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2091 
2092   /* put together the new matrix in MATSEQSBAIJ format */
2093 
2094   b    = (Mat_SeqSBAIJ*)(fact)->data;
2095   b->singlemalloc = PETSC_FALSE;
2096   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2097   b->j    = uj;
2098   b->i    = ui;
2099   b->diag = 0;
2100   b->ilen = 0;
2101   b->imax = 0;
2102   b->row  = perm;
2103   b->col  = perm;
2104   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2105   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2106   b->icol = iperm;
2107   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2108   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2109   ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2110   b->maxnz   = b->nz = ui[am];
2111   b->free_a  = PETSC_TRUE;
2112   b->free_ij = PETSC_TRUE;
2113 
2114   (fact)->info.factor_mallocs    = reallocs;
2115   (fact)->info.fill_ratio_given  = fill;
2116   if (ai[am] != 0) {
2117     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2118   } else {
2119     (fact)->info.fill_ratio_needed = 0.0;
2120   }
2121   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2122   PetscFunctionReturn(0);
2123 }
2124 
2125 #undef __FUNCT__
2126 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ"
2127 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2128 {
2129   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2130   Mat_SeqSBAIJ       *b;
2131   PetscErrorCode     ierr;
2132   PetscTruth         perm_identity;
2133   PetscReal          fill = info->fill;
2134   const PetscInt     *rip,*riip;
2135   PetscInt           i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow;
2136   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
2137   PetscInt           nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr;
2138   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2139   PetscBT            lnkbt;
2140   IS                 iperm;
2141 
2142   PetscFunctionBegin;
2143   if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n);
2144   /* check whether perm is the identity mapping */
2145   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2146   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2147   ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2148   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2149 
2150   /* initialization */
2151   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2152   ui[0] = 0;
2153 
2154   /* jl: linked list for storing indices of the pivot rows
2155      il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2156   ierr = PetscMalloc((3*am+1)*sizeof(PetscInt)+am*sizeof(PetscInt**),&jl);CHKERRQ(ierr);
2157   il     = jl + am;
2158   cols   = il + am;
2159   ui_ptr = (PetscInt**)(cols + am);
2160   for (i=0; i<am; i++){
2161     jl[i] = am; il[i] = 0;
2162   }
2163 
2164   /* create and initialize a linked list for storing column indices of the active row k */
2165   nlnk = am + 1;
2166   ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2167 
2168   /* initial FreeSpace size is fill*(ai[am]+1) */
2169   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2170   current_space = free_space;
2171 
2172   for (k=0; k<am; k++){  /* for each active row k */
2173     /* initialize lnk by the column indices of row rip[k] of A */
2174     nzk   = 0;
2175     ncols = ai[rip[k]+1] - ai[rip[k]];
2176     if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2177     ncols_upper = 0;
2178     for (j=0; j<ncols; j++){
2179       i = riip[*(aj + ai[rip[k]] + j)];
2180       if (i >= k){ /* only take upper triangular entry */
2181         cols[ncols_upper] = i;
2182         ncols_upper++;
2183       }
2184     }
2185     ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2186     nzk += nlnk;
2187 
2188     /* update lnk by computing fill-in for each pivot row to be merged in */
2189     prow = jl[k]; /* 1st pivot row */
2190 
2191     while (prow < k){
2192       nextprow = jl[prow];
2193       /* merge prow into k-th row */
2194       jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2195       jmax = ui[prow+1];
2196       ncols = jmax-jmin;
2197       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2198       ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2199       nzk += nlnk;
2200 
2201       /* update il and jl for prow */
2202       if (jmin < jmax){
2203         il[prow] = jmin;
2204         j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
2205       }
2206       prow = nextprow;
2207     }
2208 
2209     /* if free space is not available, make more free space */
2210     if (current_space->local_remaining<nzk) {
2211       i = am - k + 1; /* num of unfactored rows */
2212       i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2213       ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2214       reallocs++;
2215     }
2216 
2217     /* copy data into free space, then initialize lnk */
2218     ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
2219 
2220     /* add the k-th row into il and jl */
2221     if (nzk-1 > 0){
2222       i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2223       jl[k] = jl[i]; jl[i] = k;
2224       il[k] = ui[k] + 1;
2225     }
2226     ui_ptr[k] = current_space->array;
2227     current_space->array           += nzk;
2228     current_space->local_used      += nzk;
2229     current_space->local_remaining -= nzk;
2230 
2231     ui[k+1] = ui[k] + nzk;
2232   }
2233 
2234 #if defined(PETSC_USE_INFO)
2235   if (ai[am] != 0) {
2236     PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]);
2237     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2238     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2239     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2240   } else {
2241      ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2242   }
2243 #endif
2244 
2245   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2246   ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2247   ierr = PetscFree(jl);CHKERRQ(ierr);
2248 
2249   /* destroy list of free space and other temporary array(s) */
2250   ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2251   ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
2252   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2253 
2254   /* put together the new matrix in MATSEQSBAIJ format */
2255 
2256   b = (Mat_SeqSBAIJ*)(fact)->data;
2257   b->singlemalloc = PETSC_FALSE;
2258   b->free_a       = PETSC_TRUE;
2259   b->free_ij      = PETSC_TRUE;
2260   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2261   b->j    = uj;
2262   b->i    = ui;
2263   b->diag = 0;
2264   b->ilen = 0;
2265   b->imax = 0;
2266   b->row  = perm;
2267   b->col  = perm;
2268   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2269   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2270   b->icol = iperm;
2271   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2272   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2273   ierr    = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2274   b->maxnz = b->nz = ui[am];
2275 
2276   (fact)->info.factor_mallocs    = reallocs;
2277   (fact)->info.fill_ratio_given  = fill;
2278   if (ai[am] != 0) {
2279     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2280   } else {
2281     (fact)->info.fill_ratio_needed = 0.0;
2282   }
2283   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2284   PetscFunctionReturn(0);
2285 }
2286 
2287 #undef __FUNCT__
2288 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_iludt"
2289 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_iludt(Mat A,Vec bb,Vec xx)
2290 {
2291   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
2292   PetscErrorCode    ierr;
2293   PetscInt          n = A->rmap->n;
2294   const PetscInt    *ai = a->i,*aj = a->j,*vi;
2295   PetscScalar       *x,sum;
2296   const PetscScalar *b;
2297   const MatScalar   *aa = a->a,*v;
2298   PetscInt          i,nz;
2299 
2300   PetscFunctionBegin;
2301   if (!n) PetscFunctionReturn(0);
2302 
2303   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2304   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2305 
2306   /* forward solve the lower triangular */
2307   x[0] = b[0];
2308   v    = aa;
2309   vi   = aj;
2310   for (i=1; i<n; i++) {
2311     nz  = ai[i+1] - ai[i];
2312     sum = b[i];
2313     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
2314     /*    while (nz--) sum -= *v++ * x[*vi++];*/
2315     v  += nz;
2316     vi += nz;
2317     x[i] = sum;
2318   }
2319 
2320   /* backward solve the upper triangular */
2321   v   = aa + ai[n+1];
2322   vi  = aj + ai[n+1];
2323   for (i=n-1; i>=0; i--){
2324     nz = ai[2*n-i +1] - ai[2*n-i]-1;
2325     sum = x[i];
2326     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
2327     /* while (nz--) sum -= *v++ * x[*vi++]; */
2328     v   += nz;
2329     vi  += nz; vi++;
2330     x[i] = *v++ *sum; /* x[i]=aa[adiag[i]]*sum; v++; */
2331   }
2332 
2333   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
2334   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2335   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2336   PetscFunctionReturn(0);
2337 }
2338 
2339 #undef __FUNCT__
2340 #define __FUNCT__ "MatSolve_SeqAIJ_iludt"
2341 PetscErrorCode MatSolve_SeqAIJ_iludt(Mat A,Vec bb,Vec xx)
2342 {
2343   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
2344   IS                iscol = a->col,isrow = a->row;
2345   PetscErrorCode    ierr;
2346   PetscInt          i,n=A->rmap->n,*vi,*ai = a->i,*aj = a->j,*adiag=a->diag;
2347   PetscInt          nz;
2348   const PetscInt    *rout,*cout,*r,*c;
2349   PetscScalar       *x,*tmp,*tmps;
2350   const PetscScalar *b;
2351   const MatScalar   *aa = a->a,*v;
2352 
2353   PetscFunctionBegin;
2354   if (!n) PetscFunctionReturn(0);
2355 
2356   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2357   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2358   tmp  = a->solve_work;
2359 
2360   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
2361   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
2362 
2363   /* forward solve the lower triangular */
2364   tmp[0] = b[*r++];
2365   tmps   = tmp;
2366   v      = aa;
2367   vi     = aj;
2368   for (i=1; i<n; i++) {
2369     nz  = ai[i+1] - ai[i];
2370     tmp[i] = b[*r++];
2371     PetscSparseDenseMinusDot(tmp[i],tmps,v,vi,nz);
2372     v += nz; vi += nz;
2373   }
2374 
2375   /* backward solve the upper triangular */
2376   v   = aa + adiag[n] + 1;
2377   vi  = aj + adiag[n] + 1;
2378   for (i=n-1; i>=0; i--){
2379     nz  = adiag[i] - adiag[i+1] - 1;
2380     PetscSparseDenseMinusDot(tmp[i],tmps,v,vi,nz);
2381     x[*c--] = tmp[i] = tmp[i]*aa[adiag[i]];
2382     v += nz+1; vi += nz+1;
2383   }
2384 
2385   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
2386   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
2387   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2388   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2389   ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr);
2390   PetscFunctionReturn(0);
2391 }
2392 
2393 #undef __FUNCT__
2394 #define __FUNCT__ "MatILUDTFactor_SeqAIJ"
2395 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact)
2396 {
2397   Mat                B = *fact;
2398   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b;
2399   IS                 isicol;
2400   PetscErrorCode     ierr;
2401   const PetscInt     *r,*ic;
2402   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag;
2403   PetscInt           *bi,*bj,*bdiag,*bdiag_rev;
2404   PetscInt           row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au;
2405   PetscInt           nlnk,*lnk;
2406   PetscBT            lnkbt;
2407   PetscTruth         row_identity,icol_identity,both_identity;
2408   MatScalar          *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp;
2409   const PetscInt     *ics;
2410   PetscInt           j,nz,*pj,*bjtmp,k,ncut,*jtmp;
2411   PetscReal          dt=info->dt,dtcol=info->dtcol,shift=info->shiftinblocks;
2412   PetscInt           dtcount=(PetscInt)info->dtcount,nnz_max;
2413   PetscTruth         missing;
2414 
2415   PetscFunctionBegin;
2416 
2417   if (dt      == PETSC_DEFAULT) dt      = 0.005;
2418   if (dtcol   == PETSC_DEFAULT) dtcol   = 0.01; /* XXX unused! */
2419   if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax);
2420 
2421   /* ------- symbolic factorization, can be reused ---------*/
2422   ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
2423   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
2424   adiag=a->diag;
2425 
2426   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
2427 
2428   /* bdiag is location of diagonal in factor */
2429   ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
2430   bdiag_rev = bdiag + n+1;
2431 
2432   /* allocate row pointers bi */
2433   ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
2434 
2435   /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */
2436   if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */
2437   nnz_max  = ai[n]+2*n*dtcount+2;
2438 
2439   ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
2440   ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr);
2441 
2442   /* put together the new matrix */
2443   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
2444   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
2445   b    = (Mat_SeqAIJ*)(B)->data;
2446   b->free_a       = PETSC_TRUE;
2447   b->free_ij      = PETSC_TRUE;
2448   b->singlemalloc = PETSC_FALSE;
2449   b->a          = ba;
2450   b->j          = bj;
2451   b->i          = bi;
2452   b->diag       = bdiag;
2453   b->ilen       = 0;
2454   b->imax       = 0;
2455   b->row        = isrow;
2456   b->col        = iscol;
2457   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
2458   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
2459   b->icol       = isicol;
2460   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2461 
2462   ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2463   b->maxnz = nnz_max;
2464 
2465   (B)->factor                = MAT_FACTOR_ILUDT;
2466   (B)->info.factor_mallocs   = 0;
2467   (B)->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]);
2468   CHKMEMQ;
2469   /* ------- end of symbolic factorization ---------*/
2470 
2471   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
2472   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
2473   ics  = ic;
2474 
2475   /* linked list for storing column indices of the active row */
2476   nlnk = n + 1;
2477   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2478 
2479   /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */
2480   ierr = PetscMalloc((2*n+1)*sizeof(PetscInt),&im);CHKERRQ(ierr);
2481   jtmp = im + n;
2482   /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */
2483   ierr = PetscMalloc((2*n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
2484   ierr = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr);
2485   vtmp = rtmp + n;
2486 
2487   bi[0]    = 0;
2488   bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */
2489   bdiag_rev[n] = bdiag[0];
2490   bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */
2491   for (i=0; i<n; i++) {
2492     /* copy initial fill into linked list */
2493     nzi = 0; /* nonzeros for active row i */
2494     nzi = ai[r[i]+1] - ai[r[i]];
2495     if (!nzi) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
2496     nzi_al = adiag[r[i]] - ai[r[i]];
2497     nzi_au = ai[r[i]+1] - adiag[r[i]] -1;
2498     ajtmp = aj + ai[r[i]];
2499     ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2500 
2501     /* load in initial (unfactored row) */
2502     aatmp = a->a + ai[r[i]];
2503     for (j=0; j<nzi; j++) {
2504       rtmp[ics[*ajtmp++]] = *aatmp++;
2505     }
2506 
2507     /* add pivot rows into linked list */
2508     row = lnk[n];
2509     while (row < i ) {
2510       nzi_bl = bi[row+1] - bi[row] + 1;
2511       bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */
2512       ierr  = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr);
2513       nzi  += nlnk;
2514       row   = lnk[row];
2515     }
2516 
2517     /* copy data from lnk into jtmp, then initialize lnk */
2518     ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr);
2519 
2520     /* numerical factorization */
2521     bjtmp = jtmp;
2522     row   = *bjtmp++; /* 1st pivot row */
2523     while  ( row < i ) {
2524       pc         = rtmp + row;
2525       pv         = ba + bdiag[row]; /* 1./(diag of the pivot row) */
2526       multiplier = (*pc) * (*pv);
2527       *pc        = multiplier;
2528       if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */
2529         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
2530         pv         = ba + bdiag[row+1] + 1;
2531         /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */
2532         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
2533         for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
2534         ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
2535       }
2536       row = *bjtmp++;
2537     }
2538 
2539     /* copy sparse rtmp into contiguous vtmp; separate L and U part */
2540     diag_tmp = rtmp[i];  /* save diagonal value - may not needed?? */
2541     nzi_bl = 0; j = 0;
2542     while (jtmp[j] < i){ /* Note: jtmp is sorted */
2543       vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
2544       nzi_bl++; j++;
2545     }
2546     nzi_bu = nzi - nzi_bl -1;
2547     while (j < nzi){
2548       vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
2549       j++;
2550     }
2551 
2552     bjtmp = bj + bi[i];
2553     batmp = ba + bi[i];
2554     /* apply level dropping rule to L part */
2555     ncut = nzi_al + dtcount;
2556     if (ncut < nzi_bl){
2557       ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr);
2558       ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr);
2559     } else {
2560       ncut = nzi_bl;
2561     }
2562     for (j=0; j<ncut; j++){
2563       bjtmp[j] = jtmp[j];
2564       batmp[j] = vtmp[j];
2565       /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */
2566     }
2567     bi[i+1] = bi[i] + ncut;
2568     nzi = ncut + 1;
2569 
2570     /* apply level dropping rule to U part */
2571     ncut = nzi_au + dtcount;
2572     if (ncut < nzi_bu){
2573       ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr);
2574       ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr);
2575     } else {
2576       ncut = nzi_bu;
2577     }
2578     nzi += ncut;
2579 
2580     /* mark bdiagonal */
2581     bdiag[i+1]       = bdiag[i] - (ncut + 1);
2582     bdiag_rev[n-i-1] = bdiag[i+1];
2583     bi[2*n - i]      = bi[2*n - i +1] - (ncut + 1);
2584     bjtmp = bj + bdiag[i];
2585     batmp = ba + bdiag[i];
2586     *bjtmp = i;
2587     *batmp = diag_tmp; /* rtmp[i]; */
2588     if (*batmp == 0.0) {
2589       *batmp = dt+shift;
2590       /* printf(" row %d add shift %g\n",i,shift); */
2591     }
2592     *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */
2593     /* printf(" (%d,%g),",*bjtmp,*batmp); */
2594 
2595     bjtmp = bj + bdiag[i+1]+1;
2596     batmp = ba + bdiag[i+1]+1;
2597     for (k=0; k<ncut; k++){
2598       bjtmp[k] = jtmp[nzi_bl+1+k];
2599       batmp[k] = vtmp[nzi_bl+1+k];
2600       /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */
2601     }
2602     /* printf("\n"); */
2603 
2604     im[i]   = nzi; /* used by PetscLLAddSortedLU() */
2605     /*
2606     printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]);
2607     printf(" ----------------------------\n");
2608     */
2609   } /* for (i=0; i<n; i++) */
2610   /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */
2611   if (bi[n] >= bdiag[n]) SETERRQ2(PETSC_ERR_ARG_SIZ,"end of L array %d cannot >= the beginning of U array %d",bi[n],bdiag[n]);
2612 
2613   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
2614   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
2615 
2616   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2617   ierr = PetscFree(im);CHKERRQ(ierr);
2618   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2619 
2620   ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr);
2621   b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n];
2622 
2623   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
2624   ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr);
2625   both_identity = (PetscTruth) (row_identity && icol_identity);
2626   if (row_identity && icol_identity) {
2627     B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_iludt;
2628   } else {
2629     B->ops->solve = MatSolve_SeqAIJ_iludt;
2630   }
2631 
2632   B->ops->lufactorsymbolic  = MatILUDTFactorSymbolic_SeqAIJ;
2633   B->ops->lufactornumeric   = MatILUDTFactorNumeric_SeqAIJ;
2634   B->ops->solveadd          = 0;
2635   B->ops->solvetranspose    = 0;
2636   B->ops->solvetransposeadd = 0;
2637   B->ops->matsolve          = 0;
2638   B->assembled              = PETSC_TRUE;
2639   B->preallocated           = PETSC_TRUE;
2640   PetscFunctionReturn(0);
2641 }
2642 
2643 /* a wraper of MatILUDTFactor_SeqAIJ() */
2644 #undef __FUNCT__
2645 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ"
2646 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info)
2647 {
2648   PetscErrorCode     ierr;
2649 
2650   PetscFunctionBegin;
2651   ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr);
2652 
2653   fact->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ;
2654   PetscFunctionReturn(0);
2655 }
2656 
2657 /*
2658    same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors
2659    - intend to replace existing MatLUFactorNumeric_SeqAIJ()
2660 */
2661 #undef __FUNCT__
2662 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ"
2663 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info)
2664 {
2665   Mat            C=fact;
2666   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
2667   IS             isrow = b->row,isicol = b->icol;
2668   PetscErrorCode ierr;
2669   const PetscInt *r,*ic,*ics;
2670   PetscInt       i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
2671   PetscInt       *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj;
2672   MatScalar      *rtmp,*pc,multiplier,*v,*pv,*aa=a->a;
2673   PetscReal      dt=info->dt,shift=info->shiftinblocks;
2674   PetscTruth     row_identity, col_identity;
2675 
2676   PetscFunctionBegin;
2677   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
2678   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
2679   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
2680   ics  = ic;
2681 
2682   for (i=0; i<n; i++){
2683     /* initialize rtmp array */
2684     nzl   = bi[i+1] - bi[i];       /* num of nozeros in L(i,:) */
2685     bjtmp = bj + bi[i];
2686     for  (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0;
2687     rtmp[i] = 0.0;
2688     nzu   = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */
2689     bjtmp = bj + bdiag[i+1] + 1;
2690     for  (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0;
2691 
2692     /* load in initial unfactored row of A */
2693     /* printf("row %d\n",i); */
2694     nz    = ai[r[i]+1] - ai[r[i]];
2695     ajtmp = aj + ai[r[i]];
2696     v     = aa + ai[r[i]];
2697     for (j=0; j<nz; j++) {
2698       rtmp[ics[*ajtmp++]] = v[j];
2699       /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */
2700     }
2701     /* printf("\n"); */
2702 
2703     /* numerical factorization */
2704     bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */
2705     nzl   = bi[i+1] - bi[i]; /* num of entries in L(i,:) */
2706     k = 0;
2707     while (k < nzl){
2708       row   = *bjtmp++;
2709       /* printf("  prow %d\n",row); */
2710       pc         = rtmp + row;
2711       pv         = b->a + bdiag[row]; /* 1./(diag of the pivot row) */
2712       multiplier = (*pc) * (*pv);
2713       *pc        = multiplier;
2714       if (PetscAbsScalar(multiplier) > dt){
2715         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
2716         pv         = b->a + bdiag[row+1] + 1;
2717         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
2718         for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
2719         /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */
2720       }
2721       k++;
2722     }
2723 
2724     /* finished row so stick it into b->a */
2725     /* L-part */
2726     pv = b->a + bi[i] ;
2727     pj = bj + bi[i] ;
2728     nzl = bi[i+1] - bi[i];
2729     for (j=0; j<nzl; j++) {
2730       pv[j] = rtmp[pj[j]];
2731       /* printf(" (%d,%g),",pj[j],pv[j]); */
2732     }
2733 
2734     /* diagonal: invert diagonal entries for simplier triangular solves */
2735     if (rtmp[i] == 0.0) rtmp[i] = dt+shift;
2736     b->a[bdiag[i]] = 1.0/rtmp[i];
2737     /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */
2738 
2739     /* U-part */
2740     pv = b->a + bdiag[i+1] + 1;
2741     pj = bj + bdiag[i+1] + 1;
2742     nzu = bdiag[i] - bdiag[i+1] - 1;
2743     for (j=0; j<nzu; j++) {
2744       pv[j] = rtmp[pj[j]];
2745       /* printf(" (%d,%g),",pj[j],pv[j]); */
2746     }
2747     /* printf("\n"); */
2748   }
2749 
2750   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2751   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
2752   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
2753 
2754   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
2755   ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
2756   if (row_identity && col_identity) {
2757     C->ops->solve   = MatSolve_SeqAIJ_NaturalOrdering_iludt;
2758   } else {
2759     C->ops->solve   = MatSolve_SeqAIJ_iludt;
2760   }
2761   C->ops->solveadd           = 0;
2762   C->ops->solvetranspose     = 0;
2763   C->ops->solvetransposeadd  = 0;
2764   C->ops->matsolve           = 0;
2765   C->assembled    = PETSC_TRUE;
2766   C->preallocated = PETSC_TRUE;
2767   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
2768   PetscFunctionReturn(0);
2769 }
2770