xref: /petsc/src/mat/impls/aij/seq/aijfact.c (revision b47f5a650138ab9e0a4c0a285dbeaacb3c401bd4)
1 #define PETSCMAT_DLL
2 
3 
4 #include "../src/mat/impls/aij/seq/aij.h"
5 #include "../src/mat/impls/sbaij/seq/sbaij.h"
6 #include "petscbt.h"
7 #include "../src/mat/utils/freespace.h"
8 
9 EXTERN_C_BEGIN
10 #undef __FUNCT__
11 #define __FUNCT__ "MatOrdering_Flow_SeqAIJ"
12 /*
13       Computes an ordering to get most of the large numerical values in the lower triangular part of the matrix
14 */
15 PetscErrorCode MatOrdering_Flow_SeqAIJ(Mat mat,const MatOrderingType type,IS *irow,IS *icol)
16 {
17   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)mat->data;
18   PetscErrorCode    ierr;
19   PetscInt          i,j,jj,k, kk,n = mat->rmap->n, current = 0, newcurrent = 0,*order;
20   const PetscInt    *ai = a->i, *aj = a->j;
21   const PetscScalar *aa = a->a;
22   PetscTruth        *done;
23   PetscReal         best,past = 0,future;
24 
25   PetscFunctionBegin;
26   /* pick initial row */
27   best = -1;
28   for (i=0; i<n; i++) {
29     future = 0.0;
30     for (j=ai[i]; j<ai[i+1]; j++) {
31       if (aj[j] != i) future  += PetscAbsScalar(aa[j]); else past = PetscAbsScalar(aa[j]);
32     }
33     if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */
34     if (past/future > best) {
35       best = past/future;
36       current = i;
37     }
38   }
39 
40   ierr = PetscMalloc(n*sizeof(PetscTruth),&done);CHKERRQ(ierr);
41   ierr = PetscMemzero(done,n*sizeof(PetscTruth));CHKERRQ(ierr);
42   ierr = PetscMalloc(n*sizeof(PetscInt),&order);CHKERRQ(ierr);
43   order[0] = current;
44   for (i=0; i<n-1; i++) {
45     done[current] = PETSC_TRUE;
46     best          = -1;
47     /* loop over all neighbors of current pivot */
48     for (j=ai[current]; j<ai[current+1]; j++) {
49       jj = aj[j];
50       if (done[jj]) continue;
51       /* loop over columns of potential next row computing weights for below and above diagonal */
52       past = future = 0.0;
53       for (k=ai[jj]; k<ai[jj+1]; k++) {
54         kk = aj[k];
55         if (done[kk]) past += PetscAbsScalar(aa[k]);
56         else if (kk != jj) future  += PetscAbsScalar(aa[k]);
57       }
58       if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */
59       if (past/future > best) {
60         best = past/future;
61         newcurrent = jj;
62       }
63     }
64     if (best == -1) { /* no neighbors to select from so select best of all that remain */
65       best = -1;
66       for (k=0; k<n; k++) {
67         if (done[k]) continue;
68         future = 0.0;
69         past   = 0.0;
70         for (j=ai[k]; j<ai[k+1]; j++) {
71           kk = aj[j];
72           if (done[kk]) past += PetscAbsScalar(aa[j]);
73           else if (kk != k) future  += PetscAbsScalar(aa[j]);
74         }
75         if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */
76         if (past/future > best) {
77           best = past/future;
78           newcurrent = k;
79         }
80       }
81     }
82     if (current == newcurrent) SETERRQ(PETSC_ERR_PLIB,"newcurrent cannot be current");
83     current = newcurrent;
84     order[i+1] = current;
85   }
86   ierr = ISCreateGeneral(PETSC_COMM_SELF,n,order,irow);CHKERRQ(ierr);
87   *icol = *irow;
88   ierr = PetscObjectReference((PetscObject)*irow);CHKERRQ(ierr);
89   ierr = PetscFree(done);CHKERRQ(ierr);
90   ierr = PetscFree(order);CHKERRQ(ierr);
91   PetscFunctionReturn(0);
92 }
93 EXTERN_C_END
94 
95 EXTERN_C_BEGIN
96 #undef __FUNCT__
97 #define __FUNCT__ "MatGetFactorAvailable_seqaij_petsc"
98 PetscErrorCode MatGetFactorAvailable_seqaij_petsc(Mat A,MatFactorType ftype,PetscTruth *flg)
99 {
100   PetscFunctionBegin;
101   *flg = PETSC_TRUE;
102   PetscFunctionReturn(0);
103 }
104 EXTERN_C_END
105 
106 EXTERN_C_BEGIN
107 #undef __FUNCT__
108 #define __FUNCT__ "MatGetFactor_seqaij_petsc"
109 PetscErrorCode MatGetFactor_seqaij_petsc(Mat A,MatFactorType ftype,Mat *B)
110 {
111   PetscInt           n = A->rmap->n;
112   PetscErrorCode     ierr;
113 
114   PetscFunctionBegin;
115   ierr = MatCreate(((PetscObject)A)->comm,B);CHKERRQ(ierr);
116   ierr = MatSetSizes(*B,n,n,n,n);CHKERRQ(ierr);
117   if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT){
118     ierr = MatSetType(*B,MATSEQAIJ);CHKERRQ(ierr);
119     (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqAIJ;
120     (*B)->ops->lufactorsymbolic  = MatLUFactorSymbolic_SeqAIJ;
121     (*B)->ops->iludtfactor       = MatILUDTFactor_SeqAIJ;
122   } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) {
123     ierr = MatSetType(*B,MATSEQSBAIJ);CHKERRQ(ierr);
124     ierr = MatSeqSBAIJSetPreallocation(*B,1,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
125     (*B)->ops->iccfactorsymbolic      = MatICCFactorSymbolic_SeqAIJ;
126     (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJ;
127   } else SETERRQ(PETSC_ERR_SUP,"Factor type not supported");
128   (*B)->factor = ftype;
129   PetscFunctionReturn(0);
130 }
131 EXTERN_C_END
132 
133 EXTERN PetscErrorCode Mat_CheckInode(Mat,PetscTruth);
134 #undef __FUNCT__
135 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ"
136 PetscErrorCode MatLUFactorSymbolic_SeqAIJ(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
137 {
138   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
139   IS                 isicol;
140   PetscErrorCode     ierr;
141   const PetscInt     *r,*ic;
142   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j;
143   PetscInt           *bi,*bj,*ajtmp;
144   PetscInt           *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im;
145   PetscReal          f;
146   PetscInt           nlnk,*lnk,k,**bi_ptr;
147   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
148   PetscBT            lnkbt;
149   PetscTruth         newdatastruct= PETSC_FALSE;
150 
151   PetscFunctionBegin;
152   ierr = PetscOptionsGetTruth(PETSC_NULL,"-lu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
153   if(newdatastruct){
154     ierr = MatLUFactorSymbolic_SeqAIJ_newdatastruct(B,A,isrow,iscol,info);CHKERRQ(ierr);
155     PetscFunctionReturn(0);
156   }
157 
158   if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square");
159   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
160   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
161   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
162 
163   /* get new row pointers */
164   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
165   bi[0] = 0;
166 
167   /* bdiag is location of diagonal in factor */
168   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
169   bdiag[0] = 0;
170 
171   /* linked list for storing column indices of the active row */
172   nlnk = n + 1;
173   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
174 
175   ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr);
176 
177   /* initial FreeSpace size is f*(ai[n]+1) */
178   f = info->fill;
179   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
180   current_space = free_space;
181 
182   for (i=0; i<n; i++) {
183     /* copy previous fill into linked list */
184     nzi = 0;
185     nnz = ai[r[i]+1] - ai[r[i]];
186     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
187     ajtmp = aj + ai[r[i]];
188     ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
189     nzi += nlnk;
190 
191     /* add pivot rows into linked list */
192     row = lnk[n];
193     while (row < i) {
194       nzbd    = bdiag[row] - bi[row] + 1; /* num of entries in the row with column index <= row */
195       ajtmp   = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */
196       ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr);
197       nzi += nlnk;
198       row  = lnk[row];
199     }
200     bi[i+1] = bi[i] + nzi;
201     im[i]   = nzi;
202 
203     /* mark bdiag */
204     nzbd = 0;
205     nnz  = nzi;
206     k    = lnk[n];
207     while (nnz-- && k < i){
208       nzbd++;
209       k = lnk[k];
210     }
211     bdiag[i] = bi[i] + nzbd;
212 
213     /* if free space is not available, make more free space */
214     if (current_space->local_remaining<nzi) {
215       nnz = (n - i)*nzi; /* estimated and max additional space needed */
216       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
217       reallocs++;
218     }
219 
220     /* copy data into free space, then initialize lnk */
221     ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
222     bi_ptr[i] = current_space->array;
223     current_space->array           += nzi;
224     current_space->local_used      += nzi;
225     current_space->local_remaining -= nzi;
226   }
227 #if defined(PETSC_USE_INFO)
228   if (ai[n] != 0) {
229     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
230     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
231     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
232     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr);
233     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
234   } else {
235     ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr);
236   }
237 #endif
238 
239   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
240   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
241 
242   /* destroy list of free space and other temporary array(s) */
243   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
244   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
245   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
246   ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr);
247 
248   /* put together the new matrix */
249   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
250   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
251   b    = (Mat_SeqAIJ*)(B)->data;
252   b->free_a       = PETSC_TRUE;
253   b->free_ij      = PETSC_TRUE;
254   b->singlemalloc = PETSC_FALSE;
255   ierr          = PetscMalloc((bi[n]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
256   b->j          = bj;
257   b->i          = bi;
258   b->diag       = bdiag;
259   b->ilen       = 0;
260   b->imax       = 0;
261   b->row        = isrow;
262   b->col        = iscol;
263   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
264   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
265   b->icol       = isicol;
266   ierr          = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
267 
268   /* In b structure:  Free imax, ilen, old a, old j.  Allocate solve_work, new a, new j */
269   ierr = PetscLogObjectMemory(B,(bi[n]-n)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
270   b->maxnz = b->nz = bi[n] ;
271 
272   (B)->factor                = MAT_FACTOR_LU;
273   (B)->info.factor_mallocs   = reallocs;
274   (B)->info.fill_ratio_given = f;
275 
276   if (ai[n]) {
277     (B)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
278   } else {
279     (B)->info.fill_ratio_needed = 0.0;
280   }
281   (B)->ops->lufactornumeric  = MatLUFactorNumeric_SeqAIJ;
282   (B)->ops->solve            = MatSolve_SeqAIJ;
283   (B)->ops->solvetranspose   = MatSolveTranspose_SeqAIJ;
284   /* switch to inodes if appropriate */
285   ierr = MatLUFactorSymbolic_SeqAIJ_Inode(B,A,isrow,iscol,info);CHKERRQ(ierr);
286   PetscFunctionReturn(0);
287 }
288 
289 #undef __FUNCT__
290 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ_newdatastruct"
291 PetscErrorCode MatLUFactorSymbolic_SeqAIJ_newdatastruct(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
292 {
293   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
294   IS                 isicol;
295   PetscErrorCode     ierr;
296   const PetscInt     *r,*ic;
297   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j;
298   PetscInt           *bi,*bj,*ajtmp;
299   PetscInt           *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im;
300   PetscReal          f;
301   PetscInt           nlnk,*lnk,k,**bi_ptr;
302   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
303   PetscBT            lnkbt;
304 
305   PetscFunctionBegin;
306   if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square");
307   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
308   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
309   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
310 
311   /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
312   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
313   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
314   bi[0] = bdiag[0] = 0;
315 
316   /* linked list for storing column indices of the active row */
317   nlnk = n + 1;
318   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
319 
320   ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr);
321 
322   /* initial FreeSpace size is f*(ai[n]+1) */
323   f = info->fill;
324   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
325   current_space = free_space;
326 
327   for (i=0; i<n; i++) {
328     /* copy previous fill into linked list */
329     nzi = 0;
330     nnz = ai[r[i]+1] - ai[r[i]];
331     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
332     ajtmp = aj + ai[r[i]];
333     ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
334     nzi += nlnk;
335 
336     /* add pivot rows into linked list */
337     row = lnk[n];
338     while (row < i){
339       nzbd  = bdiag[row] + 1; /* num of entries in the row with column index <= row */
340       ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */
341       ierr  = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr);
342       nzi  += nlnk;
343       row   = lnk[row];
344     }
345     bi[i+1] = bi[i] + nzi;
346     im[i]   = nzi;
347 
348     /* mark bdiag */
349     nzbd = 0;
350     nnz  = nzi;
351     k    = lnk[n];
352     while (nnz-- && k < i){
353       nzbd++;
354       k = lnk[k];
355     }
356     bdiag[i] = nzbd; /* note: bdiag[i] = nnzL as input for PetscFreeSpaceContiguous_LU() */
357 
358     /* if free space is not available, make more free space */
359     if (current_space->local_remaining<nzi) {
360       nnz = 2*(n - i)*nzi; /* estimated and max additional space needed */
361       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
362       reallocs++;
363     }
364 
365     /* copy data into free space, then initialize lnk */
366     ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
367     bi_ptr[i] = current_space->array;
368     current_space->array           += nzi;
369     current_space->local_used      += nzi;
370     current_space->local_remaining -= nzi;
371   }
372 #if defined(PETSC_USE_INFO)
373   if (ai[n] != 0) {
374     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
375     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
376     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
377     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr);
378     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
379   } else {
380     ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr);
381   }
382 #endif
383 
384   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
385   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
386 
387   /* destroy list of free space and other temporary array(s) */
388   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
389   ierr = PetscFreeSpaceContiguous_LU_v2(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr);
390   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
391   ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr);
392 
393   /* put together the new matrix */
394   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
395   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
396   b    = (Mat_SeqAIJ*)(B)->data;
397   b->free_a       = PETSC_TRUE;
398   b->free_ij      = PETSC_TRUE;
399   b->singlemalloc = PETSC_FALSE;
400   ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
401   b->j          = bj;
402   b->i          = bi;
403   b->diag       = bdiag;
404   b->ilen       = 0;
405   b->imax       = 0;
406   b->row        = isrow;
407   b->col        = iscol;
408   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
409   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
410   b->icol       = isicol;
411   ierr          = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
412 
413   /* In b structure:  Free imax, ilen, old a, old j.  Allocate solve_work, new a, new j */
414   ierr = PetscLogObjectMemory(B,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
415   b->maxnz = b->nz = bdiag[0]+1;
416   (B)->factor                = MAT_FACTOR_LU;
417   (B)->info.factor_mallocs   = reallocs;
418   (B)->info.fill_ratio_given = f;
419 
420   if (ai[n]) {
421     (B)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]);
422   } else {
423     (B)->info.fill_ratio_needed = 0.0;
424   }
425   (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct;
426   /* switch to inodes if appropriate */
427   ierr = Mat_CheckInode(B,PETSC_FALSE);CHKERRQ(ierr); /* Mat_CheckInode_FactorLU(B,PETSC_FALSE) ??? */
428   PetscFunctionReturn(0);
429 }
430 
431 /*
432     Trouble in factorization, should we dump the original matrix?
433 */
434 #undef __FUNCT__
435 #define __FUNCT__ "MatFactorDumpMatrix"
436 PetscErrorCode MatFactorDumpMatrix(Mat A)
437 {
438   PetscErrorCode ierr;
439   PetscTruth     flg = PETSC_FALSE;
440 
441   PetscFunctionBegin;
442   ierr = PetscOptionsGetTruth(PETSC_NULL,"-mat_factor_dump_on_error",&flg,PETSC_NULL);CHKERRQ(ierr);
443   if (flg) {
444     PetscViewer viewer;
445     char        filename[PETSC_MAX_PATH_LEN];
446 
447     ierr = PetscSNPrintf(filename,PETSC_MAX_PATH_LEN,"matrix_factor_error.%d",PetscGlobalRank);CHKERRQ(ierr);
448     ierr = PetscViewerBinaryOpen(((PetscObject)A)->comm,filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr);
449     ierr = MatView(A,viewer);CHKERRQ(ierr);
450     ierr = PetscViewerDestroy(viewer);CHKERRQ(ierr);
451   }
452   PetscFunctionReturn(0);
453 }
454 
455 extern PetscErrorCode MatSolve_SeqAIJ_Inode(Mat,Vec,Vec);
456 
457 #undef __FUNCT__
458 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_newdatastruct"
459 PetscErrorCode MatLUFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info)
460 {
461   Mat            C=B;
462   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
463   IS             isrow = b->row,isicol = b->icol;
464   PetscErrorCode ierr;
465   const PetscInt *r,*ic,*ics;
466   PetscInt       i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
467   PetscInt       *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj;
468   MatScalar      *rtmp,*pc,multiplier,*v,*pv,*aa=a->a;
469   PetscTruth     row_identity,col_identity;
470 
471   LUShift_Ctx    sctx;
472   PetscInt       *ddiag,newshift;
473   PetscReal      rs;
474   MatScalar      d;
475 
476   PetscFunctionBegin;
477   /* MatPivotSetUp(): initialize shift context sctx */
478   ierr = PetscMemzero(&sctx,sizeof(LUShift_Ctx));CHKERRQ(ierr);
479 
480   /* if both shift schemes are chosen by user, only use info->shiftpd */
481   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
482     ddiag          = a->diag;
483     sctx.shift_top = info->zeropivot;
484     for (i=0; i<n; i++) {
485       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
486       d  = (aa)[ddiag[i]];
487       rs = -PetscAbsScalar(d) - PetscRealPart(d);
488       v  = aa+ai[i];
489       nz = ai[i+1] - ai[i];
490       for (j=0; j<nz; j++)
491 	rs += PetscAbsScalar(v[j]);
492       if (rs>sctx.shift_top) sctx.shift_top = rs;
493     }
494     sctx.shift_top   *= 1.1;
495     sctx.nshift_max   = 5;
496     sctx.shift_lo     = 0.;
497     sctx.shift_hi     = 1.;
498   }
499 
500   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
501   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
502   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
503   ics  = ic;
504 
505   do {
506     sctx.lushift = PETSC_FALSE;
507     for (i=0; i<n; i++){
508       /* zero rtmp */
509       /* L part */
510       nz    = bi[i+1] - bi[i];
511       bjtmp = bj + bi[i];
512       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
513 
514       /* U part */
515       nz = bdiag[i]-bdiag[i+1];
516       bjtmp = bj + bdiag[i+1]+1;
517       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
518 
519       /* load in initial (unfactored row) */
520       nz    = ai[r[i]+1] - ai[r[i]];
521       ajtmp = aj + ai[r[i]];
522       v     = aa + ai[r[i]];
523       for (j=0; j<nz; j++) {
524         rtmp[ics[ajtmp[j]]] = v[j];
525       }
526       /* ZeropivotApply() */
527       rtmp[i] += sctx.shift_amount;  /* shift the diagonal of the matrix */
528 
529       /* elimination */
530       bjtmp = bj + bi[i];
531       row   = *bjtmp++;
532       nzL   = bi[i+1] - bi[i];
533       for(k=0; k < nzL;k++) {
534         pc = rtmp + row;
535         if (*pc != 0.0) {
536           pv         = b->a + bdiag[row];
537           multiplier = *pc * (*pv);
538           *pc        = multiplier;
539           pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
540 	  pv = b->a + bdiag[row+1]+1;
541 	  nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */
542           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
543           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
544         }
545         row = *bjtmp++;
546       }
547 
548       /* finished row so stick it into b->a */
549       rs = 0.0;
550       /* L part */
551       pv   = b->a + bi[i] ;
552       pj   = b->j + bi[i] ;
553       nz   = bi[i+1] - bi[i];
554       for (j=0; j<nz; j++) {
555         pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]);
556       }
557 
558       /* U part */
559       pv = b->a + bdiag[i+1]+1;
560       pj = b->j + bdiag[i+1]+1;
561       nz = bdiag[i] - bdiag[i+1]-1;
562       for (j=0; j<nz; j++) {
563         pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]);
564       }
565 
566       /* MatPivotCheck() */
567       sctx.rs  = rs;
568       sctx.pv  = rtmp[i];
569       /* ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); */
570       if (info->shiftnz){
571         ierr = MatPivotCheck_nz(info,sctx,i,newshift);CHKERRQ(ierr);
572       } else if (info->shiftpd){
573         ierr = MatPivotCheck_pd(info,sctx,i,newshift);CHKERRQ(ierr);
574       } else if (info->shiftinblocks){
575         ierr = MatPivotCheck_inblocks(info,sctx,i,newshift);CHKERRQ(ierr);
576       } else {
577         ierr = MatPivotCheck_none(info,sctx,i,newshift);CHKERRQ(ierr);
578       }
579       rtmp[i] = sctx.pv;
580       if (newshift == 1) break;
581 
582       /* Mark diagonal and invert diagonal for simplier triangular solves */
583       pv  = b->a + bdiag[i];
584       *pv = 1.0/rtmp[i];
585 
586     } /* endof for (i=0; i<n; i++){ */
587 
588     /* MatPivotRefine() */
589     if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max){
590       /*
591        * if no shift in this attempt & shifting & started shifting & can refine,
592        * then try lower shift
593        */
594       sctx.shift_hi       = sctx.shift_fraction;
595       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
596       sctx.shift_amount   = sctx.shift_fraction * sctx.shift_top;
597       sctx.lushift        = PETSC_TRUE;
598       sctx.nshift++;
599     }
600   } while (sctx.lushift);
601 
602   ierr = PetscFree(rtmp);CHKERRQ(ierr);
603   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
604   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
605   if (b->inode.use){
606     SETERRQ(1,"MatSolve_SeqAIJ_Inode_newdatastruct not done yet");
607     /* C->ops->solve   = MatSolve_SeqAIJ_Inode_newdatastruct; not done yet! */
608   } else {
609     ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
610     ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
611     if (row_identity && col_identity) {
612       C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct;
613     } else {
614       C->ops->solve = MatSolve_SeqAIJ_newdatastruct;
615     }
616   }
617   C->ops->solveadd           = MatSolveAdd_SeqAIJ_newdatastruct;
618   C->ops->solvetranspose     = MatSolveTranspose_SeqAIJ_newdatastruct;
619   C->ops->solvetransposeadd  = MatSolveTransposeAdd_SeqAIJ_newdatastruct;
620   C->ops->matsolve           = 0;
621   C->assembled    = PETSC_TRUE;
622   C->preallocated = PETSC_TRUE;
623   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
624 
625   /* MatPivotView() */
626   if (sctx.nshift){
627     if (info->shiftpd) {
628       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);
629     } else if (info->shiftnz) {
630       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
631     } else if (info->shiftinblocks){
632       ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftinblocks);CHKERRQ(ierr);
633     }
634   }
635   PetscFunctionReturn(0);
636 }
637 
638 #undef __FUNCT__
639 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ"
640 PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info)
641 {
642   Mat             C=B;
643   Mat_SeqAIJ      *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
644   IS              isrow = b->row,isicol = b->icol;
645   PetscErrorCode  ierr;
646   const PetscInt   *r,*ic,*ics;
647   PetscInt        nz,row,i,j,n=A->rmap->n,diag;
648   const PetscInt  *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
649   const PetscInt  *ajtmp,*bjtmp,*diag_offset = b->diag,*pj;
650   MatScalar       *pv,*rtmp,*pc,multiplier,d;
651   const MatScalar *v,*aa=a->a;
652   PetscReal       rs=0.0;
653   LUShift_Ctx     sctx;
654   PetscInt        newshift,*ddiag;
655 
656   PetscFunctionBegin;
657   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
658   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
659   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
660   ics  = ic;
661 
662   /* initialize shift context sctx */
663   sctx.nshift         = 0;
664   sctx.nshift_max     = 0;
665   sctx.shift_top      = 0.0;
666   sctx.shift_lo       = 0.0;
667   sctx.shift_hi       = 0.0;
668   sctx.shift_fraction = 0.0;
669   sctx.shift_amount   = 0.0;
670 
671   /* if both shift schemes are chosen by user, only use info->shiftpd */
672   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
673     ddiag          = a->diag;
674     sctx.shift_top = info->zeropivot;
675     for (i=0; i<n; i++) {
676       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
677       d  = (aa)[ddiag[i]];
678       rs = -PetscAbsScalar(d) - PetscRealPart(d);
679       v  = aa+ai[i];
680       nz = ai[i+1] - ai[i];
681       for (j=0; j<nz; j++)
682 	rs += PetscAbsScalar(v[j]);
683       if (rs>sctx.shift_top) sctx.shift_top = rs;
684     }
685     sctx.shift_top   *= 1.1;
686     sctx.nshift_max   = 5;
687     sctx.shift_lo     = 0.;
688     sctx.shift_hi     = 1.;
689   }
690 
691   do {
692     sctx.lushift = PETSC_FALSE;
693     for (i=0; i<n; i++){
694       nz    = bi[i+1] - bi[i];
695       bjtmp = bj + bi[i];
696       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
697 
698       /* load in initial (unfactored row) */
699       nz    = ai[r[i]+1] - ai[r[i]];
700       ajtmp = aj + ai[r[i]];
701       v     = aa + ai[r[i]];
702       for (j=0; j<nz; j++) {
703         rtmp[ics[ajtmp[j]]] = v[j];
704       }
705       rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */
706       /* if (sctx.shift_amount > 0.0) printf("row %d, shift %g\n",i,sctx.shift_amount); */
707 
708       row = *bjtmp++;
709       while  (row < i) {
710         pc = rtmp + row;
711         if (*pc != 0.0) {
712           pv         = b->a + diag_offset[row];
713           pj         = b->j + diag_offset[row] + 1;
714           multiplier = *pc / *pv++;
715           *pc        = multiplier;
716           nz         = bi[row+1] - diag_offset[row] - 1;
717           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
718           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
719         }
720         row = *bjtmp++;
721       }
722       /* finished row so stick it into b->a */
723       pv   = b->a + bi[i] ;
724       pj   = b->j + bi[i] ;
725       nz   = bi[i+1] - bi[i];
726       diag = diag_offset[i] - bi[i];
727       rs   = 0.0;
728       for (j=0; j<nz; j++) {
729         pv[j] = rtmp[pj[j]];
730         rs   += PetscAbsScalar(pv[j]);
731       }
732       rs   -= PetscAbsScalar(pv[diag]);
733 
734       /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */
735       sctx.rs  = rs;
736       sctx.pv  = pv[diag];
737       ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr);
738       if (newshift == 1) break;
739     }
740 
741     if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
742       /*
743        * if no shift in this attempt & shifting & started shifting & can refine,
744        * then try lower shift
745        */
746       sctx.shift_hi       = sctx.shift_fraction;
747       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
748       sctx.shift_amount   = sctx.shift_fraction * sctx.shift_top;
749       sctx.lushift        = PETSC_TRUE;
750       sctx.nshift++;
751     }
752   } while (sctx.lushift);
753 
754   /* invert diagonal entries for simplier triangular solves */
755   for (i=0; i<n; i++) {
756     b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]];
757   }
758   ierr = PetscFree(rtmp);CHKERRQ(ierr);
759   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
760   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
761   if (b->inode.use) {
762     C->ops->solve   = MatSolve_SeqAIJ_Inode;
763   } else {
764     PetscTruth row_identity, col_identity;
765     ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
766     ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
767     if (row_identity && col_identity) {
768       C->ops->solve   = MatSolve_SeqAIJ_NaturalOrdering;
769     } else {
770       C->ops->solve   = MatSolve_SeqAIJ;
771     }
772   }
773   C->ops->solveadd           = MatSolveAdd_SeqAIJ;
774   C->ops->solvetranspose     = MatSolveTranspose_SeqAIJ;
775   C->ops->solvetransposeadd  = MatSolveTransposeAdd_SeqAIJ;
776   C->ops->matsolve           = MatMatSolve_SeqAIJ;
777   C->assembled    = PETSC_TRUE;
778   C->preallocated = PETSC_TRUE;
779   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
780   if (sctx.nshift){
781      if (info->shiftpd) {
782       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);
783     } else if (info->shiftnz) {
784       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
785     }
786   }
787   PetscFunctionReturn(0);
788 }
789 
790 /*
791    This routine implements inplace ILU(0) with row or/and column permutations.
792    Input:
793      A - original matrix
794    Output;
795      A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i]
796          a->j (col index) is permuted by the inverse of colperm, then sorted
797          a->a reordered accordingly with a->j
798          a->diag (ptr to diagonal elements) is updated.
799 */
800 #undef __FUNCT__
801 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_InplaceWithPerm"
802 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info)
803 {
804   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
805   IS             isrow = a->row,isicol = a->icol;
806   PetscErrorCode ierr;
807   const PetscInt *r,*ic,*ics;
808   PetscInt       i,j,n=A->rmap->n,*ai=a->i,*aj=a->j;
809   PetscInt       *ajtmp,nz,row;
810   PetscInt       *diag = a->diag,nbdiag,*pj;
811   PetscScalar    *rtmp,*pc,multiplier,d;
812   MatScalar      *v,*pv;
813   PetscReal      rs;
814   LUShift_Ctx    sctx;
815   PetscInt       newshift;
816 
817   PetscFunctionBegin;
818   if (A != B) SETERRQ(PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address");
819   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
820   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
821   ierr  = PetscMalloc((n+1)*sizeof(PetscScalar),&rtmp);CHKERRQ(ierr);
822   ierr  = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr);
823   ics = ic;
824 
825   sctx.shift_top      = 0.;
826   sctx.nshift_max     = 0;
827   sctx.shift_lo       = 0.;
828   sctx.shift_hi       = 0.;
829   sctx.shift_fraction = 0.;
830 
831   /* if both shift schemes are chosen by user, only use info->shiftpd */
832   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
833     sctx.shift_top = 0.;
834     for (i=0; i<n; i++) {
835       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
836       d  = (a->a)[diag[i]];
837       rs = -PetscAbsScalar(d) - PetscRealPart(d);
838       v  = a->a+ai[i];
839       nz = ai[i+1] - ai[i];
840       for (j=0; j<nz; j++)
841 	rs += PetscAbsScalar(v[j]);
842       if (rs>sctx.shift_top) sctx.shift_top = rs;
843     }
844     if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot;
845     sctx.shift_top    *= 1.1;
846     sctx.nshift_max   = 5;
847     sctx.shift_lo     = 0.;
848     sctx.shift_hi     = 1.;
849   }
850 
851   sctx.shift_amount = 0.;
852   sctx.nshift       = 0;
853   do {
854     sctx.lushift = PETSC_FALSE;
855     for (i=0; i<n; i++){
856       /* load in initial unfactored row */
857       nz    = ai[r[i]+1] - ai[r[i]];
858       ajtmp = aj + ai[r[i]];
859       v     = a->a + ai[r[i]];
860       /* sort permuted ajtmp and values v accordingly */
861       for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]];
862       ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr);
863 
864       diag[r[i]] = ai[r[i]];
865       for (j=0; j<nz; j++) {
866         rtmp[ajtmp[j]] = v[j];
867         if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */
868       }
869       rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */
870 
871       row = *ajtmp++;
872       while  (row < i) {
873         pc = rtmp + row;
874         if (*pc != 0.0) {
875           pv         = a->a + diag[r[row]];
876           pj         = aj + diag[r[row]] + 1;
877 
878           multiplier = *pc / *pv++;
879           *pc        = multiplier;
880           nz         = ai[r[row]+1] - diag[r[row]] - 1;
881           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
882           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
883         }
884         row = *ajtmp++;
885       }
886       /* finished row so overwrite it onto a->a */
887       pv   = a->a + ai[r[i]] ;
888       pj   = aj + ai[r[i]] ;
889       nz   = ai[r[i]+1] - ai[r[i]];
890       nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */
891 
892       rs   = 0.0;
893       for (j=0; j<nz; j++) {
894         pv[j] = rtmp[pj[j]];
895         if (j != nbdiag) rs += PetscAbsScalar(pv[j]);
896       }
897 
898       /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */
899       sctx.rs  = rs;
900       sctx.pv  = pv[nbdiag];
901       ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr);
902       if (newshift == 1) break;
903     }
904 
905     if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
906       /*
907        * if no shift in this attempt & shifting & started shifting & can refine,
908        * then try lower shift
909        */
910       sctx.shift_hi        = sctx.shift_fraction;
911       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
912       sctx.shift_amount    = sctx.shift_fraction * sctx.shift_top;
913       sctx.lushift         = PETSC_TRUE;
914       sctx.nshift++;
915     }
916   } while (sctx.lushift);
917 
918   /* invert diagonal entries for simplier triangular solves */
919   for (i=0; i<n; i++) {
920     a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]];
921   }
922 
923   ierr = PetscFree(rtmp);CHKERRQ(ierr);
924   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
925   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
926   A->ops->solve             = MatSolve_SeqAIJ_InplaceWithPerm;
927   A->ops->solveadd          = MatSolveAdd_SeqAIJ;
928   A->ops->solvetranspose    = MatSolveTranspose_SeqAIJ;
929   A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ;
930   A->assembled = PETSC_TRUE;
931   A->preallocated = PETSC_TRUE;
932   ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr);
933   if (sctx.nshift){
934     if (info->shiftpd) {
935       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);
936     } else if (info->shiftnz) {
937       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
938     }
939   }
940   PetscFunctionReturn(0);
941 }
942 
943 /* ----------------------------------------------------------- */
944 #undef __FUNCT__
945 #define __FUNCT__ "MatLUFactor_SeqAIJ"
946 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info)
947 {
948   PetscErrorCode ierr;
949   Mat            C;
950 
951   PetscFunctionBegin;
952   ierr = MatGetFactor(A,MAT_SOLVER_PETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr);
953   ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr);
954   ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr);
955   A->ops->solve            = C->ops->solve;
956   A->ops->solvetranspose   = C->ops->solvetranspose;
957   ierr = MatHeaderCopy(A,C);CHKERRQ(ierr);
958   ierr = PetscLogObjectParent(A,((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr);
959   PetscFunctionReturn(0);
960 }
961 /* ----------------------------------------------------------- */
962 
963 
964 #undef __FUNCT__
965 #define __FUNCT__ "MatSolve_SeqAIJ"
966 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx)
967 {
968   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
969   IS                iscol = a->col,isrow = a->row;
970   PetscErrorCode    ierr;
971   PetscInt          i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
972   PetscInt          nz;
973   const PetscInt    *rout,*cout,*r,*c;
974   PetscScalar       *x,*tmp,*tmps,sum;
975   const PetscScalar *b;
976   const MatScalar   *aa = a->a,*v;
977 
978   PetscFunctionBegin;
979   if (!n) PetscFunctionReturn(0);
980 
981   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
982   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
983   tmp  = a->solve_work;
984 
985   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
986   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
987 
988   /* forward solve the lower triangular */
989   tmp[0] = b[*r++];
990   tmps   = tmp;
991   for (i=1; i<n; i++) {
992     v   = aa + ai[i] ;
993     vi  = aj + ai[i] ;
994     nz  = a->diag[i] - ai[i];
995     sum = b[*r++];
996     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
997     tmp[i] = sum;
998   }
999 
1000   /* backward solve the upper triangular */
1001   for (i=n-1; i>=0; i--){
1002     v   = aa + a->diag[i] + 1;
1003     vi  = aj + a->diag[i] + 1;
1004     nz  = ai[i+1] - a->diag[i] - 1;
1005     sum = tmp[i];
1006     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1007     x[*c--] = tmp[i] = sum*aa[a->diag[i]];
1008   }
1009 
1010   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1011   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1012   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1013   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1014   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1015   PetscFunctionReturn(0);
1016 }
1017 
1018 #undef __FUNCT__
1019 #define __FUNCT__ "MatMatSolve_SeqAIJ"
1020 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X)
1021 {
1022   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1023   IS              iscol = a->col,isrow = a->row;
1024   PetscErrorCode  ierr;
1025   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1026   PetscInt        nz,neq;
1027   const PetscInt  *rout,*cout,*r,*c;
1028   PetscScalar     *x,*b,*tmp,*tmps,sum;
1029   const MatScalar *aa = a->a,*v;
1030   PetscTruth      bisdense,xisdense;
1031 
1032   PetscFunctionBegin;
1033   if (!n) PetscFunctionReturn(0);
1034 
1035   ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr);
1036   if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix");
1037   ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr);
1038   if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix");
1039 
1040   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
1041   ierr = MatGetArray(X,&x);CHKERRQ(ierr);
1042 
1043   tmp  = a->solve_work;
1044   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1045   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1046 
1047   for (neq=0; neq<B->cmap->n; neq++){
1048     /* forward solve the lower triangular */
1049     tmp[0] = b[r[0]];
1050     tmps   = tmp;
1051     for (i=1; i<n; i++) {
1052       v   = aa + ai[i] ;
1053       vi  = aj + ai[i] ;
1054       nz  = a->diag[i] - ai[i];
1055       sum = b[r[i]];
1056       PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1057       tmp[i] = sum;
1058     }
1059     /* backward solve the upper triangular */
1060     for (i=n-1; i>=0; i--){
1061       v   = aa + a->diag[i] + 1;
1062       vi  = aj + a->diag[i] + 1;
1063       nz  = ai[i+1] - a->diag[i] - 1;
1064       sum = tmp[i];
1065       PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1066       x[c[i]] = tmp[i] = sum*aa[a->diag[i]];
1067     }
1068 
1069     b += n;
1070     x += n;
1071   }
1072   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1073   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1074   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
1075   ierr = MatRestoreArray(X,&x);CHKERRQ(ierr);
1076   ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr);
1077   PetscFunctionReturn(0);
1078 }
1079 
1080 #undef __FUNCT__
1081 #define __FUNCT__ "MatSolve_SeqAIJ_InplaceWithPerm"
1082 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx)
1083 {
1084   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1085   IS              iscol = a->col,isrow = a->row;
1086   PetscErrorCode  ierr;
1087   const PetscInt  *r,*c,*rout,*cout;
1088   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1089   PetscInt        nz,row;
1090   PetscScalar     *x,*b,*tmp,*tmps,sum;
1091   const MatScalar *aa = a->a,*v;
1092 
1093   PetscFunctionBegin;
1094   if (!n) PetscFunctionReturn(0);
1095 
1096   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
1097   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1098   tmp  = a->solve_work;
1099 
1100   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1101   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1102 
1103   /* forward solve the lower triangular */
1104   tmp[0] = b[*r++];
1105   tmps   = tmp;
1106   for (row=1; row<n; row++) {
1107     i   = rout[row]; /* permuted row */
1108     v   = aa + ai[i] ;
1109     vi  = aj + ai[i] ;
1110     nz  = a->diag[i] - ai[i];
1111     sum = b[*r++];
1112     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1113     tmp[row] = sum;
1114   }
1115 
1116   /* backward solve the upper triangular */
1117   for (row=n-1; row>=0; row--){
1118     i   = rout[row]; /* permuted row */
1119     v   = aa + a->diag[i] + 1;
1120     vi  = aj + a->diag[i] + 1;
1121     nz  = ai[i+1] - a->diag[i] - 1;
1122     sum = tmp[row];
1123     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1124     x[*c--] = tmp[row] = sum*aa[a->diag[i]];
1125   }
1126 
1127   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1128   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1129   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
1130   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1131   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1132   PetscFunctionReturn(0);
1133 }
1134 
1135 /* ----------------------------------------------------------- */
1136 #include "../src/mat/impls/aij/seq/ftn-kernels/fsolve.h"
1137 #undef __FUNCT__
1138 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering"
1139 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx)
1140 {
1141   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1142   PetscErrorCode    ierr;
1143   PetscInt          n = A->rmap->n;
1144   const PetscInt    *ai = a->i,*aj = a->j,*adiag = a->diag;
1145   PetscScalar       *x;
1146   const PetscScalar *b;
1147   const MatScalar   *aa = a->a;
1148 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ)
1149   PetscInt          adiag_i,i,nz,ai_i;
1150   const PetscInt    *vi;
1151   const MatScalar   *v;
1152   PetscScalar       sum;
1153 #endif
1154 
1155   PetscFunctionBegin;
1156   if (!n) PetscFunctionReturn(0);
1157 
1158   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1159   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1160 
1161 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ)
1162   fortransolveaij_(&n,x,ai,aj,adiag,aa,b);
1163 #else
1164   /* forward solve the lower triangular */
1165   x[0] = b[0];
1166   for (i=1; i<n; i++) {
1167     ai_i = ai[i];
1168     v    = aa + ai_i;
1169     vi   = aj + ai_i;
1170     nz   = adiag[i] - ai_i;
1171     sum  = b[i];
1172     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
1173     x[i] = sum;
1174   }
1175 
1176   /* backward solve the upper triangular */
1177   for (i=n-1; i>=0; i--){
1178     adiag_i = adiag[i];
1179     v       = aa + adiag_i + 1;
1180     vi      = aj + adiag_i + 1;
1181     nz      = ai[i+1] - adiag_i - 1;
1182     sum     = x[i];
1183     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
1184     x[i]    = sum*aa[adiag_i];
1185   }
1186 #endif
1187   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1188   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1189   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1190   PetscFunctionReturn(0);
1191 }
1192 
1193 #undef __FUNCT__
1194 #define __FUNCT__ "MatSolveAdd_SeqAIJ"
1195 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx)
1196 {
1197   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1198   IS                iscol = a->col,isrow = a->row;
1199   PetscErrorCode    ierr;
1200   PetscInt          i, n = A->rmap->n,j;
1201   PetscInt          nz;
1202   const PetscInt    *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j;
1203   PetscScalar       *x,*tmp,sum;
1204   const PetscScalar *b;
1205   const MatScalar   *aa = a->a,*v;
1206 
1207   PetscFunctionBegin;
1208   if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);}
1209 
1210   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1211   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1212   tmp  = a->solve_work;
1213 
1214   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1215   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1216 
1217   /* forward solve the lower triangular */
1218   tmp[0] = b[*r++];
1219   for (i=1; i<n; i++) {
1220     v   = aa + ai[i] ;
1221     vi  = aj + ai[i] ;
1222     nz  = a->diag[i] - ai[i];
1223     sum = b[*r++];
1224     for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1225     tmp[i] = sum;
1226   }
1227 
1228   /* backward solve the upper triangular */
1229   for (i=n-1; i>=0; i--){
1230     v   = aa + a->diag[i] + 1;
1231     vi  = aj + a->diag[i] + 1;
1232     nz  = ai[i+1] - a->diag[i] - 1;
1233     sum = tmp[i];
1234     for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1235     tmp[i] = sum*aa[a->diag[i]];
1236     x[*c--] += tmp[i];
1237   }
1238 
1239   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1240   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1241   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1242   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1243   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1244 
1245   PetscFunctionReturn(0);
1246 }
1247 
1248 #undef __FUNCT__
1249 #define __FUNCT__ "MatSolveAdd_SeqAIJ_newdatastruct"
1250 PetscErrorCode MatSolveAdd_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec yy,Vec xx)
1251 {
1252   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1253   IS                iscol = a->col,isrow = a->row;
1254   PetscErrorCode    ierr;
1255   PetscInt          i, n = A->rmap->n,j;
1256   PetscInt          nz;
1257   const PetscInt    *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag;
1258   PetscScalar       *x,*tmp,sum;
1259   const PetscScalar *b;
1260   const MatScalar   *aa = a->a,*v;
1261 
1262   PetscFunctionBegin;
1263   if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);}
1264 
1265   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1266   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1267   tmp  = a->solve_work;
1268 
1269   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1270   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1271 
1272   /* forward solve the lower triangular */
1273   tmp[0] = b[r[0]];
1274   v      = aa;
1275   vi     = aj;
1276   for (i=1; i<n; i++) {
1277     nz  = ai[i+1] - ai[i];
1278     sum = b[r[i]];
1279     for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1280     tmp[i] = sum;
1281     v += nz; vi += nz;
1282   }
1283 
1284   /* backward solve the upper triangular */
1285   v  = aa + adiag[n-1];
1286   vi = aj + adiag[n-1];
1287   for (i=n-1; i>=0; i--){
1288     nz  = adiag[i] - adiag[i+1] - 1;
1289     sum = tmp[i];
1290     for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1291     tmp[i] = sum*v[nz];
1292     x[c[i]] += tmp[i];
1293     v += nz+1; vi += nz+1;
1294   }
1295 
1296   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1297   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1298   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1299   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1300   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1301 
1302   PetscFunctionReturn(0);
1303 }
1304 
1305 #undef __FUNCT__
1306 #define __FUNCT__ "MatSolveTranspose_SeqAIJ"
1307 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx)
1308 {
1309   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1310   IS                iscol = a->col,isrow = a->row;
1311   PetscErrorCode    ierr;
1312   const PetscInt    *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi;
1313   PetscInt          i,n = A->rmap->n,j;
1314   PetscInt          nz;
1315   PetscScalar       *x,*tmp,s1;
1316   const MatScalar   *aa = a->a,*v;
1317   const PetscScalar *b;
1318 
1319   PetscFunctionBegin;
1320   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1321   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1322   tmp  = a->solve_work;
1323 
1324   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1325   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1326 
1327   /* copy the b into temp work space according to permutation */
1328   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1329 
1330   /* forward solve the U^T */
1331   for (i=0; i<n; i++) {
1332     v   = aa + diag[i] ;
1333     vi  = aj + diag[i] + 1;
1334     nz  = ai[i+1] - diag[i] - 1;
1335     s1  = tmp[i];
1336     s1 *= (*v++);  /* multiply by inverse of diagonal entry */
1337     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1338     tmp[i] = s1;
1339   }
1340 
1341   /* backward solve the L^T */
1342   for (i=n-1; i>=0; i--){
1343     v   = aa + diag[i] - 1 ;
1344     vi  = aj + diag[i] - 1 ;
1345     nz  = diag[i] - ai[i];
1346     s1  = tmp[i];
1347     for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j];
1348   }
1349 
1350   /* copy tmp into x according to permutation */
1351   for (i=0; i<n; i++) x[r[i]] = tmp[i];
1352 
1353   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1354   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1355   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1356   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1357 
1358   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1359   PetscFunctionReturn(0);
1360 }
1361 
1362 #undef __FUNCT__
1363 #define __FUNCT__ "MatSolveTranspose_SeqAIJ_newdatastruct"
1364 PetscErrorCode MatSolveTranspose_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec xx)
1365 {
1366   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1367   IS                iscol = a->col,isrow = a->row;
1368   PetscErrorCode    ierr;
1369   const PetscInt    *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi;
1370   PetscInt          i,n = A->rmap->n,j;
1371   PetscInt          nz;
1372   PetscScalar       *x,*tmp,s1;
1373   const MatScalar   *aa = a->a,*v;
1374   const PetscScalar *b;
1375 
1376   PetscFunctionBegin;
1377   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1378   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1379   tmp  = a->solve_work;
1380 
1381   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1382   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1383 
1384   /* copy the b into temp work space according to permutation */
1385   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1386 
1387   /* forward solve the U^T */
1388   for (i=0; i<n; i++) {
1389     v   = aa + adiag[i+1] + 1;
1390     vi  = aj + adiag[i+1] + 1;
1391     nz  = adiag[i] - adiag[i+1] - 1;
1392     s1  = tmp[i];
1393     s1 *= v[nz];  /* multiply by inverse of diagonal entry */
1394     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1395     tmp[i] = s1;
1396   }
1397 
1398   /* backward solve the L^T */
1399   for (i=n-1; i>=0; i--){
1400     v   = aa + ai[i];
1401     vi  = aj + ai[i];
1402     nz  = ai[i+1] - ai[i];
1403     s1  = tmp[i];
1404     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1405   }
1406 
1407   /* copy tmp into x according to permutation */
1408   for (i=0; i<n; i++) x[r[i]] = tmp[i];
1409 
1410   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1411   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1412   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1413   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1414 
1415   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1416   PetscFunctionReturn(0);
1417 }
1418 
1419 #undef __FUNCT__
1420 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ"
1421 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx)
1422 {
1423   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1424   IS                iscol = a->col,isrow = a->row;
1425   PetscErrorCode    ierr;
1426   const PetscInt    *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi;
1427   PetscInt          i,n = A->rmap->n,j;
1428   PetscInt          nz;
1429   PetscScalar       *x,*tmp,s1;
1430   const MatScalar   *aa = a->a,*v;
1431   const PetscScalar *b;
1432 
1433   PetscFunctionBegin;
1434   if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);}
1435   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1436   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1437   tmp  = a->solve_work;
1438 
1439   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1440   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1441 
1442   /* copy the b into temp work space according to permutation */
1443   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1444 
1445   /* forward solve the U^T */
1446   for (i=0; i<n; i++) {
1447     v   = aa + diag[i] ;
1448     vi  = aj + diag[i] + 1;
1449     nz  = ai[i+1] - diag[i] - 1;
1450     s1  = tmp[i];
1451     s1 *= (*v++);  /* multiply by inverse of diagonal entry */
1452     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1453     tmp[i] = s1;
1454   }
1455 
1456   /* backward solve the L^T */
1457   for (i=n-1; i>=0; i--){
1458     v   = aa + diag[i] - 1 ;
1459     vi  = aj + diag[i] - 1 ;
1460     nz  = diag[i] - ai[i];
1461     s1  = tmp[i];
1462     for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j];
1463   }
1464 
1465   /* copy tmp into x according to permutation */
1466   for (i=0; i<n; i++) x[r[i]] += tmp[i];
1467 
1468   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1469   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1470   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1471   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1472 
1473   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1474   PetscFunctionReturn(0);
1475 }
1476 
1477 #undef __FUNCT__
1478 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ_newdatastruct"
1479 PetscErrorCode MatSolveTransposeAdd_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec zz,Vec xx)
1480 {
1481   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1482   IS                iscol = a->col,isrow = a->row;
1483   PetscErrorCode    ierr;
1484   const PetscInt    *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi;
1485   PetscInt          i,n = A->rmap->n,j;
1486   PetscInt          nz;
1487   PetscScalar       *x,*tmp,s1;
1488   const MatScalar   *aa = a->a,*v;
1489   const PetscScalar *b;
1490 
1491   PetscFunctionBegin;
1492   if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);}
1493   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1494   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1495   tmp  = a->solve_work;
1496 
1497   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1498   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1499 
1500   /* copy the b into temp work space according to permutation */
1501   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1502 
1503   /* forward solve the U^T */
1504   for (i=0; i<n; i++) {
1505     v   = aa + adiag[i+1] + 1;
1506     vi  = aj + adiag[i+1] + 1;
1507     nz  = adiag[i] - adiag[i+1] - 1;
1508     s1  = tmp[i];
1509     s1 *= v[nz];  /* multiply by inverse of diagonal entry */
1510     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1511     tmp[i] = s1;
1512   }
1513 
1514 
1515   /* backward solve the L^T */
1516   for (i=n-1; i>=0; i--){
1517     v   = aa + ai[i] ;
1518     vi  = aj + ai[i];
1519     nz  = ai[i+1] - ai[i];
1520     s1  = tmp[i];
1521     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1522   }
1523 
1524   /* copy tmp into x according to permutation */
1525   for (i=0; i<n; i++) x[r[i]] += tmp[i];
1526 
1527   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1528   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1529   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1530   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1531 
1532   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1533   PetscFunctionReturn(0);
1534 }
1535 
1536 /* ----------------------------------------------------------------*/
1537 
1538 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption,PetscTruth);
1539 
1540 /*
1541    ilu() under revised new data structure.
1542    Factored arrays bj and ba are stored as
1543      L(0,:), L(1,:), ...,L(n-1,:),  U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:)
1544 
1545    bi=fact->i is an array of size n+1, in which
1546    bi+
1547      bi[i]:  points to 1st entry of L(i,:),i=0,...,n-1
1548      bi[n]:  points to L(n-1,n-1)+1
1549 
1550   bdiag=fact->diag is an array of size n+1,in which
1551      bdiag[i]: points to diagonal of U(i,:), i=0,...,n-1
1552      bdiag[n]: points to entry of U(n-1,0)-1
1553 
1554    U(i,:) contains bdiag[i] as its last entry, i.e.,
1555     U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i])
1556 */
1557 #undef __FUNCT__
1558 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct"
1559 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1560 {
1561 
1562   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1563   PetscErrorCode     ierr;
1564   PetscInt           n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag;
1565   PetscInt           i,j,nz,*bi,*bj,*bdiag;
1566   PetscTruth         missing;
1567   IS                 isicol;
1568 
1569   PetscFunctionBegin;
1570   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);
1571   ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
1572   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
1573   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1574 
1575   ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr);
1576   b    = (Mat_SeqAIJ*)(fact)->data;
1577 
1578   /* allocate matrix arrays for new data structure */
1579   ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,n+1,PetscInt,&b->i);CHKERRQ(ierr);
1580   ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));CHKERRQ(ierr);
1581   b->singlemalloc = PETSC_TRUE;
1582   if (!b->diag){
1583     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr);
1584     ierr = PetscLogObjectMemory(fact,(n+1)*sizeof(PetscInt));CHKERRQ(ierr);
1585   }
1586   bdiag = b->diag;
1587 
1588   if (n > 0) {
1589     ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr);
1590   }
1591 
1592   /* set bi and bj with new data structure */
1593   bi = b->i;
1594   bj = b->j;
1595 
1596   /* L part */
1597   bi[0] = 0;
1598   for (i=0; i<n; i++){
1599     nz = adiag[i] - ai[i];
1600     bi[i+1] = bi[i] + nz;
1601     aj = a->j + ai[i];
1602     for (j=0; j<nz; j++){
1603       *bj = aj[j]; bj++;
1604     }
1605   }
1606 
1607   /* U part */
1608   bdiag[n] = bi[n]-1;
1609   for (i=n-1; i>=0; i--){
1610     nz = ai[i+1] - adiag[i] - 1;
1611     aj = a->j + adiag[i] + 1;
1612     for (j=0; j<nz; j++){
1613       *bj = aj[j]; bj++;
1614     }
1615     /* diag[i] */
1616     *bj = i; bj++;
1617     bdiag[i] = bdiag[i+1] + nz + 1;
1618   }
1619 
1620   fact->factor                 = MAT_FACTOR_ILU;
1621   fact->info.factor_mallocs    = 0;
1622   fact->info.fill_ratio_given  = info->fill;
1623   fact->info.fill_ratio_needed = 1.0;
1624   fact->ops->lufactornumeric   = MatLUFactorNumeric_SeqAIJ_newdatastruct;
1625 
1626   b       = (Mat_SeqAIJ*)(fact)->data;
1627   b->row  = isrow;
1628   b->col  = iscol;
1629   b->icol = isicol;
1630   ierr    = PetscMalloc((fact->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1631   ierr    = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1632   ierr    = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1633   PetscFunctionReturn(0);
1634 }
1635 
1636 #undef __FUNCT__
1637 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_newdatastruct"
1638 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1639 {
1640   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1641   IS                 isicol;
1642   PetscErrorCode     ierr;
1643   const PetscInt     *r,*ic;
1644   PetscInt           n=A->rmap->n,*ai=a->i,*aj=a->j;
1645   PetscInt           *bi,*cols,nnz,*cols_lvl;
1646   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1647   PetscInt           i,levels,diagonal_fill;
1648   PetscTruth         col_identity,row_identity;
1649   PetscReal          f;
1650   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
1651   PetscBT            lnkbt;
1652   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
1653   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1654   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1655 
1656   PetscFunctionBegin;
1657   /* printf("MatILUFactorSymbolic_SeqAIJ_newdatastruct ...\n"); */
1658   levels = (PetscInt)info->levels;
1659   ierr   = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1660   ierr   = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
1661 
1662   if (!levels && row_identity && col_identity) {
1663     /* special case: ilu(0) with natural ordering */
1664     ierr = MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1665     ierr = Mat_CheckInode(fact,PETSC_FALSE);CHKERRQ(ierr); /* Mat_CheckInode_FactorLU(fact,PETSC_FALSE) ??? */
1666     PetscFunctionReturn(0);
1667   }
1668 
1669   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);
1670   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1671   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1672   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1673 
1674   /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
1675   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1676   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
1677   bi[0] = bdiag[0] = 0;
1678 
1679   ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr);
1680 
1681   /* create a linked list for storing column indices of the active row */
1682   nlnk = n + 1;
1683   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1684 
1685   /* initial FreeSpace size is f*(ai[n]+1) */
1686   f             = info->fill;
1687   diagonal_fill = (PetscInt)info->diagonal_fill;
1688   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
1689   current_space = free_space;
1690   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
1691   current_space_lvl = free_space_lvl;
1692 
1693   for (i=0; i<n; i++) {
1694     nzi = 0;
1695     /* copy current row into linked list */
1696     nnz  = ai[r[i]+1] - ai[r[i]];
1697     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1698     cols = aj + ai[r[i]];
1699     lnk[i] = -1; /* marker to indicate if diagonal exists */
1700     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1701     nzi += nlnk;
1702 
1703     /* make sure diagonal entry is included */
1704     if (diagonal_fill && lnk[i] == -1) {
1705       fm = n;
1706       while (lnk[fm] < i) fm = lnk[fm];
1707       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
1708       lnk[fm]    = i;
1709       lnk_lvl[i] = 0;
1710       nzi++; dcount++;
1711     }
1712 
1713     /* add pivot rows into the active row */
1714     nzbd = 0;
1715     prow = lnk[n];
1716     while (prow < i) {
1717       nnz      = bdiag[prow];
1718       cols     = bj_ptr[prow] + nnz + 1;
1719       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1720       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
1721       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
1722       nzi += nlnk;
1723       prow = lnk[prow];
1724       nzbd++;
1725     }
1726     bdiag[i] = nzbd;
1727     bi[i+1]  = bi[i] + nzi;
1728 
1729     /* if free space is not available, make more free space */
1730     if (current_space->local_remaining<nzi) {
1731       nnz = 2*nzi*(n - i); /* estimated and max additional space needed */
1732       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
1733       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
1734       reallocs++;
1735     }
1736 
1737     /* copy data into free_space and free_space_lvl, then initialize lnk */
1738     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1739     bj_ptr[i]    = current_space->array;
1740     bjlvl_ptr[i] = current_space_lvl->array;
1741 
1742     /* make sure the active row i has diagonal entry */
1743     if (*(bj_ptr[i]+bdiag[i]) != i) {
1744       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
1745     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
1746     }
1747 
1748     current_space->array           += nzi;
1749     current_space->local_used      += nzi;
1750     current_space->local_remaining -= nzi;
1751     current_space_lvl->array           += nzi;
1752     current_space_lvl->local_used      += nzi;
1753     current_space_lvl->local_remaining -= nzi;
1754   }
1755 
1756   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1757   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1758 
1759   /* destroy list of free space and other temporary arrays */
1760   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
1761 
1762   /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */
1763   ierr = PetscFreeSpaceContiguous_LU_v2(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr);
1764 
1765   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1766   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
1767   ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr);
1768 
1769 #if defined(PETSC_USE_INFO)
1770   {
1771     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1772     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
1773     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
1774     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
1775     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
1776     if (diagonal_fill) {
1777       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
1778     }
1779   }
1780 #endif
1781 
1782   /* put together the new matrix */
1783   ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
1784   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
1785   b = (Mat_SeqAIJ*)(fact)->data;
1786   b->free_a       = PETSC_TRUE;
1787   b->free_ij      = PETSC_TRUE;
1788   b->singlemalloc = PETSC_FALSE;
1789   ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
1790   b->j          = bj;
1791   b->i          = bi;
1792   b->diag       = bdiag;
1793   b->ilen       = 0;
1794   b->imax       = 0;
1795   b->row        = isrow;
1796   b->col        = iscol;
1797   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1798   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1799   b->icol       = isicol;
1800   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1801   /* In b structure:  Free imax, ilen, old a, old j.
1802      Allocate bdiag, solve_work, new a, new j */
1803   ierr = PetscLogObjectMemory(fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
1804   b->maxnz = b->nz = bdiag[0]+1;
1805   (fact)->info.factor_mallocs    = reallocs;
1806   (fact)->info.fill_ratio_given  = f;
1807   (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]);
1808   (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct;
1809   ierr = Mat_CheckInode(fact,PETSC_FALSE);CHKERRQ(ierr); /* Mat_CheckInode_FactorLU(fact,PETSC_FALSE) ??? */
1810   PetscFunctionReturn(0);
1811 }
1812 
1813 #undef __FUNCT__
1814 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ"
1815 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1816 {
1817   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1818   IS                 isicol;
1819   PetscErrorCode     ierr;
1820   const PetscInt     *r,*ic;
1821   PetscInt           n=A->rmap->n,*ai=a->i,*aj=a->j,d;
1822   PetscInt           *bi,*cols,nnz,*cols_lvl;
1823   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1824   PetscInt           i,levels,diagonal_fill;
1825   PetscTruth         col_identity,row_identity;
1826   PetscReal          f;
1827   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
1828   PetscBT            lnkbt;
1829   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
1830   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1831   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1832   PetscTruth         missing;
1833   PetscTruth         newdatastruct=PETSC_FALSE;
1834 
1835   PetscFunctionBegin;
1836   ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
1837   if(newdatastruct){
1838     ierr = MatILUFactorSymbolic_SeqAIJ_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1839     PetscFunctionReturn(0);
1840   }
1841 
1842   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);
1843   f             = info->fill;
1844   levels        = (PetscInt)info->levels;
1845   diagonal_fill = (PetscInt)info->diagonal_fill;
1846   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1847 
1848   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1849   ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
1850   if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */
1851     ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr);
1852     (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ;
1853 
1854     fact->factor = MAT_FACTOR_ILU;
1855     (fact)->info.factor_mallocs    = 0;
1856     (fact)->info.fill_ratio_given  = info->fill;
1857     (fact)->info.fill_ratio_needed = 1.0;
1858     b               = (Mat_SeqAIJ*)(fact)->data;
1859     ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
1860     if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
1861     b->row              = isrow;
1862     b->col              = iscol;
1863     b->icol             = isicol;
1864     ierr                = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1865     ierr                = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1866     ierr                = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1867     ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1868     PetscFunctionReturn(0);
1869   }
1870 
1871   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1872   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1873 
1874   /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
1875   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1876   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
1877   bi[0] = bdiag[0] = 0;
1878 
1879   ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr);
1880 
1881   /* create a linked list for storing column indices of the active row */
1882   nlnk = n + 1;
1883   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1884 
1885   /* initial FreeSpace size is f*(ai[n]+1) */
1886   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
1887   current_space = free_space;
1888   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
1889   current_space_lvl = free_space_lvl;
1890 
1891   for (i=0; i<n; i++) {
1892     nzi = 0;
1893     /* copy current row into linked list */
1894     nnz  = ai[r[i]+1] - ai[r[i]];
1895     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1896     cols = aj + ai[r[i]];
1897     lnk[i] = -1; /* marker to indicate if diagonal exists */
1898     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1899     nzi += nlnk;
1900 
1901     /* make sure diagonal entry is included */
1902     if (diagonal_fill && lnk[i] == -1) {
1903       fm = n;
1904       while (lnk[fm] < i) fm = lnk[fm];
1905       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
1906       lnk[fm]    = i;
1907       lnk_lvl[i] = 0;
1908       nzi++; dcount++;
1909     }
1910 
1911     /* add pivot rows into the active row */
1912     nzbd = 0;
1913     prow = lnk[n];
1914     while (prow < i) {
1915       nnz      = bdiag[prow];
1916       cols     = bj_ptr[prow] + nnz + 1;
1917       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1918       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
1919       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
1920       nzi += nlnk;
1921       prow = lnk[prow];
1922       nzbd++;
1923     }
1924     bdiag[i] = nzbd;
1925     bi[i+1]  = bi[i] + nzi;
1926 
1927     /* if free space is not available, make more free space */
1928     if (current_space->local_remaining<nzi) {
1929       nnz = nzi*(n - i); /* estimated and max additional space needed */
1930       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
1931       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
1932       reallocs++;
1933     }
1934 
1935     /* copy data into free_space and free_space_lvl, then initialize lnk */
1936     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1937     bj_ptr[i]    = current_space->array;
1938     bjlvl_ptr[i] = current_space_lvl->array;
1939 
1940     /* make sure the active row i has diagonal entry */
1941     if (*(bj_ptr[i]+bdiag[i]) != i) {
1942       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
1943     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
1944     }
1945 
1946     current_space->array           += nzi;
1947     current_space->local_used      += nzi;
1948     current_space->local_remaining -= nzi;
1949     current_space_lvl->array           += nzi;
1950     current_space_lvl->local_used      += nzi;
1951     current_space_lvl->local_remaining -= nzi;
1952   }
1953 
1954   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1955   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1956 
1957   /* destroy list of free space and other temporary arrays */
1958   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
1959   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */
1960   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1961   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
1962   ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr);
1963 
1964 #if defined(PETSC_USE_INFO)
1965   {
1966     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1967     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
1968     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
1969     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
1970     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
1971     if (diagonal_fill) {
1972       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
1973     }
1974   }
1975 #endif
1976 
1977   /* put together the new matrix */
1978   ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
1979   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
1980   b = (Mat_SeqAIJ*)(fact)->data;
1981   b->free_a       = PETSC_TRUE;
1982   b->free_ij      = PETSC_TRUE;
1983   b->singlemalloc = PETSC_FALSE;
1984   ierr = PetscMalloc(bi[n]*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
1985   b->j          = bj;
1986   b->i          = bi;
1987   for (i=0; i<n; i++) bdiag[i] += bi[i];
1988   b->diag       = bdiag;
1989   b->ilen       = 0;
1990   b->imax       = 0;
1991   b->row        = isrow;
1992   b->col        = iscol;
1993   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1994   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1995   b->icol       = isicol;
1996   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1997   /* In b structure:  Free imax, ilen, old a, old j.
1998      Allocate bdiag, solve_work, new a, new j */
1999   ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
2000   b->maxnz             = b->nz = bi[n] ;
2001   (fact)->info.factor_mallocs    = reallocs;
2002   (fact)->info.fill_ratio_given  = f;
2003   (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
2004   (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ;
2005   ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr);
2006   PetscFunctionReturn(0);
2007 }
2008 
2009 #undef __FUNCT__
2010 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ_newdatastruct"
2011 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info)
2012 {
2013   Mat            C = B;
2014   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
2015   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
2016   IS             ip=b->row,iip = b->icol;
2017   PetscErrorCode ierr;
2018   const PetscInt *rip,*riip;
2019   PetscInt       i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp;
2020   PetscInt       *ai=a->i,*aj=a->j;
2021   PetscInt       k,jmin,jmax,*c2r,*il,col,nexti,ili,nz;
2022   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
2023   PetscTruth     perm_identity;
2024 
2025   LUShift_Ctx    sctx;
2026   PetscInt       newshift;
2027   PetscReal      rs;
2028   MatScalar      d,*v;
2029 
2030   PetscFunctionBegin;
2031   /* MatPivotSetUp(): initialize shift context sctx */
2032   ierr = PetscMemzero(&sctx,sizeof(LUShift_Ctx));CHKERRQ(ierr);
2033 
2034   /* if both shift schemes are chosen by user, only use info->shiftpd */
2035   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
2036     sctx.shift_top = info->zeropivot;
2037     for (i=0; i<mbs; i++) {
2038       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
2039       d  = (aa)[a->diag[i]];
2040       rs = -PetscAbsScalar(d) - PetscRealPart(d);
2041       v  = aa+ai[i];
2042       nz = ai[i+1] - ai[i];
2043       for (j=0; j<nz; j++)
2044 	rs += PetscAbsScalar(v[j]);
2045       if (rs>sctx.shift_top) sctx.shift_top = rs;
2046     }
2047     sctx.shift_top   *= 1.1;
2048     sctx.nshift_max   = 5;
2049     sctx.shift_lo     = 0.;
2050     sctx.shift_hi     = 1.;
2051   }
2052 
2053   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
2054   ierr  = ISGetIndices(iip,&riip);CHKERRQ(ierr);
2055 
2056   /* allocate working arrays
2057      c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col
2058      il:  for active k row, il[i] gives the index of the 1st nonzero entry in U[i,k:n-1] in bj and ba arrays
2059   */
2060   ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&c2r);CHKERRQ(ierr);
2061 
2062   do {
2063     sctx.lushift = PETSC_FALSE;
2064 
2065     for (i=0; i<mbs; i++) c2r[i] = mbs;
2066     il[0] = 0;
2067 
2068     for (k = 0; k<mbs; k++){
2069       /* zero rtmp */
2070       nz = bi[k+1] - bi[k];
2071       bjtmp = bj + bi[k];
2072       for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
2073 
2074       /* load in initial unfactored row */
2075       bval = ba + bi[k];
2076       jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2077       for (j = jmin; j < jmax; j++){
2078         col = riip[aj[j]];
2079         if (col >= k){ /* only take upper triangular entry */
2080           rtmp[col] = aa[j];
2081           *bval++   = 0.0; /* for in-place factorization */
2082         }
2083       }
2084       /* shift the diagonal of the matrix: ZeropivotApply() */
2085       rtmp[k] += sctx.shift_amount;  /* shift the diagonal of the matrix */
2086 
2087       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
2088       dk = rtmp[k];
2089       i  = c2r[k]; /* first row to be added to k_th row  */
2090 
2091       while (i < k){
2092         nexti = c2r[i]; /* next row to be added to k_th row */
2093 
2094         /* compute multiplier, update diag(k) and U(i,k) */
2095         ili   = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2096         uikdi = - ba[ili]*ba[bdiag[i]];  /* diagonal(k) */
2097         dk   += uikdi*ba[ili]; /* update diag[k] */
2098         ba[ili] = uikdi; /* -U(i,k) */
2099 
2100         /* add multiple of row i to k-th row */
2101         jmin = ili + 1; jmax = bi[i+1];
2102         if (jmin < jmax){
2103           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2104           /* update il and c2r for row i */
2105           il[i] = jmin;
2106           j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i;
2107         }
2108         i = nexti;
2109       }
2110 
2111       /* copy data into U(k,:) */
2112       rs   = 0.0;
2113       jmin = bi[k]; jmax = bi[k+1]-1;
2114       if (jmin < jmax) {
2115         for (j=jmin; j<jmax; j++){
2116           col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]);
2117         }
2118         /* add the k-th row into il and c2r */
2119         il[k] = jmin;
2120         i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k;
2121       }
2122 
2123       /* MatPivotCheck() */
2124       sctx.rs  = rs;
2125       sctx.pv  = dk;
2126       if (info->shiftnz){
2127         ierr = MatPivotCheck_nz(info,sctx,k,newshift);CHKERRQ(ierr);
2128       } else if (info->shiftpd){
2129         ierr = MatPivotCheck_pd(info,sctx,k,newshift);CHKERRQ(ierr);
2130       } else if (info->shiftinblocks){
2131         ierr = MatPivotCheck_inblocks(info,sctx,k,newshift);CHKERRQ(ierr);
2132       } else {
2133         ierr = MatPivotCheck_none(info,sctx,k,newshift);CHKERRQ(ierr);
2134       }
2135       dk = sctx.pv;
2136       if (newshift == 1) break;
2137 
2138       ba[bdiag[k]] = 1.0/dk; /* U(k,k) */
2139     }
2140   } while (sctx.lushift);
2141 
2142   ierr = PetscFree3(rtmp,il,c2r);CHKERRQ(ierr);
2143   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2144   ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr);
2145 
2146   ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
2147   if (perm_identity){
2148     (B)->ops->solve           = MatSolve_SeqSBAIJ_1_NaturalOrdering_newdatastruct;
2149     (B)->ops->solvetranspose  = 0;
2150     (B)->ops->forwardsolve    = 0;
2151     (B)->ops->backwardsolve   = 0;
2152   } else {
2153     (B)->ops->solve           = MatSolve_SeqSBAIJ_1_newdatastruct;
2154     (B)->ops->solvetranspose  = 0;
2155     (B)->ops->forwardsolve    = 0;
2156     (B)->ops->backwardsolve   = 0;
2157   }
2158 
2159   C->assembled    = PETSC_TRUE;
2160   C->preallocated = PETSC_TRUE;
2161   ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr);
2162 
2163   /* MatPivotView() */
2164   if (sctx.nshift){
2165     if (info->shiftpd) {
2166       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);
2167     } else if (info->shiftnz) {
2168       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2169     } else if (info->shiftinblocks){
2170       ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftinblocks);CHKERRQ(ierr);
2171     }
2172   }
2173   PetscFunctionReturn(0);
2174 }
2175 
2176 #undef __FUNCT__
2177 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ"
2178 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info)
2179 {
2180   Mat            C = B;
2181   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
2182   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
2183   IS             ip=b->row,iip = b->icol;
2184   PetscErrorCode ierr;
2185   const PetscInt *rip,*riip;
2186   PetscInt       i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol,*bjtmp;
2187   PetscInt       *ai=a->i,*aj=a->j;
2188   PetscInt       k,jmin,jmax,*jl,*il,col,nexti,ili,nz;
2189   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
2190   PetscReal      zeropivot,rs,shiftnz;
2191   PetscReal      shiftpd;
2192   ChShift_Ctx    sctx;
2193   PetscInt       newshift;
2194   PetscTruth     perm_identity;
2195 
2196   PetscFunctionBegin;
2197   shiftnz   = info->shiftnz;
2198   shiftpd   = info->shiftpd;
2199   zeropivot = info->zeropivot;
2200 
2201   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
2202   ierr  = ISGetIndices(iip,&riip);CHKERRQ(ierr);
2203 
2204   /* initialization */
2205   ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&jl);CHKERRQ(ierr);
2206   sctx.shift_amount = 0;
2207   sctx.nshift       = 0;
2208   do {
2209     sctx.chshift = PETSC_FALSE;
2210     for (i=0; i<mbs; i++) jl[i] = mbs;
2211     il[0] = 0;
2212 
2213     for (k = 0; k<mbs; k++){
2214       /* zero rtmp */
2215       nz = bi[k+1] - bi[k];
2216       bjtmp = bj + bi[k];
2217       for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
2218 
2219       bval = ba + bi[k];
2220       /* initialize k-th row by the perm[k]-th row of A */
2221       jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2222       for (j = jmin; j < jmax; j++){
2223         col = riip[aj[j]];
2224         if (col >= k){ /* only take upper triangular entry */
2225           rtmp[col] = aa[j];
2226           *bval++  = 0.0; /* for in-place factorization */
2227         }
2228       }
2229       /* shift the diagonal of the matrix */
2230       if (sctx.nshift) rtmp[k] += sctx.shift_amount;
2231 
2232       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
2233       dk = rtmp[k];
2234       i = jl[k]; /* first row to be added to k_th row  */
2235 
2236       while (i < k){
2237         nexti = jl[i]; /* next row to be added to k_th row */
2238 
2239         /* compute multiplier, update diag(k) and U(i,k) */
2240         ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2241         uikdi = - ba[ili]*ba[bi[i]];  /* diagonal(k) */
2242         dk += uikdi*ba[ili];
2243         ba[ili] = uikdi; /* -U(i,k) */
2244 
2245         /* add multiple of row i to k-th row */
2246         jmin = ili + 1; jmax = bi[i+1];
2247         if (jmin < jmax){
2248           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2249           /* update il and jl for row i */
2250           il[i] = jmin;
2251           j = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
2252         }
2253         i = nexti;
2254       }
2255 
2256       /* shift the diagonals when zero pivot is detected */
2257       /* compute rs=sum of abs(off-diagonal) */
2258       rs   = 0.0;
2259       jmin = bi[k]+1;
2260       nz   = bi[k+1] - jmin;
2261       bcol = bj + jmin;
2262       for (j=0; j<nz; j++) {
2263         rs += PetscAbsScalar(rtmp[bcol[j]]);
2264       }
2265 
2266       sctx.rs = rs;
2267       sctx.pv = dk;
2268       ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr);
2269 
2270       if (newshift == 1) {
2271         if (!sctx.shift_amount) {
2272           sctx.shift_amount = 1e-5;
2273         }
2274         break;
2275       }
2276 
2277       /* copy data into U(k,:) */
2278       ba[bi[k]] = 1.0/dk; /* U(k,k) */
2279       jmin = bi[k]+1; jmax = bi[k+1];
2280       if (jmin < jmax) {
2281         for (j=jmin; j<jmax; j++){
2282           col = bj[j]; ba[j] = rtmp[col];
2283         }
2284         /* add the k-th row into il and jl */
2285         il[k] = jmin;
2286         i = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
2287       }
2288     }
2289   } while (sctx.chshift);
2290   ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr);
2291   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2292   ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr);
2293 
2294   ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
2295   if (perm_identity){
2296     (B)->ops->solve           = MatSolve_SeqSBAIJ_1_NaturalOrdering;
2297     (B)->ops->solvetranspose  = MatSolve_SeqSBAIJ_1_NaturalOrdering;
2298     (B)->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering;
2299     (B)->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering;
2300   } else {
2301     (B)->ops->solve           = MatSolve_SeqSBAIJ_1;
2302     (B)->ops->solvetranspose  = MatSolve_SeqSBAIJ_1;
2303     (B)->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1;
2304     (B)->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1;
2305   }
2306 
2307   C->assembled    = PETSC_TRUE;
2308   C->preallocated = PETSC_TRUE;
2309   ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr);
2310   if (sctx.nshift){
2311     if (shiftnz) {
2312       ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2313     } else if (shiftpd) {
2314       ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2315     }
2316   }
2317   PetscFunctionReturn(0);
2318 }
2319 
2320 /*
2321    icc() under revised new data structure.
2322    Factored arrays bj and ba are stored as
2323      U(0,:),...,U(i,:),U(n-1,:)
2324 
2325    ui=fact->i is an array of size n+1, in which
2326    ui+
2327      ui[i]:  points to 1st entry of U(i,:),i=0,...,n-1
2328      ui[n]:  points to U(n-1,n-1)+1
2329 
2330   udiag=fact->diag is an array of size n,in which
2331      udiag[i]: points to diagonal of U(i,:), i=0,...,n-1
2332 
2333    U(i,:) contains udiag[i] as its last entry, i.e.,
2334     U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i])
2335 */
2336 
2337 #undef __FUNCT__
2338 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ_newdatastruct"
2339 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2340 {
2341   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2342   Mat_SeqSBAIJ       *b;
2343   PetscErrorCode     ierr;
2344   PetscTruth         perm_identity,missing;
2345   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag;
2346   const PetscInt     *rip,*riip;
2347   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
2348   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL,d;
2349   PetscInt           ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
2350   PetscReal          fill=info->fill,levels=info->levels;
2351   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2352   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
2353   PetscBT            lnkbt;
2354   IS                 iperm;
2355 
2356   PetscFunctionBegin;
2357   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);
2358   ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
2359   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
2360   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2361   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2362 
2363   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2364   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2365   ui[0] = 0;
2366 
2367   /* ICC(0) without matrix ordering: simply rearrange column indices */
2368   if (!levels && perm_identity) {
2369     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2370     cols = uj;
2371     for (i=0; i<am; i++) {
2372       ncols    = ai[i+1] - a->diag[i];
2373       ui[i+1]  = ui[i] + ncols;
2374       udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */
2375 
2376       aj   = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */
2377       ncols--; /* exclude diagonal */
2378       for (j=0; j<ncols; j++) *cols++ = aj[j];
2379       *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */
2380     }
2381   } else { /* case: levels>0 || (levels=0 && !perm_identity) */
2382     ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2383     ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2384 
2385     /* initialization */
2386     ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr);
2387 
2388     /* jl: linked list for storing indices of the pivot rows
2389        il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2390     ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr);
2391     for (i=0; i<am; i++){
2392       jl[i] = am; il[i] = 0;
2393     }
2394 
2395     /* create and initialize a linked list for storing column indices of the active row k */
2396     nlnk = am + 1;
2397     ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2398 
2399     /* initial FreeSpace size is fill*(ai[am]+1) */
2400     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2401     current_space = free_space;
2402     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr);
2403     current_space_lvl = free_space_lvl;
2404 
2405     for (k=0; k<am; k++){  /* for each active row k */
2406       /* initialize lnk by the column indices of row rip[k] of A */
2407       nzk   = 0;
2408       ncols = ai[rip[k]+1] - ai[rip[k]];
2409       if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2410       ncols_upper = 0;
2411       for (j=0; j<ncols; j++){
2412         i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2413         if (riip[i] >= k){ /* only take upper triangular entry */
2414           ajtmp[ncols_upper] = i;
2415           ncols_upper++;
2416         }
2417       }
2418       ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2419       nzk += nlnk;
2420 
2421       /* update lnk by computing fill-in for each pivot row to be merged in */
2422       prow = jl[k]; /* 1st pivot row */
2423 
2424       while (prow < k){
2425         nextprow = jl[prow];
2426 
2427         /* merge prow into k-th row */
2428         jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2429         jmax = ui[prow+1];
2430         ncols = jmax-jmin;
2431         i     = jmin - ui[prow];
2432         cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2433         uj    = uj_lvl_ptr[prow] + i; /* levels of cols */
2434         j     = *(uj - 1);
2435         ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr);
2436         nzk += nlnk;
2437 
2438         /* update il and jl for prow */
2439         if (jmin < jmax){
2440           il[prow] = jmin;
2441           j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2442         }
2443         prow = nextprow;
2444       }
2445 
2446       /* if free space is not available, make more free space */
2447       if (current_space->local_remaining<nzk) {
2448         i  = am - k + 1; /* num of unfactored rows */
2449         i *= PetscMin(nzk, i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */
2450         ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2451         ierr = PetscFreeSpaceGet(i,&current_space_lvl);CHKERRQ(ierr);
2452         reallocs++;
2453       }
2454 
2455       /* copy data into free_space and free_space_lvl, then initialize lnk */
2456       if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2457       ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
2458 
2459       /* add the k-th row into il and jl */
2460       if (nzk > 1){
2461         i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2462         jl[k] = jl[i]; jl[i] = k;
2463         il[k] = ui[k] + 1;
2464       }
2465       uj_ptr[k]     = current_space->array;
2466       uj_lvl_ptr[k] = current_space_lvl->array;
2467 
2468       current_space->array           += nzk;
2469       current_space->local_used      += nzk;
2470       current_space->local_remaining -= nzk;
2471 
2472       current_space_lvl->array           += nzk;
2473       current_space_lvl->local_used      += nzk;
2474       current_space_lvl->local_remaining -= nzk;
2475 
2476       ui[k+1] = ui[k] + nzk;
2477     }
2478 
2479 #if defined(PETSC_USE_INFO)
2480     if (ai[am] != 0) {
2481       PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]);
2482       ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2483       ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2484       ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2485     } else {
2486       ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2487     }
2488 #endif
2489 
2490     ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2491     ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2492     ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr);
2493     ierr = PetscFree(ajtmp);CHKERRQ(ierr);
2494 
2495     /* destroy list of free space and other temporary array(s) */
2496     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2497     ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor in newdatastruct */
2498     ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2499     ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2500 
2501   } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2502 
2503   /* put together the new matrix in MATSEQSBAIJ format */
2504 
2505   b    = (Mat_SeqSBAIJ*)(fact)->data;
2506   b->singlemalloc = PETSC_FALSE;
2507   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2508   b->j    = uj;
2509   b->i    = ui;
2510   b->diag = udiag;
2511   b->free_diag = PETSC_TRUE;
2512   b->ilen = 0;
2513   b->imax = 0;
2514   b->row  = perm;
2515   b->col  = perm;
2516   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2517   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2518   b->icol = iperm;
2519   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2520   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2521   ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2522   b->maxnz   = b->nz = ui[am];
2523   b->free_a  = PETSC_TRUE;
2524   b->free_ij = PETSC_TRUE;
2525 
2526   (fact)->info.factor_mallocs    = reallocs;
2527   (fact)->info.fill_ratio_given  = fill;
2528   if (ai[am] != 0) {
2529     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2530   } else {
2531     (fact)->info.fill_ratio_needed = 0.0;
2532   }
2533   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_newdatastruct;
2534   PetscFunctionReturn(0);
2535 }
2536 
2537 #undef __FUNCT__
2538 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ"
2539 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2540 {
2541   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2542   Mat_SeqSBAIJ       *b;
2543   PetscErrorCode     ierr;
2544   PetscTruth         perm_identity,missing;
2545   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag;
2546   const PetscInt     *rip,*riip;
2547   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
2548   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL,d;
2549   PetscInt           ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
2550   PetscReal          fill=info->fill,levels=info->levels;
2551   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2552   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
2553   PetscBT            lnkbt;
2554   IS                 iperm;
2555   PetscTruth         newdatastruct=PETSC_FALSE;
2556 
2557   PetscFunctionBegin;
2558   ierr = PetscOptionsGetTruth(PETSC_NULL,"-icc_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
2559   if(newdatastruct){
2560     ierr = MatICCFactorSymbolic_SeqAIJ_newdatastruct(fact,A,perm,info);CHKERRQ(ierr);
2561     PetscFunctionReturn(0);
2562   }
2563 
2564   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);
2565   ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
2566   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
2567   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2568   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2569 
2570   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2571   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2572   ui[0] = 0;
2573 
2574   /* ICC(0) without matrix ordering: simply copies fill pattern */
2575   if (!levels && perm_identity) {
2576 
2577     for (i=0; i<am; i++) {
2578       ui[i+1]  = ui[i] + ai[i+1] - a->diag[i];
2579       udiag[i] = ui[i];
2580     }
2581     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2582     cols = uj;
2583     for (i=0; i<am; i++) {
2584       aj    = a->j + a->diag[i];
2585       ncols = ui[i+1] - ui[i];
2586       for (j=0; j<ncols; j++) *cols++ = *aj++;
2587     }
2588   } else { /* case: levels>0 || (levels=0 && !perm_identity) */
2589     ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2590     ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2591 
2592     /* initialization */
2593     ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr);
2594 
2595     /* jl: linked list for storing indices of the pivot rows
2596        il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2597     ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr);
2598     for (i=0; i<am; i++){
2599       jl[i] = am; il[i] = 0;
2600     }
2601 
2602     /* create and initialize a linked list for storing column indices of the active row k */
2603     nlnk = am + 1;
2604     ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2605 
2606     /* initial FreeSpace size is fill*(ai[am]+1) */
2607     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2608     current_space = free_space;
2609     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr);
2610     current_space_lvl = free_space_lvl;
2611 
2612     for (k=0; k<am; k++){  /* for each active row k */
2613       /* initialize lnk by the column indices of row rip[k] of A */
2614       nzk   = 0;
2615       ncols = ai[rip[k]+1] - ai[rip[k]];
2616       if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2617       ncols_upper = 0;
2618       for (j=0; j<ncols; j++){
2619         i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2620         if (riip[i] >= k){ /* only take upper triangular entry */
2621           ajtmp[ncols_upper] = i;
2622           ncols_upper++;
2623         }
2624       }
2625       ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2626       nzk += nlnk;
2627 
2628       /* update lnk by computing fill-in for each pivot row to be merged in */
2629       prow = jl[k]; /* 1st pivot row */
2630 
2631       while (prow < k){
2632         nextprow = jl[prow];
2633 
2634         /* merge prow into k-th row */
2635         jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2636         jmax = ui[prow+1];
2637         ncols = jmax-jmin;
2638         i     = jmin - ui[prow];
2639         cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2640         uj    = uj_lvl_ptr[prow] + i; /* levels of cols */
2641         j     = *(uj - 1);
2642         ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr);
2643         nzk += nlnk;
2644 
2645         /* update il and jl for prow */
2646         if (jmin < jmax){
2647           il[prow] = jmin;
2648           j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2649         }
2650         prow = nextprow;
2651       }
2652 
2653       /* if free space is not available, make more free space */
2654       if (current_space->local_remaining<nzk) {
2655         i = am - k + 1; /* num of unfactored rows */
2656         i *= PetscMin(nzk, (i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2657         ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2658         ierr = PetscFreeSpaceGet(i,&current_space_lvl);CHKERRQ(ierr);
2659         reallocs++;
2660       }
2661 
2662       /* copy data into free_space and free_space_lvl, then initialize lnk */
2663       if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2664       ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
2665 
2666       /* add the k-th row into il and jl */
2667       if (nzk > 1){
2668         i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2669         jl[k] = jl[i]; jl[i] = k;
2670         il[k] = ui[k] + 1;
2671       }
2672       uj_ptr[k]     = current_space->array;
2673       uj_lvl_ptr[k] = current_space_lvl->array;
2674 
2675       current_space->array           += nzk;
2676       current_space->local_used      += nzk;
2677       current_space->local_remaining -= nzk;
2678 
2679       current_space_lvl->array           += nzk;
2680       current_space_lvl->local_used      += nzk;
2681       current_space_lvl->local_remaining -= nzk;
2682 
2683       ui[k+1] = ui[k] + nzk;
2684     }
2685 
2686 #if defined(PETSC_USE_INFO)
2687     if (ai[am] != 0) {
2688       PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]);
2689       ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2690       ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2691       ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2692     } else {
2693       ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2694     }
2695 #endif
2696 
2697     ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2698     ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2699     ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr);
2700     ierr = PetscFree(ajtmp);CHKERRQ(ierr);
2701 
2702     /* destroy list of free space and other temporary array(s) */
2703     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2704     ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
2705     ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2706     ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2707 
2708   } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2709 
2710   /* put together the new matrix in MATSEQSBAIJ format */
2711 
2712   b    = (Mat_SeqSBAIJ*)(fact)->data;
2713   b->singlemalloc = PETSC_FALSE;
2714   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2715   b->j    = uj;
2716   b->i    = ui;
2717   b->diag = udiag;
2718   b->free_diag = PETSC_TRUE;
2719   b->ilen = 0;
2720   b->imax = 0;
2721   b->row  = perm;
2722   b->col  = perm;
2723   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2724   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2725   b->icol = iperm;
2726   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2727   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2728   ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2729   b->maxnz   = b->nz = ui[am];
2730   b->free_a  = PETSC_TRUE;
2731   b->free_ij = PETSC_TRUE;
2732 
2733   (fact)->info.factor_mallocs    = reallocs;
2734   (fact)->info.fill_ratio_given  = fill;
2735   if (ai[am] != 0) {
2736     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2737   } else {
2738     (fact)->info.fill_ratio_needed = 0.0;
2739   }
2740   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2741   PetscFunctionReturn(0);
2742 }
2743 
2744 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2745 {
2746   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2747   Mat_SeqSBAIJ       *b;
2748   PetscErrorCode     ierr;
2749   PetscTruth         perm_identity;
2750   PetscReal          fill = info->fill;
2751   const PetscInt     *rip,*riip;
2752   PetscInt           i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow;
2753   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
2754   PetscInt           nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr,*udiag;
2755   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2756   PetscBT            lnkbt;
2757   IS                 iperm;
2758 
2759   PetscFunctionBegin;
2760   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);
2761   /* check whether perm is the identity mapping */
2762   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2763   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2764   ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2765   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2766 
2767   /* initialization */
2768   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2769   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2770   ui[0] = 0;
2771 
2772   /* jl: linked list for storing indices of the pivot rows
2773      il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2774   ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr);
2775   for (i=0; i<am; i++){
2776     jl[i] = am; il[i] = 0;
2777   }
2778 
2779   /* create and initialize a linked list for storing column indices of the active row k */
2780   nlnk = am + 1;
2781   ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2782 
2783   /* initial FreeSpace size is fill*(ai[am]+1) */
2784   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2785   current_space = free_space;
2786 
2787   for (k=0; k<am; k++){  /* for each active row k */
2788     /* initialize lnk by the column indices of row rip[k] of A */
2789     nzk   = 0;
2790     ncols = ai[rip[k]+1] - ai[rip[k]];
2791     if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2792     ncols_upper = 0;
2793     for (j=0; j<ncols; j++){
2794       i = riip[*(aj + ai[rip[k]] + j)];
2795       if (i >= k){ /* only take upper triangular entry */
2796         cols[ncols_upper] = i;
2797         ncols_upper++;
2798       }
2799     }
2800     ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2801     nzk += nlnk;
2802 
2803     /* update lnk by computing fill-in for each pivot row to be merged in */
2804     prow = jl[k]; /* 1st pivot row */
2805 
2806     while (prow < k){
2807       nextprow = jl[prow];
2808       /* merge prow into k-th row */
2809       jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2810       jmax = ui[prow+1];
2811       ncols = jmax-jmin;
2812       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2813       ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2814       nzk += nlnk;
2815 
2816       /* update il and jl for prow */
2817       if (jmin < jmax){
2818         il[prow] = jmin;
2819         j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
2820       }
2821       prow = nextprow;
2822     }
2823 
2824     /* if free space is not available, make more free space */
2825     if (current_space->local_remaining<nzk) {
2826       i  = am - k + 1; /* num of unfactored rows */
2827       i *= PetscMin(nzk,i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */
2828       ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2829       reallocs++;
2830     }
2831 
2832     /* copy data into free space, then initialize lnk */
2833     ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
2834 
2835     /* add the k-th row into il and jl */
2836     if (nzk-1 > 0){
2837       i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2838       jl[k] = jl[i]; jl[i] = k;
2839       il[k] = ui[k] + 1;
2840     }
2841     ui_ptr[k] = current_space->array;
2842     current_space->array           += nzk;
2843     current_space->local_used      += nzk;
2844     current_space->local_remaining -= nzk;
2845 
2846     ui[k+1] = ui[k] + nzk;
2847   }
2848 
2849 #if defined(PETSC_USE_INFO)
2850   if (ai[am] != 0) {
2851     PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]);
2852     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2853     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2854     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2855   } else {
2856      ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2857   }
2858 #endif
2859 
2860   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2861   ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2862   ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr);
2863 
2864   /* destroy list of free space and other temporary array(s) */
2865   ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2866   ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor in newdatastruct */
2867   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2868 
2869   /* put together the new matrix in MATSEQSBAIJ format */
2870 
2871   b = (Mat_SeqSBAIJ*)(fact)->data;
2872   b->singlemalloc = PETSC_FALSE;
2873   b->free_a       = PETSC_TRUE;
2874   b->free_ij      = PETSC_TRUE;
2875   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2876   b->j    = uj;
2877   b->i    = ui;
2878   b->diag = udiag;
2879   b->free_diag = PETSC_TRUE;
2880   b->ilen = 0;
2881   b->imax = 0;
2882   b->row  = perm;
2883   b->col  = perm;
2884   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2885   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2886   b->icol = iperm;
2887   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2888   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2889   ierr    = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2890   b->maxnz = b->nz = ui[am];
2891 
2892   (fact)->info.factor_mallocs    = reallocs;
2893   (fact)->info.fill_ratio_given  = fill;
2894   if (ai[am] != 0) {
2895     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2896   } else {
2897     (fact)->info.fill_ratio_needed = 0.0;
2898   }
2899   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_newdatastruct;
2900   PetscFunctionReturn(0);
2901 }
2902 
2903 #undef __FUNCT__
2904 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ"
2905 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2906 {
2907   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2908   Mat_SeqSBAIJ       *b;
2909   PetscErrorCode     ierr;
2910   PetscTruth         perm_identity;
2911   PetscReal          fill = info->fill;
2912   const PetscInt     *rip,*riip;
2913   PetscInt           i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow;
2914   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
2915   PetscInt           nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr;
2916   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2917   PetscBT            lnkbt;
2918   IS                 iperm;
2919   PetscTruth         newdatastruct=PETSC_FALSE;
2920 
2921   PetscFunctionBegin;
2922   ierr = PetscOptionsGetTruth(PETSC_NULL,"-cholesky_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
2923   if(newdatastruct){
2924     ierr = MatCholeskyFactorSymbolic_SeqAIJ_newdatastruct(fact,A,perm,info);CHKERRQ(ierr);
2925     PetscFunctionReturn(0);
2926   }
2927 
2928   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);
2929   /* check whether perm is the identity mapping */
2930   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2931   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2932   ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2933   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2934 
2935   /* initialization */
2936   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2937   ui[0] = 0;
2938 
2939   /* jl: linked list for storing indices of the pivot rows
2940      il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2941   ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr);
2942   for (i=0; i<am; i++){
2943     jl[i] = am; il[i] = 0;
2944   }
2945 
2946   /* create and initialize a linked list for storing column indices of the active row k */
2947   nlnk = am + 1;
2948   ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2949 
2950   /* initial FreeSpace size is fill*(ai[am]+1) */
2951   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2952   current_space = free_space;
2953 
2954   for (k=0; k<am; k++){  /* for each active row k */
2955     /* initialize lnk by the column indices of row rip[k] of A */
2956     nzk   = 0;
2957     ncols = ai[rip[k]+1] - ai[rip[k]];
2958     if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2959     ncols_upper = 0;
2960     for (j=0; j<ncols; j++){
2961       i = riip[*(aj + ai[rip[k]] + j)];
2962       if (i >= k){ /* only take upper triangular entry */
2963         cols[ncols_upper] = i;
2964         ncols_upper++;
2965       }
2966     }
2967     ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2968     nzk += nlnk;
2969 
2970     /* update lnk by computing fill-in for each pivot row to be merged in */
2971     prow = jl[k]; /* 1st pivot row */
2972 
2973     while (prow < k){
2974       nextprow = jl[prow];
2975       /* merge prow into k-th row */
2976       jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2977       jmax = ui[prow+1];
2978       ncols = jmax-jmin;
2979       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2980       ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2981       nzk += nlnk;
2982 
2983       /* update il and jl for prow */
2984       if (jmin < jmax){
2985         il[prow] = jmin;
2986         j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
2987       }
2988       prow = nextprow;
2989     }
2990 
2991     /* if free space is not available, make more free space */
2992     if (current_space->local_remaining<nzk) {
2993       i = am - k + 1; /* num of unfactored rows */
2994       i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2995       ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2996       reallocs++;
2997     }
2998 
2999     /* copy data into free space, then initialize lnk */
3000     ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
3001 
3002     /* add the k-th row into il and jl */
3003     if (nzk-1 > 0){
3004       i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
3005       jl[k] = jl[i]; jl[i] = k;
3006       il[k] = ui[k] + 1;
3007     }
3008     ui_ptr[k] = current_space->array;
3009     current_space->array           += nzk;
3010     current_space->local_used      += nzk;
3011     current_space->local_remaining -= nzk;
3012 
3013     ui[k+1] = ui[k] + nzk;
3014   }
3015 
3016 #if defined(PETSC_USE_INFO)
3017   if (ai[am] != 0) {
3018     PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]);
3019     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
3020     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
3021     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
3022   } else {
3023      ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
3024   }
3025 #endif
3026 
3027   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
3028   ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
3029   ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr);
3030 
3031   /* destroy list of free space and other temporary array(s) */
3032   ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
3033   ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
3034   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
3035 
3036   /* put together the new matrix in MATSEQSBAIJ format */
3037 
3038   b = (Mat_SeqSBAIJ*)(fact)->data;
3039   b->singlemalloc = PETSC_FALSE;
3040   b->free_a       = PETSC_TRUE;
3041   b->free_ij      = PETSC_TRUE;
3042   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
3043   b->j    = uj;
3044   b->i    = ui;
3045   b->diag = 0;
3046   b->ilen = 0;
3047   b->imax = 0;
3048   b->row  = perm;
3049   b->col  = perm;
3050   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
3051   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
3052   b->icol = iperm;
3053   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
3054   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
3055   ierr    = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
3056   b->maxnz = b->nz = ui[am];
3057 
3058   (fact)->info.factor_mallocs    = reallocs;
3059   (fact)->info.fill_ratio_given  = fill;
3060   if (ai[am] != 0) {
3061     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
3062   } else {
3063     (fact)->info.fill_ratio_needed = 0.0;
3064   }
3065   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
3066   PetscFunctionReturn(0);
3067 }
3068 
3069 #undef __FUNCT__
3070 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_newdatastruct"
3071 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx)
3072 {
3073   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
3074   PetscErrorCode    ierr;
3075   PetscInt          n = A->rmap->n;
3076   const PetscInt    *ai = a->i,*aj = a->j,*adiag = a->diag,*vi;
3077   PetscScalar       *x,sum;
3078   const PetscScalar *b;
3079   const MatScalar   *aa = a->a,*v;
3080   PetscInt          i,nz;
3081 
3082   PetscFunctionBegin;
3083   if (!n) PetscFunctionReturn(0);
3084 
3085   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3086   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3087 
3088   /* forward solve the lower triangular */
3089   x[0] = b[0];
3090   v    = aa;
3091   vi   = aj;
3092   for (i=1; i<n; i++) {
3093     nz  = ai[i+1] - ai[i];
3094     sum = b[i];
3095     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
3096     v  += nz;
3097     vi += nz;
3098     x[i] = sum;
3099   }
3100 
3101   /* backward solve the upper triangular */
3102   for (i=n-1; i>=0; i--){
3103     v   = aa + adiag[i+1] + 1;
3104     vi  = aj + adiag[i+1] + 1;
3105     nz = adiag[i] - adiag[i+1]-1;
3106     sum = x[i];
3107     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
3108     x[i] = sum*v[nz]; /* x[i]=aa[adiag[i]]*sum; v++; */
3109   }
3110 
3111   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
3112   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3113   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3114   PetscFunctionReturn(0);
3115 }
3116 
3117 #undef __FUNCT__
3118 #define __FUNCT__ "MatSolve_SeqAIJ_newdatastruct"
3119 PetscErrorCode MatSolve_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec xx)
3120 {
3121   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
3122   IS                iscol = a->col,isrow = a->row;
3123   PetscErrorCode    ierr;
3124   PetscInt          i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz;
3125   const PetscInt    *rout,*cout,*r,*c;
3126   PetscScalar       *x,*tmp,sum;
3127   const PetscScalar *b;
3128   const MatScalar   *aa = a->a,*v;
3129 
3130   PetscFunctionBegin;
3131   if (!n) PetscFunctionReturn(0);
3132 
3133   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3134   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3135   tmp  = a->solve_work;
3136 
3137   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
3138   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
3139 
3140   /* forward solve the lower triangular */
3141   tmp[0] = b[r[0]];
3142   v      = aa;
3143   vi     = aj;
3144   for (i=1; i<n; i++) {
3145     nz  = ai[i+1] - ai[i];
3146     sum = b[r[i]];
3147     PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
3148     tmp[i] = sum;
3149     v += nz; vi += nz;
3150   }
3151 
3152   /* backward solve the upper triangular */
3153   for (i=n-1; i>=0; i--){
3154     v   = aa + adiag[i+1]+1;
3155     vi  = aj + adiag[i+1]+1;
3156     nz  = adiag[i]-adiag[i+1]-1;
3157     sum = tmp[i];
3158     PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
3159     x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */
3160   }
3161 
3162   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
3163   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
3164   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3165   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3166   ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr);
3167   PetscFunctionReturn(0);
3168 }
3169 
3170 #undef __FUNCT__
3171 #define __FUNCT__ "MatILUDTFactor_SeqAIJ"
3172 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact)
3173 {
3174   Mat                B = *fact;
3175   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b;
3176   IS                 isicol;
3177   PetscErrorCode     ierr;
3178   const PetscInt     *r,*ic;
3179   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag;
3180   PetscInt           *bi,*bj,*bdiag,*bdiag_rev;
3181   PetscInt           row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au;
3182   PetscInt           nlnk,*lnk;
3183   PetscBT            lnkbt;
3184   PetscTruth         row_identity,icol_identity,both_identity;
3185   MatScalar          *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp;
3186   const PetscInt     *ics;
3187   PetscInt           j,nz,*pj,*bjtmp,k,ncut,*jtmp;
3188   PetscReal          dt=info->dt,dtcol=info->dtcol,shift=info->shiftinblocks;
3189   PetscInt           dtcount=(PetscInt)info->dtcount,nnz_max;
3190   PetscTruth         missing;
3191 
3192   PetscFunctionBegin;
3193 
3194   if (dt      == PETSC_DEFAULT) dt      = 0.005;
3195   if (dtcol   == PETSC_DEFAULT) dtcol   = 0.01; /* XXX unused! */
3196   if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax);
3197 
3198   /* ------- symbolic factorization, can be reused ---------*/
3199   ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
3200   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
3201   adiag=a->diag;
3202 
3203   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
3204 
3205   /* bdiag is location of diagonal in factor */
3206   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);     /* becomes b->diag */
3207   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag_rev);CHKERRQ(ierr); /* temporary */
3208 
3209   /* allocate row pointers bi */
3210   ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
3211 
3212   /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */
3213   if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */
3214   nnz_max  = ai[n]+2*n*dtcount+2;
3215 
3216   ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
3217   ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr);
3218 
3219   /* put together the new matrix */
3220   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
3221   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
3222   b    = (Mat_SeqAIJ*)(B)->data;
3223   b->free_a       = PETSC_TRUE;
3224   b->free_ij      = PETSC_TRUE;
3225   b->singlemalloc = PETSC_FALSE;
3226   b->a          = ba;
3227   b->j          = bj;
3228   b->i          = bi;
3229   b->diag       = bdiag;
3230   b->ilen       = 0;
3231   b->imax       = 0;
3232   b->row        = isrow;
3233   b->col        = iscol;
3234   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
3235   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
3236   b->icol       = isicol;
3237   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
3238 
3239   ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
3240   b->maxnz = nnz_max;
3241 
3242   (B)->factor                = MAT_FACTOR_ILUDT;
3243   (B)->info.factor_mallocs   = 0;
3244   (B)->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]);
3245   CHKMEMQ;
3246   /* ------- end of symbolic factorization ---------*/
3247 
3248   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
3249   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
3250   ics  = ic;
3251 
3252   /* linked list for storing column indices of the active row */
3253   nlnk = n + 1;
3254   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3255 
3256   /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */
3257   ierr = PetscMalloc2(n,PetscInt,&im,n,PetscInt,&jtmp);CHKERRQ(ierr);
3258   /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */
3259   ierr = PetscMalloc2(n,MatScalar,&rtmp,n,MatScalar,&vtmp);CHKERRQ(ierr);
3260   ierr = PetscMemzero(rtmp,n*sizeof(MatScalar));CHKERRQ(ierr);
3261 
3262   bi[0]    = 0;
3263   bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */
3264   bdiag_rev[n] = bdiag[0];
3265   bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */
3266   for (i=0; i<n; i++) {
3267     /* copy initial fill into linked list */
3268     nzi = 0; /* nonzeros for active row i */
3269     nzi = ai[r[i]+1] - ai[r[i]];
3270     if (!nzi) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
3271     nzi_al = adiag[r[i]] - ai[r[i]];
3272     nzi_au = ai[r[i]+1] - adiag[r[i]] -1;
3273     ajtmp = aj + ai[r[i]];
3274     ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3275 
3276     /* load in initial (unfactored row) */
3277     aatmp = a->a + ai[r[i]];
3278     for (j=0; j<nzi; j++) {
3279       rtmp[ics[*ajtmp++]] = *aatmp++;
3280     }
3281 
3282     /* add pivot rows into linked list */
3283     row = lnk[n];
3284     while (row < i ) {
3285       nzi_bl = bi[row+1] - bi[row] + 1;
3286       bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */
3287       ierr  = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr);
3288       nzi  += nlnk;
3289       row   = lnk[row];
3290     }
3291 
3292     /* copy data from lnk into jtmp, then initialize lnk */
3293     ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr);
3294 
3295     /* numerical factorization */
3296     bjtmp = jtmp;
3297     row   = *bjtmp++; /* 1st pivot row */
3298     while  ( row < i ) {
3299       pc         = rtmp + row;
3300       pv         = ba + bdiag[row]; /* 1./(diag of the pivot row) */
3301       multiplier = (*pc) * (*pv);
3302       *pc        = multiplier;
3303       if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */
3304         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
3305         pv         = ba + bdiag[row+1] + 1;
3306         /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */
3307         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
3308         for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
3309         ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
3310       }
3311       row = *bjtmp++;
3312     }
3313 
3314     /* copy sparse rtmp into contiguous vtmp; separate L and U part */
3315     diag_tmp = rtmp[i];  /* save diagonal value - may not needed?? */
3316     nzi_bl = 0; j = 0;
3317     while (jtmp[j] < i){ /* Note: jtmp is sorted */
3318       vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
3319       nzi_bl++; j++;
3320     }
3321     nzi_bu = nzi - nzi_bl -1;
3322     while (j < nzi){
3323       vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
3324       j++;
3325     }
3326 
3327     bjtmp = bj + bi[i];
3328     batmp = ba + bi[i];
3329     /* apply level dropping rule to L part */
3330     ncut = nzi_al + dtcount;
3331     if (ncut < nzi_bl){
3332       ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr);
3333       ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr);
3334     } else {
3335       ncut = nzi_bl;
3336     }
3337     for (j=0; j<ncut; j++){
3338       bjtmp[j] = jtmp[j];
3339       batmp[j] = vtmp[j];
3340       /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */
3341     }
3342     bi[i+1] = bi[i] + ncut;
3343     nzi = ncut + 1;
3344 
3345     /* apply level dropping rule to U part */
3346     ncut = nzi_au + dtcount;
3347     if (ncut < nzi_bu){
3348       ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr);
3349       ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr);
3350     } else {
3351       ncut = nzi_bu;
3352     }
3353     nzi += ncut;
3354 
3355     /* mark bdiagonal */
3356     bdiag[i+1]       = bdiag[i] - (ncut + 1);
3357     bdiag_rev[n-i-1] = bdiag[i+1];
3358     bi[2*n - i]      = bi[2*n - i +1] - (ncut + 1);
3359     bjtmp = bj + bdiag[i];
3360     batmp = ba + bdiag[i];
3361     *bjtmp = i;
3362     *batmp = diag_tmp; /* rtmp[i]; */
3363     if (*batmp == 0.0) {
3364       *batmp = dt+shift;
3365       /* printf(" row %d add shift %g\n",i,shift); */
3366     }
3367     *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */
3368     /* printf(" (%d,%g),",*bjtmp,*batmp); */
3369 
3370     bjtmp = bj + bdiag[i+1]+1;
3371     batmp = ba + bdiag[i+1]+1;
3372     for (k=0; k<ncut; k++){
3373       bjtmp[k] = jtmp[nzi_bl+1+k];
3374       batmp[k] = vtmp[nzi_bl+1+k];
3375       /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */
3376     }
3377     /* printf("\n"); */
3378 
3379     im[i]   = nzi; /* used by PetscLLAddSortedLU() */
3380     /*
3381     printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]);
3382     printf(" ----------------------------\n");
3383     */
3384   } /* for (i=0; i<n; i++) */
3385   /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */
3386   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]);
3387 
3388   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
3389   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
3390 
3391   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
3392   ierr = PetscFree2(im,jtmp);CHKERRQ(ierr);
3393   ierr = PetscFree2(rtmp,vtmp);CHKERRQ(ierr);
3394   ierr = PetscFree(bdiag_rev);CHKERRQ(ierr);
3395 
3396   ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr);
3397   b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n];
3398 
3399   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
3400   ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr);
3401   both_identity = (PetscTruth) (row_identity && icol_identity);
3402   if (row_identity && icol_identity) {
3403     B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct;
3404   } else {
3405     B->ops->solve = MatSolve_SeqAIJ_newdatastruct;
3406   }
3407 
3408   B->ops->lufactorsymbolic  = MatILUDTFactorSymbolic_SeqAIJ;
3409   B->ops->lufactornumeric   = MatILUDTFactorNumeric_SeqAIJ;
3410   B->ops->solveadd          = 0;
3411   B->ops->solvetranspose    = 0;
3412   B->ops->solvetransposeadd = 0;
3413   B->ops->matsolve          = 0;
3414   B->assembled              = PETSC_TRUE;
3415   B->preallocated           = PETSC_TRUE;
3416   PetscFunctionReturn(0);
3417 }
3418 
3419 /* a wraper of MatILUDTFactor_SeqAIJ() */
3420 #undef __FUNCT__
3421 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ"
3422 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info)
3423 {
3424   PetscErrorCode     ierr;
3425 
3426   PetscFunctionBegin;
3427   ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr);
3428 
3429   fact->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ;
3430   PetscFunctionReturn(0);
3431 }
3432 
3433 /*
3434    same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors
3435    - intend to replace existing MatLUFactorNumeric_SeqAIJ()
3436 */
3437 #undef __FUNCT__
3438 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ"
3439 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info)
3440 {
3441   Mat            C=fact;
3442   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
3443   IS             isrow = b->row,isicol = b->icol;
3444   PetscErrorCode ierr;
3445   const PetscInt *r,*ic,*ics;
3446   PetscInt       i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
3447   PetscInt       *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj;
3448   MatScalar      *rtmp,*pc,multiplier,*v,*pv,*aa=a->a;
3449   PetscReal      dt=info->dt,shift=info->shiftinblocks;
3450   PetscTruth     row_identity, col_identity;
3451 
3452   PetscFunctionBegin;
3453   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
3454   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
3455   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
3456   ics  = ic;
3457 
3458   for (i=0; i<n; i++){
3459     /* initialize rtmp array */
3460     nzl   = bi[i+1] - bi[i];       /* num of nozeros in L(i,:) */
3461     bjtmp = bj + bi[i];
3462     for  (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0;
3463     rtmp[i] = 0.0;
3464     nzu   = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */
3465     bjtmp = bj + bdiag[i+1] + 1;
3466     for  (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0;
3467 
3468     /* load in initial unfactored row of A */
3469     /* printf("row %d\n",i); */
3470     nz    = ai[r[i]+1] - ai[r[i]];
3471     ajtmp = aj + ai[r[i]];
3472     v     = aa + ai[r[i]];
3473     for (j=0; j<nz; j++) {
3474       rtmp[ics[*ajtmp++]] = v[j];
3475       /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */
3476     }
3477     /* printf("\n"); */
3478 
3479     /* numerical factorization */
3480     bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */
3481     nzl   = bi[i+1] - bi[i]; /* num of entries in L(i,:) */
3482     k = 0;
3483     while (k < nzl){
3484       row   = *bjtmp++;
3485       /* printf("  prow %d\n",row); */
3486       pc         = rtmp + row;
3487       pv         = b->a + bdiag[row]; /* 1./(diag of the pivot row) */
3488       multiplier = (*pc) * (*pv);
3489       *pc        = multiplier;
3490       if (PetscAbsScalar(multiplier) > dt){
3491         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
3492         pv         = b->a + bdiag[row+1] + 1;
3493         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
3494         for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
3495         /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */
3496       }
3497       k++;
3498     }
3499 
3500     /* finished row so stick it into b->a */
3501     /* L-part */
3502     pv = b->a + bi[i] ;
3503     pj = bj + bi[i] ;
3504     nzl = bi[i+1] - bi[i];
3505     for (j=0; j<nzl; j++) {
3506       pv[j] = rtmp[pj[j]];
3507       /* printf(" (%d,%g),",pj[j],pv[j]); */
3508     }
3509 
3510     /* diagonal: invert diagonal entries for simplier triangular solves */
3511     if (rtmp[i] == 0.0) rtmp[i] = dt+shift;
3512     b->a[bdiag[i]] = 1.0/rtmp[i];
3513     /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */
3514 
3515     /* U-part */
3516     pv = b->a + bdiag[i+1] + 1;
3517     pj = bj + bdiag[i+1] + 1;
3518     nzu = bdiag[i] - bdiag[i+1] - 1;
3519     for (j=0; j<nzu; j++) {
3520       pv[j] = rtmp[pj[j]];
3521       /* printf(" (%d,%g),",pj[j],pv[j]); */
3522     }
3523     /* printf("\n"); */
3524   }
3525 
3526   ierr = PetscFree(rtmp);CHKERRQ(ierr);
3527   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
3528   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
3529 
3530   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
3531   ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
3532   if (row_identity && col_identity) {
3533     C->ops->solve   = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct;
3534   } else {
3535     C->ops->solve   = MatSolve_SeqAIJ_newdatastruct;
3536   }
3537   C->ops->solveadd           = 0;
3538   C->ops->solvetranspose     = 0;
3539   C->ops->solvetransposeadd  = 0;
3540   C->ops->matsolve           = 0;
3541   C->assembled    = PETSC_TRUE;
3542   C->preallocated = PETSC_TRUE;
3543   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
3544   PetscFunctionReturn(0);
3545 }
3546