xref: /petsc/src/mat/impls/aij/seq/aijfact.c (revision 35e7444da1e6edf29ca585d75dc3fe3d2c63a6e4)
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   } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) {
122     ierr = MatSetType(*B,MATSEQSBAIJ);CHKERRQ(ierr);
123     ierr = MatSeqSBAIJSetPreallocation(*B,1,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
124     (*B)->ops->iccfactorsymbolic      = MatICCFactorSymbolic_SeqAIJ;
125     (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJ;
126   } else SETERRQ(PETSC_ERR_SUP,"Factor type not supported");
127   (*B)->factor = ftype;
128   PetscFunctionReturn(0);
129 }
130 EXTERN_C_END
131 
132 #undef __FUNCT__
133 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ_inplace"
134 PetscErrorCode MatLUFactorSymbolic_SeqAIJ_inplace(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
135 {
136   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
137   IS                 isicol;
138   PetscErrorCode     ierr;
139   const PetscInt     *r,*ic;
140   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j;
141   PetscInt           *bi,*bj,*ajtmp;
142   PetscInt           *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im;
143   PetscReal          f;
144   PetscInt           nlnk,*lnk,k,**bi_ptr;
145   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
146   PetscBT            lnkbt;
147 
148   PetscFunctionBegin;
149   if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square");
150   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
151   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
152   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
153 
154   /* get new row pointers */
155   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
156   bi[0] = 0;
157 
158   /* bdiag is location of diagonal in factor */
159   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
160   bdiag[0] = 0;
161 
162   /* linked list for storing column indices of the active row */
163   nlnk = n + 1;
164   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
165 
166   ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr);
167 
168   /* initial FreeSpace size is f*(ai[n]+1) */
169   f = info->fill;
170   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
171   current_space = free_space;
172 
173   for (i=0; i<n; i++) {
174     /* copy previous fill into linked list */
175     nzi = 0;
176     nnz = ai[r[i]+1] - ai[r[i]];
177     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
178     ajtmp = aj + ai[r[i]];
179     ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
180     nzi += nlnk;
181 
182     /* add pivot rows into linked list */
183     row = lnk[n];
184     while (row < i) {
185       nzbd    = bdiag[row] - bi[row] + 1; /* num of entries in the row with column index <= row */
186       ajtmp   = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */
187       ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr);
188       nzi += nlnk;
189       row  = lnk[row];
190     }
191     bi[i+1] = bi[i] + nzi;
192     im[i]   = nzi;
193 
194     /* mark bdiag */
195     nzbd = 0;
196     nnz  = nzi;
197     k    = lnk[n];
198     while (nnz-- && k < i){
199       nzbd++;
200       k = lnk[k];
201     }
202     bdiag[i] = bi[i] + nzbd;
203 
204     /* if free space is not available, make more free space */
205     if (current_space->local_remaining<nzi) {
206       nnz = (n - i)*nzi; /* estimated and max additional space needed */
207       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
208       reallocs++;
209     }
210 
211     /* copy data into free space, then initialize lnk */
212     ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
213     bi_ptr[i] = current_space->array;
214     current_space->array           += nzi;
215     current_space->local_used      += nzi;
216     current_space->local_remaining -= nzi;
217   }
218 #if defined(PETSC_USE_INFO)
219   if (ai[n] != 0) {
220     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
221     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
222     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
223     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr);
224     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
225   } else {
226     ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr);
227   }
228 #endif
229 
230   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
231   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
232 
233   /* destroy list of free space and other temporary array(s) */
234   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
235   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
236   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
237   ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr);
238 
239   /* put together the new matrix */
240   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
241   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
242   b    = (Mat_SeqAIJ*)(B)->data;
243   b->free_a       = PETSC_TRUE;
244   b->free_ij      = PETSC_TRUE;
245   b->singlemalloc = PETSC_FALSE;
246   ierr          = PetscMalloc((bi[n]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
247   b->j          = bj;
248   b->i          = bi;
249   b->diag       = bdiag;
250   b->ilen       = 0;
251   b->imax       = 0;
252   b->row        = isrow;
253   b->col        = iscol;
254   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
255   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
256   b->icol       = isicol;
257   ierr          = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
258 
259   /* In b structure:  Free imax, ilen, old a, old j.  Allocate solve_work, new a, new j */
260   ierr = PetscLogObjectMemory(B,(bi[n]-n)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
261   b->maxnz = b->nz = bi[n] ;
262 
263   (B)->factor                = MAT_FACTOR_LU;
264   (B)->info.factor_mallocs   = reallocs;
265   (B)->info.fill_ratio_given = f;
266 
267   if (ai[n]) {
268     (B)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
269   } else {
270     (B)->info.fill_ratio_needed = 0.0;
271   }
272   (B)->ops->lufactornumeric  = MatLUFactorNumeric_SeqAIJ_inplace;
273   (B)->ops->solve            = MatSolve_SeqAIJ_inplace;
274   (B)->ops->solvetranspose   = MatSolveTranspose_SeqAIJ_inplace;
275   /* switch to inodes if appropriate */
276   ierr = MatLUFactorSymbolic_SeqAIJ_Inode(B,A,isrow,iscol,info);CHKERRQ(ierr);
277   PetscFunctionReturn(0);
278 }
279 
280 #undef __FUNCT__
281 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ"
282 PetscErrorCode MatLUFactorSymbolic_SeqAIJ(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
283 {
284   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
285   IS                 isicol;
286   PetscErrorCode     ierr;
287   const PetscInt     *r,*ic;
288   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j;
289   PetscInt           *bi,*bj,*ajtmp;
290   PetscInt           *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im;
291   PetscReal          f;
292   PetscInt           nlnk,*lnk,k,**bi_ptr;
293   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
294   PetscBT            lnkbt;
295   PetscTruth         olddatastruct= PETSC_FALSE;
296 
297   PetscFunctionBegin;
298   ierr = PetscOptionsGetTruth(PETSC_NULL,"-lu_old",&olddatastruct,PETSC_NULL);CHKERRQ(ierr);
299   if(olddatastruct){
300     ierr = MatLUFactorSymbolic_SeqAIJ_inplace(B,A,isrow,iscol,info);CHKERRQ(ierr);
301     PetscFunctionReturn(0);
302   }
303   if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square");
304   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
305   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
306   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
307 
308   /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
309   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
310   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
311   bi[0] = bdiag[0] = 0;
312 
313   /* linked list for storing column indices of the active row */
314   nlnk = n + 1;
315   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
316 
317   ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr);
318 
319   /* initial FreeSpace size is f*(ai[n]+1) */
320   f = info->fill;
321   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
322   current_space = free_space;
323 
324   for (i=0; i<n; i++) {
325     /* copy previous fill into linked list */
326     nzi = 0;
327     nnz = ai[r[i]+1] - ai[r[i]];
328     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
329     ajtmp = aj + ai[r[i]];
330     ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
331     nzi += nlnk;
332 
333     /* add pivot rows into linked list */
334     row = lnk[n];
335     while (row < i){
336       nzbd  = bdiag[row] + 1; /* num of entries in the row with column index <= row */
337       ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */
338       ierr  = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr);
339       nzi  += nlnk;
340       row   = lnk[row];
341     }
342     bi[i+1] = bi[i] + nzi;
343     im[i]   = nzi;
344 
345     /* mark bdiag */
346     nzbd = 0;
347     nnz  = nzi;
348     k    = lnk[n];
349     while (nnz-- && k < i){
350       nzbd++;
351       k = lnk[k];
352     }
353     bdiag[i] = nzbd; /* note: bdiag[i] = nnzL as input for PetscFreeSpaceContiguous_LU() */
354 
355     /* if free space is not available, make more free space */
356     if (current_space->local_remaining<nzi) {
357       nnz = 2*(n - i)*nzi; /* estimated and max additional space needed */
358       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
359       reallocs++;
360     }
361 
362     /* copy data into free space, then initialize lnk */
363     ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
364     bi_ptr[i] = current_space->array;
365     current_space->array           += nzi;
366     current_space->local_used      += nzi;
367     current_space->local_remaining -= nzi;
368   }
369 #if defined(PETSC_USE_INFO)
370   if (ai[n] != 0) {
371     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
372     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
373     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
374     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr);
375     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
376   } else {
377     ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr);
378   }
379 #endif
380 
381   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
382   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
383 
384   /* destroy list of free space and other temporary array(s) */
385   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
386   ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr);
387   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
388   ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr);
389 
390   /* put together the new matrix */
391   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
392   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
393   b    = (Mat_SeqAIJ*)(B)->data;
394   b->free_a       = PETSC_TRUE;
395   b->free_ij      = PETSC_TRUE;
396   b->singlemalloc = PETSC_FALSE;
397   ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
398   b->j          = bj;
399   b->i          = bi;
400   b->diag       = bdiag;
401   b->ilen       = 0;
402   b->imax       = 0;
403   b->row        = isrow;
404   b->col        = iscol;
405   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
406   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
407   b->icol       = isicol;
408   ierr          = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
409 
410   /* In b structure:  Free imax, ilen, old a, old j.  Allocate solve_work, new a, new j */
411   ierr = PetscLogObjectMemory(B,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
412   b->maxnz = b->nz = bdiag[0]+1;
413   B->factor                = MAT_FACTOR_LU;
414   B->info.factor_mallocs   = reallocs;
415   B->info.fill_ratio_given = f;
416 
417   if (ai[n]) {
418     B->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]);
419   } else {
420     B->info.fill_ratio_needed = 0.0;
421   }
422   B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ;
423   /* switch to inodes if appropriate */
424   ierr = Mat_CheckInode_FactorLU(B,PETSC_FALSE);CHKERRQ(ierr);
425   PetscFunctionReturn(0);
426 }
427 
428 /*
429     Trouble in factorization, should we dump the original matrix?
430 */
431 #undef __FUNCT__
432 #define __FUNCT__ "MatFactorDumpMatrix"
433 PetscErrorCode MatFactorDumpMatrix(Mat A)
434 {
435   PetscErrorCode ierr;
436   PetscTruth     flg = PETSC_FALSE;
437 
438   PetscFunctionBegin;
439   ierr = PetscOptionsGetTruth(PETSC_NULL,"-mat_factor_dump_on_error",&flg,PETSC_NULL);CHKERRQ(ierr);
440   if (flg) {
441     PetscViewer viewer;
442     char        filename[PETSC_MAX_PATH_LEN];
443 
444     ierr = PetscSNPrintf(filename,PETSC_MAX_PATH_LEN,"matrix_factor_error.%d",PetscGlobalRank);CHKERRQ(ierr);
445     ierr = PetscViewerBinaryOpen(((PetscObject)A)->comm,filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr);
446     ierr = MatView(A,viewer);CHKERRQ(ierr);
447     ierr = PetscViewerDestroy(viewer);CHKERRQ(ierr);
448   }
449   PetscFunctionReturn(0);
450 }
451 
452 #undef __FUNCT__
453 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ"
454 PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info)
455 {
456   Mat            C=B;
457   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
458   IS             isrow = b->row,isicol = b->icol;
459   PetscErrorCode ierr;
460   const PetscInt *r,*ic,*ics;
461   PetscInt       i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
462   PetscInt       *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj;
463   MatScalar      *rtmp,*pc,multiplier,*v,*pv,*aa=a->a;
464   PetscTruth     row_identity,col_identity;
465 
466   LUShift_Ctx    sctx;
467   PetscInt       *ddiag,newshift;
468   PetscReal      rs;
469   MatScalar      d;
470 
471   PetscFunctionBegin;
472   /* MatPivotSetUp(): initialize shift context sctx */
473   ierr = PetscMemzero(&sctx,sizeof(LUShift_Ctx));CHKERRQ(ierr);
474 
475   /* if both shift schemes are chosen by user, only use info->shiftpd */
476   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
477     ddiag          = a->diag;
478     sctx.shift_top = info->zeropivot;
479     for (i=0; i<n; i++) {
480       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
481       d  = (aa)[ddiag[i]];
482       rs = -PetscAbsScalar(d) - PetscRealPart(d);
483       v  = aa+ai[i];
484       nz = ai[i+1] - ai[i];
485       for (j=0; j<nz; j++)
486 	rs += PetscAbsScalar(v[j]);
487       if (rs>sctx.shift_top) sctx.shift_top = rs;
488     }
489     sctx.shift_top   *= 1.1;
490     sctx.nshift_max   = 5;
491     sctx.shift_lo     = 0.;
492     sctx.shift_hi     = 1.;
493   }
494 
495   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
496   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
497   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
498   ics  = ic;
499 
500   do {
501     sctx.lushift = PETSC_FALSE;
502     for (i=0; i<n; i++){
503       /* zero rtmp */
504       /* L part */
505       nz    = bi[i+1] - bi[i];
506       bjtmp = bj + bi[i];
507       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
508 
509       /* U part */
510       nz = bdiag[i]-bdiag[i+1];
511       bjtmp = bj + bdiag[i+1]+1;
512       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
513 
514       /* load in initial (unfactored row) */
515       nz    = ai[r[i]+1] - ai[r[i]];
516       ajtmp = aj + ai[r[i]];
517       v     = aa + ai[r[i]];
518       for (j=0; j<nz; j++) {
519         rtmp[ics[ajtmp[j]]] = v[j];
520       }
521       /* ZeropivotApply() */
522       rtmp[i] += sctx.shift_amount;  /* shift the diagonal of the matrix */
523 
524       /* elimination */
525       bjtmp = bj + bi[i];
526       row   = *bjtmp++;
527       nzL   = bi[i+1] - bi[i];
528       for(k=0; k < nzL;k++) {
529         pc = rtmp + row;
530         if (*pc != 0.0) {
531           pv         = b->a + bdiag[row];
532           multiplier = *pc * (*pv);
533           *pc        = multiplier;
534           pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
535 	  pv = b->a + bdiag[row+1]+1;
536 	  nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */
537           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
538           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
539         }
540         row = *bjtmp++;
541       }
542 
543       /* finished row so stick it into b->a */
544       rs = 0.0;
545       /* L part */
546       pv   = b->a + bi[i] ;
547       pj   = b->j + bi[i] ;
548       nz   = bi[i+1] - bi[i];
549       for (j=0; j<nz; j++) {
550         pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]);
551       }
552 
553       /* U part */
554       pv = b->a + bdiag[i+1]+1;
555       pj = b->j + bdiag[i+1]+1;
556       nz = bdiag[i] - bdiag[i+1]-1;
557       for (j=0; j<nz; j++) {
558         pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]);
559       }
560 
561       /* MatPivotCheck() */
562       sctx.rs  = rs;
563       sctx.pv  = rtmp[i];
564       if (info->shiftnz){
565         ierr = MatPivotCheck_nz(info,sctx,i,newshift);CHKERRQ(ierr);
566       } else if (info->shiftpd){
567         ierr = MatPivotCheck_pd(info,sctx,i,newshift);CHKERRQ(ierr);
568       } else if (info->shiftinblocks){
569         ierr = MatPivotCheck_inblocks(info,sctx,i,newshift);CHKERRQ(ierr);
570       } else {
571         ierr = MatPivotCheck_none(info,sctx,i,newshift);CHKERRQ(ierr);
572       }
573       rtmp[i] = sctx.pv;
574       if (newshift == 1) break;
575 
576       /* Mark diagonal and invert diagonal for simplier triangular solves */
577       pv  = b->a + bdiag[i];
578       *pv = 1.0/rtmp[i];
579 
580     } /* endof for (i=0; i<n; i++){ */
581 
582     /* MatPivotRefine() */
583     if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max){
584       /*
585        * if no shift in this attempt & shifting & started shifting & can refine,
586        * then try lower shift
587        */
588       sctx.shift_hi       = sctx.shift_fraction;
589       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
590       sctx.shift_amount   = sctx.shift_fraction * sctx.shift_top;
591       sctx.lushift        = PETSC_TRUE;
592       sctx.nshift++;
593     }
594   } while (sctx.lushift);
595 
596   ierr = PetscFree(rtmp);CHKERRQ(ierr);
597   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
598   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
599   if (b->inode.use){
600     C->ops->solve   = MatSolve_SeqAIJ_Inode;
601   } else {
602     ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
603     ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
604     if (row_identity && col_identity) {
605       C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering;
606     } else {
607       C->ops->solve = MatSolve_SeqAIJ;
608     }
609   }
610   C->ops->solveadd           = MatSolveAdd_SeqAIJ;
611   C->ops->solvetranspose     = MatSolveTranspose_SeqAIJ;
612   C->ops->solvetransposeadd  = MatSolveTransposeAdd_SeqAIJ;
613   C->ops->matsolve           = MatMatSolve_SeqAIJ;
614   C->assembled    = PETSC_TRUE;
615   C->preallocated = PETSC_TRUE;
616   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
617 
618   /* MatPivotView() */
619   if (sctx.nshift){
620     if (info->shiftpd) {
621       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);
622     } else if (info->shiftnz) {
623       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
624     } else if (info->shiftinblocks){
625       ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftinblocks);CHKERRQ(ierr);
626     }
627   }
628   PetscFunctionReturn(0);
629 }
630 
631 #undef __FUNCT__
632 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_inplace"
633 PetscErrorCode MatLUFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info)
634 {
635   Mat             C=B;
636   Mat_SeqAIJ      *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
637   IS              isrow = b->row,isicol = b->icol;
638   PetscErrorCode  ierr;
639   const PetscInt   *r,*ic,*ics;
640   PetscInt        nz,row,i,j,n=A->rmap->n,diag;
641   const PetscInt  *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
642   const PetscInt  *ajtmp,*bjtmp,*diag_offset = b->diag,*pj;
643   MatScalar       *pv,*rtmp,*pc,multiplier,d;
644   const MatScalar *v,*aa=a->a;
645   PetscReal       rs=0.0;
646   LUShift_Ctx     sctx;
647   PetscInt        newshift,*ddiag;
648 
649   PetscFunctionBegin;
650   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
651   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
652   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
653   ics  = ic;
654 
655   /* initialize shift context sctx */
656   sctx.nshift         = 0;
657   sctx.nshift_max     = 0;
658   sctx.shift_top      = 0.0;
659   sctx.shift_lo       = 0.0;
660   sctx.shift_hi       = 0.0;
661   sctx.shift_fraction = 0.0;
662   sctx.shift_amount   = 0.0;
663 
664   /* if both shift schemes are chosen by user, only use info->shiftpd */
665   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
666     ddiag          = a->diag;
667     sctx.shift_top = info->zeropivot;
668     for (i=0; i<n; i++) {
669       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
670       d  = (aa)[ddiag[i]];
671       rs = -PetscAbsScalar(d) - PetscRealPart(d);
672       v  = aa+ai[i];
673       nz = ai[i+1] - ai[i];
674       for (j=0; j<nz; j++)
675 	rs += PetscAbsScalar(v[j]);
676       if (rs>sctx.shift_top) sctx.shift_top = rs;
677     }
678     sctx.shift_top   *= 1.1;
679     sctx.nshift_max   = 5;
680     sctx.shift_lo     = 0.;
681     sctx.shift_hi     = 1.;
682   }
683 
684   do {
685     sctx.lushift = PETSC_FALSE;
686     for (i=0; i<n; i++){
687       nz    = bi[i+1] - bi[i];
688       bjtmp = bj + bi[i];
689       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
690 
691       /* load in initial (unfactored row) */
692       nz    = ai[r[i]+1] - ai[r[i]];
693       ajtmp = aj + ai[r[i]];
694       v     = aa + ai[r[i]];
695       for (j=0; j<nz; j++) {
696         rtmp[ics[ajtmp[j]]] = v[j];
697       }
698       rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */
699       /* if (sctx.shift_amount > 0.0) printf("row %d, shift %g\n",i,sctx.shift_amount); */
700 
701       row = *bjtmp++;
702       while  (row < i) {
703         pc = rtmp + row;
704         if (*pc != 0.0) {
705           pv         = b->a + diag_offset[row];
706           pj         = b->j + diag_offset[row] + 1;
707           multiplier = *pc / *pv++;
708           *pc        = multiplier;
709           nz         = bi[row+1] - diag_offset[row] - 1;
710           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
711           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
712         }
713         row = *bjtmp++;
714       }
715       /* finished row so stick it into b->a */
716       pv   = b->a + bi[i] ;
717       pj   = b->j + bi[i] ;
718       nz   = bi[i+1] - bi[i];
719       diag = diag_offset[i] - bi[i];
720       rs   = 0.0;
721       for (j=0; j<nz; j++) {
722         pv[j] = rtmp[pj[j]];
723         rs   += PetscAbsScalar(pv[j]);
724       }
725       rs   -= PetscAbsScalar(pv[diag]);
726 
727       /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */
728       sctx.rs  = rs;
729       sctx.pv  = pv[diag];
730       ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr);
731       if (newshift == 1) break;
732     }
733 
734     if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
735       /*
736        * if no shift in this attempt & shifting & started shifting & can refine,
737        * then try lower shift
738        */
739       sctx.shift_hi       = sctx.shift_fraction;
740       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
741       sctx.shift_amount   = sctx.shift_fraction * sctx.shift_top;
742       sctx.lushift        = PETSC_TRUE;
743       sctx.nshift++;
744     }
745   } while (sctx.lushift);
746 
747   /* invert diagonal entries for simplier triangular solves */
748   for (i=0; i<n; i++) {
749     b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]];
750   }
751   ierr = PetscFree(rtmp);CHKERRQ(ierr);
752   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
753   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
754   if (b->inode.use) {
755     C->ops->solve   = MatSolve_SeqAIJ_Inode_inplace;
756   } else {
757     PetscTruth row_identity, col_identity;
758     ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
759     ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
760     if (row_identity && col_identity) {
761       C->ops->solve   = MatSolve_SeqAIJ_NaturalOrdering_inplace;
762     } else {
763       C->ops->solve   = MatSolve_SeqAIJ_inplace;
764     }
765   }
766   C->ops->solveadd           = MatSolveAdd_SeqAIJ_inplace;
767   C->ops->solvetranspose     = MatSolveTranspose_SeqAIJ_inplace;
768   C->ops->solvetransposeadd  = MatSolveTransposeAdd_SeqAIJ_inplace;
769   C->ops->matsolve           = MatMatSolve_SeqAIJ_inplace;
770   C->assembled    = PETSC_TRUE;
771   C->preallocated = PETSC_TRUE;
772   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
773   if (sctx.nshift){
774      if (info->shiftpd) {
775       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);
776     } else if (info->shiftnz) {
777       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
778     }
779   }
780   PetscFunctionReturn(0);
781 }
782 
783 /*
784    This routine implements inplace ILU(0) with row or/and column permutations.
785    Input:
786      A - original matrix
787    Output;
788      A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i]
789          a->j (col index) is permuted by the inverse of colperm, then sorted
790          a->a reordered accordingly with a->j
791          a->diag (ptr to diagonal elements) is updated.
792 */
793 #undef __FUNCT__
794 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_InplaceWithPerm"
795 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info)
796 {
797   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
798   IS             isrow = a->row,isicol = a->icol;
799   PetscErrorCode ierr;
800   const PetscInt *r,*ic,*ics;
801   PetscInt       i,j,n=A->rmap->n,*ai=a->i,*aj=a->j;
802   PetscInt       *ajtmp,nz,row;
803   PetscInt       *diag = a->diag,nbdiag,*pj;
804   PetscScalar    *rtmp,*pc,multiplier,d;
805   MatScalar      *v,*pv;
806   PetscReal      rs;
807   LUShift_Ctx    sctx;
808   PetscInt       newshift;
809 
810   PetscFunctionBegin;
811   if (A != B) SETERRQ(PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address");
812   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
813   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
814   ierr  = PetscMalloc((n+1)*sizeof(PetscScalar),&rtmp);CHKERRQ(ierr);
815   ierr  = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr);
816   ics = ic;
817 
818   sctx.shift_top      = 0.;
819   sctx.nshift_max     = 0;
820   sctx.shift_lo       = 0.;
821   sctx.shift_hi       = 0.;
822   sctx.shift_fraction = 0.;
823 
824   /* if both shift schemes are chosen by user, only use info->shiftpd */
825   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
826     sctx.shift_top = 0.;
827     for (i=0; i<n; i++) {
828       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
829       d  = (a->a)[diag[i]];
830       rs = -PetscAbsScalar(d) - PetscRealPart(d);
831       v  = a->a+ai[i];
832       nz = ai[i+1] - ai[i];
833       for (j=0; j<nz; j++)
834 	rs += PetscAbsScalar(v[j]);
835       if (rs>sctx.shift_top) sctx.shift_top = rs;
836     }
837     if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot;
838     sctx.shift_top    *= 1.1;
839     sctx.nshift_max   = 5;
840     sctx.shift_lo     = 0.;
841     sctx.shift_hi     = 1.;
842   }
843 
844   sctx.shift_amount = 0.;
845   sctx.nshift       = 0;
846   do {
847     sctx.lushift = PETSC_FALSE;
848     for (i=0; i<n; i++){
849       /* load in initial unfactored row */
850       nz    = ai[r[i]+1] - ai[r[i]];
851       ajtmp = aj + ai[r[i]];
852       v     = a->a + ai[r[i]];
853       /* sort permuted ajtmp and values v accordingly */
854       for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]];
855       ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr);
856 
857       diag[r[i]] = ai[r[i]];
858       for (j=0; j<nz; j++) {
859         rtmp[ajtmp[j]] = v[j];
860         if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */
861       }
862       rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */
863 
864       row = *ajtmp++;
865       while  (row < i) {
866         pc = rtmp + row;
867         if (*pc != 0.0) {
868           pv         = a->a + diag[r[row]];
869           pj         = aj + diag[r[row]] + 1;
870 
871           multiplier = *pc / *pv++;
872           *pc        = multiplier;
873           nz         = ai[r[row]+1] - diag[r[row]] - 1;
874           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
875           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
876         }
877         row = *ajtmp++;
878       }
879       /* finished row so overwrite it onto a->a */
880       pv   = a->a + ai[r[i]] ;
881       pj   = aj + ai[r[i]] ;
882       nz   = ai[r[i]+1] - ai[r[i]];
883       nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */
884 
885       rs   = 0.0;
886       for (j=0; j<nz; j++) {
887         pv[j] = rtmp[pj[j]];
888         if (j != nbdiag) rs += PetscAbsScalar(pv[j]);
889       }
890 
891       /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */
892       sctx.rs  = rs;
893       sctx.pv  = pv[nbdiag];
894       ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr);
895       if (newshift == 1) break;
896     }
897 
898     if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
899       /*
900        * if no shift in this attempt & shifting & started shifting & can refine,
901        * then try lower shift
902        */
903       sctx.shift_hi        = sctx.shift_fraction;
904       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
905       sctx.shift_amount    = sctx.shift_fraction * sctx.shift_top;
906       sctx.lushift         = PETSC_TRUE;
907       sctx.nshift++;
908     }
909   } while (sctx.lushift);
910 
911   /* invert diagonal entries for simplier triangular solves */
912   for (i=0; i<n; i++) {
913     a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]];
914   }
915 
916   ierr = PetscFree(rtmp);CHKERRQ(ierr);
917   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
918   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
919   A->ops->solve             = MatSolve_SeqAIJ_InplaceWithPerm;
920   A->ops->solveadd          = MatSolveAdd_SeqAIJ_inplace;
921   A->ops->solvetranspose    = MatSolveTranspose_SeqAIJ_inplace;
922   A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_inplace;
923   A->assembled = PETSC_TRUE;
924   A->preallocated = PETSC_TRUE;
925   ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr);
926   if (sctx.nshift){
927     if (info->shiftpd) {
928       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);
929     } else if (info->shiftnz) {
930       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
931     }
932   }
933   PetscFunctionReturn(0);
934 }
935 
936 /* ----------------------------------------------------------- */
937 #undef __FUNCT__
938 #define __FUNCT__ "MatLUFactor_SeqAIJ"
939 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info)
940 {
941   PetscErrorCode ierr;
942   Mat            C;
943 
944   PetscFunctionBegin;
945   ierr = MatGetFactor(A,MAT_SOLVER_PETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr);
946   ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr);
947   ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr);
948   A->ops->solve            = C->ops->solve;
949   A->ops->solvetranspose   = C->ops->solvetranspose;
950   ierr = MatHeaderCopy(A,C);CHKERRQ(ierr);
951   ierr = PetscLogObjectParent(A,((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr);
952   PetscFunctionReturn(0);
953 }
954 /* ----------------------------------------------------------- */
955 
956 
957 #undef __FUNCT__
958 #define __FUNCT__ "MatSolve_SeqAIJ_inplace"
959 PetscErrorCode MatSolve_SeqAIJ_inplace(Mat A,Vec bb,Vec xx)
960 {
961   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
962   IS                iscol = a->col,isrow = a->row;
963   PetscErrorCode    ierr;
964   PetscInt          i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
965   PetscInt          nz;
966   const PetscInt    *rout,*cout,*r,*c;
967   PetscScalar       *x,*tmp,*tmps,sum;
968   const PetscScalar *b;
969   const MatScalar   *aa = a->a,*v;
970 
971   PetscFunctionBegin;
972   if (!n) PetscFunctionReturn(0);
973 
974   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
975   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
976   tmp  = a->solve_work;
977 
978   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
979   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
980 
981   /* forward solve the lower triangular */
982   tmp[0] = b[*r++];
983   tmps   = tmp;
984   for (i=1; i<n; i++) {
985     v   = aa + ai[i] ;
986     vi  = aj + ai[i] ;
987     nz  = a->diag[i] - ai[i];
988     sum = b[*r++];
989     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
990     tmp[i] = sum;
991   }
992 
993   /* backward solve the upper triangular */
994   for (i=n-1; i>=0; i--){
995     v   = aa + a->diag[i] + 1;
996     vi  = aj + a->diag[i] + 1;
997     nz  = ai[i+1] - a->diag[i] - 1;
998     sum = tmp[i];
999     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1000     x[*c--] = tmp[i] = sum*aa[a->diag[i]];
1001   }
1002 
1003   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1004   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1005   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1006   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1007   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1008   PetscFunctionReturn(0);
1009 }
1010 
1011 #undef __FUNCT__
1012 #define __FUNCT__ "MatMatSolve_SeqAIJ_inplace"
1013 PetscErrorCode MatMatSolve_SeqAIJ_inplace(Mat A,Mat B,Mat X)
1014 {
1015   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1016   IS              iscol = a->col,isrow = a->row;
1017   PetscErrorCode  ierr;
1018   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1019   PetscInt        nz,neq;
1020   const PetscInt  *rout,*cout,*r,*c;
1021   PetscScalar     *x,*b,*tmp,*tmps,sum;
1022   const MatScalar *aa = a->a,*v;
1023   PetscTruth      bisdense,xisdense;
1024 
1025   PetscFunctionBegin;
1026   if (!n) PetscFunctionReturn(0);
1027 
1028   ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr);
1029   if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix");
1030   ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr);
1031   if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix");
1032 
1033   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
1034   ierr = MatGetArray(X,&x);CHKERRQ(ierr);
1035 
1036   tmp  = a->solve_work;
1037   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1038   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1039 
1040   for (neq=0; neq<B->cmap->n; neq++){
1041     /* forward solve the lower triangular */
1042     tmp[0] = b[r[0]];
1043     tmps   = tmp;
1044     for (i=1; i<n; i++) {
1045       v   = aa + ai[i] ;
1046       vi  = aj + ai[i] ;
1047       nz  = a->diag[i] - ai[i];
1048       sum = b[r[i]];
1049       PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1050       tmp[i] = sum;
1051     }
1052     /* backward solve the upper triangular */
1053     for (i=n-1; i>=0; i--){
1054       v   = aa + a->diag[i] + 1;
1055       vi  = aj + a->diag[i] + 1;
1056       nz  = ai[i+1] - a->diag[i] - 1;
1057       sum = tmp[i];
1058       PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1059       x[c[i]] = tmp[i] = sum*aa[a->diag[i]];
1060     }
1061 
1062     b += n;
1063     x += n;
1064   }
1065   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1066   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1067   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
1068   ierr = MatRestoreArray(X,&x);CHKERRQ(ierr);
1069   ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr);
1070   PetscFunctionReturn(0);
1071 }
1072 
1073 #undef __FUNCT__
1074 #define __FUNCT__ "MatMatSolve_SeqAIJ"
1075 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X)
1076 {
1077   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1078   IS              iscol = a->col,isrow = a->row;
1079   PetscErrorCode  ierr;
1080   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag;
1081   PetscInt        nz,neq;
1082   const PetscInt  *rout,*cout,*r,*c;
1083   PetscScalar     *x,*b,*tmp,sum;
1084   const MatScalar *aa = a->a,*v;
1085   PetscTruth      bisdense,xisdense;
1086 
1087   PetscFunctionBegin;
1088   if (!n) PetscFunctionReturn(0);
1089 
1090   ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr);
1091   if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix");
1092   ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr);
1093   if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix");
1094 
1095   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
1096   ierr = MatGetArray(X,&x);CHKERRQ(ierr);
1097 
1098   tmp  = a->solve_work;
1099   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1100   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1101 
1102   for (neq=0; neq<B->cmap->n; neq++){
1103     /* forward solve the lower triangular */
1104     tmp[0] = b[r[0]];
1105     v      = aa;
1106     vi     = aj;
1107     for (i=1; i<n; i++) {
1108       nz  = ai[i+1] - ai[i];
1109       sum = b[r[i]];
1110       PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
1111       tmp[i] = sum;
1112       v += nz; vi += nz;
1113     }
1114 
1115     /* backward solve the upper triangular */
1116     for (i=n-1; i>=0; i--){
1117       v   = aa + adiag[i+1]+1;
1118       vi  = aj + adiag[i+1]+1;
1119       nz  = adiag[i]-adiag[i+1]-1;
1120       sum = tmp[i];
1121       PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
1122       x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */
1123     }
1124 
1125     b += n;
1126     x += n;
1127   }
1128   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1129   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1130   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
1131   ierr = MatRestoreArray(X,&x);CHKERRQ(ierr);
1132   ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr);
1133   PetscFunctionReturn(0);
1134 }
1135 
1136 #undef __FUNCT__
1137 #define __FUNCT__ "MatSolve_SeqAIJ_InplaceWithPerm"
1138 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx)
1139 {
1140   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1141   IS              iscol = a->col,isrow = a->row;
1142   PetscErrorCode  ierr;
1143   const PetscInt  *r,*c,*rout,*cout;
1144   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1145   PetscInt        nz,row;
1146   PetscScalar     *x,*b,*tmp,*tmps,sum;
1147   const MatScalar *aa = a->a,*v;
1148 
1149   PetscFunctionBegin;
1150   if (!n) PetscFunctionReturn(0);
1151 
1152   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
1153   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1154   tmp  = a->solve_work;
1155 
1156   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1157   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1158 
1159   /* forward solve the lower triangular */
1160   tmp[0] = b[*r++];
1161   tmps   = tmp;
1162   for (row=1; row<n; row++) {
1163     i   = rout[row]; /* permuted row */
1164     v   = aa + ai[i] ;
1165     vi  = aj + ai[i] ;
1166     nz  = a->diag[i] - ai[i];
1167     sum = b[*r++];
1168     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1169     tmp[row] = sum;
1170   }
1171 
1172   /* backward solve the upper triangular */
1173   for (row=n-1; row>=0; row--){
1174     i   = rout[row]; /* permuted row */
1175     v   = aa + a->diag[i] + 1;
1176     vi  = aj + a->diag[i] + 1;
1177     nz  = ai[i+1] - a->diag[i] - 1;
1178     sum = tmp[row];
1179     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1180     x[*c--] = tmp[row] = sum*aa[a->diag[i]];
1181   }
1182 
1183   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1184   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1185   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
1186   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1187   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1188   PetscFunctionReturn(0);
1189 }
1190 
1191 /* ----------------------------------------------------------- */
1192 #include "../src/mat/impls/aij/seq/ftn-kernels/fsolve.h"
1193 #undef __FUNCT__
1194 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_inplace"
1195 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_inplace(Mat A,Vec bb,Vec xx)
1196 {
1197   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1198   PetscErrorCode    ierr;
1199   PetscInt          n = A->rmap->n;
1200   const PetscInt    *ai = a->i,*aj = a->j,*adiag = a->diag;
1201   PetscScalar       *x;
1202   const PetscScalar *b;
1203   const MatScalar   *aa = a->a;
1204 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ)
1205   PetscInt          adiag_i,i,nz,ai_i;
1206   const PetscInt    *vi;
1207   const MatScalar   *v;
1208   PetscScalar       sum;
1209 #endif
1210 
1211   PetscFunctionBegin;
1212   if (!n) PetscFunctionReturn(0);
1213 
1214   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1215   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1216 
1217 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ)
1218   fortransolveaij_(&n,x,ai,aj,adiag,aa,b);
1219 #else
1220   /* forward solve the lower triangular */
1221   x[0] = b[0];
1222   for (i=1; i<n; i++) {
1223     ai_i = ai[i];
1224     v    = aa + ai_i;
1225     vi   = aj + ai_i;
1226     nz   = adiag[i] - ai_i;
1227     sum  = b[i];
1228     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
1229     x[i] = sum;
1230   }
1231 
1232   /* backward solve the upper triangular */
1233   for (i=n-1; i>=0; i--){
1234     adiag_i = adiag[i];
1235     v       = aa + adiag_i + 1;
1236     vi      = aj + adiag_i + 1;
1237     nz      = ai[i+1] - adiag_i - 1;
1238     sum     = x[i];
1239     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
1240     x[i]    = sum*aa[adiag_i];
1241   }
1242 #endif
1243   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1244   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1245   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1246   PetscFunctionReturn(0);
1247 }
1248 
1249 #undef __FUNCT__
1250 #define __FUNCT__ "MatSolveAdd_SeqAIJ_inplace"
1251 PetscErrorCode MatSolveAdd_SeqAIJ_inplace(Mat A,Vec bb,Vec yy,Vec xx)
1252 {
1253   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1254   IS                iscol = a->col,isrow = a->row;
1255   PetscErrorCode    ierr;
1256   PetscInt          i, n = A->rmap->n,j;
1257   PetscInt          nz;
1258   const PetscInt    *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j;
1259   PetscScalar       *x,*tmp,sum;
1260   const PetscScalar *b;
1261   const MatScalar   *aa = a->a,*v;
1262 
1263   PetscFunctionBegin;
1264   if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);}
1265 
1266   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1267   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1268   tmp  = a->solve_work;
1269 
1270   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1271   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1272 
1273   /* forward solve the lower triangular */
1274   tmp[0] = b[*r++];
1275   for (i=1; i<n; i++) {
1276     v   = aa + ai[i] ;
1277     vi  = aj + ai[i] ;
1278     nz  = a->diag[i] - ai[i];
1279     sum = b[*r++];
1280     for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1281     tmp[i] = sum;
1282   }
1283 
1284   /* backward solve the upper triangular */
1285   for (i=n-1; i>=0; i--){
1286     v   = aa + a->diag[i] + 1;
1287     vi  = aj + a->diag[i] + 1;
1288     nz  = ai[i+1] - a->diag[i] - 1;
1289     sum = tmp[i];
1290     for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1291     tmp[i] = sum*aa[a->diag[i]];
1292     x[*c--] += tmp[i];
1293   }
1294 
1295   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1296   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1297   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1298   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1299   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1300 
1301   PetscFunctionReturn(0);
1302 }
1303 
1304 #undef __FUNCT__
1305 #define __FUNCT__ "MatSolveAdd_SeqAIJ"
1306 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx)
1307 {
1308   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1309   IS                iscol = a->col,isrow = a->row;
1310   PetscErrorCode    ierr;
1311   PetscInt          i, n = A->rmap->n,j;
1312   PetscInt          nz;
1313   const PetscInt    *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag;
1314   PetscScalar       *x,*tmp,sum;
1315   const PetscScalar *b;
1316   const MatScalar   *aa = a->a,*v;
1317 
1318   PetscFunctionBegin;
1319   if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);}
1320 
1321   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1322   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1323   tmp  = a->solve_work;
1324 
1325   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1326   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1327 
1328   /* forward solve the lower triangular */
1329   tmp[0] = b[r[0]];
1330   v      = aa;
1331   vi     = aj;
1332   for (i=1; i<n; i++) {
1333     nz  = ai[i+1] - ai[i];
1334     sum = b[r[i]];
1335     for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1336     tmp[i] = sum;
1337     v += nz; vi += nz;
1338   }
1339 
1340   /* backward solve the upper triangular */
1341   v  = aa + adiag[n-1];
1342   vi = aj + adiag[n-1];
1343   for (i=n-1; i>=0; i--){
1344     nz  = adiag[i] - adiag[i+1] - 1;
1345     sum = tmp[i];
1346     for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1347     tmp[i] = sum*v[nz];
1348     x[c[i]] += tmp[i];
1349     v += nz+1; vi += nz+1;
1350   }
1351 
1352   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1353   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1354   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1355   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1356   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1357 
1358   PetscFunctionReturn(0);
1359 }
1360 
1361 #undef __FUNCT__
1362 #define __FUNCT__ "MatSolveTranspose_SeqAIJ_inplace"
1363 PetscErrorCode MatSolveTranspose_SeqAIJ_inplace(Mat A,Vec bb,Vec xx)
1364 {
1365   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1366   IS                iscol = a->col,isrow = a->row;
1367   PetscErrorCode    ierr;
1368   const PetscInt    *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi;
1369   PetscInt          i,n = A->rmap->n,j;
1370   PetscInt          nz;
1371   PetscScalar       *x,*tmp,s1;
1372   const MatScalar   *aa = a->a,*v;
1373   const PetscScalar *b;
1374 
1375   PetscFunctionBegin;
1376   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1377   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1378   tmp  = a->solve_work;
1379 
1380   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1381   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1382 
1383   /* copy the b into temp work space according to permutation */
1384   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1385 
1386   /* forward solve the U^T */
1387   for (i=0; i<n; i++) {
1388     v   = aa + diag[i] ;
1389     vi  = aj + diag[i] + 1;
1390     nz  = ai[i+1] - diag[i] - 1;
1391     s1  = tmp[i];
1392     s1 *= (*v++);  /* multiply by inverse of diagonal entry */
1393     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1394     tmp[i] = s1;
1395   }
1396 
1397   /* backward solve the L^T */
1398   for (i=n-1; i>=0; i--){
1399     v   = aa + diag[i] - 1 ;
1400     vi  = aj + diag[i] - 1 ;
1401     nz  = diag[i] - ai[i];
1402     s1  = tmp[i];
1403     for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j];
1404   }
1405 
1406   /* copy tmp into x according to permutation */
1407   for (i=0; i<n; i++) x[r[i]] = tmp[i];
1408 
1409   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1410   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1411   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1412   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1413 
1414   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1415   PetscFunctionReturn(0);
1416 }
1417 
1418 #undef __FUNCT__
1419 #define __FUNCT__ "MatSolveTranspose_SeqAIJ"
1420 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx)
1421 {
1422   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1423   IS                iscol = a->col,isrow = a->row;
1424   PetscErrorCode    ierr;
1425   const PetscInt    *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi;
1426   PetscInt          i,n = A->rmap->n,j;
1427   PetscInt          nz;
1428   PetscScalar       *x,*tmp,s1;
1429   const MatScalar   *aa = a->a,*v;
1430   const PetscScalar *b;
1431 
1432   PetscFunctionBegin;
1433   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1434   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1435   tmp  = a->solve_work;
1436 
1437   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1438   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1439 
1440   /* copy the b into temp work space according to permutation */
1441   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1442 
1443   /* forward solve the U^T */
1444   for (i=0; i<n; i++) {
1445     v   = aa + adiag[i+1] + 1;
1446     vi  = aj + adiag[i+1] + 1;
1447     nz  = adiag[i] - adiag[i+1] - 1;
1448     s1  = tmp[i];
1449     s1 *= v[nz];  /* multiply by inverse of diagonal entry */
1450     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1451     tmp[i] = s1;
1452   }
1453 
1454   /* backward solve the L^T */
1455   for (i=n-1; i>=0; i--){
1456     v   = aa + ai[i];
1457     vi  = aj + ai[i];
1458     nz  = ai[i+1] - ai[i];
1459     s1  = tmp[i];
1460     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1461   }
1462 
1463   /* copy tmp into x according to permutation */
1464   for (i=0; i<n; i++) x[r[i]] = tmp[i];
1465 
1466   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1467   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1468   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1469   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1470 
1471   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1472   PetscFunctionReturn(0);
1473 }
1474 
1475 #undef __FUNCT__
1476 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ_inplace"
1477 PetscErrorCode MatSolveTransposeAdd_SeqAIJ_inplace(Mat A,Vec bb,Vec zz,Vec xx)
1478 {
1479   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1480   IS                iscol = a->col,isrow = a->row;
1481   PetscErrorCode    ierr;
1482   const PetscInt    *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi;
1483   PetscInt          i,n = A->rmap->n,j;
1484   PetscInt          nz;
1485   PetscScalar       *x,*tmp,s1;
1486   const MatScalar   *aa = a->a,*v;
1487   const PetscScalar *b;
1488 
1489   PetscFunctionBegin;
1490   if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);}
1491   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1492   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1493   tmp  = a->solve_work;
1494 
1495   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1496   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1497 
1498   /* copy the b into temp work space according to permutation */
1499   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1500 
1501   /* forward solve the U^T */
1502   for (i=0; i<n; i++) {
1503     v   = aa + diag[i] ;
1504     vi  = aj + diag[i] + 1;
1505     nz  = ai[i+1] - diag[i] - 1;
1506     s1  = tmp[i];
1507     s1 *= (*v++);  /* multiply by inverse of diagonal entry */
1508     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1509     tmp[i] = s1;
1510   }
1511 
1512   /* backward solve the L^T */
1513   for (i=n-1; i>=0; i--){
1514     v   = aa + diag[i] - 1 ;
1515     vi  = aj + diag[i] - 1 ;
1516     nz  = diag[i] - ai[i];
1517     s1  = tmp[i];
1518     for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j];
1519   }
1520 
1521   /* copy tmp into x according to permutation */
1522   for (i=0; i<n; i++) x[r[i]] += tmp[i];
1523 
1524   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1525   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1526   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1527   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1528 
1529   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1530   PetscFunctionReturn(0);
1531 }
1532 
1533 #undef __FUNCT__
1534 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ"
1535 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx)
1536 {
1537   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1538   IS                iscol = a->col,isrow = a->row;
1539   PetscErrorCode    ierr;
1540   const PetscInt    *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi;
1541   PetscInt          i,n = A->rmap->n,j;
1542   PetscInt          nz;
1543   PetscScalar       *x,*tmp,s1;
1544   const MatScalar   *aa = a->a,*v;
1545   const PetscScalar *b;
1546 
1547   PetscFunctionBegin;
1548   if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);}
1549   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1550   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1551   tmp  = a->solve_work;
1552 
1553   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1554   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1555 
1556   /* copy the b into temp work space according to permutation */
1557   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1558 
1559   /* forward solve the U^T */
1560   for (i=0; i<n; i++) {
1561     v   = aa + adiag[i+1] + 1;
1562     vi  = aj + adiag[i+1] + 1;
1563     nz  = adiag[i] - adiag[i+1] - 1;
1564     s1  = tmp[i];
1565     s1 *= v[nz];  /* multiply by inverse of diagonal entry */
1566     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1567     tmp[i] = s1;
1568   }
1569 
1570 
1571   /* backward solve the L^T */
1572   for (i=n-1; i>=0; i--){
1573     v   = aa + ai[i] ;
1574     vi  = aj + ai[i];
1575     nz  = ai[i+1] - ai[i];
1576     s1  = tmp[i];
1577     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1578   }
1579 
1580   /* copy tmp into x according to permutation */
1581   for (i=0; i<n; i++) x[r[i]] += tmp[i];
1582 
1583   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1584   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1585   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1586   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1587 
1588   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1589   PetscFunctionReturn(0);
1590 }
1591 
1592 /* ----------------------------------------------------------------*/
1593 
1594 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption,PetscTruth);
1595 
1596 /*
1597    ilu() under revised new data structure.
1598    Factored arrays bj and ba are stored as
1599      L(0,:), L(1,:), ...,L(n-1,:),  U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:)
1600 
1601    bi=fact->i is an array of size n+1, in which
1602    bi+
1603      bi[i]:  points to 1st entry of L(i,:),i=0,...,n-1
1604      bi[n]:  points to L(n-1,n-1)+1
1605 
1606   bdiag=fact->diag is an array of size n+1,in which
1607      bdiag[i]: points to diagonal of U(i,:), i=0,...,n-1
1608      bdiag[n]: points to entry of U(n-1,0)-1
1609 
1610    U(i,:) contains bdiag[i] as its last entry, i.e.,
1611     U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i])
1612 */
1613 #undef __FUNCT__
1614 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0"
1615 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1616 {
1617 
1618   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1619   PetscErrorCode     ierr;
1620   PetscInt           n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag;
1621   PetscInt           i,j,nz,*bi,*bj,*bdiag;
1622   PetscTruth         missing;
1623   IS                 isicol;
1624 
1625   PetscFunctionBegin;
1626   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);
1627   ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
1628   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
1629   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1630 
1631   ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr);
1632   b    = (Mat_SeqAIJ*)(fact)->data;
1633 
1634   /* allocate matrix arrays for new data structure */
1635   ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,n+1,PetscInt,&b->i);CHKERRQ(ierr);
1636   ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));CHKERRQ(ierr);
1637   b->singlemalloc = PETSC_TRUE;
1638   if (!b->diag){
1639     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr);
1640     ierr = PetscLogObjectMemory(fact,(n+1)*sizeof(PetscInt));CHKERRQ(ierr);
1641   }
1642   bdiag = b->diag;
1643 
1644   if (n > 0) {
1645     ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr);
1646   }
1647 
1648   /* set bi and bj with new data structure */
1649   bi = b->i;
1650   bj = b->j;
1651 
1652   /* L part */
1653   bi[0] = 0;
1654   for (i=0; i<n; i++){
1655     nz = adiag[i] - ai[i];
1656     bi[i+1] = bi[i] + nz;
1657     aj = a->j + ai[i];
1658     for (j=0; j<nz; j++){
1659       *bj = aj[j]; bj++;
1660     }
1661   }
1662 
1663   /* U part */
1664   bdiag[n] = bi[n]-1;
1665   for (i=n-1; i>=0; i--){
1666     nz = ai[i+1] - adiag[i] - 1;
1667     aj = a->j + adiag[i] + 1;
1668     for (j=0; j<nz; j++){
1669       *bj = aj[j]; bj++;
1670     }
1671     /* diag[i] */
1672     *bj = i; bj++;
1673     bdiag[i] = bdiag[i+1] + nz + 1;
1674   }
1675 
1676   fact->factor                 = MAT_FACTOR_ILU;
1677   fact->info.factor_mallocs    = 0;
1678   fact->info.fill_ratio_given  = info->fill;
1679   fact->info.fill_ratio_needed = 1.0;
1680   fact->ops->lufactornumeric   = MatLUFactorNumeric_SeqAIJ;
1681 
1682   b       = (Mat_SeqAIJ*)(fact)->data;
1683   b->row  = isrow;
1684   b->col  = iscol;
1685   b->icol = isicol;
1686   ierr    = PetscMalloc((fact->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1687   ierr    = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1688   ierr    = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1689   PetscFunctionReturn(0);
1690 }
1691 
1692 #undef __FUNCT__
1693 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ"
1694 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1695 {
1696   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1697   IS                 isicol;
1698   PetscErrorCode     ierr;
1699   const PetscInt     *r,*ic;
1700   PetscInt           n=A->rmap->n,*ai=a->i,*aj=a->j;
1701   PetscInt           *bi,*cols,nnz,*cols_lvl;
1702   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1703   PetscInt           i,levels,diagonal_fill;
1704   PetscTruth         col_identity,row_identity;
1705   PetscReal          f;
1706   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
1707   PetscBT            lnkbt;
1708   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
1709   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1710   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1711   PetscTruth         olddatastruct=PETSC_FALSE;
1712 
1713   PetscFunctionBegin;
1714   ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_old",&olddatastruct,PETSC_NULL);CHKERRQ(ierr);
1715   if(olddatastruct){
1716     ierr = MatILUFactorSymbolic_SeqAIJ_inplace(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1717     PetscFunctionReturn(0);
1718   }
1719 
1720   levels = (PetscInt)info->levels;
1721   ierr   = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1722   ierr   = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
1723 
1724   if (!levels && row_identity && col_identity) {
1725     /* special case: ilu(0) with natural ordering */
1726     ierr = MatILUFactorSymbolic_SeqAIJ_ilu0(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1727     ierr = Mat_CheckInode_FactorLU(fact,PETSC_FALSE);CHKERRQ(ierr);
1728     PetscFunctionReturn(0);
1729   }
1730 
1731   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);
1732   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1733   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1734   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1735 
1736   /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
1737   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1738   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
1739   bi[0] = bdiag[0] = 0;
1740 
1741   ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr);
1742 
1743   /* create a linked list for storing column indices of the active row */
1744   nlnk = n + 1;
1745   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1746 
1747   /* initial FreeSpace size is f*(ai[n]+1) */
1748   f             = info->fill;
1749   diagonal_fill = (PetscInt)info->diagonal_fill;
1750   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
1751   current_space = free_space;
1752   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
1753   current_space_lvl = free_space_lvl;
1754 
1755   for (i=0; i<n; i++) {
1756     nzi = 0;
1757     /* copy current row into linked list */
1758     nnz  = ai[r[i]+1] - ai[r[i]];
1759     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1760     cols = aj + ai[r[i]];
1761     lnk[i] = -1; /* marker to indicate if diagonal exists */
1762     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1763     nzi += nlnk;
1764 
1765     /* make sure diagonal entry is included */
1766     if (diagonal_fill && lnk[i] == -1) {
1767       fm = n;
1768       while (lnk[fm] < i) fm = lnk[fm];
1769       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
1770       lnk[fm]    = i;
1771       lnk_lvl[i] = 0;
1772       nzi++; dcount++;
1773     }
1774 
1775     /* add pivot rows into the active row */
1776     nzbd = 0;
1777     prow = lnk[n];
1778     while (prow < i) {
1779       nnz      = bdiag[prow];
1780       cols     = bj_ptr[prow] + nnz + 1;
1781       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1782       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
1783       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
1784       nzi += nlnk;
1785       prow = lnk[prow];
1786       nzbd++;
1787     }
1788     bdiag[i] = nzbd;
1789     bi[i+1]  = bi[i] + nzi;
1790 
1791     /* if free space is not available, make more free space */
1792     if (current_space->local_remaining<nzi) {
1793       nnz = 2*nzi*(n - i); /* estimated and max additional space needed */
1794       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
1795       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
1796       reallocs++;
1797     }
1798 
1799     /* copy data into free_space and free_space_lvl, then initialize lnk */
1800     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1801     bj_ptr[i]    = current_space->array;
1802     bjlvl_ptr[i] = current_space_lvl->array;
1803 
1804     /* make sure the active row i has diagonal entry */
1805     if (*(bj_ptr[i]+bdiag[i]) != i) {
1806       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
1807     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
1808     }
1809 
1810     current_space->array           += nzi;
1811     current_space->local_used      += nzi;
1812     current_space->local_remaining -= nzi;
1813     current_space_lvl->array           += nzi;
1814     current_space_lvl->local_used      += nzi;
1815     current_space_lvl->local_remaining -= nzi;
1816   }
1817 
1818   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1819   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1820 
1821   /* destroy list of free space and other temporary arrays */
1822   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
1823 
1824   /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */
1825   ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr);
1826 
1827   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1828   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
1829   ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr);
1830 
1831 #if defined(PETSC_USE_INFO)
1832   {
1833     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1834     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
1835     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
1836     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
1837     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
1838     if (diagonal_fill) {
1839       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
1840     }
1841   }
1842 #endif
1843 
1844   /* put together the new matrix */
1845   ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
1846   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
1847   b = (Mat_SeqAIJ*)(fact)->data;
1848   b->free_a       = PETSC_TRUE;
1849   b->free_ij      = PETSC_TRUE;
1850   b->singlemalloc = PETSC_FALSE;
1851   ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
1852   b->j          = bj;
1853   b->i          = bi;
1854   b->diag       = bdiag;
1855   b->ilen       = 0;
1856   b->imax       = 0;
1857   b->row        = isrow;
1858   b->col        = iscol;
1859   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1860   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1861   b->icol       = isicol;
1862   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1863   /* In b structure:  Free imax, ilen, old a, old j.
1864      Allocate bdiag, solve_work, new a, new j */
1865   ierr = PetscLogObjectMemory(fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
1866   b->maxnz = b->nz = bdiag[0]+1;
1867   (fact)->info.factor_mallocs    = reallocs;
1868   (fact)->info.fill_ratio_given  = f;
1869   (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]);
1870   (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ;
1871   ierr = Mat_CheckInode_FactorLU(fact,PETSC_FALSE);CHKERRQ(ierr);
1872   PetscFunctionReturn(0);
1873 }
1874 
1875 #undef __FUNCT__
1876 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_inplace"
1877 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1878 {
1879   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1880   IS                 isicol;
1881   PetscErrorCode     ierr;
1882   const PetscInt     *r,*ic;
1883   PetscInt           n=A->rmap->n,*ai=a->i,*aj=a->j,d;
1884   PetscInt           *bi,*cols,nnz,*cols_lvl;
1885   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1886   PetscInt           i,levels,diagonal_fill;
1887   PetscTruth         col_identity,row_identity;
1888   PetscReal          f;
1889   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
1890   PetscBT            lnkbt;
1891   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
1892   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1893   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1894   PetscTruth         missing;
1895 
1896   PetscFunctionBegin;
1897   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);
1898   f             = info->fill;
1899   levels        = (PetscInt)info->levels;
1900   diagonal_fill = (PetscInt)info->diagonal_fill;
1901   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1902 
1903   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1904   ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
1905   if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */
1906     ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr);
1907     (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ_inplace;
1908 
1909     fact->factor = MAT_FACTOR_ILU;
1910     (fact)->info.factor_mallocs    = 0;
1911     (fact)->info.fill_ratio_given  = info->fill;
1912     (fact)->info.fill_ratio_needed = 1.0;
1913     b               = (Mat_SeqAIJ*)(fact)->data;
1914     ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
1915     if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
1916     b->row              = isrow;
1917     b->col              = iscol;
1918     b->icol             = isicol;
1919     ierr                = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1920     ierr                = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1921     ierr                = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1922     ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1923     PetscFunctionReturn(0);
1924   }
1925 
1926   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1927   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1928 
1929   /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
1930   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1931   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
1932   bi[0] = bdiag[0] = 0;
1933 
1934   ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr);
1935 
1936   /* create a linked list for storing column indices of the active row */
1937   nlnk = n + 1;
1938   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1939 
1940   /* initial FreeSpace size is f*(ai[n]+1) */
1941   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
1942   current_space = free_space;
1943   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
1944   current_space_lvl = free_space_lvl;
1945 
1946   for (i=0; i<n; i++) {
1947     nzi = 0;
1948     /* copy current row into linked list */
1949     nnz  = ai[r[i]+1] - ai[r[i]];
1950     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1951     cols = aj + ai[r[i]];
1952     lnk[i] = -1; /* marker to indicate if diagonal exists */
1953     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1954     nzi += nlnk;
1955 
1956     /* make sure diagonal entry is included */
1957     if (diagonal_fill && lnk[i] == -1) {
1958       fm = n;
1959       while (lnk[fm] < i) fm = lnk[fm];
1960       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
1961       lnk[fm]    = i;
1962       lnk_lvl[i] = 0;
1963       nzi++; dcount++;
1964     }
1965 
1966     /* add pivot rows into the active row */
1967     nzbd = 0;
1968     prow = lnk[n];
1969     while (prow < i) {
1970       nnz      = bdiag[prow];
1971       cols     = bj_ptr[prow] + nnz + 1;
1972       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1973       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
1974       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
1975       nzi += nlnk;
1976       prow = lnk[prow];
1977       nzbd++;
1978     }
1979     bdiag[i] = nzbd;
1980     bi[i+1]  = bi[i] + nzi;
1981 
1982     /* if free space is not available, make more free space */
1983     if (current_space->local_remaining<nzi) {
1984       nnz = nzi*(n - i); /* estimated and max additional space needed */
1985       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
1986       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
1987       reallocs++;
1988     }
1989 
1990     /* copy data into free_space and free_space_lvl, then initialize lnk */
1991     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1992     bj_ptr[i]    = current_space->array;
1993     bjlvl_ptr[i] = current_space_lvl->array;
1994 
1995     /* make sure the active row i has diagonal entry */
1996     if (*(bj_ptr[i]+bdiag[i]) != i) {
1997       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
1998     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
1999     }
2000 
2001     current_space->array           += nzi;
2002     current_space->local_used      += nzi;
2003     current_space->local_remaining -= nzi;
2004     current_space_lvl->array           += nzi;
2005     current_space_lvl->local_used      += nzi;
2006     current_space_lvl->local_remaining -= nzi;
2007   }
2008 
2009   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
2010   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
2011 
2012   /* destroy list of free space and other temporary arrays */
2013   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
2014   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */
2015   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2016   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2017   ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr);
2018 
2019 #if defined(PETSC_USE_INFO)
2020   {
2021     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
2022     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
2023     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2024     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
2025     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
2026     if (diagonal_fill) {
2027       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
2028     }
2029   }
2030 #endif
2031 
2032   /* put together the new matrix */
2033   ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
2034   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
2035   b = (Mat_SeqAIJ*)(fact)->data;
2036   b->free_a       = PETSC_TRUE;
2037   b->free_ij      = PETSC_TRUE;
2038   b->singlemalloc = PETSC_FALSE;
2039   ierr = PetscMalloc(bi[n]*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
2040   b->j          = bj;
2041   b->i          = bi;
2042   for (i=0; i<n; i++) bdiag[i] += bi[i];
2043   b->diag       = bdiag;
2044   b->ilen       = 0;
2045   b->imax       = 0;
2046   b->row        = isrow;
2047   b->col        = iscol;
2048   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
2049   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
2050   b->icol       = isicol;
2051   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2052   /* In b structure:  Free imax, ilen, old a, old j.
2053      Allocate bdiag, solve_work, new a, new j */
2054   ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
2055   b->maxnz             = b->nz = bi[n] ;
2056   (fact)->info.factor_mallocs    = reallocs;
2057   (fact)->info.fill_ratio_given  = f;
2058   (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
2059   (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ_inplace;
2060   ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr);
2061   PetscFunctionReturn(0);
2062 }
2063 
2064 #undef __FUNCT__
2065 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ"
2066 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info)
2067 {
2068   Mat            C = B;
2069   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
2070   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
2071   IS             ip=b->row,iip = b->icol;
2072   PetscErrorCode ierr;
2073   const PetscInt *rip,*riip;
2074   PetscInt       i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp;
2075   PetscInt       *ai=a->i,*aj=a->j;
2076   PetscInt       k,jmin,jmax,*c2r,*il,col,nexti,ili,nz;
2077   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
2078   PetscTruth     perm_identity;
2079 
2080   LUShift_Ctx    sctx;
2081   PetscInt       newshift;
2082   PetscReal      rs;
2083   MatScalar      d,*v;
2084 
2085   PetscFunctionBegin;
2086   /* MatPivotSetUp(): initialize shift context sctx */
2087   ierr = PetscMemzero(&sctx,sizeof(LUShift_Ctx));CHKERRQ(ierr);
2088 
2089   /* if both shift schemes are chosen by user, only use info->shiftpd */
2090   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
2091     sctx.shift_top = info->zeropivot;
2092     for (i=0; i<mbs; i++) {
2093       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
2094       d  = (aa)[a->diag[i]];
2095       rs = -PetscAbsScalar(d) - PetscRealPart(d);
2096       v  = aa+ai[i];
2097       nz = ai[i+1] - ai[i];
2098       for (j=0; j<nz; j++)
2099 	rs += PetscAbsScalar(v[j]);
2100       if (rs>sctx.shift_top) sctx.shift_top = rs;
2101     }
2102     sctx.shift_top   *= 1.1;
2103     sctx.nshift_max   = 5;
2104     sctx.shift_lo     = 0.;
2105     sctx.shift_hi     = 1.;
2106   }
2107 
2108   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
2109   ierr  = ISGetIndices(iip,&riip);CHKERRQ(ierr);
2110 
2111   /* allocate working arrays
2112      c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col
2113      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
2114   */
2115   ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&c2r);CHKERRQ(ierr);
2116 
2117   do {
2118     sctx.lushift = PETSC_FALSE;
2119 
2120     for (i=0; i<mbs; i++) c2r[i] = mbs;
2121     il[0] = 0;
2122 
2123     for (k = 0; k<mbs; k++){
2124       /* zero rtmp */
2125       nz = bi[k+1] - bi[k];
2126       bjtmp = bj + bi[k];
2127       for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
2128 
2129       /* load in initial unfactored row */
2130       bval = ba + bi[k];
2131       jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2132       for (j = jmin; j < jmax; j++){
2133         col = riip[aj[j]];
2134         if (col >= k){ /* only take upper triangular entry */
2135           rtmp[col] = aa[j];
2136           *bval++   = 0.0; /* for in-place factorization */
2137         }
2138       }
2139       /* shift the diagonal of the matrix: ZeropivotApply() */
2140       rtmp[k] += sctx.shift_amount;  /* shift the diagonal of the matrix */
2141 
2142       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
2143       dk = rtmp[k];
2144       i  = c2r[k]; /* first row to be added to k_th row  */
2145 
2146       while (i < k){
2147         nexti = c2r[i]; /* next row to be added to k_th row */
2148 
2149         /* compute multiplier, update diag(k) and U(i,k) */
2150         ili   = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2151         uikdi = - ba[ili]*ba[bdiag[i]];  /* diagonal(k) */
2152         dk   += uikdi*ba[ili]; /* update diag[k] */
2153         ba[ili] = uikdi; /* -U(i,k) */
2154 
2155         /* add multiple of row i to k-th row */
2156         jmin = ili + 1; jmax = bi[i+1];
2157         if (jmin < jmax){
2158           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2159           /* update il and c2r for row i */
2160           il[i] = jmin;
2161           j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i;
2162         }
2163         i = nexti;
2164       }
2165 
2166       /* copy data into U(k,:) */
2167       rs   = 0.0;
2168       jmin = bi[k]; jmax = bi[k+1]-1;
2169       if (jmin < jmax) {
2170         for (j=jmin; j<jmax; j++){
2171           col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]);
2172         }
2173         /* add the k-th row into il and c2r */
2174         il[k] = jmin;
2175         i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k;
2176       }
2177 
2178       /* MatPivotCheck() */
2179       sctx.rs  = rs;
2180       sctx.pv  = dk;
2181       if (info->shiftnz){
2182         ierr = MatPivotCheck_nz(info,sctx,k,newshift);CHKERRQ(ierr);
2183       } else if (info->shiftpd){
2184         ierr = MatPivotCheck_pd(info,sctx,k,newshift);CHKERRQ(ierr);
2185       } else if (info->shiftinblocks){
2186         ierr = MatPivotCheck_inblocks(info,sctx,k,newshift);CHKERRQ(ierr);
2187       } else {
2188         ierr = MatPivotCheck_none(info,sctx,k,newshift);CHKERRQ(ierr);
2189       }
2190       dk = sctx.pv;
2191       if (newshift == 1) break;
2192 
2193       ba[bdiag[k]] = 1.0/dk; /* U(k,k) */
2194     }
2195   } while (sctx.lushift);
2196 
2197   ierr = PetscFree3(rtmp,il,c2r);CHKERRQ(ierr);
2198   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2199   ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr);
2200 
2201   ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
2202   if (perm_identity){
2203     B->ops->solve           = MatSolve_SeqSBAIJ_1_NaturalOrdering;
2204     B->ops->solvetranspose  = MatSolve_SeqSBAIJ_1_NaturalOrdering;
2205     B->ops->forwardsolve    = 0;
2206     B->ops->backwardsolve   = 0;
2207   } else {
2208     B->ops->solve           = MatSolve_SeqSBAIJ_1;
2209     B->ops->solvetranspose  = MatSolve_SeqSBAIJ_1;
2210     B->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1;
2211     B->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1;
2212   }
2213 
2214   C->assembled    = PETSC_TRUE;
2215   C->preallocated = PETSC_TRUE;
2216   ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr);
2217 
2218   /* MatPivotView() */
2219   if (sctx.nshift){
2220     if (info->shiftpd) {
2221       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);
2222     } else if (info->shiftnz) {
2223       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2224     } else if (info->shiftinblocks){
2225       ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftinblocks);CHKERRQ(ierr);
2226     }
2227   }
2228   PetscFunctionReturn(0);
2229 }
2230 
2231 #undef __FUNCT__
2232 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ_inplace"
2233 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info)
2234 {
2235   Mat            C = B;
2236   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
2237   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
2238   IS             ip=b->row,iip = b->icol;
2239   PetscErrorCode ierr;
2240   const PetscInt *rip,*riip;
2241   PetscInt       i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol,*bjtmp;
2242   PetscInt       *ai=a->i,*aj=a->j;
2243   PetscInt       k,jmin,jmax,*jl,*il,col,nexti,ili,nz;
2244   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
2245   PetscReal      zeropivot,rs,shiftnz;
2246   PetscReal      shiftpd;
2247   ChShift_Ctx    sctx;
2248   PetscInt       newshift;
2249   PetscTruth     perm_identity;
2250 
2251   PetscFunctionBegin;
2252   shiftnz   = info->shiftnz;
2253   shiftpd   = info->shiftpd;
2254   zeropivot = info->zeropivot;
2255 
2256   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
2257   ierr  = ISGetIndices(iip,&riip);CHKERRQ(ierr);
2258 
2259   /* initialization */
2260   ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&jl);CHKERRQ(ierr);
2261   sctx.shift_amount = 0;
2262   sctx.nshift       = 0;
2263   do {
2264     sctx.chshift = PETSC_FALSE;
2265     for (i=0; i<mbs; i++) jl[i] = mbs;
2266     il[0] = 0;
2267 
2268     for (k = 0; k<mbs; k++){
2269       /* zero rtmp */
2270       nz = bi[k+1] - bi[k];
2271       bjtmp = bj + bi[k];
2272       for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
2273 
2274       bval = ba + bi[k];
2275       /* initialize k-th row by the perm[k]-th row of A */
2276       jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2277       for (j = jmin; j < jmax; j++){
2278         col = riip[aj[j]];
2279         if (col >= k){ /* only take upper triangular entry */
2280           rtmp[col] = aa[j];
2281           *bval++  = 0.0; /* for in-place factorization */
2282         }
2283       }
2284       /* shift the diagonal of the matrix */
2285       if (sctx.nshift) rtmp[k] += sctx.shift_amount;
2286 
2287       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
2288       dk = rtmp[k];
2289       i = jl[k]; /* first row to be added to k_th row  */
2290 
2291       while (i < k){
2292         nexti = jl[i]; /* next row to be added to k_th row */
2293 
2294         /* compute multiplier, update diag(k) and U(i,k) */
2295         ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2296         uikdi = - ba[ili]*ba[bi[i]];  /* diagonal(k) */
2297         dk += uikdi*ba[ili];
2298         ba[ili] = uikdi; /* -U(i,k) */
2299 
2300         /* add multiple of row i to k-th row */
2301         jmin = ili + 1; jmax = bi[i+1];
2302         if (jmin < jmax){
2303           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2304           /* update il and jl for row i */
2305           il[i] = jmin;
2306           j = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
2307         }
2308         i = nexti;
2309       }
2310 
2311       /* shift the diagonals when zero pivot is detected */
2312       /* compute rs=sum of abs(off-diagonal) */
2313       rs   = 0.0;
2314       jmin = bi[k]+1;
2315       nz   = bi[k+1] - jmin;
2316       bcol = bj + jmin;
2317       for (j=0; j<nz; j++) {
2318         rs += PetscAbsScalar(rtmp[bcol[j]]);
2319       }
2320 
2321       sctx.rs = rs;
2322       sctx.pv = dk;
2323       ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr);
2324 
2325       if (newshift == 1) {
2326         if (!sctx.shift_amount) {
2327           sctx.shift_amount = 1e-5;
2328         }
2329         break;
2330       }
2331 
2332       /* copy data into U(k,:) */
2333       ba[bi[k]] = 1.0/dk; /* U(k,k) */
2334       jmin = bi[k]+1; jmax = bi[k+1];
2335       if (jmin < jmax) {
2336         for (j=jmin; j<jmax; j++){
2337           col = bj[j]; ba[j] = rtmp[col];
2338         }
2339         /* add the k-th row into il and jl */
2340         il[k] = jmin;
2341         i = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
2342       }
2343     }
2344   } while (sctx.chshift);
2345   ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr);
2346   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2347   ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr);
2348 
2349   ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
2350   if (perm_identity){
2351     B->ops->solve           = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
2352     B->ops->solvetranspose  = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
2353     B->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
2354     B->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
2355   } else {
2356     B->ops->solve           = MatSolve_SeqSBAIJ_1_inplace;
2357     B->ops->solvetranspose  = MatSolve_SeqSBAIJ_1_inplace;
2358     B->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1_inplace;
2359     B->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1_inplace;
2360   }
2361 
2362   C->assembled    = PETSC_TRUE;
2363   C->preallocated = PETSC_TRUE;
2364   ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr);
2365   if (sctx.nshift){
2366     if (shiftnz) {
2367       ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2368     } else if (shiftpd) {
2369       ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2370     }
2371   }
2372   PetscFunctionReturn(0);
2373 }
2374 
2375 /*
2376    icc() under revised new data structure.
2377    Factored arrays bj and ba are stored as
2378      U(0,:),...,U(i,:),U(n-1,:)
2379 
2380    ui=fact->i is an array of size n+1, in which
2381    ui+
2382      ui[i]:  points to 1st entry of U(i,:),i=0,...,n-1
2383      ui[n]:  points to U(n-1,n-1)+1
2384 
2385   udiag=fact->diag is an array of size n,in which
2386      udiag[i]: points to diagonal of U(i,:), i=0,...,n-1
2387 
2388    U(i,:) contains udiag[i] as its last entry, i.e.,
2389     U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i])
2390 */
2391 
2392 #undef __FUNCT__
2393 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ"
2394 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2395 {
2396   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2397   Mat_SeqSBAIJ       *b;
2398   PetscErrorCode     ierr;
2399   PetscTruth         perm_identity,missing;
2400   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag;
2401   const PetscInt     *rip,*riip;
2402   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
2403   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL,d;
2404   PetscInt           ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
2405   PetscReal          fill=info->fill,levels=info->levels;
2406   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2407   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
2408   PetscBT            lnkbt;
2409   IS                 iperm;
2410   PetscTruth         olddatastruct=PETSC_FALSE;
2411 
2412   PetscFunctionBegin;
2413   ierr = PetscOptionsGetTruth(PETSC_NULL,"-icc_old",&olddatastruct,PETSC_NULL);CHKERRQ(ierr);
2414   if(olddatastruct){
2415     ierr = MatICCFactorSymbolic_SeqAIJ_inplace(fact,A,perm,info);CHKERRQ(ierr);
2416     PetscFunctionReturn(0);
2417   }
2418   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);
2419   ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
2420   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
2421   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2422   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2423 
2424   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2425   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2426   ui[0] = 0;
2427 
2428   /* ICC(0) without matrix ordering: simply rearrange column indices */
2429   if (!levels && perm_identity) {
2430     for (i=0; i<am; i++) {
2431       ncols    = ai[i+1] - a->diag[i];
2432       ui[i+1]  = ui[i] + ncols;
2433       udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */
2434     }
2435     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2436     cols = uj;
2437     for (i=0; i<am; i++) {
2438       aj    = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */
2439       ncols = ai[i+1] - a->diag[i] -1;
2440       for (j=0; j<ncols; j++) *cols++ = aj[j];
2441       *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */
2442     }
2443   } else { /* case: levels>0 || (levels=0 && !perm_identity) */
2444     ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2445     ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2446 
2447     /* initialization */
2448     ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr);
2449 
2450     /* jl: linked list for storing indices of the pivot rows
2451        il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2452     ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr);
2453     for (i=0; i<am; i++){
2454       jl[i] = am; il[i] = 0;
2455     }
2456 
2457     /* create and initialize a linked list for storing column indices of the active row k */
2458     nlnk = am + 1;
2459     ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2460 
2461     /* initial FreeSpace size is fill*(ai[am]+1) */
2462     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2463     current_space = free_space;
2464     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr);
2465     current_space_lvl = free_space_lvl;
2466 
2467     for (k=0; k<am; k++){  /* for each active row k */
2468       /* initialize lnk by the column indices of row rip[k] of A */
2469       nzk   = 0;
2470       ncols = ai[rip[k]+1] - ai[rip[k]];
2471       if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2472       ncols_upper = 0;
2473       for (j=0; j<ncols; j++){
2474         i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2475         if (riip[i] >= k){ /* only take upper triangular entry */
2476           ajtmp[ncols_upper] = i;
2477           ncols_upper++;
2478         }
2479       }
2480       ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2481       nzk += nlnk;
2482 
2483       /* update lnk by computing fill-in for each pivot row to be merged in */
2484       prow = jl[k]; /* 1st pivot row */
2485 
2486       while (prow < k){
2487         nextprow = jl[prow];
2488 
2489         /* merge prow into k-th row */
2490         jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2491         jmax = ui[prow+1];
2492         ncols = jmax-jmin;
2493         i     = jmin - ui[prow];
2494         cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2495         uj    = uj_lvl_ptr[prow] + i; /* levels of cols */
2496         j     = *(uj - 1);
2497         ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr);
2498         nzk += nlnk;
2499 
2500         /* update il and jl for prow */
2501         if (jmin < jmax){
2502           il[prow] = jmin;
2503           j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2504         }
2505         prow = nextprow;
2506       }
2507 
2508       /* if free space is not available, make more free space */
2509       if (current_space->local_remaining<nzk) {
2510         i  = am - k + 1; /* num of unfactored rows */
2511         i *= PetscMin(nzk, i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */
2512         ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2513         ierr = PetscFreeSpaceGet(i,&current_space_lvl);CHKERRQ(ierr);
2514         reallocs++;
2515       }
2516 
2517       /* copy data into free_space and free_space_lvl, then initialize lnk */
2518       if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2519       ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
2520 
2521       /* add the k-th row into il and jl */
2522       if (nzk > 1){
2523         i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2524         jl[k] = jl[i]; jl[i] = k;
2525         il[k] = ui[k] + 1;
2526       }
2527       uj_ptr[k]     = current_space->array;
2528       uj_lvl_ptr[k] = current_space_lvl->array;
2529 
2530       current_space->array           += nzk;
2531       current_space->local_used      += nzk;
2532       current_space->local_remaining -= nzk;
2533 
2534       current_space_lvl->array           += nzk;
2535       current_space_lvl->local_used      += nzk;
2536       current_space_lvl->local_remaining -= nzk;
2537 
2538       ui[k+1] = ui[k] + nzk;
2539     }
2540 
2541 #if defined(PETSC_USE_INFO)
2542     if (ai[am] != 0) {
2543       PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]);
2544       ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2545       ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2546       ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2547     } else {
2548       ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2549     }
2550 #endif
2551 
2552     ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2553     ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2554     ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr);
2555     ierr = PetscFree(ajtmp);CHKERRQ(ierr);
2556 
2557     /* destroy list of free space and other temporary array(s) */
2558     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2559     ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor  */
2560     ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2561     ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2562 
2563   } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2564 
2565   /* put together the new matrix in MATSEQSBAIJ format */
2566   b    = (Mat_SeqSBAIJ*)(fact)->data;
2567   b->singlemalloc = PETSC_FALSE;
2568   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2569   b->j    = uj;
2570   b->i    = ui;
2571   b->diag = udiag;
2572   b->free_diag = PETSC_TRUE;
2573   b->ilen = 0;
2574   b->imax = 0;
2575   b->row  = perm;
2576   b->col  = perm;
2577   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2578   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2579   b->icol = iperm;
2580   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2581   ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2582   ierr = PetscLogObjectMemory(fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2583   b->maxnz   = b->nz = ui[am];
2584   b->free_a  = PETSC_TRUE;
2585   b->free_ij = PETSC_TRUE;
2586 
2587   fact->info.factor_mallocs    = reallocs;
2588   fact->info.fill_ratio_given  = fill;
2589   if (ai[am] != 0) {
2590     fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2591   } else {
2592     fact->info.fill_ratio_needed = 0.0;
2593   }
2594   fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2595   PetscFunctionReturn(0);
2596 }
2597 
2598 #undef __FUNCT__
2599 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ_inplace"
2600 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2601 {
2602   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2603   Mat_SeqSBAIJ       *b;
2604   PetscErrorCode     ierr;
2605   PetscTruth         perm_identity,missing;
2606   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag;
2607   const PetscInt     *rip,*riip;
2608   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
2609   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL,d;
2610   PetscInt           ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
2611   PetscReal          fill=info->fill,levels=info->levels;
2612   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2613   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
2614   PetscBT            lnkbt;
2615   IS                 iperm;
2616 
2617   PetscFunctionBegin;
2618   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);
2619   ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
2620   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
2621   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2622   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2623 
2624   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2625   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2626   ui[0] = 0;
2627 
2628   /* ICC(0) without matrix ordering: simply copies fill pattern */
2629   if (!levels && perm_identity) {
2630 
2631     for (i=0; i<am; i++) {
2632       ui[i+1]  = ui[i] + ai[i+1] - a->diag[i];
2633       udiag[i] = ui[i];
2634     }
2635     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2636     cols = uj;
2637     for (i=0; i<am; i++) {
2638       aj    = a->j + a->diag[i];
2639       ncols = ui[i+1] - ui[i];
2640       for (j=0; j<ncols; j++) *cols++ = *aj++;
2641     }
2642   } else { /* case: levels>0 || (levels=0 && !perm_identity) */
2643     ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2644     ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2645 
2646     /* initialization */
2647     ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr);
2648 
2649     /* jl: linked list for storing indices of the pivot rows
2650        il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2651     ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr);
2652     for (i=0; i<am; i++){
2653       jl[i] = am; il[i] = 0;
2654     }
2655 
2656     /* create and initialize a linked list for storing column indices of the active row k */
2657     nlnk = am + 1;
2658     ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2659 
2660     /* initial FreeSpace size is fill*(ai[am]+1) */
2661     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2662     current_space = free_space;
2663     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr);
2664     current_space_lvl = free_space_lvl;
2665 
2666     for (k=0; k<am; k++){  /* for each active row k */
2667       /* initialize lnk by the column indices of row rip[k] of A */
2668       nzk   = 0;
2669       ncols = ai[rip[k]+1] - ai[rip[k]];
2670       if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2671       ncols_upper = 0;
2672       for (j=0; j<ncols; j++){
2673         i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2674         if (riip[i] >= k){ /* only take upper triangular entry */
2675           ajtmp[ncols_upper] = i;
2676           ncols_upper++;
2677         }
2678       }
2679       ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2680       nzk += nlnk;
2681 
2682       /* update lnk by computing fill-in for each pivot row to be merged in */
2683       prow = jl[k]; /* 1st pivot row */
2684 
2685       while (prow < k){
2686         nextprow = jl[prow];
2687 
2688         /* merge prow into k-th row */
2689         jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2690         jmax = ui[prow+1];
2691         ncols = jmax-jmin;
2692         i     = jmin - ui[prow];
2693         cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2694         uj    = uj_lvl_ptr[prow] + i; /* levels of cols */
2695         j     = *(uj - 1);
2696         ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr);
2697         nzk += nlnk;
2698 
2699         /* update il and jl for prow */
2700         if (jmin < jmax){
2701           il[prow] = jmin;
2702           j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2703         }
2704         prow = nextprow;
2705       }
2706 
2707       /* if free space is not available, make more free space */
2708       if (current_space->local_remaining<nzk) {
2709         i = am - k + 1; /* num of unfactored rows */
2710         i *= PetscMin(nzk, (i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2711         ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2712         ierr = PetscFreeSpaceGet(i,&current_space_lvl);CHKERRQ(ierr);
2713         reallocs++;
2714       }
2715 
2716       /* copy data into free_space and free_space_lvl, then initialize lnk */
2717       if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2718       ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
2719 
2720       /* add the k-th row into il and jl */
2721       if (nzk > 1){
2722         i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2723         jl[k] = jl[i]; jl[i] = k;
2724         il[k] = ui[k] + 1;
2725       }
2726       uj_ptr[k]     = current_space->array;
2727       uj_lvl_ptr[k] = current_space_lvl->array;
2728 
2729       current_space->array           += nzk;
2730       current_space->local_used      += nzk;
2731       current_space->local_remaining -= nzk;
2732 
2733       current_space_lvl->array           += nzk;
2734       current_space_lvl->local_used      += nzk;
2735       current_space_lvl->local_remaining -= nzk;
2736 
2737       ui[k+1] = ui[k] + nzk;
2738     }
2739 
2740 #if defined(PETSC_USE_INFO)
2741     if (ai[am] != 0) {
2742       PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]);
2743       ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2744       ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2745       ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2746     } else {
2747       ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2748     }
2749 #endif
2750 
2751     ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2752     ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2753     ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr);
2754     ierr = PetscFree(ajtmp);CHKERRQ(ierr);
2755 
2756     /* destroy list of free space and other temporary array(s) */
2757     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2758     ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
2759     ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2760     ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2761 
2762   } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2763 
2764   /* put together the new matrix in MATSEQSBAIJ format */
2765 
2766   b    = (Mat_SeqSBAIJ*)fact->data;
2767   b->singlemalloc = PETSC_FALSE;
2768   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2769   b->j    = uj;
2770   b->i    = ui;
2771   b->diag = udiag;
2772   b->free_diag = PETSC_TRUE;
2773   b->ilen = 0;
2774   b->imax = 0;
2775   b->row  = perm;
2776   b->col  = perm;
2777   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2778   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2779   b->icol = iperm;
2780   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2781   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2782   ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2783   b->maxnz   = b->nz = ui[am];
2784   b->free_a  = PETSC_TRUE;
2785   b->free_ij = PETSC_TRUE;
2786 
2787   fact->info.factor_mallocs    = reallocs;
2788   fact->info.fill_ratio_given  = fill;
2789   if (ai[am] != 0) {
2790     fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2791   } else {
2792     fact->info.fill_ratio_needed = 0.0;
2793   }
2794   fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace;
2795   PetscFunctionReturn(0);
2796 }
2797 
2798 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2799 {
2800   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2801   Mat_SeqSBAIJ       *b;
2802   PetscErrorCode     ierr;
2803   PetscTruth         perm_identity;
2804   PetscReal          fill = info->fill;
2805   const PetscInt     *rip,*riip;
2806   PetscInt           i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow;
2807   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
2808   PetscInt           nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr,*udiag;
2809   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2810   PetscBT            lnkbt;
2811   IS                 iperm;
2812   PetscTruth         olddatastruct=PETSC_FALSE;
2813 
2814   PetscFunctionBegin;
2815   ierr = PetscOptionsGetTruth(PETSC_NULL,"-cholesky_old",&olddatastruct,PETSC_NULL);CHKERRQ(ierr);
2816   if(olddatastruct){
2817     ierr = MatCholeskyFactorSymbolic_SeqAIJ_inplace(fact,A,perm,info);CHKERRQ(ierr);
2818     PetscFunctionReturn(0);
2819   }
2820   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);
2821   /* check whether perm is the identity mapping */
2822   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2823   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2824   ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2825   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2826 
2827   /* initialization */
2828   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2829   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2830   ui[0] = 0;
2831 
2832   /* jl: linked list for storing indices of the pivot rows
2833      il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2834   ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr);
2835   for (i=0; i<am; i++){
2836     jl[i] = am; il[i] = 0;
2837   }
2838 
2839   /* create and initialize a linked list for storing column indices of the active row k */
2840   nlnk = am + 1;
2841   ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2842 
2843   /* initial FreeSpace size is fill*(ai[am]+1) */
2844   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2845   current_space = free_space;
2846 
2847   for (k=0; k<am; k++){  /* for each active row k */
2848     /* initialize lnk by the column indices of row rip[k] of A */
2849     nzk   = 0;
2850     ncols = ai[rip[k]+1] - ai[rip[k]];
2851     if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2852     ncols_upper = 0;
2853     for (j=0; j<ncols; j++){
2854       i = riip[*(aj + ai[rip[k]] + j)];
2855       if (i >= k){ /* only take upper triangular entry */
2856         cols[ncols_upper] = i;
2857         ncols_upper++;
2858       }
2859     }
2860     ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2861     nzk += nlnk;
2862 
2863     /* update lnk by computing fill-in for each pivot row to be merged in */
2864     prow = jl[k]; /* 1st pivot row */
2865 
2866     while (prow < k){
2867       nextprow = jl[prow];
2868       /* merge prow into k-th row */
2869       jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2870       jmax = ui[prow+1];
2871       ncols = jmax-jmin;
2872       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2873       ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2874       nzk += nlnk;
2875 
2876       /* update il and jl for prow */
2877       if (jmin < jmax){
2878         il[prow] = jmin;
2879         j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
2880       }
2881       prow = nextprow;
2882     }
2883 
2884     /* if free space is not available, make more free space */
2885     if (current_space->local_remaining<nzk) {
2886       i  = am - k + 1; /* num of unfactored rows */
2887       i *= PetscMin(nzk,i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */
2888       ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2889       reallocs++;
2890     }
2891 
2892     /* copy data into free space, then initialize lnk */
2893     ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
2894 
2895     /* add the k-th row into il and jl */
2896     if (nzk > 1){
2897       i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2898       jl[k] = jl[i]; jl[i] = k;
2899       il[k] = ui[k] + 1;
2900     }
2901     ui_ptr[k] = current_space->array;
2902     current_space->array           += nzk;
2903     current_space->local_used      += nzk;
2904     current_space->local_remaining -= nzk;
2905 
2906     ui[k+1] = ui[k] + nzk;
2907   }
2908 
2909 #if defined(PETSC_USE_INFO)
2910   if (ai[am] != 0) {
2911     PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]);
2912     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2913     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2914     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2915   } else {
2916      ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2917   }
2918 #endif
2919 
2920   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2921   ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2922   ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr);
2923 
2924   /* destroy list of free space and other temporary array(s) */
2925   ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2926   ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor */
2927   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2928 
2929   /* put together the new matrix in MATSEQSBAIJ format */
2930 
2931   b = (Mat_SeqSBAIJ*)fact->data;
2932   b->singlemalloc = PETSC_FALSE;
2933   b->free_a       = PETSC_TRUE;
2934   b->free_ij      = PETSC_TRUE;
2935   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2936   b->j    = uj;
2937   b->i    = ui;
2938   b->diag = udiag;
2939   b->free_diag = PETSC_TRUE;
2940   b->ilen = 0;
2941   b->imax = 0;
2942   b->row  = perm;
2943   b->col  = perm;
2944   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2945   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2946   b->icol = iperm;
2947   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2948   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2949   ierr    = PetscLogObjectMemory(fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2950   b->maxnz = b->nz = ui[am];
2951 
2952   fact->info.factor_mallocs    = reallocs;
2953   fact->info.fill_ratio_given  = fill;
2954   if (ai[am] != 0) {
2955     fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2956   } else {
2957     fact->info.fill_ratio_needed = 0.0;
2958   }
2959   fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2960   PetscFunctionReturn(0);
2961 }
2962 
2963 #undef __FUNCT__
2964 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ_inplace"
2965 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2966 {
2967   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2968   Mat_SeqSBAIJ       *b;
2969   PetscErrorCode     ierr;
2970   PetscTruth         perm_identity;
2971   PetscReal          fill = info->fill;
2972   const PetscInt     *rip,*riip;
2973   PetscInt           i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow;
2974   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
2975   PetscInt           nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr;
2976   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2977   PetscBT            lnkbt;
2978   IS                 iperm;
2979 
2980   PetscFunctionBegin;
2981   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);
2982   /* check whether perm is the identity mapping */
2983   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2984   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2985   ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2986   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2987 
2988   /* initialization */
2989   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2990   ui[0] = 0;
2991 
2992   /* jl: linked list for storing indices of the pivot rows
2993      il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2994   ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr);
2995   for (i=0; i<am; i++){
2996     jl[i] = am; il[i] = 0;
2997   }
2998 
2999   /* create and initialize a linked list for storing column indices of the active row k */
3000   nlnk = am + 1;
3001   ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3002 
3003   /* initial FreeSpace size is fill*(ai[am]+1) */
3004   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
3005   current_space = free_space;
3006 
3007   for (k=0; k<am; k++){  /* for each active row k */
3008     /* initialize lnk by the column indices of row rip[k] of A */
3009     nzk   = 0;
3010     ncols = ai[rip[k]+1] - ai[rip[k]];
3011     if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
3012     ncols_upper = 0;
3013     for (j=0; j<ncols; j++){
3014       i = riip[*(aj + ai[rip[k]] + j)];
3015       if (i >= k){ /* only take upper triangular entry */
3016         cols[ncols_upper] = i;
3017         ncols_upper++;
3018       }
3019     }
3020     ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3021     nzk += nlnk;
3022 
3023     /* update lnk by computing fill-in for each pivot row to be merged in */
3024     prow = jl[k]; /* 1st pivot row */
3025 
3026     while (prow < k){
3027       nextprow = jl[prow];
3028       /* merge prow into k-th row */
3029       jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
3030       jmax = ui[prow+1];
3031       ncols = jmax-jmin;
3032       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */
3033       ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3034       nzk += nlnk;
3035 
3036       /* update il and jl for prow */
3037       if (jmin < jmax){
3038         il[prow] = jmin;
3039         j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
3040       }
3041       prow = nextprow;
3042     }
3043 
3044     /* if free space is not available, make more free space */
3045     if (current_space->local_remaining<nzk) {
3046       i = am - k + 1; /* num of unfactored rows */
3047       i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
3048       ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
3049       reallocs++;
3050     }
3051 
3052     /* copy data into free space, then initialize lnk */
3053     ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
3054 
3055     /* add the k-th row into il and jl */
3056     if (nzk-1 > 0){
3057       i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
3058       jl[k] = jl[i]; jl[i] = k;
3059       il[k] = ui[k] + 1;
3060     }
3061     ui_ptr[k] = current_space->array;
3062     current_space->array           += nzk;
3063     current_space->local_used      += nzk;
3064     current_space->local_remaining -= nzk;
3065 
3066     ui[k+1] = ui[k] + nzk;
3067   }
3068 
3069 #if defined(PETSC_USE_INFO)
3070   if (ai[am] != 0) {
3071     PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]);
3072     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
3073     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
3074     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
3075   } else {
3076      ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
3077   }
3078 #endif
3079 
3080   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
3081   ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
3082   ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr);
3083 
3084   /* destroy list of free space and other temporary array(s) */
3085   ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
3086   ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
3087   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
3088 
3089   /* put together the new matrix in MATSEQSBAIJ format */
3090 
3091   b = (Mat_SeqSBAIJ*)fact->data;
3092   b->singlemalloc = PETSC_FALSE;
3093   b->free_a       = PETSC_TRUE;
3094   b->free_ij      = PETSC_TRUE;
3095   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
3096   b->j    = uj;
3097   b->i    = ui;
3098   b->diag = 0;
3099   b->ilen = 0;
3100   b->imax = 0;
3101   b->row  = perm;
3102   b->col  = perm;
3103   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
3104   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
3105   b->icol = iperm;
3106   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
3107   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
3108   ierr    = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
3109   b->maxnz = b->nz = ui[am];
3110 
3111   fact->info.factor_mallocs    = reallocs;
3112   fact->info.fill_ratio_given  = fill;
3113   if (ai[am] != 0) {
3114     fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
3115   } else {
3116     fact->info.fill_ratio_needed = 0.0;
3117   }
3118   fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace;
3119   PetscFunctionReturn(0);
3120 }
3121 
3122 #undef __FUNCT__
3123 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering"
3124 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx)
3125 {
3126   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
3127   PetscErrorCode    ierr;
3128   PetscInt          n = A->rmap->n;
3129   const PetscInt    *ai = a->i,*aj = a->j,*adiag = a->diag,*vi;
3130   PetscScalar       *x,sum;
3131   const PetscScalar *b;
3132   const MatScalar   *aa = a->a,*v;
3133   PetscInt          i,nz;
3134 
3135   PetscFunctionBegin;
3136   if (!n) PetscFunctionReturn(0);
3137 
3138   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3139   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3140 
3141   /* forward solve the lower triangular */
3142   x[0] = b[0];
3143   v    = aa;
3144   vi   = aj;
3145   for (i=1; i<n; i++) {
3146     nz  = ai[i+1] - ai[i];
3147     sum = b[i];
3148     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
3149     v  += nz;
3150     vi += nz;
3151     x[i] = sum;
3152   }
3153 
3154   /* backward solve the upper triangular */
3155   for (i=n-1; i>=0; i--){
3156     v   = aa + adiag[i+1] + 1;
3157     vi  = aj + adiag[i+1] + 1;
3158     nz = adiag[i] - adiag[i+1]-1;
3159     sum = x[i];
3160     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
3161     x[i] = sum*v[nz]; /* x[i]=aa[adiag[i]]*sum; v++; */
3162   }
3163 
3164   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
3165   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3166   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3167   PetscFunctionReturn(0);
3168 }
3169 
3170 #undef __FUNCT__
3171 #define __FUNCT__ "MatSolve_SeqAIJ"
3172 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx)
3173 {
3174   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
3175   IS                iscol = a->col,isrow = a->row;
3176   PetscErrorCode    ierr;
3177   PetscInt          i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz;
3178   const PetscInt    *rout,*cout,*r,*c;
3179   PetscScalar       *x,*tmp,sum;
3180   const PetscScalar *b;
3181   const MatScalar   *aa = a->a,*v;
3182 
3183   PetscFunctionBegin;
3184   if (!n) PetscFunctionReturn(0);
3185 
3186   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3187   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3188   tmp  = a->solve_work;
3189 
3190   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
3191   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
3192 
3193   /* forward solve the lower triangular */
3194   tmp[0] = b[r[0]];
3195   v      = aa;
3196   vi     = aj;
3197   for (i=1; i<n; i++) {
3198     nz  = ai[i+1] - ai[i];
3199     sum = b[r[i]];
3200     PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
3201     tmp[i] = sum;
3202     v += nz; vi += nz;
3203   }
3204 
3205   /* backward solve the upper triangular */
3206   for (i=n-1; i>=0; i--){
3207     v   = aa + adiag[i+1]+1;
3208     vi  = aj + adiag[i+1]+1;
3209     nz  = adiag[i]-adiag[i+1]-1;
3210     sum = tmp[i];
3211     PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
3212     x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */
3213   }
3214 
3215   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
3216   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
3217   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3218   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3219   ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr);
3220   PetscFunctionReturn(0);
3221 }
3222 
3223 #undef __FUNCT__
3224 #define __FUNCT__ "MatILUDTFactor_SeqAIJ"
3225 /*
3226     This will get a new name and become a varient of MatILUFactor_SeqAIJ() there is no longer seperate functions in the matrix function table for dt factors
3227 */
3228 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact)
3229 {
3230   Mat                B = *fact;
3231   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b;
3232   IS                 isicol;
3233   PetscErrorCode     ierr;
3234   const PetscInt     *r,*ic;
3235   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag;
3236   PetscInt           *bi,*bj,*bdiag,*bdiag_rev;
3237   PetscInt           row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au;
3238   PetscInt           nlnk,*lnk;
3239   PetscBT            lnkbt;
3240   PetscTruth         row_identity,icol_identity,both_identity;
3241   MatScalar          *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp;
3242   const PetscInt     *ics;
3243   PetscInt           j,nz,*pj,*bjtmp,k,ncut,*jtmp;
3244   PetscReal          dt=info->dt,dtcol=info->dtcol,shift=info->shiftinblocks;
3245   PetscInt           dtcount=(PetscInt)info->dtcount,nnz_max;
3246   PetscTruth         missing;
3247 
3248   PetscFunctionBegin;
3249 
3250   if (dt      == PETSC_DEFAULT) dt      = 0.005;
3251   if (dtcol   == PETSC_DEFAULT) dtcol   = 0.01; /* XXX unused! */
3252   if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax);
3253 
3254   /* ------- symbolic factorization, can be reused ---------*/
3255   ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
3256   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
3257   adiag=a->diag;
3258 
3259   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
3260 
3261   /* bdiag is location of diagonal in factor */
3262   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);     /* becomes b->diag */
3263   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag_rev);CHKERRQ(ierr); /* temporary */
3264 
3265   /* allocate row pointers bi */
3266   ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
3267 
3268   /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */
3269   if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */
3270   nnz_max  = ai[n]+2*n*dtcount+2;
3271 
3272   ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
3273   ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr);
3274 
3275   /* put together the new matrix */
3276   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
3277   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
3278   b    = (Mat_SeqAIJ*)B->data;
3279   b->free_a       = PETSC_TRUE;
3280   b->free_ij      = PETSC_TRUE;
3281   b->singlemalloc = PETSC_FALSE;
3282   b->a          = ba;
3283   b->j          = bj;
3284   b->i          = bi;
3285   b->diag       = bdiag;
3286   b->ilen       = 0;
3287   b->imax       = 0;
3288   b->row        = isrow;
3289   b->col        = iscol;
3290   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
3291   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
3292   b->icol       = isicol;
3293   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
3294 
3295   ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
3296   b->maxnz = nnz_max;
3297 
3298   B->factor                = MAT_FACTOR_ILUDT;
3299   B->info.factor_mallocs   = 0;
3300   B->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]);
3301   CHKMEMQ;
3302   /* ------- end of symbolic factorization ---------*/
3303 
3304   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
3305   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
3306   ics  = ic;
3307 
3308   /* linked list for storing column indices of the active row */
3309   nlnk = n + 1;
3310   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3311 
3312   /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */
3313   ierr = PetscMalloc2(n,PetscInt,&im,n,PetscInt,&jtmp);CHKERRQ(ierr);
3314   /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */
3315   ierr = PetscMalloc2(n,MatScalar,&rtmp,n,MatScalar,&vtmp);CHKERRQ(ierr);
3316   ierr = PetscMemzero(rtmp,n*sizeof(MatScalar));CHKERRQ(ierr);
3317 
3318   bi[0]    = 0;
3319   bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */
3320   bdiag_rev[n] = bdiag[0];
3321   bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */
3322   for (i=0; i<n; i++) {
3323     /* copy initial fill into linked list */
3324     nzi = 0; /* nonzeros for active row i */
3325     nzi = ai[r[i]+1] - ai[r[i]];
3326     if (!nzi) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
3327     nzi_al = adiag[r[i]] - ai[r[i]];
3328     nzi_au = ai[r[i]+1] - adiag[r[i]] -1;
3329     ajtmp = aj + ai[r[i]];
3330     ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3331 
3332     /* load in initial (unfactored row) */
3333     aatmp = a->a + ai[r[i]];
3334     for (j=0; j<nzi; j++) {
3335       rtmp[ics[*ajtmp++]] = *aatmp++;
3336     }
3337 
3338     /* add pivot rows into linked list */
3339     row = lnk[n];
3340     while (row < i ) {
3341       nzi_bl = bi[row+1] - bi[row] + 1;
3342       bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */
3343       ierr  = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr);
3344       nzi  += nlnk;
3345       row   = lnk[row];
3346     }
3347 
3348     /* copy data from lnk into jtmp, then initialize lnk */
3349     ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr);
3350 
3351     /* numerical factorization */
3352     bjtmp = jtmp;
3353     row   = *bjtmp++; /* 1st pivot row */
3354     while  ( row < i ) {
3355       pc         = rtmp + row;
3356       pv         = ba + bdiag[row]; /* 1./(diag of the pivot row) */
3357       multiplier = (*pc) * (*pv);
3358       *pc        = multiplier;
3359       if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */
3360         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
3361         pv         = ba + bdiag[row+1] + 1;
3362         /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */
3363         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
3364         for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
3365         ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
3366       }
3367       row = *bjtmp++;
3368     }
3369 
3370     /* copy sparse rtmp into contiguous vtmp; separate L and U part */
3371     diag_tmp = rtmp[i];  /* save diagonal value - may not needed?? */
3372     nzi_bl = 0; j = 0;
3373     while (jtmp[j] < i){ /* Note: jtmp is sorted */
3374       vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
3375       nzi_bl++; j++;
3376     }
3377     nzi_bu = nzi - nzi_bl -1;
3378     while (j < nzi){
3379       vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
3380       j++;
3381     }
3382 
3383     bjtmp = bj + bi[i];
3384     batmp = ba + bi[i];
3385     /* apply level dropping rule to L part */
3386     ncut = nzi_al + dtcount;
3387     if (ncut < nzi_bl){
3388       ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr);
3389       ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr);
3390     } else {
3391       ncut = nzi_bl;
3392     }
3393     for (j=0; j<ncut; j++){
3394       bjtmp[j] = jtmp[j];
3395       batmp[j] = vtmp[j];
3396       /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */
3397     }
3398     bi[i+1] = bi[i] + ncut;
3399     nzi = ncut + 1;
3400 
3401     /* apply level dropping rule to U part */
3402     ncut = nzi_au + dtcount;
3403     if (ncut < nzi_bu){
3404       ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr);
3405       ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr);
3406     } else {
3407       ncut = nzi_bu;
3408     }
3409     nzi += ncut;
3410 
3411     /* mark bdiagonal */
3412     bdiag[i+1]       = bdiag[i] - (ncut + 1);
3413     bdiag_rev[n-i-1] = bdiag[i+1];
3414     bi[2*n - i]      = bi[2*n - i +1] - (ncut + 1);
3415     bjtmp = bj + bdiag[i];
3416     batmp = ba + bdiag[i];
3417     *bjtmp = i;
3418     *batmp = diag_tmp; /* rtmp[i]; */
3419     if (*batmp == 0.0) {
3420       *batmp = dt+shift;
3421       /* printf(" row %d add shift %g\n",i,shift); */
3422     }
3423     *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */
3424     /* printf(" (%d,%g),",*bjtmp,*batmp); */
3425 
3426     bjtmp = bj + bdiag[i+1]+1;
3427     batmp = ba + bdiag[i+1]+1;
3428     for (k=0; k<ncut; k++){
3429       bjtmp[k] = jtmp[nzi_bl+1+k];
3430       batmp[k] = vtmp[nzi_bl+1+k];
3431       /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */
3432     }
3433     /* printf("\n"); */
3434 
3435     im[i]   = nzi; /* used by PetscLLAddSortedLU() */
3436     /*
3437     printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]);
3438     printf(" ----------------------------\n");
3439     */
3440   } /* for (i=0; i<n; i++) */
3441   /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */
3442   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]);
3443 
3444   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
3445   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
3446 
3447   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
3448   ierr = PetscFree2(im,jtmp);CHKERRQ(ierr);
3449   ierr = PetscFree2(rtmp,vtmp);CHKERRQ(ierr);
3450   ierr = PetscFree(bdiag_rev);CHKERRQ(ierr);
3451 
3452   ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr);
3453   b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n];
3454 
3455   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
3456   ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr);
3457   both_identity = (PetscTruth) (row_identity && icol_identity);
3458   if (row_identity && icol_identity) {
3459     B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering;
3460   } else {
3461     B->ops->solve = MatSolve_SeqAIJ;
3462   }
3463 
3464   B->ops->solveadd          = 0;
3465   B->ops->solvetranspose    = 0;
3466   B->ops->solvetransposeadd = 0;
3467   B->ops->matsolve          = 0;
3468   B->assembled              = PETSC_TRUE;
3469   B->preallocated           = PETSC_TRUE;
3470   PetscFunctionReturn(0);
3471 }
3472 
3473 /* a wraper of MatILUDTFactor_SeqAIJ() */
3474 #undef __FUNCT__
3475 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ"
3476 /*
3477     This will get a new name and become a varient of MatILUFactor_SeqAIJ() there is no longer seperate functions in the matrix function table for dt factors
3478 */
3479 
3480 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info)
3481 {
3482   PetscErrorCode     ierr;
3483 
3484   PetscFunctionBegin;
3485   ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr);
3486   PetscFunctionReturn(0);
3487 }
3488 
3489 /*
3490    same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors
3491    - intend to replace existing MatLUFactorNumeric_SeqAIJ()
3492 */
3493 #undef __FUNCT__
3494 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ"
3495 /*
3496     This will get a new name and become a varient of MatILUFactor_SeqAIJ() there is no longer seperate functions in the matrix function table for dt factors
3497 */
3498 
3499 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info)
3500 {
3501   Mat            C=fact;
3502   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
3503   IS             isrow = b->row,isicol = b->icol;
3504   PetscErrorCode ierr;
3505   const PetscInt *r,*ic,*ics;
3506   PetscInt       i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
3507   PetscInt       *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj;
3508   MatScalar      *rtmp,*pc,multiplier,*v,*pv,*aa=a->a;
3509   PetscReal      dt=info->dt,shift=info->shiftinblocks;
3510   PetscTruth     row_identity, col_identity;
3511 
3512   PetscFunctionBegin;
3513   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
3514   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
3515   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
3516   ics  = ic;
3517 
3518   for (i=0; i<n; i++){
3519     /* initialize rtmp array */
3520     nzl   = bi[i+1] - bi[i];       /* num of nozeros in L(i,:) */
3521     bjtmp = bj + bi[i];
3522     for  (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0;
3523     rtmp[i] = 0.0;
3524     nzu   = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */
3525     bjtmp = bj + bdiag[i+1] + 1;
3526     for  (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0;
3527 
3528     /* load in initial unfactored row of A */
3529     /* printf("row %d\n",i); */
3530     nz    = ai[r[i]+1] - ai[r[i]];
3531     ajtmp = aj + ai[r[i]];
3532     v     = aa + ai[r[i]];
3533     for (j=0; j<nz; j++) {
3534       rtmp[ics[*ajtmp++]] = v[j];
3535       /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */
3536     }
3537     /* printf("\n"); */
3538 
3539     /* numerical factorization */
3540     bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */
3541     nzl   = bi[i+1] - bi[i]; /* num of entries in L(i,:) */
3542     k = 0;
3543     while (k < nzl){
3544       row   = *bjtmp++;
3545       /* printf("  prow %d\n",row); */
3546       pc         = rtmp + row;
3547       pv         = b->a + bdiag[row]; /* 1./(diag of the pivot row) */
3548       multiplier = (*pc) * (*pv);
3549       *pc        = multiplier;
3550       if (PetscAbsScalar(multiplier) > dt){
3551         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
3552         pv         = b->a + bdiag[row+1] + 1;
3553         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
3554         for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
3555         /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */
3556       }
3557       k++;
3558     }
3559 
3560     /* finished row so stick it into b->a */
3561     /* L-part */
3562     pv = b->a + bi[i] ;
3563     pj = bj + bi[i] ;
3564     nzl = bi[i+1] - bi[i];
3565     for (j=0; j<nzl; j++) {
3566       pv[j] = rtmp[pj[j]];
3567       /* printf(" (%d,%g),",pj[j],pv[j]); */
3568     }
3569 
3570     /* diagonal: invert diagonal entries for simplier triangular solves */
3571     if (rtmp[i] == 0.0) rtmp[i] = dt+shift;
3572     b->a[bdiag[i]] = 1.0/rtmp[i];
3573     /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */
3574 
3575     /* U-part */
3576     pv = b->a + bdiag[i+1] + 1;
3577     pj = bj + bdiag[i+1] + 1;
3578     nzu = bdiag[i] - bdiag[i+1] - 1;
3579     for (j=0; j<nzu; j++) {
3580       pv[j] = rtmp[pj[j]];
3581       /* printf(" (%d,%g),",pj[j],pv[j]); */
3582     }
3583     /* printf("\n"); */
3584   }
3585 
3586   ierr = PetscFree(rtmp);CHKERRQ(ierr);
3587   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
3588   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
3589 
3590   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
3591   ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
3592   if (row_identity && col_identity) {
3593     C->ops->solve   = MatSolve_SeqAIJ_NaturalOrdering;
3594   } else {
3595     C->ops->solve   = MatSolve_SeqAIJ;
3596   }
3597   C->ops->solveadd           = 0;
3598   C->ops->solvetranspose     = 0;
3599   C->ops->solvetransposeadd  = 0;
3600   C->ops->matsolve           = 0;
3601   C->assembled    = PETSC_TRUE;
3602   C->preallocated = PETSC_TRUE;
3603   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
3604   PetscFunctionReturn(0);
3605 }
3606