xref: /petsc/src/mat/impls/aij/seq/aijfact.c (revision f284f12a577e44754165cd333f01f5e5b9a1ea57)
1 #define PETSCMAT_DLL
2 
3 
4 #include "../src/mat/impls/aij/seq/aij.h"
5 #include "../src/mat/impls/sbaij/seq/sbaij.h"
6 #include "petscbt.h"
7 #include "../src/mat/utils/freespace.h"
8 
9 EXTERN_C_BEGIN
10 #undef __FUNCT__
11 #define __FUNCT__ "MatOrdering_Flow_SeqAIJ"
12 /*
13       Computes an ordering to get most of the large numerical values in the lower triangular part of the matrix
14 */
15 PetscErrorCode MatOrdering_Flow_SeqAIJ(Mat mat,const MatOrderingType type,IS *irow,IS *icol)
16 {
17   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)mat->data;
18   PetscErrorCode    ierr;
19   PetscInt          i,j,jj,k, kk,n = mat->rmap->n, current = 0, newcurrent = 0,*order;
20   const PetscInt    *ai = a->i, *aj = a->j;
21   const PetscScalar *aa = a->a;
22   PetscTruth        *done;
23   PetscReal         best,past = 0,future;
24 
25   PetscFunctionBegin;
26   /* pick initial row */
27   best = -1;
28   for (i=0; i<n; i++) {
29     future = 0.0;
30     for (j=ai[i]; j<ai[i+1]; j++) {
31       if (aj[j] != i) future  += PetscAbsScalar(aa[j]); else past = PetscAbsScalar(aa[j]);
32     }
33     if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */
34     if (past/future > best) {
35       best = past/future;
36       current = i;
37     }
38   }
39 
40   ierr = PetscMalloc(n*sizeof(PetscTruth),&done);CHKERRQ(ierr);
41   ierr = PetscMemzero(done,n*sizeof(PetscTruth));CHKERRQ(ierr);
42   ierr = PetscMalloc(n*sizeof(PetscInt),&order);CHKERRQ(ierr);
43   order[0] = current;
44   for (i=0; i<n-1; i++) {
45     done[current] = PETSC_TRUE;
46     best          = -1;
47     /* loop over all neighbors of current pivot */
48     for (j=ai[current]; j<ai[current+1]; j++) {
49       jj = aj[j];
50       if (done[jj]) continue;
51       /* loop over columns of potential next row computing weights for below and above diagonal */
52       past = future = 0.0;
53       for (k=ai[jj]; k<ai[jj+1]; k++) {
54         kk = aj[k];
55         if (done[kk]) past += PetscAbsScalar(aa[k]);
56         else if (kk != jj) future  += PetscAbsScalar(aa[k]);
57       }
58       if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */
59       if (past/future > best) {
60         best = past/future;
61         newcurrent = jj;
62       }
63     }
64     if (best == -1) { /* no neighbors to select from so select best of all that remain */
65       best = -1;
66       for (k=0; k<n; k++) {
67         if (done[k]) continue;
68         future = 0.0;
69         past   = 0.0;
70         for (j=ai[k]; j<ai[k+1]; j++) {
71           kk = aj[j];
72           if (done[kk]) past += PetscAbsScalar(aa[j]);
73           else if (kk != k) future  += PetscAbsScalar(aa[j]);
74         }
75         if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */
76         if (past/future > best) {
77           best = past/future;
78           newcurrent = k;
79         }
80       }
81     }
82     if (current == newcurrent) SETERRQ(PETSC_ERR_PLIB,"newcurrent cannot be current");
83     current = newcurrent;
84     order[i+1] = current;
85   }
86   ierr = ISCreateGeneral(PETSC_COMM_SELF,n,order,irow);CHKERRQ(ierr);
87   *icol = *irow;
88   ierr = PetscObjectReference((PetscObject)*irow);CHKERRQ(ierr);
89   ierr = PetscFree(done);CHKERRQ(ierr);
90   ierr = PetscFree(order);CHKERRQ(ierr);
91   PetscFunctionReturn(0);
92 }
93 EXTERN_C_END
94 
95 EXTERN_C_BEGIN
96 #undef __FUNCT__
97 #define __FUNCT__ "MatGetFactorAvailable_seqaij_petsc"
98 PetscErrorCode MatGetFactorAvailable_seqaij_petsc(Mat A,MatFactorType ftype,PetscTruth *flg)
99 {
100   PetscFunctionBegin;
101   *flg = PETSC_TRUE;
102   PetscFunctionReturn(0);
103 }
104 EXTERN_C_END
105 
106 EXTERN_C_BEGIN
107 #undef __FUNCT__
108 #define __FUNCT__ "MatGetFactor_seqaij_petsc"
109 PetscErrorCode MatGetFactor_seqaij_petsc(Mat A,MatFactorType ftype,Mat *B)
110 {
111   PetscInt           n = A->rmap->n;
112   PetscErrorCode     ierr;
113 
114   PetscFunctionBegin;
115   ierr = MatCreate(((PetscObject)A)->comm,B);CHKERRQ(ierr);
116   ierr = MatSetSizes(*B,n,n,n,n);CHKERRQ(ierr);
117   if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT){
118     ierr = MatSetType(*B,MATSEQAIJ);CHKERRQ(ierr);
119     (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqAIJ;
120     (*B)->ops->lufactorsymbolic  = MatLUFactorSymbolic_SeqAIJ;
121     (*B)->ops->iludtfactor       = MatILUDTFactor_SeqAIJ;
122   } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) {
123     ierr = MatSetType(*B,MATSEQSBAIJ);CHKERRQ(ierr);
124     ierr = MatSeqSBAIJSetPreallocation(*B,1,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
125     (*B)->ops->iccfactorsymbolic      = MatICCFactorSymbolic_SeqAIJ;
126     (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJ;
127   } else SETERRQ(PETSC_ERR_SUP,"Factor type not supported");
128   (*B)->factor = ftype;
129   PetscFunctionReturn(0);
130 }
131 EXTERN_C_END
132 
133 #undef __FUNCT__
134 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ"
135 PetscErrorCode MatLUFactorSymbolic_SeqAIJ(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
136 {
137   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
138   IS                 isicol;
139   PetscErrorCode     ierr;
140   const PetscInt     *r,*ic;
141   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j;
142   PetscInt           *bi,*bj,*ajtmp;
143   PetscInt           *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im;
144   PetscReal          f;
145   PetscInt           nlnk,*lnk,k,**bi_ptr;
146   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
147   PetscBT            lnkbt;
148   PetscTruth         newdatastruct= PETSC_FALSE;
149 
150   PetscFunctionBegin;
151   ierr = PetscOptionsGetTruth(PETSC_NULL,"-lu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
152   if(newdatastruct){
153     ierr = MatLUFactorSymbolic_SeqAIJ_newdatastruct(B,A,isrow,iscol,info);CHKERRQ(ierr);
154     PetscFunctionReturn(0);
155   }
156 
157   if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square");
158   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
159   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
160   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
161 
162   /* get new row pointers */
163   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
164   bi[0] = 0;
165 
166   /* bdiag is location of diagonal in factor */
167   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
168   bdiag[0] = 0;
169 
170   /* linked list for storing column indices of the active row */
171   nlnk = n + 1;
172   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
173 
174   ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr);
175 
176   /* initial FreeSpace size is f*(ai[n]+1) */
177   f = info->fill;
178   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
179   current_space = free_space;
180 
181   for (i=0; i<n; i++) {
182     /* copy previous fill into linked list */
183     nzi = 0;
184     nnz = ai[r[i]+1] - ai[r[i]];
185     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
186     ajtmp = aj + ai[r[i]];
187     ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
188     nzi += nlnk;
189 
190     /* add pivot rows into linked list */
191     row = lnk[n];
192     while (row < i) {
193       nzbd    = bdiag[row] - bi[row] + 1; /* num of entries in the row with column index <= row */
194       ajtmp   = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */
195       ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr);
196       nzi += nlnk;
197       row  = lnk[row];
198     }
199     bi[i+1] = bi[i] + nzi;
200     im[i]   = nzi;
201 
202     /* mark bdiag */
203     nzbd = 0;
204     nnz  = nzi;
205     k    = lnk[n];
206     while (nnz-- && k < i){
207       nzbd++;
208       k = lnk[k];
209     }
210     bdiag[i] = bi[i] + nzbd;
211 
212     /* if free space is not available, make more free space */
213     if (current_space->local_remaining<nzi) {
214       nnz = (n - i)*nzi; /* estimated and max additional space needed */
215       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
216       reallocs++;
217     }
218 
219     /* copy data into free space, then initialize lnk */
220     ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
221     bi_ptr[i] = current_space->array;
222     current_space->array           += nzi;
223     current_space->local_used      += nzi;
224     current_space->local_remaining -= nzi;
225   }
226 #if defined(PETSC_USE_INFO)
227   if (ai[n] != 0) {
228     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
229     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
230     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
231     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr);
232     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
233   } else {
234     ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr);
235   }
236 #endif
237 
238   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
239   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
240 
241   /* destroy list of free space and other temporary array(s) */
242   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
243   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
244   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
245   ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr);
246 
247   /* put together the new matrix */
248   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
249   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
250   b    = (Mat_SeqAIJ*)(B)->data;
251   b->free_a       = PETSC_TRUE;
252   b->free_ij      = PETSC_TRUE;
253   b->singlemalloc = PETSC_FALSE;
254   ierr          = PetscMalloc((bi[n]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
255   b->j          = bj;
256   b->i          = bi;
257   b->diag       = bdiag;
258   b->ilen       = 0;
259   b->imax       = 0;
260   b->row        = isrow;
261   b->col        = iscol;
262   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
263   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
264   b->icol       = isicol;
265   ierr          = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
266 
267   /* In b structure:  Free imax, ilen, old a, old j.  Allocate solve_work, new a, new j */
268   ierr = PetscLogObjectMemory(B,(bi[n]-n)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
269   b->maxnz = b->nz = bi[n] ;
270 
271   (B)->factor                = MAT_FACTOR_LU;
272   (B)->info.factor_mallocs   = reallocs;
273   (B)->info.fill_ratio_given = f;
274 
275   if (ai[n]) {
276     (B)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
277   } else {
278     (B)->info.fill_ratio_needed = 0.0;
279   }
280   (B)->ops->lufactornumeric  = MatLUFactorNumeric_SeqAIJ;
281   (B)->ops->solve            = MatSolve_SeqAIJ;
282   (B)->ops->solvetranspose   = MatSolveTranspose_SeqAIJ;
283   /* switch to inodes if appropriate */
284   ierr = MatLUFactorSymbolic_SeqAIJ_Inode(B,A,isrow,iscol,info);CHKERRQ(ierr);
285   PetscFunctionReturn(0);
286 }
287 
288 #undef __FUNCT__
289 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ_newdatastruct"
290 PetscErrorCode MatLUFactorSymbolic_SeqAIJ_newdatastruct(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
291 {
292   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
293   IS                 isicol;
294   PetscErrorCode     ierr;
295   const PetscInt     *r,*ic;
296   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j;
297   PetscInt           *bi,*bj,*ajtmp;
298   PetscInt           *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im;
299   PetscReal          f;
300   PetscInt           nlnk,*lnk,k,**bi_ptr;
301   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
302   PetscBT            lnkbt;
303 
304   PetscFunctionBegin;
305   if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square");
306   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
307   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
308   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
309 
310   /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
311   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
312   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
313   bi[0] = bdiag[0] = 0;
314 
315   /* linked list for storing column indices of the active row */
316   nlnk = n + 1;
317   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
318 
319   ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr);
320 
321   /* initial FreeSpace size is f*(ai[n]+1) */
322   f = info->fill;
323   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
324   current_space = free_space;
325 
326   for (i=0; i<n; i++) {
327     /* copy previous fill into linked list */
328     nzi = 0;
329     nnz = ai[r[i]+1] - ai[r[i]];
330     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
331     ajtmp = aj + ai[r[i]];
332     ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
333     nzi += nlnk;
334 
335     /* add pivot rows into linked list */
336     row = lnk[n];
337     while (row < i){
338       nzbd  = bdiag[row] + 1; /* num of entries in the row with column index <= row */
339       ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */
340       ierr  = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr);
341       nzi  += nlnk;
342       row   = lnk[row];
343     }
344     bi[i+1] = bi[i] + nzi;
345     im[i]   = nzi;
346 
347     /* mark bdiag */
348     nzbd = 0;
349     nnz  = nzi;
350     k    = lnk[n];
351     while (nnz-- && k < i){
352       nzbd++;
353       k = lnk[k];
354     }
355     bdiag[i] = nzbd; /* note: bdiag[i] = nnzL as input for PetscFreeSpaceContiguous_LU() */
356 
357     /* if free space is not available, make more free space */
358     if (current_space->local_remaining<nzi) {
359       nnz = 2*(n - i)*nzi; /* estimated and max additional space needed */
360       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
361       reallocs++;
362     }
363 
364     /* copy data into free space, then initialize lnk */
365     ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
366     bi_ptr[i] = current_space->array;
367     current_space->array           += nzi;
368     current_space->local_used      += nzi;
369     current_space->local_remaining -= nzi;
370   }
371 #if defined(PETSC_USE_INFO)
372   if (ai[n] != 0) {
373     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
374     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
375     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
376     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr);
377     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
378   } else {
379     ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr);
380   }
381 #endif
382 
383   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
384   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
385 
386   /* destroy list of free space and other temporary array(s) */
387   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
388   ierr = PetscFreeSpaceContiguous_LU_v2(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr);
389   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
390   ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr);
391 
392   /* put together the new matrix */
393   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
394   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
395   b    = (Mat_SeqAIJ*)(B)->data;
396   b->free_a       = PETSC_TRUE;
397   b->free_ij      = PETSC_TRUE;
398   b->singlemalloc = PETSC_FALSE;
399   ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
400   b->j          = bj;
401   b->i          = bi;
402   b->diag       = bdiag;
403   b->ilen       = 0;
404   b->imax       = 0;
405   b->row        = isrow;
406   b->col        = iscol;
407   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
408   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
409   b->icol       = isicol;
410   ierr          = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
411 
412   /* In b structure:  Free imax, ilen, old a, old j.  Allocate solve_work, new a, new j */
413   ierr = PetscLogObjectMemory(B,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
414   b->maxnz = b->nz = bdiag[0]+1;
415   B->factor                = MAT_FACTOR_LU;
416   B->info.factor_mallocs   = reallocs;
417   B->info.fill_ratio_given = f;
418 
419   if (ai[n]) {
420     B->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]);
421   } else {
422     B->info.fill_ratio_needed = 0.0;
423   }
424   B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct;
425   /* switch to inodes if appropriate */
426   ierr = Mat_CheckInode_FactorLU(B,PETSC_FALSE);CHKERRQ(ierr);
427   PetscFunctionReturn(0);
428 }
429 
430 /*
431     Trouble in factorization, should we dump the original matrix?
432 */
433 #undef __FUNCT__
434 #define __FUNCT__ "MatFactorDumpMatrix"
435 PetscErrorCode MatFactorDumpMatrix(Mat A)
436 {
437   PetscErrorCode ierr;
438   PetscTruth     flg = PETSC_FALSE;
439 
440   PetscFunctionBegin;
441   ierr = PetscOptionsGetTruth(PETSC_NULL,"-mat_factor_dump_on_error",&flg,PETSC_NULL);CHKERRQ(ierr);
442   if (flg) {
443     PetscViewer viewer;
444     char        filename[PETSC_MAX_PATH_LEN];
445 
446     ierr = PetscSNPrintf(filename,PETSC_MAX_PATH_LEN,"matrix_factor_error.%d",PetscGlobalRank);CHKERRQ(ierr);
447     ierr = PetscViewerBinaryOpen(((PetscObject)A)->comm,filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr);
448     ierr = MatView(A,viewer);CHKERRQ(ierr);
449     ierr = PetscViewerDestroy(viewer);CHKERRQ(ierr);
450   }
451   PetscFunctionReturn(0);
452 }
453 
454 #undef __FUNCT__
455 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_newdatastruct"
456 PetscErrorCode MatLUFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info)
457 {
458   Mat            C=B;
459   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
460   IS             isrow = b->row,isicol = b->icol;
461   PetscErrorCode ierr;
462   const PetscInt *r,*ic,*ics;
463   PetscInt       i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
464   PetscInt       *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj;
465   MatScalar      *rtmp,*pc,multiplier,*v,*pv,*aa=a->a;
466   PetscTruth     row_identity,col_identity;
467 
468   LUShift_Ctx    sctx;
469   PetscInt       *ddiag,newshift;
470   PetscReal      rs;
471   MatScalar      d;
472 
473   PetscFunctionBegin;
474   /* MatPivotSetUp(): initialize shift context sctx */
475   ierr = PetscMemzero(&sctx,sizeof(LUShift_Ctx));CHKERRQ(ierr);
476 
477   /* if both shift schemes are chosen by user, only use info->shiftpd */
478   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
479     ddiag          = a->diag;
480     sctx.shift_top = info->zeropivot;
481     for (i=0; i<n; i++) {
482       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
483       d  = (aa)[ddiag[i]];
484       rs = -PetscAbsScalar(d) - PetscRealPart(d);
485       v  = aa+ai[i];
486       nz = ai[i+1] - ai[i];
487       for (j=0; j<nz; j++)
488 	rs += PetscAbsScalar(v[j]);
489       if (rs>sctx.shift_top) sctx.shift_top = rs;
490     }
491     sctx.shift_top   *= 1.1;
492     sctx.nshift_max   = 5;
493     sctx.shift_lo     = 0.;
494     sctx.shift_hi     = 1.;
495   }
496 
497   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
498   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
499   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
500   ics  = ic;
501 
502   do {
503     sctx.lushift = PETSC_FALSE;
504     for (i=0; i<n; i++){
505       /* zero rtmp */
506       /* L part */
507       nz    = bi[i+1] - bi[i];
508       bjtmp = bj + bi[i];
509       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
510 
511       /* U part */
512       nz = bdiag[i]-bdiag[i+1];
513       bjtmp = bj + bdiag[i+1]+1;
514       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
515 
516       /* load in initial (unfactored row) */
517       nz    = ai[r[i]+1] - ai[r[i]];
518       ajtmp = aj + ai[r[i]];
519       v     = aa + ai[r[i]];
520       for (j=0; j<nz; j++) {
521         rtmp[ics[ajtmp[j]]] = v[j];
522       }
523       /* ZeropivotApply() */
524       rtmp[i] += sctx.shift_amount;  /* shift the diagonal of the matrix */
525 
526       /* elimination */
527       bjtmp = bj + bi[i];
528       row   = *bjtmp++;
529       nzL   = bi[i+1] - bi[i];
530       for(k=0; k < nzL;k++) {
531         pc = rtmp + row;
532         if (*pc != 0.0) {
533           pv         = b->a + bdiag[row];
534           multiplier = *pc * (*pv);
535           *pc        = multiplier;
536           pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
537 	  pv = b->a + bdiag[row+1]+1;
538 	  nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */
539           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
540           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
541         }
542         row = *bjtmp++;
543       }
544 
545       /* finished row so stick it into b->a */
546       rs = 0.0;
547       /* L part */
548       pv   = b->a + bi[i] ;
549       pj   = b->j + bi[i] ;
550       nz   = bi[i+1] - bi[i];
551       for (j=0; j<nz; j++) {
552         pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]);
553       }
554 
555       /* U part */
556       pv = b->a + bdiag[i+1]+1;
557       pj = b->j + bdiag[i+1]+1;
558       nz = bdiag[i] - bdiag[i+1]-1;
559       for (j=0; j<nz; j++) {
560         pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]);
561       }
562 
563       /* MatPivotCheck() */
564       sctx.rs  = rs;
565       sctx.pv  = rtmp[i];
566       if (info->shiftnz){
567         ierr = MatPivotCheck_nz(info,sctx,i,newshift);CHKERRQ(ierr);
568       } else if (info->shiftpd){
569         ierr = MatPivotCheck_pd(info,sctx,i,newshift);CHKERRQ(ierr);
570       } else if (info->shiftinblocks){
571         ierr = MatPivotCheck_inblocks(info,sctx,i,newshift);CHKERRQ(ierr);
572       } else {
573         ierr = MatPivotCheck_none(info,sctx,i,newshift);CHKERRQ(ierr);
574       }
575       rtmp[i] = sctx.pv;
576       if (newshift == 1) break;
577 
578       /* Mark diagonal and invert diagonal for simplier triangular solves */
579       pv  = b->a + bdiag[i];
580       *pv = 1.0/rtmp[i];
581 
582     } /* endof for (i=0; i<n; i++){ */
583 
584     /* MatPivotRefine() */
585     if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max){
586       /*
587        * if no shift in this attempt & shifting & started shifting & can refine,
588        * then try lower shift
589        */
590       sctx.shift_hi       = sctx.shift_fraction;
591       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
592       sctx.shift_amount   = sctx.shift_fraction * sctx.shift_top;
593       sctx.lushift        = PETSC_TRUE;
594       sctx.nshift++;
595     }
596   } while (sctx.lushift);
597 
598   ierr = PetscFree(rtmp);CHKERRQ(ierr);
599   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
600   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
601   if (b->inode.use){
602     C->ops->solve   = MatSolve_SeqAIJ_Inode_newdatastruct;
603   } else {
604     ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
605     ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
606     if (row_identity && col_identity) {
607       C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct;
608     } else {
609       C->ops->solve = MatSolve_SeqAIJ_newdatastruct;
610     }
611   }
612   C->ops->solveadd           = MatSolveAdd_SeqAIJ_newdatastruct;
613   C->ops->solvetranspose     = MatSolveTranspose_SeqAIJ_newdatastruct;
614   C->ops->solvetransposeadd  = MatSolveTransposeAdd_SeqAIJ_newdatastruct;
615   C->ops->matsolve           = MatMatSolve_SeqAIJ_newdatastruct;
616   C->assembled    = PETSC_TRUE;
617   C->preallocated = PETSC_TRUE;
618   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
619 
620   /* MatPivotView() */
621   if (sctx.nshift){
622     if (info->shiftpd) {
623       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);
624     } else if (info->shiftnz) {
625       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
626     } else if (info->shiftinblocks){
627       ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftinblocks);CHKERRQ(ierr);
628     }
629   }
630   PetscFunctionReturn(0);
631 }
632 
633 #undef __FUNCT__
634 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ"
635 PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info)
636 {
637   Mat             C=B;
638   Mat_SeqAIJ      *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
639   IS              isrow = b->row,isicol = b->icol;
640   PetscErrorCode  ierr;
641   const PetscInt   *r,*ic,*ics;
642   PetscInt        nz,row,i,j,n=A->rmap->n,diag;
643   const PetscInt  *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
644   const PetscInt  *ajtmp,*bjtmp,*diag_offset = b->diag,*pj;
645   MatScalar       *pv,*rtmp,*pc,multiplier,d;
646   const MatScalar *v,*aa=a->a;
647   PetscReal       rs=0.0;
648   LUShift_Ctx     sctx;
649   PetscInt        newshift,*ddiag;
650 
651   PetscFunctionBegin;
652   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
653   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
654   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
655   ics  = ic;
656 
657   /* initialize shift context sctx */
658   sctx.nshift         = 0;
659   sctx.nshift_max     = 0;
660   sctx.shift_top      = 0.0;
661   sctx.shift_lo       = 0.0;
662   sctx.shift_hi       = 0.0;
663   sctx.shift_fraction = 0.0;
664   sctx.shift_amount   = 0.0;
665 
666   /* if both shift schemes are chosen by user, only use info->shiftpd */
667   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
668     ddiag          = a->diag;
669     sctx.shift_top = info->zeropivot;
670     for (i=0; i<n; i++) {
671       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
672       d  = (aa)[ddiag[i]];
673       rs = -PetscAbsScalar(d) - PetscRealPart(d);
674       v  = aa+ai[i];
675       nz = ai[i+1] - ai[i];
676       for (j=0; j<nz; j++)
677 	rs += PetscAbsScalar(v[j]);
678       if (rs>sctx.shift_top) sctx.shift_top = rs;
679     }
680     sctx.shift_top   *= 1.1;
681     sctx.nshift_max   = 5;
682     sctx.shift_lo     = 0.;
683     sctx.shift_hi     = 1.;
684   }
685 
686   do {
687     sctx.lushift = PETSC_FALSE;
688     for (i=0; i<n; i++){
689       nz    = bi[i+1] - bi[i];
690       bjtmp = bj + bi[i];
691       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
692 
693       /* load in initial (unfactored row) */
694       nz    = ai[r[i]+1] - ai[r[i]];
695       ajtmp = aj + ai[r[i]];
696       v     = aa + ai[r[i]];
697       for (j=0; j<nz; j++) {
698         rtmp[ics[ajtmp[j]]] = v[j];
699       }
700       rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */
701       /* if (sctx.shift_amount > 0.0) printf("row %d, shift %g\n",i,sctx.shift_amount); */
702 
703       row = *bjtmp++;
704       while  (row < i) {
705         pc = rtmp + row;
706         if (*pc != 0.0) {
707           pv         = b->a + diag_offset[row];
708           pj         = b->j + diag_offset[row] + 1;
709           multiplier = *pc / *pv++;
710           *pc        = multiplier;
711           nz         = bi[row+1] - diag_offset[row] - 1;
712           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
713           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
714         }
715         row = *bjtmp++;
716       }
717       /* finished row so stick it into b->a */
718       pv   = b->a + bi[i] ;
719       pj   = b->j + bi[i] ;
720       nz   = bi[i+1] - bi[i];
721       diag = diag_offset[i] - bi[i];
722       rs   = 0.0;
723       for (j=0; j<nz; j++) {
724         pv[j] = rtmp[pj[j]];
725         rs   += PetscAbsScalar(pv[j]);
726       }
727       rs   -= PetscAbsScalar(pv[diag]);
728 
729       /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */
730       sctx.rs  = rs;
731       sctx.pv  = pv[diag];
732       ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr);
733       if (newshift == 1) break;
734     }
735 
736     if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
737       /*
738        * if no shift in this attempt & shifting & started shifting & can refine,
739        * then try lower shift
740        */
741       sctx.shift_hi       = sctx.shift_fraction;
742       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
743       sctx.shift_amount   = sctx.shift_fraction * sctx.shift_top;
744       sctx.lushift        = PETSC_TRUE;
745       sctx.nshift++;
746     }
747   } while (sctx.lushift);
748 
749   /* invert diagonal entries for simplier triangular solves */
750   for (i=0; i<n; i++) {
751     b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]];
752   }
753   ierr = PetscFree(rtmp);CHKERRQ(ierr);
754   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
755   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
756   if (b->inode.use) {
757     C->ops->solve   = MatSolve_SeqAIJ_Inode;
758   } else {
759     PetscTruth row_identity, col_identity;
760     ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
761     ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
762     if (row_identity && col_identity) {
763       C->ops->solve   = MatSolve_SeqAIJ_NaturalOrdering;
764     } else {
765       C->ops->solve   = MatSolve_SeqAIJ;
766     }
767   }
768   C->ops->solveadd           = MatSolveAdd_SeqAIJ;
769   C->ops->solvetranspose     = MatSolveTranspose_SeqAIJ;
770   C->ops->solvetransposeadd  = MatSolveTransposeAdd_SeqAIJ;
771   C->ops->matsolve           = MatMatSolve_SeqAIJ;
772   C->assembled    = PETSC_TRUE;
773   C->preallocated = PETSC_TRUE;
774   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
775   if (sctx.nshift){
776      if (info->shiftpd) {
777       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);
778     } else if (info->shiftnz) {
779       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
780     }
781   }
782   PetscFunctionReturn(0);
783 }
784 
785 /*
786    This routine implements inplace ILU(0) with row or/and column permutations.
787    Input:
788      A - original matrix
789    Output;
790      A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i]
791          a->j (col index) is permuted by the inverse of colperm, then sorted
792          a->a reordered accordingly with a->j
793          a->diag (ptr to diagonal elements) is updated.
794 */
795 #undef __FUNCT__
796 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_InplaceWithPerm"
797 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info)
798 {
799   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
800   IS             isrow = a->row,isicol = a->icol;
801   PetscErrorCode ierr;
802   const PetscInt *r,*ic,*ics;
803   PetscInt       i,j,n=A->rmap->n,*ai=a->i,*aj=a->j;
804   PetscInt       *ajtmp,nz,row;
805   PetscInt       *diag = a->diag,nbdiag,*pj;
806   PetscScalar    *rtmp,*pc,multiplier,d;
807   MatScalar      *v,*pv;
808   PetscReal      rs;
809   LUShift_Ctx    sctx;
810   PetscInt       newshift;
811 
812   PetscFunctionBegin;
813   if (A != B) SETERRQ(PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address");
814   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
815   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
816   ierr  = PetscMalloc((n+1)*sizeof(PetscScalar),&rtmp);CHKERRQ(ierr);
817   ierr  = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr);
818   ics = ic;
819 
820   sctx.shift_top      = 0.;
821   sctx.nshift_max     = 0;
822   sctx.shift_lo       = 0.;
823   sctx.shift_hi       = 0.;
824   sctx.shift_fraction = 0.;
825 
826   /* if both shift schemes are chosen by user, only use info->shiftpd */
827   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
828     sctx.shift_top = 0.;
829     for (i=0; i<n; i++) {
830       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
831       d  = (a->a)[diag[i]];
832       rs = -PetscAbsScalar(d) - PetscRealPart(d);
833       v  = a->a+ai[i];
834       nz = ai[i+1] - ai[i];
835       for (j=0; j<nz; j++)
836 	rs += PetscAbsScalar(v[j]);
837       if (rs>sctx.shift_top) sctx.shift_top = rs;
838     }
839     if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot;
840     sctx.shift_top    *= 1.1;
841     sctx.nshift_max   = 5;
842     sctx.shift_lo     = 0.;
843     sctx.shift_hi     = 1.;
844   }
845 
846   sctx.shift_amount = 0.;
847   sctx.nshift       = 0;
848   do {
849     sctx.lushift = PETSC_FALSE;
850     for (i=0; i<n; i++){
851       /* load in initial unfactored row */
852       nz    = ai[r[i]+1] - ai[r[i]];
853       ajtmp = aj + ai[r[i]];
854       v     = a->a + ai[r[i]];
855       /* sort permuted ajtmp and values v accordingly */
856       for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]];
857       ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr);
858 
859       diag[r[i]] = ai[r[i]];
860       for (j=0; j<nz; j++) {
861         rtmp[ajtmp[j]] = v[j];
862         if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */
863       }
864       rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */
865 
866       row = *ajtmp++;
867       while  (row < i) {
868         pc = rtmp + row;
869         if (*pc != 0.0) {
870           pv         = a->a + diag[r[row]];
871           pj         = aj + diag[r[row]] + 1;
872 
873           multiplier = *pc / *pv++;
874           *pc        = multiplier;
875           nz         = ai[r[row]+1] - diag[r[row]] - 1;
876           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
877           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
878         }
879         row = *ajtmp++;
880       }
881       /* finished row so overwrite it onto a->a */
882       pv   = a->a + ai[r[i]] ;
883       pj   = aj + ai[r[i]] ;
884       nz   = ai[r[i]+1] - ai[r[i]];
885       nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */
886 
887       rs   = 0.0;
888       for (j=0; j<nz; j++) {
889         pv[j] = rtmp[pj[j]];
890         if (j != nbdiag) rs += PetscAbsScalar(pv[j]);
891       }
892 
893       /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */
894       sctx.rs  = rs;
895       sctx.pv  = pv[nbdiag];
896       ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr);
897       if (newshift == 1) break;
898     }
899 
900     if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
901       /*
902        * if no shift in this attempt & shifting & started shifting & can refine,
903        * then try lower shift
904        */
905       sctx.shift_hi        = sctx.shift_fraction;
906       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
907       sctx.shift_amount    = sctx.shift_fraction * sctx.shift_top;
908       sctx.lushift         = PETSC_TRUE;
909       sctx.nshift++;
910     }
911   } while (sctx.lushift);
912 
913   /* invert diagonal entries for simplier triangular solves */
914   for (i=0; i<n; i++) {
915     a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]];
916   }
917 
918   ierr = PetscFree(rtmp);CHKERRQ(ierr);
919   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
920   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
921   A->ops->solve             = MatSolve_SeqAIJ_InplaceWithPerm;
922   A->ops->solveadd          = MatSolveAdd_SeqAIJ;
923   A->ops->solvetranspose    = MatSolveTranspose_SeqAIJ;
924   A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ;
925   A->assembled = PETSC_TRUE;
926   A->preallocated = PETSC_TRUE;
927   ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr);
928   if (sctx.nshift){
929     if (info->shiftpd) {
930       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);
931     } else if (info->shiftnz) {
932       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
933     }
934   }
935   PetscFunctionReturn(0);
936 }
937 
938 /* ----------------------------------------------------------- */
939 #undef __FUNCT__
940 #define __FUNCT__ "MatLUFactor_SeqAIJ"
941 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info)
942 {
943   PetscErrorCode ierr;
944   Mat            C;
945 
946   PetscFunctionBegin;
947   ierr = MatGetFactor(A,MAT_SOLVER_PETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr);
948   ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr);
949   ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr);
950   A->ops->solve            = C->ops->solve;
951   A->ops->solvetranspose   = C->ops->solvetranspose;
952   ierr = MatHeaderCopy(A,C);CHKERRQ(ierr);
953   ierr = PetscLogObjectParent(A,((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr);
954   PetscFunctionReturn(0);
955 }
956 /* ----------------------------------------------------------- */
957 
958 
959 #undef __FUNCT__
960 #define __FUNCT__ "MatSolve_SeqAIJ"
961 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx)
962 {
963   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
964   IS                iscol = a->col,isrow = a->row;
965   PetscErrorCode    ierr;
966   PetscInt          i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
967   PetscInt          nz;
968   const PetscInt    *rout,*cout,*r,*c;
969   PetscScalar       *x,*tmp,*tmps,sum;
970   const PetscScalar *b;
971   const MatScalar   *aa = a->a,*v;
972 
973   PetscFunctionBegin;
974   if (!n) PetscFunctionReturn(0);
975 
976   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
977   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
978   tmp  = a->solve_work;
979 
980   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
981   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
982 
983   /* forward solve the lower triangular */
984   tmp[0] = b[*r++];
985   tmps   = tmp;
986   for (i=1; i<n; i++) {
987     v   = aa + ai[i] ;
988     vi  = aj + ai[i] ;
989     nz  = a->diag[i] - ai[i];
990     sum = b[*r++];
991     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
992     tmp[i] = sum;
993   }
994 
995   /* backward solve the upper triangular */
996   for (i=n-1; i>=0; i--){
997     v   = aa + a->diag[i] + 1;
998     vi  = aj + a->diag[i] + 1;
999     nz  = ai[i+1] - a->diag[i] - 1;
1000     sum = tmp[i];
1001     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1002     x[*c--] = tmp[i] = sum*aa[a->diag[i]];
1003   }
1004 
1005   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1006   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1007   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1008   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1009   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1010   PetscFunctionReturn(0);
1011 }
1012 
1013 #undef __FUNCT__
1014 #define __FUNCT__ "MatMatSolve_SeqAIJ"
1015 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X)
1016 {
1017   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1018   IS              iscol = a->col,isrow = a->row;
1019   PetscErrorCode  ierr;
1020   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1021   PetscInt        nz,neq;
1022   const PetscInt  *rout,*cout,*r,*c;
1023   PetscScalar     *x,*b,*tmp,*tmps,sum;
1024   const MatScalar *aa = a->a,*v;
1025   PetscTruth      bisdense,xisdense;
1026 
1027   PetscFunctionBegin;
1028   if (!n) PetscFunctionReturn(0);
1029 
1030   ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr);
1031   if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix");
1032   ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr);
1033   if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix");
1034 
1035   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
1036   ierr = MatGetArray(X,&x);CHKERRQ(ierr);
1037 
1038   tmp  = a->solve_work;
1039   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1040   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1041 
1042   for (neq=0; neq<B->cmap->n; neq++){
1043     /* forward solve the lower triangular */
1044     tmp[0] = b[r[0]];
1045     tmps   = tmp;
1046     for (i=1; i<n; i++) {
1047       v   = aa + ai[i] ;
1048       vi  = aj + ai[i] ;
1049       nz  = a->diag[i] - ai[i];
1050       sum = b[r[i]];
1051       PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1052       tmp[i] = sum;
1053     }
1054     /* backward solve the upper triangular */
1055     for (i=n-1; i>=0; i--){
1056       v   = aa + a->diag[i] + 1;
1057       vi  = aj + a->diag[i] + 1;
1058       nz  = ai[i+1] - a->diag[i] - 1;
1059       sum = tmp[i];
1060       PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1061       x[c[i]] = tmp[i] = sum*aa[a->diag[i]];
1062     }
1063 
1064     b += n;
1065     x += n;
1066   }
1067   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1068   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1069   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
1070   ierr = MatRestoreArray(X,&x);CHKERRQ(ierr);
1071   ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr);
1072   PetscFunctionReturn(0);
1073 }
1074 
1075 #undef __FUNCT__
1076 #define __FUNCT__ "MatMatSolve_SeqAIJ_newdatastruct"
1077 PetscErrorCode MatMatSolve_SeqAIJ_newdatastruct(Mat A,Mat B,Mat X)
1078 {
1079   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1080   IS              iscol = a->col,isrow = a->row;
1081   PetscErrorCode  ierr;
1082   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag;
1083   PetscInt        nz,neq;
1084   const PetscInt  *rout,*cout,*r,*c;
1085   PetscScalar     *x,*b,*tmp,sum;
1086   const MatScalar *aa = a->a,*v;
1087   PetscTruth      bisdense,xisdense;
1088 
1089   PetscFunctionBegin;
1090   if (!n) PetscFunctionReturn(0);
1091 
1092   ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr);
1093   if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix");
1094   ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr);
1095   if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix");
1096 
1097   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
1098   ierr = MatGetArray(X,&x);CHKERRQ(ierr);
1099 
1100   tmp  = a->solve_work;
1101   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1102   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1103 
1104   for (neq=0; neq<B->cmap->n; neq++){
1105     /* forward solve the lower triangular */
1106     tmp[0] = b[r[0]];
1107     v      = aa;
1108     vi     = aj;
1109     for (i=1; i<n; i++) {
1110       nz  = ai[i+1] - ai[i];
1111       sum = b[r[i]];
1112       PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
1113       tmp[i] = sum;
1114       v += nz; vi += nz;
1115     }
1116 
1117     /* backward solve the upper triangular */
1118     for (i=n-1; i>=0; i--){
1119       v   = aa + adiag[i+1]+1;
1120       vi  = aj + adiag[i+1]+1;
1121       nz  = adiag[i]-adiag[i+1]-1;
1122       sum = tmp[i];
1123       PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
1124       x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */
1125     }
1126 
1127     b += n;
1128     x += n;
1129   }
1130   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1131   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1132   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
1133   ierr = MatRestoreArray(X,&x);CHKERRQ(ierr);
1134   ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr);
1135   PetscFunctionReturn(0);
1136 }
1137 
1138 #undef __FUNCT__
1139 #define __FUNCT__ "MatSolve_SeqAIJ_InplaceWithPerm"
1140 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx)
1141 {
1142   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1143   IS              iscol = a->col,isrow = a->row;
1144   PetscErrorCode  ierr;
1145   const PetscInt  *r,*c,*rout,*cout;
1146   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1147   PetscInt        nz,row;
1148   PetscScalar     *x,*b,*tmp,*tmps,sum;
1149   const MatScalar *aa = a->a,*v;
1150 
1151   PetscFunctionBegin;
1152   if (!n) PetscFunctionReturn(0);
1153 
1154   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
1155   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1156   tmp  = a->solve_work;
1157 
1158   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1159   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1160 
1161   /* forward solve the lower triangular */
1162   tmp[0] = b[*r++];
1163   tmps   = tmp;
1164   for (row=1; row<n; row++) {
1165     i   = rout[row]; /* permuted row */
1166     v   = aa + ai[i] ;
1167     vi  = aj + ai[i] ;
1168     nz  = a->diag[i] - ai[i];
1169     sum = b[*r++];
1170     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1171     tmp[row] = sum;
1172   }
1173 
1174   /* backward solve the upper triangular */
1175   for (row=n-1; row>=0; row--){
1176     i   = rout[row]; /* permuted row */
1177     v   = aa + a->diag[i] + 1;
1178     vi  = aj + a->diag[i] + 1;
1179     nz  = ai[i+1] - a->diag[i] - 1;
1180     sum = tmp[row];
1181     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1182     x[*c--] = tmp[row] = sum*aa[a->diag[i]];
1183   }
1184 
1185   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1186   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1187   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
1188   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1189   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1190   PetscFunctionReturn(0);
1191 }
1192 
1193 /* ----------------------------------------------------------- */
1194 #include "../src/mat/impls/aij/seq/ftn-kernels/fsolve.h"
1195 #undef __FUNCT__
1196 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering"
1197 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx)
1198 {
1199   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1200   PetscErrorCode    ierr;
1201   PetscInt          n = A->rmap->n;
1202   const PetscInt    *ai = a->i,*aj = a->j,*adiag = a->diag;
1203   PetscScalar       *x;
1204   const PetscScalar *b;
1205   const MatScalar   *aa = a->a;
1206 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ)
1207   PetscInt          adiag_i,i,nz,ai_i;
1208   const PetscInt    *vi;
1209   const MatScalar   *v;
1210   PetscScalar       sum;
1211 #endif
1212 
1213   PetscFunctionBegin;
1214   if (!n) PetscFunctionReturn(0);
1215 
1216   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1217   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1218 
1219 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ)
1220   fortransolveaij_(&n,x,ai,aj,adiag,aa,b);
1221 #else
1222   /* forward solve the lower triangular */
1223   x[0] = b[0];
1224   for (i=1; i<n; i++) {
1225     ai_i = ai[i];
1226     v    = aa + ai_i;
1227     vi   = aj + ai_i;
1228     nz   = adiag[i] - ai_i;
1229     sum  = b[i];
1230     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
1231     x[i] = sum;
1232   }
1233 
1234   /* backward solve the upper triangular */
1235   for (i=n-1; i>=0; i--){
1236     adiag_i = adiag[i];
1237     v       = aa + adiag_i + 1;
1238     vi      = aj + adiag_i + 1;
1239     nz      = ai[i+1] - adiag_i - 1;
1240     sum     = x[i];
1241     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
1242     x[i]    = sum*aa[adiag_i];
1243   }
1244 #endif
1245   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1246   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1247   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1248   PetscFunctionReturn(0);
1249 }
1250 
1251 #undef __FUNCT__
1252 #define __FUNCT__ "MatSolveAdd_SeqAIJ"
1253 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx)
1254 {
1255   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1256   IS                iscol = a->col,isrow = a->row;
1257   PetscErrorCode    ierr;
1258   PetscInt          i, n = A->rmap->n,j;
1259   PetscInt          nz;
1260   const PetscInt    *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j;
1261   PetscScalar       *x,*tmp,sum;
1262   const PetscScalar *b;
1263   const MatScalar   *aa = a->a,*v;
1264 
1265   PetscFunctionBegin;
1266   if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);}
1267 
1268   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1269   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1270   tmp  = a->solve_work;
1271 
1272   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1273   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1274 
1275   /* forward solve the lower triangular */
1276   tmp[0] = b[*r++];
1277   for (i=1; i<n; i++) {
1278     v   = aa + ai[i] ;
1279     vi  = aj + ai[i] ;
1280     nz  = a->diag[i] - ai[i];
1281     sum = b[*r++];
1282     for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1283     tmp[i] = sum;
1284   }
1285 
1286   /* backward solve the upper triangular */
1287   for (i=n-1; i>=0; i--){
1288     v   = aa + a->diag[i] + 1;
1289     vi  = aj + a->diag[i] + 1;
1290     nz  = ai[i+1] - a->diag[i] - 1;
1291     sum = tmp[i];
1292     for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1293     tmp[i] = sum*aa[a->diag[i]];
1294     x[*c--] += tmp[i];
1295   }
1296 
1297   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1298   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1299   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1300   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1301   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1302 
1303   PetscFunctionReturn(0);
1304 }
1305 
1306 #undef __FUNCT__
1307 #define __FUNCT__ "MatSolveAdd_SeqAIJ_newdatastruct"
1308 PetscErrorCode MatSolveAdd_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec yy,Vec xx)
1309 {
1310   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1311   IS                iscol = a->col,isrow = a->row;
1312   PetscErrorCode    ierr;
1313   PetscInt          i, n = A->rmap->n,j;
1314   PetscInt          nz;
1315   const PetscInt    *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag;
1316   PetscScalar       *x,*tmp,sum;
1317   const PetscScalar *b;
1318   const MatScalar   *aa = a->a,*v;
1319 
1320   PetscFunctionBegin;
1321   if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);}
1322 
1323   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1324   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1325   tmp  = a->solve_work;
1326 
1327   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1328   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1329 
1330   /* forward solve the lower triangular */
1331   tmp[0] = b[r[0]];
1332   v      = aa;
1333   vi     = aj;
1334   for (i=1; i<n; i++) {
1335     nz  = ai[i+1] - ai[i];
1336     sum = b[r[i]];
1337     for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1338     tmp[i] = sum;
1339     v += nz; vi += nz;
1340   }
1341 
1342   /* backward solve the upper triangular */
1343   v  = aa + adiag[n-1];
1344   vi = aj + adiag[n-1];
1345   for (i=n-1; i>=0; i--){
1346     nz  = adiag[i] - adiag[i+1] - 1;
1347     sum = tmp[i];
1348     for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1349     tmp[i] = sum*v[nz];
1350     x[c[i]] += tmp[i];
1351     v += nz+1; vi += nz+1;
1352   }
1353 
1354   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1355   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1356   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1357   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1358   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1359 
1360   PetscFunctionReturn(0);
1361 }
1362 
1363 #undef __FUNCT__
1364 #define __FUNCT__ "MatSolveTranspose_SeqAIJ"
1365 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx)
1366 {
1367   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1368   IS                iscol = a->col,isrow = a->row;
1369   PetscErrorCode    ierr;
1370   const PetscInt    *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi;
1371   PetscInt          i,n = A->rmap->n,j;
1372   PetscInt          nz;
1373   PetscScalar       *x,*tmp,s1;
1374   const MatScalar   *aa = a->a,*v;
1375   const PetscScalar *b;
1376 
1377   PetscFunctionBegin;
1378   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1379   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1380   tmp  = a->solve_work;
1381 
1382   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1383   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1384 
1385   /* copy the b into temp work space according to permutation */
1386   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1387 
1388   /* forward solve the U^T */
1389   for (i=0; i<n; i++) {
1390     v   = aa + diag[i] ;
1391     vi  = aj + diag[i] + 1;
1392     nz  = ai[i+1] - diag[i] - 1;
1393     s1  = tmp[i];
1394     s1 *= (*v++);  /* multiply by inverse of diagonal entry */
1395     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1396     tmp[i] = s1;
1397   }
1398 
1399   /* backward solve the L^T */
1400   for (i=n-1; i>=0; i--){
1401     v   = aa + diag[i] - 1 ;
1402     vi  = aj + diag[i] - 1 ;
1403     nz  = diag[i] - ai[i];
1404     s1  = tmp[i];
1405     for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j];
1406   }
1407 
1408   /* copy tmp into x according to permutation */
1409   for (i=0; i<n; i++) x[r[i]] = tmp[i];
1410 
1411   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1412   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1413   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1414   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1415 
1416   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1417   PetscFunctionReturn(0);
1418 }
1419 
1420 #undef __FUNCT__
1421 #define __FUNCT__ "MatSolveTranspose_SeqAIJ_newdatastruct"
1422 PetscErrorCode MatSolveTranspose_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec xx)
1423 {
1424   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1425   IS                iscol = a->col,isrow = a->row;
1426   PetscErrorCode    ierr;
1427   const PetscInt    *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi;
1428   PetscInt          i,n = A->rmap->n,j;
1429   PetscInt          nz;
1430   PetscScalar       *x,*tmp,s1;
1431   const MatScalar   *aa = a->a,*v;
1432   const PetscScalar *b;
1433 
1434   PetscFunctionBegin;
1435   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1436   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1437   tmp  = a->solve_work;
1438 
1439   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1440   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1441 
1442   /* copy the b into temp work space according to permutation */
1443   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1444 
1445   /* forward solve the U^T */
1446   for (i=0; i<n; i++) {
1447     v   = aa + adiag[i+1] + 1;
1448     vi  = aj + adiag[i+1] + 1;
1449     nz  = adiag[i] - adiag[i+1] - 1;
1450     s1  = tmp[i];
1451     s1 *= v[nz];  /* multiply by inverse of diagonal entry */
1452     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1453     tmp[i] = s1;
1454   }
1455 
1456   /* backward solve the L^T */
1457   for (i=n-1; i>=0; i--){
1458     v   = aa + ai[i];
1459     vi  = aj + ai[i];
1460     nz  = ai[i+1] - ai[i];
1461     s1  = tmp[i];
1462     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1463   }
1464 
1465   /* copy tmp into x according to permutation */
1466   for (i=0; i<n; i++) x[r[i]] = tmp[i];
1467 
1468   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1469   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1470   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1471   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1472 
1473   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1474   PetscFunctionReturn(0);
1475 }
1476 
1477 #undef __FUNCT__
1478 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ"
1479 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx)
1480 {
1481   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1482   IS                iscol = a->col,isrow = a->row;
1483   PetscErrorCode    ierr;
1484   const PetscInt    *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi;
1485   PetscInt          i,n = A->rmap->n,j;
1486   PetscInt          nz;
1487   PetscScalar       *x,*tmp,s1;
1488   const MatScalar   *aa = a->a,*v;
1489   const PetscScalar *b;
1490 
1491   PetscFunctionBegin;
1492   if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);}
1493   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1494   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1495   tmp  = a->solve_work;
1496 
1497   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1498   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1499 
1500   /* copy the b into temp work space according to permutation */
1501   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1502 
1503   /* forward solve the U^T */
1504   for (i=0; i<n; i++) {
1505     v   = aa + diag[i] ;
1506     vi  = aj + diag[i] + 1;
1507     nz  = ai[i+1] - diag[i] - 1;
1508     s1  = tmp[i];
1509     s1 *= (*v++);  /* multiply by inverse of diagonal entry */
1510     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1511     tmp[i] = s1;
1512   }
1513 
1514   /* backward solve the L^T */
1515   for (i=n-1; i>=0; i--){
1516     v   = aa + diag[i] - 1 ;
1517     vi  = aj + diag[i] - 1 ;
1518     nz  = diag[i] - ai[i];
1519     s1  = tmp[i];
1520     for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j];
1521   }
1522 
1523   /* copy tmp into x according to permutation */
1524   for (i=0; i<n; i++) x[r[i]] += tmp[i];
1525 
1526   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1527   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1528   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1529   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1530 
1531   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1532   PetscFunctionReturn(0);
1533 }
1534 
1535 #undef __FUNCT__
1536 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ_newdatastruct"
1537 PetscErrorCode MatSolveTransposeAdd_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec zz,Vec xx)
1538 {
1539   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1540   IS                iscol = a->col,isrow = a->row;
1541   PetscErrorCode    ierr;
1542   const PetscInt    *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi;
1543   PetscInt          i,n = A->rmap->n,j;
1544   PetscInt          nz;
1545   PetscScalar       *x,*tmp,s1;
1546   const MatScalar   *aa = a->a,*v;
1547   const PetscScalar *b;
1548 
1549   PetscFunctionBegin;
1550   if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);}
1551   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1552   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1553   tmp  = a->solve_work;
1554 
1555   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1556   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1557 
1558   /* copy the b into temp work space according to permutation */
1559   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1560 
1561   /* forward solve the U^T */
1562   for (i=0; i<n; i++) {
1563     v   = aa + adiag[i+1] + 1;
1564     vi  = aj + adiag[i+1] + 1;
1565     nz  = adiag[i] - adiag[i+1] - 1;
1566     s1  = tmp[i];
1567     s1 *= v[nz];  /* multiply by inverse of diagonal entry */
1568     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1569     tmp[i] = s1;
1570   }
1571 
1572 
1573   /* backward solve the L^T */
1574   for (i=n-1; i>=0; i--){
1575     v   = aa + ai[i] ;
1576     vi  = aj + ai[i];
1577     nz  = ai[i+1] - ai[i];
1578     s1  = tmp[i];
1579     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1580   }
1581 
1582   /* copy tmp into x according to permutation */
1583   for (i=0; i<n; i++) x[r[i]] += tmp[i];
1584 
1585   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1586   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1587   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1588   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1589 
1590   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1591   PetscFunctionReturn(0);
1592 }
1593 
1594 /* ----------------------------------------------------------------*/
1595 
1596 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption,PetscTruth);
1597 
1598 /*
1599    ilu() under revised new data structure.
1600    Factored arrays bj and ba are stored as
1601      L(0,:), L(1,:), ...,L(n-1,:),  U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:)
1602 
1603    bi=fact->i is an array of size n+1, in which
1604    bi+
1605      bi[i]:  points to 1st entry of L(i,:),i=0,...,n-1
1606      bi[n]:  points to L(n-1,n-1)+1
1607 
1608   bdiag=fact->diag is an array of size n+1,in which
1609      bdiag[i]: points to diagonal of U(i,:), i=0,...,n-1
1610      bdiag[n]: points to entry of U(n-1,0)-1
1611 
1612    U(i,:) contains bdiag[i] as its last entry, i.e.,
1613     U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i])
1614 */
1615 #undef __FUNCT__
1616 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct"
1617 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1618 {
1619 
1620   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1621   PetscErrorCode     ierr;
1622   PetscInt           n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag;
1623   PetscInt           i,j,nz,*bi,*bj,*bdiag;
1624   PetscTruth         missing;
1625   IS                 isicol;
1626 
1627   PetscFunctionBegin;
1628   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);
1629   ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
1630   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
1631   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1632 
1633   ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr);
1634   b    = (Mat_SeqAIJ*)(fact)->data;
1635 
1636   /* allocate matrix arrays for new data structure */
1637   ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,n+1,PetscInt,&b->i);CHKERRQ(ierr);
1638   ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));CHKERRQ(ierr);
1639   b->singlemalloc = PETSC_TRUE;
1640   if (!b->diag){
1641     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr);
1642     ierr = PetscLogObjectMemory(fact,(n+1)*sizeof(PetscInt));CHKERRQ(ierr);
1643   }
1644   bdiag = b->diag;
1645 
1646   if (n > 0) {
1647     ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr);
1648   }
1649 
1650   /* set bi and bj with new data structure */
1651   bi = b->i;
1652   bj = b->j;
1653 
1654   /* L part */
1655   bi[0] = 0;
1656   for (i=0; i<n; i++){
1657     nz = adiag[i] - ai[i];
1658     bi[i+1] = bi[i] + nz;
1659     aj = a->j + ai[i];
1660     for (j=0; j<nz; j++){
1661       *bj = aj[j]; bj++;
1662     }
1663   }
1664 
1665   /* U part */
1666   bdiag[n] = bi[n]-1;
1667   for (i=n-1; i>=0; i--){
1668     nz = ai[i+1] - adiag[i] - 1;
1669     aj = a->j + adiag[i] + 1;
1670     for (j=0; j<nz; j++){
1671       *bj = aj[j]; bj++;
1672     }
1673     /* diag[i] */
1674     *bj = i; bj++;
1675     bdiag[i] = bdiag[i+1] + nz + 1;
1676   }
1677 
1678   fact->factor                 = MAT_FACTOR_ILU;
1679   fact->info.factor_mallocs    = 0;
1680   fact->info.fill_ratio_given  = info->fill;
1681   fact->info.fill_ratio_needed = 1.0;
1682   fact->ops->lufactornumeric   = MatLUFactorNumeric_SeqAIJ_newdatastruct;
1683 
1684   b       = (Mat_SeqAIJ*)(fact)->data;
1685   b->row  = isrow;
1686   b->col  = iscol;
1687   b->icol = isicol;
1688   ierr    = PetscMalloc((fact->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1689   ierr    = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1690   ierr    = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1691   PetscFunctionReturn(0);
1692 }
1693 
1694 #undef __FUNCT__
1695 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_newdatastruct"
1696 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1697 {
1698   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1699   IS                 isicol;
1700   PetscErrorCode     ierr;
1701   const PetscInt     *r,*ic;
1702   PetscInt           n=A->rmap->n,*ai=a->i,*aj=a->j;
1703   PetscInt           *bi,*cols,nnz,*cols_lvl;
1704   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1705   PetscInt           i,levels,diagonal_fill;
1706   PetscTruth         col_identity,row_identity;
1707   PetscReal          f;
1708   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
1709   PetscBT            lnkbt;
1710   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
1711   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1712   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1713 
1714   PetscFunctionBegin;
1715   /* printf("MatILUFactorSymbolic_SeqAIJ_newdatastruct ...\n"); */
1716   levels = (PetscInt)info->levels;
1717   ierr   = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1718   ierr   = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
1719 
1720   if (!levels && row_identity && col_identity) {
1721     /* special case: ilu(0) with natural ordering */
1722     ierr = MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1723     ierr = Mat_CheckInode_FactorLU(fact,PETSC_FALSE);CHKERRQ(ierr);
1724     PetscFunctionReturn(0);
1725   }
1726 
1727   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);
1728   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1729   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1730   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1731 
1732   /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
1733   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1734   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
1735   bi[0] = bdiag[0] = 0;
1736 
1737   ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr);
1738 
1739   /* create a linked list for storing column indices of the active row */
1740   nlnk = n + 1;
1741   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1742 
1743   /* initial FreeSpace size is f*(ai[n]+1) */
1744   f             = info->fill;
1745   diagonal_fill = (PetscInt)info->diagonal_fill;
1746   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
1747   current_space = free_space;
1748   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
1749   current_space_lvl = free_space_lvl;
1750 
1751   for (i=0; i<n; i++) {
1752     nzi = 0;
1753     /* copy current row into linked list */
1754     nnz  = ai[r[i]+1] - ai[r[i]];
1755     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1756     cols = aj + ai[r[i]];
1757     lnk[i] = -1; /* marker to indicate if diagonal exists */
1758     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1759     nzi += nlnk;
1760 
1761     /* make sure diagonal entry is included */
1762     if (diagonal_fill && lnk[i] == -1) {
1763       fm = n;
1764       while (lnk[fm] < i) fm = lnk[fm];
1765       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
1766       lnk[fm]    = i;
1767       lnk_lvl[i] = 0;
1768       nzi++; dcount++;
1769     }
1770 
1771     /* add pivot rows into the active row */
1772     nzbd = 0;
1773     prow = lnk[n];
1774     while (prow < i) {
1775       nnz      = bdiag[prow];
1776       cols     = bj_ptr[prow] + nnz + 1;
1777       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1778       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
1779       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
1780       nzi += nlnk;
1781       prow = lnk[prow];
1782       nzbd++;
1783     }
1784     bdiag[i] = nzbd;
1785     bi[i+1]  = bi[i] + nzi;
1786 
1787     /* if free space is not available, make more free space */
1788     if (current_space->local_remaining<nzi) {
1789       nnz = 2*nzi*(n - i); /* estimated and max additional space needed */
1790       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
1791       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
1792       reallocs++;
1793     }
1794 
1795     /* copy data into free_space and free_space_lvl, then initialize lnk */
1796     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1797     bj_ptr[i]    = current_space->array;
1798     bjlvl_ptr[i] = current_space_lvl->array;
1799 
1800     /* make sure the active row i has diagonal entry */
1801     if (*(bj_ptr[i]+bdiag[i]) != i) {
1802       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
1803     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
1804     }
1805 
1806     current_space->array           += nzi;
1807     current_space->local_used      += nzi;
1808     current_space->local_remaining -= nzi;
1809     current_space_lvl->array           += nzi;
1810     current_space_lvl->local_used      += nzi;
1811     current_space_lvl->local_remaining -= nzi;
1812   }
1813 
1814   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1815   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1816 
1817   /* destroy list of free space and other temporary arrays */
1818   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
1819 
1820   /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */
1821   ierr = PetscFreeSpaceContiguous_LU_v2(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr);
1822 
1823   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1824   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
1825   ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr);
1826 
1827 #if defined(PETSC_USE_INFO)
1828   {
1829     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1830     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
1831     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
1832     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
1833     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
1834     if (diagonal_fill) {
1835       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
1836     }
1837   }
1838 #endif
1839 
1840   /* put together the new matrix */
1841   ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
1842   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
1843   b = (Mat_SeqAIJ*)(fact)->data;
1844   b->free_a       = PETSC_TRUE;
1845   b->free_ij      = PETSC_TRUE;
1846   b->singlemalloc = PETSC_FALSE;
1847   ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
1848   b->j          = bj;
1849   b->i          = bi;
1850   b->diag       = bdiag;
1851   b->ilen       = 0;
1852   b->imax       = 0;
1853   b->row        = isrow;
1854   b->col        = iscol;
1855   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1856   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1857   b->icol       = isicol;
1858   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1859   /* In b structure:  Free imax, ilen, old a, old j.
1860      Allocate bdiag, solve_work, new a, new j */
1861   ierr = PetscLogObjectMemory(fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
1862   b->maxnz = b->nz = bdiag[0]+1;
1863   (fact)->info.factor_mallocs    = reallocs;
1864   (fact)->info.fill_ratio_given  = f;
1865   (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]);
1866   (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct;
1867   ierr = Mat_CheckInode_FactorLU(fact,PETSC_FALSE);CHKERRQ(ierr);
1868   PetscFunctionReturn(0);
1869 }
1870 
1871 #undef __FUNCT__
1872 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ"
1873 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1874 {
1875   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1876   IS                 isicol;
1877   PetscErrorCode     ierr;
1878   const PetscInt     *r,*ic;
1879   PetscInt           n=A->rmap->n,*ai=a->i,*aj=a->j,d;
1880   PetscInt           *bi,*cols,nnz,*cols_lvl;
1881   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1882   PetscInt           i,levels,diagonal_fill;
1883   PetscTruth         col_identity,row_identity;
1884   PetscReal          f;
1885   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
1886   PetscBT            lnkbt;
1887   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
1888   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1889   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1890   PetscTruth         missing;
1891   PetscTruth         newdatastruct=PETSC_FALSE;
1892 
1893   PetscFunctionBegin;
1894   ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
1895   if(newdatastruct){
1896     ierr = MatILUFactorSymbolic_SeqAIJ_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1897     PetscFunctionReturn(0);
1898   }
1899 
1900   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);
1901   f             = info->fill;
1902   levels        = (PetscInt)info->levels;
1903   diagonal_fill = (PetscInt)info->diagonal_fill;
1904   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1905 
1906   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1907   ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
1908   if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */
1909     ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr);
1910     (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ;
1911 
1912     fact->factor = MAT_FACTOR_ILU;
1913     (fact)->info.factor_mallocs    = 0;
1914     (fact)->info.fill_ratio_given  = info->fill;
1915     (fact)->info.fill_ratio_needed = 1.0;
1916     b               = (Mat_SeqAIJ*)(fact)->data;
1917     ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
1918     if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
1919     b->row              = isrow;
1920     b->col              = iscol;
1921     b->icol             = isicol;
1922     ierr                = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1923     ierr                = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1924     ierr                = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1925     ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1926     PetscFunctionReturn(0);
1927   }
1928 
1929   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1930   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1931 
1932   /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
1933   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1934   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
1935   bi[0] = bdiag[0] = 0;
1936 
1937   ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr);
1938 
1939   /* create a linked list for storing column indices of the active row */
1940   nlnk = n + 1;
1941   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1942 
1943   /* initial FreeSpace size is f*(ai[n]+1) */
1944   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
1945   current_space = free_space;
1946   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
1947   current_space_lvl = free_space_lvl;
1948 
1949   for (i=0; i<n; i++) {
1950     nzi = 0;
1951     /* copy current row into linked list */
1952     nnz  = ai[r[i]+1] - ai[r[i]];
1953     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1954     cols = aj + ai[r[i]];
1955     lnk[i] = -1; /* marker to indicate if diagonal exists */
1956     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1957     nzi += nlnk;
1958 
1959     /* make sure diagonal entry is included */
1960     if (diagonal_fill && lnk[i] == -1) {
1961       fm = n;
1962       while (lnk[fm] < i) fm = lnk[fm];
1963       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
1964       lnk[fm]    = i;
1965       lnk_lvl[i] = 0;
1966       nzi++; dcount++;
1967     }
1968 
1969     /* add pivot rows into the active row */
1970     nzbd = 0;
1971     prow = lnk[n];
1972     while (prow < i) {
1973       nnz      = bdiag[prow];
1974       cols     = bj_ptr[prow] + nnz + 1;
1975       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1976       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
1977       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
1978       nzi += nlnk;
1979       prow = lnk[prow];
1980       nzbd++;
1981     }
1982     bdiag[i] = nzbd;
1983     bi[i+1]  = bi[i] + nzi;
1984 
1985     /* if free space is not available, make more free space */
1986     if (current_space->local_remaining<nzi) {
1987       nnz = nzi*(n - i); /* estimated and max additional space needed */
1988       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
1989       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
1990       reallocs++;
1991     }
1992 
1993     /* copy data into free_space and free_space_lvl, then initialize lnk */
1994     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1995     bj_ptr[i]    = current_space->array;
1996     bjlvl_ptr[i] = current_space_lvl->array;
1997 
1998     /* make sure the active row i has diagonal entry */
1999     if (*(bj_ptr[i]+bdiag[i]) != i) {
2000       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
2001     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
2002     }
2003 
2004     current_space->array           += nzi;
2005     current_space->local_used      += nzi;
2006     current_space->local_remaining -= nzi;
2007     current_space_lvl->array           += nzi;
2008     current_space_lvl->local_used      += nzi;
2009     current_space_lvl->local_remaining -= nzi;
2010   }
2011 
2012   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
2013   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
2014 
2015   /* destroy list of free space and other temporary arrays */
2016   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
2017   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */
2018   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2019   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2020   ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr);
2021 
2022 #if defined(PETSC_USE_INFO)
2023   {
2024     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
2025     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
2026     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2027     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
2028     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
2029     if (diagonal_fill) {
2030       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
2031     }
2032   }
2033 #endif
2034 
2035   /* put together the new matrix */
2036   ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
2037   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
2038   b = (Mat_SeqAIJ*)(fact)->data;
2039   b->free_a       = PETSC_TRUE;
2040   b->free_ij      = PETSC_TRUE;
2041   b->singlemalloc = PETSC_FALSE;
2042   ierr = PetscMalloc(bi[n]*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
2043   b->j          = bj;
2044   b->i          = bi;
2045   for (i=0; i<n; i++) bdiag[i] += bi[i];
2046   b->diag       = bdiag;
2047   b->ilen       = 0;
2048   b->imax       = 0;
2049   b->row        = isrow;
2050   b->col        = iscol;
2051   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
2052   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
2053   b->icol       = isicol;
2054   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2055   /* In b structure:  Free imax, ilen, old a, old j.
2056      Allocate bdiag, solve_work, new a, new j */
2057   ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
2058   b->maxnz             = b->nz = bi[n] ;
2059   (fact)->info.factor_mallocs    = reallocs;
2060   (fact)->info.fill_ratio_given  = f;
2061   (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
2062   (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ;
2063   ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr);
2064   PetscFunctionReturn(0);
2065 }
2066 
2067 #undef __FUNCT__
2068 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ_newdatastruct"
2069 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info)
2070 {
2071   Mat            C = B;
2072   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
2073   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
2074   IS             ip=b->row,iip = b->icol;
2075   PetscErrorCode ierr;
2076   const PetscInt *rip,*riip;
2077   PetscInt       i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp;
2078   PetscInt       *ai=a->i,*aj=a->j;
2079   PetscInt       k,jmin,jmax,*c2r,*il,col,nexti,ili,nz;
2080   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
2081   PetscTruth     perm_identity;
2082 
2083   LUShift_Ctx    sctx;
2084   PetscInt       newshift;
2085   PetscReal      rs;
2086   MatScalar      d,*v;
2087 
2088   PetscFunctionBegin;
2089   /* MatPivotSetUp(): initialize shift context sctx */
2090   ierr = PetscMemzero(&sctx,sizeof(LUShift_Ctx));CHKERRQ(ierr);
2091 
2092   /* if both shift schemes are chosen by user, only use info->shiftpd */
2093   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
2094     sctx.shift_top = info->zeropivot;
2095     for (i=0; i<mbs; i++) {
2096       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
2097       d  = (aa)[a->diag[i]];
2098       rs = -PetscAbsScalar(d) - PetscRealPart(d);
2099       v  = aa+ai[i];
2100       nz = ai[i+1] - ai[i];
2101       for (j=0; j<nz; j++)
2102 	rs += PetscAbsScalar(v[j]);
2103       if (rs>sctx.shift_top) sctx.shift_top = rs;
2104     }
2105     sctx.shift_top   *= 1.1;
2106     sctx.nshift_max   = 5;
2107     sctx.shift_lo     = 0.;
2108     sctx.shift_hi     = 1.;
2109   }
2110 
2111   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
2112   ierr  = ISGetIndices(iip,&riip);CHKERRQ(ierr);
2113 
2114   /* allocate working arrays
2115      c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col
2116      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
2117   */
2118   ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&c2r);CHKERRQ(ierr);
2119 
2120   do {
2121     sctx.lushift = PETSC_FALSE;
2122 
2123     for (i=0; i<mbs; i++) c2r[i] = mbs;
2124     il[0] = 0;
2125 
2126     for (k = 0; k<mbs; k++){
2127       /* zero rtmp */
2128       nz = bi[k+1] - bi[k];
2129       bjtmp = bj + bi[k];
2130       for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
2131 
2132       /* load in initial unfactored row */
2133       bval = ba + bi[k];
2134       jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2135       for (j = jmin; j < jmax; j++){
2136         col = riip[aj[j]];
2137         if (col >= k){ /* only take upper triangular entry */
2138           rtmp[col] = aa[j];
2139           *bval++   = 0.0; /* for in-place factorization */
2140         }
2141       }
2142       /* shift the diagonal of the matrix: ZeropivotApply() */
2143       rtmp[k] += sctx.shift_amount;  /* shift the diagonal of the matrix */
2144 
2145       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
2146       dk = rtmp[k];
2147       i  = c2r[k]; /* first row to be added to k_th row  */
2148 
2149       while (i < k){
2150         nexti = c2r[i]; /* next row to be added to k_th row */
2151 
2152         /* compute multiplier, update diag(k) and U(i,k) */
2153         ili   = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2154         uikdi = - ba[ili]*ba[bdiag[i]];  /* diagonal(k) */
2155         dk   += uikdi*ba[ili]; /* update diag[k] */
2156         ba[ili] = uikdi; /* -U(i,k) */
2157 
2158         /* add multiple of row i to k-th row */
2159         jmin = ili + 1; jmax = bi[i+1];
2160         if (jmin < jmax){
2161           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2162           /* update il and c2r for row i */
2163           il[i] = jmin;
2164           j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i;
2165         }
2166         i = nexti;
2167       }
2168 
2169       /* copy data into U(k,:) */
2170       rs   = 0.0;
2171       jmin = bi[k]; jmax = bi[k+1]-1;
2172       if (jmin < jmax) {
2173         for (j=jmin; j<jmax; j++){
2174           col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]);
2175         }
2176         /* add the k-th row into il and c2r */
2177         il[k] = jmin;
2178         i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k;
2179       }
2180 
2181       /* MatPivotCheck() */
2182       sctx.rs  = rs;
2183       sctx.pv  = dk;
2184       if (info->shiftnz){
2185         ierr = MatPivotCheck_nz(info,sctx,k,newshift);CHKERRQ(ierr);
2186       } else if (info->shiftpd){
2187         ierr = MatPivotCheck_pd(info,sctx,k,newshift);CHKERRQ(ierr);
2188       } else if (info->shiftinblocks){
2189         ierr = MatPivotCheck_inblocks(info,sctx,k,newshift);CHKERRQ(ierr);
2190       } else {
2191         ierr = MatPivotCheck_none(info,sctx,k,newshift);CHKERRQ(ierr);
2192       }
2193       dk = sctx.pv;
2194       if (newshift == 1) break;
2195 
2196       ba[bdiag[k]] = 1.0/dk; /* U(k,k) */
2197     }
2198   } while (sctx.lushift);
2199 
2200   ierr = PetscFree3(rtmp,il,c2r);CHKERRQ(ierr);
2201   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2202   ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr);
2203 
2204   ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
2205   if (perm_identity){
2206     B->ops->solve           = MatSolve_SeqSBAIJ_1_NaturalOrdering_newdatastruct;
2207     B->ops->solvetranspose  = MatSolve_SeqSBAIJ_1_NaturalOrdering_newdatastruct;
2208     B->ops->forwardsolve    = 0;
2209     B->ops->backwardsolve   = 0;
2210   } else {
2211     B->ops->solve           = MatSolve_SeqSBAIJ_1_newdatastruct;
2212     B->ops->solvetranspose  = MatSolve_SeqSBAIJ_1_newdatastruct;
2213     B->ops->forwardsolve    = 0;
2214     B->ops->backwardsolve   = 0;
2215   }
2216 
2217   C->assembled    = PETSC_TRUE;
2218   C->preallocated = PETSC_TRUE;
2219   ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr);
2220 
2221   /* MatPivotView() */
2222   if (sctx.nshift){
2223     if (info->shiftpd) {
2224       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);
2225     } else if (info->shiftnz) {
2226       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2227     } else if (info->shiftinblocks){
2228       ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftinblocks);CHKERRQ(ierr);
2229     }
2230   }
2231   PetscFunctionReturn(0);
2232 }
2233 
2234 #undef __FUNCT__
2235 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ"
2236 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info)
2237 {
2238   Mat            C = B;
2239   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
2240   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
2241   IS             ip=b->row,iip = b->icol;
2242   PetscErrorCode ierr;
2243   const PetscInt *rip,*riip;
2244   PetscInt       i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol,*bjtmp;
2245   PetscInt       *ai=a->i,*aj=a->j;
2246   PetscInt       k,jmin,jmax,*jl,*il,col,nexti,ili,nz;
2247   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
2248   PetscReal      zeropivot,rs,shiftnz;
2249   PetscReal      shiftpd;
2250   ChShift_Ctx    sctx;
2251   PetscInt       newshift;
2252   PetscTruth     perm_identity;
2253 
2254   PetscFunctionBegin;
2255   shiftnz   = info->shiftnz;
2256   shiftpd   = info->shiftpd;
2257   zeropivot = info->zeropivot;
2258 
2259   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
2260   ierr  = ISGetIndices(iip,&riip);CHKERRQ(ierr);
2261 
2262   /* initialization */
2263   ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&jl);CHKERRQ(ierr);
2264   sctx.shift_amount = 0;
2265   sctx.nshift       = 0;
2266   do {
2267     sctx.chshift = PETSC_FALSE;
2268     for (i=0; i<mbs; i++) jl[i] = mbs;
2269     il[0] = 0;
2270 
2271     for (k = 0; k<mbs; k++){
2272       /* zero rtmp */
2273       nz = bi[k+1] - bi[k];
2274       bjtmp = bj + bi[k];
2275       for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
2276 
2277       bval = ba + bi[k];
2278       /* initialize k-th row by the perm[k]-th row of A */
2279       jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2280       for (j = jmin; j < jmax; j++){
2281         col = riip[aj[j]];
2282         if (col >= k){ /* only take upper triangular entry */
2283           rtmp[col] = aa[j];
2284           *bval++  = 0.0; /* for in-place factorization */
2285         }
2286       }
2287       /* shift the diagonal of the matrix */
2288       if (sctx.nshift) rtmp[k] += sctx.shift_amount;
2289 
2290       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
2291       dk = rtmp[k];
2292       i = jl[k]; /* first row to be added to k_th row  */
2293 
2294       while (i < k){
2295         nexti = jl[i]; /* next row to be added to k_th row */
2296 
2297         /* compute multiplier, update diag(k) and U(i,k) */
2298         ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2299         uikdi = - ba[ili]*ba[bi[i]];  /* diagonal(k) */
2300         dk += uikdi*ba[ili];
2301         ba[ili] = uikdi; /* -U(i,k) */
2302 
2303         /* add multiple of row i to k-th row */
2304         jmin = ili + 1; jmax = bi[i+1];
2305         if (jmin < jmax){
2306           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2307           /* update il and jl for row i */
2308           il[i] = jmin;
2309           j = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
2310         }
2311         i = nexti;
2312       }
2313 
2314       /* shift the diagonals when zero pivot is detected */
2315       /* compute rs=sum of abs(off-diagonal) */
2316       rs   = 0.0;
2317       jmin = bi[k]+1;
2318       nz   = bi[k+1] - jmin;
2319       bcol = bj + jmin;
2320       for (j=0; j<nz; j++) {
2321         rs += PetscAbsScalar(rtmp[bcol[j]]);
2322       }
2323 
2324       sctx.rs = rs;
2325       sctx.pv = dk;
2326       ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr);
2327 
2328       if (newshift == 1) {
2329         if (!sctx.shift_amount) {
2330           sctx.shift_amount = 1e-5;
2331         }
2332         break;
2333       }
2334 
2335       /* copy data into U(k,:) */
2336       ba[bi[k]] = 1.0/dk; /* U(k,k) */
2337       jmin = bi[k]+1; jmax = bi[k+1];
2338       if (jmin < jmax) {
2339         for (j=jmin; j<jmax; j++){
2340           col = bj[j]; ba[j] = rtmp[col];
2341         }
2342         /* add the k-th row into il and jl */
2343         il[k] = jmin;
2344         i = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
2345       }
2346     }
2347   } while (sctx.chshift);
2348   ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr);
2349   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2350   ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr);
2351 
2352   ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
2353   if (perm_identity){
2354     B->ops->solve           = MatSolve_SeqSBAIJ_1_NaturalOrdering;
2355     B->ops->solvetranspose  = MatSolve_SeqSBAIJ_1_NaturalOrdering;
2356     B->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering;
2357     B->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering;
2358   } else {
2359     B->ops->solve           = MatSolve_SeqSBAIJ_1;
2360     B->ops->solvetranspose  = MatSolve_SeqSBAIJ_1;
2361     B->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1;
2362     B->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1;
2363   }
2364 
2365   C->assembled    = PETSC_TRUE;
2366   C->preallocated = PETSC_TRUE;
2367   ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr);
2368   if (sctx.nshift){
2369     if (shiftnz) {
2370       ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2371     } else if (shiftpd) {
2372       ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2373     }
2374   }
2375   PetscFunctionReturn(0);
2376 }
2377 
2378 /*
2379    icc() under revised new data structure.
2380    Factored arrays bj and ba are stored as
2381      U(0,:),...,U(i,:),U(n-1,:)
2382 
2383    ui=fact->i is an array of size n+1, in which
2384    ui+
2385      ui[i]:  points to 1st entry of U(i,:),i=0,...,n-1
2386      ui[n]:  points to U(n-1,n-1)+1
2387 
2388   udiag=fact->diag is an array of size n,in which
2389      udiag[i]: points to diagonal of U(i,:), i=0,...,n-1
2390 
2391    U(i,:) contains udiag[i] as its last entry, i.e.,
2392     U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i])
2393 */
2394 
2395 #undef __FUNCT__
2396 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ_newdatastruct"
2397 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2398 {
2399   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2400   Mat_SeqSBAIJ       *b;
2401   PetscErrorCode     ierr;
2402   PetscTruth         perm_identity,missing;
2403   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag;
2404   const PetscInt     *rip,*riip;
2405   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
2406   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL,d;
2407   PetscInt           ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
2408   PetscReal          fill=info->fill,levels=info->levels;
2409   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2410   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
2411   PetscBT            lnkbt;
2412   IS                 iperm;
2413 
2414   PetscFunctionBegin;
2415   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);
2416   ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
2417   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
2418   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2419   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2420 
2421   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2422   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2423   ui[0] = 0;
2424 
2425   /* ICC(0) without matrix ordering: simply rearrange column indices */
2426   if (!levels && perm_identity) {
2427     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2428     cols = uj;
2429     for (i=0; i<am; i++) {
2430       ncols    = ai[i+1] - a->diag[i];
2431       ui[i+1]  = ui[i] + ncols;
2432       udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */
2433 
2434       aj   = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */
2435       ncols--; /* exclude diagonal */
2436       for (j=0; j<ncols; j++) *cols++ = aj[j];
2437       *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */
2438     }
2439   } else { /* case: levels>0 || (levels=0 && !perm_identity) */
2440     ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2441     ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2442 
2443     /* initialization */
2444     ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr);
2445 
2446     /* jl: linked list for storing indices of the pivot rows
2447        il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2448     ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr);
2449     for (i=0; i<am; i++){
2450       jl[i] = am; il[i] = 0;
2451     }
2452 
2453     /* create and initialize a linked list for storing column indices of the active row k */
2454     nlnk = am + 1;
2455     ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2456 
2457     /* initial FreeSpace size is fill*(ai[am]+1) */
2458     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2459     current_space = free_space;
2460     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr);
2461     current_space_lvl = free_space_lvl;
2462 
2463     for (k=0; k<am; k++){  /* for each active row k */
2464       /* initialize lnk by the column indices of row rip[k] of A */
2465       nzk   = 0;
2466       ncols = ai[rip[k]+1] - ai[rip[k]];
2467       if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2468       ncols_upper = 0;
2469       for (j=0; j<ncols; j++){
2470         i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2471         if (riip[i] >= k){ /* only take upper triangular entry */
2472           ajtmp[ncols_upper] = i;
2473           ncols_upper++;
2474         }
2475       }
2476       ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2477       nzk += nlnk;
2478 
2479       /* update lnk by computing fill-in for each pivot row to be merged in */
2480       prow = jl[k]; /* 1st pivot row */
2481 
2482       while (prow < k){
2483         nextprow = jl[prow];
2484 
2485         /* merge prow into k-th row */
2486         jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2487         jmax = ui[prow+1];
2488         ncols = jmax-jmin;
2489         i     = jmin - ui[prow];
2490         cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2491         uj    = uj_lvl_ptr[prow] + i; /* levels of cols */
2492         j     = *(uj - 1);
2493         ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr);
2494         nzk += nlnk;
2495 
2496         /* update il and jl for prow */
2497         if (jmin < jmax){
2498           il[prow] = jmin;
2499           j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2500         }
2501         prow = nextprow;
2502       }
2503 
2504       /* if free space is not available, make more free space */
2505       if (current_space->local_remaining<nzk) {
2506         i  = am - k + 1; /* num of unfactored rows */
2507         i *= PetscMin(nzk, i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */
2508         ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2509         ierr = PetscFreeSpaceGet(i,&current_space_lvl);CHKERRQ(ierr);
2510         reallocs++;
2511       }
2512 
2513       /* copy data into free_space and free_space_lvl, then initialize lnk */
2514       if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2515       ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
2516 
2517       /* add the k-th row into il and jl */
2518       if (nzk > 1){
2519         i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2520         jl[k] = jl[i]; jl[i] = k;
2521         il[k] = ui[k] + 1;
2522       }
2523       uj_ptr[k]     = current_space->array;
2524       uj_lvl_ptr[k] = current_space_lvl->array;
2525 
2526       current_space->array           += nzk;
2527       current_space->local_used      += nzk;
2528       current_space->local_remaining -= nzk;
2529 
2530       current_space_lvl->array           += nzk;
2531       current_space_lvl->local_used      += nzk;
2532       current_space_lvl->local_remaining -= nzk;
2533 
2534       ui[k+1] = ui[k] + nzk;
2535     }
2536 
2537 #if defined(PETSC_USE_INFO)
2538     if (ai[am] != 0) {
2539       PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]);
2540       ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2541       ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2542       ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2543     } else {
2544       ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2545     }
2546 #endif
2547 
2548     ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2549     ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2550     ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr);
2551     ierr = PetscFree(ajtmp);CHKERRQ(ierr);
2552 
2553     /* destroy list of free space and other temporary array(s) */
2554     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2555     ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor in newdatastruct */
2556     ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2557     ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2558 
2559   } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2560 
2561   /* put together the new matrix in MATSEQSBAIJ format */
2562 
2563   b    = (Mat_SeqSBAIJ*)(fact)->data;
2564   b->singlemalloc = PETSC_FALSE;
2565   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2566   b->j    = uj;
2567   b->i    = ui;
2568   b->diag = udiag;
2569   b->free_diag = PETSC_TRUE;
2570   b->ilen = 0;
2571   b->imax = 0;
2572   b->row  = perm;
2573   b->col  = perm;
2574   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2575   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2576   b->icol = iperm;
2577   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2578   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2579   ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2580   b->maxnz   = b->nz = ui[am];
2581   b->free_a  = PETSC_TRUE;
2582   b->free_ij = PETSC_TRUE;
2583 
2584   fact->info.factor_mallocs    = reallocs;
2585   fact->info.fill_ratio_given  = fill;
2586   if (ai[am] != 0) {
2587     fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2588   } else {
2589     fact->info.fill_ratio_needed = 0.0;
2590   }
2591   fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_newdatastruct;
2592   PetscFunctionReturn(0);
2593 }
2594 
2595 #undef __FUNCT__
2596 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ"
2597 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2598 {
2599   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2600   Mat_SeqSBAIJ       *b;
2601   PetscErrorCode     ierr;
2602   PetscTruth         perm_identity,missing;
2603   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag;
2604   const PetscInt     *rip,*riip;
2605   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
2606   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL,d;
2607   PetscInt           ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
2608   PetscReal          fill=info->fill,levels=info->levels;
2609   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2610   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
2611   PetscBT            lnkbt;
2612   IS                 iperm;
2613   PetscTruth         newdatastruct=PETSC_FALSE;
2614 
2615   PetscFunctionBegin;
2616   ierr = PetscOptionsGetTruth(PETSC_NULL,"-icc_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
2617   if(newdatastruct){
2618     ierr = MatICCFactorSymbolic_SeqAIJ_newdatastruct(fact,A,perm,info);CHKERRQ(ierr);
2619     PetscFunctionReturn(0);
2620   }
2621 
2622   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);
2623   ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
2624   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
2625   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2626   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2627 
2628   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2629   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2630   ui[0] = 0;
2631 
2632   /* ICC(0) without matrix ordering: simply copies fill pattern */
2633   if (!levels && perm_identity) {
2634 
2635     for (i=0; i<am; i++) {
2636       ui[i+1]  = ui[i] + ai[i+1] - a->diag[i];
2637       udiag[i] = ui[i];
2638     }
2639     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2640     cols = uj;
2641     for (i=0; i<am; i++) {
2642       aj    = a->j + a->diag[i];
2643       ncols = ui[i+1] - ui[i];
2644       for (j=0; j<ncols; j++) *cols++ = *aj++;
2645     }
2646   } else { /* case: levels>0 || (levels=0 && !perm_identity) */
2647     ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2648     ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2649 
2650     /* initialization */
2651     ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr);
2652 
2653     /* jl: linked list for storing indices of the pivot rows
2654        il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2655     ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr);
2656     for (i=0; i<am; i++){
2657       jl[i] = am; il[i] = 0;
2658     }
2659 
2660     /* create and initialize a linked list for storing column indices of the active row k */
2661     nlnk = am + 1;
2662     ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2663 
2664     /* initial FreeSpace size is fill*(ai[am]+1) */
2665     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2666     current_space = free_space;
2667     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr);
2668     current_space_lvl = free_space_lvl;
2669 
2670     for (k=0; k<am; k++){  /* for each active row k */
2671       /* initialize lnk by the column indices of row rip[k] of A */
2672       nzk   = 0;
2673       ncols = ai[rip[k]+1] - ai[rip[k]];
2674       if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2675       ncols_upper = 0;
2676       for (j=0; j<ncols; j++){
2677         i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2678         if (riip[i] >= k){ /* only take upper triangular entry */
2679           ajtmp[ncols_upper] = i;
2680           ncols_upper++;
2681         }
2682       }
2683       ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2684       nzk += nlnk;
2685 
2686       /* update lnk by computing fill-in for each pivot row to be merged in */
2687       prow = jl[k]; /* 1st pivot row */
2688 
2689       while (prow < k){
2690         nextprow = jl[prow];
2691 
2692         /* merge prow into k-th row */
2693         jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2694         jmax = ui[prow+1];
2695         ncols = jmax-jmin;
2696         i     = jmin - ui[prow];
2697         cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2698         uj    = uj_lvl_ptr[prow] + i; /* levels of cols */
2699         j     = *(uj - 1);
2700         ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr);
2701         nzk += nlnk;
2702 
2703         /* update il and jl for prow */
2704         if (jmin < jmax){
2705           il[prow] = jmin;
2706           j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2707         }
2708         prow = nextprow;
2709       }
2710 
2711       /* if free space is not available, make more free space */
2712       if (current_space->local_remaining<nzk) {
2713         i = am - k + 1; /* num of unfactored rows */
2714         i *= PetscMin(nzk, (i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2715         ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2716         ierr = PetscFreeSpaceGet(i,&current_space_lvl);CHKERRQ(ierr);
2717         reallocs++;
2718       }
2719 
2720       /* copy data into free_space and free_space_lvl, then initialize lnk */
2721       if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2722       ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
2723 
2724       /* add the k-th row into il and jl */
2725       if (nzk > 1){
2726         i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2727         jl[k] = jl[i]; jl[i] = k;
2728         il[k] = ui[k] + 1;
2729       }
2730       uj_ptr[k]     = current_space->array;
2731       uj_lvl_ptr[k] = current_space_lvl->array;
2732 
2733       current_space->array           += nzk;
2734       current_space->local_used      += nzk;
2735       current_space->local_remaining -= nzk;
2736 
2737       current_space_lvl->array           += nzk;
2738       current_space_lvl->local_used      += nzk;
2739       current_space_lvl->local_remaining -= nzk;
2740 
2741       ui[k+1] = ui[k] + nzk;
2742     }
2743 
2744 #if defined(PETSC_USE_INFO)
2745     if (ai[am] != 0) {
2746       PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]);
2747       ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2748       ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2749       ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2750     } else {
2751       ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2752     }
2753 #endif
2754 
2755     ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2756     ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2757     ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr);
2758     ierr = PetscFree(ajtmp);CHKERRQ(ierr);
2759 
2760     /* destroy list of free space and other temporary array(s) */
2761     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2762     ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
2763     ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2764     ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2765 
2766   } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2767 
2768   /* put together the new matrix in MATSEQSBAIJ format */
2769 
2770   b    = (Mat_SeqSBAIJ*)fact->data;
2771   b->singlemalloc = PETSC_FALSE;
2772   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2773   b->j    = uj;
2774   b->i    = ui;
2775   b->diag = udiag;
2776   b->free_diag = PETSC_TRUE;
2777   b->ilen = 0;
2778   b->imax = 0;
2779   b->row  = perm;
2780   b->col  = perm;
2781   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2782   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2783   b->icol = iperm;
2784   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2785   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2786   ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2787   b->maxnz   = b->nz = ui[am];
2788   b->free_a  = PETSC_TRUE;
2789   b->free_ij = PETSC_TRUE;
2790 
2791   fact->info.factor_mallocs    = reallocs;
2792   fact->info.fill_ratio_given  = fill;
2793   if (ai[am] != 0) {
2794     fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2795   } else {
2796     fact->info.fill_ratio_needed = 0.0;
2797   }
2798   fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2799   PetscFunctionReturn(0);
2800 }
2801 
2802 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2803 {
2804   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2805   Mat_SeqSBAIJ       *b;
2806   PetscErrorCode     ierr;
2807   PetscTruth         perm_identity;
2808   PetscReal          fill = info->fill;
2809   const PetscInt     *rip,*riip;
2810   PetscInt           i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow;
2811   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
2812   PetscInt           nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr,*udiag;
2813   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2814   PetscBT            lnkbt;
2815   IS                 iperm;
2816 
2817   PetscFunctionBegin;
2818   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);
2819   /* check whether perm is the identity mapping */
2820   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2821   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2822   ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2823   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2824 
2825   /* initialization */
2826   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2827   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2828   ui[0] = 0;
2829 
2830   /* jl: linked list for storing indices of the pivot rows
2831      il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2832   ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr);
2833   for (i=0; i<am; i++){
2834     jl[i] = am; il[i] = 0;
2835   }
2836 
2837   /* create and initialize a linked list for storing column indices of the active row k */
2838   nlnk = am + 1;
2839   ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2840 
2841   /* initial FreeSpace size is fill*(ai[am]+1) */
2842   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2843   current_space = free_space;
2844 
2845   for (k=0; k<am; k++){  /* for each active row k */
2846     /* initialize lnk by the column indices of row rip[k] of A */
2847     nzk   = 0;
2848     ncols = ai[rip[k]+1] - ai[rip[k]];
2849     if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2850     ncols_upper = 0;
2851     for (j=0; j<ncols; j++){
2852       i = riip[*(aj + ai[rip[k]] + j)];
2853       if (i >= k){ /* only take upper triangular entry */
2854         cols[ncols_upper] = i;
2855         ncols_upper++;
2856       }
2857     }
2858     ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2859     nzk += nlnk;
2860 
2861     /* update lnk by computing fill-in for each pivot row to be merged in */
2862     prow = jl[k]; /* 1st pivot row */
2863 
2864     while (prow < k){
2865       nextprow = jl[prow];
2866       /* merge prow into k-th row */
2867       jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2868       jmax = ui[prow+1];
2869       ncols = jmax-jmin;
2870       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2871       ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2872       nzk += nlnk;
2873 
2874       /* update il and jl for prow */
2875       if (jmin < jmax){
2876         il[prow] = jmin;
2877         j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
2878       }
2879       prow = nextprow;
2880     }
2881 
2882     /* if free space is not available, make more free space */
2883     if (current_space->local_remaining<nzk) {
2884       i  = am - k + 1; /* num of unfactored rows */
2885       i *= PetscMin(nzk,i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */
2886       ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2887       reallocs++;
2888     }
2889 
2890     /* copy data into free space, then initialize lnk */
2891     ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
2892 
2893     /* add the k-th row into il and jl */
2894     if (nzk-1 > 0){
2895       i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2896       jl[k] = jl[i]; jl[i] = k;
2897       il[k] = ui[k] + 1;
2898     }
2899     ui_ptr[k] = current_space->array;
2900     current_space->array           += nzk;
2901     current_space->local_used      += nzk;
2902     current_space->local_remaining -= nzk;
2903 
2904     ui[k+1] = ui[k] + nzk;
2905   }
2906 
2907 #if defined(PETSC_USE_INFO)
2908   if (ai[am] != 0) {
2909     PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]);
2910     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2911     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2912     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2913   } else {
2914      ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2915   }
2916 #endif
2917 
2918   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2919   ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2920   ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr);
2921 
2922   /* destroy list of free space and other temporary array(s) */
2923   ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2924   ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor in newdatastruct */
2925   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2926 
2927   /* put together the new matrix in MATSEQSBAIJ format */
2928 
2929   b = (Mat_SeqSBAIJ*)fact->data;
2930   b->singlemalloc = PETSC_FALSE;
2931   b->free_a       = PETSC_TRUE;
2932   b->free_ij      = PETSC_TRUE;
2933   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2934   b->j    = uj;
2935   b->i    = ui;
2936   b->diag = udiag;
2937   b->free_diag = PETSC_TRUE;
2938   b->ilen = 0;
2939   b->imax = 0;
2940   b->row  = perm;
2941   b->col  = perm;
2942   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2943   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2944   b->icol = iperm;
2945   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2946   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2947   ierr    = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2948   b->maxnz = b->nz = ui[am];
2949 
2950   fact->info.factor_mallocs    = reallocs;
2951   fact->info.fill_ratio_given  = fill;
2952   if (ai[am] != 0) {
2953     fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2954   } else {
2955     fact->info.fill_ratio_needed = 0.0;
2956   }
2957   fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_newdatastruct;
2958   PetscFunctionReturn(0);
2959 }
2960 
2961 #undef __FUNCT__
2962 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ"
2963 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2964 {
2965   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2966   Mat_SeqSBAIJ       *b;
2967   PetscErrorCode     ierr;
2968   PetscTruth         perm_identity;
2969   PetscReal          fill = info->fill;
2970   const PetscInt     *rip,*riip;
2971   PetscInt           i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow;
2972   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
2973   PetscInt           nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr;
2974   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2975   PetscBT            lnkbt;
2976   IS                 iperm;
2977   PetscTruth         newdatastruct=PETSC_FALSE;
2978 
2979   PetscFunctionBegin;
2980   ierr = PetscOptionsGetTruth(PETSC_NULL,"-cholesky_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
2981   if(newdatastruct){
2982     ierr = MatCholeskyFactorSymbolic_SeqAIJ_newdatastruct(fact,A,perm,info);CHKERRQ(ierr);
2983     PetscFunctionReturn(0);
2984   }
2985 
2986   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);
2987   /* check whether perm is the identity mapping */
2988   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2989   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2990   ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2991   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2992 
2993   /* initialization */
2994   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2995   ui[0] = 0;
2996 
2997   /* jl: linked list for storing indices of the pivot rows
2998      il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2999   ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr);
3000   for (i=0; i<am; i++){
3001     jl[i] = am; il[i] = 0;
3002   }
3003 
3004   /* create and initialize a linked list for storing column indices of the active row k */
3005   nlnk = am + 1;
3006   ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3007 
3008   /* initial FreeSpace size is fill*(ai[am]+1) */
3009   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
3010   current_space = free_space;
3011 
3012   for (k=0; k<am; k++){  /* for each active row k */
3013     /* initialize lnk by the column indices of row rip[k] of A */
3014     nzk   = 0;
3015     ncols = ai[rip[k]+1] - ai[rip[k]];
3016     if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
3017     ncols_upper = 0;
3018     for (j=0; j<ncols; j++){
3019       i = riip[*(aj + ai[rip[k]] + j)];
3020       if (i >= k){ /* only take upper triangular entry */
3021         cols[ncols_upper] = i;
3022         ncols_upper++;
3023       }
3024     }
3025     ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3026     nzk += nlnk;
3027 
3028     /* update lnk by computing fill-in for each pivot row to be merged in */
3029     prow = jl[k]; /* 1st pivot row */
3030 
3031     while (prow < k){
3032       nextprow = jl[prow];
3033       /* merge prow into k-th row */
3034       jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
3035       jmax = ui[prow+1];
3036       ncols = jmax-jmin;
3037       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */
3038       ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3039       nzk += nlnk;
3040 
3041       /* update il and jl for prow */
3042       if (jmin < jmax){
3043         il[prow] = jmin;
3044         j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
3045       }
3046       prow = nextprow;
3047     }
3048 
3049     /* if free space is not available, make more free space */
3050     if (current_space->local_remaining<nzk) {
3051       i = am - k + 1; /* num of unfactored rows */
3052       i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
3053       ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
3054       reallocs++;
3055     }
3056 
3057     /* copy data into free space, then initialize lnk */
3058     ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
3059 
3060     /* add the k-th row into il and jl */
3061     if (nzk-1 > 0){
3062       i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
3063       jl[k] = jl[i]; jl[i] = k;
3064       il[k] = ui[k] + 1;
3065     }
3066     ui_ptr[k] = current_space->array;
3067     current_space->array           += nzk;
3068     current_space->local_used      += nzk;
3069     current_space->local_remaining -= nzk;
3070 
3071     ui[k+1] = ui[k] + nzk;
3072   }
3073 
3074 #if defined(PETSC_USE_INFO)
3075   if (ai[am] != 0) {
3076     PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]);
3077     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
3078     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
3079     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
3080   } else {
3081      ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
3082   }
3083 #endif
3084 
3085   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
3086   ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
3087   ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr);
3088 
3089   /* destroy list of free space and other temporary array(s) */
3090   ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
3091   ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
3092   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
3093 
3094   /* put together the new matrix in MATSEQSBAIJ format */
3095 
3096   b = (Mat_SeqSBAIJ*)fact->data;
3097   b->singlemalloc = PETSC_FALSE;
3098   b->free_a       = PETSC_TRUE;
3099   b->free_ij      = PETSC_TRUE;
3100   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
3101   b->j    = uj;
3102   b->i    = ui;
3103   b->diag = 0;
3104   b->ilen = 0;
3105   b->imax = 0;
3106   b->row  = perm;
3107   b->col  = perm;
3108   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
3109   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
3110   b->icol = iperm;
3111   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
3112   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
3113   ierr    = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
3114   b->maxnz = b->nz = ui[am];
3115 
3116   fact->info.factor_mallocs    = reallocs;
3117   fact->info.fill_ratio_given  = fill;
3118   if (ai[am] != 0) {
3119     fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
3120   } else {
3121     fact->info.fill_ratio_needed = 0.0;
3122   }
3123   fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
3124   PetscFunctionReturn(0);
3125 }
3126 
3127 #undef __FUNCT__
3128 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_newdatastruct"
3129 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx)
3130 {
3131   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
3132   PetscErrorCode    ierr;
3133   PetscInt          n = A->rmap->n;
3134   const PetscInt    *ai = a->i,*aj = a->j,*adiag = a->diag,*vi;
3135   PetscScalar       *x,sum;
3136   const PetscScalar *b;
3137   const MatScalar   *aa = a->a,*v;
3138   PetscInt          i,nz;
3139 
3140   PetscFunctionBegin;
3141   if (!n) PetscFunctionReturn(0);
3142 
3143   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3144   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3145 
3146   /* forward solve the lower triangular */
3147   x[0] = b[0];
3148   v    = aa;
3149   vi   = aj;
3150   for (i=1; i<n; i++) {
3151     nz  = ai[i+1] - ai[i];
3152     sum = b[i];
3153     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
3154     v  += nz;
3155     vi += nz;
3156     x[i] = sum;
3157   }
3158 
3159   /* backward solve the upper triangular */
3160   for (i=n-1; i>=0; i--){
3161     v   = aa + adiag[i+1] + 1;
3162     vi  = aj + adiag[i+1] + 1;
3163     nz = adiag[i] - adiag[i+1]-1;
3164     sum = x[i];
3165     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
3166     x[i] = sum*v[nz]; /* x[i]=aa[adiag[i]]*sum; v++; */
3167   }
3168 
3169   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
3170   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3171   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3172   PetscFunctionReturn(0);
3173 }
3174 
3175 #undef __FUNCT__
3176 #define __FUNCT__ "MatSolve_SeqAIJ_newdatastruct"
3177 PetscErrorCode MatSolve_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec xx)
3178 {
3179   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
3180   IS                iscol = a->col,isrow = a->row;
3181   PetscErrorCode    ierr;
3182   PetscInt          i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz;
3183   const PetscInt    *rout,*cout,*r,*c;
3184   PetscScalar       *x,*tmp,sum;
3185   const PetscScalar *b;
3186   const MatScalar   *aa = a->a,*v;
3187 
3188   PetscFunctionBegin;
3189   if (!n) PetscFunctionReturn(0);
3190 
3191   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3192   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3193   tmp  = a->solve_work;
3194 
3195   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
3196   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
3197 
3198   /* forward solve the lower triangular */
3199   tmp[0] = b[r[0]];
3200   v      = aa;
3201   vi     = aj;
3202   for (i=1; i<n; i++) {
3203     nz  = ai[i+1] - ai[i];
3204     sum = b[r[i]];
3205     PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
3206     tmp[i] = sum;
3207     v += nz; vi += nz;
3208   }
3209 
3210   /* backward solve the upper triangular */
3211   for (i=n-1; i>=0; i--){
3212     v   = aa + adiag[i+1]+1;
3213     vi  = aj + adiag[i+1]+1;
3214     nz  = adiag[i]-adiag[i+1]-1;
3215     sum = tmp[i];
3216     PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
3217     x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */
3218   }
3219 
3220   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
3221   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
3222   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3223   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3224   ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr);
3225   PetscFunctionReturn(0);
3226 }
3227 
3228 #undef __FUNCT__
3229 #define __FUNCT__ "MatILUDTFactor_SeqAIJ"
3230 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact)
3231 {
3232   Mat                B = *fact;
3233   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b;
3234   IS                 isicol;
3235   PetscErrorCode     ierr;
3236   const PetscInt     *r,*ic;
3237   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag;
3238   PetscInt           *bi,*bj,*bdiag,*bdiag_rev;
3239   PetscInt           row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au;
3240   PetscInt           nlnk,*lnk;
3241   PetscBT            lnkbt;
3242   PetscTruth         row_identity,icol_identity,both_identity;
3243   MatScalar          *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp;
3244   const PetscInt     *ics;
3245   PetscInt           j,nz,*pj,*bjtmp,k,ncut,*jtmp;
3246   PetscReal          dt=info->dt,dtcol=info->dtcol,shift=info->shiftinblocks;
3247   PetscInt           dtcount=(PetscInt)info->dtcount,nnz_max;
3248   PetscTruth         missing;
3249 
3250   PetscFunctionBegin;
3251 
3252   if (dt      == PETSC_DEFAULT) dt      = 0.005;
3253   if (dtcol   == PETSC_DEFAULT) dtcol   = 0.01; /* XXX unused! */
3254   if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax);
3255 
3256   /* ------- symbolic factorization, can be reused ---------*/
3257   ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
3258   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
3259   adiag=a->diag;
3260 
3261   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
3262 
3263   /* bdiag is location of diagonal in factor */
3264   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);     /* becomes b->diag */
3265   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag_rev);CHKERRQ(ierr); /* temporary */
3266 
3267   /* allocate row pointers bi */
3268   ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
3269 
3270   /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */
3271   if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */
3272   nnz_max  = ai[n]+2*n*dtcount+2;
3273 
3274   ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
3275   ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr);
3276 
3277   /* put together the new matrix */
3278   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
3279   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
3280   b    = (Mat_SeqAIJ*)B->data;
3281   b->free_a       = PETSC_TRUE;
3282   b->free_ij      = PETSC_TRUE;
3283   b->singlemalloc = PETSC_FALSE;
3284   b->a          = ba;
3285   b->j          = bj;
3286   b->i          = bi;
3287   b->diag       = bdiag;
3288   b->ilen       = 0;
3289   b->imax       = 0;
3290   b->row        = isrow;
3291   b->col        = iscol;
3292   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
3293   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
3294   b->icol       = isicol;
3295   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
3296 
3297   ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
3298   b->maxnz = nnz_max;
3299 
3300   B->factor                = MAT_FACTOR_ILUDT;
3301   B->info.factor_mallocs   = 0;
3302   B->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]);
3303   CHKMEMQ;
3304   /* ------- end of symbolic factorization ---------*/
3305 
3306   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
3307   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
3308   ics  = ic;
3309 
3310   /* linked list for storing column indices of the active row */
3311   nlnk = n + 1;
3312   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3313 
3314   /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */
3315   ierr = PetscMalloc2(n,PetscInt,&im,n,PetscInt,&jtmp);CHKERRQ(ierr);
3316   /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */
3317   ierr = PetscMalloc2(n,MatScalar,&rtmp,n,MatScalar,&vtmp);CHKERRQ(ierr);
3318   ierr = PetscMemzero(rtmp,n*sizeof(MatScalar));CHKERRQ(ierr);
3319 
3320   bi[0]    = 0;
3321   bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */
3322   bdiag_rev[n] = bdiag[0];
3323   bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */
3324   for (i=0; i<n; i++) {
3325     /* copy initial fill into linked list */
3326     nzi = 0; /* nonzeros for active row i */
3327     nzi = ai[r[i]+1] - ai[r[i]];
3328     if (!nzi) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
3329     nzi_al = adiag[r[i]] - ai[r[i]];
3330     nzi_au = ai[r[i]+1] - adiag[r[i]] -1;
3331     ajtmp = aj + ai[r[i]];
3332     ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3333 
3334     /* load in initial (unfactored row) */
3335     aatmp = a->a + ai[r[i]];
3336     for (j=0; j<nzi; j++) {
3337       rtmp[ics[*ajtmp++]] = *aatmp++;
3338     }
3339 
3340     /* add pivot rows into linked list */
3341     row = lnk[n];
3342     while (row < i ) {
3343       nzi_bl = bi[row+1] - bi[row] + 1;
3344       bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */
3345       ierr  = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr);
3346       nzi  += nlnk;
3347       row   = lnk[row];
3348     }
3349 
3350     /* copy data from lnk into jtmp, then initialize lnk */
3351     ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr);
3352 
3353     /* numerical factorization */
3354     bjtmp = jtmp;
3355     row   = *bjtmp++; /* 1st pivot row */
3356     while  ( row < i ) {
3357       pc         = rtmp + row;
3358       pv         = ba + bdiag[row]; /* 1./(diag of the pivot row) */
3359       multiplier = (*pc) * (*pv);
3360       *pc        = multiplier;
3361       if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */
3362         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
3363         pv         = ba + bdiag[row+1] + 1;
3364         /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */
3365         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
3366         for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
3367         ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
3368       }
3369       row = *bjtmp++;
3370     }
3371 
3372     /* copy sparse rtmp into contiguous vtmp; separate L and U part */
3373     diag_tmp = rtmp[i];  /* save diagonal value - may not needed?? */
3374     nzi_bl = 0; j = 0;
3375     while (jtmp[j] < i){ /* Note: jtmp is sorted */
3376       vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
3377       nzi_bl++; j++;
3378     }
3379     nzi_bu = nzi - nzi_bl -1;
3380     while (j < nzi){
3381       vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
3382       j++;
3383     }
3384 
3385     bjtmp = bj + bi[i];
3386     batmp = ba + bi[i];
3387     /* apply level dropping rule to L part */
3388     ncut = nzi_al + dtcount;
3389     if (ncut < nzi_bl){
3390       ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr);
3391       ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr);
3392     } else {
3393       ncut = nzi_bl;
3394     }
3395     for (j=0; j<ncut; j++){
3396       bjtmp[j] = jtmp[j];
3397       batmp[j] = vtmp[j];
3398       /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */
3399     }
3400     bi[i+1] = bi[i] + ncut;
3401     nzi = ncut + 1;
3402 
3403     /* apply level dropping rule to U part */
3404     ncut = nzi_au + dtcount;
3405     if (ncut < nzi_bu){
3406       ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr);
3407       ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr);
3408     } else {
3409       ncut = nzi_bu;
3410     }
3411     nzi += ncut;
3412 
3413     /* mark bdiagonal */
3414     bdiag[i+1]       = bdiag[i] - (ncut + 1);
3415     bdiag_rev[n-i-1] = bdiag[i+1];
3416     bi[2*n - i]      = bi[2*n - i +1] - (ncut + 1);
3417     bjtmp = bj + bdiag[i];
3418     batmp = ba + bdiag[i];
3419     *bjtmp = i;
3420     *batmp = diag_tmp; /* rtmp[i]; */
3421     if (*batmp == 0.0) {
3422       *batmp = dt+shift;
3423       /* printf(" row %d add shift %g\n",i,shift); */
3424     }
3425     *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */
3426     /* printf(" (%d,%g),",*bjtmp,*batmp); */
3427 
3428     bjtmp = bj + bdiag[i+1]+1;
3429     batmp = ba + bdiag[i+1]+1;
3430     for (k=0; k<ncut; k++){
3431       bjtmp[k] = jtmp[nzi_bl+1+k];
3432       batmp[k] = vtmp[nzi_bl+1+k];
3433       /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */
3434     }
3435     /* printf("\n"); */
3436 
3437     im[i]   = nzi; /* used by PetscLLAddSortedLU() */
3438     /*
3439     printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]);
3440     printf(" ----------------------------\n");
3441     */
3442   } /* for (i=0; i<n; i++) */
3443   /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */
3444   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]);
3445 
3446   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
3447   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
3448 
3449   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
3450   ierr = PetscFree2(im,jtmp);CHKERRQ(ierr);
3451   ierr = PetscFree2(rtmp,vtmp);CHKERRQ(ierr);
3452   ierr = PetscFree(bdiag_rev);CHKERRQ(ierr);
3453 
3454   ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr);
3455   b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n];
3456 
3457   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
3458   ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr);
3459   both_identity = (PetscTruth) (row_identity && icol_identity);
3460   if (row_identity && icol_identity) {
3461     B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct;
3462   } else {
3463     B->ops->solve = MatSolve_SeqAIJ_newdatastruct;
3464   }
3465 
3466   B->ops->lufactorsymbolic  = MatILUDTFactorSymbolic_SeqAIJ;
3467   B->ops->lufactornumeric   = MatILUDTFactorNumeric_SeqAIJ;
3468   B->ops->solveadd          = 0;
3469   B->ops->solvetranspose    = 0;
3470   B->ops->solvetransposeadd = 0;
3471   B->ops->matsolve          = 0;
3472   B->assembled              = PETSC_TRUE;
3473   B->preallocated           = PETSC_TRUE;
3474   PetscFunctionReturn(0);
3475 }
3476 
3477 /* a wraper of MatILUDTFactor_SeqAIJ() */
3478 #undef __FUNCT__
3479 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ"
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 
3487   fact->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ;
3488   PetscFunctionReturn(0);
3489 }
3490 
3491 /*
3492    same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors
3493    - intend to replace existing MatLUFactorNumeric_SeqAIJ()
3494 */
3495 #undef __FUNCT__
3496 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ"
3497 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info)
3498 {
3499   Mat            C=fact;
3500   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
3501   IS             isrow = b->row,isicol = b->icol;
3502   PetscErrorCode ierr;
3503   const PetscInt *r,*ic,*ics;
3504   PetscInt       i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
3505   PetscInt       *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj;
3506   MatScalar      *rtmp,*pc,multiplier,*v,*pv,*aa=a->a;
3507   PetscReal      dt=info->dt,shift=info->shiftinblocks;
3508   PetscTruth     row_identity, col_identity;
3509 
3510   PetscFunctionBegin;
3511   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
3512   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
3513   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
3514   ics  = ic;
3515 
3516   for (i=0; i<n; i++){
3517     /* initialize rtmp array */
3518     nzl   = bi[i+1] - bi[i];       /* num of nozeros in L(i,:) */
3519     bjtmp = bj + bi[i];
3520     for  (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0;
3521     rtmp[i] = 0.0;
3522     nzu   = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */
3523     bjtmp = bj + bdiag[i+1] + 1;
3524     for  (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0;
3525 
3526     /* load in initial unfactored row of A */
3527     /* printf("row %d\n",i); */
3528     nz    = ai[r[i]+1] - ai[r[i]];
3529     ajtmp = aj + ai[r[i]];
3530     v     = aa + ai[r[i]];
3531     for (j=0; j<nz; j++) {
3532       rtmp[ics[*ajtmp++]] = v[j];
3533       /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */
3534     }
3535     /* printf("\n"); */
3536 
3537     /* numerical factorization */
3538     bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */
3539     nzl   = bi[i+1] - bi[i]; /* num of entries in L(i,:) */
3540     k = 0;
3541     while (k < nzl){
3542       row   = *bjtmp++;
3543       /* printf("  prow %d\n",row); */
3544       pc         = rtmp + row;
3545       pv         = b->a + bdiag[row]; /* 1./(diag of the pivot row) */
3546       multiplier = (*pc) * (*pv);
3547       *pc        = multiplier;
3548       if (PetscAbsScalar(multiplier) > dt){
3549         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
3550         pv         = b->a + bdiag[row+1] + 1;
3551         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
3552         for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
3553         /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */
3554       }
3555       k++;
3556     }
3557 
3558     /* finished row so stick it into b->a */
3559     /* L-part */
3560     pv = b->a + bi[i] ;
3561     pj = bj + bi[i] ;
3562     nzl = bi[i+1] - bi[i];
3563     for (j=0; j<nzl; j++) {
3564       pv[j] = rtmp[pj[j]];
3565       /* printf(" (%d,%g),",pj[j],pv[j]); */
3566     }
3567 
3568     /* diagonal: invert diagonal entries for simplier triangular solves */
3569     if (rtmp[i] == 0.0) rtmp[i] = dt+shift;
3570     b->a[bdiag[i]] = 1.0/rtmp[i];
3571     /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */
3572 
3573     /* U-part */
3574     pv = b->a + bdiag[i+1] + 1;
3575     pj = bj + bdiag[i+1] + 1;
3576     nzu = bdiag[i] - bdiag[i+1] - 1;
3577     for (j=0; j<nzu; j++) {
3578       pv[j] = rtmp[pj[j]];
3579       /* printf(" (%d,%g),",pj[j],pv[j]); */
3580     }
3581     /* printf("\n"); */
3582   }
3583 
3584   ierr = PetscFree(rtmp);CHKERRQ(ierr);
3585   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
3586   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
3587 
3588   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
3589   ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
3590   if (row_identity && col_identity) {
3591     C->ops->solve   = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct;
3592   } else {
3593     C->ops->solve   = MatSolve_SeqAIJ_newdatastruct;
3594   }
3595   C->ops->solveadd           = 0;
3596   C->ops->solvetranspose     = 0;
3597   C->ops->solvetransposeadd  = 0;
3598   C->ops->matsolve           = 0;
3599   C->assembled    = PETSC_TRUE;
3600   C->preallocated = PETSC_TRUE;
3601   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
3602   PetscFunctionReturn(0);
3603 }
3604