xref: /petsc/src/mat/impls/aij/seq/aijfact.c (revision ea2e366bc2bac138971abc659b36c7d209d5705b)
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_COMM_SELF,PETSC_ERR_PLIB,"newcurrent cannot be current");
83     current = newcurrent;
84     order[i+1] = current;
85   }
86   ierr = ISCreateGeneral(PETSC_COMM_SELF,n,order,irow);CHKERRQ(ierr);
87   *icol = *irow;
88   ierr = PetscObjectReference((PetscObject)*irow);CHKERRQ(ierr);
89   ierr = PetscFree(done);CHKERRQ(ierr);
90   ierr = PetscFree(order);CHKERRQ(ierr);
91   PetscFunctionReturn(0);
92 }
93 EXTERN_C_END
94 
95 EXTERN_C_BEGIN
96 #undef __FUNCT__
97 #define __FUNCT__ "MatGetFactorAvailable_seqaij_petsc"
98 PetscErrorCode MatGetFactorAvailable_seqaij_petsc(Mat A,MatFactorType ftype,PetscTruth *flg)
99 {
100   PetscFunctionBegin;
101   *flg = PETSC_TRUE;
102   PetscFunctionReturn(0);
103 }
104 EXTERN_C_END
105 
106 EXTERN_C_BEGIN
107 #undef __FUNCT__
108 #define __FUNCT__ "MatGetFactor_seqaij_petsc"
109 PetscErrorCode MatGetFactor_seqaij_petsc(Mat A,MatFactorType ftype,Mat *B)
110 {
111   PetscInt           n = A->rmap->n;
112   PetscErrorCode     ierr;
113 
114   PetscFunctionBegin;
115   ierr = MatCreate(((PetscObject)A)->comm,B);CHKERRQ(ierr);
116   ierr = MatSetSizes(*B,n,n,n,n);CHKERRQ(ierr);
117   if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT){
118     ierr = MatSetType(*B,MATSEQAIJ);CHKERRQ(ierr);
119     (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqAIJ;
120     (*B)->ops->lufactorsymbolic  = MatLUFactorSymbolic_SeqAIJ;
121   } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) {
122     ierr = MatSetType(*B,MATSEQSBAIJ);CHKERRQ(ierr);
123     ierr = MatSeqSBAIJSetPreallocation(*B,1,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
124     (*B)->ops->iccfactorsymbolic      = MatICCFactorSymbolic_SeqAIJ;
125     (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJ;
126   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor type not supported");
127   (*B)->factortype = ftype;
128   PetscFunctionReturn(0);
129 }
130 EXTERN_C_END
131 
132 #undef __FUNCT__
133 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ_inplace"
134 PetscErrorCode MatLUFactorSymbolic_SeqAIJ_inplace(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
135 {
136   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
137   IS                 isicol;
138   PetscErrorCode     ierr;
139   const PetscInt     *r,*ic;
140   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j;
141   PetscInt           *bi,*bj,*ajtmp;
142   PetscInt           *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im;
143   PetscReal          f;
144   PetscInt           nlnk,*lnk,k,**bi_ptr;
145   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
146   PetscBT            lnkbt;
147 
148   PetscFunctionBegin;
149   if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"matrix must be square");
150   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
151   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
152   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
153 
154   /* get new row pointers */
155   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
156   bi[0] = 0;
157 
158   /* bdiag is location of diagonal in factor */
159   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
160   bdiag[0] = 0;
161 
162   /* linked list for storing column indices of the active row */
163   nlnk = n + 1;
164   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
165 
166   ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr);
167 
168   /* initial FreeSpace size is f*(ai[n]+1) */
169   f = info->fill;
170   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
171   current_space = free_space;
172 
173   for (i=0; i<n; i++) {
174     /* copy previous fill into linked list */
175     nzi = 0;
176     nnz = ai[r[i]+1] - ai[r[i]];
177     if (!nnz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
178     ajtmp = aj + ai[r[i]];
179     ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
180     nzi += nlnk;
181 
182     /* add pivot rows into linked list */
183     row = lnk[n];
184     while (row < i) {
185       nzbd    = bdiag[row] - bi[row] + 1; /* num of entries in the row with column index <= row */
186       ajtmp   = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */
187       ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr);
188       nzi += nlnk;
189       row  = lnk[row];
190     }
191     bi[i+1] = bi[i] + nzi;
192     im[i]   = nzi;
193 
194     /* mark bdiag */
195     nzbd = 0;
196     nnz  = nzi;
197     k    = lnk[n];
198     while (nnz-- && k < i){
199       nzbd++;
200       k = lnk[k];
201     }
202     bdiag[i] = bi[i] + nzbd;
203 
204     /* if free space is not available, make more free space */
205     if (current_space->local_remaining<nzi) {
206       nnz = (n - i)*nzi; /* estimated and max additional space needed */
207       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
208       reallocs++;
209     }
210 
211     /* copy data into free space, then initialize lnk */
212     ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
213     bi_ptr[i] = current_space->array;
214     current_space->array           += nzi;
215     current_space->local_used      += nzi;
216     current_space->local_remaining -= nzi;
217   }
218 #if defined(PETSC_USE_INFO)
219   if (ai[n] != 0) {
220     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
221     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
222     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
223     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr);
224     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
225   } else {
226     ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr);
227   }
228 #endif
229 
230   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
231   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
232 
233   /* destroy list of free space and other temporary array(s) */
234   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
235   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
236   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
237   ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr);
238 
239   /* put together the new matrix */
240   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
241   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
242   b    = (Mat_SeqAIJ*)(B)->data;
243   b->free_a       = PETSC_TRUE;
244   b->free_ij      = PETSC_TRUE;
245   b->singlemalloc = PETSC_FALSE;
246   ierr          = PetscMalloc((bi[n]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
247   b->j          = bj;
248   b->i          = bi;
249   b->diag       = bdiag;
250   b->ilen       = 0;
251   b->imax       = 0;
252   b->row        = isrow;
253   b->col        = iscol;
254   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
255   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
256   b->icol       = isicol;
257   ierr          = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
258 
259   /* In b structure:  Free imax, ilen, old a, old j.  Allocate solve_work, new a, new j */
260   ierr = PetscLogObjectMemory(B,(bi[n]-n)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
261   b->maxnz = b->nz = bi[n] ;
262 
263   (B)->factortype            = MAT_FACTOR_LU;
264   (B)->info.factor_mallocs   = reallocs;
265   (B)->info.fill_ratio_given = f;
266 
267   if (ai[n]) {
268     (B)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
269   } else {
270     (B)->info.fill_ratio_needed = 0.0;
271   }
272   (B)->ops->lufactornumeric  = MatLUFactorNumeric_SeqAIJ_inplace;
273   if (a->inode.size) {
274     (B)->ops->lufactornumeric  = MatLUFactorNumeric_SeqAIJ_Inode_inplace;
275   }
276   PetscFunctionReturn(0);
277 }
278 
279 #undef __FUNCT__
280 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ"
281 PetscErrorCode MatLUFactorSymbolic_SeqAIJ(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
282 {
283   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
284   IS                 isicol;
285   PetscErrorCode     ierr;
286   const PetscInt     *r,*ic;
287   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j;
288   PetscInt           *bi,*bj,*ajtmp;
289   PetscInt           *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im;
290   PetscReal          f;
291   PetscInt           nlnk,*lnk,k,**bi_ptr;
292   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
293   PetscBT            lnkbt;
294   PetscTruth         olddatastruct=PETSC_FALSE;
295 
296   PetscFunctionBegin;
297   /* Uncomment the oldatastruct part only while testing new data structure for MatSolve() */
298   ierr = PetscOptionsGetTruth(PETSC_NULL,"-lu_old",&olddatastruct,PETSC_NULL);CHKERRQ(ierr);
299   if(olddatastruct){
300     ierr = MatLUFactorSymbolic_SeqAIJ_inplace(B,A,isrow,iscol,info);CHKERRQ(ierr);
301     PetscFunctionReturn(0);
302   }
303 
304   if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"matrix must be square");
305   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
306   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
307   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
308 
309   /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
310   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
311   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
312   bi[0] = bdiag[0] = 0;
313 
314   /* linked list for storing column indices of the active row */
315   nlnk = n + 1;
316   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
317 
318   ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr);
319 
320   /* initial FreeSpace size is f*(ai[n]+1) */
321   f = info->fill;
322   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
323   current_space = free_space;
324 
325   for (i=0; i<n; i++) {
326     /* copy previous fill into linked list */
327     nzi = 0;
328     nnz = ai[r[i]+1] - ai[r[i]];
329     if (!nnz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
330     ajtmp = aj + ai[r[i]];
331     ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
332     nzi += nlnk;
333 
334     /* add pivot rows into linked list */
335     row = lnk[n];
336     while (row < i){
337       nzbd  = bdiag[row] + 1; /* num of entries in the row with column index <= row */
338       ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */
339       ierr  = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr);
340       nzi  += nlnk;
341       row   = lnk[row];
342     }
343     bi[i+1] = bi[i] + nzi;
344     im[i]   = nzi;
345 
346     /* mark bdiag */
347     nzbd = 0;
348     nnz  = nzi;
349     k    = lnk[n];
350     while (nnz-- && k < i){
351       nzbd++;
352       k = lnk[k];
353     }
354     bdiag[i] = nzbd; /* note: bdiag[i] = nnzL as input for PetscFreeSpaceContiguous_LU() */
355 
356     /* if free space is not available, make more free space */
357     if (current_space->local_remaining<nzi) {
358       nnz = 2*(n - i)*nzi; /* estimated and max additional space needed */
359       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
360       reallocs++;
361     }
362 
363     /* copy data into free space, then initialize lnk */
364     ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
365     bi_ptr[i] = current_space->array;
366     current_space->array           += nzi;
367     current_space->local_used      += nzi;
368     current_space->local_remaining -= nzi;
369   }
370 #if defined(PETSC_USE_INFO)
371   if (ai[n] != 0) {
372     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
373     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
374     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
375     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr);
376     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
377   } else {
378     ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr);
379   }
380 #endif
381 
382   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
383   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
384 
385   /* destroy list of free space and other temporary array(s) */
386   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
387   ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr);
388   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
389   ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr);
390 
391   /* put together the new matrix */
392   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
393   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
394   b    = (Mat_SeqAIJ*)(B)->data;
395   b->free_a       = PETSC_TRUE;
396   b->free_ij      = PETSC_TRUE;
397   b->singlemalloc = PETSC_FALSE;
398   ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
399   b->j          = bj;
400   b->i          = bi;
401   b->diag       = bdiag;
402   b->ilen       = 0;
403   b->imax       = 0;
404   b->row        = isrow;
405   b->col        = iscol;
406   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
407   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
408   b->icol       = isicol;
409   ierr          = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
410 
411   /* In b structure:  Free imax, ilen, old a, old j.  Allocate solve_work, new a, new j */
412   ierr = PetscLogObjectMemory(B,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
413   b->maxnz = b->nz = bdiag[0]+1;
414   B->factortype            = MAT_FACTOR_LU;
415   B->info.factor_mallocs   = reallocs;
416   B->info.fill_ratio_given = f;
417 
418   if (ai[n]) {
419     B->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]);
420   } else {
421     B->info.fill_ratio_needed = 0.0;
422   }
423   B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ;
424   if (a->inode.size) {
425     B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode;
426   }
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"
456 PetscErrorCode MatLUFactorNumeric_SeqAIJ(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   const PetscInt   n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bdiag=b->diag;
464   PetscInt         i,j,k,nz,nzL,row,*pj;
465   const PetscInt   *ajtmp,*bjtmp;
466   MatScalar        *rtmp,*pc,multiplier,*pv;
467   const  MatScalar *aa=a->a,*v;
468   PetscTruth       row_identity,col_identity;
469   FactorShiftCtx   sctx;
470   const PetscInt   *ddiag;
471   PetscReal        rs;
472   MatScalar        d;
473   PetscInt         newshift = 0;
474 
475   PetscFunctionBegin;
476   /* MatPivotSetUp(): initialize shift context sctx */
477   ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr);
478 
479   if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
480     ddiag          = a->diag;
481     sctx.shift_top = info->zeropivot;
482     for (i=0; i<n; i++) {
483       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
484       d  = (aa)[ddiag[i]];
485       rs = -PetscAbsScalar(d) - PetscRealPart(d);
486       v  = aa+ai[i];
487       nz = ai[i+1] - ai[i];
488       for (j=0; j<nz; j++)
489 	rs += PetscAbsScalar(v[j]);
490       if (rs>sctx.shift_top) sctx.shift_top = rs;
491     }
492     sctx.shift_top   *= 1.1;
493     sctx.nshift_max   = 5;
494     sctx.shift_lo     = 0.;
495     sctx.shift_hi     = 1.;
496   }
497 
498   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
499   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
500   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
501   ics  = ic;
502 
503   do {
504     sctx.useshift = PETSC_FALSE;
505     for (i=0; i<n; i++){
506       /* zero rtmp */
507       /* L part */
508       nz    = bi[i+1] - bi[i];
509       bjtmp = bj + bi[i];
510       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
511 
512       /* U part */
513       nz = bdiag[i]-bdiag[i+1];
514       bjtmp = bj + bdiag[i+1]+1;
515       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
516 
517       /* load in initial (unfactored row) */
518       nz    = ai[r[i]+1] - ai[r[i]];
519       ajtmp = aj + ai[r[i]];
520       v     = aa + ai[r[i]];
521       for (j=0; j<nz; j++) {
522         rtmp[ics[ajtmp[j]]] = v[j];
523       }
524       /* ZeropivotApply() */
525       rtmp[i] += sctx.shift_amount;  /* shift the diagonal of the matrix */
526 
527       /* elimination */
528       bjtmp = bj + bi[i];
529       row   = *bjtmp++;
530       nzL   = bi[i+1] - bi[i];
531       for(k=0; k < nzL;k++) {
532         pc = rtmp + row;
533         if (*pc != 0.0) {
534           pv         = b->a + bdiag[row];
535           multiplier = *pc * (*pv);
536           *pc        = multiplier;
537           pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
538 	  pv = b->a + bdiag[row+1]+1;
539 	  nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */
540           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
541           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
542         }
543         row = *bjtmp++;
544       }
545 
546       /* finished row so stick it into b->a */
547       rs = 0.0;
548       /* L part */
549       pv   = b->a + bi[i] ;
550       pj   = b->j + bi[i] ;
551       nz   = bi[i+1] - bi[i];
552       for (j=0; j<nz; j++) {
553         pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]);
554       }
555 
556       /* U part */
557       pv = b->a + bdiag[i+1]+1;
558       pj = b->j + bdiag[i+1]+1;
559       nz = bdiag[i] - bdiag[i+1]-1;
560       for (j=0; j<nz; j++) {
561         pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]);
562       }
563 
564       sctx.rs  = rs;
565       sctx.pv  = rtmp[i];
566       ierr = MatPivotCheck(info,&sctx,i,&newshift);CHKERRQ(ierr);
567       if(newshift == 1) break;
568       rtmp[i] = sctx.pv;
569 
570       /* Mark diagonal and invert diagonal for simplier triangular solves */
571       pv  = b->a + bdiag[i];
572       *pv = 1.0/rtmp[i];
573 
574     } /* endof for (i=0; i<n; i++){ */
575 
576     /* MatPivotRefine() */
577     if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.useshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max){
578       /*
579        * if no shift in this attempt & shifting & started shifting & can refine,
580        * then try lower shift
581        */
582       sctx.shift_hi       = sctx.shift_fraction;
583       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
584       sctx.shift_amount   = sctx.shift_fraction * sctx.shift_top;
585       sctx.useshift        = PETSC_TRUE;
586       sctx.nshift++;
587     }
588   } while (sctx.useshift);
589 
590   ierr = PetscFree(rtmp);CHKERRQ(ierr);
591   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
592   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
593 
594   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
595   ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
596   if (row_identity && col_identity) {
597     C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering;
598   } else {
599     C->ops->solve = MatSolve_SeqAIJ;
600   }
601   C->ops->solveadd           = MatSolveAdd_SeqAIJ;
602   C->ops->solvetranspose     = MatSolveTranspose_SeqAIJ;
603   C->ops->solvetransposeadd  = MatSolveTransposeAdd_SeqAIJ;
604   C->ops->matsolve           = MatMatSolve_SeqAIJ;
605   C->assembled    = PETSC_TRUE;
606   C->preallocated = PETSC_TRUE;
607   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
608 
609   /* MatShiftView(A,info,&sctx) */
610   if (sctx.nshift){
611     if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
612       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);
613     } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
614       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
615     } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS){
616       ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftamount);CHKERRQ(ierr);
617     }
618   }
619   ierr = Mat_CheckInode_FactorLU(C,PETSC_FALSE);CHKERRQ(ierr);
620   PetscFunctionReturn(0);
621 }
622 
623 #undef __FUNCT__
624 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_inplace"
625 PetscErrorCode MatLUFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info)
626 {
627   Mat             C=B;
628   Mat_SeqAIJ      *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
629   IS              isrow = b->row,isicol = b->icol;
630   PetscErrorCode  ierr;
631   const PetscInt   *r,*ic,*ics;
632   PetscInt        nz,row,i,j,n=A->rmap->n,diag;
633   const PetscInt  *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
634   const PetscInt  *ajtmp,*bjtmp,*diag_offset = b->diag,*pj;
635   MatScalar       *pv,*rtmp,*pc,multiplier,d;
636   const MatScalar *v,*aa=a->a;
637   PetscReal       rs=0.0;
638   FactorShiftCtx  sctx;
639   PetscInt        newshift;
640   const PetscInt  *ddiag;
641   PetscTruth      row_identity, col_identity;
642 
643   PetscFunctionBegin;
644   /* MatPivotSetUp(): initialize shift context sctx */
645   ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr);
646 
647   if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
648     ddiag          = a->diag;
649     sctx.shift_top = info->zeropivot;
650     for (i=0; i<n; i++) {
651       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
652       d  = (aa)[ddiag[i]];
653       rs = -PetscAbsScalar(d) - PetscRealPart(d);
654       v  = aa+ai[i];
655       nz = ai[i+1] - ai[i];
656       for (j=0; j<nz; j++)
657 	rs += PetscAbsScalar(v[j]);
658       if (rs>sctx.shift_top) sctx.shift_top = rs;
659     }
660     sctx.shift_top   *= 1.1;
661     sctx.nshift_max   = 5;
662     sctx.shift_lo     = 0.;
663     sctx.shift_hi     = 1.;
664   }
665 
666   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
667   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
668   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
669   ics  = ic;
670 
671   do {
672     sctx.useshift = PETSC_FALSE;
673     for (i=0; i<n; i++){
674       nz    = bi[i+1] - bi[i];
675       bjtmp = bj + bi[i];
676       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
677 
678       /* load in initial (unfactored row) */
679       nz    = ai[r[i]+1] - ai[r[i]];
680       ajtmp = aj + ai[r[i]];
681       v     = aa + ai[r[i]];
682       for (j=0; j<nz; j++) {
683         rtmp[ics[ajtmp[j]]] = v[j];
684       }
685       rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */
686 
687       row = *bjtmp++;
688       while  (row < i) {
689         pc = rtmp + row;
690         if (*pc != 0.0) {
691           pv         = b->a + diag_offset[row];
692           pj         = b->j + diag_offset[row] + 1;
693           multiplier = *pc / *pv++;
694           *pc        = multiplier;
695           nz         = bi[row+1] - diag_offset[row] - 1;
696           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
697           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
698         }
699         row = *bjtmp++;
700       }
701       /* finished row so stick it into b->a */
702       pv   = b->a + bi[i] ;
703       pj   = b->j + bi[i] ;
704       nz   = bi[i+1] - bi[i];
705       diag = diag_offset[i] - bi[i];
706       rs   = 0.0;
707       for (j=0; j<nz; j++) {
708         pv[j] = rtmp[pj[j]];
709         rs   += PetscAbsScalar(pv[j]);
710       }
711       rs   -= PetscAbsScalar(pv[diag]);
712 
713       sctx.rs  = rs;
714       sctx.pv  = pv[diag];
715       ierr = MatPivotCheck(info,&sctx,i,&newshift);CHKERRQ(ierr);
716       if (newshift == 1) break;
717       pv[diag] = sctx.pv;
718     }
719 
720     if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.useshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
721       /*
722        * if no shift in this attempt & shifting & started shifting & can refine,
723        * then try lower shift
724        */
725       sctx.shift_hi       = sctx.shift_fraction;
726       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
727       sctx.shift_amount   = sctx.shift_fraction * sctx.shift_top;
728       sctx.useshift        = PETSC_TRUE;
729       sctx.nshift++;
730     }
731   } while (sctx.useshift);
732 
733   /* invert diagonal entries for simplier triangular solves */
734   for (i=0; i<n; i++) {
735     b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]];
736   }
737   ierr = PetscFree(rtmp);CHKERRQ(ierr);
738   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
739   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
740 
741   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
742   ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
743   if (row_identity && col_identity) {
744     C->ops->solve   = MatSolve_SeqAIJ_NaturalOrdering_inplace;
745   } else {
746     C->ops->solve   = MatSolve_SeqAIJ_inplace;
747   }
748   C->ops->solveadd           = MatSolveAdd_SeqAIJ_inplace;
749   C->ops->solvetranspose     = MatSolveTranspose_SeqAIJ_inplace;
750   C->ops->solvetransposeadd  = MatSolveTransposeAdd_SeqAIJ_inplace;
751   C->ops->matsolve           = MatMatSolve_SeqAIJ_inplace;
752   C->assembled    = PETSC_TRUE;
753   C->preallocated = PETSC_TRUE;
754   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
755   if (sctx.nshift){
756      if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
757       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);
758     } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
759       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
760     }
761   }
762   (C)->ops->solve            = MatSolve_SeqAIJ_inplace;
763   (C)->ops->solvetranspose   = MatSolveTranspose_SeqAIJ_inplace;
764   ierr = Mat_CheckInode(C,PETSC_FALSE);CHKERRQ(ierr);
765   PetscFunctionReturn(0);
766 }
767 
768 /*
769    This routine implements inplace ILU(0) with row or/and column permutations.
770    Input:
771      A - original matrix
772    Output;
773      A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i]
774          a->j (col index) is permuted by the inverse of colperm, then sorted
775          a->a reordered accordingly with a->j
776          a->diag (ptr to diagonal elements) is updated.
777 */
778 #undef __FUNCT__
779 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_InplaceWithPerm"
780 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info)
781 {
782   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
783   IS             isrow = a->row,isicol = a->icol;
784   PetscErrorCode ierr;
785   const PetscInt *r,*ic,*ics;
786   PetscInt       i,j,n=A->rmap->n,*ai=a->i,*aj=a->j;
787   PetscInt       *ajtmp,nz,row;
788   PetscInt       *diag = a->diag,nbdiag,*pj;
789   PetscScalar    *rtmp,*pc,multiplier,d;
790   MatScalar      *pv,*v;
791   PetscReal      rs;
792   FactorShiftCtx sctx;
793   PetscInt       newshift = 0;
794   const  MatScalar *aa=a->a,*vtmp;
795 
796   PetscFunctionBegin;
797   if (A != B) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address");
798 
799   /* MatPivotSetUp(): initialize shift context sctx */
800   ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr);
801 
802   if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
803     const PetscInt   *ddiag = a->diag;
804     sctx.shift_top = info->zeropivot;
805     for (i=0; i<n; i++) {
806       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
807       d  = (aa)[ddiag[i]];
808       rs = -PetscAbsScalar(d) - PetscRealPart(d);
809       vtmp  = aa+ai[i];
810       nz = ai[i+1] - ai[i];
811       for (j=0; j<nz; j++)
812 	rs += PetscAbsScalar(vtmp[j]);
813       if (rs>sctx.shift_top) sctx.shift_top = rs;
814     }
815     sctx.shift_top   *= 1.1;
816     sctx.nshift_max   = 5;
817     sctx.shift_lo     = 0.;
818     sctx.shift_hi     = 1.;
819   }
820 
821   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
822   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
823   ierr  = PetscMalloc((n+1)*sizeof(PetscScalar),&rtmp);CHKERRQ(ierr);
824   ierr  = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr);
825   ics = ic;
826 
827 #if defined(MV)
828   sctx.shift_top      = 0.;
829   sctx.nshift_max     = 0;
830   sctx.shift_lo       = 0.;
831   sctx.shift_hi       = 0.;
832   sctx.shift_fraction = 0.;
833 
834   if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
835     sctx.shift_top = 0.;
836     for (i=0; i<n; i++) {
837       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
838       d  = (a->a)[diag[i]];
839       rs = -PetscAbsScalar(d) - PetscRealPart(d);
840       v  = a->a+ai[i];
841       nz = ai[i+1] - ai[i];
842       for (j=0; j<nz; j++)
843 	rs += PetscAbsScalar(v[j]);
844       if (rs>sctx.shift_top) sctx.shift_top = rs;
845     }
846     if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot;
847     sctx.shift_top    *= 1.1;
848     sctx.nshift_max   = 5;
849     sctx.shift_lo     = 0.;
850     sctx.shift_hi     = 1.;
851   }
852 
853   sctx.shift_amount = 0.;
854   sctx.nshift       = 0;
855 #endif
856 
857   do {
858     sctx.useshift = PETSC_FALSE;
859     for (i=0; i<n; i++){
860       /* load in initial unfactored row */
861       nz    = ai[r[i]+1] - ai[r[i]];
862       ajtmp = aj + ai[r[i]];
863       v     = a->a + ai[r[i]];
864       /* sort permuted ajtmp and values v accordingly */
865       for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]];
866       ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr);
867 
868       diag[r[i]] = ai[r[i]];
869       for (j=0; j<nz; j++) {
870         rtmp[ajtmp[j]] = v[j];
871         if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */
872       }
873       rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */
874 
875       row = *ajtmp++;
876       while  (row < i) {
877         pc = rtmp + row;
878         if (*pc != 0.0) {
879           pv         = a->a + diag[r[row]];
880           pj         = aj + diag[r[row]] + 1;
881 
882           multiplier = *pc / *pv++;
883           *pc        = multiplier;
884           nz         = ai[r[row]+1] - diag[r[row]] - 1;
885           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
886           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
887         }
888         row = *ajtmp++;
889       }
890       /* finished row so overwrite it onto a->a */
891       pv   = a->a + ai[r[i]] ;
892       pj   = aj + ai[r[i]] ;
893       nz   = ai[r[i]+1] - ai[r[i]];
894       nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */
895 
896       rs   = 0.0;
897       for (j=0; j<nz; j++) {
898         pv[j] = rtmp[pj[j]];
899         if (j != nbdiag) rs += PetscAbsScalar(pv[j]);
900       }
901 
902       sctx.rs  = rs;
903       sctx.pv  = pv[nbdiag];
904       ierr = MatPivotCheck(info,&sctx,i,&newshift);CHKERRQ(ierr);
905       if (newshift == 1) break;
906       pv[nbdiag] = sctx.pv;
907     }
908 
909     if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.useshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
910       /*
911        * if no shift in this attempt & shifting & started shifting & can refine,
912        * then try lower shift
913        */
914       sctx.shift_hi        = sctx.shift_fraction;
915       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
916       sctx.shift_amount    = sctx.shift_fraction * sctx.shift_top;
917       sctx.useshift         = PETSC_TRUE;
918       sctx.nshift++;
919     }
920   } while (sctx.useshift);
921 
922   /* invert diagonal entries for simplier triangular solves */
923   for (i=0; i<n; i++) {
924     a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]];
925   }
926 
927   ierr = PetscFree(rtmp);CHKERRQ(ierr);
928   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
929   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
930   A->ops->solve             = MatSolve_SeqAIJ_InplaceWithPerm;
931   A->ops->solveadd          = MatSolveAdd_SeqAIJ_inplace;
932   A->ops->solvetranspose    = MatSolveTranspose_SeqAIJ_inplace;
933   A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_inplace;
934   A->assembled = PETSC_TRUE;
935   A->preallocated = PETSC_TRUE;
936   ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr);
937   if (sctx.nshift){
938     if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
939       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);
940     } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
941       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
942     }
943   }
944   PetscFunctionReturn(0);
945 }
946 
947 /* ----------------------------------------------------------- */
948 #undef __FUNCT__
949 #define __FUNCT__ "MatLUFactor_SeqAIJ"
950 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info)
951 {
952   PetscErrorCode ierr;
953   Mat            C;
954 
955   PetscFunctionBegin;
956   ierr = MatGetFactor(A,MAT_SOLVER_PETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr);
957   ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr);
958   ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr);
959   A->ops->solve            = C->ops->solve;
960   A->ops->solvetranspose   = C->ops->solvetranspose;
961   ierr = MatHeaderCopy(A,C);CHKERRQ(ierr);
962   ierr = PetscLogObjectParent(A,((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr);
963   PetscFunctionReturn(0);
964 }
965 /* ----------------------------------------------------------- */
966 
967 
968 #undef __FUNCT__
969 #define __FUNCT__ "MatSolve_SeqAIJ_inplace"
970 PetscErrorCode MatSolve_SeqAIJ_inplace(Mat A,Vec bb,Vec xx)
971 {
972   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
973   IS                iscol = a->col,isrow = a->row;
974   PetscErrorCode    ierr;
975   PetscInt          i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
976   PetscInt          nz;
977   const PetscInt    *rout,*cout,*r,*c;
978   PetscScalar       *x,*tmp,*tmps,sum;
979   const PetscScalar *b;
980   const MatScalar   *aa = a->a,*v;
981 
982   PetscFunctionBegin;
983   if (!n) PetscFunctionReturn(0);
984 
985   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
986   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
987   tmp  = a->solve_work;
988 
989   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
990   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
991 
992   /* forward solve the lower triangular */
993   tmp[0] = b[*r++];
994   tmps   = tmp;
995   for (i=1; i<n; i++) {
996     v   = aa + ai[i] ;
997     vi  = aj + ai[i] ;
998     nz  = a->diag[i] - ai[i];
999     sum = b[*r++];
1000     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1001     tmp[i] = sum;
1002   }
1003 
1004   /* backward solve the upper triangular */
1005   for (i=n-1; i>=0; i--){
1006     v   = aa + a->diag[i] + 1;
1007     vi  = aj + a->diag[i] + 1;
1008     nz  = ai[i+1] - a->diag[i] - 1;
1009     sum = tmp[i];
1010     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1011     x[*c--] = tmp[i] = sum*aa[a->diag[i]];
1012   }
1013 
1014   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1015   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1016   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1017   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1018   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1019   PetscFunctionReturn(0);
1020 }
1021 
1022 #undef __FUNCT__
1023 #define __FUNCT__ "MatMatSolve_SeqAIJ_inplace"
1024 PetscErrorCode MatMatSolve_SeqAIJ_inplace(Mat A,Mat B,Mat X)
1025 {
1026   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1027   IS              iscol = a->col,isrow = a->row;
1028   PetscErrorCode  ierr;
1029   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1030   PetscInt        nz,neq;
1031   const PetscInt  *rout,*cout,*r,*c;
1032   PetscScalar     *x,*b,*tmp,*tmps,sum;
1033   const MatScalar *aa = a->a,*v;
1034   PetscTruth      bisdense,xisdense;
1035 
1036   PetscFunctionBegin;
1037   if (!n) PetscFunctionReturn(0);
1038 
1039   ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr);
1040   if (!bisdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix");
1041   ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr);
1042   if (!xisdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix");
1043 
1044   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
1045   ierr = MatGetArray(X,&x);CHKERRQ(ierr);
1046 
1047   tmp  = a->solve_work;
1048   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1049   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1050 
1051   for (neq=0; neq<B->cmap->n; neq++){
1052     /* forward solve the lower triangular */
1053     tmp[0] = b[r[0]];
1054     tmps   = tmp;
1055     for (i=1; i<n; i++) {
1056       v   = aa + ai[i] ;
1057       vi  = aj + ai[i] ;
1058       nz  = a->diag[i] - ai[i];
1059       sum = b[r[i]];
1060       PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1061       tmp[i] = sum;
1062     }
1063     /* backward solve the upper triangular */
1064     for (i=n-1; i>=0; i--){
1065       v   = aa + a->diag[i] + 1;
1066       vi  = aj + a->diag[i] + 1;
1067       nz  = ai[i+1] - a->diag[i] - 1;
1068       sum = tmp[i];
1069       PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1070       x[c[i]] = tmp[i] = sum*aa[a->diag[i]];
1071     }
1072 
1073     b += n;
1074     x += n;
1075   }
1076   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1077   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1078   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
1079   ierr = MatRestoreArray(X,&x);CHKERRQ(ierr);
1080   ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr);
1081   PetscFunctionReturn(0);
1082 }
1083 
1084 #undef __FUNCT__
1085 #define __FUNCT__ "MatMatSolve_SeqAIJ"
1086 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X)
1087 {
1088   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1089   IS              iscol = a->col,isrow = a->row;
1090   PetscErrorCode  ierr;
1091   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag;
1092   PetscInt        nz,neq;
1093   const PetscInt  *rout,*cout,*r,*c;
1094   PetscScalar     *x,*b,*tmp,sum;
1095   const MatScalar *aa = a->a,*v;
1096   PetscTruth      bisdense,xisdense;
1097 
1098   PetscFunctionBegin;
1099   if (!n) PetscFunctionReturn(0);
1100 
1101   ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr);
1102   if (!bisdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix");
1103   ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr);
1104   if (!xisdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix");
1105 
1106   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
1107   ierr = MatGetArray(X,&x);CHKERRQ(ierr);
1108 
1109   tmp  = a->solve_work;
1110   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1111   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1112 
1113   for (neq=0; neq<B->cmap->n; neq++){
1114     /* forward solve the lower triangular */
1115     tmp[0] = b[r[0]];
1116     v      = aa;
1117     vi     = aj;
1118     for (i=1; i<n; i++) {
1119       nz  = ai[i+1] - ai[i];
1120       sum = b[r[i]];
1121       PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
1122       tmp[i] = sum;
1123       v += nz; vi += nz;
1124     }
1125 
1126     /* backward solve the upper triangular */
1127     for (i=n-1; i>=0; i--){
1128       v   = aa + adiag[i+1]+1;
1129       vi  = aj + adiag[i+1]+1;
1130       nz  = adiag[i]-adiag[i+1]-1;
1131       sum = tmp[i];
1132       PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
1133       x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */
1134     }
1135 
1136     b += n;
1137     x += n;
1138   }
1139   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1140   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1141   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
1142   ierr = MatRestoreArray(X,&x);CHKERRQ(ierr);
1143   ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr);
1144   PetscFunctionReturn(0);
1145 }
1146 
1147 #undef __FUNCT__
1148 #define __FUNCT__ "MatSolve_SeqAIJ_InplaceWithPerm"
1149 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx)
1150 {
1151   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1152   IS              iscol = a->col,isrow = a->row;
1153   PetscErrorCode  ierr;
1154   const PetscInt  *r,*c,*rout,*cout;
1155   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1156   PetscInt        nz,row;
1157   PetscScalar     *x,*b,*tmp,*tmps,sum;
1158   const MatScalar *aa = a->a,*v;
1159 
1160   PetscFunctionBegin;
1161   if (!n) PetscFunctionReturn(0);
1162 
1163   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
1164   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1165   tmp  = a->solve_work;
1166 
1167   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1168   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1169 
1170   /* forward solve the lower triangular */
1171   tmp[0] = b[*r++];
1172   tmps   = tmp;
1173   for (row=1; row<n; row++) {
1174     i   = rout[row]; /* permuted row */
1175     v   = aa + ai[i] ;
1176     vi  = aj + ai[i] ;
1177     nz  = a->diag[i] - ai[i];
1178     sum = b[*r++];
1179     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1180     tmp[row] = sum;
1181   }
1182 
1183   /* backward solve the upper triangular */
1184   for (row=n-1; row>=0; row--){
1185     i   = rout[row]; /* permuted row */
1186     v   = aa + a->diag[i] + 1;
1187     vi  = aj + a->diag[i] + 1;
1188     nz  = ai[i+1] - a->diag[i] - 1;
1189     sum = tmp[row];
1190     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1191     x[*c--] = tmp[row] = sum*aa[a->diag[i]];
1192   }
1193 
1194   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1195   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1196   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
1197   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1198   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1199   PetscFunctionReturn(0);
1200 }
1201 
1202 /* ----------------------------------------------------------- */
1203 #include "../src/mat/impls/aij/seq/ftn-kernels/fsolve.h"
1204 #undef __FUNCT__
1205 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_inplace"
1206 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_inplace(Mat A,Vec bb,Vec xx)
1207 {
1208   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1209   PetscErrorCode    ierr;
1210   PetscInt          n = A->rmap->n;
1211   const PetscInt    *ai = a->i,*aj = a->j,*adiag = a->diag;
1212   PetscScalar       *x;
1213   const PetscScalar *b;
1214   const MatScalar   *aa = a->a;
1215 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ)
1216   PetscInt          adiag_i,i,nz,ai_i;
1217   const PetscInt    *vi;
1218   const MatScalar   *v;
1219   PetscScalar       sum;
1220 #endif
1221 
1222   PetscFunctionBegin;
1223   if (!n) PetscFunctionReturn(0);
1224 
1225   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1226   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1227 
1228 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ)
1229   fortransolveaij_(&n,x,ai,aj,adiag,aa,b);
1230 #else
1231   /* forward solve the lower triangular */
1232   x[0] = b[0];
1233   for (i=1; i<n; i++) {
1234     ai_i = ai[i];
1235     v    = aa + ai_i;
1236     vi   = aj + ai_i;
1237     nz   = adiag[i] - ai_i;
1238     sum  = b[i];
1239     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
1240     x[i] = sum;
1241   }
1242 
1243   /* backward solve the upper triangular */
1244   for (i=n-1; i>=0; i--){
1245     adiag_i = adiag[i];
1246     v       = aa + adiag_i + 1;
1247     vi      = aj + adiag_i + 1;
1248     nz      = ai[i+1] - adiag_i - 1;
1249     sum     = x[i];
1250     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
1251     x[i]    = sum*aa[adiag_i];
1252   }
1253 #endif
1254   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1255   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1256   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1257   PetscFunctionReturn(0);
1258 }
1259 
1260 #undef __FUNCT__
1261 #define __FUNCT__ "MatSolveAdd_SeqAIJ_inplace"
1262 PetscErrorCode MatSolveAdd_SeqAIJ_inplace(Mat A,Vec bb,Vec yy,Vec xx)
1263 {
1264   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1265   IS                iscol = a->col,isrow = a->row;
1266   PetscErrorCode    ierr;
1267   PetscInt          i, n = A->rmap->n,j;
1268   PetscInt          nz;
1269   const PetscInt    *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j;
1270   PetscScalar       *x,*tmp,sum;
1271   const PetscScalar *b;
1272   const MatScalar   *aa = a->a,*v;
1273 
1274   PetscFunctionBegin;
1275   if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);}
1276 
1277   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1278   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1279   tmp  = a->solve_work;
1280 
1281   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1282   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1283 
1284   /* forward solve the lower triangular */
1285   tmp[0] = b[*r++];
1286   for (i=1; i<n; i++) {
1287     v   = aa + ai[i] ;
1288     vi  = aj + ai[i] ;
1289     nz  = a->diag[i] - ai[i];
1290     sum = b[*r++];
1291     for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1292     tmp[i] = sum;
1293   }
1294 
1295   /* backward solve the upper triangular */
1296   for (i=n-1; i>=0; i--){
1297     v   = aa + a->diag[i] + 1;
1298     vi  = aj + a->diag[i] + 1;
1299     nz  = ai[i+1] - a->diag[i] - 1;
1300     sum = tmp[i];
1301     for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1302     tmp[i] = sum*aa[a->diag[i]];
1303     x[*c--] += tmp[i];
1304   }
1305 
1306   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1307   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1308   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1309   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1310   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1311 
1312   PetscFunctionReturn(0);
1313 }
1314 
1315 #undef __FUNCT__
1316 #define __FUNCT__ "MatSolveAdd_SeqAIJ"
1317 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx)
1318 {
1319   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1320   IS                iscol = a->col,isrow = a->row;
1321   PetscErrorCode    ierr;
1322   PetscInt          i, n = A->rmap->n,j;
1323   PetscInt          nz;
1324   const PetscInt    *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag;
1325   PetscScalar       *x,*tmp,sum;
1326   const PetscScalar *b;
1327   const MatScalar   *aa = a->a,*v;
1328 
1329   PetscFunctionBegin;
1330   if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);}
1331 
1332   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1333   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1334   tmp  = a->solve_work;
1335 
1336   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1337   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1338 
1339   /* forward solve the lower triangular */
1340   tmp[0] = b[r[0]];
1341   v      = aa;
1342   vi     = aj;
1343   for (i=1; i<n; i++) {
1344     nz  = ai[i+1] - ai[i];
1345     sum = b[r[i]];
1346     for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1347     tmp[i] = sum;
1348     v += nz; vi += nz;
1349   }
1350 
1351   /* backward solve the upper triangular */
1352   v  = aa + adiag[n-1];
1353   vi = aj + adiag[n-1];
1354   for (i=n-1; i>=0; i--){
1355     nz  = adiag[i] - adiag[i+1] - 1;
1356     sum = tmp[i];
1357     for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1358     tmp[i] = sum*v[nz];
1359     x[c[i]] += tmp[i];
1360     v += nz+1; vi += nz+1;
1361   }
1362 
1363   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1364   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1365   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1366   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1367   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1368 
1369   PetscFunctionReturn(0);
1370 }
1371 
1372 #undef __FUNCT__
1373 #define __FUNCT__ "MatSolveTranspose_SeqAIJ_inplace"
1374 PetscErrorCode MatSolveTranspose_SeqAIJ_inplace(Mat A,Vec bb,Vec xx)
1375 {
1376   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1377   IS                iscol = a->col,isrow = a->row;
1378   PetscErrorCode    ierr;
1379   const PetscInt    *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi;
1380   PetscInt          i,n = A->rmap->n,j;
1381   PetscInt          nz;
1382   PetscScalar       *x,*tmp,s1;
1383   const MatScalar   *aa = a->a,*v;
1384   const PetscScalar *b;
1385 
1386   PetscFunctionBegin;
1387   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1388   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1389   tmp  = a->solve_work;
1390 
1391   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1392   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1393 
1394   /* copy the b into temp work space according to permutation */
1395   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1396 
1397   /* forward solve the U^T */
1398   for (i=0; i<n; i++) {
1399     v   = aa + diag[i] ;
1400     vi  = aj + diag[i] + 1;
1401     nz  = ai[i+1] - diag[i] - 1;
1402     s1  = tmp[i];
1403     s1 *= (*v++);  /* multiply by inverse of diagonal entry */
1404     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1405     tmp[i] = s1;
1406   }
1407 
1408   /* backward solve the L^T */
1409   for (i=n-1; i>=0; i--){
1410     v   = aa + diag[i] - 1 ;
1411     vi  = aj + diag[i] - 1 ;
1412     nz  = diag[i] - ai[i];
1413     s1  = tmp[i];
1414     for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j];
1415   }
1416 
1417   /* copy tmp into x according to permutation */
1418   for (i=0; i<n; i++) x[r[i]] = tmp[i];
1419 
1420   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1421   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1422   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1423   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1424 
1425   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1426   PetscFunctionReturn(0);
1427 }
1428 
1429 #undef __FUNCT__
1430 #define __FUNCT__ "MatSolveTranspose_SeqAIJ"
1431 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx)
1432 {
1433   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1434   IS                iscol = a->col,isrow = a->row;
1435   PetscErrorCode    ierr;
1436   const PetscInt    *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi;
1437   PetscInt          i,n = A->rmap->n,j;
1438   PetscInt          nz;
1439   PetscScalar       *x,*tmp,s1;
1440   const MatScalar   *aa = a->a,*v;
1441   const PetscScalar *b;
1442 
1443   PetscFunctionBegin;
1444   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1445   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1446   tmp  = a->solve_work;
1447 
1448   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1449   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1450 
1451   /* copy the b into temp work space according to permutation */
1452   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1453 
1454   /* forward solve the U^T */
1455   for (i=0; i<n; i++) {
1456     v   = aa + adiag[i+1] + 1;
1457     vi  = aj + adiag[i+1] + 1;
1458     nz  = adiag[i] - adiag[i+1] - 1;
1459     s1  = tmp[i];
1460     s1 *= v[nz];  /* multiply by inverse of diagonal entry */
1461     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1462     tmp[i] = s1;
1463   }
1464 
1465   /* backward solve the L^T */
1466   for (i=n-1; i>=0; i--){
1467     v   = aa + ai[i];
1468     vi  = aj + ai[i];
1469     nz  = ai[i+1] - ai[i];
1470     s1  = tmp[i];
1471     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1472   }
1473 
1474   /* copy tmp into x according to permutation */
1475   for (i=0; i<n; i++) x[r[i]] = tmp[i];
1476 
1477   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1478   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1479   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1480   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1481 
1482   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1483   PetscFunctionReturn(0);
1484 }
1485 
1486 #undef __FUNCT__
1487 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ_inplace"
1488 PetscErrorCode MatSolveTransposeAdd_SeqAIJ_inplace(Mat A,Vec bb,Vec zz,Vec xx)
1489 {
1490   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1491   IS                iscol = a->col,isrow = a->row;
1492   PetscErrorCode    ierr;
1493   const PetscInt    *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi;
1494   PetscInt          i,n = A->rmap->n,j;
1495   PetscInt          nz;
1496   PetscScalar       *x,*tmp,s1;
1497   const MatScalar   *aa = a->a,*v;
1498   const PetscScalar *b;
1499 
1500   PetscFunctionBegin;
1501   if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);}
1502   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1503   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1504   tmp  = a->solve_work;
1505 
1506   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1507   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1508 
1509   /* copy the b into temp work space according to permutation */
1510   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1511 
1512   /* forward solve the U^T */
1513   for (i=0; i<n; i++) {
1514     v   = aa + diag[i] ;
1515     vi  = aj + diag[i] + 1;
1516     nz  = ai[i+1] - diag[i] - 1;
1517     s1  = tmp[i];
1518     s1 *= (*v++);  /* multiply by inverse of diagonal entry */
1519     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1520     tmp[i] = s1;
1521   }
1522 
1523   /* backward solve the L^T */
1524   for (i=n-1; i>=0; i--){
1525     v   = aa + diag[i] - 1 ;
1526     vi  = aj + diag[i] - 1 ;
1527     nz  = diag[i] - ai[i];
1528     s1  = tmp[i];
1529     for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j];
1530   }
1531 
1532   /* copy tmp into x according to permutation */
1533   for (i=0; i<n; i++) x[r[i]] += tmp[i];
1534 
1535   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1536   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1537   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1538   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1539 
1540   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1541   PetscFunctionReturn(0);
1542 }
1543 
1544 #undef __FUNCT__
1545 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ"
1546 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx)
1547 {
1548   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1549   IS                iscol = a->col,isrow = a->row;
1550   PetscErrorCode    ierr;
1551   const PetscInt    *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi;
1552   PetscInt          i,n = A->rmap->n,j;
1553   PetscInt          nz;
1554   PetscScalar       *x,*tmp,s1;
1555   const MatScalar   *aa = a->a,*v;
1556   const PetscScalar *b;
1557 
1558   PetscFunctionBegin;
1559   if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);}
1560   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1561   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1562   tmp  = a->solve_work;
1563 
1564   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1565   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1566 
1567   /* copy the b into temp work space according to permutation */
1568   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1569 
1570   /* forward solve the U^T */
1571   for (i=0; i<n; i++) {
1572     v   = aa + adiag[i+1] + 1;
1573     vi  = aj + adiag[i+1] + 1;
1574     nz  = adiag[i] - adiag[i+1] - 1;
1575     s1  = tmp[i];
1576     s1 *= v[nz];  /* multiply by inverse of diagonal entry */
1577     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1578     tmp[i] = s1;
1579   }
1580 
1581 
1582   /* backward solve the L^T */
1583   for (i=n-1; i>=0; i--){
1584     v   = aa + ai[i] ;
1585     vi  = aj + ai[i];
1586     nz  = ai[i+1] - ai[i];
1587     s1  = tmp[i];
1588     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1589   }
1590 
1591   /* copy tmp into x according to permutation */
1592   for (i=0; i<n; i++) x[r[i]] += tmp[i];
1593 
1594   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1595   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1596   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1597   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1598 
1599   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1600   PetscFunctionReturn(0);
1601 }
1602 
1603 /* ----------------------------------------------------------------*/
1604 
1605 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption,PetscTruth);
1606 
1607 /*
1608    ilu() under revised new data structure.
1609    Factored arrays bj and ba are stored as
1610      L(0,:), L(1,:), ...,L(n-1,:),  U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:)
1611 
1612    bi=fact->i is an array of size n+1, in which
1613    bi+
1614      bi[i]:  points to 1st entry of L(i,:),i=0,...,n-1
1615      bi[n]:  points to L(n-1,n-1)+1
1616 
1617   bdiag=fact->diag is an array of size n+1,in which
1618      bdiag[i]: points to diagonal of U(i,:), i=0,...,n-1
1619      bdiag[n]: points to entry of U(n-1,0)-1
1620 
1621    U(i,:) contains bdiag[i] as its last entry, i.e.,
1622     U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i])
1623 */
1624 #undef __FUNCT__
1625 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0"
1626 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1627 {
1628 
1629   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1630   PetscErrorCode     ierr;
1631   const PetscInt     n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag;
1632   PetscInt           i,j,k=0,nz,*bi,*bj,*bdiag;
1633   PetscTruth         missing;
1634   IS                 isicol;
1635 
1636   PetscFunctionBegin;
1637   if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n);
1638   ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
1639   if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
1640   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1641 
1642   ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr);
1643   b    = (Mat_SeqAIJ*)(fact)->data;
1644 
1645   /* allocate matrix arrays for new data structure */
1646   ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,n+1,PetscInt,&b->i);CHKERRQ(ierr);
1647   ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));CHKERRQ(ierr);
1648   b->singlemalloc = PETSC_TRUE;
1649   if (!b->diag){
1650     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr);
1651     ierr = PetscLogObjectMemory(fact,(n+1)*sizeof(PetscInt));CHKERRQ(ierr);
1652   }
1653   bdiag = b->diag;
1654 
1655   if (n > 0) {
1656     ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr);
1657   }
1658 
1659   /* set bi and bj with new data structure */
1660   bi = b->i;
1661   bj = b->j;
1662 
1663   /* L part */
1664   bi[0] = 0;
1665   for (i=0; i<n; i++){
1666     nz = adiag[i] - ai[i];
1667     bi[i+1] = bi[i] + nz;
1668     aj = a->j + ai[i];
1669     for (j=0; j<nz; j++){
1670       /*   *bj = aj[j]; bj++; */
1671       bj[k++] = aj[j];
1672     }
1673   }
1674 
1675   /* U part */
1676   bdiag[n] = bi[n]-1;
1677   for (i=n-1; i>=0; i--){
1678     nz = ai[i+1] - adiag[i] - 1;
1679     aj = a->j + adiag[i] + 1;
1680     for (j=0; j<nz; j++){
1681       /*      *bj = aj[j]; bj++; */
1682       bj[k++] = aj[j];
1683     }
1684     /* diag[i] */
1685     /*    *bj = i; bj++; */
1686     bj[k++] = i;
1687     bdiag[i] = bdiag[i+1] + nz + 1;
1688   }
1689 
1690   fact->factortype             = MAT_FACTOR_ILU;
1691   fact->info.factor_mallocs    = 0;
1692   fact->info.fill_ratio_given  = info->fill;
1693   fact->info.fill_ratio_needed = 1.0;
1694   fact->ops->lufactornumeric   = MatLUFactorNumeric_SeqAIJ;
1695 
1696   b       = (Mat_SeqAIJ*)(fact)->data;
1697   b->row  = isrow;
1698   b->col  = iscol;
1699   b->icol = isicol;
1700   ierr    = PetscMalloc((fact->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1701   ierr    = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1702   ierr    = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1703   PetscFunctionReturn(0);
1704 }
1705 
1706 #undef __FUNCT__
1707 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ"
1708 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1709 {
1710   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1711   IS                 isicol;
1712   PetscErrorCode     ierr;
1713   const PetscInt     *r,*ic;
1714   PetscInt           n=A->rmap->n,*ai=a->i,*aj=a->j;
1715   PetscInt           *bi,*cols,nnz,*cols_lvl;
1716   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1717   PetscInt           i,levels,diagonal_fill;
1718   PetscTruth         col_identity,row_identity;
1719   PetscReal          f;
1720   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
1721   PetscBT            lnkbt;
1722   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
1723   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1724   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1725 
1726   PetscFunctionBegin;
1727   /* Uncomment the old data struct part only while testing new data structure for MatSolve() */
1728   /*
1729   PetscTruth         olddatastruct=PETSC_FALSE;
1730   ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_old",&olddatastruct,PETSC_NULL);CHKERRQ(ierr);
1731   if(olddatastruct){
1732     ierr = MatILUFactorSymbolic_SeqAIJ_inplace(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1733     PetscFunctionReturn(0);
1734   }
1735   */
1736 
1737   levels = (PetscInt)info->levels;
1738   ierr   = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1739   ierr   = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
1740 
1741   if (!levels && row_identity && col_identity) {
1742     /* special case: ilu(0) with natural ordering */
1743     ierr = MatILUFactorSymbolic_SeqAIJ_ilu0(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1744     if (a->inode.size) {
1745       fact->ops->lufactornumeric  = MatLUFactorNumeric_SeqAIJ_Inode;
1746     }
1747     PetscFunctionReturn(0);
1748   }
1749 
1750   if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n);
1751   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1752   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1753   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1754 
1755   /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
1756   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1757   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
1758   bi[0] = bdiag[0] = 0;
1759 
1760   ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr);
1761 
1762   /* create a linked list for storing column indices of the active row */
1763   nlnk = n + 1;
1764   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1765 
1766   /* initial FreeSpace size is f*(ai[n]+1) */
1767   f             = info->fill;
1768   diagonal_fill = (PetscInt)info->diagonal_fill;
1769   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
1770   current_space = free_space;
1771   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
1772   current_space_lvl = free_space_lvl;
1773 
1774   for (i=0; i<n; i++) {
1775     nzi = 0;
1776     /* copy current row into linked list */
1777     nnz  = ai[r[i]+1] - ai[r[i]];
1778     if (!nnz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1779     cols = aj + ai[r[i]];
1780     lnk[i] = -1; /* marker to indicate if diagonal exists */
1781     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1782     nzi += nlnk;
1783 
1784     /* make sure diagonal entry is included */
1785     if (diagonal_fill && lnk[i] == -1) {
1786       fm = n;
1787       while (lnk[fm] < i) fm = lnk[fm];
1788       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
1789       lnk[fm]    = i;
1790       lnk_lvl[i] = 0;
1791       nzi++; dcount++;
1792     }
1793 
1794     /* add pivot rows into the active row */
1795     nzbd = 0;
1796     prow = lnk[n];
1797     while (prow < i) {
1798       nnz      = bdiag[prow];
1799       cols     = bj_ptr[prow] + nnz + 1;
1800       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1801       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
1802       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
1803       nzi += nlnk;
1804       prow = lnk[prow];
1805       nzbd++;
1806     }
1807     bdiag[i] = nzbd;
1808     bi[i+1]  = bi[i] + nzi;
1809 
1810     /* if free space is not available, make more free space */
1811     if (current_space->local_remaining<nzi) {
1812       nnz = 2*nzi*(n - i); /* estimated and max additional space needed */
1813       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
1814       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
1815       reallocs++;
1816     }
1817 
1818     /* copy data into free_space and free_space_lvl, then initialize lnk */
1819     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1820     bj_ptr[i]    = current_space->array;
1821     bjlvl_ptr[i] = current_space_lvl->array;
1822 
1823     /* make sure the active row i has diagonal entry */
1824     if (*(bj_ptr[i]+bdiag[i]) != i) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\ntry running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
1825 
1826     current_space->array           += nzi;
1827     current_space->local_used      += nzi;
1828     current_space->local_remaining -= nzi;
1829     current_space_lvl->array           += nzi;
1830     current_space_lvl->local_used      += nzi;
1831     current_space_lvl->local_remaining -= nzi;
1832   }
1833 
1834   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1835   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1836 
1837   /* destroy list of free space and other temporary arrays */
1838   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
1839 
1840   /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */
1841   ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr);
1842 
1843   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1844   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
1845   ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr);
1846 
1847 #if defined(PETSC_USE_INFO)
1848   {
1849     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1850     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
1851     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
1852     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
1853     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
1854     if (diagonal_fill) {
1855       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
1856     }
1857   }
1858 #endif
1859 
1860   /* put together the new matrix */
1861   ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
1862   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
1863   b = (Mat_SeqAIJ*)(fact)->data;
1864   b->free_a       = PETSC_TRUE;
1865   b->free_ij      = PETSC_TRUE;
1866   b->singlemalloc = PETSC_FALSE;
1867   ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
1868   b->j          = bj;
1869   b->i          = bi;
1870   b->diag       = bdiag;
1871   b->ilen       = 0;
1872   b->imax       = 0;
1873   b->row        = isrow;
1874   b->col        = iscol;
1875   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1876   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1877   b->icol       = isicol;
1878   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1879   /* In b structure:  Free imax, ilen, old a, old j.
1880      Allocate bdiag, solve_work, new a, new j */
1881   ierr = PetscLogObjectMemory(fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
1882   b->maxnz = b->nz = bdiag[0]+1;
1883   (fact)->info.factor_mallocs    = reallocs;
1884   (fact)->info.fill_ratio_given  = f;
1885   (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]);
1886   (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ;
1887   if (a->inode.size) {
1888     (fact)->ops->lufactornumeric  = MatLUFactorNumeric_SeqAIJ_Inode;
1889   }
1890   PetscFunctionReturn(0);
1891 }
1892 
1893 #undef __FUNCT__
1894 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_inplace"
1895 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1896 {
1897   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1898   IS                 isicol;
1899   PetscErrorCode     ierr;
1900   const PetscInt     *r,*ic;
1901   PetscInt           n=A->rmap->n,*ai=a->i,*aj=a->j,d;
1902   PetscInt           *bi,*cols,nnz,*cols_lvl;
1903   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1904   PetscInt           i,levels,diagonal_fill;
1905   PetscTruth         col_identity,row_identity;
1906   PetscReal          f;
1907   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
1908   PetscBT            lnkbt;
1909   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
1910   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1911   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1912   PetscTruth         missing;
1913 
1914   PetscFunctionBegin;
1915   if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n);
1916   f             = info->fill;
1917   levels        = (PetscInt)info->levels;
1918   diagonal_fill = (PetscInt)info->diagonal_fill;
1919   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1920 
1921   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1922   ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
1923   if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */
1924     ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr);
1925     (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ_inplace;
1926     if (a->inode.size) {
1927       (fact)->ops->lufactornumeric  = MatLUFactorNumeric_SeqAIJ_Inode_inplace;
1928     }
1929     fact->factortype = MAT_FACTOR_ILU;
1930     (fact)->info.factor_mallocs    = 0;
1931     (fact)->info.fill_ratio_given  = info->fill;
1932     (fact)->info.fill_ratio_needed = 1.0;
1933     b               = (Mat_SeqAIJ*)(fact)->data;
1934     ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
1935     if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
1936     b->row              = isrow;
1937     b->col              = iscol;
1938     b->icol             = isicol;
1939     ierr                = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1940     ierr                = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1941     ierr                = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1942     PetscFunctionReturn(0);
1943   }
1944 
1945   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1946   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1947 
1948   /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
1949   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1950   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
1951   bi[0] = bdiag[0] = 0;
1952 
1953   ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr);
1954 
1955   /* create a linked list for storing column indices of the active row */
1956   nlnk = n + 1;
1957   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1958 
1959   /* initial FreeSpace size is f*(ai[n]+1) */
1960   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
1961   current_space = free_space;
1962   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
1963   current_space_lvl = free_space_lvl;
1964 
1965   for (i=0; i<n; i++) {
1966     nzi = 0;
1967     /* copy current row into linked list */
1968     nnz  = ai[r[i]+1] - ai[r[i]];
1969     if (!nnz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1970     cols = aj + ai[r[i]];
1971     lnk[i] = -1; /* marker to indicate if diagonal exists */
1972     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1973     nzi += nlnk;
1974 
1975     /* make sure diagonal entry is included */
1976     if (diagonal_fill && lnk[i] == -1) {
1977       fm = n;
1978       while (lnk[fm] < i) fm = lnk[fm];
1979       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
1980       lnk[fm]    = i;
1981       lnk_lvl[i] = 0;
1982       nzi++; dcount++;
1983     }
1984 
1985     /* add pivot rows into the active row */
1986     nzbd = 0;
1987     prow = lnk[n];
1988     while (prow < i) {
1989       nnz      = bdiag[prow];
1990       cols     = bj_ptr[prow] + nnz + 1;
1991       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1992       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
1993       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
1994       nzi += nlnk;
1995       prow = lnk[prow];
1996       nzbd++;
1997     }
1998     bdiag[i] = nzbd;
1999     bi[i+1]  = bi[i] + nzi;
2000 
2001     /* if free space is not available, make more free space */
2002     if (current_space->local_remaining<nzi) {
2003       nnz = nzi*(n - i); /* estimated and max additional space needed */
2004       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
2005       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
2006       reallocs++;
2007     }
2008 
2009     /* copy data into free_space and free_space_lvl, then initialize lnk */
2010     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
2011     bj_ptr[i]    = current_space->array;
2012     bjlvl_ptr[i] = current_space_lvl->array;
2013 
2014     /* make sure the active row i has diagonal entry */
2015     if (*(bj_ptr[i]+bdiag[i]) != i) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\ntry running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
2016 
2017     current_space->array           += nzi;
2018     current_space->local_used      += nzi;
2019     current_space->local_remaining -= nzi;
2020     current_space_lvl->array           += nzi;
2021     current_space_lvl->local_used      += nzi;
2022     current_space_lvl->local_remaining -= nzi;
2023   }
2024 
2025   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
2026   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
2027 
2028   /* destroy list of free space and other temporary arrays */
2029   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
2030   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */
2031   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2032   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2033   ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr);
2034 
2035 #if defined(PETSC_USE_INFO)
2036   {
2037     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
2038     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
2039     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2040     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
2041     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
2042     if (diagonal_fill) {
2043       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
2044     }
2045   }
2046 #endif
2047 
2048   /* put together the new matrix */
2049   ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
2050   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
2051   b = (Mat_SeqAIJ*)(fact)->data;
2052   b->free_a       = PETSC_TRUE;
2053   b->free_ij      = PETSC_TRUE;
2054   b->singlemalloc = PETSC_FALSE;
2055   ierr = PetscMalloc(bi[n]*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
2056   b->j          = bj;
2057   b->i          = bi;
2058   for (i=0; i<n; i++) bdiag[i] += bi[i];
2059   b->diag       = bdiag;
2060   b->ilen       = 0;
2061   b->imax       = 0;
2062   b->row        = isrow;
2063   b->col        = iscol;
2064   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
2065   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
2066   b->icol       = isicol;
2067   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2068   /* In b structure:  Free imax, ilen, old a, old j.
2069      Allocate bdiag, solve_work, new a, new j */
2070   ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
2071   b->maxnz             = b->nz = bi[n] ;
2072   (fact)->info.factor_mallocs    = reallocs;
2073   (fact)->info.fill_ratio_given  = f;
2074   (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
2075   (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ_inplace;
2076   if (a->inode.size) {
2077     (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace;
2078   }
2079   PetscFunctionReturn(0);
2080 }
2081 
2082 #undef __FUNCT__
2083 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ"
2084 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info)
2085 {
2086   Mat            C = B;
2087   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
2088   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
2089   IS             ip=b->row,iip = b->icol;
2090   PetscErrorCode ierr;
2091   const PetscInt *rip,*riip;
2092   PetscInt       i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp;
2093   PetscInt       *ai=a->i,*aj=a->j;
2094   PetscInt       k,jmin,jmax,*c2r,*il,col,nexti,ili,nz;
2095   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
2096   PetscTruth     perm_identity;
2097   PetscInt       newshift = 0;
2098 
2099   FactorShiftCtx sctx;
2100   PetscReal      rs;
2101   MatScalar      d,*v;
2102 
2103   PetscFunctionBegin;
2104   /* MatPivotSetUp(): initialize shift context sctx */
2105   ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr);
2106 
2107   if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
2108     sctx.shift_top = info->zeropivot;
2109     for (i=0; i<mbs; i++) {
2110       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
2111       d  = (aa)[a->diag[i]];
2112       rs = -PetscAbsScalar(d) - PetscRealPart(d);
2113       v  = aa+ai[i];
2114       nz = ai[i+1] - ai[i];
2115       for (j=0; j<nz; j++)
2116 	rs += PetscAbsScalar(v[j]);
2117       if (rs>sctx.shift_top) sctx.shift_top = rs;
2118     }
2119     sctx.shift_top   *= 1.1;
2120     sctx.nshift_max   = 5;
2121     sctx.shift_lo     = 0.;
2122     sctx.shift_hi     = 1.;
2123   }
2124 
2125   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
2126   ierr  = ISGetIndices(iip,&riip);CHKERRQ(ierr);
2127 
2128   /* allocate working arrays
2129      c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col
2130      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
2131   */
2132   ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&c2r);CHKERRQ(ierr);
2133 
2134   do {
2135     sctx.useshift = PETSC_FALSE;
2136 
2137     for (i=0; i<mbs; i++) c2r[i] = mbs;
2138     il[0] = 0;
2139 
2140     for (k = 0; k<mbs; k++){
2141       /* zero rtmp */
2142       nz = bi[k+1] - bi[k];
2143       bjtmp = bj + bi[k];
2144       for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
2145 
2146       /* load in initial unfactored row */
2147       bval = ba + bi[k];
2148       jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2149       for (j = jmin; j < jmax; j++){
2150         col = riip[aj[j]];
2151         if (col >= k){ /* only take upper triangular entry */
2152           rtmp[col] = aa[j];
2153           *bval++   = 0.0; /* for in-place factorization */
2154         }
2155       }
2156       /* shift the diagonal of the matrix: ZeropivotApply() */
2157       rtmp[k] += sctx.shift_amount;  /* shift the diagonal of the matrix */
2158 
2159       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
2160       dk = rtmp[k];
2161       i  = c2r[k]; /* first row to be added to k_th row  */
2162 
2163       while (i < k){
2164         nexti = c2r[i]; /* next row to be added to k_th row */
2165 
2166         /* compute multiplier, update diag(k) and U(i,k) */
2167         ili   = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2168         uikdi = - ba[ili]*ba[bdiag[i]];  /* diagonal(k) */
2169         dk   += uikdi*ba[ili]; /* update diag[k] */
2170         ba[ili] = uikdi; /* -U(i,k) */
2171 
2172         /* add multiple of row i to k-th row */
2173         jmin = ili + 1; jmax = bi[i+1];
2174         if (jmin < jmax){
2175           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2176           /* update il and c2r for row i */
2177           il[i] = jmin;
2178           j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i;
2179         }
2180         i = nexti;
2181       }
2182 
2183       /* copy data into U(k,:) */
2184       rs   = 0.0;
2185       jmin = bi[k]; jmax = bi[k+1]-1;
2186       if (jmin < jmax) {
2187         for (j=jmin; j<jmax; j++){
2188           col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]);
2189         }
2190         /* add the k-th row into il and c2r */
2191         il[k] = jmin;
2192         i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k;
2193       }
2194 
2195       /* MatPivotCheck() */
2196       sctx.rs  = rs;
2197       sctx.pv  = dk;
2198       ierr = MatPivotCheck(info,&sctx,i,&newshift);CHKERRQ(ierr);
2199       if(newshift == 1) break;
2200       dk = sctx.pv;
2201 
2202       ba[bdiag[k]] = 1.0/dk; /* U(k,k) */
2203     }
2204   } while (sctx.useshift);
2205 
2206   ierr = PetscFree3(rtmp,il,c2r);CHKERRQ(ierr);
2207   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2208   ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr);
2209 
2210   ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
2211   if (perm_identity){
2212     B->ops->solve           = MatSolve_SeqSBAIJ_1_NaturalOrdering;
2213     B->ops->solvetranspose  = MatSolve_SeqSBAIJ_1_NaturalOrdering;
2214     B->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering;
2215     B->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering;
2216   } else {
2217     B->ops->solve           = MatSolve_SeqSBAIJ_1;
2218     B->ops->solvetranspose  = MatSolve_SeqSBAIJ_1;
2219     B->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1;
2220     B->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1;
2221   }
2222 
2223   C->assembled    = PETSC_TRUE;
2224   C->preallocated = PETSC_TRUE;
2225   ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr);
2226 
2227   /* MatPivotView() */
2228   if (sctx.nshift){
2229     if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
2230       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);
2231     } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
2232       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2233     } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS){
2234       ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftamount);CHKERRQ(ierr);
2235     }
2236   }
2237   PetscFunctionReturn(0);
2238 }
2239 
2240 #undef __FUNCT__
2241 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ_inplace"
2242 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info)
2243 {
2244   Mat            C = B;
2245   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
2246   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
2247   IS             ip=b->row,iip = b->icol;
2248   PetscErrorCode ierr;
2249   const PetscInt *rip,*riip;
2250   PetscInt       i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol,*bjtmp;
2251   PetscInt       *ai=a->i,*aj=a->j;
2252   PetscInt       k,jmin,jmax,*jl,*il,col,nexti,ili,nz;
2253   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
2254   PetscInt       newshift;
2255   PetscTruth     perm_identity;
2256   FactorShiftCtx sctx;
2257   PetscReal      rs;
2258   MatScalar      d,*v;
2259 
2260   PetscFunctionBegin;
2261   /* MatPivotSetUp(): initialize shift context sctx */
2262   ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr);
2263 
2264   if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
2265     sctx.shift_top = info->zeropivot;
2266     for (i=0; i<mbs; i++) {
2267       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
2268       d  = (aa)[a->diag[i]];
2269       rs = -PetscAbsScalar(d) - PetscRealPart(d);
2270       v  = aa+ai[i];
2271       nz = ai[i+1] - ai[i];
2272       for (j=0; j<nz; j++)
2273 	rs += PetscAbsScalar(v[j]);
2274       if (rs>sctx.shift_top) sctx.shift_top = rs;
2275     }
2276     sctx.shift_top   *= 1.1;
2277     sctx.nshift_max   = 5;
2278     sctx.shift_lo     = 0.;
2279     sctx.shift_hi     = 1.;
2280   }
2281 
2282   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
2283   ierr  = ISGetIndices(iip,&riip);CHKERRQ(ierr);
2284 
2285   /* initialization */
2286   ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&jl);CHKERRQ(ierr);
2287 
2288   do {
2289     sctx.useshift = PETSC_FALSE;
2290 
2291     for (i=0; i<mbs; i++) jl[i] = mbs;
2292     il[0] = 0;
2293 
2294     for (k = 0; k<mbs; k++){
2295       /* zero rtmp */
2296       nz = bi[k+1] - bi[k];
2297       bjtmp = bj + bi[k];
2298       for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
2299 
2300       bval = ba + bi[k];
2301       /* initialize k-th row by the perm[k]-th row of A */
2302       jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2303       for (j = jmin; j < jmax; j++){
2304         col = riip[aj[j]];
2305         if (col >= k){ /* only take upper triangular entry */
2306           rtmp[col] = aa[j];
2307           *bval++  = 0.0; /* for in-place factorization */
2308         }
2309       }
2310       /* shift the diagonal of the matrix */
2311       if (sctx.nshift) rtmp[k] += sctx.shift_amount;
2312 
2313       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
2314       dk = rtmp[k];
2315       i = jl[k]; /* first row to be added to k_th row  */
2316 
2317       while (i < k){
2318         nexti = jl[i]; /* next row to be added to k_th row */
2319 
2320         /* compute multiplier, update diag(k) and U(i,k) */
2321         ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2322         uikdi = - ba[ili]*ba[bi[i]];  /* diagonal(k) */
2323         dk += uikdi*ba[ili];
2324         ba[ili] = uikdi; /* -U(i,k) */
2325 
2326         /* add multiple of row i to k-th row */
2327         jmin = ili + 1; jmax = bi[i+1];
2328         if (jmin < jmax){
2329           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2330           /* update il and jl for row i */
2331           il[i] = jmin;
2332           j = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
2333         }
2334         i = nexti;
2335       }
2336 
2337       /* shift the diagonals when zero pivot is detected */
2338       /* compute rs=sum of abs(off-diagonal) */
2339       rs   = 0.0;
2340       jmin = bi[k]+1;
2341       nz   = bi[k+1] - jmin;
2342       bcol = bj + jmin;
2343       for (j=0; j<nz; j++) {
2344         rs += PetscAbsScalar(rtmp[bcol[j]]);
2345       }
2346 
2347       sctx.rs = rs;
2348       sctx.pv = dk;
2349       ierr = MatPivotCheck(info,&sctx,k,&newshift);CHKERRQ(ierr);
2350       if (newshift == 1) break;
2351       dk = sctx.pv;
2352 
2353       /* copy data into U(k,:) */
2354       ba[bi[k]] = 1.0/dk; /* U(k,k) */
2355       jmin = bi[k]+1; jmax = bi[k+1];
2356       if (jmin < jmax) {
2357         for (j=jmin; j<jmax; j++){
2358           col = bj[j]; ba[j] = rtmp[col];
2359         }
2360         /* add the k-th row into il and jl */
2361         il[k] = jmin;
2362         i = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
2363       }
2364     }
2365   } while (sctx.useshift);
2366 
2367   ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr);
2368   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2369   ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr);
2370 
2371   ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
2372   if (perm_identity){
2373     B->ops->solve           = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
2374     B->ops->solvetranspose  = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
2375     B->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
2376     B->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
2377   } else {
2378     B->ops->solve           = MatSolve_SeqSBAIJ_1_inplace;
2379     B->ops->solvetranspose  = MatSolve_SeqSBAIJ_1_inplace;
2380     B->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1_inplace;
2381     B->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1_inplace;
2382   }
2383 
2384   C->assembled    = PETSC_TRUE;
2385   C->preallocated = PETSC_TRUE;
2386   ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr);
2387   if (sctx.nshift){
2388     if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
2389       ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2390     } else if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
2391       ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2392     }
2393   }
2394   PetscFunctionReturn(0);
2395 }
2396 
2397 /*
2398    icc() under revised new data structure.
2399    Factored arrays bj and ba are stored as
2400      U(0,:),...,U(i,:),U(n-1,:)
2401 
2402    ui=fact->i is an array of size n+1, in which
2403    ui+
2404      ui[i]:  points to 1st entry of U(i,:),i=0,...,n-1
2405      ui[n]:  points to U(n-1,n-1)+1
2406 
2407   udiag=fact->diag is an array of size n,in which
2408      udiag[i]: points to diagonal of U(i,:), i=0,...,n-1
2409 
2410    U(i,:) contains udiag[i] as its last entry, i.e.,
2411     U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i])
2412 */
2413 
2414 #undef __FUNCT__
2415 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ"
2416 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2417 {
2418   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2419   Mat_SeqSBAIJ       *b;
2420   PetscErrorCode     ierr;
2421   PetscTruth         perm_identity,missing;
2422   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag;
2423   const PetscInt     *rip,*riip;
2424   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
2425   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL,d;
2426   PetscInt           ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
2427   PetscReal          fill=info->fill,levels=info->levels;
2428   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2429   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
2430   PetscBT            lnkbt;
2431   IS                 iperm;
2432 
2433   PetscFunctionBegin;
2434   if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n);
2435   ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
2436   if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
2437   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2438   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2439 
2440   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2441   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2442   ui[0] = 0;
2443 
2444   /* ICC(0) without matrix ordering: simply rearrange column indices */
2445   if (!levels && perm_identity) {
2446     for (i=0; i<am; i++) {
2447       ncols    = ai[i+1] - a->diag[i];
2448       ui[i+1]  = ui[i] + ncols;
2449       udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */
2450     }
2451     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2452     cols = uj;
2453     for (i=0; i<am; i++) {
2454       aj    = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */
2455       ncols = ai[i+1] - a->diag[i] -1;
2456       for (j=0; j<ncols; j++) *cols++ = aj[j];
2457       *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */
2458     }
2459   } else { /* case: levels>0 || (levels=0 && !perm_identity) */
2460     ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2461     ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2462 
2463     /* initialization */
2464     ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr);
2465 
2466     /* jl: linked list for storing indices of the pivot rows
2467        il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2468     ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr);
2469     for (i=0; i<am; i++){
2470       jl[i] = am; il[i] = 0;
2471     }
2472 
2473     /* create and initialize a linked list for storing column indices of the active row k */
2474     nlnk = am + 1;
2475     ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2476 
2477     /* initial FreeSpace size is fill*(ai[am]+1) */
2478     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2479     current_space = free_space;
2480     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr);
2481     current_space_lvl = free_space_lvl;
2482 
2483     for (k=0; k<am; k++){  /* for each active row k */
2484       /* initialize lnk by the column indices of row rip[k] of A */
2485       nzk   = 0;
2486       ncols = ai[rip[k]+1] - ai[rip[k]];
2487       if (!ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2488       ncols_upper = 0;
2489       for (j=0; j<ncols; j++){
2490         i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2491         if (riip[i] >= k){ /* only take upper triangular entry */
2492           ajtmp[ncols_upper] = i;
2493           ncols_upper++;
2494         }
2495       }
2496       ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2497       nzk += nlnk;
2498 
2499       /* update lnk by computing fill-in for each pivot row to be merged in */
2500       prow = jl[k]; /* 1st pivot row */
2501 
2502       while (prow < k){
2503         nextprow = jl[prow];
2504 
2505         /* merge prow into k-th row */
2506         jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2507         jmax = ui[prow+1];
2508         ncols = jmax-jmin;
2509         i     = jmin - ui[prow];
2510         cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2511         uj    = uj_lvl_ptr[prow] + i; /* levels of cols */
2512         j     = *(uj - 1);
2513         ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr);
2514         nzk += nlnk;
2515 
2516         /* update il and jl for prow */
2517         if (jmin < jmax){
2518           il[prow] = jmin;
2519           j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2520         }
2521         prow = nextprow;
2522       }
2523 
2524       /* if free space is not available, make more free space */
2525       if (current_space->local_remaining<nzk) {
2526         i  = am - k + 1; /* num of unfactored rows */
2527         i *= PetscMin(nzk, i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */
2528         ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2529         ierr = PetscFreeSpaceGet(i,&current_space_lvl);CHKERRQ(ierr);
2530         reallocs++;
2531       }
2532 
2533       /* copy data into free_space and free_space_lvl, then initialize lnk */
2534       if (nzk == 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2535       ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
2536 
2537       /* add the k-th row into il and jl */
2538       if (nzk > 1){
2539         i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2540         jl[k] = jl[i]; jl[i] = k;
2541         il[k] = ui[k] + 1;
2542       }
2543       uj_ptr[k]     = current_space->array;
2544       uj_lvl_ptr[k] = current_space_lvl->array;
2545 
2546       current_space->array           += nzk;
2547       current_space->local_used      += nzk;
2548       current_space->local_remaining -= nzk;
2549 
2550       current_space_lvl->array           += nzk;
2551       current_space_lvl->local_used      += nzk;
2552       current_space_lvl->local_remaining -= nzk;
2553 
2554       ui[k+1] = ui[k] + nzk;
2555     }
2556 
2557 #if defined(PETSC_USE_INFO)
2558     if (ai[am] != 0) {
2559       PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]);
2560       ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2561       ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2562       ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2563     } else {
2564       ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2565     }
2566 #endif
2567 
2568     ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2569     ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2570     ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr);
2571     ierr = PetscFree(ajtmp);CHKERRQ(ierr);
2572 
2573     /* destroy list of free space and other temporary array(s) */
2574     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2575     ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor  */
2576     ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2577     ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2578 
2579   } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2580 
2581   /* put together the new matrix in MATSEQSBAIJ format */
2582   b    = (Mat_SeqSBAIJ*)(fact)->data;
2583   b->singlemalloc = PETSC_FALSE;
2584   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2585   b->j    = uj;
2586   b->i    = ui;
2587   b->diag = udiag;
2588   b->free_diag = PETSC_TRUE;
2589   b->ilen = 0;
2590   b->imax = 0;
2591   b->row  = perm;
2592   b->col  = perm;
2593   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2594   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2595   b->icol = iperm;
2596   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2597   ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2598   ierr = PetscLogObjectMemory(fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2599   b->maxnz   = b->nz = ui[am];
2600   b->free_a  = PETSC_TRUE;
2601   b->free_ij = PETSC_TRUE;
2602 
2603   fact->info.factor_mallocs    = reallocs;
2604   fact->info.fill_ratio_given  = fill;
2605   if (ai[am] != 0) {
2606     fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2607   } else {
2608     fact->info.fill_ratio_needed = 0.0;
2609   }
2610   fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2611   PetscFunctionReturn(0);
2612 }
2613 
2614 #undef __FUNCT__
2615 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ_inplace"
2616 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2617 {
2618   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2619   Mat_SeqSBAIJ       *b;
2620   PetscErrorCode     ierr;
2621   PetscTruth         perm_identity,missing;
2622   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag;
2623   const PetscInt     *rip,*riip;
2624   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
2625   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL,d;
2626   PetscInt           ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
2627   PetscReal          fill=info->fill,levels=info->levels;
2628   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2629   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
2630   PetscBT            lnkbt;
2631   IS                 iperm;
2632 
2633   PetscFunctionBegin;
2634   if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n);
2635   ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
2636   if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
2637   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2638   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2639 
2640   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2641   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2642   ui[0] = 0;
2643 
2644   /* ICC(0) without matrix ordering: simply copies fill pattern */
2645   if (!levels && perm_identity) {
2646 
2647     for (i=0; i<am; i++) {
2648       ui[i+1]  = ui[i] + ai[i+1] - a->diag[i];
2649       udiag[i] = ui[i];
2650     }
2651     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2652     cols = uj;
2653     for (i=0; i<am; i++) {
2654       aj    = a->j + a->diag[i];
2655       ncols = ui[i+1] - ui[i];
2656       for (j=0; j<ncols; j++) *cols++ = *aj++;
2657     }
2658   } else { /* case: levels>0 || (levels=0 && !perm_identity) */
2659     ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2660     ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2661 
2662     /* initialization */
2663     ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr);
2664 
2665     /* jl: linked list for storing indices of the pivot rows
2666        il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2667     ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr);
2668     for (i=0; i<am; i++){
2669       jl[i] = am; il[i] = 0;
2670     }
2671 
2672     /* create and initialize a linked list for storing column indices of the active row k */
2673     nlnk = am + 1;
2674     ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2675 
2676     /* initial FreeSpace size is fill*(ai[am]+1) */
2677     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2678     current_space = free_space;
2679     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr);
2680     current_space_lvl = free_space_lvl;
2681 
2682     for (k=0; k<am; k++){  /* for each active row k */
2683       /* initialize lnk by the column indices of row rip[k] of A */
2684       nzk   = 0;
2685       ncols = ai[rip[k]+1] - ai[rip[k]];
2686       if (!ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2687       ncols_upper = 0;
2688       for (j=0; j<ncols; j++){
2689         i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2690         if (riip[i] >= k){ /* only take upper triangular entry */
2691           ajtmp[ncols_upper] = i;
2692           ncols_upper++;
2693         }
2694       }
2695       ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2696       nzk += nlnk;
2697 
2698       /* update lnk by computing fill-in for each pivot row to be merged in */
2699       prow = jl[k]; /* 1st pivot row */
2700 
2701       while (prow < k){
2702         nextprow = jl[prow];
2703 
2704         /* merge prow into k-th row */
2705         jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2706         jmax = ui[prow+1];
2707         ncols = jmax-jmin;
2708         i     = jmin - ui[prow];
2709         cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2710         uj    = uj_lvl_ptr[prow] + i; /* levels of cols */
2711         j     = *(uj - 1);
2712         ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr);
2713         nzk += nlnk;
2714 
2715         /* update il and jl for prow */
2716         if (jmin < jmax){
2717           il[prow] = jmin;
2718           j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2719         }
2720         prow = nextprow;
2721       }
2722 
2723       /* if free space is not available, make more free space */
2724       if (current_space->local_remaining<nzk) {
2725         i = am - k + 1; /* num of unfactored rows */
2726         i *= PetscMin(nzk, (i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2727         ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2728         ierr = PetscFreeSpaceGet(i,&current_space_lvl);CHKERRQ(ierr);
2729         reallocs++;
2730       }
2731 
2732       /* copy data into free_space and free_space_lvl, then initialize lnk */
2733       if (!nzk) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2734       ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
2735 
2736       /* add the k-th row into il and jl */
2737       if (nzk > 1){
2738         i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2739         jl[k] = jl[i]; jl[i] = k;
2740         il[k] = ui[k] + 1;
2741       }
2742       uj_ptr[k]     = current_space->array;
2743       uj_lvl_ptr[k] = current_space_lvl->array;
2744 
2745       current_space->array           += nzk;
2746       current_space->local_used      += nzk;
2747       current_space->local_remaining -= nzk;
2748 
2749       current_space_lvl->array           += nzk;
2750       current_space_lvl->local_used      += nzk;
2751       current_space_lvl->local_remaining -= nzk;
2752 
2753       ui[k+1] = ui[k] + nzk;
2754     }
2755 
2756 #if defined(PETSC_USE_INFO)
2757     if (ai[am] != 0) {
2758       PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]);
2759       ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2760       ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2761       ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2762     } else {
2763       ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2764     }
2765 #endif
2766 
2767     ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2768     ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2769     ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr);
2770     ierr = PetscFree(ajtmp);CHKERRQ(ierr);
2771 
2772     /* destroy list of free space and other temporary array(s) */
2773     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2774     ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
2775     ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2776     ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2777 
2778   } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2779 
2780   /* put together the new matrix in MATSEQSBAIJ format */
2781 
2782   b    = (Mat_SeqSBAIJ*)fact->data;
2783   b->singlemalloc = PETSC_FALSE;
2784   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2785   b->j    = uj;
2786   b->i    = ui;
2787   b->diag = udiag;
2788   b->free_diag = PETSC_TRUE;
2789   b->ilen = 0;
2790   b->imax = 0;
2791   b->row  = perm;
2792   b->col  = perm;
2793   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2794   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2795   b->icol = iperm;
2796   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2797   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2798   ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2799   b->maxnz   = b->nz = ui[am];
2800   b->free_a  = PETSC_TRUE;
2801   b->free_ij = PETSC_TRUE;
2802 
2803   fact->info.factor_mallocs    = reallocs;
2804   fact->info.fill_ratio_given  = fill;
2805   if (ai[am] != 0) {
2806     fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2807   } else {
2808     fact->info.fill_ratio_needed = 0.0;
2809   }
2810   fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace;
2811   PetscFunctionReturn(0);
2812 }
2813 
2814 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2815 {
2816   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2817   Mat_SeqSBAIJ       *b;
2818   PetscErrorCode     ierr;
2819   PetscTruth         perm_identity;
2820   PetscReal          fill = info->fill;
2821   const PetscInt     *rip,*riip;
2822   PetscInt           i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow;
2823   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
2824   PetscInt           nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr,*udiag;
2825   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2826   PetscBT            lnkbt;
2827   IS                 iperm;
2828 
2829   PetscFunctionBegin;
2830   if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n);
2831   /* check whether perm is the identity mapping */
2832   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2833   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2834   ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2835   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2836 
2837   /* initialization */
2838   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2839   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2840   ui[0] = 0;
2841 
2842   /* jl: linked list for storing indices of the pivot rows
2843      il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2844   ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr);
2845   for (i=0; i<am; i++){
2846     jl[i] = am; il[i] = 0;
2847   }
2848 
2849   /* create and initialize a linked list for storing column indices of the active row k */
2850   nlnk = am + 1;
2851   ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2852 
2853   /* initial FreeSpace size is fill*(ai[am]+1) */
2854   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2855   current_space = free_space;
2856 
2857   for (k=0; k<am; k++){  /* for each active row k */
2858     /* initialize lnk by the column indices of row rip[k] of A */
2859     nzk   = 0;
2860     ncols = ai[rip[k]+1] - ai[rip[k]];
2861     if (!ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2862     ncols_upper = 0;
2863     for (j=0; j<ncols; j++){
2864       i = riip[*(aj + ai[rip[k]] + j)];
2865       if (i >= k){ /* only take upper triangular entry */
2866         cols[ncols_upper] = i;
2867         ncols_upper++;
2868       }
2869     }
2870     ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2871     nzk += nlnk;
2872 
2873     /* update lnk by computing fill-in for each pivot row to be merged in */
2874     prow = jl[k]; /* 1st pivot row */
2875 
2876     while (prow < k){
2877       nextprow = jl[prow];
2878       /* merge prow into k-th row */
2879       jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2880       jmax = ui[prow+1];
2881       ncols = jmax-jmin;
2882       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2883       ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2884       nzk += nlnk;
2885 
2886       /* update il and jl for prow */
2887       if (jmin < jmax){
2888         il[prow] = jmin;
2889         j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
2890       }
2891       prow = nextprow;
2892     }
2893 
2894     /* if free space is not available, make more free space */
2895     if (current_space->local_remaining<nzk) {
2896       i  = am - k + 1; /* num of unfactored rows */
2897       i *= PetscMin(nzk,i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */
2898       ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2899       reallocs++;
2900     }
2901 
2902     /* copy data into free space, then initialize lnk */
2903     ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
2904 
2905     /* add the k-th row into il and jl */
2906     if (nzk > 1){
2907       i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2908       jl[k] = jl[i]; jl[i] = k;
2909       il[k] = ui[k] + 1;
2910     }
2911     ui_ptr[k] = current_space->array;
2912     current_space->array           += nzk;
2913     current_space->local_used      += nzk;
2914     current_space->local_remaining -= nzk;
2915 
2916     ui[k+1] = ui[k] + nzk;
2917   }
2918 
2919 #if defined(PETSC_USE_INFO)
2920   if (ai[am] != 0) {
2921     PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]);
2922     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2923     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2924     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2925   } else {
2926      ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2927   }
2928 #endif
2929 
2930   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2931   ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2932   ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr);
2933 
2934   /* destroy list of free space and other temporary array(s) */
2935   ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2936   ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor */
2937   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2938 
2939   /* put together the new matrix in MATSEQSBAIJ format */
2940 
2941   b = (Mat_SeqSBAIJ*)fact->data;
2942   b->singlemalloc = PETSC_FALSE;
2943   b->free_a       = PETSC_TRUE;
2944   b->free_ij      = PETSC_TRUE;
2945   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2946   b->j    = uj;
2947   b->i    = ui;
2948   b->diag = udiag;
2949   b->free_diag = PETSC_TRUE;
2950   b->ilen = 0;
2951   b->imax = 0;
2952   b->row  = perm;
2953   b->col  = perm;
2954   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2955   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2956   b->icol = iperm;
2957   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2958   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2959   ierr    = PetscLogObjectMemory(fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2960   b->maxnz = b->nz = ui[am];
2961 
2962   fact->info.factor_mallocs    = reallocs;
2963   fact->info.fill_ratio_given  = fill;
2964   if (ai[am] != 0) {
2965     fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2966   } else {
2967     fact->info.fill_ratio_needed = 0.0;
2968   }
2969   fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2970   PetscFunctionReturn(0);
2971 }
2972 
2973 #undef __FUNCT__
2974 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ_inplace"
2975 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2976 {
2977   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2978   Mat_SeqSBAIJ       *b;
2979   PetscErrorCode     ierr;
2980   PetscTruth         perm_identity;
2981   PetscReal          fill = info->fill;
2982   const PetscInt     *rip,*riip;
2983   PetscInt           i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow;
2984   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
2985   PetscInt           nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr;
2986   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2987   PetscBT            lnkbt;
2988   IS                 iperm;
2989 
2990   PetscFunctionBegin;
2991   if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n);
2992   /* check whether perm is the identity mapping */
2993   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2994   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2995   ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2996   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2997 
2998   /* initialization */
2999   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
3000   ui[0] = 0;
3001 
3002   /* jl: linked list for storing indices of the pivot rows
3003      il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
3004   ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr);
3005   for (i=0; i<am; i++){
3006     jl[i] = am; il[i] = 0;
3007   }
3008 
3009   /* create and initialize a linked list for storing column indices of the active row k */
3010   nlnk = am + 1;
3011   ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3012 
3013   /* initial FreeSpace size is fill*(ai[am]+1) */
3014   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
3015   current_space = free_space;
3016 
3017   for (k=0; k<am; k++){  /* for each active row k */
3018     /* initialize lnk by the column indices of row rip[k] of A */
3019     nzk   = 0;
3020     ncols = ai[rip[k]+1] - ai[rip[k]];
3021     if (!ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
3022     ncols_upper = 0;
3023     for (j=0; j<ncols; j++){
3024       i = riip[*(aj + ai[rip[k]] + j)];
3025       if (i >= k){ /* only take upper triangular entry */
3026         cols[ncols_upper] = i;
3027         ncols_upper++;
3028       }
3029     }
3030     ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3031     nzk += nlnk;
3032 
3033     /* update lnk by computing fill-in for each pivot row to be merged in */
3034     prow = jl[k]; /* 1st pivot row */
3035 
3036     while (prow < k){
3037       nextprow = jl[prow];
3038       /* merge prow into k-th row */
3039       jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
3040       jmax = ui[prow+1];
3041       ncols = jmax-jmin;
3042       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */
3043       ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3044       nzk += nlnk;
3045 
3046       /* update il and jl for prow */
3047       if (jmin < jmax){
3048         il[prow] = jmin;
3049         j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
3050       }
3051       prow = nextprow;
3052     }
3053 
3054     /* if free space is not available, make more free space */
3055     if (current_space->local_remaining<nzk) {
3056       i = am - k + 1; /* num of unfactored rows */
3057       i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
3058       ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
3059       reallocs++;
3060     }
3061 
3062     /* copy data into free space, then initialize lnk */
3063     ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
3064 
3065     /* add the k-th row into il and jl */
3066     if (nzk-1 > 0){
3067       i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
3068       jl[k] = jl[i]; jl[i] = k;
3069       il[k] = ui[k] + 1;
3070     }
3071     ui_ptr[k] = current_space->array;
3072     current_space->array           += nzk;
3073     current_space->local_used      += nzk;
3074     current_space->local_remaining -= nzk;
3075 
3076     ui[k+1] = ui[k] + nzk;
3077   }
3078 
3079 #if defined(PETSC_USE_INFO)
3080   if (ai[am] != 0) {
3081     PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]);
3082     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
3083     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
3084     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
3085   } else {
3086      ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
3087   }
3088 #endif
3089 
3090   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
3091   ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
3092   ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr);
3093 
3094   /* destroy list of free space and other temporary array(s) */
3095   ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
3096   ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
3097   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
3098 
3099   /* put together the new matrix in MATSEQSBAIJ format */
3100 
3101   b = (Mat_SeqSBAIJ*)fact->data;
3102   b->singlemalloc = PETSC_FALSE;
3103   b->free_a       = PETSC_TRUE;
3104   b->free_ij      = PETSC_TRUE;
3105   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
3106   b->j    = uj;
3107   b->i    = ui;
3108   b->diag = 0;
3109   b->ilen = 0;
3110   b->imax = 0;
3111   b->row  = perm;
3112   b->col  = perm;
3113   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
3114   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
3115   b->icol = iperm;
3116   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
3117   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
3118   ierr    = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
3119   b->maxnz = b->nz = ui[am];
3120 
3121   fact->info.factor_mallocs    = reallocs;
3122   fact->info.fill_ratio_given  = fill;
3123   if (ai[am] != 0) {
3124     fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
3125   } else {
3126     fact->info.fill_ratio_needed = 0.0;
3127   }
3128   fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace;
3129   PetscFunctionReturn(0);
3130 }
3131 
3132 #undef __FUNCT__
3133 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering"
3134 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx)
3135 {
3136   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
3137   PetscErrorCode    ierr;
3138   PetscInt          n = A->rmap->n;
3139   const PetscInt    *ai = a->i,*aj = a->j,*adiag = a->diag,*vi;
3140   PetscScalar       *x,sum;
3141   const PetscScalar *b;
3142   const MatScalar   *aa = a->a,*v;
3143   PetscInt          i,nz;
3144 
3145   PetscFunctionBegin;
3146   if (!n) PetscFunctionReturn(0);
3147 
3148   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3149   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3150 
3151   /* forward solve the lower triangular */
3152   x[0] = b[0];
3153   v    = aa;
3154   vi   = aj;
3155   for (i=1; i<n; i++) {
3156     nz  = ai[i+1] - ai[i];
3157     sum = b[i];
3158     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
3159     v  += nz;
3160     vi += nz;
3161     x[i] = sum;
3162   }
3163 
3164   /* backward solve the upper triangular */
3165   for (i=n-1; i>=0; i--){
3166     v   = aa + adiag[i+1] + 1;
3167     vi  = aj + adiag[i+1] + 1;
3168     nz = adiag[i] - adiag[i+1]-1;
3169     sum = x[i];
3170     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
3171     x[i] = sum*v[nz]; /* x[i]=aa[adiag[i]]*sum; v++; */
3172   }
3173 
3174   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
3175   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3176   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3177   PetscFunctionReturn(0);
3178 }
3179 
3180 #undef __FUNCT__
3181 #define __FUNCT__ "MatSolve_SeqAIJ"
3182 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx)
3183 {
3184   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
3185   IS                iscol = a->col,isrow = a->row;
3186   PetscErrorCode    ierr;
3187   PetscInt          i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz;
3188   const PetscInt    *rout,*cout,*r,*c;
3189   PetscScalar       *x,*tmp,sum;
3190   const PetscScalar *b;
3191   const MatScalar   *aa = a->a,*v;
3192 
3193   PetscFunctionBegin;
3194   if (!n) PetscFunctionReturn(0);
3195 
3196   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3197   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3198   tmp  = a->solve_work;
3199 
3200   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
3201   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
3202 
3203   /* forward solve the lower triangular */
3204   tmp[0] = b[r[0]];
3205   v      = aa;
3206   vi     = aj;
3207   for (i=1; i<n; i++) {
3208     nz  = ai[i+1] - ai[i];
3209     sum = b[r[i]];
3210     PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
3211     tmp[i] = sum;
3212     v += nz; vi += nz;
3213   }
3214 
3215   /* backward solve the upper triangular */
3216   for (i=n-1; i>=0; i--){
3217     v   = aa + adiag[i+1]+1;
3218     vi  = aj + adiag[i+1]+1;
3219     nz  = adiag[i]-adiag[i+1]-1;
3220     sum = tmp[i];
3221     PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
3222     x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */
3223   }
3224 
3225   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
3226   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
3227   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3228   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3229   ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr);
3230   PetscFunctionReturn(0);
3231 }
3232 
3233 #undef __FUNCT__
3234 #define __FUNCT__ "MatILUDTFactor_SeqAIJ"
3235 /*
3236     This will get a new name and become a varient of MatILUFactor_SeqAIJ() there is no longer seperate functions in the matrix function table for dt factors
3237 */
3238 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact)
3239 {
3240   Mat                B = *fact;
3241   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b;
3242   IS                 isicol;
3243   PetscErrorCode     ierr;
3244   const PetscInt     *r,*ic;
3245   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag;
3246   PetscInt           *bi,*bj,*bdiag,*bdiag_rev;
3247   PetscInt           row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au;
3248   PetscInt           nlnk,*lnk;
3249   PetscBT            lnkbt;
3250   PetscTruth         row_identity,icol_identity,both_identity;
3251   MatScalar          *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp;
3252   const PetscInt     *ics;
3253   PetscInt           j,nz,*pj,*bjtmp,k,ncut,*jtmp;
3254   PetscReal          dt=info->dt,dtcol=info->dtcol,shift=info->shiftamount;
3255   PetscInt           dtcount=(PetscInt)info->dtcount,nnz_max;
3256   PetscTruth         missing;
3257 
3258   PetscFunctionBegin;
3259 
3260   if (dt      == PETSC_DEFAULT) dt      = 0.005;
3261   if (dtcol   == PETSC_DEFAULT) dtcol   = 0.01; /* XXX unused! */
3262   if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax);
3263 
3264   /* ------- symbolic factorization, can be reused ---------*/
3265   ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
3266   if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
3267   adiag=a->diag;
3268 
3269   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
3270 
3271   /* bdiag is location of diagonal in factor */
3272   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);     /* becomes b->diag */
3273   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag_rev);CHKERRQ(ierr); /* temporary */
3274 
3275   /* allocate row pointers bi */
3276   ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
3277 
3278   /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */
3279   if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */
3280   nnz_max  = ai[n]+2*n*dtcount+2;
3281 
3282   ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
3283   ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr);
3284 
3285   /* put together the new matrix */
3286   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
3287   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
3288   b    = (Mat_SeqAIJ*)B->data;
3289   b->free_a       = PETSC_TRUE;
3290   b->free_ij      = PETSC_TRUE;
3291   b->singlemalloc = PETSC_FALSE;
3292   b->a          = ba;
3293   b->j          = bj;
3294   b->i          = bi;
3295   b->diag       = bdiag;
3296   b->ilen       = 0;
3297   b->imax       = 0;
3298   b->row        = isrow;
3299   b->col        = iscol;
3300   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
3301   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
3302   b->icol       = isicol;
3303   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
3304 
3305   ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
3306   b->maxnz = nnz_max;
3307 
3308   B->factortype            = MAT_FACTOR_ILUDT;
3309   B->info.factor_mallocs   = 0;
3310   B->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]);
3311   CHKMEMQ;
3312   /* ------- end of symbolic factorization ---------*/
3313 
3314   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
3315   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
3316   ics  = ic;
3317 
3318   /* linked list for storing column indices of the active row */
3319   nlnk = n + 1;
3320   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3321 
3322   /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */
3323   ierr = PetscMalloc2(n,PetscInt,&im,n,PetscInt,&jtmp);CHKERRQ(ierr);
3324   /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */
3325   ierr = PetscMalloc2(n,MatScalar,&rtmp,n,MatScalar,&vtmp);CHKERRQ(ierr);
3326   ierr = PetscMemzero(rtmp,n*sizeof(MatScalar));CHKERRQ(ierr);
3327 
3328   bi[0]    = 0;
3329   bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */
3330   bdiag_rev[n] = bdiag[0];
3331   bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */
3332   for (i=0; i<n; i++) {
3333     /* copy initial fill into linked list */
3334     nzi = 0; /* nonzeros for active row i */
3335     nzi = ai[r[i]+1] - ai[r[i]];
3336     if (!nzi) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
3337     nzi_al = adiag[r[i]] - ai[r[i]];
3338     nzi_au = ai[r[i]+1] - adiag[r[i]] -1;
3339     ajtmp = aj + ai[r[i]];
3340     ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3341 
3342     /* load in initial (unfactored row) */
3343     aatmp = a->a + ai[r[i]];
3344     for (j=0; j<nzi; j++) {
3345       rtmp[ics[*ajtmp++]] = *aatmp++;
3346     }
3347 
3348     /* add pivot rows into linked list */
3349     row = lnk[n];
3350     while (row < i ) {
3351       nzi_bl = bi[row+1] - bi[row] + 1;
3352       bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */
3353       ierr  = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr);
3354       nzi  += nlnk;
3355       row   = lnk[row];
3356     }
3357 
3358     /* copy data from lnk into jtmp, then initialize lnk */
3359     ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr);
3360 
3361     /* numerical factorization */
3362     bjtmp = jtmp;
3363     row   = *bjtmp++; /* 1st pivot row */
3364     while  ( row < i ) {
3365       pc         = rtmp + row;
3366       pv         = ba + bdiag[row]; /* 1./(diag of the pivot row) */
3367       multiplier = (*pc) * (*pv);
3368       *pc        = multiplier;
3369       if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */
3370         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
3371         pv         = ba + bdiag[row+1] + 1;
3372         /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */
3373         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
3374         for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
3375         ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
3376       }
3377       row = *bjtmp++;
3378     }
3379 
3380     /* copy sparse rtmp into contiguous vtmp; separate L and U part */
3381     diag_tmp = rtmp[i];  /* save diagonal value - may not needed?? */
3382     nzi_bl = 0; j = 0;
3383     while (jtmp[j] < i){ /* Note: jtmp is sorted */
3384       vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
3385       nzi_bl++; j++;
3386     }
3387     nzi_bu = nzi - nzi_bl -1;
3388     while (j < nzi){
3389       vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
3390       j++;
3391     }
3392 
3393     bjtmp = bj + bi[i];
3394     batmp = ba + bi[i];
3395     /* apply level dropping rule to L part */
3396     ncut = nzi_al + dtcount;
3397     if (ncut < nzi_bl){
3398       ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr);
3399       ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr);
3400     } else {
3401       ncut = nzi_bl;
3402     }
3403     for (j=0; j<ncut; j++){
3404       bjtmp[j] = jtmp[j];
3405       batmp[j] = vtmp[j];
3406       /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */
3407     }
3408     bi[i+1] = bi[i] + ncut;
3409     nzi = ncut + 1;
3410 
3411     /* apply level dropping rule to U part */
3412     ncut = nzi_au + dtcount;
3413     if (ncut < nzi_bu){
3414       ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr);
3415       ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr);
3416     } else {
3417       ncut = nzi_bu;
3418     }
3419     nzi += ncut;
3420 
3421     /* mark bdiagonal */
3422     bdiag[i+1]       = bdiag[i] - (ncut + 1);
3423     bdiag_rev[n-i-1] = bdiag[i+1];
3424     bi[2*n - i]      = bi[2*n - i +1] - (ncut + 1);
3425     bjtmp = bj + bdiag[i];
3426     batmp = ba + bdiag[i];
3427     *bjtmp = i;
3428     *batmp = diag_tmp; /* rtmp[i]; */
3429     if (*batmp == 0.0) {
3430       *batmp = dt+shift;
3431       /* printf(" row %d add shift %g\n",i,shift); */
3432     }
3433     *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */
3434     /* printf(" (%d,%g),",*bjtmp,*batmp); */
3435 
3436     bjtmp = bj + bdiag[i+1]+1;
3437     batmp = ba + bdiag[i+1]+1;
3438     for (k=0; k<ncut; k++){
3439       bjtmp[k] = jtmp[nzi_bl+1+k];
3440       batmp[k] = vtmp[nzi_bl+1+k];
3441       /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */
3442     }
3443     /* printf("\n"); */
3444 
3445     im[i]   = nzi; /* used by PetscLLAddSortedLU() */
3446     /*
3447     printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]);
3448     printf(" ----------------------------\n");
3449     */
3450   } /* for (i=0; i<n; i++) */
3451   /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */
3452   if (bi[n] >= bdiag[n]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"end of L array %d cannot >= the beginning of U array %d",bi[n],bdiag[n]);
3453 
3454   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
3455   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
3456 
3457   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
3458   ierr = PetscFree2(im,jtmp);CHKERRQ(ierr);
3459   ierr = PetscFree2(rtmp,vtmp);CHKERRQ(ierr);
3460   ierr = PetscFree(bdiag_rev);CHKERRQ(ierr);
3461 
3462   ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr);
3463   b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n];
3464 
3465   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
3466   ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr);
3467   both_identity = (PetscTruth) (row_identity && icol_identity);
3468   if (row_identity && icol_identity) {
3469     B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering;
3470   } else {
3471     B->ops->solve = MatSolve_SeqAIJ;
3472   }
3473 
3474   B->ops->solveadd          = 0;
3475   B->ops->solvetranspose    = 0;
3476   B->ops->solvetransposeadd = 0;
3477   B->ops->matsolve          = 0;
3478   B->assembled              = PETSC_TRUE;
3479   B->preallocated           = PETSC_TRUE;
3480   PetscFunctionReturn(0);
3481 }
3482 
3483 /* a wraper of MatILUDTFactor_SeqAIJ() */
3484 #undef __FUNCT__
3485 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ"
3486 /*
3487     This will get a new name and become a varient of MatILUFactor_SeqAIJ() there is no longer seperate functions in the matrix function table for dt factors
3488 */
3489 
3490 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info)
3491 {
3492   PetscErrorCode     ierr;
3493 
3494   PetscFunctionBegin;
3495   ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr);
3496   PetscFunctionReturn(0);
3497 }
3498 
3499 /*
3500    same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors
3501    - intend to replace existing MatLUFactorNumeric_SeqAIJ()
3502 */
3503 #undef __FUNCT__
3504 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ"
3505 /*
3506     This will get a new name and become a varient of MatILUFactor_SeqAIJ() there is no longer seperate functions in the matrix function table for dt factors
3507 */
3508 
3509 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info)
3510 {
3511   Mat            C=fact;
3512   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
3513   IS             isrow = b->row,isicol = b->icol;
3514   PetscErrorCode ierr;
3515   const PetscInt *r,*ic,*ics;
3516   PetscInt       i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
3517   PetscInt       *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj;
3518   MatScalar      *rtmp,*pc,multiplier,*v,*pv,*aa=a->a;
3519   PetscReal      dt=info->dt,shift=info->shiftamount;
3520   PetscTruth     row_identity, col_identity;
3521 
3522   PetscFunctionBegin;
3523   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
3524   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
3525   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
3526   ics  = ic;
3527 
3528   for (i=0; i<n; i++){
3529     /* initialize rtmp array */
3530     nzl   = bi[i+1] - bi[i];       /* num of nozeros in L(i,:) */
3531     bjtmp = bj + bi[i];
3532     for  (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0;
3533     rtmp[i] = 0.0;
3534     nzu   = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */
3535     bjtmp = bj + bdiag[i+1] + 1;
3536     for  (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0;
3537 
3538     /* load in initial unfactored row of A */
3539     /* printf("row %d\n",i); */
3540     nz    = ai[r[i]+1] - ai[r[i]];
3541     ajtmp = aj + ai[r[i]];
3542     v     = aa + ai[r[i]];
3543     for (j=0; j<nz; j++) {
3544       rtmp[ics[*ajtmp++]] = v[j];
3545       /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */
3546     }
3547     /* printf("\n"); */
3548 
3549     /* numerical factorization */
3550     bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */
3551     nzl   = bi[i+1] - bi[i]; /* num of entries in L(i,:) */
3552     k = 0;
3553     while (k < nzl){
3554       row   = *bjtmp++;
3555       /* printf("  prow %d\n",row); */
3556       pc         = rtmp + row;
3557       pv         = b->a + bdiag[row]; /* 1./(diag of the pivot row) */
3558       multiplier = (*pc) * (*pv);
3559       *pc        = multiplier;
3560       if (PetscAbsScalar(multiplier) > dt){
3561         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
3562         pv         = b->a + bdiag[row+1] + 1;
3563         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
3564         for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
3565         /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */
3566       }
3567       k++;
3568     }
3569 
3570     /* finished row so stick it into b->a */
3571     /* L-part */
3572     pv = b->a + bi[i] ;
3573     pj = bj + bi[i] ;
3574     nzl = bi[i+1] - bi[i];
3575     for (j=0; j<nzl; j++) {
3576       pv[j] = rtmp[pj[j]];
3577       /* printf(" (%d,%g),",pj[j],pv[j]); */
3578     }
3579 
3580     /* diagonal: invert diagonal entries for simplier triangular solves */
3581     if (rtmp[i] == 0.0) rtmp[i] = dt+shift;
3582     b->a[bdiag[i]] = 1.0/rtmp[i];
3583     /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */
3584 
3585     /* U-part */
3586     pv = b->a + bdiag[i+1] + 1;
3587     pj = bj + bdiag[i+1] + 1;
3588     nzu = bdiag[i] - bdiag[i+1] - 1;
3589     for (j=0; j<nzu; j++) {
3590       pv[j] = rtmp[pj[j]];
3591       /* printf(" (%d,%g),",pj[j],pv[j]); */
3592     }
3593     /* printf("\n"); */
3594   }
3595 
3596   ierr = PetscFree(rtmp);CHKERRQ(ierr);
3597   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
3598   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
3599 
3600   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
3601   ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
3602   if (row_identity && col_identity) {
3603     C->ops->solve   = MatSolve_SeqAIJ_NaturalOrdering;
3604   } else {
3605     C->ops->solve   = MatSolve_SeqAIJ;
3606   }
3607   C->ops->solveadd           = 0;
3608   C->ops->solvetranspose     = 0;
3609   C->ops->solvetransposeadd  = 0;
3610   C->ops->matsolve           = 0;
3611   C->assembled    = PETSC_TRUE;
3612   C->preallocated = PETSC_TRUE;
3613   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
3614   PetscFunctionReturn(0);
3615 }
3616