xref: /petsc/src/mat/impls/aij/seq/aijfact.c (revision a32cbb58efe773605c619767ecb22dbf0b1d6daf)
1 #define PETSCMAT_DLL
2 
3 
4 #include "../src/mat/impls/aij/seq/aij.h"
5 #include "../src/mat/impls/sbaij/seq/sbaij.h"
6 #include "petscbt.h"
7 #include "../src/mat/utils/freespace.h"
8 
9 EXTERN_C_BEGIN
10 #undef __FUNCT__
11 #define __FUNCT__ "MatOrdering_Flow_SeqAIJ"
12 /*
13       Computes an ordering to get most of the large numerical values in the lower triangular part of the matrix
14 */
15 PetscErrorCode MatOrdering_Flow_SeqAIJ(Mat mat,const MatOrderingType type,IS *irow,IS *icol)
16 {
17   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)mat->data;
18   PetscErrorCode    ierr;
19   PetscInt          i,j,jj,k, kk,n = mat->rmap->n, current = 0, newcurrent = 0,*order;
20   const PetscInt    *ai = a->i, *aj = a->j;
21   const PetscScalar *aa = a->a;
22   PetscTruth        *done;
23   PetscReal         best,past = 0,future;
24 
25   PetscFunctionBegin;
26   /* pick initial row */
27   best = -1;
28   for (i=0; i<n; i++) {
29     future = 0.0;
30     for (j=ai[i]; j<ai[i+1]; j++) {
31       if (aj[j] != i) future  += PetscAbsScalar(aa[j]); else past = PetscAbsScalar(aa[j]);
32     }
33     if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */
34     if (past/future > best) {
35       best = past/future;
36       current = i;
37     }
38   }
39 
40   ierr = PetscMalloc(n*sizeof(PetscTruth),&done);CHKERRQ(ierr);
41   ierr = PetscMemzero(done,n*sizeof(PetscTruth));CHKERRQ(ierr);
42   ierr = PetscMalloc(n*sizeof(PetscInt),&order);CHKERRQ(ierr);
43   order[0] = current;
44   for (i=0; i<n-1; i++) {
45     done[current] = PETSC_TRUE;
46     best          = -1;
47     /* loop over all neighbors of current pivot */
48     for (j=ai[current]; j<ai[current+1]; j++) {
49       jj = aj[j];
50       if (done[jj]) continue;
51       /* loop over columns of potential next row computing weights for below and above diagonal */
52       past = future = 0.0;
53       for (k=ai[jj]; k<ai[jj+1]; k++) {
54         kk = aj[k];
55         if (done[kk]) past += PetscAbsScalar(aa[k]);
56         else if (kk != jj) future  += PetscAbsScalar(aa[k]);
57       }
58       if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */
59       if (past/future > best) {
60         best = past/future;
61         newcurrent = jj;
62       }
63     }
64     if (best == -1) { /* no neighbors to select from so select best of all that remain */
65       best = -1;
66       for (k=0; k<n; k++) {
67         if (done[k]) continue;
68         future = 0.0;
69         past   = 0.0;
70         for (j=ai[k]; j<ai[k+1]; j++) {
71           kk = aj[j];
72           if (done[kk]) past += PetscAbsScalar(aa[j]);
73           else if (kk != k) future  += PetscAbsScalar(aa[j]);
74         }
75         if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */
76         if (past/future > best) {
77           best = past/future;
78           newcurrent = k;
79         }
80       }
81     }
82     if (current == newcurrent) SETERRQ(PETSC_ERR_PLIB,"newcurrent cannot be current");
83     current = newcurrent;
84     order[i+1] = current;
85   }
86   ierr = ISCreateGeneral(PETSC_COMM_SELF,n,order,irow);CHKERRQ(ierr);
87   *icol = *irow;
88   ierr = PetscObjectReference((PetscObject)*irow);CHKERRQ(ierr);
89   ierr = PetscFree(done);CHKERRQ(ierr);
90   ierr = PetscFree(order);CHKERRQ(ierr);
91   PetscFunctionReturn(0);
92 }
93 EXTERN_C_END
94 
95 EXTERN_C_BEGIN
96 #undef __FUNCT__
97 #define __FUNCT__ "MatGetFactorAvailable_seqaij_petsc"
98 PetscErrorCode MatGetFactorAvailable_seqaij_petsc(Mat A,MatFactorType ftype,PetscTruth *flg)
99 {
100   PetscFunctionBegin;
101   *flg = PETSC_TRUE;
102   PetscFunctionReturn(0);
103 }
104 EXTERN_C_END
105 
106 EXTERN_C_BEGIN
107 #undef __FUNCT__
108 #define __FUNCT__ "MatGetFactor_seqaij_petsc"
109 PetscErrorCode MatGetFactor_seqaij_petsc(Mat A,MatFactorType ftype,Mat *B)
110 {
111   PetscInt           n = A->rmap->n;
112   PetscErrorCode     ierr;
113 
114   PetscFunctionBegin;
115   ierr = MatCreate(((PetscObject)A)->comm,B);CHKERRQ(ierr);
116   ierr = MatSetSizes(*B,n,n,n,n);CHKERRQ(ierr);
117   if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT){
118     ierr = MatSetType(*B,MATSEQAIJ);CHKERRQ(ierr);
119     (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqAIJ;
120     (*B)->ops->lufactorsymbolic  = MatLUFactorSymbolic_SeqAIJ;
121   } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) {
122     ierr = MatSetType(*B,MATSEQSBAIJ);CHKERRQ(ierr);
123     ierr = MatSeqSBAIJSetPreallocation(*B,1,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
124     (*B)->ops->iccfactorsymbolic      = MatICCFactorSymbolic_SeqAIJ;
125     (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJ;
126   } else SETERRQ(PETSC_ERR_SUP,"Factor type not supported");
127   (*B)->factor = ftype;
128   PetscFunctionReturn(0);
129 }
130 EXTERN_C_END
131 
132 #undef __FUNCT__
133 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ_inplace"
134 PetscErrorCode MatLUFactorSymbolic_SeqAIJ_inplace(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
135 {
136   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
137   IS                 isicol;
138   PetscErrorCode     ierr;
139   const PetscInt     *r,*ic;
140   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j;
141   PetscInt           *bi,*bj,*ajtmp;
142   PetscInt           *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im;
143   PetscReal          f;
144   PetscInt           nlnk,*lnk,k,**bi_ptr;
145   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
146   PetscBT            lnkbt;
147 
148   PetscFunctionBegin;
149   if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square");
150   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
151   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
152   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
153 
154   /* get new row pointers */
155   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
156   bi[0] = 0;
157 
158   /* bdiag is location of diagonal in factor */
159   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
160   bdiag[0] = 0;
161 
162   /* linked list for storing column indices of the active row */
163   nlnk = n + 1;
164   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
165 
166   ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr);
167 
168   /* initial FreeSpace size is f*(ai[n]+1) */
169   f = info->fill;
170   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
171   current_space = free_space;
172 
173   for (i=0; i<n; i++) {
174     /* copy previous fill into linked list */
175     nzi = 0;
176     nnz = ai[r[i]+1] - ai[r[i]];
177     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
178     ajtmp = aj + ai[r[i]];
179     ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
180     nzi += nlnk;
181 
182     /* add pivot rows into linked list */
183     row = lnk[n];
184     while (row < i) {
185       nzbd    = bdiag[row] - bi[row] + 1; /* num of entries in the row with column index <= row */
186       ajtmp   = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */
187       ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr);
188       nzi += nlnk;
189       row  = lnk[row];
190     }
191     bi[i+1] = bi[i] + nzi;
192     im[i]   = nzi;
193 
194     /* mark bdiag */
195     nzbd = 0;
196     nnz  = nzi;
197     k    = lnk[n];
198     while (nnz-- && k < i){
199       nzbd++;
200       k = lnk[k];
201     }
202     bdiag[i] = bi[i] + nzbd;
203 
204     /* if free space is not available, make more free space */
205     if (current_space->local_remaining<nzi) {
206       nnz = (n - i)*nzi; /* estimated and max additional space needed */
207       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
208       reallocs++;
209     }
210 
211     /* copy data into free space, then initialize lnk */
212     ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
213     bi_ptr[i] = current_space->array;
214     current_space->array           += nzi;
215     current_space->local_used      += nzi;
216     current_space->local_remaining -= nzi;
217   }
218 #if defined(PETSC_USE_INFO)
219   if (ai[n] != 0) {
220     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
221     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
222     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
223     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr);
224     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
225   } else {
226     ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr);
227   }
228 #endif
229 
230   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
231   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
232 
233   /* destroy list of free space and other temporary array(s) */
234   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
235   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
236   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
237   ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr);
238 
239   /* put together the new matrix */
240   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
241   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
242   b    = (Mat_SeqAIJ*)(B)->data;
243   b->free_a       = PETSC_TRUE;
244   b->free_ij      = PETSC_TRUE;
245   b->singlemalloc = PETSC_FALSE;
246   ierr          = PetscMalloc((bi[n]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
247   b->j          = bj;
248   b->i          = bi;
249   b->diag       = bdiag;
250   b->ilen       = 0;
251   b->imax       = 0;
252   b->row        = isrow;
253   b->col        = iscol;
254   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
255   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
256   b->icol       = isicol;
257   ierr          = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
258 
259   /* In b structure:  Free imax, ilen, old a, old j.  Allocate solve_work, new a, new j */
260   ierr = PetscLogObjectMemory(B,(bi[n]-n)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
261   b->maxnz = b->nz = bi[n] ;
262 
263   (B)->factor                = MAT_FACTOR_LU;
264   (B)->info.factor_mallocs   = reallocs;
265   (B)->info.fill_ratio_given = f;
266 
267   if (ai[n]) {
268     (B)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
269   } else {
270     (B)->info.fill_ratio_needed = 0.0;
271   }
272   (B)->ops->lufactornumeric  = MatLUFactorNumeric_SeqAIJ_inplace;
273   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 
305   if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square");
306   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
307   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
308   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
309 
310   /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
311   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
312   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
313   bi[0] = bdiag[0] = 0;
314 
315   /* linked list for storing column indices of the active row */
316   nlnk = n + 1;
317   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
318 
319   ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr);
320 
321   /* initial FreeSpace size is f*(ai[n]+1) */
322   f = info->fill;
323   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
324   current_space = free_space;
325 
326   for (i=0; i<n; i++) {
327     /* copy previous fill into linked list */
328     nzi = 0;
329     nnz = ai[r[i]+1] - ai[r[i]];
330     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
331     ajtmp = aj + ai[r[i]];
332     ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
333     nzi += nlnk;
334 
335     /* add pivot rows into linked list */
336     row = lnk[n];
337     while (row < i){
338       nzbd  = bdiag[row] + 1; /* num of entries in the row with column index <= row */
339       ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */
340       ierr  = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr);
341       nzi  += nlnk;
342       row   = lnk[row];
343     }
344     bi[i+1] = bi[i] + nzi;
345     im[i]   = nzi;
346 
347     /* mark bdiag */
348     nzbd = 0;
349     nnz  = nzi;
350     k    = lnk[n];
351     while (nnz-- && k < i){
352       nzbd++;
353       k = lnk[k];
354     }
355     bdiag[i] = nzbd; /* note: bdiag[i] = nnzL as input for PetscFreeSpaceContiguous_LU() */
356 
357     /* if free space is not available, make more free space */
358     if (current_space->local_remaining<nzi) {
359       nnz = 2*(n - i)*nzi; /* estimated and max additional space needed */
360       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
361       reallocs++;
362     }
363 
364     /* copy data into free space, then initialize lnk */
365     ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
366     bi_ptr[i] = current_space->array;
367     current_space->array           += nzi;
368     current_space->local_used      += nzi;
369     current_space->local_remaining -= nzi;
370   }
371 #if defined(PETSC_USE_INFO)
372   if (ai[n] != 0) {
373     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
374     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
375     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
376     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr);
377     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
378   } else {
379     ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr);
380   }
381 #endif
382 
383   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
384   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
385 
386   /* destroy list of free space and other temporary array(s) */
387   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
388   ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr);
389   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
390   ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr);
391 
392   /* put together the new matrix */
393   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
394   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
395   b    = (Mat_SeqAIJ*)(B)->data;
396   b->free_a       = PETSC_TRUE;
397   b->free_ij      = PETSC_TRUE;
398   b->singlemalloc = PETSC_FALSE;
399   ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
400   b->j          = bj;
401   b->i          = bi;
402   b->diag       = bdiag;
403   b->ilen       = 0;
404   b->imax       = 0;
405   b->row        = isrow;
406   b->col        = iscol;
407   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
408   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
409   b->icol       = isicol;
410   ierr          = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
411 
412   /* In b structure:  Free imax, ilen, old a, old j.  Allocate solve_work, new a, new j */
413   ierr = PetscLogObjectMemory(B,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
414   b->maxnz = b->nz = bdiag[0]+1;
415   B->factor                = MAT_FACTOR_LU;
416   B->info.factor_mallocs   = reallocs;
417   B->info.fill_ratio_given = f;
418 
419   if (ai[n]) {
420     B->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]);
421   } else {
422     B->info.fill_ratio_needed = 0.0;
423   }
424   B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ;
425   if (a->inode.size) {
426     B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode;
427   }
428   PetscFunctionReturn(0);
429 }
430 
431 /*
432     Trouble in factorization, should we dump the original matrix?
433 */
434 #undef __FUNCT__
435 #define __FUNCT__ "MatFactorDumpMatrix"
436 PetscErrorCode MatFactorDumpMatrix(Mat A)
437 {
438   PetscErrorCode ierr;
439   PetscTruth     flg = PETSC_FALSE;
440 
441   PetscFunctionBegin;
442   ierr = PetscOptionsGetTruth(PETSC_NULL,"-mat_factor_dump_on_error",&flg,PETSC_NULL);CHKERRQ(ierr);
443   if (flg) {
444     PetscViewer viewer;
445     char        filename[PETSC_MAX_PATH_LEN];
446 
447     ierr = PetscSNPrintf(filename,PETSC_MAX_PATH_LEN,"matrix_factor_error.%d",PetscGlobalRank);CHKERRQ(ierr);
448     ierr = PetscViewerBinaryOpen(((PetscObject)A)->comm,filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr);
449     ierr = MatView(A,viewer);CHKERRQ(ierr);
450     ierr = PetscViewerDestroy(viewer);CHKERRQ(ierr);
451   }
452   PetscFunctionReturn(0);
453 }
454 
455 #undef __FUNCT__
456 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ"
457 PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info)
458 {
459   Mat              C=B;
460   Mat_SeqAIJ       *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
461   IS               isrow = b->row,isicol = b->icol;
462   PetscErrorCode   ierr;
463   const PetscInt   *r,*ic,*ics;
464   const PetscInt   n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bdiag=b->diag;
465   PetscInt         i,j,k,nz,nzL,row,*pj;
466   const PetscInt   *ajtmp,*bjtmp;
467   MatScalar        *rtmp,*pc,multiplier,*pv;
468   const  MatScalar *aa=a->a,*v;
469   PetscTruth       row_identity,col_identity;
470   FactorShiftCtx   sctx;
471   const PetscInt   *ddiag;
472   PetscReal        rs;
473   MatScalar        d;
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);CHKERRQ(ierr);
567       rtmp[i] = sctx.pv;
568 
569       /* Mark diagonal and invert diagonal for simplier triangular solves */
570       pv  = b->a + bdiag[i];
571       *pv = 1.0/rtmp[i];
572 
573     } /* endof for (i=0; i<n; i++){ */
574 
575     /* MatPivotRefine() */
576     if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.useshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max){
577       /*
578        * if no shift in this attempt & shifting & started shifting & can refine,
579        * then try lower shift
580        */
581       sctx.shift_hi       = sctx.shift_fraction;
582       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
583       sctx.shift_amount   = sctx.shift_fraction * sctx.shift_top;
584       sctx.useshift        = PETSC_TRUE;
585       sctx.nshift++;
586     }
587   } while (sctx.useshift);
588 
589   ierr = PetscFree(rtmp);CHKERRQ(ierr);
590   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
591   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
592 
593   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
594   ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
595   if (row_identity && col_identity) {
596     C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering;
597   } else {
598     C->ops->solve = MatSolve_SeqAIJ;
599   }
600   C->ops->solveadd           = MatSolveAdd_SeqAIJ;
601   C->ops->solvetranspose     = MatSolveTranspose_SeqAIJ;
602   C->ops->solvetransposeadd  = MatSolveTransposeAdd_SeqAIJ;
603   C->ops->matsolve           = MatMatSolve_SeqAIJ;
604   C->assembled    = PETSC_TRUE;
605   C->preallocated = PETSC_TRUE;
606   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
607 
608   /* MatShiftView(A,info,&sctx) */
609   if (sctx.nshift){
610     if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
611       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);
612     } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
613       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
614     } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS){
615       ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftamount);CHKERRQ(ierr);
616     }
617   }
618   ierr = Mat_CheckInode_FactorLU(C,PETSC_FALSE);CHKERRQ(ierr);
619   PetscFunctionReturn(0);
620 }
621 
622 #undef __FUNCT__
623 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_inplace"
624 PetscErrorCode MatLUFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info)
625 {
626   Mat             C=B;
627   Mat_SeqAIJ      *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
628   IS              isrow = b->row,isicol = b->icol;
629   PetscErrorCode  ierr;
630   const PetscInt   *r,*ic,*ics;
631   PetscInt        nz,row,i,j,n=A->rmap->n,diag;
632   const PetscInt  *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
633   const PetscInt  *ajtmp,*bjtmp,*diag_offset = b->diag,*pj;
634   MatScalar       *pv,*rtmp,*pc,multiplier,d;
635   const MatScalar *v,*aa=a->a;
636   PetscReal       rs=0.0;
637   FactorShiftCtx  sctx;
638   PetscInt        newshift;
639   const PetscInt  *ddiag;
640   PetscTruth      row_identity, col_identity;
641 
642   PetscFunctionBegin;
643   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
644   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
645   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
646   ics  = ic;
647 
648   /* initialize shift context sctx */
649   sctx.nshift         = 0;
650   sctx.nshift_max     = 0;
651   sctx.shift_top      = 0.0;
652   sctx.shift_lo       = 0.0;
653   sctx.shift_hi       = 0.0;
654   sctx.shift_fraction = 0.0;
655   sctx.shift_amount   = 0.0;
656 
657   if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
658     ddiag          = a->diag;
659     sctx.shift_top = info->zeropivot;
660     for (i=0; i<n; i++) {
661       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
662       d  = (aa)[ddiag[i]];
663       rs = -PetscAbsScalar(d) - PetscRealPart(d);
664       v  = aa+ai[i];
665       nz = ai[i+1] - ai[i];
666       for (j=0; j<nz; j++)
667 	rs += PetscAbsScalar(v[j]);
668       if (rs>sctx.shift_top) sctx.shift_top = rs;
669     }
670     sctx.shift_top   *= 1.1;
671     sctx.nshift_max   = 5;
672     sctx.shift_lo     = 0.;
673     sctx.shift_hi     = 1.;
674   }
675 
676   do {
677     sctx.useshift = PETSC_FALSE;
678     for (i=0; i<n; i++){
679       nz    = bi[i+1] - bi[i];
680       bjtmp = bj + bi[i];
681       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
682 
683       /* load in initial (unfactored row) */
684       nz    = ai[r[i]+1] - ai[r[i]];
685       ajtmp = aj + ai[r[i]];
686       v     = aa + ai[r[i]];
687       for (j=0; j<nz; j++) {
688         rtmp[ics[ajtmp[j]]] = v[j];
689       }
690       rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */
691       /* if (sctx.shift_amount > 0.0) printf("row %d, shift %g\n",i,sctx.shift_amount); */
692 
693       row = *bjtmp++;
694       while  (row < i) {
695         pc = rtmp + row;
696         if (*pc != 0.0) {
697           pv         = b->a + diag_offset[row];
698           pj         = b->j + diag_offset[row] + 1;
699           multiplier = *pc / *pv++;
700           *pc        = multiplier;
701           nz         = bi[row+1] - diag_offset[row] - 1;
702           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
703           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
704         }
705         row = *bjtmp++;
706       }
707       /* finished row so stick it into b->a */
708       pv   = b->a + bi[i] ;
709       pj   = b->j + bi[i] ;
710       nz   = bi[i+1] - bi[i];
711       diag = diag_offset[i] - bi[i];
712       rs   = 0.0;
713       for (j=0; j<nz; j++) {
714         pv[j] = rtmp[pj[j]];
715         rs   += PetscAbsScalar(pv[j]);
716       }
717       rs   -= PetscAbsScalar(pv[diag]);
718 
719       /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */
720       sctx.rs  = rs;
721       sctx.pv  = pv[diag];
722       ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr);
723       if (newshift == 1) break;
724     }
725 
726     if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.useshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
727       /*
728        * if no shift in this attempt & shifting & started shifting & can refine,
729        * then try lower shift
730        */
731       sctx.shift_hi       = sctx.shift_fraction;
732       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
733       sctx.shift_amount   = sctx.shift_fraction * sctx.shift_top;
734       sctx.useshift        = PETSC_TRUE;
735       sctx.nshift++;
736     }
737   } while (sctx.useshift);
738 
739   /* invert diagonal entries for simplier triangular solves */
740   for (i=0; i<n; i++) {
741     b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]];
742   }
743   ierr = PetscFree(rtmp);CHKERRQ(ierr);
744   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
745   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
746 
747   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
748   ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
749   if (row_identity && col_identity) {
750     C->ops->solve   = MatSolve_SeqAIJ_NaturalOrdering_inplace;
751   } else {
752     C->ops->solve   = MatSolve_SeqAIJ_inplace;
753   }
754   C->ops->solveadd           = MatSolveAdd_SeqAIJ_inplace;
755   C->ops->solvetranspose     = MatSolveTranspose_SeqAIJ_inplace;
756   C->ops->solvetransposeadd  = MatSolveTransposeAdd_SeqAIJ_inplace;
757   C->ops->matsolve           = MatMatSolve_SeqAIJ_inplace;
758   C->assembled    = PETSC_TRUE;
759   C->preallocated = PETSC_TRUE;
760   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
761   if (sctx.nshift){
762      if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
763       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);
764     } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
765       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
766     }
767   }
768   (C)->ops->solve            = MatSolve_SeqAIJ_inplace;
769   (C)->ops->solvetranspose   = MatSolveTranspose_SeqAIJ_inplace;
770   ierr = Mat_CheckInode(C,PETSC_FALSE);CHKERRQ(ierr);
771   PetscFunctionReturn(0);
772 }
773 
774 /*
775    This routine implements inplace ILU(0) with row or/and column permutations.
776    Input:
777      A - original matrix
778    Output;
779      A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i]
780          a->j (col index) is permuted by the inverse of colperm, then sorted
781          a->a reordered accordingly with a->j
782          a->diag (ptr to diagonal elements) is updated.
783 */
784 #undef __FUNCT__
785 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_InplaceWithPerm"
786 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info)
787 {
788   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
789   IS             isrow = a->row,isicol = a->icol;
790   PetscErrorCode ierr;
791   const PetscInt *r,*ic,*ics;
792   PetscInt       i,j,n=A->rmap->n,*ai=a->i,*aj=a->j;
793   PetscInt       *ajtmp,nz,row;
794   PetscInt       *diag = a->diag,nbdiag,*pj;
795   PetscScalar    *rtmp,*pc,multiplier,d;
796   MatScalar      *v,*pv;
797   PetscReal      rs;
798   FactorShiftCtx sctx;
799   PetscInt       newshift;
800 
801   PetscFunctionBegin;
802   if (A != B) SETERRQ(PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address");
803   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
804   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
805   ierr  = PetscMalloc((n+1)*sizeof(PetscScalar),&rtmp);CHKERRQ(ierr);
806   ierr  = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr);
807   ics = ic;
808 
809   sctx.shift_top      = 0.;
810   sctx.nshift_max     = 0;
811   sctx.shift_lo       = 0.;
812   sctx.shift_hi       = 0.;
813   sctx.shift_fraction = 0.;
814 
815   if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
816     sctx.shift_top = 0.;
817     for (i=0; i<n; i++) {
818       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
819       d  = (a->a)[diag[i]];
820       rs = -PetscAbsScalar(d) - PetscRealPart(d);
821       v  = a->a+ai[i];
822       nz = ai[i+1] - ai[i];
823       for (j=0; j<nz; j++)
824 	rs += PetscAbsScalar(v[j]);
825       if (rs>sctx.shift_top) sctx.shift_top = rs;
826     }
827     if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot;
828     sctx.shift_top    *= 1.1;
829     sctx.nshift_max   = 5;
830     sctx.shift_lo     = 0.;
831     sctx.shift_hi     = 1.;
832   }
833 
834   sctx.shift_amount = 0.;
835   sctx.nshift       = 0;
836   do {
837     sctx.useshift = PETSC_FALSE;
838     for (i=0; i<n; i++){
839       /* load in initial unfactored row */
840       nz    = ai[r[i]+1] - ai[r[i]];
841       ajtmp = aj + ai[r[i]];
842       v     = a->a + ai[r[i]];
843       /* sort permuted ajtmp and values v accordingly */
844       for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]];
845       ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr);
846 
847       diag[r[i]] = ai[r[i]];
848       for (j=0; j<nz; j++) {
849         rtmp[ajtmp[j]] = v[j];
850         if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */
851       }
852       rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */
853 
854       row = *ajtmp++;
855       while  (row < i) {
856         pc = rtmp + row;
857         if (*pc != 0.0) {
858           pv         = a->a + diag[r[row]];
859           pj         = aj + diag[r[row]] + 1;
860 
861           multiplier = *pc / *pv++;
862           *pc        = multiplier;
863           nz         = ai[r[row]+1] - diag[r[row]] - 1;
864           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
865           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
866         }
867         row = *ajtmp++;
868       }
869       /* finished row so overwrite it onto a->a */
870       pv   = a->a + ai[r[i]] ;
871       pj   = aj + ai[r[i]] ;
872       nz   = ai[r[i]+1] - ai[r[i]];
873       nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */
874 
875       rs   = 0.0;
876       for (j=0; j<nz; j++) {
877         pv[j] = rtmp[pj[j]];
878         if (j != nbdiag) rs += PetscAbsScalar(pv[j]);
879       }
880 
881       /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */
882       sctx.rs  = rs;
883       sctx.pv  = pv[nbdiag];
884       ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr);
885       if (newshift == 1) break;
886     }
887 
888     if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.useshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
889       /*
890        * if no shift in this attempt & shifting & started shifting & can refine,
891        * then try lower shift
892        */
893       sctx.shift_hi        = sctx.shift_fraction;
894       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
895       sctx.shift_amount    = sctx.shift_fraction * sctx.shift_top;
896       sctx.useshift         = PETSC_TRUE;
897       sctx.nshift++;
898     }
899   } while (sctx.useshift);
900 
901   /* invert diagonal entries for simplier triangular solves */
902   for (i=0; i<n; i++) {
903     a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]];
904   }
905 
906   ierr = PetscFree(rtmp);CHKERRQ(ierr);
907   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
908   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
909   A->ops->solve             = MatSolve_SeqAIJ_InplaceWithPerm;
910   A->ops->solveadd          = MatSolveAdd_SeqAIJ_inplace;
911   A->ops->solvetranspose    = MatSolveTranspose_SeqAIJ_inplace;
912   A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_inplace;
913   A->assembled = PETSC_TRUE;
914   A->preallocated = PETSC_TRUE;
915   ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr);
916   if (sctx.nshift){
917     if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
918       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);
919     } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
920       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
921     }
922   }
923   PetscFunctionReturn(0);
924 }
925 
926 /* ----------------------------------------------------------- */
927 #undef __FUNCT__
928 #define __FUNCT__ "MatLUFactor_SeqAIJ"
929 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info)
930 {
931   PetscErrorCode ierr;
932   Mat            C;
933 
934   PetscFunctionBegin;
935   ierr = MatGetFactor(A,MAT_SOLVER_PETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr);
936   ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr);
937   ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr);
938   A->ops->solve            = C->ops->solve;
939   A->ops->solvetranspose   = C->ops->solvetranspose;
940   ierr = MatHeaderCopy(A,C);CHKERRQ(ierr);
941   ierr = PetscLogObjectParent(A,((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr);
942   PetscFunctionReturn(0);
943 }
944 /* ----------------------------------------------------------- */
945 
946 
947 #undef __FUNCT__
948 #define __FUNCT__ "MatSolve_SeqAIJ_inplace"
949 PetscErrorCode MatSolve_SeqAIJ_inplace(Mat A,Vec bb,Vec xx)
950 {
951   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
952   IS                iscol = a->col,isrow = a->row;
953   PetscErrorCode    ierr;
954   PetscInt          i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
955   PetscInt          nz;
956   const PetscInt    *rout,*cout,*r,*c;
957   PetscScalar       *x,*tmp,*tmps,sum;
958   const PetscScalar *b;
959   const MatScalar   *aa = a->a,*v;
960 
961   PetscFunctionBegin;
962   if (!n) PetscFunctionReturn(0);
963 
964   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
965   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
966   tmp  = a->solve_work;
967 
968   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
969   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
970 
971   /* forward solve the lower triangular */
972   tmp[0] = b[*r++];
973   tmps   = tmp;
974   for (i=1; i<n; i++) {
975     v   = aa + ai[i] ;
976     vi  = aj + ai[i] ;
977     nz  = a->diag[i] - ai[i];
978     sum = b[*r++];
979     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
980     tmp[i] = sum;
981   }
982 
983   /* backward solve the upper triangular */
984   for (i=n-1; i>=0; i--){
985     v   = aa + a->diag[i] + 1;
986     vi  = aj + a->diag[i] + 1;
987     nz  = ai[i+1] - a->diag[i] - 1;
988     sum = tmp[i];
989     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
990     x[*c--] = tmp[i] = sum*aa[a->diag[i]];
991   }
992 
993   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
994   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
995   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
996   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
997   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
998   PetscFunctionReturn(0);
999 }
1000 
1001 #undef __FUNCT__
1002 #define __FUNCT__ "MatMatSolve_SeqAIJ_inplace"
1003 PetscErrorCode MatMatSolve_SeqAIJ_inplace(Mat A,Mat B,Mat X)
1004 {
1005   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1006   IS              iscol = a->col,isrow = a->row;
1007   PetscErrorCode  ierr;
1008   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1009   PetscInt        nz,neq;
1010   const PetscInt  *rout,*cout,*r,*c;
1011   PetscScalar     *x,*b,*tmp,*tmps,sum;
1012   const MatScalar *aa = a->a,*v;
1013   PetscTruth      bisdense,xisdense;
1014 
1015   PetscFunctionBegin;
1016   if (!n) PetscFunctionReturn(0);
1017 
1018   ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr);
1019   if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix");
1020   ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr);
1021   if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix");
1022 
1023   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
1024   ierr = MatGetArray(X,&x);CHKERRQ(ierr);
1025 
1026   tmp  = a->solve_work;
1027   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1028   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1029 
1030   for (neq=0; neq<B->cmap->n; neq++){
1031     /* forward solve the lower triangular */
1032     tmp[0] = b[r[0]];
1033     tmps   = tmp;
1034     for (i=1; i<n; i++) {
1035       v   = aa + ai[i] ;
1036       vi  = aj + ai[i] ;
1037       nz  = a->diag[i] - ai[i];
1038       sum = b[r[i]];
1039       PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1040       tmp[i] = sum;
1041     }
1042     /* backward solve the upper triangular */
1043     for (i=n-1; i>=0; i--){
1044       v   = aa + a->diag[i] + 1;
1045       vi  = aj + a->diag[i] + 1;
1046       nz  = ai[i+1] - a->diag[i] - 1;
1047       sum = tmp[i];
1048       PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1049       x[c[i]] = tmp[i] = sum*aa[a->diag[i]];
1050     }
1051 
1052     b += n;
1053     x += n;
1054   }
1055   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1056   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1057   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
1058   ierr = MatRestoreArray(X,&x);CHKERRQ(ierr);
1059   ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr);
1060   PetscFunctionReturn(0);
1061 }
1062 
1063 #undef __FUNCT__
1064 #define __FUNCT__ "MatMatSolve_SeqAIJ"
1065 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X)
1066 {
1067   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1068   IS              iscol = a->col,isrow = a->row;
1069   PetscErrorCode  ierr;
1070   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag;
1071   PetscInt        nz,neq;
1072   const PetscInt  *rout,*cout,*r,*c;
1073   PetscScalar     *x,*b,*tmp,sum;
1074   const MatScalar *aa = a->a,*v;
1075   PetscTruth      bisdense,xisdense;
1076 
1077   PetscFunctionBegin;
1078   if (!n) PetscFunctionReturn(0);
1079 
1080   ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr);
1081   if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix");
1082   ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr);
1083   if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix");
1084 
1085   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
1086   ierr = MatGetArray(X,&x);CHKERRQ(ierr);
1087 
1088   tmp  = a->solve_work;
1089   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1090   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1091 
1092   for (neq=0; neq<B->cmap->n; neq++){
1093     /* forward solve the lower triangular */
1094     tmp[0] = b[r[0]];
1095     v      = aa;
1096     vi     = aj;
1097     for (i=1; i<n; i++) {
1098       nz  = ai[i+1] - ai[i];
1099       sum = b[r[i]];
1100       PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
1101       tmp[i] = sum;
1102       v += nz; vi += nz;
1103     }
1104 
1105     /* backward solve the upper triangular */
1106     for (i=n-1; i>=0; i--){
1107       v   = aa + adiag[i+1]+1;
1108       vi  = aj + adiag[i+1]+1;
1109       nz  = adiag[i]-adiag[i+1]-1;
1110       sum = tmp[i];
1111       PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
1112       x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */
1113     }
1114 
1115     b += n;
1116     x += n;
1117   }
1118   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1119   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1120   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
1121   ierr = MatRestoreArray(X,&x);CHKERRQ(ierr);
1122   ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr);
1123   PetscFunctionReturn(0);
1124 }
1125 
1126 #undef __FUNCT__
1127 #define __FUNCT__ "MatSolve_SeqAIJ_InplaceWithPerm"
1128 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx)
1129 {
1130   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1131   IS              iscol = a->col,isrow = a->row;
1132   PetscErrorCode  ierr;
1133   const PetscInt  *r,*c,*rout,*cout;
1134   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1135   PetscInt        nz,row;
1136   PetscScalar     *x,*b,*tmp,*tmps,sum;
1137   const MatScalar *aa = a->a,*v;
1138 
1139   PetscFunctionBegin;
1140   if (!n) PetscFunctionReturn(0);
1141 
1142   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
1143   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1144   tmp  = a->solve_work;
1145 
1146   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1147   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1148 
1149   /* forward solve the lower triangular */
1150   tmp[0] = b[*r++];
1151   tmps   = tmp;
1152   for (row=1; row<n; row++) {
1153     i   = rout[row]; /* permuted row */
1154     v   = aa + ai[i] ;
1155     vi  = aj + ai[i] ;
1156     nz  = a->diag[i] - ai[i];
1157     sum = b[*r++];
1158     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1159     tmp[row] = sum;
1160   }
1161 
1162   /* backward solve the upper triangular */
1163   for (row=n-1; row>=0; row--){
1164     i   = rout[row]; /* permuted row */
1165     v   = aa + a->diag[i] + 1;
1166     vi  = aj + a->diag[i] + 1;
1167     nz  = ai[i+1] - a->diag[i] - 1;
1168     sum = tmp[row];
1169     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1170     x[*c--] = tmp[row] = sum*aa[a->diag[i]];
1171   }
1172 
1173   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1174   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1175   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
1176   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1177   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1178   PetscFunctionReturn(0);
1179 }
1180 
1181 /* ----------------------------------------------------------- */
1182 #include "../src/mat/impls/aij/seq/ftn-kernels/fsolve.h"
1183 #undef __FUNCT__
1184 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_inplace"
1185 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_inplace(Mat A,Vec bb,Vec xx)
1186 {
1187   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1188   PetscErrorCode    ierr;
1189   PetscInt          n = A->rmap->n;
1190   const PetscInt    *ai = a->i,*aj = a->j,*adiag = a->diag;
1191   PetscScalar       *x;
1192   const PetscScalar *b;
1193   const MatScalar   *aa = a->a;
1194 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ)
1195   PetscInt          adiag_i,i,nz,ai_i;
1196   const PetscInt    *vi;
1197   const MatScalar   *v;
1198   PetscScalar       sum;
1199 #endif
1200 
1201   PetscFunctionBegin;
1202   if (!n) PetscFunctionReturn(0);
1203 
1204   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1205   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1206 
1207 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ)
1208   fortransolveaij_(&n,x,ai,aj,adiag,aa,b);
1209 #else
1210   /* forward solve the lower triangular */
1211   x[0] = b[0];
1212   for (i=1; i<n; i++) {
1213     ai_i = ai[i];
1214     v    = aa + ai_i;
1215     vi   = aj + ai_i;
1216     nz   = adiag[i] - ai_i;
1217     sum  = b[i];
1218     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
1219     x[i] = sum;
1220   }
1221 
1222   /* backward solve the upper triangular */
1223   for (i=n-1; i>=0; i--){
1224     adiag_i = adiag[i];
1225     v       = aa + adiag_i + 1;
1226     vi      = aj + adiag_i + 1;
1227     nz      = ai[i+1] - adiag_i - 1;
1228     sum     = x[i];
1229     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
1230     x[i]    = sum*aa[adiag_i];
1231   }
1232 #endif
1233   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1234   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1235   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1236   PetscFunctionReturn(0);
1237 }
1238 
1239 #undef __FUNCT__
1240 #define __FUNCT__ "MatSolveAdd_SeqAIJ_inplace"
1241 PetscErrorCode MatSolveAdd_SeqAIJ_inplace(Mat A,Vec bb,Vec yy,Vec xx)
1242 {
1243   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1244   IS                iscol = a->col,isrow = a->row;
1245   PetscErrorCode    ierr;
1246   PetscInt          i, n = A->rmap->n,j;
1247   PetscInt          nz;
1248   const PetscInt    *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j;
1249   PetscScalar       *x,*tmp,sum;
1250   const PetscScalar *b;
1251   const MatScalar   *aa = a->a,*v;
1252 
1253   PetscFunctionBegin;
1254   if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);}
1255 
1256   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1257   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1258   tmp  = a->solve_work;
1259 
1260   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1261   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1262 
1263   /* forward solve the lower triangular */
1264   tmp[0] = b[*r++];
1265   for (i=1; i<n; i++) {
1266     v   = aa + ai[i] ;
1267     vi  = aj + ai[i] ;
1268     nz  = a->diag[i] - ai[i];
1269     sum = b[*r++];
1270     for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1271     tmp[i] = sum;
1272   }
1273 
1274   /* backward solve the upper triangular */
1275   for (i=n-1; i>=0; i--){
1276     v   = aa + a->diag[i] + 1;
1277     vi  = aj + a->diag[i] + 1;
1278     nz  = ai[i+1] - a->diag[i] - 1;
1279     sum = tmp[i];
1280     for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1281     tmp[i] = sum*aa[a->diag[i]];
1282     x[*c--] += tmp[i];
1283   }
1284 
1285   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1286   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1287   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1288   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1289   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1290 
1291   PetscFunctionReturn(0);
1292 }
1293 
1294 #undef __FUNCT__
1295 #define __FUNCT__ "MatSolveAdd_SeqAIJ"
1296 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx)
1297 {
1298   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1299   IS                iscol = a->col,isrow = a->row;
1300   PetscErrorCode    ierr;
1301   PetscInt          i, n = A->rmap->n,j;
1302   PetscInt          nz;
1303   const PetscInt    *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag;
1304   PetscScalar       *x,*tmp,sum;
1305   const PetscScalar *b;
1306   const MatScalar   *aa = a->a,*v;
1307 
1308   PetscFunctionBegin;
1309   if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);}
1310 
1311   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1312   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1313   tmp  = a->solve_work;
1314 
1315   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1316   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1317 
1318   /* forward solve the lower triangular */
1319   tmp[0] = b[r[0]];
1320   v      = aa;
1321   vi     = aj;
1322   for (i=1; i<n; i++) {
1323     nz  = ai[i+1] - ai[i];
1324     sum = b[r[i]];
1325     for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1326     tmp[i] = sum;
1327     v += nz; vi += nz;
1328   }
1329 
1330   /* backward solve the upper triangular */
1331   v  = aa + adiag[n-1];
1332   vi = aj + adiag[n-1];
1333   for (i=n-1; i>=0; i--){
1334     nz  = adiag[i] - adiag[i+1] - 1;
1335     sum = tmp[i];
1336     for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1337     tmp[i] = sum*v[nz];
1338     x[c[i]] += tmp[i];
1339     v += nz+1; vi += nz+1;
1340   }
1341 
1342   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1343   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1344   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1345   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1346   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1347 
1348   PetscFunctionReturn(0);
1349 }
1350 
1351 #undef __FUNCT__
1352 #define __FUNCT__ "MatSolveTranspose_SeqAIJ_inplace"
1353 PetscErrorCode MatSolveTranspose_SeqAIJ_inplace(Mat A,Vec bb,Vec xx)
1354 {
1355   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1356   IS                iscol = a->col,isrow = a->row;
1357   PetscErrorCode    ierr;
1358   const PetscInt    *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi;
1359   PetscInt          i,n = A->rmap->n,j;
1360   PetscInt          nz;
1361   PetscScalar       *x,*tmp,s1;
1362   const MatScalar   *aa = a->a,*v;
1363   const PetscScalar *b;
1364 
1365   PetscFunctionBegin;
1366   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1367   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1368   tmp  = a->solve_work;
1369 
1370   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1371   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1372 
1373   /* copy the b into temp work space according to permutation */
1374   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1375 
1376   /* forward solve the U^T */
1377   for (i=0; i<n; i++) {
1378     v   = aa + diag[i] ;
1379     vi  = aj + diag[i] + 1;
1380     nz  = ai[i+1] - diag[i] - 1;
1381     s1  = tmp[i];
1382     s1 *= (*v++);  /* multiply by inverse of diagonal entry */
1383     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1384     tmp[i] = s1;
1385   }
1386 
1387   /* backward solve the L^T */
1388   for (i=n-1; i>=0; i--){
1389     v   = aa + diag[i] - 1 ;
1390     vi  = aj + diag[i] - 1 ;
1391     nz  = diag[i] - ai[i];
1392     s1  = tmp[i];
1393     for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j];
1394   }
1395 
1396   /* copy tmp into x according to permutation */
1397   for (i=0; i<n; i++) x[r[i]] = tmp[i];
1398 
1399   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1400   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1401   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1402   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1403 
1404   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1405   PetscFunctionReturn(0);
1406 }
1407 
1408 #undef __FUNCT__
1409 #define __FUNCT__ "MatSolveTranspose_SeqAIJ"
1410 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx)
1411 {
1412   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1413   IS                iscol = a->col,isrow = a->row;
1414   PetscErrorCode    ierr;
1415   const PetscInt    *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi;
1416   PetscInt          i,n = A->rmap->n,j;
1417   PetscInt          nz;
1418   PetscScalar       *x,*tmp,s1;
1419   const MatScalar   *aa = a->a,*v;
1420   const PetscScalar *b;
1421 
1422   PetscFunctionBegin;
1423   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1424   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1425   tmp  = a->solve_work;
1426 
1427   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1428   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1429 
1430   /* copy the b into temp work space according to permutation */
1431   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1432 
1433   /* forward solve the U^T */
1434   for (i=0; i<n; i++) {
1435     v   = aa + adiag[i+1] + 1;
1436     vi  = aj + adiag[i+1] + 1;
1437     nz  = adiag[i] - adiag[i+1] - 1;
1438     s1  = tmp[i];
1439     s1 *= v[nz];  /* multiply by inverse of diagonal entry */
1440     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1441     tmp[i] = s1;
1442   }
1443 
1444   /* backward solve the L^T */
1445   for (i=n-1; i>=0; i--){
1446     v   = aa + ai[i];
1447     vi  = aj + ai[i];
1448     nz  = ai[i+1] - ai[i];
1449     s1  = tmp[i];
1450     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1451   }
1452 
1453   /* copy tmp into x according to permutation */
1454   for (i=0; i<n; i++) x[r[i]] = tmp[i];
1455 
1456   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1457   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1458   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1459   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1460 
1461   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1462   PetscFunctionReturn(0);
1463 }
1464 
1465 #undef __FUNCT__
1466 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ_inplace"
1467 PetscErrorCode MatSolveTransposeAdd_SeqAIJ_inplace(Mat A,Vec bb,Vec zz,Vec xx)
1468 {
1469   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1470   IS                iscol = a->col,isrow = a->row;
1471   PetscErrorCode    ierr;
1472   const PetscInt    *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi;
1473   PetscInt          i,n = A->rmap->n,j;
1474   PetscInt          nz;
1475   PetscScalar       *x,*tmp,s1;
1476   const MatScalar   *aa = a->a,*v;
1477   const PetscScalar *b;
1478 
1479   PetscFunctionBegin;
1480   if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);}
1481   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1482   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1483   tmp  = a->solve_work;
1484 
1485   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1486   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1487 
1488   /* copy the b into temp work space according to permutation */
1489   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1490 
1491   /* forward solve the U^T */
1492   for (i=0; i<n; i++) {
1493     v   = aa + diag[i] ;
1494     vi  = aj + diag[i] + 1;
1495     nz  = ai[i+1] - diag[i] - 1;
1496     s1  = tmp[i];
1497     s1 *= (*v++);  /* multiply by inverse of diagonal entry */
1498     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1499     tmp[i] = s1;
1500   }
1501 
1502   /* backward solve the L^T */
1503   for (i=n-1; i>=0; i--){
1504     v   = aa + diag[i] - 1 ;
1505     vi  = aj + diag[i] - 1 ;
1506     nz  = diag[i] - ai[i];
1507     s1  = tmp[i];
1508     for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j];
1509   }
1510 
1511   /* copy tmp into x according to permutation */
1512   for (i=0; i<n; i++) x[r[i]] += tmp[i];
1513 
1514   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1515   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1516   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1517   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1518 
1519   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1520   PetscFunctionReturn(0);
1521 }
1522 
1523 #undef __FUNCT__
1524 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ"
1525 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx)
1526 {
1527   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1528   IS                iscol = a->col,isrow = a->row;
1529   PetscErrorCode    ierr;
1530   const PetscInt    *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi;
1531   PetscInt          i,n = A->rmap->n,j;
1532   PetscInt          nz;
1533   PetscScalar       *x,*tmp,s1;
1534   const MatScalar   *aa = a->a,*v;
1535   const PetscScalar *b;
1536 
1537   PetscFunctionBegin;
1538   if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);}
1539   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1540   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1541   tmp  = a->solve_work;
1542 
1543   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1544   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1545 
1546   /* copy the b into temp work space according to permutation */
1547   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1548 
1549   /* forward solve the U^T */
1550   for (i=0; i<n; i++) {
1551     v   = aa + adiag[i+1] + 1;
1552     vi  = aj + adiag[i+1] + 1;
1553     nz  = adiag[i] - adiag[i+1] - 1;
1554     s1  = tmp[i];
1555     s1 *= v[nz];  /* multiply by inverse of diagonal entry */
1556     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1557     tmp[i] = s1;
1558   }
1559 
1560 
1561   /* backward solve the L^T */
1562   for (i=n-1; i>=0; i--){
1563     v   = aa + ai[i] ;
1564     vi  = aj + ai[i];
1565     nz  = ai[i+1] - ai[i];
1566     s1  = tmp[i];
1567     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1568   }
1569 
1570   /* copy tmp into x according to permutation */
1571   for (i=0; i<n; i++) x[r[i]] += tmp[i];
1572 
1573   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1574   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1575   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1576   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1577 
1578   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1579   PetscFunctionReturn(0);
1580 }
1581 
1582 /* ----------------------------------------------------------------*/
1583 
1584 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption,PetscTruth);
1585 
1586 /*
1587    ilu() under revised new data structure.
1588    Factored arrays bj and ba are stored as
1589      L(0,:), L(1,:), ...,L(n-1,:),  U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:)
1590 
1591    bi=fact->i is an array of size n+1, in which
1592    bi+
1593      bi[i]:  points to 1st entry of L(i,:),i=0,...,n-1
1594      bi[n]:  points to L(n-1,n-1)+1
1595 
1596   bdiag=fact->diag is an array of size n+1,in which
1597      bdiag[i]: points to diagonal of U(i,:), i=0,...,n-1
1598      bdiag[n]: points to entry of U(n-1,0)-1
1599 
1600    U(i,:) contains bdiag[i] as its last entry, i.e.,
1601     U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i])
1602 */
1603 #undef __FUNCT__
1604 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0"
1605 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1606 {
1607 
1608   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1609   PetscErrorCode     ierr;
1610   const PetscInt     n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag;
1611   PetscInt           i,j,k=0,nz,*bi,*bj,*bdiag;
1612   PetscTruth         missing;
1613   IS                 isicol;
1614 
1615   PetscFunctionBegin;
1616   if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n);
1617   ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
1618   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
1619   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1620 
1621   ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr);
1622   b    = (Mat_SeqAIJ*)(fact)->data;
1623 
1624   /* allocate matrix arrays for new data structure */
1625   ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,n+1,PetscInt,&b->i);CHKERRQ(ierr);
1626   ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));CHKERRQ(ierr);
1627   b->singlemalloc = PETSC_TRUE;
1628   if (!b->diag){
1629     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr);
1630     ierr = PetscLogObjectMemory(fact,(n+1)*sizeof(PetscInt));CHKERRQ(ierr);
1631   }
1632   bdiag = b->diag;
1633 
1634   if (n > 0) {
1635     ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr);
1636   }
1637 
1638   /* set bi and bj with new data structure */
1639   bi = b->i;
1640   bj = b->j;
1641 
1642   /* L part */
1643   bi[0] = 0;
1644   for (i=0; i<n; i++){
1645     nz = adiag[i] - ai[i];
1646     bi[i+1] = bi[i] + nz;
1647     aj = a->j + ai[i];
1648     for (j=0; j<nz; j++){
1649       /*   *bj = aj[j]; bj++; */
1650       bj[k++] = aj[j];
1651     }
1652   }
1653 
1654   /* U part */
1655   bdiag[n] = bi[n]-1;
1656   for (i=n-1; i>=0; i--){
1657     nz = ai[i+1] - adiag[i] - 1;
1658     aj = a->j + adiag[i] + 1;
1659     for (j=0; j<nz; j++){
1660       /*      *bj = aj[j]; bj++; */
1661       bj[k++] = aj[j];
1662     }
1663     /* diag[i] */
1664     /*    *bj = i; bj++; */
1665     bj[k++] = i;
1666     bdiag[i] = bdiag[i+1] + nz + 1;
1667   }
1668 
1669   fact->factor                 = MAT_FACTOR_ILU;
1670   fact->info.factor_mallocs    = 0;
1671   fact->info.fill_ratio_given  = info->fill;
1672   fact->info.fill_ratio_needed = 1.0;
1673   fact->ops->lufactornumeric   = MatLUFactorNumeric_SeqAIJ;
1674 
1675   b       = (Mat_SeqAIJ*)(fact)->data;
1676   b->row  = isrow;
1677   b->col  = iscol;
1678   b->icol = isicol;
1679   ierr    = PetscMalloc((fact->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1680   ierr    = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1681   ierr    = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1682   PetscFunctionReturn(0);
1683 }
1684 
1685 #undef __FUNCT__
1686 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ"
1687 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1688 {
1689   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1690   IS                 isicol;
1691   PetscErrorCode     ierr;
1692   const PetscInt     *r,*ic;
1693   PetscInt           n=A->rmap->n,*ai=a->i,*aj=a->j;
1694   PetscInt           *bi,*cols,nnz,*cols_lvl;
1695   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1696   PetscInt           i,levels,diagonal_fill;
1697   PetscTruth         col_identity,row_identity;
1698   PetscReal          f;
1699   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
1700   PetscBT            lnkbt;
1701   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
1702   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1703   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1704   PetscTruth         olddatastruct=PETSC_FALSE;
1705 
1706   PetscFunctionBegin;
1707   /* Uncomment the old data struct part only while testing new data structure for MatSolve() */
1708   ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_old",&olddatastruct,PETSC_NULL);CHKERRQ(ierr);
1709   if(olddatastruct){
1710     ierr = MatILUFactorSymbolic_SeqAIJ_inplace(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1711     PetscFunctionReturn(0);
1712   }
1713 
1714   levels = (PetscInt)info->levels;
1715   ierr   = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1716   ierr   = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
1717 
1718   if (!levels && row_identity && col_identity) {
1719     /* special case: ilu(0) with natural ordering */
1720     ierr = MatILUFactorSymbolic_SeqAIJ_ilu0(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1721     ierr = Mat_CheckInode_FactorLU(fact,PETSC_FALSE);CHKERRQ(ierr);
1722     PetscFunctionReturn(0);
1723   }
1724 
1725   if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n);
1726   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1727   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1728   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1729 
1730   /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
1731   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1732   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
1733   bi[0] = bdiag[0] = 0;
1734 
1735   ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr);
1736 
1737   /* create a linked list for storing column indices of the active row */
1738   nlnk = n + 1;
1739   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1740 
1741   /* initial FreeSpace size is f*(ai[n]+1) */
1742   f             = info->fill;
1743   diagonal_fill = (PetscInt)info->diagonal_fill;
1744   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
1745   current_space = free_space;
1746   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
1747   current_space_lvl = free_space_lvl;
1748 
1749   for (i=0; i<n; i++) {
1750     nzi = 0;
1751     /* copy current row into linked list */
1752     nnz  = ai[r[i]+1] - ai[r[i]];
1753     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1754     cols = aj + ai[r[i]];
1755     lnk[i] = -1; /* marker to indicate if diagonal exists */
1756     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1757     nzi += nlnk;
1758 
1759     /* make sure diagonal entry is included */
1760     if (diagonal_fill && lnk[i] == -1) {
1761       fm = n;
1762       while (lnk[fm] < i) fm = lnk[fm];
1763       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
1764       lnk[fm]    = i;
1765       lnk_lvl[i] = 0;
1766       nzi++; dcount++;
1767     }
1768 
1769     /* add pivot rows into the active row */
1770     nzbd = 0;
1771     prow = lnk[n];
1772     while (prow < i) {
1773       nnz      = bdiag[prow];
1774       cols     = bj_ptr[prow] + nnz + 1;
1775       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1776       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
1777       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
1778       nzi += nlnk;
1779       prow = lnk[prow];
1780       nzbd++;
1781     }
1782     bdiag[i] = nzbd;
1783     bi[i+1]  = bi[i] + nzi;
1784 
1785     /* if free space is not available, make more free space */
1786     if (current_space->local_remaining<nzi) {
1787       nnz = 2*nzi*(n - i); /* estimated and max additional space needed */
1788       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
1789       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
1790       reallocs++;
1791     }
1792 
1793     /* copy data into free_space and free_space_lvl, then initialize lnk */
1794     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1795     bj_ptr[i]    = current_space->array;
1796     bjlvl_ptr[i] = current_space_lvl->array;
1797 
1798     /* make sure the active row i has diagonal entry */
1799     if (*(bj_ptr[i]+bdiag[i]) != i) {
1800       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
1801     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
1802     }
1803 
1804     current_space->array           += nzi;
1805     current_space->local_used      += nzi;
1806     current_space->local_remaining -= nzi;
1807     current_space_lvl->array           += nzi;
1808     current_space_lvl->local_used      += nzi;
1809     current_space_lvl->local_remaining -= nzi;
1810   }
1811 
1812   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1813   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1814 
1815   /* destroy list of free space and other temporary arrays */
1816   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
1817 
1818   /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */
1819   ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr);
1820 
1821   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1822   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
1823   ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr);
1824 
1825 #if defined(PETSC_USE_INFO)
1826   {
1827     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1828     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
1829     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
1830     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
1831     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
1832     if (diagonal_fill) {
1833       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
1834     }
1835   }
1836 #endif
1837 
1838   /* put together the new matrix */
1839   ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
1840   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
1841   b = (Mat_SeqAIJ*)(fact)->data;
1842   b->free_a       = PETSC_TRUE;
1843   b->free_ij      = PETSC_TRUE;
1844   b->singlemalloc = PETSC_FALSE;
1845   ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
1846   b->j          = bj;
1847   b->i          = bi;
1848   b->diag       = bdiag;
1849   b->ilen       = 0;
1850   b->imax       = 0;
1851   b->row        = isrow;
1852   b->col        = iscol;
1853   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1854   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1855   b->icol       = isicol;
1856   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1857   /* In b structure:  Free imax, ilen, old a, old j.
1858      Allocate bdiag, solve_work, new a, new j */
1859   ierr = PetscLogObjectMemory(fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
1860   b->maxnz = b->nz = bdiag[0]+1;
1861   (fact)->info.factor_mallocs    = reallocs;
1862   (fact)->info.fill_ratio_given  = f;
1863   (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]);
1864   (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ;
1865   if (a->inode.size) {
1866     (fact)->ops->lufactornumeric  = MatLUFactorNumeric_SeqAIJ_Inode;
1867   }
1868   PetscFunctionReturn(0);
1869 }
1870 
1871 #undef __FUNCT__
1872 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_inplace"
1873 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1874 {
1875   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1876   IS                 isicol;
1877   PetscErrorCode     ierr;
1878   const PetscInt     *r,*ic;
1879   PetscInt           n=A->rmap->n,*ai=a->i,*aj=a->j,d;
1880   PetscInt           *bi,*cols,nnz,*cols_lvl;
1881   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1882   PetscInt           i,levels,diagonal_fill;
1883   PetscTruth         col_identity,row_identity;
1884   PetscReal          f;
1885   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
1886   PetscBT            lnkbt;
1887   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
1888   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1889   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1890   PetscTruth         missing;
1891 
1892   PetscFunctionBegin;
1893   if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n);
1894   f             = info->fill;
1895   levels        = (PetscInt)info->levels;
1896   diagonal_fill = (PetscInt)info->diagonal_fill;
1897   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1898 
1899   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1900   ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
1901   if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */
1902     ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr);
1903     (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ_inplace;
1904     if (a->inode.size) {
1905       (fact)->ops->lufactornumeric  = MatLUFactorNumeric_SeqAIJ_Inode_inplace;
1906     }
1907     fact->factor = MAT_FACTOR_ILU;
1908     (fact)->info.factor_mallocs    = 0;
1909     (fact)->info.fill_ratio_given  = info->fill;
1910     (fact)->info.fill_ratio_needed = 1.0;
1911     b               = (Mat_SeqAIJ*)(fact)->data;
1912     ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
1913     if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
1914     b->row              = isrow;
1915     b->col              = iscol;
1916     b->icol             = isicol;
1917     ierr                = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1918     ierr                = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1919     ierr                = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1920     PetscFunctionReturn(0);
1921   }
1922 
1923   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1924   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1925 
1926   /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
1927   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1928   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
1929   bi[0] = bdiag[0] = 0;
1930 
1931   ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr);
1932 
1933   /* create a linked list for storing column indices of the active row */
1934   nlnk = n + 1;
1935   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1936 
1937   /* initial FreeSpace size is f*(ai[n]+1) */
1938   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
1939   current_space = free_space;
1940   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
1941   current_space_lvl = free_space_lvl;
1942 
1943   for (i=0; i<n; i++) {
1944     nzi = 0;
1945     /* copy current row into linked list */
1946     nnz  = ai[r[i]+1] - ai[r[i]];
1947     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1948     cols = aj + ai[r[i]];
1949     lnk[i] = -1; /* marker to indicate if diagonal exists */
1950     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1951     nzi += nlnk;
1952 
1953     /* make sure diagonal entry is included */
1954     if (diagonal_fill && lnk[i] == -1) {
1955       fm = n;
1956       while (lnk[fm] < i) fm = lnk[fm];
1957       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
1958       lnk[fm]    = i;
1959       lnk_lvl[i] = 0;
1960       nzi++; dcount++;
1961     }
1962 
1963     /* add pivot rows into the active row */
1964     nzbd = 0;
1965     prow = lnk[n];
1966     while (prow < i) {
1967       nnz      = bdiag[prow];
1968       cols     = bj_ptr[prow] + nnz + 1;
1969       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1970       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
1971       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
1972       nzi += nlnk;
1973       prow = lnk[prow];
1974       nzbd++;
1975     }
1976     bdiag[i] = nzbd;
1977     bi[i+1]  = bi[i] + nzi;
1978 
1979     /* if free space is not available, make more free space */
1980     if (current_space->local_remaining<nzi) {
1981       nnz = nzi*(n - i); /* estimated and max additional space needed */
1982       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
1983       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
1984       reallocs++;
1985     }
1986 
1987     /* copy data into free_space and free_space_lvl, then initialize lnk */
1988     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1989     bj_ptr[i]    = current_space->array;
1990     bjlvl_ptr[i] = current_space_lvl->array;
1991 
1992     /* make sure the active row i has diagonal entry */
1993     if (*(bj_ptr[i]+bdiag[i]) != i) {
1994       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
1995     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
1996     }
1997 
1998     current_space->array           += nzi;
1999     current_space->local_used      += nzi;
2000     current_space->local_remaining -= nzi;
2001     current_space_lvl->array           += nzi;
2002     current_space_lvl->local_used      += nzi;
2003     current_space_lvl->local_remaining -= nzi;
2004   }
2005 
2006   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
2007   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
2008 
2009   /* destroy list of free space and other temporary arrays */
2010   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
2011   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */
2012   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2013   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2014   ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr);
2015 
2016 #if defined(PETSC_USE_INFO)
2017   {
2018     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
2019     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
2020     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2021     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
2022     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
2023     if (diagonal_fill) {
2024       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
2025     }
2026   }
2027 #endif
2028 
2029   /* put together the new matrix */
2030   ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
2031   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
2032   b = (Mat_SeqAIJ*)(fact)->data;
2033   b->free_a       = PETSC_TRUE;
2034   b->free_ij      = PETSC_TRUE;
2035   b->singlemalloc = PETSC_FALSE;
2036   ierr = PetscMalloc(bi[n]*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
2037   b->j          = bj;
2038   b->i          = bi;
2039   for (i=0; i<n; i++) bdiag[i] += bi[i];
2040   b->diag       = bdiag;
2041   b->ilen       = 0;
2042   b->imax       = 0;
2043   b->row        = isrow;
2044   b->col        = iscol;
2045   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
2046   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
2047   b->icol       = isicol;
2048   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2049   /* In b structure:  Free imax, ilen, old a, old j.
2050      Allocate bdiag, solve_work, new a, new j */
2051   ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
2052   b->maxnz             = b->nz = bi[n] ;
2053   (fact)->info.factor_mallocs    = reallocs;
2054   (fact)->info.fill_ratio_given  = f;
2055   (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
2056   (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ_inplace;
2057   if (a->inode.size) {
2058     (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace;
2059   }
2060   PetscFunctionReturn(0);
2061 }
2062 
2063 #undef __FUNCT__
2064 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ"
2065 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info)
2066 {
2067   Mat            C = B;
2068   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
2069   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
2070   IS             ip=b->row,iip = b->icol;
2071   PetscErrorCode ierr;
2072   const PetscInt *rip,*riip;
2073   PetscInt       i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp;
2074   PetscInt       *ai=a->i,*aj=a->j;
2075   PetscInt       k,jmin,jmax,*c2r,*il,col,nexti,ili,nz;
2076   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
2077   PetscTruth     perm_identity;
2078 
2079   FactorShiftCtx sctx;
2080   PetscReal      rs;
2081   MatScalar      d,*v;
2082 
2083   PetscFunctionBegin;
2084   /* MatPivotSetUp(): initialize shift context sctx */
2085   ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr);
2086 
2087   if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
2088     sctx.shift_top = info->zeropivot;
2089     for (i=0; i<mbs; i++) {
2090       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
2091       d  = (aa)[a->diag[i]];
2092       rs = -PetscAbsScalar(d) - PetscRealPart(d);
2093       v  = aa+ai[i];
2094       nz = ai[i+1] - ai[i];
2095       for (j=0; j<nz; j++)
2096 	rs += PetscAbsScalar(v[j]);
2097       if (rs>sctx.shift_top) sctx.shift_top = rs;
2098     }
2099     sctx.shift_top   *= 1.1;
2100     sctx.nshift_max   = 5;
2101     sctx.shift_lo     = 0.;
2102     sctx.shift_hi     = 1.;
2103   }
2104 
2105   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
2106   ierr  = ISGetIndices(iip,&riip);CHKERRQ(ierr);
2107 
2108   /* allocate working arrays
2109      c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col
2110      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
2111   */
2112   ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&c2r);CHKERRQ(ierr);
2113 
2114   do {
2115     sctx.useshift = PETSC_FALSE;
2116 
2117     for (i=0; i<mbs; i++) c2r[i] = mbs;
2118     il[0] = 0;
2119 
2120     for (k = 0; k<mbs; k++){
2121       /* zero rtmp */
2122       nz = bi[k+1] - bi[k];
2123       bjtmp = bj + bi[k];
2124       for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
2125 
2126       /* load in initial unfactored row */
2127       bval = ba + bi[k];
2128       jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2129       for (j = jmin; j < jmax; j++){
2130         col = riip[aj[j]];
2131         if (col >= k){ /* only take upper triangular entry */
2132           rtmp[col] = aa[j];
2133           *bval++   = 0.0; /* for in-place factorization */
2134         }
2135       }
2136       /* shift the diagonal of the matrix: ZeropivotApply() */
2137       rtmp[k] += sctx.shift_amount;  /* shift the diagonal of the matrix */
2138 
2139       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
2140       dk = rtmp[k];
2141       i  = c2r[k]; /* first row to be added to k_th row  */
2142 
2143       while (i < k){
2144         nexti = c2r[i]; /* next row to be added to k_th row */
2145 
2146         /* compute multiplier, update diag(k) and U(i,k) */
2147         ili   = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2148         uikdi = - ba[ili]*ba[bdiag[i]];  /* diagonal(k) */
2149         dk   += uikdi*ba[ili]; /* update diag[k] */
2150         ba[ili] = uikdi; /* -U(i,k) */
2151 
2152         /* add multiple of row i to k-th row */
2153         jmin = ili + 1; jmax = bi[i+1];
2154         if (jmin < jmax){
2155           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2156           /* update il and c2r for row i */
2157           il[i] = jmin;
2158           j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i;
2159         }
2160         i = nexti;
2161       }
2162 
2163       /* copy data into U(k,:) */
2164       rs   = 0.0;
2165       jmin = bi[k]; jmax = bi[k+1]-1;
2166       if (jmin < jmax) {
2167         for (j=jmin; j<jmax; j++){
2168           col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]);
2169         }
2170         /* add the k-th row into il and c2r */
2171         il[k] = jmin;
2172         i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k;
2173       }
2174 
2175       /* MatPivotCheck() */
2176       sctx.rs  = rs;
2177       sctx.pv  = dk;
2178       ierr = MatPivotCheck(info,sctx,i);CHKERRQ(ierr);
2179       dk = sctx.pv;
2180 
2181       ba[bdiag[k]] = 1.0/dk; /* U(k,k) */
2182     }
2183   } while (sctx.useshift);
2184 
2185   ierr = PetscFree3(rtmp,il,c2r);CHKERRQ(ierr);
2186   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2187   ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr);
2188 
2189   ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
2190   if (perm_identity){
2191     B->ops->solve           = MatSolve_SeqSBAIJ_1_NaturalOrdering;
2192     B->ops->solvetranspose  = MatSolve_SeqSBAIJ_1_NaturalOrdering;
2193     B->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering;
2194     B->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering;
2195   } else {
2196     B->ops->solve           = MatSolve_SeqSBAIJ_1;
2197     B->ops->solvetranspose  = MatSolve_SeqSBAIJ_1;
2198     B->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1;
2199     B->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1;
2200   }
2201 
2202   C->assembled    = PETSC_TRUE;
2203   C->preallocated = PETSC_TRUE;
2204   ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr);
2205 
2206   /* MatPivotView() */
2207   if (sctx.nshift){
2208     if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
2209       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);
2210     } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
2211       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2212     } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS){
2213       ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftamount);CHKERRQ(ierr);
2214     }
2215   }
2216   PetscFunctionReturn(0);
2217 }
2218 
2219 #undef __FUNCT__
2220 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ_inplace"
2221 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info)
2222 {
2223   Mat            C = B;
2224   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
2225   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
2226   IS             ip=b->row,iip = b->icol;
2227   PetscErrorCode ierr;
2228   const PetscInt *rip,*riip;
2229   PetscInt       i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol,*bjtmp;
2230   PetscInt       *ai=a->i,*aj=a->j;
2231   PetscInt       k,jmin,jmax,*jl,*il,col,nexti,ili,nz;
2232   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
2233   PetscReal      zeropivot,rs;
2234   ChShift_Ctx    sctx;
2235   PetscInt       newshift;
2236   PetscTruth     perm_identity;
2237 
2238   PetscFunctionBegin;
2239   zeropivot = info->zeropivot;
2240 
2241   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
2242   ierr  = ISGetIndices(iip,&riip);CHKERRQ(ierr);
2243 
2244   /* initialization */
2245   ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&jl);CHKERRQ(ierr);
2246   sctx.shift_amount = 0;
2247   sctx.nshift       = 0;
2248   do {
2249     sctx.chshift = PETSC_FALSE;
2250     for (i=0; i<mbs; i++) jl[i] = mbs;
2251     il[0] = 0;
2252 
2253     for (k = 0; k<mbs; k++){
2254       /* zero rtmp */
2255       nz = bi[k+1] - bi[k];
2256       bjtmp = bj + bi[k];
2257       for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
2258 
2259       bval = ba + bi[k];
2260       /* initialize k-th row by the perm[k]-th row of A */
2261       jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2262       for (j = jmin; j < jmax; j++){
2263         col = riip[aj[j]];
2264         if (col >= k){ /* only take upper triangular entry */
2265           rtmp[col] = aa[j];
2266           *bval++  = 0.0; /* for in-place factorization */
2267         }
2268       }
2269       /* shift the diagonal of the matrix */
2270       if (sctx.nshift) rtmp[k] += sctx.shift_amount;
2271 
2272       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
2273       dk = rtmp[k];
2274       i = jl[k]; /* first row to be added to k_th row  */
2275 
2276       while (i < k){
2277         nexti = jl[i]; /* next row to be added to k_th row */
2278 
2279         /* compute multiplier, update diag(k) and U(i,k) */
2280         ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2281         uikdi = - ba[ili]*ba[bi[i]];  /* diagonal(k) */
2282         dk += uikdi*ba[ili];
2283         ba[ili] = uikdi; /* -U(i,k) */
2284 
2285         /* add multiple of row i to k-th row */
2286         jmin = ili + 1; jmax = bi[i+1];
2287         if (jmin < jmax){
2288           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2289           /* update il and jl for row i */
2290           il[i] = jmin;
2291           j = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
2292         }
2293         i = nexti;
2294       }
2295 
2296       /* shift the diagonals when zero pivot is detected */
2297       /* compute rs=sum of abs(off-diagonal) */
2298       rs   = 0.0;
2299       jmin = bi[k]+1;
2300       nz   = bi[k+1] - jmin;
2301       bcol = bj + jmin;
2302       for (j=0; j<nz; j++) {
2303         rs += PetscAbsScalar(rtmp[bcol[j]]);
2304       }
2305 
2306       sctx.rs = rs;
2307       sctx.pv = dk;
2308       ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr);
2309 
2310       if (newshift == 1) {
2311         if (!sctx.shift_amount) {
2312           sctx.shift_amount = 1e-5;
2313         }
2314         break;
2315       }
2316 
2317       /* copy data into U(k,:) */
2318       ba[bi[k]] = 1.0/dk; /* U(k,k) */
2319       jmin = bi[k]+1; jmax = bi[k+1];
2320       if (jmin < jmax) {
2321         for (j=jmin; j<jmax; j++){
2322           col = bj[j]; ba[j] = rtmp[col];
2323         }
2324         /* add the k-th row into il and jl */
2325         il[k] = jmin;
2326         i = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
2327       }
2328     }
2329   } while (sctx.chshift);
2330   ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr);
2331   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2332   ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr);
2333 
2334   ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
2335   if (perm_identity){
2336     B->ops->solve           = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
2337     B->ops->solvetranspose  = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
2338     B->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
2339     B->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
2340   } else {
2341     B->ops->solve           = MatSolve_SeqSBAIJ_1_inplace;
2342     B->ops->solvetranspose  = MatSolve_SeqSBAIJ_1_inplace;
2343     B->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1_inplace;
2344     B->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1_inplace;
2345   }
2346 
2347   C->assembled    = PETSC_TRUE;
2348   C->preallocated = PETSC_TRUE;
2349   ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr);
2350   if (sctx.nshift){
2351     if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
2352       ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2353     } else if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
2354       ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2355     }
2356   }
2357   PetscFunctionReturn(0);
2358 }
2359 
2360 /*
2361    icc() under revised new data structure.
2362    Factored arrays bj and ba are stored as
2363      U(0,:),...,U(i,:),U(n-1,:)
2364 
2365    ui=fact->i is an array of size n+1, in which
2366    ui+
2367      ui[i]:  points to 1st entry of U(i,:),i=0,...,n-1
2368      ui[n]:  points to U(n-1,n-1)+1
2369 
2370   udiag=fact->diag is an array of size n,in which
2371      udiag[i]: points to diagonal of U(i,:), i=0,...,n-1
2372 
2373    U(i,:) contains udiag[i] as its last entry, i.e.,
2374     U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i])
2375 */
2376 
2377 #undef __FUNCT__
2378 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ"
2379 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2380 {
2381   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2382   Mat_SeqSBAIJ       *b;
2383   PetscErrorCode     ierr;
2384   PetscTruth         perm_identity,missing;
2385   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag;
2386   const PetscInt     *rip,*riip;
2387   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
2388   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL,d;
2389   PetscInt           ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
2390   PetscReal          fill=info->fill,levels=info->levels;
2391   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2392   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
2393   PetscBT            lnkbt;
2394   IS                 iperm;
2395 
2396   PetscFunctionBegin;
2397   if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n);
2398   ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
2399   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
2400   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2401   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2402 
2403   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2404   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2405   ui[0] = 0;
2406 
2407   /* ICC(0) without matrix ordering: simply rearrange column indices */
2408   if (!levels && perm_identity) {
2409     for (i=0; i<am; i++) {
2410       ncols    = ai[i+1] - a->diag[i];
2411       ui[i+1]  = ui[i] + ncols;
2412       udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */
2413     }
2414     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2415     cols = uj;
2416     for (i=0; i<am; i++) {
2417       aj    = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */
2418       ncols = ai[i+1] - a->diag[i] -1;
2419       for (j=0; j<ncols; j++) *cols++ = aj[j];
2420       *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */
2421     }
2422   } else { /* case: levels>0 || (levels=0 && !perm_identity) */
2423     ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2424     ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2425 
2426     /* initialization */
2427     ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr);
2428 
2429     /* jl: linked list for storing indices of the pivot rows
2430        il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2431     ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr);
2432     for (i=0; i<am; i++){
2433       jl[i] = am; il[i] = 0;
2434     }
2435 
2436     /* create and initialize a linked list for storing column indices of the active row k */
2437     nlnk = am + 1;
2438     ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2439 
2440     /* initial FreeSpace size is fill*(ai[am]+1) */
2441     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2442     current_space = free_space;
2443     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr);
2444     current_space_lvl = free_space_lvl;
2445 
2446     for (k=0; k<am; k++){  /* for each active row k */
2447       /* initialize lnk by the column indices of row rip[k] of A */
2448       nzk   = 0;
2449       ncols = ai[rip[k]+1] - ai[rip[k]];
2450       if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2451       ncols_upper = 0;
2452       for (j=0; j<ncols; j++){
2453         i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2454         if (riip[i] >= k){ /* only take upper triangular entry */
2455           ajtmp[ncols_upper] = i;
2456           ncols_upper++;
2457         }
2458       }
2459       ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2460       nzk += nlnk;
2461 
2462       /* update lnk by computing fill-in for each pivot row to be merged in */
2463       prow = jl[k]; /* 1st pivot row */
2464 
2465       while (prow < k){
2466         nextprow = jl[prow];
2467 
2468         /* merge prow into k-th row */
2469         jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2470         jmax = ui[prow+1];
2471         ncols = jmax-jmin;
2472         i     = jmin - ui[prow];
2473         cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2474         uj    = uj_lvl_ptr[prow] + i; /* levels of cols */
2475         j     = *(uj - 1);
2476         ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr);
2477         nzk += nlnk;
2478 
2479         /* update il and jl for prow */
2480         if (jmin < jmax){
2481           il[prow] = jmin;
2482           j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2483         }
2484         prow = nextprow;
2485       }
2486 
2487       /* if free space is not available, make more free space */
2488       if (current_space->local_remaining<nzk) {
2489         i  = am - k + 1; /* num of unfactored rows */
2490         i *= PetscMin(nzk, i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */
2491         ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2492         ierr = PetscFreeSpaceGet(i,&current_space_lvl);CHKERRQ(ierr);
2493         reallocs++;
2494       }
2495 
2496       /* copy data into free_space and free_space_lvl, then initialize lnk */
2497       if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2498       ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
2499 
2500       /* add the k-th row into il and jl */
2501       if (nzk > 1){
2502         i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2503         jl[k] = jl[i]; jl[i] = k;
2504         il[k] = ui[k] + 1;
2505       }
2506       uj_ptr[k]     = current_space->array;
2507       uj_lvl_ptr[k] = current_space_lvl->array;
2508 
2509       current_space->array           += nzk;
2510       current_space->local_used      += nzk;
2511       current_space->local_remaining -= nzk;
2512 
2513       current_space_lvl->array           += nzk;
2514       current_space_lvl->local_used      += nzk;
2515       current_space_lvl->local_remaining -= nzk;
2516 
2517       ui[k+1] = ui[k] + nzk;
2518     }
2519 
2520 #if defined(PETSC_USE_INFO)
2521     if (ai[am] != 0) {
2522       PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]);
2523       ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2524       ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2525       ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2526     } else {
2527       ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2528     }
2529 #endif
2530 
2531     ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2532     ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2533     ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr);
2534     ierr = PetscFree(ajtmp);CHKERRQ(ierr);
2535 
2536     /* destroy list of free space and other temporary array(s) */
2537     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2538     ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor  */
2539     ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2540     ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2541 
2542   } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2543 
2544   /* put together the new matrix in MATSEQSBAIJ format */
2545   b    = (Mat_SeqSBAIJ*)(fact)->data;
2546   b->singlemalloc = PETSC_FALSE;
2547   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2548   b->j    = uj;
2549   b->i    = ui;
2550   b->diag = udiag;
2551   b->free_diag = PETSC_TRUE;
2552   b->ilen = 0;
2553   b->imax = 0;
2554   b->row  = perm;
2555   b->col  = perm;
2556   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2557   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2558   b->icol = iperm;
2559   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2560   ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2561   ierr = PetscLogObjectMemory(fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2562   b->maxnz   = b->nz = ui[am];
2563   b->free_a  = PETSC_TRUE;
2564   b->free_ij = PETSC_TRUE;
2565 
2566   fact->info.factor_mallocs    = reallocs;
2567   fact->info.fill_ratio_given  = fill;
2568   if (ai[am] != 0) {
2569     fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2570   } else {
2571     fact->info.fill_ratio_needed = 0.0;
2572   }
2573   fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2574   PetscFunctionReturn(0);
2575 }
2576 
2577 #undef __FUNCT__
2578 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ_inplace"
2579 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2580 {
2581   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2582   Mat_SeqSBAIJ       *b;
2583   PetscErrorCode     ierr;
2584   PetscTruth         perm_identity,missing;
2585   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag;
2586   const PetscInt     *rip,*riip;
2587   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
2588   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL,d;
2589   PetscInt           ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
2590   PetscReal          fill=info->fill,levels=info->levels;
2591   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2592   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
2593   PetscBT            lnkbt;
2594   IS                 iperm;
2595 
2596   PetscFunctionBegin;
2597   if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n);
2598   ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
2599   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
2600   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2601   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2602 
2603   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2604   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2605   ui[0] = 0;
2606 
2607   /* ICC(0) without matrix ordering: simply copies fill pattern */
2608   if (!levels && perm_identity) {
2609 
2610     for (i=0; i<am; i++) {
2611       ui[i+1]  = ui[i] + ai[i+1] - a->diag[i];
2612       udiag[i] = ui[i];
2613     }
2614     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2615     cols = uj;
2616     for (i=0; i<am; i++) {
2617       aj    = a->j + a->diag[i];
2618       ncols = ui[i+1] - ui[i];
2619       for (j=0; j<ncols; j++) *cols++ = *aj++;
2620     }
2621   } else { /* case: levels>0 || (levels=0 && !perm_identity) */
2622     ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2623     ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2624 
2625     /* initialization */
2626     ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr);
2627 
2628     /* jl: linked list for storing indices of the pivot rows
2629        il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2630     ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr);
2631     for (i=0; i<am; i++){
2632       jl[i] = am; il[i] = 0;
2633     }
2634 
2635     /* create and initialize a linked list for storing column indices of the active row k */
2636     nlnk = am + 1;
2637     ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2638 
2639     /* initial FreeSpace size is fill*(ai[am]+1) */
2640     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2641     current_space = free_space;
2642     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr);
2643     current_space_lvl = free_space_lvl;
2644 
2645     for (k=0; k<am; k++){  /* for each active row k */
2646       /* initialize lnk by the column indices of row rip[k] of A */
2647       nzk   = 0;
2648       ncols = ai[rip[k]+1] - ai[rip[k]];
2649       if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2650       ncols_upper = 0;
2651       for (j=0; j<ncols; j++){
2652         i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2653         if (riip[i] >= k){ /* only take upper triangular entry */
2654           ajtmp[ncols_upper] = i;
2655           ncols_upper++;
2656         }
2657       }
2658       ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2659       nzk += nlnk;
2660 
2661       /* update lnk by computing fill-in for each pivot row to be merged in */
2662       prow = jl[k]; /* 1st pivot row */
2663 
2664       while (prow < k){
2665         nextprow = jl[prow];
2666 
2667         /* merge prow into k-th row */
2668         jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2669         jmax = ui[prow+1];
2670         ncols = jmax-jmin;
2671         i     = jmin - ui[prow];
2672         cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2673         uj    = uj_lvl_ptr[prow] + i; /* levels of cols */
2674         j     = *(uj - 1);
2675         ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr);
2676         nzk += nlnk;
2677 
2678         /* update il and jl for prow */
2679         if (jmin < jmax){
2680           il[prow] = jmin;
2681           j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2682         }
2683         prow = nextprow;
2684       }
2685 
2686       /* if free space is not available, make more free space */
2687       if (current_space->local_remaining<nzk) {
2688         i = am - k + 1; /* num of unfactored rows */
2689         i *= PetscMin(nzk, (i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2690         ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2691         ierr = PetscFreeSpaceGet(i,&current_space_lvl);CHKERRQ(ierr);
2692         reallocs++;
2693       }
2694 
2695       /* copy data into free_space and free_space_lvl, then initialize lnk */
2696       if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2697       ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
2698 
2699       /* add the k-th row into il and jl */
2700       if (nzk > 1){
2701         i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2702         jl[k] = jl[i]; jl[i] = k;
2703         il[k] = ui[k] + 1;
2704       }
2705       uj_ptr[k]     = current_space->array;
2706       uj_lvl_ptr[k] = current_space_lvl->array;
2707 
2708       current_space->array           += nzk;
2709       current_space->local_used      += nzk;
2710       current_space->local_remaining -= nzk;
2711 
2712       current_space_lvl->array           += nzk;
2713       current_space_lvl->local_used      += nzk;
2714       current_space_lvl->local_remaining -= nzk;
2715 
2716       ui[k+1] = ui[k] + nzk;
2717     }
2718 
2719 #if defined(PETSC_USE_INFO)
2720     if (ai[am] != 0) {
2721       PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]);
2722       ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2723       ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2724       ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2725     } else {
2726       ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2727     }
2728 #endif
2729 
2730     ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2731     ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2732     ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr);
2733     ierr = PetscFree(ajtmp);CHKERRQ(ierr);
2734 
2735     /* destroy list of free space and other temporary array(s) */
2736     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2737     ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
2738     ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2739     ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2740 
2741   } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2742 
2743   /* put together the new matrix in MATSEQSBAIJ format */
2744 
2745   b    = (Mat_SeqSBAIJ*)fact->data;
2746   b->singlemalloc = PETSC_FALSE;
2747   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2748   b->j    = uj;
2749   b->i    = ui;
2750   b->diag = udiag;
2751   b->free_diag = PETSC_TRUE;
2752   b->ilen = 0;
2753   b->imax = 0;
2754   b->row  = perm;
2755   b->col  = perm;
2756   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2757   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2758   b->icol = iperm;
2759   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2760   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2761   ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2762   b->maxnz   = b->nz = ui[am];
2763   b->free_a  = PETSC_TRUE;
2764   b->free_ij = PETSC_TRUE;
2765 
2766   fact->info.factor_mallocs    = reallocs;
2767   fact->info.fill_ratio_given  = fill;
2768   if (ai[am] != 0) {
2769     fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2770   } else {
2771     fact->info.fill_ratio_needed = 0.0;
2772   }
2773   fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace;
2774   PetscFunctionReturn(0);
2775 }
2776 
2777 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2778 {
2779   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2780   Mat_SeqSBAIJ       *b;
2781   PetscErrorCode     ierr;
2782   PetscTruth         perm_identity;
2783   PetscReal          fill = info->fill;
2784   const PetscInt     *rip,*riip;
2785   PetscInt           i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow;
2786   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
2787   PetscInt           nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr,*udiag;
2788   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2789   PetscBT            lnkbt;
2790   IS                 iperm;
2791 
2792   PetscFunctionBegin;
2793   if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n);
2794   /* check whether perm is the identity mapping */
2795   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2796   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2797   ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2798   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2799 
2800   /* initialization */
2801   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2802   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2803   ui[0] = 0;
2804 
2805   /* jl: linked list for storing indices of the pivot rows
2806      il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2807   ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr);
2808   for (i=0; i<am; i++){
2809     jl[i] = am; il[i] = 0;
2810   }
2811 
2812   /* create and initialize a linked list for storing column indices of the active row k */
2813   nlnk = am + 1;
2814   ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2815 
2816   /* initial FreeSpace size is fill*(ai[am]+1) */
2817   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2818   current_space = free_space;
2819 
2820   for (k=0; k<am; k++){  /* for each active row k */
2821     /* initialize lnk by the column indices of row rip[k] of A */
2822     nzk   = 0;
2823     ncols = ai[rip[k]+1] - ai[rip[k]];
2824     if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2825     ncols_upper = 0;
2826     for (j=0; j<ncols; j++){
2827       i = riip[*(aj + ai[rip[k]] + j)];
2828       if (i >= k){ /* only take upper triangular entry */
2829         cols[ncols_upper] = i;
2830         ncols_upper++;
2831       }
2832     }
2833     ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2834     nzk += nlnk;
2835 
2836     /* update lnk by computing fill-in for each pivot row to be merged in */
2837     prow = jl[k]; /* 1st pivot row */
2838 
2839     while (prow < k){
2840       nextprow = jl[prow];
2841       /* merge prow into k-th row */
2842       jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2843       jmax = ui[prow+1];
2844       ncols = jmax-jmin;
2845       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2846       ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2847       nzk += nlnk;
2848 
2849       /* update il and jl for prow */
2850       if (jmin < jmax){
2851         il[prow] = jmin;
2852         j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
2853       }
2854       prow = nextprow;
2855     }
2856 
2857     /* if free space is not available, make more free space */
2858     if (current_space->local_remaining<nzk) {
2859       i  = am - k + 1; /* num of unfactored rows */
2860       i *= PetscMin(nzk,i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */
2861       ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2862       reallocs++;
2863     }
2864 
2865     /* copy data into free space, then initialize lnk */
2866     ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
2867 
2868     /* add the k-th row into il and jl */
2869     if (nzk > 1){
2870       i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2871       jl[k] = jl[i]; jl[i] = k;
2872       il[k] = ui[k] + 1;
2873     }
2874     ui_ptr[k] = current_space->array;
2875     current_space->array           += nzk;
2876     current_space->local_used      += nzk;
2877     current_space->local_remaining -= nzk;
2878 
2879     ui[k+1] = ui[k] + nzk;
2880   }
2881 
2882 #if defined(PETSC_USE_INFO)
2883   if (ai[am] != 0) {
2884     PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]);
2885     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2886     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2887     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2888   } else {
2889      ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2890   }
2891 #endif
2892 
2893   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2894   ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2895   ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr);
2896 
2897   /* destroy list of free space and other temporary array(s) */
2898   ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2899   ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor */
2900   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2901 
2902   /* put together the new matrix in MATSEQSBAIJ format */
2903 
2904   b = (Mat_SeqSBAIJ*)fact->data;
2905   b->singlemalloc = PETSC_FALSE;
2906   b->free_a       = PETSC_TRUE;
2907   b->free_ij      = PETSC_TRUE;
2908   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2909   b->j    = uj;
2910   b->i    = ui;
2911   b->diag = udiag;
2912   b->free_diag = PETSC_TRUE;
2913   b->ilen = 0;
2914   b->imax = 0;
2915   b->row  = perm;
2916   b->col  = perm;
2917   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2918   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2919   b->icol = iperm;
2920   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2921   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2922   ierr    = PetscLogObjectMemory(fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2923   b->maxnz = b->nz = ui[am];
2924 
2925   fact->info.factor_mallocs    = reallocs;
2926   fact->info.fill_ratio_given  = fill;
2927   if (ai[am] != 0) {
2928     fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2929   } else {
2930     fact->info.fill_ratio_needed = 0.0;
2931   }
2932   fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2933   PetscFunctionReturn(0);
2934 }
2935 
2936 #undef __FUNCT__
2937 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ_inplace"
2938 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2939 {
2940   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2941   Mat_SeqSBAIJ       *b;
2942   PetscErrorCode     ierr;
2943   PetscTruth         perm_identity;
2944   PetscReal          fill = info->fill;
2945   const PetscInt     *rip,*riip;
2946   PetscInt           i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow;
2947   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
2948   PetscInt           nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr;
2949   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2950   PetscBT            lnkbt;
2951   IS                 iperm;
2952 
2953   PetscFunctionBegin;
2954   if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n);
2955   /* check whether perm is the identity mapping */
2956   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2957   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2958   ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2959   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2960 
2961   /* initialization */
2962   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2963   ui[0] = 0;
2964 
2965   /* jl: linked list for storing indices of the pivot rows
2966      il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2967   ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr);
2968   for (i=0; i<am; i++){
2969     jl[i] = am; il[i] = 0;
2970   }
2971 
2972   /* create and initialize a linked list for storing column indices of the active row k */
2973   nlnk = am + 1;
2974   ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2975 
2976   /* initial FreeSpace size is fill*(ai[am]+1) */
2977   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2978   current_space = free_space;
2979 
2980   for (k=0; k<am; k++){  /* for each active row k */
2981     /* initialize lnk by the column indices of row rip[k] of A */
2982     nzk   = 0;
2983     ncols = ai[rip[k]+1] - ai[rip[k]];
2984     if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2985     ncols_upper = 0;
2986     for (j=0; j<ncols; j++){
2987       i = riip[*(aj + ai[rip[k]] + j)];
2988       if (i >= k){ /* only take upper triangular entry */
2989         cols[ncols_upper] = i;
2990         ncols_upper++;
2991       }
2992     }
2993     ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2994     nzk += nlnk;
2995 
2996     /* update lnk by computing fill-in for each pivot row to be merged in */
2997     prow = jl[k]; /* 1st pivot row */
2998 
2999     while (prow < k){
3000       nextprow = jl[prow];
3001       /* merge prow into k-th row */
3002       jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
3003       jmax = ui[prow+1];
3004       ncols = jmax-jmin;
3005       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */
3006       ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3007       nzk += nlnk;
3008 
3009       /* update il and jl for prow */
3010       if (jmin < jmax){
3011         il[prow] = jmin;
3012         j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
3013       }
3014       prow = nextprow;
3015     }
3016 
3017     /* if free space is not available, make more free space */
3018     if (current_space->local_remaining<nzk) {
3019       i = am - k + 1; /* num of unfactored rows */
3020       i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
3021       ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
3022       reallocs++;
3023     }
3024 
3025     /* copy data into free space, then initialize lnk */
3026     ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
3027 
3028     /* add the k-th row into il and jl */
3029     if (nzk-1 > 0){
3030       i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
3031       jl[k] = jl[i]; jl[i] = k;
3032       il[k] = ui[k] + 1;
3033     }
3034     ui_ptr[k] = current_space->array;
3035     current_space->array           += nzk;
3036     current_space->local_used      += nzk;
3037     current_space->local_remaining -= nzk;
3038 
3039     ui[k+1] = ui[k] + nzk;
3040   }
3041 
3042 #if defined(PETSC_USE_INFO)
3043   if (ai[am] != 0) {
3044     PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]);
3045     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
3046     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
3047     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
3048   } else {
3049      ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
3050   }
3051 #endif
3052 
3053   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
3054   ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
3055   ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr);
3056 
3057   /* destroy list of free space and other temporary array(s) */
3058   ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
3059   ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
3060   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
3061 
3062   /* put together the new matrix in MATSEQSBAIJ format */
3063 
3064   b = (Mat_SeqSBAIJ*)fact->data;
3065   b->singlemalloc = PETSC_FALSE;
3066   b->free_a       = PETSC_TRUE;
3067   b->free_ij      = PETSC_TRUE;
3068   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
3069   b->j    = uj;
3070   b->i    = ui;
3071   b->diag = 0;
3072   b->ilen = 0;
3073   b->imax = 0;
3074   b->row  = perm;
3075   b->col  = perm;
3076   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
3077   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
3078   b->icol = iperm;
3079   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
3080   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
3081   ierr    = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
3082   b->maxnz = b->nz = ui[am];
3083 
3084   fact->info.factor_mallocs    = reallocs;
3085   fact->info.fill_ratio_given  = fill;
3086   if (ai[am] != 0) {
3087     fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
3088   } else {
3089     fact->info.fill_ratio_needed = 0.0;
3090   }
3091   fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace;
3092   PetscFunctionReturn(0);
3093 }
3094 
3095 #undef __FUNCT__
3096 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering"
3097 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx)
3098 {
3099   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
3100   PetscErrorCode    ierr;
3101   PetscInt          n = A->rmap->n;
3102   const PetscInt    *ai = a->i,*aj = a->j,*adiag = a->diag,*vi;
3103   PetscScalar       *x,sum;
3104   const PetscScalar *b;
3105   const MatScalar   *aa = a->a,*v;
3106   PetscInt          i,nz;
3107 
3108   PetscFunctionBegin;
3109   if (!n) PetscFunctionReturn(0);
3110 
3111   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3112   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3113 
3114   /* forward solve the lower triangular */
3115   x[0] = b[0];
3116   v    = aa;
3117   vi   = aj;
3118   for (i=1; i<n; i++) {
3119     nz  = ai[i+1] - ai[i];
3120     sum = b[i];
3121     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
3122     v  += nz;
3123     vi += nz;
3124     x[i] = sum;
3125   }
3126 
3127   /* backward solve the upper triangular */
3128   for (i=n-1; i>=0; i--){
3129     v   = aa + adiag[i+1] + 1;
3130     vi  = aj + adiag[i+1] + 1;
3131     nz = adiag[i] - adiag[i+1]-1;
3132     sum = x[i];
3133     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
3134     x[i] = sum*v[nz]; /* x[i]=aa[adiag[i]]*sum; v++; */
3135   }
3136 
3137   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
3138   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3139   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3140   PetscFunctionReturn(0);
3141 }
3142 
3143 #undef __FUNCT__
3144 #define __FUNCT__ "MatSolve_SeqAIJ"
3145 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx)
3146 {
3147   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
3148   IS                iscol = a->col,isrow = a->row;
3149   PetscErrorCode    ierr;
3150   PetscInt          i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz;
3151   const PetscInt    *rout,*cout,*r,*c;
3152   PetscScalar       *x,*tmp,sum;
3153   const PetscScalar *b;
3154   const MatScalar   *aa = a->a,*v;
3155 
3156   PetscFunctionBegin;
3157   if (!n) PetscFunctionReturn(0);
3158 
3159   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3160   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3161   tmp  = a->solve_work;
3162 
3163   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
3164   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
3165 
3166   /* forward solve the lower triangular */
3167   tmp[0] = b[r[0]];
3168   v      = aa;
3169   vi     = aj;
3170   for (i=1; i<n; i++) {
3171     nz  = ai[i+1] - ai[i];
3172     sum = b[r[i]];
3173     PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
3174     tmp[i] = sum;
3175     v += nz; vi += nz;
3176   }
3177 
3178   /* backward solve the upper triangular */
3179   for (i=n-1; i>=0; i--){
3180     v   = aa + adiag[i+1]+1;
3181     vi  = aj + adiag[i+1]+1;
3182     nz  = adiag[i]-adiag[i+1]-1;
3183     sum = tmp[i];
3184     PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
3185     x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */
3186   }
3187 
3188   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
3189   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
3190   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3191   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3192   ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr);
3193   PetscFunctionReturn(0);
3194 }
3195 
3196 #undef __FUNCT__
3197 #define __FUNCT__ "MatILUDTFactor_SeqAIJ"
3198 /*
3199     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
3200 */
3201 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact)
3202 {
3203   Mat                B = *fact;
3204   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b;
3205   IS                 isicol;
3206   PetscErrorCode     ierr;
3207   const PetscInt     *r,*ic;
3208   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag;
3209   PetscInt           *bi,*bj,*bdiag,*bdiag_rev;
3210   PetscInt           row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au;
3211   PetscInt           nlnk,*lnk;
3212   PetscBT            lnkbt;
3213   PetscTruth         row_identity,icol_identity,both_identity;
3214   MatScalar          *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp;
3215   const PetscInt     *ics;
3216   PetscInt           j,nz,*pj,*bjtmp,k,ncut,*jtmp;
3217   PetscReal          dt=info->dt,dtcol=info->dtcol,shift=info->shiftamount;
3218   PetscInt           dtcount=(PetscInt)info->dtcount,nnz_max;
3219   PetscTruth         missing;
3220 
3221   PetscFunctionBegin;
3222 
3223   if (dt      == PETSC_DEFAULT) dt      = 0.005;
3224   if (dtcol   == PETSC_DEFAULT) dtcol   = 0.01; /* XXX unused! */
3225   if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax);
3226 
3227   /* ------- symbolic factorization, can be reused ---------*/
3228   ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
3229   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
3230   adiag=a->diag;
3231 
3232   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
3233 
3234   /* bdiag is location of diagonal in factor */
3235   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);     /* becomes b->diag */
3236   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag_rev);CHKERRQ(ierr); /* temporary */
3237 
3238   /* allocate row pointers bi */
3239   ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
3240 
3241   /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */
3242   if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */
3243   nnz_max  = ai[n]+2*n*dtcount+2;
3244 
3245   ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
3246   ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr);
3247 
3248   /* put together the new matrix */
3249   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
3250   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
3251   b    = (Mat_SeqAIJ*)B->data;
3252   b->free_a       = PETSC_TRUE;
3253   b->free_ij      = PETSC_TRUE;
3254   b->singlemalloc = PETSC_FALSE;
3255   b->a          = ba;
3256   b->j          = bj;
3257   b->i          = bi;
3258   b->diag       = bdiag;
3259   b->ilen       = 0;
3260   b->imax       = 0;
3261   b->row        = isrow;
3262   b->col        = iscol;
3263   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
3264   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
3265   b->icol       = isicol;
3266   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
3267 
3268   ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
3269   b->maxnz = nnz_max;
3270 
3271   B->factor                = MAT_FACTOR_ILUDT;
3272   B->info.factor_mallocs   = 0;
3273   B->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]);
3274   CHKMEMQ;
3275   /* ------- end of symbolic factorization ---------*/
3276 
3277   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
3278   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
3279   ics  = ic;
3280 
3281   /* linked list for storing column indices of the active row */
3282   nlnk = n + 1;
3283   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3284 
3285   /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */
3286   ierr = PetscMalloc2(n,PetscInt,&im,n,PetscInt,&jtmp);CHKERRQ(ierr);
3287   /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */
3288   ierr = PetscMalloc2(n,MatScalar,&rtmp,n,MatScalar,&vtmp);CHKERRQ(ierr);
3289   ierr = PetscMemzero(rtmp,n*sizeof(MatScalar));CHKERRQ(ierr);
3290 
3291   bi[0]    = 0;
3292   bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */
3293   bdiag_rev[n] = bdiag[0];
3294   bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */
3295   for (i=0; i<n; i++) {
3296     /* copy initial fill into linked list */
3297     nzi = 0; /* nonzeros for active row i */
3298     nzi = ai[r[i]+1] - ai[r[i]];
3299     if (!nzi) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
3300     nzi_al = adiag[r[i]] - ai[r[i]];
3301     nzi_au = ai[r[i]+1] - adiag[r[i]] -1;
3302     ajtmp = aj + ai[r[i]];
3303     ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3304 
3305     /* load in initial (unfactored row) */
3306     aatmp = a->a + ai[r[i]];
3307     for (j=0; j<nzi; j++) {
3308       rtmp[ics[*ajtmp++]] = *aatmp++;
3309     }
3310 
3311     /* add pivot rows into linked list */
3312     row = lnk[n];
3313     while (row < i ) {
3314       nzi_bl = bi[row+1] - bi[row] + 1;
3315       bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */
3316       ierr  = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr);
3317       nzi  += nlnk;
3318       row   = lnk[row];
3319     }
3320 
3321     /* copy data from lnk into jtmp, then initialize lnk */
3322     ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr);
3323 
3324     /* numerical factorization */
3325     bjtmp = jtmp;
3326     row   = *bjtmp++; /* 1st pivot row */
3327     while  ( row < i ) {
3328       pc         = rtmp + row;
3329       pv         = ba + bdiag[row]; /* 1./(diag of the pivot row) */
3330       multiplier = (*pc) * (*pv);
3331       *pc        = multiplier;
3332       if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */
3333         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
3334         pv         = ba + bdiag[row+1] + 1;
3335         /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */
3336         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
3337         for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
3338         ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
3339       }
3340       row = *bjtmp++;
3341     }
3342 
3343     /* copy sparse rtmp into contiguous vtmp; separate L and U part */
3344     diag_tmp = rtmp[i];  /* save diagonal value - may not needed?? */
3345     nzi_bl = 0; j = 0;
3346     while (jtmp[j] < i){ /* Note: jtmp is sorted */
3347       vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
3348       nzi_bl++; j++;
3349     }
3350     nzi_bu = nzi - nzi_bl -1;
3351     while (j < nzi){
3352       vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
3353       j++;
3354     }
3355 
3356     bjtmp = bj + bi[i];
3357     batmp = ba + bi[i];
3358     /* apply level dropping rule to L part */
3359     ncut = nzi_al + dtcount;
3360     if (ncut < nzi_bl){
3361       ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr);
3362       ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr);
3363     } else {
3364       ncut = nzi_bl;
3365     }
3366     for (j=0; j<ncut; j++){
3367       bjtmp[j] = jtmp[j];
3368       batmp[j] = vtmp[j];
3369       /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */
3370     }
3371     bi[i+1] = bi[i] + ncut;
3372     nzi = ncut + 1;
3373 
3374     /* apply level dropping rule to U part */
3375     ncut = nzi_au + dtcount;
3376     if (ncut < nzi_bu){
3377       ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr);
3378       ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr);
3379     } else {
3380       ncut = nzi_bu;
3381     }
3382     nzi += ncut;
3383 
3384     /* mark bdiagonal */
3385     bdiag[i+1]       = bdiag[i] - (ncut + 1);
3386     bdiag_rev[n-i-1] = bdiag[i+1];
3387     bi[2*n - i]      = bi[2*n - i +1] - (ncut + 1);
3388     bjtmp = bj + bdiag[i];
3389     batmp = ba + bdiag[i];
3390     *bjtmp = i;
3391     *batmp = diag_tmp; /* rtmp[i]; */
3392     if (*batmp == 0.0) {
3393       *batmp = dt+shift;
3394       /* printf(" row %d add shift %g\n",i,shift); */
3395     }
3396     *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */
3397     /* printf(" (%d,%g),",*bjtmp,*batmp); */
3398 
3399     bjtmp = bj + bdiag[i+1]+1;
3400     batmp = ba + bdiag[i+1]+1;
3401     for (k=0; k<ncut; k++){
3402       bjtmp[k] = jtmp[nzi_bl+1+k];
3403       batmp[k] = vtmp[nzi_bl+1+k];
3404       /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */
3405     }
3406     /* printf("\n"); */
3407 
3408     im[i]   = nzi; /* used by PetscLLAddSortedLU() */
3409     /*
3410     printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]);
3411     printf(" ----------------------------\n");
3412     */
3413   } /* for (i=0; i<n; i++) */
3414   /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */
3415   if (bi[n] >= bdiag[n]) SETERRQ2(PETSC_ERR_ARG_SIZ,"end of L array %d cannot >= the beginning of U array %d",bi[n],bdiag[n]);
3416 
3417   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
3418   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
3419 
3420   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
3421   ierr = PetscFree2(im,jtmp);CHKERRQ(ierr);
3422   ierr = PetscFree2(rtmp,vtmp);CHKERRQ(ierr);
3423   ierr = PetscFree(bdiag_rev);CHKERRQ(ierr);
3424 
3425   ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr);
3426   b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n];
3427 
3428   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
3429   ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr);
3430   both_identity = (PetscTruth) (row_identity && icol_identity);
3431   if (row_identity && icol_identity) {
3432     B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering;
3433   } else {
3434     B->ops->solve = MatSolve_SeqAIJ;
3435   }
3436 
3437   B->ops->solveadd          = 0;
3438   B->ops->solvetranspose    = 0;
3439   B->ops->solvetransposeadd = 0;
3440   B->ops->matsolve          = 0;
3441   B->assembled              = PETSC_TRUE;
3442   B->preallocated           = PETSC_TRUE;
3443   PetscFunctionReturn(0);
3444 }
3445 
3446 /* a wraper of MatILUDTFactor_SeqAIJ() */
3447 #undef __FUNCT__
3448 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ"
3449 /*
3450     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
3451 */
3452 
3453 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info)
3454 {
3455   PetscErrorCode     ierr;
3456 
3457   PetscFunctionBegin;
3458   ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr);
3459   PetscFunctionReturn(0);
3460 }
3461 
3462 /*
3463    same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors
3464    - intend to replace existing MatLUFactorNumeric_SeqAIJ()
3465 */
3466 #undef __FUNCT__
3467 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ"
3468 /*
3469     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
3470 */
3471 
3472 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info)
3473 {
3474   Mat            C=fact;
3475   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
3476   IS             isrow = b->row,isicol = b->icol;
3477   PetscErrorCode ierr;
3478   const PetscInt *r,*ic,*ics;
3479   PetscInt       i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
3480   PetscInt       *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj;
3481   MatScalar      *rtmp,*pc,multiplier,*v,*pv,*aa=a->a;
3482   PetscReal      dt=info->dt,shift=info->shiftamount;
3483   PetscTruth     row_identity, col_identity;
3484 
3485   PetscFunctionBegin;
3486   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
3487   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
3488   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
3489   ics  = ic;
3490 
3491   for (i=0; i<n; i++){
3492     /* initialize rtmp array */
3493     nzl   = bi[i+1] - bi[i];       /* num of nozeros in L(i,:) */
3494     bjtmp = bj + bi[i];
3495     for  (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0;
3496     rtmp[i] = 0.0;
3497     nzu   = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */
3498     bjtmp = bj + bdiag[i+1] + 1;
3499     for  (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0;
3500 
3501     /* load in initial unfactored row of A */
3502     /* printf("row %d\n",i); */
3503     nz    = ai[r[i]+1] - ai[r[i]];
3504     ajtmp = aj + ai[r[i]];
3505     v     = aa + ai[r[i]];
3506     for (j=0; j<nz; j++) {
3507       rtmp[ics[*ajtmp++]] = v[j];
3508       /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */
3509     }
3510     /* printf("\n"); */
3511 
3512     /* numerical factorization */
3513     bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */
3514     nzl   = bi[i+1] - bi[i]; /* num of entries in L(i,:) */
3515     k = 0;
3516     while (k < nzl){
3517       row   = *bjtmp++;
3518       /* printf("  prow %d\n",row); */
3519       pc         = rtmp + row;
3520       pv         = b->a + bdiag[row]; /* 1./(diag of the pivot row) */
3521       multiplier = (*pc) * (*pv);
3522       *pc        = multiplier;
3523       if (PetscAbsScalar(multiplier) > dt){
3524         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
3525         pv         = b->a + bdiag[row+1] + 1;
3526         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
3527         for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
3528         /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */
3529       }
3530       k++;
3531     }
3532 
3533     /* finished row so stick it into b->a */
3534     /* L-part */
3535     pv = b->a + bi[i] ;
3536     pj = bj + bi[i] ;
3537     nzl = bi[i+1] - bi[i];
3538     for (j=0; j<nzl; j++) {
3539       pv[j] = rtmp[pj[j]];
3540       /* printf(" (%d,%g),",pj[j],pv[j]); */
3541     }
3542 
3543     /* diagonal: invert diagonal entries for simplier triangular solves */
3544     if (rtmp[i] == 0.0) rtmp[i] = dt+shift;
3545     b->a[bdiag[i]] = 1.0/rtmp[i];
3546     /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */
3547 
3548     /* U-part */
3549     pv = b->a + bdiag[i+1] + 1;
3550     pj = bj + bdiag[i+1] + 1;
3551     nzu = bdiag[i] - bdiag[i+1] - 1;
3552     for (j=0; j<nzu; j++) {
3553       pv[j] = rtmp[pj[j]];
3554       /* printf(" (%d,%g),",pj[j],pv[j]); */
3555     }
3556     /* printf("\n"); */
3557   }
3558 
3559   ierr = PetscFree(rtmp);CHKERRQ(ierr);
3560   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
3561   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
3562 
3563   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
3564   ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
3565   if (row_identity && col_identity) {
3566     C->ops->solve   = MatSolve_SeqAIJ_NaturalOrdering;
3567   } else {
3568     C->ops->solve   = MatSolve_SeqAIJ;
3569   }
3570   C->ops->solveadd           = 0;
3571   C->ops->solvetranspose     = 0;
3572   C->ops->solvetransposeadd  = 0;
3573   C->ops->matsolve           = 0;
3574   C->assembled    = PETSC_TRUE;
3575   C->preallocated = PETSC_TRUE;
3576   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
3577   PetscFunctionReturn(0);
3578 }
3579