xref: /petsc/src/mat/impls/aij/seq/aijfact.c (revision 753ebd1d069d7a4e86ed47ccb83df941bd1fb5db)
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;
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 = PetscMalloc(n*sizeof(PetscInt),&order);CHKERRQ(ierr);
42   ierr = PetscMemzero(done,n*sizeof(PetscTruth));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;
69         past   = 0;
70         for (j=ai[k]; j<ai[k+1]; j++) {
71           kk = aj[j];
72           if (done[kk]) past += PetscAbsScalar(aa[j]);
73           else if (kk != k) future  += PetscAbsScalar(aa[j]);
74         }
75         if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */
76         if (past/future > best) {
77           best = past/future;
78           newcurrent = k;
79         }
80       }
81     }
82     if (current == newcurrent) SETERRQ(PETSC_ERR_PLIB,"newcurrent cannot be current");
83     current = newcurrent;
84     order[i+1] = current;
85   }
86   ierr = ISCreateGeneral(PETSC_COMM_SELF,n,order,irow);CHKERRQ(ierr);
87   *icol = *irow;
88   ierr = PetscObjectReference((PetscObject)*irow);CHKERRQ(ierr);
89   ierr = PetscFree(done);CHKERRQ(ierr);
90   ierr = PetscFree(order);CHKERRQ(ierr);
91   PetscFunctionReturn(0);
92 }
93 EXTERN_C_END
94 
95 EXTERN_C_BEGIN
96 #undef __FUNCT__
97 #define __FUNCT__ "MatGetFactorAvailable_seqaij_petsc"
98 PetscErrorCode MatGetFactorAvailable_seqaij_petsc(Mat A,MatFactorType ftype,PetscTruth *flg)
99 {
100   PetscFunctionBegin;
101   *flg = PETSC_TRUE;
102   PetscFunctionReturn(0);
103 }
104 EXTERN_C_END
105 
106 EXTERN_C_BEGIN
107 #undef __FUNCT__
108 #define __FUNCT__ "MatGetFactor_seqaij_petsc"
109 PetscErrorCode MatGetFactor_seqaij_petsc(Mat A,MatFactorType ftype,Mat *B)
110 {
111   PetscInt           n = A->rmap->n;
112   PetscErrorCode     ierr;
113 
114   PetscFunctionBegin;
115   ierr = MatCreate(((PetscObject)A)->comm,B);CHKERRQ(ierr);
116   ierr = MatSetSizes(*B,n,n,n,n);CHKERRQ(ierr);
117   if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT){
118     ierr = MatSetType(*B,MATSEQAIJ);CHKERRQ(ierr);
119     (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqAIJ;
120     (*B)->ops->lufactorsymbolic  = MatLUFactorSymbolic_SeqAIJ;
121     (*B)->ops->iludtfactor       = MatILUDTFactor_SeqAIJ;
122   } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) {
123     ierr = MatSetType(*B,MATSEQSBAIJ);CHKERRQ(ierr);
124     ierr = MatSeqSBAIJSetPreallocation(*B,1,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
125     (*B)->ops->iccfactorsymbolic      = MatICCFactorSymbolic_SeqAIJ;
126     (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJ;
127   } else SETERRQ(PETSC_ERR_SUP,"Factor type not supported");
128   (*B)->factor = ftype;
129   PetscFunctionReturn(0);
130 }
131 EXTERN_C_END
132 
133 #undef __FUNCT__
134 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ"
135 PetscErrorCode MatLUFactorSymbolic_SeqAIJ(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
136 {
137   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
138   IS                 isicol;
139   PetscErrorCode     ierr;
140   const PetscInt     *r,*ic;
141   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j;
142   PetscInt           *bi,*bj,*ajtmp;
143   PetscInt           *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im;
144   PetscReal          f;
145   PetscInt           nlnk,*lnk,k,**bi_ptr;
146   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
147   PetscBT            lnkbt;
148   PetscTruth         newdatastruct= PETSC_FALSE;
149 
150   PetscFunctionBegin;
151   ierr = PetscOptionsGetTruth(PETSC_NULL,"-lu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
152   if(newdatastruct){
153     ierr = MatLUFactorSymbolic_SeqAIJ_newdatastruct(B,A,isrow,iscol,info);CHKERRQ(ierr);
154     PetscFunctionReturn(0);
155   }
156 
157 
158   if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square");
159   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
160   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
161   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
162 
163   /* get new row pointers */
164   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
165   bi[0] = 0;
166 
167   /* bdiag is location of diagonal in factor */
168   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
169   bdiag[0] = 0;
170 
171   /* linked list for storing column indices of the active row */
172   nlnk = n + 1;
173   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
174 
175   ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr);
176 
177   /* initial FreeSpace size is f*(ai[n]+1) */
178   f = info->fill;
179   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
180   current_space = free_space;
181 
182   for (i=0; i<n; i++) {
183     /* copy previous fill into linked list */
184     nzi = 0;
185     nnz = ai[r[i]+1] - ai[r[i]];
186     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
187     ajtmp = aj + ai[r[i]];
188     ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
189     nzi += nlnk;
190 
191     /* add pivot rows into linked list */
192     row = lnk[n];
193     while (row < i) {
194       nzbd    = bdiag[row] - bi[row] + 1; /* num of entries in the row with column index <= row */
195       ajtmp   = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */
196       ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr);
197       nzi += nlnk;
198       row  = lnk[row];
199     }
200     bi[i+1] = bi[i] + nzi;
201     im[i]   = nzi;
202 
203     /* mark bdiag */
204     nzbd = 0;
205     nnz  = nzi;
206     k    = lnk[n];
207     while (nnz-- && k < i){
208       nzbd++;
209       k = lnk[k];
210     }
211     bdiag[i] = bi[i] + nzbd;
212 
213     /* if free space is not available, make more free space */
214     if (current_space->local_remaining<nzi) {
215       nnz = (n - i)*nzi; /* estimated and max additional space needed */
216       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
217       reallocs++;
218     }
219 
220     /* copy data into free space, then initialize lnk */
221     ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
222     bi_ptr[i] = current_space->array;
223     current_space->array           += nzi;
224     current_space->local_used      += nzi;
225     current_space->local_remaining -= nzi;
226   }
227 #if defined(PETSC_USE_INFO)
228   if (ai[n] != 0) {
229     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
230     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
231     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
232     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr);
233     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
234   } else {
235     ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr);
236   }
237 #endif
238 
239   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
240   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
241 
242   /* destroy list of free space and other temporary array(s) */
243   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
244   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
245   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
246   ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr);
247 
248   /* put together the new matrix */
249   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
250   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
251   b    = (Mat_SeqAIJ*)(B)->data;
252   b->free_a       = PETSC_TRUE;
253   b->free_ij      = PETSC_TRUE;
254   b->singlemalloc = PETSC_FALSE;
255   ierr          = PetscMalloc((bi[n]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
256   b->j          = bj;
257   b->i          = bi;
258   b->diag       = bdiag;
259   b->ilen       = 0;
260   b->imax       = 0;
261   b->row        = isrow;
262   b->col        = iscol;
263   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
264   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
265   b->icol       = isicol;
266   ierr          = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
267 
268   /* In b structure:  Free imax, ilen, old a, old j.  Allocate solve_work, new a, new j */
269   ierr = PetscLogObjectMemory(B,(bi[n]-n)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
270   b->maxnz = b->nz = bi[n] ;
271 
272   (B)->factor                = MAT_FACTOR_LU;
273   (B)->info.factor_mallocs   = reallocs;
274   (B)->info.fill_ratio_given = f;
275 
276   if (ai[n]) {
277     (B)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
278   } else {
279     (B)->info.fill_ratio_needed = 0.0;
280   }
281   (B)->ops->lufactornumeric  = MatLUFactorNumeric_SeqAIJ;
282   (B)->ops->solve            = MatSolve_SeqAIJ;
283   (B)->ops->solvetranspose   = MatSolveTranspose_SeqAIJ;
284   /* switch to inodes if appropriate */
285   ierr = MatLUFactorSymbolic_SeqAIJ_Inode(B,A,isrow,iscol,info);CHKERRQ(ierr);
286   PetscFunctionReturn(0);
287 }
288 
289 #undef __FUNCT__
290 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ_newdatastruct"
291 PetscErrorCode MatLUFactorSymbolic_SeqAIJ_newdatastruct(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
292 {
293   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
294   IS                 isicol;
295   PetscErrorCode     ierr;
296   const PetscInt     *r,*ic;
297   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j;
298   PetscInt           *bi,*bj,*ajtmp;
299   PetscInt           *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im;
300   PetscReal          f;
301   PetscInt           nlnk,*lnk,k,**bi_ptr;
302   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
303   PetscBT            lnkbt;
304 
305   PetscFunctionBegin;
306   if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square");
307   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
308   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
309   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
310 
311   /* get new row pointers */
312   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
313   bi[0] = 0;
314 
315   /* bdiag is location of diagonal in factor */
316   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
317   bdiag[0] = 0;
318 
319   /* linked list for storing column indices of the active row */
320   nlnk = n + 1;
321   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
322 
323   ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr);
324 
325   /* initial FreeSpace size is f*(ai[n]+1) */
326   f = info->fill;
327   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
328   current_space = free_space;
329 
330   for (i=0; i<n; i++) {
331     /* copy previous fill into linked list */
332     nzi = 0;
333     nnz = ai[r[i]+1] - ai[r[i]];
334     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
335     ajtmp = aj + ai[r[i]];
336     ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
337     nzi += nlnk;
338 
339     /* add pivot rows into linked list */
340     row = lnk[n];
341     while (row < i){
342       nzbd  = bdiag[row] + 1; /* num of entries in the row with column index <= row */
343       ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */
344       ierr  = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr);
345       nzi  += nlnk;
346       row   = lnk[row];
347     }
348     bi[i+1] = bi[i] + nzi;
349     im[i]   = nzi;
350 
351     /* mark bdiag */
352     nzbd = 0;
353     nnz  = nzi;
354     k    = lnk[n];
355     while (nnz-- && k < i){
356       nzbd++;
357       k = lnk[k];
358     }
359     bdiag[i] = nzbd; /* note: bdiag[i] = nnzL as input for PetscFreeSpaceContiguous_LU() */
360 
361     /* if free space is not available, make more free space */
362     if (current_space->local_remaining<nzi) {
363       nnz = 2*(n - i)*nzi; /* estimated and max additional space needed */
364       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
365       reallocs++;
366     }
367 
368     /* copy data into free space, then initialize lnk */
369     ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
370     bi_ptr[i] = current_space->array;
371     current_space->array           += nzi;
372     current_space->local_used      += nzi;
373     current_space->local_remaining -= nzi;
374   }
375 #if defined(PETSC_USE_INFO)
376   if (ai[n] != 0) {
377     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
378     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
379     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
380     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr);
381     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
382   } else {
383     ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr);
384   }
385 #endif
386 
387   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
388   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
389 
390   /* destroy list of free space and other temporary array(s) */
391   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
392   ierr = PetscFreeSpaceContiguous_LU_v2(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr);
393   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
394   ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr);
395 
396   /* put together the new matrix */
397   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
398   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
399   b    = (Mat_SeqAIJ*)(B)->data;
400   b->free_a       = PETSC_TRUE;
401   b->free_ij      = PETSC_TRUE;
402   b->singlemalloc = PETSC_FALSE;
403   ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
404   b->j          = bj;
405   b->i          = bi;
406   b->diag       = bdiag;
407   b->ilen       = 0;
408   b->imax       = 0;
409   b->row        = isrow;
410   b->col        = iscol;
411   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
412   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
413   b->icol       = isicol;
414   ierr          = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
415 
416   /* In b structure:  Free imax, ilen, old a, old j.  Allocate solve_work, new a, new j */
417   ierr = PetscLogObjectMemory(B,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
418   b->maxnz = b->nz = bdiag[0]+1;
419   (B)->factor                = MAT_FACTOR_LU;
420   (B)->info.factor_mallocs   = reallocs;
421   (B)->info.fill_ratio_given = f;
422 
423   if (ai[n]) {
424     (B)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]);
425   } else {
426     (B)->info.fill_ratio_needed = 0.0;
427   }
428   (B)->ops->lufactornumeric  = MatLUFactorNumeric_SeqAIJ_newdatastruct;
429   PetscFunctionReturn(0);
430 }
431 
432 /*
433     Trouble in factorization, should we dump the original matrix?
434 */
435 #undef __FUNCT__
436 #define __FUNCT__ "MatFactorDumpMatrix"
437 PetscErrorCode MatFactorDumpMatrix(Mat A)
438 {
439   PetscErrorCode ierr;
440   PetscTruth     flg = PETSC_FALSE;
441 
442   PetscFunctionBegin;
443   ierr = PetscOptionsGetTruth(PETSC_NULL,"-mat_factor_dump_on_error",&flg,PETSC_NULL);CHKERRQ(ierr);
444   if (flg) {
445     PetscViewer viewer;
446     char        filename[PETSC_MAX_PATH_LEN];
447 
448     ierr = PetscSNPrintf(filename,PETSC_MAX_PATH_LEN,"matrix_factor_error.%d",PetscGlobalRank);CHKERRQ(ierr);
449     ierr = PetscViewerBinaryOpen(((PetscObject)A)->comm,filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr);
450     ierr = MatView(A,viewer);CHKERRQ(ierr);
451     ierr = PetscViewerDestroy(viewer);CHKERRQ(ierr);
452   }
453   PetscFunctionReturn(0);
454 }
455 
456 extern PetscErrorCode MatSolve_SeqAIJ_Inode(Mat,Vec,Vec);
457 
458 #undef __FUNCT__
459 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_newdatastruct"
460 PetscErrorCode MatLUFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info)
461 {
462   Mat            C=B;
463   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
464   IS             isrow = b->row,isicol = b->icol;
465   PetscErrorCode ierr;
466   const PetscInt *r,*ic,*ics;
467   PetscInt       i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
468   PetscInt       *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj;
469   MatScalar      *rtmp,*pc,multiplier,*v,*pv,*aa=a->a;
470   PetscTruth     row_identity,col_identity;
471 
472   LUShift_Ctx    sctx;
473   PetscInt       *ddiag,newshift;
474   PetscReal      rs;
475   MatScalar      d;
476 
477   PetscFunctionBegin;
478   /* MatPivotSetUp(): initialize shift context sctx */
479   ierr = PetscMemzero(&sctx,sizeof(LUShift_Ctx));CHKERRQ(ierr);
480 
481   /* if both shift schemes are chosen by user, only use info->shiftpd */
482   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
483     ddiag          = a->diag;
484     sctx.shift_top = info->zeropivot;
485     for (i=0; i<n; i++) {
486       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
487       d  = (aa)[ddiag[i]];
488       rs = -PetscAbsScalar(d) - PetscRealPart(d);
489       v  = aa+ai[i];
490       nz = ai[i+1] - ai[i];
491       for (j=0; j<nz; j++)
492 	rs += PetscAbsScalar(v[j]);
493       if (rs>sctx.shift_top) sctx.shift_top = rs;
494     }
495     sctx.shift_top   *= 1.1;
496     sctx.nshift_max   = 5;
497     sctx.shift_lo     = 0.;
498     sctx.shift_hi     = 1.;
499   }
500 
501   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
502   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
503   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
504   ics  = ic;
505 
506   do {
507     sctx.lushift = PETSC_FALSE;
508     for (i=0; i<n; i++){
509       /* zero rtmp */
510       /* L part */
511       nz    = bi[i+1] - bi[i];
512       bjtmp = bj + bi[i];
513       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
514 
515       /* U part */
516       nz = bdiag[i]-bdiag[i+1];
517       bjtmp = bj + bdiag[i+1]+1;
518       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
519 
520       /* load in initial (unfactored row) */
521       nz    = ai[r[i]+1] - ai[r[i]];
522       ajtmp = aj + ai[r[i]];
523       v     = aa + ai[r[i]];
524       for (j=0; j<nz; j++) {
525         rtmp[ics[ajtmp[j]]] = v[j];
526       }
527       /* ZeropivotApply() */
528       rtmp[ics[r[i]]] += sctx.shift_amount;  /* shift the diagonal of the matrix */
529 
530       /* elimination */
531       bjtmp = bj + bi[i];
532       row   = *bjtmp++;
533       nzL   = bi[i+1] - bi[i];
534       for(k=0; k < nzL;k++) {
535         pc = rtmp + row;
536         if (*pc != 0.0) {
537           pv         = b->a + bdiag[row];
538           multiplier = *pc * (*pv);
539           *pc        = multiplier;
540           pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
541 	  pv = b->a + bdiag[row+1]+1;
542 	  nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */
543           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
544           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
545         }
546         row = *bjtmp++;
547       }
548 
549       /* finished row so stick it into b->a */
550       rs = 0.0;
551       /* L part */
552       pv   = b->a + bi[i] ;
553       pj   = b->j + bi[i] ;
554       nz   = bi[i+1] - bi[i];
555       for (j=0; j<nz; j++) {
556         pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]);
557       }
558 
559       /* U part */
560       pv = b->a + bdiag[i+1]+1;
561       pj = b->j + bdiag[i+1]+1;
562       nz = bdiag[i] - bdiag[i+1]-1;
563       for (j=0; j<nz; j++) {
564         pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]);
565       }
566 
567       /* MatPivotCheck() */
568       sctx.rs  = rs;
569       sctx.pv  = rtmp[i];
570       /* ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); */
571       if (info->shiftnz){
572         ierr = MatPivotCheck_nz(info,sctx,i,newshift);CHKERRQ(ierr);
573       } else if (info->shiftpd){
574         ierr = MatPivotCheck_pd(info,sctx,i,newshift);CHKERRQ(ierr);
575       } else if (info->shiftinblocks){
576         ierr = MatPivotCheck_inblocks(info,sctx,i,newshift);CHKERRQ(ierr);
577       } else {
578         ierr = MatPivotCheck_none(info,sctx,i,newshift);CHKERRQ(ierr);
579       }
580       rtmp[i] = sctx.pv;
581       if (newshift == 1) break;
582 
583       /* Mark diagonal and invert diagonal for simplier triangular solves */
584       pv  = b->a + bdiag[i];
585       *pv = 1.0/rtmp[i];
586 
587     } /* endof for (i=0; i<n; i++){ */
588 
589     /* MatPivotRefine() */
590     if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max){
591       /*
592        * if no shift in this attempt & shifting & started shifting & can refine,
593        * then try lower shift
594        */
595       sctx.shift_hi       = sctx.shift_fraction;
596       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
597       sctx.shift_amount   = sctx.shift_fraction * sctx.shift_top;
598       sctx.lushift        = PETSC_TRUE;
599       sctx.nshift++;
600     }
601   } while (sctx.lushift);
602 
603   ierr = PetscFree(rtmp);CHKERRQ(ierr);
604   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
605   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
606 
607   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
608   ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
609   if (row_identity && col_identity) {
610     C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct_v2;
611   } else {
612     C->ops->solve = MatSolve_SeqAIJ_newdatastruct_v2;
613   }
614 
615   C->ops->solveadd           = 0;
616   C->ops->solvetranspose     = 0;
617   C->ops->solvetransposeadd  = 0;
618   C->ops->matsolve           = 0;
619   C->assembled    = PETSC_TRUE;
620   C->preallocated = PETSC_TRUE;
621   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
622 
623   /* MatPivotView() */
624   if (sctx.nshift){
625     if (info->shiftpd) {
626       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);
627     } else if (info->shiftnz) {
628       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
629     } else if (info->shiftinblocks){
630       ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftinblocks);CHKERRQ(ierr);
631     }
632   }
633   PetscFunctionReturn(0);
634 }
635 
636 #undef __FUNCT__
637 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ"
638 PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info)
639 {
640   Mat             C=B;
641   Mat_SeqAIJ      *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
642   IS              isrow = b->row,isicol = b->icol;
643   PetscErrorCode  ierr;
644   const PetscInt   *r,*ic,*ics;
645   PetscInt        nz,row,i,j,n=A->rmap->n,diag;
646   const PetscInt  *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
647   const PetscInt  *ajtmp,*bjtmp,*diag_offset = b->diag,*pj;
648   MatScalar       *pv,*rtmp,*pc,multiplier,d;
649   const MatScalar *v,*aa=a->a;
650   PetscReal       rs=0.0;
651   LUShift_Ctx     sctx;
652   PetscInt        newshift,*ddiag;
653 
654   PetscFunctionBegin;
655   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
656   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
657   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
658   ics  = ic;
659 
660   /* initialize shift context sctx */
661   sctx.nshift         = 0;
662   sctx.nshift_max     = 0;
663   sctx.shift_top      = 0.0;
664   sctx.shift_lo       = 0.0;
665   sctx.shift_hi       = 0.0;
666   sctx.shift_fraction = 0.0;
667   sctx.shift_amount   = 0.0;
668 
669   /* if both shift schemes are chosen by user, only use info->shiftpd */
670   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
671     ddiag          = a->diag;
672     sctx.shift_top = info->zeropivot;
673     for (i=0; i<n; i++) {
674       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
675       d  = (aa)[ddiag[i]];
676       rs = -PetscAbsScalar(d) - PetscRealPart(d);
677       v  = aa+ai[i];
678       nz = ai[i+1] - ai[i];
679       for (j=0; j<nz; j++)
680 	rs += PetscAbsScalar(v[j]);
681       if (rs>sctx.shift_top) sctx.shift_top = rs;
682     }
683     sctx.shift_top   *= 1.1;
684     sctx.nshift_max   = 5;
685     sctx.shift_lo     = 0.;
686     sctx.shift_hi     = 1.;
687   }
688 
689   do {
690     sctx.lushift = PETSC_FALSE;
691     for (i=0; i<n; i++){
692       nz    = bi[i+1] - bi[i];
693       bjtmp = bj + bi[i];
694       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
695 
696       /* load in initial (unfactored row) */
697       nz    = ai[r[i]+1] - ai[r[i]];
698       ajtmp = aj + ai[r[i]];
699       v     = aa + ai[r[i]];
700       for (j=0; j<nz; j++) {
701         rtmp[ics[ajtmp[j]]] = v[j];
702       }
703       rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */
704       /* if (sctx.shift_amount > 0.0) printf("row %d, shift %g\n",i,sctx.shift_amount); */
705 
706       row = *bjtmp++;
707       while  (row < i) {
708         pc = rtmp + row;
709         if (*pc != 0.0) {
710           pv         = b->a + diag_offset[row];
711           pj         = b->j + diag_offset[row] + 1;
712           multiplier = *pc / *pv++;
713           *pc        = multiplier;
714           nz         = bi[row+1] - diag_offset[row] - 1;
715           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
716           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
717         }
718         row = *bjtmp++;
719       }
720       /* finished row so stick it into b->a */
721       pv   = b->a + bi[i] ;
722       pj   = b->j + bi[i] ;
723       nz   = bi[i+1] - bi[i];
724       diag = diag_offset[i] - bi[i];
725       rs   = 0.0;
726       for (j=0; j<nz; j++) {
727         pv[j] = rtmp[pj[j]];
728         rs   += PetscAbsScalar(pv[j]);
729       }
730       rs   -= PetscAbsScalar(pv[diag]);
731 
732       /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */
733       sctx.rs  = rs;
734       sctx.pv  = pv[diag];
735       ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr);
736       if (newshift == 1) break;
737     }
738 
739     if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
740       /*
741        * if no shift in this attempt & shifting & started shifting & can refine,
742        * then try lower shift
743        */
744       sctx.shift_hi       = sctx.shift_fraction;
745       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
746       sctx.shift_amount   = sctx.shift_fraction * sctx.shift_top;
747       sctx.lushift        = PETSC_TRUE;
748       sctx.nshift++;
749     }
750   } while (sctx.lushift);
751 
752   /* invert diagonal entries for simplier triangular solves */
753   for (i=0; i<n; i++) {
754     b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]];
755   }
756   ierr = PetscFree(rtmp);CHKERRQ(ierr);
757   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
758   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
759   if (b->inode.use) {
760     C->ops->solve   = MatSolve_SeqAIJ_Inode;
761   } else {
762     PetscTruth row_identity, col_identity;
763     ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
764     ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
765     if (row_identity && col_identity) {
766       C->ops->solve   = MatSolve_SeqAIJ_NaturalOrdering;
767     } else {
768       C->ops->solve   = MatSolve_SeqAIJ;
769     }
770   }
771   C->ops->solveadd           = MatSolveAdd_SeqAIJ;
772   C->ops->solvetranspose     = MatSolveTranspose_SeqAIJ;
773   C->ops->solvetransposeadd  = MatSolveTransposeAdd_SeqAIJ;
774   C->ops->matsolve           = MatMatSolve_SeqAIJ;
775   C->assembled    = PETSC_TRUE;
776   C->preallocated = PETSC_TRUE;
777   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
778   if (sctx.nshift){
779      if (info->shiftpd) {
780       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);
781     } else if (info->shiftnz) {
782       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
783     }
784   }
785   PetscFunctionReturn(0);
786 }
787 
788 /*
789    This routine implements inplace ILU(0) with row or/and column permutations.
790    Input:
791      A - original matrix
792    Output;
793      A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i]
794          a->j (col index) is permuted by the inverse of colperm, then sorted
795          a->a reordered accordingly with a->j
796          a->diag (ptr to diagonal elements) is updated.
797 */
798 #undef __FUNCT__
799 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_InplaceWithPerm"
800 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info)
801 {
802   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
803   IS             isrow = a->row,isicol = a->icol;
804   PetscErrorCode ierr;
805   const PetscInt *r,*ic,*ics;
806   PetscInt       i,j,n=A->rmap->n,*ai=a->i,*aj=a->j;
807   PetscInt       *ajtmp,nz,row;
808   PetscInt       *diag = a->diag,nbdiag,*pj;
809   PetscScalar    *rtmp,*pc,multiplier,d;
810   MatScalar      *v,*pv;
811   PetscReal      rs;
812   LUShift_Ctx    sctx;
813   PetscInt       newshift;
814 
815   PetscFunctionBegin;
816   if (A != B) SETERRQ(PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address");
817   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
818   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
819   ierr  = PetscMalloc((n+1)*sizeof(PetscScalar),&rtmp);CHKERRQ(ierr);
820   ierr  = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr);
821   ics = ic;
822 
823   sctx.shift_top      = 0;
824   sctx.nshift_max     = 0;
825   sctx.shift_lo       = 0;
826   sctx.shift_hi       = 0;
827   sctx.shift_fraction = 0;
828 
829   /* if both shift schemes are chosen by user, only use info->shiftpd */
830   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
831     sctx.shift_top = 0;
832     for (i=0; i<n; i++) {
833       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
834       d  = (a->a)[diag[i]];
835       rs = -PetscAbsScalar(d) - PetscRealPart(d);
836       v  = a->a+ai[i];
837       nz = ai[i+1] - ai[i];
838       for (j=0; j<nz; j++)
839 	rs += PetscAbsScalar(v[j]);
840       if (rs>sctx.shift_top) sctx.shift_top = rs;
841     }
842     if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot;
843     sctx.shift_top    *= 1.1;
844     sctx.nshift_max   = 5;
845     sctx.shift_lo     = 0.;
846     sctx.shift_hi     = 1.;
847   }
848 
849   sctx.shift_amount = 0;
850   sctx.nshift       = 0;
851   do {
852     sctx.lushift = PETSC_FALSE;
853     for (i=0; i<n; i++){
854       /* load in initial unfactored row */
855       nz    = ai[r[i]+1] - ai[r[i]];
856       ajtmp = aj + ai[r[i]];
857       v     = a->a + ai[r[i]];
858       /* sort permuted ajtmp and values v accordingly */
859       for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]];
860       ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr);
861 
862       diag[r[i]] = ai[r[i]];
863       for (j=0; j<nz; j++) {
864         rtmp[ajtmp[j]] = v[j];
865         if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */
866       }
867       rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */
868 
869       row = *ajtmp++;
870       while  (row < i) {
871         pc = rtmp + row;
872         if (*pc != 0.0) {
873           pv         = a->a + diag[r[row]];
874           pj         = aj + diag[r[row]] + 1;
875 
876           multiplier = *pc / *pv++;
877           *pc        = multiplier;
878           nz         = ai[r[row]+1] - diag[r[row]] - 1;
879           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
880           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
881         }
882         row = *ajtmp++;
883       }
884       /* finished row so overwrite it onto a->a */
885       pv   = a->a + ai[r[i]] ;
886       pj   = aj + ai[r[i]] ;
887       nz   = ai[r[i]+1] - ai[r[i]];
888       nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */
889 
890       rs   = 0.0;
891       for (j=0; j<nz; j++) {
892         pv[j] = rtmp[pj[j]];
893         if (j != nbdiag) rs += PetscAbsScalar(pv[j]);
894       }
895 
896       /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */
897       sctx.rs  = rs;
898       sctx.pv  = pv[nbdiag];
899       ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr);
900       if (newshift == 1) break;
901     }
902 
903     if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
904       /*
905        * if no shift in this attempt & shifting & started shifting & can refine,
906        * then try lower shift
907        */
908       sctx.shift_hi        = sctx.shift_fraction;
909       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
910       sctx.shift_amount    = sctx.shift_fraction * sctx.shift_top;
911       sctx.lushift         = PETSC_TRUE;
912       sctx.nshift++;
913     }
914   } while (sctx.lushift);
915 
916   /* invert diagonal entries for simplier triangular solves */
917   for (i=0; i<n; i++) {
918     a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]];
919   }
920 
921   ierr = PetscFree(rtmp);CHKERRQ(ierr);
922   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
923   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
924   A->ops->solve             = MatSolve_SeqAIJ_InplaceWithPerm;
925   A->ops->solveadd          = MatSolveAdd_SeqAIJ;
926   A->ops->solvetranspose    = MatSolveTranspose_SeqAIJ;
927   A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ;
928   A->assembled = PETSC_TRUE;
929   A->preallocated = PETSC_TRUE;
930   ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr);
931   if (sctx.nshift){
932     if (info->shiftpd) {
933       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);
934     } else if (info->shiftnz) {
935       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
936     }
937   }
938   PetscFunctionReturn(0);
939 }
940 
941 /* ----------------------------------------------------------- */
942 #undef __FUNCT__
943 #define __FUNCT__ "MatLUFactor_SeqAIJ"
944 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info)
945 {
946   PetscErrorCode ierr;
947   Mat            C;
948 
949   PetscFunctionBegin;
950   ierr = MatGetFactor(A,MAT_SOLVER_PETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr);
951   ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr);
952   ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr);
953   A->ops->solve            = C->ops->solve;
954   A->ops->solvetranspose   = C->ops->solvetranspose;
955   ierr = MatHeaderCopy(A,C);CHKERRQ(ierr);
956   ierr = PetscLogObjectParent(A,((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr);
957   PetscFunctionReturn(0);
958 }
959 /* ----------------------------------------------------------- */
960 
961 
962 #undef __FUNCT__
963 #define __FUNCT__ "MatSolve_SeqAIJ"
964 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx)
965 {
966   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
967   IS                iscol = a->col,isrow = a->row;
968   PetscErrorCode    ierr;
969   PetscInt          i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
970   PetscInt          nz;
971   const PetscInt    *rout,*cout,*r,*c;
972   PetscScalar       *x,*tmp,*tmps,sum;
973   const PetscScalar *b;
974   const MatScalar   *aa = a->a,*v;
975 
976   PetscFunctionBegin;
977   if (!n) PetscFunctionReturn(0);
978 
979   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
980   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
981   tmp  = a->solve_work;
982 
983   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
984   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
985 
986   /* forward solve the lower triangular */
987   tmp[0] = b[*r++];
988   tmps   = tmp;
989   for (i=1; i<n; i++) {
990     v   = aa + ai[i] ;
991     vi  = aj + ai[i] ;
992     nz  = a->diag[i] - ai[i];
993     sum = b[*r++];
994     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
995     tmp[i] = sum;
996   }
997 
998   /* backward solve the upper triangular */
999   for (i=n-1; i>=0; i--){
1000     v   = aa + a->diag[i] + 1;
1001     vi  = aj + a->diag[i] + 1;
1002     nz  = ai[i+1] - a->diag[i] - 1;
1003     sum = tmp[i];
1004     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1005     x[*c--] = tmp[i] = sum*aa[a->diag[i]];
1006   }
1007 
1008   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1009   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1010   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1011   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1012   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1013   PetscFunctionReturn(0);
1014 }
1015 
1016 #undef __FUNCT__
1017 #define __FUNCT__ "MatMatSolve_SeqAIJ"
1018 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X)
1019 {
1020   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1021   IS              iscol = a->col,isrow = a->row;
1022   PetscErrorCode  ierr;
1023   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1024   PetscInt        nz,neq;
1025   const PetscInt  *rout,*cout,*r,*c;
1026   PetscScalar     *x,*b,*tmp,*tmps,sum;
1027   const MatScalar *aa = a->a,*v;
1028   PetscTruth      bisdense,xisdense;
1029 
1030   PetscFunctionBegin;
1031   if (!n) PetscFunctionReturn(0);
1032 
1033   ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr);
1034   if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix");
1035   ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr);
1036   if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix");
1037 
1038   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
1039   ierr = MatGetArray(X,&x);CHKERRQ(ierr);
1040 
1041   tmp  = a->solve_work;
1042   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1043   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1044 
1045   for (neq=0; neq<B->cmap->n; neq++){
1046     /* forward solve the lower triangular */
1047     tmp[0] = b[r[0]];
1048     tmps   = tmp;
1049     for (i=1; i<n; i++) {
1050       v   = aa + ai[i] ;
1051       vi  = aj + ai[i] ;
1052       nz  = a->diag[i] - ai[i];
1053       sum = b[r[i]];
1054       PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1055       tmp[i] = sum;
1056     }
1057     /* backward solve the upper triangular */
1058     for (i=n-1; i>=0; i--){
1059       v   = aa + a->diag[i] + 1;
1060       vi  = aj + a->diag[i] + 1;
1061       nz  = ai[i+1] - a->diag[i] - 1;
1062       sum = tmp[i];
1063       PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1064       x[c[i]] = tmp[i] = sum*aa[a->diag[i]];
1065     }
1066 
1067     b += n;
1068     x += n;
1069   }
1070   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1071   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1072   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
1073   ierr = MatRestoreArray(X,&x);CHKERRQ(ierr);
1074   ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr);
1075   PetscFunctionReturn(0);
1076 }
1077 
1078 #undef __FUNCT__
1079 #define __FUNCT__ "MatSolve_SeqAIJ_InplaceWithPerm"
1080 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx)
1081 {
1082   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1083   IS              iscol = a->col,isrow = a->row;
1084   PetscErrorCode  ierr;
1085   const PetscInt  *r,*c,*rout,*cout;
1086   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1087   PetscInt        nz,row;
1088   PetscScalar     *x,*b,*tmp,*tmps,sum;
1089   const MatScalar *aa = a->a,*v;
1090 
1091   PetscFunctionBegin;
1092   if (!n) PetscFunctionReturn(0);
1093 
1094   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
1095   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1096   tmp  = a->solve_work;
1097 
1098   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1099   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1100 
1101   /* forward solve the lower triangular */
1102   tmp[0] = b[*r++];
1103   tmps   = tmp;
1104   for (row=1; row<n; row++) {
1105     i   = rout[row]; /* permuted row */
1106     v   = aa + ai[i] ;
1107     vi  = aj + ai[i] ;
1108     nz  = a->diag[i] - ai[i];
1109     sum = b[*r++];
1110     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1111     tmp[row] = sum;
1112   }
1113 
1114   /* backward solve the upper triangular */
1115   for (row=n-1; row>=0; row--){
1116     i   = rout[row]; /* permuted row */
1117     v   = aa + a->diag[i] + 1;
1118     vi  = aj + a->diag[i] + 1;
1119     nz  = ai[i+1] - a->diag[i] - 1;
1120     sum = tmp[row];
1121     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1122     x[*c--] = tmp[row] = sum*aa[a->diag[i]];
1123   }
1124 
1125   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1126   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1127   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
1128   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1129   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1130   PetscFunctionReturn(0);
1131 }
1132 
1133 /* ----------------------------------------------------------- */
1134 #include "../src/mat/impls/aij/seq/ftn-kernels/fsolve.h"
1135 #undef __FUNCT__
1136 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering"
1137 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx)
1138 {
1139   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1140   PetscErrorCode    ierr;
1141   PetscInt          n = A->rmap->n;
1142   const PetscInt    *ai = a->i,*aj = a->j,*adiag = a->diag;
1143   PetscScalar       *x;
1144   const PetscScalar *b;
1145   const MatScalar   *aa = a->a;
1146 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ)
1147   PetscInt          adiag_i,i,nz,ai_i;
1148   const PetscInt    *vi;
1149   const MatScalar   *v;
1150   PetscScalar       sum;
1151 #endif
1152 
1153   PetscFunctionBegin;
1154   if (!n) PetscFunctionReturn(0);
1155 
1156   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1157   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1158 
1159 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ)
1160   fortransolveaij_(&n,x,ai,aj,adiag,aa,b);
1161 #else
1162   /* forward solve the lower triangular */
1163   x[0] = b[0];
1164   for (i=1; i<n; i++) {
1165     ai_i = ai[i];
1166     v    = aa + ai_i;
1167     vi   = aj + ai_i;
1168     nz   = adiag[i] - ai_i;
1169     sum  = b[i];
1170     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
1171     x[i] = sum;
1172   }
1173 
1174   /* backward solve the upper triangular */
1175   for (i=n-1; i>=0; i--){
1176     adiag_i = adiag[i];
1177     v       = aa + adiag_i + 1;
1178     vi      = aj + adiag_i + 1;
1179     nz      = ai[i+1] - adiag_i - 1;
1180     sum     = x[i];
1181     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
1182     x[i]    = sum*aa[adiag_i];
1183   }
1184 #endif
1185   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1186   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1187   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1188   PetscFunctionReturn(0);
1189 }
1190 
1191 #undef __FUNCT__
1192 #define __FUNCT__ "MatSolveAdd_SeqAIJ"
1193 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx)
1194 {
1195   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1196   IS                iscol = a->col,isrow = a->row;
1197   PetscErrorCode    ierr;
1198   PetscInt          i, n = A->rmap->n,j;
1199   PetscInt          nz;
1200   const PetscInt    *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j;
1201   PetscScalar       *x,*tmp,sum;
1202   const PetscScalar *b;
1203   const MatScalar   *aa = a->a,*v;
1204 
1205   PetscFunctionBegin;
1206   if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);}
1207 
1208   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1209   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1210   tmp  = a->solve_work;
1211 
1212   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1213   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1214 
1215   /* forward solve the lower triangular */
1216   tmp[0] = b[*r++];
1217   for (i=1; i<n; i++) {
1218     v   = aa + ai[i] ;
1219     vi  = aj + ai[i] ;
1220     nz  = a->diag[i] - ai[i];
1221     sum = b[*r++];
1222     for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1223     tmp[i] = sum;
1224   }
1225 
1226   /* backward solve the upper triangular */
1227   for (i=n-1; i>=0; i--){
1228     v   = aa + a->diag[i] + 1;
1229     vi  = aj + a->diag[i] + 1;
1230     nz  = ai[i+1] - a->diag[i] - 1;
1231     sum = tmp[i];
1232     for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1233     tmp[i] = sum*aa[a->diag[i]];
1234     x[*c--] += tmp[i];
1235   }
1236 
1237   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1238   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1239   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1240   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1241   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1242 
1243   PetscFunctionReturn(0);
1244 }
1245 
1246 #undef __FUNCT__
1247 #define __FUNCT__ "MatSolveTranspose_SeqAIJ"
1248 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx)
1249 {
1250   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1251   IS                iscol = a->col,isrow = a->row;
1252   PetscErrorCode    ierr;
1253   const PetscInt    *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi;
1254   PetscInt          i,n = A->rmap->n,j;
1255   PetscInt          nz;
1256   PetscScalar       *x,*tmp,s1;
1257   const MatScalar   *aa = a->a,*v;
1258   const PetscScalar *b;
1259 
1260   PetscFunctionBegin;
1261   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1262   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1263   tmp  = a->solve_work;
1264 
1265   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1266   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1267 
1268   /* copy the b into temp work space according to permutation */
1269   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1270 
1271   /* forward solve the U^T */
1272   for (i=0; i<n; i++) {
1273     v   = aa + diag[i] ;
1274     vi  = aj + diag[i] + 1;
1275     nz  = ai[i+1] - diag[i] - 1;
1276     s1  = tmp[i];
1277     s1 *= (*v++);  /* multiply by inverse of diagonal entry */
1278     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1279     tmp[i] = s1;
1280   }
1281 
1282   /* backward solve the L^T */
1283   for (i=n-1; i>=0; i--){
1284     v   = aa + diag[i] - 1 ;
1285     vi  = aj + diag[i] - 1 ;
1286     nz  = diag[i] - ai[i];
1287     s1  = tmp[i];
1288     for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j];
1289   }
1290 
1291   /* copy tmp into x according to permutation */
1292   for (i=0; i<n; i++) x[r[i]] = tmp[i];
1293 
1294   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1295   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1296   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1297   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1298 
1299   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1300   PetscFunctionReturn(0);
1301 }
1302 
1303 #undef __FUNCT__
1304 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ"
1305 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx)
1306 {
1307   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1308   IS                iscol = a->col,isrow = a->row;
1309   PetscErrorCode    ierr;
1310   const PetscInt    *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi;
1311   PetscInt          i,n = A->rmap->n,j;
1312   PetscInt          nz;
1313   PetscScalar       *x,*tmp,s1;
1314   const MatScalar   *aa = a->a,*v;
1315   const PetscScalar *b;
1316 
1317   PetscFunctionBegin;
1318   if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);}
1319   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1320   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1321   tmp  = a->solve_work;
1322 
1323   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1324   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1325 
1326   /* copy the b into temp work space according to permutation */
1327   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1328 
1329   /* forward solve the U^T */
1330   for (i=0; i<n; i++) {
1331     v   = aa + diag[i] ;
1332     vi  = aj + diag[i] + 1;
1333     nz  = ai[i+1] - diag[i] - 1;
1334     s1  = tmp[i];
1335     s1 *= (*v++);  /* multiply by inverse of diagonal entry */
1336     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1337     tmp[i] = s1;
1338   }
1339 
1340   /* backward solve the L^T */
1341   for (i=n-1; i>=0; i--){
1342     v   = aa + diag[i] - 1 ;
1343     vi  = aj + diag[i] - 1 ;
1344     nz  = diag[i] - ai[i];
1345     s1  = tmp[i];
1346     for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j];
1347   }
1348 
1349   /* copy tmp into x according to permutation */
1350   for (i=0; i<n; i++) x[r[i]] += tmp[i];
1351 
1352   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1353   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1354   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1355   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1356 
1357   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1358   PetscFunctionReturn(0);
1359 }
1360 
1361 /* ----------------------------------------------------------------*/
1362 EXTERN PetscErrorCode Mat_CheckInode(Mat,PetscTruth);
1363 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption,PetscTruth);
1364 
1365 /*
1366    ilu() under revised new data structure.
1367    Factored arrays bj and ba are stored as
1368      L(0,:), L(1,:), ...,L(n-1,:),  U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:)
1369 
1370    bi=fact->i is an array of size n+1, in which
1371    bi+
1372      bi[i]:  points to 1st entry of L(i,:),i=0,...,n-1
1373      bi[n]:  points to L(n-1,n-1)+1
1374 
1375   bdiag=fact->diag is an array of size n+1,in which
1376      bdiag[i]: points to diagonal of U(i,:), i=0,...,n-1
1377      bdiag[n]: points to diagonal of U(n-1,0)-1
1378 
1379    U(i,:) contains bdiag[i] as its last entry, i.e.,
1380     U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i])
1381 */
1382 #undef __FUNCT__
1383 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct"
1384 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1385 {
1386 
1387   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1388   PetscErrorCode     ierr;
1389   PetscInt           n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag;
1390   PetscInt           i,j,nz,*bi,*bj,*bdiag,bi_temp;
1391   PetscTruth         missing;
1392   IS                 isicol;
1393 
1394   PetscFunctionBegin;
1395   /* printf("MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct ...\n"); */
1396   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);
1397   ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
1398   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
1399   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1400 
1401   ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr);
1402   b    = (Mat_SeqAIJ*)(fact)->data;
1403 
1404   /* allocate matrix arrays for new data structure */
1405   ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,n+1,PetscInt,&b->i);CHKERRQ(ierr);
1406   ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));CHKERRQ(ierr);
1407   b->singlemalloc = PETSC_TRUE;
1408   if (!b->diag){
1409     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr);
1410     ierr = PetscLogObjectMemory(fact,(n+1)*sizeof(PetscInt));CHKERRQ(ierr);
1411   }
1412   bdiag = b->diag;
1413 
1414   if (n > 0) {
1415     ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr);
1416   }
1417 
1418   /* set bi and bj with new data structure */
1419   bi = b->i;
1420   bj = b->j;
1421 
1422   /* L part */
1423   bi[0] = 0;
1424   for (i=0; i<n; i++){
1425     nz = adiag[i] - ai[i];
1426     bi[i+1] = bi[i] + nz;
1427     aj = a->j + ai[i];
1428     for (j=0; j<nz; j++){
1429       *bj = aj[j]; bj++;
1430     }
1431   }
1432 
1433   /* U part */
1434   bi_temp = bi[n];
1435   bdiag[n] = bi[n]-1;
1436   for (i=n-1; i>=0; i--){
1437     nz = ai[i+1] - adiag[i] - 1;
1438     bi_temp = bi_temp + nz + 1;
1439     aj = a->j + adiag[i] + 1;
1440     for (j=0; j<nz; j++){
1441       *bj = aj[j]; bj++;
1442     }
1443     /* diag[i] */
1444     *bj = i; bj++;
1445     bdiag[i] = bi_temp - 1;
1446   }
1447 
1448   fact->factor                 = MAT_FACTOR_ILU;
1449   fact->info.factor_mallocs    = 0;
1450   fact->info.fill_ratio_given  = info->fill;
1451   fact->info.fill_ratio_needed = 1.0;
1452   fact->ops->lufactornumeric   = MatLUFactorNumeric_SeqAIJ_newdatastruct;
1453 
1454   b       = (Mat_SeqAIJ*)(fact)->data;
1455   b->row  = isrow;
1456   b->col  = iscol;
1457   b->icol = isicol;
1458   ierr    = PetscMalloc((fact->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1459   ierr    = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1460   ierr    = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1461   PetscFunctionReturn(0);
1462 }
1463 
1464 #undef __FUNCT__
1465 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_newdatastruct"
1466 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1467 {
1468   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1469   IS                 isicol;
1470   PetscErrorCode     ierr;
1471   const PetscInt     *r,*ic;
1472   PetscInt           n=A->rmap->n,*ai=a->i,*aj=a->j;
1473   PetscInt           *bi,*cols,nnz,*cols_lvl;
1474   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1475   PetscInt           i,levels,diagonal_fill;
1476   PetscTruth         col_identity,row_identity;
1477   PetscReal          f;
1478   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
1479   PetscBT            lnkbt;
1480   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
1481   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1482   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1483 
1484   PetscFunctionBegin;
1485   /* printf("MatILUFactorSymbolic_SeqAIJ_newdatastruct ...\n"); */
1486   levels = (PetscInt)info->levels;
1487   ierr   = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1488   ierr   = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
1489 
1490   if (!levels && row_identity && col_identity) {
1491     /* special case: ilu(0) with natural ordering */
1492     ierr = MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1493     PetscFunctionReturn(0);
1494   }
1495 
1496   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);
1497   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1498   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1499   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1500 
1501   /* get new row pointers */
1502   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1503   bi[0] = 0;
1504   /* bdiag is location of diagonal in factor */
1505   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
1506   bdiag[0]  = 0;
1507 
1508   ierr = PetscMalloc((2*n+1)*sizeof(PetscInt**),&bj_ptr);CHKERRQ(ierr);
1509   bjlvl_ptr = (PetscInt**)(bj_ptr + n);
1510 
1511   /* create a linked list for storing column indices of the active row */
1512   nlnk = n + 1;
1513   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1514 
1515   /* initial FreeSpace size is f*(ai[n]+1) */
1516   f             = info->fill;
1517   diagonal_fill = (PetscInt)info->diagonal_fill;
1518   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
1519   current_space = free_space;
1520   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
1521   current_space_lvl = free_space_lvl;
1522 
1523   for (i=0; i<n; i++) {
1524     nzi = 0;
1525     /* copy current row into linked list */
1526     nnz  = ai[r[i]+1] - ai[r[i]];
1527     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1528     cols = aj + ai[r[i]];
1529     lnk[i] = -1; /* marker to indicate if diagonal exists */
1530     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1531     nzi += nlnk;
1532 
1533     /* make sure diagonal entry is included */
1534     if (diagonal_fill && lnk[i] == -1) {
1535       fm = n;
1536       while (lnk[fm] < i) fm = lnk[fm];
1537       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
1538       lnk[fm]    = i;
1539       lnk_lvl[i] = 0;
1540       nzi++; dcount++;
1541     }
1542 
1543     /* add pivot rows into the active row */
1544     nzbd = 0;
1545     prow = lnk[n];
1546     while (prow < i) {
1547       nnz      = bdiag[prow];
1548       cols     = bj_ptr[prow] + nnz + 1;
1549       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1550       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
1551       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
1552       nzi += nlnk;
1553       prow = lnk[prow];
1554       nzbd++;
1555     }
1556     bdiag[i] = nzbd;
1557     bi[i+1]  = bi[i] + nzi;
1558 
1559     /* if free space is not available, make more free space */
1560     if (current_space->local_remaining<nzi) {
1561       nnz = 2*nzi*(n - i); /* estimated and max additional space needed */
1562       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
1563       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
1564       reallocs++;
1565     }
1566 
1567     /* copy data into free_space and free_space_lvl, then initialize lnk */
1568     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1569     bj_ptr[i]    = current_space->array;
1570     bjlvl_ptr[i] = current_space_lvl->array;
1571 
1572     /* make sure the active row i has diagonal entry */
1573     if (*(bj_ptr[i]+bdiag[i]) != i) {
1574       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
1575     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
1576     }
1577 
1578     current_space->array           += nzi;
1579     current_space->local_used      += nzi;
1580     current_space->local_remaining -= nzi;
1581     current_space_lvl->array           += nzi;
1582     current_space_lvl->local_used      += nzi;
1583     current_space_lvl->local_remaining -= nzi;
1584   }
1585 
1586   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1587   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1588 
1589   /* destroy list of free space and other temporary arrays */
1590   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
1591 
1592   /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */
1593   ierr = PetscFreeSpaceContiguous_LU_v2(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr);
1594 
1595   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1596   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
1597   ierr = PetscFree(bj_ptr);CHKERRQ(ierr);
1598 
1599 #if defined(PETSC_USE_INFO)
1600   {
1601     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1602     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
1603     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
1604     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
1605     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
1606     if (diagonal_fill) {
1607       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
1608     }
1609   }
1610 #endif
1611 
1612   /* put together the new matrix */
1613   ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
1614   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
1615   b = (Mat_SeqAIJ*)(fact)->data;
1616   b->free_a       = PETSC_TRUE;
1617   b->free_ij      = PETSC_TRUE;
1618   b->singlemalloc = PETSC_FALSE;
1619   ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
1620   b->j          = bj;
1621   b->i          = bi;
1622   b->diag       = bdiag;
1623   b->ilen       = 0;
1624   b->imax       = 0;
1625   b->row        = isrow;
1626   b->col        = iscol;
1627   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1628   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1629   b->icol       = isicol;
1630   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1631   /* In b structure:  Free imax, ilen, old a, old j.
1632      Allocate bdiag, solve_work, new a, new j */
1633   ierr = PetscLogObjectMemory(fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
1634   b->maxnz = b->nz = bdiag[0]+1;
1635   (fact)->info.factor_mallocs    = reallocs;
1636   (fact)->info.fill_ratio_given  = f;
1637   (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]);
1638   (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct;
1639   /* ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */
1640   PetscFunctionReturn(0);
1641 }
1642 
1643 #undef __FUNCT__
1644 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ"
1645 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1646 {
1647   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1648   IS                 isicol;
1649   PetscErrorCode     ierr;
1650   const PetscInt     *r,*ic;
1651   PetscInt           n=A->rmap->n,*ai=a->i,*aj=a->j,d;
1652   PetscInt           *bi,*cols,nnz,*cols_lvl;
1653   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1654   PetscInt           i,levels,diagonal_fill;
1655   PetscTruth         col_identity,row_identity;
1656   PetscReal          f;
1657   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
1658   PetscBT            lnkbt;
1659   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
1660   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1661   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1662   PetscTruth         missing;
1663   PetscTruth         newdatastruct=PETSC_FALSE;
1664 
1665   PetscFunctionBegin;
1666   ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
1667   if(newdatastruct){
1668     ierr = MatILUFactorSymbolic_SeqAIJ_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1669     PetscFunctionReturn(0);
1670   }
1671 
1672   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);
1673   f             = info->fill;
1674   levels        = (PetscInt)info->levels;
1675   diagonal_fill = (PetscInt)info->diagonal_fill;
1676   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1677 
1678   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1679   ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
1680   if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */
1681     ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr);
1682     (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ;
1683 
1684     fact->factor = MAT_FACTOR_ILU;
1685     (fact)->info.factor_mallocs    = 0;
1686     (fact)->info.fill_ratio_given  = info->fill;
1687     (fact)->info.fill_ratio_needed = 1.0;
1688     b               = (Mat_SeqAIJ*)(fact)->data;
1689     ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
1690     if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
1691     b->row              = isrow;
1692     b->col              = iscol;
1693     b->icol             = isicol;
1694     ierr                = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1695     ierr                = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1696     ierr                = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1697     ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1698     PetscFunctionReturn(0);
1699   }
1700 
1701   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1702   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1703 
1704   /* get new row pointers */
1705   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1706   bi[0] = 0;
1707   /* bdiag is location of diagonal in factor */
1708   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
1709   bdiag[0]  = 0;
1710 
1711   ierr = PetscMalloc((2*n+1)*sizeof(PetscInt**),&bj_ptr);CHKERRQ(ierr);
1712   bjlvl_ptr = (PetscInt**)(bj_ptr + n);
1713 
1714   /* create a linked list for storing column indices of the active row */
1715   nlnk = n + 1;
1716   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1717 
1718   /* initial FreeSpace size is f*(ai[n]+1) */
1719   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
1720   current_space = free_space;
1721   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
1722   current_space_lvl = free_space_lvl;
1723 
1724   for (i=0; i<n; i++) {
1725     nzi = 0;
1726     /* copy current row into linked list */
1727     nnz  = ai[r[i]+1] - ai[r[i]];
1728     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1729     cols = aj + ai[r[i]];
1730     lnk[i] = -1; /* marker to indicate if diagonal exists */
1731     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1732     nzi += nlnk;
1733 
1734     /* make sure diagonal entry is included */
1735     if (diagonal_fill && lnk[i] == -1) {
1736       fm = n;
1737       while (lnk[fm] < i) fm = lnk[fm];
1738       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
1739       lnk[fm]    = i;
1740       lnk_lvl[i] = 0;
1741       nzi++; dcount++;
1742     }
1743 
1744     /* add pivot rows into the active row */
1745     nzbd = 0;
1746     prow = lnk[n];
1747     while (prow < i) {
1748       nnz      = bdiag[prow];
1749       cols     = bj_ptr[prow] + nnz + 1;
1750       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1751       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
1752       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
1753       nzi += nlnk;
1754       prow = lnk[prow];
1755       nzbd++;
1756     }
1757     bdiag[i] = nzbd;
1758     bi[i+1]  = bi[i] + nzi;
1759 
1760     /* if free space is not available, make more free space */
1761     if (current_space->local_remaining<nzi) {
1762       nnz = nzi*(n - i); /* estimated and max additional space needed */
1763       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
1764       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
1765       reallocs++;
1766     }
1767 
1768     /* copy data into free_space and free_space_lvl, then initialize lnk */
1769     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1770     bj_ptr[i]    = current_space->array;
1771     bjlvl_ptr[i] = current_space_lvl->array;
1772 
1773     /* make sure the active row i has diagonal entry */
1774     if (*(bj_ptr[i]+bdiag[i]) != i) {
1775       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
1776     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
1777     }
1778 
1779     current_space->array           += nzi;
1780     current_space->local_used      += nzi;
1781     current_space->local_remaining -= nzi;
1782     current_space_lvl->array           += nzi;
1783     current_space_lvl->local_used      += nzi;
1784     current_space_lvl->local_remaining -= nzi;
1785   }
1786 
1787   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1788   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1789 
1790   /* destroy list of free space and other temporary arrays */
1791   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
1792   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */
1793   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1794   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
1795   ierr = PetscFree(bj_ptr);CHKERRQ(ierr);
1796 
1797 #if defined(PETSC_USE_INFO)
1798   {
1799     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1800     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
1801     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
1802     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
1803     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
1804     if (diagonal_fill) {
1805       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
1806     }
1807   }
1808 #endif
1809 
1810   /* put together the new matrix */
1811   ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
1812   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
1813   b = (Mat_SeqAIJ*)(fact)->data;
1814   b->free_a       = PETSC_TRUE;
1815   b->free_ij      = PETSC_TRUE;
1816   b->singlemalloc = PETSC_FALSE;
1817   ierr = PetscMalloc( (bi[n] )*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
1818   b->j          = bj;
1819   b->i          = bi;
1820   for (i=0; i<n; i++) bdiag[i] += bi[i];
1821   b->diag       = bdiag;
1822   b->ilen       = 0;
1823   b->imax       = 0;
1824   b->row        = isrow;
1825   b->col        = iscol;
1826   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1827   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1828   b->icol       = isicol;
1829   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1830   /* In b structure:  Free imax, ilen, old a, old j.
1831      Allocate bdiag, solve_work, new a, new j */
1832   ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
1833   b->maxnz             = b->nz = bi[n] ;
1834   (fact)->info.factor_mallocs    = reallocs;
1835   (fact)->info.fill_ratio_given  = f;
1836   (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1837   (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ;
1838   ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1839   PetscFunctionReturn(0);
1840 }
1841 
1842 #undef __FUNCT__
1843 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ_newdatastruct"
1844 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info)
1845 {
1846   Mat            C = B;
1847   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1848   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
1849   IS             ip=b->row,iip = b->icol;
1850   PetscErrorCode ierr;
1851   const PetscInt *rip,*riip;
1852   PetscInt       i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp;
1853   PetscInt       *ai=a->i,*aj=a->j;
1854   PetscInt       k,jmin,jmax,*c2r,*il,col,nexti,ili,nz;
1855   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
1856   PetscReal      zeropivot,shiftnz;
1857   PetscReal      shiftpd;
1858   PetscTruth     perm_identity;
1859 
1860   PetscFunctionBegin;
1861 
1862   shiftnz   = info->shiftnz;
1863   shiftpd   = info->shiftpd;
1864   zeropivot = info->zeropivot;
1865 
1866   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
1867   ierr  = ISGetIndices(iip,&riip);CHKERRQ(ierr);
1868 
1869   /* allocate working arrays
1870      c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col
1871      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
1872   */
1873   nz   = (2*mbs+1)*sizeof(PetscInt)+mbs*sizeof(MatScalar);
1874   ierr = PetscMalloc(nz,&il);CHKERRQ(ierr);
1875   c2r  = il + mbs;
1876   rtmp = (MatScalar*)(c2r + mbs);
1877 
1878   for (i=0; i<mbs; i++) {
1879     c2r[i] = mbs;
1880   }
1881   il[0] = 0;
1882 
1883   for (k = 0; k<mbs; k++){
1884     /* zero rtmp */
1885     nz = bi[k+1] - bi[k];
1886     bjtmp = bj + bi[k];
1887     for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
1888 
1889     /* load in initial unfactored row */
1890     bval = ba + bi[k];
1891     jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
1892     for (j = jmin; j < jmax; j++){
1893       col = riip[aj[j]];
1894       if (col >= k){ /* only take upper triangular entry */
1895         rtmp[col] = aa[j];
1896         *bval++   = 0.0; /* for in-place factorization */
1897       }
1898     }
1899     /* shift the diagonal of the matrix */
1900 
1901     /* modify k-th row by adding in those rows i with U(i,k)!=0 */
1902     dk = rtmp[k];
1903     i  = c2r[k]; /* first row to be added to k_th row  */
1904 
1905     while (i < k){
1906       nexti = c2r[i]; /* next row to be added to k_th row */
1907 
1908       /* compute multiplier, update diag(k) and U(i,k) */
1909       ili   = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
1910       uikdi = - ba[ili]*ba[bdiag[i]];  /* diagonal(k) */
1911       dk   += uikdi*ba[ili]; /* update diag[k] */
1912       ba[ili] = uikdi; /* -U(i,k) */
1913 
1914       /* add multiple of row i to k-th row */
1915       jmin = ili + 1; jmax = bi[i+1];
1916       if (jmin < jmax){
1917         for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
1918         /* update il and c2r for row i */
1919         il[i] = jmin;
1920         j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i;
1921       }
1922       i = nexti;
1923     }
1924 
1925     /* copy data into U(k,:) */
1926     ba[bdiag[k]] = 1.0/dk; /* U(k,k) */
1927     jmin = bi[k]; jmax = bi[k+1]-1;
1928     if (jmin < jmax) {
1929       for (j=jmin; j<jmax; j++){
1930         col = bj[j]; ba[j] = rtmp[col];
1931       }
1932       /* add the k-th row into il and c2r */
1933       il[k] = jmin;
1934       i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k;
1935     }
1936   }
1937 
1938   ierr = PetscFree(il);CHKERRQ(ierr);
1939   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
1940   ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr);
1941 
1942   ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
1943   if (perm_identity){
1944     (B)->ops->solve           = MatSolve_SeqSBAIJ_1_NaturalOrdering_newdatastruct;
1945     (B)->ops->solvetranspose  = 0;
1946     (B)->ops->forwardsolve    = 0;
1947     (B)->ops->backwardsolve   = 0;
1948   } else {
1949     (B)->ops->solve           = MatSolve_SeqSBAIJ_1_newdatastruct;
1950     (B)->ops->solvetranspose  = 0;
1951     (B)->ops->forwardsolve    = 0;
1952     (B)->ops->backwardsolve   = 0;
1953   }
1954 
1955   C->assembled    = PETSC_TRUE;
1956   C->preallocated = PETSC_TRUE;
1957   ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr);
1958   PetscFunctionReturn(0);
1959 }
1960 
1961 #undef __FUNCT__
1962 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ"
1963 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info)
1964 {
1965   Mat            C = B;
1966   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1967   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
1968   IS             ip=b->row,iip = b->icol;
1969   PetscErrorCode ierr;
1970   const PetscInt *rip,*riip;
1971   PetscInt       i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol;
1972   PetscInt       *ai=a->i,*aj=a->j;
1973   PetscInt       k,jmin,jmax,*jl,*il,col,nexti,ili,nz;
1974   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
1975   PetscReal      zeropivot,rs,shiftnz;
1976   PetscReal      shiftpd;
1977   ChShift_Ctx    sctx;
1978   PetscInt       newshift;
1979   PetscTruth     perm_identity;
1980 
1981   PetscFunctionBegin;
1982   shiftnz   = info->shiftnz;
1983   shiftpd   = info->shiftpd;
1984   zeropivot = info->zeropivot;
1985 
1986   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
1987   ierr  = ISGetIndices(iip,&riip);CHKERRQ(ierr);
1988 
1989   /* initialization */
1990   nz   = (2*mbs+1)*sizeof(PetscInt)+mbs*sizeof(MatScalar);
1991   ierr = PetscMalloc(nz,&il);CHKERRQ(ierr);
1992   jl   = il + mbs;
1993   rtmp = (MatScalar*)(jl + mbs);
1994 
1995   sctx.shift_amount = 0;
1996   sctx.nshift       = 0;
1997   do {
1998     sctx.chshift = PETSC_FALSE;
1999     for (i=0; i<mbs; i++) {
2000       rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0;
2001     }
2002 
2003     for (k = 0; k<mbs; k++){
2004       bval = ba + bi[k];
2005       /* initialize k-th row by the perm[k]-th row of A */
2006       jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2007       for (j = jmin; j < jmax; j++){
2008         col = riip[aj[j]];
2009         if (col >= k){ /* only take upper triangular entry */
2010           rtmp[col] = aa[j];
2011           *bval++  = 0.0; /* for in-place factorization */
2012         }
2013       }
2014       /* shift the diagonal of the matrix */
2015       if (sctx.nshift) rtmp[k] += sctx.shift_amount;
2016 
2017       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
2018       dk = rtmp[k];
2019       i = jl[k]; /* first row to be added to k_th row  */
2020 
2021       while (i < k){
2022         nexti = jl[i]; /* next row to be added to k_th row */
2023 
2024         /* compute multiplier, update diag(k) and U(i,k) */
2025         ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2026         uikdi = - ba[ili]*ba[bi[i]];  /* diagonal(k) */
2027         dk += uikdi*ba[ili];
2028         ba[ili] = uikdi; /* -U(i,k) */
2029 
2030         /* add multiple of row i to k-th row */
2031         jmin = ili + 1; jmax = bi[i+1];
2032         if (jmin < jmax){
2033           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2034           /* update il and jl for row i */
2035           il[i] = jmin;
2036           j = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
2037         }
2038         i = nexti;
2039       }
2040 
2041       /* shift the diagonals when zero pivot is detected */
2042       /* compute rs=sum of abs(off-diagonal) */
2043       rs   = 0.0;
2044       jmin = bi[k]+1;
2045       nz   = bi[k+1] - jmin;
2046       bcol = bj + jmin;
2047       for (j=0; j<nz; j++) {
2048         rs += PetscAbsScalar(rtmp[bcol[j]]);
2049       }
2050 
2051       sctx.rs = rs;
2052       sctx.pv = dk;
2053       ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr);
2054 
2055       if (newshift == 1) {
2056         if (!sctx.shift_amount) {
2057           sctx.shift_amount = 1e-5;
2058         }
2059         break;
2060       }
2061 
2062       /* copy data into U(k,:) */
2063       ba[bi[k]] = 1.0/dk; /* U(k,k) */
2064       jmin = bi[k]+1; jmax = bi[k+1];
2065       if (jmin < jmax) {
2066         for (j=jmin; j<jmax; j++){
2067           col = bj[j]; ba[j] = rtmp[col]; rtmp[col] = 0.0;
2068         }
2069         /* add the k-th row into il and jl */
2070         il[k] = jmin;
2071         i = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
2072       }
2073     }
2074   } while (sctx.chshift);
2075   ierr = PetscFree(il);CHKERRQ(ierr);
2076 
2077   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2078   ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr);
2079 
2080   ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
2081   if (perm_identity){
2082     (B)->ops->solve           = MatSolve_SeqSBAIJ_1_NaturalOrdering;
2083     (B)->ops->solvetranspose  = MatSolve_SeqSBAIJ_1_NaturalOrdering;
2084     (B)->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering;
2085     (B)->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering;
2086   } else {
2087     (B)->ops->solve           = MatSolve_SeqSBAIJ_1;
2088     (B)->ops->solvetranspose  = MatSolve_SeqSBAIJ_1;
2089     (B)->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1;
2090     (B)->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1;
2091   }
2092 
2093   C->assembled    = PETSC_TRUE;
2094   C->preallocated = PETSC_TRUE;
2095   ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr);
2096   if (sctx.nshift){
2097     if (shiftnz) {
2098       ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2099     } else if (shiftpd) {
2100       ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2101     }
2102   }
2103   PetscFunctionReturn(0);
2104 }
2105 
2106 /*
2107    icc() under revised new data structure.
2108    Factored arrays bj and ba are stored as
2109      U(0,:),...,U(i,:),U(n-1,:)
2110 
2111    ui=fact->i is an array of size n+1, in which
2112    ui+
2113      ui[i]:  points to 1st entry of U(i,:),i=0,...,n-1
2114      ui[n]:  points to U(n-1,n-1)+1
2115 
2116   udiag=fact->diag is an array of size n,in which
2117      udiag[i]: points to diagonal of U(i,:), i=0,...,n-1
2118 
2119    U(i,:) contains udiag[i] as its last entry, i.e.,
2120     U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i])
2121 */
2122 
2123 #undef __FUNCT__
2124 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ_newdatastruct"
2125 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2126 {
2127   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2128   Mat_SeqSBAIJ       *b;
2129   PetscErrorCode     ierr;
2130   PetscTruth         perm_identity,missing;
2131   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag;
2132   const PetscInt     *rip,*riip;
2133   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
2134   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL,d;
2135   PetscInt           ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
2136   PetscReal          fill=info->fill,levels=info->levels;
2137   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2138   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
2139   PetscBT            lnkbt;
2140   IS                 iperm;
2141 
2142   PetscFunctionBegin;
2143   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);
2144   ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
2145   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
2146   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2147   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2148 
2149   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2150   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2151   ui[0] = 0;
2152 
2153   /* ICC(0) without matrix ordering: simply rearrange column indices */
2154   if (!levels && perm_identity) {
2155 
2156     for (i=0; i<am; i++) {
2157       ui[i+1]  = ui[i] + ai[i+1] - a->diag[i];
2158       udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */
2159     }
2160     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2161     cols = uj;
2162     for (i=0; i<am; i++) {
2163       aj    = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */
2164       ncols = ui[i+1] - ui[i] - 1;
2165       for (j=0; j<ncols; j++) *cols++ = aj[j];
2166       *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */
2167     }
2168   } else { /* case: levels>0 || (levels=0 && !perm_identity) */
2169     if (levels) SETERRQ(PETSC_ERR_ARG_WRONG,"not done yet");
2170     ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2171     ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2172 
2173     /* initialization */
2174     ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr);
2175 
2176     /* jl: linked list for storing indices of the pivot rows
2177        il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2178     ierr = PetscMalloc((2*am+1)*sizeof(PetscInt)+2*am*sizeof(PetscInt**),&jl);CHKERRQ(ierr);
2179     il         = jl + am;
2180     uj_ptr     = (PetscInt**)(il + am);
2181     uj_lvl_ptr = (PetscInt**)(uj_ptr + am);
2182     for (i=0; i<am; i++){
2183       jl[i] = am; il[i] = 0;
2184     }
2185 
2186     /* create and initialize a linked list for storing column indices of the active row k */
2187     nlnk = am + 1;
2188     ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2189 
2190     /* initial FreeSpace size is fill*(ai[am]+1) */
2191     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2192     current_space = free_space;
2193     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr);
2194     current_space_lvl = free_space_lvl;
2195 
2196     for (k=0; k<am; k++){  /* for each active row k */
2197       /* initialize lnk by the column indices of row rip[k] of A */
2198       nzk   = 0;
2199       ncols = ai[rip[k]+1] - ai[rip[k]];
2200       if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2201       ncols_upper = 0;
2202       for (j=0; j<ncols; j++){
2203         i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2204         if (riip[i] >= k){ /* only take upper triangular entry */
2205           ajtmp[ncols_upper] = i;
2206           ncols_upper++;
2207         }
2208       }
2209       ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2210       nzk += nlnk;
2211 
2212       /* update lnk by computing fill-in for each pivot row to be merged in */
2213       prow = jl[k]; /* 1st pivot row */
2214 
2215       while (prow < k){
2216         nextprow = jl[prow];
2217 
2218         /* merge prow into k-th row */
2219         jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2220         jmax = ui[prow+1];
2221         ncols = jmax-jmin;
2222         i     = jmin - ui[prow];
2223         cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2224         uj    = uj_lvl_ptr[prow] + i; /* levels of cols */
2225         j     = *(uj - 1);
2226         ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr);
2227         nzk += nlnk;
2228 
2229         /* update il and jl for prow */
2230         if (jmin < jmax){
2231           il[prow] = jmin;
2232           j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2233         }
2234         prow = nextprow;
2235       }
2236 
2237       /* if free space is not available, make more free space */
2238       if (current_space->local_remaining<nzk) {
2239         i = am - k + 1; /* num of unfactored rows */
2240         i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2241         ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2242         ierr = PetscFreeSpaceGet(i,&current_space_lvl);CHKERRQ(ierr);
2243         reallocs++;
2244       }
2245 
2246       /* copy data into free_space and free_space_lvl, then initialize lnk */
2247       if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2248       ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
2249 
2250       /* add the k-th row into il and jl */
2251       if (nzk > 1){
2252         i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2253         jl[k] = jl[i]; jl[i] = k;
2254         il[k] = ui[k] + 1;
2255       }
2256       uj_ptr[k]     = current_space->array;
2257       uj_lvl_ptr[k] = current_space_lvl->array;
2258 
2259       current_space->array           += nzk;
2260       current_space->local_used      += nzk;
2261       current_space->local_remaining -= nzk;
2262 
2263       current_space_lvl->array           += nzk;
2264       current_space_lvl->local_used      += nzk;
2265       current_space_lvl->local_remaining -= nzk;
2266 
2267       ui[k+1] = ui[k] + nzk;
2268     }
2269 
2270 #if defined(PETSC_USE_INFO)
2271     if (ai[am] != 0) {
2272       PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]);
2273       ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2274       ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2275       ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2276     } else {
2277       ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2278     }
2279 #endif
2280 
2281     ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2282     ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2283     ierr = PetscFree(jl);CHKERRQ(ierr);
2284     ierr = PetscFree(ajtmp);CHKERRQ(ierr);
2285 
2286     /* destroy list of free space and other temporary array(s) */
2287     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2288     ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr);
2289     ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2290     ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2291 
2292   } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2293 
2294   /* put together the new matrix in MATSEQSBAIJ format */
2295 
2296   b    = (Mat_SeqSBAIJ*)(fact)->data;
2297   b->singlemalloc = PETSC_FALSE;
2298   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2299   b->j    = uj;
2300   b->i    = ui;
2301   b->diag = udiag;
2302   b->free_diag = PETSC_TRUE;
2303   b->ilen = 0;
2304   b->imax = 0;
2305   b->row  = perm;
2306   b->col  = perm;
2307   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2308   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2309   b->icol = iperm;
2310   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2311   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2312   ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2313   b->maxnz   = b->nz = ui[am];
2314   b->free_a  = PETSC_TRUE;
2315   b->free_ij = PETSC_TRUE;
2316 
2317   (fact)->info.factor_mallocs    = reallocs;
2318   (fact)->info.fill_ratio_given  = fill;
2319   if (ai[am] != 0) {
2320     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2321   } else {
2322     (fact)->info.fill_ratio_needed = 0.0;
2323   }
2324   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_newdatastruct;
2325   PetscFunctionReturn(0);
2326 }
2327 
2328 #undef __FUNCT__
2329 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ"
2330 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2331 {
2332   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2333   Mat_SeqSBAIJ       *b;
2334   PetscErrorCode     ierr;
2335   PetscTruth         perm_identity,missing;
2336   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag;
2337   const PetscInt     *rip,*riip;
2338   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
2339   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL,d;
2340   PetscInt           ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
2341   PetscReal          fill=info->fill,levels=info->levels;
2342   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2343   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
2344   PetscBT            lnkbt;
2345   IS                 iperm;
2346   PetscTruth         newdatastruct=PETSC_FALSE;
2347 
2348   PetscFunctionBegin;
2349   ierr = PetscOptionsGetTruth(PETSC_NULL,"-icc_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
2350   if(newdatastruct){
2351     ierr = MatICCFactorSymbolic_SeqAIJ_newdatastruct(fact,A,perm,info);CHKERRQ(ierr);
2352     PetscFunctionReturn(0);
2353   }
2354 
2355   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);
2356   ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
2357   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
2358   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2359   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2360 
2361   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2362   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2363   ui[0] = 0;
2364 
2365   /* ICC(0) without matrix ordering: simply copies fill pattern */
2366   if (!levels && perm_identity) {
2367 
2368     for (i=0; i<am; i++) {
2369       ui[i+1]  = ui[i] + ai[i+1] - a->diag[i];
2370       udiag[i] = ui[i];
2371     }
2372     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2373     cols = uj;
2374     for (i=0; i<am; i++) {
2375       aj    = a->j + a->diag[i];
2376       ncols = ui[i+1] - ui[i];
2377       for (j=0; j<ncols; j++) *cols++ = *aj++;
2378     }
2379   } else { /* case: levels>0 || (levels=0 && !perm_identity) */
2380     ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2381     ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2382 
2383     /* initialization */
2384     ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr);
2385 
2386     /* jl: linked list for storing indices of the pivot rows
2387        il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2388     ierr = PetscMalloc((2*am+1)*sizeof(PetscInt)+2*am*sizeof(PetscInt**),&jl);CHKERRQ(ierr);
2389     il         = jl + am;
2390     uj_ptr     = (PetscInt**)(il + am);
2391     uj_lvl_ptr = (PetscInt**)(uj_ptr + am);
2392     for (i=0; i<am; i++){
2393       jl[i] = am; il[i] = 0;
2394     }
2395 
2396     /* create and initialize a linked list for storing column indices of the active row k */
2397     nlnk = am + 1;
2398     ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2399 
2400     /* initial FreeSpace size is fill*(ai[am]+1) */
2401     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2402     current_space = free_space;
2403     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr);
2404     current_space_lvl = free_space_lvl;
2405 
2406     for (k=0; k<am; k++){  /* for each active row k */
2407       /* initialize lnk by the column indices of row rip[k] of A */
2408       nzk   = 0;
2409       ncols = ai[rip[k]+1] - ai[rip[k]];
2410       if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2411       ncols_upper = 0;
2412       for (j=0; j<ncols; j++){
2413         i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2414         if (riip[i] >= k){ /* only take upper triangular entry */
2415           ajtmp[ncols_upper] = i;
2416           ncols_upper++;
2417         }
2418       }
2419       ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2420       nzk += nlnk;
2421 
2422       /* update lnk by computing fill-in for each pivot row to be merged in */
2423       prow = jl[k]; /* 1st pivot row */
2424 
2425       while (prow < k){
2426         nextprow = jl[prow];
2427 
2428         /* merge prow into k-th row */
2429         jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2430         jmax = ui[prow+1];
2431         ncols = jmax-jmin;
2432         i     = jmin - ui[prow];
2433         cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2434         uj    = uj_lvl_ptr[prow] + i; /* levels of cols */
2435         j     = *(uj - 1);
2436         ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr);
2437         nzk += nlnk;
2438 
2439         /* update il and jl for prow */
2440         if (jmin < jmax){
2441           il[prow] = jmin;
2442           j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2443         }
2444         prow = nextprow;
2445       }
2446 
2447       /* if free space is not available, make more free space */
2448       if (current_space->local_remaining<nzk) {
2449         i = am - k + 1; /* num of unfactored rows */
2450         i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2451         ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2452         ierr = PetscFreeSpaceGet(i,&current_space_lvl);CHKERRQ(ierr);
2453         reallocs++;
2454       }
2455 
2456       /* copy data into free_space and free_space_lvl, then initialize lnk */
2457       if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2458       ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
2459 
2460       /* add the k-th row into il and jl */
2461       if (nzk > 1){
2462         i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2463         jl[k] = jl[i]; jl[i] = k;
2464         il[k] = ui[k] + 1;
2465       }
2466       uj_ptr[k]     = current_space->array;
2467       uj_lvl_ptr[k] = current_space_lvl->array;
2468 
2469       current_space->array           += nzk;
2470       current_space->local_used      += nzk;
2471       current_space->local_remaining -= nzk;
2472 
2473       current_space_lvl->array           += nzk;
2474       current_space_lvl->local_used      += nzk;
2475       current_space_lvl->local_remaining -= nzk;
2476 
2477       ui[k+1] = ui[k] + nzk;
2478     }
2479 
2480 #if defined(PETSC_USE_INFO)
2481     if (ai[am] != 0) {
2482       PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]);
2483       ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2484       ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2485       ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2486     } else {
2487       ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2488     }
2489 #endif
2490 
2491     ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2492     ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2493     ierr = PetscFree(jl);CHKERRQ(ierr);
2494     ierr = PetscFree(ajtmp);CHKERRQ(ierr);
2495 
2496     /* destroy list of free space and other temporary array(s) */
2497     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2498     ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
2499     ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2500     ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2501 
2502   } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2503 
2504   /* put together the new matrix in MATSEQSBAIJ format */
2505 
2506   b    = (Mat_SeqSBAIJ*)(fact)->data;
2507   b->singlemalloc = PETSC_FALSE;
2508   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2509   b->j    = uj;
2510   b->i    = ui;
2511   b->diag = udiag;
2512   b->free_diag = PETSC_TRUE;
2513   b->ilen = 0;
2514   b->imax = 0;
2515   b->row  = perm;
2516   b->col  = perm;
2517   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2518   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2519   b->icol = iperm;
2520   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2521   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2522   ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2523   b->maxnz   = b->nz = ui[am];
2524   b->free_a  = PETSC_TRUE;
2525   b->free_ij = PETSC_TRUE;
2526 
2527   (fact)->info.factor_mallocs    = reallocs;
2528   (fact)->info.fill_ratio_given  = fill;
2529   if (ai[am] != 0) {
2530     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2531   } else {
2532     (fact)->info.fill_ratio_needed = 0.0;
2533   }
2534   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2535   PetscFunctionReturn(0);
2536 }
2537 
2538 #undef __FUNCT__
2539 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ"
2540 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2541 {
2542   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2543   Mat_SeqSBAIJ       *b;
2544   PetscErrorCode     ierr;
2545   PetscTruth         perm_identity;
2546   PetscReal          fill = info->fill;
2547   const PetscInt     *rip,*riip;
2548   PetscInt           i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow;
2549   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
2550   PetscInt           nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr;
2551   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2552   PetscBT            lnkbt;
2553   IS                 iperm;
2554 
2555   PetscFunctionBegin;
2556   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);
2557   /* check whether perm is the identity mapping */
2558   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2559   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2560   ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2561   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2562 
2563   /* initialization */
2564   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2565   ui[0] = 0;
2566 
2567   /* jl: linked list for storing indices of the pivot rows
2568      il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2569   ierr = PetscMalloc((3*am+1)*sizeof(PetscInt)+am*sizeof(PetscInt**),&jl);CHKERRQ(ierr);
2570   il     = jl + am;
2571   cols   = il + am;
2572   ui_ptr = (PetscInt**)(cols + am);
2573   for (i=0; i<am; i++){
2574     jl[i] = am; il[i] = 0;
2575   }
2576 
2577   /* create and initialize a linked list for storing column indices of the active row k */
2578   nlnk = am + 1;
2579   ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2580 
2581   /* initial FreeSpace size is fill*(ai[am]+1) */
2582   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2583   current_space = free_space;
2584 
2585   for (k=0; k<am; k++){  /* for each active row k */
2586     /* initialize lnk by the column indices of row rip[k] of A */
2587     nzk   = 0;
2588     ncols = ai[rip[k]+1] - ai[rip[k]];
2589     if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2590     ncols_upper = 0;
2591     for (j=0; j<ncols; j++){
2592       i = riip[*(aj + ai[rip[k]] + j)];
2593       if (i >= k){ /* only take upper triangular entry */
2594         cols[ncols_upper] = i;
2595         ncols_upper++;
2596       }
2597     }
2598     ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2599     nzk += nlnk;
2600 
2601     /* update lnk by computing fill-in for each pivot row to be merged in */
2602     prow = jl[k]; /* 1st pivot row */
2603 
2604     while (prow < k){
2605       nextprow = jl[prow];
2606       /* merge prow into k-th row */
2607       jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2608       jmax = ui[prow+1];
2609       ncols = jmax-jmin;
2610       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2611       ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2612       nzk += nlnk;
2613 
2614       /* update il and jl for prow */
2615       if (jmin < jmax){
2616         il[prow] = jmin;
2617         j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
2618       }
2619       prow = nextprow;
2620     }
2621 
2622     /* if free space is not available, make more free space */
2623     if (current_space->local_remaining<nzk) {
2624       i = am - k + 1; /* num of unfactored rows */
2625       i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2626       ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2627       reallocs++;
2628     }
2629 
2630     /* copy data into free space, then initialize lnk */
2631     ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
2632 
2633     /* add the k-th row into il and jl */
2634     if (nzk-1 > 0){
2635       i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2636       jl[k] = jl[i]; jl[i] = k;
2637       il[k] = ui[k] + 1;
2638     }
2639     ui_ptr[k] = current_space->array;
2640     current_space->array           += nzk;
2641     current_space->local_used      += nzk;
2642     current_space->local_remaining -= nzk;
2643 
2644     ui[k+1] = ui[k] + nzk;
2645   }
2646 
2647 #if defined(PETSC_USE_INFO)
2648   if (ai[am] != 0) {
2649     PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]);
2650     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2651     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2652     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2653   } else {
2654      ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2655   }
2656 #endif
2657 
2658   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2659   ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2660   ierr = PetscFree(jl);CHKERRQ(ierr);
2661 
2662   /* destroy list of free space and other temporary array(s) */
2663   ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2664   ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
2665   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2666 
2667   /* put together the new matrix in MATSEQSBAIJ format */
2668 
2669   b = (Mat_SeqSBAIJ*)(fact)->data;
2670   b->singlemalloc = PETSC_FALSE;
2671   b->free_a       = PETSC_TRUE;
2672   b->free_ij      = PETSC_TRUE;
2673   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2674   b->j    = uj;
2675   b->i    = ui;
2676   b->diag = 0;
2677   b->ilen = 0;
2678   b->imax = 0;
2679   b->row  = perm;
2680   b->col  = perm;
2681   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2682   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2683   b->icol = iperm;
2684   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2685   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2686   ierr    = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2687   b->maxnz = b->nz = ui[am];
2688 
2689   (fact)->info.factor_mallocs    = reallocs;
2690   (fact)->info.fill_ratio_given  = fill;
2691   if (ai[am] != 0) {
2692     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2693   } else {
2694     (fact)->info.fill_ratio_needed = 0.0;
2695   }
2696   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2697   PetscFunctionReturn(0);
2698 }
2699 
2700 #undef __FUNCT__
2701 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_newdatastruct"
2702 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx)
2703 {
2704   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
2705   PetscErrorCode    ierr;
2706   PetscInt          n = A->rmap->n;
2707   const PetscInt    *ai = a->i,*aj = a->j,*vi;
2708   PetscScalar       *x,sum;
2709   const PetscScalar *b;
2710   const MatScalar   *aa = a->a,*v;
2711   PetscInt          i,nz;
2712 
2713   PetscFunctionBegin;
2714   if (!n) PetscFunctionReturn(0);
2715 
2716   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2717   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2718 
2719   /* forward solve the lower triangular */
2720   x[0] = b[0];
2721   v    = aa;
2722   vi   = aj;
2723   for (i=1; i<n; i++) {
2724     nz  = ai[i+1] - ai[i];
2725     sum = b[i];
2726     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
2727     v  += nz;
2728     vi += nz;
2729     x[i] = sum;
2730   }
2731 
2732   /* backward solve the upper triangular */
2733   v   = aa + ai[n+1];
2734   vi  = aj + ai[n+1];
2735   for (i=n-1; i>=0; i--){
2736     nz = ai[2*n-i +1] - ai[2*n-i]-1;
2737     sum = x[i];
2738     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
2739     v   += nz;
2740     vi  += nz; vi++;
2741     x[i] = *v++ *sum; /* x[i]=aa[adiag[i]]*sum; v++; */
2742   }
2743 
2744   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
2745   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2746   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2747   PetscFunctionReturn(0);
2748 }
2749 
2750 #undef __FUNCT__
2751 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_newdatastruct_v2"
2752 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct_v2(Mat A,Vec bb,Vec xx)
2753 {
2754   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
2755   PetscErrorCode    ierr;
2756   PetscInt          n = A->rmap->n;
2757   const PetscInt    *ai = a->i,*aj = a->j,*adiag = a->diag,*vi;
2758   PetscScalar       *x,sum;
2759   const PetscScalar *b;
2760   const MatScalar   *aa = a->a,*v;
2761   PetscInt          i,nz;
2762 
2763   PetscFunctionBegin;
2764   if (!n) PetscFunctionReturn(0);
2765 
2766   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2767   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2768 
2769   /* forward solve the lower triangular */
2770   x[0] = b[0];
2771   v    = aa;
2772   vi   = aj;
2773   for (i=1; i<n; i++) {
2774     nz  = ai[i+1] - ai[i];
2775     sum = b[i];
2776     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
2777     v  += nz;
2778     vi += nz;
2779     x[i] = sum;
2780   }
2781 
2782   /* backward solve the upper triangular */
2783   /*  v   = aa + ai[n+1];
2784       vi  = aj + ai[n+1]; */
2785   v  = aa + adiag[n-1];
2786   vi = aj + adiag[n-1];
2787   for (i=n-1; i>=0; i--){
2788     nz = adiag[i] - adiag[i+1]-1;
2789     sum = x[i];
2790     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
2791     v   += nz;
2792     vi  += nz; vi++;
2793     x[i] = *v++ *sum; /* x[i]=aa[adiag[i]]*sum; v++; */
2794   }
2795 
2796   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
2797   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2798   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2799   PetscFunctionReturn(0);
2800 }
2801 
2802 #undef __FUNCT__
2803 #define __FUNCT__ "MatSolve_SeqAIJ_newdatastruct"
2804 PetscErrorCode MatSolve_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec xx)
2805 {
2806   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
2807   IS                iscol = a->col,isrow = a->row;
2808   PetscErrorCode    ierr;
2809   PetscInt          i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,nz,k;
2810   const PetscInt    *rout,*cout,*r,*c;
2811   PetscScalar       *x,*tmp,*tmps,sum;
2812   const PetscScalar *b;
2813   const MatScalar   *aa = a->a,*v;
2814 
2815   PetscFunctionBegin;
2816   if (!n) PetscFunctionReturn(0);
2817 
2818   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2819   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2820   tmp  = a->solve_work;
2821 
2822   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
2823   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
2824 
2825   /* forward solve the lower triangular */
2826   tmp[0] = b[*r++];
2827   tmps   = tmp;
2828   v      = aa;
2829   vi     = aj;
2830   for (i=1; i<n; i++) {
2831     nz  = ai[i+1] - ai[i];
2832     sum = b[*r++];
2833     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
2834     tmp[i] = sum;
2835     v += nz; vi += nz;
2836   }
2837 
2838   /* backward solve the upper triangular */
2839   k  = n+1;
2840   v  = aa + ai[k]; /* 1st entry of U(n-1,:) */
2841   vi = aj + ai[k];
2842   for (i=n-1; i>=0; i--){
2843     k  = 2*n-i;
2844     nz = ai[k +1] - ai[k] - 1;
2845     sum = tmp[i];
2846     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
2847     x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */
2848     v += nz+1; vi += nz+1;
2849   }
2850 
2851   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
2852   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
2853   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2854   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2855   ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr);
2856   PetscFunctionReturn(0);
2857 }
2858 
2859 #undef __FUNCT__
2860 #define __FUNCT__ "MatSolve_SeqAIJ_newdatastruct_v2"
2861 PetscErrorCode MatSolve_SeqAIJ_newdatastruct_v2(Mat A,Vec bb,Vec xx)
2862 {
2863   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
2864   IS                iscol = a->col,isrow = a->row;
2865   PetscErrorCode    ierr;
2866   PetscInt          i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz;
2867   const PetscInt    *rout,*cout,*r,*c;
2868   PetscScalar       *x,*tmp,sum;
2869   const PetscScalar *b;
2870   const MatScalar   *aa = a->a,*v;
2871 
2872   PetscFunctionBegin;
2873   if (!n) PetscFunctionReturn(0);
2874 
2875   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2876   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2877   tmp  = a->solve_work;
2878 
2879   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
2880   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
2881 
2882   /* forward solve the lower triangular */
2883   /*  tmp[0] = b[*r++]; */
2884   tmp[0] = b[r[0]];
2885   v      = aa;
2886   vi     = aj;
2887   for (i=1; i<n; i++) {
2888     nz  = ai[i+1] - ai[i];
2889     sum = b[r[i]];
2890     PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
2891     tmp[i] = sum;
2892     v += nz; vi += nz;
2893   }
2894 
2895   /* backward solve the upper triangular */
2896   /*  v  = aa + ai[k]; *//* 1st entry of U(n-1,:) */
2897   /* vi = aj + ai[k]; */
2898   v  = aa + adiag[n-1];
2899   vi = aj + adiag[n-1];
2900   for (i=n-1; i>=0; i--){
2901     /* nz = ai[k +1] - ai[k] - 1;*/
2902     nz = adiag[i]-adiag[i+1]-1;
2903     sum = tmp[i];
2904     PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
2905     x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */
2906     v += nz+1; vi += nz+1;
2907   }
2908 
2909   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
2910   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
2911   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2912   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2913   ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr);
2914   PetscFunctionReturn(0);
2915 }
2916 
2917 #undef __FUNCT__
2918 #define __FUNCT__ "MatILUDTFactor_SeqAIJ"
2919 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact)
2920 {
2921   Mat                B = *fact;
2922   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b;
2923   IS                 isicol;
2924   PetscErrorCode     ierr;
2925   const PetscInt     *r,*ic;
2926   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag;
2927   PetscInt           *bi,*bj,*bdiag,*bdiag_rev;
2928   PetscInt           row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au;
2929   PetscInt           nlnk,*lnk;
2930   PetscBT            lnkbt;
2931   PetscTruth         row_identity,icol_identity,both_identity;
2932   MatScalar          *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp;
2933   const PetscInt     *ics;
2934   PetscInt           j,nz,*pj,*bjtmp,k,ncut,*jtmp;
2935   PetscReal          dt=info->dt,dtcol=info->dtcol,shift=info->shiftinblocks;
2936   PetscInt           dtcount=(PetscInt)info->dtcount,nnz_max;
2937   PetscTruth         missing;
2938 
2939   PetscFunctionBegin;
2940 
2941   if (dt      == PETSC_DEFAULT) dt      = 0.005;
2942   if (dtcol   == PETSC_DEFAULT) dtcol   = 0.01; /* XXX unused! */
2943   if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax);
2944 
2945   /* ------- symbolic factorization, can be reused ---------*/
2946   ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
2947   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
2948   adiag=a->diag;
2949 
2950   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
2951 
2952   /* bdiag is location of diagonal in factor */
2953   ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
2954   bdiag_rev = bdiag + n+1;
2955 
2956   /* allocate row pointers bi */
2957   ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
2958 
2959   /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */
2960   if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */
2961   nnz_max  = ai[n]+2*n*dtcount+2;
2962 
2963   ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
2964   ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr);
2965 
2966   /* put together the new matrix */
2967   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
2968   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
2969   b    = (Mat_SeqAIJ*)(B)->data;
2970   b->free_a       = PETSC_TRUE;
2971   b->free_ij      = PETSC_TRUE;
2972   b->singlemalloc = PETSC_FALSE;
2973   b->a          = ba;
2974   b->j          = bj;
2975   b->i          = bi;
2976   b->diag       = bdiag;
2977   b->ilen       = 0;
2978   b->imax       = 0;
2979   b->row        = isrow;
2980   b->col        = iscol;
2981   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
2982   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
2983   b->icol       = isicol;
2984   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2985 
2986   ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2987   b->maxnz = nnz_max;
2988 
2989   (B)->factor                = MAT_FACTOR_ILUDT;
2990   (B)->info.factor_mallocs   = 0;
2991   (B)->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]);
2992   CHKMEMQ;
2993   /* ------- end of symbolic factorization ---------*/
2994 
2995   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
2996   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
2997   ics  = ic;
2998 
2999   /* linked list for storing column indices of the active row */
3000   nlnk = n + 1;
3001   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3002 
3003   /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */
3004   ierr = PetscMalloc((2*n+1)*sizeof(PetscInt),&im);CHKERRQ(ierr);
3005   jtmp = im + n;
3006   /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */
3007   ierr = PetscMalloc((2*n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
3008   ierr = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr);
3009   vtmp = rtmp + n;
3010 
3011   bi[0]    = 0;
3012   bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */
3013   bdiag_rev[n] = bdiag[0];
3014   bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */
3015   for (i=0; i<n; i++) {
3016     /* copy initial fill into linked list */
3017     nzi = 0; /* nonzeros for active row i */
3018     nzi = ai[r[i]+1] - ai[r[i]];
3019     if (!nzi) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
3020     nzi_al = adiag[r[i]] - ai[r[i]];
3021     nzi_au = ai[r[i]+1] - adiag[r[i]] -1;
3022     ajtmp = aj + ai[r[i]];
3023     ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3024 
3025     /* load in initial (unfactored row) */
3026     aatmp = a->a + ai[r[i]];
3027     for (j=0; j<nzi; j++) {
3028       rtmp[ics[*ajtmp++]] = *aatmp++;
3029     }
3030 
3031     /* add pivot rows into linked list */
3032     row = lnk[n];
3033     while (row < i ) {
3034       nzi_bl = bi[row+1] - bi[row] + 1;
3035       bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */
3036       ierr  = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr);
3037       nzi  += nlnk;
3038       row   = lnk[row];
3039     }
3040 
3041     /* copy data from lnk into jtmp, then initialize lnk */
3042     ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr);
3043 
3044     /* numerical factorization */
3045     bjtmp = jtmp;
3046     row   = *bjtmp++; /* 1st pivot row */
3047     while  ( row < i ) {
3048       pc         = rtmp + row;
3049       pv         = ba + bdiag[row]; /* 1./(diag of the pivot row) */
3050       multiplier = (*pc) * (*pv);
3051       *pc        = multiplier;
3052       if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */
3053         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
3054         pv         = ba + bdiag[row+1] + 1;
3055         /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */
3056         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
3057         for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
3058         ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
3059       }
3060       row = *bjtmp++;
3061     }
3062 
3063     /* copy sparse rtmp into contiguous vtmp; separate L and U part */
3064     diag_tmp = rtmp[i];  /* save diagonal value - may not needed?? */
3065     nzi_bl = 0; j = 0;
3066     while (jtmp[j] < i){ /* Note: jtmp is sorted */
3067       vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
3068       nzi_bl++; j++;
3069     }
3070     nzi_bu = nzi - nzi_bl -1;
3071     while (j < nzi){
3072       vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
3073       j++;
3074     }
3075 
3076     bjtmp = bj + bi[i];
3077     batmp = ba + bi[i];
3078     /* apply level dropping rule to L part */
3079     ncut = nzi_al + dtcount;
3080     if (ncut < nzi_bl){
3081       ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr);
3082       ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr);
3083     } else {
3084       ncut = nzi_bl;
3085     }
3086     for (j=0; j<ncut; j++){
3087       bjtmp[j] = jtmp[j];
3088       batmp[j] = vtmp[j];
3089       /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */
3090     }
3091     bi[i+1] = bi[i] + ncut;
3092     nzi = ncut + 1;
3093 
3094     /* apply level dropping rule to U part */
3095     ncut = nzi_au + dtcount;
3096     if (ncut < nzi_bu){
3097       ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr);
3098       ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr);
3099     } else {
3100       ncut = nzi_bu;
3101     }
3102     nzi += ncut;
3103 
3104     /* mark bdiagonal */
3105     bdiag[i+1]       = bdiag[i] - (ncut + 1);
3106     bdiag_rev[n-i-1] = bdiag[i+1];
3107     bi[2*n - i]      = bi[2*n - i +1] - (ncut + 1);
3108     bjtmp = bj + bdiag[i];
3109     batmp = ba + bdiag[i];
3110     *bjtmp = i;
3111     *batmp = diag_tmp; /* rtmp[i]; */
3112     if (*batmp == 0.0) {
3113       *batmp = dt+shift;
3114       /* printf(" row %d add shift %g\n",i,shift); */
3115     }
3116     *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */
3117     /* printf(" (%d,%g),",*bjtmp,*batmp); */
3118 
3119     bjtmp = bj + bdiag[i+1]+1;
3120     batmp = ba + bdiag[i+1]+1;
3121     for (k=0; k<ncut; k++){
3122       bjtmp[k] = jtmp[nzi_bl+1+k];
3123       batmp[k] = vtmp[nzi_bl+1+k];
3124       /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */
3125     }
3126     /* printf("\n"); */
3127 
3128     im[i]   = nzi; /* used by PetscLLAddSortedLU() */
3129     /*
3130     printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]);
3131     printf(" ----------------------------\n");
3132     */
3133   } /* for (i=0; i<n; i++) */
3134   /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */
3135   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]);
3136 
3137   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
3138   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
3139 
3140   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
3141   ierr = PetscFree(im);CHKERRQ(ierr);
3142   ierr = PetscFree(rtmp);CHKERRQ(ierr);
3143 
3144   ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr);
3145   b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n];
3146 
3147   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
3148   ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr);
3149   both_identity = (PetscTruth) (row_identity && icol_identity);
3150   if (row_identity && icol_identity) {
3151     B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct;
3152   } else {
3153     B->ops->solve = MatSolve_SeqAIJ_newdatastruct;
3154   }
3155 
3156   B->ops->lufactorsymbolic  = MatILUDTFactorSymbolic_SeqAIJ;
3157   B->ops->lufactornumeric   = MatILUDTFactorNumeric_SeqAIJ;
3158   B->ops->solveadd          = 0;
3159   B->ops->solvetranspose    = 0;
3160   B->ops->solvetransposeadd = 0;
3161   B->ops->matsolve          = 0;
3162   B->assembled              = PETSC_TRUE;
3163   B->preallocated           = PETSC_TRUE;
3164   PetscFunctionReturn(0);
3165 }
3166 
3167 /* a wraper of MatILUDTFactor_SeqAIJ() */
3168 #undef __FUNCT__
3169 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ"
3170 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info)
3171 {
3172   PetscErrorCode     ierr;
3173 
3174   PetscFunctionBegin;
3175   ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr);
3176 
3177   fact->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ;
3178   PetscFunctionReturn(0);
3179 }
3180 
3181 /*
3182    same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors
3183    - intend to replace existing MatLUFactorNumeric_SeqAIJ()
3184 */
3185 #undef __FUNCT__
3186 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ"
3187 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info)
3188 {
3189   Mat            C=fact;
3190   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
3191   IS             isrow = b->row,isicol = b->icol;
3192   PetscErrorCode ierr;
3193   const PetscInt *r,*ic,*ics;
3194   PetscInt       i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
3195   PetscInt       *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj;
3196   MatScalar      *rtmp,*pc,multiplier,*v,*pv,*aa=a->a;
3197   PetscReal      dt=info->dt,shift=info->shiftinblocks;
3198   PetscTruth     row_identity, col_identity;
3199 
3200   PetscFunctionBegin;
3201   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
3202   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
3203   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
3204   ics  = ic;
3205 
3206   for (i=0; i<n; i++){
3207     /* initialize rtmp array */
3208     nzl   = bi[i+1] - bi[i];       /* num of nozeros in L(i,:) */
3209     bjtmp = bj + bi[i];
3210     for  (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0;
3211     rtmp[i] = 0.0;
3212     nzu   = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */
3213     bjtmp = bj + bdiag[i+1] + 1;
3214     for  (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0;
3215 
3216     /* load in initial unfactored row of A */
3217     /* printf("row %d\n",i); */
3218     nz    = ai[r[i]+1] - ai[r[i]];
3219     ajtmp = aj + ai[r[i]];
3220     v     = aa + ai[r[i]];
3221     for (j=0; j<nz; j++) {
3222       rtmp[ics[*ajtmp++]] = v[j];
3223       /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */
3224     }
3225     /* printf("\n"); */
3226 
3227     /* numerical factorization */
3228     bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */
3229     nzl   = bi[i+1] - bi[i]; /* num of entries in L(i,:) */
3230     k = 0;
3231     while (k < nzl){
3232       row   = *bjtmp++;
3233       /* printf("  prow %d\n",row); */
3234       pc         = rtmp + row;
3235       pv         = b->a + bdiag[row]; /* 1./(diag of the pivot row) */
3236       multiplier = (*pc) * (*pv);
3237       *pc        = multiplier;
3238       if (PetscAbsScalar(multiplier) > dt){
3239         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
3240         pv         = b->a + bdiag[row+1] + 1;
3241         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
3242         for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
3243         /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */
3244       }
3245       k++;
3246     }
3247 
3248     /* finished row so stick it into b->a */
3249     /* L-part */
3250     pv = b->a + bi[i] ;
3251     pj = bj + bi[i] ;
3252     nzl = bi[i+1] - bi[i];
3253     for (j=0; j<nzl; j++) {
3254       pv[j] = rtmp[pj[j]];
3255       /* printf(" (%d,%g),",pj[j],pv[j]); */
3256     }
3257 
3258     /* diagonal: invert diagonal entries for simplier triangular solves */
3259     if (rtmp[i] == 0.0) rtmp[i] = dt+shift;
3260     b->a[bdiag[i]] = 1.0/rtmp[i];
3261     /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */
3262 
3263     /* U-part */
3264     pv = b->a + bdiag[i+1] + 1;
3265     pj = bj + bdiag[i+1] + 1;
3266     nzu = bdiag[i] - bdiag[i+1] - 1;
3267     for (j=0; j<nzu; j++) {
3268       pv[j] = rtmp[pj[j]];
3269       /* printf(" (%d,%g),",pj[j],pv[j]); */
3270     }
3271     /* printf("\n"); */
3272   }
3273 
3274   ierr = PetscFree(rtmp);CHKERRQ(ierr);
3275   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
3276   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
3277 
3278   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
3279   ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
3280   if (row_identity && col_identity) {
3281     C->ops->solve   = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct;
3282   } else {
3283     C->ops->solve   = MatSolve_SeqAIJ_newdatastruct;
3284   }
3285   C->ops->solveadd           = 0;
3286   C->ops->solvetranspose     = 0;
3287   C->ops->solvetransposeadd  = 0;
3288   C->ops->matsolve           = 0;
3289   C->assembled    = PETSC_TRUE;
3290   C->preallocated = PETSC_TRUE;
3291   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
3292   PetscFunctionReturn(0);
3293 }
3294