xref: /petsc/src/mat/impls/aij/seq/aijfact.c (revision 71fd2e92b2fee25f70818ffc1dca9fc57f8584d7)
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 
1392   PetscFunctionBegin;
1393   ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr);
1394   b    = (Mat_SeqAIJ*)(fact)->data;
1395 
1396   /* allocate matrix arrays for new data structure */
1397   ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,n+1,PetscInt,&b->i);CHKERRQ(ierr);
1398   ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));CHKERRQ(ierr);
1399   b->singlemalloc = PETSC_TRUE;
1400   if (!b->diag){
1401     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr);
1402     ierr = PetscLogObjectMemory(fact,(n+1)*sizeof(PetscInt));CHKERRQ(ierr);
1403   }
1404   bdiag = b->diag;
1405 
1406   if (n > 0) {
1407     ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr);
1408   }
1409 
1410   /* set bi and bj with new data structure */
1411   bi = b->i;
1412   bj = b->j;
1413 
1414   /* L part */
1415   bi[0] = 0;
1416   for (i=0; i<n; i++){
1417     nz = adiag[i] - ai[i];
1418     bi[i+1] = bi[i] + nz;
1419     aj = a->j + ai[i];
1420     for (j=0; j<nz; j++){
1421       *bj = aj[j]; bj++;
1422     }
1423   }
1424 
1425   /* U part */
1426   /* bi[n+1] = bi[n]; */
1427   bi_temp = bi[n];
1428   bdiag[n] = bi[n]-1;
1429   for (i=n-1; i>=0; i--){
1430     nz = ai[i+1] - adiag[i] - 1;
1431     /*  bi[2*n-i+1] = bi[2*n-i] + nz + 1; */
1432     bi_temp = bi_temp + nz + 1;
1433     aj = a->j + adiag[i] + 1;
1434     for (j=0; j<nz; j++){
1435       *bj = aj[j]; bj++;
1436     }
1437     /* diag[i] */
1438     *bj = i; bj++;
1439     /*   bdiag[i] = bi[2*n-i+1]-1; */
1440     bdiag[i] = bi_temp - 1;
1441   }
1442   PetscFunctionReturn(0);
1443 }
1444 
1445 #undef __FUNCT__
1446 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_newdatastruct"
1447 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1448 {
1449   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1450   IS                 isicol;
1451   PetscErrorCode     ierr;
1452   const PetscInt     *r,*ic;
1453   PetscInt           n=A->rmap->n,*ai=a->i,*aj=a->j,d;
1454   PetscInt           *bi,*cols,nnz,*cols_lvl;
1455   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1456   PetscInt           i,levels,diagonal_fill;
1457   PetscTruth         col_identity,row_identity;
1458   PetscReal          f;
1459   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
1460   PetscBT            lnkbt;
1461   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
1462   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1463   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1464   PetscTruth         missing;
1465 
1466   PetscFunctionBegin;
1467   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);
1468   f             = info->fill;
1469   levels        = (PetscInt)info->levels;
1470   diagonal_fill = (PetscInt)info->diagonal_fill;
1471   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1472 
1473   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1474   ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
1475 
1476   if (!levels && row_identity && col_identity) {
1477     /* special case: ilu(0) with natural ordering */
1478     ierr = MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1479     (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ_newdatastruct;
1480 
1481     fact->factor = MAT_FACTOR_ILU;
1482     (fact)->info.factor_mallocs    = 0;
1483     (fact)->info.fill_ratio_given  = info->fill;
1484     (fact)->info.fill_ratio_needed = 1.0;
1485     b               = (Mat_SeqAIJ*)(fact)->data;
1486     ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
1487     if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
1488     b->row              = isrow;
1489     b->col              = iscol;
1490     b->icol             = isicol;
1491     ierr                = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1492     ierr                = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1493     ierr                = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1494     /* ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */
1495     PetscFunctionReturn(0);
1496   }
1497 
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   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
1517   current_space = free_space;
1518   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
1519   current_space_lvl = free_space_lvl;
1520 
1521   for (i=0; i<n; i++) {
1522     nzi = 0;
1523     /* copy current row into linked list */
1524     nnz  = ai[r[i]+1] - ai[r[i]];
1525     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1526     cols = aj + ai[r[i]];
1527     lnk[i] = -1; /* marker to indicate if diagonal exists */
1528     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1529     nzi += nlnk;
1530 
1531     /* make sure diagonal entry is included */
1532     if (diagonal_fill && lnk[i] == -1) {
1533       fm = n;
1534       while (lnk[fm] < i) fm = lnk[fm];
1535       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
1536       lnk[fm]    = i;
1537       lnk_lvl[i] = 0;
1538       nzi++; dcount++;
1539     }
1540 
1541     /* add pivot rows into the active row */
1542     nzbd = 0;
1543     prow = lnk[n];
1544     while (prow < i) {
1545       nnz      = bdiag[prow];
1546       cols     = bj_ptr[prow] + nnz + 1;
1547       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1548       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
1549       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
1550       nzi += nlnk;
1551       prow = lnk[prow];
1552       nzbd++;
1553     }
1554     bdiag[i] = nzbd;
1555     bi[i+1]  = bi[i] + nzi;
1556 
1557     /* if free space is not available, make more free space */
1558     if (current_space->local_remaining<nzi) {
1559       nnz = 2*nzi*(n - i); /* estimated and max additional space needed */
1560       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
1561       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
1562       reallocs++;
1563     }
1564 
1565     /* copy data into free_space and free_space_lvl, then initialize lnk */
1566     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1567     bj_ptr[i]    = current_space->array;
1568     bjlvl_ptr[i] = current_space_lvl->array;
1569 
1570     /* make sure the active row i has diagonal entry */
1571     if (*(bj_ptr[i]+bdiag[i]) != i) {
1572       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
1573     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
1574     }
1575 
1576     current_space->array           += nzi;
1577     current_space->local_used      += nzi;
1578     current_space->local_remaining -= nzi;
1579     current_space_lvl->array           += nzi;
1580     current_space_lvl->local_used      += nzi;
1581     current_space_lvl->local_remaining -= nzi;
1582   }
1583 
1584   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1585   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1586 
1587   /* destroy list of free space and other temporary arrays */
1588   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
1589 
1590   /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */
1591   ierr = PetscFreeSpaceContiguous_LU_v2(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr);
1592 
1593   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1594   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
1595   ierr = PetscFree(bj_ptr);CHKERRQ(ierr);
1596 
1597 #if defined(PETSC_USE_INFO)
1598   {
1599     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1600     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
1601     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
1602     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
1603     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
1604     if (diagonal_fill) {
1605       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
1606     }
1607   }
1608 #endif
1609 
1610   /* put together the new matrix */
1611   ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
1612   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
1613   b = (Mat_SeqAIJ*)(fact)->data;
1614   b->free_a       = PETSC_TRUE;
1615   b->free_ij      = PETSC_TRUE;
1616   b->singlemalloc = PETSC_FALSE;
1617   ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
1618   b->j          = bj;
1619   b->i          = bi;
1620   b->diag       = bdiag;
1621   b->ilen       = 0;
1622   b->imax       = 0;
1623   b->row        = isrow;
1624   b->col        = iscol;
1625   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1626   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1627   b->icol       = isicol;
1628   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1629   /* In b structure:  Free imax, ilen, old a, old j.
1630      Allocate bdiag, solve_work, new a, new j */
1631   ierr = PetscLogObjectMemory(fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
1632   b->maxnz = b->nz = bdiag[0]+1;
1633   (fact)->info.factor_mallocs    = reallocs;
1634   (fact)->info.fill_ratio_given  = f;
1635   (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]);
1636   (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct;
1637   /* ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */
1638   PetscFunctionReturn(0);
1639 }
1640 
1641 #undef __FUNCT__
1642 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ"
1643 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1644 {
1645   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1646   IS                 isicol;
1647   PetscErrorCode     ierr;
1648   const PetscInt     *r,*ic;
1649   PetscInt           n=A->rmap->n,*ai=a->i,*aj=a->j,d;
1650   PetscInt           *bi,*cols,nnz,*cols_lvl;
1651   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1652   PetscInt           i,levels,diagonal_fill;
1653   PetscTruth         col_identity,row_identity;
1654   PetscReal          f;
1655   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
1656   PetscBT            lnkbt;
1657   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
1658   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1659   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1660   PetscTruth         missing;
1661   PetscTruth         newdatastruct=PETSC_FALSE;
1662 
1663   PetscFunctionBegin;
1664   ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
1665   if(newdatastruct){
1666     ierr = MatILUFactorSymbolic_SeqAIJ_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1667     PetscFunctionReturn(0);
1668   }
1669 
1670   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);
1671   f             = info->fill;
1672   levels        = (PetscInt)info->levels;
1673   diagonal_fill = (PetscInt)info->diagonal_fill;
1674   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1675 
1676   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1677   ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
1678   if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */
1679     ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr);
1680     (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ;
1681 
1682     fact->factor = MAT_FACTOR_ILU;
1683     (fact)->info.factor_mallocs    = 0;
1684     (fact)->info.fill_ratio_given  = info->fill;
1685     (fact)->info.fill_ratio_needed = 1.0;
1686     b               = (Mat_SeqAIJ*)(fact)->data;
1687     ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
1688     if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
1689     b->row              = isrow;
1690     b->col              = iscol;
1691     b->icol             = isicol;
1692     ierr                = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1693     ierr                = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1694     ierr                = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1695     ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1696     PetscFunctionReturn(0);
1697   }
1698 
1699   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1700   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1701 
1702   /* get new row pointers */
1703   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1704   bi[0] = 0;
1705   /* bdiag is location of diagonal in factor */
1706   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
1707   bdiag[0]  = 0;
1708 
1709   ierr = PetscMalloc((2*n+1)*sizeof(PetscInt**),&bj_ptr);CHKERRQ(ierr);
1710   bjlvl_ptr = (PetscInt**)(bj_ptr + n);
1711 
1712   /* create a linked list for storing column indices of the active row */
1713   nlnk = n + 1;
1714   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1715 
1716   /* initial FreeSpace size is f*(ai[n]+1) */
1717   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
1718   current_space = free_space;
1719   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
1720   current_space_lvl = free_space_lvl;
1721 
1722   for (i=0; i<n; i++) {
1723     nzi = 0;
1724     /* copy current row into linked list */
1725     nnz  = ai[r[i]+1] - ai[r[i]];
1726     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1727     cols = aj + ai[r[i]];
1728     lnk[i] = -1; /* marker to indicate if diagonal exists */
1729     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1730     nzi += nlnk;
1731 
1732     /* make sure diagonal entry is included */
1733     if (diagonal_fill && lnk[i] == -1) {
1734       fm = n;
1735       while (lnk[fm] < i) fm = lnk[fm];
1736       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
1737       lnk[fm]    = i;
1738       lnk_lvl[i] = 0;
1739       nzi++; dcount++;
1740     }
1741 
1742     /* add pivot rows into the active row */
1743     nzbd = 0;
1744     prow = lnk[n];
1745     while (prow < i) {
1746       nnz      = bdiag[prow];
1747       cols     = bj_ptr[prow] + nnz + 1;
1748       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1749       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
1750       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
1751       nzi += nlnk;
1752       prow = lnk[prow];
1753       nzbd++;
1754     }
1755     bdiag[i] = nzbd;
1756     bi[i+1]  = bi[i] + nzi;
1757 
1758     /* if free space is not available, make more free space */
1759     if (current_space->local_remaining<nzi) {
1760       nnz = nzi*(n - i); /* estimated and max additional space needed */
1761       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
1762       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
1763       reallocs++;
1764     }
1765 
1766     /* copy data into free_space and free_space_lvl, then initialize lnk */
1767     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1768     bj_ptr[i]    = current_space->array;
1769     bjlvl_ptr[i] = current_space_lvl->array;
1770 
1771     /* make sure the active row i has diagonal entry */
1772     if (*(bj_ptr[i]+bdiag[i]) != i) {
1773       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
1774     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
1775     }
1776 
1777     current_space->array           += nzi;
1778     current_space->local_used      += nzi;
1779     current_space->local_remaining -= nzi;
1780     current_space_lvl->array           += nzi;
1781     current_space_lvl->local_used      += nzi;
1782     current_space_lvl->local_remaining -= nzi;
1783   }
1784 
1785   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1786   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1787 
1788   /* destroy list of free space and other temporary arrays */
1789   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
1790   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */
1791   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1792   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
1793   ierr = PetscFree(bj_ptr);CHKERRQ(ierr);
1794 
1795 #if defined(PETSC_USE_INFO)
1796   {
1797     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1798     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
1799     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
1800     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
1801     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
1802     if (diagonal_fill) {
1803       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
1804     }
1805   }
1806 #endif
1807 
1808   /* put together the new matrix */
1809   ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
1810   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
1811   b = (Mat_SeqAIJ*)(fact)->data;
1812   b->free_a       = PETSC_TRUE;
1813   b->free_ij      = PETSC_TRUE;
1814   b->singlemalloc = PETSC_FALSE;
1815   ierr = PetscMalloc( (bi[n] )*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
1816   b->j          = bj;
1817   b->i          = bi;
1818   for (i=0; i<n; i++) bdiag[i] += bi[i];
1819   b->diag       = bdiag;
1820   b->ilen       = 0;
1821   b->imax       = 0;
1822   b->row        = isrow;
1823   b->col        = iscol;
1824   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1825   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1826   b->icol       = isicol;
1827   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1828   /* In b structure:  Free imax, ilen, old a, old j.
1829      Allocate bdiag, solve_work, new a, new j */
1830   ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
1831   b->maxnz             = b->nz = bi[n] ;
1832   (fact)->info.factor_mallocs    = reallocs;
1833   (fact)->info.fill_ratio_given  = f;
1834   (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1835   (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ;
1836   ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1837   PetscFunctionReturn(0);
1838 }
1839 
1840 #undef __FUNCT__
1841 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ_newdatastruct"
1842 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info)
1843 {
1844   Mat            C = B;
1845   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1846   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
1847   IS             ip=b->row,iip = b->icol;
1848   PetscErrorCode ierr;
1849   const PetscInt *rip,*riip;
1850   PetscInt       i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp;
1851   PetscInt       *ai=a->i,*aj=a->j;
1852   PetscInt       k,jmin,jmax,*c2r,*il,col,nexti,ili,nz;
1853   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
1854   PetscReal      zeropivot,shiftnz;
1855   PetscReal      shiftpd;
1856   PetscTruth     perm_identity;
1857 
1858   PetscFunctionBegin;
1859 
1860   shiftnz   = info->shiftnz;
1861   shiftpd   = info->shiftpd;
1862   zeropivot = info->zeropivot;
1863 
1864   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
1865   ierr  = ISGetIndices(iip,&riip);CHKERRQ(ierr);
1866 
1867   /* allocate working arrays
1868      c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col
1869      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
1870   */
1871   nz   = (2*mbs+1)*sizeof(PetscInt)+mbs*sizeof(MatScalar);
1872   ierr = PetscMalloc(nz,&il);CHKERRQ(ierr);
1873   c2r  = il + mbs;
1874   rtmp = (MatScalar*)(c2r + mbs);
1875 
1876   for (i=0; i<mbs; i++) {
1877     c2r[i] = mbs;
1878   }
1879   il[0] = 0;
1880 
1881   for (k = 0; k<mbs; k++){
1882     /* zero rtmp */
1883     nz = bi[k+1] - bi[k];
1884     bjtmp = bj + bi[k];
1885     for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
1886 
1887     /* load in initial unfactored row */
1888     bval = ba + bi[k];
1889     jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
1890     for (j = jmin; j < jmax; j++){
1891       col = riip[aj[j]];
1892       if (col >= k){ /* only take upper triangular entry */
1893         rtmp[col] = aa[j];
1894         *bval++   = 0.0; /* for in-place factorization */
1895       }
1896     }
1897     /* shift the diagonal of the matrix */
1898 
1899     /* modify k-th row by adding in those rows i with U(i,k)!=0 */
1900     dk = rtmp[k];
1901     i  = c2r[k]; /* first row to be added to k_th row  */
1902 
1903     while (i < k){
1904       nexti = c2r[i]; /* next row to be added to k_th row */
1905 
1906       /* compute multiplier, update diag(k) and U(i,k) */
1907       ili   = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
1908       uikdi = - ba[ili]*ba[bdiag[i]];  /* diagonal(k) */
1909       dk   += uikdi*ba[ili]; /* update diag[k] */
1910       ba[ili] = uikdi; /* -U(i,k) */
1911 
1912       /* add multiple of row i to k-th row */
1913       jmin = ili + 1; jmax = bi[i+1];
1914       if (jmin < jmax){
1915         for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
1916         /* update il and c2r for row i */
1917         il[i] = jmin;
1918         j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i;
1919       }
1920       i = nexti;
1921     }
1922 
1923     /* copy data into U(k,:) */
1924     ba[bdiag[k]] = 1.0/dk; /* U(k,k) */
1925     jmin = bi[k]; jmax = bi[k+1]-1;
1926     if (jmin < jmax) {
1927       for (j=jmin; j<jmax; j++){
1928         col = bj[j]; ba[j] = rtmp[col];
1929       }
1930       /* add the k-th row into il and c2r */
1931       il[k] = jmin;
1932       i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k;
1933     }
1934   }
1935 
1936   ierr = PetscFree(il);CHKERRQ(ierr);
1937   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
1938   ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr);
1939 
1940   ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
1941   if (perm_identity){
1942     (B)->ops->solve           = MatSolve_SeqSBAIJ_1_NaturalOrdering_newdatastruct;
1943     (B)->ops->solvetranspose  = 0;
1944     (B)->ops->forwardsolve    = 0;
1945     (B)->ops->backwardsolve   = 0;
1946   } else {
1947     (B)->ops->solve           = MatSolve_SeqSBAIJ_1_newdatastruct;
1948     (B)->ops->solvetranspose  = 0;
1949     (B)->ops->forwardsolve    = 0;
1950     (B)->ops->backwardsolve   = 0;
1951   }
1952 
1953   C->assembled    = PETSC_TRUE;
1954   C->preallocated = PETSC_TRUE;
1955   ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr);
1956   PetscFunctionReturn(0);
1957 }
1958 
1959 #undef __FUNCT__
1960 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ"
1961 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info)
1962 {
1963   Mat            C = B;
1964   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1965   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
1966   IS             ip=b->row,iip = b->icol;
1967   PetscErrorCode ierr;
1968   const PetscInt *rip,*riip;
1969   PetscInt       i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol;
1970   PetscInt       *ai=a->i,*aj=a->j;
1971   PetscInt       k,jmin,jmax,*jl,*il,col,nexti,ili,nz;
1972   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
1973   PetscReal      zeropivot,rs,shiftnz;
1974   PetscReal      shiftpd;
1975   ChShift_Ctx    sctx;
1976   PetscInt       newshift;
1977   PetscTruth     perm_identity;
1978 
1979   PetscFunctionBegin;
1980   shiftnz   = info->shiftnz;
1981   shiftpd   = info->shiftpd;
1982   zeropivot = info->zeropivot;
1983 
1984   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
1985   ierr  = ISGetIndices(iip,&riip);CHKERRQ(ierr);
1986 
1987   /* initialization */
1988   nz   = (2*mbs+1)*sizeof(PetscInt)+mbs*sizeof(MatScalar);
1989   ierr = PetscMalloc(nz,&il);CHKERRQ(ierr);
1990   jl   = il + mbs;
1991   rtmp = (MatScalar*)(jl + mbs);
1992 
1993   sctx.shift_amount = 0;
1994   sctx.nshift       = 0;
1995   do {
1996     sctx.chshift = PETSC_FALSE;
1997     for (i=0; i<mbs; i++) {
1998       rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0;
1999     }
2000 
2001     for (k = 0; k<mbs; k++){
2002       bval = ba + bi[k];
2003       /* initialize k-th row by the perm[k]-th row of A */
2004       jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2005       for (j = jmin; j < jmax; j++){
2006         col = riip[aj[j]];
2007         if (col >= k){ /* only take upper triangular entry */
2008           rtmp[col] = aa[j];
2009           *bval++  = 0.0; /* for in-place factorization */
2010         }
2011       }
2012       /* shift the diagonal of the matrix */
2013       if (sctx.nshift) rtmp[k] += sctx.shift_amount;
2014 
2015       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
2016       dk = rtmp[k];
2017       i = jl[k]; /* first row to be added to k_th row  */
2018 
2019       while (i < k){
2020         nexti = jl[i]; /* next row to be added to k_th row */
2021 
2022         /* compute multiplier, update diag(k) and U(i,k) */
2023         ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2024         uikdi = - ba[ili]*ba[bi[i]];  /* diagonal(k) */
2025         dk += uikdi*ba[ili];
2026         ba[ili] = uikdi; /* -U(i,k) */
2027 
2028         /* add multiple of row i to k-th row */
2029         jmin = ili + 1; jmax = bi[i+1];
2030         if (jmin < jmax){
2031           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2032           /* update il and jl for row i */
2033           il[i] = jmin;
2034           j = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
2035         }
2036         i = nexti;
2037       }
2038 
2039       /* shift the diagonals when zero pivot is detected */
2040       /* compute rs=sum of abs(off-diagonal) */
2041       rs   = 0.0;
2042       jmin = bi[k]+1;
2043       nz   = bi[k+1] - jmin;
2044       bcol = bj + jmin;
2045       for (j=0; j<nz; j++) {
2046         rs += PetscAbsScalar(rtmp[bcol[j]]);
2047       }
2048 
2049       sctx.rs = rs;
2050       sctx.pv = dk;
2051       ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr);
2052 
2053       if (newshift == 1) {
2054         if (!sctx.shift_amount) {
2055           sctx.shift_amount = 1e-5;
2056         }
2057         break;
2058       }
2059 
2060       /* copy data into U(k,:) */
2061       ba[bi[k]] = 1.0/dk; /* U(k,k) */
2062       jmin = bi[k]+1; jmax = bi[k+1];
2063       if (jmin < jmax) {
2064         for (j=jmin; j<jmax; j++){
2065           col = bj[j]; ba[j] = rtmp[col]; rtmp[col] = 0.0;
2066         }
2067         /* add the k-th row into il and jl */
2068         il[k] = jmin;
2069         i = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
2070       }
2071     }
2072   } while (sctx.chshift);
2073   ierr = PetscFree(il);CHKERRQ(ierr);
2074 
2075   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2076   ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr);
2077 
2078   ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
2079   if (perm_identity){
2080     (B)->ops->solve           = MatSolve_SeqSBAIJ_1_NaturalOrdering;
2081     (B)->ops->solvetranspose  = MatSolve_SeqSBAIJ_1_NaturalOrdering;
2082     (B)->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering;
2083     (B)->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering;
2084   } else {
2085     (B)->ops->solve           = MatSolve_SeqSBAIJ_1;
2086     (B)->ops->solvetranspose  = MatSolve_SeqSBAIJ_1;
2087     (B)->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1;
2088     (B)->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1;
2089   }
2090 
2091   C->assembled    = PETSC_TRUE;
2092   C->preallocated = PETSC_TRUE;
2093   ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr);
2094   if (sctx.nshift){
2095     if (shiftnz) {
2096       ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2097     } else if (shiftpd) {
2098       ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2099     }
2100   }
2101   PetscFunctionReturn(0);
2102 }
2103 
2104 /*
2105    icc() under revised new data structure.
2106    Factored arrays bj and ba are stored as
2107      U(0,:),...,U(i,:),U(n-1,:)
2108 
2109    ui=fact->i is an array of size n+1, in which
2110    ui+
2111      ui[i]:  points to 1st entry of U(i,:),i=0,...,n-1
2112      ui[n]:  points to U(n-1,n-1)+1
2113 
2114   udiag=fact->diag is an array of size n,in which
2115      udiag[i]: points to diagonal of U(i,:), i=0,...,n-1
2116 
2117    U(i,:) contains udiag[i] as its last entry, i.e.,
2118     U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i])
2119 */
2120 
2121 #undef __FUNCT__
2122 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ_newdatastruct"
2123 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2124 {
2125   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2126   Mat_SeqSBAIJ       *b;
2127   PetscErrorCode     ierr;
2128   PetscTruth         perm_identity,missing;
2129   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag;
2130   const PetscInt     *rip,*riip;
2131   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
2132   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL,d;
2133   PetscInt           ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
2134   PetscReal          fill=info->fill,levels=info->levels;
2135   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2136   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
2137   PetscBT            lnkbt;
2138   IS                 iperm;
2139 
2140   PetscFunctionBegin;
2141   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);
2142   ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
2143   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
2144   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2145   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2146 
2147   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2148   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2149   ui[0] = 0;
2150 
2151   /* ICC(0) without matrix ordering: simply rearrange column indices */
2152   if (!levels && perm_identity) {
2153 
2154     for (i=0; i<am; i++) {
2155       ui[i+1]  = ui[i] + ai[i+1] - a->diag[i];
2156       udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */
2157     }
2158     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2159     cols = uj;
2160     for (i=0; i<am; i++) {
2161       aj    = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */
2162       ncols = ui[i+1] - ui[i] - 1;
2163       for (j=0; j<ncols; j++) *cols++ = aj[j];
2164       *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */
2165     }
2166   } else { /* case: levels>0 || (levels=0 && !perm_identity) */
2167     if (levels) SETERRQ(PETSC_ERR_ARG_WRONG,"not done yet");
2168     ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2169     ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2170 
2171     /* initialization */
2172     ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr);
2173 
2174     /* jl: linked list for storing indices of the pivot rows
2175        il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2176     ierr = PetscMalloc((2*am+1)*sizeof(PetscInt)+2*am*sizeof(PetscInt**),&jl);CHKERRQ(ierr);
2177     il         = jl + am;
2178     uj_ptr     = (PetscInt**)(il + am);
2179     uj_lvl_ptr = (PetscInt**)(uj_ptr + am);
2180     for (i=0; i<am; i++){
2181       jl[i] = am; il[i] = 0;
2182     }
2183 
2184     /* create and initialize a linked list for storing column indices of the active row k */
2185     nlnk = am + 1;
2186     ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2187 
2188     /* initial FreeSpace size is fill*(ai[am]+1) */
2189     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2190     current_space = free_space;
2191     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr);
2192     current_space_lvl = free_space_lvl;
2193 
2194     for (k=0; k<am; k++){  /* for each active row k */
2195       /* initialize lnk by the column indices of row rip[k] of A */
2196       nzk   = 0;
2197       ncols = ai[rip[k]+1] - ai[rip[k]];
2198       if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2199       ncols_upper = 0;
2200       for (j=0; j<ncols; j++){
2201         i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2202         if (riip[i] >= k){ /* only take upper triangular entry */
2203           ajtmp[ncols_upper] = i;
2204           ncols_upper++;
2205         }
2206       }
2207       ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2208       nzk += nlnk;
2209 
2210       /* update lnk by computing fill-in for each pivot row to be merged in */
2211       prow = jl[k]; /* 1st pivot row */
2212 
2213       while (prow < k){
2214         nextprow = jl[prow];
2215 
2216         /* merge prow into k-th row */
2217         jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2218         jmax = ui[prow+1];
2219         ncols = jmax-jmin;
2220         i     = jmin - ui[prow];
2221         cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2222         uj    = uj_lvl_ptr[prow] + i; /* levels of cols */
2223         j     = *(uj - 1);
2224         ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr);
2225         nzk += nlnk;
2226 
2227         /* update il and jl for prow */
2228         if (jmin < jmax){
2229           il[prow] = jmin;
2230           j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2231         }
2232         prow = nextprow;
2233       }
2234 
2235       /* if free space is not available, make more free space */
2236       if (current_space->local_remaining<nzk) {
2237         i = am - k + 1; /* num of unfactored rows */
2238         i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2239         ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2240         ierr = PetscFreeSpaceGet(i,&current_space_lvl);CHKERRQ(ierr);
2241         reallocs++;
2242       }
2243 
2244       /* copy data into free_space and free_space_lvl, then initialize lnk */
2245       if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2246       ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
2247 
2248       /* add the k-th row into il and jl */
2249       if (nzk > 1){
2250         i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2251         jl[k] = jl[i]; jl[i] = k;
2252         il[k] = ui[k] + 1;
2253       }
2254       uj_ptr[k]     = current_space->array;
2255       uj_lvl_ptr[k] = current_space_lvl->array;
2256 
2257       current_space->array           += nzk;
2258       current_space->local_used      += nzk;
2259       current_space->local_remaining -= nzk;
2260 
2261       current_space_lvl->array           += nzk;
2262       current_space_lvl->local_used      += nzk;
2263       current_space_lvl->local_remaining -= nzk;
2264 
2265       ui[k+1] = ui[k] + nzk;
2266     }
2267 
2268 #if defined(PETSC_USE_INFO)
2269     if (ai[am] != 0) {
2270       PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]);
2271       ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2272       ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2273       ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2274     } else {
2275       ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2276     }
2277 #endif
2278 
2279     ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2280     ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2281     ierr = PetscFree(jl);CHKERRQ(ierr);
2282     ierr = PetscFree(ajtmp);CHKERRQ(ierr);
2283 
2284     /* destroy list of free space and other temporary array(s) */
2285     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2286     ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr);
2287     ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2288     ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2289 
2290   } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2291 
2292   /* put together the new matrix in MATSEQSBAIJ format */
2293 
2294   b    = (Mat_SeqSBAIJ*)(fact)->data;
2295   b->singlemalloc = PETSC_FALSE;
2296   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2297   b->j    = uj;
2298   b->i    = ui;
2299   b->diag = udiag;
2300   b->free_diag = PETSC_TRUE;
2301   b->ilen = 0;
2302   b->imax = 0;
2303   b->row  = perm;
2304   b->col  = perm;
2305   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2306   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2307   b->icol = iperm;
2308   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2309   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2310   ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2311   b->maxnz   = b->nz = ui[am];
2312   b->free_a  = PETSC_TRUE;
2313   b->free_ij = PETSC_TRUE;
2314 
2315   (fact)->info.factor_mallocs    = reallocs;
2316   (fact)->info.fill_ratio_given  = fill;
2317   if (ai[am] != 0) {
2318     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2319   } else {
2320     (fact)->info.fill_ratio_needed = 0.0;
2321   }
2322   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_newdatastruct;
2323   PetscFunctionReturn(0);
2324 }
2325 
2326 #undef __FUNCT__
2327 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ"
2328 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2329 {
2330   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2331   Mat_SeqSBAIJ       *b;
2332   PetscErrorCode     ierr;
2333   PetscTruth         perm_identity,missing;
2334   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag;
2335   const PetscInt     *rip,*riip;
2336   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
2337   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL,d;
2338   PetscInt           ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
2339   PetscReal          fill=info->fill,levels=info->levels;
2340   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2341   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
2342   PetscBT            lnkbt;
2343   IS                 iperm;
2344   PetscTruth         newdatastruct=PETSC_FALSE;
2345 
2346   PetscFunctionBegin;
2347   ierr = PetscOptionsGetTruth(PETSC_NULL,"-icc_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
2348   if(newdatastruct){
2349     ierr = MatICCFactorSymbolic_SeqAIJ_newdatastruct(fact,A,perm,info);CHKERRQ(ierr);
2350     PetscFunctionReturn(0);
2351   }
2352 
2353   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);
2354   ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
2355   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
2356   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2357   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2358 
2359   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2360   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2361   ui[0] = 0;
2362 
2363   /* ICC(0) without matrix ordering: simply copies fill pattern */
2364   if (!levels && perm_identity) {
2365 
2366     for (i=0; i<am; i++) {
2367       ui[i+1]  = ui[i] + ai[i+1] - a->diag[i];
2368       udiag[i] = ui[i];
2369     }
2370     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2371     cols = uj;
2372     for (i=0; i<am; i++) {
2373       aj    = a->j + a->diag[i];
2374       ncols = ui[i+1] - ui[i];
2375       for (j=0; j<ncols; j++) *cols++ = *aj++;
2376     }
2377   } else { /* case: levels>0 || (levels=0 && !perm_identity) */
2378     ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2379     ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2380 
2381     /* initialization */
2382     ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr);
2383 
2384     /* jl: linked list for storing indices of the pivot rows
2385        il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2386     ierr = PetscMalloc((2*am+1)*sizeof(PetscInt)+2*am*sizeof(PetscInt**),&jl);CHKERRQ(ierr);
2387     il         = jl + am;
2388     uj_ptr     = (PetscInt**)(il + am);
2389     uj_lvl_ptr = (PetscInt**)(uj_ptr + am);
2390     for (i=0; i<am; i++){
2391       jl[i] = am; il[i] = 0;
2392     }
2393 
2394     /* create and initialize a linked list for storing column indices of the active row k */
2395     nlnk = am + 1;
2396     ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2397 
2398     /* initial FreeSpace size is fill*(ai[am]+1) */
2399     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2400     current_space = free_space;
2401     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr);
2402     current_space_lvl = free_space_lvl;
2403 
2404     for (k=0; k<am; k++){  /* for each active row k */
2405       /* initialize lnk by the column indices of row rip[k] of A */
2406       nzk   = 0;
2407       ncols = ai[rip[k]+1] - ai[rip[k]];
2408       if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2409       ncols_upper = 0;
2410       for (j=0; j<ncols; j++){
2411         i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2412         if (riip[i] >= k){ /* only take upper triangular entry */
2413           ajtmp[ncols_upper] = i;
2414           ncols_upper++;
2415         }
2416       }
2417       ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2418       nzk += nlnk;
2419 
2420       /* update lnk by computing fill-in for each pivot row to be merged in */
2421       prow = jl[k]; /* 1st pivot row */
2422 
2423       while (prow < k){
2424         nextprow = jl[prow];
2425 
2426         /* merge prow into k-th row */
2427         jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2428         jmax = ui[prow+1];
2429         ncols = jmax-jmin;
2430         i     = jmin - ui[prow];
2431         cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2432         uj    = uj_lvl_ptr[prow] + i; /* levels of cols */
2433         j     = *(uj - 1);
2434         ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr);
2435         nzk += nlnk;
2436 
2437         /* update il and jl for prow */
2438         if (jmin < jmax){
2439           il[prow] = jmin;
2440           j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2441         }
2442         prow = nextprow;
2443       }
2444 
2445       /* if free space is not available, make more free space */
2446       if (current_space->local_remaining<nzk) {
2447         i = am - k + 1; /* num of unfactored rows */
2448         i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2449         ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2450         ierr = PetscFreeSpaceGet(i,&current_space_lvl);CHKERRQ(ierr);
2451         reallocs++;
2452       }
2453 
2454       /* copy data into free_space and free_space_lvl, then initialize lnk */
2455       if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2456       ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
2457 
2458       /* add the k-th row into il and jl */
2459       if (nzk > 1){
2460         i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2461         jl[k] = jl[i]; jl[i] = k;
2462         il[k] = ui[k] + 1;
2463       }
2464       uj_ptr[k]     = current_space->array;
2465       uj_lvl_ptr[k] = current_space_lvl->array;
2466 
2467       current_space->array           += nzk;
2468       current_space->local_used      += nzk;
2469       current_space->local_remaining -= nzk;
2470 
2471       current_space_lvl->array           += nzk;
2472       current_space_lvl->local_used      += nzk;
2473       current_space_lvl->local_remaining -= nzk;
2474 
2475       ui[k+1] = ui[k] + nzk;
2476     }
2477 
2478 #if defined(PETSC_USE_INFO)
2479     if (ai[am] != 0) {
2480       PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]);
2481       ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2482       ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2483       ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2484     } else {
2485       ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2486     }
2487 #endif
2488 
2489     ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2490     ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2491     ierr = PetscFree(jl);CHKERRQ(ierr);
2492     ierr = PetscFree(ajtmp);CHKERRQ(ierr);
2493 
2494     /* destroy list of free space and other temporary array(s) */
2495     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2496     ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
2497     ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2498     ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2499 
2500   } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2501 
2502   /* put together the new matrix in MATSEQSBAIJ format */
2503 
2504   b    = (Mat_SeqSBAIJ*)(fact)->data;
2505   b->singlemalloc = PETSC_FALSE;
2506   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2507   b->j    = uj;
2508   b->i    = ui;
2509   b->diag = udiag;
2510   b->free_diag = PETSC_TRUE;
2511   b->ilen = 0;
2512   b->imax = 0;
2513   b->row  = perm;
2514   b->col  = perm;
2515   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2516   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2517   b->icol = iperm;
2518   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2519   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2520   ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2521   b->maxnz   = b->nz = ui[am];
2522   b->free_a  = PETSC_TRUE;
2523   b->free_ij = PETSC_TRUE;
2524 
2525   (fact)->info.factor_mallocs    = reallocs;
2526   (fact)->info.fill_ratio_given  = fill;
2527   if (ai[am] != 0) {
2528     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2529   } else {
2530     (fact)->info.fill_ratio_needed = 0.0;
2531   }
2532   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2533   PetscFunctionReturn(0);
2534 }
2535 
2536 #undef __FUNCT__
2537 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ"
2538 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2539 {
2540   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2541   Mat_SeqSBAIJ       *b;
2542   PetscErrorCode     ierr;
2543   PetscTruth         perm_identity;
2544   PetscReal          fill = info->fill;
2545   const PetscInt     *rip,*riip;
2546   PetscInt           i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow;
2547   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
2548   PetscInt           nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr;
2549   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2550   PetscBT            lnkbt;
2551   IS                 iperm;
2552 
2553   PetscFunctionBegin;
2554   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);
2555   /* check whether perm is the identity mapping */
2556   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2557   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2558   ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2559   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2560 
2561   /* initialization */
2562   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2563   ui[0] = 0;
2564 
2565   /* jl: linked list for storing indices of the pivot rows
2566      il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2567   ierr = PetscMalloc((3*am+1)*sizeof(PetscInt)+am*sizeof(PetscInt**),&jl);CHKERRQ(ierr);
2568   il     = jl + am;
2569   cols   = il + am;
2570   ui_ptr = (PetscInt**)(cols + am);
2571   for (i=0; i<am; i++){
2572     jl[i] = am; il[i] = 0;
2573   }
2574 
2575   /* create and initialize a linked list for storing column indices of the active row k */
2576   nlnk = am + 1;
2577   ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2578 
2579   /* initial FreeSpace size is fill*(ai[am]+1) */
2580   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2581   current_space = free_space;
2582 
2583   for (k=0; k<am; k++){  /* for each active row k */
2584     /* initialize lnk by the column indices of row rip[k] of A */
2585     nzk   = 0;
2586     ncols = ai[rip[k]+1] - ai[rip[k]];
2587     if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2588     ncols_upper = 0;
2589     for (j=0; j<ncols; j++){
2590       i = riip[*(aj + ai[rip[k]] + j)];
2591       if (i >= k){ /* only take upper triangular entry */
2592         cols[ncols_upper] = i;
2593         ncols_upper++;
2594       }
2595     }
2596     ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2597     nzk += nlnk;
2598 
2599     /* update lnk by computing fill-in for each pivot row to be merged in */
2600     prow = jl[k]; /* 1st pivot row */
2601 
2602     while (prow < k){
2603       nextprow = jl[prow];
2604       /* merge prow into k-th row */
2605       jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2606       jmax = ui[prow+1];
2607       ncols = jmax-jmin;
2608       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2609       ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2610       nzk += nlnk;
2611 
2612       /* update il and jl for prow */
2613       if (jmin < jmax){
2614         il[prow] = jmin;
2615         j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
2616       }
2617       prow = nextprow;
2618     }
2619 
2620     /* if free space is not available, make more free space */
2621     if (current_space->local_remaining<nzk) {
2622       i = am - k + 1; /* num of unfactored rows */
2623       i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2624       ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2625       reallocs++;
2626     }
2627 
2628     /* copy data into free space, then initialize lnk */
2629     ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
2630 
2631     /* add the k-th row into il and jl */
2632     if (nzk-1 > 0){
2633       i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2634       jl[k] = jl[i]; jl[i] = k;
2635       il[k] = ui[k] + 1;
2636     }
2637     ui_ptr[k] = current_space->array;
2638     current_space->array           += nzk;
2639     current_space->local_used      += nzk;
2640     current_space->local_remaining -= nzk;
2641 
2642     ui[k+1] = ui[k] + nzk;
2643   }
2644 
2645 #if defined(PETSC_USE_INFO)
2646   if (ai[am] != 0) {
2647     PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]);
2648     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2649     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2650     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2651   } else {
2652      ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2653   }
2654 #endif
2655 
2656   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2657   ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2658   ierr = PetscFree(jl);CHKERRQ(ierr);
2659 
2660   /* destroy list of free space and other temporary array(s) */
2661   ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2662   ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
2663   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2664 
2665   /* put together the new matrix in MATSEQSBAIJ format */
2666 
2667   b = (Mat_SeqSBAIJ*)(fact)->data;
2668   b->singlemalloc = PETSC_FALSE;
2669   b->free_a       = PETSC_TRUE;
2670   b->free_ij      = PETSC_TRUE;
2671   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2672   b->j    = uj;
2673   b->i    = ui;
2674   b->diag = 0;
2675   b->ilen = 0;
2676   b->imax = 0;
2677   b->row  = perm;
2678   b->col  = perm;
2679   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2680   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2681   b->icol = iperm;
2682   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2683   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2684   ierr    = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2685   b->maxnz = b->nz = ui[am];
2686 
2687   (fact)->info.factor_mallocs    = reallocs;
2688   (fact)->info.fill_ratio_given  = fill;
2689   if (ai[am] != 0) {
2690     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2691   } else {
2692     (fact)->info.fill_ratio_needed = 0.0;
2693   }
2694   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2695   PetscFunctionReturn(0);
2696 }
2697 
2698 #undef __FUNCT__
2699 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_newdatastruct"
2700 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx)
2701 {
2702   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
2703   PetscErrorCode    ierr;
2704   PetscInt          n = A->rmap->n;
2705   const PetscInt    *ai = a->i,*aj = a->j,*vi;
2706   PetscScalar       *x,sum;
2707   const PetscScalar *b;
2708   const MatScalar   *aa = a->a,*v;
2709   PetscInt          i,nz;
2710 
2711   PetscFunctionBegin;
2712   if (!n) PetscFunctionReturn(0);
2713 
2714   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2715   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2716 
2717   /* forward solve the lower triangular */
2718   x[0] = b[0];
2719   v    = aa;
2720   vi   = aj;
2721   for (i=1; i<n; i++) {
2722     nz  = ai[i+1] - ai[i];
2723     sum = b[i];
2724     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
2725     v  += nz;
2726     vi += nz;
2727     x[i] = sum;
2728   }
2729 
2730   /* backward solve the upper triangular */
2731   v   = aa + ai[n+1];
2732   vi  = aj + ai[n+1];
2733   for (i=n-1; i>=0; i--){
2734     nz = ai[2*n-i +1] - ai[2*n-i]-1;
2735     sum = x[i];
2736     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
2737     v   += nz;
2738     vi  += nz; vi++;
2739     x[i] = *v++ *sum; /* x[i]=aa[adiag[i]]*sum; v++; */
2740   }
2741 
2742   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
2743   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2744   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2745   PetscFunctionReturn(0);
2746 }
2747 
2748 #undef __FUNCT__
2749 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_newdatastruct_v2"
2750 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct_v2(Mat A,Vec bb,Vec xx)
2751 {
2752   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
2753   PetscErrorCode    ierr;
2754   PetscInt          n = A->rmap->n;
2755   const PetscInt    *ai = a->i,*aj = a->j,*adiag = a->diag,*vi;
2756   PetscScalar       *x,sum;
2757   const PetscScalar *b;
2758   const MatScalar   *aa = a->a,*v;
2759   PetscInt          i,nz;
2760 
2761   PetscFunctionBegin;
2762   if (!n) PetscFunctionReturn(0);
2763 
2764   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2765   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2766 
2767   /* forward solve the lower triangular */
2768   x[0] = b[0];
2769   v    = aa;
2770   vi   = aj;
2771   for (i=1; i<n; i++) {
2772     nz  = ai[i+1] - ai[i];
2773     sum = b[i];
2774     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
2775     v  += nz;
2776     vi += nz;
2777     x[i] = sum;
2778   }
2779 
2780   /* backward solve the upper triangular */
2781   /*  v   = aa + ai[n+1];
2782       vi  = aj + ai[n+1]; */
2783   v  = aa + adiag[n-1];
2784   vi = aj + adiag[n-1];
2785   for (i=n-1; i>=0; i--){
2786     nz = adiag[i] - adiag[i+1]-1;
2787     sum = x[i];
2788     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
2789     v   += nz;
2790     vi  += nz; vi++;
2791     x[i] = *v++ *sum; /* x[i]=aa[adiag[i]]*sum; v++; */
2792   }
2793 
2794   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
2795   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2796   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2797   PetscFunctionReturn(0);
2798 }
2799 
2800 #undef __FUNCT__
2801 #define __FUNCT__ "MatSolve_SeqAIJ_newdatastruct"
2802 PetscErrorCode MatSolve_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec xx)
2803 {
2804   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
2805   IS                iscol = a->col,isrow = a->row;
2806   PetscErrorCode    ierr;
2807   PetscInt          i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,nz,k;
2808   const PetscInt    *rout,*cout,*r,*c;
2809   PetscScalar       *x,*tmp,*tmps,sum;
2810   const PetscScalar *b;
2811   const MatScalar   *aa = a->a,*v;
2812 
2813   PetscFunctionBegin;
2814   if (!n) PetscFunctionReturn(0);
2815 
2816   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2817   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2818   tmp  = a->solve_work;
2819 
2820   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
2821   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
2822 
2823   /* forward solve the lower triangular */
2824   tmp[0] = b[*r++];
2825   tmps   = tmp;
2826   v      = aa;
2827   vi     = aj;
2828   for (i=1; i<n; i++) {
2829     nz  = ai[i+1] - ai[i];
2830     sum = b[*r++];
2831     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
2832     tmp[i] = sum;
2833     v += nz; vi += nz;
2834   }
2835 
2836   /* backward solve the upper triangular */
2837   k  = n+1;
2838   v  = aa + ai[k]; /* 1st entry of U(n-1,:) */
2839   vi = aj + ai[k];
2840   for (i=n-1; i>=0; i--){
2841     k  = 2*n-i;
2842     nz = ai[k +1] - ai[k] - 1;
2843     sum = tmp[i];
2844     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
2845     x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */
2846     v += nz+1; vi += nz+1;
2847   }
2848 
2849   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
2850   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
2851   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2852   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2853   ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr);
2854   PetscFunctionReturn(0);
2855 }
2856 
2857 #undef __FUNCT__
2858 #define __FUNCT__ "MatSolve_SeqAIJ_newdatastruct_v2"
2859 PetscErrorCode MatSolve_SeqAIJ_newdatastruct_v2(Mat A,Vec bb,Vec xx)
2860 {
2861   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
2862   IS                iscol = a->col,isrow = a->row;
2863   PetscErrorCode    ierr;
2864   PetscInt          i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz;
2865   const PetscInt    *rout,*cout,*r,*c;
2866   PetscScalar       *x,*tmp,sum;
2867   const PetscScalar *b;
2868   const MatScalar   *aa = a->a,*v;
2869 
2870   PetscFunctionBegin;
2871   if (!n) PetscFunctionReturn(0);
2872 
2873   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2874   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2875   tmp  = a->solve_work;
2876 
2877   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
2878   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
2879 
2880   /* forward solve the lower triangular */
2881   /*  tmp[0] = b[*r++]; */
2882   tmp[0] = b[r[0]];
2883   v      = aa;
2884   vi     = aj;
2885   for (i=1; i<n; i++) {
2886     nz  = ai[i+1] - ai[i];
2887     sum = b[r[i]];
2888     PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
2889     tmp[i] = sum;
2890     v += nz; vi += nz;
2891   }
2892 
2893   /* backward solve the upper triangular */
2894   /*  v  = aa + ai[k]; *//* 1st entry of U(n-1,:) */
2895   /* vi = aj + ai[k]; */
2896   v  = aa + adiag[n-1];
2897   vi = aj + adiag[n-1];
2898   for (i=n-1; i>=0; i--){
2899     /* nz = ai[k +1] - ai[k] - 1;*/
2900     nz = adiag[i]-adiag[i+1]-1;
2901     sum = tmp[i];
2902     PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
2903     x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */
2904     v += nz+1; vi += nz+1;
2905   }
2906 
2907   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
2908   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
2909   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2910   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2911   ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr);
2912   PetscFunctionReturn(0);
2913 }
2914 
2915 #undef __FUNCT__
2916 #define __FUNCT__ "MatILUDTFactor_SeqAIJ"
2917 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact)
2918 {
2919   Mat                B = *fact;
2920   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b;
2921   IS                 isicol;
2922   PetscErrorCode     ierr;
2923   const PetscInt     *r,*ic;
2924   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag;
2925   PetscInt           *bi,*bj,*bdiag,*bdiag_rev;
2926   PetscInt           row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au;
2927   PetscInt           nlnk,*lnk;
2928   PetscBT            lnkbt;
2929   PetscTruth         row_identity,icol_identity,both_identity;
2930   MatScalar          *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp;
2931   const PetscInt     *ics;
2932   PetscInt           j,nz,*pj,*bjtmp,k,ncut,*jtmp;
2933   PetscReal          dt=info->dt,dtcol=info->dtcol,shift=info->shiftinblocks;
2934   PetscInt           dtcount=(PetscInt)info->dtcount,nnz_max;
2935   PetscTruth         missing;
2936 
2937   PetscFunctionBegin;
2938 
2939   if (dt      == PETSC_DEFAULT) dt      = 0.005;
2940   if (dtcol   == PETSC_DEFAULT) dtcol   = 0.01; /* XXX unused! */
2941   if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax);
2942 
2943   /* ------- symbolic factorization, can be reused ---------*/
2944   ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
2945   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
2946   adiag=a->diag;
2947 
2948   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
2949 
2950   /* bdiag is location of diagonal in factor */
2951   ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
2952   bdiag_rev = bdiag + n+1;
2953 
2954   /* allocate row pointers bi */
2955   ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
2956 
2957   /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */
2958   if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */
2959   nnz_max  = ai[n]+2*n*dtcount+2;
2960 
2961   ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
2962   ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr);
2963 
2964   /* put together the new matrix */
2965   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
2966   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
2967   b    = (Mat_SeqAIJ*)(B)->data;
2968   b->free_a       = PETSC_TRUE;
2969   b->free_ij      = PETSC_TRUE;
2970   b->singlemalloc = PETSC_FALSE;
2971   b->a          = ba;
2972   b->j          = bj;
2973   b->i          = bi;
2974   b->diag       = bdiag;
2975   b->ilen       = 0;
2976   b->imax       = 0;
2977   b->row        = isrow;
2978   b->col        = iscol;
2979   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
2980   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
2981   b->icol       = isicol;
2982   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2983 
2984   ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2985   b->maxnz = nnz_max;
2986 
2987   (B)->factor                = MAT_FACTOR_ILUDT;
2988   (B)->info.factor_mallocs   = 0;
2989   (B)->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]);
2990   CHKMEMQ;
2991   /* ------- end of symbolic factorization ---------*/
2992 
2993   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
2994   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
2995   ics  = ic;
2996 
2997   /* linked list for storing column indices of the active row */
2998   nlnk = n + 1;
2999   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3000 
3001   /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */
3002   ierr = PetscMalloc((2*n+1)*sizeof(PetscInt),&im);CHKERRQ(ierr);
3003   jtmp = im + n;
3004   /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */
3005   ierr = PetscMalloc((2*n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
3006   ierr = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr);
3007   vtmp = rtmp + n;
3008 
3009   bi[0]    = 0;
3010   bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */
3011   bdiag_rev[n] = bdiag[0];
3012   bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */
3013   for (i=0; i<n; i++) {
3014     /* copy initial fill into linked list */
3015     nzi = 0; /* nonzeros for active row i */
3016     nzi = ai[r[i]+1] - ai[r[i]];
3017     if (!nzi) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
3018     nzi_al = adiag[r[i]] - ai[r[i]];
3019     nzi_au = ai[r[i]+1] - adiag[r[i]] -1;
3020     ajtmp = aj + ai[r[i]];
3021     ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3022 
3023     /* load in initial (unfactored row) */
3024     aatmp = a->a + ai[r[i]];
3025     for (j=0; j<nzi; j++) {
3026       rtmp[ics[*ajtmp++]] = *aatmp++;
3027     }
3028 
3029     /* add pivot rows into linked list */
3030     row = lnk[n];
3031     while (row < i ) {
3032       nzi_bl = bi[row+1] - bi[row] + 1;
3033       bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */
3034       ierr  = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr);
3035       nzi  += nlnk;
3036       row   = lnk[row];
3037     }
3038 
3039     /* copy data from lnk into jtmp, then initialize lnk */
3040     ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr);
3041 
3042     /* numerical factorization */
3043     bjtmp = jtmp;
3044     row   = *bjtmp++; /* 1st pivot row */
3045     while  ( row < i ) {
3046       pc         = rtmp + row;
3047       pv         = ba + bdiag[row]; /* 1./(diag of the pivot row) */
3048       multiplier = (*pc) * (*pv);
3049       *pc        = multiplier;
3050       if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */
3051         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
3052         pv         = ba + bdiag[row+1] + 1;
3053         /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */
3054         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
3055         for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
3056         ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
3057       }
3058       row = *bjtmp++;
3059     }
3060 
3061     /* copy sparse rtmp into contiguous vtmp; separate L and U part */
3062     diag_tmp = rtmp[i];  /* save diagonal value - may not needed?? */
3063     nzi_bl = 0; j = 0;
3064     while (jtmp[j] < i){ /* Note: jtmp is sorted */
3065       vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
3066       nzi_bl++; j++;
3067     }
3068     nzi_bu = nzi - nzi_bl -1;
3069     while (j < nzi){
3070       vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
3071       j++;
3072     }
3073 
3074     bjtmp = bj + bi[i];
3075     batmp = ba + bi[i];
3076     /* apply level dropping rule to L part */
3077     ncut = nzi_al + dtcount;
3078     if (ncut < nzi_bl){
3079       ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr);
3080       ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr);
3081     } else {
3082       ncut = nzi_bl;
3083     }
3084     for (j=0; j<ncut; j++){
3085       bjtmp[j] = jtmp[j];
3086       batmp[j] = vtmp[j];
3087       /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */
3088     }
3089     bi[i+1] = bi[i] + ncut;
3090     nzi = ncut + 1;
3091 
3092     /* apply level dropping rule to U part */
3093     ncut = nzi_au + dtcount;
3094     if (ncut < nzi_bu){
3095       ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr);
3096       ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr);
3097     } else {
3098       ncut = nzi_bu;
3099     }
3100     nzi += ncut;
3101 
3102     /* mark bdiagonal */
3103     bdiag[i+1]       = bdiag[i] - (ncut + 1);
3104     bdiag_rev[n-i-1] = bdiag[i+1];
3105     bi[2*n - i]      = bi[2*n - i +1] - (ncut + 1);
3106     bjtmp = bj + bdiag[i];
3107     batmp = ba + bdiag[i];
3108     *bjtmp = i;
3109     *batmp = diag_tmp; /* rtmp[i]; */
3110     if (*batmp == 0.0) {
3111       *batmp = dt+shift;
3112       /* printf(" row %d add shift %g\n",i,shift); */
3113     }
3114     *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */
3115     /* printf(" (%d,%g),",*bjtmp,*batmp); */
3116 
3117     bjtmp = bj + bdiag[i+1]+1;
3118     batmp = ba + bdiag[i+1]+1;
3119     for (k=0; k<ncut; k++){
3120       bjtmp[k] = jtmp[nzi_bl+1+k];
3121       batmp[k] = vtmp[nzi_bl+1+k];
3122       /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */
3123     }
3124     /* printf("\n"); */
3125 
3126     im[i]   = nzi; /* used by PetscLLAddSortedLU() */
3127     /*
3128     printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]);
3129     printf(" ----------------------------\n");
3130     */
3131   } /* for (i=0; i<n; i++) */
3132   /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */
3133   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]);
3134 
3135   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
3136   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
3137 
3138   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
3139   ierr = PetscFree(im);CHKERRQ(ierr);
3140   ierr = PetscFree(rtmp);CHKERRQ(ierr);
3141 
3142   ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr);
3143   b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n];
3144 
3145   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
3146   ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr);
3147   both_identity = (PetscTruth) (row_identity && icol_identity);
3148   if (row_identity && icol_identity) {
3149     B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct;
3150   } else {
3151     B->ops->solve = MatSolve_SeqAIJ_newdatastruct;
3152   }
3153 
3154   B->ops->lufactorsymbolic  = MatILUDTFactorSymbolic_SeqAIJ;
3155   B->ops->lufactornumeric   = MatILUDTFactorNumeric_SeqAIJ;
3156   B->ops->solveadd          = 0;
3157   B->ops->solvetranspose    = 0;
3158   B->ops->solvetransposeadd = 0;
3159   B->ops->matsolve          = 0;
3160   B->assembled              = PETSC_TRUE;
3161   B->preallocated           = PETSC_TRUE;
3162   PetscFunctionReturn(0);
3163 }
3164 
3165 /* a wraper of MatILUDTFactor_SeqAIJ() */
3166 #undef __FUNCT__
3167 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ"
3168 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info)
3169 {
3170   PetscErrorCode     ierr;
3171 
3172   PetscFunctionBegin;
3173   ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr);
3174 
3175   fact->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ;
3176   PetscFunctionReturn(0);
3177 }
3178 
3179 /*
3180    same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors
3181    - intend to replace existing MatLUFactorNumeric_SeqAIJ()
3182 */
3183 #undef __FUNCT__
3184 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ"
3185 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info)
3186 {
3187   Mat            C=fact;
3188   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
3189   IS             isrow = b->row,isicol = b->icol;
3190   PetscErrorCode ierr;
3191   const PetscInt *r,*ic,*ics;
3192   PetscInt       i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
3193   PetscInt       *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj;
3194   MatScalar      *rtmp,*pc,multiplier,*v,*pv,*aa=a->a;
3195   PetscReal      dt=info->dt,shift=info->shiftinblocks;
3196   PetscTruth     row_identity, col_identity;
3197 
3198   PetscFunctionBegin;
3199   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
3200   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
3201   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
3202   ics  = ic;
3203 
3204   for (i=0; i<n; i++){
3205     /* initialize rtmp array */
3206     nzl   = bi[i+1] - bi[i];       /* num of nozeros in L(i,:) */
3207     bjtmp = bj + bi[i];
3208     for  (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0;
3209     rtmp[i] = 0.0;
3210     nzu   = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */
3211     bjtmp = bj + bdiag[i+1] + 1;
3212     for  (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0;
3213 
3214     /* load in initial unfactored row of A */
3215     /* printf("row %d\n",i); */
3216     nz    = ai[r[i]+1] - ai[r[i]];
3217     ajtmp = aj + ai[r[i]];
3218     v     = aa + ai[r[i]];
3219     for (j=0; j<nz; j++) {
3220       rtmp[ics[*ajtmp++]] = v[j];
3221       /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */
3222     }
3223     /* printf("\n"); */
3224 
3225     /* numerical factorization */
3226     bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */
3227     nzl   = bi[i+1] - bi[i]; /* num of entries in L(i,:) */
3228     k = 0;
3229     while (k < nzl){
3230       row   = *bjtmp++;
3231       /* printf("  prow %d\n",row); */
3232       pc         = rtmp + row;
3233       pv         = b->a + bdiag[row]; /* 1./(diag of the pivot row) */
3234       multiplier = (*pc) * (*pv);
3235       *pc        = multiplier;
3236       if (PetscAbsScalar(multiplier) > dt){
3237         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
3238         pv         = b->a + bdiag[row+1] + 1;
3239         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
3240         for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
3241         /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */
3242       }
3243       k++;
3244     }
3245 
3246     /* finished row so stick it into b->a */
3247     /* L-part */
3248     pv = b->a + bi[i] ;
3249     pj = bj + bi[i] ;
3250     nzl = bi[i+1] - bi[i];
3251     for (j=0; j<nzl; j++) {
3252       pv[j] = rtmp[pj[j]];
3253       /* printf(" (%d,%g),",pj[j],pv[j]); */
3254     }
3255 
3256     /* diagonal: invert diagonal entries for simplier triangular solves */
3257     if (rtmp[i] == 0.0) rtmp[i] = dt+shift;
3258     b->a[bdiag[i]] = 1.0/rtmp[i];
3259     /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */
3260 
3261     /* U-part */
3262     pv = b->a + bdiag[i+1] + 1;
3263     pj = bj + bdiag[i+1] + 1;
3264     nzu = bdiag[i] - bdiag[i+1] - 1;
3265     for (j=0; j<nzu; j++) {
3266       pv[j] = rtmp[pj[j]];
3267       /* printf(" (%d,%g),",pj[j],pv[j]); */
3268     }
3269     /* printf("\n"); */
3270   }
3271 
3272   ierr = PetscFree(rtmp);CHKERRQ(ierr);
3273   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
3274   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
3275 
3276   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
3277   ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
3278   if (row_identity && col_identity) {
3279     C->ops->solve   = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct;
3280   } else {
3281     C->ops->solve   = MatSolve_SeqAIJ_newdatastruct;
3282   }
3283   C->ops->solveadd           = 0;
3284   C->ops->solvetranspose     = 0;
3285   C->ops->solvetransposeadd  = 0;
3286   C->ops->matsolve           = 0;
3287   C->assembled    = PETSC_TRUE;
3288   C->preallocated = PETSC_TRUE;
3289   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
3290   PetscFunctionReturn(0);
3291 }
3292