xref: /petsc/src/mat/impls/aij/seq/aijfact.c (revision 3c0119df2676a4fbbc7265b2085dad9f43e7110f)
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 = PetscMemzero(done,n*sizeof(PetscTruth));CHKERRQ(ierr);
42   ierr = PetscMalloc(n*sizeof(PetscInt),&order);CHKERRQ(ierr);
43   order[0] = current;
44   for (i=0; i<n-1; i++) {
45     done[current] = PETSC_TRUE;
46     best          = -1;
47     /* loop over all neighbors of current pivot */
48     for (j=ai[current]; j<ai[current+1]; j++) {
49       jj = aj[j];
50       if (done[jj]) continue;
51       /* loop over columns of potential next row computing weights for below and above diagonal */
52       past = future = 0.0;
53       for (k=ai[jj]; k<ai[jj+1]; k++) {
54         kk = aj[k];
55         if (done[kk]) past += PetscAbsScalar(aa[k]);
56         else if (kk != jj) future  += PetscAbsScalar(aa[k]);
57       }
58       if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */
59       if (past/future > best) {
60         best = past/future;
61         newcurrent = jj;
62       }
63     }
64     if (best == -1) { /* no neighbors to select from so select best of all that remain */
65       best = -1;
66       for (k=0; k<n; k++) {
67         if (done[k]) continue;
68         future = 0;
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 and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
312   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
313   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
314   bi[0] = bdiag[0] = 0;
315 
316   /* linked list for storing column indices of the active row */
317   nlnk = n + 1;
318   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
319 
320   ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr);
321 
322   /* initial FreeSpace size is f*(ai[n]+1) */
323   f = info->fill;
324   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
325   current_space = free_space;
326 
327   for (i=0; i<n; i++) {
328     /* copy previous fill into linked list */
329     nzi = 0;
330     nnz = ai[r[i]+1] - ai[r[i]];
331     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
332     ajtmp = aj + ai[r[i]];
333     ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
334     nzi += nlnk;
335 
336     /* add pivot rows into linked list */
337     row = lnk[n];
338     while (row < i){
339       nzbd  = bdiag[row] + 1; /* num of entries in the row with column index <= row */
340       ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */
341       ierr  = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr);
342       nzi  += nlnk;
343       row   = lnk[row];
344     }
345     bi[i+1] = bi[i] + nzi;
346     im[i]   = nzi;
347 
348     /* mark bdiag */
349     nzbd = 0;
350     nnz  = nzi;
351     k    = lnk[n];
352     while (nnz-- && k < i){
353       nzbd++;
354       k = lnk[k];
355     }
356     bdiag[i] = nzbd; /* note: bdiag[i] = nnzL as input for PetscFreeSpaceContiguous_LU() */
357 
358     /* if free space is not available, make more free space */
359     if (current_space->local_remaining<nzi) {
360       nnz = 2*(n - i)*nzi; /* estimated and max additional space needed */
361       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
362       reallocs++;
363     }
364 
365     /* copy data into free space, then initialize lnk */
366     ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
367     bi_ptr[i] = current_space->array;
368     current_space->array           += nzi;
369     current_space->local_used      += nzi;
370     current_space->local_remaining -= nzi;
371   }
372 #if defined(PETSC_USE_INFO)
373   if (ai[n] != 0) {
374     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
375     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
376     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
377     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr);
378     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
379   } else {
380     ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr);
381   }
382 #endif
383 
384   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
385   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
386 
387   /* destroy list of free space and other temporary array(s) */
388   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
389   ierr = PetscFreeSpaceContiguous_LU_v2(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr);
390   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
391   ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr);
392 
393   /* put together the new matrix */
394   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
395   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
396   b    = (Mat_SeqAIJ*)(B)->data;
397   b->free_a       = PETSC_TRUE;
398   b->free_ij      = PETSC_TRUE;
399   b->singlemalloc = PETSC_FALSE;
400   ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
401   b->j          = bj;
402   b->i          = bi;
403   b->diag       = bdiag;
404   b->ilen       = 0;
405   b->imax       = 0;
406   b->row        = isrow;
407   b->col        = iscol;
408   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
409   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
410   b->icol       = isicol;
411   ierr          = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
412 
413   /* In b structure:  Free imax, ilen, old a, old j.  Allocate solve_work, new a, new j */
414   ierr = PetscLogObjectMemory(B,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
415   b->maxnz = b->nz = bdiag[0]+1;
416   (B)->factor                = MAT_FACTOR_LU;
417   (B)->info.factor_mallocs   = reallocs;
418   (B)->info.fill_ratio_given = f;
419 
420   if (ai[n]) {
421     (B)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]);
422   } else {
423     (B)->info.fill_ratio_needed = 0.0;
424   }
425   (B)->ops->lufactornumeric  = MatLUFactorNumeric_SeqAIJ_newdatastruct;
426   PetscFunctionReturn(0);
427 }
428 
429 /*
430     Trouble in factorization, should we dump the original matrix?
431 */
432 #undef __FUNCT__
433 #define __FUNCT__ "MatFactorDumpMatrix"
434 PetscErrorCode MatFactorDumpMatrix(Mat A)
435 {
436   PetscErrorCode ierr;
437   PetscTruth     flg = PETSC_FALSE;
438 
439   PetscFunctionBegin;
440   ierr = PetscOptionsGetTruth(PETSC_NULL,"-mat_factor_dump_on_error",&flg,PETSC_NULL);CHKERRQ(ierr);
441   if (flg) {
442     PetscViewer viewer;
443     char        filename[PETSC_MAX_PATH_LEN];
444 
445     ierr = PetscSNPrintf(filename,PETSC_MAX_PATH_LEN,"matrix_factor_error.%d",PetscGlobalRank);CHKERRQ(ierr);
446     ierr = PetscViewerBinaryOpen(((PetscObject)A)->comm,filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr);
447     ierr = MatView(A,viewer);CHKERRQ(ierr);
448     ierr = PetscViewerDestroy(viewer);CHKERRQ(ierr);
449   }
450   PetscFunctionReturn(0);
451 }
452 
453 extern PetscErrorCode MatSolve_SeqAIJ_Inode(Mat,Vec,Vec);
454 
455 #undef __FUNCT__
456 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_newdatastruct"
457 PetscErrorCode MatLUFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info)
458 {
459   Mat            C=B;
460   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
461   IS             isrow = b->row,isicol = b->icol;
462   PetscErrorCode ierr;
463   const PetscInt *r,*ic,*ics;
464   PetscInt       i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
465   PetscInt       *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj;
466   MatScalar      *rtmp,*pc,multiplier,*v,*pv,*aa=a->a;
467   PetscTruth     row_identity,col_identity;
468 
469   LUShift_Ctx    sctx;
470   PetscInt       *ddiag,newshift;
471   PetscReal      rs;
472   MatScalar      d;
473 
474   PetscFunctionBegin;
475   /* MatPivotSetUp(): initialize shift context sctx */
476   ierr = PetscMemzero(&sctx,sizeof(LUShift_Ctx));CHKERRQ(ierr);
477 
478   /* if both shift schemes are chosen by user, only use info->shiftpd */
479   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
480     ddiag          = a->diag;
481     sctx.shift_top = info->zeropivot;
482     for (i=0; i<n; i++) {
483       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
484       d  = (aa)[ddiag[i]];
485       rs = -PetscAbsScalar(d) - PetscRealPart(d);
486       v  = aa+ai[i];
487       nz = ai[i+1] - ai[i];
488       for (j=0; j<nz; j++)
489 	rs += PetscAbsScalar(v[j]);
490       if (rs>sctx.shift_top) sctx.shift_top = rs;
491     }
492     sctx.shift_top   *= 1.1;
493     sctx.nshift_max   = 5;
494     sctx.shift_lo     = 0.;
495     sctx.shift_hi     = 1.;
496   }
497 
498   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
499   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
500   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
501   ics  = ic;
502 
503   do {
504     sctx.lushift = PETSC_FALSE;
505     for (i=0; i<n; i++){
506       /* zero rtmp */
507       /* L part */
508       nz    = bi[i+1] - bi[i];
509       bjtmp = bj + bi[i];
510       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
511 
512       /* U part */
513       nz = bdiag[i]-bdiag[i+1];
514       bjtmp = bj + bdiag[i+1]+1;
515       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
516 
517       /* load in initial (unfactored row) */
518       nz    = ai[r[i]+1] - ai[r[i]];
519       ajtmp = aj + ai[r[i]];
520       v     = aa + ai[r[i]];
521       for (j=0; j<nz; j++) {
522         rtmp[ics[ajtmp[j]]] = v[j];
523       }
524       /* ZeropivotApply() */
525       rtmp[i] += sctx.shift_amount;  /* shift the diagonal of the matrix */
526 
527       /* elimination */
528       bjtmp = bj + bi[i];
529       row   = *bjtmp++;
530       nzL   = bi[i+1] - bi[i];
531       for(k=0; k < nzL;k++) {
532         pc = rtmp + row;
533         if (*pc != 0.0) {
534           pv         = b->a + bdiag[row];
535           multiplier = *pc * (*pv);
536           *pc        = multiplier;
537           pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
538 	  pv = b->a + bdiag[row+1]+1;
539 	  nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */
540           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
541           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
542         }
543         row = *bjtmp++;
544       }
545 
546       /* finished row so stick it into b->a */
547       rs = 0.0;
548       /* L part */
549       pv   = b->a + bi[i] ;
550       pj   = b->j + bi[i] ;
551       nz   = bi[i+1] - bi[i];
552       for (j=0; j<nz; j++) {
553         pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]);
554       }
555 
556       /* U part */
557       pv = b->a + bdiag[i+1]+1;
558       pj = b->j + bdiag[i+1]+1;
559       nz = bdiag[i] - bdiag[i+1]-1;
560       for (j=0; j<nz; j++) {
561         pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]);
562       }
563 
564       /* MatPivotCheck() */
565       sctx.rs  = rs;
566       sctx.pv  = rtmp[i];
567       /* ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); */
568       if (info->shiftnz){
569         ierr = MatPivotCheck_nz(info,sctx,i,newshift);CHKERRQ(ierr);
570       } else if (info->shiftpd){
571         ierr = MatPivotCheck_pd(info,sctx,i,newshift);CHKERRQ(ierr);
572       } else if (info->shiftinblocks){
573         ierr = MatPivotCheck_inblocks(info,sctx,i,newshift);CHKERRQ(ierr);
574       } else {
575         ierr = MatPivotCheck_none(info,sctx,i,newshift);CHKERRQ(ierr);
576       }
577       rtmp[i] = sctx.pv;
578       if (newshift == 1) break;
579 
580       /* Mark diagonal and invert diagonal for simplier triangular solves */
581       pv  = b->a + bdiag[i];
582       *pv = 1.0/rtmp[i];
583 
584     } /* endof for (i=0; i<n; i++){ */
585 
586     /* MatPivotRefine() */
587     if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max){
588       /*
589        * if no shift in this attempt & shifting & started shifting & can refine,
590        * then try lower shift
591        */
592       sctx.shift_hi       = sctx.shift_fraction;
593       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
594       sctx.shift_amount   = sctx.shift_fraction * sctx.shift_top;
595       sctx.lushift        = PETSC_TRUE;
596       sctx.nshift++;
597     }
598   } while (sctx.lushift);
599 
600   ierr = PetscFree(rtmp);CHKERRQ(ierr);
601   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
602   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
603 
604   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
605   ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
606   if (row_identity && col_identity) {
607     C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct;
608   } else {
609     C->ops->solve = MatSolve_SeqAIJ_newdatastruct;
610   }
611 
612   C->ops->solveadd           = MatSolveAdd_SeqAIJ_newdatastruct;
613   C->ops->solvetranspose     = MatSolveTranspose_SeqAIJ_newdatastruct;
614   C->ops->solvetransposeadd  = 0;
615   C->ops->matsolve           = 0;
616   C->assembled    = PETSC_TRUE;
617   C->preallocated = PETSC_TRUE;
618   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
619 
620   /* MatPivotView() */
621   if (sctx.nshift){
622     if (info->shiftpd) {
623       ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %G, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,sctx.shift_amount,sctx.shift_fraction,sctx.shift_top);CHKERRQ(ierr);
624     } else if (info->shiftnz) {
625       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
626     } else if (info->shiftinblocks){
627       ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftinblocks);CHKERRQ(ierr);
628     }
629   }
630   PetscFunctionReturn(0);
631 }
632 
633 #undef __FUNCT__
634 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ"
635 PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info)
636 {
637   Mat             C=B;
638   Mat_SeqAIJ      *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
639   IS              isrow = b->row,isicol = b->icol;
640   PetscErrorCode  ierr;
641   const PetscInt   *r,*ic,*ics;
642   PetscInt        nz,row,i,j,n=A->rmap->n,diag;
643   const PetscInt  *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
644   const PetscInt  *ajtmp,*bjtmp,*diag_offset = b->diag,*pj;
645   MatScalar       *pv,*rtmp,*pc,multiplier,d;
646   const MatScalar *v,*aa=a->a;
647   PetscReal       rs=0.0;
648   LUShift_Ctx     sctx;
649   PetscInt        newshift,*ddiag;
650 
651   PetscFunctionBegin;
652   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
653   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
654   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
655   ics  = ic;
656 
657   /* initialize shift context sctx */
658   sctx.nshift         = 0;
659   sctx.nshift_max     = 0;
660   sctx.shift_top      = 0.0;
661   sctx.shift_lo       = 0.0;
662   sctx.shift_hi       = 0.0;
663   sctx.shift_fraction = 0.0;
664   sctx.shift_amount   = 0.0;
665 
666   /* if both shift schemes are chosen by user, only use info->shiftpd */
667   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
668     ddiag          = a->diag;
669     sctx.shift_top = info->zeropivot;
670     for (i=0; i<n; i++) {
671       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
672       d  = (aa)[ddiag[i]];
673       rs = -PetscAbsScalar(d) - PetscRealPart(d);
674       v  = aa+ai[i];
675       nz = ai[i+1] - ai[i];
676       for (j=0; j<nz; j++)
677 	rs += PetscAbsScalar(v[j]);
678       if (rs>sctx.shift_top) sctx.shift_top = rs;
679     }
680     sctx.shift_top   *= 1.1;
681     sctx.nshift_max   = 5;
682     sctx.shift_lo     = 0.;
683     sctx.shift_hi     = 1.;
684   }
685 
686   do {
687     sctx.lushift = PETSC_FALSE;
688     for (i=0; i<n; i++){
689       nz    = bi[i+1] - bi[i];
690       bjtmp = bj + bi[i];
691       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
692 
693       /* load in initial (unfactored row) */
694       nz    = ai[r[i]+1] - ai[r[i]];
695       ajtmp = aj + ai[r[i]];
696       v     = aa + ai[r[i]];
697       for (j=0; j<nz; j++) {
698         rtmp[ics[ajtmp[j]]] = v[j];
699       }
700       rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */
701       /* if (sctx.shift_amount > 0.0) printf("row %d, shift %g\n",i,sctx.shift_amount); */
702 
703       row = *bjtmp++;
704       while  (row < i) {
705         pc = rtmp + row;
706         if (*pc != 0.0) {
707           pv         = b->a + diag_offset[row];
708           pj         = b->j + diag_offset[row] + 1;
709           multiplier = *pc / *pv++;
710           *pc        = multiplier;
711           nz         = bi[row+1] - diag_offset[row] - 1;
712           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
713           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
714         }
715         row = *bjtmp++;
716       }
717       /* finished row so stick it into b->a */
718       pv   = b->a + bi[i] ;
719       pj   = b->j + bi[i] ;
720       nz   = bi[i+1] - bi[i];
721       diag = diag_offset[i] - bi[i];
722       rs   = 0.0;
723       for (j=0; j<nz; j++) {
724         pv[j] = rtmp[pj[j]];
725         rs   += PetscAbsScalar(pv[j]);
726       }
727       rs   -= PetscAbsScalar(pv[diag]);
728 
729       /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */
730       sctx.rs  = rs;
731       sctx.pv  = pv[diag];
732       ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr);
733       if (newshift == 1) break;
734     }
735 
736     if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
737       /*
738        * if no shift in this attempt & shifting & started shifting & can refine,
739        * then try lower shift
740        */
741       sctx.shift_hi       = sctx.shift_fraction;
742       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
743       sctx.shift_amount   = sctx.shift_fraction * sctx.shift_top;
744       sctx.lushift        = PETSC_TRUE;
745       sctx.nshift++;
746     }
747   } while (sctx.lushift);
748 
749   /* invert diagonal entries for simplier triangular solves */
750   for (i=0; i<n; i++) {
751     b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]];
752   }
753   ierr = PetscFree(rtmp);CHKERRQ(ierr);
754   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
755   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
756   if (b->inode.use) {
757     C->ops->solve   = MatSolve_SeqAIJ_Inode;
758   } else {
759     PetscTruth row_identity, col_identity;
760     ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
761     ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
762     if (row_identity && col_identity) {
763       C->ops->solve   = MatSolve_SeqAIJ_NaturalOrdering;
764     } else {
765       C->ops->solve   = MatSolve_SeqAIJ;
766     }
767   }
768   C->ops->solveadd           = MatSolveAdd_SeqAIJ;
769   C->ops->solvetranspose     = MatSolveTranspose_SeqAIJ;
770   C->ops->solvetransposeadd  = MatSolveTransposeAdd_SeqAIJ;
771   C->ops->matsolve           = MatMatSolve_SeqAIJ;
772   C->assembled    = PETSC_TRUE;
773   C->preallocated = PETSC_TRUE;
774   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
775   if (sctx.nshift){
776      if (info->shiftpd) {
777       ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %G, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,sctx.shift_amount,sctx.shift_fraction,sctx.shift_top);CHKERRQ(ierr);
778     } else if (info->shiftnz) {
779       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
780     }
781   }
782   PetscFunctionReturn(0);
783 }
784 
785 /*
786    This routine implements inplace ILU(0) with row or/and column permutations.
787    Input:
788      A - original matrix
789    Output;
790      A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i]
791          a->j (col index) is permuted by the inverse of colperm, then sorted
792          a->a reordered accordingly with a->j
793          a->diag (ptr to diagonal elements) is updated.
794 */
795 #undef __FUNCT__
796 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_InplaceWithPerm"
797 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info)
798 {
799   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
800   IS             isrow = a->row,isicol = a->icol;
801   PetscErrorCode ierr;
802   const PetscInt *r,*ic,*ics;
803   PetscInt       i,j,n=A->rmap->n,*ai=a->i,*aj=a->j;
804   PetscInt       *ajtmp,nz,row;
805   PetscInt       *diag = a->diag,nbdiag,*pj;
806   PetscScalar    *rtmp,*pc,multiplier,d;
807   MatScalar      *v,*pv;
808   PetscReal      rs;
809   LUShift_Ctx    sctx;
810   PetscInt       newshift;
811 
812   PetscFunctionBegin;
813   if (A != B) SETERRQ(PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address");
814   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
815   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
816   ierr  = PetscMalloc((n+1)*sizeof(PetscScalar),&rtmp);CHKERRQ(ierr);
817   ierr  = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr);
818   ics = ic;
819 
820   sctx.shift_top      = 0;
821   sctx.nshift_max     = 0;
822   sctx.shift_lo       = 0;
823   sctx.shift_hi       = 0;
824   sctx.shift_fraction = 0;
825 
826   /* if both shift schemes are chosen by user, only use info->shiftpd */
827   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
828     sctx.shift_top = 0;
829     for (i=0; i<n; i++) {
830       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
831       d  = (a->a)[diag[i]];
832       rs = -PetscAbsScalar(d) - PetscRealPart(d);
833       v  = a->a+ai[i];
834       nz = ai[i+1] - ai[i];
835       for (j=0; j<nz; j++)
836 	rs += PetscAbsScalar(v[j]);
837       if (rs>sctx.shift_top) sctx.shift_top = rs;
838     }
839     if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot;
840     sctx.shift_top    *= 1.1;
841     sctx.nshift_max   = 5;
842     sctx.shift_lo     = 0.;
843     sctx.shift_hi     = 1.;
844   }
845 
846   sctx.shift_amount = 0;
847   sctx.nshift       = 0;
848   do {
849     sctx.lushift = PETSC_FALSE;
850     for (i=0; i<n; i++){
851       /* load in initial unfactored row */
852       nz    = ai[r[i]+1] - ai[r[i]];
853       ajtmp = aj + ai[r[i]];
854       v     = a->a + ai[r[i]];
855       /* sort permuted ajtmp and values v accordingly */
856       for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]];
857       ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr);
858 
859       diag[r[i]] = ai[r[i]];
860       for (j=0; j<nz; j++) {
861         rtmp[ajtmp[j]] = v[j];
862         if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */
863       }
864       rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */
865 
866       row = *ajtmp++;
867       while  (row < i) {
868         pc = rtmp + row;
869         if (*pc != 0.0) {
870           pv         = a->a + diag[r[row]];
871           pj         = aj + diag[r[row]] + 1;
872 
873           multiplier = *pc / *pv++;
874           *pc        = multiplier;
875           nz         = ai[r[row]+1] - diag[r[row]] - 1;
876           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
877           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
878         }
879         row = *ajtmp++;
880       }
881       /* finished row so overwrite it onto a->a */
882       pv   = a->a + ai[r[i]] ;
883       pj   = aj + ai[r[i]] ;
884       nz   = ai[r[i]+1] - ai[r[i]];
885       nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */
886 
887       rs   = 0.0;
888       for (j=0; j<nz; j++) {
889         pv[j] = rtmp[pj[j]];
890         if (j != nbdiag) rs += PetscAbsScalar(pv[j]);
891       }
892 
893       /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */
894       sctx.rs  = rs;
895       sctx.pv  = pv[nbdiag];
896       ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr);
897       if (newshift == 1) break;
898     }
899 
900     if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
901       /*
902        * if no shift in this attempt & shifting & started shifting & can refine,
903        * then try lower shift
904        */
905       sctx.shift_hi        = sctx.shift_fraction;
906       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
907       sctx.shift_amount    = sctx.shift_fraction * sctx.shift_top;
908       sctx.lushift         = PETSC_TRUE;
909       sctx.nshift++;
910     }
911   } while (sctx.lushift);
912 
913   /* invert diagonal entries for simplier triangular solves */
914   for (i=0; i<n; i++) {
915     a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]];
916   }
917 
918   ierr = PetscFree(rtmp);CHKERRQ(ierr);
919   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
920   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
921   A->ops->solve             = MatSolve_SeqAIJ_InplaceWithPerm;
922   A->ops->solveadd          = MatSolveAdd_SeqAIJ;
923   A->ops->solvetranspose    = MatSolveTranspose_SeqAIJ;
924   A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ;
925   A->assembled = PETSC_TRUE;
926   A->preallocated = PETSC_TRUE;
927   ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr);
928   if (sctx.nshift){
929     if (info->shiftpd) {
930       ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %G, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,sctx.shift_amount,sctx.shift_fraction,sctx.shift_top);CHKERRQ(ierr);
931     } else if (info->shiftnz) {
932       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
933     }
934   }
935   PetscFunctionReturn(0);
936 }
937 
938 /* ----------------------------------------------------------- */
939 #undef __FUNCT__
940 #define __FUNCT__ "MatLUFactor_SeqAIJ"
941 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info)
942 {
943   PetscErrorCode ierr;
944   Mat            C;
945 
946   PetscFunctionBegin;
947   ierr = MatGetFactor(A,MAT_SOLVER_PETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr);
948   ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr);
949   ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr);
950   A->ops->solve            = C->ops->solve;
951   A->ops->solvetranspose   = C->ops->solvetranspose;
952   ierr = MatHeaderCopy(A,C);CHKERRQ(ierr);
953   ierr = PetscLogObjectParent(A,((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr);
954   PetscFunctionReturn(0);
955 }
956 /* ----------------------------------------------------------- */
957 
958 
959 #undef __FUNCT__
960 #define __FUNCT__ "MatSolve_SeqAIJ"
961 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx)
962 {
963   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
964   IS                iscol = a->col,isrow = a->row;
965   PetscErrorCode    ierr;
966   PetscInt          i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
967   PetscInt          nz;
968   const PetscInt    *rout,*cout,*r,*c;
969   PetscScalar       *x,*tmp,*tmps,sum;
970   const PetscScalar *b;
971   const MatScalar   *aa = a->a,*v;
972 
973   PetscFunctionBegin;
974   if (!n) PetscFunctionReturn(0);
975 
976   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
977   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
978   tmp  = a->solve_work;
979 
980   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
981   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
982 
983   /* forward solve the lower triangular */
984   tmp[0] = b[*r++];
985   tmps   = tmp;
986   for (i=1; i<n; i++) {
987     v   = aa + ai[i] ;
988     vi  = aj + ai[i] ;
989     nz  = a->diag[i] - ai[i];
990     sum = b[*r++];
991     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
992     tmp[i] = sum;
993   }
994 
995   /* backward solve the upper triangular */
996   for (i=n-1; i>=0; i--){
997     v   = aa + a->diag[i] + 1;
998     vi  = aj + a->diag[i] + 1;
999     nz  = ai[i+1] - a->diag[i] - 1;
1000     sum = tmp[i];
1001     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1002     x[*c--] = tmp[i] = sum*aa[a->diag[i]];
1003   }
1004 
1005   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1006   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1007   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1008   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1009   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1010   PetscFunctionReturn(0);
1011 }
1012 
1013 #undef __FUNCT__
1014 #define __FUNCT__ "MatMatSolve_SeqAIJ"
1015 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X)
1016 {
1017   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1018   IS              iscol = a->col,isrow = a->row;
1019   PetscErrorCode  ierr;
1020   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1021   PetscInt        nz,neq;
1022   const PetscInt  *rout,*cout,*r,*c;
1023   PetscScalar     *x,*b,*tmp,*tmps,sum;
1024   const MatScalar *aa = a->a,*v;
1025   PetscTruth      bisdense,xisdense;
1026 
1027   PetscFunctionBegin;
1028   if (!n) PetscFunctionReturn(0);
1029 
1030   ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr);
1031   if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix");
1032   ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr);
1033   if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix");
1034 
1035   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
1036   ierr = MatGetArray(X,&x);CHKERRQ(ierr);
1037 
1038   tmp  = a->solve_work;
1039   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1040   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1041 
1042   for (neq=0; neq<B->cmap->n; neq++){
1043     /* forward solve the lower triangular */
1044     tmp[0] = b[r[0]];
1045     tmps   = tmp;
1046     for (i=1; i<n; i++) {
1047       v   = aa + ai[i] ;
1048       vi  = aj + ai[i] ;
1049       nz  = a->diag[i] - ai[i];
1050       sum = b[r[i]];
1051       PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1052       tmp[i] = sum;
1053     }
1054     /* backward solve the upper triangular */
1055     for (i=n-1; i>=0; i--){
1056       v   = aa + a->diag[i] + 1;
1057       vi  = aj + a->diag[i] + 1;
1058       nz  = ai[i+1] - a->diag[i] - 1;
1059       sum = tmp[i];
1060       PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1061       x[c[i]] = tmp[i] = sum*aa[a->diag[i]];
1062     }
1063 
1064     b += n;
1065     x += n;
1066   }
1067   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1068   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1069   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
1070   ierr = MatRestoreArray(X,&x);CHKERRQ(ierr);
1071   ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr);
1072   PetscFunctionReturn(0);
1073 }
1074 
1075 #undef __FUNCT__
1076 #define __FUNCT__ "MatSolve_SeqAIJ_InplaceWithPerm"
1077 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx)
1078 {
1079   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1080   IS              iscol = a->col,isrow = a->row;
1081   PetscErrorCode  ierr;
1082   const PetscInt  *r,*c,*rout,*cout;
1083   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1084   PetscInt        nz,row;
1085   PetscScalar     *x,*b,*tmp,*tmps,sum;
1086   const MatScalar *aa = a->a,*v;
1087 
1088   PetscFunctionBegin;
1089   if (!n) PetscFunctionReturn(0);
1090 
1091   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
1092   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1093   tmp  = a->solve_work;
1094 
1095   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1096   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1097 
1098   /* forward solve the lower triangular */
1099   tmp[0] = b[*r++];
1100   tmps   = tmp;
1101   for (row=1; row<n; row++) {
1102     i   = rout[row]; /* permuted row */
1103     v   = aa + ai[i] ;
1104     vi  = aj + ai[i] ;
1105     nz  = a->diag[i] - ai[i];
1106     sum = b[*r++];
1107     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1108     tmp[row] = sum;
1109   }
1110 
1111   /* backward solve the upper triangular */
1112   for (row=n-1; row>=0; row--){
1113     i   = rout[row]; /* permuted row */
1114     v   = aa + a->diag[i] + 1;
1115     vi  = aj + a->diag[i] + 1;
1116     nz  = ai[i+1] - a->diag[i] - 1;
1117     sum = tmp[row];
1118     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1119     x[*c--] = tmp[row] = sum*aa[a->diag[i]];
1120   }
1121 
1122   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1123   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1124   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
1125   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1126   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1127   PetscFunctionReturn(0);
1128 }
1129 
1130 /* ----------------------------------------------------------- */
1131 #include "../src/mat/impls/aij/seq/ftn-kernels/fsolve.h"
1132 #undef __FUNCT__
1133 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering"
1134 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx)
1135 {
1136   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1137   PetscErrorCode    ierr;
1138   PetscInt          n = A->rmap->n;
1139   const PetscInt    *ai = a->i,*aj = a->j,*adiag = a->diag;
1140   PetscScalar       *x;
1141   const PetscScalar *b;
1142   const MatScalar   *aa = a->a;
1143 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ)
1144   PetscInt          adiag_i,i,nz,ai_i;
1145   const PetscInt    *vi;
1146   const MatScalar   *v;
1147   PetscScalar       sum;
1148 #endif
1149 
1150   PetscFunctionBegin;
1151   if (!n) PetscFunctionReturn(0);
1152 
1153   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1154   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1155 
1156 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ)
1157   fortransolveaij_(&n,x,ai,aj,adiag,aa,b);
1158 #else
1159   /* forward solve the lower triangular */
1160   x[0] = b[0];
1161   for (i=1; i<n; i++) {
1162     ai_i = ai[i];
1163     v    = aa + ai_i;
1164     vi   = aj + ai_i;
1165     nz   = adiag[i] - ai_i;
1166     sum  = b[i];
1167     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
1168     x[i] = sum;
1169   }
1170 
1171   /* backward solve the upper triangular */
1172   for (i=n-1; i>=0; i--){
1173     adiag_i = adiag[i];
1174     v       = aa + adiag_i + 1;
1175     vi      = aj + adiag_i + 1;
1176     nz      = ai[i+1] - adiag_i - 1;
1177     sum     = x[i];
1178     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
1179     x[i]    = sum*aa[adiag_i];
1180   }
1181 #endif
1182   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1183   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1184   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1185   PetscFunctionReturn(0);
1186 }
1187 
1188 #undef __FUNCT__
1189 #define __FUNCT__ "MatSolveAdd_SeqAIJ"
1190 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx)
1191 {
1192   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1193   IS                iscol = a->col,isrow = a->row;
1194   PetscErrorCode    ierr;
1195   PetscInt          i, n = A->rmap->n,j;
1196   PetscInt          nz;
1197   const PetscInt    *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j;
1198   PetscScalar       *x,*tmp,sum;
1199   const PetscScalar *b;
1200   const MatScalar   *aa = a->a,*v;
1201 
1202   PetscFunctionBegin;
1203   if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);}
1204 
1205   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1206   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1207   tmp  = a->solve_work;
1208 
1209   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1210   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1211 
1212   /* forward solve the lower triangular */
1213   tmp[0] = b[*r++];
1214   for (i=1; i<n; i++) {
1215     v   = aa + ai[i] ;
1216     vi  = aj + ai[i] ;
1217     nz  = a->diag[i] - ai[i];
1218     sum = b[*r++];
1219     for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1220     tmp[i] = sum;
1221   }
1222 
1223   /* backward solve the upper triangular */
1224   for (i=n-1; i>=0; i--){
1225     v   = aa + a->diag[i] + 1;
1226     vi  = aj + a->diag[i] + 1;
1227     nz  = ai[i+1] - a->diag[i] - 1;
1228     sum = tmp[i];
1229     for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1230     tmp[i] = sum*aa[a->diag[i]];
1231     x[*c--] += tmp[i];
1232   }
1233 
1234   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1235   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1236   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1237   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1238   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1239 
1240   PetscFunctionReturn(0);
1241 }
1242 
1243 #undef __FUNCT__
1244 #define __FUNCT__ "MatSolveAdd_SeqAIJ_newdatastruct"
1245 PetscErrorCode MatSolveAdd_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec yy,Vec xx)
1246 {
1247   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1248   IS                iscol = a->col,isrow = a->row;
1249   PetscErrorCode    ierr;
1250   PetscInt          i, n = A->rmap->n,j;
1251   PetscInt          nz;
1252   const PetscInt    *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag;
1253   PetscScalar       *x,*tmp,sum;
1254   const PetscScalar *b;
1255   const MatScalar   *aa = a->a,*v;
1256 
1257   PetscFunctionBegin;
1258   if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);}
1259 
1260   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1261   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1262   tmp  = a->solve_work;
1263 
1264   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1265   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1266 
1267   /* forward solve the lower triangular */
1268   tmp[0] = b[r[0]];
1269   v      = aa;
1270   vi     = aj;
1271   for (i=1; i<n; i++) {
1272     nz  = ai[i+1] - ai[i];
1273     sum = b[r[i]];
1274     for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1275     tmp[i] = sum;
1276     v += nz; vi += nz;
1277   }
1278 
1279   /* backward solve the upper triangular */
1280   v  = aa + adiag[n-1];
1281   vi = aj + adiag[n-1];
1282   for (i=n-1; i>=0; i--){
1283     nz  = adiag[i] - adiag[i+1] - 1;
1284     sum = tmp[i];
1285     for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1286     tmp[i] = sum*v[nz];
1287     x[c[i]] += tmp[i];
1288     v += nz+1; vi += nz+1;
1289   }
1290 
1291   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1292   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1293   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1294   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1295   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1296 
1297   PetscFunctionReturn(0);
1298 }
1299 
1300 #undef __FUNCT__
1301 #define __FUNCT__ "MatSolveTranspose_SeqAIJ"
1302 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx)
1303 {
1304   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1305   IS                iscol = a->col,isrow = a->row;
1306   PetscErrorCode    ierr;
1307   const PetscInt    *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi;
1308   PetscInt          i,n = A->rmap->n,j;
1309   PetscInt          nz;
1310   PetscScalar       *x,*tmp,s1;
1311   const MatScalar   *aa = a->a,*v;
1312   const PetscScalar *b;
1313 
1314   PetscFunctionBegin;
1315   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1316   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1317   tmp  = a->solve_work;
1318 
1319   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1320   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1321 
1322   /* copy the b into temp work space according to permutation */
1323   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1324 
1325   /* forward solve the U^T */
1326   for (i=0; i<n; i++) {
1327     v   = aa + diag[i] ;
1328     vi  = aj + diag[i] + 1;
1329     nz  = ai[i+1] - diag[i] - 1;
1330     s1  = tmp[i];
1331     s1 *= (*v++);  /* multiply by inverse of diagonal entry */
1332     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1333     tmp[i] = s1;
1334   }
1335 
1336   /* backward solve the L^T */
1337   for (i=n-1; i>=0; i--){
1338     v   = aa + diag[i] - 1 ;
1339     vi  = aj + diag[i] - 1 ;
1340     nz  = diag[i] - ai[i];
1341     s1  = tmp[i];
1342     for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j];
1343   }
1344 
1345   /* copy tmp into x according to permutation */
1346   for (i=0; i<n; i++) x[r[i]] = tmp[i];
1347 
1348   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1349   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1350   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1351   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1352 
1353   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1354   PetscFunctionReturn(0);
1355 }
1356 
1357 #undef __FUNCT__
1358 #define __FUNCT__ "MatSolveTranspose_SeqAIJ_newdatastruct"
1359 PetscErrorCode MatSolveTranspose_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec xx)
1360 {
1361   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1362   IS                iscol = a->col,isrow = a->row;
1363   PetscErrorCode    ierr;
1364   const PetscInt    *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi;
1365   PetscInt          i,n = A->rmap->n,j;
1366   PetscInt          nz;
1367   PetscScalar       *x,*tmp,s1;
1368   const MatScalar   *aa = a->a,*v;
1369   const PetscScalar *b;
1370 
1371   PetscFunctionBegin;
1372   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1373   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1374   tmp  = a->solve_work;
1375 
1376   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1377   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1378 
1379   /* copy the b into temp work space according to permutation */
1380   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1381 
1382   /* forward solve the U^T */
1383   for (i=0; i<n; i++) {
1384     v   = aa + adiag[i+1] + 1;
1385     vi  = aj + adiag[i+1] + 1;
1386     nz  = adiag[i] - adiag[i+1] - 1;
1387     s1  = tmp[i];
1388     s1 *= v[nz];  /* multiply by inverse of diagonal entry */
1389     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1390     tmp[i] = s1;
1391   }
1392 
1393   /* backward solve the L^T */
1394   for (i=n-1; i>=0; i--){
1395     v   = aa + ai[i];
1396     vi  = aj + ai[i];
1397     nz  = ai[i+1] - ai[i];
1398     s1  = tmp[i];
1399     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1400   }
1401 
1402   /* copy tmp into x according to permutation */
1403   for (i=0; i<n; i++) x[r[i]] = tmp[i];
1404 
1405   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1406   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1407   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1408   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1409 
1410   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1411   PetscFunctionReturn(0);
1412 }
1413 
1414 #undef __FUNCT__
1415 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ"
1416 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx)
1417 {
1418   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1419   IS                iscol = a->col,isrow = a->row;
1420   PetscErrorCode    ierr;
1421   const PetscInt    *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi;
1422   PetscInt          i,n = A->rmap->n,j;
1423   PetscInt          nz;
1424   PetscScalar       *x,*tmp,s1;
1425   const MatScalar   *aa = a->a,*v;
1426   const PetscScalar *b;
1427 
1428   PetscFunctionBegin;
1429   if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);}
1430   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1431   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1432   tmp  = a->solve_work;
1433 
1434   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1435   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1436 
1437   /* copy the b into temp work space according to permutation */
1438   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1439 
1440   /* forward solve the U^T */
1441   for (i=0; i<n; i++) {
1442     v   = aa + diag[i] ;
1443     vi  = aj + diag[i] + 1;
1444     nz  = ai[i+1] - diag[i] - 1;
1445     s1  = tmp[i];
1446     s1 *= (*v++);  /* multiply by inverse of diagonal entry */
1447     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1448     tmp[i] = s1;
1449   }
1450 
1451   /* backward solve the L^T */
1452   for (i=n-1; i>=0; i--){
1453     v   = aa + diag[i] - 1 ;
1454     vi  = aj + diag[i] - 1 ;
1455     nz  = diag[i] - ai[i];
1456     s1  = tmp[i];
1457     for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j];
1458   }
1459 
1460   /* copy tmp into x according to permutation */
1461   for (i=0; i<n; i++) x[r[i]] += tmp[i];
1462 
1463   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1464   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1465   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1466   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1467 
1468   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1469   PetscFunctionReturn(0);
1470 }
1471 
1472 /* ----------------------------------------------------------------*/
1473 EXTERN PetscErrorCode Mat_CheckInode(Mat,PetscTruth);
1474 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption,PetscTruth);
1475 
1476 /*
1477    ilu() under revised new data structure.
1478    Factored arrays bj and ba are stored as
1479      L(0,:), L(1,:), ...,L(n-1,:),  U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:)
1480 
1481    bi=fact->i is an array of size n+1, in which
1482    bi+
1483      bi[i]:  points to 1st entry of L(i,:),i=0,...,n-1
1484      bi[n]:  points to L(n-1,n-1)+1
1485 
1486   bdiag=fact->diag is an array of size n+1,in which
1487      bdiag[i]: points to diagonal of U(i,:), i=0,...,n-1
1488      bdiag[n]: points to entry of U(n-1,0)-1
1489 
1490    U(i,:) contains bdiag[i] as its last entry, i.e.,
1491     U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i])
1492 */
1493 #undef __FUNCT__
1494 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct"
1495 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1496 {
1497 
1498   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1499   PetscErrorCode     ierr;
1500   PetscInt           n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag;
1501   PetscInt           i,j,nz,*bi,*bj,*bdiag;
1502   PetscTruth         missing;
1503   IS                 isicol;
1504 
1505   PetscFunctionBegin;
1506   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);
1507   ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
1508   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
1509   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1510 
1511   ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr);
1512   b    = (Mat_SeqAIJ*)(fact)->data;
1513 
1514   /* allocate matrix arrays for new data structure */
1515   ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,n+1,PetscInt,&b->i);CHKERRQ(ierr);
1516   ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));CHKERRQ(ierr);
1517   b->singlemalloc = PETSC_TRUE;
1518   if (!b->diag){
1519     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr);
1520     ierr = PetscLogObjectMemory(fact,(n+1)*sizeof(PetscInt));CHKERRQ(ierr);
1521   }
1522   bdiag = b->diag;
1523 
1524   if (n > 0) {
1525     ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr);
1526   }
1527 
1528   /* set bi and bj with new data structure */
1529   bi = b->i;
1530   bj = b->j;
1531 
1532   /* L part */
1533   bi[0] = 0;
1534   for (i=0; i<n; i++){
1535     nz = adiag[i] - ai[i];
1536     bi[i+1] = bi[i] + nz;
1537     aj = a->j + ai[i];
1538     for (j=0; j<nz; j++){
1539       *bj = aj[j]; bj++;
1540     }
1541   }
1542 
1543   /* U part */
1544   bdiag[n] = bi[n]-1;
1545   for (i=n-1; i>=0; i--){
1546     nz = ai[i+1] - adiag[i] - 1;
1547     aj = a->j + adiag[i] + 1;
1548     for (j=0; j<nz; j++){
1549       *bj = aj[j]; bj++;
1550     }
1551     /* diag[i] */
1552     *bj = i; bj++;
1553     bdiag[i] = bdiag[i+1] + nz + 1;
1554   }
1555 
1556   fact->factor                 = MAT_FACTOR_ILU;
1557   fact->info.factor_mallocs    = 0;
1558   fact->info.fill_ratio_given  = info->fill;
1559   fact->info.fill_ratio_needed = 1.0;
1560   fact->ops->lufactornumeric   = MatLUFactorNumeric_SeqAIJ_newdatastruct;
1561 
1562   b       = (Mat_SeqAIJ*)(fact)->data;
1563   b->row  = isrow;
1564   b->col  = iscol;
1565   b->icol = isicol;
1566   ierr    = PetscMalloc((fact->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1567   ierr    = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1568   ierr    = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1569   PetscFunctionReturn(0);
1570 }
1571 
1572 #undef __FUNCT__
1573 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_newdatastruct"
1574 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1575 {
1576   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1577   IS                 isicol;
1578   PetscErrorCode     ierr;
1579   const PetscInt     *r,*ic;
1580   PetscInt           n=A->rmap->n,*ai=a->i,*aj=a->j;
1581   PetscInt           *bi,*cols,nnz,*cols_lvl;
1582   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1583   PetscInt           i,levels,diagonal_fill;
1584   PetscTruth         col_identity,row_identity;
1585   PetscReal          f;
1586   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
1587   PetscBT            lnkbt;
1588   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
1589   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1590   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1591 
1592   PetscFunctionBegin;
1593   /* printf("MatILUFactorSymbolic_SeqAIJ_newdatastruct ...\n"); */
1594   levels = (PetscInt)info->levels;
1595   ierr   = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1596   ierr   = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
1597 
1598   if (!levels && row_identity && col_identity) {
1599     /* special case: ilu(0) with natural ordering */
1600     ierr = MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1601     PetscFunctionReturn(0);
1602   }
1603 
1604   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);
1605   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1606   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1607   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1608 
1609   /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
1610   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1611   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
1612   bi[0] = bdiag[0] = 0;
1613 
1614   ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr);
1615 
1616   /* create a linked list for storing column indices of the active row */
1617   nlnk = n + 1;
1618   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1619 
1620   /* initial FreeSpace size is f*(ai[n]+1) */
1621   f             = info->fill;
1622   diagonal_fill = (PetscInt)info->diagonal_fill;
1623   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
1624   current_space = free_space;
1625   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
1626   current_space_lvl = free_space_lvl;
1627 
1628   for (i=0; i<n; i++) {
1629     nzi = 0;
1630     /* copy current row into linked list */
1631     nnz  = ai[r[i]+1] - ai[r[i]];
1632     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1633     cols = aj + ai[r[i]];
1634     lnk[i] = -1; /* marker to indicate if diagonal exists */
1635     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1636     nzi += nlnk;
1637 
1638     /* make sure diagonal entry is included */
1639     if (diagonal_fill && lnk[i] == -1) {
1640       fm = n;
1641       while (lnk[fm] < i) fm = lnk[fm];
1642       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
1643       lnk[fm]    = i;
1644       lnk_lvl[i] = 0;
1645       nzi++; dcount++;
1646     }
1647 
1648     /* add pivot rows into the active row */
1649     nzbd = 0;
1650     prow = lnk[n];
1651     while (prow < i) {
1652       nnz      = bdiag[prow];
1653       cols     = bj_ptr[prow] + nnz + 1;
1654       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1655       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
1656       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
1657       nzi += nlnk;
1658       prow = lnk[prow];
1659       nzbd++;
1660     }
1661     bdiag[i] = nzbd;
1662     bi[i+1]  = bi[i] + nzi;
1663 
1664     /* if free space is not available, make more free space */
1665     if (current_space->local_remaining<nzi) {
1666       nnz = 2*nzi*(n - i); /* estimated and max additional space needed */
1667       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
1668       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
1669       reallocs++;
1670     }
1671 
1672     /* copy data into free_space and free_space_lvl, then initialize lnk */
1673     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1674     bj_ptr[i]    = current_space->array;
1675     bjlvl_ptr[i] = current_space_lvl->array;
1676 
1677     /* make sure the active row i has diagonal entry */
1678     if (*(bj_ptr[i]+bdiag[i]) != i) {
1679       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
1680     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
1681     }
1682 
1683     current_space->array           += nzi;
1684     current_space->local_used      += nzi;
1685     current_space->local_remaining -= nzi;
1686     current_space_lvl->array           += nzi;
1687     current_space_lvl->local_used      += nzi;
1688     current_space_lvl->local_remaining -= nzi;
1689   }
1690 
1691   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1692   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1693 
1694   /* destroy list of free space and other temporary arrays */
1695   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
1696 
1697   /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */
1698   ierr = PetscFreeSpaceContiguous_LU_v2(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr);
1699 
1700   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1701   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
1702   ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr);
1703 
1704 #if defined(PETSC_USE_INFO)
1705   {
1706     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1707     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
1708     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
1709     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
1710     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
1711     if (diagonal_fill) {
1712       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
1713     }
1714   }
1715 #endif
1716 
1717   /* put together the new matrix */
1718   ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
1719   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
1720   b = (Mat_SeqAIJ*)(fact)->data;
1721   b->free_a       = PETSC_TRUE;
1722   b->free_ij      = PETSC_TRUE;
1723   b->singlemalloc = PETSC_FALSE;
1724   ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
1725   b->j          = bj;
1726   b->i          = bi;
1727   b->diag       = bdiag;
1728   b->ilen       = 0;
1729   b->imax       = 0;
1730   b->row        = isrow;
1731   b->col        = iscol;
1732   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1733   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1734   b->icol       = isicol;
1735   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1736   /* In b structure:  Free imax, ilen, old a, old j.
1737      Allocate bdiag, solve_work, new a, new j */
1738   ierr = PetscLogObjectMemory(fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
1739   b->maxnz = b->nz = bdiag[0]+1;
1740   (fact)->info.factor_mallocs    = reallocs;
1741   (fact)->info.fill_ratio_given  = f;
1742   (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]);
1743   (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct;
1744   /* ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */
1745   PetscFunctionReturn(0);
1746 }
1747 
1748 #undef __FUNCT__
1749 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ"
1750 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1751 {
1752   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1753   IS                 isicol;
1754   PetscErrorCode     ierr;
1755   const PetscInt     *r,*ic;
1756   PetscInt           n=A->rmap->n,*ai=a->i,*aj=a->j,d;
1757   PetscInt           *bi,*cols,nnz,*cols_lvl;
1758   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1759   PetscInt           i,levels,diagonal_fill;
1760   PetscTruth         col_identity,row_identity;
1761   PetscReal          f;
1762   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
1763   PetscBT            lnkbt;
1764   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
1765   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1766   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1767   PetscTruth         missing;
1768   PetscTruth         newdatastruct=PETSC_FALSE;
1769 
1770   PetscFunctionBegin;
1771   ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
1772   if(newdatastruct){
1773     ierr = MatILUFactorSymbolic_SeqAIJ_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1774     PetscFunctionReturn(0);
1775   }
1776 
1777   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);
1778   f             = info->fill;
1779   levels        = (PetscInt)info->levels;
1780   diagonal_fill = (PetscInt)info->diagonal_fill;
1781   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1782 
1783   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1784   ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
1785   if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */
1786     ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr);
1787     (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ;
1788 
1789     fact->factor = MAT_FACTOR_ILU;
1790     (fact)->info.factor_mallocs    = 0;
1791     (fact)->info.fill_ratio_given  = info->fill;
1792     (fact)->info.fill_ratio_needed = 1.0;
1793     b               = (Mat_SeqAIJ*)(fact)->data;
1794     ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
1795     if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
1796     b->row              = isrow;
1797     b->col              = iscol;
1798     b->icol             = isicol;
1799     ierr                = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1800     ierr                = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1801     ierr                = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1802     ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1803     PetscFunctionReturn(0);
1804   }
1805 
1806   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1807   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1808 
1809   /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
1810   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1811   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
1812   bi[0] = bdiag[0] = 0;
1813 
1814   ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr);
1815 
1816   /* create a linked list for storing column indices of the active row */
1817   nlnk = n + 1;
1818   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1819 
1820   /* initial FreeSpace size is f*(ai[n]+1) */
1821   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
1822   current_space = free_space;
1823   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
1824   current_space_lvl = free_space_lvl;
1825 
1826   for (i=0; i<n; i++) {
1827     nzi = 0;
1828     /* copy current row into linked list */
1829     nnz  = ai[r[i]+1] - ai[r[i]];
1830     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1831     cols = aj + ai[r[i]];
1832     lnk[i] = -1; /* marker to indicate if diagonal exists */
1833     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1834     nzi += nlnk;
1835 
1836     /* make sure diagonal entry is included */
1837     if (diagonal_fill && lnk[i] == -1) {
1838       fm = n;
1839       while (lnk[fm] < i) fm = lnk[fm];
1840       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
1841       lnk[fm]    = i;
1842       lnk_lvl[i] = 0;
1843       nzi++; dcount++;
1844     }
1845 
1846     /* add pivot rows into the active row */
1847     nzbd = 0;
1848     prow = lnk[n];
1849     while (prow < i) {
1850       nnz      = bdiag[prow];
1851       cols     = bj_ptr[prow] + nnz + 1;
1852       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1853       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
1854       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
1855       nzi += nlnk;
1856       prow = lnk[prow];
1857       nzbd++;
1858     }
1859     bdiag[i] = nzbd;
1860     bi[i+1]  = bi[i] + nzi;
1861 
1862     /* if free space is not available, make more free space */
1863     if (current_space->local_remaining<nzi) {
1864       nnz = nzi*(n - i); /* estimated and max additional space needed */
1865       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
1866       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
1867       reallocs++;
1868     }
1869 
1870     /* copy data into free_space and free_space_lvl, then initialize lnk */
1871     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1872     bj_ptr[i]    = current_space->array;
1873     bjlvl_ptr[i] = current_space_lvl->array;
1874 
1875     /* make sure the active row i has diagonal entry */
1876     if (*(bj_ptr[i]+bdiag[i]) != i) {
1877       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
1878     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
1879     }
1880 
1881     current_space->array           += nzi;
1882     current_space->local_used      += nzi;
1883     current_space->local_remaining -= nzi;
1884     current_space_lvl->array           += nzi;
1885     current_space_lvl->local_used      += nzi;
1886     current_space_lvl->local_remaining -= nzi;
1887   }
1888 
1889   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1890   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1891 
1892   /* destroy list of free space and other temporary arrays */
1893   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
1894   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */
1895   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1896   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
1897   ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr);
1898 
1899 #if defined(PETSC_USE_INFO)
1900   {
1901     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1902     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
1903     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
1904     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
1905     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
1906     if (diagonal_fill) {
1907       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
1908     }
1909   }
1910 #endif
1911 
1912   /* put together the new matrix */
1913   ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
1914   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
1915   b = (Mat_SeqAIJ*)(fact)->data;
1916   b->free_a       = PETSC_TRUE;
1917   b->free_ij      = PETSC_TRUE;
1918   b->singlemalloc = PETSC_FALSE;
1919   ierr = PetscMalloc(bi[n]*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
1920   b->j          = bj;
1921   b->i          = bi;
1922   for (i=0; i<n; i++) bdiag[i] += bi[i];
1923   b->diag       = bdiag;
1924   b->ilen       = 0;
1925   b->imax       = 0;
1926   b->row        = isrow;
1927   b->col        = iscol;
1928   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1929   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1930   b->icol       = isicol;
1931   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1932   /* In b structure:  Free imax, ilen, old a, old j.
1933      Allocate bdiag, solve_work, new a, new j */
1934   ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
1935   b->maxnz             = b->nz = bi[n] ;
1936   (fact)->info.factor_mallocs    = reallocs;
1937   (fact)->info.fill_ratio_given  = f;
1938   (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1939   (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ;
1940   ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1941   PetscFunctionReturn(0);
1942 }
1943 
1944 #undef __FUNCT__
1945 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ_newdatastruct"
1946 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info)
1947 {
1948   Mat            C = B;
1949   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1950   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
1951   IS             ip=b->row,iip = b->icol;
1952   PetscErrorCode ierr;
1953   const PetscInt *rip,*riip;
1954   PetscInt       i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp;
1955   PetscInt       *ai=a->i,*aj=a->j;
1956   PetscInt       k,jmin,jmax,*c2r,*il,col,nexti,ili,nz;
1957   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
1958   PetscTruth     perm_identity;
1959 
1960   LUShift_Ctx    sctx;
1961   PetscInt       newshift;
1962   PetscReal      rs;
1963   MatScalar      d,*v;
1964 
1965   PetscFunctionBegin;
1966   /* MatPivotSetUp(): initialize shift context sctx */
1967   ierr = PetscMemzero(&sctx,sizeof(LUShift_Ctx));CHKERRQ(ierr);
1968 
1969   /* if both shift schemes are chosen by user, only use info->shiftpd */
1970   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
1971     sctx.shift_top = info->zeropivot;
1972     for (i=0; i<mbs; i++) {
1973       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
1974       d  = (aa)[a->diag[i]];
1975       rs = -PetscAbsScalar(d) - PetscRealPart(d);
1976       v  = aa+ai[i];
1977       nz = ai[i+1] - ai[i];
1978       for (j=0; j<nz; j++)
1979 	rs += PetscAbsScalar(v[j]);
1980       if (rs>sctx.shift_top) sctx.shift_top = rs;
1981     }
1982     sctx.shift_top   *= 1.1;
1983     sctx.nshift_max   = 5;
1984     sctx.shift_lo     = 0.;
1985     sctx.shift_hi     = 1.;
1986   }
1987 
1988   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
1989   ierr  = ISGetIndices(iip,&riip);CHKERRQ(ierr);
1990 
1991   /* allocate working arrays
1992      c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col
1993      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
1994   */
1995   ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&c2r);CHKERRQ(ierr);
1996 
1997   do {
1998     sctx.lushift = PETSC_FALSE;
1999 
2000     for (i=0; i<mbs; i++) c2r[i] = mbs;
2001     il[0] = 0;
2002 
2003     for (k = 0; k<mbs; k++){
2004       /* zero rtmp */
2005       nz = bi[k+1] - bi[k];
2006       bjtmp = bj + bi[k];
2007       for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
2008 
2009       /* load in initial unfactored row */
2010       bval = ba + bi[k];
2011       jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2012       for (j = jmin; j < jmax; j++){
2013         col = riip[aj[j]];
2014         if (col >= k){ /* only take upper triangular entry */
2015           rtmp[col] = aa[j];
2016           *bval++   = 0.0; /* for in-place factorization */
2017         }
2018       }
2019       /* shift the diagonal of the matrix: ZeropivotApply() */
2020       rtmp[k] += sctx.shift_amount;  /* shift the diagonal of the matrix */
2021 
2022       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
2023       dk = rtmp[k];
2024       i  = c2r[k]; /* first row to be added to k_th row  */
2025 
2026       while (i < k){
2027         nexti = c2r[i]; /* next row to be added to k_th row */
2028 
2029         /* compute multiplier, update diag(k) and U(i,k) */
2030         ili   = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2031         uikdi = - ba[ili]*ba[bdiag[i]];  /* diagonal(k) */
2032         dk   += uikdi*ba[ili]; /* update diag[k] */
2033         ba[ili] = uikdi; /* -U(i,k) */
2034 
2035         /* add multiple of row i to k-th row */
2036         jmin = ili + 1; jmax = bi[i+1];
2037         if (jmin < jmax){
2038           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2039           /* update il and c2r for row i */
2040           il[i] = jmin;
2041           j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i;
2042         }
2043         i = nexti;
2044       }
2045 
2046       /* copy data into U(k,:) */
2047       rs   = 0.0;
2048       jmin = bi[k]; jmax = bi[k+1]-1;
2049       if (jmin < jmax) {
2050         for (j=jmin; j<jmax; j++){
2051           col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]);
2052         }
2053         /* add the k-th row into il and c2r */
2054         il[k] = jmin;
2055         i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k;
2056       }
2057 
2058       /* MatPivotCheck() */
2059       sctx.rs  = rs;
2060       sctx.pv  = dk;
2061       if (info->shiftnz){
2062         ierr = MatPivotCheck_nz(info,sctx,k,newshift);CHKERRQ(ierr);
2063       } else if (info->shiftpd){
2064         ierr = MatPivotCheck_pd(info,sctx,k,newshift);CHKERRQ(ierr);
2065       } else if (info->shiftinblocks){
2066         ierr = MatPivotCheck_inblocks(info,sctx,k,newshift);CHKERRQ(ierr);
2067       } else {
2068         ierr = MatPivotCheck_none(info,sctx,k,newshift);CHKERRQ(ierr);
2069       }
2070       dk = sctx.pv;
2071       if (newshift == 1) break;
2072 
2073       ba[bdiag[k]] = 1.0/dk; /* U(k,k) */
2074     }
2075   } while (sctx.lushift);
2076 
2077   ierr = PetscFree3(rtmp,il,c2r);CHKERRQ(ierr);
2078   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2079   ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr);
2080 
2081   ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
2082   if (perm_identity){
2083     (B)->ops->solve           = MatSolve_SeqSBAIJ_1_NaturalOrdering_newdatastruct;
2084     (B)->ops->solvetranspose  = 0;
2085     (B)->ops->forwardsolve    = 0;
2086     (B)->ops->backwardsolve   = 0;
2087   } else {
2088     (B)->ops->solve           = MatSolve_SeqSBAIJ_1_newdatastruct;
2089     (B)->ops->solvetranspose  = 0;
2090     (B)->ops->forwardsolve    = 0;
2091     (B)->ops->backwardsolve   = 0;
2092   }
2093 
2094   C->assembled    = PETSC_TRUE;
2095   C->preallocated = PETSC_TRUE;
2096   ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr);
2097 
2098   /* MatPivotView() */
2099   if (sctx.nshift){
2100     if (info->shiftpd) {
2101       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);
2102     } else if (info->shiftnz) {
2103       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2104     } else if (info->shiftinblocks){
2105       ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftinblocks);CHKERRQ(ierr);
2106     }
2107   }
2108   PetscFunctionReturn(0);
2109 }
2110 
2111 #undef __FUNCT__
2112 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ"
2113 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info)
2114 {
2115   Mat            C = B;
2116   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
2117   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
2118   IS             ip=b->row,iip = b->icol;
2119   PetscErrorCode ierr;
2120   const PetscInt *rip,*riip;
2121   PetscInt       i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol,*bjtmp;
2122   PetscInt       *ai=a->i,*aj=a->j;
2123   PetscInt       k,jmin,jmax,*jl,*il,col,nexti,ili,nz;
2124   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
2125   PetscReal      zeropivot,rs,shiftnz;
2126   PetscReal      shiftpd;
2127   ChShift_Ctx    sctx;
2128   PetscInt       newshift;
2129   PetscTruth     perm_identity;
2130 
2131   PetscFunctionBegin;
2132   shiftnz   = info->shiftnz;
2133   shiftpd   = info->shiftpd;
2134   zeropivot = info->zeropivot;
2135 
2136   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
2137   ierr  = ISGetIndices(iip,&riip);CHKERRQ(ierr);
2138 
2139   /* initialization */
2140   ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&jl);CHKERRQ(ierr);
2141   sctx.shift_amount = 0;
2142   sctx.nshift       = 0;
2143   do {
2144     sctx.chshift = PETSC_FALSE;
2145     for (i=0; i<mbs; i++) jl[i] = mbs;
2146     il[0] = 0;
2147 
2148     for (k = 0; k<mbs; k++){
2149       /* zero rtmp */
2150       nz = bi[k+1] - bi[k];
2151       bjtmp = bj + bi[k];
2152       for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
2153 
2154       bval = ba + bi[k];
2155       /* initialize k-th row by the perm[k]-th row of A */
2156       jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2157       for (j = jmin; j < jmax; j++){
2158         col = riip[aj[j]];
2159         if (col >= k){ /* only take upper triangular entry */
2160           rtmp[col] = aa[j];
2161           *bval++  = 0.0; /* for in-place factorization */
2162         }
2163       }
2164       /* shift the diagonal of the matrix */
2165       if (sctx.nshift) rtmp[k] += sctx.shift_amount;
2166 
2167       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
2168       dk = rtmp[k];
2169       i = jl[k]; /* first row to be added to k_th row  */
2170 
2171       while (i < k){
2172         nexti = jl[i]; /* next row to be added to k_th row */
2173 
2174         /* compute multiplier, update diag(k) and U(i,k) */
2175         ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2176         uikdi = - ba[ili]*ba[bi[i]];  /* diagonal(k) */
2177         dk += uikdi*ba[ili];
2178         ba[ili] = uikdi; /* -U(i,k) */
2179 
2180         /* add multiple of row i to k-th row */
2181         jmin = ili + 1; jmax = bi[i+1];
2182         if (jmin < jmax){
2183           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2184           /* update il and jl for row i */
2185           il[i] = jmin;
2186           j = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
2187         }
2188         i = nexti;
2189       }
2190 
2191       /* shift the diagonals when zero pivot is detected */
2192       /* compute rs=sum of abs(off-diagonal) */
2193       rs   = 0.0;
2194       jmin = bi[k]+1;
2195       nz   = bi[k+1] - jmin;
2196       bcol = bj + jmin;
2197       for (j=0; j<nz; j++) {
2198         rs += PetscAbsScalar(rtmp[bcol[j]]);
2199       }
2200 
2201       sctx.rs = rs;
2202       sctx.pv = dk;
2203       ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr);
2204 
2205       if (newshift == 1) {
2206         if (!sctx.shift_amount) {
2207           sctx.shift_amount = 1e-5;
2208         }
2209         break;
2210       }
2211 
2212       /* copy data into U(k,:) */
2213       ba[bi[k]] = 1.0/dk; /* U(k,k) */
2214       jmin = bi[k]+1; jmax = bi[k+1];
2215       if (jmin < jmax) {
2216         for (j=jmin; j<jmax; j++){
2217           col = bj[j]; ba[j] = rtmp[col];
2218         }
2219         /* add the k-th row into il and jl */
2220         il[k] = jmin;
2221         i = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
2222       }
2223     }
2224   } while (sctx.chshift);
2225   ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr);
2226   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2227   ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr);
2228 
2229   ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
2230   if (perm_identity){
2231     (B)->ops->solve           = MatSolve_SeqSBAIJ_1_NaturalOrdering;
2232     (B)->ops->solvetranspose  = MatSolve_SeqSBAIJ_1_NaturalOrdering;
2233     (B)->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering;
2234     (B)->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering;
2235   } else {
2236     (B)->ops->solve           = MatSolve_SeqSBAIJ_1;
2237     (B)->ops->solvetranspose  = MatSolve_SeqSBAIJ_1;
2238     (B)->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1;
2239     (B)->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1;
2240   }
2241 
2242   C->assembled    = PETSC_TRUE;
2243   C->preallocated = PETSC_TRUE;
2244   ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr);
2245   if (sctx.nshift){
2246     if (shiftnz) {
2247       ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2248     } else if (shiftpd) {
2249       ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2250     }
2251   }
2252   PetscFunctionReturn(0);
2253 }
2254 
2255 /*
2256    icc() under revised new data structure.
2257    Factored arrays bj and ba are stored as
2258      U(0,:),...,U(i,:),U(n-1,:)
2259 
2260    ui=fact->i is an array of size n+1, in which
2261    ui+
2262      ui[i]:  points to 1st entry of U(i,:),i=0,...,n-1
2263      ui[n]:  points to U(n-1,n-1)+1
2264 
2265   udiag=fact->diag is an array of size n,in which
2266      udiag[i]: points to diagonal of U(i,:), i=0,...,n-1
2267 
2268    U(i,:) contains udiag[i] as its last entry, i.e.,
2269     U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i])
2270 */
2271 
2272 #undef __FUNCT__
2273 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ_newdatastruct"
2274 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2275 {
2276   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2277   Mat_SeqSBAIJ       *b;
2278   PetscErrorCode     ierr;
2279   PetscTruth         perm_identity,missing;
2280   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag;
2281   const PetscInt     *rip,*riip;
2282   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
2283   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL,d;
2284   PetscInt           ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
2285   PetscReal          fill=info->fill,levels=info->levels;
2286   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2287   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
2288   PetscBT            lnkbt;
2289   IS                 iperm;
2290 
2291   PetscFunctionBegin;
2292   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);
2293   ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
2294   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
2295   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2296   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2297 
2298   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2299   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2300   ui[0] = 0;
2301 
2302   /* ICC(0) without matrix ordering: simply rearrange column indices */
2303   if (!levels && perm_identity) {
2304     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2305     cols = uj;
2306     for (i=0; i<am; i++) {
2307       ncols    = ai[i+1] - a->diag[i];
2308       ui[i+1]  = ui[i] + ncols;
2309       udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */
2310 
2311       aj   = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */
2312       ncols--; /* exclude diagonal */
2313       for (j=0; j<ncols; j++) *cols++ = aj[j];
2314       *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */
2315     }
2316   } else { /* case: levels>0 || (levels=0 && !perm_identity) */
2317     ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2318     ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2319 
2320     /* initialization */
2321     ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr);
2322 
2323     /* jl: linked list for storing indices of the pivot rows
2324        il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2325     ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr);
2326     for (i=0; i<am; i++){
2327       jl[i] = am; il[i] = 0;
2328     }
2329 
2330     /* create and initialize a linked list for storing column indices of the active row k */
2331     nlnk = am + 1;
2332     ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2333 
2334     /* initial FreeSpace size is fill*(ai[am]+1) */
2335     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2336     current_space = free_space;
2337     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr);
2338     current_space_lvl = free_space_lvl;
2339 
2340     for (k=0; k<am; k++){  /* for each active row k */
2341       /* initialize lnk by the column indices of row rip[k] of A */
2342       nzk   = 0;
2343       ncols = ai[rip[k]+1] - ai[rip[k]];
2344       if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2345       ncols_upper = 0;
2346       for (j=0; j<ncols; j++){
2347         i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2348         if (riip[i] >= k){ /* only take upper triangular entry */
2349           ajtmp[ncols_upper] = i;
2350           ncols_upper++;
2351         }
2352       }
2353       ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2354       nzk += nlnk;
2355 
2356       /* update lnk by computing fill-in for each pivot row to be merged in */
2357       prow = jl[k]; /* 1st pivot row */
2358 
2359       while (prow < k){
2360         nextprow = jl[prow];
2361 
2362         /* merge prow into k-th row */
2363         jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2364         jmax = ui[prow+1];
2365         ncols = jmax-jmin;
2366         i     = jmin - ui[prow];
2367         cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2368         uj    = uj_lvl_ptr[prow] + i; /* levels of cols */
2369         j     = *(uj - 1);
2370         ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr);
2371         nzk += nlnk;
2372 
2373         /* update il and jl for prow */
2374         if (jmin < jmax){
2375           il[prow] = jmin;
2376           j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2377         }
2378         prow = nextprow;
2379       }
2380 
2381       /* if free space is not available, make more free space */
2382       if (current_space->local_remaining<nzk) {
2383         i  = am - k + 1; /* num of unfactored rows */
2384         i *= PetscMin(nzk, i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */
2385         ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2386         ierr = PetscFreeSpaceGet(i,&current_space_lvl);CHKERRQ(ierr);
2387         reallocs++;
2388       }
2389 
2390       /* copy data into free_space and free_space_lvl, then initialize lnk */
2391       if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2392       ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
2393 
2394       /* add the k-th row into il and jl */
2395       if (nzk > 1){
2396         i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2397         jl[k] = jl[i]; jl[i] = k;
2398         il[k] = ui[k] + 1;
2399       }
2400       uj_ptr[k]     = current_space->array;
2401       uj_lvl_ptr[k] = current_space_lvl->array;
2402 
2403       current_space->array           += nzk;
2404       current_space->local_used      += nzk;
2405       current_space->local_remaining -= nzk;
2406 
2407       current_space_lvl->array           += nzk;
2408       current_space_lvl->local_used      += nzk;
2409       current_space_lvl->local_remaining -= nzk;
2410 
2411       ui[k+1] = ui[k] + nzk;
2412     }
2413 
2414 #if defined(PETSC_USE_INFO)
2415     if (ai[am] != 0) {
2416       PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]);
2417       ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2418       ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2419       ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2420     } else {
2421       ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2422     }
2423 #endif
2424 
2425     ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2426     ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2427     ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr);
2428     ierr = PetscFree(ajtmp);CHKERRQ(ierr);
2429 
2430     /* destroy list of free space and other temporary array(s) */
2431     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2432     ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor in newdatastruct */
2433     ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2434     ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2435 
2436   } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2437 
2438   /* put together the new matrix in MATSEQSBAIJ format */
2439 
2440   b    = (Mat_SeqSBAIJ*)(fact)->data;
2441   b->singlemalloc = PETSC_FALSE;
2442   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2443   b->j    = uj;
2444   b->i    = ui;
2445   b->diag = udiag;
2446   b->free_diag = PETSC_TRUE;
2447   b->ilen = 0;
2448   b->imax = 0;
2449   b->row  = perm;
2450   b->col  = perm;
2451   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2452   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2453   b->icol = iperm;
2454   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2455   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2456   ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2457   b->maxnz   = b->nz = ui[am];
2458   b->free_a  = PETSC_TRUE;
2459   b->free_ij = PETSC_TRUE;
2460 
2461   (fact)->info.factor_mallocs    = reallocs;
2462   (fact)->info.fill_ratio_given  = fill;
2463   if (ai[am] != 0) {
2464     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2465   } else {
2466     (fact)->info.fill_ratio_needed = 0.0;
2467   }
2468   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_newdatastruct;
2469   PetscFunctionReturn(0);
2470 }
2471 
2472 #undef __FUNCT__
2473 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ"
2474 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2475 {
2476   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2477   Mat_SeqSBAIJ       *b;
2478   PetscErrorCode     ierr;
2479   PetscTruth         perm_identity,missing;
2480   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag;
2481   const PetscInt     *rip,*riip;
2482   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
2483   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL,d;
2484   PetscInt           ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
2485   PetscReal          fill=info->fill,levels=info->levels;
2486   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2487   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
2488   PetscBT            lnkbt;
2489   IS                 iperm;
2490   PetscTruth         newdatastruct=PETSC_FALSE;
2491 
2492   PetscFunctionBegin;
2493   ierr = PetscOptionsGetTruth(PETSC_NULL,"-icc_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
2494   if(newdatastruct){
2495     ierr = MatICCFactorSymbolic_SeqAIJ_newdatastruct(fact,A,perm,info);CHKERRQ(ierr);
2496     PetscFunctionReturn(0);
2497   }
2498 
2499   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);
2500   ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
2501   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
2502   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2503   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2504 
2505   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2506   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2507   ui[0] = 0;
2508 
2509   /* ICC(0) without matrix ordering: simply copies fill pattern */
2510   if (!levels && perm_identity) {
2511 
2512     for (i=0; i<am; i++) {
2513       ui[i+1]  = ui[i] + ai[i+1] - a->diag[i];
2514       udiag[i] = ui[i];
2515     }
2516     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2517     cols = uj;
2518     for (i=0; i<am; i++) {
2519       aj    = a->j + a->diag[i];
2520       ncols = ui[i+1] - ui[i];
2521       for (j=0; j<ncols; j++) *cols++ = *aj++;
2522     }
2523   } else { /* case: levels>0 || (levels=0 && !perm_identity) */
2524     ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2525     ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2526 
2527     /* initialization */
2528     ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr);
2529 
2530     /* jl: linked list for storing indices of the pivot rows
2531        il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2532     ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr);
2533     for (i=0; i<am; i++){
2534       jl[i] = am; il[i] = 0;
2535     }
2536 
2537     /* create and initialize a linked list for storing column indices of the active row k */
2538     nlnk = am + 1;
2539     ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2540 
2541     /* initial FreeSpace size is fill*(ai[am]+1) */
2542     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2543     current_space = free_space;
2544     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr);
2545     current_space_lvl = free_space_lvl;
2546 
2547     for (k=0; k<am; k++){  /* for each active row k */
2548       /* initialize lnk by the column indices of row rip[k] of A */
2549       nzk   = 0;
2550       ncols = ai[rip[k]+1] - ai[rip[k]];
2551       if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2552       ncols_upper = 0;
2553       for (j=0; j<ncols; j++){
2554         i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2555         if (riip[i] >= k){ /* only take upper triangular entry */
2556           ajtmp[ncols_upper] = i;
2557           ncols_upper++;
2558         }
2559       }
2560       ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2561       nzk += nlnk;
2562 
2563       /* update lnk by computing fill-in for each pivot row to be merged in */
2564       prow = jl[k]; /* 1st pivot row */
2565 
2566       while (prow < k){
2567         nextprow = jl[prow];
2568 
2569         /* merge prow into k-th row */
2570         jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2571         jmax = ui[prow+1];
2572         ncols = jmax-jmin;
2573         i     = jmin - ui[prow];
2574         cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2575         uj    = uj_lvl_ptr[prow] + i; /* levels of cols */
2576         j     = *(uj - 1);
2577         ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr);
2578         nzk += nlnk;
2579 
2580         /* update il and jl for prow */
2581         if (jmin < jmax){
2582           il[prow] = jmin;
2583           j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2584         }
2585         prow = nextprow;
2586       }
2587 
2588       /* if free space is not available, make more free space */
2589       if (current_space->local_remaining<nzk) {
2590         i = am - k + 1; /* num of unfactored rows */
2591         i *= PetscMin(nzk, (i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2592         ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2593         ierr = PetscFreeSpaceGet(i,&current_space_lvl);CHKERRQ(ierr);
2594         reallocs++;
2595       }
2596 
2597       /* copy data into free_space and free_space_lvl, then initialize lnk */
2598       if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2599       ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
2600 
2601       /* add the k-th row into il and jl */
2602       if (nzk > 1){
2603         i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2604         jl[k] = jl[i]; jl[i] = k;
2605         il[k] = ui[k] + 1;
2606       }
2607       uj_ptr[k]     = current_space->array;
2608       uj_lvl_ptr[k] = current_space_lvl->array;
2609 
2610       current_space->array           += nzk;
2611       current_space->local_used      += nzk;
2612       current_space->local_remaining -= nzk;
2613 
2614       current_space_lvl->array           += nzk;
2615       current_space_lvl->local_used      += nzk;
2616       current_space_lvl->local_remaining -= nzk;
2617 
2618       ui[k+1] = ui[k] + nzk;
2619     }
2620 
2621 #if defined(PETSC_USE_INFO)
2622     if (ai[am] != 0) {
2623       PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]);
2624       ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2625       ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2626       ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2627     } else {
2628       ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2629     }
2630 #endif
2631 
2632     ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2633     ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2634     ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr);
2635     ierr = PetscFree(ajtmp);CHKERRQ(ierr);
2636 
2637     /* destroy list of free space and other temporary array(s) */
2638     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2639     ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
2640     ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2641     ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2642 
2643   } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2644 
2645   /* put together the new matrix in MATSEQSBAIJ format */
2646 
2647   b    = (Mat_SeqSBAIJ*)(fact)->data;
2648   b->singlemalloc = PETSC_FALSE;
2649   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2650   b->j    = uj;
2651   b->i    = ui;
2652   b->diag = udiag;
2653   b->free_diag = PETSC_TRUE;
2654   b->ilen = 0;
2655   b->imax = 0;
2656   b->row  = perm;
2657   b->col  = perm;
2658   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2659   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2660   b->icol = iperm;
2661   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2662   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2663   ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2664   b->maxnz   = b->nz = ui[am];
2665   b->free_a  = PETSC_TRUE;
2666   b->free_ij = PETSC_TRUE;
2667 
2668   (fact)->info.factor_mallocs    = reallocs;
2669   (fact)->info.fill_ratio_given  = fill;
2670   if (ai[am] != 0) {
2671     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2672   } else {
2673     (fact)->info.fill_ratio_needed = 0.0;
2674   }
2675   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2676   PetscFunctionReturn(0);
2677 }
2678 
2679 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2680 {
2681   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2682   Mat_SeqSBAIJ       *b;
2683   PetscErrorCode     ierr;
2684   PetscTruth         perm_identity;
2685   PetscReal          fill = info->fill;
2686   const PetscInt     *rip,*riip;
2687   PetscInt           i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow;
2688   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
2689   PetscInt           nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr,*udiag;
2690   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2691   PetscBT            lnkbt;
2692   IS                 iperm;
2693 
2694   PetscFunctionBegin;
2695   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);
2696   /* check whether perm is the identity mapping */
2697   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2698   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2699   ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2700   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2701 
2702   /* initialization */
2703   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2704   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2705   ui[0] = 0;
2706 
2707   /* jl: linked list for storing indices of the pivot rows
2708      il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2709   ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr);
2710   for (i=0; i<am; i++){
2711     jl[i] = am; il[i] = 0;
2712   }
2713 
2714   /* create and initialize a linked list for storing column indices of the active row k */
2715   nlnk = am + 1;
2716   ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2717 
2718   /* initial FreeSpace size is fill*(ai[am]+1) */
2719   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2720   current_space = free_space;
2721 
2722   for (k=0; k<am; k++){  /* for each active row k */
2723     /* initialize lnk by the column indices of row rip[k] of A */
2724     nzk   = 0;
2725     ncols = ai[rip[k]+1] - ai[rip[k]];
2726     if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2727     ncols_upper = 0;
2728     for (j=0; j<ncols; j++){
2729       i = riip[*(aj + ai[rip[k]] + j)];
2730       if (i >= k){ /* only take upper triangular entry */
2731         cols[ncols_upper] = i;
2732         ncols_upper++;
2733       }
2734     }
2735     ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2736     nzk += nlnk;
2737 
2738     /* update lnk by computing fill-in for each pivot row to be merged in */
2739     prow = jl[k]; /* 1st pivot row */
2740 
2741     while (prow < k){
2742       nextprow = jl[prow];
2743       /* merge prow into k-th row */
2744       jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2745       jmax = ui[prow+1];
2746       ncols = jmax-jmin;
2747       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2748       ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2749       nzk += nlnk;
2750 
2751       /* update il and jl for prow */
2752       if (jmin < jmax){
2753         il[prow] = jmin;
2754         j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
2755       }
2756       prow = nextprow;
2757     }
2758 
2759     /* if free space is not available, make more free space */
2760     if (current_space->local_remaining<nzk) {
2761       i  = am - k + 1; /* num of unfactored rows */
2762       i *= PetscMin(nzk,i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */
2763       ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2764       reallocs++;
2765     }
2766 
2767     /* copy data into free space, then initialize lnk */
2768     ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
2769 
2770     /* add the k-th row into il and jl */
2771     if (nzk-1 > 0){
2772       i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2773       jl[k] = jl[i]; jl[i] = k;
2774       il[k] = ui[k] + 1;
2775     }
2776     ui_ptr[k] = current_space->array;
2777     current_space->array           += nzk;
2778     current_space->local_used      += nzk;
2779     current_space->local_remaining -= nzk;
2780 
2781     ui[k+1] = ui[k] + nzk;
2782   }
2783 
2784 #if defined(PETSC_USE_INFO)
2785   if (ai[am] != 0) {
2786     PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]);
2787     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2788     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2789     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2790   } else {
2791      ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2792   }
2793 #endif
2794 
2795   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2796   ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2797   ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr);
2798 
2799   /* destroy list of free space and other temporary array(s) */
2800   ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2801   ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor in newdatastruct */
2802   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2803 
2804   /* put together the new matrix in MATSEQSBAIJ format */
2805 
2806   b = (Mat_SeqSBAIJ*)(fact)->data;
2807   b->singlemalloc = PETSC_FALSE;
2808   b->free_a       = PETSC_TRUE;
2809   b->free_ij      = PETSC_TRUE;
2810   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2811   b->j    = uj;
2812   b->i    = ui;
2813   b->diag = udiag;
2814   b->free_diag = PETSC_TRUE;
2815   b->ilen = 0;
2816   b->imax = 0;
2817   b->row  = perm;
2818   b->col  = perm;
2819   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2820   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2821   b->icol = iperm;
2822   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2823   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2824   ierr    = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2825   b->maxnz = b->nz = ui[am];
2826 
2827   (fact)->info.factor_mallocs    = reallocs;
2828   (fact)->info.fill_ratio_given  = fill;
2829   if (ai[am] != 0) {
2830     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2831   } else {
2832     (fact)->info.fill_ratio_needed = 0.0;
2833   }
2834   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_newdatastruct;
2835   PetscFunctionReturn(0);
2836 }
2837 
2838 #undef __FUNCT__
2839 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ"
2840 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2841 {
2842   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2843   Mat_SeqSBAIJ       *b;
2844   PetscErrorCode     ierr;
2845   PetscTruth         perm_identity;
2846   PetscReal          fill = info->fill;
2847   const PetscInt     *rip,*riip;
2848   PetscInt           i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow;
2849   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
2850   PetscInt           nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr;
2851   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2852   PetscBT            lnkbt;
2853   IS                 iperm;
2854   PetscTruth         newdatastruct=PETSC_FALSE;
2855 
2856   PetscFunctionBegin;
2857   ierr = PetscOptionsGetTruth(PETSC_NULL,"-cholesky_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
2858   if(newdatastruct){
2859     ierr = MatCholeskyFactorSymbolic_SeqAIJ_newdatastruct(fact,A,perm,info);CHKERRQ(ierr);
2860     PetscFunctionReturn(0);
2861   }
2862 
2863   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);
2864   /* check whether perm is the identity mapping */
2865   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2866   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2867   ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2868   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2869 
2870   /* initialization */
2871   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2872   ui[0] = 0;
2873 
2874   /* jl: linked list for storing indices of the pivot rows
2875      il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2876   ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr);
2877   for (i=0; i<am; i++){
2878     jl[i] = am; il[i] = 0;
2879   }
2880 
2881   /* create and initialize a linked list for storing column indices of the active row k */
2882   nlnk = am + 1;
2883   ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2884 
2885   /* initial FreeSpace size is fill*(ai[am]+1) */
2886   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2887   current_space = free_space;
2888 
2889   for (k=0; k<am; k++){  /* for each active row k */
2890     /* initialize lnk by the column indices of row rip[k] of A */
2891     nzk   = 0;
2892     ncols = ai[rip[k]+1] - ai[rip[k]];
2893     if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2894     ncols_upper = 0;
2895     for (j=0; j<ncols; j++){
2896       i = riip[*(aj + ai[rip[k]] + j)];
2897       if (i >= k){ /* only take upper triangular entry */
2898         cols[ncols_upper] = i;
2899         ncols_upper++;
2900       }
2901     }
2902     ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2903     nzk += nlnk;
2904 
2905     /* update lnk by computing fill-in for each pivot row to be merged in */
2906     prow = jl[k]; /* 1st pivot row */
2907 
2908     while (prow < k){
2909       nextprow = jl[prow];
2910       /* merge prow into k-th row */
2911       jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2912       jmax = ui[prow+1];
2913       ncols = jmax-jmin;
2914       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2915       ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2916       nzk += nlnk;
2917 
2918       /* update il and jl for prow */
2919       if (jmin < jmax){
2920         il[prow] = jmin;
2921         j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
2922       }
2923       prow = nextprow;
2924     }
2925 
2926     /* if free space is not available, make more free space */
2927     if (current_space->local_remaining<nzk) {
2928       i = am - k + 1; /* num of unfactored rows */
2929       i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2930       ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2931       reallocs++;
2932     }
2933 
2934     /* copy data into free space, then initialize lnk */
2935     ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
2936 
2937     /* add the k-th row into il and jl */
2938     if (nzk-1 > 0){
2939       i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2940       jl[k] = jl[i]; jl[i] = k;
2941       il[k] = ui[k] + 1;
2942     }
2943     ui_ptr[k] = current_space->array;
2944     current_space->array           += nzk;
2945     current_space->local_used      += nzk;
2946     current_space->local_remaining -= nzk;
2947 
2948     ui[k+1] = ui[k] + nzk;
2949   }
2950 
2951 #if defined(PETSC_USE_INFO)
2952   if (ai[am] != 0) {
2953     PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]);
2954     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2955     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2956     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2957   } else {
2958      ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2959   }
2960 #endif
2961 
2962   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2963   ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2964   ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr);
2965 
2966   /* destroy list of free space and other temporary array(s) */
2967   ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2968   ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
2969   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2970 
2971   /* put together the new matrix in MATSEQSBAIJ format */
2972 
2973   b = (Mat_SeqSBAIJ*)(fact)->data;
2974   b->singlemalloc = PETSC_FALSE;
2975   b->free_a       = PETSC_TRUE;
2976   b->free_ij      = PETSC_TRUE;
2977   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2978   b->j    = uj;
2979   b->i    = ui;
2980   b->diag = 0;
2981   b->ilen = 0;
2982   b->imax = 0;
2983   b->row  = perm;
2984   b->col  = perm;
2985   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2986   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2987   b->icol = iperm;
2988   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2989   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2990   ierr    = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2991   b->maxnz = b->nz = ui[am];
2992 
2993   (fact)->info.factor_mallocs    = reallocs;
2994   (fact)->info.fill_ratio_given  = fill;
2995   if (ai[am] != 0) {
2996     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2997   } else {
2998     (fact)->info.fill_ratio_needed = 0.0;
2999   }
3000   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
3001   PetscFunctionReturn(0);
3002 }
3003 
3004 #if defined(OLD_ROUTINE_TO_BE_REPLACED)
3005 #undef __FUNCT__
3006 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_newdatastruct"
3007 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx)
3008 {
3009   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
3010   PetscErrorCode    ierr;
3011   PetscInt          n = A->rmap->n;
3012   const PetscInt    *ai = a->i,*aj = a->j,*vi;
3013   PetscScalar       *x,sum;
3014   const PetscScalar *b;
3015   const MatScalar   *aa = a->a,*v;
3016   PetscInt          i,nz;
3017 
3018   PetscFunctionBegin;
3019   if (!n) PetscFunctionReturn(0);
3020 
3021   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3022   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3023 
3024   /* forward solve the lower triangular */
3025   x[0] = b[0];
3026   v    = aa;
3027   vi   = aj;
3028   for (i=1; i<n; i++) {
3029     nz  = ai[i+1] - ai[i];
3030     sum = b[i];
3031     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
3032     v  += nz;
3033     vi += nz;
3034     x[i] = sum;
3035   }
3036 
3037   /* backward solve the upper triangular */
3038   v   = aa + ai[n+1];
3039   vi  = aj + ai[n+1];
3040   for (i=n-1; i>=0; i--){
3041     nz = ai[2*n-i +1] - ai[2*n-i]-1;
3042     sum = x[i];
3043     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
3044     v   += nz;
3045     vi  += nz; vi++;
3046     x[i] = *v++ *sum; /* x[i]=aa[adiag[i]]*sum; v++; */
3047   }
3048 
3049   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
3050   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3051   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3052   PetscFunctionReturn(0);
3053 }
3054 #endif
3055 
3056 #undef __FUNCT__
3057 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_newdatastruct"
3058 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx)
3059 {
3060   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
3061   PetscErrorCode    ierr;
3062   PetscInt          n = A->rmap->n;
3063   const PetscInt    *ai = a->i,*aj = a->j,*adiag = a->diag,*vi;
3064   PetscScalar       *x,sum;
3065   const PetscScalar *b;
3066   const MatScalar   *aa = a->a,*v;
3067   PetscInt          i,nz;
3068 
3069   PetscFunctionBegin;
3070   if (!n) PetscFunctionReturn(0);
3071 
3072   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3073   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3074 
3075   /* forward solve the lower triangular */
3076   x[0] = b[0];
3077   v    = aa;
3078   vi   = aj;
3079   for (i=1; i<n; i++) {
3080     nz  = ai[i+1] - ai[i];
3081     sum = b[i];
3082     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
3083     v  += nz;
3084     vi += nz;
3085     x[i] = sum;
3086   }
3087 
3088   /* backward solve the upper triangular */
3089   for (i=n-1; i>=0; i--){
3090     v   = aa + adiag[i+1] + 1;
3091     vi  = aj + adiag[i+1] + 1;
3092     nz = adiag[i] - adiag[i+1]-1;
3093     sum = x[i];
3094     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
3095     x[i] = sum*v[nz]; /* x[i]=aa[adiag[i]]*sum; v++; */
3096   }
3097 
3098   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
3099   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3100   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3101   PetscFunctionReturn(0);
3102 }
3103 
3104 #if defined(OLD_ROUTINE_TO_BE_REPLACED)
3105 #undef __FUNCT__
3106 #define __FUNCT__ "MatSolve_SeqAIJ_newdatastruct"
3107 PetscErrorCode MatSolve_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec xx)
3108 {
3109   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
3110   IS                iscol = a->col,isrow = a->row;
3111   PetscErrorCode    ierr;
3112   PetscInt          i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,nz,k;
3113   const PetscInt    *rout,*cout,*r,*c;
3114   PetscScalar       *x,*tmp,*tmps,sum;
3115   const PetscScalar *b;
3116   const MatScalar   *aa = a->a,*v;
3117 
3118   PetscFunctionBegin;
3119   if (!n) PetscFunctionReturn(0);
3120 
3121   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3122   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3123   tmp  = a->solve_work;
3124 
3125   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
3126   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
3127 
3128   /* forward solve the lower triangular */
3129   tmp[0] = b[*r++];
3130   tmps   = tmp;
3131   v      = aa;
3132   vi     = aj;
3133   for (i=1; i<n; i++) {
3134     nz  = ai[i+1] - ai[i];
3135     sum = b[*r++];
3136     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
3137     tmp[i] = sum;
3138     v += nz; vi += nz;
3139   }
3140 
3141   /* backward solve the upper triangular */
3142   k  = n+1;
3143   v  = aa + ai[k]; /* 1st entry of U(n-1,:) */
3144   vi = aj + ai[k];
3145   for (i=n-1; i>=0; i--){
3146     k  = 2*n-i;
3147     nz = ai[k +1] - ai[k] - 1;
3148     sum = tmp[i];
3149     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
3150     x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */
3151     v += nz+1; vi += nz+1;
3152   }
3153 
3154   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
3155   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
3156   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3157   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3158   ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr);
3159   PetscFunctionReturn(0);
3160 }
3161 #endif
3162 
3163 #undef __FUNCT__
3164 #define __FUNCT__ "MatSolve_SeqAIJ_newdatastruct"
3165 PetscErrorCode MatSolve_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec xx)
3166 {
3167   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
3168   IS                iscol = a->col,isrow = a->row;
3169   PetscErrorCode    ierr;
3170   PetscInt          i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz;
3171   const PetscInt    *rout,*cout,*r,*c;
3172   PetscScalar       *x,*tmp,sum;
3173   const PetscScalar *b;
3174   const MatScalar   *aa = a->a,*v;
3175 
3176   PetscFunctionBegin;
3177   if (!n) PetscFunctionReturn(0);
3178 
3179   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3180   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3181   tmp  = a->solve_work;
3182 
3183   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
3184   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
3185 
3186   /* forward solve the lower triangular */
3187   tmp[0] = b[r[0]];
3188   v      = aa;
3189   vi     = aj;
3190   for (i=1; i<n; i++) {
3191     nz  = ai[i+1] - ai[i];
3192     sum = b[r[i]];
3193     PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
3194     tmp[i] = sum;
3195     v += nz; vi += nz;
3196   }
3197 
3198   /* backward solve the upper triangular */
3199   for (i=n-1; i>=0; i--){
3200     v   = aa + adiag[i+1]+1;
3201     vi  = aj + adiag[i+1]+1;
3202     nz  = adiag[i]-adiag[i+1]-1;
3203     sum = tmp[i];
3204     PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
3205     x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */
3206   }
3207 
3208   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
3209   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
3210   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3211   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3212   ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr);
3213   PetscFunctionReturn(0);
3214 }
3215 
3216 #undef __FUNCT__
3217 #define __FUNCT__ "MatILUDTFactor_SeqAIJ"
3218 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact)
3219 {
3220   Mat                B = *fact;
3221   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b;
3222   IS                 isicol;
3223   PetscErrorCode     ierr;
3224   const PetscInt     *r,*ic;
3225   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag;
3226   PetscInt           *bi,*bj,*bdiag,*bdiag_rev;
3227   PetscInt           row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au;
3228   PetscInt           nlnk,*lnk;
3229   PetscBT            lnkbt;
3230   PetscTruth         row_identity,icol_identity,both_identity;
3231   MatScalar          *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp;
3232   const PetscInt     *ics;
3233   PetscInt           j,nz,*pj,*bjtmp,k,ncut,*jtmp;
3234   PetscReal          dt=info->dt,dtcol=info->dtcol,shift=info->shiftinblocks;
3235   PetscInt           dtcount=(PetscInt)info->dtcount,nnz_max;
3236   PetscTruth         missing;
3237 
3238   PetscFunctionBegin;
3239 
3240   if (dt      == PETSC_DEFAULT) dt      = 0.005;
3241   if (dtcol   == PETSC_DEFAULT) dtcol   = 0.01; /* XXX unused! */
3242   if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax);
3243 
3244   /* ------- symbolic factorization, can be reused ---------*/
3245   ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
3246   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
3247   adiag=a->diag;
3248 
3249   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
3250 
3251   /* bdiag is location of diagonal in factor */
3252   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);     /* becomes b->diag */
3253   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag_rev);CHKERRQ(ierr); /* temporary */
3254 
3255   /* allocate row pointers bi */
3256   ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
3257 
3258   /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */
3259   if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */
3260   nnz_max  = ai[n]+2*n*dtcount+2;
3261 
3262   ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
3263   ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr);
3264 
3265   /* put together the new matrix */
3266   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
3267   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
3268   b    = (Mat_SeqAIJ*)(B)->data;
3269   b->free_a       = PETSC_TRUE;
3270   b->free_ij      = PETSC_TRUE;
3271   b->singlemalloc = PETSC_FALSE;
3272   b->a          = ba;
3273   b->j          = bj;
3274   b->i          = bi;
3275   b->diag       = bdiag;
3276   b->ilen       = 0;
3277   b->imax       = 0;
3278   b->row        = isrow;
3279   b->col        = iscol;
3280   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
3281   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
3282   b->icol       = isicol;
3283   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
3284 
3285   ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
3286   b->maxnz = nnz_max;
3287 
3288   (B)->factor                = MAT_FACTOR_ILUDT;
3289   (B)->info.factor_mallocs   = 0;
3290   (B)->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]);
3291   CHKMEMQ;
3292   /* ------- end of symbolic factorization ---------*/
3293 
3294   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
3295   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
3296   ics  = ic;
3297 
3298   /* linked list for storing column indices of the active row */
3299   nlnk = n + 1;
3300   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3301 
3302   /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */
3303   ierr = PetscMalloc2(n,PetscInt,&im,n,PetscInt,&jtmp);CHKERRQ(ierr);
3304   /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */
3305   ierr = PetscMalloc2(n,MatScalar,&rtmp,n,MatScalar,&vtmp);CHKERRQ(ierr);
3306   ierr = PetscMemzero(rtmp,n*sizeof(MatScalar));CHKERRQ(ierr);
3307 
3308   bi[0]    = 0;
3309   bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */
3310   bdiag_rev[n] = bdiag[0];
3311   bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */
3312   for (i=0; i<n; i++) {
3313     /* copy initial fill into linked list */
3314     nzi = 0; /* nonzeros for active row i */
3315     nzi = ai[r[i]+1] - ai[r[i]];
3316     if (!nzi) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
3317     nzi_al = adiag[r[i]] - ai[r[i]];
3318     nzi_au = ai[r[i]+1] - adiag[r[i]] -1;
3319     ajtmp = aj + ai[r[i]];
3320     ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3321 
3322     /* load in initial (unfactored row) */
3323     aatmp = a->a + ai[r[i]];
3324     for (j=0; j<nzi; j++) {
3325       rtmp[ics[*ajtmp++]] = *aatmp++;
3326     }
3327 
3328     /* add pivot rows into linked list */
3329     row = lnk[n];
3330     while (row < i ) {
3331       nzi_bl = bi[row+1] - bi[row] + 1;
3332       bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */
3333       ierr  = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr);
3334       nzi  += nlnk;
3335       row   = lnk[row];
3336     }
3337 
3338     /* copy data from lnk into jtmp, then initialize lnk */
3339     ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr);
3340 
3341     /* numerical factorization */
3342     bjtmp = jtmp;
3343     row   = *bjtmp++; /* 1st pivot row */
3344     while  ( row < i ) {
3345       pc         = rtmp + row;
3346       pv         = ba + bdiag[row]; /* 1./(diag of the pivot row) */
3347       multiplier = (*pc) * (*pv);
3348       *pc        = multiplier;
3349       if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */
3350         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
3351         pv         = ba + bdiag[row+1] + 1;
3352         /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */
3353         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
3354         for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
3355         ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
3356       }
3357       row = *bjtmp++;
3358     }
3359 
3360     /* copy sparse rtmp into contiguous vtmp; separate L and U part */
3361     diag_tmp = rtmp[i];  /* save diagonal value - may not needed?? */
3362     nzi_bl = 0; j = 0;
3363     while (jtmp[j] < i){ /* Note: jtmp is sorted */
3364       vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
3365       nzi_bl++; j++;
3366     }
3367     nzi_bu = nzi - nzi_bl -1;
3368     while (j < nzi){
3369       vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
3370       j++;
3371     }
3372 
3373     bjtmp = bj + bi[i];
3374     batmp = ba + bi[i];
3375     /* apply level dropping rule to L part */
3376     ncut = nzi_al + dtcount;
3377     if (ncut < nzi_bl){
3378       ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr);
3379       ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr);
3380     } else {
3381       ncut = nzi_bl;
3382     }
3383     for (j=0; j<ncut; j++){
3384       bjtmp[j] = jtmp[j];
3385       batmp[j] = vtmp[j];
3386       /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */
3387     }
3388     bi[i+1] = bi[i] + ncut;
3389     nzi = ncut + 1;
3390 
3391     /* apply level dropping rule to U part */
3392     ncut = nzi_au + dtcount;
3393     if (ncut < nzi_bu){
3394       ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr);
3395       ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr);
3396     } else {
3397       ncut = nzi_bu;
3398     }
3399     nzi += ncut;
3400 
3401     /* mark bdiagonal */
3402     bdiag[i+1]       = bdiag[i] - (ncut + 1);
3403     bdiag_rev[n-i-1] = bdiag[i+1];
3404     bi[2*n - i]      = bi[2*n - i +1] - (ncut + 1);
3405     bjtmp = bj + bdiag[i];
3406     batmp = ba + bdiag[i];
3407     *bjtmp = i;
3408     *batmp = diag_tmp; /* rtmp[i]; */
3409     if (*batmp == 0.0) {
3410       *batmp = dt+shift;
3411       /* printf(" row %d add shift %g\n",i,shift); */
3412     }
3413     *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */
3414     /* printf(" (%d,%g),",*bjtmp,*batmp); */
3415 
3416     bjtmp = bj + bdiag[i+1]+1;
3417     batmp = ba + bdiag[i+1]+1;
3418     for (k=0; k<ncut; k++){
3419       bjtmp[k] = jtmp[nzi_bl+1+k];
3420       batmp[k] = vtmp[nzi_bl+1+k];
3421       /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */
3422     }
3423     /* printf("\n"); */
3424 
3425     im[i]   = nzi; /* used by PetscLLAddSortedLU() */
3426     /*
3427     printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]);
3428     printf(" ----------------------------\n");
3429     */
3430   } /* for (i=0; i<n; i++) */
3431   /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */
3432   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]);
3433 
3434   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
3435   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
3436 
3437   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
3438   ierr = PetscFree2(im,jtmp);CHKERRQ(ierr);
3439   ierr = PetscFree2(rtmp,vtmp);CHKERRQ(ierr);
3440   ierr = PetscFree(bdiag_rev);CHKERRQ(ierr);
3441 
3442   ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr);
3443   b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n];
3444 
3445   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
3446   ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr);
3447   both_identity = (PetscTruth) (row_identity && icol_identity);
3448   if (row_identity && icol_identity) {
3449     B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct;
3450   } else {
3451     B->ops->solve = MatSolve_SeqAIJ_newdatastruct;
3452   }
3453 
3454   B->ops->lufactorsymbolic  = MatILUDTFactorSymbolic_SeqAIJ;
3455   B->ops->lufactornumeric   = MatILUDTFactorNumeric_SeqAIJ;
3456   B->ops->solveadd          = 0;
3457   B->ops->solvetranspose    = 0;
3458   B->ops->solvetransposeadd = 0;
3459   B->ops->matsolve          = 0;
3460   B->assembled              = PETSC_TRUE;
3461   B->preallocated           = PETSC_TRUE;
3462   PetscFunctionReturn(0);
3463 }
3464 
3465 /* a wraper of MatILUDTFactor_SeqAIJ() */
3466 #undef __FUNCT__
3467 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ"
3468 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info)
3469 {
3470   PetscErrorCode     ierr;
3471 
3472   PetscFunctionBegin;
3473   ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr);
3474 
3475   fact->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ;
3476   PetscFunctionReturn(0);
3477 }
3478 
3479 /*
3480    same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors
3481    - intend to replace existing MatLUFactorNumeric_SeqAIJ()
3482 */
3483 #undef __FUNCT__
3484 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ"
3485 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info)
3486 {
3487   Mat            C=fact;
3488   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
3489   IS             isrow = b->row,isicol = b->icol;
3490   PetscErrorCode ierr;
3491   const PetscInt *r,*ic,*ics;
3492   PetscInt       i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
3493   PetscInt       *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj;
3494   MatScalar      *rtmp,*pc,multiplier,*v,*pv,*aa=a->a;
3495   PetscReal      dt=info->dt,shift=info->shiftinblocks;
3496   PetscTruth     row_identity, col_identity;
3497 
3498   PetscFunctionBegin;
3499   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
3500   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
3501   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
3502   ics  = ic;
3503 
3504   for (i=0; i<n; i++){
3505     /* initialize rtmp array */
3506     nzl   = bi[i+1] - bi[i];       /* num of nozeros in L(i,:) */
3507     bjtmp = bj + bi[i];
3508     for  (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0;
3509     rtmp[i] = 0.0;
3510     nzu   = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */
3511     bjtmp = bj + bdiag[i+1] + 1;
3512     for  (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0;
3513 
3514     /* load in initial unfactored row of A */
3515     /* printf("row %d\n",i); */
3516     nz    = ai[r[i]+1] - ai[r[i]];
3517     ajtmp = aj + ai[r[i]];
3518     v     = aa + ai[r[i]];
3519     for (j=0; j<nz; j++) {
3520       rtmp[ics[*ajtmp++]] = v[j];
3521       /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */
3522     }
3523     /* printf("\n"); */
3524 
3525     /* numerical factorization */
3526     bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */
3527     nzl   = bi[i+1] - bi[i]; /* num of entries in L(i,:) */
3528     k = 0;
3529     while (k < nzl){
3530       row   = *bjtmp++;
3531       /* printf("  prow %d\n",row); */
3532       pc         = rtmp + row;
3533       pv         = b->a + bdiag[row]; /* 1./(diag of the pivot row) */
3534       multiplier = (*pc) * (*pv);
3535       *pc        = multiplier;
3536       if (PetscAbsScalar(multiplier) > dt){
3537         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
3538         pv         = b->a + bdiag[row+1] + 1;
3539         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
3540         for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
3541         /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */
3542       }
3543       k++;
3544     }
3545 
3546     /* finished row so stick it into b->a */
3547     /* L-part */
3548     pv = b->a + bi[i] ;
3549     pj = bj + bi[i] ;
3550     nzl = bi[i+1] - bi[i];
3551     for (j=0; j<nzl; j++) {
3552       pv[j] = rtmp[pj[j]];
3553       /* printf(" (%d,%g),",pj[j],pv[j]); */
3554     }
3555 
3556     /* diagonal: invert diagonal entries for simplier triangular solves */
3557     if (rtmp[i] == 0.0) rtmp[i] = dt+shift;
3558     b->a[bdiag[i]] = 1.0/rtmp[i];
3559     /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */
3560 
3561     /* U-part */
3562     pv = b->a + bdiag[i+1] + 1;
3563     pj = bj + bdiag[i+1] + 1;
3564     nzu = bdiag[i] - bdiag[i+1] - 1;
3565     for (j=0; j<nzu; j++) {
3566       pv[j] = rtmp[pj[j]];
3567       /* printf(" (%d,%g),",pj[j],pv[j]); */
3568     }
3569     /* printf("\n"); */
3570   }
3571 
3572   ierr = PetscFree(rtmp);CHKERRQ(ierr);
3573   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
3574   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
3575 
3576   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
3577   ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
3578   if (row_identity && col_identity) {
3579     C->ops->solve   = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct;
3580   } else {
3581     C->ops->solve   = MatSolve_SeqAIJ_newdatastruct;
3582   }
3583   C->ops->solveadd           = 0;
3584   C->ops->solvetranspose     = 0;
3585   C->ops->solvetransposeadd  = 0;
3586   C->ops->matsolve           = 0;
3587   C->assembled    = PETSC_TRUE;
3588   C->preallocated = PETSC_TRUE;
3589   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
3590   PetscFunctionReturn(0);
3591 }
3592