xref: /petsc/src/mat/impls/aij/seq/aijfact.c (revision ee0bf03dc93d4c7c8a89c171f526ef710b24ee2e)
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_v2;
608   } else {
609     C->ops->solve = MatSolve_SeqAIJ_newdatastruct_v2;
610   }
611 
612   C->ops->solveadd           = 0;
613   C->ops->solvetranspose     = 0;
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__ "MatSolveTranspose_SeqAIJ"
1245 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx)
1246 {
1247   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1248   IS                iscol = a->col,isrow = a->row;
1249   PetscErrorCode    ierr;
1250   const PetscInt    *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi;
1251   PetscInt          i,n = A->rmap->n,j;
1252   PetscInt          nz;
1253   PetscScalar       *x,*tmp,s1;
1254   const MatScalar   *aa = a->a,*v;
1255   const PetscScalar *b;
1256 
1257   PetscFunctionBegin;
1258   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1259   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1260   tmp  = a->solve_work;
1261 
1262   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1263   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1264 
1265   /* copy the b into temp work space according to permutation */
1266   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1267 
1268   /* forward solve the U^T */
1269   for (i=0; i<n; i++) {
1270     v   = aa + diag[i] ;
1271     vi  = aj + diag[i] + 1;
1272     nz  = ai[i+1] - diag[i] - 1;
1273     s1  = tmp[i];
1274     s1 *= (*v++);  /* multiply by inverse of diagonal entry */
1275     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1276     tmp[i] = s1;
1277   }
1278 
1279   /* backward solve the L^T */
1280   for (i=n-1; i>=0; i--){
1281     v   = aa + diag[i] - 1 ;
1282     vi  = aj + diag[i] - 1 ;
1283     nz  = diag[i] - ai[i];
1284     s1  = tmp[i];
1285     for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j];
1286   }
1287 
1288   /* copy tmp into x according to permutation */
1289   for (i=0; i<n; i++) x[r[i]] = tmp[i];
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 
1296   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1297   PetscFunctionReturn(0);
1298 }
1299 
1300 #undef __FUNCT__
1301 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ"
1302 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,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   if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);}
1316   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1317   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1318   tmp  = a->solve_work;
1319 
1320   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1321   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1322 
1323   /* copy the b into temp work space according to permutation */
1324   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1325 
1326   /* forward solve the U^T */
1327   for (i=0; i<n; i++) {
1328     v   = aa + diag[i] ;
1329     vi  = aj + diag[i] + 1;
1330     nz  = ai[i+1] - diag[i] - 1;
1331     s1  = tmp[i];
1332     s1 *= (*v++);  /* multiply by inverse of diagonal entry */
1333     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1334     tmp[i] = s1;
1335   }
1336 
1337   /* backward solve the L^T */
1338   for (i=n-1; i>=0; i--){
1339     v   = aa + diag[i] - 1 ;
1340     vi  = aj + diag[i] - 1 ;
1341     nz  = diag[i] - ai[i];
1342     s1  = tmp[i];
1343     for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j];
1344   }
1345 
1346   /* copy tmp into x according to permutation */
1347   for (i=0; i<n; i++) x[r[i]] += tmp[i];
1348 
1349   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1350   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1351   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1352   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1353 
1354   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1355   PetscFunctionReturn(0);
1356 }
1357 
1358 /* ----------------------------------------------------------------*/
1359 EXTERN PetscErrorCode Mat_CheckInode(Mat,PetscTruth);
1360 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption,PetscTruth);
1361 
1362 /*
1363    ilu() under revised new data structure.
1364    Factored arrays bj and ba are stored as
1365      L(0,:), L(1,:), ...,L(n-1,:),  U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:)
1366 
1367    bi=fact->i is an array of size n+1, in which
1368    bi+
1369      bi[i]:  points to 1st entry of L(i,:),i=0,...,n-1
1370      bi[n]:  points to L(n-1,n-1)+1
1371 
1372   bdiag=fact->diag is an array of size n+1,in which
1373      bdiag[i]: points to diagonal of U(i,:), i=0,...,n-1
1374      bdiag[n]: points to diagonal of U(n-1,0)-1
1375 
1376    U(i,:) contains bdiag[i] as its last entry, i.e.,
1377     U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i])
1378 */
1379 #undef __FUNCT__
1380 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct"
1381 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1382 {
1383 
1384   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1385   PetscErrorCode     ierr;
1386   PetscInt           n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag;
1387   PetscInt           i,j,nz,*bi,*bj,*bdiag,bi_temp;
1388   PetscTruth         missing;
1389   IS                 isicol;
1390 
1391   PetscFunctionBegin;
1392   /* printf("MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct ...\n"); */
1393   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);
1394   ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
1395   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
1396   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1397 
1398   ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr);
1399   b    = (Mat_SeqAIJ*)(fact)->data;
1400 
1401   /* allocate matrix arrays for new data structure */
1402   ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,n+1,PetscInt,&b->i);CHKERRQ(ierr);
1403   ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));CHKERRQ(ierr);
1404   b->singlemalloc = PETSC_TRUE;
1405   if (!b->diag){
1406     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr);
1407     ierr = PetscLogObjectMemory(fact,(n+1)*sizeof(PetscInt));CHKERRQ(ierr);
1408   }
1409   bdiag = b->diag;
1410 
1411   if (n > 0) {
1412     ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr);
1413   }
1414 
1415   /* set bi and bj with new data structure */
1416   bi = b->i;
1417   bj = b->j;
1418 
1419   /* L part */
1420   bi[0] = 0;
1421   for (i=0; i<n; i++){
1422     nz = adiag[i] - ai[i];
1423     bi[i+1] = bi[i] + nz;
1424     aj = a->j + ai[i];
1425     for (j=0; j<nz; j++){
1426       *bj = aj[j]; bj++;
1427     }
1428   }
1429 
1430   /* U part */
1431   bi_temp = bi[n];
1432   bdiag[n] = bi[n]-1;
1433   for (i=n-1; i>=0; i--){
1434     nz = ai[i+1] - adiag[i] - 1;
1435     bi_temp = bi_temp + nz + 1;
1436     aj = a->j + adiag[i] + 1;
1437     for (j=0; j<nz; j++){
1438       *bj = aj[j]; bj++;
1439     }
1440     /* diag[i] */
1441     *bj = i; bj++;
1442     bdiag[i] = bi_temp - 1;
1443   }
1444 
1445   fact->factor                 = MAT_FACTOR_ILU;
1446   fact->info.factor_mallocs    = 0;
1447   fact->info.fill_ratio_given  = info->fill;
1448   fact->info.fill_ratio_needed = 1.0;
1449   fact->ops->lufactornumeric   = MatLUFactorNumeric_SeqAIJ_newdatastruct;
1450 
1451   b       = (Mat_SeqAIJ*)(fact)->data;
1452   b->row  = isrow;
1453   b->col  = iscol;
1454   b->icol = isicol;
1455   ierr    = PetscMalloc((fact->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1456   ierr    = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1457   ierr    = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1458   PetscFunctionReturn(0);
1459 }
1460 
1461 #undef __FUNCT__
1462 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_newdatastruct"
1463 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1464 {
1465   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1466   IS                 isicol;
1467   PetscErrorCode     ierr;
1468   const PetscInt     *r,*ic;
1469   PetscInt           n=A->rmap->n,*ai=a->i,*aj=a->j;
1470   PetscInt           *bi,*cols,nnz,*cols_lvl;
1471   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1472   PetscInt           i,levels,diagonal_fill;
1473   PetscTruth         col_identity,row_identity;
1474   PetscReal          f;
1475   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
1476   PetscBT            lnkbt;
1477   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
1478   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1479   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1480 
1481   PetscFunctionBegin;
1482   /* printf("MatILUFactorSymbolic_SeqAIJ_newdatastruct ...\n"); */
1483   levels = (PetscInt)info->levels;
1484   ierr   = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1485   ierr   = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
1486 
1487   if (!levels && row_identity && col_identity) {
1488     /* special case: ilu(0) with natural ordering */
1489     ierr = MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1490     PetscFunctionReturn(0);
1491   }
1492 
1493   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);
1494   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1495   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1496   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1497 
1498   /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
1499   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1500   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
1501   bi[0] = bdiag[0] = 0;
1502 
1503   ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr);
1504 
1505   /* create a linked list for storing column indices of the active row */
1506   nlnk = n + 1;
1507   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1508 
1509   /* initial FreeSpace size is f*(ai[n]+1) */
1510   f             = info->fill;
1511   diagonal_fill = (PetscInt)info->diagonal_fill;
1512   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
1513   current_space = free_space;
1514   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
1515   current_space_lvl = free_space_lvl;
1516 
1517   for (i=0; i<n; i++) {
1518     nzi = 0;
1519     /* copy current row into linked list */
1520     nnz  = ai[r[i]+1] - ai[r[i]];
1521     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1522     cols = aj + ai[r[i]];
1523     lnk[i] = -1; /* marker to indicate if diagonal exists */
1524     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1525     nzi += nlnk;
1526 
1527     /* make sure diagonal entry is included */
1528     if (diagonal_fill && lnk[i] == -1) {
1529       fm = n;
1530       while (lnk[fm] < i) fm = lnk[fm];
1531       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
1532       lnk[fm]    = i;
1533       lnk_lvl[i] = 0;
1534       nzi++; dcount++;
1535     }
1536 
1537     /* add pivot rows into the active row */
1538     nzbd = 0;
1539     prow = lnk[n];
1540     while (prow < i) {
1541       nnz      = bdiag[prow];
1542       cols     = bj_ptr[prow] + nnz + 1;
1543       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1544       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
1545       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
1546       nzi += nlnk;
1547       prow = lnk[prow];
1548       nzbd++;
1549     }
1550     bdiag[i] = nzbd;
1551     bi[i+1]  = bi[i] + nzi;
1552 
1553     /* if free space is not available, make more free space */
1554     if (current_space->local_remaining<nzi) {
1555       nnz = 2*nzi*(n - i); /* estimated and max additional space needed */
1556       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
1557       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
1558       reallocs++;
1559     }
1560 
1561     /* copy data into free_space and free_space_lvl, then initialize lnk */
1562     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1563     bj_ptr[i]    = current_space->array;
1564     bjlvl_ptr[i] = current_space_lvl->array;
1565 
1566     /* make sure the active row i has diagonal entry */
1567     if (*(bj_ptr[i]+bdiag[i]) != i) {
1568       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
1569     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
1570     }
1571 
1572     current_space->array           += nzi;
1573     current_space->local_used      += nzi;
1574     current_space->local_remaining -= nzi;
1575     current_space_lvl->array           += nzi;
1576     current_space_lvl->local_used      += nzi;
1577     current_space_lvl->local_remaining -= nzi;
1578   }
1579 
1580   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1581   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1582 
1583   /* destroy list of free space and other temporary arrays */
1584   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
1585 
1586   /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */
1587   ierr = PetscFreeSpaceContiguous_LU_v2(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr);
1588 
1589   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1590   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
1591   ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr);
1592 
1593 #if defined(PETSC_USE_INFO)
1594   {
1595     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1596     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
1597     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
1598     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
1599     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
1600     if (diagonal_fill) {
1601       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
1602     }
1603   }
1604 #endif
1605 
1606   /* put together the new matrix */
1607   ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
1608   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
1609   b = (Mat_SeqAIJ*)(fact)->data;
1610   b->free_a       = PETSC_TRUE;
1611   b->free_ij      = PETSC_TRUE;
1612   b->singlemalloc = PETSC_FALSE;
1613   ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
1614   b->j          = bj;
1615   b->i          = bi;
1616   b->diag       = bdiag;
1617   b->ilen       = 0;
1618   b->imax       = 0;
1619   b->row        = isrow;
1620   b->col        = iscol;
1621   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1622   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1623   b->icol       = isicol;
1624   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1625   /* In b structure:  Free imax, ilen, old a, old j.
1626      Allocate bdiag, solve_work, new a, new j */
1627   ierr = PetscLogObjectMemory(fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
1628   b->maxnz = b->nz = bdiag[0]+1;
1629   (fact)->info.factor_mallocs    = reallocs;
1630   (fact)->info.fill_ratio_given  = f;
1631   (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]);
1632   (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct;
1633   /* ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */
1634   PetscFunctionReturn(0);
1635 }
1636 
1637 #undef __FUNCT__
1638 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ"
1639 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1640 {
1641   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1642   IS                 isicol;
1643   PetscErrorCode     ierr;
1644   const PetscInt     *r,*ic;
1645   PetscInt           n=A->rmap->n,*ai=a->i,*aj=a->j,d;
1646   PetscInt           *bi,*cols,nnz,*cols_lvl;
1647   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1648   PetscInt           i,levels,diagonal_fill;
1649   PetscTruth         col_identity,row_identity;
1650   PetscReal          f;
1651   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
1652   PetscBT            lnkbt;
1653   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
1654   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1655   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1656   PetscTruth         missing;
1657   PetscTruth         newdatastruct=PETSC_FALSE;
1658 
1659   PetscFunctionBegin;
1660   ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
1661   if(newdatastruct){
1662     ierr = MatILUFactorSymbolic_SeqAIJ_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1663     PetscFunctionReturn(0);
1664   }
1665 
1666   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);
1667   f             = info->fill;
1668   levels        = (PetscInt)info->levels;
1669   diagonal_fill = (PetscInt)info->diagonal_fill;
1670   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1671 
1672   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1673   ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
1674   if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */
1675     ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr);
1676     (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ;
1677 
1678     fact->factor = MAT_FACTOR_ILU;
1679     (fact)->info.factor_mallocs    = 0;
1680     (fact)->info.fill_ratio_given  = info->fill;
1681     (fact)->info.fill_ratio_needed = 1.0;
1682     b               = (Mat_SeqAIJ*)(fact)->data;
1683     ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
1684     if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
1685     b->row              = isrow;
1686     b->col              = iscol;
1687     b->icol             = isicol;
1688     ierr                = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1689     ierr                = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1690     ierr                = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1691     ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1692     PetscFunctionReturn(0);
1693   }
1694 
1695   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1696   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1697 
1698   /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
1699   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1700   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
1701   bi[0] = bdiag[0] = 0;
1702 
1703   ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr);
1704 
1705   /* create a linked list for storing column indices of the active row */
1706   nlnk = n + 1;
1707   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1708 
1709   /* initial FreeSpace size is f*(ai[n]+1) */
1710   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
1711   current_space = free_space;
1712   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
1713   current_space_lvl = free_space_lvl;
1714 
1715   for (i=0; i<n; i++) {
1716     nzi = 0;
1717     /* copy current row into linked list */
1718     nnz  = ai[r[i]+1] - ai[r[i]];
1719     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1720     cols = aj + ai[r[i]];
1721     lnk[i] = -1; /* marker to indicate if diagonal exists */
1722     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1723     nzi += nlnk;
1724 
1725     /* make sure diagonal entry is included */
1726     if (diagonal_fill && lnk[i] == -1) {
1727       fm = n;
1728       while (lnk[fm] < i) fm = lnk[fm];
1729       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
1730       lnk[fm]    = i;
1731       lnk_lvl[i] = 0;
1732       nzi++; dcount++;
1733     }
1734 
1735     /* add pivot rows into the active row */
1736     nzbd = 0;
1737     prow = lnk[n];
1738     while (prow < i) {
1739       nnz      = bdiag[prow];
1740       cols     = bj_ptr[prow] + nnz + 1;
1741       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1742       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
1743       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
1744       nzi += nlnk;
1745       prow = lnk[prow];
1746       nzbd++;
1747     }
1748     bdiag[i] = nzbd;
1749     bi[i+1]  = bi[i] + nzi;
1750 
1751     /* if free space is not available, make more free space */
1752     if (current_space->local_remaining<nzi) {
1753       nnz = nzi*(n - i); /* estimated and max additional space needed */
1754       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
1755       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
1756       reallocs++;
1757     }
1758 
1759     /* copy data into free_space and free_space_lvl, then initialize lnk */
1760     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1761     bj_ptr[i]    = current_space->array;
1762     bjlvl_ptr[i] = current_space_lvl->array;
1763 
1764     /* make sure the active row i has diagonal entry */
1765     if (*(bj_ptr[i]+bdiag[i]) != i) {
1766       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
1767     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
1768     }
1769 
1770     current_space->array           += nzi;
1771     current_space->local_used      += nzi;
1772     current_space->local_remaining -= nzi;
1773     current_space_lvl->array           += nzi;
1774     current_space_lvl->local_used      += nzi;
1775     current_space_lvl->local_remaining -= nzi;
1776   }
1777 
1778   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1779   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1780 
1781   /* destroy list of free space and other temporary arrays */
1782   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
1783   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */
1784   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1785   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
1786   ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr);
1787 
1788 #if defined(PETSC_USE_INFO)
1789   {
1790     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1791     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
1792     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
1793     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
1794     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
1795     if (diagonal_fill) {
1796       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
1797     }
1798   }
1799 #endif
1800 
1801   /* put together the new matrix */
1802   ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
1803   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
1804   b = (Mat_SeqAIJ*)(fact)->data;
1805   b->free_a       = PETSC_TRUE;
1806   b->free_ij      = PETSC_TRUE;
1807   b->singlemalloc = PETSC_FALSE;
1808   ierr = PetscMalloc(bi[n]*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
1809   b->j          = bj;
1810   b->i          = bi;
1811   for (i=0; i<n; i++) bdiag[i] += bi[i];
1812   b->diag       = bdiag;
1813   b->ilen       = 0;
1814   b->imax       = 0;
1815   b->row        = isrow;
1816   b->col        = iscol;
1817   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1818   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1819   b->icol       = isicol;
1820   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1821   /* In b structure:  Free imax, ilen, old a, old j.
1822      Allocate bdiag, solve_work, new a, new j */
1823   ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
1824   b->maxnz             = b->nz = bi[n] ;
1825   (fact)->info.factor_mallocs    = reallocs;
1826   (fact)->info.fill_ratio_given  = f;
1827   (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1828   (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ;
1829   ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1830   PetscFunctionReturn(0);
1831 }
1832 
1833 #undef __FUNCT__
1834 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ_newdatastruct"
1835 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info)
1836 {
1837   Mat            C = B;
1838   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1839   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
1840   IS             ip=b->row,iip = b->icol;
1841   PetscErrorCode ierr;
1842   const PetscInt *rip,*riip;
1843   PetscInt       i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp;
1844   PetscInt       *ai=a->i,*aj=a->j;
1845   PetscInt       k,jmin,jmax,*c2r,*il,col,nexti,ili,nz;
1846   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
1847   PetscTruth     perm_identity;
1848 
1849   LUShift_Ctx    sctx;
1850   PetscInt       newshift;
1851   PetscReal      rs;
1852   MatScalar      d,*v;
1853 
1854   PetscFunctionBegin;
1855   /* MatPivotSetUp(): initialize shift context sctx */
1856   ierr = PetscMemzero(&sctx,sizeof(LUShift_Ctx));CHKERRQ(ierr);
1857 
1858   /* if both shift schemes are chosen by user, only use info->shiftpd */
1859   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
1860     sctx.shift_top = info->zeropivot;
1861     for (i=0; i<mbs; i++) {
1862       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
1863       d  = (aa)[a->diag[i]];
1864       rs = -PetscAbsScalar(d) - PetscRealPart(d);
1865       v  = aa+ai[i];
1866       nz = ai[i+1] - ai[i];
1867       for (j=0; j<nz; j++)
1868 	rs += PetscAbsScalar(v[j]);
1869       if (rs>sctx.shift_top) sctx.shift_top = rs;
1870     }
1871     sctx.shift_top   *= 1.1;
1872     sctx.nshift_max   = 5;
1873     sctx.shift_lo     = 0.;
1874     sctx.shift_hi     = 1.;
1875   }
1876 
1877   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
1878   ierr  = ISGetIndices(iip,&riip);CHKERRQ(ierr);
1879 
1880   /* allocate working arrays
1881      c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col
1882      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
1883   */
1884   ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&c2r);CHKERRQ(ierr);
1885 
1886   do {
1887     sctx.lushift = PETSC_FALSE;
1888 
1889     for (i=0; i<mbs; i++) c2r[i] = mbs;
1890     il[0] = 0;
1891 
1892     for (k = 0; k<mbs; k++){
1893       /* zero rtmp */
1894       nz = bi[k+1] - bi[k];
1895       bjtmp = bj + bi[k];
1896       for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
1897 
1898       /* load in initial unfactored row */
1899       bval = ba + bi[k];
1900       jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
1901       for (j = jmin; j < jmax; j++){
1902         col = riip[aj[j]];
1903         if (col >= k){ /* only take upper triangular entry */
1904           rtmp[col] = aa[j];
1905           *bval++   = 0.0; /* for in-place factorization */
1906         }
1907       }
1908       /* shift the diagonal of the matrix: ZeropivotApply() */
1909       rtmp[k] += sctx.shift_amount;  /* shift the diagonal of the matrix */
1910 
1911       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
1912       dk = rtmp[k];
1913       i  = c2r[k]; /* first row to be added to k_th row  */
1914 
1915       while (i < k){
1916         nexti = c2r[i]; /* next row to be added to k_th row */
1917 
1918         /* compute multiplier, update diag(k) and U(i,k) */
1919         ili   = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
1920         uikdi = - ba[ili]*ba[bdiag[i]];  /* diagonal(k) */
1921         dk   += uikdi*ba[ili]; /* update diag[k] */
1922         ba[ili] = uikdi; /* -U(i,k) */
1923 
1924         /* add multiple of row i to k-th row */
1925         jmin = ili + 1; jmax = bi[i+1];
1926         if (jmin < jmax){
1927           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
1928           /* update il and c2r for row i */
1929           il[i] = jmin;
1930           j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i;
1931         }
1932         i = nexti;
1933       }
1934 
1935       /* copy data into U(k,:) */
1936       rs   = 0.0;
1937       jmin = bi[k]; jmax = bi[k+1]-1;
1938       if (jmin < jmax) {
1939         for (j=jmin; j<jmax; j++){
1940           col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]);
1941         }
1942         /* add the k-th row into il and c2r */
1943         il[k] = jmin;
1944         i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k;
1945       }
1946 
1947       /* MatPivotCheck() */
1948       sctx.rs  = rs;
1949       sctx.pv  = dk;
1950       if (info->shiftnz){
1951         ierr = MatPivotCheck_nz(info,sctx,k,newshift);CHKERRQ(ierr);
1952       } else if (info->shiftpd){
1953         ierr = MatPivotCheck_pd(info,sctx,k,newshift);CHKERRQ(ierr);
1954       } else if (info->shiftinblocks){
1955         ierr = MatPivotCheck_inblocks(info,sctx,k,newshift);CHKERRQ(ierr);
1956       } else {
1957         ierr = MatPivotCheck_none(info,sctx,k,newshift);CHKERRQ(ierr);
1958       }
1959       dk = sctx.pv;
1960       if (newshift == 1) break;
1961 
1962       ba[bdiag[k]] = 1.0/dk; /* U(k,k) */
1963     }
1964   } while (sctx.lushift);
1965 
1966   ierr = PetscFree3(rtmp,il,c2r);CHKERRQ(ierr);
1967   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
1968   ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr);
1969 
1970   ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
1971   if (perm_identity){
1972     (B)->ops->solve           = MatSolve_SeqSBAIJ_1_NaturalOrdering_newdatastruct;
1973     (B)->ops->solvetranspose  = 0;
1974     (B)->ops->forwardsolve    = 0;
1975     (B)->ops->backwardsolve   = 0;
1976   } else {
1977     (B)->ops->solve           = MatSolve_SeqSBAIJ_1_newdatastruct;
1978     (B)->ops->solvetranspose  = 0;
1979     (B)->ops->forwardsolve    = 0;
1980     (B)->ops->backwardsolve   = 0;
1981   }
1982 
1983   C->assembled    = PETSC_TRUE;
1984   C->preallocated = PETSC_TRUE;
1985   ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr);
1986 
1987   /* MatPivotView() */
1988   if (sctx.nshift){
1989     if (info->shiftpd) {
1990       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);
1991     } else if (info->shiftnz) {
1992       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
1993     } else if (info->shiftinblocks){
1994       ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftinblocks);CHKERRQ(ierr);
1995     }
1996   }
1997   PetscFunctionReturn(0);
1998 }
1999 
2000 #undef __FUNCT__
2001 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ"
2002 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info)
2003 {
2004   Mat            C = B;
2005   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
2006   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
2007   IS             ip=b->row,iip = b->icol;
2008   PetscErrorCode ierr;
2009   const PetscInt *rip,*riip;
2010   PetscInt       i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol,*bjtmp;
2011   PetscInt       *ai=a->i,*aj=a->j;
2012   PetscInt       k,jmin,jmax,*jl,*il,col,nexti,ili,nz;
2013   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
2014   PetscReal      zeropivot,rs,shiftnz;
2015   PetscReal      shiftpd;
2016   ChShift_Ctx    sctx;
2017   PetscInt       newshift;
2018   PetscTruth     perm_identity;
2019 
2020   PetscFunctionBegin;
2021   shiftnz   = info->shiftnz;
2022   shiftpd   = info->shiftpd;
2023   zeropivot = info->zeropivot;
2024 
2025   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
2026   ierr  = ISGetIndices(iip,&riip);CHKERRQ(ierr);
2027 
2028   /* initialization */
2029   ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&jl);CHKERRQ(ierr);
2030   sctx.shift_amount = 0;
2031   sctx.nshift       = 0;
2032   do {
2033     sctx.chshift = PETSC_FALSE;
2034     for (i=0; i<mbs; i++) jl[i] = mbs;
2035     il[0] = 0;
2036 
2037     for (k = 0; k<mbs; k++){
2038       /* zero rtmp */
2039       nz = bi[k+1] - bi[k];
2040       bjtmp = bj + bi[k];
2041       for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
2042 
2043       bval = ba + bi[k];
2044       /* initialize k-th row by the perm[k]-th row of A */
2045       jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2046       for (j = jmin; j < jmax; j++){
2047         col = riip[aj[j]];
2048         if (col >= k){ /* only take upper triangular entry */
2049           rtmp[col] = aa[j];
2050           *bval++  = 0.0; /* for in-place factorization */
2051         }
2052       }
2053       /* shift the diagonal of the matrix */
2054       if (sctx.nshift) rtmp[k] += sctx.shift_amount;
2055 
2056       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
2057       dk = rtmp[k];
2058       i = jl[k]; /* first row to be added to k_th row  */
2059 
2060       while (i < k){
2061         nexti = jl[i]; /* next row to be added to k_th row */
2062 
2063         /* compute multiplier, update diag(k) and U(i,k) */
2064         ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2065         uikdi = - ba[ili]*ba[bi[i]];  /* diagonal(k) */
2066         dk += uikdi*ba[ili];
2067         ba[ili] = uikdi; /* -U(i,k) */
2068 
2069         /* add multiple of row i to k-th row */
2070         jmin = ili + 1; jmax = bi[i+1];
2071         if (jmin < jmax){
2072           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2073           /* update il and jl for row i */
2074           il[i] = jmin;
2075           j = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
2076         }
2077         i = nexti;
2078       }
2079 
2080       /* shift the diagonals when zero pivot is detected */
2081       /* compute rs=sum of abs(off-diagonal) */
2082       rs   = 0.0;
2083       jmin = bi[k]+1;
2084       nz   = bi[k+1] - jmin;
2085       bcol = bj + jmin;
2086       for (j=0; j<nz; j++) {
2087         rs += PetscAbsScalar(rtmp[bcol[j]]);
2088       }
2089 
2090       sctx.rs = rs;
2091       sctx.pv = dk;
2092       ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr);
2093 
2094       if (newshift == 1) {
2095         if (!sctx.shift_amount) {
2096           sctx.shift_amount = 1e-5;
2097         }
2098         break;
2099       }
2100 
2101       /* copy data into U(k,:) */
2102       ba[bi[k]] = 1.0/dk; /* U(k,k) */
2103       jmin = bi[k]+1; jmax = bi[k+1];
2104       if (jmin < jmax) {
2105         for (j=jmin; j<jmax; j++){
2106           col = bj[j]; ba[j] = rtmp[col]; rtmp[col] = 0.0;
2107         }
2108         /* add the k-th row into il and jl */
2109         il[k] = jmin;
2110         i = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
2111       }
2112     }
2113   } while (sctx.chshift);
2114   ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr);
2115   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2116   ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr);
2117 
2118   ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
2119   if (perm_identity){
2120     (B)->ops->solve           = MatSolve_SeqSBAIJ_1_NaturalOrdering;
2121     (B)->ops->solvetranspose  = MatSolve_SeqSBAIJ_1_NaturalOrdering;
2122     (B)->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering;
2123     (B)->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering;
2124   } else {
2125     (B)->ops->solve           = MatSolve_SeqSBAIJ_1;
2126     (B)->ops->solvetranspose  = MatSolve_SeqSBAIJ_1;
2127     (B)->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1;
2128     (B)->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1;
2129   }
2130 
2131   C->assembled    = PETSC_TRUE;
2132   C->preallocated = PETSC_TRUE;
2133   ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr);
2134   if (sctx.nshift){
2135     if (shiftnz) {
2136       ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2137     } else if (shiftpd) {
2138       ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2139     }
2140   }
2141   PetscFunctionReturn(0);
2142 }
2143 
2144 /*
2145    icc() under revised new data structure.
2146    Factored arrays bj and ba are stored as
2147      U(0,:),...,U(i,:),U(n-1,:)
2148 
2149    ui=fact->i is an array of size n+1, in which
2150    ui+
2151      ui[i]:  points to 1st entry of U(i,:),i=0,...,n-1
2152      ui[n]:  points to U(n-1,n-1)+1
2153 
2154   udiag=fact->diag is an array of size n,in which
2155      udiag[i]: points to diagonal of U(i,:), i=0,...,n-1
2156 
2157    U(i,:) contains udiag[i] as its last entry, i.e.,
2158     U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i])
2159 */
2160 
2161 #undef __FUNCT__
2162 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ_newdatastruct"
2163 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2164 {
2165   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2166   Mat_SeqSBAIJ       *b;
2167   PetscErrorCode     ierr;
2168   PetscTruth         perm_identity,missing;
2169   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag;
2170   const PetscInt     *rip,*riip;
2171   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
2172   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL,d;
2173   PetscInt           ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
2174   PetscReal          fill=info->fill,levels=info->levels;
2175   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2176   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
2177   PetscBT            lnkbt;
2178   IS                 iperm;
2179 
2180   PetscFunctionBegin;
2181   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);
2182   ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
2183   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
2184   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2185   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2186 
2187   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2188   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2189   ui[0] = 0;
2190 
2191   /* ICC(0) without matrix ordering: simply rearrange column indices */
2192   if (!levels && perm_identity) {
2193     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2194     cols = uj;
2195     for (i=0; i<am; i++) {
2196       ncols    = ai[i+1] - a->diag[i];
2197       ui[i+1]  = ui[i] + ncols;
2198       udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */
2199 
2200       aj   = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */
2201       ncols--; /* exclude diagonal */
2202       for (j=0; j<ncols; j++) *cols++ = aj[j];
2203       *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */
2204     }
2205   } else { /* case: levels>0 || (levels=0 && !perm_identity) */
2206     ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2207     ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2208 
2209     /* initialization */
2210     ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr);
2211 
2212     /* jl: linked list for storing indices of the pivot rows
2213        il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2214     ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr);
2215     for (i=0; i<am; i++){
2216       jl[i] = am; il[i] = 0;
2217     }
2218 
2219     /* create and initialize a linked list for storing column indices of the active row k */
2220     nlnk = am + 1;
2221     ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2222 
2223     /* initial FreeSpace size is fill*(ai[am]+1) */
2224     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2225     current_space = free_space;
2226     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr);
2227     current_space_lvl = free_space_lvl;
2228 
2229     for (k=0; k<am; k++){  /* for each active row k */
2230       /* initialize lnk by the column indices of row rip[k] of A */
2231       nzk   = 0;
2232       ncols = ai[rip[k]+1] - ai[rip[k]];
2233       if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2234       ncols_upper = 0;
2235       for (j=0; j<ncols; j++){
2236         i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2237         if (riip[i] >= k){ /* only take upper triangular entry */
2238           ajtmp[ncols_upper] = i;
2239           ncols_upper++;
2240         }
2241       }
2242       ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2243       nzk += nlnk;
2244 
2245       /* update lnk by computing fill-in for each pivot row to be merged in */
2246       prow = jl[k]; /* 1st pivot row */
2247 
2248       while (prow < k){
2249         nextprow = jl[prow];
2250 
2251         /* merge prow into k-th row */
2252         jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2253         jmax = ui[prow+1];
2254         ncols = jmax-jmin;
2255         i     = jmin - ui[prow];
2256         cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2257         uj    = uj_lvl_ptr[prow] + i; /* levels of cols */
2258         j     = *(uj - 1);
2259         ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr);
2260         nzk += nlnk;
2261 
2262         /* update il and jl for prow */
2263         if (jmin < jmax){
2264           il[prow] = jmin;
2265           j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2266         }
2267         prow = nextprow;
2268       }
2269 
2270       /* if free space is not available, make more free space */
2271       if (current_space->local_remaining<nzk) {
2272         i = am - k + 1; /* num of unfactored rows */
2273         i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2274         ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2275         ierr = PetscFreeSpaceGet(i,&current_space_lvl);CHKERRQ(ierr);
2276         reallocs++;
2277       }
2278 
2279       /* copy data into free_space and free_space_lvl, then initialize lnk */
2280       if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2281       ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
2282 
2283       /* add the k-th row into il and jl */
2284       if (nzk > 1){
2285         i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2286         jl[k] = jl[i]; jl[i] = k;
2287         il[k] = ui[k] + 1;
2288       }
2289       uj_ptr[k]     = current_space->array;
2290       uj_lvl_ptr[k] = current_space_lvl->array;
2291 
2292       current_space->array           += nzk;
2293       current_space->local_used      += nzk;
2294       current_space->local_remaining -= nzk;
2295 
2296       current_space_lvl->array           += nzk;
2297       current_space_lvl->local_used      += nzk;
2298       current_space_lvl->local_remaining -= nzk;
2299 
2300       ui[k+1] = ui[k] + nzk;
2301     }
2302 
2303 #if defined(PETSC_USE_INFO)
2304     if (ai[am] != 0) {
2305       PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]);
2306       ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2307       ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2308       ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2309     } else {
2310       ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2311     }
2312 #endif
2313 
2314     ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2315     ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2316     ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr);
2317     ierr = PetscFree(ajtmp);CHKERRQ(ierr);
2318 
2319     /* destroy list of free space and other temporary array(s) */
2320     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2321     ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor in newdatastruct */
2322     ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2323     ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2324 
2325   } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2326 
2327   /* put together the new matrix in MATSEQSBAIJ format */
2328 
2329   b    = (Mat_SeqSBAIJ*)(fact)->data;
2330   b->singlemalloc = PETSC_FALSE;
2331   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2332   b->j    = uj;
2333   b->i    = ui;
2334   b->diag = udiag;
2335   b->free_diag = PETSC_TRUE;
2336   b->ilen = 0;
2337   b->imax = 0;
2338   b->row  = perm;
2339   b->col  = perm;
2340   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2341   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2342   b->icol = iperm;
2343   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2344   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2345   ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2346   b->maxnz   = b->nz = ui[am];
2347   b->free_a  = PETSC_TRUE;
2348   b->free_ij = PETSC_TRUE;
2349 
2350   (fact)->info.factor_mallocs    = reallocs;
2351   (fact)->info.fill_ratio_given  = fill;
2352   if (ai[am] != 0) {
2353     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2354   } else {
2355     (fact)->info.fill_ratio_needed = 0.0;
2356   }
2357   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_newdatastruct;
2358   PetscFunctionReturn(0);
2359 }
2360 
2361 #undef __FUNCT__
2362 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ"
2363 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2364 {
2365   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2366   Mat_SeqSBAIJ       *b;
2367   PetscErrorCode     ierr;
2368   PetscTruth         perm_identity,missing;
2369   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag;
2370   const PetscInt     *rip,*riip;
2371   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
2372   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL,d;
2373   PetscInt           ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
2374   PetscReal          fill=info->fill,levels=info->levels;
2375   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2376   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
2377   PetscBT            lnkbt;
2378   IS                 iperm;
2379   PetscTruth         newdatastruct=PETSC_FALSE;
2380 
2381   PetscFunctionBegin;
2382   ierr = PetscOptionsGetTruth(PETSC_NULL,"-icc_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
2383   if(newdatastruct){
2384     ierr = MatICCFactorSymbolic_SeqAIJ_newdatastruct(fact,A,perm,info);CHKERRQ(ierr);
2385     PetscFunctionReturn(0);
2386   }
2387 
2388   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);
2389   ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
2390   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
2391   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2392   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2393 
2394   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2395   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2396   ui[0] = 0;
2397 
2398   /* ICC(0) without matrix ordering: simply copies fill pattern */
2399   if (!levels && perm_identity) {
2400 
2401     for (i=0; i<am; i++) {
2402       ui[i+1]  = ui[i] + ai[i+1] - a->diag[i];
2403       udiag[i] = ui[i];
2404     }
2405     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2406     cols = uj;
2407     for (i=0; i<am; i++) {
2408       aj    = a->j + a->diag[i];
2409       ncols = ui[i+1] - ui[i];
2410       for (j=0; j<ncols; j++) *cols++ = *aj++;
2411     }
2412   } else { /* case: levels>0 || (levels=0 && !perm_identity) */
2413     ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2414     ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2415 
2416     /* initialization */
2417     ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr);
2418 
2419     /* jl: linked list for storing indices of the pivot rows
2420        il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2421     ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr);
2422     for (i=0; i<am; i++){
2423       jl[i] = am; il[i] = 0;
2424     }
2425 
2426     /* create and initialize a linked list for storing column indices of the active row k */
2427     nlnk = am + 1;
2428     ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2429 
2430     /* initial FreeSpace size is fill*(ai[am]+1) */
2431     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2432     current_space = free_space;
2433     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr);
2434     current_space_lvl = free_space_lvl;
2435 
2436     for (k=0; k<am; k++){  /* for each active row k */
2437       /* initialize lnk by the column indices of row rip[k] of A */
2438       nzk   = 0;
2439       ncols = ai[rip[k]+1] - ai[rip[k]];
2440       if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2441       ncols_upper = 0;
2442       for (j=0; j<ncols; j++){
2443         i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2444         if (riip[i] >= k){ /* only take upper triangular entry */
2445           ajtmp[ncols_upper] = i;
2446           ncols_upper++;
2447         }
2448       }
2449       ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2450       nzk += nlnk;
2451 
2452       /* update lnk by computing fill-in for each pivot row to be merged in */
2453       prow = jl[k]; /* 1st pivot row */
2454 
2455       while (prow < k){
2456         nextprow = jl[prow];
2457 
2458         /* merge prow into k-th row */
2459         jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2460         jmax = ui[prow+1];
2461         ncols = jmax-jmin;
2462         i     = jmin - ui[prow];
2463         cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2464         uj    = uj_lvl_ptr[prow] + i; /* levels of cols */
2465         j     = *(uj - 1);
2466         ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr);
2467         nzk += nlnk;
2468 
2469         /* update il and jl for prow */
2470         if (jmin < jmax){
2471           il[prow] = jmin;
2472           j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2473         }
2474         prow = nextprow;
2475       }
2476 
2477       /* if free space is not available, make more free space */
2478       if (current_space->local_remaining<nzk) {
2479         i = am - k + 1; /* num of unfactored rows */
2480         i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2481         ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2482         ierr = PetscFreeSpaceGet(i,&current_space_lvl);CHKERRQ(ierr);
2483         reallocs++;
2484       }
2485 
2486       /* copy data into free_space and free_space_lvl, then initialize lnk */
2487       if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2488       ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
2489 
2490       /* add the k-th row into il and jl */
2491       if (nzk > 1){
2492         i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2493         jl[k] = jl[i]; jl[i] = k;
2494         il[k] = ui[k] + 1;
2495       }
2496       uj_ptr[k]     = current_space->array;
2497       uj_lvl_ptr[k] = current_space_lvl->array;
2498 
2499       current_space->array           += nzk;
2500       current_space->local_used      += nzk;
2501       current_space->local_remaining -= nzk;
2502 
2503       current_space_lvl->array           += nzk;
2504       current_space_lvl->local_used      += nzk;
2505       current_space_lvl->local_remaining -= nzk;
2506 
2507       ui[k+1] = ui[k] + nzk;
2508     }
2509 
2510 #if defined(PETSC_USE_INFO)
2511     if (ai[am] != 0) {
2512       PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]);
2513       ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2514       ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2515       ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2516     } else {
2517       ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2518     }
2519 #endif
2520 
2521     ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2522     ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2523     ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr);
2524     ierr = PetscFree(ajtmp);CHKERRQ(ierr);
2525 
2526     /* destroy list of free space and other temporary array(s) */
2527     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2528     ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
2529     ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2530     ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2531 
2532   } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2533 
2534   /* put together the new matrix in MATSEQSBAIJ format */
2535 
2536   b    = (Mat_SeqSBAIJ*)(fact)->data;
2537   b->singlemalloc = PETSC_FALSE;
2538   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2539   b->j    = uj;
2540   b->i    = ui;
2541   b->diag = udiag;
2542   b->free_diag = PETSC_TRUE;
2543   b->ilen = 0;
2544   b->imax = 0;
2545   b->row  = perm;
2546   b->col  = perm;
2547   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2548   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2549   b->icol = iperm;
2550   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2551   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2552   ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2553   b->maxnz   = b->nz = ui[am];
2554   b->free_a  = PETSC_TRUE;
2555   b->free_ij = PETSC_TRUE;
2556 
2557   (fact)->info.factor_mallocs    = reallocs;
2558   (fact)->info.fill_ratio_given  = fill;
2559   if (ai[am] != 0) {
2560     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2561   } else {
2562     (fact)->info.fill_ratio_needed = 0.0;
2563   }
2564   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2565   PetscFunctionReturn(0);
2566 }
2567 
2568 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2569 {
2570   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2571   Mat_SeqSBAIJ       *b;
2572   PetscErrorCode     ierr;
2573   PetscTruth         perm_identity;
2574   PetscReal          fill = info->fill;
2575   const PetscInt     *rip,*riip;
2576   PetscInt           i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow;
2577   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
2578   PetscInt           nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr,*udiag;
2579   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2580   PetscBT            lnkbt;
2581   IS                 iperm;
2582 
2583   PetscFunctionBegin;
2584   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);
2585   /* check whether perm is the identity mapping */
2586   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2587   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2588   ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2589   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2590 
2591   /* initialization */
2592   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2593   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2594   ui[0] = 0;
2595 
2596   /* jl: linked list for storing indices of the pivot rows
2597      il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2598   ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr);
2599   for (i=0; i<am; i++){
2600     jl[i] = am; il[i] = 0;
2601   }
2602 
2603   /* create and initialize a linked list for storing column indices of the active row k */
2604   nlnk = am + 1;
2605   ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2606 
2607   /* initial FreeSpace size is fill*(ai[am]+1) */
2608   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2609   current_space = free_space;
2610 
2611   for (k=0; k<am; k++){  /* for each active row k */
2612     /* initialize lnk by the column indices of row rip[k] of A */
2613     nzk   = 0;
2614     ncols = ai[rip[k]+1] - ai[rip[k]];
2615     if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2616     ncols_upper = 0;
2617     for (j=0; j<ncols; j++){
2618       i = riip[*(aj + ai[rip[k]] + j)];
2619       if (i >= k){ /* only take upper triangular entry */
2620         cols[ncols_upper] = i;
2621         ncols_upper++;
2622       }
2623     }
2624     ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2625     nzk += nlnk;
2626 
2627     /* update lnk by computing fill-in for each pivot row to be merged in */
2628     prow = jl[k]; /* 1st pivot row */
2629 
2630     while (prow < k){
2631       nextprow = jl[prow];
2632       /* merge prow into k-th row */
2633       jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2634       jmax = ui[prow+1];
2635       ncols = jmax-jmin;
2636       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2637       ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2638       nzk += nlnk;
2639 
2640       /* update il and jl for prow */
2641       if (jmin < jmax){
2642         il[prow] = jmin;
2643         j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
2644       }
2645       prow = nextprow;
2646     }
2647 
2648     /* if free space is not available, make more free space */
2649     if (current_space->local_remaining<nzk) {
2650       i = am - k + 1; /* num of unfactored rows */
2651       i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2652       ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2653       reallocs++;
2654     }
2655 
2656     /* copy data into free space, then initialize lnk */
2657     ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
2658 
2659     /* add the k-th row into il and jl */
2660     if (nzk-1 > 0){
2661       i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2662       jl[k] = jl[i]; jl[i] = k;
2663       il[k] = ui[k] + 1;
2664     }
2665     ui_ptr[k] = current_space->array;
2666     current_space->array           += nzk;
2667     current_space->local_used      += nzk;
2668     current_space->local_remaining -= nzk;
2669 
2670     ui[k+1] = ui[k] + nzk;
2671   }
2672 
2673 #if defined(PETSC_USE_INFO)
2674   if (ai[am] != 0) {
2675     PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]);
2676     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2677     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2678     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2679   } else {
2680      ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2681   }
2682 #endif
2683 
2684   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2685   ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2686   ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr);
2687 
2688   /* destroy list of free space and other temporary array(s) */
2689   ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2690   ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor in newdatastruct */
2691   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2692 
2693   /* put together the new matrix in MATSEQSBAIJ format */
2694 
2695   b = (Mat_SeqSBAIJ*)(fact)->data;
2696   b->singlemalloc = PETSC_FALSE;
2697   b->free_a       = PETSC_TRUE;
2698   b->free_ij      = PETSC_TRUE;
2699   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2700   b->j    = uj;
2701   b->i    = ui;
2702   b->diag = udiag;
2703   b->free_diag = PETSC_TRUE;
2704   b->ilen = 0;
2705   b->imax = 0;
2706   b->row  = perm;
2707   b->col  = perm;
2708   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2709   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2710   b->icol = iperm;
2711   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2712   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2713   ierr    = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2714   b->maxnz = b->nz = ui[am];
2715 
2716   (fact)->info.factor_mallocs    = reallocs;
2717   (fact)->info.fill_ratio_given  = fill;
2718   if (ai[am] != 0) {
2719     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2720   } else {
2721     (fact)->info.fill_ratio_needed = 0.0;
2722   }
2723   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_newdatastruct;
2724   PetscFunctionReturn(0);
2725 }
2726 
2727 #undef __FUNCT__
2728 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ"
2729 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2730 {
2731   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2732   Mat_SeqSBAIJ       *b;
2733   PetscErrorCode     ierr;
2734   PetscTruth         perm_identity;
2735   PetscReal          fill = info->fill;
2736   const PetscInt     *rip,*riip;
2737   PetscInt           i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow;
2738   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
2739   PetscInt           nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr;
2740   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2741   PetscBT            lnkbt;
2742   IS                 iperm;
2743   PetscTruth         newdatastruct=PETSC_FALSE;
2744 
2745   PetscFunctionBegin;
2746   ierr = PetscOptionsGetTruth(PETSC_NULL,"-cholesky_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
2747   if(newdatastruct){
2748     ierr = MatCholeskyFactorSymbolic_SeqAIJ_newdatastruct(fact,A,perm,info);CHKERRQ(ierr);
2749     PetscFunctionReturn(0);
2750   }
2751 
2752   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);
2753   /* check whether perm is the identity mapping */
2754   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2755   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2756   ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2757   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2758 
2759   /* initialization */
2760   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2761   ui[0] = 0;
2762 
2763   /* jl: linked list for storing indices of the pivot rows
2764      il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2765   ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr);
2766   for (i=0; i<am; i++){
2767     jl[i] = am; il[i] = 0;
2768   }
2769 
2770   /* create and initialize a linked list for storing column indices of the active row k */
2771   nlnk = am + 1;
2772   ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2773 
2774   /* initial FreeSpace size is fill*(ai[am]+1) */
2775   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2776   current_space = free_space;
2777 
2778   for (k=0; k<am; k++){  /* for each active row k */
2779     /* initialize lnk by the column indices of row rip[k] of A */
2780     nzk   = 0;
2781     ncols = ai[rip[k]+1] - ai[rip[k]];
2782     if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2783     ncols_upper = 0;
2784     for (j=0; j<ncols; j++){
2785       i = riip[*(aj + ai[rip[k]] + j)];
2786       if (i >= k){ /* only take upper triangular entry */
2787         cols[ncols_upper] = i;
2788         ncols_upper++;
2789       }
2790     }
2791     ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2792     nzk += nlnk;
2793 
2794     /* update lnk by computing fill-in for each pivot row to be merged in */
2795     prow = jl[k]; /* 1st pivot row */
2796 
2797     while (prow < k){
2798       nextprow = jl[prow];
2799       /* merge prow into k-th row */
2800       jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2801       jmax = ui[prow+1];
2802       ncols = jmax-jmin;
2803       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2804       ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2805       nzk += nlnk;
2806 
2807       /* update il and jl for prow */
2808       if (jmin < jmax){
2809         il[prow] = jmin;
2810         j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
2811       }
2812       prow = nextprow;
2813     }
2814 
2815     /* if free space is not available, make more free space */
2816     if (current_space->local_remaining<nzk) {
2817       i = am - k + 1; /* num of unfactored rows */
2818       i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2819       ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2820       reallocs++;
2821     }
2822 
2823     /* copy data into free space, then initialize lnk */
2824     ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
2825 
2826     /* add the k-th row into il and jl */
2827     if (nzk-1 > 0){
2828       i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2829       jl[k] = jl[i]; jl[i] = k;
2830       il[k] = ui[k] + 1;
2831     }
2832     ui_ptr[k] = current_space->array;
2833     current_space->array           += nzk;
2834     current_space->local_used      += nzk;
2835     current_space->local_remaining -= nzk;
2836 
2837     ui[k+1] = ui[k] + nzk;
2838   }
2839 
2840 #if defined(PETSC_USE_INFO)
2841   if (ai[am] != 0) {
2842     PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]);
2843     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2844     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2845     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2846   } else {
2847      ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2848   }
2849 #endif
2850 
2851   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2852   ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2853   ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr);
2854 
2855   /* destroy list of free space and other temporary array(s) */
2856   ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2857   ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
2858   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2859 
2860   /* put together the new matrix in MATSEQSBAIJ format */
2861 
2862   b = (Mat_SeqSBAIJ*)(fact)->data;
2863   b->singlemalloc = PETSC_FALSE;
2864   b->free_a       = PETSC_TRUE;
2865   b->free_ij      = PETSC_TRUE;
2866   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2867   b->j    = uj;
2868   b->i    = ui;
2869   b->diag = 0;
2870   b->ilen = 0;
2871   b->imax = 0;
2872   b->row  = perm;
2873   b->col  = perm;
2874   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2875   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2876   b->icol = iperm;
2877   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2878   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2879   ierr    = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2880   b->maxnz = b->nz = ui[am];
2881 
2882   (fact)->info.factor_mallocs    = reallocs;
2883   (fact)->info.fill_ratio_given  = fill;
2884   if (ai[am] != 0) {
2885     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2886   } else {
2887     (fact)->info.fill_ratio_needed = 0.0;
2888   }
2889   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2890   PetscFunctionReturn(0);
2891 }
2892 
2893 #undef __FUNCT__
2894 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_newdatastruct"
2895 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx)
2896 {
2897   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
2898   PetscErrorCode    ierr;
2899   PetscInt          n = A->rmap->n;
2900   const PetscInt    *ai = a->i,*aj = a->j,*vi;
2901   PetscScalar       *x,sum;
2902   const PetscScalar *b;
2903   const MatScalar   *aa = a->a,*v;
2904   PetscInt          i,nz;
2905 
2906   PetscFunctionBegin;
2907   if (!n) PetscFunctionReturn(0);
2908 
2909   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2910   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2911 
2912   /* forward solve the lower triangular */
2913   x[0] = b[0];
2914   v    = aa;
2915   vi   = aj;
2916   for (i=1; i<n; i++) {
2917     nz  = ai[i+1] - ai[i];
2918     sum = b[i];
2919     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
2920     v  += nz;
2921     vi += nz;
2922     x[i] = sum;
2923   }
2924 
2925   /* backward solve the upper triangular */
2926   v   = aa + ai[n+1];
2927   vi  = aj + ai[n+1];
2928   for (i=n-1; i>=0; i--){
2929     nz = ai[2*n-i +1] - ai[2*n-i]-1;
2930     sum = x[i];
2931     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
2932     v   += nz;
2933     vi  += nz; vi++;
2934     x[i] = *v++ *sum; /* x[i]=aa[adiag[i]]*sum; v++; */
2935   }
2936 
2937   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
2938   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2939   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2940   PetscFunctionReturn(0);
2941 }
2942 
2943 #undef __FUNCT__
2944 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_newdatastruct_v2"
2945 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct_v2(Mat A,Vec bb,Vec xx)
2946 {
2947   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
2948   PetscErrorCode    ierr;
2949   PetscInt          n = A->rmap->n;
2950   const PetscInt    *ai = a->i,*aj = a->j,*adiag = a->diag,*vi;
2951   PetscScalar       *x,sum;
2952   const PetscScalar *b;
2953   const MatScalar   *aa = a->a,*v;
2954   PetscInt          i,nz;
2955 
2956   PetscFunctionBegin;
2957   if (!n) PetscFunctionReturn(0);
2958 
2959   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2960   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2961 
2962   /* forward solve the lower triangular */
2963   x[0] = b[0];
2964   v    = aa;
2965   vi   = aj;
2966   for (i=1; i<n; i++) {
2967     nz  = ai[i+1] - ai[i];
2968     sum = b[i];
2969     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
2970     v  += nz;
2971     vi += nz;
2972     x[i] = sum;
2973   }
2974 
2975   /* backward solve the upper triangular */
2976   /*  v   = aa + ai[n+1];
2977       vi  = aj + ai[n+1]; */
2978   v  = aa + adiag[n-1];
2979   vi = aj + adiag[n-1];
2980   for (i=n-1; i>=0; i--){
2981     nz = adiag[i] - adiag[i+1]-1;
2982     sum = x[i];
2983     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
2984     v   += nz;
2985     vi  += nz; vi++;
2986     x[i] = *v++ *sum; /* x[i]=aa[adiag[i]]*sum; v++; */
2987   }
2988 
2989   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
2990   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2991   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2992   PetscFunctionReturn(0);
2993 }
2994 
2995 #undef __FUNCT__
2996 #define __FUNCT__ "MatSolve_SeqAIJ_newdatastruct"
2997 PetscErrorCode MatSolve_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec xx)
2998 {
2999   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
3000   IS                iscol = a->col,isrow = a->row;
3001   PetscErrorCode    ierr;
3002   PetscInt          i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,nz,k;
3003   const PetscInt    *rout,*cout,*r,*c;
3004   PetscScalar       *x,*tmp,*tmps,sum;
3005   const PetscScalar *b;
3006   const MatScalar   *aa = a->a,*v;
3007 
3008   PetscFunctionBegin;
3009   if (!n) PetscFunctionReturn(0);
3010 
3011   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3012   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3013   tmp  = a->solve_work;
3014 
3015   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
3016   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
3017 
3018   /* forward solve the lower triangular */
3019   tmp[0] = b[*r++];
3020   tmps   = tmp;
3021   v      = aa;
3022   vi     = aj;
3023   for (i=1; i<n; i++) {
3024     nz  = ai[i+1] - ai[i];
3025     sum = b[*r++];
3026     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
3027     tmp[i] = sum;
3028     v += nz; vi += nz;
3029   }
3030 
3031   /* backward solve the upper triangular */
3032   k  = n+1;
3033   v  = aa + ai[k]; /* 1st entry of U(n-1,:) */
3034   vi = aj + ai[k];
3035   for (i=n-1; i>=0; i--){
3036     k  = 2*n-i;
3037     nz = ai[k +1] - ai[k] - 1;
3038     sum = tmp[i];
3039     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
3040     x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */
3041     v += nz+1; vi += nz+1;
3042   }
3043 
3044   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
3045   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
3046   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3047   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3048   ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr);
3049   PetscFunctionReturn(0);
3050 }
3051 
3052 #undef __FUNCT__
3053 #define __FUNCT__ "MatSolve_SeqAIJ_newdatastruct_v2"
3054 PetscErrorCode MatSolve_SeqAIJ_newdatastruct_v2(Mat A,Vec bb,Vec xx)
3055 {
3056   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
3057   IS                iscol = a->col,isrow = a->row;
3058   PetscErrorCode    ierr;
3059   PetscInt          i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz;
3060   const PetscInt    *rout,*cout,*r,*c;
3061   PetscScalar       *x,*tmp,sum;
3062   const PetscScalar *b;
3063   const MatScalar   *aa = a->a,*v;
3064 
3065   PetscFunctionBegin;
3066   if (!n) PetscFunctionReturn(0);
3067 
3068   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3069   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3070   tmp  = a->solve_work;
3071 
3072   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
3073   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
3074 
3075   /* forward solve the lower triangular */
3076   /*  tmp[0] = b[*r++]; */
3077   tmp[0] = b[r[0]];
3078   v      = aa;
3079   vi     = aj;
3080   for (i=1; i<n; i++) {
3081     nz  = ai[i+1] - ai[i];
3082     sum = b[r[i]];
3083     PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
3084     tmp[i] = sum;
3085     v += nz; vi += nz;
3086   }
3087 
3088   /* backward solve the upper triangular */
3089   /*  v  = aa + ai[k]; *//* 1st entry of U(n-1,:) */
3090   /* vi = aj + ai[k]; */
3091   v  = aa + adiag[n-1];
3092   vi = aj + adiag[n-1];
3093   for (i=n-1; i>=0; i--){
3094     /* nz = ai[k +1] - ai[k] - 1;*/
3095     nz = adiag[i]-adiag[i+1]-1;
3096     sum = tmp[i];
3097     PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
3098     x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */
3099     v += nz+1; vi += nz+1;
3100   }
3101 
3102   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
3103   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
3104   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3105   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3106   ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr);
3107   PetscFunctionReturn(0);
3108 }
3109 
3110 #undef __FUNCT__
3111 #define __FUNCT__ "MatILUDTFactor_SeqAIJ"
3112 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact)
3113 {
3114   Mat                B = *fact;
3115   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b;
3116   IS                 isicol;
3117   PetscErrorCode     ierr;
3118   const PetscInt     *r,*ic;
3119   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag;
3120   PetscInt           *bi,*bj,*bdiag,*bdiag_rev;
3121   PetscInt           row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au;
3122   PetscInt           nlnk,*lnk;
3123   PetscBT            lnkbt;
3124   PetscTruth         row_identity,icol_identity,both_identity;
3125   MatScalar          *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp;
3126   const PetscInt     *ics;
3127   PetscInt           j,nz,*pj,*bjtmp,k,ncut,*jtmp;
3128   PetscReal          dt=info->dt,dtcol=info->dtcol,shift=info->shiftinblocks;
3129   PetscInt           dtcount=(PetscInt)info->dtcount,nnz_max;
3130   PetscTruth         missing;
3131 
3132   PetscFunctionBegin;
3133 
3134   if (dt      == PETSC_DEFAULT) dt      = 0.005;
3135   if (dtcol   == PETSC_DEFAULT) dtcol   = 0.01; /* XXX unused! */
3136   if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax);
3137 
3138   /* ------- symbolic factorization, can be reused ---------*/
3139   ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
3140   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
3141   adiag=a->diag;
3142 
3143   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
3144 
3145   /* bdiag is location of diagonal in factor */
3146   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);     /* becomes b->diag */
3147   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag_rev);CHKERRQ(ierr); /* temporary */
3148 
3149   /* allocate row pointers bi */
3150   ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
3151 
3152   /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */
3153   if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */
3154   nnz_max  = ai[n]+2*n*dtcount+2;
3155 
3156   ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
3157   ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr);
3158 
3159   /* put together the new matrix */
3160   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
3161   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
3162   b    = (Mat_SeqAIJ*)(B)->data;
3163   b->free_a       = PETSC_TRUE;
3164   b->free_ij      = PETSC_TRUE;
3165   b->singlemalloc = PETSC_FALSE;
3166   b->a          = ba;
3167   b->j          = bj;
3168   b->i          = bi;
3169   b->diag       = bdiag;
3170   b->ilen       = 0;
3171   b->imax       = 0;
3172   b->row        = isrow;
3173   b->col        = iscol;
3174   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
3175   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
3176   b->icol       = isicol;
3177   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
3178 
3179   ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
3180   b->maxnz = nnz_max;
3181 
3182   (B)->factor                = MAT_FACTOR_ILUDT;
3183   (B)->info.factor_mallocs   = 0;
3184   (B)->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]);
3185   CHKMEMQ;
3186   /* ------- end of symbolic factorization ---------*/
3187 
3188   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
3189   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
3190   ics  = ic;
3191 
3192   /* linked list for storing column indices of the active row */
3193   nlnk = n + 1;
3194   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3195 
3196   /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */
3197   ierr = PetscMalloc2(n,PetscInt,&im,n,PetscInt,&jtmp);CHKERRQ(ierr);
3198   /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */
3199   ierr = PetscMalloc2(n,MatScalar,&rtmp,n,MatScalar,&vtmp);CHKERRQ(ierr);
3200   ierr = PetscMemzero(rtmp,n*sizeof(MatScalar));CHKERRQ(ierr);
3201 
3202   bi[0]    = 0;
3203   bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */
3204   bdiag_rev[n] = bdiag[0];
3205   bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */
3206   for (i=0; i<n; i++) {
3207     /* copy initial fill into linked list */
3208     nzi = 0; /* nonzeros for active row i */
3209     nzi = ai[r[i]+1] - ai[r[i]];
3210     if (!nzi) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
3211     nzi_al = adiag[r[i]] - ai[r[i]];
3212     nzi_au = ai[r[i]+1] - adiag[r[i]] -1;
3213     ajtmp = aj + ai[r[i]];
3214     ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3215 
3216     /* load in initial (unfactored row) */
3217     aatmp = a->a + ai[r[i]];
3218     for (j=0; j<nzi; j++) {
3219       rtmp[ics[*ajtmp++]] = *aatmp++;
3220     }
3221 
3222     /* add pivot rows into linked list */
3223     row = lnk[n];
3224     while (row < i ) {
3225       nzi_bl = bi[row+1] - bi[row] + 1;
3226       bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */
3227       ierr  = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr);
3228       nzi  += nlnk;
3229       row   = lnk[row];
3230     }
3231 
3232     /* copy data from lnk into jtmp, then initialize lnk */
3233     ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr);
3234 
3235     /* numerical factorization */
3236     bjtmp = jtmp;
3237     row   = *bjtmp++; /* 1st pivot row */
3238     while  ( row < i ) {
3239       pc         = rtmp + row;
3240       pv         = ba + bdiag[row]; /* 1./(diag of the pivot row) */
3241       multiplier = (*pc) * (*pv);
3242       *pc        = multiplier;
3243       if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */
3244         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
3245         pv         = ba + bdiag[row+1] + 1;
3246         /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */
3247         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
3248         for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
3249         ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
3250       }
3251       row = *bjtmp++;
3252     }
3253 
3254     /* copy sparse rtmp into contiguous vtmp; separate L and U part */
3255     diag_tmp = rtmp[i];  /* save diagonal value - may not needed?? */
3256     nzi_bl = 0; j = 0;
3257     while (jtmp[j] < i){ /* Note: jtmp is sorted */
3258       vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
3259       nzi_bl++; j++;
3260     }
3261     nzi_bu = nzi - nzi_bl -1;
3262     while (j < nzi){
3263       vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
3264       j++;
3265     }
3266 
3267     bjtmp = bj + bi[i];
3268     batmp = ba + bi[i];
3269     /* apply level dropping rule to L part */
3270     ncut = nzi_al + dtcount;
3271     if (ncut < nzi_bl){
3272       ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr);
3273       ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr);
3274     } else {
3275       ncut = nzi_bl;
3276     }
3277     for (j=0; j<ncut; j++){
3278       bjtmp[j] = jtmp[j];
3279       batmp[j] = vtmp[j];
3280       /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */
3281     }
3282     bi[i+1] = bi[i] + ncut;
3283     nzi = ncut + 1;
3284 
3285     /* apply level dropping rule to U part */
3286     ncut = nzi_au + dtcount;
3287     if (ncut < nzi_bu){
3288       ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr);
3289       ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr);
3290     } else {
3291       ncut = nzi_bu;
3292     }
3293     nzi += ncut;
3294 
3295     /* mark bdiagonal */
3296     bdiag[i+1]       = bdiag[i] - (ncut + 1);
3297     bdiag_rev[n-i-1] = bdiag[i+1];
3298     bi[2*n - i]      = bi[2*n - i +1] - (ncut + 1);
3299     bjtmp = bj + bdiag[i];
3300     batmp = ba + bdiag[i];
3301     *bjtmp = i;
3302     *batmp = diag_tmp; /* rtmp[i]; */
3303     if (*batmp == 0.0) {
3304       *batmp = dt+shift;
3305       /* printf(" row %d add shift %g\n",i,shift); */
3306     }
3307     *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */
3308     /* printf(" (%d,%g),",*bjtmp,*batmp); */
3309 
3310     bjtmp = bj + bdiag[i+1]+1;
3311     batmp = ba + bdiag[i+1]+1;
3312     for (k=0; k<ncut; k++){
3313       bjtmp[k] = jtmp[nzi_bl+1+k];
3314       batmp[k] = vtmp[nzi_bl+1+k];
3315       /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */
3316     }
3317     /* printf("\n"); */
3318 
3319     im[i]   = nzi; /* used by PetscLLAddSortedLU() */
3320     /*
3321     printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]);
3322     printf(" ----------------------------\n");
3323     */
3324   } /* for (i=0; i<n; i++) */
3325   /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */
3326   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]);
3327 
3328   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
3329   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
3330 
3331   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
3332   ierr = PetscFree2(im,jtmp);CHKERRQ(ierr);
3333   ierr = PetscFree2(rtmp,vtmp);CHKERRQ(ierr);
3334   ierr = PetscFree(bdiag_rev);CHKERRQ(ierr);
3335 
3336   ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr);
3337   b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n];
3338 
3339   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
3340   ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr);
3341   both_identity = (PetscTruth) (row_identity && icol_identity);
3342   if (row_identity && icol_identity) {
3343     B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct;
3344   } else {
3345     B->ops->solve = MatSolve_SeqAIJ_newdatastruct;
3346   }
3347 
3348   B->ops->lufactorsymbolic  = MatILUDTFactorSymbolic_SeqAIJ;
3349   B->ops->lufactornumeric   = MatILUDTFactorNumeric_SeqAIJ;
3350   B->ops->solveadd          = 0;
3351   B->ops->solvetranspose    = 0;
3352   B->ops->solvetransposeadd = 0;
3353   B->ops->matsolve          = 0;
3354   B->assembled              = PETSC_TRUE;
3355   B->preallocated           = PETSC_TRUE;
3356   PetscFunctionReturn(0);
3357 }
3358 
3359 /* a wraper of MatILUDTFactor_SeqAIJ() */
3360 #undef __FUNCT__
3361 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ"
3362 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info)
3363 {
3364   PetscErrorCode     ierr;
3365 
3366   PetscFunctionBegin;
3367   ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr);
3368 
3369   fact->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ;
3370   PetscFunctionReturn(0);
3371 }
3372 
3373 /*
3374    same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors
3375    - intend to replace existing MatLUFactorNumeric_SeqAIJ()
3376 */
3377 #undef __FUNCT__
3378 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ"
3379 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info)
3380 {
3381   Mat            C=fact;
3382   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
3383   IS             isrow = b->row,isicol = b->icol;
3384   PetscErrorCode ierr;
3385   const PetscInt *r,*ic,*ics;
3386   PetscInt       i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
3387   PetscInt       *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj;
3388   MatScalar      *rtmp,*pc,multiplier,*v,*pv,*aa=a->a;
3389   PetscReal      dt=info->dt,shift=info->shiftinblocks;
3390   PetscTruth     row_identity, col_identity;
3391 
3392   PetscFunctionBegin;
3393   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
3394   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
3395   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
3396   ics  = ic;
3397 
3398   for (i=0; i<n; i++){
3399     /* initialize rtmp array */
3400     nzl   = bi[i+1] - bi[i];       /* num of nozeros in L(i,:) */
3401     bjtmp = bj + bi[i];
3402     for  (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0;
3403     rtmp[i] = 0.0;
3404     nzu   = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */
3405     bjtmp = bj + bdiag[i+1] + 1;
3406     for  (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0;
3407 
3408     /* load in initial unfactored row of A */
3409     /* printf("row %d\n",i); */
3410     nz    = ai[r[i]+1] - ai[r[i]];
3411     ajtmp = aj + ai[r[i]];
3412     v     = aa + ai[r[i]];
3413     for (j=0; j<nz; j++) {
3414       rtmp[ics[*ajtmp++]] = v[j];
3415       /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */
3416     }
3417     /* printf("\n"); */
3418 
3419     /* numerical factorization */
3420     bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */
3421     nzl   = bi[i+1] - bi[i]; /* num of entries in L(i,:) */
3422     k = 0;
3423     while (k < nzl){
3424       row   = *bjtmp++;
3425       /* printf("  prow %d\n",row); */
3426       pc         = rtmp + row;
3427       pv         = b->a + bdiag[row]; /* 1./(diag of the pivot row) */
3428       multiplier = (*pc) * (*pv);
3429       *pc        = multiplier;
3430       if (PetscAbsScalar(multiplier) > dt){
3431         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
3432         pv         = b->a + bdiag[row+1] + 1;
3433         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
3434         for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
3435         /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */
3436       }
3437       k++;
3438     }
3439 
3440     /* finished row so stick it into b->a */
3441     /* L-part */
3442     pv = b->a + bi[i] ;
3443     pj = bj + bi[i] ;
3444     nzl = bi[i+1] - bi[i];
3445     for (j=0; j<nzl; j++) {
3446       pv[j] = rtmp[pj[j]];
3447       /* printf(" (%d,%g),",pj[j],pv[j]); */
3448     }
3449 
3450     /* diagonal: invert diagonal entries for simplier triangular solves */
3451     if (rtmp[i] == 0.0) rtmp[i] = dt+shift;
3452     b->a[bdiag[i]] = 1.0/rtmp[i];
3453     /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */
3454 
3455     /* U-part */
3456     pv = b->a + bdiag[i+1] + 1;
3457     pj = bj + bdiag[i+1] + 1;
3458     nzu = bdiag[i] - bdiag[i+1] - 1;
3459     for (j=0; j<nzu; j++) {
3460       pv[j] = rtmp[pj[j]];
3461       /* printf(" (%d,%g),",pj[j],pv[j]); */
3462     }
3463     /* printf("\n"); */
3464   }
3465 
3466   ierr = PetscFree(rtmp);CHKERRQ(ierr);
3467   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
3468   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
3469 
3470   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
3471   ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
3472   if (row_identity && col_identity) {
3473     C->ops->solve   = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct;
3474   } else {
3475     C->ops->solve   = MatSolve_SeqAIJ_newdatastruct;
3476   }
3477   C->ops->solveadd           = 0;
3478   C->ops->solvetranspose     = 0;
3479   C->ops->solvetransposeadd  = 0;
3480   C->ops->matsolve           = 0;
3481   C->assembled    = PETSC_TRUE;
3482   C->preallocated = PETSC_TRUE;
3483   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
3484   PetscFunctionReturn(0);
3485 }
3486