xref: /petsc/src/mat/impls/aij/seq/aijfact.c (revision 113a72286af6bf0c0c69994a35bdec5fae9787dc)
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     = MatSolveTranspose_SeqAIJ_newdatastruct_v2;
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 
1301 #undef __FUNCT__
1302 #define __FUNCT__ "MatSolveTranspose_SeqAIJ_newdatastruct_v2"
1303 PetscErrorCode MatSolveTranspose_SeqAIJ_newdatastruct_v2(Mat A,Vec bb,Vec xx)
1304 {
1305   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1306   IS                iscol = a->col,isrow = a->row;
1307   PetscErrorCode    ierr;
1308   const PetscInt    *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi;
1309   PetscInt          i,n = A->rmap->n,j;
1310   PetscInt          nz;
1311   PetscScalar       *x,*tmp,s1;
1312   const MatScalar   *aa = a->a,*v;
1313   const PetscScalar *b;
1314 
1315   PetscFunctionBegin;
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 + adiag[i+1] + 1;
1329     vi  = aj + adiag[i+1] + 1;
1330     nz  = adiag[i] - adiag[i+1] - 1;
1331     s1  = tmp[i];
1332     s1 *= v[nz];  /* 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 + ai[i];
1340     vi  = aj + ai[i];
1341     nz  = ai[i+1] - 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 #undef __FUNCT__
1359 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ"
1360 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx)
1361 {
1362   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1363   IS                iscol = a->col,isrow = a->row;
1364   PetscErrorCode    ierr;
1365   const PetscInt    *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi;
1366   PetscInt          i,n = A->rmap->n,j;
1367   PetscInt          nz;
1368   PetscScalar       *x,*tmp,s1;
1369   const MatScalar   *aa = a->a,*v;
1370   const PetscScalar *b;
1371 
1372   PetscFunctionBegin;
1373   if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);}
1374   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1375   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1376   tmp  = a->solve_work;
1377 
1378   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1379   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1380 
1381   /* copy the b into temp work space according to permutation */
1382   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1383 
1384   /* forward solve the U^T */
1385   for (i=0; i<n; i++) {
1386     v   = aa + diag[i] ;
1387     vi  = aj + diag[i] + 1;
1388     nz  = ai[i+1] - diag[i] - 1;
1389     s1  = tmp[i];
1390     s1 *= (*v++);  /* multiply by inverse of diagonal entry */
1391     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1392     tmp[i] = s1;
1393   }
1394 
1395   /* backward solve the L^T */
1396   for (i=n-1; i>=0; i--){
1397     v   = aa + diag[i] - 1 ;
1398     vi  = aj + diag[i] - 1 ;
1399     nz  = diag[i] - ai[i];
1400     s1  = tmp[i];
1401     for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j];
1402   }
1403 
1404   /* copy tmp into x according to permutation */
1405   for (i=0; i<n; i++) x[r[i]] += tmp[i];
1406 
1407   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1408   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1409   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1410   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1411 
1412   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1413   PetscFunctionReturn(0);
1414 }
1415 
1416 /* ----------------------------------------------------------------*/
1417 EXTERN PetscErrorCode Mat_CheckInode(Mat,PetscTruth);
1418 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption,PetscTruth);
1419 
1420 /*
1421    ilu() under revised new data structure.
1422    Factored arrays bj and ba are stored as
1423      L(0,:), L(1,:), ...,L(n-1,:),  U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:)
1424 
1425    bi=fact->i is an array of size n+1, in which
1426    bi+
1427      bi[i]:  points to 1st entry of L(i,:),i=0,...,n-1
1428      bi[n]:  points to L(n-1,n-1)+1
1429 
1430   bdiag=fact->diag is an array of size n+1,in which
1431      bdiag[i]: points to diagonal of U(i,:), i=0,...,n-1
1432      bdiag[n]: points to entry of U(n-1,0)-1
1433 
1434    U(i,:) contains bdiag[i] as its last entry, i.e.,
1435     U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i])
1436 */
1437 #undef __FUNCT__
1438 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct"
1439 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1440 {
1441 
1442   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1443   PetscErrorCode     ierr;
1444   PetscInt           n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag;
1445   PetscInt           i,j,nz,*bi,*bj,*bdiag;
1446   PetscTruth         missing;
1447   IS                 isicol;
1448 
1449   PetscFunctionBegin;
1450   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);
1451   ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
1452   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
1453   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1454 
1455   ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr);
1456   b    = (Mat_SeqAIJ*)(fact)->data;
1457 
1458   /* allocate matrix arrays for new data structure */
1459   ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,n+1,PetscInt,&b->i);CHKERRQ(ierr);
1460   ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));CHKERRQ(ierr);
1461   b->singlemalloc = PETSC_TRUE;
1462   if (!b->diag){
1463     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr);
1464     ierr = PetscLogObjectMemory(fact,(n+1)*sizeof(PetscInt));CHKERRQ(ierr);
1465   }
1466   bdiag = b->diag;
1467 
1468   if (n > 0) {
1469     ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr);
1470   }
1471 
1472   /* set bi and bj with new data structure */
1473   bi = b->i;
1474   bj = b->j;
1475 
1476   /* L part */
1477   bi[0] = 0;
1478   for (i=0; i<n; i++){
1479     nz = adiag[i] - ai[i];
1480     bi[i+1] = bi[i] + nz;
1481     aj = a->j + ai[i];
1482     for (j=0; j<nz; j++){
1483       *bj = aj[j]; bj++;
1484     }
1485   }
1486 
1487   /* U part */
1488   bdiag[n] = bi[n]-1;
1489   for (i=n-1; i>=0; i--){
1490     nz = ai[i+1] - adiag[i] - 1;
1491     aj = a->j + adiag[i] + 1;
1492     for (j=0; j<nz; j++){
1493       *bj = aj[j]; bj++;
1494     }
1495     /* diag[i] */
1496     *bj = i; bj++;
1497     bdiag[i] = bdiag[i+1] + nz + 1;
1498   }
1499 
1500   fact->factor                 = MAT_FACTOR_ILU;
1501   fact->info.factor_mallocs    = 0;
1502   fact->info.fill_ratio_given  = info->fill;
1503   fact->info.fill_ratio_needed = 1.0;
1504   fact->ops->lufactornumeric   = MatLUFactorNumeric_SeqAIJ_newdatastruct;
1505 
1506   b       = (Mat_SeqAIJ*)(fact)->data;
1507   b->row  = isrow;
1508   b->col  = iscol;
1509   b->icol = isicol;
1510   ierr    = PetscMalloc((fact->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1511   ierr    = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1512   ierr    = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1513   PetscFunctionReturn(0);
1514 }
1515 
1516 #undef __FUNCT__
1517 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_newdatastruct"
1518 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1519 {
1520   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1521   IS                 isicol;
1522   PetscErrorCode     ierr;
1523   const PetscInt     *r,*ic;
1524   PetscInt           n=A->rmap->n,*ai=a->i,*aj=a->j;
1525   PetscInt           *bi,*cols,nnz,*cols_lvl;
1526   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1527   PetscInt           i,levels,diagonal_fill;
1528   PetscTruth         col_identity,row_identity;
1529   PetscReal          f;
1530   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
1531   PetscBT            lnkbt;
1532   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
1533   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1534   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1535 
1536   PetscFunctionBegin;
1537   /* printf("MatILUFactorSymbolic_SeqAIJ_newdatastruct ...\n"); */
1538   levels = (PetscInt)info->levels;
1539   ierr   = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1540   ierr   = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
1541 
1542   if (!levels && row_identity && col_identity) {
1543     /* special case: ilu(0) with natural ordering */
1544     ierr = MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1545     PetscFunctionReturn(0);
1546   }
1547 
1548   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);
1549   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1550   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1551   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1552 
1553   /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
1554   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1555   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
1556   bi[0] = bdiag[0] = 0;
1557 
1558   ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr);
1559 
1560   /* create a linked list for storing column indices of the active row */
1561   nlnk = n + 1;
1562   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1563 
1564   /* initial FreeSpace size is f*(ai[n]+1) */
1565   f             = info->fill;
1566   diagonal_fill = (PetscInt)info->diagonal_fill;
1567   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
1568   current_space = free_space;
1569   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
1570   current_space_lvl = free_space_lvl;
1571 
1572   for (i=0; i<n; i++) {
1573     nzi = 0;
1574     /* copy current row into linked list */
1575     nnz  = ai[r[i]+1] - ai[r[i]];
1576     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1577     cols = aj + ai[r[i]];
1578     lnk[i] = -1; /* marker to indicate if diagonal exists */
1579     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1580     nzi += nlnk;
1581 
1582     /* make sure diagonal entry is included */
1583     if (diagonal_fill && lnk[i] == -1) {
1584       fm = n;
1585       while (lnk[fm] < i) fm = lnk[fm];
1586       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
1587       lnk[fm]    = i;
1588       lnk_lvl[i] = 0;
1589       nzi++; dcount++;
1590     }
1591 
1592     /* add pivot rows into the active row */
1593     nzbd = 0;
1594     prow = lnk[n];
1595     while (prow < i) {
1596       nnz      = bdiag[prow];
1597       cols     = bj_ptr[prow] + nnz + 1;
1598       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1599       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
1600       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
1601       nzi += nlnk;
1602       prow = lnk[prow];
1603       nzbd++;
1604     }
1605     bdiag[i] = nzbd;
1606     bi[i+1]  = bi[i] + nzi;
1607 
1608     /* if free space is not available, make more free space */
1609     if (current_space->local_remaining<nzi) {
1610       nnz = 2*nzi*(n - i); /* estimated and max additional space needed */
1611       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
1612       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
1613       reallocs++;
1614     }
1615 
1616     /* copy data into free_space and free_space_lvl, then initialize lnk */
1617     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1618     bj_ptr[i]    = current_space->array;
1619     bjlvl_ptr[i] = current_space_lvl->array;
1620 
1621     /* make sure the active row i has diagonal entry */
1622     if (*(bj_ptr[i]+bdiag[i]) != i) {
1623       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
1624     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
1625     }
1626 
1627     current_space->array           += nzi;
1628     current_space->local_used      += nzi;
1629     current_space->local_remaining -= nzi;
1630     current_space_lvl->array           += nzi;
1631     current_space_lvl->local_used      += nzi;
1632     current_space_lvl->local_remaining -= nzi;
1633   }
1634 
1635   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1636   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1637 
1638   /* destroy list of free space and other temporary arrays */
1639   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
1640 
1641   /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */
1642   ierr = PetscFreeSpaceContiguous_LU_v2(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr);
1643 
1644   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1645   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
1646   ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr);
1647 
1648 #if defined(PETSC_USE_INFO)
1649   {
1650     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1651     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
1652     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
1653     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
1654     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
1655     if (diagonal_fill) {
1656       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
1657     }
1658   }
1659 #endif
1660 
1661   /* put together the new matrix */
1662   ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
1663   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
1664   b = (Mat_SeqAIJ*)(fact)->data;
1665   b->free_a       = PETSC_TRUE;
1666   b->free_ij      = PETSC_TRUE;
1667   b->singlemalloc = PETSC_FALSE;
1668   ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
1669   b->j          = bj;
1670   b->i          = bi;
1671   b->diag       = bdiag;
1672   b->ilen       = 0;
1673   b->imax       = 0;
1674   b->row        = isrow;
1675   b->col        = iscol;
1676   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1677   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1678   b->icol       = isicol;
1679   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1680   /* In b structure:  Free imax, ilen, old a, old j.
1681      Allocate bdiag, solve_work, new a, new j */
1682   ierr = PetscLogObjectMemory(fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
1683   b->maxnz = b->nz = bdiag[0]+1;
1684   (fact)->info.factor_mallocs    = reallocs;
1685   (fact)->info.fill_ratio_given  = f;
1686   (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]);
1687   (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct;
1688   /* ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */
1689   PetscFunctionReturn(0);
1690 }
1691 
1692 #undef __FUNCT__
1693 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ"
1694 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1695 {
1696   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1697   IS                 isicol;
1698   PetscErrorCode     ierr;
1699   const PetscInt     *r,*ic;
1700   PetscInt           n=A->rmap->n,*ai=a->i,*aj=a->j,d;
1701   PetscInt           *bi,*cols,nnz,*cols_lvl;
1702   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1703   PetscInt           i,levels,diagonal_fill;
1704   PetscTruth         col_identity,row_identity;
1705   PetscReal          f;
1706   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
1707   PetscBT            lnkbt;
1708   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
1709   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1710   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1711   PetscTruth         missing;
1712   PetscTruth         newdatastruct=PETSC_FALSE;
1713 
1714   PetscFunctionBegin;
1715   ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
1716   if(newdatastruct){
1717     ierr = MatILUFactorSymbolic_SeqAIJ_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1718     PetscFunctionReturn(0);
1719   }
1720 
1721   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);
1722   f             = info->fill;
1723   levels        = (PetscInt)info->levels;
1724   diagonal_fill = (PetscInt)info->diagonal_fill;
1725   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1726 
1727   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1728   ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
1729   if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */
1730     ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr);
1731     (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ;
1732 
1733     fact->factor = MAT_FACTOR_ILU;
1734     (fact)->info.factor_mallocs    = 0;
1735     (fact)->info.fill_ratio_given  = info->fill;
1736     (fact)->info.fill_ratio_needed = 1.0;
1737     b               = (Mat_SeqAIJ*)(fact)->data;
1738     ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
1739     if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
1740     b->row              = isrow;
1741     b->col              = iscol;
1742     b->icol             = isicol;
1743     ierr                = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1744     ierr                = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1745     ierr                = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1746     ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1747     PetscFunctionReturn(0);
1748   }
1749 
1750   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1751   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1752 
1753   /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
1754   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1755   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
1756   bi[0] = bdiag[0] = 0;
1757 
1758   ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr);
1759 
1760   /* create a linked list for storing column indices of the active row */
1761   nlnk = n + 1;
1762   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1763 
1764   /* initial FreeSpace size is f*(ai[n]+1) */
1765   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
1766   current_space = free_space;
1767   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
1768   current_space_lvl = free_space_lvl;
1769 
1770   for (i=0; i<n; i++) {
1771     nzi = 0;
1772     /* copy current row into linked list */
1773     nnz  = ai[r[i]+1] - ai[r[i]];
1774     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1775     cols = aj + ai[r[i]];
1776     lnk[i] = -1; /* marker to indicate if diagonal exists */
1777     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1778     nzi += nlnk;
1779 
1780     /* make sure diagonal entry is included */
1781     if (diagonal_fill && lnk[i] == -1) {
1782       fm = n;
1783       while (lnk[fm] < i) fm = lnk[fm];
1784       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
1785       lnk[fm]    = i;
1786       lnk_lvl[i] = 0;
1787       nzi++; dcount++;
1788     }
1789 
1790     /* add pivot rows into the active row */
1791     nzbd = 0;
1792     prow = lnk[n];
1793     while (prow < i) {
1794       nnz      = bdiag[prow];
1795       cols     = bj_ptr[prow] + nnz + 1;
1796       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1797       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
1798       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
1799       nzi += nlnk;
1800       prow = lnk[prow];
1801       nzbd++;
1802     }
1803     bdiag[i] = nzbd;
1804     bi[i+1]  = bi[i] + nzi;
1805 
1806     /* if free space is not available, make more free space */
1807     if (current_space->local_remaining<nzi) {
1808       nnz = nzi*(n - i); /* estimated and max additional space needed */
1809       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
1810       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
1811       reallocs++;
1812     }
1813 
1814     /* copy data into free_space and free_space_lvl, then initialize lnk */
1815     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1816     bj_ptr[i]    = current_space->array;
1817     bjlvl_ptr[i] = current_space_lvl->array;
1818 
1819     /* make sure the active row i has diagonal entry */
1820     if (*(bj_ptr[i]+bdiag[i]) != i) {
1821       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
1822     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
1823     }
1824 
1825     current_space->array           += nzi;
1826     current_space->local_used      += nzi;
1827     current_space->local_remaining -= nzi;
1828     current_space_lvl->array           += nzi;
1829     current_space_lvl->local_used      += nzi;
1830     current_space_lvl->local_remaining -= nzi;
1831   }
1832 
1833   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1834   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1835 
1836   /* destroy list of free space and other temporary arrays */
1837   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
1838   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */
1839   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1840   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
1841   ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr);
1842 
1843 #if defined(PETSC_USE_INFO)
1844   {
1845     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1846     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
1847     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
1848     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
1849     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
1850     if (diagonal_fill) {
1851       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
1852     }
1853   }
1854 #endif
1855 
1856   /* put together the new matrix */
1857   ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
1858   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
1859   b = (Mat_SeqAIJ*)(fact)->data;
1860   b->free_a       = PETSC_TRUE;
1861   b->free_ij      = PETSC_TRUE;
1862   b->singlemalloc = PETSC_FALSE;
1863   ierr = PetscMalloc(bi[n]*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
1864   b->j          = bj;
1865   b->i          = bi;
1866   for (i=0; i<n; i++) bdiag[i] += bi[i];
1867   b->diag       = bdiag;
1868   b->ilen       = 0;
1869   b->imax       = 0;
1870   b->row        = isrow;
1871   b->col        = iscol;
1872   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1873   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1874   b->icol       = isicol;
1875   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1876   /* In b structure:  Free imax, ilen, old a, old j.
1877      Allocate bdiag, solve_work, new a, new j */
1878   ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
1879   b->maxnz             = b->nz = bi[n] ;
1880   (fact)->info.factor_mallocs    = reallocs;
1881   (fact)->info.fill_ratio_given  = f;
1882   (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1883   (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ;
1884   ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1885   PetscFunctionReturn(0);
1886 }
1887 
1888 #undef __FUNCT__
1889 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ_newdatastruct"
1890 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info)
1891 {
1892   Mat            C = B;
1893   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1894   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
1895   IS             ip=b->row,iip = b->icol;
1896   PetscErrorCode ierr;
1897   const PetscInt *rip,*riip;
1898   PetscInt       i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp;
1899   PetscInt       *ai=a->i,*aj=a->j;
1900   PetscInt       k,jmin,jmax,*c2r,*il,col,nexti,ili,nz;
1901   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
1902   PetscTruth     perm_identity;
1903 
1904   LUShift_Ctx    sctx;
1905   PetscInt       newshift;
1906   PetscReal      rs;
1907   MatScalar      d,*v;
1908 
1909   PetscFunctionBegin;
1910   /* MatPivotSetUp(): initialize shift context sctx */
1911   ierr = PetscMemzero(&sctx,sizeof(LUShift_Ctx));CHKERRQ(ierr);
1912 
1913   /* if both shift schemes are chosen by user, only use info->shiftpd */
1914   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
1915     sctx.shift_top = info->zeropivot;
1916     for (i=0; i<mbs; i++) {
1917       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
1918       d  = (aa)[a->diag[i]];
1919       rs = -PetscAbsScalar(d) - PetscRealPart(d);
1920       v  = aa+ai[i];
1921       nz = ai[i+1] - ai[i];
1922       for (j=0; j<nz; j++)
1923 	rs += PetscAbsScalar(v[j]);
1924       if (rs>sctx.shift_top) sctx.shift_top = rs;
1925     }
1926     sctx.shift_top   *= 1.1;
1927     sctx.nshift_max   = 5;
1928     sctx.shift_lo     = 0.;
1929     sctx.shift_hi     = 1.;
1930   }
1931 
1932   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
1933   ierr  = ISGetIndices(iip,&riip);CHKERRQ(ierr);
1934 
1935   /* allocate working arrays
1936      c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col
1937      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
1938   */
1939   ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&c2r);CHKERRQ(ierr);
1940 
1941   do {
1942     sctx.lushift = PETSC_FALSE;
1943 
1944     for (i=0; i<mbs; i++) c2r[i] = mbs;
1945     il[0] = 0;
1946 
1947     for (k = 0; k<mbs; k++){
1948       /* zero rtmp */
1949       nz = bi[k+1] - bi[k];
1950       bjtmp = bj + bi[k];
1951       for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
1952 
1953       /* load in initial unfactored row */
1954       bval = ba + bi[k];
1955       jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
1956       for (j = jmin; j < jmax; j++){
1957         col = riip[aj[j]];
1958         if (col >= k){ /* only take upper triangular entry */
1959           rtmp[col] = aa[j];
1960           *bval++   = 0.0; /* for in-place factorization */
1961         }
1962       }
1963       /* shift the diagonal of the matrix: ZeropivotApply() */
1964       rtmp[k] += sctx.shift_amount;  /* shift the diagonal of the matrix */
1965 
1966       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
1967       dk = rtmp[k];
1968       i  = c2r[k]; /* first row to be added to k_th row  */
1969 
1970       while (i < k){
1971         nexti = c2r[i]; /* next row to be added to k_th row */
1972 
1973         /* compute multiplier, update diag(k) and U(i,k) */
1974         ili   = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
1975         uikdi = - ba[ili]*ba[bdiag[i]];  /* diagonal(k) */
1976         dk   += uikdi*ba[ili]; /* update diag[k] */
1977         ba[ili] = uikdi; /* -U(i,k) */
1978 
1979         /* add multiple of row i to k-th row */
1980         jmin = ili + 1; jmax = bi[i+1];
1981         if (jmin < jmax){
1982           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
1983           /* update il and c2r for row i */
1984           il[i] = jmin;
1985           j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i;
1986         }
1987         i = nexti;
1988       }
1989 
1990       /* copy data into U(k,:) */
1991       rs   = 0.0;
1992       jmin = bi[k]; jmax = bi[k+1]-1;
1993       if (jmin < jmax) {
1994         for (j=jmin; j<jmax; j++){
1995           col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]);
1996         }
1997         /* add the k-th row into il and c2r */
1998         il[k] = jmin;
1999         i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k;
2000       }
2001 
2002       /* MatPivotCheck() */
2003       sctx.rs  = rs;
2004       sctx.pv  = dk;
2005       if (info->shiftnz){
2006         ierr = MatPivotCheck_nz(info,sctx,k,newshift);CHKERRQ(ierr);
2007       } else if (info->shiftpd){
2008         ierr = MatPivotCheck_pd(info,sctx,k,newshift);CHKERRQ(ierr);
2009       } else if (info->shiftinblocks){
2010         ierr = MatPivotCheck_inblocks(info,sctx,k,newshift);CHKERRQ(ierr);
2011       } else {
2012         ierr = MatPivotCheck_none(info,sctx,k,newshift);CHKERRQ(ierr);
2013       }
2014       dk = sctx.pv;
2015       if (newshift == 1) break;
2016 
2017       ba[bdiag[k]] = 1.0/dk; /* U(k,k) */
2018     }
2019   } while (sctx.lushift);
2020 
2021   ierr = PetscFree3(rtmp,il,c2r);CHKERRQ(ierr);
2022   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2023   ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr);
2024 
2025   ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
2026   if (perm_identity){
2027     (B)->ops->solve           = MatSolve_SeqSBAIJ_1_NaturalOrdering_newdatastruct;
2028     (B)->ops->solvetranspose  = 0;
2029     (B)->ops->forwardsolve    = 0;
2030     (B)->ops->backwardsolve   = 0;
2031   } else {
2032     (B)->ops->solve           = MatSolve_SeqSBAIJ_1_newdatastruct;
2033     (B)->ops->solvetranspose  = 0;
2034     (B)->ops->forwardsolve    = 0;
2035     (B)->ops->backwardsolve   = 0;
2036   }
2037 
2038   C->assembled    = PETSC_TRUE;
2039   C->preallocated = PETSC_TRUE;
2040   ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr);
2041 
2042   /* MatPivotView() */
2043   if (sctx.nshift){
2044     if (info->shiftpd) {
2045       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);
2046     } else if (info->shiftnz) {
2047       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2048     } else if (info->shiftinblocks){
2049       ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftinblocks);CHKERRQ(ierr);
2050     }
2051   }
2052   PetscFunctionReturn(0);
2053 }
2054 
2055 #undef __FUNCT__
2056 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ"
2057 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info)
2058 {
2059   Mat            C = B;
2060   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
2061   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
2062   IS             ip=b->row,iip = b->icol;
2063   PetscErrorCode ierr;
2064   const PetscInt *rip,*riip;
2065   PetscInt       i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol,*bjtmp;
2066   PetscInt       *ai=a->i,*aj=a->j;
2067   PetscInt       k,jmin,jmax,*jl,*il,col,nexti,ili,nz;
2068   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
2069   PetscReal      zeropivot,rs,shiftnz;
2070   PetscReal      shiftpd;
2071   ChShift_Ctx    sctx;
2072   PetscInt       newshift;
2073   PetscTruth     perm_identity;
2074 
2075   PetscFunctionBegin;
2076   shiftnz   = info->shiftnz;
2077   shiftpd   = info->shiftpd;
2078   zeropivot = info->zeropivot;
2079 
2080   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
2081   ierr  = ISGetIndices(iip,&riip);CHKERRQ(ierr);
2082 
2083   /* initialization */
2084   ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&jl);CHKERRQ(ierr);
2085   sctx.shift_amount = 0;
2086   sctx.nshift       = 0;
2087   do {
2088     sctx.chshift = PETSC_FALSE;
2089     for (i=0; i<mbs; i++) jl[i] = mbs;
2090     il[0] = 0;
2091 
2092     for (k = 0; k<mbs; k++){
2093       /* zero rtmp */
2094       nz = bi[k+1] - bi[k];
2095       bjtmp = bj + bi[k];
2096       for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
2097 
2098       bval = ba + bi[k];
2099       /* initialize k-th row by the perm[k]-th row of A */
2100       jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2101       for (j = jmin; j < jmax; j++){
2102         col = riip[aj[j]];
2103         if (col >= k){ /* only take upper triangular entry */
2104           rtmp[col] = aa[j];
2105           *bval++  = 0.0; /* for in-place factorization */
2106         }
2107       }
2108       /* shift the diagonal of the matrix */
2109       if (sctx.nshift) rtmp[k] += sctx.shift_amount;
2110 
2111       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
2112       dk = rtmp[k];
2113       i = jl[k]; /* first row to be added to k_th row  */
2114 
2115       while (i < k){
2116         nexti = jl[i]; /* next row to be added to k_th row */
2117 
2118         /* compute multiplier, update diag(k) and U(i,k) */
2119         ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2120         uikdi = - ba[ili]*ba[bi[i]];  /* diagonal(k) */
2121         dk += uikdi*ba[ili];
2122         ba[ili] = uikdi; /* -U(i,k) */
2123 
2124         /* add multiple of row i to k-th row */
2125         jmin = ili + 1; jmax = bi[i+1];
2126         if (jmin < jmax){
2127           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2128           /* update il and jl for row i */
2129           il[i] = jmin;
2130           j = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
2131         }
2132         i = nexti;
2133       }
2134 
2135       /* shift the diagonals when zero pivot is detected */
2136       /* compute rs=sum of abs(off-diagonal) */
2137       rs   = 0.0;
2138       jmin = bi[k]+1;
2139       nz   = bi[k+1] - jmin;
2140       bcol = bj + jmin;
2141       for (j=0; j<nz; j++) {
2142         rs += PetscAbsScalar(rtmp[bcol[j]]);
2143       }
2144 
2145       sctx.rs = rs;
2146       sctx.pv = dk;
2147       ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr);
2148 
2149       if (newshift == 1) {
2150         if (!sctx.shift_amount) {
2151           sctx.shift_amount = 1e-5;
2152         }
2153         break;
2154       }
2155 
2156       /* copy data into U(k,:) */
2157       ba[bi[k]] = 1.0/dk; /* U(k,k) */
2158       jmin = bi[k]+1; jmax = bi[k+1];
2159       if (jmin < jmax) {
2160         for (j=jmin; j<jmax; j++){
2161           col = bj[j]; ba[j] = rtmp[col];
2162         }
2163         /* add the k-th row into il and jl */
2164         il[k] = jmin;
2165         i = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
2166       }
2167     }
2168   } while (sctx.chshift);
2169   ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr);
2170   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2171   ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr);
2172 
2173   ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
2174   if (perm_identity){
2175     (B)->ops->solve           = MatSolve_SeqSBAIJ_1_NaturalOrdering;
2176     (B)->ops->solvetranspose  = MatSolve_SeqSBAIJ_1_NaturalOrdering;
2177     (B)->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering;
2178     (B)->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering;
2179   } else {
2180     (B)->ops->solve           = MatSolve_SeqSBAIJ_1;
2181     (B)->ops->solvetranspose  = MatSolve_SeqSBAIJ_1;
2182     (B)->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1;
2183     (B)->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1;
2184   }
2185 
2186   C->assembled    = PETSC_TRUE;
2187   C->preallocated = PETSC_TRUE;
2188   ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr);
2189   if (sctx.nshift){
2190     if (shiftnz) {
2191       ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2192     } else if (shiftpd) {
2193       ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2194     }
2195   }
2196   PetscFunctionReturn(0);
2197 }
2198 
2199 /*
2200    icc() under revised new data structure.
2201    Factored arrays bj and ba are stored as
2202      U(0,:),...,U(i,:),U(n-1,:)
2203 
2204    ui=fact->i is an array of size n+1, in which
2205    ui+
2206      ui[i]:  points to 1st entry of U(i,:),i=0,...,n-1
2207      ui[n]:  points to U(n-1,n-1)+1
2208 
2209   udiag=fact->diag is an array of size n,in which
2210      udiag[i]: points to diagonal of U(i,:), i=0,...,n-1
2211 
2212    U(i,:) contains udiag[i] as its last entry, i.e.,
2213     U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i])
2214 */
2215 
2216 #undef __FUNCT__
2217 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ_newdatastruct"
2218 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2219 {
2220   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2221   Mat_SeqSBAIJ       *b;
2222   PetscErrorCode     ierr;
2223   PetscTruth         perm_identity,missing;
2224   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag;
2225   const PetscInt     *rip,*riip;
2226   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
2227   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL,d;
2228   PetscInt           ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
2229   PetscReal          fill=info->fill,levels=info->levels;
2230   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2231   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
2232   PetscBT            lnkbt;
2233   IS                 iperm;
2234 
2235   PetscFunctionBegin;
2236   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);
2237   ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
2238   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
2239   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2240   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2241 
2242   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2243   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2244   ui[0] = 0;
2245 
2246   /* ICC(0) without matrix ordering: simply rearrange column indices */
2247   if (!levels && perm_identity) {
2248     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2249     cols = uj;
2250     for (i=0; i<am; i++) {
2251       ncols    = ai[i+1] - a->diag[i];
2252       ui[i+1]  = ui[i] + ncols;
2253       udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */
2254 
2255       aj   = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */
2256       ncols--; /* exclude diagonal */
2257       for (j=0; j<ncols; j++) *cols++ = aj[j];
2258       *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */
2259     }
2260   } else { /* case: levels>0 || (levels=0 && !perm_identity) */
2261     ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2262     ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2263 
2264     /* initialization */
2265     ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr);
2266 
2267     /* jl: linked list for storing indices of the pivot rows
2268        il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2269     ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr);
2270     for (i=0; i<am; i++){
2271       jl[i] = am; il[i] = 0;
2272     }
2273 
2274     /* create and initialize a linked list for storing column indices of the active row k */
2275     nlnk = am + 1;
2276     ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2277 
2278     /* initial FreeSpace size is fill*(ai[am]+1) */
2279     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2280     current_space = free_space;
2281     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr);
2282     current_space_lvl = free_space_lvl;
2283 
2284     for (k=0; k<am; k++){  /* for each active row k */
2285       /* initialize lnk by the column indices of row rip[k] of A */
2286       nzk   = 0;
2287       ncols = ai[rip[k]+1] - ai[rip[k]];
2288       if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2289       ncols_upper = 0;
2290       for (j=0; j<ncols; j++){
2291         i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2292         if (riip[i] >= k){ /* only take upper triangular entry */
2293           ajtmp[ncols_upper] = i;
2294           ncols_upper++;
2295         }
2296       }
2297       ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2298       nzk += nlnk;
2299 
2300       /* update lnk by computing fill-in for each pivot row to be merged in */
2301       prow = jl[k]; /* 1st pivot row */
2302 
2303       while (prow < k){
2304         nextprow = jl[prow];
2305 
2306         /* merge prow into k-th row */
2307         jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2308         jmax = ui[prow+1];
2309         ncols = jmax-jmin;
2310         i     = jmin - ui[prow];
2311         cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2312         uj    = uj_lvl_ptr[prow] + i; /* levels of cols */
2313         j     = *(uj - 1);
2314         ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr);
2315         nzk += nlnk;
2316 
2317         /* update il and jl for prow */
2318         if (jmin < jmax){
2319           il[prow] = jmin;
2320           j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2321         }
2322         prow = nextprow;
2323       }
2324 
2325       /* if free space is not available, make more free space */
2326       if (current_space->local_remaining<nzk) {
2327         i  = am - k + 1; /* num of unfactored rows */
2328         i *= PetscMin(nzk, i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */
2329         ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2330         ierr = PetscFreeSpaceGet(i,&current_space_lvl);CHKERRQ(ierr);
2331         reallocs++;
2332       }
2333 
2334       /* copy data into free_space and free_space_lvl, then initialize lnk */
2335       if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2336       ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
2337 
2338       /* add the k-th row into il and jl */
2339       if (nzk > 1){
2340         i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2341         jl[k] = jl[i]; jl[i] = k;
2342         il[k] = ui[k] + 1;
2343       }
2344       uj_ptr[k]     = current_space->array;
2345       uj_lvl_ptr[k] = current_space_lvl->array;
2346 
2347       current_space->array           += nzk;
2348       current_space->local_used      += nzk;
2349       current_space->local_remaining -= nzk;
2350 
2351       current_space_lvl->array           += nzk;
2352       current_space_lvl->local_used      += nzk;
2353       current_space_lvl->local_remaining -= nzk;
2354 
2355       ui[k+1] = ui[k] + nzk;
2356     }
2357 
2358 #if defined(PETSC_USE_INFO)
2359     if (ai[am] != 0) {
2360       PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]);
2361       ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2362       ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2363       ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2364     } else {
2365       ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2366     }
2367 #endif
2368 
2369     ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2370     ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2371     ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr);
2372     ierr = PetscFree(ajtmp);CHKERRQ(ierr);
2373 
2374     /* destroy list of free space and other temporary array(s) */
2375     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2376     ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor in newdatastruct */
2377     ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2378     ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2379 
2380   } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2381 
2382   /* put together the new matrix in MATSEQSBAIJ format */
2383 
2384   b    = (Mat_SeqSBAIJ*)(fact)->data;
2385   b->singlemalloc = PETSC_FALSE;
2386   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2387   b->j    = uj;
2388   b->i    = ui;
2389   b->diag = udiag;
2390   b->free_diag = PETSC_TRUE;
2391   b->ilen = 0;
2392   b->imax = 0;
2393   b->row  = perm;
2394   b->col  = perm;
2395   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2396   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2397   b->icol = iperm;
2398   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2399   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2400   ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2401   b->maxnz   = b->nz = ui[am];
2402   b->free_a  = PETSC_TRUE;
2403   b->free_ij = PETSC_TRUE;
2404 
2405   (fact)->info.factor_mallocs    = reallocs;
2406   (fact)->info.fill_ratio_given  = fill;
2407   if (ai[am] != 0) {
2408     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2409   } else {
2410     (fact)->info.fill_ratio_needed = 0.0;
2411   }
2412   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_newdatastruct;
2413   PetscFunctionReturn(0);
2414 }
2415 
2416 #undef __FUNCT__
2417 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ"
2418 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2419 {
2420   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2421   Mat_SeqSBAIJ       *b;
2422   PetscErrorCode     ierr;
2423   PetscTruth         perm_identity,missing;
2424   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag;
2425   const PetscInt     *rip,*riip;
2426   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
2427   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL,d;
2428   PetscInt           ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
2429   PetscReal          fill=info->fill,levels=info->levels;
2430   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2431   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
2432   PetscBT            lnkbt;
2433   IS                 iperm;
2434   PetscTruth         newdatastruct=PETSC_FALSE;
2435 
2436   PetscFunctionBegin;
2437   ierr = PetscOptionsGetTruth(PETSC_NULL,"-icc_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
2438   if(newdatastruct){
2439     ierr = MatICCFactorSymbolic_SeqAIJ_newdatastruct(fact,A,perm,info);CHKERRQ(ierr);
2440     PetscFunctionReturn(0);
2441   }
2442 
2443   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);
2444   ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
2445   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
2446   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2447   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2448 
2449   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2450   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2451   ui[0] = 0;
2452 
2453   /* ICC(0) without matrix ordering: simply copies fill pattern */
2454   if (!levels && perm_identity) {
2455 
2456     for (i=0; i<am; i++) {
2457       ui[i+1]  = ui[i] + ai[i+1] - a->diag[i];
2458       udiag[i] = ui[i];
2459     }
2460     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2461     cols = uj;
2462     for (i=0; i<am; i++) {
2463       aj    = a->j + a->diag[i];
2464       ncols = ui[i+1] - ui[i];
2465       for (j=0; j<ncols; j++) *cols++ = *aj++;
2466     }
2467   } else { /* case: levels>0 || (levels=0 && !perm_identity) */
2468     ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2469     ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2470 
2471     /* initialization */
2472     ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr);
2473 
2474     /* jl: linked list for storing indices of the pivot rows
2475        il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2476     ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr);
2477     for (i=0; i<am; i++){
2478       jl[i] = am; il[i] = 0;
2479     }
2480 
2481     /* create and initialize a linked list for storing column indices of the active row k */
2482     nlnk = am + 1;
2483     ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2484 
2485     /* initial FreeSpace size is fill*(ai[am]+1) */
2486     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2487     current_space = free_space;
2488     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr);
2489     current_space_lvl = free_space_lvl;
2490 
2491     for (k=0; k<am; k++){  /* for each active row k */
2492       /* initialize lnk by the column indices of row rip[k] of A */
2493       nzk   = 0;
2494       ncols = ai[rip[k]+1] - ai[rip[k]];
2495       if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2496       ncols_upper = 0;
2497       for (j=0; j<ncols; j++){
2498         i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2499         if (riip[i] >= k){ /* only take upper triangular entry */
2500           ajtmp[ncols_upper] = i;
2501           ncols_upper++;
2502         }
2503       }
2504       ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2505       nzk += nlnk;
2506 
2507       /* update lnk by computing fill-in for each pivot row to be merged in */
2508       prow = jl[k]; /* 1st pivot row */
2509 
2510       while (prow < k){
2511         nextprow = jl[prow];
2512 
2513         /* merge prow into k-th row */
2514         jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2515         jmax = ui[prow+1];
2516         ncols = jmax-jmin;
2517         i     = jmin - ui[prow];
2518         cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2519         uj    = uj_lvl_ptr[prow] + i; /* levels of cols */
2520         j     = *(uj - 1);
2521         ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr);
2522         nzk += nlnk;
2523 
2524         /* update il and jl for prow */
2525         if (jmin < jmax){
2526           il[prow] = jmin;
2527           j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2528         }
2529         prow = nextprow;
2530       }
2531 
2532       /* if free space is not available, make more free space */
2533       if (current_space->local_remaining<nzk) {
2534         i = am - k + 1; /* num of unfactored rows */
2535         i *= PetscMin(nzk, (i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2536         ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2537         ierr = PetscFreeSpaceGet(i,&current_space_lvl);CHKERRQ(ierr);
2538         reallocs++;
2539       }
2540 
2541       /* copy data into free_space and free_space_lvl, then initialize lnk */
2542       if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2543       ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
2544 
2545       /* add the k-th row into il and jl */
2546       if (nzk > 1){
2547         i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2548         jl[k] = jl[i]; jl[i] = k;
2549         il[k] = ui[k] + 1;
2550       }
2551       uj_ptr[k]     = current_space->array;
2552       uj_lvl_ptr[k] = current_space_lvl->array;
2553 
2554       current_space->array           += nzk;
2555       current_space->local_used      += nzk;
2556       current_space->local_remaining -= nzk;
2557 
2558       current_space_lvl->array           += nzk;
2559       current_space_lvl->local_used      += nzk;
2560       current_space_lvl->local_remaining -= nzk;
2561 
2562       ui[k+1] = ui[k] + nzk;
2563     }
2564 
2565 #if defined(PETSC_USE_INFO)
2566     if (ai[am] != 0) {
2567       PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]);
2568       ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2569       ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2570       ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2571     } else {
2572       ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2573     }
2574 #endif
2575 
2576     ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2577     ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2578     ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr);
2579     ierr = PetscFree(ajtmp);CHKERRQ(ierr);
2580 
2581     /* destroy list of free space and other temporary array(s) */
2582     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2583     ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
2584     ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2585     ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2586 
2587   } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2588 
2589   /* put together the new matrix in MATSEQSBAIJ format */
2590 
2591   b    = (Mat_SeqSBAIJ*)(fact)->data;
2592   b->singlemalloc = PETSC_FALSE;
2593   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2594   b->j    = uj;
2595   b->i    = ui;
2596   b->diag = udiag;
2597   b->free_diag = PETSC_TRUE;
2598   b->ilen = 0;
2599   b->imax = 0;
2600   b->row  = perm;
2601   b->col  = perm;
2602   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2603   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2604   b->icol = iperm;
2605   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2606   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2607   ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2608   b->maxnz   = b->nz = ui[am];
2609   b->free_a  = PETSC_TRUE;
2610   b->free_ij = PETSC_TRUE;
2611 
2612   (fact)->info.factor_mallocs    = reallocs;
2613   (fact)->info.fill_ratio_given  = fill;
2614   if (ai[am] != 0) {
2615     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2616   } else {
2617     (fact)->info.fill_ratio_needed = 0.0;
2618   }
2619   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2620   PetscFunctionReturn(0);
2621 }
2622 
2623 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2624 {
2625   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2626   Mat_SeqSBAIJ       *b;
2627   PetscErrorCode     ierr;
2628   PetscTruth         perm_identity;
2629   PetscReal          fill = info->fill;
2630   const PetscInt     *rip,*riip;
2631   PetscInt           i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow;
2632   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
2633   PetscInt           nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr,*udiag;
2634   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2635   PetscBT            lnkbt;
2636   IS                 iperm;
2637 
2638   PetscFunctionBegin;
2639   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);
2640   /* check whether perm is the identity mapping */
2641   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2642   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2643   ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2644   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2645 
2646   /* initialization */
2647   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2648   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2649   ui[0] = 0;
2650 
2651   /* jl: linked list for storing indices of the pivot rows
2652      il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2653   ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr);
2654   for (i=0; i<am; i++){
2655     jl[i] = am; il[i] = 0;
2656   }
2657 
2658   /* create and initialize a linked list for storing column indices of the active row k */
2659   nlnk = am + 1;
2660   ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2661 
2662   /* initial FreeSpace size is fill*(ai[am]+1) */
2663   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2664   current_space = free_space;
2665 
2666   for (k=0; k<am; k++){  /* for each active row k */
2667     /* initialize lnk by the column indices of row rip[k] of A */
2668     nzk   = 0;
2669     ncols = ai[rip[k]+1] - ai[rip[k]];
2670     if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2671     ncols_upper = 0;
2672     for (j=0; j<ncols; j++){
2673       i = riip[*(aj + ai[rip[k]] + j)];
2674       if (i >= k){ /* only take upper triangular entry */
2675         cols[ncols_upper] = i;
2676         ncols_upper++;
2677       }
2678     }
2679     ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2680     nzk += nlnk;
2681 
2682     /* update lnk by computing fill-in for each pivot row to be merged in */
2683     prow = jl[k]; /* 1st pivot row */
2684 
2685     while (prow < k){
2686       nextprow = jl[prow];
2687       /* merge prow into k-th row */
2688       jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2689       jmax = ui[prow+1];
2690       ncols = jmax-jmin;
2691       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2692       ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2693       nzk += nlnk;
2694 
2695       /* update il and jl for prow */
2696       if (jmin < jmax){
2697         il[prow] = jmin;
2698         j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
2699       }
2700       prow = nextprow;
2701     }
2702 
2703     /* if free space is not available, make more free space */
2704     if (current_space->local_remaining<nzk) {
2705       i  = am - k + 1; /* num of unfactored rows */
2706       i *= PetscMin(nzk,i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */
2707       ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2708       reallocs++;
2709     }
2710 
2711     /* copy data into free space, then initialize lnk */
2712     ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
2713 
2714     /* add the k-th row into il and jl */
2715     if (nzk-1 > 0){
2716       i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2717       jl[k] = jl[i]; jl[i] = k;
2718       il[k] = ui[k] + 1;
2719     }
2720     ui_ptr[k] = current_space->array;
2721     current_space->array           += nzk;
2722     current_space->local_used      += nzk;
2723     current_space->local_remaining -= nzk;
2724 
2725     ui[k+1] = ui[k] + nzk;
2726   }
2727 
2728 #if defined(PETSC_USE_INFO)
2729   if (ai[am] != 0) {
2730     PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]);
2731     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2732     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2733     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2734   } else {
2735      ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2736   }
2737 #endif
2738 
2739   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2740   ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2741   ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr);
2742 
2743   /* destroy list of free space and other temporary array(s) */
2744   ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2745   ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor in newdatastruct */
2746   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2747 
2748   /* put together the new matrix in MATSEQSBAIJ format */
2749 
2750   b = (Mat_SeqSBAIJ*)(fact)->data;
2751   b->singlemalloc = PETSC_FALSE;
2752   b->free_a       = PETSC_TRUE;
2753   b->free_ij      = PETSC_TRUE;
2754   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2755   b->j    = uj;
2756   b->i    = ui;
2757   b->diag = udiag;
2758   b->free_diag = PETSC_TRUE;
2759   b->ilen = 0;
2760   b->imax = 0;
2761   b->row  = perm;
2762   b->col  = perm;
2763   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2764   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2765   b->icol = iperm;
2766   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2767   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2768   ierr    = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2769   b->maxnz = b->nz = ui[am];
2770 
2771   (fact)->info.factor_mallocs    = reallocs;
2772   (fact)->info.fill_ratio_given  = fill;
2773   if (ai[am] != 0) {
2774     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2775   } else {
2776     (fact)->info.fill_ratio_needed = 0.0;
2777   }
2778   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_newdatastruct;
2779   PetscFunctionReturn(0);
2780 }
2781 
2782 #undef __FUNCT__
2783 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ"
2784 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2785 {
2786   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2787   Mat_SeqSBAIJ       *b;
2788   PetscErrorCode     ierr;
2789   PetscTruth         perm_identity;
2790   PetscReal          fill = info->fill;
2791   const PetscInt     *rip,*riip;
2792   PetscInt           i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow;
2793   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
2794   PetscInt           nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr;
2795   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2796   PetscBT            lnkbt;
2797   IS                 iperm;
2798   PetscTruth         newdatastruct=PETSC_FALSE;
2799 
2800   PetscFunctionBegin;
2801   ierr = PetscOptionsGetTruth(PETSC_NULL,"-cholesky_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
2802   if(newdatastruct){
2803     ierr = MatCholeskyFactorSymbolic_SeqAIJ_newdatastruct(fact,A,perm,info);CHKERRQ(ierr);
2804     PetscFunctionReturn(0);
2805   }
2806 
2807   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);
2808   /* check whether perm is the identity mapping */
2809   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2810   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2811   ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2812   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2813 
2814   /* initialization */
2815   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2816   ui[0] = 0;
2817 
2818   /* jl: linked list for storing indices of the pivot rows
2819      il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2820   ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr);
2821   for (i=0; i<am; i++){
2822     jl[i] = am; il[i] = 0;
2823   }
2824 
2825   /* create and initialize a linked list for storing column indices of the active row k */
2826   nlnk = am + 1;
2827   ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2828 
2829   /* initial FreeSpace size is fill*(ai[am]+1) */
2830   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2831   current_space = free_space;
2832 
2833   for (k=0; k<am; k++){  /* for each active row k */
2834     /* initialize lnk by the column indices of row rip[k] of A */
2835     nzk   = 0;
2836     ncols = ai[rip[k]+1] - ai[rip[k]];
2837     if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2838     ncols_upper = 0;
2839     for (j=0; j<ncols; j++){
2840       i = riip[*(aj + ai[rip[k]] + j)];
2841       if (i >= k){ /* only take upper triangular entry */
2842         cols[ncols_upper] = i;
2843         ncols_upper++;
2844       }
2845     }
2846     ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2847     nzk += nlnk;
2848 
2849     /* update lnk by computing fill-in for each pivot row to be merged in */
2850     prow = jl[k]; /* 1st pivot row */
2851 
2852     while (prow < k){
2853       nextprow = jl[prow];
2854       /* merge prow into k-th row */
2855       jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2856       jmax = ui[prow+1];
2857       ncols = jmax-jmin;
2858       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2859       ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2860       nzk += nlnk;
2861 
2862       /* update il and jl for prow */
2863       if (jmin < jmax){
2864         il[prow] = jmin;
2865         j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
2866       }
2867       prow = nextprow;
2868     }
2869 
2870     /* if free space is not available, make more free space */
2871     if (current_space->local_remaining<nzk) {
2872       i = am - k + 1; /* num of unfactored rows */
2873       i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2874       ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2875       reallocs++;
2876     }
2877 
2878     /* copy data into free space, then initialize lnk */
2879     ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
2880 
2881     /* add the k-th row into il and jl */
2882     if (nzk-1 > 0){
2883       i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2884       jl[k] = jl[i]; jl[i] = k;
2885       il[k] = ui[k] + 1;
2886     }
2887     ui_ptr[k] = current_space->array;
2888     current_space->array           += nzk;
2889     current_space->local_used      += nzk;
2890     current_space->local_remaining -= nzk;
2891 
2892     ui[k+1] = ui[k] + nzk;
2893   }
2894 
2895 #if defined(PETSC_USE_INFO)
2896   if (ai[am] != 0) {
2897     PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]);
2898     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2899     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2900     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2901   } else {
2902      ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2903   }
2904 #endif
2905 
2906   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2907   ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2908   ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr);
2909 
2910   /* destroy list of free space and other temporary array(s) */
2911   ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2912   ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
2913   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2914 
2915   /* put together the new matrix in MATSEQSBAIJ format */
2916 
2917   b = (Mat_SeqSBAIJ*)(fact)->data;
2918   b->singlemalloc = PETSC_FALSE;
2919   b->free_a       = PETSC_TRUE;
2920   b->free_ij      = PETSC_TRUE;
2921   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2922   b->j    = uj;
2923   b->i    = ui;
2924   b->diag = 0;
2925   b->ilen = 0;
2926   b->imax = 0;
2927   b->row  = perm;
2928   b->col  = perm;
2929   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2930   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2931   b->icol = iperm;
2932   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2933   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2934   ierr    = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2935   b->maxnz = b->nz = ui[am];
2936 
2937   (fact)->info.factor_mallocs    = reallocs;
2938   (fact)->info.fill_ratio_given  = fill;
2939   if (ai[am] != 0) {
2940     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2941   } else {
2942     (fact)->info.fill_ratio_needed = 0.0;
2943   }
2944   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2945   PetscFunctionReturn(0);
2946 }
2947 
2948 #undef __FUNCT__
2949 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_newdatastruct"
2950 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx)
2951 {
2952   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
2953   PetscErrorCode    ierr;
2954   PetscInt          n = A->rmap->n;
2955   const PetscInt    *ai = a->i,*aj = a->j,*vi;
2956   PetscScalar       *x,sum;
2957   const PetscScalar *b;
2958   const MatScalar   *aa = a->a,*v;
2959   PetscInt          i,nz;
2960 
2961   PetscFunctionBegin;
2962   if (!n) PetscFunctionReturn(0);
2963 
2964   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2965   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2966 
2967   /* forward solve the lower triangular */
2968   x[0] = b[0];
2969   v    = aa;
2970   vi   = aj;
2971   for (i=1; i<n; i++) {
2972     nz  = ai[i+1] - ai[i];
2973     sum = b[i];
2974     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
2975     v  += nz;
2976     vi += nz;
2977     x[i] = sum;
2978   }
2979 
2980   /* backward solve the upper triangular */
2981   v   = aa + ai[n+1];
2982   vi  = aj + ai[n+1];
2983   for (i=n-1; i>=0; i--){
2984     nz = ai[2*n-i +1] - ai[2*n-i]-1;
2985     sum = x[i];
2986     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
2987     v   += nz;
2988     vi  += nz; vi++;
2989     x[i] = *v++ *sum; /* x[i]=aa[adiag[i]]*sum; v++; */
2990   }
2991 
2992   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
2993   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2994   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2995   PetscFunctionReturn(0);
2996 }
2997 
2998 #undef __FUNCT__
2999 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_newdatastruct_v2"
3000 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct_v2(Mat A,Vec bb,Vec xx)
3001 {
3002   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
3003   PetscErrorCode    ierr;
3004   PetscInt          n = A->rmap->n;
3005   const PetscInt    *ai = a->i,*aj = a->j,*adiag = a->diag,*vi;
3006   PetscScalar       *x,sum;
3007   const PetscScalar *b;
3008   const MatScalar   *aa = a->a,*v;
3009   PetscInt          i,nz;
3010 
3011   PetscFunctionBegin;
3012   if (!n) PetscFunctionReturn(0);
3013 
3014   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3015   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3016 
3017   /* forward solve the lower triangular */
3018   x[0] = b[0];
3019   v    = aa;
3020   vi   = aj;
3021   for (i=1; i<n; i++) {
3022     nz  = ai[i+1] - ai[i];
3023     sum = b[i];
3024     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
3025     v  += nz;
3026     vi += nz;
3027     x[i] = sum;
3028   }
3029 
3030   /* backward solve the upper triangular */
3031   /*  v   = aa + ai[n+1];
3032       vi  = aj + ai[n+1]; */
3033   v  = aa + adiag[n-1];
3034   vi = aj + adiag[n-1];
3035   for (i=n-1; i>=0; i--){
3036     nz = adiag[i] - adiag[i+1]-1;
3037     sum = x[i];
3038     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
3039     v   += nz;
3040     vi  += nz; vi++;
3041     x[i] = *v++ *sum; /* x[i]=aa[adiag[i]]*sum; v++; */
3042   }
3043 
3044   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
3045   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3046   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3047   PetscFunctionReturn(0);
3048 }
3049 
3050 #undef __FUNCT__
3051 #define __FUNCT__ "MatSolve_SeqAIJ_newdatastruct"
3052 PetscErrorCode MatSolve_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec xx)
3053 {
3054   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
3055   IS                iscol = a->col,isrow = a->row;
3056   PetscErrorCode    ierr;
3057   PetscInt          i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,nz,k;
3058   const PetscInt    *rout,*cout,*r,*c;
3059   PetscScalar       *x,*tmp,*tmps,sum;
3060   const PetscScalar *b;
3061   const MatScalar   *aa = a->a,*v;
3062 
3063   PetscFunctionBegin;
3064   if (!n) PetscFunctionReturn(0);
3065 
3066   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3067   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3068   tmp  = a->solve_work;
3069 
3070   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
3071   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
3072 
3073   /* forward solve the lower triangular */
3074   tmp[0] = b[*r++];
3075   tmps   = tmp;
3076   v      = aa;
3077   vi     = aj;
3078   for (i=1; i<n; i++) {
3079     nz  = ai[i+1] - ai[i];
3080     sum = b[*r++];
3081     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
3082     tmp[i] = sum;
3083     v += nz; vi += nz;
3084   }
3085 
3086   /* backward solve the upper triangular */
3087   k  = n+1;
3088   v  = aa + ai[k]; /* 1st entry of U(n-1,:) */
3089   vi = aj + ai[k];
3090   for (i=n-1; i>=0; i--){
3091     k  = 2*n-i;
3092     nz = ai[k +1] - ai[k] - 1;
3093     sum = tmp[i];
3094     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
3095     x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */
3096     v += nz+1; vi += nz+1;
3097   }
3098 
3099   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
3100   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
3101   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3102   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3103   ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr);
3104   PetscFunctionReturn(0);
3105 }
3106 
3107 #undef __FUNCT__
3108 #define __FUNCT__ "MatSolve_SeqAIJ_newdatastruct_v2"
3109 PetscErrorCode MatSolve_SeqAIJ_newdatastruct_v2(Mat A,Vec bb,Vec xx)
3110 {
3111   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
3112   IS                iscol = a->col,isrow = a->row;
3113   PetscErrorCode    ierr;
3114   PetscInt          i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz;
3115   const PetscInt    *rout,*cout,*r,*c;
3116   PetscScalar       *x,*tmp,sum;
3117   const PetscScalar *b;
3118   const MatScalar   *aa = a->a,*v;
3119 
3120   PetscFunctionBegin;
3121   if (!n) PetscFunctionReturn(0);
3122 
3123   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3124   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3125   tmp  = a->solve_work;
3126 
3127   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
3128   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
3129 
3130   /* forward solve the lower triangular */
3131   tmp[0] = b[r[0]];
3132   v      = aa;
3133   vi     = aj;
3134   for (i=1; i<n; i++) {
3135     nz  = ai[i+1] - ai[i];
3136     sum = b[r[i]];
3137     PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
3138     tmp[i] = sum;
3139     v += nz; vi += nz;
3140   }
3141 
3142   /* backward solve the upper triangular */
3143   v  = aa + adiag[n-1]; /* 1st entry of U(n-1,:) */
3144   vi = aj + adiag[n-1];
3145   for (i=n-1; i>=0; i--){
3146     nz = adiag[i]-adiag[i+1]-1;
3147     sum = tmp[i];
3148     PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
3149     x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */
3150     v += nz+1; vi += nz+1;
3151   }
3152 
3153   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
3154   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
3155   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3156   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3157   ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr);
3158   PetscFunctionReturn(0);
3159 }
3160 
3161 #undef __FUNCT__
3162 #define __FUNCT__ "MatILUDTFactor_SeqAIJ"
3163 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact)
3164 {
3165   Mat                B = *fact;
3166   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b;
3167   IS                 isicol;
3168   PetscErrorCode     ierr;
3169   const PetscInt     *r,*ic;
3170   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag;
3171   PetscInt           *bi,*bj,*bdiag,*bdiag_rev;
3172   PetscInt           row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au;
3173   PetscInt           nlnk,*lnk;
3174   PetscBT            lnkbt;
3175   PetscTruth         row_identity,icol_identity,both_identity;
3176   MatScalar          *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp;
3177   const PetscInt     *ics;
3178   PetscInt           j,nz,*pj,*bjtmp,k,ncut,*jtmp;
3179   PetscReal          dt=info->dt,dtcol=info->dtcol,shift=info->shiftinblocks;
3180   PetscInt           dtcount=(PetscInt)info->dtcount,nnz_max;
3181   PetscTruth         missing;
3182 
3183   PetscFunctionBegin;
3184 
3185   if (dt      == PETSC_DEFAULT) dt      = 0.005;
3186   if (dtcol   == PETSC_DEFAULT) dtcol   = 0.01; /* XXX unused! */
3187   if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax);
3188 
3189   /* ------- symbolic factorization, can be reused ---------*/
3190   ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
3191   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
3192   adiag=a->diag;
3193 
3194   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
3195 
3196   /* bdiag is location of diagonal in factor */
3197   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);     /* becomes b->diag */
3198   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag_rev);CHKERRQ(ierr); /* temporary */
3199 
3200   /* allocate row pointers bi */
3201   ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
3202 
3203   /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */
3204   if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */
3205   nnz_max  = ai[n]+2*n*dtcount+2;
3206 
3207   ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
3208   ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr);
3209 
3210   /* put together the new matrix */
3211   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
3212   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
3213   b    = (Mat_SeqAIJ*)(B)->data;
3214   b->free_a       = PETSC_TRUE;
3215   b->free_ij      = PETSC_TRUE;
3216   b->singlemalloc = PETSC_FALSE;
3217   b->a          = ba;
3218   b->j          = bj;
3219   b->i          = bi;
3220   b->diag       = bdiag;
3221   b->ilen       = 0;
3222   b->imax       = 0;
3223   b->row        = isrow;
3224   b->col        = iscol;
3225   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
3226   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
3227   b->icol       = isicol;
3228   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
3229 
3230   ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
3231   b->maxnz = nnz_max;
3232 
3233   (B)->factor                = MAT_FACTOR_ILUDT;
3234   (B)->info.factor_mallocs   = 0;
3235   (B)->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]);
3236   CHKMEMQ;
3237   /* ------- end of symbolic factorization ---------*/
3238 
3239   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
3240   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
3241   ics  = ic;
3242 
3243   /* linked list for storing column indices of the active row */
3244   nlnk = n + 1;
3245   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3246 
3247   /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */
3248   ierr = PetscMalloc2(n,PetscInt,&im,n,PetscInt,&jtmp);CHKERRQ(ierr);
3249   /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */
3250   ierr = PetscMalloc2(n,MatScalar,&rtmp,n,MatScalar,&vtmp);CHKERRQ(ierr);
3251   ierr = PetscMemzero(rtmp,n*sizeof(MatScalar));CHKERRQ(ierr);
3252 
3253   bi[0]    = 0;
3254   bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */
3255   bdiag_rev[n] = bdiag[0];
3256   bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */
3257   for (i=0; i<n; i++) {
3258     /* copy initial fill into linked list */
3259     nzi = 0; /* nonzeros for active row i */
3260     nzi = ai[r[i]+1] - ai[r[i]];
3261     if (!nzi) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
3262     nzi_al = adiag[r[i]] - ai[r[i]];
3263     nzi_au = ai[r[i]+1] - adiag[r[i]] -1;
3264     ajtmp = aj + ai[r[i]];
3265     ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3266 
3267     /* load in initial (unfactored row) */
3268     aatmp = a->a + ai[r[i]];
3269     for (j=0; j<nzi; j++) {
3270       rtmp[ics[*ajtmp++]] = *aatmp++;
3271     }
3272 
3273     /* add pivot rows into linked list */
3274     row = lnk[n];
3275     while (row < i ) {
3276       nzi_bl = bi[row+1] - bi[row] + 1;
3277       bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */
3278       ierr  = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr);
3279       nzi  += nlnk;
3280       row   = lnk[row];
3281     }
3282 
3283     /* copy data from lnk into jtmp, then initialize lnk */
3284     ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr);
3285 
3286     /* numerical factorization */
3287     bjtmp = jtmp;
3288     row   = *bjtmp++; /* 1st pivot row */
3289     while  ( row < i ) {
3290       pc         = rtmp + row;
3291       pv         = ba + bdiag[row]; /* 1./(diag of the pivot row) */
3292       multiplier = (*pc) * (*pv);
3293       *pc        = multiplier;
3294       if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */
3295         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
3296         pv         = ba + bdiag[row+1] + 1;
3297         /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */
3298         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
3299         for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
3300         ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
3301       }
3302       row = *bjtmp++;
3303     }
3304 
3305     /* copy sparse rtmp into contiguous vtmp; separate L and U part */
3306     diag_tmp = rtmp[i];  /* save diagonal value - may not needed?? */
3307     nzi_bl = 0; j = 0;
3308     while (jtmp[j] < i){ /* Note: jtmp is sorted */
3309       vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
3310       nzi_bl++; j++;
3311     }
3312     nzi_bu = nzi - nzi_bl -1;
3313     while (j < nzi){
3314       vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
3315       j++;
3316     }
3317 
3318     bjtmp = bj + bi[i];
3319     batmp = ba + bi[i];
3320     /* apply level dropping rule to L part */
3321     ncut = nzi_al + dtcount;
3322     if (ncut < nzi_bl){
3323       ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr);
3324       ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr);
3325     } else {
3326       ncut = nzi_bl;
3327     }
3328     for (j=0; j<ncut; j++){
3329       bjtmp[j] = jtmp[j];
3330       batmp[j] = vtmp[j];
3331       /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */
3332     }
3333     bi[i+1] = bi[i] + ncut;
3334     nzi = ncut + 1;
3335 
3336     /* apply level dropping rule to U part */
3337     ncut = nzi_au + dtcount;
3338     if (ncut < nzi_bu){
3339       ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr);
3340       ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr);
3341     } else {
3342       ncut = nzi_bu;
3343     }
3344     nzi += ncut;
3345 
3346     /* mark bdiagonal */
3347     bdiag[i+1]       = bdiag[i] - (ncut + 1);
3348     bdiag_rev[n-i-1] = bdiag[i+1];
3349     bi[2*n - i]      = bi[2*n - i +1] - (ncut + 1);
3350     bjtmp = bj + bdiag[i];
3351     batmp = ba + bdiag[i];
3352     *bjtmp = i;
3353     *batmp = diag_tmp; /* rtmp[i]; */
3354     if (*batmp == 0.0) {
3355       *batmp = dt+shift;
3356       /* printf(" row %d add shift %g\n",i,shift); */
3357     }
3358     *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */
3359     /* printf(" (%d,%g),",*bjtmp,*batmp); */
3360 
3361     bjtmp = bj + bdiag[i+1]+1;
3362     batmp = ba + bdiag[i+1]+1;
3363     for (k=0; k<ncut; k++){
3364       bjtmp[k] = jtmp[nzi_bl+1+k];
3365       batmp[k] = vtmp[nzi_bl+1+k];
3366       /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */
3367     }
3368     /* printf("\n"); */
3369 
3370     im[i]   = nzi; /* used by PetscLLAddSortedLU() */
3371     /*
3372     printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]);
3373     printf(" ----------------------------\n");
3374     */
3375   } /* for (i=0; i<n; i++) */
3376   /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */
3377   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]);
3378 
3379   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
3380   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
3381 
3382   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
3383   ierr = PetscFree2(im,jtmp);CHKERRQ(ierr);
3384   ierr = PetscFree2(rtmp,vtmp);CHKERRQ(ierr);
3385   ierr = PetscFree(bdiag_rev);CHKERRQ(ierr);
3386 
3387   ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr);
3388   b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n];
3389 
3390   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
3391   ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr);
3392   both_identity = (PetscTruth) (row_identity && icol_identity);
3393   if (row_identity && icol_identity) {
3394     B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct;
3395   } else {
3396     B->ops->solve = MatSolve_SeqAIJ_newdatastruct;
3397   }
3398 
3399   B->ops->lufactorsymbolic  = MatILUDTFactorSymbolic_SeqAIJ;
3400   B->ops->lufactornumeric   = MatILUDTFactorNumeric_SeqAIJ;
3401   B->ops->solveadd          = 0;
3402   B->ops->solvetranspose    = 0;
3403   B->ops->solvetransposeadd = 0;
3404   B->ops->matsolve          = 0;
3405   B->assembled              = PETSC_TRUE;
3406   B->preallocated           = PETSC_TRUE;
3407   PetscFunctionReturn(0);
3408 }
3409 
3410 /* a wraper of MatILUDTFactor_SeqAIJ() */
3411 #undef __FUNCT__
3412 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ"
3413 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info)
3414 {
3415   PetscErrorCode     ierr;
3416 
3417   PetscFunctionBegin;
3418   ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr);
3419 
3420   fact->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ;
3421   PetscFunctionReturn(0);
3422 }
3423 
3424 /*
3425    same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors
3426    - intend to replace existing MatLUFactorNumeric_SeqAIJ()
3427 */
3428 #undef __FUNCT__
3429 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ"
3430 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info)
3431 {
3432   Mat            C=fact;
3433   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
3434   IS             isrow = b->row,isicol = b->icol;
3435   PetscErrorCode ierr;
3436   const PetscInt *r,*ic,*ics;
3437   PetscInt       i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
3438   PetscInt       *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj;
3439   MatScalar      *rtmp,*pc,multiplier,*v,*pv,*aa=a->a;
3440   PetscReal      dt=info->dt,shift=info->shiftinblocks;
3441   PetscTruth     row_identity, col_identity;
3442 
3443   PetscFunctionBegin;
3444   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
3445   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
3446   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
3447   ics  = ic;
3448 
3449   for (i=0; i<n; i++){
3450     /* initialize rtmp array */
3451     nzl   = bi[i+1] - bi[i];       /* num of nozeros in L(i,:) */
3452     bjtmp = bj + bi[i];
3453     for  (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0;
3454     rtmp[i] = 0.0;
3455     nzu   = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */
3456     bjtmp = bj + bdiag[i+1] + 1;
3457     for  (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0;
3458 
3459     /* load in initial unfactored row of A */
3460     /* printf("row %d\n",i); */
3461     nz    = ai[r[i]+1] - ai[r[i]];
3462     ajtmp = aj + ai[r[i]];
3463     v     = aa + ai[r[i]];
3464     for (j=0; j<nz; j++) {
3465       rtmp[ics[*ajtmp++]] = v[j];
3466       /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */
3467     }
3468     /* printf("\n"); */
3469 
3470     /* numerical factorization */
3471     bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */
3472     nzl   = bi[i+1] - bi[i]; /* num of entries in L(i,:) */
3473     k = 0;
3474     while (k < nzl){
3475       row   = *bjtmp++;
3476       /* printf("  prow %d\n",row); */
3477       pc         = rtmp + row;
3478       pv         = b->a + bdiag[row]; /* 1./(diag of the pivot row) */
3479       multiplier = (*pc) * (*pv);
3480       *pc        = multiplier;
3481       if (PetscAbsScalar(multiplier) > dt){
3482         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
3483         pv         = b->a + bdiag[row+1] + 1;
3484         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
3485         for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
3486         /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */
3487       }
3488       k++;
3489     }
3490 
3491     /* finished row so stick it into b->a */
3492     /* L-part */
3493     pv = b->a + bi[i] ;
3494     pj = bj + bi[i] ;
3495     nzl = bi[i+1] - bi[i];
3496     for (j=0; j<nzl; j++) {
3497       pv[j] = rtmp[pj[j]];
3498       /* printf(" (%d,%g),",pj[j],pv[j]); */
3499     }
3500 
3501     /* diagonal: invert diagonal entries for simplier triangular solves */
3502     if (rtmp[i] == 0.0) rtmp[i] = dt+shift;
3503     b->a[bdiag[i]] = 1.0/rtmp[i];
3504     /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */
3505 
3506     /* U-part */
3507     pv = b->a + bdiag[i+1] + 1;
3508     pj = bj + bdiag[i+1] + 1;
3509     nzu = bdiag[i] - bdiag[i+1] - 1;
3510     for (j=0; j<nzu; j++) {
3511       pv[j] = rtmp[pj[j]];
3512       /* printf(" (%d,%g),",pj[j],pv[j]); */
3513     }
3514     /* printf("\n"); */
3515   }
3516 
3517   ierr = PetscFree(rtmp);CHKERRQ(ierr);
3518   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
3519   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
3520 
3521   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
3522   ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
3523   if (row_identity && col_identity) {
3524     C->ops->solve   = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct;
3525   } else {
3526     C->ops->solve   = MatSolve_SeqAIJ_newdatastruct;
3527   }
3528   C->ops->solveadd           = 0;
3529   C->ops->solvetranspose     = 0;
3530   C->ops->solvetransposeadd  = 0;
3531   C->ops->matsolve           = 0;
3532   C->assembled    = PETSC_TRUE;
3533   C->preallocated = PETSC_TRUE;
3534   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
3535   PetscFunctionReturn(0);
3536 }
3537