xref: /petsc/src/mat/impls/aij/seq/aijfact.c (revision 5c42ef9d1fa542f9a51ba066fc31dace3e81e1a2)
1 #define PETSCMAT_DLL
2 
3 
4 #include "../src/mat/impls/aij/seq/aij.h"
5 #include "../src/mat/impls/sbaij/seq/sbaij.h"
6 #include "petscbt.h"
7 #include "../src/mat/utils/freespace.h"
8 
9 EXTERN_C_BEGIN
10 #undef __FUNCT__
11 #define __FUNCT__ "MatOrdering_Flow_SeqAIJ"
12 /*
13       Computes an ordering to get most of the large numerical values in the lower triangular part of the matrix
14 */
15 PetscErrorCode MatOrdering_Flow_SeqAIJ(Mat mat,const MatOrderingType type,IS *irow,IS *icol)
16 {
17   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)mat->data;
18   PetscErrorCode    ierr;
19   PetscInt          i,j,jj,k, kk,n = mat->rmap->n, current = 0, newcurrent = 0,*order;
20   const PetscInt    *ai = a->i, *aj = a->j;
21   const PetscScalar *aa = a->a;
22   PetscTruth        *done;
23   PetscReal         best,past = 0,future;
24 
25   PetscFunctionBegin;
26   /* pick initial row */
27   best = -1;
28   for (i=0; i<n; i++) {
29     future = 0;
30     for (j=ai[i]; j<ai[i+1]; j++) {
31       if (aj[j] != i) future  += PetscAbsScalar(aa[j]); else past = PetscAbsScalar(aa[j]);
32     }
33     if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */
34     if (past/future > best) {
35       best = past/future;
36       current = i;
37     }
38   }
39 
40   ierr = PetscMalloc(n*sizeof(PetscTruth),&done);CHKERRQ(ierr);
41   ierr = PetscMemzero(done,n*sizeof(PetscTruth));CHKERRQ(ierr);
42   ierr = PetscMalloc(n*sizeof(PetscInt),&order);CHKERRQ(ierr);
43   order[0] = current;
44   for (i=0; i<n-1; i++) {
45     done[current] = PETSC_TRUE;
46     best          = -1;
47     /* loop over all neighbors of current pivot */
48     for (j=ai[current]; j<ai[current+1]; j++) {
49       jj = aj[j];
50       if (done[jj]) continue;
51       /* loop over columns of potential next row computing weights for below and above diagonal */
52       past = future = 0.0;
53       for (k=ai[jj]; k<ai[jj+1]; k++) {
54         kk = aj[k];
55         if (done[kk]) past += PetscAbsScalar(aa[k]);
56         else if (kk != jj) future  += PetscAbsScalar(aa[k]);
57       }
58       if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */
59       if (past/future > best) {
60         best = past/future;
61         newcurrent = jj;
62       }
63     }
64     if (best == -1) { /* no neighbors to select from so select best of all that remain */
65       best = -1;
66       for (k=0; k<n; k++) {
67         if (done[k]) continue;
68         future = 0;
69         past   = 0;
70         for (j=ai[k]; j<ai[k+1]; j++) {
71           kk = aj[j];
72           if (done[kk]) past += PetscAbsScalar(aa[j]);
73           else if (kk != k) future  += PetscAbsScalar(aa[j]);
74         }
75         if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */
76         if (past/future > best) {
77           best = past/future;
78           newcurrent = k;
79         }
80       }
81     }
82     if (current == newcurrent) SETERRQ(PETSC_ERR_PLIB,"newcurrent cannot be current");
83     current = newcurrent;
84     order[i+1] = current;
85   }
86   ierr = ISCreateGeneral(PETSC_COMM_SELF,n,order,irow);CHKERRQ(ierr);
87   *icol = *irow;
88   ierr = PetscObjectReference((PetscObject)*irow);CHKERRQ(ierr);
89   ierr = PetscFree(done);CHKERRQ(ierr);
90   ierr = PetscFree(order);CHKERRQ(ierr);
91   PetscFunctionReturn(0);
92 }
93 EXTERN_C_END
94 
95 EXTERN_C_BEGIN
96 #undef __FUNCT__
97 #define __FUNCT__ "MatGetFactorAvailable_seqaij_petsc"
98 PetscErrorCode MatGetFactorAvailable_seqaij_petsc(Mat A,MatFactorType ftype,PetscTruth *flg)
99 {
100   PetscFunctionBegin;
101   *flg = PETSC_TRUE;
102   PetscFunctionReturn(0);
103 }
104 EXTERN_C_END
105 
106 EXTERN_C_BEGIN
107 #undef __FUNCT__
108 #define __FUNCT__ "MatGetFactor_seqaij_petsc"
109 PetscErrorCode MatGetFactor_seqaij_petsc(Mat A,MatFactorType ftype,Mat *B)
110 {
111   PetscInt           n = A->rmap->n;
112   PetscErrorCode     ierr;
113 
114   PetscFunctionBegin;
115   ierr = MatCreate(((PetscObject)A)->comm,B);CHKERRQ(ierr);
116   ierr = MatSetSizes(*B,n,n,n,n);CHKERRQ(ierr);
117   if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT){
118     ierr = MatSetType(*B,MATSEQAIJ);CHKERRQ(ierr);
119     (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqAIJ;
120     (*B)->ops->lufactorsymbolic  = MatLUFactorSymbolic_SeqAIJ;
121     (*B)->ops->iludtfactor       = MatILUDTFactor_SeqAIJ;
122   } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) {
123     ierr = MatSetType(*B,MATSEQSBAIJ);CHKERRQ(ierr);
124     ierr = MatSeqSBAIJSetPreallocation(*B,1,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
125     (*B)->ops->iccfactorsymbolic      = MatICCFactorSymbolic_SeqAIJ;
126     (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJ;
127   } else SETERRQ(PETSC_ERR_SUP,"Factor type not supported");
128   (*B)->factor = ftype;
129   PetscFunctionReturn(0);
130 }
131 EXTERN_C_END
132 
133 #undef __FUNCT__
134 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ"
135 PetscErrorCode MatLUFactorSymbolic_SeqAIJ(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
136 {
137   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
138   IS                 isicol;
139   PetscErrorCode     ierr;
140   const PetscInt     *r,*ic;
141   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j;
142   PetscInt           *bi,*bj,*ajtmp;
143   PetscInt           *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im;
144   PetscReal          f;
145   PetscInt           nlnk,*lnk,k,**bi_ptr;
146   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
147   PetscBT            lnkbt;
148   PetscTruth         newdatastruct= PETSC_FALSE;
149 
150   PetscFunctionBegin;
151   ierr = PetscOptionsGetTruth(PETSC_NULL,"-lu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
152   if(newdatastruct){
153     ierr = MatLUFactorSymbolic_SeqAIJ_newdatastruct(B,A,isrow,iscol,info);CHKERRQ(ierr);
154     PetscFunctionReturn(0);
155   }
156 
157 
158   if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square");
159   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
160   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
161   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
162 
163   /* get new row pointers */
164   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
165   bi[0] = 0;
166 
167   /* bdiag is location of diagonal in factor */
168   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
169   bdiag[0] = 0;
170 
171   /* linked list for storing column indices of the active row */
172   nlnk = n + 1;
173   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
174 
175   ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr);
176 
177   /* initial FreeSpace size is f*(ai[n]+1) */
178   f = info->fill;
179   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
180   current_space = free_space;
181 
182   for (i=0; i<n; i++) {
183     /* copy previous fill into linked list */
184     nzi = 0;
185     nnz = ai[r[i]+1] - ai[r[i]];
186     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
187     ajtmp = aj + ai[r[i]];
188     ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
189     nzi += nlnk;
190 
191     /* add pivot rows into linked list */
192     row = lnk[n];
193     while (row < i) {
194       nzbd    = bdiag[row] - bi[row] + 1; /* num of entries in the row with column index <= row */
195       ajtmp   = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */
196       ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr);
197       nzi += nlnk;
198       row  = lnk[row];
199     }
200     bi[i+1] = bi[i] + nzi;
201     im[i]   = nzi;
202 
203     /* mark bdiag */
204     nzbd = 0;
205     nnz  = nzi;
206     k    = lnk[n];
207     while (nnz-- && k < i){
208       nzbd++;
209       k = lnk[k];
210     }
211     bdiag[i] = bi[i] + nzbd;
212 
213     /* if free space is not available, make more free space */
214     if (current_space->local_remaining<nzi) {
215       nnz = (n - i)*nzi; /* estimated and max additional space needed */
216       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
217       reallocs++;
218     }
219 
220     /* copy data into free space, then initialize lnk */
221     ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
222     bi_ptr[i] = current_space->array;
223     current_space->array           += nzi;
224     current_space->local_used      += nzi;
225     current_space->local_remaining -= nzi;
226   }
227 #if defined(PETSC_USE_INFO)
228   if (ai[n] != 0) {
229     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
230     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
231     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
232     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr);
233     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
234   } else {
235     ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr);
236   }
237 #endif
238 
239   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
240   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
241 
242   /* destroy list of free space and other temporary array(s) */
243   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
244   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
245   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
246   ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr);
247 
248   /* put together the new matrix */
249   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
250   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
251   b    = (Mat_SeqAIJ*)(B)->data;
252   b->free_a       = PETSC_TRUE;
253   b->free_ij      = PETSC_TRUE;
254   b->singlemalloc = PETSC_FALSE;
255   ierr          = PetscMalloc((bi[n]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
256   b->j          = bj;
257   b->i          = bi;
258   b->diag       = bdiag;
259   b->ilen       = 0;
260   b->imax       = 0;
261   b->row        = isrow;
262   b->col        = iscol;
263   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
264   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
265   b->icol       = isicol;
266   ierr          = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
267 
268   /* In b structure:  Free imax, ilen, old a, old j.  Allocate solve_work, new a, new j */
269   ierr = PetscLogObjectMemory(B,(bi[n]-n)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
270   b->maxnz = b->nz = bi[n] ;
271 
272   (B)->factor                = MAT_FACTOR_LU;
273   (B)->info.factor_mallocs   = reallocs;
274   (B)->info.fill_ratio_given = f;
275 
276   if (ai[n]) {
277     (B)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
278   } else {
279     (B)->info.fill_ratio_needed = 0.0;
280   }
281   (B)->ops->lufactornumeric  = MatLUFactorNumeric_SeqAIJ;
282   (B)->ops->solve            = MatSolve_SeqAIJ;
283   (B)->ops->solvetranspose   = MatSolveTranspose_SeqAIJ;
284   /* switch to inodes if appropriate */
285   ierr = MatLUFactorSymbolic_SeqAIJ_Inode(B,A,isrow,iscol,info);CHKERRQ(ierr);
286   PetscFunctionReturn(0);
287 }
288 
289 #undef __FUNCT__
290 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ_newdatastruct"
291 PetscErrorCode MatLUFactorSymbolic_SeqAIJ_newdatastruct(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
292 {
293   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
294   IS                 isicol;
295   PetscErrorCode     ierr;
296   const PetscInt     *r,*ic;
297   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j;
298   PetscInt           *bi,*bj,*ajtmp;
299   PetscInt           *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im;
300   PetscReal          f;
301   PetscInt           nlnk,*lnk,k,**bi_ptr;
302   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
303   PetscBT            lnkbt;
304 
305   PetscFunctionBegin;
306   if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square");
307   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
308   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
309   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
310 
311   /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
312   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
313   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
314   bi[0] = bdiag[0] = 0;
315 
316   /* linked list for storing column indices of the active row */
317   nlnk = n + 1;
318   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
319 
320   ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr);
321 
322   /* initial FreeSpace size is f*(ai[n]+1) */
323   f = info->fill;
324   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
325   current_space = free_space;
326 
327   for (i=0; i<n; i++) {
328     /* copy previous fill into linked list */
329     nzi = 0;
330     nnz = ai[r[i]+1] - ai[r[i]];
331     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
332     ajtmp = aj + ai[r[i]];
333     ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
334     nzi += nlnk;
335 
336     /* add pivot rows into linked list */
337     row = lnk[n];
338     while (row < i){
339       nzbd  = bdiag[row] + 1; /* num of entries in the row with column index <= row */
340       ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */
341       ierr  = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr);
342       nzi  += nlnk;
343       row   = lnk[row];
344     }
345     bi[i+1] = bi[i] + nzi;
346     im[i]   = nzi;
347 
348     /* mark bdiag */
349     nzbd = 0;
350     nnz  = nzi;
351     k    = lnk[n];
352     while (nnz-- && k < i){
353       nzbd++;
354       k = lnk[k];
355     }
356     bdiag[i] = nzbd; /* note: bdiag[i] = nnzL as input for PetscFreeSpaceContiguous_LU() */
357 
358     /* if free space is not available, make more free space */
359     if (current_space->local_remaining<nzi) {
360       nnz = 2*(n - i)*nzi; /* estimated and max additional space needed */
361       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
362       reallocs++;
363     }
364 
365     /* copy data into free space, then initialize lnk */
366     ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
367     bi_ptr[i] = current_space->array;
368     current_space->array           += nzi;
369     current_space->local_used      += nzi;
370     current_space->local_remaining -= nzi;
371   }
372 #if defined(PETSC_USE_INFO)
373   if (ai[n] != 0) {
374     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
375     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
376     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
377     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr);
378     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
379   } else {
380     ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr);
381   }
382 #endif
383 
384   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
385   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
386 
387   /* destroy list of free space and other temporary array(s) */
388   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
389   ierr = PetscFreeSpaceContiguous_LU_v2(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr);
390   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
391   ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr);
392 
393   /* put together the new matrix */
394   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
395   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
396   b    = (Mat_SeqAIJ*)(B)->data;
397   b->free_a       = PETSC_TRUE;
398   b->free_ij      = PETSC_TRUE;
399   b->singlemalloc = PETSC_FALSE;
400   ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
401   b->j          = bj;
402   b->i          = bi;
403   b->diag       = bdiag;
404   b->ilen       = 0;
405   b->imax       = 0;
406   b->row        = isrow;
407   b->col        = iscol;
408   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
409   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
410   b->icol       = isicol;
411   ierr          = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
412 
413   /* In b structure:  Free imax, ilen, old a, old j.  Allocate solve_work, new a, new j */
414   ierr = PetscLogObjectMemory(B,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
415   b->maxnz = b->nz = bdiag[0]+1;
416   (B)->factor                = MAT_FACTOR_LU;
417   (B)->info.factor_mallocs   = reallocs;
418   (B)->info.fill_ratio_given = f;
419 
420   if (ai[n]) {
421     (B)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]);
422   } else {
423     (B)->info.fill_ratio_needed = 0.0;
424   }
425   (B)->ops->lufactornumeric  = MatLUFactorNumeric_SeqAIJ_newdatastruct;
426   PetscFunctionReturn(0);
427 }
428 
429 /*
430     Trouble in factorization, should we dump the original matrix?
431 */
432 #undef __FUNCT__
433 #define __FUNCT__ "MatFactorDumpMatrix"
434 PetscErrorCode MatFactorDumpMatrix(Mat A)
435 {
436   PetscErrorCode ierr;
437   PetscTruth     flg = PETSC_FALSE;
438 
439   PetscFunctionBegin;
440   ierr = PetscOptionsGetTruth(PETSC_NULL,"-mat_factor_dump_on_error",&flg,PETSC_NULL);CHKERRQ(ierr);
441   if (flg) {
442     PetscViewer viewer;
443     char        filename[PETSC_MAX_PATH_LEN];
444 
445     ierr = PetscSNPrintf(filename,PETSC_MAX_PATH_LEN,"matrix_factor_error.%d",PetscGlobalRank);CHKERRQ(ierr);
446     ierr = PetscViewerBinaryOpen(((PetscObject)A)->comm,filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr);
447     ierr = MatView(A,viewer);CHKERRQ(ierr);
448     ierr = PetscViewerDestroy(viewer);CHKERRQ(ierr);
449   }
450   PetscFunctionReturn(0);
451 }
452 
453 extern PetscErrorCode MatSolve_SeqAIJ_Inode(Mat,Vec,Vec);
454 
455 #undef __FUNCT__
456 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_newdatastruct"
457 PetscErrorCode MatLUFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info)
458 {
459   Mat            C=B;
460   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
461   IS             isrow = b->row,isicol = b->icol;
462   PetscErrorCode ierr;
463   const PetscInt *r,*ic,*ics;
464   PetscInt       i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
465   PetscInt       *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj;
466   MatScalar      *rtmp,*pc,multiplier,*v,*pv,*aa=a->a;
467   PetscTruth     row_identity,col_identity;
468 
469   LUShift_Ctx    sctx;
470   PetscInt       *ddiag,newshift;
471   PetscReal      rs;
472   MatScalar      d;
473 
474   PetscFunctionBegin;
475   /* MatPivotSetUp(): initialize shift context sctx */
476   ierr = PetscMemzero(&sctx,sizeof(LUShift_Ctx));CHKERRQ(ierr);
477 
478   /* if both shift schemes are chosen by user, only use info->shiftpd */
479   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
480     ddiag          = a->diag;
481     sctx.shift_top = info->zeropivot;
482     for (i=0; i<n; i++) {
483       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
484       d  = (aa)[ddiag[i]];
485       rs = -PetscAbsScalar(d) - PetscRealPart(d);
486       v  = aa+ai[i];
487       nz = ai[i+1] - ai[i];
488       for (j=0; j<nz; j++)
489 	rs += PetscAbsScalar(v[j]);
490       if (rs>sctx.shift_top) sctx.shift_top = rs;
491     }
492     sctx.shift_top   *= 1.1;
493     sctx.nshift_max   = 5;
494     sctx.shift_lo     = 0.;
495     sctx.shift_hi     = 1.;
496   }
497 
498   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
499   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
500   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
501   ics  = ic;
502 
503   do {
504     sctx.lushift = PETSC_FALSE;
505     for (i=0; i<n; i++){
506       /* zero rtmp */
507       /* L part */
508       nz    = bi[i+1] - bi[i];
509       bjtmp = bj + bi[i];
510       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
511 
512       /* U part */
513       nz = bdiag[i]-bdiag[i+1];
514       bjtmp = bj + bdiag[i+1]+1;
515       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
516 
517       /* load in initial (unfactored row) */
518       nz    = ai[r[i]+1] - ai[r[i]];
519       ajtmp = aj + ai[r[i]];
520       v     = aa + ai[r[i]];
521       for (j=0; j<nz; j++) {
522         rtmp[ics[ajtmp[j]]] = v[j];
523       }
524       /* ZeropivotApply() */
525       rtmp[i] += sctx.shift_amount;  /* shift the diagonal of the matrix */
526 
527       /* elimination */
528       bjtmp = bj + bi[i];
529       row   = *bjtmp++;
530       nzL   = bi[i+1] - bi[i];
531       for(k=0; k < nzL;k++) {
532         pc = rtmp + row;
533         if (*pc != 0.0) {
534           pv         = b->a + bdiag[row];
535           multiplier = *pc * (*pv);
536           *pc        = multiplier;
537           pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
538 	  pv = b->a + bdiag[row+1]+1;
539 	  nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */
540           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
541           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
542         }
543         row = *bjtmp++;
544       }
545 
546       /* finished row so stick it into b->a */
547       rs = 0.0;
548       /* L part */
549       pv   = b->a + bi[i] ;
550       pj   = b->j + bi[i] ;
551       nz   = bi[i+1] - bi[i];
552       for (j=0; j<nz; j++) {
553         pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]);
554       }
555 
556       /* U part */
557       pv = b->a + bdiag[i+1]+1;
558       pj = b->j + bdiag[i+1]+1;
559       nz = bdiag[i] - bdiag[i+1]-1;
560       for (j=0; j<nz; j++) {
561         pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]);
562       }
563 
564       /* MatPivotCheck() */
565       sctx.rs  = rs;
566       sctx.pv  = rtmp[i];
567       /* ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); */
568       if (info->shiftnz){
569         ierr = MatPivotCheck_nz(info,sctx,i,newshift);CHKERRQ(ierr);
570       } else if (info->shiftpd){
571         ierr = MatPivotCheck_pd(info,sctx,i,newshift);CHKERRQ(ierr);
572       } else if (info->shiftinblocks){
573         ierr = MatPivotCheck_inblocks(info,sctx,i,newshift);CHKERRQ(ierr);
574       } else {
575         ierr = MatPivotCheck_none(info,sctx,i,newshift);CHKERRQ(ierr);
576       }
577       rtmp[i] = sctx.pv;
578       if (newshift == 1) break;
579 
580       /* Mark diagonal and invert diagonal for simplier triangular solves */
581       pv  = b->a + bdiag[i];
582       *pv = 1.0/rtmp[i];
583 
584     } /* endof for (i=0; i<n; i++){ */
585 
586     /* MatPivotRefine() */
587     if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max){
588       /*
589        * if no shift in this attempt & shifting & started shifting & can refine,
590        * then try lower shift
591        */
592       sctx.shift_hi       = sctx.shift_fraction;
593       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
594       sctx.shift_amount   = sctx.shift_fraction * sctx.shift_top;
595       sctx.lushift        = PETSC_TRUE;
596       sctx.nshift++;
597     }
598   } while (sctx.lushift);
599 
600   ierr = PetscFree(rtmp);CHKERRQ(ierr);
601   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
602   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
603 
604   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
605   ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
606   if (row_identity && col_identity) {
607     C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct;
608   } else {
609     C->ops->solve = MatSolve_SeqAIJ_newdatastruct;
610   }
611 
612   C->ops->solveadd           = 0;
613   C->ops->solvetranspose     = MatSolveTranspose_SeqAIJ_newdatastruct;
614   C->ops->solvetransposeadd  = 0;
615   C->ops->matsolve           = 0;
616   C->assembled    = PETSC_TRUE;
617   C->preallocated = PETSC_TRUE;
618   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
619 
620   /* MatPivotView() */
621   if (sctx.nshift){
622     if (info->shiftpd) {
623       ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %G, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,sctx.shift_amount,sctx.shift_fraction,sctx.shift_top);CHKERRQ(ierr);
624     } else if (info->shiftnz) {
625       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
626     } else if (info->shiftinblocks){
627       ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftinblocks);CHKERRQ(ierr);
628     }
629   }
630   PetscFunctionReturn(0);
631 }
632 
633 #undef __FUNCT__
634 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ"
635 PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info)
636 {
637   Mat             C=B;
638   Mat_SeqAIJ      *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
639   IS              isrow = b->row,isicol = b->icol;
640   PetscErrorCode  ierr;
641   const PetscInt   *r,*ic,*ics;
642   PetscInt        nz,row,i,j,n=A->rmap->n,diag;
643   const PetscInt  *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
644   const PetscInt  *ajtmp,*bjtmp,*diag_offset = b->diag,*pj;
645   MatScalar       *pv,*rtmp,*pc,multiplier,d;
646   const MatScalar *v,*aa=a->a;
647   PetscReal       rs=0.0;
648   LUShift_Ctx     sctx;
649   PetscInt        newshift,*ddiag;
650 
651   PetscFunctionBegin;
652   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
653   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
654   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
655   ics  = ic;
656 
657   /* initialize shift context sctx */
658   sctx.nshift         = 0;
659   sctx.nshift_max     = 0;
660   sctx.shift_top      = 0.0;
661   sctx.shift_lo       = 0.0;
662   sctx.shift_hi       = 0.0;
663   sctx.shift_fraction = 0.0;
664   sctx.shift_amount   = 0.0;
665 
666   /* if both shift schemes are chosen by user, only use info->shiftpd */
667   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
668     ddiag          = a->diag;
669     sctx.shift_top = info->zeropivot;
670     for (i=0; i<n; i++) {
671       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
672       d  = (aa)[ddiag[i]];
673       rs = -PetscAbsScalar(d) - PetscRealPart(d);
674       v  = aa+ai[i];
675       nz = ai[i+1] - ai[i];
676       for (j=0; j<nz; j++)
677 	rs += PetscAbsScalar(v[j]);
678       if (rs>sctx.shift_top) sctx.shift_top = rs;
679     }
680     sctx.shift_top   *= 1.1;
681     sctx.nshift_max   = 5;
682     sctx.shift_lo     = 0.;
683     sctx.shift_hi     = 1.;
684   }
685 
686   do {
687     sctx.lushift = PETSC_FALSE;
688     for (i=0; i<n; i++){
689       nz    = bi[i+1] - bi[i];
690       bjtmp = bj + bi[i];
691       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
692 
693       /* load in initial (unfactored row) */
694       nz    = ai[r[i]+1] - ai[r[i]];
695       ajtmp = aj + ai[r[i]];
696       v     = aa + ai[r[i]];
697       for (j=0; j<nz; j++) {
698         rtmp[ics[ajtmp[j]]] = v[j];
699       }
700       rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */
701       /* if (sctx.shift_amount > 0.0) printf("row %d, shift %g\n",i,sctx.shift_amount); */
702 
703       row = *bjtmp++;
704       while  (row < i) {
705         pc = rtmp + row;
706         if (*pc != 0.0) {
707           pv         = b->a + diag_offset[row];
708           pj         = b->j + diag_offset[row] + 1;
709           multiplier = *pc / *pv++;
710           *pc        = multiplier;
711           nz         = bi[row+1] - diag_offset[row] - 1;
712           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
713           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
714         }
715         row = *bjtmp++;
716       }
717       /* finished row so stick it into b->a */
718       pv   = b->a + bi[i] ;
719       pj   = b->j + bi[i] ;
720       nz   = bi[i+1] - bi[i];
721       diag = diag_offset[i] - bi[i];
722       rs   = 0.0;
723       for (j=0; j<nz; j++) {
724         pv[j] = rtmp[pj[j]];
725         rs   += PetscAbsScalar(pv[j]);
726       }
727       rs   -= PetscAbsScalar(pv[diag]);
728 
729       /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */
730       sctx.rs  = rs;
731       sctx.pv  = pv[diag];
732       ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr);
733       if (newshift == 1) break;
734     }
735 
736     if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
737       /*
738        * if no shift in this attempt & shifting & started shifting & can refine,
739        * then try lower shift
740        */
741       sctx.shift_hi       = sctx.shift_fraction;
742       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
743       sctx.shift_amount   = sctx.shift_fraction * sctx.shift_top;
744       sctx.lushift        = PETSC_TRUE;
745       sctx.nshift++;
746     }
747   } while (sctx.lushift);
748 
749   /* invert diagonal entries for simplier triangular solves */
750   for (i=0; i<n; i++) {
751     b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]];
752   }
753   ierr = PetscFree(rtmp);CHKERRQ(ierr);
754   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
755   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
756   if (b->inode.use) {
757     C->ops->solve   = MatSolve_SeqAIJ_Inode;
758   } else {
759     PetscTruth row_identity, col_identity;
760     ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
761     ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
762     if (row_identity && col_identity) {
763       C->ops->solve   = MatSolve_SeqAIJ_NaturalOrdering;
764     } else {
765       C->ops->solve   = MatSolve_SeqAIJ;
766     }
767   }
768   C->ops->solveadd           = MatSolveAdd_SeqAIJ;
769   C->ops->solvetranspose     = MatSolveTranspose_SeqAIJ;
770   C->ops->solvetransposeadd  = MatSolveTransposeAdd_SeqAIJ;
771   C->ops->matsolve           = MatMatSolve_SeqAIJ;
772   C->assembled    = PETSC_TRUE;
773   C->preallocated = PETSC_TRUE;
774   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
775   if (sctx.nshift){
776      if (info->shiftpd) {
777       ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %G, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,sctx.shift_amount,sctx.shift_fraction,sctx.shift_top);CHKERRQ(ierr);
778     } else if (info->shiftnz) {
779       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
780     }
781   }
782   PetscFunctionReturn(0);
783 }
784 
785 /*
786    This routine implements inplace ILU(0) with row or/and column permutations.
787    Input:
788      A - original matrix
789    Output;
790      A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i]
791          a->j (col index) is permuted by the inverse of colperm, then sorted
792          a->a reordered accordingly with a->j
793          a->diag (ptr to diagonal elements) is updated.
794 */
795 #undef __FUNCT__
796 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_InplaceWithPerm"
797 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info)
798 {
799   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
800   IS             isrow = a->row,isicol = a->icol;
801   PetscErrorCode ierr;
802   const PetscInt *r,*ic,*ics;
803   PetscInt       i,j,n=A->rmap->n,*ai=a->i,*aj=a->j;
804   PetscInt       *ajtmp,nz,row;
805   PetscInt       *diag = a->diag,nbdiag,*pj;
806   PetscScalar    *rtmp,*pc,multiplier,d;
807   MatScalar      *v,*pv;
808   PetscReal      rs;
809   LUShift_Ctx    sctx;
810   PetscInt       newshift;
811 
812   PetscFunctionBegin;
813   if (A != B) SETERRQ(PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address");
814   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
815   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
816   ierr  = PetscMalloc((n+1)*sizeof(PetscScalar),&rtmp);CHKERRQ(ierr);
817   ierr  = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr);
818   ics = ic;
819 
820   sctx.shift_top      = 0;
821   sctx.nshift_max     = 0;
822   sctx.shift_lo       = 0;
823   sctx.shift_hi       = 0;
824   sctx.shift_fraction = 0;
825 
826   /* if both shift schemes are chosen by user, only use info->shiftpd */
827   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
828     sctx.shift_top = 0;
829     for (i=0; i<n; i++) {
830       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
831       d  = (a->a)[diag[i]];
832       rs = -PetscAbsScalar(d) - PetscRealPart(d);
833       v  = a->a+ai[i];
834       nz = ai[i+1] - ai[i];
835       for (j=0; j<nz; j++)
836 	rs += PetscAbsScalar(v[j]);
837       if (rs>sctx.shift_top) sctx.shift_top = rs;
838     }
839     if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot;
840     sctx.shift_top    *= 1.1;
841     sctx.nshift_max   = 5;
842     sctx.shift_lo     = 0.;
843     sctx.shift_hi     = 1.;
844   }
845 
846   sctx.shift_amount = 0;
847   sctx.nshift       = 0;
848   do {
849     sctx.lushift = PETSC_FALSE;
850     for (i=0; i<n; i++){
851       /* load in initial unfactored row */
852       nz    = ai[r[i]+1] - ai[r[i]];
853       ajtmp = aj + ai[r[i]];
854       v     = a->a + ai[r[i]];
855       /* sort permuted ajtmp and values v accordingly */
856       for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]];
857       ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr);
858 
859       diag[r[i]] = ai[r[i]];
860       for (j=0; j<nz; j++) {
861         rtmp[ajtmp[j]] = v[j];
862         if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */
863       }
864       rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */
865 
866       row = *ajtmp++;
867       while  (row < i) {
868         pc = rtmp + row;
869         if (*pc != 0.0) {
870           pv         = a->a + diag[r[row]];
871           pj         = aj + diag[r[row]] + 1;
872 
873           multiplier = *pc / *pv++;
874           *pc        = multiplier;
875           nz         = ai[r[row]+1] - diag[r[row]] - 1;
876           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
877           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
878         }
879         row = *ajtmp++;
880       }
881       /* finished row so overwrite it onto a->a */
882       pv   = a->a + ai[r[i]] ;
883       pj   = aj + ai[r[i]] ;
884       nz   = ai[r[i]+1] - ai[r[i]];
885       nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */
886 
887       rs   = 0.0;
888       for (j=0; j<nz; j++) {
889         pv[j] = rtmp[pj[j]];
890         if (j != nbdiag) rs += PetscAbsScalar(pv[j]);
891       }
892 
893       /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */
894       sctx.rs  = rs;
895       sctx.pv  = pv[nbdiag];
896       ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr);
897       if (newshift == 1) break;
898     }
899 
900     if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
901       /*
902        * if no shift in this attempt & shifting & started shifting & can refine,
903        * then try lower shift
904        */
905       sctx.shift_hi        = sctx.shift_fraction;
906       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
907       sctx.shift_amount    = sctx.shift_fraction * sctx.shift_top;
908       sctx.lushift         = PETSC_TRUE;
909       sctx.nshift++;
910     }
911   } while (sctx.lushift);
912 
913   /* invert diagonal entries for simplier triangular solves */
914   for (i=0; i<n; i++) {
915     a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]];
916   }
917 
918   ierr = PetscFree(rtmp);CHKERRQ(ierr);
919   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
920   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
921   A->ops->solve             = MatSolve_SeqAIJ_InplaceWithPerm;
922   A->ops->solveadd          = MatSolveAdd_SeqAIJ;
923   A->ops->solvetranspose    = MatSolveTranspose_SeqAIJ;
924   A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ;
925   A->assembled = PETSC_TRUE;
926   A->preallocated = PETSC_TRUE;
927   ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr);
928   if (sctx.nshift){
929     if (info->shiftpd) {
930       ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %G, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,sctx.shift_amount,sctx.shift_fraction,sctx.shift_top);CHKERRQ(ierr);
931     } else if (info->shiftnz) {
932       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
933     }
934   }
935   PetscFunctionReturn(0);
936 }
937 
938 /* ----------------------------------------------------------- */
939 #undef __FUNCT__
940 #define __FUNCT__ "MatLUFactor_SeqAIJ"
941 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info)
942 {
943   PetscErrorCode ierr;
944   Mat            C;
945 
946   PetscFunctionBegin;
947   ierr = MatGetFactor(A,MAT_SOLVER_PETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr);
948   ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr);
949   ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr);
950   A->ops->solve            = C->ops->solve;
951   A->ops->solvetranspose   = C->ops->solvetranspose;
952   ierr = MatHeaderCopy(A,C);CHKERRQ(ierr);
953   ierr = PetscLogObjectParent(A,((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr);
954   PetscFunctionReturn(0);
955 }
956 /* ----------------------------------------------------------- */
957 
958 
959 #undef __FUNCT__
960 #define __FUNCT__ "MatSolve_SeqAIJ"
961 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx)
962 {
963   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
964   IS                iscol = a->col,isrow = a->row;
965   PetscErrorCode    ierr;
966   PetscInt          i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
967   PetscInt          nz;
968   const PetscInt    *rout,*cout,*r,*c;
969   PetscScalar       *x,*tmp,*tmps,sum;
970   const PetscScalar *b;
971   const MatScalar   *aa = a->a,*v;
972 
973   PetscFunctionBegin;
974   if (!n) PetscFunctionReturn(0);
975 
976   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
977   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
978   tmp  = a->solve_work;
979 
980   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
981   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
982 
983   /* forward solve the lower triangular */
984   tmp[0] = b[*r++];
985   tmps   = tmp;
986   for (i=1; i<n; i++) {
987     v   = aa + ai[i] ;
988     vi  = aj + ai[i] ;
989     nz  = a->diag[i] - ai[i];
990     sum = b[*r++];
991     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
992     tmp[i] = sum;
993   }
994 
995   /* backward solve the upper triangular */
996   for (i=n-1; i>=0; i--){
997     v   = aa + a->diag[i] + 1;
998     vi  = aj + a->diag[i] + 1;
999     nz  = ai[i+1] - a->diag[i] - 1;
1000     sum = tmp[i];
1001     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1002     x[*c--] = tmp[i] = sum*aa[a->diag[i]];
1003   }
1004 
1005   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1006   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1007   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1008   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1009   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1010   PetscFunctionReturn(0);
1011 }
1012 
1013 #undef __FUNCT__
1014 #define __FUNCT__ "MatMatSolve_SeqAIJ"
1015 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X)
1016 {
1017   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1018   IS              iscol = a->col,isrow = a->row;
1019   PetscErrorCode  ierr;
1020   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1021   PetscInt        nz,neq;
1022   const PetscInt  *rout,*cout,*r,*c;
1023   PetscScalar     *x,*b,*tmp,*tmps,sum;
1024   const MatScalar *aa = a->a,*v;
1025   PetscTruth      bisdense,xisdense;
1026 
1027   PetscFunctionBegin;
1028   if (!n) PetscFunctionReturn(0);
1029 
1030   ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr);
1031   if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix");
1032   ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr);
1033   if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix");
1034 
1035   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
1036   ierr = MatGetArray(X,&x);CHKERRQ(ierr);
1037 
1038   tmp  = a->solve_work;
1039   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1040   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1041 
1042   for (neq=0; neq<B->cmap->n; neq++){
1043     /* forward solve the lower triangular */
1044     tmp[0] = b[r[0]];
1045     tmps   = tmp;
1046     for (i=1; i<n; i++) {
1047       v   = aa + ai[i] ;
1048       vi  = aj + ai[i] ;
1049       nz  = a->diag[i] - ai[i];
1050       sum = b[r[i]];
1051       PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1052       tmp[i] = sum;
1053     }
1054     /* backward solve the upper triangular */
1055     for (i=n-1; i>=0; i--){
1056       v   = aa + a->diag[i] + 1;
1057       vi  = aj + a->diag[i] + 1;
1058       nz  = ai[i+1] - a->diag[i] - 1;
1059       sum = tmp[i];
1060       PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1061       x[c[i]] = tmp[i] = sum*aa[a->diag[i]];
1062     }
1063 
1064     b += n;
1065     x += n;
1066   }
1067   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1068   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1069   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
1070   ierr = MatRestoreArray(X,&x);CHKERRQ(ierr);
1071   ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr);
1072   PetscFunctionReturn(0);
1073 }
1074 
1075 #undef __FUNCT__
1076 #define __FUNCT__ "MatSolve_SeqAIJ_InplaceWithPerm"
1077 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx)
1078 {
1079   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1080   IS              iscol = a->col,isrow = a->row;
1081   PetscErrorCode  ierr;
1082   const PetscInt  *r,*c,*rout,*cout;
1083   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1084   PetscInt        nz,row;
1085   PetscScalar     *x,*b,*tmp,*tmps,sum;
1086   const MatScalar *aa = a->a,*v;
1087 
1088   PetscFunctionBegin;
1089   if (!n) PetscFunctionReturn(0);
1090 
1091   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
1092   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1093   tmp  = a->solve_work;
1094 
1095   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1096   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1097 
1098   /* forward solve the lower triangular */
1099   tmp[0] = b[*r++];
1100   tmps   = tmp;
1101   for (row=1; row<n; row++) {
1102     i   = rout[row]; /* permuted row */
1103     v   = aa + ai[i] ;
1104     vi  = aj + ai[i] ;
1105     nz  = a->diag[i] - ai[i];
1106     sum = b[*r++];
1107     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1108     tmp[row] = sum;
1109   }
1110 
1111   /* backward solve the upper triangular */
1112   for (row=n-1; row>=0; row--){
1113     i   = rout[row]; /* permuted row */
1114     v   = aa + a->diag[i] + 1;
1115     vi  = aj + a->diag[i] + 1;
1116     nz  = ai[i+1] - a->diag[i] - 1;
1117     sum = tmp[row];
1118     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1119     x[*c--] = tmp[row] = sum*aa[a->diag[i]];
1120   }
1121 
1122   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1123   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1124   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
1125   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1126   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1127   PetscFunctionReturn(0);
1128 }
1129 
1130 /* ----------------------------------------------------------- */
1131 #include "../src/mat/impls/aij/seq/ftn-kernels/fsolve.h"
1132 #undef __FUNCT__
1133 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering"
1134 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx)
1135 {
1136   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1137   PetscErrorCode    ierr;
1138   PetscInt          n = A->rmap->n;
1139   const PetscInt    *ai = a->i,*aj = a->j,*adiag = a->diag;
1140   PetscScalar       *x;
1141   const PetscScalar *b;
1142   const MatScalar   *aa = a->a;
1143 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ)
1144   PetscInt          adiag_i,i,nz,ai_i;
1145   const PetscInt    *vi;
1146   const MatScalar   *v;
1147   PetscScalar       sum;
1148 #endif
1149 
1150   PetscFunctionBegin;
1151   if (!n) PetscFunctionReturn(0);
1152 
1153   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1154   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1155 
1156 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ)
1157   fortransolveaij_(&n,x,ai,aj,adiag,aa,b);
1158 #else
1159   /* forward solve the lower triangular */
1160   x[0] = b[0];
1161   for (i=1; i<n; i++) {
1162     ai_i = ai[i];
1163     v    = aa + ai_i;
1164     vi   = aj + ai_i;
1165     nz   = adiag[i] - ai_i;
1166     sum  = b[i];
1167     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
1168     x[i] = sum;
1169   }
1170 
1171   /* backward solve the upper triangular */
1172   for (i=n-1; i>=0; i--){
1173     adiag_i = adiag[i];
1174     v       = aa + adiag_i + 1;
1175     vi      = aj + adiag_i + 1;
1176     nz      = ai[i+1] - adiag_i - 1;
1177     sum     = x[i];
1178     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
1179     x[i]    = sum*aa[adiag_i];
1180   }
1181 #endif
1182   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1183   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1184   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1185   PetscFunctionReturn(0);
1186 }
1187 
1188 #undef __FUNCT__
1189 #define __FUNCT__ "MatSolveAdd_SeqAIJ"
1190 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx)
1191 {
1192   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1193   IS                iscol = a->col,isrow = a->row;
1194   PetscErrorCode    ierr;
1195   PetscInt          i, n = A->rmap->n,j;
1196   PetscInt          nz;
1197   const PetscInt    *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j;
1198   PetscScalar       *x,*tmp,sum;
1199   const PetscScalar *b;
1200   const MatScalar   *aa = a->a,*v;
1201 
1202   PetscFunctionBegin;
1203   if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);}
1204 
1205   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1206   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1207   tmp  = a->solve_work;
1208 
1209   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1210   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1211 
1212   /* forward solve the lower triangular */
1213   tmp[0] = b[*r++];
1214   for (i=1; i<n; i++) {
1215     v   = aa + ai[i] ;
1216     vi  = aj + ai[i] ;
1217     nz  = a->diag[i] - ai[i];
1218     sum = b[*r++];
1219     for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1220     tmp[i] = sum;
1221   }
1222 
1223   /* backward solve the upper triangular */
1224   for (i=n-1; i>=0; i--){
1225     v   = aa + a->diag[i] + 1;
1226     vi  = aj + a->diag[i] + 1;
1227     nz  = ai[i+1] - a->diag[i] - 1;
1228     sum = tmp[i];
1229     for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1230     tmp[i] = sum*aa[a->diag[i]];
1231     x[*c--] += tmp[i];
1232   }
1233 
1234   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1235   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1236   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1237   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1238   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1239 
1240   PetscFunctionReturn(0);
1241 }
1242 
1243 #undef __FUNCT__
1244 #define __FUNCT__ "MatSolveTranspose_SeqAIJ"
1245 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx)
1246 {
1247   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1248   IS                iscol = a->col,isrow = a->row;
1249   PetscErrorCode    ierr;
1250   const PetscInt    *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi;
1251   PetscInt          i,n = A->rmap->n,j;
1252   PetscInt          nz;
1253   PetscScalar       *x,*tmp,s1;
1254   const MatScalar   *aa = a->a,*v;
1255   const PetscScalar *b;
1256 
1257   PetscFunctionBegin;
1258   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1259   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1260   tmp  = a->solve_work;
1261 
1262   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1263   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1264 
1265   /* copy the b into temp work space according to permutation */
1266   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1267 
1268   /* forward solve the U^T */
1269   for (i=0; i<n; i++) {
1270     v   = aa + diag[i] ;
1271     vi  = aj + diag[i] + 1;
1272     nz  = ai[i+1] - diag[i] - 1;
1273     s1  = tmp[i];
1274     s1 *= (*v++);  /* multiply by inverse of diagonal entry */
1275     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1276     tmp[i] = s1;
1277   }
1278 
1279   /* backward solve the L^T */
1280   for (i=n-1; i>=0; i--){
1281     v   = aa + diag[i] - 1 ;
1282     vi  = aj + diag[i] - 1 ;
1283     nz  = diag[i] - ai[i];
1284     s1  = tmp[i];
1285     for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j];
1286   }
1287 
1288   /* copy tmp into x according to permutation */
1289   for (i=0; i<n; i++) x[r[i]] = tmp[i];
1290 
1291   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1292   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1293   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1294   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1295 
1296   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1297   PetscFunctionReturn(0);
1298 }
1299 
1300 #undef __FUNCT__
1301 #define __FUNCT__ "MatSolveTranspose_SeqAIJ_newdatastruct"
1302 PetscErrorCode MatSolveTranspose_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec xx)
1303 {
1304   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1305   IS                iscol = a->col,isrow = a->row;
1306   PetscErrorCode    ierr;
1307   const PetscInt    *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi;
1308   PetscInt          i,n = A->rmap->n,j;
1309   PetscInt          nz;
1310   PetscScalar       *x,*tmp,s1;
1311   const MatScalar   *aa = a->a,*v;
1312   const PetscScalar *b;
1313 
1314   PetscFunctionBegin;
1315   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1316   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1317   tmp  = a->solve_work;
1318 
1319   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1320   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1321 
1322   /* copy the b into temp work space according to permutation */
1323   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1324 
1325   /* forward solve the U^T */
1326   for (i=0; i<n; i++) {
1327     v   = aa + adiag[i+1] + 1;
1328     vi  = aj + adiag[i+1] + 1;
1329     nz  = adiag[i] - adiag[i+1] - 1;
1330     s1  = tmp[i];
1331     s1 *= v[nz];  /* multiply by inverse of diagonal entry */
1332     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1333     tmp[i] = s1;
1334   }
1335 
1336   /* backward solve the L^T */
1337   for (i=n-1; i>=0; i--){
1338     v   = aa + ai[i];
1339     vi  = aj + ai[i];
1340     nz  = ai[i+1] - ai[i];
1341     s1  = tmp[i];
1342     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1343   }
1344 
1345   /* copy tmp into x according to permutation */
1346   for (i=0; i<n; i++) x[r[i]] = tmp[i];
1347 
1348   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1349   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1350   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1351   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1352 
1353   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1354   PetscFunctionReturn(0);
1355 }
1356 
1357 #undef __FUNCT__
1358 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ"
1359 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx)
1360 {
1361   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1362   IS                iscol = a->col,isrow = a->row;
1363   PetscErrorCode    ierr;
1364   const PetscInt    *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi;
1365   PetscInt          i,n = A->rmap->n,j;
1366   PetscInt          nz;
1367   PetscScalar       *x,*tmp,s1;
1368   const MatScalar   *aa = a->a,*v;
1369   const PetscScalar *b;
1370 
1371   PetscFunctionBegin;
1372   if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);}
1373   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1374   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1375   tmp  = a->solve_work;
1376 
1377   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1378   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1379 
1380   /* copy the b into temp work space according to permutation */
1381   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1382 
1383   /* forward solve the U^T */
1384   for (i=0; i<n; i++) {
1385     v   = aa + diag[i] ;
1386     vi  = aj + diag[i] + 1;
1387     nz  = ai[i+1] - diag[i] - 1;
1388     s1  = tmp[i];
1389     s1 *= (*v++);  /* multiply by inverse of diagonal entry */
1390     for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1391     tmp[i] = s1;
1392   }
1393 
1394   /* backward solve the L^T */
1395   for (i=n-1; i>=0; i--){
1396     v   = aa + diag[i] - 1 ;
1397     vi  = aj + diag[i] - 1 ;
1398     nz  = diag[i] - ai[i];
1399     s1  = tmp[i];
1400     for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j];
1401   }
1402 
1403   /* copy tmp into x according to permutation */
1404   for (i=0; i<n; i++) x[r[i]] += tmp[i];
1405 
1406   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1407   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1408   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1409   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1410 
1411   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1412   PetscFunctionReturn(0);
1413 }
1414 
1415 /* ----------------------------------------------------------------*/
1416 EXTERN PetscErrorCode Mat_CheckInode(Mat,PetscTruth);
1417 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption,PetscTruth);
1418 
1419 /*
1420    ilu() under revised new data structure.
1421    Factored arrays bj and ba are stored as
1422      L(0,:), L(1,:), ...,L(n-1,:),  U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:)
1423 
1424    bi=fact->i is an array of size n+1, in which
1425    bi+
1426      bi[i]:  points to 1st entry of L(i,:),i=0,...,n-1
1427      bi[n]:  points to L(n-1,n-1)+1
1428 
1429   bdiag=fact->diag is an array of size n+1,in which
1430      bdiag[i]: points to diagonal of U(i,:), i=0,...,n-1
1431      bdiag[n]: points to entry of U(n-1,0)-1
1432 
1433    U(i,:) contains bdiag[i] as its last entry, i.e.,
1434     U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i])
1435 */
1436 #undef __FUNCT__
1437 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct"
1438 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1439 {
1440 
1441   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1442   PetscErrorCode     ierr;
1443   PetscInt           n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag;
1444   PetscInt           i,j,nz,*bi,*bj,*bdiag;
1445   PetscTruth         missing;
1446   IS                 isicol;
1447 
1448   PetscFunctionBegin;
1449   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);
1450   ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
1451   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
1452   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1453 
1454   ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr);
1455   b    = (Mat_SeqAIJ*)(fact)->data;
1456 
1457   /* allocate matrix arrays for new data structure */
1458   ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,n+1,PetscInt,&b->i);CHKERRQ(ierr);
1459   ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));CHKERRQ(ierr);
1460   b->singlemalloc = PETSC_TRUE;
1461   if (!b->diag){
1462     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr);
1463     ierr = PetscLogObjectMemory(fact,(n+1)*sizeof(PetscInt));CHKERRQ(ierr);
1464   }
1465   bdiag = b->diag;
1466 
1467   if (n > 0) {
1468     ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr);
1469   }
1470 
1471   /* set bi and bj with new data structure */
1472   bi = b->i;
1473   bj = b->j;
1474 
1475   /* L part */
1476   bi[0] = 0;
1477   for (i=0; i<n; i++){
1478     nz = adiag[i] - ai[i];
1479     bi[i+1] = bi[i] + nz;
1480     aj = a->j + ai[i];
1481     for (j=0; j<nz; j++){
1482       *bj = aj[j]; bj++;
1483     }
1484   }
1485 
1486   /* U part */
1487   bdiag[n] = bi[n]-1;
1488   for (i=n-1; i>=0; i--){
1489     nz = ai[i+1] - adiag[i] - 1;
1490     aj = a->j + adiag[i] + 1;
1491     for (j=0; j<nz; j++){
1492       *bj = aj[j]; bj++;
1493     }
1494     /* diag[i] */
1495     *bj = i; bj++;
1496     bdiag[i] = bdiag[i+1] + nz + 1;
1497   }
1498 
1499   fact->factor                 = MAT_FACTOR_ILU;
1500   fact->info.factor_mallocs    = 0;
1501   fact->info.fill_ratio_given  = info->fill;
1502   fact->info.fill_ratio_needed = 1.0;
1503   fact->ops->lufactornumeric   = MatLUFactorNumeric_SeqAIJ_newdatastruct;
1504 
1505   b       = (Mat_SeqAIJ*)(fact)->data;
1506   b->row  = isrow;
1507   b->col  = iscol;
1508   b->icol = isicol;
1509   ierr    = PetscMalloc((fact->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1510   ierr    = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1511   ierr    = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1512   PetscFunctionReturn(0);
1513 }
1514 
1515 #undef __FUNCT__
1516 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_newdatastruct"
1517 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1518 {
1519   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1520   IS                 isicol;
1521   PetscErrorCode     ierr;
1522   const PetscInt     *r,*ic;
1523   PetscInt           n=A->rmap->n,*ai=a->i,*aj=a->j;
1524   PetscInt           *bi,*cols,nnz,*cols_lvl;
1525   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1526   PetscInt           i,levels,diagonal_fill;
1527   PetscTruth         col_identity,row_identity;
1528   PetscReal          f;
1529   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
1530   PetscBT            lnkbt;
1531   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
1532   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1533   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1534 
1535   PetscFunctionBegin;
1536   /* printf("MatILUFactorSymbolic_SeqAIJ_newdatastruct ...\n"); */
1537   levels = (PetscInt)info->levels;
1538   ierr   = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1539   ierr   = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
1540 
1541   if (!levels && row_identity && col_identity) {
1542     /* special case: ilu(0) with natural ordering */
1543     ierr = MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1544     PetscFunctionReturn(0);
1545   }
1546 
1547   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);
1548   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1549   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1550   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1551 
1552   /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
1553   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1554   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
1555   bi[0] = bdiag[0] = 0;
1556 
1557   ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr);
1558 
1559   /* create a linked list for storing column indices of the active row */
1560   nlnk = n + 1;
1561   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1562 
1563   /* initial FreeSpace size is f*(ai[n]+1) */
1564   f             = info->fill;
1565   diagonal_fill = (PetscInt)info->diagonal_fill;
1566   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
1567   current_space = free_space;
1568   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
1569   current_space_lvl = free_space_lvl;
1570 
1571   for (i=0; i<n; i++) {
1572     nzi = 0;
1573     /* copy current row into linked list */
1574     nnz  = ai[r[i]+1] - ai[r[i]];
1575     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1576     cols = aj + ai[r[i]];
1577     lnk[i] = -1; /* marker to indicate if diagonal exists */
1578     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1579     nzi += nlnk;
1580 
1581     /* make sure diagonal entry is included */
1582     if (diagonal_fill && lnk[i] == -1) {
1583       fm = n;
1584       while (lnk[fm] < i) fm = lnk[fm];
1585       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
1586       lnk[fm]    = i;
1587       lnk_lvl[i] = 0;
1588       nzi++; dcount++;
1589     }
1590 
1591     /* add pivot rows into the active row */
1592     nzbd = 0;
1593     prow = lnk[n];
1594     while (prow < i) {
1595       nnz      = bdiag[prow];
1596       cols     = bj_ptr[prow] + nnz + 1;
1597       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1598       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
1599       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
1600       nzi += nlnk;
1601       prow = lnk[prow];
1602       nzbd++;
1603     }
1604     bdiag[i] = nzbd;
1605     bi[i+1]  = bi[i] + nzi;
1606 
1607     /* if free space is not available, make more free space */
1608     if (current_space->local_remaining<nzi) {
1609       nnz = 2*nzi*(n - i); /* estimated and max additional space needed */
1610       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
1611       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
1612       reallocs++;
1613     }
1614 
1615     /* copy data into free_space and free_space_lvl, then initialize lnk */
1616     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1617     bj_ptr[i]    = current_space->array;
1618     bjlvl_ptr[i] = current_space_lvl->array;
1619 
1620     /* make sure the active row i has diagonal entry */
1621     if (*(bj_ptr[i]+bdiag[i]) != i) {
1622       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
1623     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
1624     }
1625 
1626     current_space->array           += nzi;
1627     current_space->local_used      += nzi;
1628     current_space->local_remaining -= nzi;
1629     current_space_lvl->array           += nzi;
1630     current_space_lvl->local_used      += nzi;
1631     current_space_lvl->local_remaining -= nzi;
1632   }
1633 
1634   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1635   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1636 
1637   /* destroy list of free space and other temporary arrays */
1638   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
1639 
1640   /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */
1641   ierr = PetscFreeSpaceContiguous_LU_v2(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr);
1642 
1643   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1644   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
1645   ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr);
1646 
1647 #if defined(PETSC_USE_INFO)
1648   {
1649     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1650     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
1651     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
1652     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
1653     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
1654     if (diagonal_fill) {
1655       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
1656     }
1657   }
1658 #endif
1659 
1660   /* put together the new matrix */
1661   ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
1662   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
1663   b = (Mat_SeqAIJ*)(fact)->data;
1664   b->free_a       = PETSC_TRUE;
1665   b->free_ij      = PETSC_TRUE;
1666   b->singlemalloc = PETSC_FALSE;
1667   ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
1668   b->j          = bj;
1669   b->i          = bi;
1670   b->diag       = bdiag;
1671   b->ilen       = 0;
1672   b->imax       = 0;
1673   b->row        = isrow;
1674   b->col        = iscol;
1675   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1676   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1677   b->icol       = isicol;
1678   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1679   /* In b structure:  Free imax, ilen, old a, old j.
1680      Allocate bdiag, solve_work, new a, new j */
1681   ierr = PetscLogObjectMemory(fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
1682   b->maxnz = b->nz = bdiag[0]+1;
1683   (fact)->info.factor_mallocs    = reallocs;
1684   (fact)->info.fill_ratio_given  = f;
1685   (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]);
1686   (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct;
1687   /* ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */
1688   PetscFunctionReturn(0);
1689 }
1690 
1691 #undef __FUNCT__
1692 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ"
1693 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1694 {
1695   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1696   IS                 isicol;
1697   PetscErrorCode     ierr;
1698   const PetscInt     *r,*ic;
1699   PetscInt           n=A->rmap->n,*ai=a->i,*aj=a->j,d;
1700   PetscInt           *bi,*cols,nnz,*cols_lvl;
1701   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1702   PetscInt           i,levels,diagonal_fill;
1703   PetscTruth         col_identity,row_identity;
1704   PetscReal          f;
1705   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
1706   PetscBT            lnkbt;
1707   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
1708   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1709   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1710   PetscTruth         missing;
1711   PetscTruth         newdatastruct=PETSC_FALSE;
1712 
1713   PetscFunctionBegin;
1714   ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
1715   if(newdatastruct){
1716     ierr = MatILUFactorSymbolic_SeqAIJ_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1717     PetscFunctionReturn(0);
1718   }
1719 
1720   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);
1721   f             = info->fill;
1722   levels        = (PetscInt)info->levels;
1723   diagonal_fill = (PetscInt)info->diagonal_fill;
1724   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1725 
1726   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1727   ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
1728   if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */
1729     ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr);
1730     (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ;
1731 
1732     fact->factor = MAT_FACTOR_ILU;
1733     (fact)->info.factor_mallocs    = 0;
1734     (fact)->info.fill_ratio_given  = info->fill;
1735     (fact)->info.fill_ratio_needed = 1.0;
1736     b               = (Mat_SeqAIJ*)(fact)->data;
1737     ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
1738     if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
1739     b->row              = isrow;
1740     b->col              = iscol;
1741     b->icol             = isicol;
1742     ierr                = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1743     ierr                = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1744     ierr                = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1745     ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1746     PetscFunctionReturn(0);
1747   }
1748 
1749   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1750   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1751 
1752   /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
1753   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1754   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
1755   bi[0] = bdiag[0] = 0;
1756 
1757   ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr);
1758 
1759   /* create a linked list for storing column indices of the active row */
1760   nlnk = n + 1;
1761   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1762 
1763   /* initial FreeSpace size is f*(ai[n]+1) */
1764   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
1765   current_space = free_space;
1766   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
1767   current_space_lvl = free_space_lvl;
1768 
1769   for (i=0; i<n; i++) {
1770     nzi = 0;
1771     /* copy current row into linked list */
1772     nnz  = ai[r[i]+1] - ai[r[i]];
1773     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1774     cols = aj + ai[r[i]];
1775     lnk[i] = -1; /* marker to indicate if diagonal exists */
1776     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1777     nzi += nlnk;
1778 
1779     /* make sure diagonal entry is included */
1780     if (diagonal_fill && lnk[i] == -1) {
1781       fm = n;
1782       while (lnk[fm] < i) fm = lnk[fm];
1783       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
1784       lnk[fm]    = i;
1785       lnk_lvl[i] = 0;
1786       nzi++; dcount++;
1787     }
1788 
1789     /* add pivot rows into the active row */
1790     nzbd = 0;
1791     prow = lnk[n];
1792     while (prow < i) {
1793       nnz      = bdiag[prow];
1794       cols     = bj_ptr[prow] + nnz + 1;
1795       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1796       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
1797       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
1798       nzi += nlnk;
1799       prow = lnk[prow];
1800       nzbd++;
1801     }
1802     bdiag[i] = nzbd;
1803     bi[i+1]  = bi[i] + nzi;
1804 
1805     /* if free space is not available, make more free space */
1806     if (current_space->local_remaining<nzi) {
1807       nnz = nzi*(n - i); /* estimated and max additional space needed */
1808       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
1809       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
1810       reallocs++;
1811     }
1812 
1813     /* copy data into free_space and free_space_lvl, then initialize lnk */
1814     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1815     bj_ptr[i]    = current_space->array;
1816     bjlvl_ptr[i] = current_space_lvl->array;
1817 
1818     /* make sure the active row i has diagonal entry */
1819     if (*(bj_ptr[i]+bdiag[i]) != i) {
1820       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
1821     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
1822     }
1823 
1824     current_space->array           += nzi;
1825     current_space->local_used      += nzi;
1826     current_space->local_remaining -= nzi;
1827     current_space_lvl->array           += nzi;
1828     current_space_lvl->local_used      += nzi;
1829     current_space_lvl->local_remaining -= nzi;
1830   }
1831 
1832   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1833   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1834 
1835   /* destroy list of free space and other temporary arrays */
1836   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
1837   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */
1838   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1839   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
1840   ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr);
1841 
1842 #if defined(PETSC_USE_INFO)
1843   {
1844     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1845     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
1846     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
1847     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
1848     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
1849     if (diagonal_fill) {
1850       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
1851     }
1852   }
1853 #endif
1854 
1855   /* put together the new matrix */
1856   ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
1857   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
1858   b = (Mat_SeqAIJ*)(fact)->data;
1859   b->free_a       = PETSC_TRUE;
1860   b->free_ij      = PETSC_TRUE;
1861   b->singlemalloc = PETSC_FALSE;
1862   ierr = PetscMalloc(bi[n]*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
1863   b->j          = bj;
1864   b->i          = bi;
1865   for (i=0; i<n; i++) bdiag[i] += bi[i];
1866   b->diag       = bdiag;
1867   b->ilen       = 0;
1868   b->imax       = 0;
1869   b->row        = isrow;
1870   b->col        = iscol;
1871   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1872   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1873   b->icol       = isicol;
1874   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1875   /* In b structure:  Free imax, ilen, old a, old j.
1876      Allocate bdiag, solve_work, new a, new j */
1877   ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
1878   b->maxnz             = b->nz = bi[n] ;
1879   (fact)->info.factor_mallocs    = reallocs;
1880   (fact)->info.fill_ratio_given  = f;
1881   (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1882   (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ;
1883   ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1884   PetscFunctionReturn(0);
1885 }
1886 
1887 #undef __FUNCT__
1888 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ_newdatastruct"
1889 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info)
1890 {
1891   Mat            C = B;
1892   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1893   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
1894   IS             ip=b->row,iip = b->icol;
1895   PetscErrorCode ierr;
1896   const PetscInt *rip,*riip;
1897   PetscInt       i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp;
1898   PetscInt       *ai=a->i,*aj=a->j;
1899   PetscInt       k,jmin,jmax,*c2r,*il,col,nexti,ili,nz;
1900   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
1901   PetscTruth     perm_identity;
1902 
1903   LUShift_Ctx    sctx;
1904   PetscInt       newshift;
1905   PetscReal      rs;
1906   MatScalar      d,*v;
1907 
1908   PetscFunctionBegin;
1909   /* MatPivotSetUp(): initialize shift context sctx */
1910   ierr = PetscMemzero(&sctx,sizeof(LUShift_Ctx));CHKERRQ(ierr);
1911 
1912   /* if both shift schemes are chosen by user, only use info->shiftpd */
1913   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
1914     sctx.shift_top = info->zeropivot;
1915     for (i=0; i<mbs; i++) {
1916       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
1917       d  = (aa)[a->diag[i]];
1918       rs = -PetscAbsScalar(d) - PetscRealPart(d);
1919       v  = aa+ai[i];
1920       nz = ai[i+1] - ai[i];
1921       for (j=0; j<nz; j++)
1922 	rs += PetscAbsScalar(v[j]);
1923       if (rs>sctx.shift_top) sctx.shift_top = rs;
1924     }
1925     sctx.shift_top   *= 1.1;
1926     sctx.nshift_max   = 5;
1927     sctx.shift_lo     = 0.;
1928     sctx.shift_hi     = 1.;
1929   }
1930 
1931   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
1932   ierr  = ISGetIndices(iip,&riip);CHKERRQ(ierr);
1933 
1934   /* allocate working arrays
1935      c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col
1936      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
1937   */
1938   ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&c2r);CHKERRQ(ierr);
1939 
1940   do {
1941     sctx.lushift = PETSC_FALSE;
1942 
1943     for (i=0; i<mbs; i++) c2r[i] = mbs;
1944     il[0] = 0;
1945 
1946     for (k = 0; k<mbs; k++){
1947       /* zero rtmp */
1948       nz = bi[k+1] - bi[k];
1949       bjtmp = bj + bi[k];
1950       for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
1951 
1952       /* load in initial unfactored row */
1953       bval = ba + bi[k];
1954       jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
1955       for (j = jmin; j < jmax; j++){
1956         col = riip[aj[j]];
1957         if (col >= k){ /* only take upper triangular entry */
1958           rtmp[col] = aa[j];
1959           *bval++   = 0.0; /* for in-place factorization */
1960         }
1961       }
1962       /* shift the diagonal of the matrix: ZeropivotApply() */
1963       rtmp[k] += sctx.shift_amount;  /* shift the diagonal of the matrix */
1964 
1965       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
1966       dk = rtmp[k];
1967       i  = c2r[k]; /* first row to be added to k_th row  */
1968 
1969       while (i < k){
1970         nexti = c2r[i]; /* next row to be added to k_th row */
1971 
1972         /* compute multiplier, update diag(k) and U(i,k) */
1973         ili   = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
1974         uikdi = - ba[ili]*ba[bdiag[i]];  /* diagonal(k) */
1975         dk   += uikdi*ba[ili]; /* update diag[k] */
1976         ba[ili] = uikdi; /* -U(i,k) */
1977 
1978         /* add multiple of row i to k-th row */
1979         jmin = ili + 1; jmax = bi[i+1];
1980         if (jmin < jmax){
1981           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
1982           /* update il and c2r for row i */
1983           il[i] = jmin;
1984           j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i;
1985         }
1986         i = nexti;
1987       }
1988 
1989       /* copy data into U(k,:) */
1990       rs   = 0.0;
1991       jmin = bi[k]; jmax = bi[k+1]-1;
1992       if (jmin < jmax) {
1993         for (j=jmin; j<jmax; j++){
1994           col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]);
1995         }
1996         /* add the k-th row into il and c2r */
1997         il[k] = jmin;
1998         i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k;
1999       }
2000 
2001       /* MatPivotCheck() */
2002       sctx.rs  = rs;
2003       sctx.pv  = dk;
2004       if (info->shiftnz){
2005         ierr = MatPivotCheck_nz(info,sctx,k,newshift);CHKERRQ(ierr);
2006       } else if (info->shiftpd){
2007         ierr = MatPivotCheck_pd(info,sctx,k,newshift);CHKERRQ(ierr);
2008       } else if (info->shiftinblocks){
2009         ierr = MatPivotCheck_inblocks(info,sctx,k,newshift);CHKERRQ(ierr);
2010       } else {
2011         ierr = MatPivotCheck_none(info,sctx,k,newshift);CHKERRQ(ierr);
2012       }
2013       dk = sctx.pv;
2014       if (newshift == 1) break;
2015 
2016       ba[bdiag[k]] = 1.0/dk; /* U(k,k) */
2017     }
2018   } while (sctx.lushift);
2019 
2020   ierr = PetscFree3(rtmp,il,c2r);CHKERRQ(ierr);
2021   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2022   ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr);
2023 
2024   ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
2025   if (perm_identity){
2026     (B)->ops->solve           = MatSolve_SeqSBAIJ_1_NaturalOrdering_newdatastruct;
2027     (B)->ops->solvetranspose  = 0;
2028     (B)->ops->forwardsolve    = 0;
2029     (B)->ops->backwardsolve   = 0;
2030   } else {
2031     (B)->ops->solve           = MatSolve_SeqSBAIJ_1_newdatastruct;
2032     (B)->ops->solvetranspose  = 0;
2033     (B)->ops->forwardsolve    = 0;
2034     (B)->ops->backwardsolve   = 0;
2035   }
2036 
2037   C->assembled    = PETSC_TRUE;
2038   C->preallocated = PETSC_TRUE;
2039   ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr);
2040 
2041   /* MatPivotView() */
2042   if (sctx.nshift){
2043     if (info->shiftpd) {
2044       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);
2045     } else if (info->shiftnz) {
2046       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2047     } else if (info->shiftinblocks){
2048       ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftinblocks);CHKERRQ(ierr);
2049     }
2050   }
2051   PetscFunctionReturn(0);
2052 }
2053 
2054 #undef __FUNCT__
2055 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ"
2056 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info)
2057 {
2058   Mat            C = B;
2059   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
2060   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
2061   IS             ip=b->row,iip = b->icol;
2062   PetscErrorCode ierr;
2063   const PetscInt *rip,*riip;
2064   PetscInt       i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol,*bjtmp;
2065   PetscInt       *ai=a->i,*aj=a->j;
2066   PetscInt       k,jmin,jmax,*jl,*il,col,nexti,ili,nz;
2067   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
2068   PetscReal      zeropivot,rs,shiftnz;
2069   PetscReal      shiftpd;
2070   ChShift_Ctx    sctx;
2071   PetscInt       newshift;
2072   PetscTruth     perm_identity;
2073 
2074   PetscFunctionBegin;
2075   shiftnz   = info->shiftnz;
2076   shiftpd   = info->shiftpd;
2077   zeropivot = info->zeropivot;
2078 
2079   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
2080   ierr  = ISGetIndices(iip,&riip);CHKERRQ(ierr);
2081 
2082   /* initialization */
2083   ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&jl);CHKERRQ(ierr);
2084   sctx.shift_amount = 0;
2085   sctx.nshift       = 0;
2086   do {
2087     sctx.chshift = PETSC_FALSE;
2088     for (i=0; i<mbs; i++) jl[i] = mbs;
2089     il[0] = 0;
2090 
2091     for (k = 0; k<mbs; k++){
2092       /* zero rtmp */
2093       nz = bi[k+1] - bi[k];
2094       bjtmp = bj + bi[k];
2095       for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
2096 
2097       bval = ba + bi[k];
2098       /* initialize k-th row by the perm[k]-th row of A */
2099       jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2100       for (j = jmin; j < jmax; j++){
2101         col = riip[aj[j]];
2102         if (col >= k){ /* only take upper triangular entry */
2103           rtmp[col] = aa[j];
2104           *bval++  = 0.0; /* for in-place factorization */
2105         }
2106       }
2107       /* shift the diagonal of the matrix */
2108       if (sctx.nshift) rtmp[k] += sctx.shift_amount;
2109 
2110       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
2111       dk = rtmp[k];
2112       i = jl[k]; /* first row to be added to k_th row  */
2113 
2114       while (i < k){
2115         nexti = jl[i]; /* next row to be added to k_th row */
2116 
2117         /* compute multiplier, update diag(k) and U(i,k) */
2118         ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2119         uikdi = - ba[ili]*ba[bi[i]];  /* diagonal(k) */
2120         dk += uikdi*ba[ili];
2121         ba[ili] = uikdi; /* -U(i,k) */
2122 
2123         /* add multiple of row i to k-th row */
2124         jmin = ili + 1; jmax = bi[i+1];
2125         if (jmin < jmax){
2126           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2127           /* update il and jl for row i */
2128           il[i] = jmin;
2129           j = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
2130         }
2131         i = nexti;
2132       }
2133 
2134       /* shift the diagonals when zero pivot is detected */
2135       /* compute rs=sum of abs(off-diagonal) */
2136       rs   = 0.0;
2137       jmin = bi[k]+1;
2138       nz   = bi[k+1] - jmin;
2139       bcol = bj + jmin;
2140       for (j=0; j<nz; j++) {
2141         rs += PetscAbsScalar(rtmp[bcol[j]]);
2142       }
2143 
2144       sctx.rs = rs;
2145       sctx.pv = dk;
2146       ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr);
2147 
2148       if (newshift == 1) {
2149         if (!sctx.shift_amount) {
2150           sctx.shift_amount = 1e-5;
2151         }
2152         break;
2153       }
2154 
2155       /* copy data into U(k,:) */
2156       ba[bi[k]] = 1.0/dk; /* U(k,k) */
2157       jmin = bi[k]+1; jmax = bi[k+1];
2158       if (jmin < jmax) {
2159         for (j=jmin; j<jmax; j++){
2160           col = bj[j]; ba[j] = rtmp[col];
2161         }
2162         /* add the k-th row into il and jl */
2163         il[k] = jmin;
2164         i = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
2165       }
2166     }
2167   } while (sctx.chshift);
2168   ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr);
2169   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2170   ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr);
2171 
2172   ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
2173   if (perm_identity){
2174     (B)->ops->solve           = MatSolve_SeqSBAIJ_1_NaturalOrdering;
2175     (B)->ops->solvetranspose  = MatSolve_SeqSBAIJ_1_NaturalOrdering;
2176     (B)->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering;
2177     (B)->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering;
2178   } else {
2179     (B)->ops->solve           = MatSolve_SeqSBAIJ_1;
2180     (B)->ops->solvetranspose  = MatSolve_SeqSBAIJ_1;
2181     (B)->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1;
2182     (B)->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1;
2183   }
2184 
2185   C->assembled    = PETSC_TRUE;
2186   C->preallocated = PETSC_TRUE;
2187   ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr);
2188   if (sctx.nshift){
2189     if (shiftnz) {
2190       ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2191     } else if (shiftpd) {
2192       ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2193     }
2194   }
2195   PetscFunctionReturn(0);
2196 }
2197 
2198 /*
2199    icc() under revised new data structure.
2200    Factored arrays bj and ba are stored as
2201      U(0,:),...,U(i,:),U(n-1,:)
2202 
2203    ui=fact->i is an array of size n+1, in which
2204    ui+
2205      ui[i]:  points to 1st entry of U(i,:),i=0,...,n-1
2206      ui[n]:  points to U(n-1,n-1)+1
2207 
2208   udiag=fact->diag is an array of size n,in which
2209      udiag[i]: points to diagonal of U(i,:), i=0,...,n-1
2210 
2211    U(i,:) contains udiag[i] as its last entry, i.e.,
2212     U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i])
2213 */
2214 
2215 #undef __FUNCT__
2216 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ_newdatastruct"
2217 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2218 {
2219   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2220   Mat_SeqSBAIJ       *b;
2221   PetscErrorCode     ierr;
2222   PetscTruth         perm_identity,missing;
2223   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag;
2224   const PetscInt     *rip,*riip;
2225   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
2226   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL,d;
2227   PetscInt           ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
2228   PetscReal          fill=info->fill,levels=info->levels;
2229   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2230   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
2231   PetscBT            lnkbt;
2232   IS                 iperm;
2233 
2234   PetscFunctionBegin;
2235   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);
2236   ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
2237   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
2238   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2239   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2240 
2241   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2242   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2243   ui[0] = 0;
2244 
2245   /* ICC(0) without matrix ordering: simply rearrange column indices */
2246   if (!levels && perm_identity) {
2247     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2248     cols = uj;
2249     for (i=0; i<am; i++) {
2250       ncols    = ai[i+1] - a->diag[i];
2251       ui[i+1]  = ui[i] + ncols;
2252       udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */
2253 
2254       aj   = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */
2255       ncols--; /* exclude diagonal */
2256       for (j=0; j<ncols; j++) *cols++ = aj[j];
2257       *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */
2258     }
2259   } else { /* case: levels>0 || (levels=0 && !perm_identity) */
2260     ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2261     ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2262 
2263     /* initialization */
2264     ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr);
2265 
2266     /* jl: linked list for storing indices of the pivot rows
2267        il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2268     ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr);
2269     for (i=0; i<am; i++){
2270       jl[i] = am; il[i] = 0;
2271     }
2272 
2273     /* create and initialize a linked list for storing column indices of the active row k */
2274     nlnk = am + 1;
2275     ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2276 
2277     /* initial FreeSpace size is fill*(ai[am]+1) */
2278     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2279     current_space = free_space;
2280     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr);
2281     current_space_lvl = free_space_lvl;
2282 
2283     for (k=0; k<am; k++){  /* for each active row k */
2284       /* initialize lnk by the column indices of row rip[k] of A */
2285       nzk   = 0;
2286       ncols = ai[rip[k]+1] - ai[rip[k]];
2287       if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2288       ncols_upper = 0;
2289       for (j=0; j<ncols; j++){
2290         i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2291         if (riip[i] >= k){ /* only take upper triangular entry */
2292           ajtmp[ncols_upper] = i;
2293           ncols_upper++;
2294         }
2295       }
2296       ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2297       nzk += nlnk;
2298 
2299       /* update lnk by computing fill-in for each pivot row to be merged in */
2300       prow = jl[k]; /* 1st pivot row */
2301 
2302       while (prow < k){
2303         nextprow = jl[prow];
2304 
2305         /* merge prow into k-th row */
2306         jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2307         jmax = ui[prow+1];
2308         ncols = jmax-jmin;
2309         i     = jmin - ui[prow];
2310         cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2311         uj    = uj_lvl_ptr[prow] + i; /* levels of cols */
2312         j     = *(uj - 1);
2313         ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr);
2314         nzk += nlnk;
2315 
2316         /* update il and jl for prow */
2317         if (jmin < jmax){
2318           il[prow] = jmin;
2319           j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2320         }
2321         prow = nextprow;
2322       }
2323 
2324       /* if free space is not available, make more free space */
2325       if (current_space->local_remaining<nzk) {
2326         i  = am - k + 1; /* num of unfactored rows */
2327         i *= PetscMin(nzk, i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */
2328         ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2329         ierr = PetscFreeSpaceGet(i,&current_space_lvl);CHKERRQ(ierr);
2330         reallocs++;
2331       }
2332 
2333       /* copy data into free_space and free_space_lvl, then initialize lnk */
2334       if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2335       ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
2336 
2337       /* add the k-th row into il and jl */
2338       if (nzk > 1){
2339         i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2340         jl[k] = jl[i]; jl[i] = k;
2341         il[k] = ui[k] + 1;
2342       }
2343       uj_ptr[k]     = current_space->array;
2344       uj_lvl_ptr[k] = current_space_lvl->array;
2345 
2346       current_space->array           += nzk;
2347       current_space->local_used      += nzk;
2348       current_space->local_remaining -= nzk;
2349 
2350       current_space_lvl->array           += nzk;
2351       current_space_lvl->local_used      += nzk;
2352       current_space_lvl->local_remaining -= nzk;
2353 
2354       ui[k+1] = ui[k] + nzk;
2355     }
2356 
2357 #if defined(PETSC_USE_INFO)
2358     if (ai[am] != 0) {
2359       PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]);
2360       ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2361       ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2362       ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2363     } else {
2364       ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2365     }
2366 #endif
2367 
2368     ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2369     ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2370     ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr);
2371     ierr = PetscFree(ajtmp);CHKERRQ(ierr);
2372 
2373     /* destroy list of free space and other temporary array(s) */
2374     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2375     ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor in newdatastruct */
2376     ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2377     ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2378 
2379   } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2380 
2381   /* put together the new matrix in MATSEQSBAIJ format */
2382 
2383   b    = (Mat_SeqSBAIJ*)(fact)->data;
2384   b->singlemalloc = PETSC_FALSE;
2385   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2386   b->j    = uj;
2387   b->i    = ui;
2388   b->diag = udiag;
2389   b->free_diag = PETSC_TRUE;
2390   b->ilen = 0;
2391   b->imax = 0;
2392   b->row  = perm;
2393   b->col  = perm;
2394   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2395   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2396   b->icol = iperm;
2397   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2398   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2399   ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2400   b->maxnz   = b->nz = ui[am];
2401   b->free_a  = PETSC_TRUE;
2402   b->free_ij = PETSC_TRUE;
2403 
2404   (fact)->info.factor_mallocs    = reallocs;
2405   (fact)->info.fill_ratio_given  = fill;
2406   if (ai[am] != 0) {
2407     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2408   } else {
2409     (fact)->info.fill_ratio_needed = 0.0;
2410   }
2411   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_newdatastruct;
2412   PetscFunctionReturn(0);
2413 }
2414 
2415 #undef __FUNCT__
2416 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ"
2417 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2418 {
2419   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2420   Mat_SeqSBAIJ       *b;
2421   PetscErrorCode     ierr;
2422   PetscTruth         perm_identity,missing;
2423   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag;
2424   const PetscInt     *rip,*riip;
2425   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
2426   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL,d;
2427   PetscInt           ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
2428   PetscReal          fill=info->fill,levels=info->levels;
2429   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2430   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
2431   PetscBT            lnkbt;
2432   IS                 iperm;
2433   PetscTruth         newdatastruct=PETSC_FALSE;
2434 
2435   PetscFunctionBegin;
2436   ierr = PetscOptionsGetTruth(PETSC_NULL,"-icc_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
2437   if(newdatastruct){
2438     ierr = MatICCFactorSymbolic_SeqAIJ_newdatastruct(fact,A,perm,info);CHKERRQ(ierr);
2439     PetscFunctionReturn(0);
2440   }
2441 
2442   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);
2443   ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
2444   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
2445   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2446   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2447 
2448   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2449   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2450   ui[0] = 0;
2451 
2452   /* ICC(0) without matrix ordering: simply copies fill pattern */
2453   if (!levels && perm_identity) {
2454 
2455     for (i=0; i<am; i++) {
2456       ui[i+1]  = ui[i] + ai[i+1] - a->diag[i];
2457       udiag[i] = ui[i];
2458     }
2459     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2460     cols = uj;
2461     for (i=0; i<am; i++) {
2462       aj    = a->j + a->diag[i];
2463       ncols = ui[i+1] - ui[i];
2464       for (j=0; j<ncols; j++) *cols++ = *aj++;
2465     }
2466   } else { /* case: levels>0 || (levels=0 && !perm_identity) */
2467     ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2468     ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2469 
2470     /* initialization */
2471     ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr);
2472 
2473     /* jl: linked list for storing indices of the pivot rows
2474        il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2475     ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr);
2476     for (i=0; i<am; i++){
2477       jl[i] = am; il[i] = 0;
2478     }
2479 
2480     /* create and initialize a linked list for storing column indices of the active row k */
2481     nlnk = am + 1;
2482     ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2483 
2484     /* initial FreeSpace size is fill*(ai[am]+1) */
2485     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2486     current_space = free_space;
2487     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr);
2488     current_space_lvl = free_space_lvl;
2489 
2490     for (k=0; k<am; k++){  /* for each active row k */
2491       /* initialize lnk by the column indices of row rip[k] of A */
2492       nzk   = 0;
2493       ncols = ai[rip[k]+1] - ai[rip[k]];
2494       if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2495       ncols_upper = 0;
2496       for (j=0; j<ncols; j++){
2497         i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2498         if (riip[i] >= k){ /* only take upper triangular entry */
2499           ajtmp[ncols_upper] = i;
2500           ncols_upper++;
2501         }
2502       }
2503       ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2504       nzk += nlnk;
2505 
2506       /* update lnk by computing fill-in for each pivot row to be merged in */
2507       prow = jl[k]; /* 1st pivot row */
2508 
2509       while (prow < k){
2510         nextprow = jl[prow];
2511 
2512         /* merge prow into k-th row */
2513         jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2514         jmax = ui[prow+1];
2515         ncols = jmax-jmin;
2516         i     = jmin - ui[prow];
2517         cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2518         uj    = uj_lvl_ptr[prow] + i; /* levels of cols */
2519         j     = *(uj - 1);
2520         ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr);
2521         nzk += nlnk;
2522 
2523         /* update il and jl for prow */
2524         if (jmin < jmax){
2525           il[prow] = jmin;
2526           j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2527         }
2528         prow = nextprow;
2529       }
2530 
2531       /* if free space is not available, make more free space */
2532       if (current_space->local_remaining<nzk) {
2533         i = am - k + 1; /* num of unfactored rows */
2534         i *= PetscMin(nzk, (i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2535         ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2536         ierr = PetscFreeSpaceGet(i,&current_space_lvl);CHKERRQ(ierr);
2537         reallocs++;
2538       }
2539 
2540       /* copy data into free_space and free_space_lvl, then initialize lnk */
2541       if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2542       ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
2543 
2544       /* add the k-th row into il and jl */
2545       if (nzk > 1){
2546         i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2547         jl[k] = jl[i]; jl[i] = k;
2548         il[k] = ui[k] + 1;
2549       }
2550       uj_ptr[k]     = current_space->array;
2551       uj_lvl_ptr[k] = current_space_lvl->array;
2552 
2553       current_space->array           += nzk;
2554       current_space->local_used      += nzk;
2555       current_space->local_remaining -= nzk;
2556 
2557       current_space_lvl->array           += nzk;
2558       current_space_lvl->local_used      += nzk;
2559       current_space_lvl->local_remaining -= nzk;
2560 
2561       ui[k+1] = ui[k] + nzk;
2562     }
2563 
2564 #if defined(PETSC_USE_INFO)
2565     if (ai[am] != 0) {
2566       PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]);
2567       ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2568       ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2569       ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2570     } else {
2571       ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2572     }
2573 #endif
2574 
2575     ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2576     ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2577     ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr);
2578     ierr = PetscFree(ajtmp);CHKERRQ(ierr);
2579 
2580     /* destroy list of free space and other temporary array(s) */
2581     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2582     ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
2583     ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2584     ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2585 
2586   } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2587 
2588   /* put together the new matrix in MATSEQSBAIJ format */
2589 
2590   b    = (Mat_SeqSBAIJ*)(fact)->data;
2591   b->singlemalloc = PETSC_FALSE;
2592   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2593   b->j    = uj;
2594   b->i    = ui;
2595   b->diag = udiag;
2596   b->free_diag = PETSC_TRUE;
2597   b->ilen = 0;
2598   b->imax = 0;
2599   b->row  = perm;
2600   b->col  = perm;
2601   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2602   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2603   b->icol = iperm;
2604   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2605   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2606   ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2607   b->maxnz   = b->nz = ui[am];
2608   b->free_a  = PETSC_TRUE;
2609   b->free_ij = PETSC_TRUE;
2610 
2611   (fact)->info.factor_mallocs    = reallocs;
2612   (fact)->info.fill_ratio_given  = fill;
2613   if (ai[am] != 0) {
2614     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2615   } else {
2616     (fact)->info.fill_ratio_needed = 0.0;
2617   }
2618   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2619   PetscFunctionReturn(0);
2620 }
2621 
2622 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2623 {
2624   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2625   Mat_SeqSBAIJ       *b;
2626   PetscErrorCode     ierr;
2627   PetscTruth         perm_identity;
2628   PetscReal          fill = info->fill;
2629   const PetscInt     *rip,*riip;
2630   PetscInt           i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow;
2631   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
2632   PetscInt           nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr,*udiag;
2633   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2634   PetscBT            lnkbt;
2635   IS                 iperm;
2636 
2637   PetscFunctionBegin;
2638   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);
2639   /* check whether perm is the identity mapping */
2640   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2641   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2642   ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2643   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2644 
2645   /* initialization */
2646   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2647   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2648   ui[0] = 0;
2649 
2650   /* jl: linked list for storing indices of the pivot rows
2651      il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2652   ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr);
2653   for (i=0; i<am; i++){
2654     jl[i] = am; il[i] = 0;
2655   }
2656 
2657   /* create and initialize a linked list for storing column indices of the active row k */
2658   nlnk = am + 1;
2659   ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2660 
2661   /* initial FreeSpace size is fill*(ai[am]+1) */
2662   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2663   current_space = free_space;
2664 
2665   for (k=0; k<am; k++){  /* for each active row k */
2666     /* initialize lnk by the column indices of row rip[k] of A */
2667     nzk   = 0;
2668     ncols = ai[rip[k]+1] - ai[rip[k]];
2669     if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2670     ncols_upper = 0;
2671     for (j=0; j<ncols; j++){
2672       i = riip[*(aj + ai[rip[k]] + j)];
2673       if (i >= k){ /* only take upper triangular entry */
2674         cols[ncols_upper] = i;
2675         ncols_upper++;
2676       }
2677     }
2678     ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2679     nzk += nlnk;
2680 
2681     /* update lnk by computing fill-in for each pivot row to be merged in */
2682     prow = jl[k]; /* 1st pivot row */
2683 
2684     while (prow < k){
2685       nextprow = jl[prow];
2686       /* merge prow into k-th row */
2687       jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2688       jmax = ui[prow+1];
2689       ncols = jmax-jmin;
2690       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2691       ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2692       nzk += nlnk;
2693 
2694       /* update il and jl for prow */
2695       if (jmin < jmax){
2696         il[prow] = jmin;
2697         j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
2698       }
2699       prow = nextprow;
2700     }
2701 
2702     /* if free space is not available, make more free space */
2703     if (current_space->local_remaining<nzk) {
2704       i  = am - k + 1; /* num of unfactored rows */
2705       i *= PetscMin(nzk,i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */
2706       ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2707       reallocs++;
2708     }
2709 
2710     /* copy data into free space, then initialize lnk */
2711     ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
2712 
2713     /* add the k-th row into il and jl */
2714     if (nzk-1 > 0){
2715       i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2716       jl[k] = jl[i]; jl[i] = k;
2717       il[k] = ui[k] + 1;
2718     }
2719     ui_ptr[k] = current_space->array;
2720     current_space->array           += nzk;
2721     current_space->local_used      += nzk;
2722     current_space->local_remaining -= nzk;
2723 
2724     ui[k+1] = ui[k] + nzk;
2725   }
2726 
2727 #if defined(PETSC_USE_INFO)
2728   if (ai[am] != 0) {
2729     PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]);
2730     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2731     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2732     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2733   } else {
2734      ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2735   }
2736 #endif
2737 
2738   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2739   ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2740   ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr);
2741 
2742   /* destroy list of free space and other temporary array(s) */
2743   ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2744   ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor in newdatastruct */
2745   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2746 
2747   /* put together the new matrix in MATSEQSBAIJ format */
2748 
2749   b = (Mat_SeqSBAIJ*)(fact)->data;
2750   b->singlemalloc = PETSC_FALSE;
2751   b->free_a       = PETSC_TRUE;
2752   b->free_ij      = PETSC_TRUE;
2753   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2754   b->j    = uj;
2755   b->i    = ui;
2756   b->diag = udiag;
2757   b->free_diag = PETSC_TRUE;
2758   b->ilen = 0;
2759   b->imax = 0;
2760   b->row  = perm;
2761   b->col  = perm;
2762   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2763   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2764   b->icol = iperm;
2765   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2766   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2767   ierr    = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2768   b->maxnz = b->nz = ui[am];
2769 
2770   (fact)->info.factor_mallocs    = reallocs;
2771   (fact)->info.fill_ratio_given  = fill;
2772   if (ai[am] != 0) {
2773     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2774   } else {
2775     (fact)->info.fill_ratio_needed = 0.0;
2776   }
2777   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_newdatastruct;
2778   PetscFunctionReturn(0);
2779 }
2780 
2781 #undef __FUNCT__
2782 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ"
2783 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2784 {
2785   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2786   Mat_SeqSBAIJ       *b;
2787   PetscErrorCode     ierr;
2788   PetscTruth         perm_identity;
2789   PetscReal          fill = info->fill;
2790   const PetscInt     *rip,*riip;
2791   PetscInt           i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow;
2792   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
2793   PetscInt           nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr;
2794   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2795   PetscBT            lnkbt;
2796   IS                 iperm;
2797   PetscTruth         newdatastruct=PETSC_FALSE;
2798 
2799   PetscFunctionBegin;
2800   ierr = PetscOptionsGetTruth(PETSC_NULL,"-cholesky_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
2801   if(newdatastruct){
2802     ierr = MatCholeskyFactorSymbolic_SeqAIJ_newdatastruct(fact,A,perm,info);CHKERRQ(ierr);
2803     PetscFunctionReturn(0);
2804   }
2805 
2806   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);
2807   /* check whether perm is the identity mapping */
2808   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2809   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2810   ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2811   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2812 
2813   /* initialization */
2814   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2815   ui[0] = 0;
2816 
2817   /* jl: linked list for storing indices of the pivot rows
2818      il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2819   ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr);
2820   for (i=0; i<am; i++){
2821     jl[i] = am; il[i] = 0;
2822   }
2823 
2824   /* create and initialize a linked list for storing column indices of the active row k */
2825   nlnk = am + 1;
2826   ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2827 
2828   /* initial FreeSpace size is fill*(ai[am]+1) */
2829   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2830   current_space = free_space;
2831 
2832   for (k=0; k<am; k++){  /* for each active row k */
2833     /* initialize lnk by the column indices of row rip[k] of A */
2834     nzk   = 0;
2835     ncols = ai[rip[k]+1] - ai[rip[k]];
2836     if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2837     ncols_upper = 0;
2838     for (j=0; j<ncols; j++){
2839       i = riip[*(aj + ai[rip[k]] + j)];
2840       if (i >= k){ /* only take upper triangular entry */
2841         cols[ncols_upper] = i;
2842         ncols_upper++;
2843       }
2844     }
2845     ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2846     nzk += nlnk;
2847 
2848     /* update lnk by computing fill-in for each pivot row to be merged in */
2849     prow = jl[k]; /* 1st pivot row */
2850 
2851     while (prow < k){
2852       nextprow = jl[prow];
2853       /* merge prow into k-th row */
2854       jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2855       jmax = ui[prow+1];
2856       ncols = jmax-jmin;
2857       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2858       ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2859       nzk += nlnk;
2860 
2861       /* update il and jl for prow */
2862       if (jmin < jmax){
2863         il[prow] = jmin;
2864         j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
2865       }
2866       prow = nextprow;
2867     }
2868 
2869     /* if free space is not available, make more free space */
2870     if (current_space->local_remaining<nzk) {
2871       i = am - k + 1; /* num of unfactored rows */
2872       i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2873       ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2874       reallocs++;
2875     }
2876 
2877     /* copy data into free space, then initialize lnk */
2878     ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
2879 
2880     /* add the k-th row into il and jl */
2881     if (nzk-1 > 0){
2882       i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2883       jl[k] = jl[i]; jl[i] = k;
2884       il[k] = ui[k] + 1;
2885     }
2886     ui_ptr[k] = current_space->array;
2887     current_space->array           += nzk;
2888     current_space->local_used      += nzk;
2889     current_space->local_remaining -= nzk;
2890 
2891     ui[k+1] = ui[k] + nzk;
2892   }
2893 
2894 #if defined(PETSC_USE_INFO)
2895   if (ai[am] != 0) {
2896     PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]);
2897     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2898     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2899     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2900   } else {
2901      ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2902   }
2903 #endif
2904 
2905   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2906   ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2907   ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr);
2908 
2909   /* destroy list of free space and other temporary array(s) */
2910   ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2911   ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
2912   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2913 
2914   /* put together the new matrix in MATSEQSBAIJ format */
2915 
2916   b = (Mat_SeqSBAIJ*)(fact)->data;
2917   b->singlemalloc = PETSC_FALSE;
2918   b->free_a       = PETSC_TRUE;
2919   b->free_ij      = PETSC_TRUE;
2920   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2921   b->j    = uj;
2922   b->i    = ui;
2923   b->diag = 0;
2924   b->ilen = 0;
2925   b->imax = 0;
2926   b->row  = perm;
2927   b->col  = perm;
2928   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2929   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2930   b->icol = iperm;
2931   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2932   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2933   ierr    = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2934   b->maxnz = b->nz = ui[am];
2935 
2936   (fact)->info.factor_mallocs    = reallocs;
2937   (fact)->info.fill_ratio_given  = fill;
2938   if (ai[am] != 0) {
2939     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2940   } else {
2941     (fact)->info.fill_ratio_needed = 0.0;
2942   }
2943   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2944   PetscFunctionReturn(0);
2945 }
2946 
2947 #if defined(OLD_ROUTINE_TO_BE_REPLACED)
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 #endif
2998 
2999 #undef __FUNCT__
3000 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_newdatastruct"
3001 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx)
3002 {
3003   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
3004   PetscErrorCode    ierr;
3005   PetscInt          n = A->rmap->n;
3006   const PetscInt    *ai = a->i,*aj = a->j,*adiag = a->diag,*vi;
3007   PetscScalar       *x,sum;
3008   const PetscScalar *b;
3009   const MatScalar   *aa = a->a,*v;
3010   PetscInt          i,nz;
3011 
3012   PetscFunctionBegin;
3013   if (!n) PetscFunctionReturn(0);
3014 
3015   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3016   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3017 
3018   /* forward solve the lower triangular */
3019   x[0] = b[0];
3020   v    = aa;
3021   vi   = aj;
3022   for (i=1; i<n; i++) {
3023     nz  = ai[i+1] - ai[i];
3024     sum = b[i];
3025     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
3026     v  += nz;
3027     vi += nz;
3028     x[i] = sum;
3029   }
3030 
3031   /* backward solve the upper triangular */
3032   /*  v   = aa + ai[n+1];
3033       vi  = aj + ai[n+1]; */
3034   v  = aa + adiag[n-1];
3035   vi = aj + adiag[n-1];
3036   for (i=n-1; i>=0; i--){
3037     nz = adiag[i] - adiag[i+1]-1;
3038     sum = x[i];
3039     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
3040     v   += nz;
3041     vi  += nz; vi++;
3042     x[i] = *v++ *sum; /* x[i]=aa[adiag[i]]*sum; v++; */
3043   }
3044 
3045   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
3046   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3047   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3048   PetscFunctionReturn(0);
3049 }
3050 
3051 #if defined(OLD_ROUTINE_TO_BE_REPLACED)
3052 #undef __FUNCT__
3053 #define __FUNCT__ "MatSolve_SeqAIJ_newdatastruct"
3054 PetscErrorCode MatSolve_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec xx)
3055 {
3056   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
3057   IS                iscol = a->col,isrow = a->row;
3058   PetscErrorCode    ierr;
3059   PetscInt          i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,nz,k;
3060   const PetscInt    *rout,*cout,*r,*c;
3061   PetscScalar       *x,*tmp,*tmps,sum;
3062   const PetscScalar *b;
3063   const MatScalar   *aa = a->a,*v;
3064 
3065   PetscFunctionBegin;
3066   if (!n) PetscFunctionReturn(0);
3067 
3068   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3069   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3070   tmp  = a->solve_work;
3071 
3072   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
3073   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
3074 
3075   /* forward solve the lower triangular */
3076   tmp[0] = b[*r++];
3077   tmps   = tmp;
3078   v      = aa;
3079   vi     = aj;
3080   for (i=1; i<n; i++) {
3081     nz  = ai[i+1] - ai[i];
3082     sum = b[*r++];
3083     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
3084     tmp[i] = sum;
3085     v += nz; vi += nz;
3086   }
3087 
3088   /* backward solve the upper triangular */
3089   k  = n+1;
3090   v  = aa + ai[k]; /* 1st entry of U(n-1,:) */
3091   vi = aj + ai[k];
3092   for (i=n-1; i>=0; i--){
3093     k  = 2*n-i;
3094     nz = ai[k +1] - ai[k] - 1;
3095     sum = tmp[i];
3096     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
3097     x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */
3098     v += nz+1; vi += nz+1;
3099   }
3100 
3101   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
3102   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
3103   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3104   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3105   ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr);
3106   PetscFunctionReturn(0);
3107 }
3108 #endif
3109 
3110 #undef __FUNCT__
3111 #define __FUNCT__ "MatSolve_SeqAIJ_newdatastruct"
3112 PetscErrorCode MatSolve_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec xx)
3113 {
3114   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
3115   IS                iscol = a->col,isrow = a->row;
3116   PetscErrorCode    ierr;
3117   PetscInt          i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz;
3118   const PetscInt    *rout,*cout,*r,*c;
3119   PetscScalar       *x,*tmp,sum;
3120   const PetscScalar *b;
3121   const MatScalar   *aa = a->a,*v;
3122 
3123   PetscFunctionBegin;
3124   if (!n) PetscFunctionReturn(0);
3125 
3126   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3127   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3128   tmp  = a->solve_work;
3129 
3130   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
3131   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
3132 
3133   /* forward solve the lower triangular */
3134   tmp[0] = b[r[0]];
3135   v      = aa;
3136   vi     = aj;
3137   for (i=1; i<n; i++) {
3138     nz  = ai[i+1] - ai[i];
3139     sum = b[r[i]];
3140     PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
3141     tmp[i] = sum;
3142     v += nz; vi += nz;
3143   }
3144 
3145   /* backward solve the upper triangular */
3146   v  = aa + adiag[n-1]; /* 1st entry of U(n-1,:) */
3147   vi = aj + adiag[n-1];
3148   for (i=n-1; i>=0; i--){
3149     nz = adiag[i]-adiag[i+1]-1;
3150     sum = tmp[i];
3151     PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
3152     x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */
3153     v += nz+1; vi += nz+1;
3154   }
3155 
3156   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
3157   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
3158   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3159   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3160   ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr);
3161   PetscFunctionReturn(0);
3162 }
3163 
3164 #undef __FUNCT__
3165 #define __FUNCT__ "MatILUDTFactor_SeqAIJ"
3166 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact)
3167 {
3168   Mat                B = *fact;
3169   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b;
3170   IS                 isicol;
3171   PetscErrorCode     ierr;
3172   const PetscInt     *r,*ic;
3173   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag;
3174   PetscInt           *bi,*bj,*bdiag,*bdiag_rev;
3175   PetscInt           row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au;
3176   PetscInt           nlnk,*lnk;
3177   PetscBT            lnkbt;
3178   PetscTruth         row_identity,icol_identity,both_identity;
3179   MatScalar          *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp;
3180   const PetscInt     *ics;
3181   PetscInt           j,nz,*pj,*bjtmp,k,ncut,*jtmp;
3182   PetscReal          dt=info->dt,dtcol=info->dtcol,shift=info->shiftinblocks;
3183   PetscInt           dtcount=(PetscInt)info->dtcount,nnz_max;
3184   PetscTruth         missing;
3185 
3186   PetscFunctionBegin;
3187 
3188   if (dt      == PETSC_DEFAULT) dt      = 0.005;
3189   if (dtcol   == PETSC_DEFAULT) dtcol   = 0.01; /* XXX unused! */
3190   if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax);
3191 
3192   /* ------- symbolic factorization, can be reused ---------*/
3193   ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
3194   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
3195   adiag=a->diag;
3196 
3197   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
3198 
3199   /* bdiag is location of diagonal in factor */
3200   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);     /* becomes b->diag */
3201   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag_rev);CHKERRQ(ierr); /* temporary */
3202 
3203   /* allocate row pointers bi */
3204   ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
3205 
3206   /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */
3207   if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */
3208   nnz_max  = ai[n]+2*n*dtcount+2;
3209 
3210   ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
3211   ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr);
3212 
3213   /* put together the new matrix */
3214   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
3215   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
3216   b    = (Mat_SeqAIJ*)(B)->data;
3217   b->free_a       = PETSC_TRUE;
3218   b->free_ij      = PETSC_TRUE;
3219   b->singlemalloc = PETSC_FALSE;
3220   b->a          = ba;
3221   b->j          = bj;
3222   b->i          = bi;
3223   b->diag       = bdiag;
3224   b->ilen       = 0;
3225   b->imax       = 0;
3226   b->row        = isrow;
3227   b->col        = iscol;
3228   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
3229   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
3230   b->icol       = isicol;
3231   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
3232 
3233   ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
3234   b->maxnz = nnz_max;
3235 
3236   (B)->factor                = MAT_FACTOR_ILUDT;
3237   (B)->info.factor_mallocs   = 0;
3238   (B)->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]);
3239   CHKMEMQ;
3240   /* ------- end of symbolic factorization ---------*/
3241 
3242   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
3243   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
3244   ics  = ic;
3245 
3246   /* linked list for storing column indices of the active row */
3247   nlnk = n + 1;
3248   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3249 
3250   /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */
3251   ierr = PetscMalloc2(n,PetscInt,&im,n,PetscInt,&jtmp);CHKERRQ(ierr);
3252   /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */
3253   ierr = PetscMalloc2(n,MatScalar,&rtmp,n,MatScalar,&vtmp);CHKERRQ(ierr);
3254   ierr = PetscMemzero(rtmp,n*sizeof(MatScalar));CHKERRQ(ierr);
3255 
3256   bi[0]    = 0;
3257   bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */
3258   bdiag_rev[n] = bdiag[0];
3259   bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */
3260   for (i=0; i<n; i++) {
3261     /* copy initial fill into linked list */
3262     nzi = 0; /* nonzeros for active row i */
3263     nzi = ai[r[i]+1] - ai[r[i]];
3264     if (!nzi) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
3265     nzi_al = adiag[r[i]] - ai[r[i]];
3266     nzi_au = ai[r[i]+1] - adiag[r[i]] -1;
3267     ajtmp = aj + ai[r[i]];
3268     ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3269 
3270     /* load in initial (unfactored row) */
3271     aatmp = a->a + ai[r[i]];
3272     for (j=0; j<nzi; j++) {
3273       rtmp[ics[*ajtmp++]] = *aatmp++;
3274     }
3275 
3276     /* add pivot rows into linked list */
3277     row = lnk[n];
3278     while (row < i ) {
3279       nzi_bl = bi[row+1] - bi[row] + 1;
3280       bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */
3281       ierr  = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr);
3282       nzi  += nlnk;
3283       row   = lnk[row];
3284     }
3285 
3286     /* copy data from lnk into jtmp, then initialize lnk */
3287     ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr);
3288 
3289     /* numerical factorization */
3290     bjtmp = jtmp;
3291     row   = *bjtmp++; /* 1st pivot row */
3292     while  ( row < i ) {
3293       pc         = rtmp + row;
3294       pv         = ba + bdiag[row]; /* 1./(diag of the pivot row) */
3295       multiplier = (*pc) * (*pv);
3296       *pc        = multiplier;
3297       if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */
3298         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
3299         pv         = ba + bdiag[row+1] + 1;
3300         /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */
3301         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
3302         for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
3303         ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
3304       }
3305       row = *bjtmp++;
3306     }
3307 
3308     /* copy sparse rtmp into contiguous vtmp; separate L and U part */
3309     diag_tmp = rtmp[i];  /* save diagonal value - may not needed?? */
3310     nzi_bl = 0; j = 0;
3311     while (jtmp[j] < i){ /* Note: jtmp is sorted */
3312       vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
3313       nzi_bl++; j++;
3314     }
3315     nzi_bu = nzi - nzi_bl -1;
3316     while (j < nzi){
3317       vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
3318       j++;
3319     }
3320 
3321     bjtmp = bj + bi[i];
3322     batmp = ba + bi[i];
3323     /* apply level dropping rule to L part */
3324     ncut = nzi_al + dtcount;
3325     if (ncut < nzi_bl){
3326       ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr);
3327       ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr);
3328     } else {
3329       ncut = nzi_bl;
3330     }
3331     for (j=0; j<ncut; j++){
3332       bjtmp[j] = jtmp[j];
3333       batmp[j] = vtmp[j];
3334       /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */
3335     }
3336     bi[i+1] = bi[i] + ncut;
3337     nzi = ncut + 1;
3338 
3339     /* apply level dropping rule to U part */
3340     ncut = nzi_au + dtcount;
3341     if (ncut < nzi_bu){
3342       ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr);
3343       ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr);
3344     } else {
3345       ncut = nzi_bu;
3346     }
3347     nzi += ncut;
3348 
3349     /* mark bdiagonal */
3350     bdiag[i+1]       = bdiag[i] - (ncut + 1);
3351     bdiag_rev[n-i-1] = bdiag[i+1];
3352     bi[2*n - i]      = bi[2*n - i +1] - (ncut + 1);
3353     bjtmp = bj + bdiag[i];
3354     batmp = ba + bdiag[i];
3355     *bjtmp = i;
3356     *batmp = diag_tmp; /* rtmp[i]; */
3357     if (*batmp == 0.0) {
3358       *batmp = dt+shift;
3359       /* printf(" row %d add shift %g\n",i,shift); */
3360     }
3361     *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */
3362     /* printf(" (%d,%g),",*bjtmp,*batmp); */
3363 
3364     bjtmp = bj + bdiag[i+1]+1;
3365     batmp = ba + bdiag[i+1]+1;
3366     for (k=0; k<ncut; k++){
3367       bjtmp[k] = jtmp[nzi_bl+1+k];
3368       batmp[k] = vtmp[nzi_bl+1+k];
3369       /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */
3370     }
3371     /* printf("\n"); */
3372 
3373     im[i]   = nzi; /* used by PetscLLAddSortedLU() */
3374     /*
3375     printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]);
3376     printf(" ----------------------------\n");
3377     */
3378   } /* for (i=0; i<n; i++) */
3379   /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */
3380   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]);
3381 
3382   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
3383   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
3384 
3385   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
3386   ierr = PetscFree2(im,jtmp);CHKERRQ(ierr);
3387   ierr = PetscFree2(rtmp,vtmp);CHKERRQ(ierr);
3388   ierr = PetscFree(bdiag_rev);CHKERRQ(ierr);
3389 
3390   ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr);
3391   b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n];
3392 
3393   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
3394   ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr);
3395   both_identity = (PetscTruth) (row_identity && icol_identity);
3396   if (row_identity && icol_identity) {
3397     B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct;
3398   } else {
3399     B->ops->solve = MatSolve_SeqAIJ_newdatastruct;
3400   }
3401 
3402   B->ops->lufactorsymbolic  = MatILUDTFactorSymbolic_SeqAIJ;
3403   B->ops->lufactornumeric   = MatILUDTFactorNumeric_SeqAIJ;
3404   B->ops->solveadd          = 0;
3405   B->ops->solvetranspose    = 0;
3406   B->ops->solvetransposeadd = 0;
3407   B->ops->matsolve          = 0;
3408   B->assembled              = PETSC_TRUE;
3409   B->preallocated           = PETSC_TRUE;
3410   PetscFunctionReturn(0);
3411 }
3412 
3413 /* a wraper of MatILUDTFactor_SeqAIJ() */
3414 #undef __FUNCT__
3415 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ"
3416 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info)
3417 {
3418   PetscErrorCode     ierr;
3419 
3420   PetscFunctionBegin;
3421   ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr);
3422 
3423   fact->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ;
3424   PetscFunctionReturn(0);
3425 }
3426 
3427 /*
3428    same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors
3429    - intend to replace existing MatLUFactorNumeric_SeqAIJ()
3430 */
3431 #undef __FUNCT__
3432 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ"
3433 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info)
3434 {
3435   Mat            C=fact;
3436   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
3437   IS             isrow = b->row,isicol = b->icol;
3438   PetscErrorCode ierr;
3439   const PetscInt *r,*ic,*ics;
3440   PetscInt       i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
3441   PetscInt       *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj;
3442   MatScalar      *rtmp,*pc,multiplier,*v,*pv,*aa=a->a;
3443   PetscReal      dt=info->dt,shift=info->shiftinblocks;
3444   PetscTruth     row_identity, col_identity;
3445 
3446   PetscFunctionBegin;
3447   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
3448   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
3449   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
3450   ics  = ic;
3451 
3452   for (i=0; i<n; i++){
3453     /* initialize rtmp array */
3454     nzl   = bi[i+1] - bi[i];       /* num of nozeros in L(i,:) */
3455     bjtmp = bj + bi[i];
3456     for  (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0;
3457     rtmp[i] = 0.0;
3458     nzu   = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */
3459     bjtmp = bj + bdiag[i+1] + 1;
3460     for  (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0;
3461 
3462     /* load in initial unfactored row of A */
3463     /* printf("row %d\n",i); */
3464     nz    = ai[r[i]+1] - ai[r[i]];
3465     ajtmp = aj + ai[r[i]];
3466     v     = aa + ai[r[i]];
3467     for (j=0; j<nz; j++) {
3468       rtmp[ics[*ajtmp++]] = v[j];
3469       /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */
3470     }
3471     /* printf("\n"); */
3472 
3473     /* numerical factorization */
3474     bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */
3475     nzl   = bi[i+1] - bi[i]; /* num of entries in L(i,:) */
3476     k = 0;
3477     while (k < nzl){
3478       row   = *bjtmp++;
3479       /* printf("  prow %d\n",row); */
3480       pc         = rtmp + row;
3481       pv         = b->a + bdiag[row]; /* 1./(diag of the pivot row) */
3482       multiplier = (*pc) * (*pv);
3483       *pc        = multiplier;
3484       if (PetscAbsScalar(multiplier) > dt){
3485         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
3486         pv         = b->a + bdiag[row+1] + 1;
3487         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
3488         for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
3489         /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */
3490       }
3491       k++;
3492     }
3493 
3494     /* finished row so stick it into b->a */
3495     /* L-part */
3496     pv = b->a + bi[i] ;
3497     pj = bj + bi[i] ;
3498     nzl = bi[i+1] - bi[i];
3499     for (j=0; j<nzl; j++) {
3500       pv[j] = rtmp[pj[j]];
3501       /* printf(" (%d,%g),",pj[j],pv[j]); */
3502     }
3503 
3504     /* diagonal: invert diagonal entries for simplier triangular solves */
3505     if (rtmp[i] == 0.0) rtmp[i] = dt+shift;
3506     b->a[bdiag[i]] = 1.0/rtmp[i];
3507     /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */
3508 
3509     /* U-part */
3510     pv = b->a + bdiag[i+1] + 1;
3511     pj = bj + bdiag[i+1] + 1;
3512     nzu = bdiag[i] - bdiag[i+1] - 1;
3513     for (j=0; j<nzu; j++) {
3514       pv[j] = rtmp[pj[j]];
3515       /* printf(" (%d,%g),",pj[j],pv[j]); */
3516     }
3517     /* printf("\n"); */
3518   }
3519 
3520   ierr = PetscFree(rtmp);CHKERRQ(ierr);
3521   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
3522   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
3523 
3524   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
3525   ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
3526   if (row_identity && col_identity) {
3527     C->ops->solve   = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct;
3528   } else {
3529     C->ops->solve   = MatSolve_SeqAIJ_newdatastruct;
3530   }
3531   C->ops->solveadd           = 0;
3532   C->ops->solvetranspose     = 0;
3533   C->ops->solvetransposeadd  = 0;
3534   C->ops->matsolve           = 0;
3535   C->assembled    = PETSC_TRUE;
3536   C->preallocated = PETSC_TRUE;
3537   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
3538   PetscFunctionReturn(0);
3539 }
3540