xref: /petsc/src/mat/impls/aij/seq/aijfact.c (revision 70dcbbb9ec575d8ef59c8591bf18c9c2e6e303fc)
1 #define PETSCMAT_DLL
2 
3 
4 #include "../src/mat/impls/aij/seq/aij.h"
5 #include "petscbt.h"
6 #include "../src/mat/utils/freespace.h"
7 
8 EXTERN_C_BEGIN
9 #undef __FUNCT__
10 #define __FUNCT__ "MatOrdering_Flow_SeqAIJ"
11 /*
12       Computes an ordering to get most of the large numerical values in the lower triangular part of the matrix
13 */
14 PetscErrorCode MatOrdering_Flow_SeqAIJ(Mat mat,const MatOrderingType type,IS *irow,IS *icol)
15 {
16   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)mat->data;
17   PetscErrorCode    ierr;
18   PetscInt          i,j,jj,k, kk,n = mat->rmap->n, current = 0, newcurrent = 0,*order;
19   const PetscInt    *ai = a->i, *aj = a->j;
20   const PetscScalar *aa = a->a;
21   PetscTruth        *done;
22   PetscReal         best,past = 0,future;
23 
24   PetscFunctionBegin;
25   /* pick initial row */
26   best = -1;
27   for (i=0; i<n; i++) {
28     future = 0;
29     for (j=ai[i]; j<ai[i+1]; j++) {
30       if (aj[j] != i) future  += PetscAbsScalar(aa[j]); else past = PetscAbsScalar(aa[j]);
31     }
32     if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */
33     if (past/future > best) {
34       best = past/future;
35       current = i;
36     }
37   }
38 
39   ierr = PetscMalloc(n*sizeof(PetscTruth),&done);CHKERRQ(ierr);
40   ierr = PetscMalloc(n*sizeof(PetscInt),&order);CHKERRQ(ierr);
41   ierr = PetscMemzero(done,n*sizeof(PetscTruth));CHKERRQ(ierr);
42   order[0] = current;
43   for (i=0; i<n-1; i++) {
44     done[current] = PETSC_TRUE;
45     best          = -1;
46     /* loop over all neighbors of current pivot */
47     for (j=ai[current]; j<ai[current+1]; j++) {
48       jj = aj[j];
49       if (done[jj]) continue;
50       /* loop over columns of potential next row computing weights for below and above diagonal */
51       past = future = 0.0;
52       for (k=ai[jj]; k<ai[jj+1]; k++) {
53         kk = aj[k];
54         if (done[kk]) past += PetscAbsScalar(aa[k]);
55         else if (kk != jj) future  += PetscAbsScalar(aa[k]);
56       }
57       if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */
58       if (past/future > best) {
59         best = past/future;
60         newcurrent = jj;
61       }
62     }
63     if (best == -1) { /* no neighbors to select from so select best of all that remain */
64       best = -1;
65       for (k=0; k<n; k++) {
66         if (done[k]) continue;
67         future = 0;
68         past   = 0;
69         for (j=ai[k]; j<ai[k+1]; j++) {
70           kk = aj[j];
71           if (done[kk]) past += PetscAbsScalar(aa[j]);
72           else if (kk != k) future  += PetscAbsScalar(aa[j]);
73         }
74         if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */
75         if (past/future > best) {
76           best = past/future;
77           newcurrent = k;
78         }
79       }
80     }
81     if (current == newcurrent) SETERRQ(PETSC_ERR_PLIB,"newcurrent cannot be current");
82     current = newcurrent;
83     order[i+1] = current;
84   }
85   ierr = ISCreateGeneral(PETSC_COMM_SELF,n,order,irow);CHKERRQ(ierr);
86   *icol = *irow;
87   ierr = PetscObjectReference((PetscObject)*irow);CHKERRQ(ierr);
88   ierr = PetscFree(done);CHKERRQ(ierr);
89   ierr = PetscFree(order);CHKERRQ(ierr);
90   PetscFunctionReturn(0);
91 }
92 EXTERN_C_END
93 
94 EXTERN_C_BEGIN
95 #undef __FUNCT__
96 #define __FUNCT__ "MatGetFactorAvailable_seqaij_petsc"
97 PetscErrorCode MatGetFactorAvailable_seqaij_petsc(Mat A,MatFactorType ftype,PetscTruth *flg)
98 {
99   PetscFunctionBegin;
100   *flg = PETSC_TRUE;
101   PetscFunctionReturn(0);
102 }
103 EXTERN_C_END
104 
105 EXTERN_C_BEGIN
106 #undef __FUNCT__
107 #define __FUNCT__ "MatGetFactor_seqaij_petsc"
108 PetscErrorCode MatGetFactor_seqaij_petsc(Mat A,MatFactorType ftype,Mat *B)
109 {
110   PetscInt           n = A->rmap->n;
111   PetscErrorCode     ierr;
112 
113   PetscFunctionBegin;
114   ierr = MatCreate(((PetscObject)A)->comm,B);CHKERRQ(ierr);
115   ierr = MatSetSizes(*B,n,n,n,n);CHKERRQ(ierr);
116   if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT){
117     ierr = MatSetType(*B,MATSEQAIJ);CHKERRQ(ierr);
118     (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqAIJ;
119     (*B)->ops->lufactorsymbolic  = MatLUFactorSymbolic_SeqAIJ;
120     (*B)->ops->iludtfactor       = MatILUDTFactor_SeqAIJ;
121   } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) {
122     ierr = MatSetType(*B,MATSEQSBAIJ);CHKERRQ(ierr);
123     ierr = MatSeqSBAIJSetPreallocation(*B,1,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
124     (*B)->ops->iccfactorsymbolic      = MatICCFactorSymbolic_SeqAIJ;
125     (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJ;
126   } else SETERRQ(PETSC_ERR_SUP,"Factor type not supported");
127   (*B)->factor = ftype;
128   PetscFunctionReturn(0);
129 }
130 EXTERN_C_END
131 
132 #undef __FUNCT__
133 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ"
134 PetscErrorCode MatLUFactorSymbolic_SeqAIJ(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
135 {
136   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
137   IS                 isicol;
138   PetscErrorCode     ierr;
139   const PetscInt     *r,*ic;
140   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j;
141   PetscInt           *bi,*bj,*ajtmp;
142   PetscInt           *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im;
143   PetscReal          f;
144   PetscInt           nlnk,*lnk,k,**bi_ptr;
145   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
146   PetscBT            lnkbt;
147   PetscTruth         newdatastruct=PETSC_FALSE;
148 
149   PetscFunctionBegin;
150   ierr = PetscOptionsGetTruth(PETSC_NULL,"-lu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
151   if(newdatastruct){
152     ierr = MatLUFactorSymbolic_SeqAIJ_newdatastruct(B,A,isrow,iscol,info);CHKERRQ(ierr);
153     PetscFunctionReturn(0);
154   }
155 
156   if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square");
157   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
158   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
159   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
160 
161   /* get new row pointers */
162   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
163   bi[0] = 0;
164 
165   /* bdiag is location of diagonal in factor */
166   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
167   bdiag[0] = 0;
168 
169   /* linked list for storing column indices of the active row */
170   nlnk = n + 1;
171   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
172 
173   ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr);
174 
175   /* initial FreeSpace size is f*(ai[n]+1) */
176   f = info->fill;
177   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
178   current_space = free_space;
179 
180   for (i=0; i<n; i++) {
181     /* copy previous fill into linked list */
182     nzi = 0;
183     nnz = ai[r[i]+1] - ai[r[i]];
184     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
185     ajtmp = aj + ai[r[i]];
186     ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
187     nzi += nlnk;
188 
189     /* add pivot rows into linked list */
190     row = lnk[n];
191     while (row < i) {
192       nzbd    = bdiag[row] - bi[row] + 1; /* num of entries in the row with column index <= row */
193       ajtmp   = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */
194       ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr);
195       nzi += nlnk;
196       row  = lnk[row];
197     }
198     bi[i+1] = bi[i] + nzi;
199     im[i]   = nzi;
200 
201     /* mark bdiag */
202     nzbd = 0;
203     nnz  = nzi;
204     k    = lnk[n];
205     while (nnz-- && k < i){
206       nzbd++;
207       k = lnk[k];
208     }
209     bdiag[i] = bi[i] + nzbd;
210 
211     /* if free space is not available, make more free space */
212     if (current_space->local_remaining<nzi) {
213       nnz = (n - i)*nzi; /* estimated and max additional space needed */
214       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
215       reallocs++;
216     }
217 
218     /* copy data into free space, then initialize lnk */
219     ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
220     bi_ptr[i] = current_space->array;
221     current_space->array           += nzi;
222     current_space->local_used      += nzi;
223     current_space->local_remaining -= nzi;
224   }
225 #if defined(PETSC_USE_INFO)
226   if (ai[n] != 0) {
227     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
228     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
229     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
230     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr);
231     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
232   } else {
233     ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr);
234   }
235 #endif
236 
237   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
238   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
239 
240   /* destroy list of free space and other temporary array(s) */
241   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
242   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
243   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
244   ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr);
245 
246   /* put together the new matrix */
247   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
248   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
249   b    = (Mat_SeqAIJ*)(B)->data;
250   b->free_a       = PETSC_TRUE;
251   b->free_ij      = PETSC_TRUE;
252   b->singlemalloc = PETSC_FALSE;
253   ierr          = PetscMalloc((bi[n]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
254   b->j          = bj;
255   b->i          = bi;
256   b->diag       = bdiag;
257   b->ilen       = 0;
258   b->imax       = 0;
259   b->row        = isrow;
260   b->col        = iscol;
261   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
262   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
263   b->icol       = isicol;
264   ierr          = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
265 
266   /* In b structure:  Free imax, ilen, old a, old j.  Allocate solve_work, new a, new j */
267   ierr = PetscLogObjectMemory(B,(bi[n]-n)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
268   b->maxnz = b->nz = bi[n] ;
269 
270   (B)->factor                = MAT_FACTOR_LU;
271   (B)->info.factor_mallocs   = reallocs;
272   (B)->info.fill_ratio_given = f;
273 
274   if (ai[n]) {
275     (B)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
276   } else {
277     (B)->info.fill_ratio_needed = 0.0;
278   }
279   (B)->ops->lufactornumeric  = MatLUFactorNumeric_SeqAIJ;
280   (B)->ops->solve            = MatSolve_SeqAIJ;
281   (B)->ops->solvetranspose   = MatSolveTranspose_SeqAIJ;
282   /* switch to inodes if appropriate */
283   ierr = MatLUFactorSymbolic_Inode(B,A,isrow,iscol,info);CHKERRQ(ierr);
284   PetscFunctionReturn(0);
285 }
286 
287 #undef __FUNCT__
288 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ_newdatastruct"
289 PetscErrorCode MatLUFactorSymbolic_SeqAIJ_newdatastruct(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
290 {
291   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
292   IS                 isicol;
293   PetscErrorCode     ierr;
294   const PetscInt     *r,*ic;
295   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j;
296   PetscInt           *bi,*bj,*ajtmp;
297   PetscInt           *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im;
298   PetscReal          f;
299   PetscInt           nlnk,*lnk,k,**bi_ptr;
300   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
301   PetscBT            lnkbt;
302 
303   PetscFunctionBegin;
304   if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square");
305   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
306   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
307   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
308 
309   /* get new row pointers */
310   ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
311   bi[0] = 0;
312 
313   /* bdiag is location of diagonal in factor */
314   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
315   bdiag[0] = 0;
316 
317   /* linked list for storing column indices of the active row */
318   nlnk = n + 1;
319   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
320 
321   ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr);
322 
323   /* initial FreeSpace size is f*(ai[n]+1) */
324   f = info->fill;
325   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
326   current_space = free_space;
327 
328   for (i=0; i<n; i++) {
329     /* copy previous fill into linked list */
330     nzi = 0;
331     nnz = ai[r[i]+1] - ai[r[i]];
332     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
333     ajtmp = aj + ai[r[i]];
334     ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
335     nzi += nlnk;
336 
337     /* add pivot rows into linked list */
338     row = lnk[n];
339     while (row < i){
340       nzbd  = bdiag[row] + 1; /* num of entries in the row with column index <= row */
341       ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */
342       ierr  = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr);
343       nzi  += nlnk;
344       row   = lnk[row];
345     }
346     bi[i+1] = bi[i] + nzi;
347     im[i]   = nzi;
348 
349     /* mark bdiag */
350     nzbd = 0;
351     nnz  = nzi;
352     k    = lnk[n];
353     while (nnz-- && k < i){
354       nzbd++;
355       k = lnk[k];
356     }
357     bdiag[i] = nzbd; /* note: bdiag[i] = nnzL as input for PetscFreeSpaceContiguous_newdatastruct() */
358 
359     /* if free space is not available, make more free space */
360     if (current_space->local_remaining<nzi) {
361       nnz = 2*(n - i)*nzi; /* estimated and max additional space needed */
362       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
363       reallocs++;
364     }
365 
366     /* copy data into free space, then initialize lnk */
367     ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
368     bi_ptr[i] = current_space->array;
369     current_space->array           += nzi;
370     current_space->local_used      += nzi;
371     current_space->local_remaining -= nzi;
372   }
373 #if defined(PETSC_USE_INFO)
374   if (ai[n] != 0) {
375     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
376     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
377     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
378     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr);
379     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
380   } else {
381     ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr);
382   }
383 #endif
384 
385   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
386   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
387 
388   /* destroy list of free space and other temporary array(s) */
389   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
390   ierr = PetscFreeSpaceContiguous_newdatastruct(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr);
391   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
392   ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr);
393 
394   /* put together the new matrix */
395   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
396   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
397   b    = (Mat_SeqAIJ*)(B)->data;
398   b->free_a       = PETSC_TRUE;
399   b->free_ij      = PETSC_TRUE;
400   b->singlemalloc = PETSC_FALSE;
401   ierr          = PetscMalloc((bi[2*n+1])*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
402   b->j          = bj;
403   b->i          = bi;
404   b->diag       = bdiag;
405   b->ilen       = 0;
406   b->imax       = 0;
407   b->row        = isrow;
408   b->col        = iscol;
409   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
410   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
411   b->icol       = isicol;
412   ierr          = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
413 
414   /* In b structure:  Free imax, ilen, old a, old j.  Allocate solve_work, new a, new j */
415   ierr = PetscLogObjectMemory(B,bi[2*n+1]*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
416   b->maxnz = b->nz = bi[2*n+1] ;
417 
418   (B)->factor                = MAT_FACTOR_LU;
419   (B)->info.factor_mallocs   = reallocs;
420   (B)->info.fill_ratio_given = f;
421 
422   if (ai[n]) {
423     (B)->info.fill_ratio_needed = ((PetscReal)bi[2*n+1])/((PetscReal)ai[n]);
424   } else {
425     (B)->info.fill_ratio_needed = 0.0;
426   }
427   (B)->ops->lufactornumeric  = MatLUFactorNumeric_SeqAIJ_newdatastruct;
428   PetscFunctionReturn(0);
429 }
430 
431 /*
432     Trouble in factorization, should we dump the original matrix?
433 */
434 #undef __FUNCT__
435 #define __FUNCT__ "MatFactorDumpMatrix"
436 PetscErrorCode MatFactorDumpMatrix(Mat A)
437 {
438   PetscErrorCode ierr;
439   PetscTruth     flg = PETSC_FALSE;
440 
441   PetscFunctionBegin;
442   ierr = PetscOptionsGetTruth(PETSC_NULL,"-mat_factor_dump_on_error",&flg,PETSC_NULL);CHKERRQ(ierr);
443   if (flg) {
444     PetscViewer viewer;
445     char        filename[PETSC_MAX_PATH_LEN];
446 
447     ierr = PetscSNPrintf(filename,PETSC_MAX_PATH_LEN,"matrix_factor_error.%d",PetscGlobalRank);CHKERRQ(ierr);
448     ierr = PetscViewerBinaryOpen(((PetscObject)A)->comm,filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr);
449     ierr = MatView(A,viewer);CHKERRQ(ierr);
450     ierr = PetscViewerDestroy(viewer);CHKERRQ(ierr);
451   }
452   PetscFunctionReturn(0);
453 }
454 
455 extern PetscErrorCode MatSolve_Inode(Mat,Vec,Vec);
456 
457 /* ----------------------------------------------------------- */
458 extern PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct(Mat,Vec,Vec);
459 extern PetscErrorCode MatSolve_SeqAIJ_newdatastruct(Mat,Vec,Vec);
460 
461 #undef __FUNCT__
462 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_newdatastruct"
463 PetscErrorCode MatLUFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info)
464 {
465   Mat            C=B;
466   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
467   IS             isrow = b->row,isicol = b->icol;
468   PetscErrorCode ierr;
469   const PetscInt *r,*ic,*ics;
470   PetscInt       i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
471   PetscInt       *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj;
472   MatScalar      *rtmp,*pc,multiplier,*v,*pv,*aa=a->a;
473   PetscReal      shift=info->shiftinblocks;
474   PetscTruth     row_identity, col_identity;
475 
476   PetscFunctionBegin;
477   /* printf("MatLUFactorNumeric_SeqAIJ_newdatastruct is called ...\n"); */
478   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
479   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
480   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
481   ics  = ic;
482 
483   for (i=0; i<n; i++){
484     /* zero rtmp */
485     /* L part */
486     nz    = bi[i+1] - bi[i];
487     bjtmp = bj + bi[i];
488     for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
489 
490     /* U part */
491     nz = bi[2*n-i+1] - bi[2*n-i];
492     bjtmp = bj + bi[2*n-i];
493     for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
494 
495     /* load in initial (unfactored row) */
496     nz    = ai[r[i]+1] - ai[r[i]];
497     ajtmp = aj + ai[r[i]];
498     v     = aa + ai[r[i]];
499     for (j=0; j<nz; j++) {
500       rtmp[ics[ajtmp[j]]] = v[j];
501     }
502     if (rtmp[ics[r[i]]] == 0.0){
503       rtmp[ics[r[i]]] += shift; /* shift the diagonal of the matrix */
504       /* printf("row %d, shift %g\n",i,shift); */
505     }
506 
507     /* elimination */
508     bjtmp = bj + bi[i];
509     row   = *bjtmp++;
510     nzL   = bi[i+1] - bi[i];
511     k   = 0;
512     while  (k < nzL) {
513       pc = rtmp + row;
514       if (*pc != 0.0) {
515         pv         = b->a + bdiag[row];
516         multiplier = *pc * (*pv);
517         *pc        = multiplier;
518         pj         = b->j + bi[2*n-row]; /* begining of U(row,:) */
519         pv         = b->a + bi[2*n-row];
520         nz         = bi[2*n-row+1] - bi[2*n-row] - 1; /* num of entries in U(row,:), excluding diag */
521         for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
522         ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
523       }
524       row = *bjtmp++; k++;
525     }
526 
527     /* finished row so stick it into b->a */
528     /* L part */
529     pv   = b->a + bi[i] ;
530     pj   = b->j + bi[i] ;
531     nz   = bi[i+1] - bi[i];
532     for (j=0; j<nz; j++) {
533       pv[j] = rtmp[pj[j]];
534     }
535 
536     /* Mark diagonal and invert diagonal for simplier triangular solves */
537     pv  = b->a + bdiag[i];
538     pj  = b->j + bdiag[i];
539     /* if (*pj != i)SETERRQ2(PETSC_ERR_SUP,"row %d != *pj %d",i,*pj) */
540     *pv = 1.0/rtmp[*pj];
541 
542     /* U part */
543     pv = b->a + bi[2*n-i];
544     pj = b->j + bi[2*n-i];
545     nz = bi[2*n-i+1] - bi[2*n-i] - 1;
546     for (j=0; j<nz; j++) pv[j] = rtmp[pj[j]];
547   }
548   ierr = PetscFree(rtmp);CHKERRQ(ierr);
549   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
550   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
551 
552   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
553   ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
554   if (row_identity && col_identity) {
555     C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct;
556   } else {
557     C->ops->solve = MatSolve_SeqAIJ_newdatastruct;
558   }
559 
560   C->ops->solveadd           = 0;
561   C->ops->solvetranspose     = 0;
562   C->ops->solvetransposeadd  = 0;
563   C->ops->matsolve           = 0;
564   C->assembled    = PETSC_TRUE;
565   C->preallocated = PETSC_TRUE;
566   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
567   PetscFunctionReturn(0);
568 }
569 
570 #undef __FUNCT__
571 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ"
572 PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info)
573 {
574   Mat             C=B;
575   Mat_SeqAIJ      *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
576   IS              isrow = b->row,isicol = b->icol;
577   PetscErrorCode  ierr;
578   const PetscInt   *r,*ic,*ics;
579   PetscInt        nz,row,i,j,n=A->rmap->n,diag;
580   const PetscInt  *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
581   const PetscInt  *ajtmp,*bjtmp,*diag_offset = b->diag,*pj;
582   MatScalar       *pv,*rtmp,*pc,multiplier,d;
583   const MatScalar *v,*aa=a->a;
584   PetscReal       rs=0.0;
585   LUShift_Ctx     sctx;
586   PetscInt        newshift,*ddiag;
587 
588   PetscFunctionBegin;
589   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
590   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
591   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
592   ics  = ic;
593 
594   sctx.shift_top      = 0;
595   sctx.nshift_max     = 0;
596   sctx.shift_lo       = 0;
597   sctx.shift_hi       = 0;
598   sctx.shift_fraction = 0;
599 
600   /* if both shift schemes are chosen by user, only use info->shiftpd */
601   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
602     ddiag          = a->diag;
603     sctx.shift_top = info->zeropivot;
604     for (i=0; i<n; i++) {
605       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
606       d  = (aa)[ddiag[i]];
607       rs = -PetscAbsScalar(d) - PetscRealPart(d);
608       v  = aa+ai[i];
609       nz = ai[i+1] - ai[i];
610       for (j=0; j<nz; j++)
611 	rs += PetscAbsScalar(v[j]);
612       if (rs>sctx.shift_top) sctx.shift_top = rs;
613     }
614     sctx.shift_top   *= 1.1;
615     sctx.nshift_max   = 5;
616     sctx.shift_lo     = 0.;
617     sctx.shift_hi     = 1.;
618   }
619 
620   sctx.shift_amount = 0.0;
621   sctx.nshift       = 0;
622   do {
623     sctx.lushift = PETSC_FALSE;
624     for (i=0; i<n; i++){
625       nz    = bi[i+1] - bi[i];
626       bjtmp = bj + bi[i];
627       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
628 
629       /* load in initial (unfactored row) */
630       nz    = ai[r[i]+1] - ai[r[i]];
631       ajtmp = aj + ai[r[i]];
632       v     = aa + ai[r[i]];
633       for (j=0; j<nz; j++) {
634         rtmp[ics[ajtmp[j]]] = v[j];
635       }
636       rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */
637       /* if (sctx.shift_amount > 0.0) printf("row %d, shift %g\n",i,sctx.shift_amount); */
638 
639       row = *bjtmp++;
640       while  (row < i) {
641         pc = rtmp + row;
642         if (*pc != 0.0) {
643           pv         = b->a + diag_offset[row];
644           pj         = b->j + diag_offset[row] + 1;
645           multiplier = *pc / *pv++;
646           *pc        = multiplier;
647           nz         = bi[row+1] - diag_offset[row] - 1;
648           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
649           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
650         }
651         row = *bjtmp++;
652       }
653       /* finished row so stick it into b->a */
654       pv   = b->a + bi[i] ;
655       pj   = b->j + bi[i] ;
656       nz   = bi[i+1] - bi[i];
657       diag = diag_offset[i] - bi[i];
658       rs   = 0.0;
659       for (j=0; j<nz; j++) {
660         pv[j] = rtmp[pj[j]];
661         rs   += PetscAbsScalar(pv[j]);
662       }
663       rs   -= PetscAbsScalar(pv[diag]);
664 
665       /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */
666       sctx.rs  = rs;
667       sctx.pv  = pv[diag];
668       ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr);
669       if (newshift == 1) break;
670     }
671 
672     if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
673       /*
674        * if no shift in this attempt & shifting & started shifting & can refine,
675        * then try lower shift
676        */
677       sctx.shift_hi       = sctx.shift_fraction;
678       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
679       sctx.shift_amount   = sctx.shift_fraction * sctx.shift_top;
680       sctx.lushift        = PETSC_TRUE;
681       sctx.nshift++;
682     }
683   } while (sctx.lushift);
684 
685   /* invert diagonal entries for simplier triangular solves */
686   for (i=0; i<n; i++) {
687     b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]];
688   }
689   ierr = PetscFree(rtmp);CHKERRQ(ierr);
690   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
691   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
692   if (b->inode.use) {
693     C->ops->solve   = MatSolve_Inode;
694   } else {
695     PetscTruth row_identity, col_identity;
696     ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
697     ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
698     if (row_identity && col_identity) {
699       C->ops->solve   = MatSolve_SeqAIJ_NaturalOrdering;
700     } else {
701       C->ops->solve   = MatSolve_SeqAIJ;
702     }
703   }
704   C->ops->solveadd           = MatSolveAdd_SeqAIJ;
705   C->ops->solvetranspose     = MatSolveTranspose_SeqAIJ;
706   C->ops->solvetransposeadd  = MatSolveTransposeAdd_SeqAIJ;
707   C->ops->matsolve           = MatMatSolve_SeqAIJ;
708   C->assembled    = PETSC_TRUE;
709   C->preallocated = PETSC_TRUE;
710   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
711   if (sctx.nshift){
712      if (info->shiftpd) {
713       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);
714     } else if (info->shiftnz) {
715       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
716     }
717   }
718   PetscFunctionReturn(0);
719 }
720 
721 /*
722    This routine implements inplace ILU(0) with row or/and column permutations.
723    Input:
724      A - original matrix
725    Output;
726      A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i]
727          a->j (col index) is permuted by the inverse of colperm, then sorted
728          a->a reordered accordingly with a->j
729          a->diag (ptr to diagonal elements) is updated.
730 */
731 #undef __FUNCT__
732 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_InplaceWithPerm"
733 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info)
734 {
735   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
736   IS             isrow = a->row,isicol = a->icol;
737   PetscErrorCode ierr;
738   const PetscInt *r,*ic,*ics;
739   PetscInt       i,j,n=A->rmap->n,*ai=a->i,*aj=a->j;
740   PetscInt       *ajtmp,nz,row;
741   PetscInt       *diag = a->diag,nbdiag,*pj;
742   PetscScalar    *rtmp,*pc,multiplier,d;
743   MatScalar      *v,*pv;
744   PetscReal      rs;
745   LUShift_Ctx    sctx;
746   PetscInt       newshift;
747 
748   PetscFunctionBegin;
749   if (A != B) SETERRQ(PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address");
750   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
751   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
752   ierr  = PetscMalloc((n+1)*sizeof(PetscScalar),&rtmp);CHKERRQ(ierr);
753   ierr  = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr);
754   ics = ic;
755 
756   sctx.shift_top      = 0;
757   sctx.nshift_max     = 0;
758   sctx.shift_lo       = 0;
759   sctx.shift_hi       = 0;
760   sctx.shift_fraction = 0;
761 
762   /* if both shift schemes are chosen by user, only use info->shiftpd */
763   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
764     sctx.shift_top = 0;
765     for (i=0; i<n; i++) {
766       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
767       d  = (a->a)[diag[i]];
768       rs = -PetscAbsScalar(d) - PetscRealPart(d);
769       v  = a->a+ai[i];
770       nz = ai[i+1] - ai[i];
771       for (j=0; j<nz; j++)
772 	rs += PetscAbsScalar(v[j]);
773       if (rs>sctx.shift_top) sctx.shift_top = rs;
774     }
775     if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot;
776     sctx.shift_top    *= 1.1;
777     sctx.nshift_max   = 5;
778     sctx.shift_lo     = 0.;
779     sctx.shift_hi     = 1.;
780   }
781 
782   sctx.shift_amount = 0;
783   sctx.nshift       = 0;
784   do {
785     sctx.lushift = PETSC_FALSE;
786     for (i=0; i<n; i++){
787       /* load in initial unfactored row */
788       nz    = ai[r[i]+1] - ai[r[i]];
789       ajtmp = aj + ai[r[i]];
790       v     = a->a + ai[r[i]];
791       /* sort permuted ajtmp and values v accordingly */
792       for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]];
793       ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr);
794 
795       diag[r[i]] = ai[r[i]];
796       for (j=0; j<nz; j++) {
797         rtmp[ajtmp[j]] = v[j];
798         if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */
799       }
800       rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */
801 
802       row = *ajtmp++;
803       while  (row < i) {
804         pc = rtmp + row;
805         if (*pc != 0.0) {
806           pv         = a->a + diag[r[row]];
807           pj         = aj + diag[r[row]] + 1;
808 
809           multiplier = *pc / *pv++;
810           *pc        = multiplier;
811           nz         = ai[r[row]+1] - diag[r[row]] - 1;
812           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
813           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
814         }
815         row = *ajtmp++;
816       }
817       /* finished row so overwrite it onto a->a */
818       pv   = a->a + ai[r[i]] ;
819       pj   = aj + ai[r[i]] ;
820       nz   = ai[r[i]+1] - ai[r[i]];
821       nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */
822 
823       rs   = 0.0;
824       for (j=0; j<nz; j++) {
825         pv[j] = rtmp[pj[j]];
826         if (j != nbdiag) rs += PetscAbsScalar(pv[j]);
827       }
828 
829       /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */
830       sctx.rs  = rs;
831       sctx.pv  = pv[nbdiag];
832       ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr);
833       if (newshift == 1) break;
834     }
835 
836     if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
837       /*
838        * if no shift in this attempt & shifting & started shifting & can refine,
839        * then try lower shift
840        */
841       sctx.shift_hi        = sctx.shift_fraction;
842       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
843       sctx.shift_amount    = sctx.shift_fraction * sctx.shift_top;
844       sctx.lushift         = PETSC_TRUE;
845       sctx.nshift++;
846     }
847   } while (sctx.lushift);
848 
849   /* invert diagonal entries for simplier triangular solves */
850   for (i=0; i<n; i++) {
851     a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]];
852   }
853 
854   ierr = PetscFree(rtmp);CHKERRQ(ierr);
855   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
856   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
857   A->ops->solve             = MatSolve_SeqAIJ_InplaceWithPerm;
858   A->ops->solveadd          = MatSolveAdd_SeqAIJ;
859   A->ops->solvetranspose    = MatSolveTranspose_SeqAIJ;
860   A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ;
861   A->assembled = PETSC_TRUE;
862   A->preallocated = PETSC_TRUE;
863   ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr);
864   if (sctx.nshift){
865     if (info->shiftpd) {
866       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);
867     } else if (info->shiftnz) {
868       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
869     }
870   }
871   PetscFunctionReturn(0);
872 }
873 
874 /* ----------------------------------------------------------- */
875 #undef __FUNCT__
876 #define __FUNCT__ "MatLUFactor_SeqAIJ"
877 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info)
878 {
879   PetscErrorCode ierr;
880   Mat            C;
881 
882   PetscFunctionBegin;
883   ierr = MatGetFactor(A,MAT_SOLVER_PETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr);
884   ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr);
885   ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr);
886   A->ops->solve            = C->ops->solve;
887   A->ops->solvetranspose   = C->ops->solvetranspose;
888   ierr = MatHeaderCopy(A,C);CHKERRQ(ierr);
889   ierr = PetscLogObjectParent(A,((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr);
890   PetscFunctionReturn(0);
891 }
892 /* ----------------------------------------------------------- */
893 
894 
895 #undef __FUNCT__
896 #define __FUNCT__ "MatSolve_SeqAIJ"
897 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx)
898 {
899   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
900   IS                iscol = a->col,isrow = a->row;
901   PetscErrorCode    ierr;
902   PetscInt          i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
903   PetscInt          nz;
904   const PetscInt    *rout,*cout,*r,*c;
905   PetscScalar       *x,*tmp,*tmps,sum;
906   const PetscScalar *b;
907   const MatScalar   *aa = a->a,*v;
908 
909   PetscFunctionBegin;
910   if (!n) PetscFunctionReturn(0);
911 
912   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
913   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
914   tmp  = a->solve_work;
915 
916   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
917   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
918 
919   /* forward solve the lower triangular */
920   tmp[0] = b[*r++];
921   tmps   = tmp;
922   for (i=1; i<n; i++) {
923     v   = aa + ai[i] ;
924     vi  = aj + ai[i] ;
925     nz  = a->diag[i] - ai[i];
926     sum = b[*r++];
927     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
928     tmp[i] = sum;
929   }
930 
931   /* backward solve the upper triangular */
932   for (i=n-1; i>=0; i--){
933     v   = aa + a->diag[i] + 1;
934     vi  = aj + a->diag[i] + 1;
935     nz  = ai[i+1] - a->diag[i] - 1;
936     sum = tmp[i];
937     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
938     x[*c--] = tmp[i] = sum*aa[a->diag[i]];
939   }
940 
941   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
942   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
943   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
944   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
945   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
946   PetscFunctionReturn(0);
947 }
948 
949 #undef __FUNCT__
950 #define __FUNCT__ "MatMatSolve_SeqAIJ"
951 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X)
952 {
953   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
954   IS              iscol = a->col,isrow = a->row;
955   PetscErrorCode  ierr;
956   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
957   PetscInt        nz,neq;
958   const PetscInt  *rout,*cout,*r,*c;
959   PetscScalar     *x,*b,*tmp,*tmps,sum;
960   const MatScalar *aa = a->a,*v;
961   PetscTruth      bisdense,xisdense;
962 
963   PetscFunctionBegin;
964   if (!n) PetscFunctionReturn(0);
965 
966   ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr);
967   if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix");
968   ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr);
969   if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix");
970 
971   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
972   ierr = MatGetArray(X,&x);CHKERRQ(ierr);
973 
974   tmp  = a->solve_work;
975   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
976   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
977 
978   for (neq=0; neq<B->cmap->n; neq++){
979     /* forward solve the lower triangular */
980     tmp[0] = b[r[0]];
981     tmps   = tmp;
982     for (i=1; i<n; i++) {
983       v   = aa + ai[i] ;
984       vi  = aj + ai[i] ;
985       nz  = a->diag[i] - ai[i];
986       sum = b[r[i]];
987       PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
988       tmp[i] = sum;
989     }
990     /* backward solve the upper triangular */
991     for (i=n-1; i>=0; i--){
992       v   = aa + a->diag[i] + 1;
993       vi  = aj + a->diag[i] + 1;
994       nz  = ai[i+1] - a->diag[i] - 1;
995       sum = tmp[i];
996       PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
997       x[c[i]] = tmp[i] = sum*aa[a->diag[i]];
998     }
999 
1000     b += n;
1001     x += n;
1002   }
1003   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1004   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1005   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
1006   ierr = MatRestoreArray(X,&x);CHKERRQ(ierr);
1007   ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr);
1008   PetscFunctionReturn(0);
1009 }
1010 
1011 #undef __FUNCT__
1012 #define __FUNCT__ "MatSolve_SeqAIJ_InplaceWithPerm"
1013 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx)
1014 {
1015   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1016   IS              iscol = a->col,isrow = a->row;
1017   PetscErrorCode  ierr;
1018   const PetscInt  *r,*c,*rout,*cout;
1019   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1020   PetscInt        nz,row;
1021   PetscScalar     *x,*b,*tmp,*tmps,sum;
1022   const MatScalar *aa = a->a,*v;
1023 
1024   PetscFunctionBegin;
1025   if (!n) PetscFunctionReturn(0);
1026 
1027   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
1028   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1029   tmp  = a->solve_work;
1030 
1031   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1032   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1033 
1034   /* forward solve the lower triangular */
1035   tmp[0] = b[*r++];
1036   tmps   = tmp;
1037   for (row=1; row<n; row++) {
1038     i   = rout[row]; /* permuted row */
1039     v   = aa + ai[i] ;
1040     vi  = aj + ai[i] ;
1041     nz  = a->diag[i] - ai[i];
1042     sum = b[*r++];
1043     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1044     tmp[row] = sum;
1045   }
1046 
1047   /* backward solve the upper triangular */
1048   for (row=n-1; row>=0; row--){
1049     i   = rout[row]; /* permuted row */
1050     v   = aa + a->diag[i] + 1;
1051     vi  = aj + a->diag[i] + 1;
1052     nz  = ai[i+1] - a->diag[i] - 1;
1053     sum = tmp[row];
1054     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1055     x[*c--] = tmp[row] = sum*aa[a->diag[i]];
1056   }
1057 
1058   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1059   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1060   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
1061   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1062   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1063   PetscFunctionReturn(0);
1064 }
1065 
1066 /* ----------------------------------------------------------- */
1067 #include "../src/mat/impls/aij/seq/ftn-kernels/fsolve.h"
1068 #undef __FUNCT__
1069 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering"
1070 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx)
1071 {
1072   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1073   PetscErrorCode    ierr;
1074   PetscInt          n = A->rmap->n;
1075   const PetscInt    *ai = a->i,*aj = a->j,*adiag = a->diag;
1076   PetscScalar       *x;
1077   const PetscScalar *b;
1078   const MatScalar   *aa = a->a;
1079 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ)
1080   PetscInt          adiag_i,i,nz,ai_i;
1081   const PetscInt    *vi;
1082   const MatScalar   *v;
1083   PetscScalar       sum;
1084 #endif
1085 
1086   PetscFunctionBegin;
1087   if (!n) PetscFunctionReturn(0);
1088 
1089   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1090   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1091 
1092 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ)
1093   fortransolveaij_(&n,x,ai,aj,adiag,aa,b);
1094 #else
1095   /* forward solve the lower triangular */
1096   x[0] = b[0];
1097   for (i=1; i<n; i++) {
1098     ai_i = ai[i];
1099     v    = aa + ai_i;
1100     vi   = aj + ai_i;
1101     nz   = adiag[i] - ai_i;
1102     sum  = b[i];
1103     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
1104     x[i] = sum;
1105   }
1106 
1107   /* backward solve the upper triangular */
1108   for (i=n-1; i>=0; i--){
1109     adiag_i = adiag[i];
1110     v       = aa + adiag_i + 1;
1111     vi      = aj + adiag_i + 1;
1112     nz      = ai[i+1] - adiag_i - 1;
1113     sum     = x[i];
1114     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
1115     x[i]    = sum*aa[adiag_i];
1116   }
1117 #endif
1118   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1119   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1120   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1121   PetscFunctionReturn(0);
1122 }
1123 
1124 #undef __FUNCT__
1125 #define __FUNCT__ "MatSolveAdd_SeqAIJ"
1126 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx)
1127 {
1128   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1129   IS              iscol = a->col,isrow = a->row;
1130   PetscErrorCode  ierr;
1131   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1132   PetscInt        nz;
1133   const PetscInt  *rout,*cout,*r,*c;
1134   PetscScalar     *x,*b,*tmp,sum;
1135   const MatScalar *aa = a->a,*v;
1136 
1137   PetscFunctionBegin;
1138   if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);}
1139 
1140   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
1141   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1142   tmp  = a->solve_work;
1143 
1144   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1145   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1146 
1147   /* forward solve the lower triangular */
1148   tmp[0] = b[*r++];
1149   for (i=1; i<n; i++) {
1150     v   = aa + ai[i] ;
1151     vi  = aj + ai[i] ;
1152     nz  = a->diag[i] - ai[i];
1153     sum = b[*r++];
1154     while (nz--) sum -= *v++ * tmp[*vi++ ];
1155     tmp[i] = sum;
1156   }
1157 
1158   /* backward solve the upper triangular */
1159   for (i=n-1; i>=0; i--){
1160     v   = aa + a->diag[i] + 1;
1161     vi  = aj + a->diag[i] + 1;
1162     nz  = ai[i+1] - a->diag[i] - 1;
1163     sum = tmp[i];
1164     while (nz--) sum -= *v++ * tmp[*vi++ ];
1165     tmp[i] = sum*aa[a->diag[i]];
1166     x[*c--] += tmp[i];
1167   }
1168 
1169   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1170   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1171   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
1172   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1173   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1174 
1175   PetscFunctionReturn(0);
1176 }
1177 /* -------------------------------------------------------------------*/
1178 #undef __FUNCT__
1179 #define __FUNCT__ "MatSolveTranspose_SeqAIJ"
1180 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx)
1181 {
1182   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1183   IS              iscol = a->col,isrow = a->row;
1184   PetscErrorCode  ierr;
1185   const PetscInt  *rout,*cout,*r,*c;
1186   PetscInt        i,n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1187   PetscInt        nz,*diag = a->diag;
1188   PetscScalar     *x,*b,*tmp,s1;
1189   const MatScalar *aa = a->a,*v;
1190 
1191   PetscFunctionBegin;
1192   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
1193   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1194   tmp  = a->solve_work;
1195 
1196   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1197   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1198 
1199   /* copy the b into temp work space according to permutation */
1200   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1201 
1202   /* forward solve the U^T */
1203   for (i=0; i<n; i++) {
1204     v   = aa + diag[i] ;
1205     vi  = aj + diag[i] + 1;
1206     nz  = ai[i+1] - diag[i] - 1;
1207     s1  = tmp[i];
1208     s1 *= (*v++);  /* multiply by inverse of diagonal entry */
1209     while (nz--) {
1210       tmp[*vi++ ] -= (*v++)*s1;
1211     }
1212     tmp[i] = s1;
1213   }
1214 
1215   /* backward solve the L^T */
1216   for (i=n-1; i>=0; i--){
1217     v   = aa + diag[i] - 1 ;
1218     vi  = aj + diag[i] - 1 ;
1219     nz  = diag[i] - ai[i];
1220     s1  = tmp[i];
1221     while (nz--) {
1222       tmp[*vi-- ] -= (*v--)*s1;
1223     }
1224   }
1225 
1226   /* copy tmp into x according to permutation */
1227   for (i=0; i<n; i++) x[r[i]] = tmp[i];
1228 
1229   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1230   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1231   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
1232   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1233 
1234   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1235   PetscFunctionReturn(0);
1236 }
1237 
1238 #undef __FUNCT__
1239 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ"
1240 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx)
1241 {
1242   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1243   IS              iscol = a->col,isrow = a->row;
1244   PetscErrorCode  ierr;
1245   const PetscInt  *r,*c,*rout,*cout;
1246   PetscInt        i,n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1247   PetscInt        nz,*diag = a->diag;
1248   PetscScalar     *x,*b,*tmp;
1249   const MatScalar *aa = a->a,*v;
1250 
1251   PetscFunctionBegin;
1252   if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);}
1253 
1254   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
1255   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1256   tmp = a->solve_work;
1257 
1258   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1259   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1260 
1261   /* copy the b into temp work space according to permutation */
1262   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1263 
1264   /* forward solve the U^T */
1265   for (i=0; i<n; i++) {
1266     v   = aa + diag[i] ;
1267     vi  = aj + diag[i] + 1;
1268     nz  = ai[i+1] - diag[i] - 1;
1269     tmp[i] *= *v++;
1270     while (nz--) {
1271       tmp[*vi++ ] -= (*v++)*tmp[i];
1272     }
1273   }
1274 
1275   /* backward solve the L^T */
1276   for (i=n-1; i>=0; i--){
1277     v   = aa + diag[i] - 1 ;
1278     vi  = aj + diag[i] - 1 ;
1279     nz  = diag[i] - ai[i];
1280     while (nz--) {
1281       tmp[*vi-- ] -= (*v--)*tmp[i];
1282     }
1283   }
1284 
1285   /* copy tmp into x according to permutation */
1286   for (i=0; i<n; i++) x[r[i]] += tmp[i];
1287 
1288   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1289   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1290   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
1291   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1292 
1293   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1294   PetscFunctionReturn(0);
1295 }
1296 /* ----------------------------------------------------------------*/
1297 EXTERN PetscErrorCode Mat_CheckInode(Mat,PetscTruth);
1298 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption,PetscTruth);
1299 
1300 /*
1301    ilu(0) with natural ordering under new data structure.
1302    Factored arrays bj and ba are stored as
1303      L(0,:), L(1,:), ...,L(n-1,:),  U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:)
1304 
1305    bi=fact->i is an array of size 2n+2, in which
1306    bi+
1307      bi[i]      ->  1st entry of L(i,:),i=0,...,i-1
1308      bi[n]      ->  points to L(n-1,:)+1
1309      bi[n+1]    ->  1st entry of U(n-1,:)
1310      bi[2n-i]   ->  1st entry of U(i,:)
1311      bi[2n-i+1] ->  end of U(i,:)+1, the 1st entry of U(i-1,:)
1312      bi[2n]     ->  1st entry of U(0,:)
1313      bi[2n+1]   ->  points to U(0,:)+1
1314 
1315    U(i,:) contains diag[i] as its last entry, i.e.,
1316     U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i])
1317 */
1318 #undef __FUNCT__
1319 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct"
1320 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1321 {
1322 
1323   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1324   PetscErrorCode     ierr;
1325   PetscInt           n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag;
1326   PetscInt           i,j,nz,*bi,*bj,*bdiag;
1327 
1328   PetscFunctionBegin;
1329   ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr);
1330   b    = (Mat_SeqAIJ*)(fact)->data;
1331 
1332   /* allocate matrix arrays for new data structure */
1333   ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,2*n+2,PetscInt,&b->i);CHKERRQ(ierr);
1334   ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(2*n+2)*sizeof(PetscInt));CHKERRQ(ierr);
1335   b->singlemalloc = PETSC_TRUE;
1336   if (!b->diag){
1337     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr);
1338   }
1339   bdiag = b->diag;
1340 
1341   if (n > 0) {
1342     ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr);
1343   }
1344 
1345   /* set bi and bj with new data structure */
1346   bi = b->i;
1347   bj = b->j;
1348 
1349   /* L part */
1350   bi[0] = 0;
1351   for (i=0; i<n; i++){
1352     nz = adiag[i] - ai[i];
1353     bi[i+1] = bi[i] + nz;
1354     aj = a->j + ai[i];
1355     for (j=0; j<nz; j++){
1356       *bj = aj[j]; bj++;
1357     }
1358   }
1359 
1360   /* U part */
1361   bi[n+1] = bi[n];
1362   for (i=n-1; i>=0; i--){
1363     nz = ai[i+1] - adiag[i] - 1;
1364     bi[2*n-i+1] = bi[2*n-i] + nz + 1;
1365     aj = a->j + adiag[i] + 1;
1366     for (j=0; j<nz; j++){
1367       *bj = aj[j]; bj++;
1368     }
1369     /* diag[i] */
1370     *bj = i; bj++;
1371     bdiag[i] = bi[2*n-i+1]-1;
1372   }
1373   PetscFunctionReturn(0);
1374 }
1375 
1376 #undef __FUNCT__
1377 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_newdatastruct"
1378 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1379 {
1380   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1381   IS                 isicol;
1382   PetscErrorCode     ierr;
1383   const PetscInt     *r,*ic;
1384   PetscInt           n=A->rmap->n,*ai=a->i,*aj=a->j,d;
1385   PetscInt           *bi,*cols,nnz,*cols_lvl;
1386   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1387   PetscInt           i,levels,diagonal_fill;
1388   PetscTruth         col_identity,row_identity;
1389   PetscReal          f;
1390   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
1391   PetscBT            lnkbt;
1392   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
1393   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1394   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1395   PetscTruth         missing;
1396 
1397   PetscFunctionBegin;
1398   //printf("MatILUFactorSymbolic_SeqAIJ_newdatastruct ...\n");
1399   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);
1400   f             = info->fill;
1401   levels        = (PetscInt)info->levels;
1402   diagonal_fill = (PetscInt)info->diagonal_fill;
1403   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1404 
1405   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1406   ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
1407 
1408   if (!levels && row_identity && col_identity) {
1409     /* special case: ilu(0) with natural ordering */
1410     ierr = MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1411     (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ_newdatastruct;
1412 
1413     fact->factor = MAT_FACTOR_ILU;
1414     (fact)->info.factor_mallocs    = 0;
1415     (fact)->info.fill_ratio_given  = info->fill;
1416     (fact)->info.fill_ratio_needed = 1.0;
1417     b               = (Mat_SeqAIJ*)(fact)->data;
1418     ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
1419     if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
1420     b->row              = isrow;
1421     b->col              = iscol;
1422     b->icol             = isicol;
1423     ierr                = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1424     ierr                = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1425     ierr                = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1426     /* ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */
1427     PetscFunctionReturn(0);
1428   }
1429 
1430   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1431   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1432 
1433   /* get new row pointers */
1434   ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1435   bi[0] = 0;
1436   /* bdiag is location of diagonal in factor */
1437   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
1438   bdiag[0]  = 0;
1439 
1440   ierr = PetscMalloc((2*n+1)*sizeof(PetscInt**),&bj_ptr);CHKERRQ(ierr);
1441   bjlvl_ptr = (PetscInt**)(bj_ptr + n);
1442 
1443   /* create a linked list for storing column indices of the active row */
1444   nlnk = n + 1;
1445   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1446 
1447   /* initial FreeSpace size is f*(ai[n]+1) */
1448   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
1449   current_space = free_space;
1450   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
1451   current_space_lvl = free_space_lvl;
1452 
1453   for (i=0; i<n; i++) {
1454     nzi = 0;
1455     /* copy current row into linked list */
1456     nnz  = ai[r[i]+1] - ai[r[i]];
1457     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1458     cols = aj + ai[r[i]];
1459     lnk[i] = -1; /* marker to indicate if diagonal exists */
1460     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1461     nzi += nlnk;
1462 
1463     /* make sure diagonal entry is included */
1464     if (diagonal_fill && lnk[i] == -1) {
1465       fm = n;
1466       while (lnk[fm] < i) fm = lnk[fm];
1467       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
1468       lnk[fm]    = i;
1469       lnk_lvl[i] = 0;
1470       nzi++; dcount++;
1471     }
1472 
1473     /* add pivot rows into the active row */
1474     nzbd = 0;
1475     prow = lnk[n];
1476     while (prow < i) {
1477       nnz      = bdiag[prow];
1478       cols     = bj_ptr[prow] + nnz + 1;
1479       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1480       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
1481       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
1482       nzi += nlnk;
1483       prow = lnk[prow];
1484       nzbd++;
1485     }
1486     bdiag[i] = nzbd;
1487     bi[i+1]  = bi[i] + nzi;
1488 
1489     /* if free space is not available, make more free space */
1490     if (current_space->local_remaining<nzi) {
1491       nnz = 2*nzi*(n - i); /* estimated and max additional space needed */
1492       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
1493       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
1494       reallocs++;
1495     }
1496 
1497     /* copy data into free_space and free_space_lvl, then initialize lnk */
1498     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1499     bj_ptr[i]    = current_space->array;
1500     bjlvl_ptr[i] = current_space_lvl->array;
1501 
1502     /* make sure the active row i has diagonal entry */
1503     if (*(bj_ptr[i]+bdiag[i]) != i) {
1504       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
1505     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
1506     }
1507 
1508     current_space->array           += nzi;
1509     current_space->local_used      += nzi;
1510     current_space->local_remaining -= nzi;
1511     current_space_lvl->array           += nzi;
1512     current_space_lvl->local_used      += nzi;
1513     current_space_lvl->local_remaining -= nzi;
1514   }
1515 
1516   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1517   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1518 
1519   /* destroy list of free space and other temporary arrays */
1520   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
1521 
1522   /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */
1523   ierr = PetscFreeSpaceContiguous_newdatastruct(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr);
1524 
1525   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1526   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
1527   ierr = PetscFree(bj_ptr);CHKERRQ(ierr);
1528 
1529 #if defined(PETSC_USE_INFO)
1530   {
1531     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1532     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
1533     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
1534     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
1535     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
1536     if (diagonal_fill) {
1537       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
1538     }
1539   }
1540 #endif
1541 
1542   /* put together the new matrix */
1543   ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
1544   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
1545   b = (Mat_SeqAIJ*)(fact)->data;
1546   b->free_a       = PETSC_TRUE;
1547   b->free_ij      = PETSC_TRUE;
1548   b->singlemalloc = PETSC_FALSE;
1549   ierr = PetscMalloc( (bi[2*n+1] )*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
1550   b->j          = bj;
1551   b->i          = bi;
1552   b->diag       = bdiag;
1553   b->ilen       = 0;
1554   b->imax       = 0;
1555   b->row        = isrow;
1556   b->col        = iscol;
1557   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1558   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1559   b->icol       = isicol;
1560   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1561   /* In b structure:  Free imax, ilen, old a, old j.
1562      Allocate bdiag, solve_work, new a, new j */
1563   ierr = PetscLogObjectMemory(fact,bi[2*n+1] * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
1564   b->maxnz = b->nz = bi[2*n+1] ;
1565   (fact)->info.factor_mallocs    = reallocs;
1566   (fact)->info.fill_ratio_given  = f;
1567   (fact)->info.fill_ratio_needed = ((PetscReal)bi[2*n+1])/((PetscReal)ai[n]);
1568   (fact)->ops->lufactornumeric   = MatLUFactorNumeric_SeqAIJ_newdatastruct;
1569   /* ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */
1570   PetscFunctionReturn(0);
1571 }
1572 
1573 #undef __FUNCT__
1574 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ"
1575 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1576 {
1577   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1578   IS                 isicol;
1579   PetscErrorCode     ierr;
1580   const PetscInt     *r,*ic;
1581   PetscInt           n=A->rmap->n,*ai=a->i,*aj=a->j,d;
1582   PetscInt           *bi,*cols,nnz,*cols_lvl;
1583   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1584   PetscInt           i,levels,diagonal_fill;
1585   PetscTruth         col_identity,row_identity;
1586   PetscReal          f;
1587   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
1588   PetscBT            lnkbt;
1589   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
1590   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1591   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1592   PetscTruth         missing;
1593   PetscTruth         newdatastruct=PETSC_FALSE;
1594 
1595   PetscFunctionBegin;
1596   ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
1597   if (newdatastruct){
1598     ierr = MatILUFactorSymbolic_SeqAIJ_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1599     PetscFunctionReturn(0);
1600   }
1601 
1602   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);
1603   f             = info->fill;
1604   levels        = (PetscInt)info->levels;
1605   diagonal_fill = (PetscInt)info->diagonal_fill;
1606   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1607 
1608   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1609   ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
1610   if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */
1611     ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr);
1612     (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ;
1613 
1614     fact->factor = MAT_FACTOR_ILU;
1615     (fact)->info.factor_mallocs    = 0;
1616     (fact)->info.fill_ratio_given  = info->fill;
1617     (fact)->info.fill_ratio_needed = 1.0;
1618     b               = (Mat_SeqAIJ*)(fact)->data;
1619     ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
1620     if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
1621     b->row              = isrow;
1622     b->col              = iscol;
1623     b->icol             = isicol;
1624     ierr                = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1625     ierr                = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1626     ierr                = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1627     ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1628     PetscFunctionReturn(0);
1629   }
1630 
1631   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1632   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1633 
1634   /* get new row pointers */
1635   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1636   bi[0] = 0;
1637   /* bdiag is location of diagonal in factor */
1638   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
1639   bdiag[0]  = 0;
1640 
1641   ierr = PetscMalloc((2*n+1)*sizeof(PetscInt**),&bj_ptr);CHKERRQ(ierr);
1642   bjlvl_ptr = (PetscInt**)(bj_ptr + n);
1643 
1644   /* create a linked list for storing column indices of the active row */
1645   nlnk = n + 1;
1646   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1647 
1648   /* initial FreeSpace size is f*(ai[n]+1) */
1649   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
1650   current_space = free_space;
1651   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
1652   current_space_lvl = free_space_lvl;
1653 
1654   for (i=0; i<n; i++) {
1655     nzi = 0;
1656     /* copy current row into linked list */
1657     nnz  = ai[r[i]+1] - ai[r[i]];
1658     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1659     cols = aj + ai[r[i]];
1660     lnk[i] = -1; /* marker to indicate if diagonal exists */
1661     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1662     nzi += nlnk;
1663 
1664     /* make sure diagonal entry is included */
1665     if (diagonal_fill && lnk[i] == -1) {
1666       fm = n;
1667       while (lnk[fm] < i) fm = lnk[fm];
1668       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
1669       lnk[fm]    = i;
1670       lnk_lvl[i] = 0;
1671       nzi++; dcount++;
1672     }
1673 
1674     /* add pivot rows into the active row */
1675     nzbd = 0;
1676     prow = lnk[n];
1677     while (prow < i) {
1678       nnz      = bdiag[prow];
1679       cols     = bj_ptr[prow] + nnz + 1;
1680       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1681       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
1682       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
1683       nzi += nlnk;
1684       prow = lnk[prow];
1685       nzbd++;
1686     }
1687     bdiag[i] = nzbd;
1688     bi[i+1]  = bi[i] + nzi;
1689 
1690     /* if free space is not available, make more free space */
1691     if (current_space->local_remaining<nzi) {
1692       nnz = nzi*(n - i); /* estimated and max additional space needed */
1693       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
1694       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
1695       reallocs++;
1696     }
1697 
1698     /* copy data into free_space and free_space_lvl, then initialize lnk */
1699     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1700     bj_ptr[i]    = current_space->array;
1701     bjlvl_ptr[i] = current_space_lvl->array;
1702 
1703     /* make sure the active row i has diagonal entry */
1704     if (*(bj_ptr[i]+bdiag[i]) != i) {
1705       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
1706     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
1707     }
1708 
1709     current_space->array           += nzi;
1710     current_space->local_used      += nzi;
1711     current_space->local_remaining -= nzi;
1712     current_space_lvl->array           += nzi;
1713     current_space_lvl->local_used      += nzi;
1714     current_space_lvl->local_remaining -= nzi;
1715   }
1716 
1717   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1718   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1719 
1720   /* destroy list of free space and other temporary arrays */
1721   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
1722   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */
1723   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1724   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
1725   ierr = PetscFree(bj_ptr);CHKERRQ(ierr);
1726 
1727 #if defined(PETSC_USE_INFO)
1728   {
1729     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1730     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
1731     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
1732     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
1733     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
1734     if (diagonal_fill) {
1735       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
1736     }
1737   }
1738 #endif
1739 
1740   /* put together the new matrix */
1741   ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
1742   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
1743   b = (Mat_SeqAIJ*)(fact)->data;
1744   b->free_a       = PETSC_TRUE;
1745   b->free_ij      = PETSC_TRUE;
1746   b->singlemalloc = PETSC_FALSE;
1747   ierr = PetscMalloc( (bi[n] )*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
1748   b->j          = bj;
1749   b->i          = bi;
1750   for (i=0; i<n; i++) bdiag[i] += bi[i];
1751   b->diag       = bdiag;
1752   b->ilen       = 0;
1753   b->imax       = 0;
1754   b->row        = isrow;
1755   b->col        = iscol;
1756   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1757   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1758   b->icol       = isicol;
1759   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1760   /* In b structure:  Free imax, ilen, old a, old j.
1761      Allocate bdiag, solve_work, new a, new j */
1762   ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
1763   b->maxnz             = b->nz = bi[n] ;
1764   (fact)->info.factor_mallocs    = reallocs;
1765   (fact)->info.fill_ratio_given  = f;
1766   (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1767   (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ;
1768   ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1769   PetscFunctionReturn(0);
1770 }
1771 
1772 #include "../src/mat/impls/sbaij/seq/sbaij.h"
1773 #undef __FUNCT__
1774 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ"
1775 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info)
1776 {
1777   Mat            C = B;
1778   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1779   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
1780   IS             ip=b->row,iip = b->icol;
1781   PetscErrorCode ierr;
1782   const PetscInt *rip,*riip;
1783   PetscInt       i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol;
1784   PetscInt       *ai=a->i,*aj=a->j;
1785   PetscInt       k,jmin,jmax,*jl,*il,col,nexti,ili,nz;
1786   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
1787   PetscReal      zeropivot,rs,shiftnz;
1788   PetscReal      shiftpd;
1789   ChShift_Ctx    sctx;
1790   PetscInt       newshift;
1791   PetscTruth     perm_identity;
1792 
1793   PetscFunctionBegin;
1794 
1795   shiftnz   = info->shiftnz;
1796   shiftpd   = info->shiftpd;
1797   zeropivot = info->zeropivot;
1798 
1799   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
1800   ierr  = ISGetIndices(iip,&riip);CHKERRQ(ierr);
1801 
1802   /* initialization */
1803   nz   = (2*mbs+1)*sizeof(PetscInt)+mbs*sizeof(MatScalar);
1804   ierr = PetscMalloc(nz,&il);CHKERRQ(ierr);
1805   jl   = il + mbs;
1806   rtmp = (MatScalar*)(jl + mbs);
1807 
1808   sctx.shift_amount = 0;
1809   sctx.nshift       = 0;
1810   do {
1811     sctx.chshift = PETSC_FALSE;
1812     for (i=0; i<mbs; i++) {
1813       rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0;
1814     }
1815 
1816     for (k = 0; k<mbs; k++){
1817       bval = ba + bi[k];
1818       /* initialize k-th row by the perm[k]-th row of A */
1819       jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
1820       for (j = jmin; j < jmax; j++){
1821         col = riip[aj[j]];
1822         if (col >= k){ /* only take upper triangular entry */
1823           rtmp[col] = aa[j];
1824           *bval++  = 0.0; /* for in-place factorization */
1825         }
1826       }
1827       /* shift the diagonal of the matrix */
1828       if (sctx.nshift) rtmp[k] += sctx.shift_amount;
1829 
1830       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
1831       dk = rtmp[k];
1832       i = jl[k]; /* first row to be added to k_th row  */
1833 
1834       while (i < k){
1835         nexti = jl[i]; /* next row to be added to k_th row */
1836 
1837         /* compute multiplier, update diag(k) and U(i,k) */
1838         ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
1839         uikdi = - ba[ili]*ba[bi[i]];  /* diagonal(k) */
1840         dk += uikdi*ba[ili];
1841         ba[ili] = uikdi; /* -U(i,k) */
1842 
1843         /* add multiple of row i to k-th row */
1844         jmin = ili + 1; jmax = bi[i+1];
1845         if (jmin < jmax){
1846           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
1847           /* update il and jl for row i */
1848           il[i] = jmin;
1849           j = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
1850         }
1851         i = nexti;
1852       }
1853 
1854       /* shift the diagonals when zero pivot is detected */
1855       /* compute rs=sum of abs(off-diagonal) */
1856       rs   = 0.0;
1857       jmin = bi[k]+1;
1858       nz   = bi[k+1] - jmin;
1859       bcol = bj + jmin;
1860       while (nz--){
1861         rs += PetscAbsScalar(rtmp[*bcol]);
1862         bcol++;
1863       }
1864 
1865       sctx.rs = rs;
1866       sctx.pv = dk;
1867       ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr);
1868 
1869       if (newshift == 1) {
1870         if (!sctx.shift_amount) {
1871           sctx.shift_amount = 1e-5;
1872         }
1873         break;
1874       }
1875 
1876       /* copy data into U(k,:) */
1877       ba[bi[k]] = 1.0/dk; /* U(k,k) */
1878       jmin = bi[k]+1; jmax = bi[k+1];
1879       if (jmin < jmax) {
1880         for (j=jmin; j<jmax; j++){
1881           col = bj[j]; ba[j] = rtmp[col]; rtmp[col] = 0.0;
1882         }
1883         /* add the k-th row into il and jl */
1884         il[k] = jmin;
1885         i = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
1886       }
1887     }
1888   } while (sctx.chshift);
1889   ierr = PetscFree(il);CHKERRQ(ierr);
1890 
1891   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
1892   ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr);
1893 
1894   ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
1895   if (perm_identity){
1896     (B)->ops->solve           = MatSolve_SeqSBAIJ_1_NaturalOrdering;
1897     (B)->ops->solvetranspose  = MatSolve_SeqSBAIJ_1_NaturalOrdering;
1898     (B)->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering;
1899     (B)->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering;
1900   } else {
1901     (B)->ops->solve           = MatSolve_SeqSBAIJ_1;
1902     (B)->ops->solvetranspose  = MatSolve_SeqSBAIJ_1;
1903     (B)->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1;
1904     (B)->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1;
1905   }
1906 
1907   C->assembled    = PETSC_TRUE;
1908   C->preallocated = PETSC_TRUE;
1909   ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr);
1910   if (sctx.nshift){
1911     if (shiftnz) {
1912       ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
1913     } else if (shiftpd) {
1914       ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
1915     }
1916   }
1917   PetscFunctionReturn(0);
1918 }
1919 
1920 #undef __FUNCT__
1921 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ"
1922 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
1923 {
1924   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
1925   Mat_SeqSBAIJ       *b;
1926   PetscErrorCode     ierr;
1927   PetscTruth         perm_identity,missing;
1928   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui;
1929   const PetscInt     *rip,*riip;
1930   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
1931   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL,d;
1932   PetscInt           ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
1933   PetscReal          fill=info->fill,levels=info->levels;
1934   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1935   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1936   PetscBT            lnkbt;
1937   IS                 iperm;
1938 
1939   PetscFunctionBegin;
1940   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);
1941   ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
1942   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
1943   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
1944   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
1945 
1946   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
1947   ui[0] = 0;
1948 
1949   /* ICC(0) without matrix ordering: simply copies fill pattern */
1950   if (!levels && perm_identity) {
1951 
1952     for (i=0; i<am; i++) {
1953       ui[i+1] = ui[i] + ai[i+1] - a->diag[i];
1954     }
1955     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
1956     cols = uj;
1957     for (i=0; i<am; i++) {
1958       aj    = a->j + a->diag[i];
1959       ncols = ui[i+1] - ui[i];
1960       for (j=0; j<ncols; j++) *cols++ = *aj++;
1961     }
1962   } else { /* case: levels>0 || (levels=0 && !perm_identity) */
1963     ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
1964     ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
1965 
1966     /* initialization */
1967     ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr);
1968 
1969     /* jl: linked list for storing indices of the pivot rows
1970        il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
1971     ierr = PetscMalloc((2*am+1)*sizeof(PetscInt)+2*am*sizeof(PetscInt**),&jl);CHKERRQ(ierr);
1972     il         = jl + am;
1973     uj_ptr     = (PetscInt**)(il + am);
1974     uj_lvl_ptr = (PetscInt**)(uj_ptr + am);
1975     for (i=0; i<am; i++){
1976       jl[i] = am; il[i] = 0;
1977     }
1978 
1979     /* create and initialize a linked list for storing column indices of the active row k */
1980     nlnk = am + 1;
1981     ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1982 
1983     /* initial FreeSpace size is fill*(ai[am]+1) */
1984     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
1985     current_space = free_space;
1986     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr);
1987     current_space_lvl = free_space_lvl;
1988 
1989     for (k=0; k<am; k++){  /* for each active row k */
1990       /* initialize lnk by the column indices of row rip[k] of A */
1991       nzk   = 0;
1992       ncols = ai[rip[k]+1] - ai[rip[k]];
1993       if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
1994       ncols_upper = 0;
1995       for (j=0; j<ncols; j++){
1996         i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
1997         if (riip[i] >= k){ /* only take upper triangular entry */
1998           ajtmp[ncols_upper] = i;
1999           ncols_upper++;
2000         }
2001       }
2002       ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2003       nzk += nlnk;
2004 
2005       /* update lnk by computing fill-in for each pivot row to be merged in */
2006       prow = jl[k]; /* 1st pivot row */
2007 
2008       while (prow < k){
2009         nextprow = jl[prow];
2010 
2011         /* merge prow into k-th row */
2012         jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2013         jmax = ui[prow+1];
2014         ncols = jmax-jmin;
2015         i     = jmin - ui[prow];
2016         cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2017         uj    = uj_lvl_ptr[prow] + i; /* levels of cols */
2018         j     = *(uj - 1);
2019         ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr);
2020         nzk += nlnk;
2021 
2022         /* update il and jl for prow */
2023         if (jmin < jmax){
2024           il[prow] = jmin;
2025           j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2026         }
2027         prow = nextprow;
2028       }
2029 
2030       /* if free space is not available, make more free space */
2031       if (current_space->local_remaining<nzk) {
2032         i = am - k + 1; /* num of unfactored rows */
2033         i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2034         ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2035         ierr = PetscFreeSpaceGet(i,&current_space_lvl);CHKERRQ(ierr);
2036         reallocs++;
2037       }
2038 
2039       /* copy data into free_space and free_space_lvl, then initialize lnk */
2040       if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2041       ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
2042 
2043       /* add the k-th row into il and jl */
2044       if (nzk > 1){
2045         i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2046         jl[k] = jl[i]; jl[i] = k;
2047         il[k] = ui[k] + 1;
2048       }
2049       uj_ptr[k]     = current_space->array;
2050       uj_lvl_ptr[k] = current_space_lvl->array;
2051 
2052       current_space->array           += nzk;
2053       current_space->local_used      += nzk;
2054       current_space->local_remaining -= nzk;
2055 
2056       current_space_lvl->array           += nzk;
2057       current_space_lvl->local_used      += nzk;
2058       current_space_lvl->local_remaining -= nzk;
2059 
2060       ui[k+1] = ui[k] + nzk;
2061     }
2062 
2063 #if defined(PETSC_USE_INFO)
2064     if (ai[am] != 0) {
2065       PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]);
2066       ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2067       ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2068       ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2069     } else {
2070       ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2071     }
2072 #endif
2073 
2074     ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2075     ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2076     ierr = PetscFree(jl);CHKERRQ(ierr);
2077     ierr = PetscFree(ajtmp);CHKERRQ(ierr);
2078 
2079     /* destroy list of free space and other temporary array(s) */
2080     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2081     ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
2082     ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2083     ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2084 
2085   } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2086 
2087   /* put together the new matrix in MATSEQSBAIJ format */
2088 
2089   b    = (Mat_SeqSBAIJ*)(fact)->data;
2090   b->singlemalloc = PETSC_FALSE;
2091   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2092   b->j    = uj;
2093   b->i    = ui;
2094   b->diag = 0;
2095   b->ilen = 0;
2096   b->imax = 0;
2097   b->row  = perm;
2098   b->col  = perm;
2099   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2100   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2101   b->icol = iperm;
2102   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2103   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2104   ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2105   b->maxnz   = b->nz = ui[am];
2106   b->free_a  = PETSC_TRUE;
2107   b->free_ij = PETSC_TRUE;
2108 
2109   (fact)->info.factor_mallocs    = reallocs;
2110   (fact)->info.fill_ratio_given  = fill;
2111   if (ai[am] != 0) {
2112     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2113   } else {
2114     (fact)->info.fill_ratio_needed = 0.0;
2115   }
2116   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2117   PetscFunctionReturn(0);
2118 }
2119 
2120 #undef __FUNCT__
2121 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ"
2122 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2123 {
2124   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2125   Mat_SeqSBAIJ       *b;
2126   PetscErrorCode     ierr;
2127   PetscTruth         perm_identity;
2128   PetscReal          fill = info->fill;
2129   const PetscInt     *rip,*riip;
2130   PetscInt           i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow;
2131   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
2132   PetscInt           nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr;
2133   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2134   PetscBT            lnkbt;
2135   IS                 iperm;
2136 
2137   PetscFunctionBegin;
2138   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);
2139   /* check whether perm is the identity mapping */
2140   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2141   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2142   ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2143   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2144 
2145   /* initialization */
2146   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2147   ui[0] = 0;
2148 
2149   /* jl: linked list for storing indices of the pivot rows
2150      il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2151   ierr = PetscMalloc((3*am+1)*sizeof(PetscInt)+am*sizeof(PetscInt**),&jl);CHKERRQ(ierr);
2152   il     = jl + am;
2153   cols   = il + am;
2154   ui_ptr = (PetscInt**)(cols + am);
2155   for (i=0; i<am; i++){
2156     jl[i] = am; il[i] = 0;
2157   }
2158 
2159   /* create and initialize a linked list for storing column indices of the active row k */
2160   nlnk = am + 1;
2161   ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2162 
2163   /* initial FreeSpace size is fill*(ai[am]+1) */
2164   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2165   current_space = free_space;
2166 
2167   for (k=0; k<am; k++){  /* for each active row k */
2168     /* initialize lnk by the column indices of row rip[k] of A */
2169     nzk   = 0;
2170     ncols = ai[rip[k]+1] - ai[rip[k]];
2171     if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2172     ncols_upper = 0;
2173     for (j=0; j<ncols; j++){
2174       i = riip[*(aj + ai[rip[k]] + j)];
2175       if (i >= k){ /* only take upper triangular entry */
2176         cols[ncols_upper] = i;
2177         ncols_upper++;
2178       }
2179     }
2180     ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2181     nzk += nlnk;
2182 
2183     /* update lnk by computing fill-in for each pivot row to be merged in */
2184     prow = jl[k]; /* 1st pivot row */
2185 
2186     while (prow < k){
2187       nextprow = jl[prow];
2188       /* merge prow into k-th row */
2189       jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2190       jmax = ui[prow+1];
2191       ncols = jmax-jmin;
2192       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2193       ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2194       nzk += nlnk;
2195 
2196       /* update il and jl for prow */
2197       if (jmin < jmax){
2198         il[prow] = jmin;
2199         j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
2200       }
2201       prow = nextprow;
2202     }
2203 
2204     /* if free space is not available, make more free space */
2205     if (current_space->local_remaining<nzk) {
2206       i = am - k + 1; /* num of unfactored rows */
2207       i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2208       ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2209       reallocs++;
2210     }
2211 
2212     /* copy data into free space, then initialize lnk */
2213     ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
2214 
2215     /* add the k-th row into il and jl */
2216     if (nzk-1 > 0){
2217       i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2218       jl[k] = jl[i]; jl[i] = k;
2219       il[k] = ui[k] + 1;
2220     }
2221     ui_ptr[k] = current_space->array;
2222     current_space->array           += nzk;
2223     current_space->local_used      += nzk;
2224     current_space->local_remaining -= nzk;
2225 
2226     ui[k+1] = ui[k] + nzk;
2227   }
2228 
2229 #if defined(PETSC_USE_INFO)
2230   if (ai[am] != 0) {
2231     PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]);
2232     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2233     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2234     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2235   } else {
2236      ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2237   }
2238 #endif
2239 
2240   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2241   ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2242   ierr = PetscFree(jl);CHKERRQ(ierr);
2243 
2244   /* destroy list of free space and other temporary array(s) */
2245   ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2246   ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
2247   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2248 
2249   /* put together the new matrix in MATSEQSBAIJ format */
2250 
2251   b = (Mat_SeqSBAIJ*)(fact)->data;
2252   b->singlemalloc = PETSC_FALSE;
2253   b->free_a       = PETSC_TRUE;
2254   b->free_ij      = PETSC_TRUE;
2255   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2256   b->j    = uj;
2257   b->i    = ui;
2258   b->diag = 0;
2259   b->ilen = 0;
2260   b->imax = 0;
2261   b->row  = perm;
2262   b->col  = perm;
2263   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2264   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2265   b->icol = iperm;
2266   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2267   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2268   ierr    = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2269   b->maxnz = b->nz = ui[am];
2270 
2271   (fact)->info.factor_mallocs    = reallocs;
2272   (fact)->info.fill_ratio_given  = fill;
2273   if (ai[am] != 0) {
2274     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2275   } else {
2276     (fact)->info.fill_ratio_needed = 0.0;
2277   }
2278   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2279   PetscFunctionReturn(0);
2280 }
2281 
2282 #undef __FUNCT__
2283 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_newdatastruct"
2284 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx)
2285 {
2286   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
2287   PetscErrorCode    ierr;
2288   PetscInt          n = A->rmap->n;
2289   const PetscInt    *ai = a->i,*aj = a->j,*vi;
2290   PetscScalar       *x,sum;
2291   const PetscScalar *b;
2292   const MatScalar   *aa = a->a,*v;
2293   PetscInt          i,nz;
2294 
2295   PetscFunctionBegin;
2296   if (!n) PetscFunctionReturn(0);
2297 
2298   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2299   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2300 
2301   /* forward solve the lower triangular */
2302   x[0] = b[0];
2303   v    = aa;
2304   vi   = aj;
2305   for (i=1; i<n; i++) {
2306     nz  = ai[i+1] - ai[i];
2307     sum = b[i];
2308     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
2309     /*    while (nz--) sum -= *v++ * x[*vi++];*/
2310     v  += nz;
2311     vi += nz;
2312     x[i] = sum;
2313   }
2314 
2315   /* backward solve the upper triangular */
2316   v   = aa + ai[n+1];
2317   vi  = aj + ai[n+1];
2318   for (i=n-1; i>=0; i--){
2319     nz = ai[2*n-i +1] - ai[2*n-i]-1;
2320     sum = x[i];
2321     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
2322     /* while (nz--) sum -= *v++ * x[*vi++]; */
2323     v   += nz;
2324     vi  += nz; vi++;
2325     x[i] = *v++ *sum; /* x[i]=aa[adiag[i]]*sum; v++; */
2326   }
2327 
2328   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
2329   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2330   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2331   PetscFunctionReturn(0);
2332 }
2333 
2334 #undef __FUNCT__
2335 #define __FUNCT__ "MatSolve_SeqAIJ_newdatastruct"
2336 PetscErrorCode MatSolve_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec xx)
2337 {
2338   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
2339   IS                iscol = a->col,isrow = a->row;
2340   PetscErrorCode    ierr;
2341   PetscInt          i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,nz,k;
2342   const PetscInt    *rout,*cout,*r,*c;
2343   PetscScalar       *x,*tmp,*tmps,sum;
2344   const PetscScalar *b;
2345   const MatScalar   *aa = a->a,*v;
2346 
2347   PetscFunctionBegin;
2348   if (!n) PetscFunctionReturn(0);
2349 
2350   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2351   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2352   tmp  = a->solve_work;
2353 
2354   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
2355   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
2356 
2357   /* forward solve the lower triangular */
2358   tmp[0] = b[*r++];
2359   tmps   = tmp;
2360   v      = aa;
2361   vi     = aj;
2362   for (i=1; i<n; i++) {
2363     nz  = ai[i+1] - ai[i];
2364     sum = b[*r++];
2365     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
2366     tmp[i] = sum;
2367     v += nz; vi += nz;
2368   }
2369 
2370   /* backward solve the upper triangular */
2371   k  = n+1;
2372   v  = aa + ai[k]; /* 1st entry of U(n-1,:) */
2373   vi = aj + ai[k];
2374   for (i=n-1; i>=0; i--){
2375     k  = 2*n-i;
2376     nz = ai[k +1] - ai[k] - 1;
2377     sum = tmp[i];
2378     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
2379     x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */
2380     v += nz+1; vi += nz+1;
2381   }
2382 
2383   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
2384   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
2385   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2386   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2387   ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr);
2388   PetscFunctionReturn(0);
2389 }
2390 
2391 #undef __FUNCT__
2392 #define __FUNCT__ "MatILUDTFactor_SeqAIJ"
2393 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact)
2394 {
2395   Mat                B = *fact;
2396   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b;
2397   IS                 isicol;
2398   PetscErrorCode     ierr;
2399   const PetscInt     *r,*ic;
2400   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag;
2401   PetscInt           *bi,*bj,*bdiag,*bdiag_rev;
2402   PetscInt           row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au;
2403   PetscInt           nlnk,*lnk;
2404   PetscBT            lnkbt;
2405   PetscTruth         row_identity,icol_identity,both_identity;
2406   MatScalar          *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp;
2407   const PetscInt     *ics;
2408   PetscInt           j,nz,*pj,*bjtmp,k,ncut,*jtmp;
2409   PetscReal          dt=info->dt,dtcol=info->dtcol,shift=info->shiftinblocks;
2410   PetscInt           dtcount=(PetscInt)info->dtcount,nnz_max;
2411   PetscTruth         missing;
2412 
2413   PetscFunctionBegin;
2414 
2415   if (dt      == PETSC_DEFAULT) dt      = 0.005;
2416   if (dtcol   == PETSC_DEFAULT) dtcol   = 0.01; /* XXX unused! */
2417   if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax);
2418 
2419   /* ------- symbolic factorization, can be reused ---------*/
2420   ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
2421   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
2422   adiag=a->diag;
2423 
2424   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
2425 
2426   /* bdiag is location of diagonal in factor */
2427   ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
2428   bdiag_rev = bdiag + n+1;
2429 
2430   /* allocate row pointers bi */
2431   ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
2432 
2433   /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */
2434   if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */
2435   nnz_max  = ai[n]+2*n*dtcount+2;
2436 
2437   ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
2438   ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr);
2439 
2440   /* put together the new matrix */
2441   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
2442   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
2443   b    = (Mat_SeqAIJ*)(B)->data;
2444   b->free_a       = PETSC_TRUE;
2445   b->free_ij      = PETSC_TRUE;
2446   b->singlemalloc = PETSC_FALSE;
2447   b->a          = ba;
2448   b->j          = bj;
2449   b->i          = bi;
2450   b->diag       = bdiag;
2451   b->ilen       = 0;
2452   b->imax       = 0;
2453   b->row        = isrow;
2454   b->col        = iscol;
2455   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
2456   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
2457   b->icol       = isicol;
2458   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2459 
2460   ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2461   b->maxnz = nnz_max;
2462 
2463   (B)->factor                = MAT_FACTOR_ILUDT;
2464   (B)->info.factor_mallocs   = 0;
2465   (B)->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]);
2466   CHKMEMQ;
2467   /* ------- end of symbolic factorization ---------*/
2468 
2469   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
2470   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
2471   ics  = ic;
2472 
2473   /* linked list for storing column indices of the active row */
2474   nlnk = n + 1;
2475   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2476 
2477   /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */
2478   ierr = PetscMalloc((2*n+1)*sizeof(PetscInt),&im);CHKERRQ(ierr);
2479   jtmp = im + n;
2480   /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */
2481   ierr = PetscMalloc((2*n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
2482   ierr = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr);
2483   vtmp = rtmp + n;
2484 
2485   bi[0]    = 0;
2486   bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */
2487   bdiag_rev[n] = bdiag[0];
2488   bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */
2489   for (i=0; i<n; i++) {
2490     /* copy initial fill into linked list */
2491     nzi = 0; /* nonzeros for active row i */
2492     nzi = ai[r[i]+1] - ai[r[i]];
2493     if (!nzi) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
2494     nzi_al = adiag[r[i]] - ai[r[i]];
2495     nzi_au = ai[r[i]+1] - adiag[r[i]] -1;
2496     ajtmp = aj + ai[r[i]];
2497     ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2498 
2499     /* load in initial (unfactored row) */
2500     aatmp = a->a + ai[r[i]];
2501     for (j=0; j<nzi; j++) {
2502       rtmp[ics[*ajtmp++]] = *aatmp++;
2503     }
2504 
2505     /* add pivot rows into linked list */
2506     row = lnk[n];
2507     while (row < i ) {
2508       nzi_bl = bi[row+1] - bi[row] + 1;
2509       bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */
2510       ierr  = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr);
2511       nzi  += nlnk;
2512       row   = lnk[row];
2513     }
2514 
2515     /* copy data from lnk into jtmp, then initialize lnk */
2516     ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr);
2517 
2518     /* numerical factorization */
2519     bjtmp = jtmp;
2520     row   = *bjtmp++; /* 1st pivot row */
2521     while  ( row < i ) {
2522       pc         = rtmp + row;
2523       pv         = ba + bdiag[row]; /* 1./(diag of the pivot row) */
2524       multiplier = (*pc) * (*pv);
2525       *pc        = multiplier;
2526       if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */
2527         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
2528         pv         = ba + bdiag[row+1] + 1;
2529         /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */
2530         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
2531         for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
2532         ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
2533       }
2534       row = *bjtmp++;
2535     }
2536 
2537     /* copy sparse rtmp into contiguous vtmp; separate L and U part */
2538     diag_tmp = rtmp[i];  /* save diagonal value - may not needed?? */
2539     nzi_bl = 0; j = 0;
2540     while (jtmp[j] < i){ /* Note: jtmp is sorted */
2541       vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
2542       nzi_bl++; j++;
2543     }
2544     nzi_bu = nzi - nzi_bl -1;
2545     while (j < nzi){
2546       vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
2547       j++;
2548     }
2549 
2550     bjtmp = bj + bi[i];
2551     batmp = ba + bi[i];
2552     /* apply level dropping rule to L part */
2553     ncut = nzi_al + dtcount;
2554     if (ncut < nzi_bl){
2555       ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr);
2556       ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr);
2557     } else {
2558       ncut = nzi_bl;
2559     }
2560     for (j=0; j<ncut; j++){
2561       bjtmp[j] = jtmp[j];
2562       batmp[j] = vtmp[j];
2563       /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */
2564     }
2565     bi[i+1] = bi[i] + ncut;
2566     nzi = ncut + 1;
2567 
2568     /* apply level dropping rule to U part */
2569     ncut = nzi_au + dtcount;
2570     if (ncut < nzi_bu){
2571       ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr);
2572       ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr);
2573     } else {
2574       ncut = nzi_bu;
2575     }
2576     nzi += ncut;
2577 
2578     /* mark bdiagonal */
2579     bdiag[i+1]       = bdiag[i] - (ncut + 1);
2580     bdiag_rev[n-i-1] = bdiag[i+1];
2581     bi[2*n - i]      = bi[2*n - i +1] - (ncut + 1);
2582     bjtmp = bj + bdiag[i];
2583     batmp = ba + bdiag[i];
2584     *bjtmp = i;
2585     *batmp = diag_tmp; /* rtmp[i]; */
2586     if (*batmp == 0.0) {
2587       *batmp = dt+shift;
2588       /* printf(" row %d add shift %g\n",i,shift); */
2589     }
2590     *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */
2591     /* printf(" (%d,%g),",*bjtmp,*batmp); */
2592 
2593     bjtmp = bj + bdiag[i+1]+1;
2594     batmp = ba + bdiag[i+1]+1;
2595     for (k=0; k<ncut; k++){
2596       bjtmp[k] = jtmp[nzi_bl+1+k];
2597       batmp[k] = vtmp[nzi_bl+1+k];
2598       /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */
2599     }
2600     /* printf("\n"); */
2601 
2602     im[i]   = nzi; /* used by PetscLLAddSortedLU() */
2603     /*
2604     printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]);
2605     printf(" ----------------------------\n");
2606     */
2607   } /* for (i=0; i<n; i++) */
2608   /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */
2609   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]);
2610 
2611   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
2612   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
2613 
2614   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2615   ierr = PetscFree(im);CHKERRQ(ierr);
2616   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2617 
2618   ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr);
2619   b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n];
2620 
2621   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
2622   ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr);
2623   both_identity = (PetscTruth) (row_identity && icol_identity);
2624   if (row_identity && icol_identity) {
2625     B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct;
2626   } else {
2627     B->ops->solve = MatSolve_SeqAIJ_newdatastruct;
2628   }
2629 
2630   B->ops->lufactorsymbolic  = MatILUDTFactorSymbolic_SeqAIJ;
2631   B->ops->lufactornumeric   = MatILUDTFactorNumeric_SeqAIJ;
2632   B->ops->solveadd          = 0;
2633   B->ops->solvetranspose    = 0;
2634   B->ops->solvetransposeadd = 0;
2635   B->ops->matsolve          = 0;
2636   B->assembled              = PETSC_TRUE;
2637   B->preallocated           = PETSC_TRUE;
2638   PetscFunctionReturn(0);
2639 }
2640 
2641 /* a wraper of MatILUDTFactor_SeqAIJ() */
2642 #undef __FUNCT__
2643 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ"
2644 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info)
2645 {
2646   PetscErrorCode     ierr;
2647 
2648   PetscFunctionBegin;
2649   ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr);
2650 
2651   fact->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ;
2652   PetscFunctionReturn(0);
2653 }
2654 
2655 /*
2656    same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors
2657    - intend to replace existing MatLUFactorNumeric_SeqAIJ()
2658 */
2659 #undef __FUNCT__
2660 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ"
2661 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info)
2662 {
2663   Mat            C=fact;
2664   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
2665   IS             isrow = b->row,isicol = b->icol;
2666   PetscErrorCode ierr;
2667   const PetscInt *r,*ic,*ics;
2668   PetscInt       i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
2669   PetscInt       *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj;
2670   MatScalar      *rtmp,*pc,multiplier,*v,*pv,*aa=a->a;
2671   PetscReal      dt=info->dt,shift=info->shiftinblocks;
2672   PetscTruth     row_identity, col_identity;
2673 
2674   PetscFunctionBegin;
2675   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
2676   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
2677   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
2678   ics  = ic;
2679 
2680   for (i=0; i<n; i++){
2681     /* initialize rtmp array */
2682     nzl   = bi[i+1] - bi[i];       /* num of nozeros in L(i,:) */
2683     bjtmp = bj + bi[i];
2684     for  (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0;
2685     rtmp[i] = 0.0;
2686     nzu   = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */
2687     bjtmp = bj + bdiag[i+1] + 1;
2688     for  (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0;
2689 
2690     /* load in initial unfactored row of A */
2691     /* printf("row %d\n",i); */
2692     nz    = ai[r[i]+1] - ai[r[i]];
2693     ajtmp = aj + ai[r[i]];
2694     v     = aa + ai[r[i]];
2695     for (j=0; j<nz; j++) {
2696       rtmp[ics[*ajtmp++]] = v[j];
2697       /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */
2698     }
2699     /* printf("\n"); */
2700 
2701     /* numerical factorization */
2702     bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */
2703     nzl   = bi[i+1] - bi[i]; /* num of entries in L(i,:) */
2704     k = 0;
2705     while (k < nzl){
2706       row   = *bjtmp++;
2707       /* printf("  prow %d\n",row); */
2708       pc         = rtmp + row;
2709       pv         = b->a + bdiag[row]; /* 1./(diag of the pivot row) */
2710       multiplier = (*pc) * (*pv);
2711       *pc        = multiplier;
2712       if (PetscAbsScalar(multiplier) > dt){
2713         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
2714         pv         = b->a + bdiag[row+1] + 1;
2715         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
2716         for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
2717         /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */
2718       }
2719       k++;
2720     }
2721 
2722     /* finished row so stick it into b->a */
2723     /* L-part */
2724     pv = b->a + bi[i] ;
2725     pj = bj + bi[i] ;
2726     nzl = bi[i+1] - bi[i];
2727     for (j=0; j<nzl; j++) {
2728       pv[j] = rtmp[pj[j]];
2729       /* printf(" (%d,%g),",pj[j],pv[j]); */
2730     }
2731 
2732     /* diagonal: invert diagonal entries for simplier triangular solves */
2733     if (rtmp[i] == 0.0) rtmp[i] = dt+shift;
2734     b->a[bdiag[i]] = 1.0/rtmp[i];
2735     /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */
2736 
2737     /* U-part */
2738     pv = b->a + bdiag[i+1] + 1;
2739     pj = bj + bdiag[i+1] + 1;
2740     nzu = bdiag[i] - bdiag[i+1] - 1;
2741     for (j=0; j<nzu; j++) {
2742       pv[j] = rtmp[pj[j]];
2743       /* printf(" (%d,%g),",pj[j],pv[j]); */
2744     }
2745     /* printf("\n"); */
2746   }
2747 
2748   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2749   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
2750   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
2751 
2752   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
2753   ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
2754   if (row_identity && col_identity) {
2755     C->ops->solve   = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct;
2756   } else {
2757     C->ops->solve   = MatSolve_SeqAIJ_newdatastruct;
2758   }
2759   C->ops->solveadd           = 0;
2760   C->ops->solvetranspose     = 0;
2761   C->ops->solvetransposeadd  = 0;
2762   C->ops->matsolve           = 0;
2763   C->assembled    = PETSC_TRUE;
2764   C->preallocated = PETSC_TRUE;
2765   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
2766   PetscFunctionReturn(0);
2767 }
2768