xref: /petsc/src/mat/impls/aij/seq/aijfact.c (revision 9596e0b48258fba4fca4f68feb5185896facfe69)
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   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
478   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
479   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
480   ics  = ic;
481 
482   for (i=0; i<n; i++){
483     /* zero rtmp */
484     /* L part */
485     nz    = bi[i+1] - bi[i];
486     bjtmp = bj + bi[i];
487     for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
488 
489     /* U part */
490     nz = bi[2*n-i+1] - bi[2*n-i];
491     bjtmp = bj + bi[2*n-i];
492     for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
493 
494     /* load in initial (unfactored row) */
495     nz    = ai[r[i]+1] - ai[r[i]];
496     ajtmp = aj + ai[r[i]];
497     v     = aa + ai[r[i]];
498     for (j=0; j<nz; j++) {
499       rtmp[ics[ajtmp[j]]] = v[j];
500     }
501     if (rtmp[ics[r[i]]] == 0.0){
502       rtmp[ics[r[i]]] += shift; /* shift the diagonal of the matrix */
503       /* printf("row %d, shift %g\n",i,shift); */
504     }
505 
506     /* elimination */
507     bjtmp = bj + bi[i];
508     row   = *bjtmp++;
509     nzL   = bi[i+1] - bi[i];
510     k   = 0;
511     while  (k < nzL) {
512       pc = rtmp + row;
513       if (*pc != 0.0) {
514         pv         = b->a + bdiag[row];
515         multiplier = *pc * (*pv);
516         *pc        = multiplier;
517         pj         = b->j + bi[2*n-row]; /* begining of U(row,:) */
518         pv         = b->a + bi[2*n-row];
519         nz         = bi[2*n-row+1] - bi[2*n-row] - 1; /* num of entries in U(row,:), excluding diag */
520         for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
521         ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
522       }
523       row = *bjtmp++; k++;
524     }
525 
526     /* finished row so stick it into b->a */
527     /* L part */
528     pv   = b->a + bi[i] ;
529     pj   = b->j + bi[i] ;
530     nz   = bi[i+1] - bi[i];
531     for (j=0; j<nz; j++) {
532       pv[j] = rtmp[pj[j]];
533     }
534 
535     /* Mark diagonal and invert diagonal for simplier triangular solves */
536     pv  = b->a + bdiag[i];
537     pj  = b->j + bdiag[i];
538     /* if (*pj != i)SETERRQ2(PETSC_ERR_SUP,"row %d != *pj %d",i,*pj) */
539     *pv = 1.0/rtmp[*pj];
540 
541     /* U part */
542     pv = b->a + bi[2*n-i];
543     pj = b->j + bi[2*n-i];
544     nz = bi[2*n-i+1] - bi[2*n-i] - 1;
545     for (j=0; j<nz; j++) pv[j] = rtmp[pj[j]];
546   }
547   ierr = PetscFree(rtmp);CHKERRQ(ierr);
548   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
549   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
550 
551   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
552   ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
553   if (row_identity && col_identity) {
554     C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct;
555   } else {
556     C->ops->solve = MatSolve_SeqAIJ_newdatastruct;
557   }
558 
559   C->ops->solveadd           = 0;
560   C->ops->solvetranspose     = 0;
561   C->ops->solvetransposeadd  = 0;
562   C->ops->matsolve           = 0;
563   C->assembled    = PETSC_TRUE;
564   C->preallocated = PETSC_TRUE;
565   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
566   PetscFunctionReturn(0);
567 }
568 
569 #undef __FUNCT__
570 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ"
571 PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info)
572 {
573   Mat             C=B;
574   Mat_SeqAIJ      *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
575   IS              isrow = b->row,isicol = b->icol;
576   PetscErrorCode  ierr;
577   const PetscInt   *r,*ic,*ics;
578   PetscInt        nz,row,i,j,n=A->rmap->n,diag;
579   const PetscInt  *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
580   const PetscInt  *ajtmp,*bjtmp,*diag_offset = b->diag,*pj;
581   MatScalar       *pv,*rtmp,*pc,multiplier,d;
582   const MatScalar *v,*aa=a->a;
583   PetscReal       rs=0.0;
584   LUShift_Ctx     sctx;
585   PetscInt        newshift,*ddiag;
586 
587   PetscFunctionBegin;
588   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
589   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
590   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
591   ics  = ic;
592 
593   sctx.shift_top      = 0;
594   sctx.nshift_max     = 0;
595   sctx.shift_lo       = 0;
596   sctx.shift_hi       = 0;
597   sctx.shift_fraction = 0;
598 
599   /* if both shift schemes are chosen by user, only use info->shiftpd */
600   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
601     ddiag          = a->diag;
602     sctx.shift_top = info->zeropivot;
603     for (i=0; i<n; i++) {
604       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
605       d  = (aa)[ddiag[i]];
606       rs = -PetscAbsScalar(d) - PetscRealPart(d);
607       v  = aa+ai[i];
608       nz = ai[i+1] - ai[i];
609       for (j=0; j<nz; j++)
610 	rs += PetscAbsScalar(v[j]);
611       if (rs>sctx.shift_top) sctx.shift_top = rs;
612     }
613     sctx.shift_top   *= 1.1;
614     sctx.nshift_max   = 5;
615     sctx.shift_lo     = 0.;
616     sctx.shift_hi     = 1.;
617   }
618 
619   sctx.shift_amount = 0.0;
620   sctx.nshift       = 0;
621   do {
622     sctx.lushift = PETSC_FALSE;
623     for (i=0; i<n; i++){
624       nz    = bi[i+1] - bi[i];
625       bjtmp = bj + bi[i];
626       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
627 
628       /* load in initial (unfactored row) */
629       nz    = ai[r[i]+1] - ai[r[i]];
630       ajtmp = aj + ai[r[i]];
631       v     = aa + ai[r[i]];
632       for (j=0; j<nz; j++) {
633         rtmp[ics[ajtmp[j]]] = v[j];
634       }
635       rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */
636       /* if (sctx.shift_amount > 0.0) printf("row %d, shift %g\n",i,sctx.shift_amount); */
637 
638       row = *bjtmp++;
639       while  (row < i) {
640         pc = rtmp + row;
641         if (*pc != 0.0) {
642           pv         = b->a + diag_offset[row];
643           pj         = b->j + diag_offset[row] + 1;
644           multiplier = *pc / *pv++;
645           *pc        = multiplier;
646           nz         = bi[row+1] - diag_offset[row] - 1;
647           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
648           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
649         }
650         row = *bjtmp++;
651       }
652       /* finished row so stick it into b->a */
653       pv   = b->a + bi[i] ;
654       pj   = b->j + bi[i] ;
655       nz   = bi[i+1] - bi[i];
656       diag = diag_offset[i] - bi[i];
657       rs   = 0.0;
658       for (j=0; j<nz; j++) {
659         pv[j] = rtmp[pj[j]];
660         rs   += PetscAbsScalar(pv[j]);
661       }
662       rs   -= PetscAbsScalar(pv[diag]);
663 
664       /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */
665       sctx.rs  = rs;
666       sctx.pv  = pv[diag];
667       ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr);
668       if (newshift == 1) break;
669     }
670 
671     if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
672       /*
673        * if no shift in this attempt & shifting & started shifting & can refine,
674        * then try lower shift
675        */
676       sctx.shift_hi       = sctx.shift_fraction;
677       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
678       sctx.shift_amount   = sctx.shift_fraction * sctx.shift_top;
679       sctx.lushift        = PETSC_TRUE;
680       sctx.nshift++;
681     }
682   } while (sctx.lushift);
683 
684   /* invert diagonal entries for simplier triangular solves */
685   for (i=0; i<n; i++) {
686     b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]];
687   }
688   ierr = PetscFree(rtmp);CHKERRQ(ierr);
689   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
690   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
691   if (b->inode.use) {
692     C->ops->solve   = MatSolve_Inode;
693   } else {
694     PetscTruth row_identity, col_identity;
695     ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
696     ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
697     if (row_identity && col_identity) {
698       C->ops->solve   = MatSolve_SeqAIJ_NaturalOrdering;
699     } else {
700       C->ops->solve   = MatSolve_SeqAIJ;
701     }
702   }
703   C->ops->solveadd           = MatSolveAdd_SeqAIJ;
704   C->ops->solvetranspose     = MatSolveTranspose_SeqAIJ;
705   C->ops->solvetransposeadd  = MatSolveTransposeAdd_SeqAIJ;
706   C->ops->matsolve           = MatMatSolve_SeqAIJ;
707   C->assembled    = PETSC_TRUE;
708   C->preallocated = PETSC_TRUE;
709   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
710   if (sctx.nshift){
711      if (info->shiftpd) {
712       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);
713     } else if (info->shiftnz) {
714       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
715     }
716   }
717   PetscFunctionReturn(0);
718 }
719 
720 /*
721    This routine implements inplace ILU(0) with row or/and column permutations.
722    Input:
723      A - original matrix
724    Output;
725      A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i]
726          a->j (col index) is permuted by the inverse of colperm, then sorted
727          a->a reordered accordingly with a->j
728          a->diag (ptr to diagonal elements) is updated.
729 */
730 #undef __FUNCT__
731 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_InplaceWithPerm"
732 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info)
733 {
734   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
735   IS             isrow = a->row,isicol = a->icol;
736   PetscErrorCode ierr;
737   const PetscInt *r,*ic,*ics;
738   PetscInt       i,j,n=A->rmap->n,*ai=a->i,*aj=a->j;
739   PetscInt       *ajtmp,nz,row;
740   PetscInt       *diag = a->diag,nbdiag,*pj;
741   PetscScalar    *rtmp,*pc,multiplier,d;
742   MatScalar      *v,*pv;
743   PetscReal      rs;
744   LUShift_Ctx    sctx;
745   PetscInt       newshift;
746 
747   PetscFunctionBegin;
748   if (A != B) SETERRQ(PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address");
749   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
750   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
751   ierr  = PetscMalloc((n+1)*sizeof(PetscScalar),&rtmp);CHKERRQ(ierr);
752   ierr  = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr);
753   ics = ic;
754 
755   sctx.shift_top      = 0;
756   sctx.nshift_max     = 0;
757   sctx.shift_lo       = 0;
758   sctx.shift_hi       = 0;
759   sctx.shift_fraction = 0;
760 
761   /* if both shift schemes are chosen by user, only use info->shiftpd */
762   if (info->shiftpd) { /* set sctx.shift_top=max{rs} */
763     sctx.shift_top = 0;
764     for (i=0; i<n; i++) {
765       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
766       d  = (a->a)[diag[i]];
767       rs = -PetscAbsScalar(d) - PetscRealPart(d);
768       v  = a->a+ai[i];
769       nz = ai[i+1] - ai[i];
770       for (j=0; j<nz; j++)
771 	rs += PetscAbsScalar(v[j]);
772       if (rs>sctx.shift_top) sctx.shift_top = rs;
773     }
774     if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot;
775     sctx.shift_top    *= 1.1;
776     sctx.nshift_max   = 5;
777     sctx.shift_lo     = 0.;
778     sctx.shift_hi     = 1.;
779   }
780 
781   sctx.shift_amount = 0;
782   sctx.nshift       = 0;
783   do {
784     sctx.lushift = PETSC_FALSE;
785     for (i=0; i<n; i++){
786       /* load in initial unfactored row */
787       nz    = ai[r[i]+1] - ai[r[i]];
788       ajtmp = aj + ai[r[i]];
789       v     = a->a + ai[r[i]];
790       /* sort permuted ajtmp and values v accordingly */
791       for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]];
792       ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr);
793 
794       diag[r[i]] = ai[r[i]];
795       for (j=0; j<nz; j++) {
796         rtmp[ajtmp[j]] = v[j];
797         if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */
798       }
799       rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */
800 
801       row = *ajtmp++;
802       while  (row < i) {
803         pc = rtmp + row;
804         if (*pc != 0.0) {
805           pv         = a->a + diag[r[row]];
806           pj         = aj + diag[r[row]] + 1;
807 
808           multiplier = *pc / *pv++;
809           *pc        = multiplier;
810           nz         = ai[r[row]+1] - diag[r[row]] - 1;
811           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
812           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
813         }
814         row = *ajtmp++;
815       }
816       /* finished row so overwrite it onto a->a */
817       pv   = a->a + ai[r[i]] ;
818       pj   = aj + ai[r[i]] ;
819       nz   = ai[r[i]+1] - ai[r[i]];
820       nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */
821 
822       rs   = 0.0;
823       for (j=0; j<nz; j++) {
824         pv[j] = rtmp[pj[j]];
825         if (j != nbdiag) rs += PetscAbsScalar(pv[j]);
826       }
827 
828       /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */
829       sctx.rs  = rs;
830       sctx.pv  = pv[nbdiag];
831       ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr);
832       if (newshift == 1) break;
833     }
834 
835     if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
836       /*
837        * if no shift in this attempt & shifting & started shifting & can refine,
838        * then try lower shift
839        */
840       sctx.shift_hi        = sctx.shift_fraction;
841       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
842       sctx.shift_amount    = sctx.shift_fraction * sctx.shift_top;
843       sctx.lushift         = PETSC_TRUE;
844       sctx.nshift++;
845     }
846   } while (sctx.lushift);
847 
848   /* invert diagonal entries for simplier triangular solves */
849   for (i=0; i<n; i++) {
850     a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]];
851   }
852 
853   ierr = PetscFree(rtmp);CHKERRQ(ierr);
854   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
855   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
856   A->ops->solve             = MatSolve_SeqAIJ_InplaceWithPerm;
857   A->ops->solveadd          = MatSolveAdd_SeqAIJ;
858   A->ops->solvetranspose    = MatSolveTranspose_SeqAIJ;
859   A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ;
860   A->assembled = PETSC_TRUE;
861   A->preallocated = PETSC_TRUE;
862   ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr);
863   if (sctx.nshift){
864     if (info->shiftpd) {
865       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);
866     } else if (info->shiftnz) {
867       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
868     }
869   }
870   PetscFunctionReturn(0);
871 }
872 
873 /* ----------------------------------------------------------- */
874 #undef __FUNCT__
875 #define __FUNCT__ "MatLUFactor_SeqAIJ"
876 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info)
877 {
878   PetscErrorCode ierr;
879   Mat            C;
880 
881   PetscFunctionBegin;
882   ierr = MatGetFactor(A,MAT_SOLVER_PETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr);
883   ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr);
884   ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr);
885   A->ops->solve            = C->ops->solve;
886   A->ops->solvetranspose   = C->ops->solvetranspose;
887   ierr = MatHeaderCopy(A,C);CHKERRQ(ierr);
888   ierr = PetscLogObjectParent(A,((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr);
889   PetscFunctionReturn(0);
890 }
891 /* ----------------------------------------------------------- */
892 
893 
894 #undef __FUNCT__
895 #define __FUNCT__ "MatSolve_SeqAIJ"
896 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx)
897 {
898   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
899   IS                iscol = a->col,isrow = a->row;
900   PetscErrorCode    ierr;
901   PetscInt          i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
902   PetscInt          nz;
903   const PetscInt    *rout,*cout,*r,*c;
904   PetscScalar       *x,*tmp,*tmps,sum;
905   const PetscScalar *b;
906   const MatScalar   *aa = a->a,*v;
907 
908   PetscFunctionBegin;
909   if (!n) PetscFunctionReturn(0);
910 
911   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
912   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
913   tmp  = a->solve_work;
914 
915   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
916   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
917 
918   /* forward solve the lower triangular */
919   tmp[0] = b[*r++];
920   tmps   = tmp;
921   for (i=1; i<n; i++) {
922     v   = aa + ai[i] ;
923     vi  = aj + ai[i] ;
924     nz  = a->diag[i] - ai[i];
925     sum = b[*r++];
926     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
927     tmp[i] = sum;
928   }
929 
930   /* backward solve the upper triangular */
931   for (i=n-1; i>=0; i--){
932     v   = aa + a->diag[i] + 1;
933     vi  = aj + a->diag[i] + 1;
934     nz  = ai[i+1] - a->diag[i] - 1;
935     sum = tmp[i];
936     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
937     x[*c--] = tmp[i] = sum*aa[a->diag[i]];
938   }
939 
940   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
941   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
942   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
943   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
944   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
945   PetscFunctionReturn(0);
946 }
947 
948 #undef __FUNCT__
949 #define __FUNCT__ "MatMatSolve_SeqAIJ"
950 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X)
951 {
952   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
953   IS              iscol = a->col,isrow = a->row;
954   PetscErrorCode  ierr;
955   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
956   PetscInt        nz,neq;
957   const PetscInt  *rout,*cout,*r,*c;
958   PetscScalar     *x,*b,*tmp,*tmps,sum;
959   const MatScalar *aa = a->a,*v;
960   PetscTruth      bisdense,xisdense;
961 
962   PetscFunctionBegin;
963   if (!n) PetscFunctionReturn(0);
964 
965   ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr);
966   if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix");
967   ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr);
968   if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix");
969 
970   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
971   ierr = MatGetArray(X,&x);CHKERRQ(ierr);
972 
973   tmp  = a->solve_work;
974   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
975   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
976 
977   for (neq=0; neq<B->cmap->n; neq++){
978     /* forward solve the lower triangular */
979     tmp[0] = b[r[0]];
980     tmps   = tmp;
981     for (i=1; i<n; i++) {
982       v   = aa + ai[i] ;
983       vi  = aj + ai[i] ;
984       nz  = a->diag[i] - ai[i];
985       sum = b[r[i]];
986       PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
987       tmp[i] = sum;
988     }
989     /* backward solve the upper triangular */
990     for (i=n-1; i>=0; i--){
991       v   = aa + a->diag[i] + 1;
992       vi  = aj + a->diag[i] + 1;
993       nz  = ai[i+1] - a->diag[i] - 1;
994       sum = tmp[i];
995       PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
996       x[c[i]] = tmp[i] = sum*aa[a->diag[i]];
997     }
998 
999     b += n;
1000     x += n;
1001   }
1002   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1003   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1004   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
1005   ierr = MatRestoreArray(X,&x);CHKERRQ(ierr);
1006   ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr);
1007   PetscFunctionReturn(0);
1008 }
1009 
1010 #undef __FUNCT__
1011 #define __FUNCT__ "MatSolve_SeqAIJ_InplaceWithPerm"
1012 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx)
1013 {
1014   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1015   IS              iscol = a->col,isrow = a->row;
1016   PetscErrorCode  ierr;
1017   const PetscInt  *r,*c,*rout,*cout;
1018   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1019   PetscInt        nz,row;
1020   PetscScalar     *x,*b,*tmp,*tmps,sum;
1021   const MatScalar *aa = a->a,*v;
1022 
1023   PetscFunctionBegin;
1024   if (!n) PetscFunctionReturn(0);
1025 
1026   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
1027   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1028   tmp  = a->solve_work;
1029 
1030   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1031   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1032 
1033   /* forward solve the lower triangular */
1034   tmp[0] = b[*r++];
1035   tmps   = tmp;
1036   for (row=1; row<n; row++) {
1037     i   = rout[row]; /* permuted row */
1038     v   = aa + ai[i] ;
1039     vi  = aj + ai[i] ;
1040     nz  = a->diag[i] - ai[i];
1041     sum = b[*r++];
1042     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1043     tmp[row] = sum;
1044   }
1045 
1046   /* backward solve the upper triangular */
1047   for (row=n-1; row>=0; row--){
1048     i   = rout[row]; /* permuted row */
1049     v   = aa + a->diag[i] + 1;
1050     vi  = aj + a->diag[i] + 1;
1051     nz  = ai[i+1] - a->diag[i] - 1;
1052     sum = tmp[row];
1053     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1054     x[*c--] = tmp[row] = sum*aa[a->diag[i]];
1055   }
1056 
1057   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1058   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1059   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
1060   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1061   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1062   PetscFunctionReturn(0);
1063 }
1064 
1065 /* ----------------------------------------------------------- */
1066 #include "../src/mat/impls/aij/seq/ftn-kernels/fsolve.h"
1067 #undef __FUNCT__
1068 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering"
1069 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx)
1070 {
1071   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1072   PetscErrorCode    ierr;
1073   PetscInt          n = A->rmap->n;
1074   const PetscInt    *ai = a->i,*aj = a->j,*adiag = a->diag;
1075   PetscScalar       *x;
1076   const PetscScalar *b;
1077   const MatScalar   *aa = a->a;
1078 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ)
1079   PetscInt          adiag_i,i,nz,ai_i;
1080   const PetscInt    *vi;
1081   const MatScalar   *v;
1082   PetscScalar       sum;
1083 #endif
1084 
1085   PetscFunctionBegin;
1086   if (!n) PetscFunctionReturn(0);
1087 
1088   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1089   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1090 
1091 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ)
1092   fortransolveaij_(&n,x,ai,aj,adiag,aa,b);
1093 #else
1094   /* forward solve the lower triangular */
1095   x[0] = b[0];
1096   for (i=1; i<n; i++) {
1097     ai_i = ai[i];
1098     v    = aa + ai_i;
1099     vi   = aj + ai_i;
1100     nz   = adiag[i] - ai_i;
1101     sum  = b[i];
1102     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
1103     x[i] = sum;
1104   }
1105 
1106   /* backward solve the upper triangular */
1107   for (i=n-1; i>=0; i--){
1108     adiag_i = adiag[i];
1109     v       = aa + adiag_i + 1;
1110     vi      = aj + adiag_i + 1;
1111     nz      = ai[i+1] - adiag_i - 1;
1112     sum     = x[i];
1113     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
1114     x[i]    = sum*aa[adiag_i];
1115   }
1116 #endif
1117   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
1118   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1119   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1120   PetscFunctionReturn(0);
1121 }
1122 
1123 #undef __FUNCT__
1124 #define __FUNCT__ "MatSolveAdd_SeqAIJ"
1125 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx)
1126 {
1127   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1128   IS              iscol = a->col,isrow = a->row;
1129   PetscErrorCode  ierr;
1130   PetscInt        i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1131   PetscInt        nz;
1132   const PetscInt  *rout,*cout,*r,*c;
1133   PetscScalar     *x,*b,*tmp,sum;
1134   const MatScalar *aa = a->a,*v;
1135 
1136   PetscFunctionBegin;
1137   if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);}
1138 
1139   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
1140   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1141   tmp  = a->solve_work;
1142 
1143   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1144   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1145 
1146   /* forward solve the lower triangular */
1147   tmp[0] = b[*r++];
1148   for (i=1; i<n; i++) {
1149     v   = aa + ai[i] ;
1150     vi  = aj + ai[i] ;
1151     nz  = a->diag[i] - ai[i];
1152     sum = b[*r++];
1153     while (nz--) sum -= *v++ * tmp[*vi++ ];
1154     tmp[i] = sum;
1155   }
1156 
1157   /* backward solve the upper triangular */
1158   for (i=n-1; i>=0; i--){
1159     v   = aa + a->diag[i] + 1;
1160     vi  = aj + a->diag[i] + 1;
1161     nz  = ai[i+1] - a->diag[i] - 1;
1162     sum = tmp[i];
1163     while (nz--) sum -= *v++ * tmp[*vi++ ];
1164     tmp[i] = sum*aa[a->diag[i]];
1165     x[*c--] += tmp[i];
1166   }
1167 
1168   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1169   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1170   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
1171   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1172   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1173 
1174   PetscFunctionReturn(0);
1175 }
1176 /* -------------------------------------------------------------------*/
1177 #undef __FUNCT__
1178 #define __FUNCT__ "MatSolveTranspose_SeqAIJ"
1179 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx)
1180 {
1181   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1182   IS              iscol = a->col,isrow = a->row;
1183   PetscErrorCode  ierr;
1184   const PetscInt  *rout,*cout,*r,*c;
1185   PetscInt        i,n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1186   PetscInt        nz,*diag = a->diag;
1187   PetscScalar     *x,*b,*tmp,s1;
1188   const MatScalar *aa = a->a,*v;
1189 
1190   PetscFunctionBegin;
1191   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
1192   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1193   tmp  = a->solve_work;
1194 
1195   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1196   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1197 
1198   /* copy the b into temp work space according to permutation */
1199   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1200 
1201   /* forward solve the U^T */
1202   for (i=0; i<n; i++) {
1203     v   = aa + diag[i] ;
1204     vi  = aj + diag[i] + 1;
1205     nz  = ai[i+1] - diag[i] - 1;
1206     s1  = tmp[i];
1207     s1 *= (*v++);  /* multiply by inverse of diagonal entry */
1208     while (nz--) {
1209       tmp[*vi++ ] -= (*v++)*s1;
1210     }
1211     tmp[i] = s1;
1212   }
1213 
1214   /* backward solve the L^T */
1215   for (i=n-1; i>=0; i--){
1216     v   = aa + diag[i] - 1 ;
1217     vi  = aj + diag[i] - 1 ;
1218     nz  = diag[i] - ai[i];
1219     s1  = tmp[i];
1220     while (nz--) {
1221       tmp[*vi-- ] -= (*v--)*s1;
1222     }
1223   }
1224 
1225   /* copy tmp into x according to permutation */
1226   for (i=0; i<n; i++) x[r[i]] = tmp[i];
1227 
1228   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1229   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1230   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
1231   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1232 
1233   ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr);
1234   PetscFunctionReturn(0);
1235 }
1236 
1237 #undef __FUNCT__
1238 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ"
1239 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx)
1240 {
1241   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
1242   IS              iscol = a->col,isrow = a->row;
1243   PetscErrorCode  ierr;
1244   const PetscInt  *r,*c,*rout,*cout;
1245   PetscInt        i,n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1246   PetscInt        nz,*diag = a->diag;
1247   PetscScalar     *x,*b,*tmp;
1248   const MatScalar *aa = a->a,*v;
1249 
1250   PetscFunctionBegin;
1251   if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);}
1252 
1253   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
1254   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1255   tmp = a->solve_work;
1256 
1257   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1258   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1259 
1260   /* copy the b into temp work space according to permutation */
1261   for (i=0; i<n; i++) tmp[i] = b[c[i]];
1262 
1263   /* forward solve the U^T */
1264   for (i=0; i<n; i++) {
1265     v   = aa + diag[i] ;
1266     vi  = aj + diag[i] + 1;
1267     nz  = ai[i+1] - diag[i] - 1;
1268     tmp[i] *= *v++;
1269     while (nz--) {
1270       tmp[*vi++ ] -= (*v++)*tmp[i];
1271     }
1272   }
1273 
1274   /* backward solve the L^T */
1275   for (i=n-1; i>=0; i--){
1276     v   = aa + diag[i] - 1 ;
1277     vi  = aj + diag[i] - 1 ;
1278     nz  = diag[i] - ai[i];
1279     while (nz--) {
1280       tmp[*vi-- ] -= (*v--)*tmp[i];
1281     }
1282   }
1283 
1284   /* copy tmp into x according to permutation */
1285   for (i=0; i<n; i++) x[r[i]] += tmp[i];
1286 
1287   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1288   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1289   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
1290   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1291 
1292   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1293   PetscFunctionReturn(0);
1294 }
1295 /* ----------------------------------------------------------------*/
1296 EXTERN PetscErrorCode Mat_CheckInode(Mat,PetscTruth);
1297 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption,PetscTruth);
1298 
1299 /*
1300    ilu(0) with natural ordering under new data structure.
1301    Factored arrays bj and ba are stored as
1302      L(0,:), L(1,:), ...,L(n-1,:),  U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:)
1303 
1304    bi=fact->i is an array of size 2n+2, in which
1305    bi+
1306      bi[i]      ->  1st entry of L(i,:),i=0,...,i-1
1307      bi[n]      ->  points to L(n-1,:)+1
1308      bi[n+1]    ->  1st entry of U(n-1,:)
1309      bi[2n-i]   ->  1st entry of U(i,:)
1310      bi[2n-i+1] ->  end of U(i,:)+1, the 1st entry of U(i-1,:)
1311      bi[2n]     ->  1st entry of U(0,:)
1312      bi[2n+1]   ->  points to U(0,:)+1
1313 
1314    U(i,:) contains diag[i] as its last entry, i.e.,
1315     U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i])
1316 */
1317 #undef __FUNCT__
1318 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct"
1319 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1320 {
1321 
1322   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1323   PetscErrorCode     ierr;
1324   PetscInt           n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag;
1325   PetscInt           i,j,nz,*bi,*bj,*bdiag;
1326 
1327   PetscFunctionBegin;
1328   ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr);
1329   b    = (Mat_SeqAIJ*)(fact)->data;
1330 
1331   /* allocate matrix arrays for new data structure */
1332   ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,2*n+2,PetscInt,&b->i);CHKERRQ(ierr);
1333   ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(2*n+2)*sizeof(PetscInt));CHKERRQ(ierr);
1334   b->singlemalloc = PETSC_TRUE;
1335   if (!b->diag){
1336     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr);
1337   }
1338   bdiag = b->diag;
1339 
1340   if (n > 0) {
1341     ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr);
1342   }
1343 
1344   /* set bi and bj with new data structure */
1345   bi = b->i;
1346   bj = b->j;
1347 
1348   /* L part */
1349   bi[0] = 0;
1350   for (i=0; i<n; i++){
1351     nz = adiag[i] - ai[i];
1352     bi[i+1] = bi[i] + nz;
1353     aj = a->j + ai[i];
1354     for (j=0; j<nz; j++){
1355       *bj = aj[j]; bj++;
1356     }
1357   }
1358 
1359   /* U part */
1360   bi[n+1] = bi[n];
1361   for (i=n-1; i>=0; i--){
1362     nz = ai[i+1] - adiag[i] - 1;
1363     bi[2*n-i+1] = bi[2*n-i] + nz + 1;
1364     aj = a->j + adiag[i] + 1;
1365     for (j=0; j<nz; j++){
1366       *bj = aj[j]; bj++;
1367     }
1368     /* diag[i] */
1369     *bj = i; bj++;
1370     bdiag[i] = bi[2*n-i+1]-1;
1371   }
1372   PetscFunctionReturn(0);
1373 }
1374 
1375 #undef __FUNCT__
1376 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_newdatastruct"
1377 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1378 {
1379   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1380   IS                 isicol;
1381   PetscErrorCode     ierr;
1382   const PetscInt     *r,*ic;
1383   PetscInt           n=A->rmap->n,*ai=a->i,*aj=a->j,d;
1384   PetscInt           *bi,*cols,nnz,*cols_lvl;
1385   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1386   PetscInt           i,levels,diagonal_fill;
1387   PetscTruth         col_identity,row_identity;
1388   PetscReal          f;
1389   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
1390   PetscBT            lnkbt;
1391   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
1392   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1393   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1394   PetscTruth         missing;
1395 
1396   PetscFunctionBegin;
1397   //printf("MatILUFactorSymbolic_SeqAIJ_newdatastruct ...\n");
1398   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);
1399   f             = info->fill;
1400   levels        = (PetscInt)info->levels;
1401   diagonal_fill = (PetscInt)info->diagonal_fill;
1402   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1403 
1404   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1405   ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
1406 
1407   if (!levels && row_identity && col_identity) {
1408     /* special case: ilu(0) with natural ordering */
1409     ierr = MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1410     (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ_newdatastruct;
1411 
1412     fact->factor = MAT_FACTOR_ILU;
1413     (fact)->info.factor_mallocs    = 0;
1414     (fact)->info.fill_ratio_given  = info->fill;
1415     (fact)->info.fill_ratio_needed = 1.0;
1416     b               = (Mat_SeqAIJ*)(fact)->data;
1417     ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
1418     if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
1419     b->row              = isrow;
1420     b->col              = iscol;
1421     b->icol             = isicol;
1422     ierr                = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1423     ierr                = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1424     ierr                = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1425     /* ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */
1426     PetscFunctionReturn(0);
1427   }
1428 
1429   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1430   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1431 
1432   /* get new row pointers */
1433   ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1434   bi[0] = 0;
1435   /* bdiag is location of diagonal in factor */
1436   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
1437   bdiag[0]  = 0;
1438 
1439   ierr = PetscMalloc((2*n+1)*sizeof(PetscInt**),&bj_ptr);CHKERRQ(ierr);
1440   bjlvl_ptr = (PetscInt**)(bj_ptr + n);
1441 
1442   /* create a linked list for storing column indices of the active row */
1443   nlnk = n + 1;
1444   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1445 
1446   /* initial FreeSpace size is f*(ai[n]+1) */
1447   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
1448   current_space = free_space;
1449   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
1450   current_space_lvl = free_space_lvl;
1451 
1452   for (i=0; i<n; i++) {
1453     nzi = 0;
1454     /* copy current row into linked list */
1455     nnz  = ai[r[i]+1] - ai[r[i]];
1456     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1457     cols = aj + ai[r[i]];
1458     lnk[i] = -1; /* marker to indicate if diagonal exists */
1459     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1460     nzi += nlnk;
1461 
1462     /* make sure diagonal entry is included */
1463     if (diagonal_fill && lnk[i] == -1) {
1464       fm = n;
1465       while (lnk[fm] < i) fm = lnk[fm];
1466       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
1467       lnk[fm]    = i;
1468       lnk_lvl[i] = 0;
1469       nzi++; dcount++;
1470     }
1471 
1472     /* add pivot rows into the active row */
1473     nzbd = 0;
1474     prow = lnk[n];
1475     while (prow < i) {
1476       nnz      = bdiag[prow];
1477       cols     = bj_ptr[prow] + nnz + 1;
1478       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1479       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
1480       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
1481       nzi += nlnk;
1482       prow = lnk[prow];
1483       nzbd++;
1484     }
1485     bdiag[i] = nzbd;
1486     bi[i+1]  = bi[i] + nzi;
1487 
1488     /* if free space is not available, make more free space */
1489     if (current_space->local_remaining<nzi) {
1490       nnz = 2*nzi*(n - i); /* estimated and max additional space needed */
1491       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
1492       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
1493       reallocs++;
1494     }
1495 
1496     /* copy data into free_space and free_space_lvl, then initialize lnk */
1497     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1498     bj_ptr[i]    = current_space->array;
1499     bjlvl_ptr[i] = current_space_lvl->array;
1500 
1501     /* make sure the active row i has diagonal entry */
1502     if (*(bj_ptr[i]+bdiag[i]) != i) {
1503       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
1504     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
1505     }
1506 
1507     current_space->array           += nzi;
1508     current_space->local_used      += nzi;
1509     current_space->local_remaining -= nzi;
1510     current_space_lvl->array           += nzi;
1511     current_space_lvl->local_used      += nzi;
1512     current_space_lvl->local_remaining -= nzi;
1513   }
1514 
1515   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1516   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1517 
1518   /* destroy list of free space and other temporary arrays */
1519   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
1520 
1521   /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */
1522   ierr = PetscFreeSpaceContiguous_newdatastruct(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr);
1523 
1524   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1525   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
1526   ierr = PetscFree(bj_ptr);CHKERRQ(ierr);
1527 
1528 #if defined(PETSC_USE_INFO)
1529   {
1530     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1531     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
1532     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
1533     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
1534     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
1535     if (diagonal_fill) {
1536       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
1537     }
1538   }
1539 #endif
1540 
1541   /* put together the new matrix */
1542   ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
1543   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
1544   b = (Mat_SeqAIJ*)(fact)->data;
1545   b->free_a       = PETSC_TRUE;
1546   b->free_ij      = PETSC_TRUE;
1547   b->singlemalloc = PETSC_FALSE;
1548   ierr = PetscMalloc( (bi[2*n+1] )*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
1549   b->j          = bj;
1550   b->i          = bi;
1551   b->diag       = bdiag;
1552   b->ilen       = 0;
1553   b->imax       = 0;
1554   b->row        = isrow;
1555   b->col        = iscol;
1556   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1557   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1558   b->icol       = isicol;
1559   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1560   /* In b structure:  Free imax, ilen, old a, old j.
1561      Allocate bdiag, solve_work, new a, new j */
1562   ierr = PetscLogObjectMemory(fact,bi[2*n+1] * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
1563   b->maxnz = b->nz = bi[2*n+1] ;
1564   (fact)->info.factor_mallocs    = reallocs;
1565   (fact)->info.fill_ratio_given  = f;
1566   (fact)->info.fill_ratio_needed = ((PetscReal)bi[2*n+1])/((PetscReal)ai[n]);
1567   (fact)->ops->lufactornumeric   = MatLUFactorNumeric_SeqAIJ_newdatastruct;
1568   /* ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */
1569   PetscFunctionReturn(0);
1570 }
1571 
1572 #undef __FUNCT__
1573 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ"
1574 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1575 {
1576   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b;
1577   IS                 isicol;
1578   PetscErrorCode     ierr;
1579   const PetscInt     *r,*ic;
1580   PetscInt           n=A->rmap->n,*ai=a->i,*aj=a->j,d;
1581   PetscInt           *bi,*cols,nnz,*cols_lvl;
1582   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1583   PetscInt           i,levels,diagonal_fill;
1584   PetscTruth         col_identity,row_identity;
1585   PetscReal          f;
1586   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
1587   PetscBT            lnkbt;
1588   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
1589   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1590   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
1591   PetscTruth         missing;
1592   PetscTruth         newdatastruct=PETSC_FALSE;
1593 
1594   PetscFunctionBegin;
1595   ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
1596   if (newdatastruct){
1597     ierr = MatILUFactorSymbolic_SeqAIJ_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1598     PetscFunctionReturn(0);
1599   }
1600 
1601   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);
1602   f             = info->fill;
1603   levels        = (PetscInt)info->levels;
1604   diagonal_fill = (PetscInt)info->diagonal_fill;
1605   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1606 
1607   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1608   ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
1609   if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */
1610     ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr);
1611     (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ;
1612 
1613     fact->factor = MAT_FACTOR_ILU;
1614     (fact)->info.factor_mallocs    = 0;
1615     (fact)->info.fill_ratio_given  = info->fill;
1616     (fact)->info.fill_ratio_needed = 1.0;
1617     b               = (Mat_SeqAIJ*)(fact)->data;
1618     ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
1619     if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
1620     b->row              = isrow;
1621     b->col              = iscol;
1622     b->icol             = isicol;
1623     ierr                = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1624     ierr                = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1625     ierr                = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1626     ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1627     PetscFunctionReturn(0);
1628   }
1629 
1630   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1631   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1632 
1633   /* get new row pointers */
1634   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1635   bi[0] = 0;
1636   /* bdiag is location of diagonal in factor */
1637   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
1638   bdiag[0]  = 0;
1639 
1640   ierr = PetscMalloc((2*n+1)*sizeof(PetscInt**),&bj_ptr);CHKERRQ(ierr);
1641   bjlvl_ptr = (PetscInt**)(bj_ptr + n);
1642 
1643   /* create a linked list for storing column indices of the active row */
1644   nlnk = n + 1;
1645   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1646 
1647   /* initial FreeSpace size is f*(ai[n]+1) */
1648   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
1649   current_space = free_space;
1650   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
1651   current_space_lvl = free_space_lvl;
1652 
1653   for (i=0; i<n; i++) {
1654     nzi = 0;
1655     /* copy current row into linked list */
1656     nnz  = ai[r[i]+1] - ai[r[i]];
1657     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1658     cols = aj + ai[r[i]];
1659     lnk[i] = -1; /* marker to indicate if diagonal exists */
1660     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1661     nzi += nlnk;
1662 
1663     /* make sure diagonal entry is included */
1664     if (diagonal_fill && lnk[i] == -1) {
1665       fm = n;
1666       while (lnk[fm] < i) fm = lnk[fm];
1667       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
1668       lnk[fm]    = i;
1669       lnk_lvl[i] = 0;
1670       nzi++; dcount++;
1671     }
1672 
1673     /* add pivot rows into the active row */
1674     nzbd = 0;
1675     prow = lnk[n];
1676     while (prow < i) {
1677       nnz      = bdiag[prow];
1678       cols     = bj_ptr[prow] + nnz + 1;
1679       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1680       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
1681       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
1682       nzi += nlnk;
1683       prow = lnk[prow];
1684       nzbd++;
1685     }
1686     bdiag[i] = nzbd;
1687     bi[i+1]  = bi[i] + nzi;
1688 
1689     /* if free space is not available, make more free space */
1690     if (current_space->local_remaining<nzi) {
1691       nnz = nzi*(n - i); /* estimated and max additional space needed */
1692       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
1693       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
1694       reallocs++;
1695     }
1696 
1697     /* copy data into free_space and free_space_lvl, then initialize lnk */
1698     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1699     bj_ptr[i]    = current_space->array;
1700     bjlvl_ptr[i] = current_space_lvl->array;
1701 
1702     /* make sure the active row i has diagonal entry */
1703     if (*(bj_ptr[i]+bdiag[i]) != i) {
1704       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
1705     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
1706     }
1707 
1708     current_space->array           += nzi;
1709     current_space->local_used      += nzi;
1710     current_space->local_remaining -= nzi;
1711     current_space_lvl->array           += nzi;
1712     current_space_lvl->local_used      += nzi;
1713     current_space_lvl->local_remaining -= nzi;
1714   }
1715 
1716   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1717   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1718 
1719   /* destroy list of free space and other temporary arrays */
1720   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
1721   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */
1722   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1723   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
1724   ierr = PetscFree(bj_ptr);CHKERRQ(ierr);
1725 
1726 #if defined(PETSC_USE_INFO)
1727   {
1728     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1729     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
1730     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
1731     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
1732     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
1733     if (diagonal_fill) {
1734       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
1735     }
1736   }
1737 #endif
1738 
1739   /* put together the new matrix */
1740   ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
1741   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
1742   b = (Mat_SeqAIJ*)(fact)->data;
1743   b->free_a       = PETSC_TRUE;
1744   b->free_ij      = PETSC_TRUE;
1745   b->singlemalloc = PETSC_FALSE;
1746   ierr = PetscMalloc( (bi[n] )*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);
1747   b->j          = bj;
1748   b->i          = bi;
1749   for (i=0; i<n; i++) bdiag[i] += bi[i];
1750   b->diag       = bdiag;
1751   b->ilen       = 0;
1752   b->imax       = 0;
1753   b->row        = isrow;
1754   b->col        = iscol;
1755   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1756   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1757   b->icol       = isicol;
1758   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1759   /* In b structure:  Free imax, ilen, old a, old j.
1760      Allocate bdiag, solve_work, new a, new j */
1761   ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr);
1762   b->maxnz             = b->nz = bi[n] ;
1763   (fact)->info.factor_mallocs    = reallocs;
1764   (fact)->info.fill_ratio_given  = f;
1765   (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1766   (fact)->ops->lufactornumeric =  MatLUFactorNumeric_SeqAIJ;
1767   ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr);
1768   PetscFunctionReturn(0);
1769 }
1770 
1771 #include "../src/mat/impls/sbaij/seq/sbaij.h"
1772 #undef __FUNCT__
1773 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ_newdatastruct"
1774 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info)
1775 {
1776   Mat            C = B;
1777   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1778   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
1779   IS             ip=b->row,iip = b->icol;
1780   PetscErrorCode ierr;
1781   const PetscInt *rip,*riip;
1782   PetscInt       i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp;
1783   PetscInt       *ai=a->i,*aj=a->j;
1784   PetscInt       k,jmin,jmax,*c2r,*il,col,nexti,ili,nz;
1785   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
1786   PetscReal      zeropivot,shiftnz;
1787   PetscReal      shiftpd;
1788   PetscTruth     perm_identity;
1789 
1790   PetscFunctionBegin;
1791 
1792   shiftnz   = info->shiftnz;
1793   shiftpd   = info->shiftpd;
1794   zeropivot = info->zeropivot;
1795 
1796   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
1797   ierr  = ISGetIndices(iip,&riip);CHKERRQ(ierr);
1798 
1799   /* allocate working arrays
1800      c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col
1801      il:  for active k row, il[i] gives the index of the 1st nonzero entry in U[i,k:n-1] in bj and ba arrays
1802   */
1803   nz   = (2*mbs+1)*sizeof(PetscInt)+mbs*sizeof(MatScalar);
1804   ierr = PetscMalloc(nz,&il);CHKERRQ(ierr);
1805   c2r  = il + mbs;
1806   rtmp = (MatScalar*)(c2r + mbs);
1807 
1808   for (i=0; i<mbs; i++) {
1809     c2r[i] = mbs;
1810   }
1811   il[0] = 0;
1812 
1813   for (k = 0; k<mbs; k++){
1814     /* zero rtmp */
1815     nz = bi[k+1] - bi[k];
1816     bjtmp = bj + bi[k];
1817     for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
1818 
1819     /* load in initial unfactored row */
1820     bval = ba + bi[k];
1821     jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
1822     for (j = jmin; j < jmax; j++){
1823       col = riip[aj[j]];
1824       if (col >= k){ /* only take upper triangular entry */
1825         rtmp[col] = aa[j];
1826         *bval++   = 0.0; /* for in-place factorization */
1827       }
1828     }
1829     /* shift the diagonal of the matrix */
1830 
1831     /* modify k-th row by adding in those rows i with U(i,k)!=0 */
1832     dk = rtmp[k];
1833     i  = c2r[k]; /* first row to be added to k_th row  */
1834 
1835     while (i < k){
1836       nexti = c2r[i]; /* next row to be added to k_th row */
1837 
1838       /* compute multiplier, update diag(k) and U(i,k) */
1839       ili   = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
1840       uikdi = - ba[ili]*ba[bdiag[i]];  /* diagonal(k) */
1841       dk   += uikdi*ba[ili]; /* update diag[k] */
1842       ba[ili] = uikdi; /* -U(i,k) */
1843 
1844       /* add multiple of row i to k-th row */
1845       jmin = ili + 1; jmax = bi[i+1];
1846       if (jmin < jmax){
1847         for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
1848         /* update il and c2r for row i */
1849         il[i] = jmin;
1850         j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i;
1851       }
1852       i = nexti;
1853     }
1854 
1855     /* copy data into U(k,:) */
1856     ba[bdiag[k]] = 1.0/dk; /* U(k,k) */
1857     jmin = bi[k]; jmax = bi[k+1]-1;
1858     if (jmin < jmax) {
1859       for (j=jmin; j<jmax; j++){
1860         col = bj[j]; ba[j] = rtmp[col];
1861       }
1862       /* add the k-th row into il and c2r */
1863       il[k] = jmin;
1864       i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k;
1865     }
1866   }
1867 
1868   ierr = PetscFree(il);CHKERRQ(ierr);
1869   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
1870   ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr);
1871 
1872   ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
1873   if (perm_identity){
1874     (B)->ops->solve           = MatSolve_SeqSBAIJ_1_NaturalOrdering_newdatastruct;
1875     (B)->ops->solvetranspose  = 0;
1876     (B)->ops->forwardsolve    = 0;
1877     (B)->ops->backwardsolve   = 0;
1878   } else {
1879     (B)->ops->solve           = 0;
1880     (B)->ops->solvetranspose  = 0;
1881     (B)->ops->forwardsolve    = 0;
1882     (B)->ops->backwardsolve   = 0;
1883   }
1884 
1885   C->assembled    = PETSC_TRUE;
1886   C->preallocated = PETSC_TRUE;
1887   ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr);
1888   PetscFunctionReturn(0);
1889 }
1890 
1891 #undef __FUNCT__
1892 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ"
1893 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info)
1894 {
1895   Mat            C = B;
1896   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1897   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
1898   IS             ip=b->row,iip = b->icol;
1899   PetscErrorCode ierr;
1900   const PetscInt *rip,*riip;
1901   PetscInt       i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol;
1902   PetscInt       *ai=a->i,*aj=a->j;
1903   PetscInt       k,jmin,jmax,*jl,*il,col,nexti,ili,nz;
1904   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
1905   PetscReal      zeropivot,rs,shiftnz;
1906   PetscReal      shiftpd;
1907   ChShift_Ctx    sctx;
1908   PetscInt       newshift;
1909   PetscTruth     perm_identity;
1910 
1911   PetscFunctionBegin;
1912   shiftnz   = info->shiftnz;
1913   shiftpd   = info->shiftpd;
1914   zeropivot = info->zeropivot;
1915 
1916   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
1917   ierr  = ISGetIndices(iip,&riip);CHKERRQ(ierr);
1918 
1919   /* initialization */
1920   nz   = (2*mbs+1)*sizeof(PetscInt)+mbs*sizeof(MatScalar);
1921   ierr = PetscMalloc(nz,&il);CHKERRQ(ierr);
1922   jl   = il + mbs;
1923   rtmp = (MatScalar*)(jl + mbs);
1924 
1925   sctx.shift_amount = 0;
1926   sctx.nshift       = 0;
1927   do {
1928     sctx.chshift = PETSC_FALSE;
1929     for (i=0; i<mbs; i++) {
1930       rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0;
1931     }
1932 
1933     for (k = 0; k<mbs; k++){
1934       bval = ba + bi[k];
1935       /* initialize k-th row by the perm[k]-th row of A */
1936       jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
1937       for (j = jmin; j < jmax; j++){
1938         col = riip[aj[j]];
1939         if (col >= k){ /* only take upper triangular entry */
1940           rtmp[col] = aa[j];
1941           *bval++  = 0.0; /* for in-place factorization */
1942         }
1943       }
1944       /* shift the diagonal of the matrix */
1945       if (sctx.nshift) rtmp[k] += sctx.shift_amount;
1946 
1947       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
1948       dk = rtmp[k];
1949       i = jl[k]; /* first row to be added to k_th row  */
1950 
1951       while (i < k){
1952         nexti = jl[i]; /* next row to be added to k_th row */
1953 
1954         /* compute multiplier, update diag(k) and U(i,k) */
1955         ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
1956         uikdi = - ba[ili]*ba[bi[i]];  /* diagonal(k) */
1957         dk += uikdi*ba[ili];
1958         ba[ili] = uikdi; /* -U(i,k) */
1959 
1960         /* add multiple of row i to k-th row */
1961         jmin = ili + 1; jmax = bi[i+1];
1962         if (jmin < jmax){
1963           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
1964           /* update il and jl for row i */
1965           il[i] = jmin;
1966           j = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
1967         }
1968         i = nexti;
1969       }
1970 
1971       /* shift the diagonals when zero pivot is detected */
1972       /* compute rs=sum of abs(off-diagonal) */
1973       rs   = 0.0;
1974       jmin = bi[k]+1;
1975       nz   = bi[k+1] - jmin;
1976       bcol = bj + jmin;
1977       while (nz--){
1978         rs += PetscAbsScalar(rtmp[*bcol]);
1979         bcol++;
1980       }
1981 
1982       sctx.rs = rs;
1983       sctx.pv = dk;
1984       ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr);
1985 
1986       if (newshift == 1) {
1987         if (!sctx.shift_amount) {
1988           sctx.shift_amount = 1e-5;
1989         }
1990         break;
1991       }
1992 
1993       /* copy data into U(k,:) */
1994       ba[bi[k]] = 1.0/dk; /* U(k,k) */
1995       jmin = bi[k]+1; jmax = bi[k+1];
1996       if (jmin < jmax) {
1997         for (j=jmin; j<jmax; j++){
1998           col = bj[j]; ba[j] = rtmp[col]; rtmp[col] = 0.0;
1999         }
2000         /* add the k-th row into il and jl */
2001         il[k] = jmin;
2002         i = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
2003       }
2004     }
2005   } while (sctx.chshift);
2006   ierr = PetscFree(il);CHKERRQ(ierr);
2007 
2008   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2009   ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr);
2010 
2011   ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
2012   if (perm_identity){
2013     (B)->ops->solve           = MatSolve_SeqSBAIJ_1_NaturalOrdering;
2014     (B)->ops->solvetranspose  = MatSolve_SeqSBAIJ_1_NaturalOrdering;
2015     (B)->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering;
2016     (B)->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering;
2017   } else {
2018     (B)->ops->solve           = MatSolve_SeqSBAIJ_1;
2019     (B)->ops->solvetranspose  = MatSolve_SeqSBAIJ_1;
2020     (B)->ops->forwardsolve    = MatForwardSolve_SeqSBAIJ_1;
2021     (B)->ops->backwardsolve   = MatBackwardSolve_SeqSBAIJ_1;
2022   }
2023 
2024   C->assembled    = PETSC_TRUE;
2025   C->preallocated = PETSC_TRUE;
2026   ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr);
2027   if (sctx.nshift){
2028     if (shiftnz) {
2029       ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2030     } else if (shiftpd) {
2031       ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
2032     }
2033   }
2034   PetscFunctionReturn(0);
2035 }
2036 
2037 #undef __FUNCT__
2038 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ_newdatastruct"
2039 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2040 {
2041   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2042   Mat_SeqSBAIJ       *b;
2043   PetscErrorCode     ierr;
2044   PetscTruth         perm_identity,missing;
2045   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag;
2046   const PetscInt     *rip,*riip;
2047   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
2048   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL,d;
2049   PetscInt           ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
2050   PetscReal          fill=info->fill,levels=info->levels;
2051   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2052   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
2053   PetscBT            lnkbt;
2054   IS                 iperm;
2055 
2056   PetscFunctionBegin;
2057   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);
2058   ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
2059   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
2060   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2061   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2062 
2063   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2064   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2065   ui[0] = 0;
2066 
2067   /* ICC(0) without matrix ordering: simply copies fill pattern */
2068   if (!levels && perm_identity) {
2069 
2070     for (i=0; i<am; i++) {
2071       ui[i+1]  = ui[i] + ai[i+1] - a->diag[i];
2072       udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */
2073     }
2074     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2075     cols = uj;
2076     for (i=0; i<am; i++) {
2077       aj    = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */
2078       ncols = ui[i+1] - ui[i] - 1;
2079       for (j=0; j<ncols; j++) *cols++ = aj[j];
2080       *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */
2081     }
2082   } else { /* case: levels>0 || (levels=0 && !perm_identity) */
2083     SETERRQ(1,"Not done yet");
2084     ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2085     ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2086 
2087     /* initialization */
2088     ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr);
2089 
2090     /* jl: linked list for storing indices of the pivot rows
2091        il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2092     ierr = PetscMalloc((2*am+1)*sizeof(PetscInt)+2*am*sizeof(PetscInt**),&jl);CHKERRQ(ierr);
2093     il         = jl + am;
2094     uj_ptr     = (PetscInt**)(il + am);
2095     uj_lvl_ptr = (PetscInt**)(uj_ptr + am);
2096     for (i=0; i<am; i++){
2097       jl[i] = am; il[i] = 0;
2098     }
2099 
2100     /* create and initialize a linked list for storing column indices of the active row k */
2101     nlnk = am + 1;
2102     ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2103 
2104     /* initial FreeSpace size is fill*(ai[am]+1) */
2105     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2106     current_space = free_space;
2107     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr);
2108     current_space_lvl = free_space_lvl;
2109 
2110     for (k=0; k<am; k++){  /* for each active row k */
2111       /* initialize lnk by the column indices of row rip[k] of A */
2112       nzk   = 0;
2113       ncols = ai[rip[k]+1] - ai[rip[k]];
2114       if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2115       ncols_upper = 0;
2116       for (j=0; j<ncols; j++){
2117         i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2118         if (riip[i] >= k){ /* only take upper triangular entry */
2119           ajtmp[ncols_upper] = i;
2120           ncols_upper++;
2121         }
2122       }
2123       ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2124       nzk += nlnk;
2125 
2126       /* update lnk by computing fill-in for each pivot row to be merged in */
2127       prow = jl[k]; /* 1st pivot row */
2128 
2129       while (prow < k){
2130         nextprow = jl[prow];
2131 
2132         /* merge prow into k-th row */
2133         jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2134         jmax = ui[prow+1];
2135         ncols = jmax-jmin;
2136         i     = jmin - ui[prow];
2137         cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2138         uj    = uj_lvl_ptr[prow] + i; /* levels of cols */
2139         j     = *(uj - 1);
2140         ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr);
2141         nzk += nlnk;
2142 
2143         /* update il and jl for prow */
2144         if (jmin < jmax){
2145           il[prow] = jmin;
2146           j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2147         }
2148         prow = nextprow;
2149       }
2150 
2151       /* if free space is not available, make more free space */
2152       if (current_space->local_remaining<nzk) {
2153         i = am - k + 1; /* num of unfactored rows */
2154         i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2155         ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2156         ierr = PetscFreeSpaceGet(i,&current_space_lvl);CHKERRQ(ierr);
2157         reallocs++;
2158       }
2159 
2160       /* copy data into free_space and free_space_lvl, then initialize lnk */
2161       if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2162       ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
2163 
2164       /* add the k-th row into il and jl */
2165       if (nzk > 1){
2166         i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2167         jl[k] = jl[i]; jl[i] = k;
2168         il[k] = ui[k] + 1;
2169       }
2170       uj_ptr[k]     = current_space->array;
2171       uj_lvl_ptr[k] = current_space_lvl->array;
2172 
2173       current_space->array           += nzk;
2174       current_space->local_used      += nzk;
2175       current_space->local_remaining -= nzk;
2176 
2177       current_space_lvl->array           += nzk;
2178       current_space_lvl->local_used      += nzk;
2179       current_space_lvl->local_remaining -= nzk;
2180 
2181       ui[k+1] = ui[k] + nzk;
2182     }
2183 
2184 #if defined(PETSC_USE_INFO)
2185     if (ai[am] != 0) {
2186       PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]);
2187       ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2188       ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2189       ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2190     } else {
2191       ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2192     }
2193 #endif
2194 
2195     ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2196     ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2197     ierr = PetscFree(jl);CHKERRQ(ierr);
2198     ierr = PetscFree(ajtmp);CHKERRQ(ierr);
2199 
2200     /* destroy list of free space and other temporary array(s) */
2201     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2202     ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
2203     ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2204     ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2205 
2206   } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2207 
2208   /* put together the new matrix in MATSEQSBAIJ format */
2209 
2210   b    = (Mat_SeqSBAIJ*)(fact)->data;
2211   b->singlemalloc = PETSC_FALSE;
2212   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2213   b->j    = uj;
2214   b->i    = ui;
2215   b->diag = udiag;
2216   b->ilen = 0;
2217   b->imax = 0;
2218   b->row  = perm;
2219   b->col  = perm;
2220   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2221   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2222   b->icol = iperm;
2223   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2224   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2225   ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2226   b->maxnz   = b->nz = ui[am];
2227   b->free_a  = PETSC_TRUE;
2228   b->free_ij = PETSC_TRUE;
2229 
2230   (fact)->info.factor_mallocs    = reallocs;
2231   (fact)->info.fill_ratio_given  = fill;
2232   if (ai[am] != 0) {
2233     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2234   } else {
2235     (fact)->info.fill_ratio_needed = 0.0;
2236   }
2237   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_newdatastruct;
2238   PetscFunctionReturn(0);
2239 }
2240 
2241 #undef __FUNCT__
2242 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ"
2243 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2244 {
2245   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2246   Mat_SeqSBAIJ       *b;
2247   PetscErrorCode     ierr;
2248   PetscTruth         perm_identity,missing;
2249   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag;
2250   const PetscInt     *rip,*riip;
2251   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
2252   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL,d;
2253   PetscInt           ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
2254   PetscReal          fill=info->fill,levels=info->levels;
2255   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2256   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
2257   PetscBT            lnkbt;
2258   IS                 iperm;
2259   PetscTruth         newdatastruct=PETSC_FALSE;
2260 
2261   PetscFunctionBegin;
2262   ierr = PetscOptionsGetTruth(PETSC_NULL,"-icc_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
2263   if(newdatastruct){
2264     ierr = MatICCFactorSymbolic_SeqAIJ_newdatastruct(fact,A,perm,info);CHKERRQ(ierr);
2265     PetscFunctionReturn(0);
2266   }
2267 
2268   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);
2269   ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
2270   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
2271   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2272   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2273 
2274   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2275   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr);
2276   ui[0] = 0;
2277 
2278   /* ICC(0) without matrix ordering: simply copies fill pattern */
2279   if (!levels && perm_identity) {
2280 
2281     for (i=0; i<am; i++) {
2282       ui[i+1]  = ui[i] + ai[i+1] - a->diag[i];
2283       udiag[i] = ui[i];
2284     }
2285     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2286     cols = uj;
2287     for (i=0; i<am; i++) {
2288       aj    = a->j + a->diag[i];
2289       ncols = ui[i+1] - ui[i];
2290       for (j=0; j<ncols; j++) *cols++ = *aj++;
2291     }
2292   } else { /* case: levels>0 || (levels=0 && !perm_identity) */
2293     ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2294     ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2295 
2296     /* initialization */
2297     ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr);
2298 
2299     /* jl: linked list for storing indices of the pivot rows
2300        il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2301     ierr = PetscMalloc((2*am+1)*sizeof(PetscInt)+2*am*sizeof(PetscInt**),&jl);CHKERRQ(ierr);
2302     il         = jl + am;
2303     uj_ptr     = (PetscInt**)(il + am);
2304     uj_lvl_ptr = (PetscInt**)(uj_ptr + am);
2305     for (i=0; i<am; i++){
2306       jl[i] = am; il[i] = 0;
2307     }
2308 
2309     /* create and initialize a linked list for storing column indices of the active row k */
2310     nlnk = am + 1;
2311     ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2312 
2313     /* initial FreeSpace size is fill*(ai[am]+1) */
2314     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2315     current_space = free_space;
2316     ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr);
2317     current_space_lvl = free_space_lvl;
2318 
2319     for (k=0; k<am; k++){  /* for each active row k */
2320       /* initialize lnk by the column indices of row rip[k] of A */
2321       nzk   = 0;
2322       ncols = ai[rip[k]+1] - ai[rip[k]];
2323       if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2324       ncols_upper = 0;
2325       for (j=0; j<ncols; j++){
2326         i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2327         if (riip[i] >= k){ /* only take upper triangular entry */
2328           ajtmp[ncols_upper] = i;
2329           ncols_upper++;
2330         }
2331       }
2332       ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
2333       nzk += nlnk;
2334 
2335       /* update lnk by computing fill-in for each pivot row to be merged in */
2336       prow = jl[k]; /* 1st pivot row */
2337 
2338       while (prow < k){
2339         nextprow = jl[prow];
2340 
2341         /* merge prow into k-th row */
2342         jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2343         jmax = ui[prow+1];
2344         ncols = jmax-jmin;
2345         i     = jmin - ui[prow];
2346         cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2347         uj    = uj_lvl_ptr[prow] + i; /* levels of cols */
2348         j     = *(uj - 1);
2349         ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr);
2350         nzk += nlnk;
2351 
2352         /* update il and jl for prow */
2353         if (jmin < jmax){
2354           il[prow] = jmin;
2355           j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2356         }
2357         prow = nextprow;
2358       }
2359 
2360       /* if free space is not available, make more free space */
2361       if (current_space->local_remaining<nzk) {
2362         i = am - k + 1; /* num of unfactored rows */
2363         i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2364         ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2365         ierr = PetscFreeSpaceGet(i,&current_space_lvl);CHKERRQ(ierr);
2366         reallocs++;
2367       }
2368 
2369       /* copy data into free_space and free_space_lvl, then initialize lnk */
2370       if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2371       ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
2372 
2373       /* add the k-th row into il and jl */
2374       if (nzk > 1){
2375         i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2376         jl[k] = jl[i]; jl[i] = k;
2377         il[k] = ui[k] + 1;
2378       }
2379       uj_ptr[k]     = current_space->array;
2380       uj_lvl_ptr[k] = current_space_lvl->array;
2381 
2382       current_space->array           += nzk;
2383       current_space->local_used      += nzk;
2384       current_space->local_remaining -= nzk;
2385 
2386       current_space_lvl->array           += nzk;
2387       current_space_lvl->local_used      += nzk;
2388       current_space_lvl->local_remaining -= nzk;
2389 
2390       ui[k+1] = ui[k] + nzk;
2391     }
2392 
2393 #if defined(PETSC_USE_INFO)
2394     if (ai[am] != 0) {
2395       PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]);
2396       ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2397       ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2398       ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2399     } else {
2400       ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2401     }
2402 #endif
2403 
2404     ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2405     ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2406     ierr = PetscFree(jl);CHKERRQ(ierr);
2407     ierr = PetscFree(ajtmp);CHKERRQ(ierr);
2408 
2409     /* destroy list of free space and other temporary array(s) */
2410     ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2411     ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
2412     ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2413     ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
2414 
2415   } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2416 
2417   /* put together the new matrix in MATSEQSBAIJ format */
2418 
2419   b    = (Mat_SeqSBAIJ*)(fact)->data;
2420   b->singlemalloc = PETSC_FALSE;
2421   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2422   b->j    = uj;
2423   b->i    = ui;
2424   b->diag = udiag;
2425   b->ilen = 0;
2426   b->imax = 0;
2427   b->row  = perm;
2428   b->col  = perm;
2429   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2430   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2431   b->icol = iperm;
2432   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2433   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2434   ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2435   b->maxnz   = b->nz = ui[am];
2436   b->free_a  = PETSC_TRUE;
2437   b->free_ij = PETSC_TRUE;
2438 
2439   (fact)->info.factor_mallocs    = reallocs;
2440   (fact)->info.fill_ratio_given  = fill;
2441   if (ai[am] != 0) {
2442     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2443   } else {
2444     (fact)->info.fill_ratio_needed = 0.0;
2445   }
2446   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2447   PetscFunctionReturn(0);
2448 }
2449 
2450 #undef __FUNCT__
2451 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ"
2452 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2453 {
2454   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
2455   Mat_SeqSBAIJ       *b;
2456   PetscErrorCode     ierr;
2457   PetscTruth         perm_identity;
2458   PetscReal          fill = info->fill;
2459   const PetscInt     *rip,*riip;
2460   PetscInt           i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow;
2461   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
2462   PetscInt           nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr;
2463   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
2464   PetscBT            lnkbt;
2465   IS                 iperm;
2466 
2467   PetscFunctionBegin;
2468   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);
2469   /* check whether perm is the identity mapping */
2470   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
2471   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
2472   ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
2473   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
2474 
2475   /* initialization */
2476   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
2477   ui[0] = 0;
2478 
2479   /* jl: linked list for storing indices of the pivot rows
2480      il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2481   ierr = PetscMalloc((3*am+1)*sizeof(PetscInt)+am*sizeof(PetscInt**),&jl);CHKERRQ(ierr);
2482   il     = jl + am;
2483   cols   = il + am;
2484   ui_ptr = (PetscInt**)(cols + am);
2485   for (i=0; i<am; i++){
2486     jl[i] = am; il[i] = 0;
2487   }
2488 
2489   /* create and initialize a linked list for storing column indices of the active row k */
2490   nlnk = am + 1;
2491   ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2492 
2493   /* initial FreeSpace size is fill*(ai[am]+1) */
2494   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr);
2495   current_space = free_space;
2496 
2497   for (k=0; k<am; k++){  /* for each active row k */
2498     /* initialize lnk by the column indices of row rip[k] of A */
2499     nzk   = 0;
2500     ncols = ai[rip[k]+1] - ai[rip[k]];
2501     if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2502     ncols_upper = 0;
2503     for (j=0; j<ncols; j++){
2504       i = riip[*(aj + ai[rip[k]] + j)];
2505       if (i >= k){ /* only take upper triangular entry */
2506         cols[ncols_upper] = i;
2507         ncols_upper++;
2508       }
2509     }
2510     ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2511     nzk += nlnk;
2512 
2513     /* update lnk by computing fill-in for each pivot row to be merged in */
2514     prow = jl[k]; /* 1st pivot row */
2515 
2516     while (prow < k){
2517       nextprow = jl[prow];
2518       /* merge prow into k-th row */
2519       jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
2520       jmax = ui[prow+1];
2521       ncols = jmax-jmin;
2522       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2523       ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2524       nzk += nlnk;
2525 
2526       /* update il and jl for prow */
2527       if (jmin < jmax){
2528         il[prow] = jmin;
2529         j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
2530       }
2531       prow = nextprow;
2532     }
2533 
2534     /* if free space is not available, make more free space */
2535     if (current_space->local_remaining<nzk) {
2536       i = am - k + 1; /* num of unfactored rows */
2537       i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2538       ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
2539       reallocs++;
2540     }
2541 
2542     /* copy data into free space, then initialize lnk */
2543     ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
2544 
2545     /* add the k-th row into il and jl */
2546     if (nzk-1 > 0){
2547       i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2548       jl[k] = jl[i]; jl[i] = k;
2549       il[k] = ui[k] + 1;
2550     }
2551     ui_ptr[k] = current_space->array;
2552     current_space->array           += nzk;
2553     current_space->local_used      += nzk;
2554     current_space->local_remaining -= nzk;
2555 
2556     ui[k+1] = ui[k] + nzk;
2557   }
2558 
2559 #if defined(PETSC_USE_INFO)
2560   if (ai[am] != 0) {
2561     PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]);
2562     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
2563     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
2564     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
2565   } else {
2566      ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
2567   }
2568 #endif
2569 
2570   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
2571   ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
2572   ierr = PetscFree(jl);CHKERRQ(ierr);
2573 
2574   /* destroy list of free space and other temporary array(s) */
2575   ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
2576   ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
2577   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2578 
2579   /* put together the new matrix in MATSEQSBAIJ format */
2580 
2581   b = (Mat_SeqSBAIJ*)(fact)->data;
2582   b->singlemalloc = PETSC_FALSE;
2583   b->free_a       = PETSC_TRUE;
2584   b->free_ij      = PETSC_TRUE;
2585   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
2586   b->j    = uj;
2587   b->i    = ui;
2588   b->diag = 0;
2589   b->ilen = 0;
2590   b->imax = 0;
2591   b->row  = perm;
2592   b->col  = perm;
2593   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2594   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
2595   b->icol = iperm;
2596   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2597   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2598   ierr    = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2599   b->maxnz = b->nz = ui[am];
2600 
2601   (fact)->info.factor_mallocs    = reallocs;
2602   (fact)->info.fill_ratio_given  = fill;
2603   if (ai[am] != 0) {
2604     (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2605   } else {
2606     (fact)->info.fill_ratio_needed = 0.0;
2607   }
2608   (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2609   PetscFunctionReturn(0);
2610 }
2611 
2612 #undef __FUNCT__
2613 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_newdatastruct"
2614 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx)
2615 {
2616   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
2617   PetscErrorCode    ierr;
2618   PetscInt          n = A->rmap->n;
2619   const PetscInt    *ai = a->i,*aj = a->j,*vi;
2620   PetscScalar       *x,sum;
2621   const PetscScalar *b;
2622   const MatScalar   *aa = a->a,*v;
2623   PetscInt          i,nz;
2624 
2625   PetscFunctionBegin;
2626   if (!n) PetscFunctionReturn(0);
2627 
2628   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2629   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2630 
2631   /* forward solve the lower triangular */
2632   x[0] = b[0];
2633   v    = aa;
2634   vi   = aj;
2635   for (i=1; i<n; i++) {
2636     nz  = ai[i+1] - ai[i];
2637     sum = b[i];
2638     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
2639     /*    while (nz--) sum -= *v++ * x[*vi++];*/
2640     v  += nz;
2641     vi += nz;
2642     x[i] = sum;
2643   }
2644 
2645   /* backward solve the upper triangular */
2646   v   = aa + ai[n+1];
2647   vi  = aj + ai[n+1];
2648   for (i=n-1; i>=0; i--){
2649     nz = ai[2*n-i +1] - ai[2*n-i]-1;
2650     sum = x[i];
2651     PetscSparseDenseMinusDot(sum,x,v,vi,nz);
2652     /* while (nz--) sum -= *v++ * x[*vi++]; */
2653     v   += nz;
2654     vi  += nz; vi++;
2655     x[i] = *v++ *sum; /* x[i]=aa[adiag[i]]*sum; v++; */
2656   }
2657 
2658   ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr);
2659   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2660   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2661   PetscFunctionReturn(0);
2662 }
2663 
2664 #undef __FUNCT__
2665 #define __FUNCT__ "MatSolve_SeqAIJ_newdatastruct"
2666 PetscErrorCode MatSolve_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec xx)
2667 {
2668   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
2669   IS                iscol = a->col,isrow = a->row;
2670   PetscErrorCode    ierr;
2671   PetscInt          i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,nz,k;
2672   const PetscInt    *rout,*cout,*r,*c;
2673   PetscScalar       *x,*tmp,*tmps,sum;
2674   const PetscScalar *b;
2675   const MatScalar   *aa = a->a,*v;
2676 
2677   PetscFunctionBegin;
2678   if (!n) PetscFunctionReturn(0);
2679 
2680   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2681   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2682   tmp  = a->solve_work;
2683 
2684   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
2685   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
2686 
2687   /* forward solve the lower triangular */
2688   tmp[0] = b[*r++];
2689   tmps   = tmp;
2690   v      = aa;
2691   vi     = aj;
2692   for (i=1; i<n; i++) {
2693     nz  = ai[i+1] - ai[i];
2694     sum = b[*r++];
2695     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
2696     tmp[i] = sum;
2697     v += nz; vi += nz;
2698   }
2699 
2700   /* backward solve the upper triangular */
2701   k  = n+1;
2702   v  = aa + ai[k]; /* 1st entry of U(n-1,:) */
2703   vi = aj + ai[k];
2704   for (i=n-1; i>=0; i--){
2705     k  = 2*n-i;
2706     nz = ai[k +1] - ai[k] - 1;
2707     sum = tmp[i];
2708     PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
2709     x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */
2710     v += nz+1; vi += nz+1;
2711   }
2712 
2713   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
2714   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
2715   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2716   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2717   ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr);
2718   PetscFunctionReturn(0);
2719 }
2720 
2721 #undef __FUNCT__
2722 #define __FUNCT__ "MatILUDTFactor_SeqAIJ"
2723 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact)
2724 {
2725   Mat                B = *fact;
2726   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b;
2727   IS                 isicol;
2728   PetscErrorCode     ierr;
2729   const PetscInt     *r,*ic;
2730   PetscInt           i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag;
2731   PetscInt           *bi,*bj,*bdiag,*bdiag_rev;
2732   PetscInt           row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au;
2733   PetscInt           nlnk,*lnk;
2734   PetscBT            lnkbt;
2735   PetscTruth         row_identity,icol_identity,both_identity;
2736   MatScalar          *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp;
2737   const PetscInt     *ics;
2738   PetscInt           j,nz,*pj,*bjtmp,k,ncut,*jtmp;
2739   PetscReal          dt=info->dt,dtcol=info->dtcol,shift=info->shiftinblocks;
2740   PetscInt           dtcount=(PetscInt)info->dtcount,nnz_max;
2741   PetscTruth         missing;
2742 
2743   PetscFunctionBegin;
2744 
2745   if (dt      == PETSC_DEFAULT) dt      = 0.005;
2746   if (dtcol   == PETSC_DEFAULT) dtcol   = 0.01; /* XXX unused! */
2747   if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax);
2748 
2749   /* ------- symbolic factorization, can be reused ---------*/
2750   ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
2751   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
2752   adiag=a->diag;
2753 
2754   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
2755 
2756   /* bdiag is location of diagonal in factor */
2757   ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
2758   bdiag_rev = bdiag + n+1;
2759 
2760   /* allocate row pointers bi */
2761   ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
2762 
2763   /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */
2764   if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */
2765   nnz_max  = ai[n]+2*n*dtcount+2;
2766 
2767   ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
2768   ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr);
2769 
2770   /* put together the new matrix */
2771   ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
2772   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
2773   b    = (Mat_SeqAIJ*)(B)->data;
2774   b->free_a       = PETSC_TRUE;
2775   b->free_ij      = PETSC_TRUE;
2776   b->singlemalloc = PETSC_FALSE;
2777   b->a          = ba;
2778   b->j          = bj;
2779   b->i          = bi;
2780   b->diag       = bdiag;
2781   b->ilen       = 0;
2782   b->imax       = 0;
2783   b->row        = isrow;
2784   b->col        = iscol;
2785   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
2786   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
2787   b->icol       = isicol;
2788   ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
2789 
2790   ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
2791   b->maxnz = nnz_max;
2792 
2793   (B)->factor                = MAT_FACTOR_ILUDT;
2794   (B)->info.factor_mallocs   = 0;
2795   (B)->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]);
2796   CHKMEMQ;
2797   /* ------- end of symbolic factorization ---------*/
2798 
2799   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
2800   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
2801   ics  = ic;
2802 
2803   /* linked list for storing column indices of the active row */
2804   nlnk = n + 1;
2805   ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2806 
2807   /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */
2808   ierr = PetscMalloc((2*n+1)*sizeof(PetscInt),&im);CHKERRQ(ierr);
2809   jtmp = im + n;
2810   /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */
2811   ierr = PetscMalloc((2*n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
2812   ierr = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr);
2813   vtmp = rtmp + n;
2814 
2815   bi[0]    = 0;
2816   bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */
2817   bdiag_rev[n] = bdiag[0];
2818   bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */
2819   for (i=0; i<n; i++) {
2820     /* copy initial fill into linked list */
2821     nzi = 0; /* nonzeros for active row i */
2822     nzi = ai[r[i]+1] - ai[r[i]];
2823     if (!nzi) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
2824     nzi_al = adiag[r[i]] - ai[r[i]];
2825     nzi_au = ai[r[i]+1] - adiag[r[i]] -1;
2826     ajtmp = aj + ai[r[i]];
2827     ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
2828 
2829     /* load in initial (unfactored row) */
2830     aatmp = a->a + ai[r[i]];
2831     for (j=0; j<nzi; j++) {
2832       rtmp[ics[*ajtmp++]] = *aatmp++;
2833     }
2834 
2835     /* add pivot rows into linked list */
2836     row = lnk[n];
2837     while (row < i ) {
2838       nzi_bl = bi[row+1] - bi[row] + 1;
2839       bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */
2840       ierr  = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr);
2841       nzi  += nlnk;
2842       row   = lnk[row];
2843     }
2844 
2845     /* copy data from lnk into jtmp, then initialize lnk */
2846     ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr);
2847 
2848     /* numerical factorization */
2849     bjtmp = jtmp;
2850     row   = *bjtmp++; /* 1st pivot row */
2851     while  ( row < i ) {
2852       pc         = rtmp + row;
2853       pv         = ba + bdiag[row]; /* 1./(diag of the pivot row) */
2854       multiplier = (*pc) * (*pv);
2855       *pc        = multiplier;
2856       if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */
2857         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
2858         pv         = ba + bdiag[row+1] + 1;
2859         /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */
2860         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
2861         for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
2862         ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
2863       }
2864       row = *bjtmp++;
2865     }
2866 
2867     /* copy sparse rtmp into contiguous vtmp; separate L and U part */
2868     diag_tmp = rtmp[i];  /* save diagonal value - may not needed?? */
2869     nzi_bl = 0; j = 0;
2870     while (jtmp[j] < i){ /* Note: jtmp is sorted */
2871       vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
2872       nzi_bl++; j++;
2873     }
2874     nzi_bu = nzi - nzi_bl -1;
2875     while (j < nzi){
2876       vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
2877       j++;
2878     }
2879 
2880     bjtmp = bj + bi[i];
2881     batmp = ba + bi[i];
2882     /* apply level dropping rule to L part */
2883     ncut = nzi_al + dtcount;
2884     if (ncut < nzi_bl){
2885       ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr);
2886       ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr);
2887     } else {
2888       ncut = nzi_bl;
2889     }
2890     for (j=0; j<ncut; j++){
2891       bjtmp[j] = jtmp[j];
2892       batmp[j] = vtmp[j];
2893       /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */
2894     }
2895     bi[i+1] = bi[i] + ncut;
2896     nzi = ncut + 1;
2897 
2898     /* apply level dropping rule to U part */
2899     ncut = nzi_au + dtcount;
2900     if (ncut < nzi_bu){
2901       ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr);
2902       ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr);
2903     } else {
2904       ncut = nzi_bu;
2905     }
2906     nzi += ncut;
2907 
2908     /* mark bdiagonal */
2909     bdiag[i+1]       = bdiag[i] - (ncut + 1);
2910     bdiag_rev[n-i-1] = bdiag[i+1];
2911     bi[2*n - i]      = bi[2*n - i +1] - (ncut + 1);
2912     bjtmp = bj + bdiag[i];
2913     batmp = ba + bdiag[i];
2914     *bjtmp = i;
2915     *batmp = diag_tmp; /* rtmp[i]; */
2916     if (*batmp == 0.0) {
2917       *batmp = dt+shift;
2918       /* printf(" row %d add shift %g\n",i,shift); */
2919     }
2920     *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */
2921     /* printf(" (%d,%g),",*bjtmp,*batmp); */
2922 
2923     bjtmp = bj + bdiag[i+1]+1;
2924     batmp = ba + bdiag[i+1]+1;
2925     for (k=0; k<ncut; k++){
2926       bjtmp[k] = jtmp[nzi_bl+1+k];
2927       batmp[k] = vtmp[nzi_bl+1+k];
2928       /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */
2929     }
2930     /* printf("\n"); */
2931 
2932     im[i]   = nzi; /* used by PetscLLAddSortedLU() */
2933     /*
2934     printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]);
2935     printf(" ----------------------------\n");
2936     */
2937   } /* for (i=0; i<n; i++) */
2938   /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */
2939   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]);
2940 
2941   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
2942   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
2943 
2944   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
2945   ierr = PetscFree(im);CHKERRQ(ierr);
2946   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2947 
2948   ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr);
2949   b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n];
2950 
2951   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
2952   ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr);
2953   both_identity = (PetscTruth) (row_identity && icol_identity);
2954   if (row_identity && icol_identity) {
2955     B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct;
2956   } else {
2957     B->ops->solve = MatSolve_SeqAIJ_newdatastruct;
2958   }
2959 
2960   B->ops->lufactorsymbolic  = MatILUDTFactorSymbolic_SeqAIJ;
2961   B->ops->lufactornumeric   = MatILUDTFactorNumeric_SeqAIJ;
2962   B->ops->solveadd          = 0;
2963   B->ops->solvetranspose    = 0;
2964   B->ops->solvetransposeadd = 0;
2965   B->ops->matsolve          = 0;
2966   B->assembled              = PETSC_TRUE;
2967   B->preallocated           = PETSC_TRUE;
2968   PetscFunctionReturn(0);
2969 }
2970 
2971 /* a wraper of MatILUDTFactor_SeqAIJ() */
2972 #undef __FUNCT__
2973 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ"
2974 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info)
2975 {
2976   PetscErrorCode     ierr;
2977 
2978   PetscFunctionBegin;
2979   ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr);
2980 
2981   fact->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ;
2982   PetscFunctionReturn(0);
2983 }
2984 
2985 /*
2986    same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors
2987    - intend to replace existing MatLUFactorNumeric_SeqAIJ()
2988 */
2989 #undef __FUNCT__
2990 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ"
2991 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info)
2992 {
2993   Mat            C=fact;
2994   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data;
2995   IS             isrow = b->row,isicol = b->icol;
2996   PetscErrorCode ierr;
2997   const PetscInt *r,*ic,*ics;
2998   PetscInt       i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
2999   PetscInt       *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj;
3000   MatScalar      *rtmp,*pc,multiplier,*v,*pv,*aa=a->a;
3001   PetscReal      dt=info->dt,shift=info->shiftinblocks;
3002   PetscTruth     row_identity, col_identity;
3003 
3004   PetscFunctionBegin;
3005   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
3006   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
3007   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
3008   ics  = ic;
3009 
3010   for (i=0; i<n; i++){
3011     /* initialize rtmp array */
3012     nzl   = bi[i+1] - bi[i];       /* num of nozeros in L(i,:) */
3013     bjtmp = bj + bi[i];
3014     for  (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0;
3015     rtmp[i] = 0.0;
3016     nzu   = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */
3017     bjtmp = bj + bdiag[i+1] + 1;
3018     for  (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0;
3019 
3020     /* load in initial unfactored row of A */
3021     /* printf("row %d\n",i); */
3022     nz    = ai[r[i]+1] - ai[r[i]];
3023     ajtmp = aj + ai[r[i]];
3024     v     = aa + ai[r[i]];
3025     for (j=0; j<nz; j++) {
3026       rtmp[ics[*ajtmp++]] = v[j];
3027       /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */
3028     }
3029     /* printf("\n"); */
3030 
3031     /* numerical factorization */
3032     bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */
3033     nzl   = bi[i+1] - bi[i]; /* num of entries in L(i,:) */
3034     k = 0;
3035     while (k < nzl){
3036       row   = *bjtmp++;
3037       /* printf("  prow %d\n",row); */
3038       pc         = rtmp + row;
3039       pv         = b->a + bdiag[row]; /* 1./(diag of the pivot row) */
3040       multiplier = (*pc) * (*pv);
3041       *pc        = multiplier;
3042       if (PetscAbsScalar(multiplier) > dt){
3043         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
3044         pv         = b->a + bdiag[row+1] + 1;
3045         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
3046         for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
3047         /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */
3048       }
3049       k++;
3050     }
3051 
3052     /* finished row so stick it into b->a */
3053     /* L-part */
3054     pv = b->a + bi[i] ;
3055     pj = bj + bi[i] ;
3056     nzl = bi[i+1] - bi[i];
3057     for (j=0; j<nzl; j++) {
3058       pv[j] = rtmp[pj[j]];
3059       /* printf(" (%d,%g),",pj[j],pv[j]); */
3060     }
3061 
3062     /* diagonal: invert diagonal entries for simplier triangular solves */
3063     if (rtmp[i] == 0.0) rtmp[i] = dt+shift;
3064     b->a[bdiag[i]] = 1.0/rtmp[i];
3065     /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */
3066 
3067     /* U-part */
3068     pv = b->a + bdiag[i+1] + 1;
3069     pj = bj + bdiag[i+1] + 1;
3070     nzu = bdiag[i] - bdiag[i+1] - 1;
3071     for (j=0; j<nzu; j++) {
3072       pv[j] = rtmp[pj[j]];
3073       /* printf(" (%d,%g),",pj[j],pv[j]); */
3074     }
3075     /* printf("\n"); */
3076   }
3077 
3078   ierr = PetscFree(rtmp);CHKERRQ(ierr);
3079   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
3080   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
3081 
3082   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
3083   ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
3084   if (row_identity && col_identity) {
3085     C->ops->solve   = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct;
3086   } else {
3087     C->ops->solve   = MatSolve_SeqAIJ_newdatastruct;
3088   }
3089   C->ops->solveadd           = 0;
3090   C->ops->solvetranspose     = 0;
3091   C->ops->solvetransposeadd  = 0;
3092   C->ops->matsolve           = 0;
3093   C->assembled    = PETSC_TRUE;
3094   C->preallocated = PETSC_TRUE;
3095   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
3096   PetscFunctionReturn(0);
3097 }
3098