xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision 4ffacfe27a72f4cdf51b68a3bbb6aed96040fb2f)
1 #include <../src/mat/impls/aij/mpi/mpiaij.h>   /*I "petscmat.h" I*/
2 #include <petsc/private/vecimpl.h>
3 #include <petsc/private/sfimpl.h>
4 #include <petsc/private/isimpl.h>
5 #include <petscblaslapack.h>
6 #include <petscsf.h>
7 #include <petsc/private/hashmapi.h>
8 
9 PetscErrorCode MatGetRowIJ_MPIAIJ(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *m,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
10 {
11   Mat            B;
12 
13   PetscFunctionBegin;
14   PetscCall(MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&B));
15   PetscCall(PetscObjectCompose((PetscObject)A,"MatGetRowIJ_MPIAIJ",(PetscObject)B));
16   PetscCall(MatGetRowIJ(B,oshift,symmetric,inodecompressed,m,ia,ja,done));
17   PetscFunctionReturn(0);
18 }
19 
20 PetscErrorCode MatRestoreRowIJ_MPIAIJ(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *m,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
21 {
22   Mat            B;
23 
24   PetscFunctionBegin;
25   PetscCall(PetscObjectQuery((PetscObject)A,"MatGetRowIJ_MPIAIJ",(PetscObject*)&B));
26   PetscCall(MatRestoreRowIJ(B,oshift,symmetric,inodecompressed,m,ia,ja,done));
27   PetscCall(MatDestroy(&B));
28   PetscFunctionReturn(0);
29 }
30 
31 /*MC
32    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.
33 
34    This matrix type is identical to MATSEQAIJ when constructed with a single process communicator,
35    and MATMPIAIJ otherwise.  As a result, for single process communicators,
36   MatSeqAIJSetPreallocation is supported, and similarly MatMPIAIJSetPreallocation() is supported
37   for communicators controlling multiple processes.  It is recommended that you call both of
38   the above preallocation routines for simplicity.
39 
40    Options Database Keys:
41 . -mat_type aij - sets the matrix type to "aij" during a call to MatSetFromOptions()
42 
43   Developer Notes:
44     Subclasses include MATAIJCUSPARSE, MATAIJPERM, MATAIJSELL, MATAIJMKL, MATAIJCRL, and also automatically switches over to use inodes when
45    enough exist.
46 
47   Level: beginner
48 
49 .seealso: `MatCreateAIJ()`, `MatCreateSeqAIJ()`, `MATSEQAIJ`, `MATMPIAIJ`
50 M*/
51 
52 /*MC
53    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.
54 
55    This matrix type is identical to MATSEQAIJCRL when constructed with a single process communicator,
56    and MATMPIAIJCRL otherwise.  As a result, for single process communicators,
57    MatSeqAIJSetPreallocation() is supported, and similarly MatMPIAIJSetPreallocation() is supported
58   for communicators controlling multiple processes.  It is recommended that you call both of
59   the above preallocation routines for simplicity.
60 
61    Options Database Keys:
62 . -mat_type aijcrl - sets the matrix type to "aijcrl" during a call to MatSetFromOptions()
63 
64   Level: beginner
65 
66 .seealso: `MatCreateMPIAIJCRL`, `MATSEQAIJCRL`, `MATMPIAIJCRL`, `MATSEQAIJCRL`, `MATMPIAIJCRL`
67 M*/
68 
69 static PetscErrorCode MatBindToCPU_MPIAIJ(Mat A,PetscBool flg)
70 {
71   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
72 
73   PetscFunctionBegin;
74 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_VIENNACL)
75   A->boundtocpu = flg;
76 #endif
77   if (a->A) PetscCall(MatBindToCPU(a->A,flg));
78   if (a->B) PetscCall(MatBindToCPU(a->B,flg));
79 
80   /* In addition to binding the diagonal and off-diagonal matrices, bind the local vectors used for matrix-vector products.
81    * This maybe seems a little odd for a MatBindToCPU() call to do, but it makes no sense for the binding of these vectors
82    * to differ from the parent matrix. */
83   if (a->lvec) PetscCall(VecBindToCPU(a->lvec,flg));
84   if (a->diag) PetscCall(VecBindToCPU(a->diag,flg));
85 
86   PetscFunctionReturn(0);
87 }
88 
89 PetscErrorCode MatSetBlockSizes_MPIAIJ(Mat M, PetscInt rbs, PetscInt cbs)
90 {
91   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)M->data;
92 
93   PetscFunctionBegin;
94   if (mat->A) {
95     PetscCall(MatSetBlockSizes(mat->A,rbs,cbs));
96     PetscCall(MatSetBlockSizes(mat->B,rbs,1));
97   }
98   PetscFunctionReturn(0);
99 }
100 
101 PetscErrorCode MatFindNonzeroRows_MPIAIJ(Mat M,IS *keptrows)
102 {
103   Mat_MPIAIJ      *mat = (Mat_MPIAIJ*)M->data;
104   Mat_SeqAIJ      *a   = (Mat_SeqAIJ*)mat->A->data;
105   Mat_SeqAIJ      *b   = (Mat_SeqAIJ*)mat->B->data;
106   const PetscInt  *ia,*ib;
107   const MatScalar *aa,*bb,*aav,*bav;
108   PetscInt        na,nb,i,j,*rows,cnt=0,n0rows;
109   PetscInt        m = M->rmap->n,rstart = M->rmap->rstart;
110 
111   PetscFunctionBegin;
112   *keptrows = NULL;
113 
114   ia   = a->i;
115   ib   = b->i;
116   PetscCall(MatSeqAIJGetArrayRead(mat->A,&aav));
117   PetscCall(MatSeqAIJGetArrayRead(mat->B,&bav));
118   for (i=0; i<m; i++) {
119     na = ia[i+1] - ia[i];
120     nb = ib[i+1] - ib[i];
121     if (!na && !nb) {
122       cnt++;
123       goto ok1;
124     }
125     aa = aav + ia[i];
126     for (j=0; j<na; j++) {
127       if (aa[j] != 0.0) goto ok1;
128     }
129     bb = bav + ib[i];
130     for (j=0; j <nb; j++) {
131       if (bb[j] != 0.0) goto ok1;
132     }
133     cnt++;
134 ok1:;
135   }
136   PetscCall(MPIU_Allreduce(&cnt,&n0rows,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)M)));
137   if (!n0rows) {
138     PetscCall(MatSeqAIJRestoreArrayRead(mat->A,&aav));
139     PetscCall(MatSeqAIJRestoreArrayRead(mat->B,&bav));
140     PetscFunctionReturn(0);
141   }
142   PetscCall(PetscMalloc1(M->rmap->n-cnt,&rows));
143   cnt  = 0;
144   for (i=0; i<m; i++) {
145     na = ia[i+1] - ia[i];
146     nb = ib[i+1] - ib[i];
147     if (!na && !nb) continue;
148     aa = aav + ia[i];
149     for (j=0; j<na;j++) {
150       if (aa[j] != 0.0) {
151         rows[cnt++] = rstart + i;
152         goto ok2;
153       }
154     }
155     bb = bav + ib[i];
156     for (j=0; j<nb; j++) {
157       if (bb[j] != 0.0) {
158         rows[cnt++] = rstart + i;
159         goto ok2;
160       }
161     }
162 ok2:;
163   }
164   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)M),cnt,rows,PETSC_OWN_POINTER,keptrows));
165   PetscCall(MatSeqAIJRestoreArrayRead(mat->A,&aav));
166   PetscCall(MatSeqAIJRestoreArrayRead(mat->B,&bav));
167   PetscFunctionReturn(0);
168 }
169 
170 PetscErrorCode  MatDiagonalSet_MPIAIJ(Mat Y,Vec D,InsertMode is)
171 {
172   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*) Y->data;
173   PetscBool         cong;
174 
175   PetscFunctionBegin;
176   PetscCall(MatHasCongruentLayouts(Y,&cong));
177   if (Y->assembled && cong) {
178     PetscCall(MatDiagonalSet(aij->A,D,is));
179   } else {
180     PetscCall(MatDiagonalSet_Default(Y,D,is));
181   }
182   PetscFunctionReturn(0);
183 }
184 
185 PetscErrorCode MatFindZeroDiagonals_MPIAIJ(Mat M,IS *zrows)
186 {
187   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)M->data;
188   PetscInt       i,rstart,nrows,*rows;
189 
190   PetscFunctionBegin;
191   *zrows = NULL;
192   PetscCall(MatFindZeroDiagonals_SeqAIJ_Private(aij->A,&nrows,&rows));
193   PetscCall(MatGetOwnershipRange(M,&rstart,NULL));
194   for (i=0; i<nrows; i++) rows[i] += rstart;
195   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)M),nrows,rows,PETSC_OWN_POINTER,zrows));
196   PetscFunctionReturn(0);
197 }
198 
199 PetscErrorCode MatGetColumnReductions_MPIAIJ(Mat A,PetscInt type,PetscReal *reductions)
200 {
201   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)A->data;
202   PetscInt          i,m,n,*garray = aij->garray;
203   Mat_SeqAIJ        *a_aij = (Mat_SeqAIJ*) aij->A->data;
204   Mat_SeqAIJ        *b_aij = (Mat_SeqAIJ*) aij->B->data;
205   PetscReal         *work;
206   const PetscScalar *dummy;
207 
208   PetscFunctionBegin;
209   PetscCall(MatGetSize(A,&m,&n));
210   PetscCall(PetscCalloc1(n,&work));
211   PetscCall(MatSeqAIJGetArrayRead(aij->A,&dummy));
212   PetscCall(MatSeqAIJRestoreArrayRead(aij->A,&dummy));
213   PetscCall(MatSeqAIJGetArrayRead(aij->B,&dummy));
214   PetscCall(MatSeqAIJRestoreArrayRead(aij->B,&dummy));
215   if (type == NORM_2) {
216     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
217       work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i]*a_aij->a[i]);
218     }
219     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
220       work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]*b_aij->a[i]);
221     }
222   } else if (type == NORM_1) {
223     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
224       work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i]);
225     }
226     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
227       work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]);
228     }
229   } else if (type == NORM_INFINITY) {
230     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
231       work[A->cmap->rstart + a_aij->j[i]] = PetscMax(PetscAbsScalar(a_aij->a[i]), work[A->cmap->rstart + a_aij->j[i]]);
232     }
233     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
234       work[garray[b_aij->j[i]]] = PetscMax(PetscAbsScalar(b_aij->a[i]),work[garray[b_aij->j[i]]]);
235     }
236   } else if (type == REDUCTION_SUM_REALPART || type == REDUCTION_MEAN_REALPART) {
237     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
238       work[A->cmap->rstart + a_aij->j[i]] += PetscRealPart(a_aij->a[i]);
239     }
240     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
241       work[garray[b_aij->j[i]]] += PetscRealPart(b_aij->a[i]);
242     }
243   } else if (type == REDUCTION_SUM_IMAGINARYPART || type == REDUCTION_MEAN_IMAGINARYPART) {
244     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
245       work[A->cmap->rstart + a_aij->j[i]] += PetscImaginaryPart(a_aij->a[i]);
246     }
247     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
248       work[garray[b_aij->j[i]]] += PetscImaginaryPart(b_aij->a[i]);
249     }
250   } else SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Unknown reduction type");
251   if (type == NORM_INFINITY) {
252     PetscCall(MPIU_Allreduce(work,reductions,n,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)A)));
253   } else {
254     PetscCall(MPIU_Allreduce(work,reductions,n,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)A)));
255   }
256   PetscCall(PetscFree(work));
257   if (type == NORM_2) {
258     for (i=0; i<n; i++) reductions[i] = PetscSqrtReal(reductions[i]);
259   } else if (type == REDUCTION_MEAN_REALPART || type == REDUCTION_MEAN_IMAGINARYPART) {
260     for (i=0; i<n; i++) reductions[i] /= m;
261   }
262   PetscFunctionReturn(0);
263 }
264 
265 PetscErrorCode MatFindOffBlockDiagonalEntries_MPIAIJ(Mat A,IS *is)
266 {
267   Mat_MPIAIJ      *a  = (Mat_MPIAIJ*)A->data;
268   IS              sis,gis;
269   const PetscInt  *isis,*igis;
270   PetscInt        n,*iis,nsis,ngis,rstart,i;
271 
272   PetscFunctionBegin;
273   PetscCall(MatFindOffBlockDiagonalEntries(a->A,&sis));
274   PetscCall(MatFindNonzeroRows(a->B,&gis));
275   PetscCall(ISGetSize(gis,&ngis));
276   PetscCall(ISGetSize(sis,&nsis));
277   PetscCall(ISGetIndices(sis,&isis));
278   PetscCall(ISGetIndices(gis,&igis));
279 
280   PetscCall(PetscMalloc1(ngis+nsis,&iis));
281   PetscCall(PetscArraycpy(iis,igis,ngis));
282   PetscCall(PetscArraycpy(iis+ngis,isis,nsis));
283   n    = ngis + nsis;
284   PetscCall(PetscSortRemoveDupsInt(&n,iis));
285   PetscCall(MatGetOwnershipRange(A,&rstart,NULL));
286   for (i=0; i<n; i++) iis[i] += rstart;
287   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)A),n,iis,PETSC_OWN_POINTER,is));
288 
289   PetscCall(ISRestoreIndices(sis,&isis));
290   PetscCall(ISRestoreIndices(gis,&igis));
291   PetscCall(ISDestroy(&sis));
292   PetscCall(ISDestroy(&gis));
293   PetscFunctionReturn(0);
294 }
295 
296 /*
297   Local utility routine that creates a mapping from the global column
298 number to the local number in the off-diagonal part of the local
299 storage of the matrix.  When PETSC_USE_CTABLE is used this is scalable at
300 a slightly higher hash table cost; without it it is not scalable (each processor
301 has an order N integer array but is fast to access.
302 */
303 PetscErrorCode MatCreateColmap_MPIAIJ_Private(Mat mat)
304 {
305   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
306   PetscInt       n = aij->B->cmap->n,i;
307 
308   PetscFunctionBegin;
309   PetscCheck(!n || aij->garray,PETSC_COMM_SELF,PETSC_ERR_PLIB,"MPIAIJ Matrix was assembled but is missing garray");
310 #if defined(PETSC_USE_CTABLE)
311   PetscCall(PetscTableCreate(n,mat->cmap->N+1,&aij->colmap));
312   for (i=0; i<n; i++) {
313     PetscCall(PetscTableAdd(aij->colmap,aij->garray[i]+1,i+1,INSERT_VALUES));
314   }
315 #else
316   PetscCall(PetscCalloc1(mat->cmap->N+1,&aij->colmap));
317   PetscCall(PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N+1)*sizeof(PetscInt)));
318   for (i=0; i<n; i++) aij->colmap[aij->garray[i]] = i+1;
319 #endif
320   PetscFunctionReturn(0);
321 }
322 
323 #define MatSetValues_SeqAIJ_A_Private(row,col,value,addv,orow,ocol)     \
324 { \
325     if (col <= lastcol1)  low1 = 0;     \
326     else                 high1 = nrow1; \
327     lastcol1 = col;\
328     while (high1-low1 > 5) { \
329       t = (low1+high1)/2; \
330       if (rp1[t] > col) high1 = t; \
331       else              low1  = t; \
332     } \
333       for (_i=low1; _i<high1; _i++) { \
334         if (rp1[_i] > col) break; \
335         if (rp1[_i] == col) { \
336           if (addv == ADD_VALUES) { \
337             ap1[_i] += value;   \
338             /* Not sure LogFlops will slow dow the code or not */ \
339             (void)PetscLogFlops(1.0);   \
340            } \
341           else                    ap1[_i] = value; \
342           goto a_noinsert; \
343         } \
344       }  \
345       if (value == 0.0 && ignorezeroentries && row != col) {low1 = 0; high1 = nrow1;goto a_noinsert;} \
346       if (nonew == 1) {low1 = 0; high1 = nrow1; goto a_noinsert;}                \
347       PetscCheck(nonew != -1,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at global row/column (%" PetscInt_FMT ", %" PetscInt_FMT ") into matrix", orow, ocol); \
348       MatSeqXAIJReallocateAIJ(A,am,1,nrow1,row,col,rmax1,aa,ai,aj,rp1,ap1,aimax,nonew,MatScalar); \
349       N = nrow1++ - 1; a->nz++; high1++; \
350       /* shift up all the later entries in this row */ \
351       PetscCall(PetscArraymove(rp1+_i+1,rp1+_i,N-_i+1));\
352       PetscCall(PetscArraymove(ap1+_i+1,ap1+_i,N-_i+1));\
353       rp1[_i] = col;  \
354       ap1[_i] = value;  \
355       A->nonzerostate++;\
356       a_noinsert: ; \
357       ailen[row] = nrow1; \
358 }
359 
360 #define MatSetValues_SeqAIJ_B_Private(row,col,value,addv,orow,ocol) \
361   { \
362     if (col <= lastcol2) low2 = 0;                        \
363     else high2 = nrow2;                                   \
364     lastcol2 = col;                                       \
365     while (high2-low2 > 5) {                              \
366       t = (low2+high2)/2;                                 \
367       if (rp2[t] > col) high2 = t;                        \
368       else             low2  = t;                         \
369     }                                                     \
370     for (_i=low2; _i<high2; _i++) {                       \
371       if (rp2[_i] > col) break;                           \
372       if (rp2[_i] == col) {                               \
373         if (addv == ADD_VALUES) {                         \
374           ap2[_i] += value;                               \
375           (void)PetscLogFlops(1.0);                       \
376         }                                                 \
377         else                    ap2[_i] = value;          \
378         goto b_noinsert;                                  \
379       }                                                   \
380     }                                                     \
381     if (value == 0.0 && ignorezeroentries) {low2 = 0; high2 = nrow2; goto b_noinsert;} \
382     if (nonew == 1) {low2 = 0; high2 = nrow2; goto b_noinsert;}                        \
383     PetscCheck(nonew != -1,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at global row/column (%" PetscInt_FMT ", %" PetscInt_FMT ") into matrix", orow, ocol); \
384     MatSeqXAIJReallocateAIJ(B,bm,1,nrow2,row,col,rmax2,ba,bi,bj,rp2,ap2,bimax,nonew,MatScalar); \
385     N = nrow2++ - 1; b->nz++; high2++;                    \
386     /* shift up all the later entries in this row */      \
387     PetscCall(PetscArraymove(rp2+_i+1,rp2+_i,N-_i+1));\
388     PetscCall(PetscArraymove(ap2+_i+1,ap2+_i,N-_i+1));\
389     rp2[_i] = col;                                        \
390     ap2[_i] = value;                                      \
391     B->nonzerostate++;                                    \
392     b_noinsert: ;                                         \
393     bilen[row] = nrow2;                                   \
394   }
395 
396 PetscErrorCode MatSetValuesRow_MPIAIJ(Mat A,PetscInt row,const PetscScalar v[])
397 {
398   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)A->data;
399   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)mat->A->data,*b = (Mat_SeqAIJ*)mat->B->data;
400   PetscInt       l,*garray = mat->garray,diag;
401   PetscScalar    *aa,*ba;
402 
403   PetscFunctionBegin;
404   /* code only works for square matrices A */
405 
406   /* find size of row to the left of the diagonal part */
407   PetscCall(MatGetOwnershipRange(A,&diag,NULL));
408   row  = row - diag;
409   for (l=0; l<b->i[row+1]-b->i[row]; l++) {
410     if (garray[b->j[b->i[row]+l]] > diag) break;
411   }
412   if (l) {
413     PetscCall(MatSeqAIJGetArray(mat->B,&ba));
414     PetscCall(PetscArraycpy(ba+b->i[row],v,l));
415     PetscCall(MatSeqAIJRestoreArray(mat->B,&ba));
416   }
417 
418   /* diagonal part */
419   if (a->i[row+1]-a->i[row]) {
420     PetscCall(MatSeqAIJGetArray(mat->A,&aa));
421     PetscCall(PetscArraycpy(aa+a->i[row],v+l,(a->i[row+1]-a->i[row])));
422     PetscCall(MatSeqAIJRestoreArray(mat->A,&aa));
423   }
424 
425   /* right of diagonal part */
426   if (b->i[row+1]-b->i[row]-l) {
427     PetscCall(MatSeqAIJGetArray(mat->B,&ba));
428     PetscCall(PetscArraycpy(ba+b->i[row]+l,v+l+a->i[row+1]-a->i[row],b->i[row+1]-b->i[row]-l));
429     PetscCall(MatSeqAIJRestoreArray(mat->B,&ba));
430   }
431   PetscFunctionReturn(0);
432 }
433 
434 PetscErrorCode MatSetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode addv)
435 {
436   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
437   PetscScalar    value = 0.0;
438   PetscInt       i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
439   PetscInt       cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
440   PetscBool      roworiented = aij->roworiented;
441 
442   /* Some Variables required in the macro */
443   Mat        A                    = aij->A;
444   Mat_SeqAIJ *a                   = (Mat_SeqAIJ*)A->data;
445   PetscInt   *aimax               = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
446   PetscBool  ignorezeroentries    = a->ignorezeroentries;
447   Mat        B                    = aij->B;
448   Mat_SeqAIJ *b                   = (Mat_SeqAIJ*)B->data;
449   PetscInt   *bimax               = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
450   MatScalar  *aa,*ba;
451   PetscInt   *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
452   PetscInt   nonew;
453   MatScalar  *ap1,*ap2;
454 
455   PetscFunctionBegin;
456   PetscCall(MatSeqAIJGetArray(A,&aa));
457   PetscCall(MatSeqAIJGetArray(B,&ba));
458   for (i=0; i<m; i++) {
459     if (im[i] < 0) continue;
460     PetscCheck(im[i] < mat->rmap->N,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %" PetscInt_FMT " max %" PetscInt_FMT,im[i],mat->rmap->N-1);
461     if (im[i] >= rstart && im[i] < rend) {
462       row      = im[i] - rstart;
463       lastcol1 = -1;
464       rp1      = aj + ai[row];
465       ap1      = aa + ai[row];
466       rmax1    = aimax[row];
467       nrow1    = ailen[row];
468       low1     = 0;
469       high1    = nrow1;
470       lastcol2 = -1;
471       rp2      = bj + bi[row];
472       ap2      = ba + bi[row];
473       rmax2    = bimax[row];
474       nrow2    = bilen[row];
475       low2     = 0;
476       high2    = nrow2;
477 
478       for (j=0; j<n; j++) {
479         if (v)  value = roworiented ? v[i*n+j] : v[i+j*m];
480         if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && im[i] != in[j]) continue;
481         if (in[j] >= cstart && in[j] < cend) {
482           col   = in[j] - cstart;
483           nonew = a->nonew;
484           MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
485         } else if (in[j] < 0) {
486           continue;
487         } else {
488           PetscCheck(in[j] < mat->cmap->N,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %" PetscInt_FMT " max %" PetscInt_FMT,in[j],mat->cmap->N-1);
489           if (mat->was_assembled) {
490             if (!aij->colmap) {
491               PetscCall(MatCreateColmap_MPIAIJ_Private(mat));
492             }
493 #if defined(PETSC_USE_CTABLE)
494             PetscCall(PetscTableFind(aij->colmap,in[j]+1,&col)); /* map global col ids to local ones */
495             col--;
496 #else
497             col = aij->colmap[in[j]] - 1;
498 #endif
499             if (col < 0 && !((Mat_SeqAIJ*)(aij->B->data))->nonew) { /* col < 0 means in[j] is a new col for B */
500               PetscCall(MatDisAssemble_MPIAIJ(mat)); /* Change aij->B from reduced/local format to expanded/global format */
501               col  =  in[j];
502               /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
503               B        = aij->B;
504               b        = (Mat_SeqAIJ*)B->data;
505               bimax    = b->imax; bi = b->i; bilen = b->ilen; bj = b->j; ba = b->a;
506               rp2      = bj + bi[row];
507               ap2      = ba + bi[row];
508               rmax2    = bimax[row];
509               nrow2    = bilen[row];
510               low2     = 0;
511               high2    = nrow2;
512               bm       = aij->B->rmap->n;
513               ba       = b->a;
514             } else if (col < 0 && !(ignorezeroentries && value == 0.0)) {
515               if (1 == ((Mat_SeqAIJ*)(aij->B->data))->nonew) {
516                 PetscCall(PetscInfo(mat,"Skipping of insertion of new nonzero location in off-diagonal portion of matrix %g(%" PetscInt_FMT ",%" PetscInt_FMT ")\n",(double)PetscRealPart(value),im[i],in[j]));
517               } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at global row/column (%" PetscInt_FMT ", %" PetscInt_FMT ") into matrix", im[i], in[j]);
518             }
519           } else col = in[j];
520           nonew = b->nonew;
521           MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
522         }
523       }
524     } else {
525       PetscCheck(!mat->nooffprocentries,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Setting off process row %" PetscInt_FMT " even though MatSetOption(,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) was set",im[i]);
526       if (!aij->donotstash) {
527         mat->assembled = PETSC_FALSE;
528         if (roworiented) {
529           PetscCall(MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES))));
530         } else {
531           PetscCall(MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES))));
532         }
533       }
534     }
535   }
536   PetscCall(MatSeqAIJRestoreArray(A,&aa)); /* aa, bb might have been free'd due to reallocation above. But we don't access them here */
537   PetscCall(MatSeqAIJRestoreArray(B,&ba));
538   PetscFunctionReturn(0);
539 }
540 
541 /*
542     This function sets the j and ilen arrays (of the diagonal and off-diagonal part) of an MPIAIJ-matrix.
543     The values in mat_i have to be sorted and the values in mat_j have to be sorted for each row (CSR-like).
544     No off-processor parts off the matrix are allowed here and mat->was_assembled has to be PETSC_FALSE.
545 */
546 PetscErrorCode MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(Mat mat,const PetscInt mat_j[],const PetscInt mat_i[])
547 {
548   Mat_MPIAIJ     *aij        = (Mat_MPIAIJ*)mat->data;
549   Mat            A           = aij->A; /* diagonal part of the matrix */
550   Mat            B           = aij->B; /* offdiagonal part of the matrix */
551   Mat_SeqAIJ     *a          = (Mat_SeqAIJ*)A->data;
552   Mat_SeqAIJ     *b          = (Mat_SeqAIJ*)B->data;
553   PetscInt       cstart      = mat->cmap->rstart,cend = mat->cmap->rend,col;
554   PetscInt       *ailen      = a->ilen,*aj = a->j;
555   PetscInt       *bilen      = b->ilen,*bj = b->j;
556   PetscInt       am          = aij->A->rmap->n,j;
557   PetscInt       diag_so_far = 0,dnz;
558   PetscInt       offd_so_far = 0,onz;
559 
560   PetscFunctionBegin;
561   /* Iterate over all rows of the matrix */
562   for (j=0; j<am; j++) {
563     dnz = onz = 0;
564     /*  Iterate over all non-zero columns of the current row */
565     for (col=mat_i[j]; col<mat_i[j+1]; col++) {
566       /* If column is in the diagonal */
567       if (mat_j[col] >= cstart && mat_j[col] < cend) {
568         aj[diag_so_far++] = mat_j[col] - cstart;
569         dnz++;
570       } else { /* off-diagonal entries */
571         bj[offd_so_far++] = mat_j[col];
572         onz++;
573       }
574     }
575     ailen[j] = dnz;
576     bilen[j] = onz;
577   }
578   PetscFunctionReturn(0);
579 }
580 
581 /*
582     This function sets the local j, a and ilen arrays (of the diagonal and off-diagonal part) of an MPIAIJ-matrix.
583     The values in mat_i have to be sorted and the values in mat_j have to be sorted for each row (CSR-like).
584     No off-processor parts off the matrix are allowed here, they are set at a later point by MatSetValues_MPIAIJ.
585     Also, mat->was_assembled has to be false, otherwise the statement aj[rowstart_diag+dnz_row] = mat_j[col] - cstart;
586     would not be true and the more complex MatSetValues_MPIAIJ has to be used.
587 */
588 PetscErrorCode MatSetValues_MPIAIJ_CopyFromCSRFormat(Mat mat,const PetscInt mat_j[],const PetscInt mat_i[],const PetscScalar mat_a[])
589 {
590   Mat_MPIAIJ     *aij   = (Mat_MPIAIJ*)mat->data;
591   Mat            A      = aij->A; /* diagonal part of the matrix */
592   Mat            B      = aij->B; /* offdiagonal part of the matrix */
593   Mat_SeqAIJ     *aijd  =(Mat_SeqAIJ*)(aij->A)->data,*aijo=(Mat_SeqAIJ*)(aij->B)->data;
594   Mat_SeqAIJ     *a     = (Mat_SeqAIJ*)A->data;
595   Mat_SeqAIJ     *b     = (Mat_SeqAIJ*)B->data;
596   PetscInt       cstart = mat->cmap->rstart,cend = mat->cmap->rend;
597   PetscInt       *ailen = a->ilen,*aj = a->j;
598   PetscInt       *bilen = b->ilen,*bj = b->j;
599   PetscInt       am     = aij->A->rmap->n,j;
600   PetscInt       *full_diag_i=aijd->i,*full_offd_i=aijo->i; /* These variables can also include non-local elements, which are set at a later point. */
601   PetscInt       col,dnz_row,onz_row,rowstart_diag,rowstart_offd;
602   PetscScalar    *aa = a->a,*ba = b->a;
603 
604   PetscFunctionBegin;
605   /* Iterate over all rows of the matrix */
606   for (j=0; j<am; j++) {
607     dnz_row = onz_row = 0;
608     rowstart_offd = full_offd_i[j];
609     rowstart_diag = full_diag_i[j];
610     /*  Iterate over all non-zero columns of the current row */
611     for (col=mat_i[j]; col<mat_i[j+1]; col++) {
612       /* If column is in the diagonal */
613       if (mat_j[col] >= cstart && mat_j[col] < cend) {
614         aj[rowstart_diag+dnz_row] = mat_j[col] - cstart;
615         aa[rowstart_diag+dnz_row] = mat_a[col];
616         dnz_row++;
617       } else { /* off-diagonal entries */
618         bj[rowstart_offd+onz_row] = mat_j[col];
619         ba[rowstart_offd+onz_row] = mat_a[col];
620         onz_row++;
621       }
622     }
623     ailen[j] = dnz_row;
624     bilen[j] = onz_row;
625   }
626   PetscFunctionReturn(0);
627 }
628 
629 PetscErrorCode MatGetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],PetscScalar v[])
630 {
631   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
632   PetscInt       i,j,rstart = mat->rmap->rstart,rend = mat->rmap->rend;
633   PetscInt       cstart = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
634 
635   PetscFunctionBegin;
636   for (i=0; i<m; i++) {
637     if (idxm[i] < 0) continue; /* negative row */
638     PetscCheck(idxm[i] < mat->rmap->N,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %" PetscInt_FMT " max %" PetscInt_FMT,idxm[i],mat->rmap->N-1);
639     if (idxm[i] >= rstart && idxm[i] < rend) {
640       row = idxm[i] - rstart;
641       for (j=0; j<n; j++) {
642         if (idxn[j] < 0) continue; /* negative column */
643         PetscCheck(idxn[j] < mat->cmap->N,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %" PetscInt_FMT " max %" PetscInt_FMT,idxn[j],mat->cmap->N-1);
644         if (idxn[j] >= cstart && idxn[j] < cend) {
645           col  = idxn[j] - cstart;
646           PetscCall(MatGetValues(aij->A,1,&row,1,&col,v+i*n+j));
647         } else {
648           if (!aij->colmap) {
649             PetscCall(MatCreateColmap_MPIAIJ_Private(mat));
650           }
651 #if defined(PETSC_USE_CTABLE)
652           PetscCall(PetscTableFind(aij->colmap,idxn[j]+1,&col));
653           col--;
654 #else
655           col = aij->colmap[idxn[j]] - 1;
656 #endif
657           if ((col < 0) || (aij->garray[col] != idxn[j])) *(v+i*n+j) = 0.0;
658           else {
659             PetscCall(MatGetValues(aij->B,1,&row,1,&col,v+i*n+j));
660           }
661         }
662       }
663     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only local values currently supported");
664   }
665   PetscFunctionReturn(0);
666 }
667 
668 PetscErrorCode MatAssemblyBegin_MPIAIJ(Mat mat,MatAssemblyType mode)
669 {
670   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
671   PetscInt       nstash,reallocs;
672 
673   PetscFunctionBegin;
674   if (aij->donotstash || mat->nooffprocentries) PetscFunctionReturn(0);
675 
676   PetscCall(MatStashScatterBegin_Private(mat,&mat->stash,mat->rmap->range));
677   PetscCall(MatStashGetInfo_Private(&mat->stash,&nstash,&reallocs));
678   PetscCall(PetscInfo(aij->A,"Stash has %" PetscInt_FMT " entries, uses %" PetscInt_FMT " mallocs.\n",nstash,reallocs));
679   PetscFunctionReturn(0);
680 }
681 
682 PetscErrorCode MatAssemblyEnd_MPIAIJ(Mat mat,MatAssemblyType mode)
683 {
684   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
685   PetscMPIInt    n;
686   PetscInt       i,j,rstart,ncols,flg;
687   PetscInt       *row,*col;
688   PetscBool      other_disassembled;
689   PetscScalar    *val;
690 
691   /* do not use 'b = (Mat_SeqAIJ*)aij->B->data' as B can be reset in disassembly */
692 
693   PetscFunctionBegin;
694   if (!aij->donotstash && !mat->nooffprocentries) {
695     while (1) {
696       PetscCall(MatStashScatterGetMesg_Private(&mat->stash,&n,&row,&col,&val,&flg));
697       if (!flg) break;
698 
699       for (i=0; i<n;) {
700         /* Now identify the consecutive vals belonging to the same row */
701         for (j=i,rstart=row[j]; j<n; j++) {
702           if (row[j] != rstart) break;
703         }
704         if (j < n) ncols = j-i;
705         else       ncols = n-i;
706         /* Now assemble all these values with a single function call */
707         PetscCall(MatSetValues_MPIAIJ(mat,1,row+i,ncols,col+i,val+i,mat->insertmode));
708         i    = j;
709       }
710     }
711     PetscCall(MatStashScatterEnd_Private(&mat->stash));
712   }
713 #if defined(PETSC_HAVE_DEVICE)
714   if (mat->offloadmask == PETSC_OFFLOAD_CPU) aij->A->offloadmask = PETSC_OFFLOAD_CPU;
715   /* We call MatBindToCPU() on aij->A and aij->B here, because if MatBindToCPU_MPIAIJ() is called before assembly, it cannot bind these. */
716   if (mat->boundtocpu) {
717     PetscCall(MatBindToCPU(aij->A,PETSC_TRUE));
718     PetscCall(MatBindToCPU(aij->B,PETSC_TRUE));
719   }
720 #endif
721   PetscCall(MatAssemblyBegin(aij->A,mode));
722   PetscCall(MatAssemblyEnd(aij->A,mode));
723 
724   /* determine if any processor has disassembled, if so we must
725      also disassemble ourself, in order that we may reassemble. */
726   /*
727      if nonzero structure of submatrix B cannot change then we know that
728      no processor disassembled thus we can skip this stuff
729   */
730   if (!((Mat_SeqAIJ*)aij->B->data)->nonew) {
731     PetscCall(MPIU_Allreduce(&mat->was_assembled,&other_disassembled,1,MPIU_BOOL,MPI_PROD,PetscObjectComm((PetscObject)mat)));
732     if (mat->was_assembled && !other_disassembled) { /* mat on this rank has reduced off-diag B with local col ids, but globaly it does not */
733       PetscCall(MatDisAssemble_MPIAIJ(mat));
734     }
735   }
736   if (!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) {
737     PetscCall(MatSetUpMultiply_MPIAIJ(mat));
738   }
739   PetscCall(MatSetOption(aij->B,MAT_USE_INODES,PETSC_FALSE));
740 #if defined(PETSC_HAVE_DEVICE)
741   if (mat->offloadmask == PETSC_OFFLOAD_CPU && aij->B->offloadmask != PETSC_OFFLOAD_UNALLOCATED) aij->B->offloadmask = PETSC_OFFLOAD_CPU;
742 #endif
743   PetscCall(MatAssemblyBegin(aij->B,mode));
744   PetscCall(MatAssemblyEnd(aij->B,mode));
745 
746   PetscCall(PetscFree2(aij->rowvalues,aij->rowindices));
747 
748   aij->rowvalues = NULL;
749 
750   PetscCall(VecDestroy(&aij->diag));
751 
752   /* if no new nonzero locations are allowed in matrix then only set the matrix state the first time through */
753   if ((!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) || !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
754     PetscObjectState state = aij->A->nonzerostate + aij->B->nonzerostate;
755     PetscCall(MPIU_Allreduce(&state,&mat->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)mat)));
756   }
757 #if defined(PETSC_HAVE_DEVICE)
758   mat->offloadmask = PETSC_OFFLOAD_BOTH;
759 #endif
760   PetscFunctionReturn(0);
761 }
762 
763 PetscErrorCode MatZeroEntries_MPIAIJ(Mat A)
764 {
765   Mat_MPIAIJ     *l = (Mat_MPIAIJ*)A->data;
766 
767   PetscFunctionBegin;
768   PetscCall(MatZeroEntries(l->A));
769   PetscCall(MatZeroEntries(l->B));
770   PetscFunctionReturn(0);
771 }
772 
773 PetscErrorCode MatZeroRows_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
774 {
775   Mat_MPIAIJ      *mat = (Mat_MPIAIJ *) A->data;
776   PetscObjectState sA, sB;
777   PetscInt        *lrows;
778   PetscInt         r, len;
779   PetscBool        cong, lch, gch;
780 
781   PetscFunctionBegin;
782   /* get locally owned rows */
783   PetscCall(MatZeroRowsMapLocal_Private(A,N,rows,&len,&lrows));
784   PetscCall(MatHasCongruentLayouts(A,&cong));
785   /* fix right hand side if needed */
786   if (x && b) {
787     const PetscScalar *xx;
788     PetscScalar       *bb;
789 
790     PetscCheck(cong,PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Need matching row/col layout");
791     PetscCall(VecGetArrayRead(x, &xx));
792     PetscCall(VecGetArray(b, &bb));
793     for (r = 0; r < len; ++r) bb[lrows[r]] = diag*xx[lrows[r]];
794     PetscCall(VecRestoreArrayRead(x, &xx));
795     PetscCall(VecRestoreArray(b, &bb));
796   }
797 
798   sA = mat->A->nonzerostate;
799   sB = mat->B->nonzerostate;
800 
801   if (diag != 0.0 && cong) {
802     PetscCall(MatZeroRows(mat->A, len, lrows, diag, NULL, NULL));
803     PetscCall(MatZeroRows(mat->B, len, lrows, 0.0, NULL, NULL));
804   } else if (diag != 0.0) { /* non-square or non congruent layouts -> if keepnonzeropattern is false, we allow for new insertion */
805     Mat_SeqAIJ *aijA = (Mat_SeqAIJ*)mat->A->data;
806     Mat_SeqAIJ *aijB = (Mat_SeqAIJ*)mat->B->data;
807     PetscInt   nnwA, nnwB;
808     PetscBool  nnzA, nnzB;
809 
810     nnwA = aijA->nonew;
811     nnwB = aijB->nonew;
812     nnzA = aijA->keepnonzeropattern;
813     nnzB = aijB->keepnonzeropattern;
814     if (!nnzA) {
815       PetscCall(PetscInfo(mat->A,"Requested to not keep the pattern and add a nonzero diagonal; may encounter reallocations on diagonal block.\n"));
816       aijA->nonew = 0;
817     }
818     if (!nnzB) {
819       PetscCall(PetscInfo(mat->B,"Requested to not keep the pattern and add a nonzero diagonal; may encounter reallocations on off-diagonal block.\n"));
820       aijB->nonew = 0;
821     }
822     /* Must zero here before the next loop */
823     PetscCall(MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL));
824     PetscCall(MatZeroRows(mat->B, len, lrows, 0.0, NULL, NULL));
825     for (r = 0; r < len; ++r) {
826       const PetscInt row = lrows[r] + A->rmap->rstart;
827       if (row >= A->cmap->N) continue;
828       PetscCall(MatSetValues(A, 1, &row, 1, &row, &diag, INSERT_VALUES));
829     }
830     aijA->nonew = nnwA;
831     aijB->nonew = nnwB;
832   } else {
833     PetscCall(MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL));
834     PetscCall(MatZeroRows(mat->B, len, lrows, 0.0, NULL, NULL));
835   }
836   PetscCall(PetscFree(lrows));
837   PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
838   PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
839 
840   /* reduce nonzerostate */
841   lch = (PetscBool)(sA != mat->A->nonzerostate || sB != mat->B->nonzerostate);
842   PetscCall(MPIU_Allreduce(&lch,&gch,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)A)));
843   if (gch) A->nonzerostate++;
844   PetscFunctionReturn(0);
845 }
846 
847 PetscErrorCode MatZeroRowsColumns_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
848 {
849   Mat_MPIAIJ        *l = (Mat_MPIAIJ*)A->data;
850   PetscMPIInt       n = A->rmap->n;
851   PetscInt          i,j,r,m,len = 0;
852   PetscInt          *lrows,*owners = A->rmap->range;
853   PetscMPIInt       p = 0;
854   PetscSFNode       *rrows;
855   PetscSF           sf;
856   const PetscScalar *xx;
857   PetscScalar       *bb,*mask,*aij_a;
858   Vec               xmask,lmask;
859   Mat_SeqAIJ        *aij = (Mat_SeqAIJ*)l->B->data;
860   const PetscInt    *aj, *ii,*ridx;
861   PetscScalar       *aa;
862 
863   PetscFunctionBegin;
864   /* Create SF where leaves are input rows and roots are owned rows */
865   PetscCall(PetscMalloc1(n, &lrows));
866   for (r = 0; r < n; ++r) lrows[r] = -1;
867   PetscCall(PetscMalloc1(N, &rrows));
868   for (r = 0; r < N; ++r) {
869     const PetscInt idx   = rows[r];
870     PetscCheck(idx >= 0 && A->rmap->N > idx,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row %" PetscInt_FMT " out of range [0,%" PetscInt_FMT ")",idx,A->rmap->N);
871     if (idx < owners[p] || owners[p+1] <= idx) { /* short-circuit the search if the last p owns this row too */
872       PetscCall(PetscLayoutFindOwner(A->rmap,idx,&p));
873     }
874     rrows[r].rank  = p;
875     rrows[r].index = rows[r] - owners[p];
876   }
877   PetscCall(PetscSFCreate(PetscObjectComm((PetscObject) A), &sf));
878   PetscCall(PetscSFSetGraph(sf, n, N, NULL, PETSC_OWN_POINTER, rrows, PETSC_OWN_POINTER));
879   /* Collect flags for rows to be zeroed */
880   PetscCall(PetscSFReduceBegin(sf, MPIU_INT, (PetscInt *) rows, lrows, MPI_LOR));
881   PetscCall(PetscSFReduceEnd(sf, MPIU_INT, (PetscInt *) rows, lrows, MPI_LOR));
882   PetscCall(PetscSFDestroy(&sf));
883   /* Compress and put in row numbers */
884   for (r = 0; r < n; ++r) if (lrows[r] >= 0) lrows[len++] = r;
885   /* zero diagonal part of matrix */
886   PetscCall(MatZeroRowsColumns(l->A,len,lrows,diag,x,b));
887   /* handle off diagonal part of matrix */
888   PetscCall(MatCreateVecs(A,&xmask,NULL));
889   PetscCall(VecDuplicate(l->lvec,&lmask));
890   PetscCall(VecGetArray(xmask,&bb));
891   for (i=0; i<len; i++) bb[lrows[i]] = 1;
892   PetscCall(VecRestoreArray(xmask,&bb));
893   PetscCall(VecScatterBegin(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD));
894   PetscCall(VecScatterEnd(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD));
895   PetscCall(VecDestroy(&xmask));
896   if (x && b) { /* this code is buggy when the row and column layout don't match */
897     PetscBool cong;
898 
899     PetscCall(MatHasCongruentLayouts(A,&cong));
900     PetscCheck(cong,PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Need matching row/col layout");
901     PetscCall(VecScatterBegin(l->Mvctx,x,l->lvec,INSERT_VALUES,SCATTER_FORWARD));
902     PetscCall(VecScatterEnd(l->Mvctx,x,l->lvec,INSERT_VALUES,SCATTER_FORWARD));
903     PetscCall(VecGetArrayRead(l->lvec,&xx));
904     PetscCall(VecGetArray(b,&bb));
905   }
906   PetscCall(VecGetArray(lmask,&mask));
907   /* remove zeroed rows of off diagonal matrix */
908   PetscCall(MatSeqAIJGetArray(l->B,&aij_a));
909   ii = aij->i;
910   for (i=0; i<len; i++) {
911     PetscCall(PetscArrayzero(aij_a + ii[lrows[i]],ii[lrows[i]+1] - ii[lrows[i]]));
912   }
913   /* loop over all elements of off process part of matrix zeroing removed columns*/
914   if (aij->compressedrow.use) {
915     m    = aij->compressedrow.nrows;
916     ii   = aij->compressedrow.i;
917     ridx = aij->compressedrow.rindex;
918     for (i=0; i<m; i++) {
919       n  = ii[i+1] - ii[i];
920       aj = aij->j + ii[i];
921       aa = aij_a + ii[i];
922 
923       for (j=0; j<n; j++) {
924         if (PetscAbsScalar(mask[*aj])) {
925           if (b) bb[*ridx] -= *aa*xx[*aj];
926           *aa = 0.0;
927         }
928         aa++;
929         aj++;
930       }
931       ridx++;
932     }
933   } else { /* do not use compressed row format */
934     m = l->B->rmap->n;
935     for (i=0; i<m; i++) {
936       n  = ii[i+1] - ii[i];
937       aj = aij->j + ii[i];
938       aa = aij_a + ii[i];
939       for (j=0; j<n; j++) {
940         if (PetscAbsScalar(mask[*aj])) {
941           if (b) bb[i] -= *aa*xx[*aj];
942           *aa = 0.0;
943         }
944         aa++;
945         aj++;
946       }
947     }
948   }
949   if (x && b) {
950     PetscCall(VecRestoreArray(b,&bb));
951     PetscCall(VecRestoreArrayRead(l->lvec,&xx));
952   }
953   PetscCall(MatSeqAIJRestoreArray(l->B,&aij_a));
954   PetscCall(VecRestoreArray(lmask,&mask));
955   PetscCall(VecDestroy(&lmask));
956   PetscCall(PetscFree(lrows));
957 
958   /* only change matrix nonzero state if pattern was allowed to be changed */
959   if (!((Mat_SeqAIJ*)(l->A->data))->keepnonzeropattern) {
960     PetscObjectState state = l->A->nonzerostate + l->B->nonzerostate;
961     PetscCall(MPIU_Allreduce(&state,&A->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)A)));
962   }
963   PetscFunctionReturn(0);
964 }
965 
966 PetscErrorCode MatMult_MPIAIJ(Mat A,Vec xx,Vec yy)
967 {
968   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
969   PetscInt       nt;
970   VecScatter     Mvctx = a->Mvctx;
971 
972   PetscFunctionBegin;
973   PetscCall(VecGetLocalSize(xx,&nt));
974   PetscCheck(nt == A->cmap->n,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Incompatible partition of A (%" PetscInt_FMT ") and xx (%" PetscInt_FMT ")",A->cmap->n,nt);
975   PetscCall(VecScatterBegin(Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD));
976   PetscCall((*a->A->ops->mult)(a->A,xx,yy));
977   PetscCall(VecScatterEnd(Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD));
978   PetscCall((*a->B->ops->multadd)(a->B,a->lvec,yy,yy));
979   PetscFunctionReturn(0);
980 }
981 
982 PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat A,Vec bb,Vec xx)
983 {
984   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
985 
986   PetscFunctionBegin;
987   PetscCall(MatMultDiagonalBlock(a->A,bb,xx));
988   PetscFunctionReturn(0);
989 }
990 
991 PetscErrorCode MatMultAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
992 {
993   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
994   VecScatter     Mvctx = a->Mvctx;
995 
996   PetscFunctionBegin;
997   PetscCall(VecScatterBegin(Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD));
998   PetscCall((*a->A->ops->multadd)(a->A,xx,yy,zz));
999   PetscCall(VecScatterEnd(Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD));
1000   PetscCall((*a->B->ops->multadd)(a->B,a->lvec,zz,zz));
1001   PetscFunctionReturn(0);
1002 }
1003 
1004 PetscErrorCode MatMultTranspose_MPIAIJ(Mat A,Vec xx,Vec yy)
1005 {
1006   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1007 
1008   PetscFunctionBegin;
1009   /* do nondiagonal part */
1010   PetscCall((*a->B->ops->multtranspose)(a->B,xx,a->lvec));
1011   /* do local part */
1012   PetscCall((*a->A->ops->multtranspose)(a->A,xx,yy));
1013   /* add partial results together */
1014   PetscCall(VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE));
1015   PetscCall(VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE));
1016   PetscFunctionReturn(0);
1017 }
1018 
1019 PetscErrorCode MatIsTranspose_MPIAIJ(Mat Amat,Mat Bmat,PetscReal tol,PetscBool  *f)
1020 {
1021   MPI_Comm       comm;
1022   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ*) Amat->data, *Bij;
1023   Mat            Adia = Aij->A, Bdia, Aoff,Boff,*Aoffs,*Boffs;
1024   IS             Me,Notme;
1025   PetscInt       M,N,first,last,*notme,i;
1026   PetscBool      lf;
1027   PetscMPIInt    size;
1028 
1029   PetscFunctionBegin;
1030   /* Easy test: symmetric diagonal block */
1031   Bij  = (Mat_MPIAIJ*) Bmat->data; Bdia = Bij->A;
1032   PetscCall(MatIsTranspose(Adia,Bdia,tol,&lf));
1033   PetscCall(MPIU_Allreduce(&lf,f,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)Amat)));
1034   if (!*f) PetscFunctionReturn(0);
1035   PetscCall(PetscObjectGetComm((PetscObject)Amat,&comm));
1036   PetscCallMPI(MPI_Comm_size(comm,&size));
1037   if (size == 1) PetscFunctionReturn(0);
1038 
1039   /* Hard test: off-diagonal block. This takes a MatCreateSubMatrix. */
1040   PetscCall(MatGetSize(Amat,&M,&N));
1041   PetscCall(MatGetOwnershipRange(Amat,&first,&last));
1042   PetscCall(PetscMalloc1(N-last+first,&notme));
1043   for (i=0; i<first; i++) notme[i] = i;
1044   for (i=last; i<M; i++) notme[i-last+first] = i;
1045   PetscCall(ISCreateGeneral(MPI_COMM_SELF,N-last+first,notme,PETSC_COPY_VALUES,&Notme));
1046   PetscCall(ISCreateStride(MPI_COMM_SELF,last-first,first,1,&Me));
1047   PetscCall(MatCreateSubMatrices(Amat,1,&Me,&Notme,MAT_INITIAL_MATRIX,&Aoffs));
1048   Aoff = Aoffs[0];
1049   PetscCall(MatCreateSubMatrices(Bmat,1,&Notme,&Me,MAT_INITIAL_MATRIX,&Boffs));
1050   Boff = Boffs[0];
1051   PetscCall(MatIsTranspose(Aoff,Boff,tol,f));
1052   PetscCall(MatDestroyMatrices(1,&Aoffs));
1053   PetscCall(MatDestroyMatrices(1,&Boffs));
1054   PetscCall(ISDestroy(&Me));
1055   PetscCall(ISDestroy(&Notme));
1056   PetscCall(PetscFree(notme));
1057   PetscFunctionReturn(0);
1058 }
1059 
1060 PetscErrorCode MatIsSymmetric_MPIAIJ(Mat A,PetscReal tol,PetscBool  *f)
1061 {
1062   PetscFunctionBegin;
1063   PetscCall(MatIsTranspose_MPIAIJ(A,A,tol,f));
1064   PetscFunctionReturn(0);
1065 }
1066 
1067 PetscErrorCode MatMultTransposeAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1068 {
1069   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1070 
1071   PetscFunctionBegin;
1072   /* do nondiagonal part */
1073   PetscCall((*a->B->ops->multtranspose)(a->B,xx,a->lvec));
1074   /* do local part */
1075   PetscCall((*a->A->ops->multtransposeadd)(a->A,xx,yy,zz));
1076   /* add partial results together */
1077   PetscCall(VecScatterBegin(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE));
1078   PetscCall(VecScatterEnd(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE));
1079   PetscFunctionReturn(0);
1080 }
1081 
1082 /*
1083   This only works correctly for square matrices where the subblock A->A is the
1084    diagonal block
1085 */
1086 PetscErrorCode MatGetDiagonal_MPIAIJ(Mat A,Vec v)
1087 {
1088   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1089 
1090   PetscFunctionBegin;
1091   PetscCheck(A->rmap->N == A->cmap->N,PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Supports only square matrix where A->A is diag block");
1092   PetscCheck(A->rmap->rstart == A->cmap->rstart && A->rmap->rend == A->cmap->rend,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"row partition must equal col partition");
1093   PetscCall(MatGetDiagonal(a->A,v));
1094   PetscFunctionReturn(0);
1095 }
1096 
1097 PetscErrorCode MatScale_MPIAIJ(Mat A,PetscScalar aa)
1098 {
1099   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1100 
1101   PetscFunctionBegin;
1102   PetscCall(MatScale(a->A,aa));
1103   PetscCall(MatScale(a->B,aa));
1104   PetscFunctionReturn(0);
1105 }
1106 
1107 /* Free COO stuff; must match allocation methods in MatSetPreallocationCOO_MPIAIJ() */
1108 PETSC_INTERN PetscErrorCode MatResetPreallocationCOO_MPIAIJ(Mat mat)
1109 {
1110   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1111 
1112   PetscFunctionBegin;
1113   PetscCall(PetscSFDestroy(&aij->coo_sf));
1114   PetscCall(PetscFree(aij->Aperm1));
1115   PetscCall(PetscFree(aij->Bperm1));
1116   PetscCall(PetscFree(aij->Ajmap1));
1117   PetscCall(PetscFree(aij->Bjmap1));
1118 
1119   PetscCall(PetscFree(aij->Aimap2));
1120   PetscCall(PetscFree(aij->Bimap2));
1121   PetscCall(PetscFree(aij->Aperm2));
1122   PetscCall(PetscFree(aij->Bperm2));
1123   PetscCall(PetscFree(aij->Ajmap2));
1124   PetscCall(PetscFree(aij->Bjmap2));
1125 
1126   PetscCall(PetscFree2(aij->sendbuf,aij->recvbuf));
1127   PetscCall(PetscFree(aij->Cperm1));
1128   PetscFunctionReturn(0);
1129 }
1130 
1131 PetscErrorCode MatDestroy_MPIAIJ(Mat mat)
1132 {
1133   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1134 
1135   PetscFunctionBegin;
1136 #if defined(PETSC_USE_LOG)
1137   PetscLogObjectState((PetscObject)mat,"Rows=%" PetscInt_FMT ", Cols=%" PetscInt_FMT,mat->rmap->N,mat->cmap->N);
1138 #endif
1139   PetscCall(MatStashDestroy_Private(&mat->stash));
1140   PetscCall(VecDestroy(&aij->diag));
1141   PetscCall(MatDestroy(&aij->A));
1142   PetscCall(MatDestroy(&aij->B));
1143 #if defined(PETSC_USE_CTABLE)
1144   PetscCall(PetscTableDestroy(&aij->colmap));
1145 #else
1146   PetscCall(PetscFree(aij->colmap));
1147 #endif
1148   PetscCall(PetscFree(aij->garray));
1149   PetscCall(VecDestroy(&aij->lvec));
1150   PetscCall(VecScatterDestroy(&aij->Mvctx));
1151   PetscCall(PetscFree2(aij->rowvalues,aij->rowindices));
1152   PetscCall(PetscFree(aij->ld));
1153 
1154   /* Free COO */
1155   PetscCall(MatResetPreallocationCOO_MPIAIJ(mat));
1156 
1157   PetscCall(PetscFree(mat->data));
1158 
1159   /* may be created by MatCreateMPIAIJSumSeqAIJSymbolic */
1160   PetscCall(PetscObjectCompose((PetscObject)mat,"MatMergeSeqsToMPI",NULL));
1161 
1162   PetscCall(PetscObjectChangeTypeName((PetscObject)mat,NULL));
1163   PetscCall(PetscObjectComposeFunction((PetscObject)mat,"MatStoreValues_C",NULL));
1164   PetscCall(PetscObjectComposeFunction((PetscObject)mat,"MatRetrieveValues_C",NULL));
1165   PetscCall(PetscObjectComposeFunction((PetscObject)mat,"MatIsTranspose_C",NULL));
1166   PetscCall(PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocation_C",NULL));
1167   PetscCall(PetscObjectComposeFunction((PetscObject)mat,"MatResetPreallocation_C",NULL));
1168   PetscCall(PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocationCSR_C",NULL));
1169   PetscCall(PetscObjectComposeFunction((PetscObject)mat,"MatDiagonalScaleLocal_C",NULL));
1170   PetscCall(PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_mpibaij_C",NULL));
1171   PetscCall(PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_mpisbaij_C",NULL));
1172 #if defined(PETSC_HAVE_CUDA)
1173   PetscCall(PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_mpiaijcusparse_C",NULL));
1174 #endif
1175 #if defined(PETSC_HAVE_KOKKOS_KERNELS)
1176   PetscCall(PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_mpiaijkokkos_C",NULL));
1177 #endif
1178   PetscCall(PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_mpidense_C",NULL));
1179 #if defined(PETSC_HAVE_ELEMENTAL)
1180   PetscCall(PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_elemental_C",NULL));
1181 #endif
1182 #if defined(PETSC_HAVE_SCALAPACK)
1183   PetscCall(PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_scalapack_C",NULL));
1184 #endif
1185 #if defined(PETSC_HAVE_HYPRE)
1186   PetscCall(PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_hypre_C",NULL));
1187   PetscCall(PetscObjectComposeFunction((PetscObject)mat,"MatProductSetFromOptions_transpose_mpiaij_mpiaij_C",NULL));
1188 #endif
1189   PetscCall(PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_is_C",NULL));
1190   PetscCall(PetscObjectComposeFunction((PetscObject)mat,"MatProductSetFromOptions_is_mpiaij_C",NULL));
1191   PetscCall(PetscObjectComposeFunction((PetscObject)mat,"MatProductSetFromOptions_mpiaij_mpiaij_C",NULL));
1192   PetscCall(PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetUseScalableIncreaseOverlap_C",NULL));
1193   PetscCall(PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_mpiaijperm_C",NULL));
1194   PetscCall(PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_mpiaijsell_C",NULL));
1195 #if defined(PETSC_HAVE_MKL_SPARSE)
1196   PetscCall(PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_mpiaijmkl_C",NULL));
1197 #endif
1198   PetscCall(PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_mpiaijcrl_C",NULL));
1199   PetscCall(PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_is_C",NULL));
1200   PetscCall(PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_mpisell_C",NULL));
1201   PetscCall(PetscObjectComposeFunction((PetscObject)mat,"MatSetPreallocationCOO_C",NULL));
1202   PetscCall(PetscObjectComposeFunction((PetscObject)mat,"MatSetValuesCOO_C",NULL));
1203   PetscFunctionReturn(0);
1204 }
1205 
1206 PetscErrorCode MatView_MPIAIJ_Binary(Mat mat,PetscViewer viewer)
1207 {
1208   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)mat->data;
1209   Mat_SeqAIJ        *A   = (Mat_SeqAIJ*)aij->A->data;
1210   Mat_SeqAIJ        *B   = (Mat_SeqAIJ*)aij->B->data;
1211   const PetscInt    *garray = aij->garray;
1212   const PetscScalar *aa,*ba;
1213   PetscInt          header[4],M,N,m,rs,cs,nz,cnt,i,ja,jb;
1214   PetscInt          *rowlens;
1215   PetscInt          *colidxs;
1216   PetscScalar       *matvals;
1217 
1218   PetscFunctionBegin;
1219   PetscCall(PetscViewerSetUp(viewer));
1220 
1221   M  = mat->rmap->N;
1222   N  = mat->cmap->N;
1223   m  = mat->rmap->n;
1224   rs = mat->rmap->rstart;
1225   cs = mat->cmap->rstart;
1226   nz = A->nz + B->nz;
1227 
1228   /* write matrix header */
1229   header[0] = MAT_FILE_CLASSID;
1230   header[1] = M; header[2] = N; header[3] = nz;
1231   PetscCallMPI(MPI_Reduce(&nz,&header[3],1,MPIU_INT,MPI_SUM,0,PetscObjectComm((PetscObject)mat)));
1232   PetscCall(PetscViewerBinaryWrite(viewer,header,4,PETSC_INT));
1233 
1234   /* fill in and store row lengths  */
1235   PetscCall(PetscMalloc1(m,&rowlens));
1236   for (i=0; i<m; i++) rowlens[i] = A->i[i+1] - A->i[i] + B->i[i+1] - B->i[i];
1237   PetscCall(PetscViewerBinaryWriteAll(viewer,rowlens,m,rs,M,PETSC_INT));
1238   PetscCall(PetscFree(rowlens));
1239 
1240   /* fill in and store column indices */
1241   PetscCall(PetscMalloc1(nz,&colidxs));
1242   for (cnt=0, i=0; i<m; i++) {
1243     for (jb=B->i[i]; jb<B->i[i+1]; jb++) {
1244       if (garray[B->j[jb]] > cs) break;
1245       colidxs[cnt++] = garray[B->j[jb]];
1246     }
1247     for (ja=A->i[i]; ja<A->i[i+1]; ja++)
1248       colidxs[cnt++] = A->j[ja] + cs;
1249     for (; jb<B->i[i+1]; jb++)
1250       colidxs[cnt++] = garray[B->j[jb]];
1251   }
1252   PetscCheck(cnt == nz,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Internal PETSc error: cnt = %" PetscInt_FMT " nz = %" PetscInt_FMT,cnt,nz);
1253   PetscCall(PetscViewerBinaryWriteAll(viewer,colidxs,nz,PETSC_DETERMINE,PETSC_DETERMINE,PETSC_INT));
1254   PetscCall(PetscFree(colidxs));
1255 
1256   /* fill in and store nonzero values */
1257   PetscCall(MatSeqAIJGetArrayRead(aij->A,&aa));
1258   PetscCall(MatSeqAIJGetArrayRead(aij->B,&ba));
1259   PetscCall(PetscMalloc1(nz,&matvals));
1260   for (cnt=0, i=0; i<m; i++) {
1261     for (jb=B->i[i]; jb<B->i[i+1]; jb++) {
1262       if (garray[B->j[jb]] > cs) break;
1263       matvals[cnt++] = ba[jb];
1264     }
1265     for (ja=A->i[i]; ja<A->i[i+1]; ja++)
1266       matvals[cnt++] = aa[ja];
1267     for (; jb<B->i[i+1]; jb++)
1268       matvals[cnt++] = ba[jb];
1269   }
1270   PetscCall(MatSeqAIJRestoreArrayRead(aij->A,&aa));
1271   PetscCall(MatSeqAIJRestoreArrayRead(aij->B,&ba));
1272   PetscCheck(cnt == nz,PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: cnt = %" PetscInt_FMT " nz = %" PetscInt_FMT,cnt,nz);
1273   PetscCall(PetscViewerBinaryWriteAll(viewer,matvals,nz,PETSC_DETERMINE,PETSC_DETERMINE,PETSC_SCALAR));
1274   PetscCall(PetscFree(matvals));
1275 
1276   /* write block size option to the viewer's .info file */
1277   PetscCall(MatView_Binary_BlockSizes(mat,viewer));
1278   PetscFunctionReturn(0);
1279 }
1280 
1281 #include <petscdraw.h>
1282 PetscErrorCode MatView_MPIAIJ_ASCIIorDraworSocket(Mat mat,PetscViewer viewer)
1283 {
1284   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)mat->data;
1285   PetscMPIInt       rank = aij->rank,size = aij->size;
1286   PetscBool         isdraw,iascii,isbinary;
1287   PetscViewer       sviewer;
1288   PetscViewerFormat format;
1289 
1290   PetscFunctionBegin;
1291   PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw));
1292   PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii));
1293   PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary));
1294   if (iascii) {
1295     PetscCall(PetscViewerGetFormat(viewer,&format));
1296     if (format == PETSC_VIEWER_LOAD_BALANCE) {
1297       PetscInt i,nmax = 0,nmin = PETSC_MAX_INT,navg = 0,*nz,nzlocal = ((Mat_SeqAIJ*) (aij->A->data))->nz + ((Mat_SeqAIJ*) (aij->B->data))->nz;
1298       PetscCall(PetscMalloc1(size,&nz));
1299       PetscCallMPI(MPI_Allgather(&nzlocal,1,MPIU_INT,nz,1,MPIU_INT,PetscObjectComm((PetscObject)mat)));
1300       for (i=0; i<(PetscInt)size; i++) {
1301         nmax = PetscMax(nmax,nz[i]);
1302         nmin = PetscMin(nmin,nz[i]);
1303         navg += nz[i];
1304       }
1305       PetscCall(PetscFree(nz));
1306       navg = navg/size;
1307       PetscCall(PetscViewerASCIIPrintf(viewer,"Load Balance - Nonzeros: Min %" PetscInt_FMT "  avg %" PetscInt_FMT "  max %" PetscInt_FMT "\n",nmin,navg,nmax));
1308       PetscFunctionReturn(0);
1309     }
1310     PetscCall(PetscViewerGetFormat(viewer,&format));
1311     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
1312       MatInfo   info;
1313       PetscInt *inodes=NULL;
1314 
1315       PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank));
1316       PetscCall(MatGetInfo(mat,MAT_LOCAL,&info));
1317       PetscCall(MatInodeGetInodeSizes(aij->A,NULL,&inodes,NULL));
1318       PetscCall(PetscViewerASCIIPushSynchronized(viewer));
1319       if (!inodes) {
1320         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %" PetscInt_FMT " nz %" PetscInt_FMT " nz alloced %" PetscInt_FMT " mem %g, not using I-node routines\n",
1321                                                    rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(double)info.memory));
1322       } else {
1323         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %" PetscInt_FMT " nz %" PetscInt_FMT " nz alloced %" PetscInt_FMT " mem %g, using I-node routines\n",
1324                                                    rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(double)info.memory));
1325       }
1326       PetscCall(MatGetInfo(aij->A,MAT_LOCAL,&info));
1327       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"[%d] on-diagonal part: nz %" PetscInt_FMT " \n",rank,(PetscInt)info.nz_used));
1328       PetscCall(MatGetInfo(aij->B,MAT_LOCAL,&info));
1329       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer,"[%d] off-diagonal part: nz %" PetscInt_FMT " \n",rank,(PetscInt)info.nz_used));
1330       PetscCall(PetscViewerFlush(viewer));
1331       PetscCall(PetscViewerASCIIPopSynchronized(viewer));
1332       PetscCall(PetscViewerASCIIPrintf(viewer,"Information on VecScatter used in matrix-vector product: \n"));
1333       PetscCall(VecScatterView(aij->Mvctx,viewer));
1334       PetscFunctionReturn(0);
1335     } else if (format == PETSC_VIEWER_ASCII_INFO) {
1336       PetscInt inodecount,inodelimit,*inodes;
1337       PetscCall(MatInodeGetInodeSizes(aij->A,&inodecount,&inodes,&inodelimit));
1338       if (inodes) {
1339         PetscCall(PetscViewerASCIIPrintf(viewer,"using I-node (on process 0) routines: found %" PetscInt_FMT " nodes, limit used is %" PetscInt_FMT "\n",inodecount,inodelimit));
1340       } else {
1341         PetscCall(PetscViewerASCIIPrintf(viewer,"not using I-node (on process 0) routines\n"));
1342       }
1343       PetscFunctionReturn(0);
1344     } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO) {
1345       PetscFunctionReturn(0);
1346     }
1347   } else if (isbinary) {
1348     if (size == 1) {
1349       PetscCall(PetscObjectSetName((PetscObject)aij->A,((PetscObject)mat)->name));
1350       PetscCall(MatView(aij->A,viewer));
1351     } else {
1352       PetscCall(MatView_MPIAIJ_Binary(mat,viewer));
1353     }
1354     PetscFunctionReturn(0);
1355   } else if (iascii && size == 1) {
1356     PetscCall(PetscObjectSetName((PetscObject)aij->A,((PetscObject)mat)->name));
1357     PetscCall(MatView(aij->A,viewer));
1358     PetscFunctionReturn(0);
1359   } else if (isdraw) {
1360     PetscDraw draw;
1361     PetscBool isnull;
1362     PetscCall(PetscViewerDrawGetDraw(viewer,0,&draw));
1363     PetscCall(PetscDrawIsNull(draw,&isnull));
1364     if (isnull) PetscFunctionReturn(0);
1365   }
1366 
1367   { /* assemble the entire matrix onto first processor */
1368     Mat A = NULL, Av;
1369     IS  isrow,iscol;
1370 
1371     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)mat),rank == 0 ? mat->rmap->N : 0,0,1,&isrow));
1372     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)mat),rank == 0 ? mat->cmap->N : 0,0,1,&iscol));
1373     PetscCall(MatCreateSubMatrix(mat,isrow,iscol,MAT_INITIAL_MATRIX,&A));
1374     PetscCall(MatMPIAIJGetSeqAIJ(A,&Av,NULL,NULL));
1375 /*  The commented code uses MatCreateSubMatrices instead */
1376 /*
1377     Mat *AA, A = NULL, Av;
1378     IS  isrow,iscol;
1379 
1380     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)mat),rank == 0 ? mat->rmap->N : 0,0,1,&isrow));
1381     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)mat),rank == 0 ? mat->cmap->N : 0,0,1,&iscol));
1382     PetscCall(MatCreateSubMatrices(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&AA));
1383     if (rank == 0) {
1384        PetscCall(PetscObjectReference((PetscObject)AA[0]));
1385        A    = AA[0];
1386        Av   = AA[0];
1387     }
1388     PetscCall(MatDestroySubMatrices(1,&AA));
1389 */
1390     PetscCall(ISDestroy(&iscol));
1391     PetscCall(ISDestroy(&isrow));
1392     /*
1393        Everyone has to call to draw the matrix since the graphics waits are
1394        synchronized across all processors that share the PetscDraw object
1395     */
1396     PetscCall(PetscViewerGetSubViewer(viewer,PETSC_COMM_SELF,&sviewer));
1397     if (rank == 0) {
1398       if (((PetscObject)mat)->name) {
1399         PetscCall(PetscObjectSetName((PetscObject)Av,((PetscObject)mat)->name));
1400       }
1401       PetscCall(MatView_SeqAIJ(Av,sviewer));
1402     }
1403     PetscCall(PetscViewerRestoreSubViewer(viewer,PETSC_COMM_SELF,&sviewer));
1404     PetscCall(PetscViewerFlush(viewer));
1405     PetscCall(MatDestroy(&A));
1406   }
1407   PetscFunctionReturn(0);
1408 }
1409 
1410 PetscErrorCode MatView_MPIAIJ(Mat mat,PetscViewer viewer)
1411 {
1412   PetscBool      iascii,isdraw,issocket,isbinary;
1413 
1414   PetscFunctionBegin;
1415   PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii));
1416   PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw));
1417   PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary));
1418   PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSOCKET,&issocket));
1419   if (iascii || isdraw || isbinary || issocket) {
1420     PetscCall(MatView_MPIAIJ_ASCIIorDraworSocket(mat,viewer));
1421   }
1422   PetscFunctionReturn(0);
1423 }
1424 
1425 PetscErrorCode MatSOR_MPIAIJ(Mat matin,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
1426 {
1427   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1428   Vec            bb1 = NULL;
1429   PetscBool      hasop;
1430 
1431   PetscFunctionBegin;
1432   if (flag == SOR_APPLY_UPPER) {
1433     PetscCall((*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx));
1434     PetscFunctionReturn(0);
1435   }
1436 
1437   if (its > 1 || ~flag & SOR_ZERO_INITIAL_GUESS || flag & SOR_EISENSTAT) {
1438     PetscCall(VecDuplicate(bb,&bb1));
1439   }
1440 
1441   if ((flag & SOR_LOCAL_SYMMETRIC_SWEEP) == SOR_LOCAL_SYMMETRIC_SWEEP) {
1442     if (flag & SOR_ZERO_INITIAL_GUESS) {
1443       PetscCall((*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx));
1444       its--;
1445     }
1446 
1447     while (its--) {
1448       PetscCall(VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD));
1449       PetscCall(VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD));
1450 
1451       /* update rhs: bb1 = bb - B*x */
1452       PetscCall(VecScale(mat->lvec,-1.0));
1453       PetscCall((*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1));
1454 
1455       /* local sweep */
1456       PetscCall((*mat->A->ops->sor)(mat->A,bb1,omega,SOR_SYMMETRIC_SWEEP,fshift,lits,1,xx));
1457     }
1458   } else if (flag & SOR_LOCAL_FORWARD_SWEEP) {
1459     if (flag & SOR_ZERO_INITIAL_GUESS) {
1460       PetscCall((*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx));
1461       its--;
1462     }
1463     while (its--) {
1464       PetscCall(VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD));
1465       PetscCall(VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD));
1466 
1467       /* update rhs: bb1 = bb - B*x */
1468       PetscCall(VecScale(mat->lvec,-1.0));
1469       PetscCall((*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1));
1470 
1471       /* local sweep */
1472       PetscCall((*mat->A->ops->sor)(mat->A,bb1,omega,SOR_FORWARD_SWEEP,fshift,lits,1,xx));
1473     }
1474   } else if (flag & SOR_LOCAL_BACKWARD_SWEEP) {
1475     if (flag & SOR_ZERO_INITIAL_GUESS) {
1476       PetscCall((*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx));
1477       its--;
1478     }
1479     while (its--) {
1480       PetscCall(VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD));
1481       PetscCall(VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD));
1482 
1483       /* update rhs: bb1 = bb - B*x */
1484       PetscCall(VecScale(mat->lvec,-1.0));
1485       PetscCall((*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1));
1486 
1487       /* local sweep */
1488       PetscCall((*mat->A->ops->sor)(mat->A,bb1,omega,SOR_BACKWARD_SWEEP,fshift,lits,1,xx));
1489     }
1490   } else if (flag & SOR_EISENSTAT) {
1491     Vec xx1;
1492 
1493     PetscCall(VecDuplicate(bb,&xx1));
1494     PetscCall((*mat->A->ops->sor)(mat->A,bb,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_BACKWARD_SWEEP),fshift,lits,1,xx));
1495 
1496     PetscCall(VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD));
1497     PetscCall(VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD));
1498     if (!mat->diag) {
1499       PetscCall(MatCreateVecs(matin,&mat->diag,NULL));
1500       PetscCall(MatGetDiagonal(matin,mat->diag));
1501     }
1502     PetscCall(MatHasOperation(matin,MATOP_MULT_DIAGONAL_BLOCK,&hasop));
1503     if (hasop) {
1504       PetscCall(MatMultDiagonalBlock(matin,xx,bb1));
1505     } else {
1506       PetscCall(VecPointwiseMult(bb1,mat->diag,xx));
1507     }
1508     PetscCall(VecAYPX(bb1,(omega-2.0)/omega,bb));
1509 
1510     PetscCall(MatMultAdd(mat->B,mat->lvec,bb1,bb1));
1511 
1512     /* local sweep */
1513     PetscCall((*mat->A->ops->sor)(mat->A,bb1,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_FORWARD_SWEEP),fshift,lits,1,xx1));
1514     PetscCall(VecAXPY(xx,1.0,xx1));
1515     PetscCall(VecDestroy(&xx1));
1516   } else SETERRQ(PetscObjectComm((PetscObject)matin),PETSC_ERR_SUP,"Parallel SOR not supported");
1517 
1518   PetscCall(VecDestroy(&bb1));
1519 
1520   matin->factorerrortype = mat->A->factorerrortype;
1521   PetscFunctionReturn(0);
1522 }
1523 
1524 PetscErrorCode MatPermute_MPIAIJ(Mat A,IS rowp,IS colp,Mat *B)
1525 {
1526   Mat            aA,aB,Aperm;
1527   const PetscInt *rwant,*cwant,*gcols,*ai,*bi,*aj,*bj;
1528   PetscScalar    *aa,*ba;
1529   PetscInt       i,j,m,n,ng,anz,bnz,*dnnz,*onnz,*tdnnz,*tonnz,*rdest,*cdest,*work,*gcdest;
1530   PetscSF        rowsf,sf;
1531   IS             parcolp = NULL;
1532   PetscBool      done;
1533 
1534   PetscFunctionBegin;
1535   PetscCall(MatGetLocalSize(A,&m,&n));
1536   PetscCall(ISGetIndices(rowp,&rwant));
1537   PetscCall(ISGetIndices(colp,&cwant));
1538   PetscCall(PetscMalloc3(PetscMax(m,n),&work,m,&rdest,n,&cdest));
1539 
1540   /* Invert row permutation to find out where my rows should go */
1541   PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A),&rowsf));
1542   PetscCall(PetscSFSetGraphLayout(rowsf,A->rmap,A->rmap->n,NULL,PETSC_OWN_POINTER,rwant));
1543   PetscCall(PetscSFSetFromOptions(rowsf));
1544   for (i=0; i<m; i++) work[i] = A->rmap->rstart + i;
1545   PetscCall(PetscSFReduceBegin(rowsf,MPIU_INT,work,rdest,MPI_REPLACE));
1546   PetscCall(PetscSFReduceEnd(rowsf,MPIU_INT,work,rdest,MPI_REPLACE));
1547 
1548   /* Invert column permutation to find out where my columns should go */
1549   PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A),&sf));
1550   PetscCall(PetscSFSetGraphLayout(sf,A->cmap,A->cmap->n,NULL,PETSC_OWN_POINTER,cwant));
1551   PetscCall(PetscSFSetFromOptions(sf));
1552   for (i=0; i<n; i++) work[i] = A->cmap->rstart + i;
1553   PetscCall(PetscSFReduceBegin(sf,MPIU_INT,work,cdest,MPI_REPLACE));
1554   PetscCall(PetscSFReduceEnd(sf,MPIU_INT,work,cdest,MPI_REPLACE));
1555   PetscCall(PetscSFDestroy(&sf));
1556 
1557   PetscCall(ISRestoreIndices(rowp,&rwant));
1558   PetscCall(ISRestoreIndices(colp,&cwant));
1559   PetscCall(MatMPIAIJGetSeqAIJ(A,&aA,&aB,&gcols));
1560 
1561   /* Find out where my gcols should go */
1562   PetscCall(MatGetSize(aB,NULL,&ng));
1563   PetscCall(PetscMalloc1(ng,&gcdest));
1564   PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A),&sf));
1565   PetscCall(PetscSFSetGraphLayout(sf,A->cmap,ng,NULL,PETSC_OWN_POINTER,gcols));
1566   PetscCall(PetscSFSetFromOptions(sf));
1567   PetscCall(PetscSFBcastBegin(sf,MPIU_INT,cdest,gcdest,MPI_REPLACE));
1568   PetscCall(PetscSFBcastEnd(sf,MPIU_INT,cdest,gcdest,MPI_REPLACE));
1569   PetscCall(PetscSFDestroy(&sf));
1570 
1571   PetscCall(PetscCalloc4(m,&dnnz,m,&onnz,m,&tdnnz,m,&tonnz));
1572   PetscCall(MatGetRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done));
1573   PetscCall(MatGetRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done));
1574   for (i=0; i<m; i++) {
1575     PetscInt    row = rdest[i];
1576     PetscMPIInt rowner;
1577     PetscCall(PetscLayoutFindOwner(A->rmap,row,&rowner));
1578     for (j=ai[i]; j<ai[i+1]; j++) {
1579       PetscInt    col = cdest[aj[j]];
1580       PetscMPIInt cowner;
1581       PetscCall(PetscLayoutFindOwner(A->cmap,col,&cowner)); /* Could build an index for the columns to eliminate this search */
1582       if (rowner == cowner) dnnz[i]++;
1583       else onnz[i]++;
1584     }
1585     for (j=bi[i]; j<bi[i+1]; j++) {
1586       PetscInt    col = gcdest[bj[j]];
1587       PetscMPIInt cowner;
1588       PetscCall(PetscLayoutFindOwner(A->cmap,col,&cowner));
1589       if (rowner == cowner) dnnz[i]++;
1590       else onnz[i]++;
1591     }
1592   }
1593   PetscCall(PetscSFBcastBegin(rowsf,MPIU_INT,dnnz,tdnnz,MPI_REPLACE));
1594   PetscCall(PetscSFBcastEnd(rowsf,MPIU_INT,dnnz,tdnnz,MPI_REPLACE));
1595   PetscCall(PetscSFBcastBegin(rowsf,MPIU_INT,onnz,tonnz,MPI_REPLACE));
1596   PetscCall(PetscSFBcastEnd(rowsf,MPIU_INT,onnz,tonnz,MPI_REPLACE));
1597   PetscCall(PetscSFDestroy(&rowsf));
1598 
1599   PetscCall(MatCreateAIJ(PetscObjectComm((PetscObject)A),A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N,0,tdnnz,0,tonnz,&Aperm));
1600   PetscCall(MatSeqAIJGetArray(aA,&aa));
1601   PetscCall(MatSeqAIJGetArray(aB,&ba));
1602   for (i=0; i<m; i++) {
1603     PetscInt *acols = dnnz,*bcols = onnz; /* Repurpose now-unneeded arrays */
1604     PetscInt j0,rowlen;
1605     rowlen = ai[i+1] - ai[i];
1606     for (j0=j=0; j<rowlen; j0=j) { /* rowlen could be larger than number of rows m, so sum in batches */
1607       for (; j<PetscMin(rowlen,j0+m); j++) acols[j-j0] = cdest[aj[ai[i]+j]];
1608       PetscCall(MatSetValues(Aperm,1,&rdest[i],j-j0,acols,aa+ai[i]+j0,INSERT_VALUES));
1609     }
1610     rowlen = bi[i+1] - bi[i];
1611     for (j0=j=0; j<rowlen; j0=j) {
1612       for (; j<PetscMin(rowlen,j0+m); j++) bcols[j-j0] = gcdest[bj[bi[i]+j]];
1613       PetscCall(MatSetValues(Aperm,1,&rdest[i],j-j0,bcols,ba+bi[i]+j0,INSERT_VALUES));
1614     }
1615   }
1616   PetscCall(MatAssemblyBegin(Aperm,MAT_FINAL_ASSEMBLY));
1617   PetscCall(MatAssemblyEnd(Aperm,MAT_FINAL_ASSEMBLY));
1618   PetscCall(MatRestoreRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done));
1619   PetscCall(MatRestoreRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done));
1620   PetscCall(MatSeqAIJRestoreArray(aA,&aa));
1621   PetscCall(MatSeqAIJRestoreArray(aB,&ba));
1622   PetscCall(PetscFree4(dnnz,onnz,tdnnz,tonnz));
1623   PetscCall(PetscFree3(work,rdest,cdest));
1624   PetscCall(PetscFree(gcdest));
1625   if (parcolp) PetscCall(ISDestroy(&colp));
1626   *B = Aperm;
1627   PetscFunctionReturn(0);
1628 }
1629 
1630 PetscErrorCode  MatGetGhosts_MPIAIJ(Mat mat,PetscInt *nghosts,const PetscInt *ghosts[])
1631 {
1632   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1633 
1634   PetscFunctionBegin;
1635   PetscCall(MatGetSize(aij->B,NULL,nghosts));
1636   if (ghosts) *ghosts = aij->garray;
1637   PetscFunctionReturn(0);
1638 }
1639 
1640 PetscErrorCode MatGetInfo_MPIAIJ(Mat matin,MatInfoType flag,MatInfo *info)
1641 {
1642   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1643   Mat            A    = mat->A,B = mat->B;
1644   PetscLogDouble isend[5],irecv[5];
1645 
1646   PetscFunctionBegin;
1647   info->block_size = 1.0;
1648   PetscCall(MatGetInfo(A,MAT_LOCAL,info));
1649 
1650   isend[0] = info->nz_used; isend[1] = info->nz_allocated; isend[2] = info->nz_unneeded;
1651   isend[3] = info->memory;  isend[4] = info->mallocs;
1652 
1653   PetscCall(MatGetInfo(B,MAT_LOCAL,info));
1654 
1655   isend[0] += info->nz_used; isend[1] += info->nz_allocated; isend[2] += info->nz_unneeded;
1656   isend[3] += info->memory;  isend[4] += info->mallocs;
1657   if (flag == MAT_LOCAL) {
1658     info->nz_used      = isend[0];
1659     info->nz_allocated = isend[1];
1660     info->nz_unneeded  = isend[2];
1661     info->memory       = isend[3];
1662     info->mallocs      = isend[4];
1663   } else if (flag == MAT_GLOBAL_MAX) {
1664     PetscCall(MPIU_Allreduce(isend,irecv,5,MPIU_PETSCLOGDOUBLE,MPI_MAX,PetscObjectComm((PetscObject)matin)));
1665 
1666     info->nz_used      = irecv[0];
1667     info->nz_allocated = irecv[1];
1668     info->nz_unneeded  = irecv[2];
1669     info->memory       = irecv[3];
1670     info->mallocs      = irecv[4];
1671   } else if (flag == MAT_GLOBAL_SUM) {
1672     PetscCall(MPIU_Allreduce(isend,irecv,5,MPIU_PETSCLOGDOUBLE,MPI_SUM,PetscObjectComm((PetscObject)matin)));
1673 
1674     info->nz_used      = irecv[0];
1675     info->nz_allocated = irecv[1];
1676     info->nz_unneeded  = irecv[2];
1677     info->memory       = irecv[3];
1678     info->mallocs      = irecv[4];
1679   }
1680   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
1681   info->fill_ratio_needed = 0;
1682   info->factor_mallocs    = 0;
1683   PetscFunctionReturn(0);
1684 }
1685 
1686 PetscErrorCode MatSetOption_MPIAIJ(Mat A,MatOption op,PetscBool flg)
1687 {
1688   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1689 
1690   PetscFunctionBegin;
1691   switch (op) {
1692   case MAT_NEW_NONZERO_LOCATIONS:
1693   case MAT_NEW_NONZERO_ALLOCATION_ERR:
1694   case MAT_UNUSED_NONZERO_LOCATION_ERR:
1695   case MAT_KEEP_NONZERO_PATTERN:
1696   case MAT_NEW_NONZERO_LOCATION_ERR:
1697   case MAT_USE_INODES:
1698   case MAT_IGNORE_ZERO_ENTRIES:
1699   case MAT_FORM_EXPLICIT_TRANSPOSE:
1700     MatCheckPreallocated(A,1);
1701     PetscCall(MatSetOption(a->A,op,flg));
1702     PetscCall(MatSetOption(a->B,op,flg));
1703     break;
1704   case MAT_ROW_ORIENTED:
1705     MatCheckPreallocated(A,1);
1706     a->roworiented = flg;
1707 
1708     PetscCall(MatSetOption(a->A,op,flg));
1709     PetscCall(MatSetOption(a->B,op,flg));
1710     break;
1711   case MAT_FORCE_DIAGONAL_ENTRIES:
1712   case MAT_SORTED_FULL:
1713     PetscCall(PetscInfo(A,"Option %s ignored\n",MatOptions[op]));
1714     break;
1715   case MAT_IGNORE_OFF_PROC_ENTRIES:
1716     a->donotstash = flg;
1717     break;
1718   /* Symmetry flags are handled directly by MatSetOption() and they don't affect preallocation */
1719   case MAT_SPD:
1720   case MAT_SYMMETRIC:
1721   case MAT_STRUCTURALLY_SYMMETRIC:
1722   case MAT_HERMITIAN:
1723   case MAT_SYMMETRY_ETERNAL:
1724     break;
1725   case MAT_SUBMAT_SINGLEIS:
1726     A->submat_singleis = flg;
1727     break;
1728   case MAT_STRUCTURE_ONLY:
1729     /* The option is handled directly by MatSetOption() */
1730     break;
1731   default:
1732     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %d",op);
1733   }
1734   PetscFunctionReturn(0);
1735 }
1736 
1737 PetscErrorCode MatGetRow_MPIAIJ(Mat matin,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1738 {
1739   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1740   PetscScalar    *vworkA,*vworkB,**pvA,**pvB,*v_p;
1741   PetscInt       i,*cworkA,*cworkB,**pcA,**pcB,cstart = matin->cmap->rstart;
1742   PetscInt       nztot,nzA,nzB,lrow,rstart = matin->rmap->rstart,rend = matin->rmap->rend;
1743   PetscInt       *cmap,*idx_p;
1744 
1745   PetscFunctionBegin;
1746   PetscCheck(!mat->getrowactive,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Already active");
1747   mat->getrowactive = PETSC_TRUE;
1748 
1749   if (!mat->rowvalues && (idx || v)) {
1750     /*
1751         allocate enough space to hold information from the longest row.
1752     */
1753     Mat_SeqAIJ *Aa = (Mat_SeqAIJ*)mat->A->data,*Ba = (Mat_SeqAIJ*)mat->B->data;
1754     PetscInt   max = 1,tmp;
1755     for (i=0; i<matin->rmap->n; i++) {
1756       tmp = Aa->i[i+1] - Aa->i[i] + Ba->i[i+1] - Ba->i[i];
1757       if (max < tmp) max = tmp;
1758     }
1759     PetscCall(PetscMalloc2(max,&mat->rowvalues,max,&mat->rowindices));
1760   }
1761 
1762   PetscCheck(row >= rstart && row < rend,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Only local rows");
1763   lrow = row - rstart;
1764 
1765   pvA = &vworkA; pcA = &cworkA; pvB = &vworkB; pcB = &cworkB;
1766   if (!v)   {pvA = NULL; pvB = NULL;}
1767   if (!idx) {pcA = NULL; if (!v) pcB = NULL;}
1768   PetscCall((*mat->A->ops->getrow)(mat->A,lrow,&nzA,pcA,pvA));
1769   PetscCall((*mat->B->ops->getrow)(mat->B,lrow,&nzB,pcB,pvB));
1770   nztot = nzA + nzB;
1771 
1772   cmap = mat->garray;
1773   if (v  || idx) {
1774     if (nztot) {
1775       /* Sort by increasing column numbers, assuming A and B already sorted */
1776       PetscInt imark = -1;
1777       if (v) {
1778         *v = v_p = mat->rowvalues;
1779         for (i=0; i<nzB; i++) {
1780           if (cmap[cworkB[i]] < cstart) v_p[i] = vworkB[i];
1781           else break;
1782         }
1783         imark = i;
1784         for (i=0; i<nzA; i++)     v_p[imark+i] = vworkA[i];
1785         for (i=imark; i<nzB; i++) v_p[nzA+i]   = vworkB[i];
1786       }
1787       if (idx) {
1788         *idx = idx_p = mat->rowindices;
1789         if (imark > -1) {
1790           for (i=0; i<imark; i++) {
1791             idx_p[i] = cmap[cworkB[i]];
1792           }
1793         } else {
1794           for (i=0; i<nzB; i++) {
1795             if (cmap[cworkB[i]] < cstart) idx_p[i] = cmap[cworkB[i]];
1796             else break;
1797           }
1798           imark = i;
1799         }
1800         for (i=0; i<nzA; i++)     idx_p[imark+i] = cstart + cworkA[i];
1801         for (i=imark; i<nzB; i++) idx_p[nzA+i]   = cmap[cworkB[i]];
1802       }
1803     } else {
1804       if (idx) *idx = NULL;
1805       if (v)   *v   = NULL;
1806     }
1807   }
1808   *nz  = nztot;
1809   PetscCall((*mat->A->ops->restorerow)(mat->A,lrow,&nzA,pcA,pvA));
1810   PetscCall((*mat->B->ops->restorerow)(mat->B,lrow,&nzB,pcB,pvB));
1811   PetscFunctionReturn(0);
1812 }
1813 
1814 PetscErrorCode MatRestoreRow_MPIAIJ(Mat mat,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1815 {
1816   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1817 
1818   PetscFunctionBegin;
1819   PetscCheck(aij->getrowactive,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"MatGetRow() must be called first");
1820   aij->getrowactive = PETSC_FALSE;
1821   PetscFunctionReturn(0);
1822 }
1823 
1824 PetscErrorCode MatNorm_MPIAIJ(Mat mat,NormType type,PetscReal *norm)
1825 {
1826   Mat_MPIAIJ      *aij  = (Mat_MPIAIJ*)mat->data;
1827   Mat_SeqAIJ      *amat = (Mat_SeqAIJ*)aij->A->data,*bmat = (Mat_SeqAIJ*)aij->B->data;
1828   PetscInt        i,j,cstart = mat->cmap->rstart;
1829   PetscReal       sum = 0.0;
1830   const MatScalar *v,*amata,*bmata;
1831 
1832   PetscFunctionBegin;
1833   if (aij->size == 1) {
1834     PetscCall(MatNorm(aij->A,type,norm));
1835   } else {
1836     PetscCall(MatSeqAIJGetArrayRead(aij->A,&amata));
1837     PetscCall(MatSeqAIJGetArrayRead(aij->B,&bmata));
1838     if (type == NORM_FROBENIUS) {
1839       v = amata;
1840       for (i=0; i<amat->nz; i++) {
1841         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1842       }
1843       v = bmata;
1844       for (i=0; i<bmat->nz; i++) {
1845         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1846       }
1847       PetscCall(MPIU_Allreduce(&sum,norm,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat)));
1848       *norm = PetscSqrtReal(*norm);
1849       PetscCall(PetscLogFlops(2.0*amat->nz+2.0*bmat->nz));
1850     } else if (type == NORM_1) { /* max column norm */
1851       PetscReal *tmp,*tmp2;
1852       PetscInt  *jj,*garray = aij->garray;
1853       PetscCall(PetscCalloc1(mat->cmap->N+1,&tmp));
1854       PetscCall(PetscMalloc1(mat->cmap->N+1,&tmp2));
1855       *norm = 0.0;
1856       v     = amata; jj = amat->j;
1857       for (j=0; j<amat->nz; j++) {
1858         tmp[cstart + *jj++] += PetscAbsScalar(*v);  v++;
1859       }
1860       v = bmata; jj = bmat->j;
1861       for (j=0; j<bmat->nz; j++) {
1862         tmp[garray[*jj++]] += PetscAbsScalar(*v); v++;
1863       }
1864       PetscCall(MPIU_Allreduce(tmp,tmp2,mat->cmap->N,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat)));
1865       for (j=0; j<mat->cmap->N; j++) {
1866         if (tmp2[j] > *norm) *norm = tmp2[j];
1867       }
1868       PetscCall(PetscFree(tmp));
1869       PetscCall(PetscFree(tmp2));
1870       PetscCall(PetscLogFlops(PetscMax(amat->nz+bmat->nz-1,0)));
1871     } else if (type == NORM_INFINITY) { /* max row norm */
1872       PetscReal ntemp = 0.0;
1873       for (j=0; j<aij->A->rmap->n; j++) {
1874         v   = amata + amat->i[j];
1875         sum = 0.0;
1876         for (i=0; i<amat->i[j+1]-amat->i[j]; i++) {
1877           sum += PetscAbsScalar(*v); v++;
1878         }
1879         v = bmata + bmat->i[j];
1880         for (i=0; i<bmat->i[j+1]-bmat->i[j]; i++) {
1881           sum += PetscAbsScalar(*v); v++;
1882         }
1883         if (sum > ntemp) ntemp = sum;
1884       }
1885       PetscCall(MPIU_Allreduce(&ntemp,norm,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)mat)));
1886       PetscCall(PetscLogFlops(PetscMax(amat->nz+bmat->nz-1,0)));
1887     } else SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"No support for two norm");
1888     PetscCall(MatSeqAIJRestoreArrayRead(aij->A,&amata));
1889     PetscCall(MatSeqAIJRestoreArrayRead(aij->B,&bmata));
1890   }
1891   PetscFunctionReturn(0);
1892 }
1893 
1894 PetscErrorCode MatTranspose_MPIAIJ(Mat A,MatReuse reuse,Mat *matout)
1895 {
1896   Mat_MPIAIJ      *a    =(Mat_MPIAIJ*)A->data,*b;
1897   Mat_SeqAIJ      *Aloc =(Mat_SeqAIJ*)a->A->data,*Bloc=(Mat_SeqAIJ*)a->B->data,*sub_B_diag;
1898   PetscInt        M     = A->rmap->N,N=A->cmap->N,ma,na,mb,nb,row,*cols,*cols_tmp,*B_diag_ilen,i,ncol,A_diag_ncol;
1899   const PetscInt  *ai,*aj,*bi,*bj,*B_diag_i;
1900   Mat             B,A_diag,*B_diag;
1901   const MatScalar *pbv,*bv;
1902 
1903   PetscFunctionBegin;
1904   ma = A->rmap->n; na = A->cmap->n; mb = a->B->rmap->n; nb = a->B->cmap->n;
1905   ai = Aloc->i; aj = Aloc->j;
1906   bi = Bloc->i; bj = Bloc->j;
1907   if (reuse == MAT_INITIAL_MATRIX || *matout == A) {
1908     PetscInt             *d_nnz,*g_nnz,*o_nnz;
1909     PetscSFNode          *oloc;
1910     PETSC_UNUSED PetscSF sf;
1911 
1912     PetscCall(PetscMalloc4(na,&d_nnz,na,&o_nnz,nb,&g_nnz,nb,&oloc));
1913     /* compute d_nnz for preallocation */
1914     PetscCall(PetscArrayzero(d_nnz,na));
1915     for (i=0; i<ai[ma]; i++) d_nnz[aj[i]]++;
1916     /* compute local off-diagonal contributions */
1917     PetscCall(PetscArrayzero(g_nnz,nb));
1918     for (i=0; i<bi[ma]; i++) g_nnz[bj[i]]++;
1919     /* map those to global */
1920     PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A),&sf));
1921     PetscCall(PetscSFSetGraphLayout(sf,A->cmap,nb,NULL,PETSC_USE_POINTER,a->garray));
1922     PetscCall(PetscSFSetFromOptions(sf));
1923     PetscCall(PetscArrayzero(o_nnz,na));
1924     PetscCall(PetscSFReduceBegin(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM));
1925     PetscCall(PetscSFReduceEnd(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM));
1926     PetscCall(PetscSFDestroy(&sf));
1927 
1928     PetscCall(MatCreate(PetscObjectComm((PetscObject)A),&B));
1929     PetscCall(MatSetSizes(B,A->cmap->n,A->rmap->n,N,M));
1930     PetscCall(MatSetBlockSizes(B,PetscAbs(A->cmap->bs),PetscAbs(A->rmap->bs)));
1931     PetscCall(MatSetType(B,((PetscObject)A)->type_name));
1932     PetscCall(MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz));
1933     PetscCall(PetscFree4(d_nnz,o_nnz,g_nnz,oloc));
1934   } else {
1935     B    = *matout;
1936     PetscCall(MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE));
1937   }
1938 
1939   b           = (Mat_MPIAIJ*)B->data;
1940   A_diag      = a->A;
1941   B_diag      = &b->A;
1942   sub_B_diag  = (Mat_SeqAIJ*)(*B_diag)->data;
1943   A_diag_ncol = A_diag->cmap->N;
1944   B_diag_ilen = sub_B_diag->ilen;
1945   B_diag_i    = sub_B_diag->i;
1946 
1947   /* Set ilen for diagonal of B */
1948   for (i=0; i<A_diag_ncol; i++) {
1949     B_diag_ilen[i] = B_diag_i[i+1] - B_diag_i[i];
1950   }
1951 
1952   /* Transpose the diagonal part of the matrix. In contrast to the offdiagonal part, this can be done
1953   very quickly (=without using MatSetValues), because all writes are local. */
1954   PetscCall(MatTranspose(A_diag,MAT_REUSE_MATRIX,B_diag));
1955 
1956   /* copy over the B part */
1957   PetscCall(PetscMalloc1(bi[mb],&cols));
1958   PetscCall(MatSeqAIJGetArrayRead(a->B,&bv));
1959   pbv  = bv;
1960   row  = A->rmap->rstart;
1961   for (i=0; i<bi[mb]; i++) cols[i] = a->garray[bj[i]];
1962   cols_tmp = cols;
1963   for (i=0; i<mb; i++) {
1964     ncol = bi[i+1]-bi[i];
1965     PetscCall(MatSetValues(B,ncol,cols_tmp,1,&row,pbv,INSERT_VALUES));
1966     row++;
1967     pbv += ncol; cols_tmp += ncol;
1968   }
1969   PetscCall(PetscFree(cols));
1970   PetscCall(MatSeqAIJRestoreArrayRead(a->B,&bv));
1971 
1972   PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
1973   PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
1974   if (reuse == MAT_INITIAL_MATRIX || reuse == MAT_REUSE_MATRIX) {
1975     *matout = B;
1976   } else {
1977     PetscCall(MatHeaderMerge(A,&B));
1978   }
1979   PetscFunctionReturn(0);
1980 }
1981 
1982 PetscErrorCode MatDiagonalScale_MPIAIJ(Mat mat,Vec ll,Vec rr)
1983 {
1984   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1985   Mat            a    = aij->A,b = aij->B;
1986   PetscInt       s1,s2,s3;
1987 
1988   PetscFunctionBegin;
1989   PetscCall(MatGetLocalSize(mat,&s2,&s3));
1990   if (rr) {
1991     PetscCall(VecGetLocalSize(rr,&s1));
1992     PetscCheck(s1==s3,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"right vector non-conforming local size");
1993     /* Overlap communication with computation. */
1994     PetscCall(VecScatterBegin(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD));
1995   }
1996   if (ll) {
1997     PetscCall(VecGetLocalSize(ll,&s1));
1998     PetscCheck(s1==s2,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"left vector non-conforming local size");
1999     PetscCall((*b->ops->diagonalscale)(b,ll,NULL));
2000   }
2001   /* scale  the diagonal block */
2002   PetscCall((*a->ops->diagonalscale)(a,ll,rr));
2003 
2004   if (rr) {
2005     /* Do a scatter end and then right scale the off-diagonal block */
2006     PetscCall(VecScatterEnd(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD));
2007     PetscCall((*b->ops->diagonalscale)(b,NULL,aij->lvec));
2008   }
2009   PetscFunctionReturn(0);
2010 }
2011 
2012 PetscErrorCode MatSetUnfactored_MPIAIJ(Mat A)
2013 {
2014   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2015 
2016   PetscFunctionBegin;
2017   PetscCall(MatSetUnfactored(a->A));
2018   PetscFunctionReturn(0);
2019 }
2020 
2021 PetscErrorCode MatEqual_MPIAIJ(Mat A,Mat B,PetscBool  *flag)
2022 {
2023   Mat_MPIAIJ     *matB = (Mat_MPIAIJ*)B->data,*matA = (Mat_MPIAIJ*)A->data;
2024   Mat            a,b,c,d;
2025   PetscBool      flg;
2026 
2027   PetscFunctionBegin;
2028   a = matA->A; b = matA->B;
2029   c = matB->A; d = matB->B;
2030 
2031   PetscCall(MatEqual(a,c,&flg));
2032   if (flg) {
2033     PetscCall(MatEqual(b,d,&flg));
2034   }
2035   PetscCall(MPIU_Allreduce(&flg,flag,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)A)));
2036   PetscFunctionReturn(0);
2037 }
2038 
2039 PetscErrorCode MatCopy_MPIAIJ(Mat A,Mat B,MatStructure str)
2040 {
2041   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2042   Mat_MPIAIJ     *b = (Mat_MPIAIJ*)B->data;
2043 
2044   PetscFunctionBegin;
2045   /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
2046   if ((str != SAME_NONZERO_PATTERN) || (A->ops->copy != B->ops->copy)) {
2047     /* because of the column compression in the off-processor part of the matrix a->B,
2048        the number of columns in a->B and b->B may be different, hence we cannot call
2049        the MatCopy() directly on the two parts. If need be, we can provide a more
2050        efficient copy than the MatCopy_Basic() by first uncompressing the a->B matrices
2051        then copying the submatrices */
2052     PetscCall(MatCopy_Basic(A,B,str));
2053   } else {
2054     PetscCall(MatCopy(a->A,b->A,str));
2055     PetscCall(MatCopy(a->B,b->B,str));
2056   }
2057   PetscCall(PetscObjectStateIncrease((PetscObject)B));
2058   PetscFunctionReturn(0);
2059 }
2060 
2061 PetscErrorCode MatSetUp_MPIAIJ(Mat A)
2062 {
2063   PetscFunctionBegin;
2064   PetscCall(MatMPIAIJSetPreallocation(A,PETSC_DEFAULT,NULL,PETSC_DEFAULT,NULL));
2065   PetscFunctionReturn(0);
2066 }
2067 
2068 /*
2069    Computes the number of nonzeros per row needed for preallocation when X and Y
2070    have different nonzero structure.
2071 */
2072 PetscErrorCode MatAXPYGetPreallocation_MPIX_private(PetscInt m,const PetscInt *xi,const PetscInt *xj,const PetscInt *xltog,const PetscInt *yi,const PetscInt *yj,const PetscInt *yltog,PetscInt *nnz)
2073 {
2074   PetscInt       i,j,k,nzx,nzy;
2075 
2076   PetscFunctionBegin;
2077   /* Set the number of nonzeros in the new matrix */
2078   for (i=0; i<m; i++) {
2079     const PetscInt *xjj = xj+xi[i],*yjj = yj+yi[i];
2080     nzx = xi[i+1] - xi[i];
2081     nzy = yi[i+1] - yi[i];
2082     nnz[i] = 0;
2083     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2084       for (; k<nzy && yltog[yjj[k]]<xltog[xjj[j]]; k++) nnz[i]++; /* Catch up to X */
2085       if (k<nzy && yltog[yjj[k]]==xltog[xjj[j]]) k++;             /* Skip duplicate */
2086       nnz[i]++;
2087     }
2088     for (; k<nzy; k++) nnz[i]++;
2089   }
2090   PetscFunctionReturn(0);
2091 }
2092 
2093 /* This is the same as MatAXPYGetPreallocation_SeqAIJ, except that the local-to-global map is provided */
2094 static PetscErrorCode MatAXPYGetPreallocation_MPIAIJ(Mat Y,const PetscInt *yltog,Mat X,const PetscInt *xltog,PetscInt *nnz)
2095 {
2096   PetscInt       m = Y->rmap->N;
2097   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data;
2098   Mat_SeqAIJ     *y = (Mat_SeqAIJ*)Y->data;
2099 
2100   PetscFunctionBegin;
2101   PetscCall(MatAXPYGetPreallocation_MPIX_private(m,x->i,x->j,xltog,y->i,y->j,yltog,nnz));
2102   PetscFunctionReturn(0);
2103 }
2104 
2105 PetscErrorCode MatAXPY_MPIAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
2106 {
2107   Mat_MPIAIJ     *xx = (Mat_MPIAIJ*)X->data,*yy = (Mat_MPIAIJ*)Y->data;
2108 
2109   PetscFunctionBegin;
2110   if (str == SAME_NONZERO_PATTERN) {
2111     PetscCall(MatAXPY(yy->A,a,xx->A,str));
2112     PetscCall(MatAXPY(yy->B,a,xx->B,str));
2113   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
2114     PetscCall(MatAXPY_Basic(Y,a,X,str));
2115   } else {
2116     Mat      B;
2117     PetscInt *nnz_d,*nnz_o;
2118 
2119     PetscCall(PetscMalloc1(yy->A->rmap->N,&nnz_d));
2120     PetscCall(PetscMalloc1(yy->B->rmap->N,&nnz_o));
2121     PetscCall(MatCreate(PetscObjectComm((PetscObject)Y),&B));
2122     PetscCall(PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name));
2123     PetscCall(MatSetLayouts(B,Y->rmap,Y->cmap));
2124     PetscCall(MatSetType(B,((PetscObject)Y)->type_name));
2125     PetscCall(MatAXPYGetPreallocation_SeqAIJ(yy->A,xx->A,nnz_d));
2126     PetscCall(MatAXPYGetPreallocation_MPIAIJ(yy->B,yy->garray,xx->B,xx->garray,nnz_o));
2127     PetscCall(MatMPIAIJSetPreallocation(B,0,nnz_d,0,nnz_o));
2128     PetscCall(MatAXPY_BasicWithPreallocation(B,Y,a,X,str));
2129     PetscCall(MatHeaderMerge(Y,&B));
2130     PetscCall(PetscFree(nnz_d));
2131     PetscCall(PetscFree(nnz_o));
2132   }
2133   PetscFunctionReturn(0);
2134 }
2135 
2136 PETSC_INTERN PetscErrorCode MatConjugate_SeqAIJ(Mat);
2137 
2138 PetscErrorCode MatConjugate_MPIAIJ(Mat mat)
2139 {
2140   PetscFunctionBegin;
2141   if (PetscDefined(USE_COMPLEX)) {
2142     Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
2143 
2144     PetscCall(MatConjugate_SeqAIJ(aij->A));
2145     PetscCall(MatConjugate_SeqAIJ(aij->B));
2146   }
2147   PetscFunctionReturn(0);
2148 }
2149 
2150 PetscErrorCode MatRealPart_MPIAIJ(Mat A)
2151 {
2152   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2153 
2154   PetscFunctionBegin;
2155   PetscCall(MatRealPart(a->A));
2156   PetscCall(MatRealPart(a->B));
2157   PetscFunctionReturn(0);
2158 }
2159 
2160 PetscErrorCode MatImaginaryPart_MPIAIJ(Mat A)
2161 {
2162   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2163 
2164   PetscFunctionBegin;
2165   PetscCall(MatImaginaryPart(a->A));
2166   PetscCall(MatImaginaryPart(a->B));
2167   PetscFunctionReturn(0);
2168 }
2169 
2170 PetscErrorCode MatGetRowMaxAbs_MPIAIJ(Mat A,Vec v,PetscInt idx[])
2171 {
2172   Mat_MPIAIJ        *a = (Mat_MPIAIJ*)A->data;
2173   PetscInt          i,*idxb = NULL,m = A->rmap->n;
2174   PetscScalar       *va,*vv;
2175   Vec               vB,vA;
2176   const PetscScalar *vb;
2177 
2178   PetscFunctionBegin;
2179   PetscCall(VecCreateSeq(PETSC_COMM_SELF,m,&vA));
2180   PetscCall(MatGetRowMaxAbs(a->A,vA,idx));
2181 
2182   PetscCall(VecGetArrayWrite(vA,&va));
2183   if (idx) {
2184     for (i=0; i<m; i++) {
2185       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2186     }
2187   }
2188 
2189   PetscCall(VecCreateSeq(PETSC_COMM_SELF,m,&vB));
2190   PetscCall(PetscMalloc1(m,&idxb));
2191   PetscCall(MatGetRowMaxAbs(a->B,vB,idxb));
2192 
2193   PetscCall(VecGetArrayWrite(v,&vv));
2194   PetscCall(VecGetArrayRead(vB,&vb));
2195   for (i=0; i<m; i++) {
2196     if (PetscAbsScalar(va[i]) < PetscAbsScalar(vb[i])) {
2197       vv[i] = vb[i];
2198       if (idx) idx[i] = a->garray[idxb[i]];
2199     } else {
2200       vv[i] = va[i];
2201       if (idx && PetscAbsScalar(va[i]) == PetscAbsScalar(vb[i]) && idxb[i] != -1 && idx[i] > a->garray[idxb[i]])
2202         idx[i] = a->garray[idxb[i]];
2203     }
2204   }
2205   PetscCall(VecRestoreArrayWrite(vA,&vv));
2206   PetscCall(VecRestoreArrayWrite(vA,&va));
2207   PetscCall(VecRestoreArrayRead(vB,&vb));
2208   PetscCall(PetscFree(idxb));
2209   PetscCall(VecDestroy(&vA));
2210   PetscCall(VecDestroy(&vB));
2211   PetscFunctionReturn(0);
2212 }
2213 
2214 PetscErrorCode MatGetRowMinAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2215 {
2216   Mat_MPIAIJ        *mat   = (Mat_MPIAIJ*) A->data;
2217   PetscInt          m = A->rmap->n,n = A->cmap->n;
2218   PetscInt          cstart = A->cmap->rstart,cend = A->cmap->rend;
2219   PetscInt          *cmap  = mat->garray;
2220   PetscInt          *diagIdx, *offdiagIdx;
2221   Vec               diagV, offdiagV;
2222   PetscScalar       *a, *diagA, *offdiagA;
2223   const PetscScalar *ba,*bav;
2224   PetscInt          r,j,col,ncols,*bi,*bj;
2225   Mat               B = mat->B;
2226   Mat_SeqAIJ        *b = (Mat_SeqAIJ*)B->data;
2227 
2228   PetscFunctionBegin;
2229   /* When a process holds entire A and other processes have no entry */
2230   if (A->cmap->N == n) {
2231     PetscCall(VecGetArrayWrite(v,&diagA));
2232     PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF,1,m,diagA,&diagV));
2233     PetscCall(MatGetRowMinAbs(mat->A,diagV,idx));
2234     PetscCall(VecDestroy(&diagV));
2235     PetscCall(VecRestoreArrayWrite(v,&diagA));
2236     PetscFunctionReturn(0);
2237   } else if (n == 0) {
2238     if (m) {
2239       PetscCall(VecGetArrayWrite(v,&a));
2240       for (r = 0; r < m; r++) {a[r] = 0.0; if (idx) idx[r] = -1;}
2241       PetscCall(VecRestoreArrayWrite(v,&a));
2242     }
2243     PetscFunctionReturn(0);
2244   }
2245 
2246   PetscCall(PetscMalloc2(m,&diagIdx,m,&offdiagIdx));
2247   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &diagV));
2248   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &offdiagV));
2249   PetscCall(MatGetRowMinAbs(mat->A, diagV, diagIdx));
2250 
2251   /* Get offdiagIdx[] for implicit 0.0 */
2252   PetscCall(MatSeqAIJGetArrayRead(B,&bav));
2253   ba   = bav;
2254   bi   = b->i;
2255   bj   = b->j;
2256   PetscCall(VecGetArrayWrite(offdiagV, &offdiagA));
2257   for (r = 0; r < m; r++) {
2258     ncols = bi[r+1] - bi[r];
2259     if (ncols == A->cmap->N - n) { /* Brow is dense */
2260       offdiagA[r] = *ba; offdiagIdx[r] = cmap[0];
2261     } else { /* Brow is sparse so already KNOW maximum is 0.0 or higher */
2262       offdiagA[r] = 0.0;
2263 
2264       /* Find first hole in the cmap */
2265       for (j=0; j<ncols; j++) {
2266         col = cmap[bj[j]]; /* global column number = cmap[B column number] */
2267         if (col > j && j < cstart) {
2268           offdiagIdx[r] = j; /* global column number of first implicit 0.0 */
2269           break;
2270         } else if (col > j + n && j >= cstart) {
2271           offdiagIdx[r] = j + n; /* global column number of first implicit 0.0 */
2272           break;
2273         }
2274       }
2275       if (j == ncols && ncols < A->cmap->N - n) {
2276         /* a hole is outside compressed Bcols */
2277         if (ncols == 0) {
2278           if (cstart) {
2279             offdiagIdx[r] = 0;
2280           } else offdiagIdx[r] = cend;
2281         } else { /* ncols > 0 */
2282           offdiagIdx[r] = cmap[ncols-1] + 1;
2283           if (offdiagIdx[r] == cstart) offdiagIdx[r] += n;
2284         }
2285       }
2286     }
2287 
2288     for (j=0; j<ncols; j++) {
2289       if (PetscAbsScalar(offdiagA[r]) > PetscAbsScalar(*ba)) {offdiagA[r] = *ba; offdiagIdx[r] = cmap[*bj];}
2290       ba++; bj++;
2291     }
2292   }
2293 
2294   PetscCall(VecGetArrayWrite(v, &a));
2295   PetscCall(VecGetArrayRead(diagV, (const PetscScalar**)&diagA));
2296   for (r = 0; r < m; ++r) {
2297     if (PetscAbsScalar(diagA[r]) < PetscAbsScalar(offdiagA[r])) {
2298       a[r]   = diagA[r];
2299       if (idx) idx[r] = cstart + diagIdx[r];
2300     } else if (PetscAbsScalar(diagA[r]) == PetscAbsScalar(offdiagA[r])) {
2301       a[r] = diagA[r];
2302       if (idx) {
2303         if (cstart + diagIdx[r] <= offdiagIdx[r]) {
2304           idx[r] = cstart + diagIdx[r];
2305         } else idx[r] = offdiagIdx[r];
2306       }
2307     } else {
2308       a[r]   = offdiagA[r];
2309       if (idx) idx[r] = offdiagIdx[r];
2310     }
2311   }
2312   PetscCall(MatSeqAIJRestoreArrayRead(B,&bav));
2313   PetscCall(VecRestoreArrayWrite(v, &a));
2314   PetscCall(VecRestoreArrayRead(diagV, (const PetscScalar**)&diagA));
2315   PetscCall(VecRestoreArrayWrite(offdiagV, &offdiagA));
2316   PetscCall(VecDestroy(&diagV));
2317   PetscCall(VecDestroy(&offdiagV));
2318   PetscCall(PetscFree2(diagIdx, offdiagIdx));
2319   PetscFunctionReturn(0);
2320 }
2321 
2322 PetscErrorCode MatGetRowMin_MPIAIJ(Mat A,Vec v,PetscInt idx[])
2323 {
2324   Mat_MPIAIJ        *mat = (Mat_MPIAIJ*) A->data;
2325   PetscInt          m = A->rmap->n,n = A->cmap->n;
2326   PetscInt          cstart = A->cmap->rstart,cend = A->cmap->rend;
2327   PetscInt          *cmap  = mat->garray;
2328   PetscInt          *diagIdx, *offdiagIdx;
2329   Vec               diagV, offdiagV;
2330   PetscScalar       *a, *diagA, *offdiagA;
2331   const PetscScalar *ba,*bav;
2332   PetscInt          r,j,col,ncols,*bi,*bj;
2333   Mat               B = mat->B;
2334   Mat_SeqAIJ        *b = (Mat_SeqAIJ*)B->data;
2335 
2336   PetscFunctionBegin;
2337   /* When a process holds entire A and other processes have no entry */
2338   if (A->cmap->N == n) {
2339     PetscCall(VecGetArrayWrite(v,&diagA));
2340     PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF,1,m,diagA,&diagV));
2341     PetscCall(MatGetRowMin(mat->A,diagV,idx));
2342     PetscCall(VecDestroy(&diagV));
2343     PetscCall(VecRestoreArrayWrite(v,&diagA));
2344     PetscFunctionReturn(0);
2345   } else if (n == 0) {
2346     if (m) {
2347       PetscCall(VecGetArrayWrite(v,&a));
2348       for (r = 0; r < m; r++) {a[r] = PETSC_MAX_REAL; if (idx) idx[r] = -1;}
2349       PetscCall(VecRestoreArrayWrite(v,&a));
2350     }
2351     PetscFunctionReturn(0);
2352   }
2353 
2354   PetscCall(PetscCalloc2(m,&diagIdx,m,&offdiagIdx));
2355   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &diagV));
2356   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &offdiagV));
2357   PetscCall(MatGetRowMin(mat->A, diagV, diagIdx));
2358 
2359   /* Get offdiagIdx[] for implicit 0.0 */
2360   PetscCall(MatSeqAIJGetArrayRead(B,&bav));
2361   ba   = bav;
2362   bi   = b->i;
2363   bj   = b->j;
2364   PetscCall(VecGetArrayWrite(offdiagV, &offdiagA));
2365   for (r = 0; r < m; r++) {
2366     ncols = bi[r+1] - bi[r];
2367     if (ncols == A->cmap->N - n) { /* Brow is dense */
2368       offdiagA[r] = *ba; offdiagIdx[r] = cmap[0];
2369     } else { /* Brow is sparse so already KNOW maximum is 0.0 or higher */
2370       offdiagA[r] = 0.0;
2371 
2372       /* Find first hole in the cmap */
2373       for (j=0; j<ncols; j++) {
2374         col = cmap[bj[j]]; /* global column number = cmap[B column number] */
2375         if (col > j && j < cstart) {
2376           offdiagIdx[r] = j; /* global column number of first implicit 0.0 */
2377           break;
2378         } else if (col > j + n && j >= cstart) {
2379           offdiagIdx[r] = j + n; /* global column number of first implicit 0.0 */
2380           break;
2381         }
2382       }
2383       if (j == ncols && ncols < A->cmap->N - n) {
2384         /* a hole is outside compressed Bcols */
2385         if (ncols == 0) {
2386           if (cstart) {
2387             offdiagIdx[r] = 0;
2388           } else offdiagIdx[r] = cend;
2389         } else { /* ncols > 0 */
2390           offdiagIdx[r] = cmap[ncols-1] + 1;
2391           if (offdiagIdx[r] == cstart) offdiagIdx[r] += n;
2392         }
2393       }
2394     }
2395 
2396     for (j=0; j<ncols; j++) {
2397       if (PetscRealPart(offdiagA[r]) > PetscRealPart(*ba)) {offdiagA[r] = *ba; offdiagIdx[r] = cmap[*bj];}
2398       ba++; bj++;
2399     }
2400   }
2401 
2402   PetscCall(VecGetArrayWrite(v, &a));
2403   PetscCall(VecGetArrayRead(diagV, (const PetscScalar**)&diagA));
2404   for (r = 0; r < m; ++r) {
2405     if (PetscRealPart(diagA[r]) < PetscRealPart(offdiagA[r])) {
2406       a[r]   = diagA[r];
2407       if (idx) idx[r] = cstart + diagIdx[r];
2408     } else if (PetscRealPart(diagA[r]) == PetscRealPart(offdiagA[r])) {
2409       a[r] = diagA[r];
2410       if (idx) {
2411         if (cstart + diagIdx[r] <= offdiagIdx[r]) {
2412           idx[r] = cstart + diagIdx[r];
2413         } else idx[r] = offdiagIdx[r];
2414       }
2415     } else {
2416       a[r]   = offdiagA[r];
2417       if (idx) idx[r] = offdiagIdx[r];
2418     }
2419   }
2420   PetscCall(MatSeqAIJRestoreArrayRead(B,&bav));
2421   PetscCall(VecRestoreArrayWrite(v, &a));
2422   PetscCall(VecRestoreArrayRead(diagV, (const PetscScalar**)&diagA));
2423   PetscCall(VecRestoreArrayWrite(offdiagV, &offdiagA));
2424   PetscCall(VecDestroy(&diagV));
2425   PetscCall(VecDestroy(&offdiagV));
2426   PetscCall(PetscFree2(diagIdx, offdiagIdx));
2427   PetscFunctionReturn(0);
2428 }
2429 
2430 PetscErrorCode MatGetRowMax_MPIAIJ(Mat A,Vec v,PetscInt idx[])
2431 {
2432   Mat_MPIAIJ        *mat = (Mat_MPIAIJ*)A->data;
2433   PetscInt          m = A->rmap->n,n = A->cmap->n;
2434   PetscInt          cstart = A->cmap->rstart,cend = A->cmap->rend;
2435   PetscInt          *cmap  = mat->garray;
2436   PetscInt          *diagIdx, *offdiagIdx;
2437   Vec               diagV, offdiagV;
2438   PetscScalar       *a, *diagA, *offdiagA;
2439   const PetscScalar *ba,*bav;
2440   PetscInt          r,j,col,ncols,*bi,*bj;
2441   Mat               B = mat->B;
2442   Mat_SeqAIJ        *b = (Mat_SeqAIJ*)B->data;
2443 
2444   PetscFunctionBegin;
2445   /* When a process holds entire A and other processes have no entry */
2446   if (A->cmap->N == n) {
2447     PetscCall(VecGetArrayWrite(v,&diagA));
2448     PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF,1,m,diagA,&diagV));
2449     PetscCall(MatGetRowMax(mat->A,diagV,idx));
2450     PetscCall(VecDestroy(&diagV));
2451     PetscCall(VecRestoreArrayWrite(v,&diagA));
2452     PetscFunctionReturn(0);
2453   } else if (n == 0) {
2454     if (m) {
2455       PetscCall(VecGetArrayWrite(v,&a));
2456       for (r = 0; r < m; r++) {a[r] = PETSC_MIN_REAL; if (idx) idx[r] = -1;}
2457       PetscCall(VecRestoreArrayWrite(v,&a));
2458     }
2459     PetscFunctionReturn(0);
2460   }
2461 
2462   PetscCall(PetscMalloc2(m,&diagIdx,m,&offdiagIdx));
2463   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &diagV));
2464   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &offdiagV));
2465   PetscCall(MatGetRowMax(mat->A, diagV, diagIdx));
2466 
2467   /* Get offdiagIdx[] for implicit 0.0 */
2468   PetscCall(MatSeqAIJGetArrayRead(B,&bav));
2469   ba   = bav;
2470   bi   = b->i;
2471   bj   = b->j;
2472   PetscCall(VecGetArrayWrite(offdiagV, &offdiagA));
2473   for (r = 0; r < m; r++) {
2474     ncols = bi[r+1] - bi[r];
2475     if (ncols == A->cmap->N - n) { /* Brow is dense */
2476       offdiagA[r] = *ba; offdiagIdx[r] = cmap[0];
2477     } else { /* Brow is sparse so already KNOW maximum is 0.0 or higher */
2478       offdiagA[r] = 0.0;
2479 
2480       /* Find first hole in the cmap */
2481       for (j=0; j<ncols; j++) {
2482         col = cmap[bj[j]]; /* global column number = cmap[B column number] */
2483         if (col > j && j < cstart) {
2484           offdiagIdx[r] = j; /* global column number of first implicit 0.0 */
2485           break;
2486         } else if (col > j + n && j >= cstart) {
2487           offdiagIdx[r] = j + n; /* global column number of first implicit 0.0 */
2488           break;
2489         }
2490       }
2491       if (j == ncols && ncols < A->cmap->N - n) {
2492         /* a hole is outside compressed Bcols */
2493         if (ncols == 0) {
2494           if (cstart) {
2495             offdiagIdx[r] = 0;
2496           } else offdiagIdx[r] = cend;
2497         } else { /* ncols > 0 */
2498           offdiagIdx[r] = cmap[ncols-1] + 1;
2499           if (offdiagIdx[r] == cstart) offdiagIdx[r] += n;
2500         }
2501       }
2502     }
2503 
2504     for (j=0; j<ncols; j++) {
2505       if (PetscRealPart(offdiagA[r]) < PetscRealPart(*ba)) {offdiagA[r] = *ba; offdiagIdx[r] = cmap[*bj];}
2506       ba++; bj++;
2507     }
2508   }
2509 
2510   PetscCall(VecGetArrayWrite(v,    &a));
2511   PetscCall(VecGetArrayRead(diagV,(const PetscScalar**)&diagA));
2512   for (r = 0; r < m; ++r) {
2513     if (PetscRealPart(diagA[r]) > PetscRealPart(offdiagA[r])) {
2514       a[r] = diagA[r];
2515       if (idx) idx[r] = cstart + diagIdx[r];
2516     } else if (PetscRealPart(diagA[r]) == PetscRealPart(offdiagA[r])) {
2517       a[r] = diagA[r];
2518       if (idx) {
2519         if (cstart + diagIdx[r] <= offdiagIdx[r]) {
2520           idx[r] = cstart + diagIdx[r];
2521         } else idx[r] = offdiagIdx[r];
2522       }
2523     } else {
2524       a[r] = offdiagA[r];
2525       if (idx) idx[r] = offdiagIdx[r];
2526     }
2527   }
2528   PetscCall(MatSeqAIJRestoreArrayRead(B,&bav));
2529   PetscCall(VecRestoreArrayWrite(v,       &a));
2530   PetscCall(VecRestoreArrayRead(diagV,   (const PetscScalar**)&diagA));
2531   PetscCall(VecRestoreArrayWrite(offdiagV,&offdiagA));
2532   PetscCall(VecDestroy(&diagV));
2533   PetscCall(VecDestroy(&offdiagV));
2534   PetscCall(PetscFree2(diagIdx, offdiagIdx));
2535   PetscFunctionReturn(0);
2536 }
2537 
2538 PetscErrorCode MatGetSeqNonzeroStructure_MPIAIJ(Mat mat,Mat *newmat)
2539 {
2540   Mat            *dummy;
2541 
2542   PetscFunctionBegin;
2543   PetscCall(MatCreateSubMatrix_MPIAIJ_All(mat,MAT_DO_NOT_GET_VALUES,MAT_INITIAL_MATRIX,&dummy));
2544   *newmat = *dummy;
2545   PetscCall(PetscFree(dummy));
2546   PetscFunctionReturn(0);
2547 }
2548 
2549 PetscErrorCode  MatInvertBlockDiagonal_MPIAIJ(Mat A,const PetscScalar **values)
2550 {
2551   Mat_MPIAIJ     *a = (Mat_MPIAIJ*) A->data;
2552 
2553   PetscFunctionBegin;
2554   PetscCall(MatInvertBlockDiagonal(a->A,values));
2555   A->factorerrortype = a->A->factorerrortype;
2556   PetscFunctionReturn(0);
2557 }
2558 
2559 static PetscErrorCode  MatSetRandom_MPIAIJ(Mat x,PetscRandom rctx)
2560 {
2561   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)x->data;
2562 
2563   PetscFunctionBegin;
2564   PetscCheck(x->assembled || x->preallocated,PetscObjectComm((PetscObject)x), PETSC_ERR_ARG_WRONGSTATE, "MatSetRandom on an unassembled and unpreallocated MATMPIAIJ is not allowed");
2565   PetscCall(MatSetRandom(aij->A,rctx));
2566   if (x->assembled) {
2567     PetscCall(MatSetRandom(aij->B,rctx));
2568   } else {
2569     PetscCall(MatSetRandomSkipColumnRange_SeqAIJ_Private(aij->B,x->cmap->rstart,x->cmap->rend,rctx));
2570   }
2571   PetscCall(MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY));
2572   PetscCall(MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY));
2573   PetscFunctionReturn(0);
2574 }
2575 
2576 PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ(Mat A,PetscBool sc)
2577 {
2578   PetscFunctionBegin;
2579   if (sc) A->ops->increaseoverlap = MatIncreaseOverlap_MPIAIJ_Scalable;
2580   else A->ops->increaseoverlap    = MatIncreaseOverlap_MPIAIJ;
2581   PetscFunctionReturn(0);
2582 }
2583 
2584 /*@
2585    MatMPIAIJSetUseScalableIncreaseOverlap - Determine if the matrix uses a scalable algorithm to compute the overlap
2586 
2587    Collective on Mat
2588 
2589    Input Parameters:
2590 +    A - the matrix
2591 -    sc - PETSC_TRUE indicates use the scalable algorithm (default is not to use the scalable algorithm)
2592 
2593  Level: advanced
2594 
2595 @*/
2596 PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap(Mat A,PetscBool sc)
2597 {
2598   PetscFunctionBegin;
2599   PetscTryMethod(A,"MatMPIAIJSetUseScalableIncreaseOverlap_C",(Mat,PetscBool),(A,sc));
2600   PetscFunctionReturn(0);
2601 }
2602 
2603 PetscErrorCode MatSetFromOptions_MPIAIJ(PetscOptionItems *PetscOptionsObject,Mat A)
2604 {
2605   PetscBool            sc = PETSC_FALSE,flg;
2606 
2607   PetscFunctionBegin;
2608   PetscOptionsHeadBegin(PetscOptionsObject,"MPIAIJ options");
2609   if (A->ops->increaseoverlap == MatIncreaseOverlap_MPIAIJ_Scalable) sc = PETSC_TRUE;
2610   PetscCall(PetscOptionsBool("-mat_increase_overlap_scalable","Use a scalable algorithm to compute the overlap","MatIncreaseOverlap",sc,&sc,&flg));
2611   if (flg) PetscCall(MatMPIAIJSetUseScalableIncreaseOverlap(A,sc));
2612   PetscOptionsHeadEnd();
2613   PetscFunctionReturn(0);
2614 }
2615 
2616 PetscErrorCode MatShift_MPIAIJ(Mat Y,PetscScalar a)
2617 {
2618   Mat_MPIAIJ     *maij = (Mat_MPIAIJ*)Y->data;
2619   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)maij->A->data;
2620 
2621   PetscFunctionBegin;
2622   if (!Y->preallocated) {
2623     PetscCall(MatMPIAIJSetPreallocation(Y,1,NULL,0,NULL));
2624   } else if (!aij->nz) { /* It does not matter if diagonals of Y only partially lie in maij->A. We just need an estimated preallocation. */
2625     PetscInt nonew = aij->nonew;
2626     PetscCall(MatSeqAIJSetPreallocation(maij->A,1,NULL));
2627     aij->nonew = nonew;
2628   }
2629   PetscCall(MatShift_Basic(Y,a));
2630   PetscFunctionReturn(0);
2631 }
2632 
2633 PetscErrorCode MatMissingDiagonal_MPIAIJ(Mat A,PetscBool  *missing,PetscInt *d)
2634 {
2635   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2636 
2637   PetscFunctionBegin;
2638   PetscCheck(A->rmap->n == A->cmap->n,PETSC_COMM_SELF,PETSC_ERR_SUP,"Only works for square matrices");
2639   PetscCall(MatMissingDiagonal(a->A,missing,d));
2640   if (d) {
2641     PetscInt rstart;
2642     PetscCall(MatGetOwnershipRange(A,&rstart,NULL));
2643     *d += rstart;
2644 
2645   }
2646   PetscFunctionReturn(0);
2647 }
2648 
2649 PetscErrorCode MatInvertVariableBlockDiagonal_MPIAIJ(Mat A,PetscInt nblocks,const PetscInt *bsizes,PetscScalar *diag)
2650 {
2651   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2652 
2653   PetscFunctionBegin;
2654   PetscCall(MatInvertVariableBlockDiagonal(a->A,nblocks,bsizes,diag));
2655   PetscFunctionReturn(0);
2656 }
2657 
2658 /* -------------------------------------------------------------------*/
2659 static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
2660                                        MatGetRow_MPIAIJ,
2661                                        MatRestoreRow_MPIAIJ,
2662                                        MatMult_MPIAIJ,
2663                                 /* 4*/ MatMultAdd_MPIAIJ,
2664                                        MatMultTranspose_MPIAIJ,
2665                                        MatMultTransposeAdd_MPIAIJ,
2666                                        NULL,
2667                                        NULL,
2668                                        NULL,
2669                                 /*10*/ NULL,
2670                                        NULL,
2671                                        NULL,
2672                                        MatSOR_MPIAIJ,
2673                                        MatTranspose_MPIAIJ,
2674                                 /*15*/ MatGetInfo_MPIAIJ,
2675                                        MatEqual_MPIAIJ,
2676                                        MatGetDiagonal_MPIAIJ,
2677                                        MatDiagonalScale_MPIAIJ,
2678                                        MatNorm_MPIAIJ,
2679                                 /*20*/ MatAssemblyBegin_MPIAIJ,
2680                                        MatAssemblyEnd_MPIAIJ,
2681                                        MatSetOption_MPIAIJ,
2682                                        MatZeroEntries_MPIAIJ,
2683                                 /*24*/ MatZeroRows_MPIAIJ,
2684                                        NULL,
2685                                        NULL,
2686                                        NULL,
2687                                        NULL,
2688                                 /*29*/ MatSetUp_MPIAIJ,
2689                                        NULL,
2690                                        NULL,
2691                                        MatGetDiagonalBlock_MPIAIJ,
2692                                        NULL,
2693                                 /*34*/ MatDuplicate_MPIAIJ,
2694                                        NULL,
2695                                        NULL,
2696                                        NULL,
2697                                        NULL,
2698                                 /*39*/ MatAXPY_MPIAIJ,
2699                                        MatCreateSubMatrices_MPIAIJ,
2700                                        MatIncreaseOverlap_MPIAIJ,
2701                                        MatGetValues_MPIAIJ,
2702                                        MatCopy_MPIAIJ,
2703                                 /*44*/ MatGetRowMax_MPIAIJ,
2704                                        MatScale_MPIAIJ,
2705                                        MatShift_MPIAIJ,
2706                                        MatDiagonalSet_MPIAIJ,
2707                                        MatZeroRowsColumns_MPIAIJ,
2708                                 /*49*/ MatSetRandom_MPIAIJ,
2709                                        MatGetRowIJ_MPIAIJ,
2710                                        MatRestoreRowIJ_MPIAIJ,
2711                                        NULL,
2712                                        NULL,
2713                                 /*54*/ MatFDColoringCreate_MPIXAIJ,
2714                                        NULL,
2715                                        MatSetUnfactored_MPIAIJ,
2716                                        MatPermute_MPIAIJ,
2717                                        NULL,
2718                                 /*59*/ MatCreateSubMatrix_MPIAIJ,
2719                                        MatDestroy_MPIAIJ,
2720                                        MatView_MPIAIJ,
2721                                        NULL,
2722                                        NULL,
2723                                 /*64*/ NULL,
2724                                        MatMatMatMultNumeric_MPIAIJ_MPIAIJ_MPIAIJ,
2725                                        NULL,
2726                                        NULL,
2727                                        NULL,
2728                                 /*69*/ MatGetRowMaxAbs_MPIAIJ,
2729                                        MatGetRowMinAbs_MPIAIJ,
2730                                        NULL,
2731                                        NULL,
2732                                        NULL,
2733                                        NULL,
2734                                 /*75*/ MatFDColoringApply_AIJ,
2735                                        MatSetFromOptions_MPIAIJ,
2736                                        NULL,
2737                                        NULL,
2738                                        MatFindZeroDiagonals_MPIAIJ,
2739                                 /*80*/ NULL,
2740                                        NULL,
2741                                        NULL,
2742                                 /*83*/ MatLoad_MPIAIJ,
2743                                        MatIsSymmetric_MPIAIJ,
2744                                        NULL,
2745                                        NULL,
2746                                        NULL,
2747                                        NULL,
2748                                 /*89*/ NULL,
2749                                        NULL,
2750                                        MatMatMultNumeric_MPIAIJ_MPIAIJ,
2751                                        NULL,
2752                                        NULL,
2753                                 /*94*/ MatPtAPNumeric_MPIAIJ_MPIAIJ,
2754                                        NULL,
2755                                        NULL,
2756                                        NULL,
2757                                        MatBindToCPU_MPIAIJ,
2758                                 /*99*/ MatProductSetFromOptions_MPIAIJ,
2759                                        NULL,
2760                                        NULL,
2761                                        MatConjugate_MPIAIJ,
2762                                        NULL,
2763                                 /*104*/MatSetValuesRow_MPIAIJ,
2764                                        MatRealPart_MPIAIJ,
2765                                        MatImaginaryPart_MPIAIJ,
2766                                        NULL,
2767                                        NULL,
2768                                 /*109*/NULL,
2769                                        NULL,
2770                                        MatGetRowMin_MPIAIJ,
2771                                        NULL,
2772                                        MatMissingDiagonal_MPIAIJ,
2773                                 /*114*/MatGetSeqNonzeroStructure_MPIAIJ,
2774                                        NULL,
2775                                        MatGetGhosts_MPIAIJ,
2776                                        NULL,
2777                                        NULL,
2778                                 /*119*/MatMultDiagonalBlock_MPIAIJ,
2779                                        NULL,
2780                                        NULL,
2781                                        NULL,
2782                                        MatGetMultiProcBlock_MPIAIJ,
2783                                 /*124*/MatFindNonzeroRows_MPIAIJ,
2784                                        MatGetColumnReductions_MPIAIJ,
2785                                        MatInvertBlockDiagonal_MPIAIJ,
2786                                        MatInvertVariableBlockDiagonal_MPIAIJ,
2787                                        MatCreateSubMatricesMPI_MPIAIJ,
2788                                 /*129*/NULL,
2789                                        NULL,
2790                                        NULL,
2791                                        MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ,
2792                                        NULL,
2793                                 /*134*/NULL,
2794                                        NULL,
2795                                        NULL,
2796                                        NULL,
2797                                        NULL,
2798                                 /*139*/MatSetBlockSizes_MPIAIJ,
2799                                        NULL,
2800                                        NULL,
2801                                        MatFDColoringSetUp_MPIXAIJ,
2802                                        MatFindOffBlockDiagonalEntries_MPIAIJ,
2803                                        MatCreateMPIMatConcatenateSeqMat_MPIAIJ,
2804                                 /*145*/NULL,
2805                                        NULL,
2806                                        NULL,
2807                                        MatCreateGraph_Simple_AIJ,
2808                                        MatFilter_AIJ
2809 };
2810 
2811 /* ----------------------------------------------------------------------------------------*/
2812 
2813 PetscErrorCode  MatStoreValues_MPIAIJ(Mat mat)
2814 {
2815   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2816 
2817   PetscFunctionBegin;
2818   PetscCall(MatStoreValues(aij->A));
2819   PetscCall(MatStoreValues(aij->B));
2820   PetscFunctionReturn(0);
2821 }
2822 
2823 PetscErrorCode  MatRetrieveValues_MPIAIJ(Mat mat)
2824 {
2825   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2826 
2827   PetscFunctionBegin;
2828   PetscCall(MatRetrieveValues(aij->A));
2829   PetscCall(MatRetrieveValues(aij->B));
2830   PetscFunctionReturn(0);
2831 }
2832 
2833 PetscErrorCode MatMPIAIJSetPreallocation_MPIAIJ(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
2834 {
2835   Mat_MPIAIJ     *b;
2836   PetscMPIInt    size;
2837 
2838   PetscFunctionBegin;
2839   PetscCall(PetscLayoutSetUp(B->rmap));
2840   PetscCall(PetscLayoutSetUp(B->cmap));
2841   b = (Mat_MPIAIJ*)B->data;
2842 
2843 #if defined(PETSC_USE_CTABLE)
2844   PetscCall(PetscTableDestroy(&b->colmap));
2845 #else
2846   PetscCall(PetscFree(b->colmap));
2847 #endif
2848   PetscCall(PetscFree(b->garray));
2849   PetscCall(VecDestroy(&b->lvec));
2850   PetscCall(VecScatterDestroy(&b->Mvctx));
2851 
2852   /* Because the B will have been resized we simply destroy it and create a new one each time */
2853   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)B),&size));
2854   PetscCall(MatDestroy(&b->B));
2855   PetscCall(MatCreate(PETSC_COMM_SELF,&b->B));
2856   PetscCall(MatSetSizes(b->B,B->rmap->n,size > 1 ? B->cmap->N : 0,B->rmap->n,size > 1 ? B->cmap->N : 0));
2857   PetscCall(MatSetBlockSizesFromMats(b->B,B,B));
2858   PetscCall(MatSetType(b->B,MATSEQAIJ));
2859   PetscCall(PetscLogObjectParent((PetscObject)B,(PetscObject)b->B));
2860 
2861   if (!B->preallocated) {
2862     PetscCall(MatCreate(PETSC_COMM_SELF,&b->A));
2863     PetscCall(MatSetSizes(b->A,B->rmap->n,B->cmap->n,B->rmap->n,B->cmap->n));
2864     PetscCall(MatSetBlockSizesFromMats(b->A,B,B));
2865     PetscCall(MatSetType(b->A,MATSEQAIJ));
2866     PetscCall(PetscLogObjectParent((PetscObject)B,(PetscObject)b->A));
2867   }
2868 
2869   PetscCall(MatSeqAIJSetPreallocation(b->A,d_nz,d_nnz));
2870   PetscCall(MatSeqAIJSetPreallocation(b->B,o_nz,o_nnz));
2871   B->preallocated  = PETSC_TRUE;
2872   B->was_assembled = PETSC_FALSE;
2873   B->assembled     = PETSC_FALSE;
2874   PetscFunctionReturn(0);
2875 }
2876 
2877 PetscErrorCode MatResetPreallocation_MPIAIJ(Mat B)
2878 {
2879   Mat_MPIAIJ     *b;
2880 
2881   PetscFunctionBegin;
2882   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
2883   PetscCall(PetscLayoutSetUp(B->rmap));
2884   PetscCall(PetscLayoutSetUp(B->cmap));
2885   b = (Mat_MPIAIJ*)B->data;
2886 
2887 #if defined(PETSC_USE_CTABLE)
2888   PetscCall(PetscTableDestroy(&b->colmap));
2889 #else
2890   PetscCall(PetscFree(b->colmap));
2891 #endif
2892   PetscCall(PetscFree(b->garray));
2893   PetscCall(VecDestroy(&b->lvec));
2894   PetscCall(VecScatterDestroy(&b->Mvctx));
2895 
2896   PetscCall(MatResetPreallocation(b->A));
2897   PetscCall(MatResetPreallocation(b->B));
2898   B->preallocated  = PETSC_TRUE;
2899   B->was_assembled = PETSC_FALSE;
2900   B->assembled = PETSC_FALSE;
2901   PetscFunctionReturn(0);
2902 }
2903 
2904 PetscErrorCode MatDuplicate_MPIAIJ(Mat matin,MatDuplicateOption cpvalues,Mat *newmat)
2905 {
2906   Mat            mat;
2907   Mat_MPIAIJ     *a,*oldmat = (Mat_MPIAIJ*)matin->data;
2908 
2909   PetscFunctionBegin;
2910   *newmat = NULL;
2911   PetscCall(MatCreate(PetscObjectComm((PetscObject)matin),&mat));
2912   PetscCall(MatSetSizes(mat,matin->rmap->n,matin->cmap->n,matin->rmap->N,matin->cmap->N));
2913   PetscCall(MatSetBlockSizesFromMats(mat,matin,matin));
2914   PetscCall(MatSetType(mat,((PetscObject)matin)->type_name));
2915   a       = (Mat_MPIAIJ*)mat->data;
2916 
2917   mat->factortype   = matin->factortype;
2918   mat->assembled    = matin->assembled;
2919   mat->insertmode   = NOT_SET_VALUES;
2920   mat->preallocated = matin->preallocated;
2921 
2922   a->size         = oldmat->size;
2923   a->rank         = oldmat->rank;
2924   a->donotstash   = oldmat->donotstash;
2925   a->roworiented  = oldmat->roworiented;
2926   a->rowindices   = NULL;
2927   a->rowvalues    = NULL;
2928   a->getrowactive = PETSC_FALSE;
2929 
2930   PetscCall(PetscLayoutReference(matin->rmap,&mat->rmap));
2931   PetscCall(PetscLayoutReference(matin->cmap,&mat->cmap));
2932 
2933   if (oldmat->colmap) {
2934 #if defined(PETSC_USE_CTABLE)
2935     PetscCall(PetscTableCreateCopy(oldmat->colmap,&a->colmap));
2936 #else
2937     PetscCall(PetscMalloc1(mat->cmap->N,&a->colmap));
2938     PetscCall(PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N)*sizeof(PetscInt)));
2939     PetscCall(PetscArraycpy(a->colmap,oldmat->colmap,mat->cmap->N));
2940 #endif
2941   } else a->colmap = NULL;
2942   if (oldmat->garray) {
2943     PetscInt len;
2944     len  = oldmat->B->cmap->n;
2945     PetscCall(PetscMalloc1(len+1,&a->garray));
2946     PetscCall(PetscLogObjectMemory((PetscObject)mat,len*sizeof(PetscInt)));
2947     if (len) PetscCall(PetscArraycpy(a->garray,oldmat->garray,len));
2948   } else a->garray = NULL;
2949 
2950   /* It may happen MatDuplicate is called with a non-assembled matrix
2951      In fact, MatDuplicate only requires the matrix to be preallocated
2952      This may happen inside a DMCreateMatrix_Shell */
2953   if (oldmat->lvec) {
2954     PetscCall(VecDuplicate(oldmat->lvec,&a->lvec));
2955     PetscCall(PetscLogObjectParent((PetscObject)mat,(PetscObject)a->lvec));
2956   }
2957   if (oldmat->Mvctx) {
2958     PetscCall(VecScatterCopy(oldmat->Mvctx,&a->Mvctx));
2959     PetscCall(PetscLogObjectParent((PetscObject)mat,(PetscObject)a->Mvctx));
2960   }
2961   PetscCall(MatDuplicate(oldmat->A,cpvalues,&a->A));
2962   PetscCall(PetscLogObjectParent((PetscObject)mat,(PetscObject)a->A));
2963   PetscCall(MatDuplicate(oldmat->B,cpvalues,&a->B));
2964   PetscCall(PetscLogObjectParent((PetscObject)mat,(PetscObject)a->B));
2965   PetscCall(PetscFunctionListDuplicate(((PetscObject)matin)->qlist,&((PetscObject)mat)->qlist));
2966   *newmat = mat;
2967   PetscFunctionReturn(0);
2968 }
2969 
2970 PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
2971 {
2972   PetscBool      isbinary, ishdf5;
2973 
2974   PetscFunctionBegin;
2975   PetscValidHeaderSpecific(newMat,MAT_CLASSID,1);
2976   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,2);
2977   /* force binary viewer to load .info file if it has not yet done so */
2978   PetscCall(PetscViewerSetUp(viewer));
2979   PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary));
2980   PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERHDF5,  &ishdf5));
2981   if (isbinary) {
2982     PetscCall(MatLoad_MPIAIJ_Binary(newMat,viewer));
2983   } else if (ishdf5) {
2984 #if defined(PETSC_HAVE_HDF5)
2985     PetscCall(MatLoad_AIJ_HDF5(newMat,viewer));
2986 #else
2987     SETERRQ(PetscObjectComm((PetscObject)newMat),PETSC_ERR_SUP,"HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
2988 #endif
2989   } else {
2990     SETERRQ(PetscObjectComm((PetscObject)newMat),PETSC_ERR_SUP,"Viewer type %s not yet supported for reading %s matrices",((PetscObject)viewer)->type_name,((PetscObject)newMat)->type_name);
2991   }
2992   PetscFunctionReturn(0);
2993 }
2994 
2995 PetscErrorCode MatLoad_MPIAIJ_Binary(Mat mat, PetscViewer viewer)
2996 {
2997   PetscInt       header[4],M,N,m,nz,rows,cols,sum,i;
2998   PetscInt       *rowidxs,*colidxs;
2999   PetscScalar    *matvals;
3000 
3001   PetscFunctionBegin;
3002   PetscCall(PetscViewerSetUp(viewer));
3003 
3004   /* read in matrix header */
3005   PetscCall(PetscViewerBinaryRead(viewer,header,4,NULL,PETSC_INT));
3006   PetscCheck(header[0] == MAT_FILE_CLASSID,PetscObjectComm((PetscObject)viewer),PETSC_ERR_FILE_UNEXPECTED,"Not a matrix object in file");
3007   M  = header[1]; N = header[2]; nz = header[3];
3008   PetscCheck(M >= 0,PetscObjectComm((PetscObject)viewer),PETSC_ERR_FILE_UNEXPECTED,"Matrix row size (%" PetscInt_FMT ") in file is negative",M);
3009   PetscCheck(N >= 0,PetscObjectComm((PetscObject)viewer),PETSC_ERR_FILE_UNEXPECTED,"Matrix column size (%" PetscInt_FMT ") in file is negative",N);
3010   PetscCheck(nz >= 0,PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Matrix stored in special format on disk, cannot load as MPIAIJ");
3011 
3012   /* set block sizes from the viewer's .info file */
3013   PetscCall(MatLoad_Binary_BlockSizes(mat,viewer));
3014   /* set global sizes if not set already */
3015   if (mat->rmap->N < 0) mat->rmap->N = M;
3016   if (mat->cmap->N < 0) mat->cmap->N = N;
3017   PetscCall(PetscLayoutSetUp(mat->rmap));
3018   PetscCall(PetscLayoutSetUp(mat->cmap));
3019 
3020   /* check if the matrix sizes are correct */
3021   PetscCall(MatGetSize(mat,&rows,&cols));
3022   PetscCheck(M == rows && N == cols,PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Matrix in file of different sizes (%" PetscInt_FMT ", %" PetscInt_FMT ") than the input matrix (%" PetscInt_FMT ", %" PetscInt_FMT ")",M,N,rows,cols);
3023 
3024   /* read in row lengths and build row indices */
3025   PetscCall(MatGetLocalSize(mat,&m,NULL));
3026   PetscCall(PetscMalloc1(m+1,&rowidxs));
3027   PetscCall(PetscViewerBinaryReadAll(viewer,rowidxs+1,m,PETSC_DECIDE,M,PETSC_INT));
3028   rowidxs[0] = 0; for (i=0; i<m; i++) rowidxs[i+1] += rowidxs[i];
3029   PetscCall(MPIU_Allreduce(&rowidxs[m],&sum,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)viewer)));
3030   PetscCheck(sum == nz,PetscObjectComm((PetscObject)viewer),PETSC_ERR_FILE_UNEXPECTED,"Inconsistent matrix data in file: nonzeros = %" PetscInt_FMT ", sum-row-lengths = %" PetscInt_FMT,nz,sum);
3031   /* read in column indices and matrix values */
3032   PetscCall(PetscMalloc2(rowidxs[m],&colidxs,rowidxs[m],&matvals));
3033   PetscCall(PetscViewerBinaryReadAll(viewer,colidxs,rowidxs[m],PETSC_DETERMINE,PETSC_DETERMINE,PETSC_INT));
3034   PetscCall(PetscViewerBinaryReadAll(viewer,matvals,rowidxs[m],PETSC_DETERMINE,PETSC_DETERMINE,PETSC_SCALAR));
3035   /* store matrix indices and values */
3036   PetscCall(MatMPIAIJSetPreallocationCSR(mat,rowidxs,colidxs,matvals));
3037   PetscCall(PetscFree(rowidxs));
3038   PetscCall(PetscFree2(colidxs,matvals));
3039   PetscFunctionReturn(0);
3040 }
3041 
3042 /* Not scalable because of ISAllGather() unless getting all columns. */
3043 PetscErrorCode ISGetSeqIS_Private(Mat mat,IS iscol,IS *isseq)
3044 {
3045   IS             iscol_local;
3046   PetscBool      isstride;
3047   PetscMPIInt    lisstride=0,gisstride;
3048 
3049   PetscFunctionBegin;
3050   /* check if we are grabbing all columns*/
3051   PetscCall(PetscObjectTypeCompare((PetscObject)iscol,ISSTRIDE,&isstride));
3052 
3053   if (isstride) {
3054     PetscInt  start,len,mstart,mlen;
3055     PetscCall(ISStrideGetInfo(iscol,&start,NULL));
3056     PetscCall(ISGetLocalSize(iscol,&len));
3057     PetscCall(MatGetOwnershipRangeColumn(mat,&mstart,&mlen));
3058     if (mstart == start && mlen-mstart == len) lisstride = 1;
3059   }
3060 
3061   PetscCall(MPIU_Allreduce(&lisstride,&gisstride,1,MPI_INT,MPI_MIN,PetscObjectComm((PetscObject)mat)));
3062   if (gisstride) {
3063     PetscInt N;
3064     PetscCall(MatGetSize(mat,NULL,&N));
3065     PetscCall(ISCreateStride(PETSC_COMM_SELF,N,0,1,&iscol_local));
3066     PetscCall(ISSetIdentity(iscol_local));
3067     PetscCall(PetscInfo(mat,"Optimizing for obtaining all columns of the matrix; skipping ISAllGather()\n"));
3068   } else {
3069     PetscInt cbs;
3070     PetscCall(ISGetBlockSize(iscol,&cbs));
3071     PetscCall(ISAllGather(iscol,&iscol_local));
3072     PetscCall(ISSetBlockSize(iscol_local,cbs));
3073   }
3074 
3075   *isseq = iscol_local;
3076   PetscFunctionReturn(0);
3077 }
3078 
3079 /*
3080  Used by MatCreateSubMatrix_MPIAIJ_SameRowColDist() to avoid ISAllGather() and global size of iscol_local
3081  (see MatCreateSubMatrix_MPIAIJ_nonscalable)
3082 
3083  Input Parameters:
3084    mat - matrix
3085    isrow - parallel row index set; its local indices are a subset of local columns of mat,
3086            i.e., mat->rstart <= isrow[i] < mat->rend
3087    iscol - parallel column index set; its local indices are a subset of local columns of mat,
3088            i.e., mat->cstart <= iscol[i] < mat->cend
3089  Output Parameter:
3090    isrow_d,iscol_d - sequential row and column index sets for retrieving mat->A
3091    iscol_o - sequential column index set for retrieving mat->B
3092    garray - column map; garray[i] indicates global location of iscol_o[i] in iscol
3093  */
3094 PetscErrorCode ISGetSeqIS_SameColDist_Private(Mat mat,IS isrow,IS iscol,IS *isrow_d,IS *iscol_d,IS *iscol_o,const PetscInt *garray[])
3095 {
3096   Vec            x,cmap;
3097   const PetscInt *is_idx;
3098   PetscScalar    *xarray,*cmaparray;
3099   PetscInt       ncols,isstart,*idx,m,rstart,*cmap1,count;
3100   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)mat->data;
3101   Mat            B=a->B;
3102   Vec            lvec=a->lvec,lcmap;
3103   PetscInt       i,cstart,cend,Bn=B->cmap->N;
3104   MPI_Comm       comm;
3105   VecScatter     Mvctx=a->Mvctx;
3106 
3107   PetscFunctionBegin;
3108   PetscCall(PetscObjectGetComm((PetscObject)mat,&comm));
3109   PetscCall(ISGetLocalSize(iscol,&ncols));
3110 
3111   /* (1) iscol is a sub-column vector of mat, pad it with '-1.' to form a full vector x */
3112   PetscCall(MatCreateVecs(mat,&x,NULL));
3113   PetscCall(VecSet(x,-1.0));
3114   PetscCall(VecDuplicate(x,&cmap));
3115   PetscCall(VecSet(cmap,-1.0));
3116 
3117   /* Get start indices */
3118   PetscCallMPI(MPI_Scan(&ncols,&isstart,1,MPIU_INT,MPI_SUM,comm));
3119   isstart -= ncols;
3120   PetscCall(MatGetOwnershipRangeColumn(mat,&cstart,&cend));
3121 
3122   PetscCall(ISGetIndices(iscol,&is_idx));
3123   PetscCall(VecGetArray(x,&xarray));
3124   PetscCall(VecGetArray(cmap,&cmaparray));
3125   PetscCall(PetscMalloc1(ncols,&idx));
3126   for (i=0; i<ncols; i++) {
3127     xarray[is_idx[i]-cstart]    = (PetscScalar)is_idx[i];
3128     cmaparray[is_idx[i]-cstart] = i + isstart;      /* global index of iscol[i] */
3129     idx[i]                      = is_idx[i]-cstart; /* local index of iscol[i]  */
3130   }
3131   PetscCall(VecRestoreArray(x,&xarray));
3132   PetscCall(VecRestoreArray(cmap,&cmaparray));
3133   PetscCall(ISRestoreIndices(iscol,&is_idx));
3134 
3135   /* Get iscol_d */
3136   PetscCall(ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,iscol_d));
3137   PetscCall(ISGetBlockSize(iscol,&i));
3138   PetscCall(ISSetBlockSize(*iscol_d,i));
3139 
3140   /* Get isrow_d */
3141   PetscCall(ISGetLocalSize(isrow,&m));
3142   rstart = mat->rmap->rstart;
3143   PetscCall(PetscMalloc1(m,&idx));
3144   PetscCall(ISGetIndices(isrow,&is_idx));
3145   for (i=0; i<m; i++) idx[i] = is_idx[i]-rstart;
3146   PetscCall(ISRestoreIndices(isrow,&is_idx));
3147 
3148   PetscCall(ISCreateGeneral(PETSC_COMM_SELF,m,idx,PETSC_OWN_POINTER,isrow_d));
3149   PetscCall(ISGetBlockSize(isrow,&i));
3150   PetscCall(ISSetBlockSize(*isrow_d,i));
3151 
3152   /* (2) Scatter x and cmap using aij->Mvctx to get their off-process portions (see MatMult_MPIAIJ) */
3153   PetscCall(VecScatterBegin(Mvctx,x,lvec,INSERT_VALUES,SCATTER_FORWARD));
3154   PetscCall(VecScatterEnd(Mvctx,x,lvec,INSERT_VALUES,SCATTER_FORWARD));
3155 
3156   PetscCall(VecDuplicate(lvec,&lcmap));
3157 
3158   PetscCall(VecScatterBegin(Mvctx,cmap,lcmap,INSERT_VALUES,SCATTER_FORWARD));
3159   PetscCall(VecScatterEnd(Mvctx,cmap,lcmap,INSERT_VALUES,SCATTER_FORWARD));
3160 
3161   /* (3) create sequential iscol_o (a subset of iscol) and isgarray */
3162   /* off-process column indices */
3163   count = 0;
3164   PetscCall(PetscMalloc1(Bn,&idx));
3165   PetscCall(PetscMalloc1(Bn,&cmap1));
3166 
3167   PetscCall(VecGetArray(lvec,&xarray));
3168   PetscCall(VecGetArray(lcmap,&cmaparray));
3169   for (i=0; i<Bn; i++) {
3170     if (PetscRealPart(xarray[i]) > -1.0) {
3171       idx[count]     = i;                   /* local column index in off-diagonal part B */
3172       cmap1[count] = (PetscInt)PetscRealPart(cmaparray[i]);  /* column index in submat */
3173       count++;
3174     }
3175   }
3176   PetscCall(VecRestoreArray(lvec,&xarray));
3177   PetscCall(VecRestoreArray(lcmap,&cmaparray));
3178 
3179   PetscCall(ISCreateGeneral(PETSC_COMM_SELF,count,idx,PETSC_COPY_VALUES,iscol_o));
3180   /* cannot ensure iscol_o has same blocksize as iscol! */
3181 
3182   PetscCall(PetscFree(idx));
3183   *garray = cmap1;
3184 
3185   PetscCall(VecDestroy(&x));
3186   PetscCall(VecDestroy(&cmap));
3187   PetscCall(VecDestroy(&lcmap));
3188   PetscFunctionReturn(0);
3189 }
3190 
3191 /* isrow and iscol have same processor distribution as mat, output *submat is a submatrix of local mat */
3192 PetscErrorCode MatCreateSubMatrix_MPIAIJ_SameRowColDist(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *submat)
3193 {
3194   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)mat->data,*asub;
3195   Mat            M = NULL;
3196   MPI_Comm       comm;
3197   IS             iscol_d,isrow_d,iscol_o;
3198   Mat            Asub = NULL,Bsub = NULL;
3199   PetscInt       n;
3200 
3201   PetscFunctionBegin;
3202   PetscCall(PetscObjectGetComm((PetscObject)mat,&comm));
3203 
3204   if (call == MAT_REUSE_MATRIX) {
3205     /* Retrieve isrow_d, iscol_d and iscol_o from submat */
3206     PetscCall(PetscObjectQuery((PetscObject)*submat,"isrow_d",(PetscObject*)&isrow_d));
3207     PetscCheck(isrow_d,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"isrow_d passed in was not used before, cannot reuse");
3208 
3209     PetscCall(PetscObjectQuery((PetscObject)*submat,"iscol_d",(PetscObject*)&iscol_d));
3210     PetscCheck(iscol_d,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"iscol_d passed in was not used before, cannot reuse");
3211 
3212     PetscCall(PetscObjectQuery((PetscObject)*submat,"iscol_o",(PetscObject*)&iscol_o));
3213     PetscCheck(iscol_o,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"iscol_o passed in was not used before, cannot reuse");
3214 
3215     /* Update diagonal and off-diagonal portions of submat */
3216     asub = (Mat_MPIAIJ*)(*submat)->data;
3217     PetscCall(MatCreateSubMatrix_SeqAIJ(a->A,isrow_d,iscol_d,PETSC_DECIDE,MAT_REUSE_MATRIX,&asub->A));
3218     PetscCall(ISGetLocalSize(iscol_o,&n));
3219     if (n) {
3220       PetscCall(MatCreateSubMatrix_SeqAIJ(a->B,isrow_d,iscol_o,PETSC_DECIDE,MAT_REUSE_MATRIX,&asub->B));
3221     }
3222     PetscCall(MatAssemblyBegin(*submat,MAT_FINAL_ASSEMBLY));
3223     PetscCall(MatAssemblyEnd(*submat,MAT_FINAL_ASSEMBLY));
3224 
3225   } else { /* call == MAT_INITIAL_MATRIX) */
3226     const PetscInt *garray;
3227     PetscInt        BsubN;
3228 
3229     /* Create isrow_d, iscol_d, iscol_o and isgarray (replace isgarray with array?) */
3230     PetscCall(ISGetSeqIS_SameColDist_Private(mat,isrow,iscol,&isrow_d,&iscol_d,&iscol_o,&garray));
3231 
3232     /* Create local submatrices Asub and Bsub */
3233     PetscCall(MatCreateSubMatrix_SeqAIJ(a->A,isrow_d,iscol_d,PETSC_DECIDE,MAT_INITIAL_MATRIX,&Asub));
3234     PetscCall(MatCreateSubMatrix_SeqAIJ(a->B,isrow_d,iscol_o,PETSC_DECIDE,MAT_INITIAL_MATRIX,&Bsub));
3235 
3236     /* Create submatrix M */
3237     PetscCall(MatCreateMPIAIJWithSeqAIJ(comm,Asub,Bsub,garray,&M));
3238 
3239     /* If Bsub has empty columns, compress iscol_o such that it will retrieve condensed Bsub from a->B during reuse */
3240     asub = (Mat_MPIAIJ*)M->data;
3241 
3242     PetscCall(ISGetLocalSize(iscol_o,&BsubN));
3243     n = asub->B->cmap->N;
3244     if (BsubN > n) {
3245       /* This case can be tested using ~petsc/src/tao/bound/tutorials/runplate2_3 */
3246       const PetscInt *idx;
3247       PetscInt       i,j,*idx_new,*subgarray = asub->garray;
3248       PetscCall(PetscInfo(M,"submatrix Bn %" PetscInt_FMT " != BsubN %" PetscInt_FMT ", update iscol_o\n",n,BsubN));
3249 
3250       PetscCall(PetscMalloc1(n,&idx_new));
3251       j = 0;
3252       PetscCall(ISGetIndices(iscol_o,&idx));
3253       for (i=0; i<n; i++) {
3254         if (j >= BsubN) break;
3255         while (subgarray[i] > garray[j]) j++;
3256 
3257         if (subgarray[i] == garray[j]) {
3258           idx_new[i] = idx[j++];
3259         } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"subgarray[%" PetscInt_FMT "]=%" PetscInt_FMT " cannot < garray[%" PetscInt_FMT "]=%" PetscInt_FMT,i,subgarray[i],j,garray[j]);
3260       }
3261       PetscCall(ISRestoreIndices(iscol_o,&idx));
3262 
3263       PetscCall(ISDestroy(&iscol_o));
3264       PetscCall(ISCreateGeneral(PETSC_COMM_SELF,n,idx_new,PETSC_OWN_POINTER,&iscol_o));
3265 
3266     } else if (BsubN < n) {
3267       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Columns of Bsub (%" PetscInt_FMT ") cannot be smaller than B's (%" PetscInt_FMT ")",BsubN,asub->B->cmap->N);
3268     }
3269 
3270     PetscCall(PetscFree(garray));
3271     *submat = M;
3272 
3273     /* Save isrow_d, iscol_d and iscol_o used in processor for next request */
3274     PetscCall(PetscObjectCompose((PetscObject)M,"isrow_d",(PetscObject)isrow_d));
3275     PetscCall(ISDestroy(&isrow_d));
3276 
3277     PetscCall(PetscObjectCompose((PetscObject)M,"iscol_d",(PetscObject)iscol_d));
3278     PetscCall(ISDestroy(&iscol_d));
3279 
3280     PetscCall(PetscObjectCompose((PetscObject)M,"iscol_o",(PetscObject)iscol_o));
3281     PetscCall(ISDestroy(&iscol_o));
3282   }
3283   PetscFunctionReturn(0);
3284 }
3285 
3286 PetscErrorCode MatCreateSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3287 {
3288   IS             iscol_local=NULL,isrow_d;
3289   PetscInt       csize;
3290   PetscInt       n,i,j,start,end;
3291   PetscBool      sameRowDist=PETSC_FALSE,sameDist[2],tsameDist[2];
3292   MPI_Comm       comm;
3293 
3294   PetscFunctionBegin;
3295   /* If isrow has same processor distribution as mat,
3296      call MatCreateSubMatrix_MPIAIJ_SameRowDist() to avoid using a hash table with global size of iscol */
3297   if (call == MAT_REUSE_MATRIX) {
3298     PetscCall(PetscObjectQuery((PetscObject)*newmat,"isrow_d",(PetscObject*)&isrow_d));
3299     if (isrow_d) {
3300       sameRowDist  = PETSC_TRUE;
3301       tsameDist[1] = PETSC_TRUE; /* sameColDist */
3302     } else {
3303       PetscCall(PetscObjectQuery((PetscObject)*newmat,"SubIScol",(PetscObject*)&iscol_local));
3304       if (iscol_local) {
3305         sameRowDist  = PETSC_TRUE;
3306         tsameDist[1] = PETSC_FALSE; /* !sameColDist */
3307       }
3308     }
3309   } else {
3310     /* Check if isrow has same processor distribution as mat */
3311     sameDist[0] = PETSC_FALSE;
3312     PetscCall(ISGetLocalSize(isrow,&n));
3313     if (!n) {
3314       sameDist[0] = PETSC_TRUE;
3315     } else {
3316       PetscCall(ISGetMinMax(isrow,&i,&j));
3317       PetscCall(MatGetOwnershipRange(mat,&start,&end));
3318       if (i >= start && j < end) {
3319         sameDist[0] = PETSC_TRUE;
3320       }
3321     }
3322 
3323     /* Check if iscol has same processor distribution as mat */
3324     sameDist[1] = PETSC_FALSE;
3325     PetscCall(ISGetLocalSize(iscol,&n));
3326     if (!n) {
3327       sameDist[1] = PETSC_TRUE;
3328     } else {
3329       PetscCall(ISGetMinMax(iscol,&i,&j));
3330       PetscCall(MatGetOwnershipRangeColumn(mat,&start,&end));
3331       if (i >= start && j < end) sameDist[1] = PETSC_TRUE;
3332     }
3333 
3334     PetscCall(PetscObjectGetComm((PetscObject)mat,&comm));
3335     PetscCall(MPIU_Allreduce(&sameDist,&tsameDist,2,MPIU_BOOL,MPI_LAND,comm));
3336     sameRowDist = tsameDist[0];
3337   }
3338 
3339   if (sameRowDist) {
3340     if (tsameDist[1]) { /* sameRowDist & sameColDist */
3341       /* isrow and iscol have same processor distribution as mat */
3342       PetscCall(MatCreateSubMatrix_MPIAIJ_SameRowColDist(mat,isrow,iscol,call,newmat));
3343       PetscFunctionReturn(0);
3344     } else { /* sameRowDist */
3345       /* isrow has same processor distribution as mat */
3346       if (call == MAT_INITIAL_MATRIX) {
3347         PetscBool sorted;
3348         PetscCall(ISGetSeqIS_Private(mat,iscol,&iscol_local));
3349         PetscCall(ISGetLocalSize(iscol_local,&n)); /* local size of iscol_local = global columns of newmat */
3350         PetscCall(ISGetSize(iscol,&i));
3351         PetscCheck(n == i,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"n %" PetscInt_FMT " != size of iscol %" PetscInt_FMT,n,i);
3352 
3353         PetscCall(ISSorted(iscol_local,&sorted));
3354         if (sorted) {
3355           /* MatCreateSubMatrix_MPIAIJ_SameRowDist() requires iscol_local be sorted; it can have duplicate indices */
3356           PetscCall(MatCreateSubMatrix_MPIAIJ_SameRowDist(mat,isrow,iscol,iscol_local,MAT_INITIAL_MATRIX,newmat));
3357           PetscFunctionReturn(0);
3358         }
3359       } else { /* call == MAT_REUSE_MATRIX */
3360         IS iscol_sub;
3361         PetscCall(PetscObjectQuery((PetscObject)*newmat,"SubIScol",(PetscObject*)&iscol_sub));
3362         if (iscol_sub) {
3363           PetscCall(MatCreateSubMatrix_MPIAIJ_SameRowDist(mat,isrow,iscol,NULL,call,newmat));
3364           PetscFunctionReturn(0);
3365         }
3366       }
3367     }
3368   }
3369 
3370   /* General case: iscol -> iscol_local which has global size of iscol */
3371   if (call == MAT_REUSE_MATRIX) {
3372     PetscCall(PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local));
3373     PetscCheck(iscol_local,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3374   } else {
3375     if (!iscol_local) {
3376       PetscCall(ISGetSeqIS_Private(mat,iscol,&iscol_local));
3377     }
3378   }
3379 
3380   PetscCall(ISGetLocalSize(iscol,&csize));
3381   PetscCall(MatCreateSubMatrix_MPIAIJ_nonscalable(mat,isrow,iscol_local,csize,call,newmat));
3382 
3383   if (call == MAT_INITIAL_MATRIX) {
3384     PetscCall(PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local));
3385     PetscCall(ISDestroy(&iscol_local));
3386   }
3387   PetscFunctionReturn(0);
3388 }
3389 
3390 /*@C
3391      MatCreateMPIAIJWithSeqAIJ - creates a MPIAIJ matrix using SeqAIJ matrices that contain the "diagonal"
3392          and "off-diagonal" part of the matrix in CSR format.
3393 
3394    Collective
3395 
3396    Input Parameters:
3397 +  comm - MPI communicator
3398 .  A - "diagonal" portion of matrix
3399 .  B - "off-diagonal" portion of matrix, may have empty columns, will be destroyed by this routine
3400 -  garray - global index of B columns
3401 
3402    Output Parameter:
3403 .   mat - the matrix, with input A as its local diagonal matrix
3404    Level: advanced
3405 
3406    Notes:
3407        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix.
3408        A becomes part of output mat, B is destroyed by this routine. The user cannot use A and B anymore.
3409 
3410 .seealso: `MatCreateMPIAIJWithSplitArrays()`
3411 @*/
3412 PetscErrorCode MatCreateMPIAIJWithSeqAIJ(MPI_Comm comm,Mat A,Mat B,const PetscInt garray[],Mat *mat)
3413 {
3414   Mat_MPIAIJ        *maij;
3415   Mat_SeqAIJ        *b=(Mat_SeqAIJ*)B->data,*bnew;
3416   PetscInt          *oi=b->i,*oj=b->j,i,nz,col;
3417   const PetscScalar *oa;
3418   Mat               Bnew;
3419   PetscInt          m,n,N;
3420 
3421   PetscFunctionBegin;
3422   PetscCall(MatCreate(comm,mat));
3423   PetscCall(MatGetSize(A,&m,&n));
3424   PetscCheck(m == B->rmap->N,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Am %" PetscInt_FMT " != Bm %" PetscInt_FMT,m,B->rmap->N);
3425   PetscCheck(A->rmap->bs == B->rmap->bs,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"A row bs %" PetscInt_FMT " != B row bs %" PetscInt_FMT,A->rmap->bs,B->rmap->bs);
3426   /* remove check below; When B is created using iscol_o from ISGetSeqIS_SameColDist_Private(), its bs may not be same as A */
3427   /* PetscCheck(A->cmap->bs == B->cmap->bs,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"A column bs %" PetscInt_FMT " != B column bs %" PetscInt_FMT,A->cmap->bs,B->cmap->bs); */
3428 
3429   /* Get global columns of mat */
3430   PetscCall(MPIU_Allreduce(&n,&N,1,MPIU_INT,MPI_SUM,comm));
3431 
3432   PetscCall(MatSetSizes(*mat,m,n,PETSC_DECIDE,N));
3433   PetscCall(MatSetType(*mat,MATMPIAIJ));
3434   PetscCall(MatSetBlockSizes(*mat,A->rmap->bs,A->cmap->bs));
3435   maij = (Mat_MPIAIJ*)(*mat)->data;
3436 
3437   (*mat)->preallocated = PETSC_TRUE;
3438 
3439   PetscCall(PetscLayoutSetUp((*mat)->rmap));
3440   PetscCall(PetscLayoutSetUp((*mat)->cmap));
3441 
3442   /* Set A as diagonal portion of *mat */
3443   maij->A = A;
3444 
3445   nz = oi[m];
3446   for (i=0; i<nz; i++) {
3447     col   = oj[i];
3448     oj[i] = garray[col];
3449   }
3450 
3451   /* Set Bnew as off-diagonal portion of *mat */
3452   PetscCall(MatSeqAIJGetArrayRead(B,&oa));
3453   PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,N,oi,oj,(PetscScalar*)oa,&Bnew));
3454   PetscCall(MatSeqAIJRestoreArrayRead(B,&oa));
3455   bnew        = (Mat_SeqAIJ*)Bnew->data;
3456   bnew->maxnz = b->maxnz; /* allocated nonzeros of B */
3457   maij->B     = Bnew;
3458 
3459   PetscCheck(B->rmap->N == Bnew->rmap->N,PETSC_COMM_SELF,PETSC_ERR_PLIB,"BN %" PetscInt_FMT " != BnewN %" PetscInt_FMT,B->rmap->N,Bnew->rmap->N);
3460 
3461   b->singlemalloc = PETSC_FALSE; /* B arrays are shared by Bnew */
3462   b->free_a       = PETSC_FALSE;
3463   b->free_ij      = PETSC_FALSE;
3464   PetscCall(MatDestroy(&B));
3465 
3466   bnew->singlemalloc = PETSC_TRUE; /* arrays will be freed by MatDestroy(&Bnew) */
3467   bnew->free_a       = PETSC_TRUE;
3468   bnew->free_ij      = PETSC_TRUE;
3469 
3470   /* condense columns of maij->B */
3471   PetscCall(MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE));
3472   PetscCall(MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY));
3473   PetscCall(MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY));
3474   PetscCall(MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_FALSE));
3475   PetscCall(MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE));
3476   PetscFunctionReturn(0);
3477 }
3478 
3479 extern PetscErrorCode MatCreateSubMatrices_MPIAIJ_SingleIS_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool,Mat*);
3480 
3481 PetscErrorCode MatCreateSubMatrix_MPIAIJ_SameRowDist(Mat mat,IS isrow,IS iscol,IS iscol_local,MatReuse call,Mat *newmat)
3482 {
3483   PetscInt       i,m,n,rstart,row,rend,nz,j,bs,cbs;
3484   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
3485   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)mat->data;
3486   Mat            M,Msub,B=a->B;
3487   MatScalar      *aa;
3488   Mat_SeqAIJ     *aij;
3489   PetscInt       *garray = a->garray,*colsub,Ncols;
3490   PetscInt       count,Bn=B->cmap->N,cstart=mat->cmap->rstart,cend=mat->cmap->rend;
3491   IS             iscol_sub,iscmap;
3492   const PetscInt *is_idx,*cmap;
3493   PetscBool      allcolumns=PETSC_FALSE;
3494   MPI_Comm       comm;
3495 
3496   PetscFunctionBegin;
3497   PetscCall(PetscObjectGetComm((PetscObject)mat,&comm));
3498   if (call == MAT_REUSE_MATRIX) {
3499     PetscCall(PetscObjectQuery((PetscObject)*newmat,"SubIScol",(PetscObject*)&iscol_sub));
3500     PetscCheck(iscol_sub,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"SubIScol passed in was not used before, cannot reuse");
3501     PetscCall(ISGetLocalSize(iscol_sub,&count));
3502 
3503     PetscCall(PetscObjectQuery((PetscObject)*newmat,"Subcmap",(PetscObject*)&iscmap));
3504     PetscCheck(iscmap,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Subcmap passed in was not used before, cannot reuse");
3505 
3506     PetscCall(PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Msub));
3507     PetscCheck(Msub,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3508 
3509     PetscCall(MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol_sub,MAT_REUSE_MATRIX,PETSC_FALSE,&Msub));
3510 
3511   } else { /* call == MAT_INITIAL_MATRIX) */
3512     PetscBool flg;
3513 
3514     PetscCall(ISGetLocalSize(iscol,&n));
3515     PetscCall(ISGetSize(iscol,&Ncols));
3516 
3517     /* (1) iscol -> nonscalable iscol_local */
3518     /* Check for special case: each processor gets entire matrix columns */
3519     PetscCall(ISIdentity(iscol_local,&flg));
3520     if (flg && n == mat->cmap->N) allcolumns = PETSC_TRUE;
3521     PetscCall(MPIU_Allreduce(MPI_IN_PLACE,&allcolumns,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)mat)));
3522     if (allcolumns) {
3523       iscol_sub = iscol_local;
3524       PetscCall(PetscObjectReference((PetscObject)iscol_local));
3525       PetscCall(ISCreateStride(PETSC_COMM_SELF,n,0,1,&iscmap));
3526 
3527     } else {
3528       /* (2) iscol_local -> iscol_sub and iscmap. Implementation below requires iscol_local be sorted, it can have duplicate indices */
3529       PetscInt *idx,*cmap1,k;
3530       PetscCall(PetscMalloc1(Ncols,&idx));
3531       PetscCall(PetscMalloc1(Ncols,&cmap1));
3532       PetscCall(ISGetIndices(iscol_local,&is_idx));
3533       count = 0;
3534       k     = 0;
3535       for (i=0; i<Ncols; i++) {
3536         j = is_idx[i];
3537         if (j >= cstart && j < cend) {
3538           /* diagonal part of mat */
3539           idx[count]     = j;
3540           cmap1[count++] = i; /* column index in submat */
3541         } else if (Bn) {
3542           /* off-diagonal part of mat */
3543           if (j == garray[k]) {
3544             idx[count]     = j;
3545             cmap1[count++] = i;  /* column index in submat */
3546           } else if (j > garray[k]) {
3547             while (j > garray[k] && k < Bn-1) k++;
3548             if (j == garray[k]) {
3549               idx[count]     = j;
3550               cmap1[count++] = i; /* column index in submat */
3551             }
3552           }
3553         }
3554       }
3555       PetscCall(ISRestoreIndices(iscol_local,&is_idx));
3556 
3557       PetscCall(ISCreateGeneral(PETSC_COMM_SELF,count,idx,PETSC_OWN_POINTER,&iscol_sub));
3558       PetscCall(ISGetBlockSize(iscol,&cbs));
3559       PetscCall(ISSetBlockSize(iscol_sub,cbs));
3560 
3561       PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)iscol_local),count,cmap1,PETSC_OWN_POINTER,&iscmap));
3562     }
3563 
3564     /* (3) Create sequential Msub */
3565     PetscCall(MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol_sub,MAT_INITIAL_MATRIX,allcolumns,&Msub));
3566   }
3567 
3568   PetscCall(ISGetLocalSize(iscol_sub,&count));
3569   aij  = (Mat_SeqAIJ*)(Msub)->data;
3570   ii   = aij->i;
3571   PetscCall(ISGetIndices(iscmap,&cmap));
3572 
3573   /*
3574       m - number of local rows
3575       Ncols - number of columns (same on all processors)
3576       rstart - first row in new global matrix generated
3577   */
3578   PetscCall(MatGetSize(Msub,&m,NULL));
3579 
3580   if (call == MAT_INITIAL_MATRIX) {
3581     /* (4) Create parallel newmat */
3582     PetscMPIInt    rank,size;
3583     PetscInt       csize;
3584 
3585     PetscCallMPI(MPI_Comm_size(comm,&size));
3586     PetscCallMPI(MPI_Comm_rank(comm,&rank));
3587 
3588     /*
3589         Determine the number of non-zeros in the diagonal and off-diagonal
3590         portions of the matrix in order to do correct preallocation
3591     */
3592 
3593     /* first get start and end of "diagonal" columns */
3594     PetscCall(ISGetLocalSize(iscol,&csize));
3595     if (csize == PETSC_DECIDE) {
3596       PetscCall(ISGetSize(isrow,&mglobal));
3597       if (mglobal == Ncols) { /* square matrix */
3598         nlocal = m;
3599       } else {
3600         nlocal = Ncols/size + ((Ncols % size) > rank);
3601       }
3602     } else {
3603       nlocal = csize;
3604     }
3605     PetscCallMPI(MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm));
3606     rstart = rend - nlocal;
3607     PetscCheck(rank != size - 1 || rend == Ncols,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local column sizes %" PetscInt_FMT " do not add up to total number of columns %" PetscInt_FMT,rend,Ncols);
3608 
3609     /* next, compute all the lengths */
3610     jj    = aij->j;
3611     PetscCall(PetscMalloc1(2*m+1,&dlens));
3612     olens = dlens + m;
3613     for (i=0; i<m; i++) {
3614       jend = ii[i+1] - ii[i];
3615       olen = 0;
3616       dlen = 0;
3617       for (j=0; j<jend; j++) {
3618         if (cmap[*jj] < rstart || cmap[*jj] >= rend) olen++;
3619         else dlen++;
3620         jj++;
3621       }
3622       olens[i] = olen;
3623       dlens[i] = dlen;
3624     }
3625 
3626     PetscCall(ISGetBlockSize(isrow,&bs));
3627     PetscCall(ISGetBlockSize(iscol,&cbs));
3628 
3629     PetscCall(MatCreate(comm,&M));
3630     PetscCall(MatSetSizes(M,m,nlocal,PETSC_DECIDE,Ncols));
3631     PetscCall(MatSetBlockSizes(M,bs,cbs));
3632     PetscCall(MatSetType(M,((PetscObject)mat)->type_name));
3633     PetscCall(MatMPIAIJSetPreallocation(M,0,dlens,0,olens));
3634     PetscCall(PetscFree(dlens));
3635 
3636   } else { /* call == MAT_REUSE_MATRIX */
3637     M    = *newmat;
3638     PetscCall(MatGetLocalSize(M,&i,NULL));
3639     PetscCheck(i == m,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3640     PetscCall(MatZeroEntries(M));
3641     /*
3642          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3643        rather than the slower MatSetValues().
3644     */
3645     M->was_assembled = PETSC_TRUE;
3646     M->assembled     = PETSC_FALSE;
3647   }
3648 
3649   /* (5) Set values of Msub to *newmat */
3650   PetscCall(PetscMalloc1(count,&colsub));
3651   PetscCall(MatGetOwnershipRange(M,&rstart,NULL));
3652 
3653   jj   = aij->j;
3654   PetscCall(MatSeqAIJGetArrayRead(Msub,(const PetscScalar**)&aa));
3655   for (i=0; i<m; i++) {
3656     row = rstart + i;
3657     nz  = ii[i+1] - ii[i];
3658     for (j=0; j<nz; j++) colsub[j] = cmap[jj[j]];
3659     PetscCall(MatSetValues_MPIAIJ(M,1,&row,nz,colsub,aa,INSERT_VALUES));
3660     jj += nz; aa += nz;
3661   }
3662   PetscCall(MatSeqAIJRestoreArrayRead(Msub,(const PetscScalar**)&aa));
3663   PetscCall(ISRestoreIndices(iscmap,&cmap));
3664 
3665   PetscCall(MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY));
3666   PetscCall(MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY));
3667 
3668   PetscCall(PetscFree(colsub));
3669 
3670   /* save Msub, iscol_sub and iscmap used in processor for next request */
3671   if (call == MAT_INITIAL_MATRIX) {
3672     *newmat = M;
3673     PetscCall(PetscObjectCompose((PetscObject)(*newmat),"SubMatrix",(PetscObject)Msub));
3674     PetscCall(MatDestroy(&Msub));
3675 
3676     PetscCall(PetscObjectCompose((PetscObject)(*newmat),"SubIScol",(PetscObject)iscol_sub));
3677     PetscCall(ISDestroy(&iscol_sub));
3678 
3679     PetscCall(PetscObjectCompose((PetscObject)(*newmat),"Subcmap",(PetscObject)iscmap));
3680     PetscCall(ISDestroy(&iscmap));
3681 
3682     if (iscol_local) {
3683       PetscCall(PetscObjectCompose((PetscObject)(*newmat),"ISAllGather",(PetscObject)iscol_local));
3684       PetscCall(ISDestroy(&iscol_local));
3685     }
3686   }
3687   PetscFunctionReturn(0);
3688 }
3689 
3690 /*
3691     Not great since it makes two copies of the submatrix, first an SeqAIJ
3692   in local and then by concatenating the local matrices the end result.
3693   Writing it directly would be much like MatCreateSubMatrices_MPIAIJ()
3694 
3695   Note: This requires a sequential iscol with all indices.
3696 */
3697 PetscErrorCode MatCreateSubMatrix_MPIAIJ_nonscalable(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3698 {
3699   PetscMPIInt    rank,size;
3700   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3701   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
3702   Mat            M,Mreuse;
3703   MatScalar      *aa,*vwork;
3704   MPI_Comm       comm;
3705   Mat_SeqAIJ     *aij;
3706   PetscBool      colflag,allcolumns=PETSC_FALSE;
3707 
3708   PetscFunctionBegin;
3709   PetscCall(PetscObjectGetComm((PetscObject)mat,&comm));
3710   PetscCallMPI(MPI_Comm_rank(comm,&rank));
3711   PetscCallMPI(MPI_Comm_size(comm,&size));
3712 
3713   /* Check for special case: each processor gets entire matrix columns */
3714   PetscCall(ISIdentity(iscol,&colflag));
3715   PetscCall(ISGetLocalSize(iscol,&n));
3716   if (colflag && n == mat->cmap->N) allcolumns = PETSC_TRUE;
3717   PetscCall(MPIU_Allreduce(MPI_IN_PLACE,&allcolumns,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)mat)));
3718 
3719   if (call ==  MAT_REUSE_MATRIX) {
3720     PetscCall(PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse));
3721     PetscCheck(Mreuse,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3722     PetscCall(MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,allcolumns,&Mreuse));
3723   } else {
3724     PetscCall(MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,allcolumns,&Mreuse));
3725   }
3726 
3727   /*
3728       m - number of local rows
3729       n - number of columns (same on all processors)
3730       rstart - first row in new global matrix generated
3731   */
3732   PetscCall(MatGetSize(Mreuse,&m,&n));
3733   PetscCall(MatGetBlockSizes(Mreuse,&bs,&cbs));
3734   if (call == MAT_INITIAL_MATRIX) {
3735     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3736     ii  = aij->i;
3737     jj  = aij->j;
3738 
3739     /*
3740         Determine the number of non-zeros in the diagonal and off-diagonal
3741         portions of the matrix in order to do correct preallocation
3742     */
3743 
3744     /* first get start and end of "diagonal" columns */
3745     if (csize == PETSC_DECIDE) {
3746       PetscCall(ISGetSize(isrow,&mglobal));
3747       if (mglobal == n) { /* square matrix */
3748         nlocal = m;
3749       } else {
3750         nlocal = n/size + ((n % size) > rank);
3751       }
3752     } else {
3753       nlocal = csize;
3754     }
3755     PetscCallMPI(MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm));
3756     rstart = rend - nlocal;
3757     PetscCheck(rank != size - 1 || rend == n,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local column sizes %" PetscInt_FMT " do not add up to total number of columns %" PetscInt_FMT,rend,n);
3758 
3759     /* next, compute all the lengths */
3760     PetscCall(PetscMalloc1(2*m+1,&dlens));
3761     olens = dlens + m;
3762     for (i=0; i<m; i++) {
3763       jend = ii[i+1] - ii[i];
3764       olen = 0;
3765       dlen = 0;
3766       for (j=0; j<jend; j++) {
3767         if (*jj < rstart || *jj >= rend) olen++;
3768         else dlen++;
3769         jj++;
3770       }
3771       olens[i] = olen;
3772       dlens[i] = dlen;
3773     }
3774     PetscCall(MatCreate(comm,&M));
3775     PetscCall(MatSetSizes(M,m,nlocal,PETSC_DECIDE,n));
3776     PetscCall(MatSetBlockSizes(M,bs,cbs));
3777     PetscCall(MatSetType(M,((PetscObject)mat)->type_name));
3778     PetscCall(MatMPIAIJSetPreallocation(M,0,dlens,0,olens));
3779     PetscCall(PetscFree(dlens));
3780   } else {
3781     PetscInt ml,nl;
3782 
3783     M    = *newmat;
3784     PetscCall(MatGetLocalSize(M,&ml,&nl));
3785     PetscCheck(ml == m,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3786     PetscCall(MatZeroEntries(M));
3787     /*
3788          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3789        rather than the slower MatSetValues().
3790     */
3791     M->was_assembled = PETSC_TRUE;
3792     M->assembled     = PETSC_FALSE;
3793   }
3794   PetscCall(MatGetOwnershipRange(M,&rstart,&rend));
3795   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3796   ii   = aij->i;
3797   jj   = aij->j;
3798 
3799   /* trigger copy to CPU if needed */
3800   PetscCall(MatSeqAIJGetArrayRead(Mreuse,(const PetscScalar**)&aa));
3801   for (i=0; i<m; i++) {
3802     row   = rstart + i;
3803     nz    = ii[i+1] - ii[i];
3804     cwork = jj; jj += nz;
3805     vwork = aa; aa += nz;
3806     PetscCall(MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES));
3807   }
3808   PetscCall(MatSeqAIJRestoreArrayRead(Mreuse,(const PetscScalar**)&aa));
3809 
3810   PetscCall(MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY));
3811   PetscCall(MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY));
3812   *newmat = M;
3813 
3814   /* save submatrix used in processor for next request */
3815   if (call ==  MAT_INITIAL_MATRIX) {
3816     PetscCall(PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse));
3817     PetscCall(MatDestroy(&Mreuse));
3818   }
3819   PetscFunctionReturn(0);
3820 }
3821 
3822 PetscErrorCode MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3823 {
3824   PetscInt       m,cstart, cend,j,nnz,i,d;
3825   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3826   const PetscInt *JJ;
3827   PetscBool      nooffprocentries;
3828 
3829   PetscFunctionBegin;
3830   PetscCheck(Ii[0] == 0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %" PetscInt_FMT,Ii[0]);
3831 
3832   PetscCall(PetscLayoutSetUp(B->rmap));
3833   PetscCall(PetscLayoutSetUp(B->cmap));
3834   m      = B->rmap->n;
3835   cstart = B->cmap->rstart;
3836   cend   = B->cmap->rend;
3837   rstart = B->rmap->rstart;
3838 
3839   PetscCall(PetscCalloc2(m,&d_nnz,m,&o_nnz));
3840 
3841   if (PetscDefined(USE_DEBUG)) {
3842     for (i=0; i<m; i++) {
3843       nnz = Ii[i+1]- Ii[i];
3844       JJ  = J + Ii[i];
3845       PetscCheck(nnz >= 0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %" PetscInt_FMT " has a negative %" PetscInt_FMT " number of columns",i,nnz);
3846       PetscCheck(!nnz || !(JJ[0] < 0),PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Row %" PetscInt_FMT " starts with negative column index %" PetscInt_FMT,i,JJ[0]);
3847       PetscCheck(!nnz || !(JJ[nnz-1] >= B->cmap->N),PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Row %" PetscInt_FMT " ends with too large a column index %" PetscInt_FMT " (max allowed %" PetscInt_FMT ")",i,JJ[nnz-1],B->cmap->N);
3848     }
3849   }
3850 
3851   for (i=0; i<m; i++) {
3852     nnz     = Ii[i+1]- Ii[i];
3853     JJ      = J + Ii[i];
3854     nnz_max = PetscMax(nnz_max,nnz);
3855     d       = 0;
3856     for (j=0; j<nnz; j++) {
3857       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3858     }
3859     d_nnz[i] = d;
3860     o_nnz[i] = nnz - d;
3861   }
3862   PetscCall(MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz));
3863   PetscCall(PetscFree2(d_nnz,o_nnz));
3864 
3865   for (i=0; i<m; i++) {
3866     ii   = i + rstart;
3867     PetscCall(MatSetValues_MPIAIJ(B,1,&ii,Ii[i+1] - Ii[i],J+Ii[i], v ? v + Ii[i] : NULL,INSERT_VALUES));
3868   }
3869   nooffprocentries    = B->nooffprocentries;
3870   B->nooffprocentries = PETSC_TRUE;
3871   PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
3872   PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
3873   B->nooffprocentries = nooffprocentries;
3874 
3875   PetscCall(MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE));
3876   PetscFunctionReturn(0);
3877 }
3878 
3879 /*@
3880    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3881    (the default parallel PETSc format).
3882 
3883    Collective
3884 
3885    Input Parameters:
3886 +  B - the matrix
3887 .  i - the indices into j for the start of each local row (starts with zero)
3888 .  j - the column indices for each local row (starts with zero)
3889 -  v - optional values in the matrix
3890 
3891    Level: developer
3892 
3893    Notes:
3894        The i, j, and v arrays ARE copied by this routine into the internal format used by PETSc;
3895      thus you CANNOT change the matrix entries by changing the values of v[] after you have
3896      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3897 
3898        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3899 
3900        The format which is used for the sparse matrix input, is equivalent to a
3901     row-major ordering.. i.e for the following matrix, the input data expected is
3902     as shown
3903 
3904 $        1 0 0
3905 $        2 0 3     P0
3906 $       -------
3907 $        4 5 6     P1
3908 $
3909 $     Process0 [P0]: rows_owned=[0,1]
3910 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3911 $        j =  {0,0,2}  [size = 3]
3912 $        v =  {1,2,3}  [size = 3]
3913 $
3914 $     Process1 [P1]: rows_owned=[2]
3915 $        i =  {0,3}    [size = nrow+1  = 1+1]
3916 $        j =  {0,1,2}  [size = 3]
3917 $        v =  {4,5,6}  [size = 3]
3918 
3919 .seealso: `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatCreateAIJ()`, `MATMPIAIJ`,
3920           `MatCreateSeqAIJWithArrays()`, `MatCreateMPIAIJWithSplitArrays()`
3921 @*/
3922 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3923 {
3924   PetscFunctionBegin;
3925   PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));
3926   PetscFunctionReturn(0);
3927 }
3928 
3929 /*@C
3930    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3931    (the default parallel PETSc format).  For good matrix assembly performance
3932    the user should preallocate the matrix storage by setting the parameters
3933    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3934    performance can be increased by more than a factor of 50.
3935 
3936    Collective
3937 
3938    Input Parameters:
3939 +  B - the matrix
3940 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3941            (same value is used for all local rows)
3942 .  d_nnz - array containing the number of nonzeros in the various rows of the
3943            DIAGONAL portion of the local submatrix (possibly different for each row)
3944            or NULL (PETSC_NULL_INTEGER in Fortran), if d_nz is used to specify the nonzero structure.
3945            The size of this array is equal to the number of local rows, i.e 'm'.
3946            For matrices that will be factored, you must leave room for (and set)
3947            the diagonal entry even if it is zero.
3948 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3949            submatrix (same value is used for all local rows).
3950 -  o_nnz - array containing the number of nonzeros in the various rows of the
3951            OFF-DIAGONAL portion of the local submatrix (possibly different for
3952            each row) or NULL (PETSC_NULL_INTEGER in Fortran), if o_nz is used to specify the nonzero
3953            structure. The size of this array is equal to the number
3954            of local rows, i.e 'm'.
3955 
3956    If the *_nnz parameter is given then the *_nz parameter is ignored
3957 
3958    The AIJ format (also called the Yale sparse matrix format or
3959    compressed row storage (CSR)), is fully compatible with standard Fortran 77
3960    storage.  The stored row and column indices begin with zero.
3961    See Users-Manual: ch_mat for details.
3962 
3963    The parallel matrix is partitioned such that the first m0 rows belong to
3964    process 0, the next m1 rows belong to process 1, the next m2 rows belong
3965    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
3966 
3967    The DIAGONAL portion of the local submatrix of a processor can be defined
3968    as the submatrix which is obtained by extraction the part corresponding to
3969    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
3970    first row that belongs to the processor, r2 is the last row belonging to
3971    the this processor, and c1-c2 is range of indices of the local part of a
3972    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
3973    common case of a square matrix, the row and column ranges are the same and
3974    the DIAGONAL part is also square. The remaining portion of the local
3975    submatrix (mxN) constitute the OFF-DIAGONAL portion.
3976 
3977    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3978 
3979    You can call MatGetInfo() to get information on how effective the preallocation was;
3980    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3981    You can also run with the option -info and look for messages with the string
3982    malloc in them to see if additional memory allocation was needed.
3983 
3984    Example usage:
3985 
3986    Consider the following 8x8 matrix with 34 non-zero values, that is
3987    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3988    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3989    as follows:
3990 
3991 .vb
3992             1  2  0  |  0  3  0  |  0  4
3993     Proc0   0  5  6  |  7  0  0  |  8  0
3994             9  0 10  | 11  0  0  | 12  0
3995     -------------------------------------
3996            13  0 14  | 15 16 17  |  0  0
3997     Proc1   0 18  0  | 19 20 21  |  0  0
3998             0  0  0  | 22 23  0  | 24  0
3999     -------------------------------------
4000     Proc2  25 26 27  |  0  0 28  | 29  0
4001            30  0  0  | 31 32 33  |  0 34
4002 .ve
4003 
4004    This can be represented as a collection of submatrices as:
4005 
4006 .vb
4007       A B C
4008       D E F
4009       G H I
4010 .ve
4011 
4012    Where the submatrices A,B,C are owned by proc0, D,E,F are
4013    owned by proc1, G,H,I are owned by proc2.
4014 
4015    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4016    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4017    The 'M','N' parameters are 8,8, and have the same values on all procs.
4018 
4019    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
4020    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
4021    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
4022    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
4023    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
4024    matrix, ans [DF] as another SeqAIJ matrix.
4025 
4026    When d_nz, o_nz parameters are specified, d_nz storage elements are
4027    allocated for every row of the local diagonal submatrix, and o_nz
4028    storage locations are allocated for every row of the OFF-DIAGONAL submat.
4029    One way to choose d_nz and o_nz is to use the max nonzerors per local
4030    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
4031    In this case, the values of d_nz,o_nz are:
4032 .vb
4033      proc0 : dnz = 2, o_nz = 2
4034      proc1 : dnz = 3, o_nz = 2
4035      proc2 : dnz = 1, o_nz = 4
4036 .ve
4037    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
4038    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
4039    for proc3. i.e we are using 12+15+10=37 storage locations to store
4040    34 values.
4041 
4042    When d_nnz, o_nnz parameters are specified, the storage is specified
4043    for every row, corresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
4044    In the above case the values for d_nnz,o_nnz are:
4045 .vb
4046      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
4047      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
4048      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
4049 .ve
4050    Here the space allocated is sum of all the above values i.e 34, and
4051    hence pre-allocation is perfect.
4052 
4053    Level: intermediate
4054 
4055 .seealso: `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatCreateAIJ()`, `MatMPIAIJSetPreallocationCSR()`,
4056           `MATMPIAIJ`, `MatGetInfo()`, `PetscSplitOwnership()`
4057 @*/
4058 PetscErrorCode MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
4059 {
4060   PetscFunctionBegin;
4061   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
4062   PetscValidType(B,1);
4063   PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));
4064   PetscFunctionReturn(0);
4065 }
4066 
4067 /*@
4068      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
4069          CSR format for the local rows.
4070 
4071    Collective
4072 
4073    Input Parameters:
4074 +  comm - MPI communicator
4075 .  m - number of local rows (Cannot be PETSC_DECIDE)
4076 .  n - This value should be the same as the local size used in creating the
4077        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
4078        calculated if N is given) For square matrices n is almost always m.
4079 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
4080 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
4081 .   i - row indices; that is i[0] = 0, i[row] = i[row-1] + number of elements in that row of the matrix
4082 .   j - column indices
4083 -   a - matrix values
4084 
4085    Output Parameter:
4086 .   mat - the matrix
4087 
4088    Level: intermediate
4089 
4090    Notes:
4091        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
4092      thus you CANNOT change the matrix entries by changing the values of a[] after you have
4093      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
4094 
4095        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
4096 
4097        The format which is used for the sparse matrix input, is equivalent to a
4098     row-major ordering.. i.e for the following matrix, the input data expected is
4099     as shown
4100 
4101        Once you have created the matrix you can update it with new numerical values using MatUpdateMPIAIJWithArrays
4102 
4103 $        1 0 0
4104 $        2 0 3     P0
4105 $       -------
4106 $        4 5 6     P1
4107 $
4108 $     Process0 [P0]: rows_owned=[0,1]
4109 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
4110 $        j =  {0,0,2}  [size = 3]
4111 $        v =  {1,2,3}  [size = 3]
4112 $
4113 $     Process1 [P1]: rows_owned=[2]
4114 $        i =  {0,3}    [size = nrow+1  = 1+1]
4115 $        j =  {0,1,2}  [size = 3]
4116 $        v =  {4,5,6}  [size = 3]
4117 
4118 .seealso: `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
4119           `MATMPIAIJ`, `MatCreateAIJ()`, `MatCreateMPIAIJWithSplitArrays()`, `MatUpdateMPIAIJWithArrays()`
4120 @*/
4121 PetscErrorCode MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
4122 {
4123   PetscFunctionBegin;
4124   PetscCheck(!i || !i[0],PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
4125   PetscCheck(m >= 0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
4126   PetscCall(MatCreate(comm,mat));
4127   PetscCall(MatSetSizes(*mat,m,n,M,N));
4128   /* PetscCall(MatSetBlockSizes(M,bs,cbs)); */
4129   PetscCall(MatSetType(*mat,MATMPIAIJ));
4130   PetscCall(MatMPIAIJSetPreallocationCSR(*mat,i,j,a));
4131   PetscFunctionReturn(0);
4132 }
4133 
4134 /*@
4135      MatUpdateMPIAIJWithArrays - updates a MPI AIJ matrix using arrays that contain in standard
4136          CSR format for the local rows. Only the numerical values are updated the other arrays must be identical
4137 
4138    Collective
4139 
4140    Input Parameters:
4141 +  mat - the matrix
4142 .  m - number of local rows (Cannot be PETSC_DECIDE)
4143 .  n - This value should be the same as the local size used in creating the
4144        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
4145        calculated if N is given) For square matrices n is almost always m.
4146 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
4147 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
4148 .  Ii - row indices; that is Ii[0] = 0, Ii[row] = Ii[row-1] + number of elements in that row of the matrix
4149 .  J - column indices
4150 -  v - matrix values
4151 
4152    Level: intermediate
4153 
4154 .seealso: `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
4155           `MATMPIAIJ`, `MatCreateAIJ()`, `MatCreateMPIAIJWithSplitArrays()`, `MatUpdateMPIAIJWithArrays()`
4156 @*/
4157 PetscErrorCode MatUpdateMPIAIJWithArrays(Mat mat,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
4158 {
4159   PetscInt       cstart,nnz,i,j;
4160   PetscInt       *ld;
4161   PetscBool      nooffprocentries;
4162   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ*)mat->data;
4163   Mat_SeqAIJ     *Ad  = (Mat_SeqAIJ*)Aij->A->data;
4164   PetscScalar    *ad,*ao;
4165   const PetscInt *Adi = Ad->i;
4166   PetscInt       ldi,Iii,md;
4167 
4168   PetscFunctionBegin;
4169   PetscCheck(Ii[0] == 0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
4170   PetscCheck(m >= 0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
4171   PetscCheck(m == mat->rmap->n,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Local number of rows cannot change from call to MatUpdateMPIAIJWithArrays()");
4172   PetscCheck(n == mat->cmap->n,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Local number of columns cannot change from call to MatUpdateMPIAIJWithArrays()");
4173 
4174   PetscCall(MatSeqAIJGetArrayWrite(Aij->A,&ad));
4175   PetscCall(MatSeqAIJGetArrayWrite(Aij->B,&ao));
4176   cstart = mat->cmap->rstart;
4177   if (!Aij->ld) {
4178     /* count number of entries below block diagonal */
4179     PetscCall(PetscCalloc1(m,&ld));
4180     Aij->ld = ld;
4181     for (i=0; i<m; i++) {
4182       nnz  = Ii[i+1]- Ii[i];
4183       j     = 0;
4184       while  (J[j] < cstart && j < nnz) {j++;}
4185       J    += nnz;
4186       ld[i] = j;
4187     }
4188   } else {
4189     ld = Aij->ld;
4190   }
4191 
4192   for (i=0; i<m; i++) {
4193     nnz  = Ii[i+1]- Ii[i];
4194     Iii  = Ii[i];
4195     ldi  = ld[i];
4196     md   = Adi[i+1]-Adi[i];
4197     PetscCall(PetscArraycpy(ao,v + Iii,ldi));
4198     PetscCall(PetscArraycpy(ad,v + Iii + ldi,md));
4199     PetscCall(PetscArraycpy(ao + ldi,v + Iii + ldi + md,nnz - ldi - md));
4200     ad  += md;
4201     ao  += nnz - md;
4202   }
4203   nooffprocentries      = mat->nooffprocentries;
4204   mat->nooffprocentries = PETSC_TRUE;
4205   PetscCall(MatSeqAIJRestoreArrayWrite(Aij->A,&ad));
4206   PetscCall(MatSeqAIJRestoreArrayWrite(Aij->B,&ao));
4207   PetscCall(PetscObjectStateIncrease((PetscObject)Aij->A));
4208   PetscCall(PetscObjectStateIncrease((PetscObject)Aij->B));
4209   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
4210   PetscCall(MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY));
4211   PetscCall(MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY));
4212   mat->nooffprocentries = nooffprocentries;
4213   PetscFunctionReturn(0);
4214 }
4215 
4216 /*@C
4217    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
4218    (the default parallel PETSc format).  For good matrix assembly performance
4219    the user should preallocate the matrix storage by setting the parameters
4220    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
4221    performance can be increased by more than a factor of 50.
4222 
4223    Collective
4224 
4225    Input Parameters:
4226 +  comm - MPI communicator
4227 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
4228            This value should be the same as the local size used in creating the
4229            y vector for the matrix-vector product y = Ax.
4230 .  n - This value should be the same as the local size used in creating the
4231        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
4232        calculated if N is given) For square matrices n is almost always m.
4233 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
4234 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
4235 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
4236            (same value is used for all local rows)
4237 .  d_nnz - array containing the number of nonzeros in the various rows of the
4238            DIAGONAL portion of the local submatrix (possibly different for each row)
4239            or NULL, if d_nz is used to specify the nonzero structure.
4240            The size of this array is equal to the number of local rows, i.e 'm'.
4241 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
4242            submatrix (same value is used for all local rows).
4243 -  o_nnz - array containing the number of nonzeros in the various rows of the
4244            OFF-DIAGONAL portion of the local submatrix (possibly different for
4245            each row) or NULL, if o_nz is used to specify the nonzero
4246            structure. The size of this array is equal to the number
4247            of local rows, i.e 'm'.
4248 
4249    Output Parameter:
4250 .  A - the matrix
4251 
4252    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
4253    MatXXXXSetPreallocation() paradigm instead of this routine directly.
4254    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
4255 
4256    Notes:
4257    If the *_nnz parameter is given then the *_nz parameter is ignored
4258 
4259    m,n,M,N parameters specify the size of the matrix, and its partitioning across
4260    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
4261    storage requirements for this matrix.
4262 
4263    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
4264    processor than it must be used on all processors that share the object for
4265    that argument.
4266 
4267    The user MUST specify either the local or global matrix dimensions
4268    (possibly both).
4269 
4270    The parallel matrix is partitioned across processors such that the
4271    first m0 rows belong to process 0, the next m1 rows belong to
4272    process 1, the next m2 rows belong to process 2 etc.. where
4273    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
4274    values corresponding to [m x N] submatrix.
4275 
4276    The columns are logically partitioned with the n0 columns belonging
4277    to 0th partition, the next n1 columns belonging to the next
4278    partition etc.. where n0,n1,n2... are the input parameter 'n'.
4279 
4280    The DIAGONAL portion of the local submatrix on any given processor
4281    is the submatrix corresponding to the rows and columns m,n
4282    corresponding to the given processor. i.e diagonal matrix on
4283    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
4284    etc. The remaining portion of the local submatrix [m x (N-n)]
4285    constitute the OFF-DIAGONAL portion. The example below better
4286    illustrates this concept.
4287 
4288    For a square global matrix we define each processor's diagonal portion
4289    to be its local rows and the corresponding columns (a square submatrix);
4290    each processor's off-diagonal portion encompasses the remainder of the
4291    local matrix (a rectangular submatrix).
4292 
4293    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
4294 
4295    When calling this routine with a single process communicator, a matrix of
4296    type SEQAIJ is returned.  If a matrix of type MPIAIJ is desired for this
4297    type of communicator, use the construction mechanism
4298 .vb
4299      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
4300 .ve
4301 
4302 $     MatCreate(...,&A);
4303 $     MatSetType(A,MATMPIAIJ);
4304 $     MatSetSizes(A, m,n,M,N);
4305 $     MatMPIAIJSetPreallocation(A,...);
4306 
4307    By default, this format uses inodes (identical nodes) when possible.
4308    We search for consecutive rows with the same nonzero structure, thereby
4309    reusing matrix information to achieve increased efficiency.
4310 
4311    Options Database Keys:
4312 +  -mat_no_inode  - Do not use inodes
4313 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
4314 -  -matmult_vecscatter_view <viewer> - View the vecscatter (i.e., communication pattern) used in MatMult() of sparse parallel matrices.
4315         See viewer types in manual of MatView(). Of them, ascii_matlab, draw or binary cause the vecscatter be viewed as a matrix.
4316         Entry (i,j) is the size of message (in bytes) rank i sends to rank j in one MatMult() call.
4317 
4318    Example usage:
4319 
4320    Consider the following 8x8 matrix with 34 non-zero values, that is
4321    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
4322    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
4323    as follows
4324 
4325 .vb
4326             1  2  0  |  0  3  0  |  0  4
4327     Proc0   0  5  6  |  7  0  0  |  8  0
4328             9  0 10  | 11  0  0  | 12  0
4329     -------------------------------------
4330            13  0 14  | 15 16 17  |  0  0
4331     Proc1   0 18  0  | 19 20 21  |  0  0
4332             0  0  0  | 22 23  0  | 24  0
4333     -------------------------------------
4334     Proc2  25 26 27  |  0  0 28  | 29  0
4335            30  0  0  | 31 32 33  |  0 34
4336 .ve
4337 
4338    This can be represented as a collection of submatrices as
4339 
4340 .vb
4341       A B C
4342       D E F
4343       G H I
4344 .ve
4345 
4346    Where the submatrices A,B,C are owned by proc0, D,E,F are
4347    owned by proc1, G,H,I are owned by proc2.
4348 
4349    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4350    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4351    The 'M','N' parameters are 8,8, and have the same values on all procs.
4352 
4353    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
4354    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
4355    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
4356    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
4357    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
4358    matrix, ans [DF] as another SeqAIJ matrix.
4359 
4360    When d_nz, o_nz parameters are specified, d_nz storage elements are
4361    allocated for every row of the local diagonal submatrix, and o_nz
4362    storage locations are allocated for every row of the OFF-DIAGONAL submat.
4363    One way to choose d_nz and o_nz is to use the max nonzerors per local
4364    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
4365    In this case, the values of d_nz,o_nz are
4366 .vb
4367      proc0 : dnz = 2, o_nz = 2
4368      proc1 : dnz = 3, o_nz = 2
4369      proc2 : dnz = 1, o_nz = 4
4370 .ve
4371    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
4372    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
4373    for proc3. i.e we are using 12+15+10=37 storage locations to store
4374    34 values.
4375 
4376    When d_nnz, o_nnz parameters are specified, the storage is specified
4377    for every row, corresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
4378    In the above case the values for d_nnz,o_nnz are
4379 .vb
4380      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
4381      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
4382      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
4383 .ve
4384    Here the space allocated is sum of all the above values i.e 34, and
4385    hence pre-allocation is perfect.
4386 
4387    Level: intermediate
4388 
4389 .seealso: `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
4390           `MATMPIAIJ`, `MatCreateMPIAIJWithArrays()`
4391 @*/
4392 PetscErrorCode  MatCreateAIJ(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[],Mat *A)
4393 {
4394   PetscMPIInt    size;
4395 
4396   PetscFunctionBegin;
4397   PetscCall(MatCreate(comm,A));
4398   PetscCall(MatSetSizes(*A,m,n,M,N));
4399   PetscCallMPI(MPI_Comm_size(comm,&size));
4400   if (size > 1) {
4401     PetscCall(MatSetType(*A,MATMPIAIJ));
4402     PetscCall(MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz));
4403   } else {
4404     PetscCall(MatSetType(*A,MATSEQAIJ));
4405     PetscCall(MatSeqAIJSetPreallocation(*A,d_nz,d_nnz));
4406   }
4407   PetscFunctionReturn(0);
4408 }
4409 
4410 /*@C
4411   MatMPIAIJGetSeqAIJ - Returns the local piece of this distributed matrix
4412 
4413   Not collective
4414 
4415   Input Parameter:
4416 . A - The MPIAIJ matrix
4417 
4418   Output Parameters:
4419 + Ad - The local diagonal block as a SeqAIJ matrix
4420 . Ao - The local off-diagonal block as a SeqAIJ matrix
4421 - colmap - An array mapping local column numbers of Ao to global column numbers of the parallel matrix
4422 
4423   Note: The rows in Ad and Ao are in [0, Nr), where Nr is the number of local rows on this process. The columns
4424   in Ad are in [0, Nc) where Nc is the number of local columns. The columns are Ao are in [0, Nco), where Nco is
4425   the number of nonzero columns in the local off-diagonal piece of the matrix A. The array colmap maps these
4426   local column numbers to global column numbers in the original matrix.
4427 
4428   Level: intermediate
4429 
4430 .seealso: `MatMPIAIJGetLocalMat()`, `MatMPIAIJGetLocalMatCondensed()`, `MatCreateAIJ()`, `MATMPIAIJ`, `MATSEQAIJ`
4431 @*/
4432 PetscErrorCode MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
4433 {
4434   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
4435   PetscBool      flg;
4436 
4437   PetscFunctionBegin;
4438   PetscCall(PetscStrbeginswith(((PetscObject)A)->type_name,MATMPIAIJ,&flg));
4439   PetscCheck(flg,PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"This function requires a MATMPIAIJ matrix as input");
4440   if (Ad)     *Ad     = a->A;
4441   if (Ao)     *Ao     = a->B;
4442   if (colmap) *colmap = a->garray;
4443   PetscFunctionReturn(0);
4444 }
4445 
4446 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
4447 {
4448   PetscInt       m,N,i,rstart,nnz,Ii;
4449   PetscInt       *indx;
4450   PetscScalar    *values;
4451   MatType        rootType;
4452 
4453   PetscFunctionBegin;
4454   PetscCall(MatGetSize(inmat,&m,&N));
4455   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
4456     PetscInt       *dnz,*onz,sum,bs,cbs;
4457 
4458     if (n == PETSC_DECIDE) {
4459       PetscCall(PetscSplitOwnership(comm,&n,&N));
4460     }
4461     /* Check sum(n) = N */
4462     PetscCall(MPIU_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm));
4463     PetscCheck(sum == N,PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns %" PetscInt_FMT " != global columns %" PetscInt_FMT,sum,N);
4464 
4465     PetscCallMPI(MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm));
4466     rstart -= m;
4467 
4468     MatPreallocateBegin(comm,m,n,dnz,onz);
4469     for (i=0; i<m; i++) {
4470       PetscCall(MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL));
4471       PetscCall(MatPreallocateSet(i+rstart,nnz,indx,dnz,onz));
4472       PetscCall(MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL));
4473     }
4474 
4475     PetscCall(MatCreate(comm,outmat));
4476     PetscCall(MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE));
4477     PetscCall(MatGetBlockSizes(inmat,&bs,&cbs));
4478     PetscCall(MatSetBlockSizes(*outmat,bs,cbs));
4479     PetscCall(MatGetRootType_Private(inmat,&rootType));
4480     PetscCall(MatSetType(*outmat,rootType));
4481     PetscCall(MatSeqAIJSetPreallocation(*outmat,0,dnz));
4482     PetscCall(MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz));
4483     MatPreallocateEnd(dnz,onz);
4484     PetscCall(MatSetOption(*outmat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE));
4485   }
4486 
4487   /* numeric phase */
4488   PetscCall(MatGetOwnershipRange(*outmat,&rstart,NULL));
4489   for (i=0; i<m; i++) {
4490     PetscCall(MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values));
4491     Ii   = i + rstart;
4492     PetscCall(MatSetValues(*outmat,1,&Ii,nnz,indx,values,INSERT_VALUES));
4493     PetscCall(MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values));
4494   }
4495   PetscCall(MatAssemblyBegin(*outmat,MAT_FINAL_ASSEMBLY));
4496   PetscCall(MatAssemblyEnd(*outmat,MAT_FINAL_ASSEMBLY));
4497   PetscFunctionReturn(0);
4498 }
4499 
4500 PetscErrorCode MatFileSplit(Mat A,char *outfile)
4501 {
4502   PetscMPIInt       rank;
4503   PetscInt          m,N,i,rstart,nnz;
4504   size_t            len;
4505   const PetscInt    *indx;
4506   PetscViewer       out;
4507   char              *name;
4508   Mat               B;
4509   const PetscScalar *values;
4510 
4511   PetscFunctionBegin;
4512   PetscCall(MatGetLocalSize(A,&m,NULL));
4513   PetscCall(MatGetSize(A,NULL,&N));
4514   /* Should this be the type of the diagonal block of A? */
4515   PetscCall(MatCreate(PETSC_COMM_SELF,&B));
4516   PetscCall(MatSetSizes(B,m,N,m,N));
4517   PetscCall(MatSetBlockSizesFromMats(B,A,A));
4518   PetscCall(MatSetType(B,MATSEQAIJ));
4519   PetscCall(MatSeqAIJSetPreallocation(B,0,NULL));
4520   PetscCall(MatGetOwnershipRange(A,&rstart,NULL));
4521   for (i=0; i<m; i++) {
4522     PetscCall(MatGetRow(A,i+rstart,&nnz,&indx,&values));
4523     PetscCall(MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES));
4524     PetscCall(MatRestoreRow(A,i+rstart,&nnz,&indx,&values));
4525   }
4526   PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
4527   PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
4528 
4529   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank));
4530   PetscCall(PetscStrlen(outfile,&len));
4531   PetscCall(PetscMalloc1(len+6,&name));
4532   PetscCall(PetscSNPrintf(name,len+6,"%s.%d",outfile,rank));
4533   PetscCall(PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out));
4534   PetscCall(PetscFree(name));
4535   PetscCall(MatView(B,out));
4536   PetscCall(PetscViewerDestroy(&out));
4537   PetscCall(MatDestroy(&B));
4538   PetscFunctionReturn(0);
4539 }
4540 
4541 static PetscErrorCode MatDestroy_MPIAIJ_SeqsToMPI(void *data)
4542 {
4543   Mat_Merge_SeqsToMPI *merge = (Mat_Merge_SeqsToMPI *)data;
4544 
4545   PetscFunctionBegin;
4546   if (!merge) PetscFunctionReturn(0);
4547   PetscCall(PetscFree(merge->id_r));
4548   PetscCall(PetscFree(merge->len_s));
4549   PetscCall(PetscFree(merge->len_r));
4550   PetscCall(PetscFree(merge->bi));
4551   PetscCall(PetscFree(merge->bj));
4552   PetscCall(PetscFree(merge->buf_ri[0]));
4553   PetscCall(PetscFree(merge->buf_ri));
4554   PetscCall(PetscFree(merge->buf_rj[0]));
4555   PetscCall(PetscFree(merge->buf_rj));
4556   PetscCall(PetscFree(merge->coi));
4557   PetscCall(PetscFree(merge->coj));
4558   PetscCall(PetscFree(merge->owners_co));
4559   PetscCall(PetscLayoutDestroy(&merge->rowmap));
4560   PetscCall(PetscFree(merge));
4561   PetscFunctionReturn(0);
4562 }
4563 
4564 #include <../src/mat/utils/freespace.h>
4565 #include <petscbt.h>
4566 
4567 PetscErrorCode MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
4568 {
4569   MPI_Comm            comm;
4570   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
4571   PetscMPIInt         size,rank,taga,*len_s;
4572   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
4573   PetscInt            proc,m;
4574   PetscInt            **buf_ri,**buf_rj;
4575   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
4576   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
4577   MPI_Request         *s_waits,*r_waits;
4578   MPI_Status          *status;
4579   const MatScalar     *aa,*a_a;
4580   MatScalar           **abuf_r,*ba_i;
4581   Mat_Merge_SeqsToMPI *merge;
4582   PetscContainer      container;
4583 
4584   PetscFunctionBegin;
4585   PetscCall(PetscObjectGetComm((PetscObject)mpimat,&comm));
4586   PetscCall(PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0));
4587 
4588   PetscCallMPI(MPI_Comm_size(comm,&size));
4589   PetscCallMPI(MPI_Comm_rank(comm,&rank));
4590 
4591   PetscCall(PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container));
4592   PetscCheck(container,PetscObjectComm((PetscObject)mpimat),PETSC_ERR_PLIB,"Mat not created from MatCreateMPIAIJSumSeqAIJSymbolic");
4593   PetscCall(PetscContainerGetPointer(container,(void**)&merge));
4594   PetscCall(MatSeqAIJGetArrayRead(seqmat,&a_a));
4595   aa   = a_a;
4596 
4597   bi     = merge->bi;
4598   bj     = merge->bj;
4599   buf_ri = merge->buf_ri;
4600   buf_rj = merge->buf_rj;
4601 
4602   PetscCall(PetscMalloc1(size,&status));
4603   owners = merge->rowmap->range;
4604   len_s  = merge->len_s;
4605 
4606   /* send and recv matrix values */
4607   /*-----------------------------*/
4608   PetscCall(PetscObjectGetNewTag((PetscObject)mpimat,&taga));
4609   PetscCall(PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits));
4610 
4611   PetscCall(PetscMalloc1(merge->nsend+1,&s_waits));
4612   for (proc=0,k=0; proc<size; proc++) {
4613     if (!len_s[proc]) continue;
4614     i    = owners[proc];
4615     PetscCallMPI(MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k));
4616     k++;
4617   }
4618 
4619   if (merge->nrecv) PetscCallMPI(MPI_Waitall(merge->nrecv,r_waits,status));
4620   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend,s_waits,status));
4621   PetscCall(PetscFree(status));
4622 
4623   PetscCall(PetscFree(s_waits));
4624   PetscCall(PetscFree(r_waits));
4625 
4626   /* insert mat values of mpimat */
4627   /*----------------------------*/
4628   PetscCall(PetscMalloc1(N,&ba_i));
4629   PetscCall(PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai));
4630 
4631   for (k=0; k<merge->nrecv; k++) {
4632     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4633     nrows       = *(buf_ri_k[k]);
4634     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
4635     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
4636   }
4637 
4638   /* set values of ba */
4639   m    = merge->rowmap->n;
4640   for (i=0; i<m; i++) {
4641     arow = owners[rank] + i;
4642     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
4643     bnzi = bi[i+1] - bi[i];
4644     PetscCall(PetscArrayzero(ba_i,bnzi));
4645 
4646     /* add local non-zero vals of this proc's seqmat into ba */
4647     anzi   = ai[arow+1] - ai[arow];
4648     aj     = a->j + ai[arow];
4649     aa     = a_a + ai[arow];
4650     nextaj = 0;
4651     for (j=0; nextaj<anzi; j++) {
4652       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4653         ba_i[j] += aa[nextaj++];
4654       }
4655     }
4656 
4657     /* add received vals into ba */
4658     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4659       /* i-th row */
4660       if (i == *nextrow[k]) {
4661         anzi   = *(nextai[k]+1) - *nextai[k];
4662         aj     = buf_rj[k] + *(nextai[k]);
4663         aa     = abuf_r[k] + *(nextai[k]);
4664         nextaj = 0;
4665         for (j=0; nextaj<anzi; j++) {
4666           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4667             ba_i[j] += aa[nextaj++];
4668           }
4669         }
4670         nextrow[k]++; nextai[k]++;
4671       }
4672     }
4673     PetscCall(MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES));
4674   }
4675   PetscCall(MatSeqAIJRestoreArrayRead(seqmat,&a_a));
4676   PetscCall(MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY));
4677   PetscCall(MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY));
4678 
4679   PetscCall(PetscFree(abuf_r[0]));
4680   PetscCall(PetscFree(abuf_r));
4681   PetscCall(PetscFree(ba_i));
4682   PetscCall(PetscFree3(buf_ri_k,nextrow,nextai));
4683   PetscCall(PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0));
4684   PetscFunctionReturn(0);
4685 }
4686 
4687 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4688 {
4689   Mat                 B_mpi;
4690   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
4691   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4692   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
4693   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4694   PetscInt            len,proc,*dnz,*onz,bs,cbs;
4695   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4696   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4697   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
4698   MPI_Status          *status;
4699   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
4700   PetscBT             lnkbt;
4701   Mat_Merge_SeqsToMPI *merge;
4702   PetscContainer      container;
4703 
4704   PetscFunctionBegin;
4705   PetscCall(PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0));
4706 
4707   /* make sure it is a PETSc comm */
4708   PetscCall(PetscCommDuplicate(comm,&comm,NULL));
4709   PetscCallMPI(MPI_Comm_size(comm,&size));
4710   PetscCallMPI(MPI_Comm_rank(comm,&rank));
4711 
4712   PetscCall(PetscNew(&merge));
4713   PetscCall(PetscMalloc1(size,&status));
4714 
4715   /* determine row ownership */
4716   /*---------------------------------------------------------*/
4717   PetscCall(PetscLayoutCreate(comm,&merge->rowmap));
4718   PetscCall(PetscLayoutSetLocalSize(merge->rowmap,m));
4719   PetscCall(PetscLayoutSetSize(merge->rowmap,M));
4720   PetscCall(PetscLayoutSetBlockSize(merge->rowmap,1));
4721   PetscCall(PetscLayoutSetUp(merge->rowmap));
4722   PetscCall(PetscMalloc1(size,&len_si));
4723   PetscCall(PetscMalloc1(size,&merge->len_s));
4724 
4725   m      = merge->rowmap->n;
4726   owners = merge->rowmap->range;
4727 
4728   /* determine the number of messages to send, their lengths */
4729   /*---------------------------------------------------------*/
4730   len_s = merge->len_s;
4731 
4732   len          = 0; /* length of buf_si[] */
4733   merge->nsend = 0;
4734   for (proc=0; proc<size; proc++) {
4735     len_si[proc] = 0;
4736     if (proc == rank) {
4737       len_s[proc] = 0;
4738     } else {
4739       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4740       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4741     }
4742     if (len_s[proc]) {
4743       merge->nsend++;
4744       nrows = 0;
4745       for (i=owners[proc]; i<owners[proc+1]; i++) {
4746         if (ai[i+1] > ai[i]) nrows++;
4747       }
4748       len_si[proc] = 2*(nrows+1);
4749       len         += len_si[proc];
4750     }
4751   }
4752 
4753   /* determine the number and length of messages to receive for ij-structure */
4754   /*-------------------------------------------------------------------------*/
4755   PetscCall(PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv));
4756   PetscCall(PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri));
4757 
4758   /* post the Irecv of j-structure */
4759   /*-------------------------------*/
4760   PetscCall(PetscCommGetNewTag(comm,&tagj));
4761   PetscCall(PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits));
4762 
4763   /* post the Isend of j-structure */
4764   /*--------------------------------*/
4765   PetscCall(PetscMalloc2(merge->nsend,&si_waits,merge->nsend,&sj_waits));
4766 
4767   for (proc=0, k=0; proc<size; proc++) {
4768     if (!len_s[proc]) continue;
4769     i    = owners[proc];
4770     PetscCallMPI(MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k));
4771     k++;
4772   }
4773 
4774   /* receives and sends of j-structure are complete */
4775   /*------------------------------------------------*/
4776   if (merge->nrecv) PetscCallMPI(MPI_Waitall(merge->nrecv,rj_waits,status));
4777   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend,sj_waits,status));
4778 
4779   /* send and recv i-structure */
4780   /*---------------------------*/
4781   PetscCall(PetscCommGetNewTag(comm,&tagi));
4782   PetscCall(PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits));
4783 
4784   PetscCall(PetscMalloc1(len+1,&buf_s));
4785   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4786   for (proc=0,k=0; proc<size; proc++) {
4787     if (!len_s[proc]) continue;
4788     /* form outgoing message for i-structure:
4789          buf_si[0]:                 nrows to be sent
4790                [1:nrows]:           row index (global)
4791                [nrows+1:2*nrows+1]: i-structure index
4792     */
4793     /*-------------------------------------------*/
4794     nrows       = len_si[proc]/2 - 1;
4795     buf_si_i    = buf_si + nrows+1;
4796     buf_si[0]   = nrows;
4797     buf_si_i[0] = 0;
4798     nrows       = 0;
4799     for (i=owners[proc]; i<owners[proc+1]; i++) {
4800       anzi = ai[i+1] - ai[i];
4801       if (anzi) {
4802         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4803         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4804         nrows++;
4805       }
4806     }
4807     PetscCallMPI(MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k));
4808     k++;
4809     buf_si += len_si[proc];
4810   }
4811 
4812   if (merge->nrecv) PetscCallMPI(MPI_Waitall(merge->nrecv,ri_waits,status));
4813   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend,si_waits,status));
4814 
4815   PetscCall(PetscInfo(seqmat,"nsend: %d, nrecv: %d\n",merge->nsend,merge->nrecv));
4816   for (i=0; i<merge->nrecv; i++) {
4817     PetscCall(PetscInfo(seqmat,"recv len_ri=%d, len_rj=%d from [%d]\n",len_ri[i],merge->len_r[i],merge->id_r[i]));
4818   }
4819 
4820   PetscCall(PetscFree(len_si));
4821   PetscCall(PetscFree(len_ri));
4822   PetscCall(PetscFree(rj_waits));
4823   PetscCall(PetscFree2(si_waits,sj_waits));
4824   PetscCall(PetscFree(ri_waits));
4825   PetscCall(PetscFree(buf_s));
4826   PetscCall(PetscFree(status));
4827 
4828   /* compute a local seq matrix in each processor */
4829   /*----------------------------------------------*/
4830   /* allocate bi array and free space for accumulating nonzero column info */
4831   PetscCall(PetscMalloc1(m+1,&bi));
4832   bi[0] = 0;
4833 
4834   /* create and initialize a linked list */
4835   nlnk = N+1;
4836   PetscCall(PetscLLCreate(N,N,nlnk,lnk,lnkbt));
4837 
4838   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4839   len  = ai[owners[rank+1]] - ai[owners[rank]];
4840   PetscCall(PetscFreeSpaceGet(PetscIntMultTruncate(2,len)+1,&free_space));
4841 
4842   current_space = free_space;
4843 
4844   /* determine symbolic info for each local row */
4845   PetscCall(PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai));
4846 
4847   for (k=0; k<merge->nrecv; k++) {
4848     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4849     nrows       = *buf_ri_k[k];
4850     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4851     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
4852   }
4853 
4854   MatPreallocateBegin(comm,m,n,dnz,onz);
4855   len  = 0;
4856   for (i=0; i<m; i++) {
4857     bnzi = 0;
4858     /* add local non-zero cols of this proc's seqmat into lnk */
4859     arow  = owners[rank] + i;
4860     anzi  = ai[arow+1] - ai[arow];
4861     aj    = a->j + ai[arow];
4862     PetscCall(PetscLLAddSorted(anzi,aj,N,&nlnk,lnk,lnkbt));
4863     bnzi += nlnk;
4864     /* add received col data into lnk */
4865     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4866       if (i == *nextrow[k]) { /* i-th row */
4867         anzi  = *(nextai[k]+1) - *nextai[k];
4868         aj    = buf_rj[k] + *nextai[k];
4869         PetscCall(PetscLLAddSorted(anzi,aj,N,&nlnk,lnk,lnkbt));
4870         bnzi += nlnk;
4871         nextrow[k]++; nextai[k]++;
4872       }
4873     }
4874     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4875 
4876     /* if free space is not available, make more free space */
4877     if (current_space->local_remaining<bnzi) {
4878       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(bnzi,current_space->total_array_size),&current_space));
4879       nspacedouble++;
4880     }
4881     /* copy data into free space, then initialize lnk */
4882     PetscCall(PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt));
4883     PetscCall(MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz));
4884 
4885     current_space->array           += bnzi;
4886     current_space->local_used      += bnzi;
4887     current_space->local_remaining -= bnzi;
4888 
4889     bi[i+1] = bi[i] + bnzi;
4890   }
4891 
4892   PetscCall(PetscFree3(buf_ri_k,nextrow,nextai));
4893 
4894   PetscCall(PetscMalloc1(bi[m]+1,&bj));
4895   PetscCall(PetscFreeSpaceContiguous(&free_space,bj));
4896   PetscCall(PetscLLDestroy(lnk,lnkbt));
4897 
4898   /* create symbolic parallel matrix B_mpi */
4899   /*---------------------------------------*/
4900   PetscCall(MatGetBlockSizes(seqmat,&bs,&cbs));
4901   PetscCall(MatCreate(comm,&B_mpi));
4902   if (n==PETSC_DECIDE) {
4903     PetscCall(MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N));
4904   } else {
4905     PetscCall(MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE));
4906   }
4907   PetscCall(MatSetBlockSizes(B_mpi,bs,cbs));
4908   PetscCall(MatSetType(B_mpi,MATMPIAIJ));
4909   PetscCall(MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz));
4910   MatPreallocateEnd(dnz,onz);
4911   PetscCall(MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE));
4912 
4913   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4914   B_mpi->assembled  = PETSC_FALSE;
4915   merge->bi         = bi;
4916   merge->bj         = bj;
4917   merge->buf_ri     = buf_ri;
4918   merge->buf_rj     = buf_rj;
4919   merge->coi        = NULL;
4920   merge->coj        = NULL;
4921   merge->owners_co  = NULL;
4922 
4923   PetscCall(PetscCommDestroy(&comm));
4924 
4925   /* attach the supporting struct to B_mpi for reuse */
4926   PetscCall(PetscContainerCreate(PETSC_COMM_SELF,&container));
4927   PetscCall(PetscContainerSetPointer(container,merge));
4928   PetscCall(PetscContainerSetUserDestroy(container,MatDestroy_MPIAIJ_SeqsToMPI));
4929   PetscCall(PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container));
4930   PetscCall(PetscContainerDestroy(&container));
4931   *mpimat = B_mpi;
4932 
4933   PetscCall(PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0));
4934   PetscFunctionReturn(0);
4935 }
4936 
4937 /*@C
4938       MatCreateMPIAIJSumSeqAIJ - Creates a MATMPIAIJ matrix by adding sequential
4939                  matrices from each processor
4940 
4941     Collective
4942 
4943    Input Parameters:
4944 +    comm - the communicators the parallel matrix will live on
4945 .    seqmat - the input sequential matrices
4946 .    m - number of local rows (or PETSC_DECIDE)
4947 .    n - number of local columns (or PETSC_DECIDE)
4948 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4949 
4950    Output Parameter:
4951 .    mpimat - the parallel matrix generated
4952 
4953     Level: advanced
4954 
4955    Notes:
4956      The dimensions of the sequential matrix in each processor MUST be the same.
4957      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
4958      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
4959 @*/
4960 PetscErrorCode MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
4961 {
4962   PetscMPIInt    size;
4963 
4964   PetscFunctionBegin;
4965   PetscCallMPI(MPI_Comm_size(comm,&size));
4966   if (size == 1) {
4967     PetscCall(PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0));
4968     if (scall == MAT_INITIAL_MATRIX) {
4969       PetscCall(MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat));
4970     } else {
4971       PetscCall(MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN));
4972     }
4973     PetscCall(PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0));
4974     PetscFunctionReturn(0);
4975   }
4976   PetscCall(PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0));
4977   if (scall == MAT_INITIAL_MATRIX) {
4978     PetscCall(MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat));
4979   }
4980   PetscCall(MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat));
4981   PetscCall(PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0));
4982   PetscFunctionReturn(0);
4983 }
4984 
4985 /*@
4986      MatAIJGetLocalMat - Creates a SeqAIJ from a MATAIJ matrix by taking all its local rows and putting them into a sequential matrix with
4987           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
4988           with MatGetSize()
4989 
4990     Not Collective
4991 
4992    Input Parameters:
4993 +    A - the matrix
4994 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4995 
4996    Output Parameter:
4997 .    A_loc - the local sequential matrix generated
4998 
4999     Level: developer
5000 
5001    Notes:
5002      In other words combines the two parts of a parallel MPIAIJ matrix on each process to a single matrix.
5003 
5004      Destroy the matrix with MatDestroy()
5005 
5006 .seealso: MatMPIAIJGetLocalMat()
5007 
5008 @*/
5009 PetscErrorCode MatAIJGetLocalMat(Mat A,Mat *A_loc)
5010 {
5011   PetscBool      mpi;
5012 
5013   PetscFunctionBegin;
5014   PetscCall(PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&mpi));
5015   if (mpi) {
5016     PetscCall(MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,A_loc));
5017   } else {
5018     *A_loc = A;
5019     PetscCall(PetscObjectReference((PetscObject)*A_loc));
5020   }
5021   PetscFunctionReturn(0);
5022 }
5023 
5024 /*@
5025      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MATMPIAIJ matrix by taking all its local rows and putting them into a sequential matrix with
5026           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
5027           with MatGetSize()
5028 
5029     Not Collective
5030 
5031    Input Parameters:
5032 +    A - the matrix
5033 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5034 
5035    Output Parameter:
5036 .    A_loc - the local sequential matrix generated
5037 
5038     Level: developer
5039 
5040    Notes:
5041      In other words combines the two parts of a parallel MPIAIJ matrix on each process to a single matrix.
5042 
5043      When the communicator associated with A has size 1 and MAT_INITIAL_MATRIX is requested, the matrix returned is the diagonal part of A.
5044      If MAT_REUSE_MATRIX is requested with comm size 1, MatCopy(Adiag,*A_loc,SAME_NONZERO_PATTERN) is called.
5045      This means that one can preallocate the proper sequential matrix first and then call this routine with MAT_REUSE_MATRIX to safely
5046      modify the values of the returned A_loc.
5047 
5048 .seealso: `MatGetOwnershipRange()`, `MatMPIAIJGetLocalMatCondensed()`, `MatMPIAIJGetLocalMatMerge()`
5049 @*/
5050 PetscErrorCode MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
5051 {
5052   Mat_MPIAIJ        *mpimat=(Mat_MPIAIJ*)A->data;
5053   Mat_SeqAIJ        *mat,*a,*b;
5054   PetscInt          *ai,*aj,*bi,*bj,*cmap=mpimat->garray;
5055   const PetscScalar *aa,*ba,*aav,*bav;
5056   PetscScalar       *ca,*cam;
5057   PetscMPIInt       size;
5058   PetscInt          am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
5059   PetscInt          *ci,*cj,col,ncols_d,ncols_o,jo;
5060   PetscBool         match;
5061 
5062   PetscFunctionBegin;
5063   PetscCall(PetscStrbeginswith(((PetscObject)A)->type_name,MATMPIAIJ,&match));
5064   PetscCheck(match,PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
5065   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A),&size));
5066   if (size == 1) {
5067     if (scall == MAT_INITIAL_MATRIX) {
5068       PetscCall(PetscObjectReference((PetscObject)mpimat->A));
5069       *A_loc = mpimat->A;
5070     } else if (scall == MAT_REUSE_MATRIX) {
5071       PetscCall(MatCopy(mpimat->A,*A_loc,SAME_NONZERO_PATTERN));
5072     }
5073     PetscFunctionReturn(0);
5074   }
5075 
5076   PetscCall(PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0));
5077   a = (Mat_SeqAIJ*)(mpimat->A)->data;
5078   b = (Mat_SeqAIJ*)(mpimat->B)->data;
5079   ai = a->i; aj = a->j; bi = b->i; bj = b->j;
5080   PetscCall(MatSeqAIJGetArrayRead(mpimat->A,&aav));
5081   PetscCall(MatSeqAIJGetArrayRead(mpimat->B,&bav));
5082   aa   = aav;
5083   ba   = bav;
5084   if (scall == MAT_INITIAL_MATRIX) {
5085     PetscCall(PetscMalloc1(1+am,&ci));
5086     ci[0] = 0;
5087     for (i=0; i<am; i++) {
5088       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
5089     }
5090     PetscCall(PetscMalloc1(1+ci[am],&cj));
5091     PetscCall(PetscMalloc1(1+ci[am],&ca));
5092     k    = 0;
5093     for (i=0; i<am; i++) {
5094       ncols_o = bi[i+1] - bi[i];
5095       ncols_d = ai[i+1] - ai[i];
5096       /* off-diagonal portion of A */
5097       for (jo=0; jo<ncols_o; jo++) {
5098         col = cmap[*bj];
5099         if (col >= cstart) break;
5100         cj[k]   = col; bj++;
5101         ca[k++] = *ba++;
5102       }
5103       /* diagonal portion of A */
5104       for (j=0; j<ncols_d; j++) {
5105         cj[k]   = cstart + *aj++;
5106         ca[k++] = *aa++;
5107       }
5108       /* off-diagonal portion of A */
5109       for (j=jo; j<ncols_o; j++) {
5110         cj[k]   = cmap[*bj++];
5111         ca[k++] = *ba++;
5112       }
5113     }
5114     /* put together the new matrix */
5115     PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc));
5116     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
5117     /* Since these are PETSc arrays, change flags to free them as necessary. */
5118     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
5119     mat->free_a  = PETSC_TRUE;
5120     mat->free_ij = PETSC_TRUE;
5121     mat->nonew   = 0;
5122   } else if (scall == MAT_REUSE_MATRIX) {
5123     mat  =(Mat_SeqAIJ*)(*A_loc)->data;
5124     ci   = mat->i;
5125     cj   = mat->j;
5126     PetscCall(MatSeqAIJGetArrayWrite(*A_loc,&cam));
5127     for (i=0; i<am; i++) {
5128       /* off-diagonal portion of A */
5129       ncols_o = bi[i+1] - bi[i];
5130       for (jo=0; jo<ncols_o; jo++) {
5131         col = cmap[*bj];
5132         if (col >= cstart) break;
5133         *cam++ = *ba++; bj++;
5134       }
5135       /* diagonal portion of A */
5136       ncols_d = ai[i+1] - ai[i];
5137       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
5138       /* off-diagonal portion of A */
5139       for (j=jo; j<ncols_o; j++) {
5140         *cam++ = *ba++; bj++;
5141       }
5142     }
5143     PetscCall(MatSeqAIJRestoreArrayWrite(*A_loc,&cam));
5144   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
5145   PetscCall(MatSeqAIJRestoreArrayRead(mpimat->A,&aav));
5146   PetscCall(MatSeqAIJRestoreArrayRead(mpimat->B,&bav));
5147   PetscCall(PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0));
5148   PetscFunctionReturn(0);
5149 }
5150 
5151 /*@
5152      MatMPIAIJGetLocalMatMerge - Creates a SeqAIJ from a MATMPIAIJ matrix by taking all its local rows and putting them into a sequential matrix with
5153           mlocal rows and n columns. Where n is the sum of the number of columns of the diagonal and offdiagonal part
5154 
5155     Not Collective
5156 
5157    Input Parameters:
5158 +    A - the matrix
5159 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5160 
5161    Output Parameters:
5162 +    glob - sequential IS with global indices associated with the columns of the local sequential matrix generated (can be NULL)
5163 -    A_loc - the local sequential matrix generated
5164 
5165     Level: developer
5166 
5167    Notes:
5168      This is different from MatMPIAIJGetLocalMat() since the first columns in the returning matrix are those associated with the diagonal part, then those associated with the offdiagonal part (in its local ordering)
5169 
5170 .seealso: `MatGetOwnershipRange()`, `MatMPIAIJGetLocalMat()`, `MatMPIAIJGetLocalMatCondensed()`
5171 
5172 @*/
5173 PetscErrorCode MatMPIAIJGetLocalMatMerge(Mat A,MatReuse scall,IS *glob,Mat *A_loc)
5174 {
5175   Mat            Ao,Ad;
5176   const PetscInt *cmap;
5177   PetscMPIInt    size;
5178   PetscErrorCode (*f)(Mat,MatReuse,IS*,Mat*);
5179 
5180   PetscFunctionBegin;
5181   PetscCall(MatMPIAIJGetSeqAIJ(A,&Ad,&Ao,&cmap));
5182   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A),&size));
5183   if (size == 1) {
5184     if (scall == MAT_INITIAL_MATRIX) {
5185       PetscCall(PetscObjectReference((PetscObject)Ad));
5186       *A_loc = Ad;
5187     } else if (scall == MAT_REUSE_MATRIX) {
5188       PetscCall(MatCopy(Ad,*A_loc,SAME_NONZERO_PATTERN));
5189     }
5190     if (glob) PetscCall(ISCreateStride(PetscObjectComm((PetscObject)Ad),Ad->cmap->n,Ad->cmap->rstart,1,glob));
5191     PetscFunctionReturn(0);
5192   }
5193   PetscCall(PetscObjectQueryFunction((PetscObject)A,"MatMPIAIJGetLocalMatMerge_C",&f));
5194   PetscCall(PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0));
5195   if (f) {
5196     PetscCall((*f)(A,scall,glob,A_loc));
5197   } else {
5198     Mat_SeqAIJ        *a = (Mat_SeqAIJ*)Ad->data;
5199     Mat_SeqAIJ        *b = (Mat_SeqAIJ*)Ao->data;
5200     Mat_SeqAIJ        *c;
5201     PetscInt          *ai = a->i, *aj = a->j;
5202     PetscInt          *bi = b->i, *bj = b->j;
5203     PetscInt          *ci,*cj;
5204     const PetscScalar *aa,*ba;
5205     PetscScalar       *ca;
5206     PetscInt          i,j,am,dn,on;
5207 
5208     PetscCall(MatGetLocalSize(Ad,&am,&dn));
5209     PetscCall(MatGetLocalSize(Ao,NULL,&on));
5210     PetscCall(MatSeqAIJGetArrayRead(Ad,&aa));
5211     PetscCall(MatSeqAIJGetArrayRead(Ao,&ba));
5212     if (scall == MAT_INITIAL_MATRIX) {
5213       PetscInt k;
5214       PetscCall(PetscMalloc1(1+am,&ci));
5215       PetscCall(PetscMalloc1(ai[am]+bi[am],&cj));
5216       PetscCall(PetscMalloc1(ai[am]+bi[am],&ca));
5217       ci[0] = 0;
5218       for (i=0,k=0; i<am; i++) {
5219         const PetscInt ncols_o = bi[i+1] - bi[i];
5220         const PetscInt ncols_d = ai[i+1] - ai[i];
5221         ci[i+1] = ci[i] + ncols_o + ncols_d;
5222         /* diagonal portion of A */
5223         for (j=0; j<ncols_d; j++,k++) {
5224           cj[k] = *aj++;
5225           ca[k] = *aa++;
5226         }
5227         /* off-diagonal portion of A */
5228         for (j=0; j<ncols_o; j++,k++) {
5229           cj[k] = dn + *bj++;
5230           ca[k] = *ba++;
5231         }
5232       }
5233       /* put together the new matrix */
5234       PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,dn+on,ci,cj,ca,A_loc));
5235       /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
5236       /* Since these are PETSc arrays, change flags to free them as necessary. */
5237       c          = (Mat_SeqAIJ*)(*A_loc)->data;
5238       c->free_a  = PETSC_TRUE;
5239       c->free_ij = PETSC_TRUE;
5240       c->nonew   = 0;
5241       PetscCall(MatSetType(*A_loc,((PetscObject)Ad)->type_name));
5242     } else if (scall == MAT_REUSE_MATRIX) {
5243       PetscCall(MatSeqAIJGetArrayWrite(*A_loc,&ca));
5244       for (i=0; i<am; i++) {
5245         const PetscInt ncols_d = ai[i+1] - ai[i];
5246         const PetscInt ncols_o = bi[i+1] - bi[i];
5247         /* diagonal portion of A */
5248         for (j=0; j<ncols_d; j++) *ca++ = *aa++;
5249         /* off-diagonal portion of A */
5250         for (j=0; j<ncols_o; j++) *ca++ = *ba++;
5251       }
5252       PetscCall(MatSeqAIJRestoreArrayWrite(*A_loc,&ca));
5253     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
5254     PetscCall(MatSeqAIJRestoreArrayRead(Ad,&aa));
5255     PetscCall(MatSeqAIJRestoreArrayRead(Ao,&aa));
5256     if (glob) {
5257       PetscInt cst, *gidx;
5258 
5259       PetscCall(MatGetOwnershipRangeColumn(A,&cst,NULL));
5260       PetscCall(PetscMalloc1(dn+on,&gidx));
5261       for (i=0; i<dn; i++) gidx[i]    = cst + i;
5262       for (i=0; i<on; i++) gidx[i+dn] = cmap[i];
5263       PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)Ad),dn+on,gidx,PETSC_OWN_POINTER,glob));
5264     }
5265   }
5266   PetscCall(PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0));
5267   PetscFunctionReturn(0);
5268 }
5269 
5270 /*@C
5271      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MATMPIAIJ matrix by taking all its local rows and NON-ZERO columns
5272 
5273     Not Collective
5274 
5275    Input Parameters:
5276 +    A - the matrix
5277 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5278 -    row, col - index sets of rows and columns to extract (or NULL)
5279 
5280    Output Parameter:
5281 .    A_loc - the local sequential matrix generated
5282 
5283     Level: developer
5284 
5285 .seealso: `MatGetOwnershipRange()`, `MatMPIAIJGetLocalMat()`
5286 
5287 @*/
5288 PetscErrorCode MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
5289 {
5290   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
5291   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
5292   IS             isrowa,iscola;
5293   Mat            *aloc;
5294   PetscBool      match;
5295 
5296   PetscFunctionBegin;
5297   PetscCall(PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match));
5298   PetscCheck(match,PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
5299   PetscCall(PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0));
5300   if (!row) {
5301     start = A->rmap->rstart; end = A->rmap->rend;
5302     PetscCall(ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa));
5303   } else {
5304     isrowa = *row;
5305   }
5306   if (!col) {
5307     start = A->cmap->rstart;
5308     cmap  = a->garray;
5309     nzA   = a->A->cmap->n;
5310     nzB   = a->B->cmap->n;
5311     PetscCall(PetscMalloc1(nzA+nzB, &idx));
5312     ncols = 0;
5313     for (i=0; i<nzB; i++) {
5314       if (cmap[i] < start) idx[ncols++] = cmap[i];
5315       else break;
5316     }
5317     imark = i;
5318     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
5319     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
5320     PetscCall(ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola));
5321   } else {
5322     iscola = *col;
5323   }
5324   if (scall != MAT_INITIAL_MATRIX) {
5325     PetscCall(PetscMalloc1(1,&aloc));
5326     aloc[0] = *A_loc;
5327   }
5328   PetscCall(MatCreateSubMatrices(A,1,&isrowa,&iscola,scall,&aloc));
5329   if (!col) { /* attach global id of condensed columns */
5330     PetscCall(PetscObjectCompose((PetscObject)aloc[0],"_petsc_GetLocalMatCondensed_iscol",(PetscObject)iscola));
5331   }
5332   *A_loc = aloc[0];
5333   PetscCall(PetscFree(aloc));
5334   if (!row) {
5335     PetscCall(ISDestroy(&isrowa));
5336   }
5337   if (!col) {
5338     PetscCall(ISDestroy(&iscola));
5339   }
5340   PetscCall(PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0));
5341   PetscFunctionReturn(0);
5342 }
5343 
5344 /*
5345  * Create a sequential AIJ matrix based on row indices. a whole column is extracted once a row is matched.
5346  * Row could be local or remote.The routine is designed to be scalable in memory so that nothing is based
5347  * on a global size.
5348  * */
5349 PetscErrorCode MatCreateSeqSubMatrixWithRows_Private(Mat P,IS rows,Mat *P_oth)
5350 {
5351   Mat_MPIAIJ               *p=(Mat_MPIAIJ*)P->data;
5352   Mat_SeqAIJ               *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data,*p_oth;
5353   PetscInt                 plocalsize,nrows,*ilocal,*oilocal,i,lidx,*nrcols,*nlcols,ncol;
5354   PetscMPIInt              owner;
5355   PetscSFNode              *iremote,*oiremote;
5356   const PetscInt           *lrowindices;
5357   PetscSF                  sf,osf;
5358   PetscInt                 pcstart,*roffsets,*loffsets,*pnnz,j;
5359   PetscInt                 ontotalcols,dntotalcols,ntotalcols,nout;
5360   MPI_Comm                 comm;
5361   ISLocalToGlobalMapping   mapping;
5362   const PetscScalar        *pd_a,*po_a;
5363 
5364   PetscFunctionBegin;
5365   PetscCall(PetscObjectGetComm((PetscObject)P,&comm));
5366   /* plocalsize is the number of roots
5367    * nrows is the number of leaves
5368    * */
5369   PetscCall(MatGetLocalSize(P,&plocalsize,NULL));
5370   PetscCall(ISGetLocalSize(rows,&nrows));
5371   PetscCall(PetscCalloc1(nrows,&iremote));
5372   PetscCall(ISGetIndices(rows,&lrowindices));
5373   for (i=0;i<nrows;i++) {
5374     /* Find a remote index and an owner for a row
5375      * The row could be local or remote
5376      * */
5377     owner = 0;
5378     lidx  = 0;
5379     PetscCall(PetscLayoutFindOwnerIndex(P->rmap,lrowindices[i],&owner,&lidx));
5380     iremote[i].index = lidx;
5381     iremote[i].rank  = owner;
5382   }
5383   /* Create SF to communicate how many nonzero columns for each row */
5384   PetscCall(PetscSFCreate(comm,&sf));
5385   /* SF will figure out the number of nonzero colunms for each row, and their
5386    * offsets
5387    * */
5388   PetscCall(PetscSFSetGraph(sf,plocalsize,nrows,NULL,PETSC_OWN_POINTER,iremote,PETSC_OWN_POINTER));
5389   PetscCall(PetscSFSetFromOptions(sf));
5390   PetscCall(PetscSFSetUp(sf));
5391 
5392   PetscCall(PetscCalloc1(2*(plocalsize+1),&roffsets));
5393   PetscCall(PetscCalloc1(2*plocalsize,&nrcols));
5394   PetscCall(PetscCalloc1(nrows,&pnnz));
5395   roffsets[0] = 0;
5396   roffsets[1] = 0;
5397   for (i=0;i<plocalsize;i++) {
5398     /* diag */
5399     nrcols[i*2+0] = pd->i[i+1] - pd->i[i];
5400     /* off diag */
5401     nrcols[i*2+1] = po->i[i+1] - po->i[i];
5402     /* compute offsets so that we relative location for each row */
5403     roffsets[(i+1)*2+0] = roffsets[i*2+0] + nrcols[i*2+0];
5404     roffsets[(i+1)*2+1] = roffsets[i*2+1] + nrcols[i*2+1];
5405   }
5406   PetscCall(PetscCalloc1(2*nrows,&nlcols));
5407   PetscCall(PetscCalloc1(2*nrows,&loffsets));
5408   /* 'r' means root, and 'l' means leaf */
5409   PetscCall(PetscSFBcastBegin(sf,MPIU_2INT,nrcols,nlcols,MPI_REPLACE));
5410   PetscCall(PetscSFBcastBegin(sf,MPIU_2INT,roffsets,loffsets,MPI_REPLACE));
5411   PetscCall(PetscSFBcastEnd(sf,MPIU_2INT,nrcols,nlcols,MPI_REPLACE));
5412   PetscCall(PetscSFBcastEnd(sf,MPIU_2INT,roffsets,loffsets,MPI_REPLACE));
5413   PetscCall(PetscSFDestroy(&sf));
5414   PetscCall(PetscFree(roffsets));
5415   PetscCall(PetscFree(nrcols));
5416   dntotalcols = 0;
5417   ontotalcols = 0;
5418   ncol = 0;
5419   for (i=0;i<nrows;i++) {
5420     pnnz[i] = nlcols[i*2+0] + nlcols[i*2+1];
5421     ncol = PetscMax(pnnz[i],ncol);
5422     /* diag */
5423     dntotalcols += nlcols[i*2+0];
5424     /* off diag */
5425     ontotalcols += nlcols[i*2+1];
5426   }
5427   /* We do not need to figure the right number of columns
5428    * since all the calculations will be done by going through the raw data
5429    * */
5430   PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF,nrows,ncol,0,pnnz,P_oth));
5431   PetscCall(MatSetUp(*P_oth));
5432   PetscCall(PetscFree(pnnz));
5433   p_oth = (Mat_SeqAIJ*) (*P_oth)->data;
5434   /* diag */
5435   PetscCall(PetscCalloc1(dntotalcols,&iremote));
5436   /* off diag */
5437   PetscCall(PetscCalloc1(ontotalcols,&oiremote));
5438   /* diag */
5439   PetscCall(PetscCalloc1(dntotalcols,&ilocal));
5440   /* off diag */
5441   PetscCall(PetscCalloc1(ontotalcols,&oilocal));
5442   dntotalcols = 0;
5443   ontotalcols = 0;
5444   ntotalcols  = 0;
5445   for (i=0;i<nrows;i++) {
5446     owner = 0;
5447     PetscCall(PetscLayoutFindOwnerIndex(P->rmap,lrowindices[i],&owner,NULL));
5448     /* Set iremote for diag matrix */
5449     for (j=0;j<nlcols[i*2+0];j++) {
5450       iremote[dntotalcols].index   = loffsets[i*2+0] + j;
5451       iremote[dntotalcols].rank    = owner;
5452       /* P_oth is seqAIJ so that ilocal need to point to the first part of memory */
5453       ilocal[dntotalcols++]        = ntotalcols++;
5454     }
5455     /* off diag */
5456     for (j=0;j<nlcols[i*2+1];j++) {
5457       oiremote[ontotalcols].index   = loffsets[i*2+1] + j;
5458       oiremote[ontotalcols].rank    = owner;
5459       oilocal[ontotalcols++]        = ntotalcols++;
5460     }
5461   }
5462   PetscCall(ISRestoreIndices(rows,&lrowindices));
5463   PetscCall(PetscFree(loffsets));
5464   PetscCall(PetscFree(nlcols));
5465   PetscCall(PetscSFCreate(comm,&sf));
5466   /* P serves as roots and P_oth is leaves
5467    * Diag matrix
5468    * */
5469   PetscCall(PetscSFSetGraph(sf,pd->i[plocalsize],dntotalcols,ilocal,PETSC_OWN_POINTER,iremote,PETSC_OWN_POINTER));
5470   PetscCall(PetscSFSetFromOptions(sf));
5471   PetscCall(PetscSFSetUp(sf));
5472 
5473   PetscCall(PetscSFCreate(comm,&osf));
5474   /* Off diag */
5475   PetscCall(PetscSFSetGraph(osf,po->i[plocalsize],ontotalcols,oilocal,PETSC_OWN_POINTER,oiremote,PETSC_OWN_POINTER));
5476   PetscCall(PetscSFSetFromOptions(osf));
5477   PetscCall(PetscSFSetUp(osf));
5478   PetscCall(MatSeqAIJGetArrayRead(p->A,&pd_a));
5479   PetscCall(MatSeqAIJGetArrayRead(p->B,&po_a));
5480   /* We operate on the matrix internal data for saving memory */
5481   PetscCall(PetscSFBcastBegin(sf,MPIU_SCALAR,pd_a,p_oth->a,MPI_REPLACE));
5482   PetscCall(PetscSFBcastBegin(osf,MPIU_SCALAR,po_a,p_oth->a,MPI_REPLACE));
5483   PetscCall(MatGetOwnershipRangeColumn(P,&pcstart,NULL));
5484   /* Convert to global indices for diag matrix */
5485   for (i=0;i<pd->i[plocalsize];i++) pd->j[i] += pcstart;
5486   PetscCall(PetscSFBcastBegin(sf,MPIU_INT,pd->j,p_oth->j,MPI_REPLACE));
5487   /* We want P_oth store global indices */
5488   PetscCall(ISLocalToGlobalMappingCreate(comm,1,p->B->cmap->n,p->garray,PETSC_COPY_VALUES,&mapping));
5489   /* Use memory scalable approach */
5490   PetscCall(ISLocalToGlobalMappingSetType(mapping,ISLOCALTOGLOBALMAPPINGHASH));
5491   PetscCall(ISLocalToGlobalMappingApply(mapping,po->i[plocalsize],po->j,po->j));
5492   PetscCall(PetscSFBcastBegin(osf,MPIU_INT,po->j,p_oth->j,MPI_REPLACE));
5493   PetscCall(PetscSFBcastEnd(sf,MPIU_INT,pd->j,p_oth->j,MPI_REPLACE));
5494   /* Convert back to local indices */
5495   for (i=0;i<pd->i[plocalsize];i++) pd->j[i] -= pcstart;
5496   PetscCall(PetscSFBcastEnd(osf,MPIU_INT,po->j,p_oth->j,MPI_REPLACE));
5497   nout = 0;
5498   PetscCall(ISGlobalToLocalMappingApply(mapping,IS_GTOLM_DROP,po->i[plocalsize],po->j,&nout,po->j));
5499   PetscCheck(nout == po->i[plocalsize],comm,PETSC_ERR_ARG_INCOMP,"n %" PetscInt_FMT " does not equal to nout %" PetscInt_FMT " ",po->i[plocalsize],nout);
5500   PetscCall(ISLocalToGlobalMappingDestroy(&mapping));
5501   /* Exchange values */
5502   PetscCall(PetscSFBcastEnd(sf,MPIU_SCALAR,pd_a,p_oth->a,MPI_REPLACE));
5503   PetscCall(PetscSFBcastEnd(osf,MPIU_SCALAR,po_a,p_oth->a,MPI_REPLACE));
5504   PetscCall(MatSeqAIJRestoreArrayRead(p->A,&pd_a));
5505   PetscCall(MatSeqAIJRestoreArrayRead(p->B,&po_a));
5506   /* Stop PETSc from shrinking memory */
5507   for (i=0;i<nrows;i++) p_oth->ilen[i] = p_oth->imax[i];
5508   PetscCall(MatAssemblyBegin(*P_oth,MAT_FINAL_ASSEMBLY));
5509   PetscCall(MatAssemblyEnd(*P_oth,MAT_FINAL_ASSEMBLY));
5510   /* Attach PetscSF objects to P_oth so that we can reuse it later */
5511   PetscCall(PetscObjectCompose((PetscObject)*P_oth,"diagsf",(PetscObject)sf));
5512   PetscCall(PetscObjectCompose((PetscObject)*P_oth,"offdiagsf",(PetscObject)osf));
5513   PetscCall(PetscSFDestroy(&sf));
5514   PetscCall(PetscSFDestroy(&osf));
5515   PetscFunctionReturn(0);
5516 }
5517 
5518 /*
5519  * Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
5520  * This supports MPIAIJ and MAIJ
5521  * */
5522 PetscErrorCode MatGetBrowsOfAcols_MPIXAIJ(Mat A,Mat P,PetscInt dof,MatReuse reuse,Mat *P_oth)
5523 {
5524   Mat_MPIAIJ            *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data;
5525   Mat_SeqAIJ            *p_oth;
5526   IS                    rows,map;
5527   PetscHMapI            hamp;
5528   PetscInt              i,htsize,*rowindices,off,*mapping,key,count;
5529   MPI_Comm              comm;
5530   PetscSF               sf,osf;
5531   PetscBool             has;
5532 
5533   PetscFunctionBegin;
5534   PetscCall(PetscObjectGetComm((PetscObject)A,&comm));
5535   PetscCall(PetscLogEventBegin(MAT_GetBrowsOfAocols,A,P,0,0));
5536   /* If it is the first time, create an index set of off-diag nonzero columns of A,
5537    *  and then create a submatrix (that often is an overlapping matrix)
5538    * */
5539   if (reuse == MAT_INITIAL_MATRIX) {
5540     /* Use a hash table to figure out unique keys */
5541     PetscCall(PetscHMapICreate(&hamp));
5542     PetscCall(PetscHMapIResize(hamp,a->B->cmap->n));
5543     PetscCall(PetscCalloc1(a->B->cmap->n,&mapping));
5544     count = 0;
5545     /* Assume that  a->g is sorted, otherwise the following does not make sense */
5546     for (i=0;i<a->B->cmap->n;i++) {
5547       key  = a->garray[i]/dof;
5548       PetscCall(PetscHMapIHas(hamp,key,&has));
5549       if (!has) {
5550         mapping[i] = count;
5551         PetscCall(PetscHMapISet(hamp,key,count++));
5552       } else {
5553         /* Current 'i' has the same value the previous step */
5554         mapping[i] = count-1;
5555       }
5556     }
5557     PetscCall(ISCreateGeneral(comm,a->B->cmap->n,mapping,PETSC_OWN_POINTER,&map));
5558     PetscCall(PetscHMapIGetSize(hamp,&htsize));
5559     PetscCheck(htsize==count,comm,PETSC_ERR_ARG_INCOMP," Size of hash map %" PetscInt_FMT " is inconsistent with count %" PetscInt_FMT " ",htsize,count);
5560     PetscCall(PetscCalloc1(htsize,&rowindices));
5561     off = 0;
5562     PetscCall(PetscHMapIGetKeys(hamp,&off,rowindices));
5563     PetscCall(PetscHMapIDestroy(&hamp));
5564     PetscCall(PetscSortInt(htsize,rowindices));
5565     PetscCall(ISCreateGeneral(comm,htsize,rowindices,PETSC_OWN_POINTER,&rows));
5566     /* In case, the matrix was already created but users want to recreate the matrix */
5567     PetscCall(MatDestroy(P_oth));
5568     PetscCall(MatCreateSeqSubMatrixWithRows_Private(P,rows,P_oth));
5569     PetscCall(PetscObjectCompose((PetscObject)*P_oth,"aoffdiagtopothmapping",(PetscObject)map));
5570     PetscCall(ISDestroy(&map));
5571     PetscCall(ISDestroy(&rows));
5572   } else if (reuse == MAT_REUSE_MATRIX) {
5573     /* If matrix was already created, we simply update values using SF objects
5574      * that as attached to the matrix ealier.
5575      */
5576     const PetscScalar *pd_a,*po_a;
5577 
5578     PetscCall(PetscObjectQuery((PetscObject)*P_oth,"diagsf",(PetscObject*)&sf));
5579     PetscCall(PetscObjectQuery((PetscObject)*P_oth,"offdiagsf",(PetscObject*)&osf));
5580     PetscCheck(sf && osf,comm,PETSC_ERR_ARG_NULL,"Matrix is not initialized yet");
5581     p_oth = (Mat_SeqAIJ*) (*P_oth)->data;
5582     /* Update values in place */
5583     PetscCall(MatSeqAIJGetArrayRead(p->A,&pd_a));
5584     PetscCall(MatSeqAIJGetArrayRead(p->B,&po_a));
5585     PetscCall(PetscSFBcastBegin(sf,MPIU_SCALAR,pd_a,p_oth->a,MPI_REPLACE));
5586     PetscCall(PetscSFBcastBegin(osf,MPIU_SCALAR,po_a,p_oth->a,MPI_REPLACE));
5587     PetscCall(PetscSFBcastEnd(sf,MPIU_SCALAR,pd_a,p_oth->a,MPI_REPLACE));
5588     PetscCall(PetscSFBcastEnd(osf,MPIU_SCALAR,po_a,p_oth->a,MPI_REPLACE));
5589     PetscCall(MatSeqAIJRestoreArrayRead(p->A,&pd_a));
5590     PetscCall(MatSeqAIJRestoreArrayRead(p->B,&po_a));
5591   } else SETERRQ(comm,PETSC_ERR_ARG_UNKNOWN_TYPE,"Unknown reuse type");
5592   PetscCall(PetscLogEventEnd(MAT_GetBrowsOfAocols,A,P,0,0));
5593   PetscFunctionReturn(0);
5594 }
5595 
5596 /*@C
5597   MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
5598 
5599   Collective on Mat
5600 
5601   Input Parameters:
5602 + A - the first matrix in mpiaij format
5603 . B - the second matrix in mpiaij format
5604 - scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5605 
5606   Output Parameters:
5607 + rowb - On input index sets of rows of B to extract (or NULL), modified on output
5608 . colb - On input index sets of columns of B to extract (or NULL), modified on output
5609 - B_seq - the sequential matrix generated
5610 
5611   Level: developer
5612 
5613 @*/
5614 PetscErrorCode MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
5615 {
5616   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
5617   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
5618   IS             isrowb,iscolb;
5619   Mat            *bseq=NULL;
5620 
5621   PetscFunctionBegin;
5622   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
5623     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%" PetscInt_FMT ", %" PetscInt_FMT ") != (%" PetscInt_FMT ",%" PetscInt_FMT ")",A->cmap->rstart,A->cmap->rend,B->rmap->rstart,B->rmap->rend);
5624   }
5625   PetscCall(PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0));
5626 
5627   if (scall == MAT_INITIAL_MATRIX) {
5628     start = A->cmap->rstart;
5629     cmap  = a->garray;
5630     nzA   = a->A->cmap->n;
5631     nzB   = a->B->cmap->n;
5632     PetscCall(PetscMalloc1(nzA+nzB, &idx));
5633     ncols = 0;
5634     for (i=0; i<nzB; i++) {  /* row < local row index */
5635       if (cmap[i] < start) idx[ncols++] = cmap[i];
5636       else break;
5637     }
5638     imark = i;
5639     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
5640     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
5641     PetscCall(ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb));
5642     PetscCall(ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb));
5643   } else {
5644     PetscCheck(rowb && colb,PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
5645     isrowb  = *rowb; iscolb = *colb;
5646     PetscCall(PetscMalloc1(1,&bseq));
5647     bseq[0] = *B_seq;
5648   }
5649   PetscCall(MatCreateSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq));
5650   *B_seq = bseq[0];
5651   PetscCall(PetscFree(bseq));
5652   if (!rowb) {
5653     PetscCall(ISDestroy(&isrowb));
5654   } else {
5655     *rowb = isrowb;
5656   }
5657   if (!colb) {
5658     PetscCall(ISDestroy(&iscolb));
5659   } else {
5660     *colb = iscolb;
5661   }
5662   PetscCall(PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0));
5663   PetscFunctionReturn(0);
5664 }
5665 
5666 /*
5667     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
5668     of the OFF-DIAGONAL portion of local A
5669 
5670     Collective on Mat
5671 
5672    Input Parameters:
5673 +    A,B - the matrices in mpiaij format
5674 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5675 
5676    Output Parameter:
5677 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
5678 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
5679 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
5680 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
5681 
5682     Developer Notes: This directly accesses information inside the VecScatter associated with the matrix-vector product
5683      for this matrix. This is not desirable..
5684 
5685     Level: developer
5686 
5687 */
5688 PetscErrorCode MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
5689 {
5690   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
5691   Mat_SeqAIJ             *b_oth;
5692   VecScatter             ctx;
5693   MPI_Comm               comm;
5694   const PetscMPIInt      *rprocs,*sprocs;
5695   const PetscInt         *srow,*rstarts,*sstarts;
5696   PetscInt               *rowlen,*bufj,*bufJ,ncols = 0,aBn=a->B->cmap->n,row,*b_othi,*b_othj,*rvalues=NULL,*svalues=NULL,*cols,sbs,rbs;
5697   PetscInt               i,j,k=0,l,ll,nrecvs,nsends,nrows,*rstartsj = NULL,*sstartsj,len;
5698   PetscScalar            *b_otha,*bufa,*bufA,*vals = NULL;
5699   MPI_Request            *reqs = NULL,*rwaits = NULL,*swaits = NULL;
5700   PetscMPIInt            size,tag,rank,nreqs;
5701 
5702   PetscFunctionBegin;
5703   PetscCall(PetscObjectGetComm((PetscObject)A,&comm));
5704   PetscCallMPI(MPI_Comm_size(comm,&size));
5705 
5706   if (PetscUnlikely(A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend)) {
5707     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%" PetscInt_FMT ", %" PetscInt_FMT ") != (%" PetscInt_FMT ",%" PetscInt_FMT ")",A->cmap->rstart,A->cmap->rend,B->rmap->rstart,B->rmap->rend);
5708   }
5709   PetscCall(PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0));
5710   PetscCallMPI(MPI_Comm_rank(comm,&rank));
5711 
5712   if (size == 1) {
5713     startsj_s = NULL;
5714     bufa_ptr  = NULL;
5715     *B_oth    = NULL;
5716     PetscFunctionReturn(0);
5717   }
5718 
5719   ctx = a->Mvctx;
5720   tag = ((PetscObject)ctx)->tag;
5721 
5722   PetscCall(VecScatterGetRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&srow,&sprocs,&sbs));
5723   /* rprocs[] must be ordered so that indices received from them are ordered in rvalues[], which is key to algorithms used in this subroutine */
5724   PetscCall(VecScatterGetRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL/*indices not needed*/,&rprocs,&rbs));
5725   PetscCall(PetscMPIIntCast(nsends+nrecvs,&nreqs));
5726   PetscCall(PetscMalloc1(nreqs,&reqs));
5727   rwaits = reqs;
5728   swaits = reqs + nrecvs;
5729 
5730   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
5731   if (scall == MAT_INITIAL_MATRIX) {
5732     /* i-array */
5733     /*---------*/
5734     /*  post receives */
5735     if (nrecvs) PetscCall(PetscMalloc1(rbs*(rstarts[nrecvs] - rstarts[0]),&rvalues)); /* rstarts can be NULL when nrecvs=0 */
5736     for (i=0; i<nrecvs; i++) {
5737       rowlen = rvalues + rstarts[i]*rbs;
5738       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
5739       PetscCallMPI(MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i));
5740     }
5741 
5742     /* pack the outgoing message */
5743     PetscCall(PetscMalloc2(nsends+1,&sstartsj,nrecvs+1,&rstartsj));
5744 
5745     sstartsj[0] = 0;
5746     rstartsj[0] = 0;
5747     len         = 0; /* total length of j or a array to be sent */
5748     if (nsends) {
5749       k    = sstarts[0]; /* ATTENTION: sstarts[0] and rstarts[0] are not necessarily zero */
5750       PetscCall(PetscMalloc1(sbs*(sstarts[nsends]-sstarts[0]),&svalues));
5751     }
5752     for (i=0; i<nsends; i++) {
5753       rowlen = svalues + (sstarts[i]-sstarts[0])*sbs;
5754       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
5755       for (j=0; j<nrows; j++) {
5756         row = srow[k] + B->rmap->range[rank]; /* global row idx */
5757         for (l=0; l<sbs; l++) {
5758           PetscCall(MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL)); /* rowlength */
5759 
5760           rowlen[j*sbs+l] = ncols;
5761 
5762           len += ncols;
5763           PetscCall(MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL));
5764         }
5765         k++;
5766       }
5767       PetscCallMPI(MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i));
5768 
5769       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
5770     }
5771     /* recvs and sends of i-array are completed */
5772     if (nreqs) PetscCallMPI(MPI_Waitall(nreqs,reqs,MPI_STATUSES_IGNORE));
5773     PetscCall(PetscFree(svalues));
5774 
5775     /* allocate buffers for sending j and a arrays */
5776     PetscCall(PetscMalloc1(len+1,&bufj));
5777     PetscCall(PetscMalloc1(len+1,&bufa));
5778 
5779     /* create i-array of B_oth */
5780     PetscCall(PetscMalloc1(aBn+2,&b_othi));
5781 
5782     b_othi[0] = 0;
5783     len       = 0; /* total length of j or a array to be received */
5784     k         = 0;
5785     for (i=0; i<nrecvs; i++) {
5786       rowlen = rvalues + (rstarts[i]-rstarts[0])*rbs;
5787       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of rows to be received */
5788       for (j=0; j<nrows; j++) {
5789         b_othi[k+1] = b_othi[k] + rowlen[j];
5790         PetscCall(PetscIntSumError(rowlen[j],len,&len));
5791         k++;
5792       }
5793       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
5794     }
5795     PetscCall(PetscFree(rvalues));
5796 
5797     /* allocate space for j and a arrays of B_oth */
5798     PetscCall(PetscMalloc1(b_othi[aBn]+1,&b_othj));
5799     PetscCall(PetscMalloc1(b_othi[aBn]+1,&b_otha));
5800 
5801     /* j-array */
5802     /*---------*/
5803     /*  post receives of j-array */
5804     for (i=0; i<nrecvs; i++) {
5805       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5806       PetscCallMPI(MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i));
5807     }
5808 
5809     /* pack the outgoing message j-array */
5810     if (nsends) k = sstarts[0];
5811     for (i=0; i<nsends; i++) {
5812       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5813       bufJ  = bufj+sstartsj[i];
5814       for (j=0; j<nrows; j++) {
5815         row = srow[k++] + B->rmap->range[rank];  /* global row idx */
5816         for (ll=0; ll<sbs; ll++) {
5817           PetscCall(MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL));
5818           for (l=0; l<ncols; l++) {
5819             *bufJ++ = cols[l];
5820           }
5821           PetscCall(MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL));
5822         }
5823       }
5824       PetscCallMPI(MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i));
5825     }
5826 
5827     /* recvs and sends of j-array are completed */
5828     if (nreqs) PetscCallMPI(MPI_Waitall(nreqs,reqs,MPI_STATUSES_IGNORE));
5829   } else if (scall == MAT_REUSE_MATRIX) {
5830     sstartsj = *startsj_s;
5831     rstartsj = *startsj_r;
5832     bufa     = *bufa_ptr;
5833     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
5834     PetscCall(MatSeqAIJGetArrayWrite(*B_oth,&b_otha));
5835   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not possess an object container");
5836 
5837   /* a-array */
5838   /*---------*/
5839   /*  post receives of a-array */
5840   for (i=0; i<nrecvs; i++) {
5841     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5842     PetscCallMPI(MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i));
5843   }
5844 
5845   /* pack the outgoing message a-array */
5846   if (nsends) k = sstarts[0];
5847   for (i=0; i<nsends; i++) {
5848     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5849     bufA  = bufa+sstartsj[i];
5850     for (j=0; j<nrows; j++) {
5851       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
5852       for (ll=0; ll<sbs; ll++) {
5853         PetscCall(MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals));
5854         for (l=0; l<ncols; l++) {
5855           *bufA++ = vals[l];
5856         }
5857         PetscCall(MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals));
5858       }
5859     }
5860     PetscCallMPI(MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i));
5861   }
5862   /* recvs and sends of a-array are completed */
5863   if (nreqs) PetscCallMPI(MPI_Waitall(nreqs,reqs,MPI_STATUSES_IGNORE));
5864   PetscCall(PetscFree(reqs));
5865 
5866   if (scall == MAT_INITIAL_MATRIX) {
5867     /* put together the new matrix */
5868     PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth));
5869 
5870     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
5871     /* Since these are PETSc arrays, change flags to free them as necessary. */
5872     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
5873     b_oth->free_a  = PETSC_TRUE;
5874     b_oth->free_ij = PETSC_TRUE;
5875     b_oth->nonew   = 0;
5876 
5877     PetscCall(PetscFree(bufj));
5878     if (!startsj_s || !bufa_ptr) {
5879       PetscCall(PetscFree2(sstartsj,rstartsj));
5880       PetscCall(PetscFree(bufa_ptr));
5881     } else {
5882       *startsj_s = sstartsj;
5883       *startsj_r = rstartsj;
5884       *bufa_ptr  = bufa;
5885     }
5886   } else if (scall == MAT_REUSE_MATRIX) {
5887     PetscCall(MatSeqAIJRestoreArrayWrite(*B_oth,&b_otha));
5888   }
5889 
5890   PetscCall(VecScatterRestoreRemote_Private(ctx,PETSC_TRUE,&nsends,&sstarts,&srow,&sprocs,&sbs));
5891   PetscCall(VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE,&nrecvs,&rstarts,NULL,&rprocs,&rbs));
5892   PetscCall(PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0));
5893   PetscFunctionReturn(0);
5894 }
5895 
5896 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
5897 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
5898 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJSELL(Mat,MatType,MatReuse,Mat*);
5899 #if defined(PETSC_HAVE_MKL_SPARSE)
5900 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJMKL(Mat,MatType,MatReuse,Mat*);
5901 #endif
5902 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIBAIJ(Mat,MatType,MatReuse,Mat*);
5903 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
5904 #if defined(PETSC_HAVE_ELEMENTAL)
5905 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
5906 #endif
5907 #if defined(PETSC_HAVE_SCALAPACK)
5908 PETSC_INTERN PetscErrorCode MatConvert_AIJ_ScaLAPACK(Mat,MatType,MatReuse,Mat*);
5909 #endif
5910 #if defined(PETSC_HAVE_HYPRE)
5911 PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat,MatType,MatReuse,Mat*);
5912 #endif
5913 #if defined(PETSC_HAVE_CUDA)
5914 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCUSPARSE(Mat,MatType,MatReuse,Mat*);
5915 #endif
5916 #if defined(PETSC_HAVE_KOKKOS_KERNELS)
5917 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJKokkos(Mat,MatType,MatReuse,Mat*);
5918 #endif
5919 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPISELL(Mat,MatType,MatReuse,Mat*);
5920 PETSC_INTERN PetscErrorCode MatConvert_XAIJ_IS(Mat,MatType,MatReuse,Mat*);
5921 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_IS_XAIJ(Mat);
5922 
5923 /*
5924     Computes (B'*A')' since computing B*A directly is untenable
5925 
5926                n                       p                          p
5927         [             ]       [             ]         [                 ]
5928       m [      A      ]  *  n [       B     ]   =   m [         C       ]
5929         [             ]       [             ]         [                 ]
5930 
5931 */
5932 static PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
5933 {
5934   Mat            At,Bt,Ct;
5935 
5936   PetscFunctionBegin;
5937   PetscCall(MatTranspose(A,MAT_INITIAL_MATRIX,&At));
5938   PetscCall(MatTranspose(B,MAT_INITIAL_MATRIX,&Bt));
5939   PetscCall(MatMatMult(Bt,At,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&Ct));
5940   PetscCall(MatDestroy(&At));
5941   PetscCall(MatDestroy(&Bt));
5942   PetscCall(MatTranspose(Ct,MAT_REUSE_MATRIX,&C));
5943   PetscCall(MatDestroy(&Ct));
5944   PetscFunctionReturn(0);
5945 }
5946 
5947 static PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat C)
5948 {
5949   PetscBool      cisdense;
5950 
5951   PetscFunctionBegin;
5952   PetscCheck(A->cmap->n == B->rmap->n,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"A->cmap->n %" PetscInt_FMT " != B->rmap->n %" PetscInt_FMT,A->cmap->n,B->rmap->n);
5953   PetscCall(MatSetSizes(C,A->rmap->n,B->cmap->n,A->rmap->N,B->cmap->N));
5954   PetscCall(MatSetBlockSizesFromMats(C,A,B));
5955   PetscCall(PetscObjectTypeCompareAny((PetscObject)C,&cisdense,MATMPIDENSE,MATMPIDENSECUDA,""));
5956   if (!cisdense) {
5957     PetscCall(MatSetType(C,((PetscObject)A)->type_name));
5958   }
5959   PetscCall(MatSetUp(C));
5960 
5961   C->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
5962   PetscFunctionReturn(0);
5963 }
5964 
5965 /* ----------------------------------------------------------------*/
5966 static PetscErrorCode MatProductSetFromOptions_MPIDense_MPIAIJ_AB(Mat C)
5967 {
5968   Mat_Product *product = C->product;
5969   Mat         A = product->A,B=product->B;
5970 
5971   PetscFunctionBegin;
5972   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend)
5973     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%" PetscInt_FMT ", %" PetscInt_FMT ") != (%" PetscInt_FMT ",%" PetscInt_FMT ")",A->cmap->rstart,A->cmap->rend,B->rmap->rstart,B->rmap->rend);
5974 
5975   C->ops->matmultsymbolic = MatMatMultSymbolic_MPIDense_MPIAIJ;
5976   C->ops->productsymbolic = MatProductSymbolic_AB;
5977   PetscFunctionReturn(0);
5978 }
5979 
5980 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIDense_MPIAIJ(Mat C)
5981 {
5982   Mat_Product    *product = C->product;
5983 
5984   PetscFunctionBegin;
5985   if (product->type == MATPRODUCT_AB) {
5986     PetscCall(MatProductSetFromOptions_MPIDense_MPIAIJ_AB(C));
5987   }
5988   PetscFunctionReturn(0);
5989 }
5990 
5991 /* Merge two sets of sorted nonzeros and return a CSR for the merged (sequential) matrix
5992 
5993   Input Parameters:
5994 
5995     j1,rowBegin1,rowEnd1,perm1,jmap1: describe the first set of nonzeros (Set1)
5996     j2,rowBegin2,rowEnd2,perm2,jmap2: describe the second set of nonzeros (Set2)
5997 
5998     mat: both sets' nonzeros are on m rows, where m is the number of local rows of the matrix mat
5999 
6000     For Set1, j1[] contains column indices of the nonzeros.
6001     For the k-th row (0<=k<m), [rowBegin1[k],rowEnd1[k]) index into j1[] and point to the begin/end nonzero in row k
6002     respectively (note rowEnd1[k] is not necessarily equal to rwoBegin1[k+1]). Indices in this range of j1[] are sorted,
6003     but might have repeats. jmap1[t+1] - jmap1[t] is the number of repeats for the t-th unique nonzero in Set1.
6004 
6005     Similar for Set2.
6006 
6007     This routine merges the two sets of nonzeros row by row and removes repeats.
6008 
6009   Output Parameters: (memory is allocated by the caller)
6010 
6011     i[],j[]: the CSR of the merged matrix, which has m rows.
6012     imap1[]: the k-th unique nonzero in Set1 (k=0,1,...) corresponds to imap1[k]-th unique nonzero in the merged matrix.
6013     imap2[]: similar to imap1[], but for Set2.
6014     Note we order nonzeros row-by-row and from left to right.
6015 */
6016 static PetscErrorCode MatMergeEntries_Internal(Mat mat,const PetscInt j1[],const PetscInt j2[],const PetscCount rowBegin1[],const PetscCount rowEnd1[],
6017   const PetscCount rowBegin2[],const PetscCount rowEnd2[],const PetscCount jmap1[],const PetscCount jmap2[],
6018   PetscCount imap1[],PetscCount imap2[],PetscInt i[],PetscInt j[])
6019 {
6020   PetscInt       r,m; /* Row index of mat */
6021   PetscCount     t,t1,t2,b1,e1,b2,e2;
6022 
6023   PetscFunctionBegin;
6024   PetscCall(MatGetLocalSize(mat,&m,NULL));
6025   t1   = t2 = t = 0; /* Count unique nonzeros of in Set1, Set1 and the merged respectively */
6026   i[0] = 0;
6027   for (r=0; r<m; r++) { /* Do row by row merging */
6028     b1   = rowBegin1[r];
6029     e1   = rowEnd1[r];
6030     b2   = rowBegin2[r];
6031     e2   = rowEnd2[r];
6032     while (b1 < e1 && b2 < e2) {
6033       if (j1[b1] == j2[b2]) { /* Same column index and hence same nonzero */
6034         j[t]      = j1[b1];
6035         imap1[t1] = t;
6036         imap2[t2] = t;
6037         b1       += jmap1[t1+1] - jmap1[t1]; /* Jump to next unique local nonzero */
6038         b2       += jmap2[t2+1] - jmap2[t2]; /* Jump to next unique remote nonzero */
6039         t1++; t2++; t++;
6040       } else if (j1[b1] < j2[b2]) {
6041         j[t]      = j1[b1];
6042         imap1[t1] = t;
6043         b1       += jmap1[t1+1] - jmap1[t1];
6044         t1++; t++;
6045       } else {
6046         j[t]      = j2[b2];
6047         imap2[t2] = t;
6048         b2       += jmap2[t2+1] - jmap2[t2];
6049         t2++; t++;
6050       }
6051     }
6052     /* Merge the remaining in either j1[] or j2[] */
6053     while (b1 < e1) {
6054       j[t]      = j1[b1];
6055       imap1[t1] = t;
6056       b1       += jmap1[t1+1] - jmap1[t1];
6057       t1++; t++;
6058     }
6059     while (b2 < e2) {
6060       j[t]      = j2[b2];
6061       imap2[t2] = t;
6062       b2       += jmap2[t2+1] - jmap2[t2];
6063       t2++; t++;
6064     }
6065     i[r+1] = t;
6066   }
6067   PetscFunctionReturn(0);
6068 }
6069 
6070 /* Split nonzeros in a block of local rows into two subsets: those in the diagonal block and those in the off-diagonal block
6071 
6072   Input Parameters:
6073     mat: an MPI matrix that provides row and column layout information for splitting. Let's say its number of local rows is m.
6074     n,i[],j[],perm[]: there are n input entries, belonging to m rows. Row/col indices of the entries are stored in i[] and j[]
6075       respectively, along with a permutation array perm[]. Length of the i[],j[],perm[] arrays is n.
6076 
6077       i[] is already sorted, but within a row, j[] is not sorted and might have repeats.
6078       i[] might contain negative indices at the beginning, which means the corresponding entries should be ignored in the splitting.
6079 
6080   Output Parameters:
6081     j[],perm[]: the routine needs to sort j[] within each row along with perm[].
6082     rowBegin[],rowMid[],rowEnd[]: of length m, and the memory is preallocated and zeroed by the caller.
6083       They contain indices pointing to j[]. For 0<=r<m, [rowBegin[r],rowMid[r]) point to begin/end entries of row r of the diagonal block,
6084       and [rowMid[r],rowEnd[r]) point to begin/end entries of row r of the off-diagonal block.
6085 
6086     Aperm[],Ajmap[],Atot,Annz: Arrays are allocated by this routine.
6087       Atot: number of entries belonging to the diagonal block.
6088       Annz: number of unique nonzeros belonging to the diagonal block.
6089       Aperm[Atot] stores values from perm[] for entries belonging to the diagonal block. Length of Aperm[] is Atot, though it may also count
6090         repeats (i.e., same 'i,j' pair).
6091       Ajmap[Annz+1] stores the number of repeats of each unique entry belonging to the diagonal block. More precisely, Ajmap[t+1] - Ajmap[t]
6092         is the number of repeats for the t-th unique entry in the diagonal block. Ajmap[0] is always 0.
6093 
6094       Atot: number of entries belonging to the diagonal block
6095       Annz: number of unique nonzeros belonging to the diagonal block.
6096 
6097     Bperm[], Bjmap[], Btot, Bnnz are similar but for the off-diagonal block.
6098 
6099     Aperm[],Bperm[],Ajmap[] and Bjmap[] are allocated separately by this routine with PetscMalloc1().
6100 */
6101 static PetscErrorCode MatSplitEntries_Internal(Mat mat,PetscCount n,const PetscInt i[],PetscInt j[],
6102   PetscCount perm[],PetscCount rowBegin[],PetscCount rowMid[],PetscCount rowEnd[],
6103   PetscCount *Atot_,PetscCount **Aperm_,PetscCount *Annz_,PetscCount **Ajmap_,
6104   PetscCount *Btot_,PetscCount **Bperm_,PetscCount *Bnnz_,PetscCount **Bjmap_)
6105 {
6106   PetscInt          cstart,cend,rstart,rend,row,col;
6107   PetscCount        Atot=0,Btot=0; /* Total number of nonzeros in the diagonal and off-diagonal blocks */
6108   PetscCount        Annz=0,Bnnz=0; /* Number of unique nonzeros in the diagonal and off-diagonal blocks */
6109   PetscCount        k,m,p,q,r,s,mid;
6110   PetscCount        *Aperm,*Bperm,*Ajmap,*Bjmap;
6111 
6112   PetscFunctionBegin;
6113   PetscCall(PetscLayoutGetRange(mat->rmap,&rstart,&rend));
6114   PetscCall(PetscLayoutGetRange(mat->cmap,&cstart,&cend));
6115   m    = rend - rstart;
6116 
6117   for (k=0; k<n; k++) {if (i[k]>=0) break;} /* Skip negative rows */
6118 
6119   /* Process [k,n): sort and partition each local row into diag and offdiag portions,
6120      fill rowBegin[], rowMid[], rowEnd[], and count Atot, Btot, Annz, Bnnz.
6121   */
6122   while (k<n) {
6123     row = i[k];
6124     /* Entries in [k,s) are in one row. Shift diagonal block col indices so that diag is ahead of offdiag after sorting the row */
6125     for (s=k; s<n; s++) if (i[s] != row) break;
6126     for (p=k; p<s; p++) {
6127       if (j[p] >= cstart && j[p] < cend) j[p] -= PETSC_MAX_INT; /* Shift diag columns to range of [-PETSC_MAX_INT, -1]  */
6128       else PetscAssert((j[p] >= 0) && (j[p] <= mat->cmap->N),PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column index %" PetscInt_FMT " is out of range",j[p]);
6129     }
6130     PetscCall(PetscSortIntWithCountArray(s-k,j+k,perm+k));
6131     PetscCall(PetscSortedIntUpperBound(j,k,s,-1,&mid)); /* Separate [k,s) into [k,mid) for diag and [mid,s) for offdiag */
6132     rowBegin[row-rstart] = k;
6133     rowMid[row-rstart]   = mid;
6134     rowEnd[row-rstart]   = s;
6135 
6136     /* Count nonzeros of this diag/offdiag row, which might have repeats */
6137     Atot += mid - k;
6138     Btot += s - mid;
6139 
6140     /* Count unique nonzeros of this diag/offdiag row */
6141     for (p=k; p<mid;) {
6142       col = j[p];
6143       do {j[p] += PETSC_MAX_INT; p++;} while (p<mid && j[p] == col); /* Revert the modified diagonal indices */
6144       Annz++;
6145     }
6146 
6147     for (p=mid; p<s;) {
6148       col = j[p];
6149       do {p++;} while (p<s && j[p] == col);
6150       Bnnz++;
6151     }
6152     k = s;
6153   }
6154 
6155   /* Allocation according to Atot, Btot, Annz, Bnnz */
6156   PetscCall(PetscMalloc1(Atot,&Aperm));
6157   PetscCall(PetscMalloc1(Btot,&Bperm));
6158   PetscCall(PetscMalloc1(Annz+1,&Ajmap));
6159   PetscCall(PetscMalloc1(Bnnz+1,&Bjmap));
6160 
6161   /* Re-scan indices and copy diag/offdiag permutation indices to Aperm, Bperm and also fill Ajmap and Bjmap */
6162   Ajmap[0] = Bjmap[0] = Atot = Btot = Annz = Bnnz = 0;
6163   for (r=0; r<m; r++) {
6164     k     = rowBegin[r];
6165     mid   = rowMid[r];
6166     s     = rowEnd[r];
6167     PetscCall(PetscArraycpy(Aperm+Atot,perm+k,  mid-k));
6168     PetscCall(PetscArraycpy(Bperm+Btot,perm+mid,s-mid));
6169     Atot += mid - k;
6170     Btot += s - mid;
6171 
6172     /* Scan column indices in this row and find out how many repeats each unique nonzero has */
6173     for (p=k; p<mid;) {
6174       col = j[p];
6175       q   = p;
6176       do {p++;} while (p<mid && j[p] == col);
6177       Ajmap[Annz+1] = Ajmap[Annz] + (p - q);
6178       Annz++;
6179     }
6180 
6181     for (p=mid; p<s;) {
6182       col = j[p];
6183       q   = p;
6184       do {p++;} while (p<s && j[p] == col);
6185       Bjmap[Bnnz+1] = Bjmap[Bnnz] + (p - q);
6186       Bnnz++;
6187     }
6188   }
6189   /* Output */
6190   *Aperm_ = Aperm;
6191   *Annz_  = Annz;
6192   *Atot_  = Atot;
6193   *Ajmap_ = Ajmap;
6194   *Bperm_ = Bperm;
6195   *Bnnz_  = Bnnz;
6196   *Btot_  = Btot;
6197   *Bjmap_ = Bjmap;
6198   PetscFunctionReturn(0);
6199 }
6200 
6201 /* Expand the jmap[] array to make a new one in view of nonzeros in the merged matrix
6202 
6203   Input Parameters:
6204     nnz1: number of unique nonzeros in a set that was used to produce imap[], jmap[]
6205     nnz:  number of unique nonzeros in the merged matrix
6206     imap[nnz1]: i-th nonzero in the set is the imap[i]-th nonzero in the merged matrix
6207     jmap[nnz1+1]: i-th nonzeron in the set has jmap[i+1] - jmap[i] repeats in the set
6208 
6209   Output Parameter: (memory is allocated by the caller)
6210     jmap_new[nnz+1]: i-th nonzero in the merged matrix has jmap_new[i+1] - jmap_new[i] repeats in the set
6211 
6212   Example:
6213     nnz1 = 4
6214     nnz  = 6
6215     imap = [1,3,4,5]
6216     jmap = [0,3,5,6,7]
6217    then,
6218     jmap_new = [0,0,3,3,5,6,7]
6219 */
6220 static PetscErrorCode ExpandJmap_Internal(PetscCount nnz1,PetscCount nnz,const PetscCount imap[],const PetscCount jmap[],PetscCount jmap_new[])
6221 {
6222   PetscCount k,p;
6223 
6224   PetscFunctionBegin;
6225   jmap_new[0] = 0;
6226   p = nnz; /* p loops over jmap_new[] backwards */
6227   for (k=nnz1-1; k>=0; k--) { /* k loops over imap[] */
6228     for (; p > imap[k]; p--) jmap_new[p] = jmap[k+1];
6229   }
6230   for (; p >= 0; p--) jmap_new[p] = jmap[0];
6231   PetscFunctionReturn(0);
6232 }
6233 
6234 PetscErrorCode MatSetPreallocationCOO_MPIAIJ(Mat mat, PetscCount coo_n, const PetscInt coo_i[], const PetscInt coo_j[])
6235 {
6236   MPI_Comm                  comm;
6237   PetscMPIInt               rank,size;
6238   PetscInt                  m,n,M,N,rstart,rend,cstart,cend; /* Sizes, indices of row/col, therefore with type PetscInt */
6239   PetscCount                k,p,q,rem; /* Loop variables over coo arrays */
6240   Mat_MPIAIJ                *mpiaij = (Mat_MPIAIJ*)mat->data;
6241 
6242   PetscFunctionBegin;
6243   PetscCall(PetscFree(mpiaij->garray));
6244   PetscCall(VecDestroy(&mpiaij->lvec));
6245 #if defined(PETSC_USE_CTABLE)
6246   PetscCall(PetscTableDestroy(&mpiaij->colmap));
6247 #else
6248   PetscCall(PetscFree(mpiaij->colmap));
6249 #endif
6250   PetscCall(VecScatterDestroy(&mpiaij->Mvctx));
6251   mat->assembled = PETSC_FALSE;
6252   mat->was_assembled = PETSC_FALSE;
6253   PetscCall(MatResetPreallocationCOO_MPIAIJ(mat));
6254 
6255   PetscCall(PetscObjectGetComm((PetscObject)mat,&comm));
6256   PetscCallMPI(MPI_Comm_size(comm,&size));
6257   PetscCallMPI(MPI_Comm_rank(comm,&rank));
6258   PetscCall(PetscLayoutSetUp(mat->rmap));
6259   PetscCall(PetscLayoutSetUp(mat->cmap));
6260   PetscCall(PetscLayoutGetRange(mat->rmap,&rstart,&rend));
6261   PetscCall(PetscLayoutGetRange(mat->cmap,&cstart,&cend));
6262   PetscCall(MatGetLocalSize(mat,&m,&n));
6263   PetscCall(MatGetSize(mat,&M,&N));
6264 
6265   /* ---------------------------------------------------------------------------*/
6266   /* Sort (i,j) by row along with a permutation array, so that the to-be-ignored */
6267   /* entries come first, then local rows, then remote rows.                     */
6268   /* ---------------------------------------------------------------------------*/
6269   PetscCount n1 = coo_n,*perm1;
6270   PetscInt   *i1,*j1; /* Copies of input COOs along with a permutation array */
6271   PetscCall(PetscMalloc3(n1,&i1,n1,&j1,n1,&perm1));
6272   PetscCall(PetscArraycpy(i1,coo_i,n1)); /* Make a copy since we'll modify it */
6273   PetscCall(PetscArraycpy(j1,coo_j,n1));
6274   for (k=0; k<n1; k++) perm1[k] = k;
6275 
6276   /* Manipulate indices so that entries with negative row or col indices will have smallest
6277      row indices, local entries will have greater but negative row indices, and remote entries
6278      will have positive row indices.
6279   */
6280   for (k=0; k<n1; k++) {
6281     if (i1[k] < 0 || j1[k] < 0) i1[k] = PETSC_MIN_INT; /* e.g., -2^31, minimal to move them ahead */
6282     else if (i1[k] >= rstart && i1[k] < rend) i1[k] -= PETSC_MAX_INT; /* e.g., minus 2^31-1 to shift local rows to range of [-PETSC_MAX_INT, -1] */
6283     else {
6284       PetscCheck(!mat->nooffprocentries,PETSC_COMM_SELF,PETSC_ERR_USER_INPUT,"MAT_NO_OFF_PROC_ENTRIES is set but insert to remote rows");
6285       if (mpiaij->donotstash) i1[k] = PETSC_MIN_INT; /* Ignore offproc entries as if they had negative indices */
6286     }
6287   }
6288 
6289   /* Sort by row; after that, [0,k) have ignored entires, [k,rem) have local rows and [rem,n1) have remote rows */
6290   PetscCall(PetscSortIntWithIntCountArrayPair(n1,i1,j1,perm1));
6291   for (k=0; k<n1; k++) {if (i1[k] > PETSC_MIN_INT) break;} /* Advance k to the first entry we need to take care of */
6292   PetscCall(PetscSortedIntUpperBound(i1,k,n1,rend-1-PETSC_MAX_INT,&rem)); /* rem is upper bound of the last local row */
6293   for (; k<rem; k++) i1[k] += PETSC_MAX_INT; /* Revert row indices of local rows*/
6294 
6295   /* ---------------------------------------------------------------------------*/
6296   /*           Split local rows into diag/offdiag portions                      */
6297   /* ---------------------------------------------------------------------------*/
6298   PetscCount   *rowBegin1,*rowMid1,*rowEnd1;
6299   PetscCount   *Ajmap1,*Aperm1,*Bjmap1,*Bperm1,*Cperm1;
6300   PetscCount   Annz1,Bnnz1,Atot1,Btot1;
6301 
6302   PetscCall(PetscCalloc3(m,&rowBegin1,m,&rowMid1,m,&rowEnd1));
6303   PetscCall(PetscMalloc1(n1-rem,&Cperm1));
6304   PetscCall(MatSplitEntries_Internal(mat,rem,i1,j1,perm1,rowBegin1,rowMid1,rowEnd1,&Atot1,&Aperm1,&Annz1,&Ajmap1,&Btot1,&Bperm1,&Bnnz1,&Bjmap1));
6305 
6306   /* ---------------------------------------------------------------------------*/
6307   /*           Send remote rows to their owner                                  */
6308   /* ---------------------------------------------------------------------------*/
6309   /* Find which rows should be sent to which remote ranks*/
6310   PetscInt       nsend = 0; /* Number of MPI ranks to send data to */
6311   PetscMPIInt    *sendto; /* [nsend], storing remote ranks */
6312   PetscInt       *nentries; /* [nsend], storing number of entries sent to remote ranks; Assume PetscInt is big enough for this count, and error if not */
6313   const PetscInt *ranges;
6314   PetscInt       maxNsend = size >= 128? 128 : size; /* Assume max 128 neighbors; realloc when needed */
6315 
6316   PetscCall(PetscLayoutGetRanges(mat->rmap,&ranges));
6317   PetscCall(PetscMalloc2(maxNsend,&sendto,maxNsend,&nentries));
6318   for (k=rem; k<n1;) {
6319     PetscMPIInt  owner;
6320     PetscInt     firstRow,lastRow;
6321 
6322     /* Locate a row range */
6323     firstRow = i1[k]; /* first row of this owner */
6324     PetscCall(PetscLayoutFindOwner(mat->rmap,firstRow,&owner));
6325     lastRow  = ranges[owner+1]-1; /* last row of this owner */
6326 
6327     /* Find the first index 'p' in [k,n) with i[p] belonging to next owner */
6328     PetscCall(PetscSortedIntUpperBound(i1,k,n1,lastRow,&p));
6329 
6330     /* All entries in [k,p) belong to this remote owner */
6331     if (nsend >= maxNsend) { /* Double the remote ranks arrays if not long enough */
6332       PetscMPIInt *sendto2;
6333       PetscInt    *nentries2;
6334       PetscInt    maxNsend2 = (maxNsend <= size/2) ? maxNsend*2 : size;
6335 
6336       PetscCall(PetscMalloc2(maxNsend2,&sendto2,maxNsend2,&nentries2));
6337       PetscCall(PetscArraycpy(sendto2,sendto,maxNsend));
6338       PetscCall(PetscArraycpy(nentries2,nentries2,maxNsend+1));
6339       PetscCall(PetscFree2(sendto,nentries2));
6340       sendto      = sendto2;
6341       nentries    = nentries2;
6342       maxNsend    = maxNsend2;
6343     }
6344     sendto[nsend]   = owner;
6345     nentries[nsend] = p - k;
6346     PetscCall(PetscCountCast(p-k,&nentries[nsend]));
6347     nsend++;
6348     k = p;
6349   }
6350 
6351   /* Build 1st SF to know offsets on remote to send data */
6352   PetscSF     sf1;
6353   PetscInt    nroots = 1,nroots2 = 0;
6354   PetscInt    nleaves = nsend,nleaves2 = 0;
6355   PetscInt    *offsets;
6356   PetscSFNode *iremote;
6357 
6358   PetscCall(PetscSFCreate(comm,&sf1));
6359   PetscCall(PetscMalloc1(nsend,&iremote));
6360   PetscCall(PetscMalloc1(nsend,&offsets));
6361   for (k=0; k<nsend; k++) {
6362     iremote[k].rank  = sendto[k];
6363     iremote[k].index = 0;
6364     nleaves2        += nentries[k];
6365     PetscCheck(nleaves2 >= 0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Number of SF leaves is too large for PetscInt");
6366   }
6367   PetscCall(PetscSFSetGraph(sf1,nroots,nleaves,NULL,PETSC_OWN_POINTER,iremote,PETSC_OWN_POINTER));
6368   PetscCall(PetscSFFetchAndOpWithMemTypeBegin(sf1,MPIU_INT,PETSC_MEMTYPE_HOST,&nroots2/*rootdata*/,PETSC_MEMTYPE_HOST,nentries/*leafdata*/,PETSC_MEMTYPE_HOST,offsets/*leafupdate*/,MPI_SUM));
6369   PetscCall(PetscSFFetchAndOpEnd(sf1,MPIU_INT,&nroots2,nentries,offsets,MPI_SUM)); /* Would nroots2 overflow, we check offsets[] below */
6370   PetscCall(PetscSFDestroy(&sf1));
6371   PetscAssert(nleaves2 == n1-rem,PETSC_COMM_SELF,PETSC_ERR_PLIB,"nleaves2 %" PetscInt_FMT " != number of remote entries %" PetscCount_FMT "",nleaves2,n1-rem);
6372 
6373   /* Build 2nd SF to send remote COOs to their owner */
6374   PetscSF sf2;
6375   nroots  = nroots2;
6376   nleaves = nleaves2;
6377   PetscCall(PetscSFCreate(comm,&sf2));
6378   PetscCall(PetscSFSetFromOptions(sf2));
6379   PetscCall(PetscMalloc1(nleaves,&iremote));
6380   p       = 0;
6381   for (k=0; k<nsend; k++) {
6382     PetscCheck(offsets[k] >= 0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Number of SF roots is too large for PetscInt");
6383     for (q=0; q<nentries[k]; q++,p++) {
6384       iremote[p].rank  = sendto[k];
6385       iremote[p].index = offsets[k] + q;
6386     }
6387   }
6388   PetscCall(PetscSFSetGraph(sf2,nroots,nleaves,NULL,PETSC_OWN_POINTER,iremote,PETSC_OWN_POINTER));
6389 
6390   /* sf2 only sends contiguous leafdata to contiguous rootdata. We record the permutation which will be used to fill leafdata */
6391   PetscCall(PetscArraycpy(Cperm1,perm1+rem,n1-rem));
6392 
6393   /* Send the remote COOs to their owner */
6394   PetscInt   n2 = nroots,*i2,*j2; /* Buffers for received COOs from other ranks, along with a permutation array */
6395   PetscCount *perm2; /* Though PetscInt is enough for remote entries, we use PetscCount here as we want to reuse MatSplitEntries_Internal() */
6396   PetscCall(PetscMalloc3(n2,&i2,n2,&j2,n2,&perm2));
6397   PetscCall(PetscSFReduceWithMemTypeBegin(sf2,MPIU_INT,PETSC_MEMTYPE_HOST,i1+rem,PETSC_MEMTYPE_HOST,i2,MPI_REPLACE));
6398   PetscCall(PetscSFReduceEnd(sf2,MPIU_INT,i1+rem,i2,MPI_REPLACE));
6399   PetscCall(PetscSFReduceWithMemTypeBegin(sf2,MPIU_INT,PETSC_MEMTYPE_HOST,j1+rem,PETSC_MEMTYPE_HOST,j2,MPI_REPLACE));
6400   PetscCall(PetscSFReduceEnd(sf2,MPIU_INT,j1+rem,j2,MPI_REPLACE));
6401 
6402   PetscCall(PetscFree(offsets));
6403   PetscCall(PetscFree2(sendto,nentries));
6404 
6405   /* ---------------------------------------------------------------*/
6406   /* Sort received COOs by row along with the permutation array     */
6407   /* ---------------------------------------------------------------*/
6408   for (k=0; k<n2; k++) perm2[k] = k;
6409   PetscCall(PetscSortIntWithIntCountArrayPair(n2,i2,j2,perm2));
6410 
6411   /* ---------------------------------------------------------------*/
6412   /* Split received COOs into diag/offdiag portions                 */
6413   /* ---------------------------------------------------------------*/
6414   PetscCount  *rowBegin2,*rowMid2,*rowEnd2;
6415   PetscCount  *Ajmap2,*Aperm2,*Bjmap2,*Bperm2;
6416   PetscCount  Annz2,Bnnz2,Atot2,Btot2;
6417 
6418   PetscCall(PetscCalloc3(m,&rowBegin2,m,&rowMid2,m,&rowEnd2));
6419   PetscCall(MatSplitEntries_Internal(mat,n2,i2,j2,perm2,rowBegin2,rowMid2,rowEnd2,&Atot2,&Aperm2,&Annz2,&Ajmap2,&Btot2,&Bperm2,&Bnnz2,&Bjmap2));
6420 
6421   /* --------------------------------------------------------------------------*/
6422   /* Merge local COOs with received COOs: diag with diag, offdiag with offdiag */
6423   /* --------------------------------------------------------------------------*/
6424   PetscInt   *Ai,*Bi;
6425   PetscInt   *Aj,*Bj;
6426 
6427   PetscCall(PetscMalloc1(m+1,&Ai));
6428   PetscCall(PetscMalloc1(m+1,&Bi));
6429   PetscCall(PetscMalloc1(Annz1+Annz2,&Aj)); /* Since local and remote entries might have dups, we might allocate excess memory */
6430   PetscCall(PetscMalloc1(Bnnz1+Bnnz2,&Bj));
6431 
6432   PetscCount *Aimap1,*Bimap1,*Aimap2,*Bimap2;
6433   PetscCall(PetscMalloc1(Annz1,&Aimap1));
6434   PetscCall(PetscMalloc1(Bnnz1,&Bimap1));
6435   PetscCall(PetscMalloc1(Annz2,&Aimap2));
6436   PetscCall(PetscMalloc1(Bnnz2,&Bimap2));
6437 
6438   PetscCall(MatMergeEntries_Internal(mat,j1,j2,rowBegin1,rowMid1,rowBegin2,rowMid2,Ajmap1,Ajmap2,Aimap1,Aimap2,Ai,Aj));
6439   PetscCall(MatMergeEntries_Internal(mat,j1,j2,rowMid1,  rowEnd1,rowMid2,  rowEnd2,Bjmap1,Bjmap2,Bimap1,Bimap2,Bi,Bj));
6440 
6441   /* --------------------------------------------------------------------------*/
6442   /* Expand Ajmap1/Bjmap1 to make them based off nonzeros in A/B, since we     */
6443   /* expect nonzeros in A/B most likely have local contributing entries        */
6444   /* --------------------------------------------------------------------------*/
6445   PetscInt Annz = Ai[m];
6446   PetscInt Bnnz = Bi[m];
6447   PetscCount *Ajmap1_new,*Bjmap1_new;
6448 
6449   PetscCall(PetscMalloc1(Annz+1,&Ajmap1_new));
6450   PetscCall(PetscMalloc1(Bnnz+1,&Bjmap1_new));
6451 
6452   PetscCall(ExpandJmap_Internal(Annz1,Annz,Aimap1,Ajmap1,Ajmap1_new));
6453   PetscCall(ExpandJmap_Internal(Bnnz1,Bnnz,Bimap1,Bjmap1,Bjmap1_new));
6454 
6455   PetscCall(PetscFree(Aimap1));
6456   PetscCall(PetscFree(Ajmap1));
6457   PetscCall(PetscFree(Bimap1));
6458   PetscCall(PetscFree(Bjmap1));
6459   PetscCall(PetscFree3(rowBegin1,rowMid1,rowEnd1));
6460   PetscCall(PetscFree3(rowBegin2,rowMid2,rowEnd2));
6461   PetscCall(PetscFree3(i1,j1,perm1));
6462   PetscCall(PetscFree3(i2,j2,perm2));
6463 
6464   Ajmap1 = Ajmap1_new;
6465   Bjmap1 = Bjmap1_new;
6466 
6467   /* Reallocate Aj, Bj once we know actual numbers of unique nonzeros in A and B */
6468   if (Annz < Annz1 + Annz2) {
6469     PetscInt *Aj_new;
6470     PetscCall(PetscMalloc1(Annz,&Aj_new));
6471     PetscCall(PetscArraycpy(Aj_new,Aj,Annz));
6472     PetscCall(PetscFree(Aj));
6473     Aj   = Aj_new;
6474   }
6475 
6476   if (Bnnz < Bnnz1 + Bnnz2) {
6477     PetscInt *Bj_new;
6478     PetscCall(PetscMalloc1(Bnnz,&Bj_new));
6479     PetscCall(PetscArraycpy(Bj_new,Bj,Bnnz));
6480     PetscCall(PetscFree(Bj));
6481     Bj   = Bj_new;
6482   }
6483 
6484   /* --------------------------------------------------------------------------------*/
6485   /* Create new submatrices for on-process and off-process coupling                  */
6486   /* --------------------------------------------------------------------------------*/
6487   PetscScalar   *Aa,*Ba;
6488   MatType       rtype;
6489   Mat_SeqAIJ    *a,*b;
6490   PetscCall(PetscCalloc1(Annz,&Aa)); /* Zero matrix on device */
6491   PetscCall(PetscCalloc1(Bnnz,&Ba));
6492   /* make Aj[] local, i.e, based off the start column of the diagonal portion */
6493   if (cstart) {for (k=0; k<Annz; k++) Aj[k] -= cstart;}
6494   PetscCall(MatDestroy(&mpiaij->A));
6495   PetscCall(MatDestroy(&mpiaij->B));
6496   PetscCall(MatGetRootType_Private(mat,&rtype));
6497   PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,Ai,Aj,Aa,&mpiaij->A));
6498   PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,mat->cmap->N,Bi,Bj,Ba,&mpiaij->B));
6499   PetscCall(MatSetUpMultiply_MPIAIJ(mat));
6500 
6501   a = (Mat_SeqAIJ*)mpiaij->A->data;
6502   b = (Mat_SeqAIJ*)mpiaij->B->data;
6503   a->singlemalloc = b->singlemalloc = PETSC_FALSE; /* Let newmat own Ai,Aj,Aa,Bi,Bj,Ba */
6504   a->free_a       = b->free_a       = PETSC_TRUE;
6505   a->free_ij      = b->free_ij      = PETSC_TRUE;
6506 
6507   /* conversion must happen AFTER multiply setup */
6508   PetscCall(MatConvert(mpiaij->A,rtype,MAT_INPLACE_MATRIX,&mpiaij->A));
6509   PetscCall(MatConvert(mpiaij->B,rtype,MAT_INPLACE_MATRIX,&mpiaij->B));
6510   PetscCall(VecDestroy(&mpiaij->lvec));
6511   PetscCall(MatCreateVecs(mpiaij->B,&mpiaij->lvec,NULL));
6512   PetscCall(PetscLogObjectParent((PetscObject)mat,(PetscObject)mpiaij->lvec));
6513 
6514   mpiaij->coo_n   = coo_n;
6515   mpiaij->coo_sf  = sf2;
6516   mpiaij->sendlen = nleaves;
6517   mpiaij->recvlen = nroots;
6518 
6519   mpiaij->Annz    = Annz;
6520   mpiaij->Bnnz    = Bnnz;
6521 
6522   mpiaij->Annz2   = Annz2;
6523   mpiaij->Bnnz2   = Bnnz2;
6524 
6525   mpiaij->Atot1   = Atot1;
6526   mpiaij->Atot2   = Atot2;
6527   mpiaij->Btot1   = Btot1;
6528   mpiaij->Btot2   = Btot2;
6529 
6530   mpiaij->Ajmap1  = Ajmap1;
6531   mpiaij->Aperm1  = Aperm1;
6532 
6533   mpiaij->Bjmap1  = Bjmap1;
6534   mpiaij->Bperm1  = Bperm1;
6535 
6536   mpiaij->Aimap2  = Aimap2;
6537   mpiaij->Ajmap2  = Ajmap2;
6538   mpiaij->Aperm2  = Aperm2;
6539 
6540   mpiaij->Bimap2  = Bimap2;
6541   mpiaij->Bjmap2  = Bjmap2;
6542   mpiaij->Bperm2  = Bperm2;
6543 
6544   mpiaij->Cperm1  = Cperm1;
6545 
6546   /* Allocate in preallocation. If not used, it has zero cost on host */
6547   PetscCall(PetscMalloc2(mpiaij->sendlen,&mpiaij->sendbuf,mpiaij->recvlen,&mpiaij->recvbuf));
6548   PetscFunctionReturn(0);
6549 }
6550 
6551 static PetscErrorCode MatSetValuesCOO_MPIAIJ(Mat mat,const PetscScalar v[],InsertMode imode)
6552 {
6553   Mat_MPIAIJ           *mpiaij = (Mat_MPIAIJ*)mat->data;
6554   Mat                  A = mpiaij->A,B = mpiaij->B;
6555   PetscCount           Annz = mpiaij->Annz,Annz2 = mpiaij->Annz2,Bnnz = mpiaij->Bnnz,Bnnz2 = mpiaij->Bnnz2;
6556   PetscScalar          *Aa,*Ba;
6557   PetscScalar          *sendbuf = mpiaij->sendbuf;
6558   PetscScalar          *recvbuf = mpiaij->recvbuf;
6559   const PetscCount     *Ajmap1 = mpiaij->Ajmap1,*Ajmap2 = mpiaij->Ajmap2,*Aimap2 = mpiaij->Aimap2;
6560   const PetscCount     *Bjmap1 = mpiaij->Bjmap1,*Bjmap2 = mpiaij->Bjmap2,*Bimap2 = mpiaij->Bimap2;
6561   const PetscCount     *Aperm1 = mpiaij->Aperm1,*Aperm2 = mpiaij->Aperm2,*Bperm1 = mpiaij->Bperm1,*Bperm2 = mpiaij->Bperm2;
6562   const PetscCount     *Cperm1 = mpiaij->Cperm1;
6563 
6564   PetscFunctionBegin;
6565   PetscCall(MatSeqAIJGetArray(A,&Aa)); /* Might read and write matrix values */
6566   PetscCall(MatSeqAIJGetArray(B,&Ba));
6567 
6568   /* Pack entries to be sent to remote */
6569   for (PetscCount i=0; i<mpiaij->sendlen; i++) sendbuf[i] = v[Cperm1[i]];
6570 
6571   /* Send remote entries to their owner and overlap the communication with local computation */
6572   PetscCall(PetscSFReduceWithMemTypeBegin(mpiaij->coo_sf,MPIU_SCALAR,PETSC_MEMTYPE_HOST,sendbuf,PETSC_MEMTYPE_HOST,recvbuf,MPI_REPLACE));
6573   /* Add local entries to A and B */
6574   for (PetscCount i=0; i<Annz; i++) { /* All nonzeros in A are either zero'ed or added with a value (i.e., initialized) */
6575     PetscScalar sum = 0.0; /* Do partial summation first to improve numerical stablility */
6576     for (PetscCount k=Ajmap1[i]; k<Ajmap1[i+1]; k++) sum += v[Aperm1[k]];
6577     Aa[i] = (imode == INSERT_VALUES? 0.0 : Aa[i]) + sum;
6578   }
6579   for (PetscCount i=0; i<Bnnz; i++) {
6580     PetscScalar sum = 0.0;
6581     for (PetscCount k=Bjmap1[i]; k<Bjmap1[i+1]; k++) sum += v[Bperm1[k]];
6582     Ba[i] = (imode == INSERT_VALUES? 0.0 : Ba[i]) + sum;
6583   }
6584   PetscCall(PetscSFReduceEnd(mpiaij->coo_sf,MPIU_SCALAR,sendbuf,recvbuf,MPI_REPLACE));
6585 
6586   /* Add received remote entries to A and B */
6587   for (PetscCount i=0; i<Annz2; i++) {
6588     for (PetscCount k=Ajmap2[i]; k<Ajmap2[i+1]; k++) Aa[Aimap2[i]] += recvbuf[Aperm2[k]];
6589   }
6590   for (PetscCount i=0; i<Bnnz2; i++) {
6591     for (PetscCount k=Bjmap2[i]; k<Bjmap2[i+1]; k++) Ba[Bimap2[i]] += recvbuf[Bperm2[k]];
6592   }
6593   PetscCall(MatSeqAIJRestoreArray(A,&Aa));
6594   PetscCall(MatSeqAIJRestoreArray(B,&Ba));
6595   PetscFunctionReturn(0);
6596 }
6597 
6598 /* ----------------------------------------------------------------*/
6599 
6600 /*MC
6601    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
6602 
6603    Options Database Keys:
6604 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
6605 
6606    Level: beginner
6607 
6608    Notes:
6609     MatSetValues() may be called for this matrix type with a NULL argument for the numerical values,
6610     in this case the values associated with the rows and columns one passes in are set to zero
6611     in the matrix
6612 
6613     MatSetOptions(,MAT_STRUCTURE_ONLY,PETSC_TRUE) may be called for this matrix type. In this no
6614     space is allocated for the nonzero entries and any entries passed with MatSetValues() are ignored
6615 
6616 .seealso: `MatCreateAIJ()`
6617 M*/
6618 
6619 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
6620 {
6621   Mat_MPIAIJ     *b;
6622   PetscMPIInt    size;
6623 
6624   PetscFunctionBegin;
6625   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)B),&size));
6626 
6627   PetscCall(PetscNewLog(B,&b));
6628   B->data       = (void*)b;
6629   PetscCall(PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps)));
6630   B->assembled  = PETSC_FALSE;
6631   B->insertmode = NOT_SET_VALUES;
6632   b->size       = size;
6633 
6634   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank));
6635 
6636   /* build cache for off array entries formed */
6637   PetscCall(MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash));
6638 
6639   b->donotstash  = PETSC_FALSE;
6640   b->colmap      = NULL;
6641   b->garray      = NULL;
6642   b->roworiented = PETSC_TRUE;
6643 
6644   /* stuff used for matrix vector multiply */
6645   b->lvec  = NULL;
6646   b->Mvctx = NULL;
6647 
6648   /* stuff for MatGetRow() */
6649   b->rowindices   = NULL;
6650   b->rowvalues    = NULL;
6651   b->getrowactive = PETSC_FALSE;
6652 
6653   /* flexible pointer used in CUSPARSE classes */
6654   b->spptr = NULL;
6655 
6656   PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetUseScalableIncreaseOverlap_C",MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ));
6657   PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ));
6658   PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ));
6659   PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ));
6660   PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ));
6661   PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatResetPreallocation_C",MatResetPreallocation_MPIAIJ));
6662   PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ));
6663   PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ));
6664   PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM));
6665   PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijsell_C",MatConvert_MPIAIJ_MPIAIJSELL));
6666 #if defined(PETSC_HAVE_CUDA)
6667   PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcusparse_C",MatConvert_MPIAIJ_MPIAIJCUSPARSE));
6668 #endif
6669 #if defined(PETSC_HAVE_KOKKOS_KERNELS)
6670   PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijkokkos_C",MatConvert_MPIAIJ_MPIAIJKokkos));
6671 #endif
6672 #if defined(PETSC_HAVE_MKL_SPARSE)
6673   PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijmkl_C",MatConvert_MPIAIJ_MPIAIJMKL));
6674 #endif
6675   PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL));
6676   PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpibaij_C",MatConvert_MPIAIJ_MPIBAIJ));
6677   PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ));
6678   PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpidense_C",MatConvert_MPIAIJ_MPIDense));
6679 #if defined(PETSC_HAVE_ELEMENTAL)
6680   PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_elemental_C",MatConvert_MPIAIJ_Elemental));
6681 #endif
6682 #if defined(PETSC_HAVE_SCALAPACK)
6683   PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_scalapack_C",MatConvert_AIJ_ScaLAPACK));
6684 #endif
6685   PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_is_C",MatConvert_XAIJ_IS));
6686   PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisell_C",MatConvert_MPIAIJ_MPISELL));
6687 #if defined(PETSC_HAVE_HYPRE)
6688   PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_hypre_C",MatConvert_AIJ_HYPRE));
6689   PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatProductSetFromOptions_transpose_mpiaij_mpiaij_C",MatProductSetFromOptions_Transpose_AIJ_AIJ));
6690 #endif
6691   PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatProductSetFromOptions_is_mpiaij_C",MatProductSetFromOptions_IS_XAIJ));
6692   PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatProductSetFromOptions_mpiaij_mpiaij_C",MatProductSetFromOptions_MPIAIJ));
6693   PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatSetPreallocationCOO_C",MatSetPreallocationCOO_MPIAIJ));
6694   PetscCall(PetscObjectComposeFunction((PetscObject)B,"MatSetValuesCOO_C",MatSetValuesCOO_MPIAIJ));
6695   PetscCall(PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ));
6696   PetscFunctionReturn(0);
6697 }
6698 
6699 /*@C
6700      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
6701          and "off-diagonal" part of the matrix in CSR format.
6702 
6703    Collective
6704 
6705    Input Parameters:
6706 +  comm - MPI communicator
6707 .  m - number of local rows (Cannot be PETSC_DECIDE)
6708 .  n - This value should be the same as the local size used in creating the
6709        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
6710        calculated if N is given) For square matrices n is almost always m.
6711 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
6712 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
6713 .   i - row indices for "diagonal" portion of matrix; that is i[0] = 0, i[row] = i[row-1] + number of elements in that row of the matrix
6714 .   j - column indices, which must be local, i.e., based off the start column of the diagonal portion
6715 .   a - matrix values
6716 .   oi - row indices for "off-diagonal" portion of matrix; that is oi[0] = 0, oi[row] = oi[row-1] + number of elements in that row of the matrix
6717 .   oj - column indices, which must be global, representing global columns in the MPIAIJ matrix
6718 -   oa - matrix values
6719 
6720    Output Parameter:
6721 .   mat - the matrix
6722 
6723    Level: advanced
6724 
6725    Notes:
6726        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
6727        must free the arrays once the matrix has been destroyed and not before.
6728 
6729        The i and j indices are 0 based
6730 
6731        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
6732 
6733        This sets local rows and cannot be used to set off-processor values.
6734 
6735        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
6736        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
6737        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
6738        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
6739        keep track of the underlying array. Use MatSetOption(A,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
6740        communication if it is known that only local entries will be set.
6741 
6742 .seealso: `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
6743           `MATMPIAIJ`, `MatCreateAIJ()`, `MatCreateMPIAIJWithArrays()`
6744 @*/
6745 PetscErrorCode MatCreateMPIAIJWithSplitArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,PetscInt i[],PetscInt j[],PetscScalar a[],PetscInt oi[], PetscInt oj[],PetscScalar oa[],Mat *mat)
6746 {
6747   Mat_MPIAIJ     *maij;
6748 
6749   PetscFunctionBegin;
6750   PetscCheck(m >= 0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
6751   PetscCheck(i[0] == 0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
6752   PetscCheck(oi[0] == 0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
6753   PetscCall(MatCreate(comm,mat));
6754   PetscCall(MatSetSizes(*mat,m,n,M,N));
6755   PetscCall(MatSetType(*mat,MATMPIAIJ));
6756   maij = (Mat_MPIAIJ*) (*mat)->data;
6757 
6758   (*mat)->preallocated = PETSC_TRUE;
6759 
6760   PetscCall(PetscLayoutSetUp((*mat)->rmap));
6761   PetscCall(PetscLayoutSetUp((*mat)->cmap));
6762 
6763   PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A));
6764   PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B));
6765 
6766   PetscCall(MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE));
6767   PetscCall(MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY));
6768   PetscCall(MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY));
6769   PetscCall(MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_FALSE));
6770   PetscCall(MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE));
6771   PetscFunctionReturn(0);
6772 }
6773 
6774 typedef struct {
6775   Mat       *mp;    /* intermediate products */
6776   PetscBool *mptmp; /* is the intermediate product temporary ? */
6777   PetscInt  cp;     /* number of intermediate products */
6778 
6779   /* support for MatGetBrowsOfAoCols_MPIAIJ for P_oth */
6780   PetscInt    *startsj_s,*startsj_r;
6781   PetscScalar *bufa;
6782   Mat         P_oth;
6783 
6784   /* may take advantage of merging product->B */
6785   Mat Bloc; /* B-local by merging diag and off-diag */
6786 
6787   /* cusparse does not have support to split between symbolic and numeric phases.
6788      When api_user is true, we don't need to update the numerical values
6789      of the temporary storage */
6790   PetscBool reusesym;
6791 
6792   /* support for COO values insertion */
6793   PetscScalar  *coo_v,*coo_w; /* store on-process and off-process COO scalars, and used as MPI recv/send buffers respectively */
6794   PetscInt     **own; /* own[i] points to address of on-process COO indices for Mat mp[i] */
6795   PetscInt     **off; /* off[i] points to address of off-process COO indices for Mat mp[i] */
6796   PetscBool    hasoffproc; /* if true, have off-process values insertion (i.e. AtB or PtAP) */
6797   PetscSF      sf; /* used for non-local values insertion and memory malloc */
6798   PetscMemType mtype;
6799 
6800   /* customization */
6801   PetscBool abmerge;
6802   PetscBool P_oth_bind;
6803 } MatMatMPIAIJBACKEND;
6804 
6805 PetscErrorCode MatDestroy_MatMatMPIAIJBACKEND(void *data)
6806 {
6807   MatMatMPIAIJBACKEND *mmdata = (MatMatMPIAIJBACKEND*)data;
6808   PetscInt            i;
6809 
6810   PetscFunctionBegin;
6811   PetscCall(PetscFree2(mmdata->startsj_s,mmdata->startsj_r));
6812   PetscCall(PetscFree(mmdata->bufa));
6813   PetscCall(PetscSFFree(mmdata->sf,mmdata->mtype,mmdata->coo_v));
6814   PetscCall(PetscSFFree(mmdata->sf,mmdata->mtype,mmdata->coo_w));
6815   PetscCall(MatDestroy(&mmdata->P_oth));
6816   PetscCall(MatDestroy(&mmdata->Bloc));
6817   PetscCall(PetscSFDestroy(&mmdata->sf));
6818   for (i = 0; i < mmdata->cp; i++) {
6819     PetscCall(MatDestroy(&mmdata->mp[i]));
6820   }
6821   PetscCall(PetscFree2(mmdata->mp,mmdata->mptmp));
6822   PetscCall(PetscFree(mmdata->own[0]));
6823   PetscCall(PetscFree(mmdata->own));
6824   PetscCall(PetscFree(mmdata->off[0]));
6825   PetscCall(PetscFree(mmdata->off));
6826   PetscCall(PetscFree(mmdata));
6827   PetscFunctionReturn(0);
6828 }
6829 
6830 /* Copy selected n entries with indices in idx[] of A to v[].
6831    If idx is NULL, copy the whole data array of A to v[]
6832  */
6833 static PetscErrorCode MatSeqAIJCopySubArray(Mat A, PetscInt n, const PetscInt idx[], PetscScalar v[])
6834 {
6835   PetscErrorCode (*f)(Mat,PetscInt,const PetscInt[],PetscScalar[]);
6836 
6837   PetscFunctionBegin;
6838   PetscCall(PetscObjectQueryFunction((PetscObject)A,"MatSeqAIJCopySubArray_C",&f));
6839   if (f) {
6840     PetscCall((*f)(A,n,idx,v));
6841   } else {
6842     const PetscScalar *vv;
6843 
6844     PetscCall(MatSeqAIJGetArrayRead(A,&vv));
6845     if (n && idx) {
6846       PetscScalar    *w = v;
6847       const PetscInt *oi = idx;
6848       PetscInt       j;
6849 
6850       for (j = 0; j < n; j++) *w++ = vv[*oi++];
6851     } else {
6852       PetscCall(PetscArraycpy(v,vv,n));
6853     }
6854     PetscCall(MatSeqAIJRestoreArrayRead(A,&vv));
6855   }
6856   PetscFunctionReturn(0);
6857 }
6858 
6859 static PetscErrorCode MatProductNumeric_MPIAIJBACKEND(Mat C)
6860 {
6861   MatMatMPIAIJBACKEND *mmdata;
6862   PetscInt            i,n_d,n_o;
6863 
6864   PetscFunctionBegin;
6865   MatCheckProduct(C,1);
6866   PetscCheck(C->product->data,PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data empty");
6867   mmdata = (MatMatMPIAIJBACKEND*)C->product->data;
6868   if (!mmdata->reusesym) { /* update temporary matrices */
6869     if (mmdata->P_oth) {
6870       PetscCall(MatGetBrowsOfAoCols_MPIAIJ(C->product->A,C->product->B,MAT_REUSE_MATRIX,&mmdata->startsj_s,&mmdata->startsj_r,&mmdata->bufa,&mmdata->P_oth));
6871     }
6872     if (mmdata->Bloc) {
6873       PetscCall(MatMPIAIJGetLocalMatMerge(C->product->B,MAT_REUSE_MATRIX,NULL,&mmdata->Bloc));
6874     }
6875   }
6876   mmdata->reusesym = PETSC_FALSE;
6877 
6878   for (i = 0; i < mmdata->cp; i++) {
6879     PetscCheck(mmdata->mp[i]->ops->productnumeric,PetscObjectComm((PetscObject)mmdata->mp[i]),PETSC_ERR_PLIB,"Missing numeric op for %s",MatProductTypes[mmdata->mp[i]->product->type]);
6880     PetscCall((*mmdata->mp[i]->ops->productnumeric)(mmdata->mp[i]));
6881   }
6882   for (i = 0, n_d = 0, n_o = 0; i < mmdata->cp; i++) {
6883     PetscInt noff = mmdata->off[i+1] - mmdata->off[i];
6884 
6885     if (mmdata->mptmp[i]) continue;
6886     if (noff) {
6887       PetscInt nown = mmdata->own[i+1] - mmdata->own[i];
6888 
6889       PetscCall(MatSeqAIJCopySubArray(mmdata->mp[i],noff,mmdata->off[i],mmdata->coo_w + n_o));
6890       PetscCall(MatSeqAIJCopySubArray(mmdata->mp[i],nown,mmdata->own[i],mmdata->coo_v + n_d));
6891       n_o += noff;
6892       n_d += nown;
6893     } else {
6894       Mat_SeqAIJ *mm = (Mat_SeqAIJ*)mmdata->mp[i]->data;
6895 
6896       PetscCall(MatSeqAIJCopySubArray(mmdata->mp[i],mm->nz,NULL,mmdata->coo_v + n_d));
6897       n_d += mm->nz;
6898     }
6899   }
6900   if (mmdata->hasoffproc) { /* offprocess insertion */
6901     PetscCall(PetscSFGatherBegin(mmdata->sf,MPIU_SCALAR,mmdata->coo_w,mmdata->coo_v+n_d));
6902     PetscCall(PetscSFGatherEnd(mmdata->sf,MPIU_SCALAR,mmdata->coo_w,mmdata->coo_v+n_d));
6903   }
6904   PetscCall(MatSetValuesCOO(C,mmdata->coo_v,INSERT_VALUES));
6905   PetscFunctionReturn(0);
6906 }
6907 
6908 /* Support for Pt * A, A * P, or Pt * A * P */
6909 #define MAX_NUMBER_INTERMEDIATE 4
6910 PetscErrorCode MatProductSymbolic_MPIAIJBACKEND(Mat C)
6911 {
6912   Mat_Product            *product = C->product;
6913   Mat                    A,P,mp[MAX_NUMBER_INTERMEDIATE]; /* A, P and a series of intermediate matrices */
6914   Mat_MPIAIJ             *a,*p;
6915   MatMatMPIAIJBACKEND    *mmdata;
6916   ISLocalToGlobalMapping P_oth_l2g = NULL;
6917   IS                     glob = NULL;
6918   const char             *prefix;
6919   char                   pprefix[256];
6920   const PetscInt         *globidx,*P_oth_idx;
6921   PetscInt               i,j,cp,m,n,M,N,*coo_i,*coo_j;
6922   PetscCount             ncoo,ncoo_d,ncoo_o,ncoo_oown;
6923   PetscInt               cmapt[MAX_NUMBER_INTERMEDIATE],rmapt[MAX_NUMBER_INTERMEDIATE]; /* col/row map type for each Mat in mp[]. */
6924                                                                                         /* type-0: consecutive, start from 0; type-1: consecutive with */
6925                                                                                         /* a base offset; type-2: sparse with a local to global map table */
6926   const PetscInt         *cmapa[MAX_NUMBER_INTERMEDIATE],*rmapa[MAX_NUMBER_INTERMEDIATE]; /* col/row local to global map array (table) for type-2 map type */
6927 
6928   MatProductType         ptype;
6929   PetscBool              mptmp[MAX_NUMBER_INTERMEDIATE],hasoffproc = PETSC_FALSE,iscuda,iskokk;
6930   PetscMPIInt            size;
6931 
6932   PetscFunctionBegin;
6933   MatCheckProduct(C,1);
6934   PetscCheck(!product->data,PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data not empty");
6935   ptype = product->type;
6936   if (product->A->symmetric && ptype == MATPRODUCT_AtB) {
6937     ptype = MATPRODUCT_AB;
6938     product->symbolic_used_the_fact_A_is_symmetric = PETSC_TRUE;
6939   }
6940   switch (ptype) {
6941   case MATPRODUCT_AB:
6942     A = product->A;
6943     P = product->B;
6944     m = A->rmap->n;
6945     n = P->cmap->n;
6946     M = A->rmap->N;
6947     N = P->cmap->N;
6948     hasoffproc = PETSC_FALSE; /* will not scatter mat product values to other processes */
6949     break;
6950   case MATPRODUCT_AtB:
6951     P = product->A;
6952     A = product->B;
6953     m = P->cmap->n;
6954     n = A->cmap->n;
6955     M = P->cmap->N;
6956     N = A->cmap->N;
6957     hasoffproc = PETSC_TRUE;
6958     break;
6959   case MATPRODUCT_PtAP:
6960     A = product->A;
6961     P = product->B;
6962     m = P->cmap->n;
6963     n = P->cmap->n;
6964     M = P->cmap->N;
6965     N = P->cmap->N;
6966     hasoffproc = PETSC_TRUE;
6967     break;
6968   default:
6969     SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Not for product type %s",MatProductTypes[ptype]);
6970   }
6971   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)C),&size));
6972   if (size == 1) hasoffproc = PETSC_FALSE;
6973 
6974   /* defaults */
6975   for (i=0;i<MAX_NUMBER_INTERMEDIATE;i++) {
6976     mp[i]    = NULL;
6977     mptmp[i] = PETSC_FALSE;
6978     rmapt[i] = -1;
6979     cmapt[i] = -1;
6980     rmapa[i] = NULL;
6981     cmapa[i] = NULL;
6982   }
6983 
6984   /* customization */
6985   PetscCall(PetscNew(&mmdata));
6986   mmdata->reusesym = product->api_user;
6987   if (ptype == MATPRODUCT_AB) {
6988     if (product->api_user) {
6989       PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMult","Mat");
6990       PetscCall(PetscOptionsBool("-matmatmult_backend_mergeB","Merge product->B local matrices","MatMatMult",mmdata->abmerge,&mmdata->abmerge,NULL));
6991       PetscCall(PetscOptionsBool("-matmatmult_backend_pothbind","Bind P_oth to CPU","MatBindToCPU",mmdata->P_oth_bind,&mmdata->P_oth_bind,NULL));
6992       PetscOptionsEnd();
6993     } else {
6994       PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AB","Mat");
6995       PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_mergeB","Merge product->B local matrices","MatMatMult",mmdata->abmerge,&mmdata->abmerge,NULL));
6996       PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_pothbind","Bind P_oth to CPU","MatBindToCPU",mmdata->P_oth_bind,&mmdata->P_oth_bind,NULL));
6997       PetscOptionsEnd();
6998     }
6999   } else if (ptype == MATPRODUCT_PtAP) {
7000     if (product->api_user) {
7001       PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatPtAP","Mat");
7002       PetscCall(PetscOptionsBool("-matptap_backend_pothbind","Bind P_oth to CPU","MatBindToCPU",mmdata->P_oth_bind,&mmdata->P_oth_bind,NULL));
7003       PetscOptionsEnd();
7004     } else {
7005       PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_PtAP","Mat");
7006       PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_pothbind","Bind P_oth to CPU","MatBindToCPU",mmdata->P_oth_bind,&mmdata->P_oth_bind,NULL));
7007       PetscOptionsEnd();
7008     }
7009   }
7010   a = (Mat_MPIAIJ*)A->data;
7011   p = (Mat_MPIAIJ*)P->data;
7012   PetscCall(MatSetSizes(C,m,n,M,N));
7013   PetscCall(PetscLayoutSetUp(C->rmap));
7014   PetscCall(PetscLayoutSetUp(C->cmap));
7015   PetscCall(MatSetType(C,((PetscObject)A)->type_name));
7016   PetscCall(MatGetOptionsPrefix(C,&prefix));
7017 
7018   cp   = 0;
7019   switch (ptype) {
7020   case MATPRODUCT_AB: /* A * P */
7021     PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&mmdata->startsj_s,&mmdata->startsj_r,&mmdata->bufa,&mmdata->P_oth));
7022 
7023     /* A_diag * P_local (merged or not) */
7024     if (mmdata->abmerge) { /* P's diagonal and off-diag blocks are merged to one matrix, then multiplied by A_diag */
7025       /* P is product->B */
7026       PetscCall(MatMPIAIJGetLocalMatMerge(P,MAT_INITIAL_MATRIX,&glob,&mmdata->Bloc));
7027       PetscCall(MatProductCreate(a->A,mmdata->Bloc,NULL,&mp[cp]));
7028       PetscCall(MatProductSetType(mp[cp],MATPRODUCT_AB));
7029       PetscCall(MatProductSetFill(mp[cp],product->fill));
7030       PetscCall(PetscSNPrintf(pprefix,sizeof(pprefix),"backend_p%" PetscInt_FMT "_",cp));
7031       PetscCall(MatSetOptionsPrefix(mp[cp],prefix));
7032       PetscCall(MatAppendOptionsPrefix(mp[cp],pprefix));
7033       mp[cp]->product->api_user = product->api_user;
7034       PetscCall(MatProductSetFromOptions(mp[cp]));
7035       PetscCheck(mp[cp]->ops->productsymbolic,PetscObjectComm((PetscObject)mp[cp]),PETSC_ERR_PLIB,"Missing symbolic op for %s",MatProductTypes[mp[cp]->product->type]);
7036       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
7037       PetscCall(ISGetIndices(glob,&globidx));
7038       rmapt[cp] = 1;
7039       cmapt[cp] = 2;
7040       cmapa[cp] = globidx;
7041       mptmp[cp] = PETSC_FALSE;
7042       cp++;
7043     } else { /* A_diag * P_diag and A_diag * P_off */
7044       PetscCall(MatProductCreate(a->A,p->A,NULL,&mp[cp]));
7045       PetscCall(MatProductSetType(mp[cp],MATPRODUCT_AB));
7046       PetscCall(MatProductSetFill(mp[cp],product->fill));
7047       PetscCall(PetscSNPrintf(pprefix,sizeof(pprefix),"backend_p%" PetscInt_FMT "_",cp));
7048       PetscCall(MatSetOptionsPrefix(mp[cp],prefix));
7049       PetscCall(MatAppendOptionsPrefix(mp[cp],pprefix));
7050       mp[cp]->product->api_user = product->api_user;
7051       PetscCall(MatProductSetFromOptions(mp[cp]));
7052       PetscCheck(mp[cp]->ops->productsymbolic,PetscObjectComm((PetscObject)mp[cp]),PETSC_ERR_PLIB,"Missing symbolic op for %s",MatProductTypes[mp[cp]->product->type]);
7053       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
7054       rmapt[cp] = 1;
7055       cmapt[cp] = 1;
7056       mptmp[cp] = PETSC_FALSE;
7057       cp++;
7058       PetscCall(MatProductCreate(a->A,p->B,NULL,&mp[cp]));
7059       PetscCall(MatProductSetType(mp[cp],MATPRODUCT_AB));
7060       PetscCall(MatProductSetFill(mp[cp],product->fill));
7061       PetscCall(PetscSNPrintf(pprefix,sizeof(pprefix),"backend_p%" PetscInt_FMT "_",cp));
7062       PetscCall(MatSetOptionsPrefix(mp[cp],prefix));
7063       PetscCall(MatAppendOptionsPrefix(mp[cp],pprefix));
7064       mp[cp]->product->api_user = product->api_user;
7065       PetscCall(MatProductSetFromOptions(mp[cp]));
7066       PetscCheck(mp[cp]->ops->productsymbolic,PetscObjectComm((PetscObject)mp[cp]),PETSC_ERR_PLIB,"Missing symbolic op for %s",MatProductTypes[mp[cp]->product->type]);
7067       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
7068       rmapt[cp] = 1;
7069       cmapt[cp] = 2;
7070       cmapa[cp] = p->garray;
7071       mptmp[cp] = PETSC_FALSE;
7072       cp++;
7073     }
7074 
7075     /* A_off * P_other */
7076     if (mmdata->P_oth) {
7077       PetscCall(MatSeqAIJCompactOutExtraColumns_SeqAIJ(mmdata->P_oth,&P_oth_l2g)); /* make P_oth use local col ids */
7078       PetscCall(ISLocalToGlobalMappingGetIndices(P_oth_l2g,&P_oth_idx));
7079       PetscCall(MatSetType(mmdata->P_oth,((PetscObject)(a->B))->type_name));
7080       PetscCall(MatBindToCPU(mmdata->P_oth,mmdata->P_oth_bind));
7081       PetscCall(MatProductCreate(a->B,mmdata->P_oth,NULL,&mp[cp]));
7082       PetscCall(MatProductSetType(mp[cp],MATPRODUCT_AB));
7083       PetscCall(MatProductSetFill(mp[cp],product->fill));
7084       PetscCall(PetscSNPrintf(pprefix,sizeof(pprefix),"backend_p%" PetscInt_FMT "_",cp));
7085       PetscCall(MatSetOptionsPrefix(mp[cp],prefix));
7086       PetscCall(MatAppendOptionsPrefix(mp[cp],pprefix));
7087       mp[cp]->product->api_user = product->api_user;
7088       PetscCall(MatProductSetFromOptions(mp[cp]));
7089       PetscCheck(mp[cp]->ops->productsymbolic,PetscObjectComm((PetscObject)mp[cp]),PETSC_ERR_PLIB,"Missing symbolic op for %s",MatProductTypes[mp[cp]->product->type]);
7090       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
7091       rmapt[cp] = 1;
7092       cmapt[cp] = 2;
7093       cmapa[cp] = P_oth_idx;
7094       mptmp[cp] = PETSC_FALSE;
7095       cp++;
7096     }
7097     break;
7098 
7099   case MATPRODUCT_AtB: /* (P^t * A): P_diag * A_loc + P_off * A_loc */
7100     /* A is product->B */
7101     PetscCall(MatMPIAIJGetLocalMatMerge(A,MAT_INITIAL_MATRIX,&glob,&mmdata->Bloc));
7102     if (A == P) { /* when A==P, we can take advantage of the already merged mmdata->Bloc */
7103       PetscCall(MatProductCreate(mmdata->Bloc,mmdata->Bloc,NULL,&mp[cp]));
7104       PetscCall(MatProductSetType(mp[cp],MATPRODUCT_AtB));
7105       PetscCall(MatProductSetFill(mp[cp],product->fill));
7106       PetscCall(PetscSNPrintf(pprefix,sizeof(pprefix),"backend_p%" PetscInt_FMT "_",cp));
7107       PetscCall(MatSetOptionsPrefix(mp[cp],prefix));
7108       PetscCall(MatAppendOptionsPrefix(mp[cp],pprefix));
7109       mp[cp]->product->api_user = product->api_user;
7110       PetscCall(MatProductSetFromOptions(mp[cp]));
7111       PetscCheck(mp[cp]->ops->productsymbolic,PetscObjectComm((PetscObject)mp[cp]),PETSC_ERR_PLIB,"Missing symbolic op for %s",MatProductTypes[mp[cp]->product->type]);
7112       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
7113       PetscCall(ISGetIndices(glob,&globidx));
7114       rmapt[cp] = 2;
7115       rmapa[cp] = globidx;
7116       cmapt[cp] = 2;
7117       cmapa[cp] = globidx;
7118       mptmp[cp] = PETSC_FALSE;
7119       cp++;
7120     } else {
7121       PetscCall(MatProductCreate(p->A,mmdata->Bloc,NULL,&mp[cp]));
7122       PetscCall(MatProductSetType(mp[cp],MATPRODUCT_AtB));
7123       PetscCall(MatProductSetFill(mp[cp],product->fill));
7124       PetscCall(PetscSNPrintf(pprefix,sizeof(pprefix),"backend_p%" PetscInt_FMT "_",cp));
7125       PetscCall(MatSetOptionsPrefix(mp[cp],prefix));
7126       PetscCall(MatAppendOptionsPrefix(mp[cp],pprefix));
7127       mp[cp]->product->api_user = product->api_user;
7128       PetscCall(MatProductSetFromOptions(mp[cp]));
7129       PetscCheck(mp[cp]->ops->productsymbolic,PetscObjectComm((PetscObject)mp[cp]),PETSC_ERR_PLIB,"Missing symbolic op for %s",MatProductTypes[mp[cp]->product->type]);
7130       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
7131       PetscCall(ISGetIndices(glob,&globidx));
7132       rmapt[cp] = 1;
7133       cmapt[cp] = 2;
7134       cmapa[cp] = globidx;
7135       mptmp[cp] = PETSC_FALSE;
7136       cp++;
7137       PetscCall(MatProductCreate(p->B,mmdata->Bloc,NULL,&mp[cp]));
7138       PetscCall(MatProductSetType(mp[cp],MATPRODUCT_AtB));
7139       PetscCall(MatProductSetFill(mp[cp],product->fill));
7140       PetscCall(PetscSNPrintf(pprefix,sizeof(pprefix),"backend_p%" PetscInt_FMT "_",cp));
7141       PetscCall(MatSetOptionsPrefix(mp[cp],prefix));
7142       PetscCall(MatAppendOptionsPrefix(mp[cp],pprefix));
7143       mp[cp]->product->api_user = product->api_user;
7144       PetscCall(MatProductSetFromOptions(mp[cp]));
7145       PetscCheck(mp[cp]->ops->productsymbolic,PetscObjectComm((PetscObject)mp[cp]),PETSC_ERR_PLIB,"Missing symbolic op for %s",MatProductTypes[mp[cp]->product->type]);
7146       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
7147       rmapt[cp] = 2;
7148       rmapa[cp] = p->garray;
7149       cmapt[cp] = 2;
7150       cmapa[cp] = globidx;
7151       mptmp[cp] = PETSC_FALSE;
7152       cp++;
7153     }
7154     break;
7155   case MATPRODUCT_PtAP:
7156     PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&mmdata->startsj_s,&mmdata->startsj_r,&mmdata->bufa,&mmdata->P_oth));
7157     /* P is product->B */
7158     PetscCall(MatMPIAIJGetLocalMatMerge(P,MAT_INITIAL_MATRIX,&glob,&mmdata->Bloc));
7159     PetscCall(MatProductCreate(a->A,mmdata->Bloc,NULL,&mp[cp]));
7160     PetscCall(MatProductSetType(mp[cp],MATPRODUCT_PtAP));
7161     PetscCall(MatProductSetFill(mp[cp],product->fill));
7162     PetscCall(PetscSNPrintf(pprefix,sizeof(pprefix),"backend_p%" PetscInt_FMT "_",cp));
7163     PetscCall(MatSetOptionsPrefix(mp[cp],prefix));
7164     PetscCall(MatAppendOptionsPrefix(mp[cp],pprefix));
7165     mp[cp]->product->api_user = product->api_user;
7166     PetscCall(MatProductSetFromOptions(mp[cp]));
7167     PetscCheck(mp[cp]->ops->productsymbolic,PetscObjectComm((PetscObject)mp[cp]),PETSC_ERR_PLIB,"Missing symbolic op for %s",MatProductTypes[mp[cp]->product->type]);
7168     PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
7169     PetscCall(ISGetIndices(glob,&globidx));
7170     rmapt[cp] = 2;
7171     rmapa[cp] = globidx;
7172     cmapt[cp] = 2;
7173     cmapa[cp] = globidx;
7174     mptmp[cp] = PETSC_FALSE;
7175     cp++;
7176     if (mmdata->P_oth) {
7177       PetscCall(MatSeqAIJCompactOutExtraColumns_SeqAIJ(mmdata->P_oth,&P_oth_l2g));
7178       PetscCall(ISLocalToGlobalMappingGetIndices(P_oth_l2g,&P_oth_idx));
7179       PetscCall(MatSetType(mmdata->P_oth,((PetscObject)(a->B))->type_name));
7180       PetscCall(MatBindToCPU(mmdata->P_oth,mmdata->P_oth_bind));
7181       PetscCall(MatProductCreate(a->B,mmdata->P_oth,NULL,&mp[cp]));
7182       PetscCall(MatProductSetType(mp[cp],MATPRODUCT_AB));
7183       PetscCall(MatProductSetFill(mp[cp],product->fill));
7184       PetscCall(PetscSNPrintf(pprefix,sizeof(pprefix),"backend_p%" PetscInt_FMT "_",cp));
7185       PetscCall(MatSetOptionsPrefix(mp[cp],prefix));
7186       PetscCall(MatAppendOptionsPrefix(mp[cp],pprefix));
7187       mp[cp]->product->api_user = product->api_user;
7188       PetscCall(MatProductSetFromOptions(mp[cp]));
7189       PetscCheck(mp[cp]->ops->productsymbolic,PetscObjectComm((PetscObject)mp[cp]),PETSC_ERR_PLIB,"Missing symbolic op for %s",MatProductTypes[mp[cp]->product->type]);
7190       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
7191       mptmp[cp] = PETSC_TRUE;
7192       cp++;
7193       PetscCall(MatProductCreate(mmdata->Bloc,mp[1],NULL,&mp[cp]));
7194       PetscCall(MatProductSetType(mp[cp],MATPRODUCT_AtB));
7195       PetscCall(MatProductSetFill(mp[cp],product->fill));
7196       PetscCall(PetscSNPrintf(pprefix,sizeof(pprefix),"backend_p%" PetscInt_FMT "_",cp));
7197       PetscCall(MatSetOptionsPrefix(mp[cp],prefix));
7198       PetscCall(MatAppendOptionsPrefix(mp[cp],pprefix));
7199       mp[cp]->product->api_user = product->api_user;
7200       PetscCall(MatProductSetFromOptions(mp[cp]));
7201       PetscCheck(mp[cp]->ops->productsymbolic,PetscObjectComm((PetscObject)mp[cp]),PETSC_ERR_PLIB,"Missing symbolic op for %s",MatProductTypes[mp[cp]->product->type]);
7202       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
7203       rmapt[cp] = 2;
7204       rmapa[cp] = globidx;
7205       cmapt[cp] = 2;
7206       cmapa[cp] = P_oth_idx;
7207       mptmp[cp] = PETSC_FALSE;
7208       cp++;
7209     }
7210     break;
7211   default:
7212     SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Not for product type %s",MatProductTypes[ptype]);
7213   }
7214   /* sanity check */
7215   if (size > 1) for (i = 0; i < cp; i++) PetscCheck(rmapt[i] != 2 || hasoffproc,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Unexpected offproc map type for product %" PetscInt_FMT,i);
7216 
7217   PetscCall(PetscMalloc2(cp,&mmdata->mp,cp,&mmdata->mptmp));
7218   for (i = 0; i < cp; i++) {
7219     mmdata->mp[i]    = mp[i];
7220     mmdata->mptmp[i] = mptmp[i];
7221   }
7222   mmdata->cp = cp;
7223   C->product->data       = mmdata;
7224   C->product->destroy    = MatDestroy_MatMatMPIAIJBACKEND;
7225   C->ops->productnumeric = MatProductNumeric_MPIAIJBACKEND;
7226 
7227   /* memory type */
7228   mmdata->mtype = PETSC_MEMTYPE_HOST;
7229   PetscCall(PetscObjectTypeCompareAny((PetscObject)C,&iscuda,MATSEQAIJCUSPARSE,MATMPIAIJCUSPARSE,""));
7230   PetscCall(PetscObjectTypeCompareAny((PetscObject)C,&iskokk,MATSEQAIJKOKKOS,MATMPIAIJKOKKOS,""));
7231   if (iscuda) mmdata->mtype = PETSC_MEMTYPE_CUDA;
7232   else if (iskokk) mmdata->mtype = PETSC_MEMTYPE_KOKKOS;
7233 
7234   /* prepare coo coordinates for values insertion */
7235 
7236   /* count total nonzeros of those intermediate seqaij Mats
7237     ncoo_d:    # of nonzeros of matrices that do not have offproc entries
7238     ncoo_o:    # of nonzeros (of matrices that might have offproc entries) that will be inserted to remote procs
7239     ncoo_oown: # of nonzeros (of matrices that might have offproc entries) that will be inserted locally
7240   */
7241   for (cp = 0, ncoo_d = 0, ncoo_o = 0, ncoo_oown = 0; cp < mmdata->cp; cp++) {
7242     Mat_SeqAIJ *mm = (Mat_SeqAIJ*)mp[cp]->data;
7243     if (mptmp[cp]) continue;
7244     if (rmapt[cp] == 2 && hasoffproc) { /* the rows need to be scatter to all processes (might include self) */
7245       const PetscInt *rmap = rmapa[cp];
7246       const PetscInt mr = mp[cp]->rmap->n;
7247       const PetscInt rs = C->rmap->rstart;
7248       const PetscInt re = C->rmap->rend;
7249       const PetscInt *ii  = mm->i;
7250       for (i = 0; i < mr; i++) {
7251         const PetscInt gr = rmap[i];
7252         const PetscInt nz = ii[i+1] - ii[i];
7253         if (gr < rs || gr >= re) ncoo_o += nz; /* this row is offproc */
7254         else ncoo_oown += nz; /* this row is local */
7255       }
7256     } else ncoo_d += mm->nz;
7257   }
7258 
7259   /*
7260     ncoo: total number of nonzeros (including those inserted by remote procs) belonging to this proc
7261 
7262     ncoo = ncoo_d + ncoo_oown + ncoo2, which ncoo2 is number of nonzeros inserted to me by other procs.
7263 
7264     off[0] points to a big index array, which is shared by off[1,2,...]. Similarily, for own[0].
7265 
7266     off[p]: points to the segment for matrix mp[p], storing location of nonzeros that mp[p] will insert to others
7267     own[p]: points to the segment for matrix mp[p], storing location of nonzeros that mp[p] will insert locally
7268     so, off[p+1]-off[p] is the number of nonzeros that mp[p] will send to others.
7269 
7270     coo_i/j/v[]: [ncoo] row/col/val of nonzeros belonging to this proc.
7271     Ex. coo_i[]: the beginning part (of size ncoo_d + ncoo_oown) stores i of local nonzeros, and the remaing part stores i of nonzeros I will receive.
7272   */
7273   PetscCall(PetscCalloc1(mmdata->cp+1,&mmdata->off)); /* +1 to make a csr-like data structure */
7274   PetscCall(PetscCalloc1(mmdata->cp+1,&mmdata->own));
7275 
7276   /* gather (i,j) of nonzeros inserted by remote procs */
7277   if (hasoffproc) {
7278     PetscSF  msf;
7279     PetscInt ncoo2,*coo_i2,*coo_j2;
7280 
7281     PetscCall(PetscMalloc1(ncoo_o,&mmdata->off[0]));
7282     PetscCall(PetscMalloc1(ncoo_oown,&mmdata->own[0]));
7283     PetscCall(PetscMalloc2(ncoo_o,&coo_i,ncoo_o,&coo_j)); /* to collect (i,j) of entries to be sent to others */
7284 
7285     for (cp = 0, ncoo_o = 0; cp < mmdata->cp; cp++) {
7286       Mat_SeqAIJ *mm = (Mat_SeqAIJ*)mp[cp]->data;
7287       PetscInt   *idxoff = mmdata->off[cp];
7288       PetscInt   *idxown = mmdata->own[cp];
7289       if (!mptmp[cp] && rmapt[cp] == 2) { /* row map is sparse */
7290         const PetscInt *rmap = rmapa[cp];
7291         const PetscInt *cmap = cmapa[cp];
7292         const PetscInt *ii  = mm->i;
7293         PetscInt       *coi = coo_i + ncoo_o;
7294         PetscInt       *coj = coo_j + ncoo_o;
7295         const PetscInt mr = mp[cp]->rmap->n;
7296         const PetscInt rs = C->rmap->rstart;
7297         const PetscInt re = C->rmap->rend;
7298         const PetscInt cs = C->cmap->rstart;
7299         for (i = 0; i < mr; i++) {
7300           const PetscInt *jj = mm->j + ii[i];
7301           const PetscInt gr  = rmap[i];
7302           const PetscInt nz  = ii[i+1] - ii[i];
7303           if (gr < rs || gr >= re) { /* this is an offproc row */
7304             for (j = ii[i]; j < ii[i+1]; j++) {
7305               *coi++ = gr;
7306               *idxoff++ = j;
7307             }
7308             if (!cmapt[cp]) { /* already global */
7309               for (j = 0; j < nz; j++) *coj++ = jj[j];
7310             } else if (cmapt[cp] == 1) { /* local to global for owned columns of C */
7311               for (j = 0; j < nz; j++) *coj++ = jj[j] + cs;
7312             } else { /* offdiag */
7313               for (j = 0; j < nz; j++) *coj++ = cmap[jj[j]];
7314             }
7315             ncoo_o += nz;
7316           } else { /* this is a local row */
7317             for (j = ii[i]; j < ii[i+1]; j++) *idxown++ = j;
7318           }
7319         }
7320       }
7321       mmdata->off[cp + 1] = idxoff;
7322       mmdata->own[cp + 1] = idxown;
7323     }
7324 
7325     PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)C),&mmdata->sf));
7326     PetscCall(PetscSFSetGraphLayout(mmdata->sf,C->rmap,ncoo_o/*nleaves*/,NULL/*ilocal*/,PETSC_OWN_POINTER,coo_i));
7327     PetscCall(PetscSFGetMultiSF(mmdata->sf,&msf));
7328     PetscCall(PetscSFGetGraph(msf,&ncoo2/*nroots*/,NULL,NULL,NULL));
7329     ncoo = ncoo_d + ncoo_oown + ncoo2;
7330     PetscCall(PetscMalloc2(ncoo,&coo_i2,ncoo,&coo_j2));
7331     PetscCall(PetscSFGatherBegin(mmdata->sf,MPIU_INT,coo_i,coo_i2 + ncoo_d + ncoo_oown)); /* put (i,j) of remote nonzeros at back */
7332     PetscCall(PetscSFGatherEnd(mmdata->sf,MPIU_INT,coo_i,coo_i2 + ncoo_d + ncoo_oown));
7333     PetscCall(PetscSFGatherBegin(mmdata->sf,MPIU_INT,coo_j,coo_j2 + ncoo_d + ncoo_oown));
7334     PetscCall(PetscSFGatherEnd(mmdata->sf,MPIU_INT,coo_j,coo_j2 + ncoo_d + ncoo_oown));
7335     PetscCall(PetscFree2(coo_i,coo_j));
7336     /* allocate MPI send buffer to collect nonzero values to be sent to remote procs */
7337     PetscCall(PetscSFMalloc(mmdata->sf,mmdata->mtype,ncoo_o*sizeof(PetscScalar),(void**)&mmdata->coo_w));
7338     coo_i = coo_i2;
7339     coo_j = coo_j2;
7340   } else { /* no offproc values insertion */
7341     ncoo = ncoo_d;
7342     PetscCall(PetscMalloc2(ncoo,&coo_i,ncoo,&coo_j));
7343 
7344     PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)C),&mmdata->sf));
7345     PetscCall(PetscSFSetGraph(mmdata->sf,0,0,NULL,PETSC_OWN_POINTER,NULL,PETSC_OWN_POINTER));
7346     PetscCall(PetscSFSetUp(mmdata->sf));
7347   }
7348   mmdata->hasoffproc = hasoffproc;
7349 
7350   /* gather (i,j) of nonzeros inserted locally */
7351   for (cp = 0, ncoo_d = 0; cp < mmdata->cp; cp++) {
7352     Mat_SeqAIJ     *mm = (Mat_SeqAIJ*)mp[cp]->data;
7353     PetscInt       *coi = coo_i + ncoo_d;
7354     PetscInt       *coj = coo_j + ncoo_d;
7355     const PetscInt *jj  = mm->j;
7356     const PetscInt *ii  = mm->i;
7357     const PetscInt *cmap = cmapa[cp];
7358     const PetscInt *rmap = rmapa[cp];
7359     const PetscInt mr = mp[cp]->rmap->n;
7360     const PetscInt rs = C->rmap->rstart;
7361     const PetscInt re = C->rmap->rend;
7362     const PetscInt cs = C->cmap->rstart;
7363 
7364     if (mptmp[cp]) continue;
7365     if (rmapt[cp] == 1) { /* consecutive rows */
7366       /* fill coo_i */
7367       for (i = 0; i < mr; i++) {
7368         const PetscInt gr = i + rs;
7369         for (j = ii[i]; j < ii[i+1]; j++) coi[j] = gr;
7370       }
7371       /* fill coo_j */
7372       if (!cmapt[cp]) { /* type-0, already global */
7373         PetscCall(PetscArraycpy(coj,jj,mm->nz));
7374       } else if (cmapt[cp] == 1) { /* type-1, local to global for consecutive columns of C */
7375         for (j = 0; j < mm->nz; j++) coj[j] = jj[j] + cs; /* lid + col start */
7376       } else { /* type-2, local to global for sparse columns */
7377         for (j = 0; j < mm->nz; j++) coj[j] = cmap[jj[j]];
7378       }
7379       ncoo_d += mm->nz;
7380     } else if (rmapt[cp] == 2) { /* sparse rows */
7381       for (i = 0; i < mr; i++) {
7382         const PetscInt *jj = mm->j + ii[i];
7383         const PetscInt gr  = rmap[i];
7384         const PetscInt nz  = ii[i+1] - ii[i];
7385         if (gr >= rs && gr < re) { /* local rows */
7386           for (j = ii[i]; j < ii[i+1]; j++) *coi++ = gr;
7387           if (!cmapt[cp]) { /* type-0, already global */
7388             for (j = 0; j < nz; j++) *coj++ = jj[j];
7389           } else if (cmapt[cp] == 1) { /* local to global for owned columns of C */
7390             for (j = 0; j < nz; j++) *coj++ = jj[j] + cs;
7391           } else { /* type-2, local to global for sparse columns */
7392             for (j = 0; j < nz; j++) *coj++ = cmap[jj[j]];
7393           }
7394           ncoo_d += nz;
7395         }
7396       }
7397     }
7398   }
7399   if (glob) {
7400     PetscCall(ISRestoreIndices(glob,&globidx));
7401   }
7402   PetscCall(ISDestroy(&glob));
7403   if (P_oth_l2g) {
7404     PetscCall(ISLocalToGlobalMappingRestoreIndices(P_oth_l2g,&P_oth_idx));
7405   }
7406   PetscCall(ISLocalToGlobalMappingDestroy(&P_oth_l2g));
7407   /* allocate an array to store all nonzeros (inserted locally or remotely) belonging to this proc */
7408   PetscCall(PetscSFMalloc(mmdata->sf,mmdata->mtype,ncoo*sizeof(PetscScalar),(void**)&mmdata->coo_v));
7409 
7410   /* preallocate with COO data */
7411   PetscCall(MatSetPreallocationCOO(C,ncoo,coo_i,coo_j));
7412   PetscCall(PetscFree2(coo_i,coo_j));
7413   PetscFunctionReturn(0);
7414 }
7415 
7416 PetscErrorCode MatProductSetFromOptions_MPIAIJBACKEND(Mat mat)
7417 {
7418   Mat_Product *product = mat->product;
7419 #if defined(PETSC_HAVE_DEVICE)
7420   PetscBool    match   = PETSC_FALSE;
7421   PetscBool    usecpu  = PETSC_FALSE;
7422 #else
7423   PetscBool    match   = PETSC_TRUE;
7424 #endif
7425 
7426   PetscFunctionBegin;
7427   MatCheckProduct(mat,1);
7428 #if defined(PETSC_HAVE_DEVICE)
7429   if (!product->A->boundtocpu && !product->B->boundtocpu) {
7430     PetscCall(PetscObjectTypeCompare((PetscObject)product->B,((PetscObject)product->A)->type_name,&match));
7431   }
7432   if (match) { /* we can always fallback to the CPU if requested */
7433     switch (product->type) {
7434     case MATPRODUCT_AB:
7435       if (product->api_user) {
7436         PetscOptionsBegin(PetscObjectComm((PetscObject)mat),((PetscObject)mat)->prefix,"MatMatMult","Mat");
7437         PetscCall(PetscOptionsBool("-matmatmult_backend_cpu","Use CPU code","MatMatMult",usecpu,&usecpu,NULL));
7438         PetscOptionsEnd();
7439       } else {
7440         PetscOptionsBegin(PetscObjectComm((PetscObject)mat),((PetscObject)mat)->prefix,"MatProduct_AB","Mat");
7441         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu","Use CPU code","MatMatMult",usecpu,&usecpu,NULL));
7442         PetscOptionsEnd();
7443       }
7444       break;
7445     case MATPRODUCT_AtB:
7446       if (product->api_user) {
7447         PetscOptionsBegin(PetscObjectComm((PetscObject)mat),((PetscObject)mat)->prefix,"MatTransposeMatMult","Mat");
7448         PetscCall(PetscOptionsBool("-mattransposematmult_backend_cpu","Use CPU code","MatTransposeMatMult",usecpu,&usecpu,NULL));
7449         PetscOptionsEnd();
7450       } else {
7451         PetscOptionsBegin(PetscObjectComm((PetscObject)mat),((PetscObject)mat)->prefix,"MatProduct_AtB","Mat");
7452         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu","Use CPU code","MatTransposeMatMult",usecpu,&usecpu,NULL));
7453         PetscOptionsEnd();
7454       }
7455       break;
7456     case MATPRODUCT_PtAP:
7457       if (product->api_user) {
7458         PetscOptionsBegin(PetscObjectComm((PetscObject)mat),((PetscObject)mat)->prefix,"MatPtAP","Mat");
7459         PetscCall(PetscOptionsBool("-matptap_backend_cpu","Use CPU code","MatPtAP",usecpu,&usecpu,NULL));
7460         PetscOptionsEnd();
7461       } else {
7462         PetscOptionsBegin(PetscObjectComm((PetscObject)mat),((PetscObject)mat)->prefix,"MatProduct_PtAP","Mat");
7463         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu","Use CPU code","MatPtAP",usecpu,&usecpu,NULL));
7464         PetscOptionsEnd();
7465       }
7466       break;
7467     default:
7468       break;
7469     }
7470     match = (PetscBool)!usecpu;
7471   }
7472 #endif
7473   if (match) {
7474     switch (product->type) {
7475     case MATPRODUCT_AB:
7476     case MATPRODUCT_AtB:
7477     case MATPRODUCT_PtAP:
7478       mat->ops->productsymbolic = MatProductSymbolic_MPIAIJBACKEND;
7479       break;
7480     default:
7481       break;
7482     }
7483   }
7484   /* fallback to MPIAIJ ops */
7485   if (!mat->ops->productsymbolic) PetscCall(MatProductSetFromOptions_MPIAIJ(mat));
7486   PetscFunctionReturn(0);
7487 }
7488 
7489 /*
7490    Produces a set of block column indices of the matrix row, one for each block represented in the original row
7491 
7492    n - the number of block indices in cc[]
7493    cc - the block indices (must be large enough to contain the indices)
7494 */
7495 static inline PetscErrorCode MatCollapseRow(Mat Amat,PetscInt row,PetscInt bs,PetscInt *n,PetscInt *cc)
7496 {
7497   PetscInt       cnt = -1,nidx,j;
7498   const PetscInt *idx;
7499 
7500   PetscFunctionBegin;
7501   PetscCall(MatGetRow(Amat,row,&nidx,&idx,NULL));
7502   if (nidx) {
7503     cnt = 0;
7504     cc[cnt] = idx[0]/bs;
7505     for (j=1; j<nidx; j++) {
7506       if (cc[cnt] < idx[j]/bs) cc[++cnt] = idx[j]/bs;
7507     }
7508   }
7509   PetscCall(MatRestoreRow(Amat,row,&nidx,&idx,NULL));
7510   *n = cnt+1;
7511   PetscFunctionReturn(0);
7512 }
7513 
7514 /*
7515     Produces a set of block column indices of the matrix block row, one for each block represented in the original set of rows
7516 
7517     ncollapsed - the number of block indices
7518     collapsed - the block indices (must be large enough to contain the indices)
7519 */
7520 static inline PetscErrorCode MatCollapseRows(Mat Amat,PetscInt start,PetscInt bs,PetscInt *w0,PetscInt *w1,PetscInt *w2,PetscInt *ncollapsed,PetscInt **collapsed)
7521 {
7522   PetscInt       i,nprev,*cprev = w0,ncur = 0,*ccur = w1,*merged = w2,*cprevtmp;
7523 
7524   PetscFunctionBegin;
7525   PetscCall(MatCollapseRow(Amat,start,bs,&nprev,cprev));
7526   for (i=start+1; i<start+bs; i++) {
7527     PetscCall(MatCollapseRow(Amat,i,bs,&ncur,ccur));
7528     PetscCall(PetscMergeIntArray(nprev,cprev,ncur,ccur,&nprev,&merged));
7529     cprevtmp = cprev; cprev = merged; merged = cprevtmp;
7530   }
7531   *ncollapsed = nprev;
7532   if (collapsed) *collapsed  = cprev;
7533   PetscFunctionReturn(0);
7534 }
7535 
7536 /* -------------------------------------------------------------------------- */
7537 /*
7538  MatCreateGraph_Simple_AIJ - create simple scalar matrix (graph) from potentially blocked matrix
7539 
7540  Input Parameter:
7541  . Amat - matrix
7542  - symmetrize - make the result symmetric
7543  + scale - scale with diagonal
7544 
7545  Output Parameter:
7546  . a_Gmat - output scalar graph >= 0
7547 
7548  */
7549 PETSC_INTERN PetscErrorCode MatCreateGraph_Simple_AIJ(Mat Amat, PetscBool symmetrize, PetscBool scale, Mat *a_Gmat)
7550 {
7551   PetscInt       Istart,Iend,Ii,jj,kk,ncols,nloc,NN,MM,bs;
7552   MPI_Comm       comm;
7553   Mat            Gmat;
7554   PetscBool      ismpiaij,isseqaij;
7555   Mat            a, b, c;
7556   MatType        jtype;
7557 
7558   PetscFunctionBegin;
7559   PetscCall(PetscObjectGetComm((PetscObject)Amat,&comm));
7560   PetscCall(MatGetOwnershipRange(Amat, &Istart, &Iend));
7561   PetscCall(MatGetSize(Amat, &MM, &NN));
7562   PetscCall(MatGetBlockSize(Amat, &bs));
7563   nloc = (Iend-Istart)/bs;
7564 
7565   PetscCall(PetscObjectBaseTypeCompare((PetscObject)Amat,MATSEQAIJ,&isseqaij));
7566   PetscCall(PetscObjectBaseTypeCompare((PetscObject)Amat,MATMPIAIJ,&ismpiaij));
7567   PetscCheck(isseqaij || ismpiaij,comm,PETSC_ERR_USER,"Require (MPI)AIJ matrix type");
7568 
7569   /* TODO GPU: these calls are potentially expensive if matrices are large and we want to use the GPU */
7570   /* A solution consists in providing a new API, MatAIJGetCollapsedAIJ, and each class can provide a fast
7571      implementation */
7572   if (bs > 1) {
7573     PetscCall(MatGetType(Amat,&jtype));
7574     PetscCall(MatCreate(comm, &Gmat));
7575     PetscCall(MatSetType(Gmat, jtype));
7576     PetscCall(MatSetSizes(Gmat,nloc,nloc,PETSC_DETERMINE,PETSC_DETERMINE));
7577     PetscCall(MatSetBlockSizes(Gmat, 1, 1));
7578     if (isseqaij || ((Mat_MPIAIJ*)Amat->data)->garray) {
7579       PetscInt  *d_nnz, *o_nnz;
7580       MatScalar *aa,val,AA[4096];
7581       PetscInt  *aj,*ai,AJ[4096],nc;
7582       if (isseqaij) { a = Amat; b = NULL; }
7583       else {
7584         Mat_MPIAIJ *d = (Mat_MPIAIJ*)Amat->data;
7585         a = d->A; b = d->B;
7586       }
7587       PetscCall(PetscInfo(Amat,"New bs>1 Graph. nloc=%" PetscInt_FMT "\n",nloc));
7588       PetscCall(PetscMalloc2(nloc, &d_nnz,isseqaij ? 0 : nloc, &o_nnz));
7589       for (c=a, kk=0 ; c && kk<2 ; c=b, kk++){
7590         PetscInt       *nnz = (c==a) ? d_nnz : o_nnz, nmax=0;
7591         const PetscInt *cols;
7592         for (PetscInt brow=0,jj,ok=1,j0; brow < nloc*bs; brow += bs) { // block rows
7593           PetscCall(MatGetRow(c,brow,&jj,&cols,NULL));
7594           nnz[brow/bs] = jj/bs;
7595           if (jj%bs) ok = 0;
7596           if (cols) j0 = cols[0];
7597           else j0 = -1;
7598           PetscCall(MatRestoreRow(c,brow,&jj,&cols,NULL));
7599           if (nnz[brow/bs]>nmax) nmax = nnz[brow/bs];
7600           for (PetscInt ii=1; ii < bs && nnz[brow/bs] ; ii++) { // check for non-dense blocks
7601             PetscCall(MatGetRow(c,brow+ii,&jj,&cols,NULL));
7602             if (jj%bs) ok = 0;
7603             if ((cols && j0 != cols[0]) || (!cols && j0 != -1)) ok = 0;
7604             if (nnz[brow/bs] != jj/bs) ok = 0;
7605             PetscCall(MatRestoreRow(c,brow+ii,&jj,&cols,NULL));
7606           }
7607           if (!ok) {
7608             PetscCall(PetscFree2(d_nnz,o_nnz));
7609             goto old_bs;
7610           }
7611         }
7612         PetscCheck(nmax<4096,PETSC_COMM_SELF,PETSC_ERR_USER,"Buffer %" PetscInt_FMT " too small 4096.",nmax);
7613       }
7614       PetscCall(MatSeqAIJSetPreallocation(Gmat,0,d_nnz));
7615       PetscCall(MatMPIAIJSetPreallocation(Gmat,0,d_nnz,0,o_nnz));
7616       PetscCall(PetscFree2(d_nnz,o_nnz));
7617       // diag
7618       for (PetscInt brow=0,n,grow; brow < nloc*bs; brow += bs) { // block rows
7619         Mat_SeqAIJ *aseq  = (Mat_SeqAIJ*)a->data;
7620         ai = aseq->i;
7621         n  = ai[brow+1] - ai[brow];
7622         aj = aseq->j + ai[brow];
7623         for (int k=0; k<n; k += bs) { // block columns
7624           AJ[k/bs] = aj[k]/bs + Istart/bs; // diag starts at (Istart,Istart)
7625           val = 0;
7626           for (int ii=0; ii<bs; ii++) { // rows in block
7627             aa = aseq->a + ai[brow+ii] + k;
7628             for (int jj=0; jj<bs; jj++) { // columns in block
7629               val += PetscAbs(PetscRealPart(aa[jj])); // a sort of norm
7630             }
7631           }
7632           AA[k/bs] = val;
7633         }
7634         grow = Istart/bs + brow/bs;
7635         PetscCall(MatSetValues(Gmat,1,&grow,n/bs,AJ,AA,INSERT_VALUES));
7636       }
7637       // off-diag
7638       if (ismpiaij) {
7639         Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)Amat->data;
7640         const PetscScalar *vals;
7641         const PetscInt    *cols, *garray = aij->garray;
7642         PetscCheck(garray,PETSC_COMM_SELF,PETSC_ERR_USER,"No garray ?");
7643         for (PetscInt brow=0,grow; brow < nloc*bs; brow += bs) { // block rows
7644           PetscCall(MatGetRow(b,brow,&ncols,&cols,NULL));
7645           for (int k=0,cidx=0 ; k < ncols ; k += bs, cidx++) {
7646             AA[k/bs] = 0;
7647             AJ[cidx] = garray[cols[k]]/bs;
7648           }
7649           nc = ncols/bs;
7650           PetscCall(MatRestoreRow(b,brow,&ncols,&cols,NULL));
7651           for (int ii=0; ii<bs; ii++) { // rows in block
7652             PetscCall(MatGetRow(b,brow+ii,&ncols,&cols,&vals));
7653             for (int k=0; k<ncols; k += bs) {
7654               for (int jj=0; jj<bs; jj++) { // cols in block
7655                 AA[k/bs] += PetscAbs(PetscRealPart(vals[k+jj]));
7656               }
7657             }
7658             PetscCall(MatRestoreRow(b,brow+ii,&ncols,&cols,&vals));
7659           }
7660           grow = Istart/bs + brow/bs;
7661           PetscCall(MatSetValues(Gmat,1,&grow,nc,AJ,AA,INSERT_VALUES));
7662         }
7663       }
7664       PetscCall(MatAssemblyBegin(Gmat,MAT_FINAL_ASSEMBLY));
7665       PetscCall(MatAssemblyEnd(Gmat,MAT_FINAL_ASSEMBLY));
7666     } else {
7667       const PetscScalar *vals;
7668       const PetscInt    *idx;
7669       PetscInt          *d_nnz, *o_nnz,*w0,*w1,*w2;
7670       old_bs:
7671       /*
7672        Determine the preallocation needed for the scalar matrix derived from the vector matrix.
7673        */
7674       PetscCall(PetscInfo(Amat,"OLD bs>1 CreateGraph\n"));
7675       PetscCall(PetscMalloc2(nloc, &d_nnz,isseqaij ? 0 : nloc, &o_nnz));
7676       if (isseqaij) {
7677         PetscInt max_d_nnz;
7678         /*
7679          Determine exact preallocation count for (sequential) scalar matrix
7680          */
7681         PetscCall(MatSeqAIJGetMaxRowNonzeros(Amat,&max_d_nnz));
7682         max_d_nnz = PetscMin(nloc,bs*max_d_nnz);
7683         PetscCall(PetscMalloc3(max_d_nnz, &w0,max_d_nnz, &w1,max_d_nnz, &w2));
7684         for (Ii = 0, jj = 0; Ii < Iend; Ii += bs, jj++) {
7685           PetscCall(MatCollapseRows(Amat,Ii,bs,w0,w1,w2,&d_nnz[jj],NULL));
7686         }
7687         PetscCall(PetscFree3(w0,w1,w2));
7688       } else if (ismpiaij) {
7689         Mat            Daij,Oaij;
7690         const PetscInt *garray;
7691         PetscInt       max_d_nnz;
7692         PetscCall(MatMPIAIJGetSeqAIJ(Amat,&Daij,&Oaij,&garray));
7693         /*
7694          Determine exact preallocation count for diagonal block portion of scalar matrix
7695          */
7696         PetscCall(MatSeqAIJGetMaxRowNonzeros(Daij,&max_d_nnz));
7697         max_d_nnz = PetscMin(nloc,bs*max_d_nnz);
7698         PetscCall(PetscMalloc3(max_d_nnz, &w0,max_d_nnz, &w1,max_d_nnz, &w2));
7699         for (Ii = 0, jj = 0; Ii < Iend - Istart; Ii += bs, jj++) {
7700           PetscCall(MatCollapseRows(Daij,Ii,bs,w0,w1,w2,&d_nnz[jj],NULL));
7701         }
7702         PetscCall(PetscFree3(w0,w1,w2));
7703         /*
7704          Over estimate (usually grossly over), preallocation count for off-diagonal portion of scalar matrix
7705          */
7706         for (Ii = 0, jj = 0; Ii < Iend - Istart; Ii += bs, jj++) {
7707           o_nnz[jj] = 0;
7708           for (kk=0; kk<bs; kk++) { /* rows that get collapsed to a single row */
7709             PetscCall(MatGetRow(Oaij,Ii+kk,&ncols,NULL,NULL));
7710             o_nnz[jj] += ncols;
7711             PetscCall(MatRestoreRow(Oaij,Ii+kk,&ncols,NULL,NULL));
7712           }
7713           if (o_nnz[jj] > (NN/bs-nloc)) o_nnz[jj] = NN/bs-nloc;
7714         }
7715       } else SETERRQ(comm,PETSC_ERR_USER,"Require AIJ matrix type");
7716       /* get scalar copy (norms) of matrix */
7717       PetscCall(MatSeqAIJSetPreallocation(Gmat,0,d_nnz));
7718       PetscCall(MatMPIAIJSetPreallocation(Gmat,0,d_nnz,0,o_nnz));
7719       PetscCall(PetscFree2(d_nnz,o_nnz));
7720       for (Ii = Istart; Ii < Iend; Ii++) {
7721         PetscInt dest_row = Ii/bs;
7722         PetscCall(MatGetRow(Amat,Ii,&ncols,&idx,&vals));
7723         for (jj=0; jj<ncols; jj++) {
7724           PetscInt    dest_col = idx[jj]/bs;
7725           PetscScalar sv       = PetscAbs(PetscRealPart(vals[jj]));
7726           PetscCall(MatSetValues(Gmat,1,&dest_row,1,&dest_col,&sv,ADD_VALUES));
7727         }
7728         PetscCall(MatRestoreRow(Amat,Ii,&ncols,&idx,&vals));
7729       }
7730       PetscCall(MatAssemblyBegin(Gmat,MAT_FINAL_ASSEMBLY));
7731       PetscCall(MatAssemblyEnd(Gmat,MAT_FINAL_ASSEMBLY));
7732     }
7733   } else {
7734     /* TODO GPU: optimization proposal, each class provides fast implementation of this
7735      procedure via MatAbs API */
7736     /* just copy scalar matrix & abs() */
7737     PetscCall(MatDuplicate(Amat, MAT_COPY_VALUES, &Gmat));
7738     if (isseqaij) { a = Gmat; b = NULL; }
7739     else {
7740       Mat_MPIAIJ *d = (Mat_MPIAIJ*)Gmat->data;
7741       a = d->A; b = d->B;
7742     }
7743     /* abs */
7744     for (c=a, kk=0 ; c && kk<2 ; c=b, kk++){
7745       MatInfo     info;
7746       PetscScalar *avals;
7747       PetscCall(MatGetInfo(c,MAT_LOCAL,&info));
7748       PetscCall(MatSeqAIJGetArray(c,&avals));
7749       for (int jj = 0; jj<info.nz_used; jj++) avals[jj] = PetscAbsScalar(avals[jj]);
7750       PetscCall(MatSeqAIJRestoreArray(c,&avals));
7751     }
7752   }
7753   if (symmetrize) {
7754     PetscBool issym;
7755     PetscCall(MatGetOption(Amat,MAT_SYMMETRIC,&issym));
7756     if (!issym) {
7757       Mat matTrans;
7758       PetscCall(MatTranspose(Gmat, MAT_INITIAL_MATRIX, &matTrans));
7759       PetscCall(MatAXPY(Gmat, 1.0, matTrans, Gmat->structurally_symmetric ? SAME_NONZERO_PATTERN : DIFFERENT_NONZERO_PATTERN));
7760       PetscCall(MatDestroy(&matTrans));
7761     }
7762     PetscCall(MatSetOption(Gmat,MAT_SYMMETRIC,PETSC_TRUE));
7763   } else {
7764     PetscCall(MatPropagateSymmetryOptions(Amat, Gmat));
7765   }
7766   if (scale) {
7767     /* scale c for all diagonal values = 1 or -1 */
7768     Vec               diag;
7769     PetscCall(MatCreateVecs(Gmat, &diag, NULL));
7770     PetscCall(MatGetDiagonal(Gmat, diag));
7771     PetscCall(VecReciprocal(diag));
7772     PetscCall(VecSqrtAbs(diag));
7773     PetscCall(MatDiagonalScale(Gmat, diag, diag));
7774     PetscCall(VecDestroy(&diag));
7775   }
7776   PetscCall(MatViewFromOptions(Gmat, NULL, "-mat_graph_view"));
7777   *a_Gmat = Gmat;
7778   PetscFunctionReturn(0);
7779 }
7780 
7781 /* -------------------------------------------------------------------------- */
7782 /*@C
7783    MatFilter_AIJ - filter values with small absolute values
7784      With vfilter < 0 does nothing so should not be called.
7785 
7786    Collective on Mat
7787 
7788    Input Parameters:
7789 +   Gmat - the graph
7790 .   vfilter - threshold parameter [0,1)
7791 
7792  Output Parameter:
7793  .  filteredG - output filtered scalar graph
7794 
7795    Level: developer
7796 
7797    Notes:
7798     This is called before graph coarsers are called.
7799     This could go into Mat, move 'symm' to GAMG
7800 
7801 .seealso: `PCGAMGSetThreshold()`
7802 @*/
7803 PETSC_INTERN PetscErrorCode MatFilter_AIJ(Mat Gmat,PetscReal vfilter, Mat *filteredG)
7804 {
7805   PetscInt          Istart,Iend,ncols,nnz0,nnz1, NN, MM, nloc;
7806   Mat               tGmat;
7807   MPI_Comm          comm;
7808   const PetscScalar *vals;
7809   const PetscInt    *idx;
7810   PetscInt          *d_nnz, *o_nnz, kk, *garray = NULL, *AJ, maxcols=0;
7811   MatScalar         *AA; // this is checked in graph
7812   PetscBool         isseqaij;
7813   Mat               a, b, c;
7814   MatType           jtype;
7815 
7816   PetscFunctionBegin;
7817   PetscCall(PetscObjectGetComm((PetscObject)Gmat,&comm));
7818   PetscCall(PetscObjectBaseTypeCompare((PetscObject)Gmat,MATSEQAIJ,&isseqaij));
7819   PetscCall(MatGetType(Gmat,&jtype));
7820   PetscCall(MatCreate(comm, &tGmat));
7821   PetscCall(MatSetType(tGmat, jtype));
7822 
7823   /* TODO GPU: this can be called when filter = 0 -> Probably provide MatAIJThresholdCompress that compresses the entries below a threshold?
7824                Also, if the matrix is symmetric, can we skip this
7825                operation? It can be very expensive on large matrices. */
7826 
7827   // global sizes
7828   PetscCall(MatGetSize(Gmat, &MM, &NN));
7829   PetscCall(MatGetOwnershipRange(Gmat, &Istart, &Iend));
7830   nloc = Iend - Istart;
7831   PetscCall(PetscMalloc2(nloc, &d_nnz,nloc, &o_nnz));
7832   if (isseqaij) { a = Gmat; b = NULL; }
7833   else {
7834     Mat_MPIAIJ *d = (Mat_MPIAIJ*)Gmat->data;
7835     a = d->A; b = d->B;
7836     garray = d->garray;
7837   }
7838   /* Determine upper bound on non-zeros needed in new filtered matrix */
7839   for (PetscInt row=0; row < nloc; row++) {
7840     PetscCall(MatGetRow(a,row,&ncols,NULL,NULL));
7841     d_nnz[row] = ncols;
7842     if (ncols>maxcols) maxcols=ncols;
7843     PetscCall(MatRestoreRow(a,row,&ncols,NULL,NULL));
7844   }
7845   if (b) {
7846     for (PetscInt row=0; row < nloc; row++) {
7847       PetscCall(MatGetRow(b,row,&ncols,NULL,NULL));
7848       o_nnz[row] = ncols;
7849       if (ncols>maxcols) maxcols=ncols;
7850       PetscCall(MatRestoreRow(b,row,&ncols,NULL,NULL));
7851     }
7852   }
7853   PetscCall(MatSetSizes(tGmat,nloc,nloc,MM,MM));
7854   PetscCall(MatSetBlockSizes(tGmat, 1, 1));
7855   PetscCall(MatSeqAIJSetPreallocation(tGmat,0,d_nnz));
7856   PetscCall(MatMPIAIJSetPreallocation(tGmat,0,d_nnz,0,o_nnz));
7857   PetscCall(MatSetOption(tGmat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE));
7858   PetscCall(PetscFree2(d_nnz,o_nnz));
7859   //
7860   PetscCall(PetscMalloc2(maxcols, &AA,maxcols, &AJ));
7861   nnz0 = nnz1 = 0;
7862   for (c=a, kk=0 ; c && kk<2 ; c=b, kk++){
7863     for (PetscInt row=0, grow=Istart, ncol_row, jj ; row < nloc; row++,grow++) {
7864       PetscCall(MatGetRow(c,row,&ncols,&idx,&vals));
7865       for (ncol_row=jj=0; jj<ncols; jj++,nnz0++) {
7866         PetscScalar sv = PetscAbs(PetscRealPart(vals[jj]));
7867         if (PetscRealPart(sv) > vfilter) {
7868           nnz1++;
7869           PetscInt cid = idx[jj] + Istart; //diag
7870           if (c!=a) cid = garray[idx[jj]];
7871           AA[ncol_row] = vals[jj];
7872           AJ[ncol_row] = cid;
7873           ncol_row++;
7874         }
7875       }
7876       PetscCall(MatRestoreRow(c,row,&ncols,&idx,&vals));
7877       PetscCall(MatSetValues(tGmat,1,&grow,ncol_row,AJ,AA,INSERT_VALUES));
7878     }
7879   }
7880   PetscCall(PetscFree2(AA,AJ));
7881   PetscCall(MatAssemblyBegin(tGmat,MAT_FINAL_ASSEMBLY));
7882   PetscCall(MatAssemblyEnd(tGmat,MAT_FINAL_ASSEMBLY));
7883   PetscCall(MatPropagateSymmetryOptions(Gmat,tGmat)); /* Normal Mat options are not relevant ? */
7884 
7885   PetscCall(PetscInfo(tGmat,"\t %g%% nnz after filtering, with threshold %g, %g nnz ave. (N=%" PetscInt_FMT ", max row size %d)\n",
7886                       (!nnz0) ? 1. : 100.*(double)nnz1/(double)nnz0, (double)vfilter,
7887                       (!nloc) ? 1. : (double)nnz0/(double)nloc,MM,(int)maxcols));
7888 
7889   *filteredG = tGmat;
7890   PetscCall(MatViewFromOptions(tGmat, NULL, "-mat_filter_graph_view"));
7891   PetscFunctionReturn(0);
7892 }
7893 
7894 /*
7895     Special version for direct calls from Fortran
7896 */
7897 #include <petsc/private/fortranimpl.h>
7898 
7899 /* Change these macros so can be used in void function */
7900 /* Identical to PetscCallVoid, except it assigns to *_ierr */
7901 #undef  PetscCall
7902 #define PetscCall(...) do {                                                                    \
7903     PetscErrorCode ierr_msv_mpiaij = __VA_ARGS__;                                              \
7904     if (PetscUnlikely(ierr_msv_mpiaij)) {                                                      \
7905       *_ierr = PetscError(PETSC_COMM_SELF,__LINE__,PETSC_FUNCTION_NAME,__FILE__,ierr_msv_mpiaij,PETSC_ERROR_REPEAT," "); \
7906       return;                                                                                  \
7907     }                                                                                          \
7908   } while (0)
7909 
7910 #undef SETERRQ
7911 #define SETERRQ(comm,ierr,...) do {                                                            \
7912     *_ierr = PetscError(comm,__LINE__,PETSC_FUNCTION_NAME,__FILE__,ierr,PETSC_ERROR_INITIAL,__VA_ARGS__); \
7913     return;                                                                                    \
7914   } while (0)
7915 
7916 #if defined(PETSC_HAVE_FORTRAN_CAPS)
7917 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
7918 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
7919 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
7920 #else
7921 #endif
7922 PETSC_EXTERN void matsetvaluesmpiaij_(Mat *mmat,PetscInt *mm,const PetscInt im[],PetscInt *mn,const PetscInt in[],const PetscScalar v[],InsertMode *maddv,PetscErrorCode *_ierr)
7923 {
7924   Mat          mat  = *mmat;
7925   PetscInt     m    = *mm, n = *mn;
7926   InsertMode   addv = *maddv;
7927   Mat_MPIAIJ  *aij  = (Mat_MPIAIJ*)mat->data;
7928   PetscScalar  value;
7929 
7930   MatCheckPreallocated(mat,1);
7931   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
7932   else PetscCheck(mat->insertmode == addv,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
7933   {
7934     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
7935     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
7936     PetscBool roworiented = aij->roworiented;
7937 
7938     /* Some Variables required in the macro */
7939     Mat        A                    = aij->A;
7940     Mat_SeqAIJ *a                   = (Mat_SeqAIJ*)A->data;
7941     PetscInt   *aimax               = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
7942     MatScalar  *aa;
7943     PetscBool  ignorezeroentries    = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
7944     Mat        B                    = aij->B;
7945     Mat_SeqAIJ *b                   = (Mat_SeqAIJ*)B->data;
7946     PetscInt   *bimax               = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
7947     MatScalar  *ba;
7948     /* This variable below is only for the PETSC_HAVE_VIENNACL or PETSC_HAVE_CUDA cases, but we define it in all cases because we
7949      * cannot use "#if defined" inside a macro. */
7950     PETSC_UNUSED PetscBool inserted = PETSC_FALSE;
7951 
7952     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
7953     PetscInt  nonew = a->nonew;
7954     MatScalar *ap1,*ap2;
7955 
7956     PetscFunctionBegin;
7957     PetscCall(MatSeqAIJGetArray(A,&aa));
7958     PetscCall(MatSeqAIJGetArray(B,&ba));
7959     for (i=0; i<m; i++) {
7960       if (im[i] < 0) continue;
7961       PetscCheck(im[i] < mat->rmap->N,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %" PetscInt_FMT " max %" PetscInt_FMT,im[i],mat->rmap->N-1);
7962       if (im[i] >= rstart && im[i] < rend) {
7963         row      = im[i] - rstart;
7964         lastcol1 = -1;
7965         rp1      = aj + ai[row];
7966         ap1      = aa + ai[row];
7967         rmax1    = aimax[row];
7968         nrow1    = ailen[row];
7969         low1     = 0;
7970         high1    = nrow1;
7971         lastcol2 = -1;
7972         rp2      = bj + bi[row];
7973         ap2      = ba + bi[row];
7974         rmax2    = bimax[row];
7975         nrow2    = bilen[row];
7976         low2     = 0;
7977         high2    = nrow2;
7978 
7979         for (j=0; j<n; j++) {
7980           if (roworiented) value = v[i*n+j];
7981           else value = v[i+j*m];
7982           if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && im[i] != in[j]) continue;
7983           if (in[j] >= cstart && in[j] < cend) {
7984             col = in[j] - cstart;
7985             MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
7986           } else if (in[j] < 0) continue;
7987           else if (PetscUnlikelyDebug(in[j] >= mat->cmap->N)) {
7988             /* extra brace on SETERRQ() is required for --with-errorchecking=0 - due to the next 'else' clause */
7989             SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %" PetscInt_FMT " max %" PetscInt_FMT,in[j],mat->cmap->N-1);
7990           } else {
7991             if (mat->was_assembled) {
7992               if (!aij->colmap) {
7993                 PetscCall(MatCreateColmap_MPIAIJ_Private(mat));
7994               }
7995 #if defined(PETSC_USE_CTABLE)
7996               PetscCall(PetscTableFind(aij->colmap,in[j]+1,&col));
7997               col--;
7998 #else
7999               col = aij->colmap[in[j]] - 1;
8000 #endif
8001               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
8002                 PetscCall(MatDisAssemble_MPIAIJ(mat));
8003                 col  =  in[j];
8004                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
8005                 B        = aij->B;
8006                 b        = (Mat_SeqAIJ*)B->data;
8007                 bimax    = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
8008                 rp2      = bj + bi[row];
8009                 ap2      = ba + bi[row];
8010                 rmax2    = bimax[row];
8011                 nrow2    = bilen[row];
8012                 low2     = 0;
8013                 high2    = nrow2;
8014                 bm       = aij->B->rmap->n;
8015                 ba       = b->a;
8016                 inserted = PETSC_FALSE;
8017               }
8018             } else col = in[j];
8019             MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
8020           }
8021         }
8022       } else if (!aij->donotstash) {
8023         if (roworiented) {
8024           PetscCall(MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES))));
8025         } else {
8026           PetscCall(MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES))));
8027         }
8028       }
8029     }
8030     PetscCall(MatSeqAIJRestoreArray(A,&aa));
8031     PetscCall(MatSeqAIJRestoreArray(B,&ba));
8032   }
8033   PetscFunctionReturnVoid();
8034 }
8035 
8036 /* Undefining these here since they were redefined from their original definition above! No
8037  * other PETSc functions should be defined past this point, as it is impossible to recover the
8038  * original definitions */
8039 #undef PetscCall
8040 #undef SETERRQ
8041