xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision 6a98f8dc3f2c9149905a87dc2e9d0fedaf64e09a)
1 #include <../src/mat/impls/aij/mpi/mpiaij.h>   /*I "petscmat.h" I*/
2 #include <petsc/private/vecimpl.h>
3 #include <petsc/private/vecscatterimpl.h>
4 #include <petsc/private/isimpl.h>
5 #include <petscblaslapack.h>
6 #include <petscsf.h>
7 #include <petsc/private/hashmapi.h>
8 
9 /*MC
10    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.
11 
12    This matrix type is identical to MATSEQAIJ when constructed with a single process communicator,
13    and MATMPIAIJ otherwise.  As a result, for single process communicators,
14   MatSeqAIJSetPreallocation is supported, and similarly MatMPIAIJSetPreallocation() is supported
15   for communicators controlling multiple processes.  It is recommended that you call both of
16   the above preallocation routines for simplicity.
17 
18    Options Database Keys:
19 . -mat_type aij - sets the matrix type to "aij" during a call to MatSetFromOptions()
20 
21   Developer Notes:
22     Subclasses include MATAIJCUSP, MATAIJCUSPARSE, MATAIJPERM, MATAIJSELL, MATAIJMKL, MATAIJCRL, and also automatically switches over to use inodes when
23    enough exist.
24 
25   Level: beginner
26 
27 .seealso: MatCreateAIJ(), MatCreateSeqAIJ(), MATSEQAIJ, MATMPIAIJ
28 M*/
29 
30 /*MC
31    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.
32 
33    This matrix type is identical to MATSEQAIJCRL when constructed with a single process communicator,
34    and MATMPIAIJCRL otherwise.  As a result, for single process communicators,
35    MatSeqAIJSetPreallocation() is supported, and similarly MatMPIAIJSetPreallocation() is supported
36   for communicators controlling multiple processes.  It is recommended that you call both of
37   the above preallocation routines for simplicity.
38 
39    Options Database Keys:
40 . -mat_type aijcrl - sets the matrix type to "aijcrl" during a call to MatSetFromOptions()
41 
42   Level: beginner
43 
44 .seealso: MatCreateMPIAIJCRL,MATSEQAIJCRL,MATMPIAIJCRL, MATSEQAIJCRL, MATMPIAIJCRL
45 M*/
46 
47 static PetscErrorCode MatBindToCPU_MPIAIJ(Mat A,PetscBool flg)
48 {
49   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
50   PetscErrorCode ierr;
51 
52   PetscFunctionBegin;
53 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_VIENNACL)
54   A->boundtocpu = flg;
55 #endif
56   if (a->A) {
57     ierr = MatBindToCPU(a->A,flg);CHKERRQ(ierr);
58   }
59   if (a->B) {
60     ierr = MatBindToCPU(a->B,flg);CHKERRQ(ierr);
61   }
62   PetscFunctionReturn(0);
63 }
64 
65 
66 PetscErrorCode MatSetBlockSizes_MPIAIJ(Mat M, PetscInt rbs, PetscInt cbs)
67 {
68   PetscErrorCode ierr;
69   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)M->data;
70 
71   PetscFunctionBegin;
72   if (mat->A) {
73     ierr = MatSetBlockSizes(mat->A,rbs,cbs);CHKERRQ(ierr);
74     ierr = MatSetBlockSizes(mat->B,rbs,1);CHKERRQ(ierr);
75   }
76   PetscFunctionReturn(0);
77 }
78 
79 PetscErrorCode MatFindNonzeroRows_MPIAIJ(Mat M,IS *keptrows)
80 {
81   PetscErrorCode  ierr;
82   Mat_MPIAIJ      *mat = (Mat_MPIAIJ*)M->data;
83   Mat_SeqAIJ      *a   = (Mat_SeqAIJ*)mat->A->data;
84   Mat_SeqAIJ      *b   = (Mat_SeqAIJ*)mat->B->data;
85   const PetscInt  *ia,*ib;
86   const MatScalar *aa,*bb;
87   PetscInt        na,nb,i,j,*rows,cnt=0,n0rows;
88   PetscInt        m = M->rmap->n,rstart = M->rmap->rstart;
89 
90   PetscFunctionBegin;
91   *keptrows = 0;
92   ia        = a->i;
93   ib        = b->i;
94   for (i=0; i<m; i++) {
95     na = ia[i+1] - ia[i];
96     nb = ib[i+1] - ib[i];
97     if (!na && !nb) {
98       cnt++;
99       goto ok1;
100     }
101     aa = a->a + ia[i];
102     for (j=0; j<na; j++) {
103       if (aa[j] != 0.0) goto ok1;
104     }
105     bb = b->a + ib[i];
106     for (j=0; j <nb; j++) {
107       if (bb[j] != 0.0) goto ok1;
108     }
109     cnt++;
110 ok1:;
111   }
112   ierr = MPIU_Allreduce(&cnt,&n0rows,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)M));CHKERRQ(ierr);
113   if (!n0rows) PetscFunctionReturn(0);
114   ierr = PetscMalloc1(M->rmap->n-cnt,&rows);CHKERRQ(ierr);
115   cnt  = 0;
116   for (i=0; i<m; i++) {
117     na = ia[i+1] - ia[i];
118     nb = ib[i+1] - ib[i];
119     if (!na && !nb) continue;
120     aa = a->a + ia[i];
121     for (j=0; j<na;j++) {
122       if (aa[j] != 0.0) {
123         rows[cnt++] = rstart + i;
124         goto ok2;
125       }
126     }
127     bb = b->a + ib[i];
128     for (j=0; j<nb; j++) {
129       if (bb[j] != 0.0) {
130         rows[cnt++] = rstart + i;
131         goto ok2;
132       }
133     }
134 ok2:;
135   }
136   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)M),cnt,rows,PETSC_OWN_POINTER,keptrows);CHKERRQ(ierr);
137   PetscFunctionReturn(0);
138 }
139 
140 PetscErrorCode  MatDiagonalSet_MPIAIJ(Mat Y,Vec D,InsertMode is)
141 {
142   PetscErrorCode    ierr;
143   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*) Y->data;
144   PetscBool         cong;
145 
146   PetscFunctionBegin;
147   ierr = MatHasCongruentLayouts(Y,&cong);CHKERRQ(ierr);
148   if (Y->assembled && cong) {
149     ierr = MatDiagonalSet(aij->A,D,is);CHKERRQ(ierr);
150   } else {
151     ierr = MatDiagonalSet_Default(Y,D,is);CHKERRQ(ierr);
152   }
153   PetscFunctionReturn(0);
154 }
155 
156 PetscErrorCode MatFindZeroDiagonals_MPIAIJ(Mat M,IS *zrows)
157 {
158   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)M->data;
159   PetscErrorCode ierr;
160   PetscInt       i,rstart,nrows,*rows;
161 
162   PetscFunctionBegin;
163   *zrows = NULL;
164   ierr   = MatFindZeroDiagonals_SeqAIJ_Private(aij->A,&nrows,&rows);CHKERRQ(ierr);
165   ierr   = MatGetOwnershipRange(M,&rstart,NULL);CHKERRQ(ierr);
166   for (i=0; i<nrows; i++) rows[i] += rstart;
167   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)M),nrows,rows,PETSC_OWN_POINTER,zrows);CHKERRQ(ierr);
168   PetscFunctionReturn(0);
169 }
170 
171 PetscErrorCode MatGetColumnNorms_MPIAIJ(Mat A,NormType type,PetscReal *norms)
172 {
173   PetscErrorCode ierr;
174   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)A->data;
175   PetscInt       i,n,*garray = aij->garray;
176   Mat_SeqAIJ     *a_aij = (Mat_SeqAIJ*) aij->A->data;
177   Mat_SeqAIJ     *b_aij = (Mat_SeqAIJ*) aij->B->data;
178   PetscReal      *work;
179 
180   PetscFunctionBegin;
181   ierr = MatGetSize(A,NULL,&n);CHKERRQ(ierr);
182   ierr = PetscCalloc1(n,&work);CHKERRQ(ierr);
183   if (type == NORM_2) {
184     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
185       work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i]*a_aij->a[i]);
186     }
187     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
188       work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]*b_aij->a[i]);
189     }
190   } else if (type == NORM_1) {
191     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
192       work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i]);
193     }
194     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
195       work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]);
196     }
197   } else if (type == NORM_INFINITY) {
198     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
199       work[A->cmap->rstart + a_aij->j[i]] = PetscMax(PetscAbsScalar(a_aij->a[i]), work[A->cmap->rstart + a_aij->j[i]]);
200     }
201     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
202       work[garray[b_aij->j[i]]] = PetscMax(PetscAbsScalar(b_aij->a[i]),work[garray[b_aij->j[i]]]);
203     }
204 
205   } else SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Unknown NormType");
206   if (type == NORM_INFINITY) {
207     ierr = MPIU_Allreduce(work,norms,n,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
208   } else {
209     ierr = MPIU_Allreduce(work,norms,n,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
210   }
211   ierr = PetscFree(work);CHKERRQ(ierr);
212   if (type == NORM_2) {
213     for (i=0; i<n; i++) norms[i] = PetscSqrtReal(norms[i]);
214   }
215   PetscFunctionReturn(0);
216 }
217 
218 PetscErrorCode MatFindOffBlockDiagonalEntries_MPIAIJ(Mat A,IS *is)
219 {
220   Mat_MPIAIJ      *a  = (Mat_MPIAIJ*)A->data;
221   IS              sis,gis;
222   PetscErrorCode  ierr;
223   const PetscInt  *isis,*igis;
224   PetscInt        n,*iis,nsis,ngis,rstart,i;
225 
226   PetscFunctionBegin;
227   ierr = MatFindOffBlockDiagonalEntries(a->A,&sis);CHKERRQ(ierr);
228   ierr = MatFindNonzeroRows(a->B,&gis);CHKERRQ(ierr);
229   ierr = ISGetSize(gis,&ngis);CHKERRQ(ierr);
230   ierr = ISGetSize(sis,&nsis);CHKERRQ(ierr);
231   ierr = ISGetIndices(sis,&isis);CHKERRQ(ierr);
232   ierr = ISGetIndices(gis,&igis);CHKERRQ(ierr);
233 
234   ierr = PetscMalloc1(ngis+nsis,&iis);CHKERRQ(ierr);
235   ierr = PetscArraycpy(iis,igis,ngis);CHKERRQ(ierr);
236   ierr = PetscArraycpy(iis+ngis,isis,nsis);CHKERRQ(ierr);
237   n    = ngis + nsis;
238   ierr = PetscSortRemoveDupsInt(&n,iis);CHKERRQ(ierr);
239   ierr = MatGetOwnershipRange(A,&rstart,NULL);CHKERRQ(ierr);
240   for (i=0; i<n; i++) iis[i] += rstart;
241   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)A),n,iis,PETSC_OWN_POINTER,is);CHKERRQ(ierr);
242 
243   ierr = ISRestoreIndices(sis,&isis);CHKERRQ(ierr);
244   ierr = ISRestoreIndices(gis,&igis);CHKERRQ(ierr);
245   ierr = ISDestroy(&sis);CHKERRQ(ierr);
246   ierr = ISDestroy(&gis);CHKERRQ(ierr);
247   PetscFunctionReturn(0);
248 }
249 
250 /*
251     Distributes a SeqAIJ matrix across a set of processes. Code stolen from
252     MatLoad_MPIAIJ(). Horrible lack of reuse. Should be a routine for each matrix type.
253 
254     Only for square matrices
255 
256     Used by a preconditioner, hence PETSC_EXTERN
257 */
258 PETSC_EXTERN PetscErrorCode MatDistribute_MPIAIJ(MPI_Comm comm,Mat gmat,PetscInt m,MatReuse reuse,Mat *inmat)
259 {
260   PetscMPIInt    rank,size;
261   PetscInt       *rowners,*dlens,*olens,i,rstart,rend,j,jj,nz = 0,*gmataj,cnt,row,*ld,bses[2];
262   PetscErrorCode ierr;
263   Mat            mat;
264   Mat_SeqAIJ     *gmata;
265   PetscMPIInt    tag;
266   MPI_Status     status;
267   PetscBool      aij;
268   MatScalar      *gmataa,*ao,*ad,*gmataarestore=0;
269 
270   PetscFunctionBegin;
271   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
272   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
273   if (!rank) {
274     ierr = PetscObjectTypeCompare((PetscObject)gmat,MATSEQAIJ,&aij);CHKERRQ(ierr);
275     if (!aij) SETERRQ1(PetscObjectComm((PetscObject)gmat),PETSC_ERR_SUP,"Currently no support for input matrix of type %s\n",((PetscObject)gmat)->type_name);
276   }
277   if (reuse == MAT_INITIAL_MATRIX) {
278     ierr = MatCreate(comm,&mat);CHKERRQ(ierr);
279     ierr = MatSetSizes(mat,m,m,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
280     ierr = MatGetBlockSizes(gmat,&bses[0],&bses[1]);CHKERRQ(ierr);
281     ierr = MPI_Bcast(bses,2,MPIU_INT,0,comm);CHKERRQ(ierr);
282     ierr = MatSetBlockSizes(mat,bses[0],bses[1]);CHKERRQ(ierr);
283     ierr = MatSetType(mat,MATAIJ);CHKERRQ(ierr);
284     ierr = PetscMalloc1(size+1,&rowners);CHKERRQ(ierr);
285     ierr = PetscMalloc2(m,&dlens,m,&olens);CHKERRQ(ierr);
286     ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
287 
288     rowners[0] = 0;
289     for (i=2; i<=size; i++) rowners[i] += rowners[i-1];
290     rstart = rowners[rank];
291     rend   = rowners[rank+1];
292     ierr   = PetscObjectGetNewTag((PetscObject)mat,&tag);CHKERRQ(ierr);
293     if (!rank) {
294       gmata = (Mat_SeqAIJ*) gmat->data;
295       /* send row lengths to all processors */
296       for (i=0; i<m; i++) dlens[i] = gmata->ilen[i];
297       for (i=1; i<size; i++) {
298         ierr = MPI_Send(gmata->ilen + rowners[i],rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
299       }
300       /* determine number diagonal and off-diagonal counts */
301       ierr = PetscArrayzero(olens,m);CHKERRQ(ierr);
302       ierr = PetscCalloc1(m,&ld);CHKERRQ(ierr);
303       jj   = 0;
304       for (i=0; i<m; i++) {
305         for (j=0; j<dlens[i]; j++) {
306           if (gmata->j[jj] < rstart) ld[i]++;
307           if (gmata->j[jj] < rstart || gmata->j[jj] >= rend) olens[i]++;
308           jj++;
309         }
310       }
311       /* send column indices to other processes */
312       for (i=1; i<size; i++) {
313         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
314         ierr = MPI_Send(&nz,1,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
315         ierr = MPI_Send(gmata->j + gmata->i[rowners[i]],nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
316       }
317 
318       /* send numerical values to other processes */
319       for (i=1; i<size; i++) {
320         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
321         ierr = MPI_Send(gmata->a + gmata->i[rowners[i]],nz,MPIU_SCALAR,i,tag,comm);CHKERRQ(ierr);
322       }
323       gmataa = gmata->a;
324       gmataj = gmata->j;
325 
326     } else {
327       /* receive row lengths */
328       ierr = MPI_Recv(dlens,m,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
329       /* receive column indices */
330       ierr = MPI_Recv(&nz,1,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
331       ierr = PetscMalloc2(nz,&gmataa,nz,&gmataj);CHKERRQ(ierr);
332       ierr = MPI_Recv(gmataj,nz,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
333       /* determine number diagonal and off-diagonal counts */
334       ierr = PetscArrayzero(olens,m);CHKERRQ(ierr);
335       ierr = PetscCalloc1(m,&ld);CHKERRQ(ierr);
336       jj   = 0;
337       for (i=0; i<m; i++) {
338         for (j=0; j<dlens[i]; j++) {
339           if (gmataj[jj] < rstart) ld[i]++;
340           if (gmataj[jj] < rstart || gmataj[jj] >= rend) olens[i]++;
341           jj++;
342         }
343       }
344       /* receive numerical values */
345       ierr = PetscArrayzero(gmataa,nz);CHKERRQ(ierr);
346       ierr = MPI_Recv(gmataa,nz,MPIU_SCALAR,0,tag,comm,&status);CHKERRQ(ierr);
347     }
348     /* set preallocation */
349     for (i=0; i<m; i++) {
350       dlens[i] -= olens[i];
351     }
352     ierr = MatSeqAIJSetPreallocation(mat,0,dlens);CHKERRQ(ierr);
353     ierr = MatMPIAIJSetPreallocation(mat,0,dlens,0,olens);CHKERRQ(ierr);
354 
355     for (i=0; i<m; i++) {
356       dlens[i] += olens[i];
357     }
358     cnt = 0;
359     for (i=0; i<m; i++) {
360       row  = rstart + i;
361       ierr = MatSetValues(mat,1,&row,dlens[i],gmataj+cnt,gmataa+cnt,INSERT_VALUES);CHKERRQ(ierr);
362       cnt += dlens[i];
363     }
364     if (rank) {
365       ierr = PetscFree2(gmataa,gmataj);CHKERRQ(ierr);
366     }
367     ierr = PetscFree2(dlens,olens);CHKERRQ(ierr);
368     ierr = PetscFree(rowners);CHKERRQ(ierr);
369 
370     ((Mat_MPIAIJ*)(mat->data))->ld = ld;
371 
372     *inmat = mat;
373   } else {   /* column indices are already set; only need to move over numerical values from process 0 */
374     Mat_SeqAIJ *Ad = (Mat_SeqAIJ*)((Mat_MPIAIJ*)((*inmat)->data))->A->data;
375     Mat_SeqAIJ *Ao = (Mat_SeqAIJ*)((Mat_MPIAIJ*)((*inmat)->data))->B->data;
376     mat  = *inmat;
377     ierr = PetscObjectGetNewTag((PetscObject)mat,&tag);CHKERRQ(ierr);
378     if (!rank) {
379       /* send numerical values to other processes */
380       gmata  = (Mat_SeqAIJ*) gmat->data;
381       ierr   = MatGetOwnershipRanges(mat,(const PetscInt**)&rowners);CHKERRQ(ierr);
382       gmataa = gmata->a;
383       for (i=1; i<size; i++) {
384         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
385         ierr = MPI_Send(gmataa + gmata->i[rowners[i]],nz,MPIU_SCALAR,i,tag,comm);CHKERRQ(ierr);
386       }
387       nz = gmata->i[rowners[1]]-gmata->i[rowners[0]];
388     } else {
389       /* receive numerical values from process 0*/
390       nz   = Ad->nz + Ao->nz;
391       ierr = PetscMalloc1(nz,&gmataa);CHKERRQ(ierr); gmataarestore = gmataa;
392       ierr = MPI_Recv(gmataa,nz,MPIU_SCALAR,0,tag,comm,&status);CHKERRQ(ierr);
393     }
394     /* transfer numerical values into the diagonal A and off diagonal B parts of mat */
395     ld = ((Mat_MPIAIJ*)(mat->data))->ld;
396     ad = Ad->a;
397     ao = Ao->a;
398     if (mat->rmap->n) {
399       i  = 0;
400       nz = ld[i];                                   ierr = PetscArraycpy(ao,gmataa,nz);CHKERRQ(ierr); ao += nz; gmataa += nz;
401       nz = Ad->i[i+1] - Ad->i[i];                   ierr = PetscArraycpy(ad,gmataa,nz);CHKERRQ(ierr); ad += nz; gmataa += nz;
402     }
403     for (i=1; i<mat->rmap->n; i++) {
404       nz = Ao->i[i] - Ao->i[i-1] - ld[i-1] + ld[i]; ierr = PetscArraycpy(ao,gmataa,nz);CHKERRQ(ierr); ao += nz; gmataa += nz;
405       nz = Ad->i[i+1] - Ad->i[i];                   ierr = PetscArraycpy(ad,gmataa,nz);CHKERRQ(ierr); ad += nz; gmataa += nz;
406     }
407     i--;
408     if (mat->rmap->n) {
409       nz = Ao->i[i+1] - Ao->i[i] - ld[i];           ierr = PetscArraycpy(ao,gmataa,nz);CHKERRQ(ierr);
410     }
411     if (rank) {
412       ierr = PetscFree(gmataarestore);CHKERRQ(ierr);
413     }
414   }
415   ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
416   ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
417   PetscFunctionReturn(0);
418 }
419 
420 /*
421   Local utility routine that creates a mapping from the global column
422 number to the local number in the off-diagonal part of the local
423 storage of the matrix.  When PETSC_USE_CTABLE is used this is scalable at
424 a slightly higher hash table cost; without it it is not scalable (each processor
425 has an order N integer array but is fast to acess.
426 */
427 PetscErrorCode MatCreateColmap_MPIAIJ_Private(Mat mat)
428 {
429   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
430   PetscErrorCode ierr;
431   PetscInt       n = aij->B->cmap->n,i;
432 
433   PetscFunctionBegin;
434   if (!aij->garray) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"MPIAIJ Matrix was assembled but is missing garray");
435 #if defined(PETSC_USE_CTABLE)
436   ierr = PetscTableCreate(n,mat->cmap->N+1,&aij->colmap);CHKERRQ(ierr);
437   for (i=0; i<n; i++) {
438     ierr = PetscTableAdd(aij->colmap,aij->garray[i]+1,i+1,INSERT_VALUES);CHKERRQ(ierr);
439   }
440 #else
441   ierr = PetscCalloc1(mat->cmap->N+1,&aij->colmap);CHKERRQ(ierr);
442   ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N+1)*sizeof(PetscInt));CHKERRQ(ierr);
443   for (i=0; i<n; i++) aij->colmap[aij->garray[i]] = i+1;
444 #endif
445   PetscFunctionReturn(0);
446 }
447 
448 #define MatSetValues_SeqAIJ_A_Private(row,col,value,addv,orow,ocol)     \
449 { \
450     if (col <= lastcol1)  low1 = 0;     \
451     else                 high1 = nrow1; \
452     lastcol1 = col;\
453     while (high1-low1 > 5) { \
454       t = (low1+high1)/2; \
455       if (rp1[t] > col) high1 = t; \
456       else              low1  = t; \
457     } \
458       for (_i=low1; _i<high1; _i++) { \
459         if (rp1[_i] > col) break; \
460         if (rp1[_i] == col) { \
461           if (addv == ADD_VALUES) { \
462             ap1[_i] += value;   \
463             /* Not sure LogFlops will slow dow the code or not */ \
464             (void)PetscLogFlops(1.0);   \
465            } \
466           else                    ap1[_i] = value; \
467           inserted = PETSC_TRUE; \
468           goto a_noinsert; \
469         } \
470       }  \
471       if (value == 0.0 && ignorezeroentries && row != col) {low1 = 0; high1 = nrow1;goto a_noinsert;} \
472       if (nonew == 1) {low1 = 0; high1 = nrow1; goto a_noinsert;}                \
473       if (nonew == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at global row/column (%D, %D) into matrix", orow, ocol); \
474       MatSeqXAIJReallocateAIJ(A,am,1,nrow1,row,col,rmax1,aa,ai,aj,rp1,ap1,aimax,nonew,MatScalar); \
475       N = nrow1++ - 1; a->nz++; high1++; \
476       /* shift up all the later entries in this row */ \
477       ierr = PetscArraymove(rp1+_i+1,rp1+_i,N-_i+1);CHKERRQ(ierr);\
478       ierr = PetscArraymove(ap1+_i+1,ap1+_i,N-_i+1);CHKERRQ(ierr);\
479       rp1[_i] = col;  \
480       ap1[_i] = value;  \
481       A->nonzerostate++;\
482       a_noinsert: ; \
483       ailen[row] = nrow1; \
484 }
485 
486 #define MatSetValues_SeqAIJ_B_Private(row,col,value,addv,orow,ocol) \
487   { \
488     if (col <= lastcol2) low2 = 0;                        \
489     else high2 = nrow2;                                   \
490     lastcol2 = col;                                       \
491     while (high2-low2 > 5) {                              \
492       t = (low2+high2)/2;                                 \
493       if (rp2[t] > col) high2 = t;                        \
494       else             low2  = t;                         \
495     }                                                     \
496     for (_i=low2; _i<high2; _i++) {                       \
497       if (rp2[_i] > col) break;                           \
498       if (rp2[_i] == col) {                               \
499         if (addv == ADD_VALUES) {                         \
500           ap2[_i] += value;                               \
501           (void)PetscLogFlops(1.0);                       \
502         }                                                 \
503         else                    ap2[_i] = value;          \
504         inserted = PETSC_TRUE;                            \
505         goto b_noinsert;                                  \
506       }                                                   \
507     }                                                     \
508     if (value == 0.0 && ignorezeroentries) {low2 = 0; high2 = nrow2; goto b_noinsert;} \
509     if (nonew == 1) {low2 = 0; high2 = nrow2; goto b_noinsert;}                        \
510     if (nonew == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at global row/column (%D, %D) into matrix", orow, ocol); \
511     MatSeqXAIJReallocateAIJ(B,bm,1,nrow2,row,col,rmax2,ba,bi,bj,rp2,ap2,bimax,nonew,MatScalar); \
512     N = nrow2++ - 1; b->nz++; high2++;                    \
513     /* shift up all the later entries in this row */      \
514     ierr = PetscArraymove(rp2+_i+1,rp2+_i,N-_i+1);CHKERRQ(ierr);\
515     ierr = PetscArraymove(ap2+_i+1,ap2+_i,N-_i+1);CHKERRQ(ierr);\
516     rp2[_i] = col;                                        \
517     ap2[_i] = value;                                      \
518     B->nonzerostate++;                                    \
519     b_noinsert: ;                                         \
520     bilen[row] = nrow2;                                   \
521   }
522 
523 PetscErrorCode MatSetValuesRow_MPIAIJ(Mat A,PetscInt row,const PetscScalar v[])
524 {
525   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)A->data;
526   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)mat->A->data,*b = (Mat_SeqAIJ*)mat->B->data;
527   PetscErrorCode ierr;
528   PetscInt       l,*garray = mat->garray,diag;
529 
530   PetscFunctionBegin;
531   /* code only works for square matrices A */
532 
533   /* find size of row to the left of the diagonal part */
534   ierr = MatGetOwnershipRange(A,&diag,0);CHKERRQ(ierr);
535   row  = row - diag;
536   for (l=0; l<b->i[row+1]-b->i[row]; l++) {
537     if (garray[b->j[b->i[row]+l]] > diag) break;
538   }
539   ierr = PetscArraycpy(b->a+b->i[row],v,l);CHKERRQ(ierr);
540 
541   /* diagonal part */
542   ierr = PetscArraycpy(a->a+a->i[row],v+l,(a->i[row+1]-a->i[row]));CHKERRQ(ierr);
543 
544   /* right of diagonal part */
545   ierr = PetscArraycpy(b->a+b->i[row]+l,v+l+a->i[row+1]-a->i[row],b->i[row+1]-b->i[row]-l);CHKERRQ(ierr);
546 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
547   if (A->offloadmask != PETSC_OFFLOAD_UNALLOCATED && (l || (a->i[row+1]-a->i[row]) || (b->i[row+1]-b->i[row]-l))) A->offloadmask = PETSC_OFFLOAD_CPU;
548 #endif
549   PetscFunctionReturn(0);
550 }
551 
552 PetscErrorCode MatSetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode addv)
553 {
554   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
555   PetscScalar    value = 0.0;
556   PetscErrorCode ierr;
557   PetscInt       i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
558   PetscInt       cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
559   PetscBool      roworiented = aij->roworiented;
560 
561   /* Some Variables required in the macro */
562   Mat        A                    = aij->A;
563   Mat_SeqAIJ *a                   = (Mat_SeqAIJ*)A->data;
564   PetscInt   *aimax               = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
565   MatScalar  *aa                  = a->a;
566   PetscBool  ignorezeroentries    = a->ignorezeroentries;
567   Mat        B                    = aij->B;
568   Mat_SeqAIJ *b                   = (Mat_SeqAIJ*)B->data;
569   PetscInt   *bimax               = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
570   MatScalar  *ba                  = b->a;
571   /* This variable below is only for the PETSC_HAVE_VIENNACL or PETSC_HAVE_CUDA cases, but we define it in all cases because we
572    * cannot use "#if defined" inside a macro. */
573   PETSC_UNUSED PetscBool inserted = PETSC_FALSE;
574 
575   PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
576   PetscInt  nonew;
577   MatScalar *ap1,*ap2;
578 
579   PetscFunctionBegin;
580   for (i=0; i<m; i++) {
581     if (im[i] < 0) continue;
582 #if defined(PETSC_USE_DEBUG)
583     if (im[i] >= mat->rmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %D max %D",im[i],mat->rmap->N-1);
584 #endif
585     if (im[i] >= rstart && im[i] < rend) {
586       row      = im[i] - rstart;
587       lastcol1 = -1;
588       rp1      = aj + ai[row];
589       ap1      = aa + ai[row];
590       rmax1    = aimax[row];
591       nrow1    = ailen[row];
592       low1     = 0;
593       high1    = nrow1;
594       lastcol2 = -1;
595       rp2      = bj + bi[row];
596       ap2      = ba + bi[row];
597       rmax2    = bimax[row];
598       nrow2    = bilen[row];
599       low2     = 0;
600       high2    = nrow2;
601 
602       for (j=0; j<n; j++) {
603         if (v)  value = roworiented ? v[i*n+j] : v[i+j*m];
604         if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && im[i] != in[j]) continue;
605         if (in[j] >= cstart && in[j] < cend) {
606           col   = in[j] - cstart;
607           nonew = a->nonew;
608           MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
609 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
610           if (A->offloadmask != PETSC_OFFLOAD_UNALLOCATED && inserted) A->offloadmask = PETSC_OFFLOAD_CPU;
611 #endif
612         } else if (in[j] < 0) continue;
613 #if defined(PETSC_USE_DEBUG)
614         else if (in[j] >= mat->cmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %D max %D",in[j],mat->cmap->N-1);
615 #endif
616         else {
617           if (mat->was_assembled) {
618             if (!aij->colmap) {
619               ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
620             }
621 #if defined(PETSC_USE_CTABLE)
622             ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
623             col--;
624 #else
625             col = aij->colmap[in[j]] - 1;
626 #endif
627             if (col < 0 && !((Mat_SeqAIJ*)(aij->B->data))->nonew) {
628               ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
629               col  =  in[j];
630               /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
631               B        = aij->B;
632               b        = (Mat_SeqAIJ*)B->data;
633               bimax    = b->imax; bi = b->i; bilen = b->ilen; bj = b->j; ba = b->a;
634               rp2      = bj + bi[row];
635               ap2      = ba + bi[row];
636               rmax2    = bimax[row];
637               nrow2    = bilen[row];
638               low2     = 0;
639               high2    = nrow2;
640               bm       = aij->B->rmap->n;
641               ba       = b->a;
642               inserted = PETSC_FALSE;
643             } else if (col < 0) {
644               if (1 == ((Mat_SeqAIJ*)(aij->B->data))->nonew) {
645                 ierr = PetscInfo3(mat,"Skipping of insertion of new nonzero location in off-diagonal portion of matrix %g(%D,%D)\n",(double)PetscRealPart(value),im[i],in[j]);CHKERRQ(ierr);
646               } else SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at global row/column (%D, %D) into matrix", im[i], in[j]);
647             }
648           } else col = in[j];
649           nonew = b->nonew;
650           MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
651 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
652           if (B->offloadmask != PETSC_OFFLOAD_UNALLOCATED && inserted) B->offloadmask = PETSC_OFFLOAD_CPU;
653 #endif
654         }
655       }
656     } else {
657       if (mat->nooffprocentries) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Setting off process row %D even though MatSetOption(,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) was set",im[i]);
658       if (!aij->donotstash) {
659         mat->assembled = PETSC_FALSE;
660         if (roworiented) {
661           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
662         } else {
663           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
664         }
665       }
666     }
667   }
668   PetscFunctionReturn(0);
669 }
670 
671 /*
672     This function sets the j and ilen arrays (of the diagonal and off-diagonal part) of an MPIAIJ-matrix.
673     The values in mat_i have to be sorted and the values in mat_j have to be sorted for each row (CSR-like).
674     No off-processor parts off the matrix are allowed here and mat->was_assembled has to be PETSC_FALSE.
675 */
676 PetscErrorCode MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(Mat mat,const PetscInt mat_j[],const PetscInt mat_i[])
677 {
678   Mat_MPIAIJ     *aij        = (Mat_MPIAIJ*)mat->data;
679   Mat            A           = aij->A; /* diagonal part of the matrix */
680   Mat            B           = aij->B; /* offdiagonal part of the matrix */
681   Mat_SeqAIJ     *a          = (Mat_SeqAIJ*)A->data;
682   Mat_SeqAIJ     *b          = (Mat_SeqAIJ*)B->data;
683   PetscInt       cstart      = mat->cmap->rstart,cend = mat->cmap->rend,col;
684   PetscInt       *ailen      = a->ilen,*aj = a->j;
685   PetscInt       *bilen      = b->ilen,*bj = b->j;
686   PetscInt       am          = aij->A->rmap->n,j;
687   PetscInt       diag_so_far = 0,dnz;
688   PetscInt       offd_so_far = 0,onz;
689 
690   PetscFunctionBegin;
691   /* Iterate over all rows of the matrix */
692   for (j=0; j<am; j++) {
693     dnz = onz = 0;
694     /*  Iterate over all non-zero columns of the current row */
695     for (col=mat_i[j]; col<mat_i[j+1]; col++) {
696       /* If column is in the diagonal */
697       if (mat_j[col] >= cstart && mat_j[col] < cend) {
698         aj[diag_so_far++] = mat_j[col] - cstart;
699         dnz++;
700       } else { /* off-diagonal entries */
701         bj[offd_so_far++] = mat_j[col];
702         onz++;
703       }
704     }
705     ailen[j] = dnz;
706     bilen[j] = onz;
707   }
708   PetscFunctionReturn(0);
709 }
710 
711 /*
712     This function sets the local j, a and ilen arrays (of the diagonal and off-diagonal part) of an MPIAIJ-matrix.
713     The values in mat_i have to be sorted and the values in mat_j have to be sorted for each row (CSR-like).
714     No off-processor parts off the matrix are allowed here, they are set at a later point by MatSetValues_MPIAIJ.
715     Also, mat->was_assembled has to be false, otherwise the statement aj[rowstart_diag+dnz_row] = mat_j[col] - cstart;
716     would not be true and the more complex MatSetValues_MPIAIJ has to be used.
717 */
718 PetscErrorCode MatSetValues_MPIAIJ_CopyFromCSRFormat(Mat mat,const PetscInt mat_j[],const PetscInt mat_i[],const PetscScalar mat_a[])
719 {
720   Mat_MPIAIJ     *aij   = (Mat_MPIAIJ*)mat->data;
721   Mat            A      = aij->A; /* diagonal part of the matrix */
722   Mat            B      = aij->B; /* offdiagonal part of the matrix */
723   Mat_SeqAIJ     *aijd  =(Mat_SeqAIJ*)(aij->A)->data,*aijo=(Mat_SeqAIJ*)(aij->B)->data;
724   Mat_SeqAIJ     *a     = (Mat_SeqAIJ*)A->data;
725   Mat_SeqAIJ     *b     = (Mat_SeqAIJ*)B->data;
726   PetscInt       cstart = mat->cmap->rstart,cend = mat->cmap->rend;
727   PetscInt       *ailen = a->ilen,*aj = a->j;
728   PetscInt       *bilen = b->ilen,*bj = b->j;
729   PetscInt       am     = aij->A->rmap->n,j;
730   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. */
731   PetscInt       col,dnz_row,onz_row,rowstart_diag,rowstart_offd;
732   PetscScalar    *aa = a->a,*ba = b->a;
733 
734   PetscFunctionBegin;
735   /* Iterate over all rows of the matrix */
736   for (j=0; j<am; j++) {
737     dnz_row = onz_row = 0;
738     rowstart_offd = full_offd_i[j];
739     rowstart_diag = full_diag_i[j];
740     /*  Iterate over all non-zero columns of the current row */
741     for (col=mat_i[j]; col<mat_i[j+1]; col++) {
742       /* If column is in the diagonal */
743       if (mat_j[col] >= cstart && mat_j[col] < cend) {
744         aj[rowstart_diag+dnz_row] = mat_j[col] - cstart;
745         aa[rowstart_diag+dnz_row] = mat_a[col];
746         dnz_row++;
747       } else { /* off-diagonal entries */
748         bj[rowstart_offd+onz_row] = mat_j[col];
749         ba[rowstart_offd+onz_row] = mat_a[col];
750         onz_row++;
751       }
752     }
753     ailen[j] = dnz_row;
754     bilen[j] = onz_row;
755   }
756   PetscFunctionReturn(0);
757 }
758 
759 PetscErrorCode MatGetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],PetscScalar v[])
760 {
761   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
762   PetscErrorCode ierr;
763   PetscInt       i,j,rstart = mat->rmap->rstart,rend = mat->rmap->rend;
764   PetscInt       cstart = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
765 
766   PetscFunctionBegin;
767   for (i=0; i<m; i++) {
768     if (idxm[i] < 0) continue; /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative row: %D",idxm[i]);*/
769     if (idxm[i] >= mat->rmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %D max %D",idxm[i],mat->rmap->N-1);
770     if (idxm[i] >= rstart && idxm[i] < rend) {
771       row = idxm[i] - rstart;
772       for (j=0; j<n; j++) {
773         if (idxn[j] < 0) continue; /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column: %D",idxn[j]); */
774         if (idxn[j] >= mat->cmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %D max %D",idxn[j],mat->cmap->N-1);
775         if (idxn[j] >= cstart && idxn[j] < cend) {
776           col  = idxn[j] - cstart;
777           ierr = MatGetValues(aij->A,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
778         } else {
779           if (!aij->colmap) {
780             ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
781           }
782 #if defined(PETSC_USE_CTABLE)
783           ierr = PetscTableFind(aij->colmap,idxn[j]+1,&col);CHKERRQ(ierr);
784           col--;
785 #else
786           col = aij->colmap[idxn[j]] - 1;
787 #endif
788           if ((col < 0) || (aij->garray[col] != idxn[j])) *(v+i*n+j) = 0.0;
789           else {
790             ierr = MatGetValues(aij->B,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
791           }
792         }
793       }
794     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only local values currently supported");
795   }
796   PetscFunctionReturn(0);
797 }
798 
799 extern PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat,Vec,Vec);
800 
801 PetscErrorCode MatAssemblyBegin_MPIAIJ(Mat mat,MatAssemblyType mode)
802 {
803   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
804   PetscErrorCode ierr;
805   PetscInt       nstash,reallocs;
806 
807   PetscFunctionBegin;
808   if (aij->donotstash || mat->nooffprocentries) PetscFunctionReturn(0);
809 
810   ierr = MatStashScatterBegin_Private(mat,&mat->stash,mat->rmap->range);CHKERRQ(ierr);
811   ierr = MatStashGetInfo_Private(&mat->stash,&nstash,&reallocs);CHKERRQ(ierr);
812   ierr = PetscInfo2(aij->A,"Stash has %D entries, uses %D mallocs.\n",nstash,reallocs);CHKERRQ(ierr);
813   PetscFunctionReturn(0);
814 }
815 
816 PetscErrorCode MatAssemblyEnd_MPIAIJ(Mat mat,MatAssemblyType mode)
817 {
818   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
819   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)aij->A->data;
820   PetscErrorCode ierr;
821   PetscMPIInt    n;
822   PetscInt       i,j,rstart,ncols,flg;
823   PetscInt       *row,*col;
824   PetscBool      other_disassembled;
825   PetscScalar    *val;
826 
827   /* do not use 'b = (Mat_SeqAIJ*)aij->B->data' as B can be reset in disassembly */
828 
829   PetscFunctionBegin;
830   if (!aij->donotstash && !mat->nooffprocentries) {
831     while (1) {
832       ierr = MatStashScatterGetMesg_Private(&mat->stash,&n,&row,&col,&val,&flg);CHKERRQ(ierr);
833       if (!flg) break;
834 
835       for (i=0; i<n; ) {
836         /* Now identify the consecutive vals belonging to the same row */
837         for (j=i,rstart=row[j]; j<n; j++) {
838           if (row[j] != rstart) break;
839         }
840         if (j < n) ncols = j-i;
841         else       ncols = n-i;
842         /* Now assemble all these values with a single function call */
843         ierr = MatSetValues_MPIAIJ(mat,1,row+i,ncols,col+i,val+i,mat->insertmode);CHKERRQ(ierr);
844 
845         i = j;
846       }
847     }
848     ierr = MatStashScatterEnd_Private(&mat->stash);CHKERRQ(ierr);
849   }
850 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
851   if (mat->offloadmask == PETSC_OFFLOAD_CPU) aij->A->offloadmask = PETSC_OFFLOAD_CPU;
852   /* We call MatBindToCPU() on aij->A and aij->B here, because if MatBindToCPU_MPIAIJ() is called before assembly, it cannot bind these. */
853   if (mat->boundtocpu) {
854     ierr = MatBindToCPU(aij->A,PETSC_TRUE);CHKERRQ(ierr);
855     ierr = MatBindToCPU(aij->B,PETSC_TRUE);CHKERRQ(ierr);
856   }
857 #endif
858   ierr = MatAssemblyBegin(aij->A,mode);CHKERRQ(ierr);
859   ierr = MatAssemblyEnd(aij->A,mode);CHKERRQ(ierr);
860 
861   /* determine if any processor has disassembled, if so we must
862      also disassemble ourself, in order that we may reassemble. */
863   /*
864      if nonzero structure of submatrix B cannot change then we know that
865      no processor disassembled thus we can skip this stuff
866   */
867   if (!((Mat_SeqAIJ*)aij->B->data)->nonew) {
868     ierr = MPIU_Allreduce(&mat->was_assembled,&other_disassembled,1,MPIU_BOOL,MPI_PROD,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
869     if (mat->was_assembled && !other_disassembled) {
870 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
871       aij->B->offloadmask = PETSC_OFFLOAD_BOTH; /* do not copy on the GPU when assembling inside MatDisAssemble_MPIAIJ */
872 #endif
873       ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
874     }
875   }
876   if (!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) {
877     ierr = MatSetUpMultiply_MPIAIJ(mat);CHKERRQ(ierr);
878   }
879   ierr = MatSetOption(aij->B,MAT_USE_INODES,PETSC_FALSE);CHKERRQ(ierr);
880 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
881   if (mat->offloadmask == PETSC_OFFLOAD_CPU && aij->B->offloadmask != PETSC_OFFLOAD_UNALLOCATED) aij->B->offloadmask = PETSC_OFFLOAD_CPU;
882 #endif
883   ierr = MatAssemblyBegin(aij->B,mode);CHKERRQ(ierr);
884   ierr = MatAssemblyEnd(aij->B,mode);CHKERRQ(ierr);
885 
886   ierr = PetscFree2(aij->rowvalues,aij->rowindices);CHKERRQ(ierr);
887 
888   aij->rowvalues = 0;
889 
890   ierr = VecDestroy(&aij->diag);CHKERRQ(ierr);
891   if (a->inode.size) mat->ops->multdiagonalblock = MatMultDiagonalBlock_MPIAIJ;
892 
893   /* if no new nonzero locations are allowed in matrix then only set the matrix state the first time through */
894   if ((!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) || !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
895     PetscObjectState state = aij->A->nonzerostate + aij->B->nonzerostate;
896     ierr = MPIU_Allreduce(&state,&mat->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
897   }
898 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
899   mat->offloadmask = PETSC_OFFLOAD_BOTH;
900 #endif
901   PetscFunctionReturn(0);
902 }
903 
904 PetscErrorCode MatZeroEntries_MPIAIJ(Mat A)
905 {
906   Mat_MPIAIJ     *l = (Mat_MPIAIJ*)A->data;
907   PetscErrorCode ierr;
908 
909   PetscFunctionBegin;
910   ierr = MatZeroEntries(l->A);CHKERRQ(ierr);
911   ierr = MatZeroEntries(l->B);CHKERRQ(ierr);
912   PetscFunctionReturn(0);
913 }
914 
915 PetscErrorCode MatZeroRows_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
916 {
917   Mat_MPIAIJ      *mat = (Mat_MPIAIJ *) A->data;
918   PetscObjectState sA, sB;
919   PetscInt        *lrows;
920   PetscInt         r, len;
921   PetscBool        cong, lch, gch;
922   PetscErrorCode   ierr;
923 
924   PetscFunctionBegin;
925   /* get locally owned rows */
926   ierr = MatZeroRowsMapLocal_Private(A,N,rows,&len,&lrows);CHKERRQ(ierr);
927   ierr = MatHasCongruentLayouts(A,&cong);CHKERRQ(ierr);
928   /* fix right hand side if needed */
929   if (x && b) {
930     const PetscScalar *xx;
931     PetscScalar       *bb;
932 
933     if (!cong) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Need matching row/col layout");
934     ierr = VecGetArrayRead(x, &xx);CHKERRQ(ierr);
935     ierr = VecGetArray(b, &bb);CHKERRQ(ierr);
936     for (r = 0; r < len; ++r) bb[lrows[r]] = diag*xx[lrows[r]];
937     ierr = VecRestoreArrayRead(x, &xx);CHKERRQ(ierr);
938     ierr = VecRestoreArray(b, &bb);CHKERRQ(ierr);
939   }
940 
941   sA = mat->A->nonzerostate;
942   sB = mat->B->nonzerostate;
943 
944   if (diag != 0.0 && cong) {
945     ierr = MatZeroRows(mat->A, len, lrows, diag, NULL, NULL);CHKERRQ(ierr);
946     ierr = MatZeroRows(mat->B, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
947   } else if (diag != 0.0) { /* non-square or non congruent layouts -> if keepnonzeropattern is false, we allow for new insertion */
948     Mat_SeqAIJ *aijA = (Mat_SeqAIJ*)mat->A->data;
949     Mat_SeqAIJ *aijB = (Mat_SeqAIJ*)mat->B->data;
950     PetscInt   nnwA, nnwB;
951     PetscBool  nnzA, nnzB;
952 
953     nnwA = aijA->nonew;
954     nnwB = aijB->nonew;
955     nnzA = aijA->keepnonzeropattern;
956     nnzB = aijB->keepnonzeropattern;
957     if (!nnzA) {
958       ierr = PetscInfo(mat->A,"Requested to not keep the pattern and add a nonzero diagonal; may encounter reallocations on diagonal block.\n");CHKERRQ(ierr);
959       aijA->nonew = 0;
960     }
961     if (!nnzB) {
962       ierr = PetscInfo(mat->B,"Requested to not keep the pattern and add a nonzero diagonal; may encounter reallocations on off-diagonal block.\n");CHKERRQ(ierr);
963       aijB->nonew = 0;
964     }
965     /* Must zero here before the next loop */
966     ierr = MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
967     ierr = MatZeroRows(mat->B, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
968     for (r = 0; r < len; ++r) {
969       const PetscInt row = lrows[r] + A->rmap->rstart;
970       if (row >= A->cmap->N) continue;
971       ierr = MatSetValues(A, 1, &row, 1, &row, &diag, INSERT_VALUES);CHKERRQ(ierr);
972     }
973     aijA->nonew = nnwA;
974     aijB->nonew = nnwB;
975   } else {
976     ierr = MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
977     ierr = MatZeroRows(mat->B, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
978   }
979   ierr = PetscFree(lrows);CHKERRQ(ierr);
980   ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
981   ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
982 
983   /* reduce nonzerostate */
984   lch = (PetscBool)(sA != mat->A->nonzerostate || sB != mat->B->nonzerostate);
985   ierr = MPIU_Allreduce(&lch,&gch,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
986   if (gch) A->nonzerostate++;
987   PetscFunctionReturn(0);
988 }
989 
990 PetscErrorCode MatZeroRowsColumns_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
991 {
992   Mat_MPIAIJ        *l = (Mat_MPIAIJ*)A->data;
993   PetscErrorCode    ierr;
994   PetscMPIInt       n = A->rmap->n;
995   PetscInt          i,j,r,m,len = 0;
996   PetscInt          *lrows,*owners = A->rmap->range;
997   PetscMPIInt       p = 0;
998   PetscSFNode       *rrows;
999   PetscSF           sf;
1000   const PetscScalar *xx;
1001   PetscScalar       *bb,*mask;
1002   Vec               xmask,lmask;
1003   Mat_SeqAIJ        *aij = (Mat_SeqAIJ*)l->B->data;
1004   const PetscInt    *aj, *ii,*ridx;
1005   PetscScalar       *aa;
1006 
1007   PetscFunctionBegin;
1008   /* Create SF where leaves are input rows and roots are owned rows */
1009   ierr = PetscMalloc1(n, &lrows);CHKERRQ(ierr);
1010   for (r = 0; r < n; ++r) lrows[r] = -1;
1011   ierr = PetscMalloc1(N, &rrows);CHKERRQ(ierr);
1012   for (r = 0; r < N; ++r) {
1013     const PetscInt idx   = rows[r];
1014     if (idx < 0 || A->rmap->N <= idx) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row %D out of range [0,%D)",idx,A->rmap->N);
1015     if (idx < owners[p] || owners[p+1] <= idx) { /* short-circuit the search if the last p owns this row too */
1016       ierr = PetscLayoutFindOwner(A->rmap,idx,&p);CHKERRQ(ierr);
1017     }
1018     rrows[r].rank  = p;
1019     rrows[r].index = rows[r] - owners[p];
1020   }
1021   ierr = PetscSFCreate(PetscObjectComm((PetscObject) A), &sf);CHKERRQ(ierr);
1022   ierr = PetscSFSetGraph(sf, n, N, NULL, PETSC_OWN_POINTER, rrows, PETSC_OWN_POINTER);CHKERRQ(ierr);
1023   /* Collect flags for rows to be zeroed */
1024   ierr = PetscSFReduceBegin(sf, MPIU_INT, (PetscInt *) rows, lrows, MPI_LOR);CHKERRQ(ierr);
1025   ierr = PetscSFReduceEnd(sf, MPIU_INT, (PetscInt *) rows, lrows, MPI_LOR);CHKERRQ(ierr);
1026   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1027   /* Compress and put in row numbers */
1028   for (r = 0; r < n; ++r) if (lrows[r] >= 0) lrows[len++] = r;
1029   /* zero diagonal part of matrix */
1030   ierr = MatZeroRowsColumns(l->A,len,lrows,diag,x,b);CHKERRQ(ierr);
1031   /* handle off diagonal part of matrix */
1032   ierr = MatCreateVecs(A,&xmask,NULL);CHKERRQ(ierr);
1033   ierr = VecDuplicate(l->lvec,&lmask);CHKERRQ(ierr);
1034   ierr = VecGetArray(xmask,&bb);CHKERRQ(ierr);
1035   for (i=0; i<len; i++) bb[lrows[i]] = 1;
1036   ierr = VecRestoreArray(xmask,&bb);CHKERRQ(ierr);
1037   ierr = VecScatterBegin(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1038   ierr = VecScatterEnd(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1039   ierr = VecDestroy(&xmask);CHKERRQ(ierr);
1040   if (x && b) { /* this code is buggy when the row and column layout don't match */
1041     PetscBool cong;
1042 
1043     ierr = MatHasCongruentLayouts(A,&cong);CHKERRQ(ierr);
1044     if (!cong) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Need matching row/col layout");
1045     ierr = VecScatterBegin(l->Mvctx,x,l->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1046     ierr = VecScatterEnd(l->Mvctx,x,l->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1047     ierr = VecGetArrayRead(l->lvec,&xx);CHKERRQ(ierr);
1048     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
1049   }
1050   ierr = VecGetArray(lmask,&mask);CHKERRQ(ierr);
1051   /* remove zeroed rows of off diagonal matrix */
1052   ii = aij->i;
1053   for (i=0; i<len; i++) {
1054     ierr = PetscArrayzero(aij->a + ii[lrows[i]],ii[lrows[i]+1] - ii[lrows[i]]);CHKERRQ(ierr);
1055   }
1056   /* loop over all elements of off process part of matrix zeroing removed columns*/
1057   if (aij->compressedrow.use) {
1058     m    = aij->compressedrow.nrows;
1059     ii   = aij->compressedrow.i;
1060     ridx = aij->compressedrow.rindex;
1061     for (i=0; i<m; i++) {
1062       n  = ii[i+1] - ii[i];
1063       aj = aij->j + ii[i];
1064       aa = aij->a + ii[i];
1065 
1066       for (j=0; j<n; j++) {
1067         if (PetscAbsScalar(mask[*aj])) {
1068           if (b) bb[*ridx] -= *aa*xx[*aj];
1069           *aa = 0.0;
1070         }
1071         aa++;
1072         aj++;
1073       }
1074       ridx++;
1075     }
1076   } else { /* do not use compressed row format */
1077     m = l->B->rmap->n;
1078     for (i=0; i<m; i++) {
1079       n  = ii[i+1] - ii[i];
1080       aj = aij->j + ii[i];
1081       aa = aij->a + ii[i];
1082       for (j=0; j<n; j++) {
1083         if (PetscAbsScalar(mask[*aj])) {
1084           if (b) bb[i] -= *aa*xx[*aj];
1085           *aa = 0.0;
1086         }
1087         aa++;
1088         aj++;
1089       }
1090     }
1091   }
1092   if (x && b) {
1093     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
1094     ierr = VecRestoreArrayRead(l->lvec,&xx);CHKERRQ(ierr);
1095   }
1096   ierr = VecRestoreArray(lmask,&mask);CHKERRQ(ierr);
1097   ierr = VecDestroy(&lmask);CHKERRQ(ierr);
1098   ierr = PetscFree(lrows);CHKERRQ(ierr);
1099 
1100   /* only change matrix nonzero state if pattern was allowed to be changed */
1101   if (!((Mat_SeqAIJ*)(l->A->data))->keepnonzeropattern) {
1102     PetscObjectState state = l->A->nonzerostate + l->B->nonzerostate;
1103     ierr = MPIU_Allreduce(&state,&A->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
1104   }
1105   PetscFunctionReturn(0);
1106 }
1107 
1108 PetscErrorCode MatMult_MPIAIJ(Mat A,Vec xx,Vec yy)
1109 {
1110   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1111   PetscErrorCode ierr;
1112   PetscInt       nt;
1113   VecScatter     Mvctx = a->Mvctx;
1114 
1115   PetscFunctionBegin;
1116   ierr = VecGetLocalSize(xx,&nt);CHKERRQ(ierr);
1117   if (nt != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Incompatible partition of A (%D) and xx (%D)",A->cmap->n,nt);
1118 
1119   ierr = VecScatterBegin(Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1120   ierr = (*a->A->ops->mult)(a->A,xx,yy);CHKERRQ(ierr);
1121   ierr = VecScatterEnd(Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1122   ierr = (*a->B->ops->multadd)(a->B,a->lvec,yy,yy);CHKERRQ(ierr);
1123   PetscFunctionReturn(0);
1124 }
1125 
1126 PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat A,Vec bb,Vec xx)
1127 {
1128   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1129   PetscErrorCode ierr;
1130 
1131   PetscFunctionBegin;
1132   ierr = MatMultDiagonalBlock(a->A,bb,xx);CHKERRQ(ierr);
1133   PetscFunctionReturn(0);
1134 }
1135 
1136 PetscErrorCode MatMultAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1137 {
1138   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1139   PetscErrorCode ierr;
1140   VecScatter     Mvctx = a->Mvctx;
1141 
1142   PetscFunctionBegin;
1143   if (a->Mvctx_mpi1_flg) Mvctx = a->Mvctx_mpi1;
1144   ierr = VecScatterBegin(Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1145   ierr = (*a->A->ops->multadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
1146   ierr = VecScatterEnd(Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1147   ierr = (*a->B->ops->multadd)(a->B,a->lvec,zz,zz);CHKERRQ(ierr);
1148   PetscFunctionReturn(0);
1149 }
1150 
1151 PetscErrorCode MatMultTranspose_MPIAIJ(Mat A,Vec xx,Vec yy)
1152 {
1153   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1154   PetscErrorCode ierr;
1155 
1156   PetscFunctionBegin;
1157   /* do nondiagonal part */
1158   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
1159   /* do local part */
1160   ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
1161   /* add partial results together */
1162   ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1163   ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1164   PetscFunctionReturn(0);
1165 }
1166 
1167 PetscErrorCode MatIsTranspose_MPIAIJ(Mat Amat,Mat Bmat,PetscReal tol,PetscBool  *f)
1168 {
1169   MPI_Comm       comm;
1170   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ*) Amat->data, *Bij;
1171   Mat            Adia = Aij->A, Bdia, Aoff,Boff,*Aoffs,*Boffs;
1172   IS             Me,Notme;
1173   PetscErrorCode ierr;
1174   PetscInt       M,N,first,last,*notme,i;
1175   PetscBool      lf;
1176   PetscMPIInt    size;
1177 
1178   PetscFunctionBegin;
1179   /* Easy test: symmetric diagonal block */
1180   Bij  = (Mat_MPIAIJ*) Bmat->data; Bdia = Bij->A;
1181   ierr = MatIsTranspose(Adia,Bdia,tol,&lf);CHKERRQ(ierr);
1182   ierr = MPIU_Allreduce(&lf,f,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)Amat));CHKERRQ(ierr);
1183   if (!*f) PetscFunctionReturn(0);
1184   ierr = PetscObjectGetComm((PetscObject)Amat,&comm);CHKERRQ(ierr);
1185   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1186   if (size == 1) PetscFunctionReturn(0);
1187 
1188   /* Hard test: off-diagonal block. This takes a MatCreateSubMatrix. */
1189   ierr = MatGetSize(Amat,&M,&N);CHKERRQ(ierr);
1190   ierr = MatGetOwnershipRange(Amat,&first,&last);CHKERRQ(ierr);
1191   ierr = PetscMalloc1(N-last+first,&notme);CHKERRQ(ierr);
1192   for (i=0; i<first; i++) notme[i] = i;
1193   for (i=last; i<M; i++) notme[i-last+first] = i;
1194   ierr = ISCreateGeneral(MPI_COMM_SELF,N-last+first,notme,PETSC_COPY_VALUES,&Notme);CHKERRQ(ierr);
1195   ierr = ISCreateStride(MPI_COMM_SELF,last-first,first,1,&Me);CHKERRQ(ierr);
1196   ierr = MatCreateSubMatrices(Amat,1,&Me,&Notme,MAT_INITIAL_MATRIX,&Aoffs);CHKERRQ(ierr);
1197   Aoff = Aoffs[0];
1198   ierr = MatCreateSubMatrices(Bmat,1,&Notme,&Me,MAT_INITIAL_MATRIX,&Boffs);CHKERRQ(ierr);
1199   Boff = Boffs[0];
1200   ierr = MatIsTranspose(Aoff,Boff,tol,f);CHKERRQ(ierr);
1201   ierr = MatDestroyMatrices(1,&Aoffs);CHKERRQ(ierr);
1202   ierr = MatDestroyMatrices(1,&Boffs);CHKERRQ(ierr);
1203   ierr = ISDestroy(&Me);CHKERRQ(ierr);
1204   ierr = ISDestroy(&Notme);CHKERRQ(ierr);
1205   ierr = PetscFree(notme);CHKERRQ(ierr);
1206   PetscFunctionReturn(0);
1207 }
1208 
1209 PetscErrorCode MatIsSymmetric_MPIAIJ(Mat A,PetscReal tol,PetscBool  *f)
1210 {
1211   PetscErrorCode ierr;
1212 
1213   PetscFunctionBegin;
1214   ierr = MatIsTranspose_MPIAIJ(A,A,tol,f);CHKERRQ(ierr);
1215   PetscFunctionReturn(0);
1216 }
1217 
1218 PetscErrorCode MatMultTransposeAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1219 {
1220   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1221   PetscErrorCode ierr;
1222 
1223   PetscFunctionBegin;
1224   /* do nondiagonal part */
1225   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
1226   /* do local part */
1227   ierr = (*a->A->ops->multtransposeadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
1228   /* add partial results together */
1229   ierr = VecScatterBegin(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1230   ierr = VecScatterEnd(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1231   PetscFunctionReturn(0);
1232 }
1233 
1234 /*
1235   This only works correctly for square matrices where the subblock A->A is the
1236    diagonal block
1237 */
1238 PetscErrorCode MatGetDiagonal_MPIAIJ(Mat A,Vec v)
1239 {
1240   PetscErrorCode ierr;
1241   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1242 
1243   PetscFunctionBegin;
1244   if (A->rmap->N != A->cmap->N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Supports only square matrix where A->A is diag block");
1245   if (A->rmap->rstart != A->cmap->rstart || A->rmap->rend != A->cmap->rend) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"row partition must equal col partition");
1246   ierr = MatGetDiagonal(a->A,v);CHKERRQ(ierr);
1247   PetscFunctionReturn(0);
1248 }
1249 
1250 PetscErrorCode MatScale_MPIAIJ(Mat A,PetscScalar aa)
1251 {
1252   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1253   PetscErrorCode ierr;
1254 
1255   PetscFunctionBegin;
1256   ierr = MatScale(a->A,aa);CHKERRQ(ierr);
1257   ierr = MatScale(a->B,aa);CHKERRQ(ierr);
1258   PetscFunctionReturn(0);
1259 }
1260 
1261 PetscErrorCode MatDestroy_MPIAIJ(Mat mat)
1262 {
1263   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1264   PetscErrorCode ierr;
1265 
1266   PetscFunctionBegin;
1267 #if defined(PETSC_USE_LOG)
1268   PetscLogObjectState((PetscObject)mat,"Rows=%D, Cols=%D",mat->rmap->N,mat->cmap->N);
1269 #endif
1270   ierr = MatStashDestroy_Private(&mat->stash);CHKERRQ(ierr);
1271   ierr = VecDestroy(&aij->diag);CHKERRQ(ierr);
1272   ierr = MatDestroy(&aij->A);CHKERRQ(ierr);
1273   ierr = MatDestroy(&aij->B);CHKERRQ(ierr);
1274 #if defined(PETSC_USE_CTABLE)
1275   ierr = PetscTableDestroy(&aij->colmap);CHKERRQ(ierr);
1276 #else
1277   ierr = PetscFree(aij->colmap);CHKERRQ(ierr);
1278 #endif
1279   ierr = PetscFree(aij->garray);CHKERRQ(ierr);
1280   ierr = VecDestroy(&aij->lvec);CHKERRQ(ierr);
1281   ierr = VecScatterDestroy(&aij->Mvctx);CHKERRQ(ierr);
1282   if (aij->Mvctx_mpi1) {ierr = VecScatterDestroy(&aij->Mvctx_mpi1);CHKERRQ(ierr);}
1283   ierr = PetscFree2(aij->rowvalues,aij->rowindices);CHKERRQ(ierr);
1284   ierr = PetscFree(aij->ld);CHKERRQ(ierr);
1285   ierr = PetscFree(mat->data);CHKERRQ(ierr);
1286 
1287   ierr = PetscObjectChangeTypeName((PetscObject)mat,0);CHKERRQ(ierr);
1288   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatStoreValues_C",NULL);CHKERRQ(ierr);
1289   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatRetrieveValues_C",NULL);CHKERRQ(ierr);
1290   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatIsTranspose_C",NULL);CHKERRQ(ierr);
1291   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocation_C",NULL);CHKERRQ(ierr);
1292   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatResetPreallocation_C",NULL);CHKERRQ(ierr);
1293   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocationCSR_C",NULL);CHKERRQ(ierr);
1294   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDiagonalScaleLocal_C",NULL);CHKERRQ(ierr);
1295   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_mpibaij_C",NULL);CHKERRQ(ierr);
1296   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_mpisbaij_C",NULL);CHKERRQ(ierr);
1297 #if defined(PETSC_HAVE_ELEMENTAL)
1298   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_elemental_C",NULL);CHKERRQ(ierr);
1299 #endif
1300 #if defined(PETSC_HAVE_HYPRE)
1301   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_hypre_C",NULL);CHKERRQ(ierr);
1302   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatProductSetFromOptions_transpose_mpiaij_mpiaij_C",NULL);CHKERRQ(ierr);
1303 #endif
1304   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_is_C",NULL);CHKERRQ(ierr);
1305   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatProductSetFromOptions_is_mpiaij_C",NULL);CHKERRQ(ierr);
1306   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatProductSetFromOptions_mpiaij_mpiaij_C",NULL);CHKERRQ(ierr);
1307   PetscFunctionReturn(0);
1308 }
1309 
1310 PetscErrorCode MatView_MPIAIJ_Binary(Mat mat,PetscViewer viewer)
1311 {
1312   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)mat->data;
1313   Mat_SeqAIJ        *A   = (Mat_SeqAIJ*)aij->A->data;
1314   Mat_SeqAIJ        *B   = (Mat_SeqAIJ*)aij->B->data;
1315   const PetscInt    *garray = aij->garray;
1316   PetscInt          header[4],M,N,m,rs,cs,nz,cnt,i,ja,jb;
1317   PetscInt          *rowlens;
1318   PetscInt          *colidxs;
1319   PetscScalar       *matvals;
1320   PetscErrorCode    ierr;
1321 
1322   PetscFunctionBegin;
1323   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
1324 
1325   M  = mat->rmap->N;
1326   N  = mat->cmap->N;
1327   m  = mat->rmap->n;
1328   rs = mat->rmap->rstart;
1329   cs = mat->cmap->rstart;
1330   nz = A->nz + B->nz;
1331 
1332   /* write matrix header */
1333   header[0] = MAT_FILE_CLASSID;
1334   header[1] = M; header[2] = N; header[3] = nz;
1335   ierr = MPI_Reduce(&nz,&header[3],1,MPIU_INT,MPI_SUM,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1336   ierr = PetscViewerBinaryWrite(viewer,header,4,PETSC_INT);CHKERRQ(ierr);
1337 
1338   /* fill in and store row lengths  */
1339   ierr = PetscMalloc1(m,&rowlens);CHKERRQ(ierr);
1340   for (i=0; i<m; i++) rowlens[i] = A->i[i+1] - A->i[i] + B->i[i+1] - B->i[i];
1341   ierr = PetscViewerBinaryWriteAll(viewer,rowlens,m,rs,M,PETSC_INT);CHKERRQ(ierr);
1342   ierr = PetscFree(rowlens);CHKERRQ(ierr);
1343 
1344   /* fill in and store column indices */
1345   ierr = PetscMalloc1(nz,&colidxs);CHKERRQ(ierr);
1346   for (cnt=0, i=0; i<m; i++) {
1347     for (jb=B->i[i]; jb<B->i[i+1]; jb++) {
1348       if (garray[B->j[jb]] > cs) break;
1349       colidxs[cnt++] = garray[B->j[jb]];
1350     }
1351     for (ja=A->i[i]; ja<A->i[i+1]; ja++)
1352       colidxs[cnt++] = A->j[ja] + cs;
1353     for (; jb<B->i[i+1]; jb++)
1354       colidxs[cnt++] = garray[B->j[jb]];
1355   }
1356   if (cnt != nz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: cnt = %D nz = %D",cnt,nz);
1357   ierr = PetscViewerBinaryWriteAll(viewer,colidxs,nz,PETSC_DETERMINE,PETSC_DETERMINE,PETSC_INT);CHKERRQ(ierr);
1358   ierr = PetscFree(colidxs);CHKERRQ(ierr);
1359 
1360   /* fill in and store nonzero values */
1361   ierr = PetscMalloc1(nz,&matvals);CHKERRQ(ierr);
1362   for (cnt=0, i=0; i<m; i++) {
1363     for (jb=B->i[i]; jb<B->i[i+1]; jb++) {
1364       if (garray[B->j[jb]] > cs) break;
1365       matvals[cnt++] = B->a[jb];
1366     }
1367     for (ja=A->i[i]; ja<A->i[i+1]; ja++)
1368       matvals[cnt++] = A->a[ja];
1369     for (; jb<B->i[i+1]; jb++)
1370       matvals[cnt++] = B->a[jb];
1371   }
1372   if (cnt != nz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: cnt = %D nz = %D",cnt,nz);
1373   ierr = PetscViewerBinaryWriteAll(viewer,matvals,nz,PETSC_DETERMINE,PETSC_DETERMINE,PETSC_SCALAR);CHKERRQ(ierr);
1374   ierr = PetscFree(matvals);CHKERRQ(ierr);
1375 
1376   /* write block size option to the viewer's .info file */
1377   ierr = MatView_Binary_BlockSizes(mat,viewer);CHKERRQ(ierr);
1378   PetscFunctionReturn(0);
1379 }
1380 
1381 #include <petscdraw.h>
1382 PetscErrorCode MatView_MPIAIJ_ASCIIorDraworSocket(Mat mat,PetscViewer viewer)
1383 {
1384   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)mat->data;
1385   PetscErrorCode    ierr;
1386   PetscMPIInt       rank = aij->rank,size = aij->size;
1387   PetscBool         isdraw,iascii,isbinary;
1388   PetscViewer       sviewer;
1389   PetscViewerFormat format;
1390 
1391   PetscFunctionBegin;
1392   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1393   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1394   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1395   if (iascii) {
1396     ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
1397     if (format == PETSC_VIEWER_LOAD_BALANCE) {
1398       PetscInt i,nmax = 0,nmin = PETSC_MAX_INT,navg = 0,*nz,nzlocal = ((Mat_SeqAIJ*) (aij->A->data))->nz + ((Mat_SeqAIJ*) (aij->B->data))->nz;
1399       ierr = PetscMalloc1(size,&nz);CHKERRQ(ierr);
1400       ierr = MPI_Allgather(&nzlocal,1,MPIU_INT,nz,1,MPIU_INT,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1401       for (i=0; i<(PetscInt)size; i++) {
1402         nmax = PetscMax(nmax,nz[i]);
1403         nmin = PetscMin(nmin,nz[i]);
1404         navg += nz[i];
1405       }
1406       ierr = PetscFree(nz);CHKERRQ(ierr);
1407       navg = navg/size;
1408       ierr = PetscViewerASCIIPrintf(viewer,"Load Balance - Nonzeros: Min %D  avg %D  max %D\n",nmin,navg,nmax);CHKERRQ(ierr);
1409       PetscFunctionReturn(0);
1410     }
1411     ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
1412     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
1413       MatInfo   info;
1414       PetscBool inodes;
1415 
1416       ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
1417       ierr = MatGetInfo(mat,MAT_LOCAL,&info);CHKERRQ(ierr);
1418       ierr = MatInodeGetInodeSizes(aij->A,NULL,(PetscInt**)&inodes,NULL);CHKERRQ(ierr);
1419       ierr = PetscViewerASCIIPushSynchronized(viewer);CHKERRQ(ierr);
1420       if (!inodes) {
1421         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %D nz %D nz alloced %D mem %g, not using I-node routines\n",
1422                                                   rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(double)info.memory);CHKERRQ(ierr);
1423       } else {
1424         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %D nz %D nz alloced %D mem %g, using I-node routines\n",
1425                                                   rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(double)info.memory);CHKERRQ(ierr);
1426       }
1427       ierr = MatGetInfo(aij->A,MAT_LOCAL,&info);CHKERRQ(ierr);
1428       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] on-diagonal part: nz %D \n",rank,(PetscInt)info.nz_used);CHKERRQ(ierr);
1429       ierr = MatGetInfo(aij->B,MAT_LOCAL,&info);CHKERRQ(ierr);
1430       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] off-diagonal part: nz %D \n",rank,(PetscInt)info.nz_used);CHKERRQ(ierr);
1431       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1432       ierr = PetscViewerASCIIPopSynchronized(viewer);CHKERRQ(ierr);
1433       ierr = PetscViewerASCIIPrintf(viewer,"Information on VecScatter used in matrix-vector product: \n");CHKERRQ(ierr);
1434       ierr = VecScatterView(aij->Mvctx,viewer);CHKERRQ(ierr);
1435       PetscFunctionReturn(0);
1436     } else if (format == PETSC_VIEWER_ASCII_INFO) {
1437       PetscInt inodecount,inodelimit,*inodes;
1438       ierr = MatInodeGetInodeSizes(aij->A,&inodecount,&inodes,&inodelimit);CHKERRQ(ierr);
1439       if (inodes) {
1440         ierr = PetscViewerASCIIPrintf(viewer,"using I-node (on process 0) routines: found %D nodes, limit used is %D\n",inodecount,inodelimit);CHKERRQ(ierr);
1441       } else {
1442         ierr = PetscViewerASCIIPrintf(viewer,"not using I-node (on process 0) routines\n");CHKERRQ(ierr);
1443       }
1444       PetscFunctionReturn(0);
1445     } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO) {
1446       PetscFunctionReturn(0);
1447     }
1448   } else if (isbinary) {
1449     if (size == 1) {
1450       ierr = PetscObjectSetName((PetscObject)aij->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1451       ierr = MatView(aij->A,viewer);CHKERRQ(ierr);
1452     } else {
1453       ierr = MatView_MPIAIJ_Binary(mat,viewer);CHKERRQ(ierr);
1454     }
1455     PetscFunctionReturn(0);
1456   } else if (iascii && size == 1) {
1457     ierr = PetscObjectSetName((PetscObject)aij->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1458     ierr = MatView(aij->A,viewer);CHKERRQ(ierr);
1459     PetscFunctionReturn(0);
1460   } else if (isdraw) {
1461     PetscDraw draw;
1462     PetscBool isnull;
1463     ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
1464     ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr);
1465     if (isnull) PetscFunctionReturn(0);
1466   }
1467 
1468   { /* assemble the entire matrix onto first processor */
1469     Mat A = NULL, Av;
1470     IS  isrow,iscol;
1471 
1472     ierr = ISCreateStride(PetscObjectComm((PetscObject)mat),!rank ? mat->rmap->N : 0,0,1,&isrow);CHKERRQ(ierr);
1473     ierr = ISCreateStride(PetscObjectComm((PetscObject)mat),!rank ? mat->cmap->N : 0,0,1,&iscol);CHKERRQ(ierr);
1474     ierr = MatCreateSubMatrix(mat,isrow,iscol,MAT_INITIAL_MATRIX,&A);CHKERRQ(ierr);
1475     ierr = MatMPIAIJGetSeqAIJ(A,&Av,NULL,NULL);CHKERRQ(ierr);
1476 /*  The commented code uses MatCreateSubMatrices instead */
1477 /*
1478     Mat *AA, A = NULL, Av;
1479     IS  isrow,iscol;
1480 
1481     ierr = ISCreateStride(PetscObjectComm((PetscObject)mat),!rank ? mat->rmap->N : 0,0,1,&isrow);CHKERRQ(ierr);
1482     ierr = ISCreateStride(PetscObjectComm((PetscObject)mat),!rank ? mat->cmap->N : 0,0,1,&iscol);CHKERRQ(ierr);
1483     ierr = MatCreateSubMatrices(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&AA);CHKERRQ(ierr);
1484     if (!rank) {
1485        ierr = PetscObjectReference((PetscObject)AA[0]);CHKERRQ(ierr);
1486        A    = AA[0];
1487        Av   = AA[0];
1488     }
1489     ierr = MatDestroySubMatrices(1,&AA);CHKERRQ(ierr);
1490 */
1491     ierr = ISDestroy(&iscol);CHKERRQ(ierr);
1492     ierr = ISDestroy(&isrow);CHKERRQ(ierr);
1493     /*
1494        Everyone has to call to draw the matrix since the graphics waits are
1495        synchronized across all processors that share the PetscDraw object
1496     */
1497     ierr = PetscViewerGetSubViewer(viewer,PETSC_COMM_SELF,&sviewer);CHKERRQ(ierr);
1498     if (!rank) {
1499       if (((PetscObject)mat)->name) {
1500         ierr = PetscObjectSetName((PetscObject)Av,((PetscObject)mat)->name);CHKERRQ(ierr);
1501       }
1502       ierr = MatView_SeqAIJ(Av,sviewer);CHKERRQ(ierr);
1503     }
1504     ierr = PetscViewerRestoreSubViewer(viewer,PETSC_COMM_SELF,&sviewer);CHKERRQ(ierr);
1505     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1506     ierr = MatDestroy(&A);CHKERRQ(ierr);
1507   }
1508   PetscFunctionReturn(0);
1509 }
1510 
1511 PetscErrorCode MatView_MPIAIJ(Mat mat,PetscViewer viewer)
1512 {
1513   PetscErrorCode ierr;
1514   PetscBool      iascii,isdraw,issocket,isbinary;
1515 
1516   PetscFunctionBegin;
1517   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1518   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1519   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1520   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSOCKET,&issocket);CHKERRQ(ierr);
1521   if (iascii || isdraw || isbinary || issocket) {
1522     ierr = MatView_MPIAIJ_ASCIIorDraworSocket(mat,viewer);CHKERRQ(ierr);
1523   }
1524   PetscFunctionReturn(0);
1525 }
1526 
1527 PetscErrorCode MatSOR_MPIAIJ(Mat matin,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
1528 {
1529   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1530   PetscErrorCode ierr;
1531   Vec            bb1 = 0;
1532   PetscBool      hasop;
1533 
1534   PetscFunctionBegin;
1535   if (flag == SOR_APPLY_UPPER) {
1536     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1537     PetscFunctionReturn(0);
1538   }
1539 
1540   if (its > 1 || ~flag & SOR_ZERO_INITIAL_GUESS || flag & SOR_EISENSTAT) {
1541     ierr = VecDuplicate(bb,&bb1);CHKERRQ(ierr);
1542   }
1543 
1544   if ((flag & SOR_LOCAL_SYMMETRIC_SWEEP) == SOR_LOCAL_SYMMETRIC_SWEEP) {
1545     if (flag & SOR_ZERO_INITIAL_GUESS) {
1546       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1547       its--;
1548     }
1549 
1550     while (its--) {
1551       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1552       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1553 
1554       /* update rhs: bb1 = bb - B*x */
1555       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1556       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1557 
1558       /* local sweep */
1559       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_SYMMETRIC_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1560     }
1561   } else if (flag & SOR_LOCAL_FORWARD_SWEEP) {
1562     if (flag & SOR_ZERO_INITIAL_GUESS) {
1563       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1564       its--;
1565     }
1566     while (its--) {
1567       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1568       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1569 
1570       /* update rhs: bb1 = bb - B*x */
1571       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1572       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1573 
1574       /* local sweep */
1575       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_FORWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1576     }
1577   } else if (flag & SOR_LOCAL_BACKWARD_SWEEP) {
1578     if (flag & SOR_ZERO_INITIAL_GUESS) {
1579       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1580       its--;
1581     }
1582     while (its--) {
1583       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1584       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1585 
1586       /* update rhs: bb1 = bb - B*x */
1587       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1588       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1589 
1590       /* local sweep */
1591       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_BACKWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1592     }
1593   } else if (flag & SOR_EISENSTAT) {
1594     Vec xx1;
1595 
1596     ierr = VecDuplicate(bb,&xx1);CHKERRQ(ierr);
1597     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_BACKWARD_SWEEP),fshift,lits,1,xx);CHKERRQ(ierr);
1598 
1599     ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1600     ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1601     if (!mat->diag) {
1602       ierr = MatCreateVecs(matin,&mat->diag,NULL);CHKERRQ(ierr);
1603       ierr = MatGetDiagonal(matin,mat->diag);CHKERRQ(ierr);
1604     }
1605     ierr = MatHasOperation(matin,MATOP_MULT_DIAGONAL_BLOCK,&hasop);CHKERRQ(ierr);
1606     if (hasop) {
1607       ierr = MatMultDiagonalBlock(matin,xx,bb1);CHKERRQ(ierr);
1608     } else {
1609       ierr = VecPointwiseMult(bb1,mat->diag,xx);CHKERRQ(ierr);
1610     }
1611     ierr = VecAYPX(bb1,(omega-2.0)/omega,bb);CHKERRQ(ierr);
1612 
1613     ierr = MatMultAdd(mat->B,mat->lvec,bb1,bb1);CHKERRQ(ierr);
1614 
1615     /* local sweep */
1616     ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_FORWARD_SWEEP),fshift,lits,1,xx1);CHKERRQ(ierr);
1617     ierr = VecAXPY(xx,1.0,xx1);CHKERRQ(ierr);
1618     ierr = VecDestroy(&xx1);CHKERRQ(ierr);
1619   } else SETERRQ(PetscObjectComm((PetscObject)matin),PETSC_ERR_SUP,"Parallel SOR not supported");
1620 
1621   ierr = VecDestroy(&bb1);CHKERRQ(ierr);
1622 
1623   matin->factorerrortype = mat->A->factorerrortype;
1624   PetscFunctionReturn(0);
1625 }
1626 
1627 PetscErrorCode MatPermute_MPIAIJ(Mat A,IS rowp,IS colp,Mat *B)
1628 {
1629   Mat            aA,aB,Aperm;
1630   const PetscInt *rwant,*cwant,*gcols,*ai,*bi,*aj,*bj;
1631   PetscScalar    *aa,*ba;
1632   PetscInt       i,j,m,n,ng,anz,bnz,*dnnz,*onnz,*tdnnz,*tonnz,*rdest,*cdest,*work,*gcdest;
1633   PetscSF        rowsf,sf;
1634   IS             parcolp = NULL;
1635   PetscBool      done;
1636   PetscErrorCode ierr;
1637 
1638   PetscFunctionBegin;
1639   ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
1640   ierr = ISGetIndices(rowp,&rwant);CHKERRQ(ierr);
1641   ierr = ISGetIndices(colp,&cwant);CHKERRQ(ierr);
1642   ierr = PetscMalloc3(PetscMax(m,n),&work,m,&rdest,n,&cdest);CHKERRQ(ierr);
1643 
1644   /* Invert row permutation to find out where my rows should go */
1645   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&rowsf);CHKERRQ(ierr);
1646   ierr = PetscSFSetGraphLayout(rowsf,A->rmap,A->rmap->n,NULL,PETSC_OWN_POINTER,rwant);CHKERRQ(ierr);
1647   ierr = PetscSFSetFromOptions(rowsf);CHKERRQ(ierr);
1648   for (i=0; i<m; i++) work[i] = A->rmap->rstart + i;
1649   ierr = PetscSFReduceBegin(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1650   ierr = PetscSFReduceEnd(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1651 
1652   /* Invert column permutation to find out where my columns should go */
1653   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1654   ierr = PetscSFSetGraphLayout(sf,A->cmap,A->cmap->n,NULL,PETSC_OWN_POINTER,cwant);CHKERRQ(ierr);
1655   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1656   for (i=0; i<n; i++) work[i] = A->cmap->rstart + i;
1657   ierr = PetscSFReduceBegin(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1658   ierr = PetscSFReduceEnd(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1659   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1660 
1661   ierr = ISRestoreIndices(rowp,&rwant);CHKERRQ(ierr);
1662   ierr = ISRestoreIndices(colp,&cwant);CHKERRQ(ierr);
1663   ierr = MatMPIAIJGetSeqAIJ(A,&aA,&aB,&gcols);CHKERRQ(ierr);
1664 
1665   /* Find out where my gcols should go */
1666   ierr = MatGetSize(aB,NULL,&ng);CHKERRQ(ierr);
1667   ierr = PetscMalloc1(ng,&gcdest);CHKERRQ(ierr);
1668   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1669   ierr = PetscSFSetGraphLayout(sf,A->cmap,ng,NULL,PETSC_OWN_POINTER,gcols);CHKERRQ(ierr);
1670   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1671   ierr = PetscSFBcastBegin(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1672   ierr = PetscSFBcastEnd(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1673   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1674 
1675   ierr = PetscCalloc4(m,&dnnz,m,&onnz,m,&tdnnz,m,&tonnz);CHKERRQ(ierr);
1676   ierr = MatGetRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1677   ierr = MatGetRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1678   for (i=0; i<m; i++) {
1679     PetscInt    row = rdest[i];
1680     PetscMPIInt rowner;
1681     ierr = PetscLayoutFindOwner(A->rmap,row,&rowner);CHKERRQ(ierr);
1682     for (j=ai[i]; j<ai[i+1]; j++) {
1683       PetscInt    col = cdest[aj[j]];
1684       PetscMPIInt cowner;
1685       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr); /* Could build an index for the columns to eliminate this search */
1686       if (rowner == cowner) dnnz[i]++;
1687       else onnz[i]++;
1688     }
1689     for (j=bi[i]; j<bi[i+1]; j++) {
1690       PetscInt    col = gcdest[bj[j]];
1691       PetscMPIInt cowner;
1692       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr);
1693       if (rowner == cowner) dnnz[i]++;
1694       else onnz[i]++;
1695     }
1696   }
1697   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1698   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1699   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1700   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1701   ierr = PetscSFDestroy(&rowsf);CHKERRQ(ierr);
1702 
1703   ierr = MatCreateAIJ(PetscObjectComm((PetscObject)A),A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N,0,tdnnz,0,tonnz,&Aperm);CHKERRQ(ierr);
1704   ierr = MatSeqAIJGetArray(aA,&aa);CHKERRQ(ierr);
1705   ierr = MatSeqAIJGetArray(aB,&ba);CHKERRQ(ierr);
1706   for (i=0; i<m; i++) {
1707     PetscInt *acols = dnnz,*bcols = onnz; /* Repurpose now-unneeded arrays */
1708     PetscInt j0,rowlen;
1709     rowlen = ai[i+1] - ai[i];
1710     for (j0=j=0; j<rowlen; j0=j) { /* rowlen could be larger than number of rows m, so sum in batches */
1711       for ( ; j<PetscMin(rowlen,j0+m); j++) acols[j-j0] = cdest[aj[ai[i]+j]];
1712       ierr = MatSetValues(Aperm,1,&rdest[i],j-j0,acols,aa+ai[i]+j0,INSERT_VALUES);CHKERRQ(ierr);
1713     }
1714     rowlen = bi[i+1] - bi[i];
1715     for (j0=j=0; j<rowlen; j0=j) {
1716       for ( ; j<PetscMin(rowlen,j0+m); j++) bcols[j-j0] = gcdest[bj[bi[i]+j]];
1717       ierr = MatSetValues(Aperm,1,&rdest[i],j-j0,bcols,ba+bi[i]+j0,INSERT_VALUES);CHKERRQ(ierr);
1718     }
1719   }
1720   ierr = MatAssemblyBegin(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1721   ierr = MatAssemblyEnd(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1722   ierr = MatRestoreRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1723   ierr = MatRestoreRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1724   ierr = MatSeqAIJRestoreArray(aA,&aa);CHKERRQ(ierr);
1725   ierr = MatSeqAIJRestoreArray(aB,&ba);CHKERRQ(ierr);
1726   ierr = PetscFree4(dnnz,onnz,tdnnz,tonnz);CHKERRQ(ierr);
1727   ierr = PetscFree3(work,rdest,cdest);CHKERRQ(ierr);
1728   ierr = PetscFree(gcdest);CHKERRQ(ierr);
1729   if (parcolp) {ierr = ISDestroy(&colp);CHKERRQ(ierr);}
1730   *B = Aperm;
1731   PetscFunctionReturn(0);
1732 }
1733 
1734 PetscErrorCode  MatGetGhosts_MPIAIJ(Mat mat,PetscInt *nghosts,const PetscInt *ghosts[])
1735 {
1736   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1737   PetscErrorCode ierr;
1738 
1739   PetscFunctionBegin;
1740   ierr = MatGetSize(aij->B,NULL,nghosts);CHKERRQ(ierr);
1741   if (ghosts) *ghosts = aij->garray;
1742   PetscFunctionReturn(0);
1743 }
1744 
1745 PetscErrorCode MatGetInfo_MPIAIJ(Mat matin,MatInfoType flag,MatInfo *info)
1746 {
1747   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1748   Mat            A    = mat->A,B = mat->B;
1749   PetscErrorCode ierr;
1750   PetscLogDouble isend[5],irecv[5];
1751 
1752   PetscFunctionBegin;
1753   info->block_size = 1.0;
1754   ierr             = MatGetInfo(A,MAT_LOCAL,info);CHKERRQ(ierr);
1755 
1756   isend[0] = info->nz_used; isend[1] = info->nz_allocated; isend[2] = info->nz_unneeded;
1757   isend[3] = info->memory;  isend[4] = info->mallocs;
1758 
1759   ierr = MatGetInfo(B,MAT_LOCAL,info);CHKERRQ(ierr);
1760 
1761   isend[0] += info->nz_used; isend[1] += info->nz_allocated; isend[2] += info->nz_unneeded;
1762   isend[3] += info->memory;  isend[4] += info->mallocs;
1763   if (flag == MAT_LOCAL) {
1764     info->nz_used      = isend[0];
1765     info->nz_allocated = isend[1];
1766     info->nz_unneeded  = isend[2];
1767     info->memory       = isend[3];
1768     info->mallocs      = isend[4];
1769   } else if (flag == MAT_GLOBAL_MAX) {
1770     ierr = MPIU_Allreduce(isend,irecv,5,MPIU_PETSCLOGDOUBLE,MPI_MAX,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1771 
1772     info->nz_used      = irecv[0];
1773     info->nz_allocated = irecv[1];
1774     info->nz_unneeded  = irecv[2];
1775     info->memory       = irecv[3];
1776     info->mallocs      = irecv[4];
1777   } else if (flag == MAT_GLOBAL_SUM) {
1778     ierr = MPIU_Allreduce(isend,irecv,5,MPIU_PETSCLOGDOUBLE,MPI_SUM,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1779 
1780     info->nz_used      = irecv[0];
1781     info->nz_allocated = irecv[1];
1782     info->nz_unneeded  = irecv[2];
1783     info->memory       = irecv[3];
1784     info->mallocs      = irecv[4];
1785   }
1786   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
1787   info->fill_ratio_needed = 0;
1788   info->factor_mallocs    = 0;
1789   PetscFunctionReturn(0);
1790 }
1791 
1792 PetscErrorCode MatSetOption_MPIAIJ(Mat A,MatOption op,PetscBool flg)
1793 {
1794   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1795   PetscErrorCode ierr;
1796 
1797   PetscFunctionBegin;
1798   switch (op) {
1799   case MAT_NEW_NONZERO_LOCATIONS:
1800   case MAT_NEW_NONZERO_ALLOCATION_ERR:
1801   case MAT_UNUSED_NONZERO_LOCATION_ERR:
1802   case MAT_KEEP_NONZERO_PATTERN:
1803   case MAT_NEW_NONZERO_LOCATION_ERR:
1804   case MAT_USE_INODES:
1805   case MAT_IGNORE_ZERO_ENTRIES:
1806     MatCheckPreallocated(A,1);
1807     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1808     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1809     break;
1810   case MAT_ROW_ORIENTED:
1811     MatCheckPreallocated(A,1);
1812     a->roworiented = flg;
1813 
1814     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1815     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1816     break;
1817   case MAT_NEW_DIAGONALS:
1818   case MAT_SORTED_FULL:
1819     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
1820     break;
1821   case MAT_IGNORE_OFF_PROC_ENTRIES:
1822     a->donotstash = flg;
1823     break;
1824   /* Symmetry flags are handled directly by MatSetOption() and they don't affect preallocation */
1825   case MAT_SPD:
1826   case MAT_SYMMETRIC:
1827   case MAT_STRUCTURALLY_SYMMETRIC:
1828   case MAT_HERMITIAN:
1829   case MAT_SYMMETRY_ETERNAL:
1830     break;
1831   case MAT_SUBMAT_SINGLEIS:
1832     A->submat_singleis = flg;
1833     break;
1834   case MAT_STRUCTURE_ONLY:
1835     /* The option is handled directly by MatSetOption() */
1836     break;
1837   default:
1838     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %d",op);
1839   }
1840   PetscFunctionReturn(0);
1841 }
1842 
1843 PetscErrorCode MatGetRow_MPIAIJ(Mat matin,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1844 {
1845   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1846   PetscScalar    *vworkA,*vworkB,**pvA,**pvB,*v_p;
1847   PetscErrorCode ierr;
1848   PetscInt       i,*cworkA,*cworkB,**pcA,**pcB,cstart = matin->cmap->rstart;
1849   PetscInt       nztot,nzA,nzB,lrow,rstart = matin->rmap->rstart,rend = matin->rmap->rend;
1850   PetscInt       *cmap,*idx_p;
1851 
1852   PetscFunctionBegin;
1853   if (mat->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Already active");
1854   mat->getrowactive = PETSC_TRUE;
1855 
1856   if (!mat->rowvalues && (idx || v)) {
1857     /*
1858         allocate enough space to hold information from the longest row.
1859     */
1860     Mat_SeqAIJ *Aa = (Mat_SeqAIJ*)mat->A->data,*Ba = (Mat_SeqAIJ*)mat->B->data;
1861     PetscInt   max = 1,tmp;
1862     for (i=0; i<matin->rmap->n; i++) {
1863       tmp = Aa->i[i+1] - Aa->i[i] + Ba->i[i+1] - Ba->i[i];
1864       if (max < tmp) max = tmp;
1865     }
1866     ierr = PetscMalloc2(max,&mat->rowvalues,max,&mat->rowindices);CHKERRQ(ierr);
1867   }
1868 
1869   if (row < rstart || row >= rend) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Only local rows");
1870   lrow = row - rstart;
1871 
1872   pvA = &vworkA; pcA = &cworkA; pvB = &vworkB; pcB = &cworkB;
1873   if (!v)   {pvA = 0; pvB = 0;}
1874   if (!idx) {pcA = 0; if (!v) pcB = 0;}
1875   ierr  = (*mat->A->ops->getrow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1876   ierr  = (*mat->B->ops->getrow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1877   nztot = nzA + nzB;
1878 
1879   cmap = mat->garray;
1880   if (v  || idx) {
1881     if (nztot) {
1882       /* Sort by increasing column numbers, assuming A and B already sorted */
1883       PetscInt imark = -1;
1884       if (v) {
1885         *v = v_p = mat->rowvalues;
1886         for (i=0; i<nzB; i++) {
1887           if (cmap[cworkB[i]] < cstart) v_p[i] = vworkB[i];
1888           else break;
1889         }
1890         imark = i;
1891         for (i=0; i<nzA; i++)     v_p[imark+i] = vworkA[i];
1892         for (i=imark; i<nzB; i++) v_p[nzA+i]   = vworkB[i];
1893       }
1894       if (idx) {
1895         *idx = idx_p = mat->rowindices;
1896         if (imark > -1) {
1897           for (i=0; i<imark; i++) {
1898             idx_p[i] = cmap[cworkB[i]];
1899           }
1900         } else {
1901           for (i=0; i<nzB; i++) {
1902             if (cmap[cworkB[i]] < cstart) idx_p[i] = cmap[cworkB[i]];
1903             else break;
1904           }
1905           imark = i;
1906         }
1907         for (i=0; i<nzA; i++)     idx_p[imark+i] = cstart + cworkA[i];
1908         for (i=imark; i<nzB; i++) idx_p[nzA+i]   = cmap[cworkB[i]];
1909       }
1910     } else {
1911       if (idx) *idx = 0;
1912       if (v)   *v   = 0;
1913     }
1914   }
1915   *nz  = nztot;
1916   ierr = (*mat->A->ops->restorerow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1917   ierr = (*mat->B->ops->restorerow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1918   PetscFunctionReturn(0);
1919 }
1920 
1921 PetscErrorCode MatRestoreRow_MPIAIJ(Mat mat,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1922 {
1923   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1924 
1925   PetscFunctionBegin;
1926   if (!aij->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"MatGetRow() must be called first");
1927   aij->getrowactive = PETSC_FALSE;
1928   PetscFunctionReturn(0);
1929 }
1930 
1931 PetscErrorCode MatNorm_MPIAIJ(Mat mat,NormType type,PetscReal *norm)
1932 {
1933   Mat_MPIAIJ     *aij  = (Mat_MPIAIJ*)mat->data;
1934   Mat_SeqAIJ     *amat = (Mat_SeqAIJ*)aij->A->data,*bmat = (Mat_SeqAIJ*)aij->B->data;
1935   PetscErrorCode ierr;
1936   PetscInt       i,j,cstart = mat->cmap->rstart;
1937   PetscReal      sum = 0.0;
1938   MatScalar      *v;
1939 
1940   PetscFunctionBegin;
1941   if (aij->size == 1) {
1942     ierr =  MatNorm(aij->A,type,norm);CHKERRQ(ierr);
1943   } else {
1944     if (type == NORM_FROBENIUS) {
1945       v = amat->a;
1946       for (i=0; i<amat->nz; i++) {
1947         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1948       }
1949       v = bmat->a;
1950       for (i=0; i<bmat->nz; i++) {
1951         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1952       }
1953       ierr  = MPIU_Allreduce(&sum,norm,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1954       *norm = PetscSqrtReal(*norm);
1955       ierr = PetscLogFlops(2*amat->nz+2*bmat->nz);CHKERRQ(ierr);
1956     } else if (type == NORM_1) { /* max column norm */
1957       PetscReal *tmp,*tmp2;
1958       PetscInt  *jj,*garray = aij->garray;
1959       ierr  = PetscCalloc1(mat->cmap->N+1,&tmp);CHKERRQ(ierr);
1960       ierr  = PetscMalloc1(mat->cmap->N+1,&tmp2);CHKERRQ(ierr);
1961       *norm = 0.0;
1962       v     = amat->a; jj = amat->j;
1963       for (j=0; j<amat->nz; j++) {
1964         tmp[cstart + *jj++] += PetscAbsScalar(*v);  v++;
1965       }
1966       v = bmat->a; jj = bmat->j;
1967       for (j=0; j<bmat->nz; j++) {
1968         tmp[garray[*jj++]] += PetscAbsScalar(*v); v++;
1969       }
1970       ierr = MPIU_Allreduce(tmp,tmp2,mat->cmap->N,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1971       for (j=0; j<mat->cmap->N; j++) {
1972         if (tmp2[j] > *norm) *norm = tmp2[j];
1973       }
1974       ierr = PetscFree(tmp);CHKERRQ(ierr);
1975       ierr = PetscFree(tmp2);CHKERRQ(ierr);
1976       ierr = PetscLogFlops(PetscMax(amat->nz+bmat->nz-1,0));CHKERRQ(ierr);
1977     } else if (type == NORM_INFINITY) { /* max row norm */
1978       PetscReal ntemp = 0.0;
1979       for (j=0; j<aij->A->rmap->n; j++) {
1980         v   = amat->a + amat->i[j];
1981         sum = 0.0;
1982         for (i=0; i<amat->i[j+1]-amat->i[j]; i++) {
1983           sum += PetscAbsScalar(*v); v++;
1984         }
1985         v = bmat->a + bmat->i[j];
1986         for (i=0; i<bmat->i[j+1]-bmat->i[j]; i++) {
1987           sum += PetscAbsScalar(*v); v++;
1988         }
1989         if (sum > ntemp) ntemp = sum;
1990       }
1991       ierr = MPIU_Allreduce(&ntemp,norm,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1992       ierr = PetscLogFlops(PetscMax(amat->nz+bmat->nz-1,0));CHKERRQ(ierr);
1993     } else SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"No support for two norm");
1994   }
1995   PetscFunctionReturn(0);
1996 }
1997 
1998 PetscErrorCode MatTranspose_MPIAIJ(Mat A,MatReuse reuse,Mat *matout)
1999 {
2000   Mat_MPIAIJ      *a    =(Mat_MPIAIJ*)A->data,*b;
2001   Mat_SeqAIJ      *Aloc =(Mat_SeqAIJ*)a->A->data,*Bloc=(Mat_SeqAIJ*)a->B->data,*sub_B_diag;
2002   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;
2003   const PetscInt  *ai,*aj,*bi,*bj,*B_diag_i;
2004   PetscErrorCode  ierr;
2005   Mat             B,A_diag,*B_diag;
2006   const MatScalar *array;
2007 
2008   PetscFunctionBegin;
2009   ma = A->rmap->n; na = A->cmap->n; mb = a->B->rmap->n; nb = a->B->cmap->n;
2010   ai = Aloc->i; aj = Aloc->j;
2011   bi = Bloc->i; bj = Bloc->j;
2012   if (reuse == MAT_INITIAL_MATRIX || *matout == A) {
2013     PetscInt             *d_nnz,*g_nnz,*o_nnz;
2014     PetscSFNode          *oloc;
2015     PETSC_UNUSED PetscSF sf;
2016 
2017     ierr = PetscMalloc4(na,&d_nnz,na,&o_nnz,nb,&g_nnz,nb,&oloc);CHKERRQ(ierr);
2018     /* compute d_nnz for preallocation */
2019     ierr = PetscArrayzero(d_nnz,na);CHKERRQ(ierr);
2020     for (i=0; i<ai[ma]; i++) {
2021       d_nnz[aj[i]]++;
2022     }
2023     /* compute local off-diagonal contributions */
2024     ierr = PetscArrayzero(g_nnz,nb);CHKERRQ(ierr);
2025     for (i=0; i<bi[ma]; i++) g_nnz[bj[i]]++;
2026     /* map those to global */
2027     ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
2028     ierr = PetscSFSetGraphLayout(sf,A->cmap,nb,NULL,PETSC_USE_POINTER,a->garray);CHKERRQ(ierr);
2029     ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
2030     ierr = PetscArrayzero(o_nnz,na);CHKERRQ(ierr);
2031     ierr = PetscSFReduceBegin(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
2032     ierr = PetscSFReduceEnd(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
2033     ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
2034 
2035     ierr = MatCreate(PetscObjectComm((PetscObject)A),&B);CHKERRQ(ierr);
2036     ierr = MatSetSizes(B,A->cmap->n,A->rmap->n,N,M);CHKERRQ(ierr);
2037     ierr = MatSetBlockSizes(B,PetscAbs(A->cmap->bs),PetscAbs(A->rmap->bs));CHKERRQ(ierr);
2038     ierr = MatSetType(B,((PetscObject)A)->type_name);CHKERRQ(ierr);
2039     ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
2040     ierr = PetscFree4(d_nnz,o_nnz,g_nnz,oloc);CHKERRQ(ierr);
2041   } else {
2042     B    = *matout;
2043     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
2044   }
2045 
2046   b           = (Mat_MPIAIJ*)B->data;
2047   A_diag      = a->A;
2048   B_diag      = &b->A;
2049   sub_B_diag  = (Mat_SeqAIJ*)(*B_diag)->data;
2050   A_diag_ncol = A_diag->cmap->N;
2051   B_diag_ilen = sub_B_diag->ilen;
2052   B_diag_i    = sub_B_diag->i;
2053 
2054   /* Set ilen for diagonal of B */
2055   for (i=0; i<A_diag_ncol; i++) {
2056     B_diag_ilen[i] = B_diag_i[i+1] - B_diag_i[i];
2057   }
2058 
2059   /* Transpose the diagonal part of the matrix. In contrast to the offdiagonal part, this can be done
2060   very quickly (=without using MatSetValues), because all writes are local. */
2061   ierr = MatTranspose(A_diag,MAT_REUSE_MATRIX,B_diag);CHKERRQ(ierr);
2062 
2063   /* copy over the B part */
2064   ierr  = PetscMalloc1(bi[mb],&cols);CHKERRQ(ierr);
2065   array = Bloc->a;
2066   row   = A->rmap->rstart;
2067   for (i=0; i<bi[mb]; i++) cols[i] = a->garray[bj[i]];
2068   cols_tmp = cols;
2069   for (i=0; i<mb; i++) {
2070     ncol = bi[i+1]-bi[i];
2071     ierr = MatSetValues(B,ncol,cols_tmp,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
2072     row++;
2073     array += ncol; cols_tmp += ncol;
2074   }
2075   ierr = PetscFree(cols);CHKERRQ(ierr);
2076 
2077   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2078   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2079   if (reuse == MAT_INITIAL_MATRIX || reuse == MAT_REUSE_MATRIX) {
2080     *matout = B;
2081   } else {
2082     ierr = MatHeaderMerge(A,&B);CHKERRQ(ierr);
2083   }
2084   PetscFunctionReturn(0);
2085 }
2086 
2087 PetscErrorCode MatDiagonalScale_MPIAIJ(Mat mat,Vec ll,Vec rr)
2088 {
2089   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2090   Mat            a    = aij->A,b = aij->B;
2091   PetscErrorCode ierr;
2092   PetscInt       s1,s2,s3;
2093 
2094   PetscFunctionBegin;
2095   ierr = MatGetLocalSize(mat,&s2,&s3);CHKERRQ(ierr);
2096   if (rr) {
2097     ierr = VecGetLocalSize(rr,&s1);CHKERRQ(ierr);
2098     if (s1!=s3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"right vector non-conforming local size");
2099     /* Overlap communication with computation. */
2100     ierr = VecScatterBegin(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2101   }
2102   if (ll) {
2103     ierr = VecGetLocalSize(ll,&s1);CHKERRQ(ierr);
2104     if (s1!=s2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"left vector non-conforming local size");
2105     ierr = (*b->ops->diagonalscale)(b,ll,0);CHKERRQ(ierr);
2106   }
2107   /* scale  the diagonal block */
2108   ierr = (*a->ops->diagonalscale)(a,ll,rr);CHKERRQ(ierr);
2109 
2110   if (rr) {
2111     /* Do a scatter end and then right scale the off-diagonal block */
2112     ierr = VecScatterEnd(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2113     ierr = (*b->ops->diagonalscale)(b,0,aij->lvec);CHKERRQ(ierr);
2114   }
2115   PetscFunctionReturn(0);
2116 }
2117 
2118 PetscErrorCode MatSetUnfactored_MPIAIJ(Mat A)
2119 {
2120   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2121   PetscErrorCode ierr;
2122 
2123   PetscFunctionBegin;
2124   ierr = MatSetUnfactored(a->A);CHKERRQ(ierr);
2125   PetscFunctionReturn(0);
2126 }
2127 
2128 PetscErrorCode MatEqual_MPIAIJ(Mat A,Mat B,PetscBool  *flag)
2129 {
2130   Mat_MPIAIJ     *matB = (Mat_MPIAIJ*)B->data,*matA = (Mat_MPIAIJ*)A->data;
2131   Mat            a,b,c,d;
2132   PetscBool      flg;
2133   PetscErrorCode ierr;
2134 
2135   PetscFunctionBegin;
2136   a = matA->A; b = matA->B;
2137   c = matB->A; d = matB->B;
2138 
2139   ierr = MatEqual(a,c,&flg);CHKERRQ(ierr);
2140   if (flg) {
2141     ierr = MatEqual(b,d,&flg);CHKERRQ(ierr);
2142   }
2143   ierr = MPIU_Allreduce(&flg,flag,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
2144   PetscFunctionReturn(0);
2145 }
2146 
2147 PetscErrorCode MatCopy_MPIAIJ(Mat A,Mat B,MatStructure str)
2148 {
2149   PetscErrorCode ierr;
2150   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2151   Mat_MPIAIJ     *b = (Mat_MPIAIJ*)B->data;
2152 
2153   PetscFunctionBegin;
2154   /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
2155   if ((str != SAME_NONZERO_PATTERN) || (A->ops->copy != B->ops->copy)) {
2156     /* because of the column compression in the off-processor part of the matrix a->B,
2157        the number of columns in a->B and b->B may be different, hence we cannot call
2158        the MatCopy() directly on the two parts. If need be, we can provide a more
2159        efficient copy than the MatCopy_Basic() by first uncompressing the a->B matrices
2160        then copying the submatrices */
2161     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
2162   } else {
2163     ierr = MatCopy(a->A,b->A,str);CHKERRQ(ierr);
2164     ierr = MatCopy(a->B,b->B,str);CHKERRQ(ierr);
2165   }
2166   ierr = PetscObjectStateIncrease((PetscObject)B);CHKERRQ(ierr);
2167   PetscFunctionReturn(0);
2168 }
2169 
2170 PetscErrorCode MatSetUp_MPIAIJ(Mat A)
2171 {
2172   PetscErrorCode ierr;
2173 
2174   PetscFunctionBegin;
2175   ierr = MatMPIAIJSetPreallocation(A,PETSC_DEFAULT,0,PETSC_DEFAULT,0);CHKERRQ(ierr);
2176   PetscFunctionReturn(0);
2177 }
2178 
2179 /*
2180    Computes the number of nonzeros per row needed for preallocation when X and Y
2181    have different nonzero structure.
2182 */
2183 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)
2184 {
2185   PetscInt       i,j,k,nzx,nzy;
2186 
2187   PetscFunctionBegin;
2188   /* Set the number of nonzeros in the new matrix */
2189   for (i=0; i<m; i++) {
2190     const PetscInt *xjj = xj+xi[i],*yjj = yj+yi[i];
2191     nzx = xi[i+1] - xi[i];
2192     nzy = yi[i+1] - yi[i];
2193     nnz[i] = 0;
2194     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2195       for (; k<nzy && yltog[yjj[k]]<xltog[xjj[j]]; k++) nnz[i]++; /* Catch up to X */
2196       if (k<nzy && yltog[yjj[k]]==xltog[xjj[j]]) k++;             /* Skip duplicate */
2197       nnz[i]++;
2198     }
2199     for (; k<nzy; k++) nnz[i]++;
2200   }
2201   PetscFunctionReturn(0);
2202 }
2203 
2204 /* This is the same as MatAXPYGetPreallocation_SeqAIJ, except that the local-to-global map is provided */
2205 static PetscErrorCode MatAXPYGetPreallocation_MPIAIJ(Mat Y,const PetscInt *yltog,Mat X,const PetscInt *xltog,PetscInt *nnz)
2206 {
2207   PetscErrorCode ierr;
2208   PetscInt       m = Y->rmap->N;
2209   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data;
2210   Mat_SeqAIJ     *y = (Mat_SeqAIJ*)Y->data;
2211 
2212   PetscFunctionBegin;
2213   ierr = MatAXPYGetPreallocation_MPIX_private(m,x->i,x->j,xltog,y->i,y->j,yltog,nnz);CHKERRQ(ierr);
2214   PetscFunctionReturn(0);
2215 }
2216 
2217 PetscErrorCode MatAXPY_MPIAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
2218 {
2219   PetscErrorCode ierr;
2220   Mat_MPIAIJ     *xx = (Mat_MPIAIJ*)X->data,*yy = (Mat_MPIAIJ*)Y->data;
2221   PetscBLASInt   bnz,one=1;
2222   Mat_SeqAIJ     *x,*y;
2223 
2224   PetscFunctionBegin;
2225   if (str == SAME_NONZERO_PATTERN) {
2226     PetscScalar alpha = a;
2227     x    = (Mat_SeqAIJ*)xx->A->data;
2228     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2229     y    = (Mat_SeqAIJ*)yy->A->data;
2230     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2231     x    = (Mat_SeqAIJ*)xx->B->data;
2232     y    = (Mat_SeqAIJ*)yy->B->data;
2233     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2234     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2235     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
2236     /* the MatAXPY_Basic* subroutines calls MatAssembly, so the matrix on the GPU
2237        will be updated */
2238 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
2239     if (Y->offloadmask != PETSC_OFFLOAD_UNALLOCATED) {
2240       Y->offloadmask = PETSC_OFFLOAD_CPU;
2241     }
2242 #endif
2243   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
2244     ierr = MatAXPY_Basic(Y,a,X,str);CHKERRQ(ierr);
2245   } else {
2246     Mat      B;
2247     PetscInt *nnz_d,*nnz_o;
2248     ierr = PetscMalloc1(yy->A->rmap->N,&nnz_d);CHKERRQ(ierr);
2249     ierr = PetscMalloc1(yy->B->rmap->N,&nnz_o);CHKERRQ(ierr);
2250     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
2251     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
2252     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
2253     ierr = MatSetBlockSizesFromMats(B,Y,Y);CHKERRQ(ierr);
2254     ierr = MatSetType(B,MATMPIAIJ);CHKERRQ(ierr);
2255     ierr = MatAXPYGetPreallocation_SeqAIJ(yy->A,xx->A,nnz_d);CHKERRQ(ierr);
2256     ierr = MatAXPYGetPreallocation_MPIAIJ(yy->B,yy->garray,xx->B,xx->garray,nnz_o);CHKERRQ(ierr);
2257     ierr = MatMPIAIJSetPreallocation(B,0,nnz_d,0,nnz_o);CHKERRQ(ierr);
2258     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
2259     ierr = MatHeaderReplace(Y,&B);CHKERRQ(ierr);
2260     ierr = PetscFree(nnz_d);CHKERRQ(ierr);
2261     ierr = PetscFree(nnz_o);CHKERRQ(ierr);
2262   }
2263   PetscFunctionReturn(0);
2264 }
2265 
2266 extern PetscErrorCode  MatConjugate_SeqAIJ(Mat);
2267 
2268 PetscErrorCode  MatConjugate_MPIAIJ(Mat mat)
2269 {
2270 #if defined(PETSC_USE_COMPLEX)
2271   PetscErrorCode ierr;
2272   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2273 
2274   PetscFunctionBegin;
2275   ierr = MatConjugate_SeqAIJ(aij->A);CHKERRQ(ierr);
2276   ierr = MatConjugate_SeqAIJ(aij->B);CHKERRQ(ierr);
2277 #else
2278   PetscFunctionBegin;
2279 #endif
2280   PetscFunctionReturn(0);
2281 }
2282 
2283 PetscErrorCode MatRealPart_MPIAIJ(Mat A)
2284 {
2285   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2286   PetscErrorCode ierr;
2287 
2288   PetscFunctionBegin;
2289   ierr = MatRealPart(a->A);CHKERRQ(ierr);
2290   ierr = MatRealPart(a->B);CHKERRQ(ierr);
2291   PetscFunctionReturn(0);
2292 }
2293 
2294 PetscErrorCode MatImaginaryPart_MPIAIJ(Mat A)
2295 {
2296   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2297   PetscErrorCode ierr;
2298 
2299   PetscFunctionBegin;
2300   ierr = MatImaginaryPart(a->A);CHKERRQ(ierr);
2301   ierr = MatImaginaryPart(a->B);CHKERRQ(ierr);
2302   PetscFunctionReturn(0);
2303 }
2304 
2305 PetscErrorCode MatGetRowMaxAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2306 {
2307   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2308   PetscErrorCode ierr;
2309   PetscInt       i,*idxb = 0;
2310   PetscScalar    *va,*vb;
2311   Vec            vtmp;
2312 
2313   PetscFunctionBegin;
2314   ierr = MatGetRowMaxAbs(a->A,v,idx);CHKERRQ(ierr);
2315   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2316   if (idx) {
2317     for (i=0; i<A->rmap->n; i++) {
2318       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2319     }
2320   }
2321 
2322   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2323   if (idx) {
2324     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2325   }
2326   ierr = MatGetRowMaxAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2327   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2328 
2329   for (i=0; i<A->rmap->n; i++) {
2330     if (PetscAbsScalar(va[i]) < PetscAbsScalar(vb[i])) {
2331       va[i] = vb[i];
2332       if (idx) idx[i] = a->garray[idxb[i]];
2333     }
2334   }
2335 
2336   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2337   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2338   ierr = PetscFree(idxb);CHKERRQ(ierr);
2339   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2340   PetscFunctionReturn(0);
2341 }
2342 
2343 PetscErrorCode MatGetRowMinAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2344 {
2345   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2346   PetscErrorCode ierr;
2347   PetscInt       i,*idxb = 0;
2348   PetscScalar    *va,*vb;
2349   Vec            vtmp;
2350 
2351   PetscFunctionBegin;
2352   ierr = MatGetRowMinAbs(a->A,v,idx);CHKERRQ(ierr);
2353   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2354   if (idx) {
2355     for (i=0; i<A->cmap->n; i++) {
2356       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2357     }
2358   }
2359 
2360   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2361   if (idx) {
2362     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2363   }
2364   ierr = MatGetRowMinAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2365   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2366 
2367   for (i=0; i<A->rmap->n; i++) {
2368     if (PetscAbsScalar(va[i]) > PetscAbsScalar(vb[i])) {
2369       va[i] = vb[i];
2370       if (idx) idx[i] = a->garray[idxb[i]];
2371     }
2372   }
2373 
2374   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2375   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2376   ierr = PetscFree(idxb);CHKERRQ(ierr);
2377   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2378   PetscFunctionReturn(0);
2379 }
2380 
2381 PetscErrorCode MatGetRowMin_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2382 {
2383   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2384   PetscInt       n      = A->rmap->n;
2385   PetscInt       cstart = A->cmap->rstart;
2386   PetscInt       *cmap  = mat->garray;
2387   PetscInt       *diagIdx, *offdiagIdx;
2388   Vec            diagV, offdiagV;
2389   PetscScalar    *a, *diagA, *offdiagA;
2390   PetscInt       r;
2391   PetscErrorCode ierr;
2392 
2393   PetscFunctionBegin;
2394   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2395   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &diagV);CHKERRQ(ierr);
2396   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &offdiagV);CHKERRQ(ierr);
2397   ierr = MatGetRowMin(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2398   ierr = MatGetRowMin(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2399   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2400   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2401   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2402   for (r = 0; r < n; ++r) {
2403     if (PetscAbsScalar(diagA[r]) <= PetscAbsScalar(offdiagA[r])) {
2404       a[r]   = diagA[r];
2405       idx[r] = cstart + diagIdx[r];
2406     } else {
2407       a[r]   = offdiagA[r];
2408       idx[r] = cmap[offdiagIdx[r]];
2409     }
2410   }
2411   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2412   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2413   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2414   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2415   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2416   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2417   PetscFunctionReturn(0);
2418 }
2419 
2420 PetscErrorCode MatGetRowMax_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2421 {
2422   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2423   PetscInt       n      = A->rmap->n;
2424   PetscInt       cstart = A->cmap->rstart;
2425   PetscInt       *cmap  = mat->garray;
2426   PetscInt       *diagIdx, *offdiagIdx;
2427   Vec            diagV, offdiagV;
2428   PetscScalar    *a, *diagA, *offdiagA;
2429   PetscInt       r;
2430   PetscErrorCode ierr;
2431 
2432   PetscFunctionBegin;
2433   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2434   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &diagV);CHKERRQ(ierr);
2435   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &offdiagV);CHKERRQ(ierr);
2436   ierr = MatGetRowMax(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2437   ierr = MatGetRowMax(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2438   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2439   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2440   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2441   for (r = 0; r < n; ++r) {
2442     if (PetscAbsScalar(diagA[r]) >= PetscAbsScalar(offdiagA[r])) {
2443       a[r]   = diagA[r];
2444       idx[r] = cstart + diagIdx[r];
2445     } else {
2446       a[r]   = offdiagA[r];
2447       idx[r] = cmap[offdiagIdx[r]];
2448     }
2449   }
2450   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2451   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2452   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2453   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2454   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2455   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2456   PetscFunctionReturn(0);
2457 }
2458 
2459 PetscErrorCode MatGetSeqNonzeroStructure_MPIAIJ(Mat mat,Mat *newmat)
2460 {
2461   PetscErrorCode ierr;
2462   Mat            *dummy;
2463 
2464   PetscFunctionBegin;
2465   ierr    = MatCreateSubMatrix_MPIAIJ_All(mat,MAT_DO_NOT_GET_VALUES,MAT_INITIAL_MATRIX,&dummy);CHKERRQ(ierr);
2466   *newmat = *dummy;
2467   ierr    = PetscFree(dummy);CHKERRQ(ierr);
2468   PetscFunctionReturn(0);
2469 }
2470 
2471 PetscErrorCode  MatInvertBlockDiagonal_MPIAIJ(Mat A,const PetscScalar **values)
2472 {
2473   Mat_MPIAIJ     *a = (Mat_MPIAIJ*) A->data;
2474   PetscErrorCode ierr;
2475 
2476   PetscFunctionBegin;
2477   ierr = MatInvertBlockDiagonal(a->A,values);CHKERRQ(ierr);
2478   A->factorerrortype = a->A->factorerrortype;
2479   PetscFunctionReturn(0);
2480 }
2481 
2482 static PetscErrorCode  MatSetRandom_MPIAIJ(Mat x,PetscRandom rctx)
2483 {
2484   PetscErrorCode ierr;
2485   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)x->data;
2486 
2487   PetscFunctionBegin;
2488   if (!x->assembled && !x->preallocated) SETERRQ(PetscObjectComm((PetscObject)x), PETSC_ERR_ARG_WRONGSTATE, "MatSetRandom on an unassembled and unpreallocated MATMPIAIJ is not allowed");
2489   ierr = MatSetRandom(aij->A,rctx);CHKERRQ(ierr);
2490   if (x->assembled) {
2491     ierr = MatSetRandom(aij->B,rctx);CHKERRQ(ierr);
2492   } else {
2493     ierr = MatSetRandomSkipColumnRange_SeqAIJ_Private(aij->B,x->cmap->rstart,x->cmap->rend,rctx);CHKERRQ(ierr);
2494   }
2495   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2496   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2497   PetscFunctionReturn(0);
2498 }
2499 
2500 PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ(Mat A,PetscBool sc)
2501 {
2502   PetscFunctionBegin;
2503   if (sc) A->ops->increaseoverlap = MatIncreaseOverlap_MPIAIJ_Scalable;
2504   else A->ops->increaseoverlap    = MatIncreaseOverlap_MPIAIJ;
2505   PetscFunctionReturn(0);
2506 }
2507 
2508 /*@
2509    MatMPIAIJSetUseScalableIncreaseOverlap - Determine if the matrix uses a scalable algorithm to compute the overlap
2510 
2511    Collective on Mat
2512 
2513    Input Parameters:
2514 +    A - the matrix
2515 -    sc - PETSC_TRUE indicates use the scalable algorithm (default is not to use the scalable algorithm)
2516 
2517  Level: advanced
2518 
2519 @*/
2520 PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap(Mat A,PetscBool sc)
2521 {
2522   PetscErrorCode       ierr;
2523 
2524   PetscFunctionBegin;
2525   ierr = PetscTryMethod(A,"MatMPIAIJSetUseScalableIncreaseOverlap_C",(Mat,PetscBool),(A,sc));CHKERRQ(ierr);
2526   PetscFunctionReturn(0);
2527 }
2528 
2529 PetscErrorCode MatSetFromOptions_MPIAIJ(PetscOptionItems *PetscOptionsObject,Mat A)
2530 {
2531   PetscErrorCode       ierr;
2532   PetscBool            sc = PETSC_FALSE,flg;
2533 
2534   PetscFunctionBegin;
2535   ierr = PetscOptionsHead(PetscOptionsObject,"MPIAIJ options");CHKERRQ(ierr);
2536   if (A->ops->increaseoverlap == MatIncreaseOverlap_MPIAIJ_Scalable) sc = PETSC_TRUE;
2537   ierr = PetscOptionsBool("-mat_increase_overlap_scalable","Use a scalable algorithm to compute the overlap","MatIncreaseOverlap",sc,&sc,&flg);CHKERRQ(ierr);
2538   if (flg) {
2539     ierr = MatMPIAIJSetUseScalableIncreaseOverlap(A,sc);CHKERRQ(ierr);
2540   }
2541   ierr = PetscOptionsTail();CHKERRQ(ierr);
2542   PetscFunctionReturn(0);
2543 }
2544 
2545 PetscErrorCode MatShift_MPIAIJ(Mat Y,PetscScalar a)
2546 {
2547   PetscErrorCode ierr;
2548   Mat_MPIAIJ     *maij = (Mat_MPIAIJ*)Y->data;
2549   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)maij->A->data;
2550 
2551   PetscFunctionBegin;
2552   if (!Y->preallocated) {
2553     ierr = MatMPIAIJSetPreallocation(Y,1,NULL,0,NULL);CHKERRQ(ierr);
2554   } else if (!aij->nz) {
2555     PetscInt nonew = aij->nonew;
2556     ierr = MatSeqAIJSetPreallocation(maij->A,1,NULL);CHKERRQ(ierr);
2557     aij->nonew = nonew;
2558   }
2559   ierr = MatShift_Basic(Y,a);CHKERRQ(ierr);
2560   PetscFunctionReturn(0);
2561 }
2562 
2563 PetscErrorCode MatMissingDiagonal_MPIAIJ(Mat A,PetscBool  *missing,PetscInt *d)
2564 {
2565   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2566   PetscErrorCode ierr;
2567 
2568   PetscFunctionBegin;
2569   if (A->rmap->n != A->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only works for square matrices");
2570   ierr = MatMissingDiagonal(a->A,missing,d);CHKERRQ(ierr);
2571   if (d) {
2572     PetscInt rstart;
2573     ierr = MatGetOwnershipRange(A,&rstart,NULL);CHKERRQ(ierr);
2574     *d += rstart;
2575 
2576   }
2577   PetscFunctionReturn(0);
2578 }
2579 
2580 PetscErrorCode MatInvertVariableBlockDiagonal_MPIAIJ(Mat A,PetscInt nblocks,const PetscInt *bsizes,PetscScalar *diag)
2581 {
2582   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2583   PetscErrorCode ierr;
2584 
2585   PetscFunctionBegin;
2586   ierr = MatInvertVariableBlockDiagonal(a->A,nblocks,bsizes,diag);CHKERRQ(ierr);
2587   PetscFunctionReturn(0);
2588 }
2589 
2590 /* -------------------------------------------------------------------*/
2591 static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
2592                                        MatGetRow_MPIAIJ,
2593                                        MatRestoreRow_MPIAIJ,
2594                                        MatMult_MPIAIJ,
2595                                 /* 4*/ MatMultAdd_MPIAIJ,
2596                                        MatMultTranspose_MPIAIJ,
2597                                        MatMultTransposeAdd_MPIAIJ,
2598                                        0,
2599                                        0,
2600                                        0,
2601                                 /*10*/ 0,
2602                                        0,
2603                                        0,
2604                                        MatSOR_MPIAIJ,
2605                                        MatTranspose_MPIAIJ,
2606                                 /*15*/ MatGetInfo_MPIAIJ,
2607                                        MatEqual_MPIAIJ,
2608                                        MatGetDiagonal_MPIAIJ,
2609                                        MatDiagonalScale_MPIAIJ,
2610                                        MatNorm_MPIAIJ,
2611                                 /*20*/ MatAssemblyBegin_MPIAIJ,
2612                                        MatAssemblyEnd_MPIAIJ,
2613                                        MatSetOption_MPIAIJ,
2614                                        MatZeroEntries_MPIAIJ,
2615                                 /*24*/ MatZeroRows_MPIAIJ,
2616                                        0,
2617                                        0,
2618                                        0,
2619                                        0,
2620                                 /*29*/ MatSetUp_MPIAIJ,
2621                                        0,
2622                                        0,
2623                                        MatGetDiagonalBlock_MPIAIJ,
2624                                        0,
2625                                 /*34*/ MatDuplicate_MPIAIJ,
2626                                        0,
2627                                        0,
2628                                        0,
2629                                        0,
2630                                 /*39*/ MatAXPY_MPIAIJ,
2631                                        MatCreateSubMatrices_MPIAIJ,
2632                                        MatIncreaseOverlap_MPIAIJ,
2633                                        MatGetValues_MPIAIJ,
2634                                        MatCopy_MPIAIJ,
2635                                 /*44*/ MatGetRowMax_MPIAIJ,
2636                                        MatScale_MPIAIJ,
2637                                        MatShift_MPIAIJ,
2638                                        MatDiagonalSet_MPIAIJ,
2639                                        MatZeroRowsColumns_MPIAIJ,
2640                                 /*49*/ MatSetRandom_MPIAIJ,
2641                                        0,
2642                                        0,
2643                                        0,
2644                                        0,
2645                                 /*54*/ MatFDColoringCreate_MPIXAIJ,
2646                                        0,
2647                                        MatSetUnfactored_MPIAIJ,
2648                                        MatPermute_MPIAIJ,
2649                                        0,
2650                                 /*59*/ MatCreateSubMatrix_MPIAIJ,
2651                                        MatDestroy_MPIAIJ,
2652                                        MatView_MPIAIJ,
2653                                        0,
2654                                        0,
2655                                 /*64*/ 0,
2656                                        MatMatMatMultNumeric_MPIAIJ_MPIAIJ_MPIAIJ,
2657                                        0,
2658                                        0,
2659                                        0,
2660                                 /*69*/ MatGetRowMaxAbs_MPIAIJ,
2661                                        MatGetRowMinAbs_MPIAIJ,
2662                                        0,
2663                                        0,
2664                                        0,
2665                                        0,
2666                                 /*75*/ MatFDColoringApply_AIJ,
2667                                        MatSetFromOptions_MPIAIJ,
2668                                        0,
2669                                        0,
2670                                        MatFindZeroDiagonals_MPIAIJ,
2671                                 /*80*/ 0,
2672                                        0,
2673                                        0,
2674                                 /*83*/ MatLoad_MPIAIJ,
2675                                        MatIsSymmetric_MPIAIJ,
2676                                        0,
2677                                        0,
2678                                        0,
2679                                        0,
2680                                 /*89*/ 0,
2681                                        0,
2682                                        MatMatMultNumeric_MPIAIJ_MPIAIJ,
2683                                        0,
2684                                        0,
2685                                 /*94*/ MatPtAPNumeric_MPIAIJ_MPIAIJ,
2686                                        0,
2687                                        0,
2688                                        0,
2689                                        MatBindToCPU_MPIAIJ,
2690                                 /*99*/ MatProductSetFromOptions_MPIAIJ,
2691                                        0,
2692                                        0,
2693                                        MatConjugate_MPIAIJ,
2694                                        0,
2695                                 /*104*/MatSetValuesRow_MPIAIJ,
2696                                        MatRealPart_MPIAIJ,
2697                                        MatImaginaryPart_MPIAIJ,
2698                                        0,
2699                                        0,
2700                                 /*109*/0,
2701                                        0,
2702                                        MatGetRowMin_MPIAIJ,
2703                                        0,
2704                                        MatMissingDiagonal_MPIAIJ,
2705                                 /*114*/MatGetSeqNonzeroStructure_MPIAIJ,
2706                                        0,
2707                                        MatGetGhosts_MPIAIJ,
2708                                        0,
2709                                        0,
2710                                 /*119*/0,
2711                                        0,
2712                                        0,
2713                                        0,
2714                                        MatGetMultiProcBlock_MPIAIJ,
2715                                 /*124*/MatFindNonzeroRows_MPIAIJ,
2716                                        MatGetColumnNorms_MPIAIJ,
2717                                        MatInvertBlockDiagonal_MPIAIJ,
2718                                        MatInvertVariableBlockDiagonal_MPIAIJ,
2719                                        MatCreateSubMatricesMPI_MPIAIJ,
2720                                 /*129*/0,
2721                                        0,
2722                                        0,
2723                                        MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ,
2724                                        0,
2725                                 /*134*/0,
2726                                        0,
2727                                        0,
2728                                        0,
2729                                        0,
2730                                 /*139*/MatSetBlockSizes_MPIAIJ,
2731                                        0,
2732                                        0,
2733                                        MatFDColoringSetUp_MPIXAIJ,
2734                                        MatFindOffBlockDiagonalEntries_MPIAIJ,
2735                                        MatCreateMPIMatConcatenateSeqMat_MPIAIJ,
2736                                 /*145*/0,
2737                                        0,
2738                                        0
2739 };
2740 
2741 /* ----------------------------------------------------------------------------------------*/
2742 
2743 PetscErrorCode  MatStoreValues_MPIAIJ(Mat mat)
2744 {
2745   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2746   PetscErrorCode ierr;
2747 
2748   PetscFunctionBegin;
2749   ierr = MatStoreValues(aij->A);CHKERRQ(ierr);
2750   ierr = MatStoreValues(aij->B);CHKERRQ(ierr);
2751   PetscFunctionReturn(0);
2752 }
2753 
2754 PetscErrorCode  MatRetrieveValues_MPIAIJ(Mat mat)
2755 {
2756   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2757   PetscErrorCode ierr;
2758 
2759   PetscFunctionBegin;
2760   ierr = MatRetrieveValues(aij->A);CHKERRQ(ierr);
2761   ierr = MatRetrieveValues(aij->B);CHKERRQ(ierr);
2762   PetscFunctionReturn(0);
2763 }
2764 
2765 PetscErrorCode  MatMPIAIJSetPreallocation_MPIAIJ(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
2766 {
2767   Mat_MPIAIJ     *b;
2768   PetscErrorCode ierr;
2769   PetscMPIInt    size;
2770 
2771   PetscFunctionBegin;
2772   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
2773   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
2774   b = (Mat_MPIAIJ*)B->data;
2775 
2776 #if defined(PETSC_USE_CTABLE)
2777   ierr = PetscTableDestroy(&b->colmap);CHKERRQ(ierr);
2778 #else
2779   ierr = PetscFree(b->colmap);CHKERRQ(ierr);
2780 #endif
2781   ierr = PetscFree(b->garray);CHKERRQ(ierr);
2782   ierr = VecDestroy(&b->lvec);CHKERRQ(ierr);
2783   ierr = VecScatterDestroy(&b->Mvctx);CHKERRQ(ierr);
2784 
2785   /* Because the B will have been resized we simply destroy it and create a new one each time */
2786   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
2787   ierr = MatDestroy(&b->B);CHKERRQ(ierr);
2788   ierr = MatCreate(PETSC_COMM_SELF,&b->B);CHKERRQ(ierr);
2789   ierr = MatSetSizes(b->B,B->rmap->n,size > 1 ? B->cmap->N : 0,B->rmap->n,size > 1 ? B->cmap->N : 0);CHKERRQ(ierr);
2790   ierr = MatSetBlockSizesFromMats(b->B,B,B);CHKERRQ(ierr);
2791   ierr = MatSetType(b->B,MATSEQAIJ);CHKERRQ(ierr);
2792   ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->B);CHKERRQ(ierr);
2793 
2794   if (!B->preallocated) {
2795     ierr = MatCreate(PETSC_COMM_SELF,&b->A);CHKERRQ(ierr);
2796     ierr = MatSetSizes(b->A,B->rmap->n,B->cmap->n,B->rmap->n,B->cmap->n);CHKERRQ(ierr);
2797     ierr = MatSetBlockSizesFromMats(b->A,B,B);CHKERRQ(ierr);
2798     ierr = MatSetType(b->A,MATSEQAIJ);CHKERRQ(ierr);
2799     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->A);CHKERRQ(ierr);
2800   }
2801 
2802   ierr = MatSeqAIJSetPreallocation(b->A,d_nz,d_nnz);CHKERRQ(ierr);
2803   ierr = MatSeqAIJSetPreallocation(b->B,o_nz,o_nnz);CHKERRQ(ierr);
2804   B->preallocated  = PETSC_TRUE;
2805   B->was_assembled = PETSC_FALSE;
2806   B->assembled     = PETSC_FALSE;
2807   PetscFunctionReturn(0);
2808 }
2809 
2810 PetscErrorCode MatResetPreallocation_MPIAIJ(Mat B)
2811 {
2812   Mat_MPIAIJ     *b;
2813   PetscErrorCode ierr;
2814 
2815   PetscFunctionBegin;
2816   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
2817   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
2818   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
2819   b = (Mat_MPIAIJ*)B->data;
2820 
2821 #if defined(PETSC_USE_CTABLE)
2822   ierr = PetscTableDestroy(&b->colmap);CHKERRQ(ierr);
2823 #else
2824   ierr = PetscFree(b->colmap);CHKERRQ(ierr);
2825 #endif
2826   ierr = PetscFree(b->garray);CHKERRQ(ierr);
2827   ierr = VecDestroy(&b->lvec);CHKERRQ(ierr);
2828   ierr = VecScatterDestroy(&b->Mvctx);CHKERRQ(ierr);
2829 
2830   ierr = MatResetPreallocation(b->A);CHKERRQ(ierr);
2831   ierr = MatResetPreallocation(b->B);CHKERRQ(ierr);
2832   B->preallocated  = PETSC_TRUE;
2833   B->was_assembled = PETSC_FALSE;
2834   B->assembled = PETSC_FALSE;
2835   PetscFunctionReturn(0);
2836 }
2837 
2838 PetscErrorCode MatDuplicate_MPIAIJ(Mat matin,MatDuplicateOption cpvalues,Mat *newmat)
2839 {
2840   Mat            mat;
2841   Mat_MPIAIJ     *a,*oldmat = (Mat_MPIAIJ*)matin->data;
2842   PetscErrorCode ierr;
2843 
2844   PetscFunctionBegin;
2845   *newmat = 0;
2846   ierr    = MatCreate(PetscObjectComm((PetscObject)matin),&mat);CHKERRQ(ierr);
2847   ierr    = MatSetSizes(mat,matin->rmap->n,matin->cmap->n,matin->rmap->N,matin->cmap->N);CHKERRQ(ierr);
2848   ierr    = MatSetBlockSizesFromMats(mat,matin,matin);CHKERRQ(ierr);
2849   ierr    = MatSetType(mat,((PetscObject)matin)->type_name);CHKERRQ(ierr);
2850   a       = (Mat_MPIAIJ*)mat->data;
2851 
2852   mat->factortype   = matin->factortype;
2853   mat->assembled    = matin->assembled;
2854   mat->insertmode   = NOT_SET_VALUES;
2855   mat->preallocated = matin->preallocated;
2856 
2857   a->size         = oldmat->size;
2858   a->rank         = oldmat->rank;
2859   a->donotstash   = oldmat->donotstash;
2860   a->roworiented  = oldmat->roworiented;
2861   a->rowindices   = NULL;
2862   a->rowvalues    = NULL;
2863   a->getrowactive = PETSC_FALSE;
2864 
2865   ierr = PetscLayoutReference(matin->rmap,&mat->rmap);CHKERRQ(ierr);
2866   ierr = PetscLayoutReference(matin->cmap,&mat->cmap);CHKERRQ(ierr);
2867 
2868   if (oldmat->colmap) {
2869 #if defined(PETSC_USE_CTABLE)
2870     ierr = PetscTableCreateCopy(oldmat->colmap,&a->colmap);CHKERRQ(ierr);
2871 #else
2872     ierr = PetscMalloc1(mat->cmap->N,&a->colmap);CHKERRQ(ierr);
2873     ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2874     ierr = PetscArraycpy(a->colmap,oldmat->colmap,mat->cmap->N);CHKERRQ(ierr);
2875 #endif
2876   } else a->colmap = NULL;
2877   if (oldmat->garray) {
2878     PetscInt len;
2879     len  = oldmat->B->cmap->n;
2880     ierr = PetscMalloc1(len+1,&a->garray);CHKERRQ(ierr);
2881     ierr = PetscLogObjectMemory((PetscObject)mat,len*sizeof(PetscInt));CHKERRQ(ierr);
2882     if (len) { ierr = PetscArraycpy(a->garray,oldmat->garray,len);CHKERRQ(ierr); }
2883   } else a->garray = NULL;
2884 
2885   /* It may happen MatDuplicate is called with a non-assembled matrix
2886      In fact, MatDuplicate only requires the matrix to be preallocated
2887      This may happen inside a DMCreateMatrix_Shell */
2888   if (oldmat->lvec) {
2889     ierr = VecDuplicate(oldmat->lvec,&a->lvec);CHKERRQ(ierr);
2890     ierr = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->lvec);CHKERRQ(ierr);
2891   }
2892   if (oldmat->Mvctx) {
2893     ierr = VecScatterCopy(oldmat->Mvctx,&a->Mvctx);CHKERRQ(ierr);
2894     ierr = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->Mvctx);CHKERRQ(ierr);
2895   }
2896   if (oldmat->Mvctx_mpi1) {
2897     ierr = VecScatterCopy(oldmat->Mvctx_mpi1,&a->Mvctx_mpi1);CHKERRQ(ierr);
2898     ierr = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->Mvctx_mpi1);CHKERRQ(ierr);
2899   }
2900 
2901   ierr    = MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
2902   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->A);CHKERRQ(ierr);
2903   ierr    = MatDuplicate(oldmat->B,cpvalues,&a->B);CHKERRQ(ierr);
2904   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->B);CHKERRQ(ierr);
2905   ierr    = PetscFunctionListDuplicate(((PetscObject)matin)->qlist,&((PetscObject)mat)->qlist);CHKERRQ(ierr);
2906   *newmat = mat;
2907   PetscFunctionReturn(0);
2908 }
2909 
2910 PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
2911 {
2912   PetscBool      isbinary, ishdf5;
2913   PetscErrorCode ierr;
2914 
2915   PetscFunctionBegin;
2916   PetscValidHeaderSpecific(newMat,MAT_CLASSID,1);
2917   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,2);
2918   /* force binary viewer to load .info file if it has not yet done so */
2919   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
2920   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
2921   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERHDF5,  &ishdf5);CHKERRQ(ierr);
2922   if (isbinary) {
2923     ierr = MatLoad_MPIAIJ_Binary(newMat,viewer);CHKERRQ(ierr);
2924   } else if (ishdf5) {
2925 #if defined(PETSC_HAVE_HDF5)
2926     ierr = MatLoad_AIJ_HDF5(newMat,viewer);CHKERRQ(ierr);
2927 #else
2928     SETERRQ(PetscObjectComm((PetscObject)newMat),PETSC_ERR_SUP,"HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
2929 #endif
2930   } else {
2931     SETERRQ2(PetscObjectComm((PetscObject)newMat),PETSC_ERR_SUP,"Viewer type %s not yet supported for reading %s matrices",((PetscObject)viewer)->type_name,((PetscObject)newMat)->type_name);
2932   }
2933   PetscFunctionReturn(0);
2934 }
2935 
2936 PetscErrorCode MatLoad_MPIAIJ_Binary(Mat mat, PetscViewer viewer)
2937 {
2938   PetscInt       header[4],M,N,m,nz,rows,cols,sum,i;
2939   PetscInt       *rowidxs,*colidxs;
2940   PetscScalar    *matvals;
2941   PetscErrorCode ierr;
2942 
2943   PetscFunctionBegin;
2944   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
2945 
2946   /* read in matrix header */
2947   ierr = PetscViewerBinaryRead(viewer,header,4,NULL,PETSC_INT);CHKERRQ(ierr);
2948   if (header[0] != MAT_FILE_CLASSID) SETERRQ(PetscObjectComm((PetscObject)viewer),PETSC_ERR_FILE_UNEXPECTED,"Not a matrix object in file");
2949   M  = header[1]; N = header[2]; nz = header[3];
2950   if (M < 0) SETERRQ1(PetscObjectComm((PetscObject)viewer),PETSC_ERR_FILE_UNEXPECTED,"Matrix row size (%D) in file is negative",M);
2951   if (N < 0) SETERRQ1(PetscObjectComm((PetscObject)viewer),PETSC_ERR_FILE_UNEXPECTED,"Matrix column size (%D) in file is negative",N);
2952   if (nz < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Matrix stored in special format on disk, cannot load as MPIAIJ");
2953 
2954   /* set block sizes from the viewer's .info file */
2955   ierr = MatLoad_Binary_BlockSizes(mat,viewer);CHKERRQ(ierr);
2956   /* set global sizes if not set already */
2957   if (mat->rmap->N < 0) mat->rmap->N = M;
2958   if (mat->cmap->N < 0) mat->cmap->N = N;
2959   ierr = PetscLayoutSetUp(mat->rmap);CHKERRQ(ierr);
2960   ierr = PetscLayoutSetUp(mat->cmap);CHKERRQ(ierr);
2961 
2962   /* check if the matrix sizes are correct */
2963   ierr = MatGetSize(mat,&rows,&cols);CHKERRQ(ierr);
2964   if (M != rows || N != cols) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Matrix in file of different sizes (%D, %D) than the input matrix (%D, %D)",M,N,rows,cols);
2965 
2966   /* read in row lengths and build row indices */
2967   ierr = MatGetLocalSize(mat,&m,NULL);CHKERRQ(ierr);
2968   ierr = PetscMalloc1(m+1,&rowidxs);CHKERRQ(ierr);
2969   ierr = PetscViewerBinaryReadAll(viewer,rowidxs+1,m,PETSC_DECIDE,M,PETSC_INT);CHKERRQ(ierr);
2970   rowidxs[0] = 0; for (i=0; i<m; i++) rowidxs[i+1] += rowidxs[i];
2971   ierr = MPIU_Allreduce(&rowidxs[m],&sum,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)viewer));CHKERRQ(ierr);
2972   if (sum != nz) SETERRQ2(PetscObjectComm((PetscObject)viewer),PETSC_ERR_FILE_UNEXPECTED,"Inconsistent matrix data in file: nonzeros = %D, sum-row-lengths = %D\n",nz,sum);
2973   /* read in column indices and matrix values */
2974   ierr = PetscMalloc2(rowidxs[m],&colidxs,rowidxs[m],&matvals);CHKERRQ(ierr);
2975   ierr = PetscViewerBinaryReadAll(viewer,colidxs,rowidxs[m],PETSC_DETERMINE,PETSC_DETERMINE,PETSC_INT);CHKERRQ(ierr);
2976   ierr = PetscViewerBinaryReadAll(viewer,matvals,rowidxs[m],PETSC_DETERMINE,PETSC_DETERMINE,PETSC_SCALAR);CHKERRQ(ierr);
2977   /* store matrix indices and values */
2978   ierr = MatMPIAIJSetPreallocationCSR(mat,rowidxs,colidxs,matvals);CHKERRQ(ierr);
2979   ierr = PetscFree(rowidxs);CHKERRQ(ierr);
2980   ierr = PetscFree2(colidxs,matvals);CHKERRQ(ierr);
2981   PetscFunctionReturn(0);
2982 }
2983 
2984 /* Not scalable because of ISAllGather() unless getting all columns. */
2985 PetscErrorCode ISGetSeqIS_Private(Mat mat,IS iscol,IS *isseq)
2986 {
2987   PetscErrorCode ierr;
2988   IS             iscol_local;
2989   PetscBool      isstride;
2990   PetscMPIInt    lisstride=0,gisstride;
2991 
2992   PetscFunctionBegin;
2993   /* check if we are grabbing all columns*/
2994   ierr = PetscObjectTypeCompare((PetscObject)iscol,ISSTRIDE,&isstride);CHKERRQ(ierr);
2995 
2996   if (isstride) {
2997     PetscInt  start,len,mstart,mlen;
2998     ierr = ISStrideGetInfo(iscol,&start,NULL);CHKERRQ(ierr);
2999     ierr = ISGetLocalSize(iscol,&len);CHKERRQ(ierr);
3000     ierr = MatGetOwnershipRangeColumn(mat,&mstart,&mlen);CHKERRQ(ierr);
3001     if (mstart == start && mlen-mstart == len) lisstride = 1;
3002   }
3003 
3004   ierr = MPIU_Allreduce(&lisstride,&gisstride,1,MPI_INT,MPI_MIN,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
3005   if (gisstride) {
3006     PetscInt N;
3007     ierr = MatGetSize(mat,NULL,&N);CHKERRQ(ierr);
3008     ierr = ISCreateStride(PETSC_COMM_SELF,N,0,1,&iscol_local);CHKERRQ(ierr);
3009     ierr = ISSetIdentity(iscol_local);CHKERRQ(ierr);
3010     ierr = PetscInfo(mat,"Optimizing for obtaining all columns of the matrix; skipping ISAllGather()\n");CHKERRQ(ierr);
3011   } else {
3012     PetscInt cbs;
3013     ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
3014     ierr = ISAllGather(iscol,&iscol_local);CHKERRQ(ierr);
3015     ierr = ISSetBlockSize(iscol_local,cbs);CHKERRQ(ierr);
3016   }
3017 
3018   *isseq = iscol_local;
3019   PetscFunctionReturn(0);
3020 }
3021 
3022 /*
3023  Used by MatCreateSubMatrix_MPIAIJ_SameRowColDist() to avoid ISAllGather() and global size of iscol_local
3024  (see MatCreateSubMatrix_MPIAIJ_nonscalable)
3025 
3026  Input Parameters:
3027    mat - matrix
3028    isrow - parallel row index set; its local indices are a subset of local columns of mat,
3029            i.e., mat->rstart <= isrow[i] < mat->rend
3030    iscol - parallel column index set; its local indices are a subset of local columns of mat,
3031            i.e., mat->cstart <= iscol[i] < mat->cend
3032  Output Parameter:
3033    isrow_d,iscol_d - sequential row and column index sets for retrieving mat->A
3034    iscol_o - sequential column index set for retrieving mat->B
3035    garray - column map; garray[i] indicates global location of iscol_o[i] in iscol
3036  */
3037 PetscErrorCode ISGetSeqIS_SameColDist_Private(Mat mat,IS isrow,IS iscol,IS *isrow_d,IS *iscol_d,IS *iscol_o,const PetscInt *garray[])
3038 {
3039   PetscErrorCode ierr;
3040   Vec            x,cmap;
3041   const PetscInt *is_idx;
3042   PetscScalar    *xarray,*cmaparray;
3043   PetscInt       ncols,isstart,*idx,m,rstart,*cmap1,count;
3044   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)mat->data;
3045   Mat            B=a->B;
3046   Vec            lvec=a->lvec,lcmap;
3047   PetscInt       i,cstart,cend,Bn=B->cmap->N;
3048   MPI_Comm       comm;
3049   VecScatter     Mvctx=a->Mvctx;
3050 
3051   PetscFunctionBegin;
3052   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3053   ierr = ISGetLocalSize(iscol,&ncols);CHKERRQ(ierr);
3054 
3055   /* (1) iscol is a sub-column vector of mat, pad it with '-1.' to form a full vector x */
3056   ierr = MatCreateVecs(mat,&x,NULL);CHKERRQ(ierr);
3057   ierr = VecSet(x,-1.0);CHKERRQ(ierr);
3058   ierr = VecDuplicate(x,&cmap);CHKERRQ(ierr);
3059   ierr = VecSet(cmap,-1.0);CHKERRQ(ierr);
3060 
3061   /* Get start indices */
3062   ierr = MPI_Scan(&ncols,&isstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3063   isstart -= ncols;
3064   ierr = MatGetOwnershipRangeColumn(mat,&cstart,&cend);CHKERRQ(ierr);
3065 
3066   ierr = ISGetIndices(iscol,&is_idx);CHKERRQ(ierr);
3067   ierr = VecGetArray(x,&xarray);CHKERRQ(ierr);
3068   ierr = VecGetArray(cmap,&cmaparray);CHKERRQ(ierr);
3069   ierr = PetscMalloc1(ncols,&idx);CHKERRQ(ierr);
3070   for (i=0; i<ncols; i++) {
3071     xarray[is_idx[i]-cstart]    = (PetscScalar)is_idx[i];
3072     cmaparray[is_idx[i]-cstart] = i + isstart;      /* global index of iscol[i] */
3073     idx[i]                      = is_idx[i]-cstart; /* local index of iscol[i]  */
3074   }
3075   ierr = VecRestoreArray(x,&xarray);CHKERRQ(ierr);
3076   ierr = VecRestoreArray(cmap,&cmaparray);CHKERRQ(ierr);
3077   ierr = ISRestoreIndices(iscol,&is_idx);CHKERRQ(ierr);
3078 
3079   /* Get iscol_d */
3080   ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,iscol_d);CHKERRQ(ierr);
3081   ierr = ISGetBlockSize(iscol,&i);CHKERRQ(ierr);
3082   ierr = ISSetBlockSize(*iscol_d,i);CHKERRQ(ierr);
3083 
3084   /* Get isrow_d */
3085   ierr = ISGetLocalSize(isrow,&m);CHKERRQ(ierr);
3086   rstart = mat->rmap->rstart;
3087   ierr = PetscMalloc1(m,&idx);CHKERRQ(ierr);
3088   ierr = ISGetIndices(isrow,&is_idx);CHKERRQ(ierr);
3089   for (i=0; i<m; i++) idx[i] = is_idx[i]-rstart;
3090   ierr = ISRestoreIndices(isrow,&is_idx);CHKERRQ(ierr);
3091 
3092   ierr = ISCreateGeneral(PETSC_COMM_SELF,m,idx,PETSC_OWN_POINTER,isrow_d);CHKERRQ(ierr);
3093   ierr = ISGetBlockSize(isrow,&i);CHKERRQ(ierr);
3094   ierr = ISSetBlockSize(*isrow_d,i);CHKERRQ(ierr);
3095 
3096   /* (2) Scatter x and cmap using aij->Mvctx to get their off-process portions (see MatMult_MPIAIJ) */
3097   ierr = VecScatterBegin(Mvctx,x,lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3098   ierr = VecScatterEnd(Mvctx,x,lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3099 
3100   ierr = VecDuplicate(lvec,&lcmap);CHKERRQ(ierr);
3101 
3102   ierr = VecScatterBegin(Mvctx,cmap,lcmap,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3103   ierr = VecScatterEnd(Mvctx,cmap,lcmap,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3104 
3105   /* (3) create sequential iscol_o (a subset of iscol) and isgarray */
3106   /* off-process column indices */
3107   count = 0;
3108   ierr = PetscMalloc1(Bn,&idx);CHKERRQ(ierr);
3109   ierr = PetscMalloc1(Bn,&cmap1);CHKERRQ(ierr);
3110 
3111   ierr = VecGetArray(lvec,&xarray);CHKERRQ(ierr);
3112   ierr = VecGetArray(lcmap,&cmaparray);CHKERRQ(ierr);
3113   for (i=0; i<Bn; i++) {
3114     if (PetscRealPart(xarray[i]) > -1.0) {
3115       idx[count]     = i;                   /* local column index in off-diagonal part B */
3116       cmap1[count] = (PetscInt)PetscRealPart(cmaparray[i]);  /* column index in submat */
3117       count++;
3118     }
3119   }
3120   ierr = VecRestoreArray(lvec,&xarray);CHKERRQ(ierr);
3121   ierr = VecRestoreArray(lcmap,&cmaparray);CHKERRQ(ierr);
3122 
3123   ierr = ISCreateGeneral(PETSC_COMM_SELF,count,idx,PETSC_COPY_VALUES,iscol_o);CHKERRQ(ierr);
3124   /* cannot ensure iscol_o has same blocksize as iscol! */
3125 
3126   ierr = PetscFree(idx);CHKERRQ(ierr);
3127   *garray = cmap1;
3128 
3129   ierr = VecDestroy(&x);CHKERRQ(ierr);
3130   ierr = VecDestroy(&cmap);CHKERRQ(ierr);
3131   ierr = VecDestroy(&lcmap);CHKERRQ(ierr);
3132   PetscFunctionReturn(0);
3133 }
3134 
3135 /* isrow and iscol have same processor distribution as mat, output *submat is a submatrix of local mat */
3136 PetscErrorCode MatCreateSubMatrix_MPIAIJ_SameRowColDist(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *submat)
3137 {
3138   PetscErrorCode ierr;
3139   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)mat->data,*asub;
3140   Mat            M = NULL;
3141   MPI_Comm       comm;
3142   IS             iscol_d,isrow_d,iscol_o;
3143   Mat            Asub = NULL,Bsub = NULL;
3144   PetscInt       n;
3145 
3146   PetscFunctionBegin;
3147   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3148 
3149   if (call == MAT_REUSE_MATRIX) {
3150     /* Retrieve isrow_d, iscol_d and iscol_o from submat */
3151     ierr = PetscObjectQuery((PetscObject)*submat,"isrow_d",(PetscObject*)&isrow_d);CHKERRQ(ierr);
3152     if (!isrow_d) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"isrow_d passed in was not used before, cannot reuse");
3153 
3154     ierr = PetscObjectQuery((PetscObject)*submat,"iscol_d",(PetscObject*)&iscol_d);CHKERRQ(ierr);
3155     if (!iscol_d) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"iscol_d passed in was not used before, cannot reuse");
3156 
3157     ierr = PetscObjectQuery((PetscObject)*submat,"iscol_o",(PetscObject*)&iscol_o);CHKERRQ(ierr);
3158     if (!iscol_o) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"iscol_o passed in was not used before, cannot reuse");
3159 
3160     /* Update diagonal and off-diagonal portions of submat */
3161     asub = (Mat_MPIAIJ*)(*submat)->data;
3162     ierr = MatCreateSubMatrix_SeqAIJ(a->A,isrow_d,iscol_d,PETSC_DECIDE,MAT_REUSE_MATRIX,&asub->A);CHKERRQ(ierr);
3163     ierr = ISGetLocalSize(iscol_o,&n);CHKERRQ(ierr);
3164     if (n) {
3165       ierr = MatCreateSubMatrix_SeqAIJ(a->B,isrow_d,iscol_o,PETSC_DECIDE,MAT_REUSE_MATRIX,&asub->B);CHKERRQ(ierr);
3166     }
3167     ierr = MatAssemblyBegin(*submat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3168     ierr = MatAssemblyEnd(*submat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3169 
3170   } else { /* call == MAT_INITIAL_MATRIX) */
3171     const PetscInt *garray;
3172     PetscInt        BsubN;
3173 
3174     /* Create isrow_d, iscol_d, iscol_o and isgarray (replace isgarray with array?) */
3175     ierr = ISGetSeqIS_SameColDist_Private(mat,isrow,iscol,&isrow_d,&iscol_d,&iscol_o,&garray);CHKERRQ(ierr);
3176 
3177     /* Create local submatrices Asub and Bsub */
3178     ierr = MatCreateSubMatrix_SeqAIJ(a->A,isrow_d,iscol_d,PETSC_DECIDE,MAT_INITIAL_MATRIX,&Asub);CHKERRQ(ierr);
3179     ierr = MatCreateSubMatrix_SeqAIJ(a->B,isrow_d,iscol_o,PETSC_DECIDE,MAT_INITIAL_MATRIX,&Bsub);CHKERRQ(ierr);
3180 
3181     /* Create submatrix M */
3182     ierr = MatCreateMPIAIJWithSeqAIJ(comm,Asub,Bsub,garray,&M);CHKERRQ(ierr);
3183 
3184     /* If Bsub has empty columns, compress iscol_o such that it will retrieve condensed Bsub from a->B during reuse */
3185     asub = (Mat_MPIAIJ*)M->data;
3186 
3187     ierr = ISGetLocalSize(iscol_o,&BsubN);CHKERRQ(ierr);
3188     n = asub->B->cmap->N;
3189     if (BsubN > n) {
3190       /* This case can be tested using ~petsc/src/tao/bound/tutorials/runplate2_3 */
3191       const PetscInt *idx;
3192       PetscInt       i,j,*idx_new,*subgarray = asub->garray;
3193       ierr = PetscInfo2(M,"submatrix Bn %D != BsubN %D, update iscol_o\n",n,BsubN);CHKERRQ(ierr);
3194 
3195       ierr = PetscMalloc1(n,&idx_new);CHKERRQ(ierr);
3196       j = 0;
3197       ierr = ISGetIndices(iscol_o,&idx);CHKERRQ(ierr);
3198       for (i=0; i<n; i++) {
3199         if (j >= BsubN) break;
3200         while (subgarray[i] > garray[j]) j++;
3201 
3202         if (subgarray[i] == garray[j]) {
3203           idx_new[i] = idx[j++];
3204         } else SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"subgarray[%D]=%D cannot < garray[%D]=%D",i,subgarray[i],j,garray[j]);
3205       }
3206       ierr = ISRestoreIndices(iscol_o,&idx);CHKERRQ(ierr);
3207 
3208       ierr = ISDestroy(&iscol_o);CHKERRQ(ierr);
3209       ierr = ISCreateGeneral(PETSC_COMM_SELF,n,idx_new,PETSC_OWN_POINTER,&iscol_o);CHKERRQ(ierr);
3210 
3211     } else if (BsubN < n) {
3212       SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Columns of Bsub cannot be smaller than B's",BsubN,asub->B->cmap->N);
3213     }
3214 
3215     ierr = PetscFree(garray);CHKERRQ(ierr);
3216     *submat = M;
3217 
3218     /* Save isrow_d, iscol_d and iscol_o used in processor for next request */
3219     ierr = PetscObjectCompose((PetscObject)M,"isrow_d",(PetscObject)isrow_d);CHKERRQ(ierr);
3220     ierr = ISDestroy(&isrow_d);CHKERRQ(ierr);
3221 
3222     ierr = PetscObjectCompose((PetscObject)M,"iscol_d",(PetscObject)iscol_d);CHKERRQ(ierr);
3223     ierr = ISDestroy(&iscol_d);CHKERRQ(ierr);
3224 
3225     ierr = PetscObjectCompose((PetscObject)M,"iscol_o",(PetscObject)iscol_o);CHKERRQ(ierr);
3226     ierr = ISDestroy(&iscol_o);CHKERRQ(ierr);
3227   }
3228   PetscFunctionReturn(0);
3229 }
3230 
3231 PetscErrorCode MatCreateSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3232 {
3233   PetscErrorCode ierr;
3234   IS             iscol_local=NULL,isrow_d;
3235   PetscInt       csize;
3236   PetscInt       n,i,j,start,end;
3237   PetscBool      sameRowDist=PETSC_FALSE,sameDist[2],tsameDist[2];
3238   MPI_Comm       comm;
3239 
3240   PetscFunctionBegin;
3241   /* If isrow has same processor distribution as mat,
3242      call MatCreateSubMatrix_MPIAIJ_SameRowDist() to avoid using a hash table with global size of iscol */
3243   if (call == MAT_REUSE_MATRIX) {
3244     ierr = PetscObjectQuery((PetscObject)*newmat,"isrow_d",(PetscObject*)&isrow_d);CHKERRQ(ierr);
3245     if (isrow_d) {
3246       sameRowDist  = PETSC_TRUE;
3247       tsameDist[1] = PETSC_TRUE; /* sameColDist */
3248     } else {
3249       ierr = PetscObjectQuery((PetscObject)*newmat,"SubIScol",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3250       if (iscol_local) {
3251         sameRowDist  = PETSC_TRUE;
3252         tsameDist[1] = PETSC_FALSE; /* !sameColDist */
3253       }
3254     }
3255   } else {
3256     /* Check if isrow has same processor distribution as mat */
3257     sameDist[0] = PETSC_FALSE;
3258     ierr = ISGetLocalSize(isrow,&n);CHKERRQ(ierr);
3259     if (!n) {
3260       sameDist[0] = PETSC_TRUE;
3261     } else {
3262       ierr = ISGetMinMax(isrow,&i,&j);CHKERRQ(ierr);
3263       ierr = MatGetOwnershipRange(mat,&start,&end);CHKERRQ(ierr);
3264       if (i >= start && j < end) {
3265         sameDist[0] = PETSC_TRUE;
3266       }
3267     }
3268 
3269     /* Check if iscol has same processor distribution as mat */
3270     sameDist[1] = PETSC_FALSE;
3271     ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr);
3272     if (!n) {
3273       sameDist[1] = PETSC_TRUE;
3274     } else {
3275       ierr = ISGetMinMax(iscol,&i,&j);CHKERRQ(ierr);
3276       ierr = MatGetOwnershipRangeColumn(mat,&start,&end);CHKERRQ(ierr);
3277       if (i >= start && j < end) sameDist[1] = PETSC_TRUE;
3278     }
3279 
3280     ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3281     ierr = MPIU_Allreduce(&sameDist,&tsameDist,2,MPIU_BOOL,MPI_LAND,comm);CHKERRQ(ierr);
3282     sameRowDist = tsameDist[0];
3283   }
3284 
3285   if (sameRowDist) {
3286     if (tsameDist[1]) { /* sameRowDist & sameColDist */
3287       /* isrow and iscol have same processor distribution as mat */
3288       ierr = MatCreateSubMatrix_MPIAIJ_SameRowColDist(mat,isrow,iscol,call,newmat);CHKERRQ(ierr);
3289       PetscFunctionReturn(0);
3290     } else { /* sameRowDist */
3291       /* isrow has same processor distribution as mat */
3292       if (call == MAT_INITIAL_MATRIX) {
3293         PetscBool sorted;
3294         ierr = ISGetSeqIS_Private(mat,iscol,&iscol_local);CHKERRQ(ierr);
3295         ierr = ISGetLocalSize(iscol_local,&n);CHKERRQ(ierr); /* local size of iscol_local = global columns of newmat */
3296         ierr = ISGetSize(iscol,&i);CHKERRQ(ierr);
3297         if (n != i) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"n %d != size of iscol %d",n,i);
3298 
3299         ierr = ISSorted(iscol_local,&sorted);CHKERRQ(ierr);
3300         if (sorted) {
3301           /* MatCreateSubMatrix_MPIAIJ_SameRowDist() requires iscol_local be sorted; it can have duplicate indices */
3302           ierr = MatCreateSubMatrix_MPIAIJ_SameRowDist(mat,isrow,iscol,iscol_local,MAT_INITIAL_MATRIX,newmat);CHKERRQ(ierr);
3303           PetscFunctionReturn(0);
3304         }
3305       } else { /* call == MAT_REUSE_MATRIX */
3306         IS    iscol_sub;
3307         ierr = PetscObjectQuery((PetscObject)*newmat,"SubIScol",(PetscObject*)&iscol_sub);CHKERRQ(ierr);
3308         if (iscol_sub) {
3309           ierr = MatCreateSubMatrix_MPIAIJ_SameRowDist(mat,isrow,iscol,NULL,call,newmat);CHKERRQ(ierr);
3310           PetscFunctionReturn(0);
3311         }
3312       }
3313     }
3314   }
3315 
3316   /* General case: iscol -> iscol_local which has global size of iscol */
3317   if (call == MAT_REUSE_MATRIX) {
3318     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3319     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3320   } else {
3321     if (!iscol_local) {
3322       ierr = ISGetSeqIS_Private(mat,iscol,&iscol_local);CHKERRQ(ierr);
3323     }
3324   }
3325 
3326   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3327   ierr = MatCreateSubMatrix_MPIAIJ_nonscalable(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
3328 
3329   if (call == MAT_INITIAL_MATRIX) {
3330     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3331     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3332   }
3333   PetscFunctionReturn(0);
3334 }
3335 
3336 /*@C
3337      MatCreateMPIAIJWithSeqAIJ - creates a MPIAIJ matrix using SeqAIJ matrices that contain the "diagonal"
3338          and "off-diagonal" part of the matrix in CSR format.
3339 
3340    Collective
3341 
3342    Input Parameters:
3343 +  comm - MPI communicator
3344 .  A - "diagonal" portion of matrix
3345 .  B - "off-diagonal" portion of matrix, may have empty columns, will be destroyed by this routine
3346 -  garray - global index of B columns
3347 
3348    Output Parameter:
3349 .   mat - the matrix, with input A as its local diagonal matrix
3350    Level: advanced
3351 
3352    Notes:
3353        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix.
3354        A becomes part of output mat, B is destroyed by this routine. The user cannot use A and B anymore.
3355 
3356 .seealso: MatCreateMPIAIJWithSplitArrays()
3357 @*/
3358 PetscErrorCode MatCreateMPIAIJWithSeqAIJ(MPI_Comm comm,Mat A,Mat B,const PetscInt garray[],Mat *mat)
3359 {
3360   PetscErrorCode ierr;
3361   Mat_MPIAIJ     *maij;
3362   Mat_SeqAIJ     *b=(Mat_SeqAIJ*)B->data,*bnew;
3363   PetscInt       *oi=b->i,*oj=b->j,i,nz,col;
3364   PetscScalar    *oa=b->a;
3365   Mat            Bnew;
3366   PetscInt       m,n,N;
3367 
3368   PetscFunctionBegin;
3369   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
3370   ierr = MatGetSize(A,&m,&n);CHKERRQ(ierr);
3371   if (m != B->rmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Am %D != Bm %D",m,B->rmap->N);
3372   if (A->rmap->bs != B->rmap->bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"A row bs %D != B row bs %D",A->rmap->bs,B->rmap->bs);
3373   /* remove check below; When B is created using iscol_o from ISGetSeqIS_SameColDist_Private(), its bs may not be same as A */
3374   /* if (A->cmap->bs != B->cmap->bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"A column bs %D != B column bs %D",A->cmap->bs,B->cmap->bs); */
3375 
3376   /* Get global columns of mat */
3377   ierr = MPIU_Allreduce(&n,&N,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3378 
3379   ierr = MatSetSizes(*mat,m,n,PETSC_DECIDE,N);CHKERRQ(ierr);
3380   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
3381   ierr = MatSetBlockSizes(*mat,A->rmap->bs,A->cmap->bs);CHKERRQ(ierr);
3382   maij = (Mat_MPIAIJ*)(*mat)->data;
3383 
3384   (*mat)->preallocated = PETSC_TRUE;
3385 
3386   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
3387   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
3388 
3389   /* Set A as diagonal portion of *mat */
3390   maij->A = A;
3391 
3392   nz = oi[m];
3393   for (i=0; i<nz; i++) {
3394     col   = oj[i];
3395     oj[i] = garray[col];
3396   }
3397 
3398    /* Set Bnew as off-diagonal portion of *mat */
3399   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,N,oi,oj,oa,&Bnew);CHKERRQ(ierr);
3400   bnew        = (Mat_SeqAIJ*)Bnew->data;
3401   bnew->maxnz = b->maxnz; /* allocated nonzeros of B */
3402   maij->B     = Bnew;
3403 
3404   if (B->rmap->N != Bnew->rmap->N) SETERRQ2(PETSC_COMM_SELF,0,"BN %d != BnewN %d",B->rmap->N,Bnew->rmap->N);
3405 
3406   b->singlemalloc = PETSC_FALSE; /* B arrays are shared by Bnew */
3407   b->free_a       = PETSC_FALSE;
3408   b->free_ij      = PETSC_FALSE;
3409   ierr = MatDestroy(&B);CHKERRQ(ierr);
3410 
3411   bnew->singlemalloc = PETSC_TRUE; /* arrays will be freed by MatDestroy(&Bnew) */
3412   bnew->free_a       = PETSC_TRUE;
3413   bnew->free_ij      = PETSC_TRUE;
3414 
3415   /* condense columns of maij->B */
3416   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
3417   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3418   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3419   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_FALSE);CHKERRQ(ierr);
3420   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3421   PetscFunctionReturn(0);
3422 }
3423 
3424 extern PetscErrorCode MatCreateSubMatrices_MPIAIJ_SingleIS_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool,Mat*);
3425 
3426 PetscErrorCode MatCreateSubMatrix_MPIAIJ_SameRowDist(Mat mat,IS isrow,IS iscol,IS iscol_local,MatReuse call,Mat *newmat)
3427 {
3428   PetscErrorCode ierr;
3429   PetscInt       i,m,n,rstart,row,rend,nz,j,bs,cbs;
3430   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
3431   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)mat->data;
3432   Mat            M,Msub,B=a->B;
3433   MatScalar      *aa;
3434   Mat_SeqAIJ     *aij;
3435   PetscInt       *garray = a->garray,*colsub,Ncols;
3436   PetscInt       count,Bn=B->cmap->N,cstart=mat->cmap->rstart,cend=mat->cmap->rend;
3437   IS             iscol_sub,iscmap;
3438   const PetscInt *is_idx,*cmap;
3439   PetscBool      allcolumns=PETSC_FALSE;
3440   MPI_Comm       comm;
3441 
3442   PetscFunctionBegin;
3443   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3444 
3445   if (call == MAT_REUSE_MATRIX) {
3446     ierr = PetscObjectQuery((PetscObject)*newmat,"SubIScol",(PetscObject*)&iscol_sub);CHKERRQ(ierr);
3447     if (!iscol_sub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"SubIScol passed in was not used before, cannot reuse");
3448     ierr = ISGetLocalSize(iscol_sub,&count);CHKERRQ(ierr);
3449 
3450     ierr = PetscObjectQuery((PetscObject)*newmat,"Subcmap",(PetscObject*)&iscmap);CHKERRQ(ierr);
3451     if (!iscmap) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Subcmap passed in was not used before, cannot reuse");
3452 
3453     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Msub);CHKERRQ(ierr);
3454     if (!Msub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3455 
3456     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol_sub,MAT_REUSE_MATRIX,PETSC_FALSE,&Msub);CHKERRQ(ierr);
3457 
3458   } else { /* call == MAT_INITIAL_MATRIX) */
3459     PetscBool flg;
3460 
3461     ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr);
3462     ierr = ISGetSize(iscol,&Ncols);CHKERRQ(ierr);
3463 
3464     /* (1) iscol -> nonscalable iscol_local */
3465     /* Check for special case: each processor gets entire matrix columns */
3466     ierr = ISIdentity(iscol_local,&flg);CHKERRQ(ierr);
3467     if (flg && n == mat->cmap->N) allcolumns = PETSC_TRUE;
3468     if (allcolumns) {
3469       iscol_sub = iscol_local;
3470       ierr = PetscObjectReference((PetscObject)iscol_local);CHKERRQ(ierr);
3471       ierr = ISCreateStride(PETSC_COMM_SELF,n,0,1,&iscmap);CHKERRQ(ierr);
3472 
3473     } else {
3474       /* (2) iscol_local -> iscol_sub and iscmap. Implementation below requires iscol_local be sorted, it can have duplicate indices */
3475       PetscInt *idx,*cmap1,k;
3476       ierr = PetscMalloc1(Ncols,&idx);CHKERRQ(ierr);
3477       ierr = PetscMalloc1(Ncols,&cmap1);CHKERRQ(ierr);
3478       ierr = ISGetIndices(iscol_local,&is_idx);CHKERRQ(ierr);
3479       count = 0;
3480       k     = 0;
3481       for (i=0; i<Ncols; i++) {
3482         j = is_idx[i];
3483         if (j >= cstart && j < cend) {
3484           /* diagonal part of mat */
3485           idx[count]     = j;
3486           cmap1[count++] = i; /* column index in submat */
3487         } else if (Bn) {
3488           /* off-diagonal part of mat */
3489           if (j == garray[k]) {
3490             idx[count]     = j;
3491             cmap1[count++] = i;  /* column index in submat */
3492           } else if (j > garray[k]) {
3493             while (j > garray[k] && k < Bn-1) k++;
3494             if (j == garray[k]) {
3495               idx[count]     = j;
3496               cmap1[count++] = i; /* column index in submat */
3497             }
3498           }
3499         }
3500       }
3501       ierr = ISRestoreIndices(iscol_local,&is_idx);CHKERRQ(ierr);
3502 
3503       ierr = ISCreateGeneral(PETSC_COMM_SELF,count,idx,PETSC_OWN_POINTER,&iscol_sub);CHKERRQ(ierr);
3504       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
3505       ierr = ISSetBlockSize(iscol_sub,cbs);CHKERRQ(ierr);
3506 
3507       ierr = ISCreateGeneral(PetscObjectComm((PetscObject)iscol_local),count,cmap1,PETSC_OWN_POINTER,&iscmap);CHKERRQ(ierr);
3508     }
3509 
3510     /* (3) Create sequential Msub */
3511     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol_sub,MAT_INITIAL_MATRIX,allcolumns,&Msub);CHKERRQ(ierr);
3512   }
3513 
3514   ierr = ISGetLocalSize(iscol_sub,&count);CHKERRQ(ierr);
3515   aij  = (Mat_SeqAIJ*)(Msub)->data;
3516   ii   = aij->i;
3517   ierr = ISGetIndices(iscmap,&cmap);CHKERRQ(ierr);
3518 
3519   /*
3520       m - number of local rows
3521       Ncols - number of columns (same on all processors)
3522       rstart - first row in new global matrix generated
3523   */
3524   ierr = MatGetSize(Msub,&m,NULL);CHKERRQ(ierr);
3525 
3526   if (call == MAT_INITIAL_MATRIX) {
3527     /* (4) Create parallel newmat */
3528     PetscMPIInt    rank,size;
3529     PetscInt       csize;
3530 
3531     ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3532     ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3533 
3534     /*
3535         Determine the number of non-zeros in the diagonal and off-diagonal
3536         portions of the matrix in order to do correct preallocation
3537     */
3538 
3539     /* first get start and end of "diagonal" columns */
3540     ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3541     if (csize == PETSC_DECIDE) {
3542       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3543       if (mglobal == Ncols) { /* square matrix */
3544         nlocal = m;
3545       } else {
3546         nlocal = Ncols/size + ((Ncols % size) > rank);
3547       }
3548     } else {
3549       nlocal = csize;
3550     }
3551     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3552     rstart = rend - nlocal;
3553     if (rank == size - 1 && rend != Ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local column sizes %D do not add up to total number of columns %D",rend,Ncols);
3554 
3555     /* next, compute all the lengths */
3556     jj    = aij->j;
3557     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3558     olens = dlens + m;
3559     for (i=0; i<m; i++) {
3560       jend = ii[i+1] - ii[i];
3561       olen = 0;
3562       dlen = 0;
3563       for (j=0; j<jend; j++) {
3564         if (cmap[*jj] < rstart || cmap[*jj] >= rend) olen++;
3565         else dlen++;
3566         jj++;
3567       }
3568       olens[i] = olen;
3569       dlens[i] = dlen;
3570     }
3571 
3572     ierr = ISGetBlockSize(isrow,&bs);CHKERRQ(ierr);
3573     ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
3574 
3575     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3576     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,Ncols);CHKERRQ(ierr);
3577     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3578     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3579     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3580     ierr = PetscFree(dlens);CHKERRQ(ierr);
3581 
3582   } else { /* call == MAT_REUSE_MATRIX */
3583     M    = *newmat;
3584     ierr = MatGetLocalSize(M,&i,NULL);CHKERRQ(ierr);
3585     if (i != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3586     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3587     /*
3588          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3589        rather than the slower MatSetValues().
3590     */
3591     M->was_assembled = PETSC_TRUE;
3592     M->assembled     = PETSC_FALSE;
3593   }
3594 
3595   /* (5) Set values of Msub to *newmat */
3596   ierr = PetscMalloc1(count,&colsub);CHKERRQ(ierr);
3597   ierr = MatGetOwnershipRange(M,&rstart,NULL);CHKERRQ(ierr);
3598 
3599   jj   = aij->j;
3600   aa   = aij->a;
3601   for (i=0; i<m; i++) {
3602     row = rstart + i;
3603     nz  = ii[i+1] - ii[i];
3604     for (j=0; j<nz; j++) colsub[j] = cmap[jj[j]];
3605     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,colsub,aa,INSERT_VALUES);CHKERRQ(ierr);
3606     jj += nz; aa += nz;
3607   }
3608   ierr = ISRestoreIndices(iscmap,&cmap);CHKERRQ(ierr);
3609 
3610   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3611   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3612 
3613   ierr = PetscFree(colsub);CHKERRQ(ierr);
3614 
3615   /* save Msub, iscol_sub and iscmap used in processor for next request */
3616   if (call ==  MAT_INITIAL_MATRIX) {
3617     *newmat = M;
3618     ierr = PetscObjectCompose((PetscObject)(*newmat),"SubMatrix",(PetscObject)Msub);CHKERRQ(ierr);
3619     ierr = MatDestroy(&Msub);CHKERRQ(ierr);
3620 
3621     ierr = PetscObjectCompose((PetscObject)(*newmat),"SubIScol",(PetscObject)iscol_sub);CHKERRQ(ierr);
3622     ierr = ISDestroy(&iscol_sub);CHKERRQ(ierr);
3623 
3624     ierr = PetscObjectCompose((PetscObject)(*newmat),"Subcmap",(PetscObject)iscmap);CHKERRQ(ierr);
3625     ierr = ISDestroy(&iscmap);CHKERRQ(ierr);
3626 
3627     if (iscol_local) {
3628       ierr = PetscObjectCompose((PetscObject)(*newmat),"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3629       ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3630     }
3631   }
3632   PetscFunctionReturn(0);
3633 }
3634 
3635 /*
3636     Not great since it makes two copies of the submatrix, first an SeqAIJ
3637   in local and then by concatenating the local matrices the end result.
3638   Writing it directly would be much like MatCreateSubMatrices_MPIAIJ()
3639 
3640   Note: This requires a sequential iscol with all indices.
3641 */
3642 PetscErrorCode MatCreateSubMatrix_MPIAIJ_nonscalable(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3643 {
3644   PetscErrorCode ierr;
3645   PetscMPIInt    rank,size;
3646   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3647   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
3648   Mat            M,Mreuse;
3649   MatScalar      *aa,*vwork;
3650   MPI_Comm       comm;
3651   Mat_SeqAIJ     *aij;
3652   PetscBool      colflag,allcolumns=PETSC_FALSE;
3653 
3654   PetscFunctionBegin;
3655   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3656   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3657   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3658 
3659   /* Check for special case: each processor gets entire matrix columns */
3660   ierr = ISIdentity(iscol,&colflag);CHKERRQ(ierr);
3661   ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr);
3662   if (colflag && n == mat->cmap->N) allcolumns = PETSC_TRUE;
3663 
3664   if (call ==  MAT_REUSE_MATRIX) {
3665     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3666     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3667     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,allcolumns,&Mreuse);CHKERRQ(ierr);
3668   } else {
3669     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,allcolumns,&Mreuse);CHKERRQ(ierr);
3670   }
3671 
3672   /*
3673       m - number of local rows
3674       n - number of columns (same on all processors)
3675       rstart - first row in new global matrix generated
3676   */
3677   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3678   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3679   if (call == MAT_INITIAL_MATRIX) {
3680     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3681     ii  = aij->i;
3682     jj  = aij->j;
3683 
3684     /*
3685         Determine the number of non-zeros in the diagonal and off-diagonal
3686         portions of the matrix in order to do correct preallocation
3687     */
3688 
3689     /* first get start and end of "diagonal" columns */
3690     if (csize == PETSC_DECIDE) {
3691       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3692       if (mglobal == n) { /* square matrix */
3693         nlocal = m;
3694       } else {
3695         nlocal = n/size + ((n % size) > rank);
3696       }
3697     } else {
3698       nlocal = csize;
3699     }
3700     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3701     rstart = rend - nlocal;
3702     if (rank == size - 1 && rend != n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local column sizes %D do not add up to total number of columns %D",rend,n);
3703 
3704     /* next, compute all the lengths */
3705     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3706     olens = dlens + m;
3707     for (i=0; i<m; i++) {
3708       jend = ii[i+1] - ii[i];
3709       olen = 0;
3710       dlen = 0;
3711       for (j=0; j<jend; j++) {
3712         if (*jj < rstart || *jj >= rend) olen++;
3713         else dlen++;
3714         jj++;
3715       }
3716       olens[i] = olen;
3717       dlens[i] = dlen;
3718     }
3719     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3720     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3721     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3722     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3723     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3724     ierr = PetscFree(dlens);CHKERRQ(ierr);
3725   } else {
3726     PetscInt ml,nl;
3727 
3728     M    = *newmat;
3729     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3730     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3731     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3732     /*
3733          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3734        rather than the slower MatSetValues().
3735     */
3736     M->was_assembled = PETSC_TRUE;
3737     M->assembled     = PETSC_FALSE;
3738   }
3739   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3740   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3741   ii   = aij->i;
3742   jj   = aij->j;
3743   aa   = aij->a;
3744   for (i=0; i<m; i++) {
3745     row   = rstart + i;
3746     nz    = ii[i+1] - ii[i];
3747     cwork = jj;     jj += nz;
3748     vwork = aa;     aa += nz;
3749     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3750   }
3751 
3752   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3753   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3754   *newmat = M;
3755 
3756   /* save submatrix used in processor for next request */
3757   if (call ==  MAT_INITIAL_MATRIX) {
3758     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3759     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3760   }
3761   PetscFunctionReturn(0);
3762 }
3763 
3764 PetscErrorCode MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3765 {
3766   PetscInt       m,cstart, cend,j,nnz,i,d;
3767   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3768   const PetscInt *JJ;
3769   PetscErrorCode ierr;
3770   PetscBool      nooffprocentries;
3771 
3772   PetscFunctionBegin;
3773   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3774 
3775   ierr   = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3776   ierr   = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3777   m      = B->rmap->n;
3778   cstart = B->cmap->rstart;
3779   cend   = B->cmap->rend;
3780   rstart = B->rmap->rstart;
3781 
3782   ierr = PetscCalloc2(m,&d_nnz,m,&o_nnz);CHKERRQ(ierr);
3783 
3784 #if defined(PETSC_USE_DEBUG)
3785   for (i=0; i<m; i++) {
3786     nnz = Ii[i+1]- Ii[i];
3787     JJ  = J + Ii[i];
3788     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3789     if (nnz && (JJ[0] < 0)) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,JJ[0]);
3790     if (nnz && (JJ[nnz-1] >= B->cmap->N)) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Row %D ends with too large a column index %D (max allowed %D)",i,JJ[nnz-1],B->cmap->N);
3791   }
3792 #endif
3793 
3794   for (i=0; i<m; i++) {
3795     nnz     = Ii[i+1]- Ii[i];
3796     JJ      = J + Ii[i];
3797     nnz_max = PetscMax(nnz_max,nnz);
3798     d       = 0;
3799     for (j=0; j<nnz; j++) {
3800       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3801     }
3802     d_nnz[i] = d;
3803     o_nnz[i] = nnz - d;
3804   }
3805   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3806   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3807 
3808   for (i=0; i<m; i++) {
3809     ii   = i + rstart;
3810     ierr = MatSetValues_MPIAIJ(B,1,&ii,Ii[i+1] - Ii[i],J+Ii[i], v ? v + Ii[i] : NULL,INSERT_VALUES);CHKERRQ(ierr);
3811   }
3812   nooffprocentries    = B->nooffprocentries;
3813   B->nooffprocentries = PETSC_TRUE;
3814   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3815   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3816   B->nooffprocentries = nooffprocentries;
3817 
3818   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3819   PetscFunctionReturn(0);
3820 }
3821 
3822 /*@
3823    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3824    (the default parallel PETSc format).
3825 
3826    Collective
3827 
3828    Input Parameters:
3829 +  B - the matrix
3830 .  i - the indices into j for the start of each local row (starts with zero)
3831 .  j - the column indices for each local row (starts with zero)
3832 -  v - optional values in the matrix
3833 
3834    Level: developer
3835 
3836    Notes:
3837        The i, j, and v arrays ARE copied by this routine into the internal format used by PETSc;
3838      thus you CANNOT change the matrix entries by changing the values of v[] after you have
3839      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3840 
3841        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3842 
3843        The format which is used for the sparse matrix input, is equivalent to a
3844     row-major ordering.. i.e for the following matrix, the input data expected is
3845     as shown
3846 
3847 $        1 0 0
3848 $        2 0 3     P0
3849 $       -------
3850 $        4 5 6     P1
3851 $
3852 $     Process0 [P0]: rows_owned=[0,1]
3853 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3854 $        j =  {0,0,2}  [size = 3]
3855 $        v =  {1,2,3}  [size = 3]
3856 $
3857 $     Process1 [P1]: rows_owned=[2]
3858 $        i =  {0,3}    [size = nrow+1  = 1+1]
3859 $        j =  {0,1,2}  [size = 3]
3860 $        v =  {4,5,6}  [size = 3]
3861 
3862 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MATMPIAIJ,
3863           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3864 @*/
3865 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3866 {
3867   PetscErrorCode ierr;
3868 
3869   PetscFunctionBegin;
3870   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3871   PetscFunctionReturn(0);
3872 }
3873 
3874 /*@C
3875    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3876    (the default parallel PETSc format).  For good matrix assembly performance
3877    the user should preallocate the matrix storage by setting the parameters
3878    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3879    performance can be increased by more than a factor of 50.
3880 
3881    Collective
3882 
3883    Input Parameters:
3884 +  B - the matrix
3885 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3886            (same value is used for all local rows)
3887 .  d_nnz - array containing the number of nonzeros in the various rows of the
3888            DIAGONAL portion of the local submatrix (possibly different for each row)
3889            or NULL (PETSC_NULL_INTEGER in Fortran), if d_nz is used to specify the nonzero structure.
3890            The size of this array is equal to the number of local rows, i.e 'm'.
3891            For matrices that will be factored, you must leave room for (and set)
3892            the diagonal entry even if it is zero.
3893 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3894            submatrix (same value is used for all local rows).
3895 -  o_nnz - array containing the number of nonzeros in the various rows of the
3896            OFF-DIAGONAL portion of the local submatrix (possibly different for
3897            each row) or NULL (PETSC_NULL_INTEGER in Fortran), if o_nz is used to specify the nonzero
3898            structure. The size of this array is equal to the number
3899            of local rows, i.e 'm'.
3900 
3901    If the *_nnz parameter is given then the *_nz parameter is ignored
3902 
3903    The AIJ format (also called the Yale sparse matrix format or
3904    compressed row storage (CSR)), is fully compatible with standard Fortran 77
3905    storage.  The stored row and column indices begin with zero.
3906    See Users-Manual: ch_mat for details.
3907 
3908    The parallel matrix is partitioned such that the first m0 rows belong to
3909    process 0, the next m1 rows belong to process 1, the next m2 rows belong
3910    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
3911 
3912    The DIAGONAL portion of the local submatrix of a processor can be defined
3913    as the submatrix which is obtained by extraction the part corresponding to
3914    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
3915    first row that belongs to the processor, r2 is the last row belonging to
3916    the this processor, and c1-c2 is range of indices of the local part of a
3917    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
3918    common case of a square matrix, the row and column ranges are the same and
3919    the DIAGONAL part is also square. The remaining portion of the local
3920    submatrix (mxN) constitute the OFF-DIAGONAL portion.
3921 
3922    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3923 
3924    You can call MatGetInfo() to get information on how effective the preallocation was;
3925    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3926    You can also run with the option -info and look for messages with the string
3927    malloc in them to see if additional memory allocation was needed.
3928 
3929    Example usage:
3930 
3931    Consider the following 8x8 matrix with 34 non-zero values, that is
3932    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3933    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3934    as follows:
3935 
3936 .vb
3937             1  2  0  |  0  3  0  |  0  4
3938     Proc0   0  5  6  |  7  0  0  |  8  0
3939             9  0 10  | 11  0  0  | 12  0
3940     -------------------------------------
3941            13  0 14  | 15 16 17  |  0  0
3942     Proc1   0 18  0  | 19 20 21  |  0  0
3943             0  0  0  | 22 23  0  | 24  0
3944     -------------------------------------
3945     Proc2  25 26 27  |  0  0 28  | 29  0
3946            30  0  0  | 31 32 33  |  0 34
3947 .ve
3948 
3949    This can be represented as a collection of submatrices as:
3950 
3951 .vb
3952       A B C
3953       D E F
3954       G H I
3955 .ve
3956 
3957    Where the submatrices A,B,C are owned by proc0, D,E,F are
3958    owned by proc1, G,H,I are owned by proc2.
3959 
3960    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3961    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3962    The 'M','N' parameters are 8,8, and have the same values on all procs.
3963 
3964    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3965    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3966    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3967    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3968    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3969    matrix, ans [DF] as another SeqAIJ matrix.
3970 
3971    When d_nz, o_nz parameters are specified, d_nz storage elements are
3972    allocated for every row of the local diagonal submatrix, and o_nz
3973    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3974    One way to choose d_nz and o_nz is to use the max nonzerors per local
3975    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3976    In this case, the values of d_nz,o_nz are:
3977 .vb
3978      proc0 : dnz = 2, o_nz = 2
3979      proc1 : dnz = 3, o_nz = 2
3980      proc2 : dnz = 1, o_nz = 4
3981 .ve
3982    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3983    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3984    for proc3. i.e we are using 12+15+10=37 storage locations to store
3985    34 values.
3986 
3987    When d_nnz, o_nnz parameters are specified, the storage is specified
3988    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3989    In the above case the values for d_nnz,o_nnz are:
3990 .vb
3991      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3992      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3993      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3994 .ve
3995    Here the space allocated is sum of all the above values i.e 34, and
3996    hence pre-allocation is perfect.
3997 
3998    Level: intermediate
3999 
4000 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
4001           MATMPIAIJ, MatGetInfo(), PetscSplitOwnership()
4002 @*/
4003 PetscErrorCode MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
4004 {
4005   PetscErrorCode ierr;
4006 
4007   PetscFunctionBegin;
4008   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
4009   PetscValidType(B,1);
4010   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
4011   PetscFunctionReturn(0);
4012 }
4013 
4014 /*@
4015      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
4016          CSR format for the local rows.
4017 
4018    Collective
4019 
4020    Input Parameters:
4021 +  comm - MPI communicator
4022 .  m - number of local rows (Cannot be PETSC_DECIDE)
4023 .  n - This value should be the same as the local size used in creating the
4024        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
4025        calculated if N is given) For square matrices n is almost always m.
4026 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
4027 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
4028 .   i - row indices; that is i[0] = 0, i[row] = i[row-1] + number of elements in that row of the matrix
4029 .   j - column indices
4030 -   a - matrix values
4031 
4032    Output Parameter:
4033 .   mat - the matrix
4034 
4035    Level: intermediate
4036 
4037    Notes:
4038        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
4039      thus you CANNOT change the matrix entries by changing the values of a[] after you have
4040      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
4041 
4042        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
4043 
4044        The format which is used for the sparse matrix input, is equivalent to a
4045     row-major ordering.. i.e for the following matrix, the input data expected is
4046     as shown
4047 
4048        Once you have created the matrix you can update it with new numerical values using MatUpdateMPIAIJWithArrays
4049 
4050 $        1 0 0
4051 $        2 0 3     P0
4052 $       -------
4053 $        4 5 6     P1
4054 $
4055 $     Process0 [P0]: rows_owned=[0,1]
4056 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
4057 $        j =  {0,0,2}  [size = 3]
4058 $        v =  {1,2,3}  [size = 3]
4059 $
4060 $     Process1 [P1]: rows_owned=[2]
4061 $        i =  {0,3}    [size = nrow+1  = 1+1]
4062 $        j =  {0,1,2}  [size = 3]
4063 $        v =  {4,5,6}  [size = 3]
4064 
4065 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
4066           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays(), MatUpdateMPIAIJWithArrays()
4067 @*/
4068 PetscErrorCode MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
4069 {
4070   PetscErrorCode ierr;
4071 
4072   PetscFunctionBegin;
4073   if (i && i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
4074   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
4075   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4076   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
4077   /* ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr); */
4078   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
4079   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
4080   PetscFunctionReturn(0);
4081 }
4082 
4083 /*@
4084      MatUpdateMPIAIJWithArrays - updates a MPI AIJ matrix using arrays that contain in standard
4085          CSR format for the local rows. Only the numerical values are updated the other arrays must be identical
4086 
4087    Collective
4088 
4089    Input Parameters:
4090 +  mat - the matrix
4091 .  m - number of local rows (Cannot be PETSC_DECIDE)
4092 .  n - This value should be the same as the local size used in creating the
4093        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
4094        calculated if N is given) For square matrices n is almost always m.
4095 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
4096 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
4097 .  Ii - row indices; that is Ii[0] = 0, Ii[row] = Ii[row-1] + number of elements in that row of the matrix
4098 .  J - column indices
4099 -  v - matrix values
4100 
4101    Level: intermediate
4102 
4103 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
4104           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays(), MatUpdateMPIAIJWithArrays()
4105 @*/
4106 PetscErrorCode MatUpdateMPIAIJWithArrays(Mat mat,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
4107 {
4108   PetscErrorCode ierr;
4109   PetscInt       cstart,nnz,i,j;
4110   PetscInt       *ld;
4111   PetscBool      nooffprocentries;
4112   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ*)mat->data;
4113   Mat_SeqAIJ     *Ad  = (Mat_SeqAIJ*)Aij->A->data, *Ao  = (Mat_SeqAIJ*)Aij->B->data;
4114   PetscScalar    *ad = Ad->a, *ao = Ao->a;
4115   const PetscInt *Adi = Ad->i;
4116   PetscInt       ldi,Iii,md;
4117 
4118   PetscFunctionBegin;
4119   if (Ii[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
4120   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
4121   if (m != mat->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Local number of rows cannot change from call to MatUpdateMPIAIJWithArrays()");
4122   if (n != mat->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Local number of columns cannot change from call to MatUpdateMPIAIJWithArrays()");
4123 
4124   cstart = mat->cmap->rstart;
4125   if (!Aij->ld) {
4126     /* count number of entries below block diagonal */
4127     ierr    = PetscCalloc1(m,&ld);CHKERRQ(ierr);
4128     Aij->ld = ld;
4129     for (i=0; i<m; i++) {
4130       nnz  = Ii[i+1]- Ii[i];
4131       j     = 0;
4132       while  (J[j] < cstart && j < nnz) {j++;}
4133       J    += nnz;
4134       ld[i] = j;
4135     }
4136   } else {
4137     ld = Aij->ld;
4138   }
4139 
4140   for (i=0; i<m; i++) {
4141     nnz  = Ii[i+1]- Ii[i];
4142     Iii  = Ii[i];
4143     ldi  = ld[i];
4144     md   = Adi[i+1]-Adi[i];
4145     ierr = PetscArraycpy(ao,v + Iii,ldi);CHKERRQ(ierr);
4146     ierr = PetscArraycpy(ad,v + Iii + ldi,md);CHKERRQ(ierr);
4147     ierr = PetscArraycpy(ao + ldi,v + Iii + ldi + md,nnz - ldi - md);CHKERRQ(ierr);
4148     ad  += md;
4149     ao  += nnz - md;
4150   }
4151   nooffprocentries      = mat->nooffprocentries;
4152   mat->nooffprocentries = PETSC_TRUE;
4153   ierr = PetscObjectStateIncrease((PetscObject)Aij->A);CHKERRQ(ierr);
4154   ierr = PetscObjectStateIncrease((PetscObject)Aij->B);CHKERRQ(ierr);
4155   ierr = PetscObjectStateIncrease((PetscObject)mat);CHKERRQ(ierr);
4156   ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4157   ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4158   mat->nooffprocentries = nooffprocentries;
4159   PetscFunctionReturn(0);
4160 }
4161 
4162 /*@C
4163    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
4164    (the default parallel PETSc format).  For good matrix assembly performance
4165    the user should preallocate the matrix storage by setting the parameters
4166    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
4167    performance can be increased by more than a factor of 50.
4168 
4169    Collective
4170 
4171    Input Parameters:
4172 +  comm - MPI communicator
4173 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
4174            This value should be the same as the local size used in creating the
4175            y vector for the matrix-vector product y = Ax.
4176 .  n - This value should be the same as the local size used in creating the
4177        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
4178        calculated if N is given) For square matrices n is almost always m.
4179 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
4180 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
4181 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
4182            (same value is used for all local rows)
4183 .  d_nnz - array containing the number of nonzeros in the various rows of the
4184            DIAGONAL portion of the local submatrix (possibly different for each row)
4185            or NULL, if d_nz is used to specify the nonzero structure.
4186            The size of this array is equal to the number of local rows, i.e 'm'.
4187 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
4188            submatrix (same value is used for all local rows).
4189 -  o_nnz - array containing the number of nonzeros in the various rows of the
4190            OFF-DIAGONAL portion of the local submatrix (possibly different for
4191            each row) or NULL, if o_nz is used to specify the nonzero
4192            structure. The size of this array is equal to the number
4193            of local rows, i.e 'm'.
4194 
4195    Output Parameter:
4196 .  A - the matrix
4197 
4198    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
4199    MatXXXXSetPreallocation() paradigm instead of this routine directly.
4200    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
4201 
4202    Notes:
4203    If the *_nnz parameter is given then the *_nz parameter is ignored
4204 
4205    m,n,M,N parameters specify the size of the matrix, and its partitioning across
4206    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
4207    storage requirements for this matrix.
4208 
4209    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
4210    processor than it must be used on all processors that share the object for
4211    that argument.
4212 
4213    The user MUST specify either the local or global matrix dimensions
4214    (possibly both).
4215 
4216    The parallel matrix is partitioned across processors such that the
4217    first m0 rows belong to process 0, the next m1 rows belong to
4218    process 1, the next m2 rows belong to process 2 etc.. where
4219    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
4220    values corresponding to [m x N] submatrix.
4221 
4222    The columns are logically partitioned with the n0 columns belonging
4223    to 0th partition, the next n1 columns belonging to the next
4224    partition etc.. where n0,n1,n2... are the input parameter 'n'.
4225 
4226    The DIAGONAL portion of the local submatrix on any given processor
4227    is the submatrix corresponding to the rows and columns m,n
4228    corresponding to the given processor. i.e diagonal matrix on
4229    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
4230    etc. The remaining portion of the local submatrix [m x (N-n)]
4231    constitute the OFF-DIAGONAL portion. The example below better
4232    illustrates this concept.
4233 
4234    For a square global matrix we define each processor's diagonal portion
4235    to be its local rows and the corresponding columns (a square submatrix);
4236    each processor's off-diagonal portion encompasses the remainder of the
4237    local matrix (a rectangular submatrix).
4238 
4239    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
4240 
4241    When calling this routine with a single process communicator, a matrix of
4242    type SEQAIJ is returned.  If a matrix of type MPIAIJ is desired for this
4243    type of communicator, use the construction mechanism
4244 .vb
4245      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
4246 .ve
4247 
4248 $     MatCreate(...,&A);
4249 $     MatSetType(A,MATMPIAIJ);
4250 $     MatSetSizes(A, m,n,M,N);
4251 $     MatMPIAIJSetPreallocation(A,...);
4252 
4253    By default, this format uses inodes (identical nodes) when possible.
4254    We search for consecutive rows with the same nonzero structure, thereby
4255    reusing matrix information to achieve increased efficiency.
4256 
4257    Options Database Keys:
4258 +  -mat_no_inode  - Do not use inodes
4259 -  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
4260 
4261 
4262 
4263    Example usage:
4264 
4265    Consider the following 8x8 matrix with 34 non-zero values, that is
4266    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
4267    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
4268    as follows
4269 
4270 .vb
4271             1  2  0  |  0  3  0  |  0  4
4272     Proc0   0  5  6  |  7  0  0  |  8  0
4273             9  0 10  | 11  0  0  | 12  0
4274     -------------------------------------
4275            13  0 14  | 15 16 17  |  0  0
4276     Proc1   0 18  0  | 19 20 21  |  0  0
4277             0  0  0  | 22 23  0  | 24  0
4278     -------------------------------------
4279     Proc2  25 26 27  |  0  0 28  | 29  0
4280            30  0  0  | 31 32 33  |  0 34
4281 .ve
4282 
4283    This can be represented as a collection of submatrices as
4284 
4285 .vb
4286       A B C
4287       D E F
4288       G H I
4289 .ve
4290 
4291    Where the submatrices A,B,C are owned by proc0, D,E,F are
4292    owned by proc1, G,H,I are owned by proc2.
4293 
4294    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4295    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4296    The 'M','N' parameters are 8,8, and have the same values on all procs.
4297 
4298    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
4299    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
4300    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
4301    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
4302    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
4303    matrix, ans [DF] as another SeqAIJ matrix.
4304 
4305    When d_nz, o_nz parameters are specified, d_nz storage elements are
4306    allocated for every row of the local diagonal submatrix, and o_nz
4307    storage locations are allocated for every row of the OFF-DIAGONAL submat.
4308    One way to choose d_nz and o_nz is to use the max nonzerors per local
4309    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
4310    In this case, the values of d_nz,o_nz are
4311 .vb
4312      proc0 : dnz = 2, o_nz = 2
4313      proc1 : dnz = 3, o_nz = 2
4314      proc2 : dnz = 1, o_nz = 4
4315 .ve
4316    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
4317    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
4318    for proc3. i.e we are using 12+15+10=37 storage locations to store
4319    34 values.
4320 
4321    When d_nnz, o_nnz parameters are specified, the storage is specified
4322    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
4323    In the above case the values for d_nnz,o_nnz are
4324 .vb
4325      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
4326      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
4327      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
4328 .ve
4329    Here the space allocated is sum of all the above values i.e 34, and
4330    hence pre-allocation is perfect.
4331 
4332    Level: intermediate
4333 
4334 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
4335           MATMPIAIJ, MatCreateMPIAIJWithArrays()
4336 @*/
4337 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)
4338 {
4339   PetscErrorCode ierr;
4340   PetscMPIInt    size;
4341 
4342   PetscFunctionBegin;
4343   ierr = MatCreate(comm,A);CHKERRQ(ierr);
4344   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
4345   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4346   if (size > 1) {
4347     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
4348     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
4349   } else {
4350     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
4351     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
4352   }
4353   PetscFunctionReturn(0);
4354 }
4355 
4356 /*@C
4357   MatMPIAIJGetSeqAIJ - Returns the local piece of this distributed matrix
4358 
4359   Not collective
4360 
4361   Input Parameter:
4362 . A - The MPIAIJ matrix
4363 
4364   Output Parameters:
4365 + Ad - The local diagonal block as a SeqAIJ matrix
4366 . Ao - The local off-diagonal block as a SeqAIJ matrix
4367 - colmap - An array mapping local column numbers of Ao to global column numbers of the parallel matrix
4368 
4369   Note: The rows in Ad and Ao are in [0, Nr), where Nr is the number of local rows on this process. The columns
4370   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
4371   the number of nonzero columns in the local off-diagonal piece of the matrix A. The array colmap maps these
4372   local column numbers to global column numbers in the original matrix.
4373 
4374   Level: intermediate
4375 
4376 .seealso: MatMPIAIJGetLocalMat(), MatMPIAIJGetLocalMatCondensed(), MatCreateAIJ(), MATMPIAJ, MATSEQAIJ
4377 @*/
4378 PetscErrorCode MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
4379 {
4380   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
4381   PetscBool      flg;
4382   PetscErrorCode ierr;
4383 
4384   PetscFunctionBegin;
4385   ierr = PetscStrbeginswith(((PetscObject)A)->type_name,MATMPIAIJ,&flg);CHKERRQ(ierr);
4386   if (!flg) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"This function requires a MATMPIAIJ matrix as input");
4387   if (Ad)     *Ad     = a->A;
4388   if (Ao)     *Ao     = a->B;
4389   if (colmap) *colmap = a->garray;
4390   PetscFunctionReturn(0);
4391 }
4392 
4393 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
4394 {
4395   PetscErrorCode ierr;
4396   PetscInt       m,N,i,rstart,nnz,Ii;
4397   PetscInt       *indx;
4398   PetscScalar    *values;
4399 
4400   PetscFunctionBegin;
4401   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
4402   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
4403     PetscInt       *dnz,*onz,sum,bs,cbs;
4404 
4405     if (n == PETSC_DECIDE) {
4406       ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
4407     }
4408     /* Check sum(n) = N */
4409     ierr = MPIU_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4410     if (sum != N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns %D != global columns %D",sum,N);
4411 
4412     ierr    = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4413     rstart -= m;
4414 
4415     ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4416     for (i=0; i<m; i++) {
4417       ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
4418       ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
4419       ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
4420     }
4421 
4422     ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
4423     ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4424     ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
4425     ierr = MatSetBlockSizes(*outmat,bs,cbs);CHKERRQ(ierr);
4426     ierr = MatSetType(*outmat,MATAIJ);CHKERRQ(ierr);
4427     ierr = MatSeqAIJSetPreallocation(*outmat,0,dnz);CHKERRQ(ierr);
4428     ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
4429     ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4430   }
4431 
4432   /* numeric phase */
4433   ierr = MatGetOwnershipRange(*outmat,&rstart,NULL);CHKERRQ(ierr);
4434   for (i=0; i<m; i++) {
4435     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4436     Ii   = i + rstart;
4437     ierr = MatSetValues(*outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4438     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4439   }
4440   ierr = MatAssemblyBegin(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4441   ierr = MatAssemblyEnd(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4442   PetscFunctionReturn(0);
4443 }
4444 
4445 PetscErrorCode MatFileSplit(Mat A,char *outfile)
4446 {
4447   PetscErrorCode    ierr;
4448   PetscMPIInt       rank;
4449   PetscInt          m,N,i,rstart,nnz;
4450   size_t            len;
4451   const PetscInt    *indx;
4452   PetscViewer       out;
4453   char              *name;
4454   Mat               B;
4455   const PetscScalar *values;
4456 
4457   PetscFunctionBegin;
4458   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
4459   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
4460   /* Should this be the type of the diagonal block of A? */
4461   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
4462   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
4463   ierr = MatSetBlockSizesFromMats(B,A,A);CHKERRQ(ierr);
4464   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
4465   ierr = MatSeqAIJSetPreallocation(B,0,NULL);CHKERRQ(ierr);
4466   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
4467   for (i=0; i<m; i++) {
4468     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4469     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4470     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4471   }
4472   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4473   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4474 
4475   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
4476   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
4477   ierr = PetscMalloc1(len+5,&name);CHKERRQ(ierr);
4478   sprintf(name,"%s.%d",outfile,rank);
4479   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
4480   ierr = PetscFree(name);CHKERRQ(ierr);
4481   ierr = MatView(B,out);CHKERRQ(ierr);
4482   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
4483   ierr = MatDestroy(&B);CHKERRQ(ierr);
4484   PetscFunctionReturn(0);
4485 }
4486 
4487 PetscErrorCode MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
4488 {
4489   PetscErrorCode      ierr;
4490   Mat_Merge_SeqsToMPI *merge;
4491   PetscContainer      container;
4492 
4493   PetscFunctionBegin;
4494   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4495   if (container) {
4496     ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4497     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
4498     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
4499     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
4500     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
4501     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
4502     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
4503     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
4504     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
4505     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
4506     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
4507     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
4508     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
4509     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
4510     ierr = PetscFree(merge);CHKERRQ(ierr);
4511     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
4512   }
4513   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
4514   PetscFunctionReturn(0);
4515 }
4516 
4517 #include <../src/mat/utils/freespace.h>
4518 #include <petscbt.h>
4519 
4520 PetscErrorCode MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
4521 {
4522   PetscErrorCode      ierr;
4523   MPI_Comm            comm;
4524   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
4525   PetscMPIInt         size,rank,taga,*len_s;
4526   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
4527   PetscInt            proc,m;
4528   PetscInt            **buf_ri,**buf_rj;
4529   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
4530   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
4531   MPI_Request         *s_waits,*r_waits;
4532   MPI_Status          *status;
4533   MatScalar           *aa=a->a;
4534   MatScalar           **abuf_r,*ba_i;
4535   Mat_Merge_SeqsToMPI *merge;
4536   PetscContainer      container;
4537 
4538   PetscFunctionBegin;
4539   ierr = PetscObjectGetComm((PetscObject)mpimat,&comm);CHKERRQ(ierr);
4540   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4541 
4542   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4543   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4544 
4545   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4546   ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4547 
4548   bi     = merge->bi;
4549   bj     = merge->bj;
4550   buf_ri = merge->buf_ri;
4551   buf_rj = merge->buf_rj;
4552 
4553   ierr   = PetscMalloc1(size,&status);CHKERRQ(ierr);
4554   owners = merge->rowmap->range;
4555   len_s  = merge->len_s;
4556 
4557   /* send and recv matrix values */
4558   /*-----------------------------*/
4559   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
4560   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
4561 
4562   ierr = PetscMalloc1(merge->nsend+1,&s_waits);CHKERRQ(ierr);
4563   for (proc=0,k=0; proc<size; proc++) {
4564     if (!len_s[proc]) continue;
4565     i    = owners[proc];
4566     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
4567     k++;
4568   }
4569 
4570   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
4571   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
4572   ierr = PetscFree(status);CHKERRQ(ierr);
4573 
4574   ierr = PetscFree(s_waits);CHKERRQ(ierr);
4575   ierr = PetscFree(r_waits);CHKERRQ(ierr);
4576 
4577   /* insert mat values of mpimat */
4578   /*----------------------------*/
4579   ierr = PetscMalloc1(N,&ba_i);CHKERRQ(ierr);
4580   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4581 
4582   for (k=0; k<merge->nrecv; k++) {
4583     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4584     nrows       = *(buf_ri_k[k]);
4585     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
4586     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4587   }
4588 
4589   /* set values of ba */
4590   m = merge->rowmap->n;
4591   for (i=0; i<m; i++) {
4592     arow = owners[rank] + i;
4593     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
4594     bnzi = bi[i+1] - bi[i];
4595     ierr = PetscArrayzero(ba_i,bnzi);CHKERRQ(ierr);
4596 
4597     /* add local non-zero vals of this proc's seqmat into ba */
4598     anzi   = ai[arow+1] - ai[arow];
4599     aj     = a->j + ai[arow];
4600     aa     = a->a + ai[arow];
4601     nextaj = 0;
4602     for (j=0; nextaj<anzi; j++) {
4603       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4604         ba_i[j] += aa[nextaj++];
4605       }
4606     }
4607 
4608     /* add received vals into ba */
4609     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4610       /* i-th row */
4611       if (i == *nextrow[k]) {
4612         anzi   = *(nextai[k]+1) - *nextai[k];
4613         aj     = buf_rj[k] + *(nextai[k]);
4614         aa     = abuf_r[k] + *(nextai[k]);
4615         nextaj = 0;
4616         for (j=0; nextaj<anzi; j++) {
4617           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4618             ba_i[j] += aa[nextaj++];
4619           }
4620         }
4621         nextrow[k]++; nextai[k]++;
4622       }
4623     }
4624     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
4625   }
4626   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4627   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4628 
4629   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
4630   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
4631   ierr = PetscFree(ba_i);CHKERRQ(ierr);
4632   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4633   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4634   PetscFunctionReturn(0);
4635 }
4636 
4637 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4638 {
4639   PetscErrorCode      ierr;
4640   Mat                 B_mpi;
4641   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
4642   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4643   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
4644   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4645   PetscInt            len,proc,*dnz,*onz,bs,cbs;
4646   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4647   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4648   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
4649   MPI_Status          *status;
4650   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
4651   PetscBT             lnkbt;
4652   Mat_Merge_SeqsToMPI *merge;
4653   PetscContainer      container;
4654 
4655   PetscFunctionBegin;
4656   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4657 
4658   /* make sure it is a PETSc comm */
4659   ierr = PetscCommDuplicate(comm,&comm,NULL);CHKERRQ(ierr);
4660   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4661   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4662 
4663   ierr = PetscNew(&merge);CHKERRQ(ierr);
4664   ierr = PetscMalloc1(size,&status);CHKERRQ(ierr);
4665 
4666   /* determine row ownership */
4667   /*---------------------------------------------------------*/
4668   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
4669   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
4670   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
4671   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
4672   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
4673   ierr = PetscMalloc1(size,&len_si);CHKERRQ(ierr);
4674   ierr = PetscMalloc1(size,&merge->len_s);CHKERRQ(ierr);
4675 
4676   m      = merge->rowmap->n;
4677   owners = merge->rowmap->range;
4678 
4679   /* determine the number of messages to send, their lengths */
4680   /*---------------------------------------------------------*/
4681   len_s = merge->len_s;
4682 
4683   len          = 0; /* length of buf_si[] */
4684   merge->nsend = 0;
4685   for (proc=0; proc<size; proc++) {
4686     len_si[proc] = 0;
4687     if (proc == rank) {
4688       len_s[proc] = 0;
4689     } else {
4690       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4691       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4692     }
4693     if (len_s[proc]) {
4694       merge->nsend++;
4695       nrows = 0;
4696       for (i=owners[proc]; i<owners[proc+1]; i++) {
4697         if (ai[i+1] > ai[i]) nrows++;
4698       }
4699       len_si[proc] = 2*(nrows+1);
4700       len         += len_si[proc];
4701     }
4702   }
4703 
4704   /* determine the number and length of messages to receive for ij-structure */
4705   /*-------------------------------------------------------------------------*/
4706   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
4707   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
4708 
4709   /* post the Irecv of j-structure */
4710   /*-------------------------------*/
4711   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
4712   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
4713 
4714   /* post the Isend of j-structure */
4715   /*--------------------------------*/
4716   ierr = PetscMalloc2(merge->nsend,&si_waits,merge->nsend,&sj_waits);CHKERRQ(ierr);
4717 
4718   for (proc=0, k=0; proc<size; proc++) {
4719     if (!len_s[proc]) continue;
4720     i    = owners[proc];
4721     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
4722     k++;
4723   }
4724 
4725   /* receives and sends of j-structure are complete */
4726   /*------------------------------------------------*/
4727   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
4728   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
4729 
4730   /* send and recv i-structure */
4731   /*---------------------------*/
4732   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
4733   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
4734 
4735   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
4736   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4737   for (proc=0,k=0; proc<size; proc++) {
4738     if (!len_s[proc]) continue;
4739     /* form outgoing message for i-structure:
4740          buf_si[0]:                 nrows to be sent
4741                [1:nrows]:           row index (global)
4742                [nrows+1:2*nrows+1]: i-structure index
4743     */
4744     /*-------------------------------------------*/
4745     nrows       = len_si[proc]/2 - 1;
4746     buf_si_i    = buf_si + nrows+1;
4747     buf_si[0]   = nrows;
4748     buf_si_i[0] = 0;
4749     nrows       = 0;
4750     for (i=owners[proc]; i<owners[proc+1]; i++) {
4751       anzi = ai[i+1] - ai[i];
4752       if (anzi) {
4753         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4754         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4755         nrows++;
4756       }
4757     }
4758     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4759     k++;
4760     buf_si += len_si[proc];
4761   }
4762 
4763   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4764   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4765 
4766   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4767   for (i=0; i<merge->nrecv; i++) {
4768     ierr = PetscInfo3(seqmat,"recv len_ri=%D, len_rj=%D from [%D]\n",len_ri[i],merge->len_r[i],merge->id_r[i]);CHKERRQ(ierr);
4769   }
4770 
4771   ierr = PetscFree(len_si);CHKERRQ(ierr);
4772   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4773   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4774   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4775   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4776   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4777   ierr = PetscFree(status);CHKERRQ(ierr);
4778 
4779   /* compute a local seq matrix in each processor */
4780   /*----------------------------------------------*/
4781   /* allocate bi array and free space for accumulating nonzero column info */
4782   ierr  = PetscMalloc1(m+1,&bi);CHKERRQ(ierr);
4783   bi[0] = 0;
4784 
4785   /* create and initialize a linked list */
4786   nlnk = N+1;
4787   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4788 
4789   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4790   len  = ai[owners[rank+1]] - ai[owners[rank]];
4791   ierr = PetscFreeSpaceGet(PetscIntMultTruncate(2,len)+1,&free_space);CHKERRQ(ierr);
4792 
4793   current_space = free_space;
4794 
4795   /* determine symbolic info for each local row */
4796   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4797 
4798   for (k=0; k<merge->nrecv; k++) {
4799     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4800     nrows       = *buf_ri_k[k];
4801     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4802     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4803   }
4804 
4805   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4806   len  = 0;
4807   for (i=0; i<m; i++) {
4808     bnzi = 0;
4809     /* add local non-zero cols of this proc's seqmat into lnk */
4810     arow  = owners[rank] + i;
4811     anzi  = ai[arow+1] - ai[arow];
4812     aj    = a->j + ai[arow];
4813     ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4814     bnzi += nlnk;
4815     /* add received col data into lnk */
4816     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4817       if (i == *nextrow[k]) { /* i-th row */
4818         anzi  = *(nextai[k]+1) - *nextai[k];
4819         aj    = buf_rj[k] + *nextai[k];
4820         ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4821         bnzi += nlnk;
4822         nextrow[k]++; nextai[k]++;
4823       }
4824     }
4825     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4826 
4827     /* if free space is not available, make more free space */
4828     if (current_space->local_remaining<bnzi) {
4829       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(bnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
4830       nspacedouble++;
4831     }
4832     /* copy data into free space, then initialize lnk */
4833     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4834     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
4835 
4836     current_space->array           += bnzi;
4837     current_space->local_used      += bnzi;
4838     current_space->local_remaining -= bnzi;
4839 
4840     bi[i+1] = bi[i] + bnzi;
4841   }
4842 
4843   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4844 
4845   ierr = PetscMalloc1(bi[m]+1,&bj);CHKERRQ(ierr);
4846   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
4847   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4848 
4849   /* create symbolic parallel matrix B_mpi */
4850   /*---------------------------------------*/
4851   ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
4852   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
4853   if (n==PETSC_DECIDE) {
4854     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
4855   } else {
4856     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4857   }
4858   ierr = MatSetBlockSizes(B_mpi,bs,cbs);CHKERRQ(ierr);
4859   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
4860   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
4861   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4862   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
4863 
4864   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4865   B_mpi->assembled    = PETSC_FALSE;
4866   B_mpi->ops->destroy = MatDestroy_MPIAIJ_SeqsToMPI;
4867   merge->bi           = bi;
4868   merge->bj           = bj;
4869   merge->buf_ri       = buf_ri;
4870   merge->buf_rj       = buf_rj;
4871   merge->coi          = NULL;
4872   merge->coj          = NULL;
4873   merge->owners_co    = NULL;
4874 
4875   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
4876 
4877   /* attach the supporting struct to B_mpi for reuse */
4878   ierr    = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
4879   ierr    = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
4880   ierr    = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
4881   ierr    = PetscContainerDestroy(&container);CHKERRQ(ierr);
4882   *mpimat = B_mpi;
4883 
4884   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4885   PetscFunctionReturn(0);
4886 }
4887 
4888 /*@C
4889       MatCreateMPIAIJSumSeqAIJ - Creates a MATMPIAIJ matrix by adding sequential
4890                  matrices from each processor
4891 
4892     Collective
4893 
4894    Input Parameters:
4895 +    comm - the communicators the parallel matrix will live on
4896 .    seqmat - the input sequential matrices
4897 .    m - number of local rows (or PETSC_DECIDE)
4898 .    n - number of local columns (or PETSC_DECIDE)
4899 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4900 
4901    Output Parameter:
4902 .    mpimat - the parallel matrix generated
4903 
4904     Level: advanced
4905 
4906    Notes:
4907      The dimensions of the sequential matrix in each processor MUST be the same.
4908      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
4909      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
4910 @*/
4911 PetscErrorCode MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
4912 {
4913   PetscErrorCode ierr;
4914   PetscMPIInt    size;
4915 
4916   PetscFunctionBegin;
4917   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4918   if (size == 1) {
4919     ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4920     if (scall == MAT_INITIAL_MATRIX) {
4921       ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
4922     } else {
4923       ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4924     }
4925     ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4926     PetscFunctionReturn(0);
4927   }
4928   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4929   if (scall == MAT_INITIAL_MATRIX) {
4930     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
4931   }
4932   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
4933   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4934   PetscFunctionReturn(0);
4935 }
4936 
4937 /*@
4938      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MATMPIAIJ matrix by taking all its local rows and putting them into a sequential matrix with
4939           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
4940           with MatGetSize()
4941 
4942     Not Collective
4943 
4944    Input Parameters:
4945 +    A - the matrix
4946 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4947 
4948    Output Parameter:
4949 .    A_loc - the local sequential matrix generated
4950 
4951     Level: developer
4952 
4953    Notes:
4954      When the communicator associated with A has size 1 and MAT_INITIAL_MATRIX is requested, the matrix returned is the diagonal part of A.
4955      If MAT_REUSE_MATRIX is requested with comm size 1, MatCopy(Adiag,*A_loc,SAME_NONZERO_PATTERN) is called.
4956      This means that one can preallocate the proper sequential matrix first and then call this routine with MAT_REUSE_MATRIX to safely
4957      modify the values of the returned A_loc.
4958 
4959 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMatCondensed()
4960 
4961 @*/
4962 PetscErrorCode MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
4963 {
4964   PetscErrorCode ierr;
4965   Mat_MPIAIJ     *mpimat=(Mat_MPIAIJ*)A->data;
4966   Mat_SeqAIJ     *mat,*a,*b;
4967   PetscInt       *ai,*aj,*bi,*bj,*cmap=mpimat->garray;
4968   MatScalar      *aa,*ba,*cam;
4969   PetscScalar    *ca;
4970   PetscMPIInt    size;
4971   PetscInt       am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
4972   PetscInt       *ci,*cj,col,ncols_d,ncols_o,jo;
4973   PetscBool      match;
4974 
4975   PetscFunctionBegin;
4976   ierr = PetscStrbeginswith(((PetscObject)A)->type_name,MATMPIAIJ,&match);CHKERRQ(ierr);
4977   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
4978   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)A),&size);CHKERRQ(ierr);
4979   if (size == 1) {
4980     if (scall == MAT_INITIAL_MATRIX) {
4981       ierr = PetscObjectReference((PetscObject)mpimat->A);CHKERRQ(ierr);
4982       *A_loc = mpimat->A;
4983     } else if (scall == MAT_REUSE_MATRIX) {
4984       ierr = MatCopy(mpimat->A,*A_loc,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4985     }
4986     PetscFunctionReturn(0);
4987   }
4988 
4989   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4990   a = (Mat_SeqAIJ*)(mpimat->A)->data;
4991   b = (Mat_SeqAIJ*)(mpimat->B)->data;
4992   ai = a->i; aj = a->j; bi = b->i; bj = b->j;
4993   aa = a->a; ba = b->a;
4994   if (scall == MAT_INITIAL_MATRIX) {
4995     ierr  = PetscMalloc1(1+am,&ci);CHKERRQ(ierr);
4996     ci[0] = 0;
4997     for (i=0; i<am; i++) {
4998       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
4999     }
5000     ierr = PetscMalloc1(1+ci[am],&cj);CHKERRQ(ierr);
5001     ierr = PetscMalloc1(1+ci[am],&ca);CHKERRQ(ierr);
5002     k    = 0;
5003     for (i=0; i<am; i++) {
5004       ncols_o = bi[i+1] - bi[i];
5005       ncols_d = ai[i+1] - ai[i];
5006       /* off-diagonal portion of A */
5007       for (jo=0; jo<ncols_o; jo++) {
5008         col = cmap[*bj];
5009         if (col >= cstart) break;
5010         cj[k]   = col; bj++;
5011         ca[k++] = *ba++;
5012       }
5013       /* diagonal portion of A */
5014       for (j=0; j<ncols_d; j++) {
5015         cj[k]   = cstart + *aj++;
5016         ca[k++] = *aa++;
5017       }
5018       /* off-diagonal portion of A */
5019       for (j=jo; j<ncols_o; j++) {
5020         cj[k]   = cmap[*bj++];
5021         ca[k++] = *ba++;
5022       }
5023     }
5024     /* put together the new matrix */
5025     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
5026     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
5027     /* Since these are PETSc arrays, change flags to free them as necessary. */
5028     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
5029     mat->free_a  = PETSC_TRUE;
5030     mat->free_ij = PETSC_TRUE;
5031     mat->nonew   = 0;
5032   } else if (scall == MAT_REUSE_MATRIX) {
5033     mat=(Mat_SeqAIJ*)(*A_loc)->data;
5034     ci = mat->i; cj = mat->j; cam = mat->a;
5035     for (i=0; i<am; i++) {
5036       /* off-diagonal portion of A */
5037       ncols_o = bi[i+1] - bi[i];
5038       for (jo=0; jo<ncols_o; jo++) {
5039         col = cmap[*bj];
5040         if (col >= cstart) break;
5041         *cam++ = *ba++; bj++;
5042       }
5043       /* diagonal portion of A */
5044       ncols_d = ai[i+1] - ai[i];
5045       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
5046       /* off-diagonal portion of A */
5047       for (j=jo; j<ncols_o; j++) {
5048         *cam++ = *ba++; bj++;
5049       }
5050     }
5051   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
5052   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
5053   PetscFunctionReturn(0);
5054 }
5055 
5056 /*@C
5057      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MATMPIAIJ matrix by taking all its local rows and NON-ZERO columns
5058 
5059     Not Collective
5060 
5061    Input Parameters:
5062 +    A - the matrix
5063 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5064 -    row, col - index sets of rows and columns to extract (or NULL)
5065 
5066    Output Parameter:
5067 .    A_loc - the local sequential matrix generated
5068 
5069     Level: developer
5070 
5071 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
5072 
5073 @*/
5074 PetscErrorCode MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
5075 {
5076   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
5077   PetscErrorCode ierr;
5078   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
5079   IS             isrowa,iscola;
5080   Mat            *aloc;
5081   PetscBool      match;
5082 
5083   PetscFunctionBegin;
5084   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
5085   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
5086   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
5087   if (!row) {
5088     start = A->rmap->rstart; end = A->rmap->rend;
5089     ierr  = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
5090   } else {
5091     isrowa = *row;
5092   }
5093   if (!col) {
5094     start = A->cmap->rstart;
5095     cmap  = a->garray;
5096     nzA   = a->A->cmap->n;
5097     nzB   = a->B->cmap->n;
5098     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
5099     ncols = 0;
5100     for (i=0; i<nzB; i++) {
5101       if (cmap[i] < start) idx[ncols++] = cmap[i];
5102       else break;
5103     }
5104     imark = i;
5105     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
5106     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
5107     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
5108   } else {
5109     iscola = *col;
5110   }
5111   if (scall != MAT_INITIAL_MATRIX) {
5112     ierr    = PetscMalloc1(1,&aloc);CHKERRQ(ierr);
5113     aloc[0] = *A_loc;
5114   }
5115   ierr = MatCreateSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
5116   if (!col) { /* attach global id of condensed columns */
5117     ierr = PetscObjectCompose((PetscObject)aloc[0],"_petsc_GetLocalMatCondensed_iscol",(PetscObject)iscola);CHKERRQ(ierr);
5118   }
5119   *A_loc = aloc[0];
5120   ierr   = PetscFree(aloc);CHKERRQ(ierr);
5121   if (!row) {
5122     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
5123   }
5124   if (!col) {
5125     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
5126   }
5127   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
5128   PetscFunctionReturn(0);
5129 }
5130 
5131 /*
5132  * Destroy a mat that may be composed with PetscSF communication objects.
5133  * The SF objects were created in MatCreateSeqSubMatrixWithRows_Private.
5134  * */
5135 PetscErrorCode MatDestroy_SeqAIJ_PetscSF(Mat mat)
5136 {
5137   PetscSF          sf,osf;
5138   IS               map;
5139   PetscErrorCode   ierr;
5140 
5141   PetscFunctionBegin;
5142   ierr = PetscObjectQuery((PetscObject)mat,"diagsf",(PetscObject*)&sf);CHKERRQ(ierr);
5143   ierr = PetscObjectQuery((PetscObject)mat,"offdiagsf",(PetscObject*)&osf);CHKERRQ(ierr);
5144   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
5145   ierr = PetscSFDestroy(&osf);CHKERRQ(ierr);
5146   ierr = PetscObjectQuery((PetscObject)mat,"aoffdiagtopothmapping",(PetscObject*)&map);CHKERRQ(ierr);
5147   ierr = ISDestroy(&map);CHKERRQ(ierr);
5148   ierr = MatDestroy_SeqAIJ(mat);CHKERRQ(ierr);
5149   PetscFunctionReturn(0);
5150 }
5151 
5152 /*
5153  * Create a sequential AIJ matrix based on row indices. a whole column is extracted once a row is matched.
5154  * Row could be local or remote.The routine is designed to be scalable in memory so that nothing is based
5155  * on a global size.
5156  * */
5157 PetscErrorCode MatCreateSeqSubMatrixWithRows_Private(Mat P,IS rows,Mat *P_oth)
5158 {
5159   Mat_MPIAIJ               *p=(Mat_MPIAIJ*)P->data;
5160   Mat_SeqAIJ               *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data,*p_oth;
5161   PetscInt                 plocalsize,nrows,*ilocal,*oilocal,i,lidx,*nrcols,*nlcols,ncol;
5162   PetscMPIInt              owner;
5163   PetscSFNode              *iremote,*oiremote;
5164   const PetscInt           *lrowindices;
5165   PetscErrorCode           ierr;
5166   PetscSF                  sf,osf;
5167   PetscInt                 pcstart,*roffsets,*loffsets,*pnnz,j;
5168   PetscInt                 ontotalcols,dntotalcols,ntotalcols,nout;
5169   MPI_Comm                 comm;
5170   ISLocalToGlobalMapping   mapping;
5171 
5172   PetscFunctionBegin;
5173   ierr = PetscObjectGetComm((PetscObject)P,&comm);CHKERRQ(ierr);
5174   /* plocalsize is the number of roots
5175    * nrows is the number of leaves
5176    * */
5177   ierr = MatGetLocalSize(P,&plocalsize,NULL);CHKERRQ(ierr);
5178   ierr = ISGetLocalSize(rows,&nrows);CHKERRQ(ierr);
5179   ierr = PetscCalloc1(nrows,&iremote);CHKERRQ(ierr);
5180   ierr = ISGetIndices(rows,&lrowindices);CHKERRQ(ierr);
5181   for (i=0;i<nrows;i++) {
5182     /* Find a remote index and an owner for a row
5183      * The row could be local or remote
5184      * */
5185     owner = 0;
5186     lidx  = 0;
5187     ierr = PetscLayoutFindOwnerIndex(P->rmap,lrowindices[i],&owner,&lidx);CHKERRQ(ierr);
5188     iremote[i].index = lidx;
5189     iremote[i].rank  = owner;
5190   }
5191   /* Create SF to communicate how many nonzero columns for each row */
5192   ierr = PetscSFCreate(comm,&sf);CHKERRQ(ierr);
5193   /* SF will figure out the number of nonzero colunms for each row, and their
5194    * offsets
5195    * */
5196   ierr = PetscSFSetGraph(sf,plocalsize,nrows,NULL,PETSC_OWN_POINTER,iremote,PETSC_OWN_POINTER);CHKERRQ(ierr);
5197   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
5198   ierr = PetscSFSetUp(sf);CHKERRQ(ierr);
5199 
5200   ierr = PetscCalloc1(2*(plocalsize+1),&roffsets);CHKERRQ(ierr);
5201   ierr = PetscCalloc1(2*plocalsize,&nrcols);CHKERRQ(ierr);
5202   ierr = PetscCalloc1(nrows,&pnnz);CHKERRQ(ierr);
5203   roffsets[0] = 0;
5204   roffsets[1] = 0;
5205   for (i=0;i<plocalsize;i++) {
5206     /* diag */
5207     nrcols[i*2+0] = pd->i[i+1] - pd->i[i];
5208     /* off diag */
5209     nrcols[i*2+1] = po->i[i+1] - po->i[i];
5210     /* compute offsets so that we relative location for each row */
5211     roffsets[(i+1)*2+0] = roffsets[i*2+0] + nrcols[i*2+0];
5212     roffsets[(i+1)*2+1] = roffsets[i*2+1] + nrcols[i*2+1];
5213   }
5214   ierr = PetscCalloc1(2*nrows,&nlcols);CHKERRQ(ierr);
5215   ierr = PetscCalloc1(2*nrows,&loffsets);CHKERRQ(ierr);
5216   /* 'r' means root, and 'l' means leaf */
5217   ierr = PetscSFBcastBegin(sf,MPIU_2INT,nrcols,nlcols);CHKERRQ(ierr);
5218   ierr = PetscSFBcastBegin(sf,MPIU_2INT,roffsets,loffsets);CHKERRQ(ierr);
5219   ierr = PetscSFBcastEnd(sf,MPIU_2INT,nrcols,nlcols);CHKERRQ(ierr);
5220   ierr = PetscSFBcastEnd(sf,MPIU_2INT,roffsets,loffsets);CHKERRQ(ierr);
5221   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
5222   ierr = PetscFree(roffsets);CHKERRQ(ierr);
5223   ierr = PetscFree(nrcols);CHKERRQ(ierr);
5224   dntotalcols = 0;
5225   ontotalcols = 0;
5226   ncol = 0;
5227   for (i=0;i<nrows;i++) {
5228     pnnz[i] = nlcols[i*2+0] + nlcols[i*2+1];
5229     ncol = PetscMax(pnnz[i],ncol);
5230     /* diag */
5231     dntotalcols += nlcols[i*2+0];
5232     /* off diag */
5233     ontotalcols += nlcols[i*2+1];
5234   }
5235   /* We do not need to figure the right number of columns
5236    * since all the calculations will be done by going through the raw data
5237    * */
5238   ierr = MatCreateSeqAIJ(PETSC_COMM_SELF,nrows,ncol,0,pnnz,P_oth);CHKERRQ(ierr);
5239   ierr = MatSetUp(*P_oth);CHKERRQ(ierr);
5240   ierr = PetscFree(pnnz);CHKERRQ(ierr);
5241   p_oth = (Mat_SeqAIJ*) (*P_oth)->data;
5242   /* diag */
5243   ierr = PetscCalloc1(dntotalcols,&iremote);CHKERRQ(ierr);
5244   /* off diag */
5245   ierr = PetscCalloc1(ontotalcols,&oiremote);CHKERRQ(ierr);
5246   /* diag */
5247   ierr = PetscCalloc1(dntotalcols,&ilocal);CHKERRQ(ierr);
5248   /* off diag */
5249   ierr = PetscCalloc1(ontotalcols,&oilocal);CHKERRQ(ierr);
5250   dntotalcols = 0;
5251   ontotalcols = 0;
5252   ntotalcols  = 0;
5253   for (i=0;i<nrows;i++) {
5254     owner = 0;
5255     ierr = PetscLayoutFindOwnerIndex(P->rmap,lrowindices[i],&owner,NULL);CHKERRQ(ierr);
5256     /* Set iremote for diag matrix */
5257     for (j=0;j<nlcols[i*2+0];j++) {
5258       iremote[dntotalcols].index   = loffsets[i*2+0] + j;
5259       iremote[dntotalcols].rank    = owner;
5260       /* P_oth is seqAIJ so that ilocal need to point to the first part of memory */
5261       ilocal[dntotalcols++]        = ntotalcols++;
5262     }
5263     /* off diag */
5264     for (j=0;j<nlcols[i*2+1];j++) {
5265       oiremote[ontotalcols].index   = loffsets[i*2+1] + j;
5266       oiremote[ontotalcols].rank    = owner;
5267       oilocal[ontotalcols++]        = ntotalcols++;
5268     }
5269   }
5270   ierr = ISRestoreIndices(rows,&lrowindices);CHKERRQ(ierr);
5271   ierr = PetscFree(loffsets);CHKERRQ(ierr);
5272   ierr = PetscFree(nlcols);CHKERRQ(ierr);
5273   ierr = PetscSFCreate(comm,&sf);CHKERRQ(ierr);
5274   /* P serves as roots and P_oth is leaves
5275    * Diag matrix
5276    * */
5277   ierr = PetscSFSetGraph(sf,pd->i[plocalsize],dntotalcols,ilocal,PETSC_OWN_POINTER,iremote,PETSC_OWN_POINTER);CHKERRQ(ierr);
5278   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
5279   ierr = PetscSFSetUp(sf);CHKERRQ(ierr);
5280 
5281   ierr = PetscSFCreate(comm,&osf);CHKERRQ(ierr);
5282   /* Off diag */
5283   ierr = PetscSFSetGraph(osf,po->i[plocalsize],ontotalcols,oilocal,PETSC_OWN_POINTER,oiremote,PETSC_OWN_POINTER);CHKERRQ(ierr);
5284   ierr = PetscSFSetFromOptions(osf);CHKERRQ(ierr);
5285   ierr = PetscSFSetUp(osf);CHKERRQ(ierr);
5286   /* We operate on the matrix internal data for saving memory */
5287   ierr = PetscSFBcastBegin(sf,MPIU_SCALAR,pd->a,p_oth->a);CHKERRQ(ierr);
5288   ierr = PetscSFBcastBegin(osf,MPIU_SCALAR,po->a,p_oth->a);CHKERRQ(ierr);
5289   ierr = MatGetOwnershipRangeColumn(P,&pcstart,NULL);CHKERRQ(ierr);
5290   /* Convert to global indices for diag matrix */
5291   for (i=0;i<pd->i[plocalsize];i++) pd->j[i] += pcstart;
5292   ierr = PetscSFBcastBegin(sf,MPIU_INT,pd->j,p_oth->j);CHKERRQ(ierr);
5293   /* We want P_oth store global indices */
5294   ierr = ISLocalToGlobalMappingCreate(comm,1,p->B->cmap->n,p->garray,PETSC_COPY_VALUES,&mapping);CHKERRQ(ierr);
5295   /* Use memory scalable approach */
5296   ierr = ISLocalToGlobalMappingSetType(mapping,ISLOCALTOGLOBALMAPPINGHASH);CHKERRQ(ierr);
5297   ierr = ISLocalToGlobalMappingApply(mapping,po->i[plocalsize],po->j,po->j);CHKERRQ(ierr);
5298   ierr = PetscSFBcastBegin(osf,MPIU_INT,po->j,p_oth->j);CHKERRQ(ierr);
5299   ierr = PetscSFBcastEnd(sf,MPIU_INT,pd->j,p_oth->j);CHKERRQ(ierr);
5300   /* Convert back to local indices */
5301   for (i=0;i<pd->i[plocalsize];i++) pd->j[i] -= pcstart;
5302   ierr = PetscSFBcastEnd(osf,MPIU_INT,po->j,p_oth->j);CHKERRQ(ierr);
5303   nout = 0;
5304   ierr = ISGlobalToLocalMappingApply(mapping,IS_GTOLM_DROP,po->i[plocalsize],po->j,&nout,po->j);CHKERRQ(ierr);
5305   if (nout != po->i[plocalsize]) SETERRQ2(comm,PETSC_ERR_ARG_INCOMP,"n %D does not equal to nout %D \n",po->i[plocalsize],nout);
5306   ierr = ISLocalToGlobalMappingDestroy(&mapping);CHKERRQ(ierr);
5307   /* Exchange values */
5308   ierr = PetscSFBcastEnd(sf,MPIU_SCALAR,pd->a,p_oth->a);CHKERRQ(ierr);
5309   ierr = PetscSFBcastEnd(osf,MPIU_SCALAR,po->a,p_oth->a);CHKERRQ(ierr);
5310   /* Stop PETSc from shrinking memory */
5311   for (i=0;i<nrows;i++) p_oth->ilen[i] = p_oth->imax[i];
5312   ierr = MatAssemblyBegin(*P_oth,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5313   ierr = MatAssemblyEnd(*P_oth,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5314   /* Attach PetscSF objects to P_oth so that we can reuse it later */
5315   ierr = PetscObjectCompose((PetscObject)*P_oth,"diagsf",(PetscObject)sf);CHKERRQ(ierr);
5316   ierr = PetscObjectCompose((PetscObject)*P_oth,"offdiagsf",(PetscObject)osf);CHKERRQ(ierr);
5317   /* ``New MatDestroy" takes care of PetscSF objects as well */
5318   (*P_oth)->ops->destroy = MatDestroy_SeqAIJ_PetscSF;
5319   PetscFunctionReturn(0);
5320 }
5321 
5322 /*
5323  * Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
5324  * This supports MPIAIJ and MAIJ
5325  * */
5326 PetscErrorCode MatGetBrowsOfAcols_MPIXAIJ(Mat A,Mat P,PetscInt dof,MatReuse reuse,Mat *P_oth)
5327 {
5328   Mat_MPIAIJ            *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data;
5329   Mat_SeqAIJ            *p_oth;
5330   Mat_SeqAIJ            *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
5331   IS                    rows,map;
5332   PetscHMapI            hamp;
5333   PetscInt              i,htsize,*rowindices,off,*mapping,key,count;
5334   MPI_Comm              comm;
5335   PetscSF               sf,osf;
5336   PetscBool             has;
5337   PetscErrorCode        ierr;
5338 
5339   PetscFunctionBegin;
5340   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
5341   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,P,0,0);CHKERRQ(ierr);
5342   /* If it is the first time, create an index set of off-diag nonzero columns of A,
5343    *  and then create a submatrix (that often is an overlapping matrix)
5344    * */
5345   if (reuse==MAT_INITIAL_MATRIX) {
5346     /* Use a hash table to figure out unique keys */
5347     ierr = PetscHMapICreate(&hamp);CHKERRQ(ierr);
5348     ierr = PetscHMapIResize(hamp,a->B->cmap->n);CHKERRQ(ierr);
5349     ierr = PetscCalloc1(a->B->cmap->n,&mapping);CHKERRQ(ierr);
5350     count = 0;
5351     /* Assume that  a->g is sorted, otherwise the following does not make sense */
5352     for (i=0;i<a->B->cmap->n;i++) {
5353       key  = a->garray[i]/dof;
5354       ierr = PetscHMapIHas(hamp,key,&has);CHKERRQ(ierr);
5355       if (!has) {
5356         mapping[i] = count;
5357         ierr = PetscHMapISet(hamp,key,count++);CHKERRQ(ierr);
5358       } else {
5359         /* Current 'i' has the same value the previous step */
5360         mapping[i] = count-1;
5361       }
5362     }
5363     ierr = ISCreateGeneral(comm,a->B->cmap->n,mapping,PETSC_OWN_POINTER,&map);CHKERRQ(ierr);
5364     ierr = PetscHMapIGetSize(hamp,&htsize);CHKERRQ(ierr);
5365     if (htsize!=count) SETERRQ2(comm,PETSC_ERR_ARG_INCOMP," Size of hash map %D is inconsistent with count %D \n",htsize,count);CHKERRQ(ierr);
5366     ierr = PetscCalloc1(htsize,&rowindices);CHKERRQ(ierr);
5367     off = 0;
5368     ierr = PetscHMapIGetKeys(hamp,&off,rowindices);CHKERRQ(ierr);
5369     ierr = PetscHMapIDestroy(&hamp);CHKERRQ(ierr);
5370     ierr = PetscSortInt(htsize,rowindices);CHKERRQ(ierr);
5371     ierr = ISCreateGeneral(comm,htsize,rowindices,PETSC_OWN_POINTER,&rows);CHKERRQ(ierr);
5372     /* In case, the matrix was already created but users want to recreate the matrix */
5373     ierr = MatDestroy(P_oth);CHKERRQ(ierr);
5374     ierr = MatCreateSeqSubMatrixWithRows_Private(P,rows,P_oth);CHKERRQ(ierr);
5375     ierr = PetscObjectCompose((PetscObject)*P_oth,"aoffdiagtopothmapping",(PetscObject)map);CHKERRQ(ierr);
5376     ierr = ISDestroy(&rows);CHKERRQ(ierr);
5377   } else if (reuse==MAT_REUSE_MATRIX) {
5378     /* If matrix was already created, we simply update values using SF objects
5379      * that as attached to the matrix ealier.
5380      *  */
5381     ierr = PetscObjectQuery((PetscObject)*P_oth,"diagsf",(PetscObject*)&sf);CHKERRQ(ierr);
5382     ierr = PetscObjectQuery((PetscObject)*P_oth,"offdiagsf",(PetscObject*)&osf);CHKERRQ(ierr);
5383     if (!sf || !osf) {
5384       SETERRQ(comm,PETSC_ERR_ARG_NULL,"Matrix is not initialized yet \n");
5385     }
5386     p_oth = (Mat_SeqAIJ*) (*P_oth)->data;
5387     /* Update values in place */
5388     ierr = PetscSFBcastBegin(sf,MPIU_SCALAR,pd->a,p_oth->a);CHKERRQ(ierr);
5389     ierr = PetscSFBcastBegin(osf,MPIU_SCALAR,po->a,p_oth->a);CHKERRQ(ierr);
5390     ierr = PetscSFBcastEnd(sf,MPIU_SCALAR,pd->a,p_oth->a);CHKERRQ(ierr);
5391     ierr = PetscSFBcastEnd(osf,MPIU_SCALAR,po->a,p_oth->a);CHKERRQ(ierr);
5392   } else {
5393     SETERRQ(comm,PETSC_ERR_ARG_UNKNOWN_TYPE,"Unknown reuse type \n");
5394   }
5395   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,P,0,0);CHKERRQ(ierr);
5396   PetscFunctionReturn(0);
5397 }
5398 
5399 /*@C
5400     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
5401 
5402     Collective on Mat
5403 
5404    Input Parameters:
5405 +    A,B - the matrices in mpiaij format
5406 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5407 -    rowb, colb - index sets of rows and columns of B to extract (or NULL)
5408 
5409    Output Parameter:
5410 +    rowb, colb - index sets of rows and columns of B to extract
5411 -    B_seq - the sequential matrix generated
5412 
5413     Level: developer
5414 
5415 @*/
5416 PetscErrorCode MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
5417 {
5418   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
5419   PetscErrorCode ierr;
5420   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
5421   IS             isrowb,iscolb;
5422   Mat            *bseq=NULL;
5423 
5424   PetscFunctionBegin;
5425   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
5426     SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%D, %D) != (%D,%D)",A->cmap->rstart,A->cmap->rend,B->rmap->rstart,B->rmap->rend);
5427   }
5428   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
5429 
5430   if (scall == MAT_INITIAL_MATRIX) {
5431     start = A->cmap->rstart;
5432     cmap  = a->garray;
5433     nzA   = a->A->cmap->n;
5434     nzB   = a->B->cmap->n;
5435     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
5436     ncols = 0;
5437     for (i=0; i<nzB; i++) {  /* row < local row index */
5438       if (cmap[i] < start) idx[ncols++] = cmap[i];
5439       else break;
5440     }
5441     imark = i;
5442     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
5443     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
5444     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
5445     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
5446   } else {
5447     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
5448     isrowb  = *rowb; iscolb = *colb;
5449     ierr    = PetscMalloc1(1,&bseq);CHKERRQ(ierr);
5450     bseq[0] = *B_seq;
5451   }
5452   ierr   = MatCreateSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
5453   *B_seq = bseq[0];
5454   ierr   = PetscFree(bseq);CHKERRQ(ierr);
5455   if (!rowb) {
5456     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
5457   } else {
5458     *rowb = isrowb;
5459   }
5460   if (!colb) {
5461     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
5462   } else {
5463     *colb = iscolb;
5464   }
5465   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
5466   PetscFunctionReturn(0);
5467 }
5468 
5469 /*
5470     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
5471     of the OFF-DIAGONAL portion of local A
5472 
5473     Collective on Mat
5474 
5475    Input Parameters:
5476 +    A,B - the matrices in mpiaij format
5477 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5478 
5479    Output Parameter:
5480 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
5481 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
5482 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
5483 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
5484 
5485     Developer Notes: This directly accesses information inside the VecScatter associated with the matrix-vector product
5486      for this matrix. This is not desirable..
5487 
5488     Level: developer
5489 
5490 */
5491 PetscErrorCode MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
5492 {
5493   PetscErrorCode         ierr;
5494   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
5495   Mat_SeqAIJ             *b_oth;
5496   VecScatter             ctx;
5497   MPI_Comm               comm;
5498   const PetscMPIInt      *rprocs,*sprocs;
5499   const PetscInt         *srow,*rstarts,*sstarts;
5500   PetscInt               *rowlen,*bufj,*bufJ,ncols = 0,aBn=a->B->cmap->n,row,*b_othi,*b_othj,*rvalues=NULL,*svalues=NULL,*cols,sbs,rbs;
5501   PetscInt               i,j,k=0,l,ll,nrecvs,nsends,nrows,*rstartsj = 0,*sstartsj,len;
5502   PetscScalar            *b_otha,*bufa,*bufA,*vals = NULL;
5503   MPI_Request            *rwaits = NULL,*swaits = NULL;
5504   MPI_Status             rstatus;
5505   PetscMPIInt            jj,size,tag,rank,nsends_mpi,nrecvs_mpi;
5506 
5507   PetscFunctionBegin;
5508   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
5509   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
5510 
5511   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
5512     SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%d, %d) != (%d,%d)",A->cmap->rstart,A->cmap->rend,B->rmap->rstart,B->rmap->rend);
5513   }
5514   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5515   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
5516 
5517   if (size == 1) {
5518     startsj_s = NULL;
5519     bufa_ptr  = NULL;
5520     *B_oth    = NULL;
5521     PetscFunctionReturn(0);
5522   }
5523 
5524   ctx = a->Mvctx;
5525   tag = ((PetscObject)ctx)->tag;
5526 
5527   if (ctx->inuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE," Scatter ctx already in use");
5528   ierr = VecScatterGetRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&srow,&sprocs,&sbs);CHKERRQ(ierr);
5529   /* rprocs[] must be ordered so that indices received from them are ordered in rvalues[], which is key to algorithms used in this subroutine */
5530   ierr = VecScatterGetRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL/*indices not needed*/,&rprocs,&rbs);CHKERRQ(ierr);
5531   ierr = PetscMPIIntCast(nsends,&nsends_mpi);CHKERRQ(ierr);
5532   ierr = PetscMPIIntCast(nrecvs,&nrecvs_mpi);CHKERRQ(ierr);
5533   ierr = PetscMalloc2(nrecvs,&rwaits,nsends,&swaits);CHKERRQ(ierr);
5534 
5535   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
5536   if (scall == MAT_INITIAL_MATRIX) {
5537     /* i-array */
5538     /*---------*/
5539     /*  post receives */
5540     if (nrecvs) {ierr = PetscMalloc1(rbs*(rstarts[nrecvs] - rstarts[0]),&rvalues);CHKERRQ(ierr);} /* rstarts can be NULL when nrecvs=0 */
5541     for (i=0; i<nrecvs; i++) {
5542       rowlen = rvalues + rstarts[i]*rbs;
5543       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
5544       ierr   = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5545     }
5546 
5547     /* pack the outgoing message */
5548     ierr = PetscMalloc2(nsends+1,&sstartsj,nrecvs+1,&rstartsj);CHKERRQ(ierr);
5549 
5550     sstartsj[0] = 0;
5551     rstartsj[0] = 0;
5552     len         = 0; /* total length of j or a array to be sent */
5553     if (nsends) {
5554       k    = sstarts[0]; /* ATTENTION: sstarts[0] and rstarts[0] are not necessarily zero */
5555       ierr = PetscMalloc1(sbs*(sstarts[nsends]-sstarts[0]),&svalues);CHKERRQ(ierr);
5556     }
5557     for (i=0; i<nsends; i++) {
5558       rowlen = svalues + (sstarts[i]-sstarts[0])*sbs;
5559       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
5560       for (j=0; j<nrows; j++) {
5561         row = srow[k] + B->rmap->range[rank]; /* global row idx */
5562         for (l=0; l<sbs; l++) {
5563           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr); /* rowlength */
5564 
5565           rowlen[j*sbs+l] = ncols;
5566 
5567           len += ncols;
5568           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr);
5569         }
5570         k++;
5571       }
5572       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5573 
5574       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
5575     }
5576     /* recvs and sends of i-array are completed */
5577     i = nrecvs;
5578     while (i--) {
5579       ierr = MPI_Waitany(nrecvs_mpi,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5580     }
5581     if (nsends) {ierr = MPI_Waitall(nsends_mpi,swaits,MPI_STATUSES_IGNORE);CHKERRQ(ierr);}
5582     ierr = PetscFree(svalues);CHKERRQ(ierr);
5583 
5584     /* allocate buffers for sending j and a arrays */
5585     ierr = PetscMalloc1(len+1,&bufj);CHKERRQ(ierr);
5586     ierr = PetscMalloc1(len+1,&bufa);CHKERRQ(ierr);
5587 
5588     /* create i-array of B_oth */
5589     ierr = PetscMalloc1(aBn+2,&b_othi);CHKERRQ(ierr);
5590 
5591     b_othi[0] = 0;
5592     len       = 0; /* total length of j or a array to be received */
5593     k         = 0;
5594     for (i=0; i<nrecvs; i++) {
5595       rowlen = rvalues + (rstarts[i]-rstarts[0])*rbs;
5596       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of rows to be received */
5597       for (j=0; j<nrows; j++) {
5598         b_othi[k+1] = b_othi[k] + rowlen[j];
5599         ierr = PetscIntSumError(rowlen[j],len,&len);CHKERRQ(ierr);
5600         k++;
5601       }
5602       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
5603     }
5604     ierr = PetscFree(rvalues);CHKERRQ(ierr);
5605 
5606     /* allocate space for j and a arrrays of B_oth */
5607     ierr = PetscMalloc1(b_othi[aBn]+1,&b_othj);CHKERRQ(ierr);
5608     ierr = PetscMalloc1(b_othi[aBn]+1,&b_otha);CHKERRQ(ierr);
5609 
5610     /* j-array */
5611     /*---------*/
5612     /*  post receives of j-array */
5613     for (i=0; i<nrecvs; i++) {
5614       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5615       ierr  = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5616     }
5617 
5618     /* pack the outgoing message j-array */
5619     if (nsends) k = sstarts[0];
5620     for (i=0; i<nsends; i++) {
5621       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5622       bufJ  = bufj+sstartsj[i];
5623       for (j=0; j<nrows; j++) {
5624         row = srow[k++] + B->rmap->range[rank];  /* global row idx */
5625         for (ll=0; ll<sbs; ll++) {
5626           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
5627           for (l=0; l<ncols; l++) {
5628             *bufJ++ = cols[l];
5629           }
5630           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
5631         }
5632       }
5633       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5634     }
5635 
5636     /* recvs and sends of j-array are completed */
5637     i = nrecvs;
5638     while (i--) {
5639       ierr = MPI_Waitany(nrecvs_mpi,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5640     }
5641     if (nsends) {ierr = MPI_Waitall(nsends_mpi,swaits,MPI_STATUSES_IGNORE);CHKERRQ(ierr);}
5642   } else if (scall == MAT_REUSE_MATRIX) {
5643     sstartsj = *startsj_s;
5644     rstartsj = *startsj_r;
5645     bufa     = *bufa_ptr;
5646     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
5647     b_otha   = b_oth->a;
5648   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
5649 
5650   /* a-array */
5651   /*---------*/
5652   /*  post receives of a-array */
5653   for (i=0; i<nrecvs; i++) {
5654     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5655     ierr  = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5656   }
5657 
5658   /* pack the outgoing message a-array */
5659   if (nsends) k = sstarts[0];
5660   for (i=0; i<nsends; i++) {
5661     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5662     bufA  = bufa+sstartsj[i];
5663     for (j=0; j<nrows; j++) {
5664       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
5665       for (ll=0; ll<sbs; ll++) {
5666         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
5667         for (l=0; l<ncols; l++) {
5668           *bufA++ = vals[l];
5669         }
5670         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
5671       }
5672     }
5673     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5674   }
5675   /* recvs and sends of a-array are completed */
5676   i = nrecvs;
5677   while (i--) {
5678     ierr = MPI_Waitany(nrecvs_mpi,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5679   }
5680   if (nsends) {ierr = MPI_Waitall(nsends_mpi,swaits,MPI_STATUSES_IGNORE);CHKERRQ(ierr);}
5681   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
5682 
5683   if (scall == MAT_INITIAL_MATRIX) {
5684     /* put together the new matrix */
5685     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
5686 
5687     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
5688     /* Since these are PETSc arrays, change flags to free them as necessary. */
5689     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
5690     b_oth->free_a  = PETSC_TRUE;
5691     b_oth->free_ij = PETSC_TRUE;
5692     b_oth->nonew   = 0;
5693 
5694     ierr = PetscFree(bufj);CHKERRQ(ierr);
5695     if (!startsj_s || !bufa_ptr) {
5696       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
5697       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
5698     } else {
5699       *startsj_s = sstartsj;
5700       *startsj_r = rstartsj;
5701       *bufa_ptr  = bufa;
5702     }
5703   }
5704 
5705   ierr = VecScatterRestoreRemote_Private(ctx,PETSC_TRUE,&nsends,&sstarts,&srow,&sprocs,&sbs);CHKERRQ(ierr);
5706   ierr = VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE,&nrecvs,&rstarts,NULL,&rprocs,&rbs);CHKERRQ(ierr);
5707   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5708   PetscFunctionReturn(0);
5709 }
5710 
5711 /*@C
5712   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
5713 
5714   Not Collective
5715 
5716   Input Parameters:
5717 . A - The matrix in mpiaij format
5718 
5719   Output Parameter:
5720 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
5721 . colmap - A map from global column index to local index into lvec
5722 - multScatter - A scatter from the argument of a matrix-vector product to lvec
5723 
5724   Level: developer
5725 
5726 @*/
5727 #if defined(PETSC_USE_CTABLE)
5728 PetscErrorCode MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
5729 #else
5730 PetscErrorCode MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
5731 #endif
5732 {
5733   Mat_MPIAIJ *a;
5734 
5735   PetscFunctionBegin;
5736   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
5737   PetscValidPointer(lvec, 2);
5738   PetscValidPointer(colmap, 3);
5739   PetscValidPointer(multScatter, 4);
5740   a = (Mat_MPIAIJ*) A->data;
5741   if (lvec) *lvec = a->lvec;
5742   if (colmap) *colmap = a->colmap;
5743   if (multScatter) *multScatter = a->Mvctx;
5744   PetscFunctionReturn(0);
5745 }
5746 
5747 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
5748 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
5749 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJSELL(Mat,MatType,MatReuse,Mat*);
5750 #if defined(PETSC_HAVE_MKL_SPARSE)
5751 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJMKL(Mat,MatType,MatReuse,Mat*);
5752 #endif
5753 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIBAIJ(Mat,MatType,MatReuse,Mat*);
5754 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
5755 #if defined(PETSC_HAVE_ELEMENTAL)
5756 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
5757 #endif
5758 #if defined(PETSC_HAVE_HYPRE)
5759 PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat,MatType,MatReuse,Mat*);
5760 #endif
5761 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPISELL(Mat,MatType,MatReuse,Mat*);
5762 PETSC_INTERN PetscErrorCode MatConvert_XAIJ_IS(Mat,MatType,MatReuse,Mat*);
5763 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_IS_XAIJ(Mat);
5764 
5765 /*
5766     Computes (B'*A')' since computing B*A directly is untenable
5767 
5768                n                       p                          p
5769         (              )       (              )         (                  )
5770       m (      A       )  *  n (       B      )   =   m (         C        )
5771         (              )       (              )         (                  )
5772 
5773 */
5774 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
5775 {
5776   PetscErrorCode ierr;
5777   Mat            At,Bt,Ct;
5778 
5779   PetscFunctionBegin;
5780   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
5781   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
5782   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
5783   ierr = MatDestroy(&At);CHKERRQ(ierr);
5784   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
5785   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
5786   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
5787   PetscFunctionReturn(0);
5788 }
5789 
5790 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat C)
5791 {
5792   PetscErrorCode ierr;
5793   PetscInt       m=A->rmap->n,n=B->cmap->n;
5794 
5795   PetscFunctionBegin;
5796   if (A->cmap->n != B->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"A->cmap->n %d != B->rmap->n %d\n",A->cmap->n,B->rmap->n);
5797   ierr = MatSetSizes(C,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
5798   ierr = MatSetBlockSizesFromMats(C,A,B);CHKERRQ(ierr);
5799   ierr = MatSetType(C,MATMPIDENSE);CHKERRQ(ierr);
5800   ierr = MatMPIDenseSetPreallocation(C,NULL);CHKERRQ(ierr);
5801   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5802   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5803 
5804   C->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
5805   PetscFunctionReturn(0);
5806 }
5807 
5808 /* ----------------------------------------------------------------*/
5809 static PetscErrorCode MatProductSetFromOptions_MPIDense_MPIAIJ_AB(Mat C)
5810 {
5811   Mat_Product *product = C->product;
5812   Mat         A = product->A,B=product->B;
5813 
5814   PetscFunctionBegin;
5815   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend)
5816     SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%D, %D) != (%D,%D)",A->cmap->rstart,A->cmap->rend,B->rmap->rstart,B->rmap->rend);
5817 
5818   C->ops->matmultsymbolic = MatMatMultSymbolic_MPIDense_MPIAIJ;
5819   C->ops->productsymbolic = MatProductSymbolic_AB;
5820   PetscFunctionReturn(0);
5821 }
5822 
5823 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIDense_MPIAIJ(Mat C)
5824 {
5825   PetscErrorCode ierr;
5826   Mat_Product    *product = C->product;
5827 
5828   PetscFunctionBegin;
5829   if (product->type == MATPRODUCT_AB) {
5830     ierr = MatProductSetFromOptions_MPIDense_MPIAIJ_AB(C);CHKERRQ(ierr);
5831   } else SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_SUP,"MatProduct type is not supported");
5832   PetscFunctionReturn(0);
5833 }
5834 /* ----------------------------------------------------------------*/
5835 
5836 /*MC
5837    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
5838 
5839    Options Database Keys:
5840 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
5841 
5842    Level: beginner
5843 
5844    Notes:
5845     MatSetValues() may be called for this matrix type with a NULL argument for the numerical values,
5846     in this case the values associated with the rows and columns one passes in are set to zero
5847     in the matrix
5848 
5849     MatSetOptions(,MAT_STRUCTURE_ONLY,PETSC_TRUE) may be called for this matrix type. In this no
5850     space is allocated for the nonzero entries and any entries passed with MatSetValues() are ignored
5851 
5852 .seealso: MatCreateAIJ()
5853 M*/
5854 
5855 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
5856 {
5857   Mat_MPIAIJ     *b;
5858   PetscErrorCode ierr;
5859   PetscMPIInt    size;
5860 
5861   PetscFunctionBegin;
5862   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
5863 
5864   ierr          = PetscNewLog(B,&b);CHKERRQ(ierr);
5865   B->data       = (void*)b;
5866   ierr          = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
5867   B->assembled  = PETSC_FALSE;
5868   B->insertmode = NOT_SET_VALUES;
5869   b->size       = size;
5870 
5871   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank);CHKERRQ(ierr);
5872 
5873   /* build cache for off array entries formed */
5874   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash);CHKERRQ(ierr);
5875 
5876   b->donotstash  = PETSC_FALSE;
5877   b->colmap      = 0;
5878   b->garray      = 0;
5879   b->roworiented = PETSC_TRUE;
5880 
5881   /* stuff used for matrix vector multiply */
5882   b->lvec  = NULL;
5883   b->Mvctx = NULL;
5884 
5885   /* stuff for MatGetRow() */
5886   b->rowindices   = 0;
5887   b->rowvalues    = 0;
5888   b->getrowactive = PETSC_FALSE;
5889 
5890   /* flexible pointer used in CUSP/CUSPARSE classes */
5891   b->spptr = NULL;
5892 
5893   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetUseScalableIncreaseOverlap_C",MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ);CHKERRQ(ierr);
5894   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ);CHKERRQ(ierr);
5895   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
5896   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
5897   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
5898   ierr = PetscObjectComposeFunction((PetscObject)B,"MatResetPreallocation_C",MatResetPreallocation_MPIAIJ);CHKERRQ(ierr);
5899   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
5900   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
5901   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
5902   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijsell_C",MatConvert_MPIAIJ_MPIAIJSELL);CHKERRQ(ierr);
5903 #if defined(PETSC_HAVE_MKL_SPARSE)
5904   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijmkl_C",MatConvert_MPIAIJ_MPIAIJMKL);CHKERRQ(ierr);
5905 #endif
5906   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
5907   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpibaij_C",MatConvert_MPIAIJ_MPIBAIJ);CHKERRQ(ierr);
5908   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
5909 #if defined(PETSC_HAVE_ELEMENTAL)
5910   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_elemental_C",MatConvert_MPIAIJ_Elemental);CHKERRQ(ierr);
5911 #endif
5912   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_is_C",MatConvert_XAIJ_IS);CHKERRQ(ierr);
5913   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisell_C",MatConvert_MPIAIJ_MPISELL);CHKERRQ(ierr);
5914   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
5915   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
5916 #if defined(PETSC_HAVE_HYPRE)
5917   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_hypre_C",MatConvert_AIJ_HYPRE);CHKERRQ(ierr);
5918   ierr = PetscObjectComposeFunction((PetscObject)B,"MatProductSetFromOptions_transpose_mpiaij_mpiaij_C",MatProductSetFromOptions_Transpose_AIJ_AIJ);CHKERRQ(ierr);
5919 #endif
5920   ierr = PetscObjectComposeFunction((PetscObject)B,"MatProductSetFromOptions_is_mpiaij_C",MatProductSetFromOptions_IS_XAIJ);CHKERRQ(ierr);
5921   ierr = PetscObjectComposeFunction((PetscObject)B,"MatProductSetFromOptions_mpiaij_mpiaij_C",MatProductSetFromOptions_MPIAIJ);CHKERRQ(ierr);
5922   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
5923   PetscFunctionReturn(0);
5924 }
5925 
5926 /*@C
5927      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
5928          and "off-diagonal" part of the matrix in CSR format.
5929 
5930    Collective
5931 
5932    Input Parameters:
5933 +  comm - MPI communicator
5934 .  m - number of local rows (Cannot be PETSC_DECIDE)
5935 .  n - This value should be the same as the local size used in creating the
5936        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
5937        calculated if N is given) For square matrices n is almost always m.
5938 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
5939 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
5940 .   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
5941 .   j - column indices
5942 .   a - matrix values
5943 .   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
5944 .   oj - column indices
5945 -   oa - matrix values
5946 
5947    Output Parameter:
5948 .   mat - the matrix
5949 
5950    Level: advanced
5951 
5952    Notes:
5953        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
5954        must free the arrays once the matrix has been destroyed and not before.
5955 
5956        The i and j indices are 0 based
5957 
5958        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
5959 
5960        This sets local rows and cannot be used to set off-processor values.
5961 
5962        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
5963        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
5964        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
5965        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
5966        keep track of the underlying array. Use MatSetOption(A,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
5967        communication if it is known that only local entries will be set.
5968 
5969 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
5970           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
5971 @*/
5972 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)
5973 {
5974   PetscErrorCode ierr;
5975   Mat_MPIAIJ     *maij;
5976 
5977   PetscFunctionBegin;
5978   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
5979   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
5980   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
5981   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
5982   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
5983   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
5984   maij = (Mat_MPIAIJ*) (*mat)->data;
5985 
5986   (*mat)->preallocated = PETSC_TRUE;
5987 
5988   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
5989   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
5990 
5991   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
5992   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
5993 
5994   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5995   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5996   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5997   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5998 
5999   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
6000   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
6001   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
6002   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_FALSE);CHKERRQ(ierr);
6003   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
6004   PetscFunctionReturn(0);
6005 }
6006 
6007 /*
6008     Special version for direct calls from Fortran
6009 */
6010 #include <petsc/private/fortranimpl.h>
6011 
6012 /* Change these macros so can be used in void function */
6013 #undef CHKERRQ
6014 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
6015 #undef SETERRQ2
6016 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
6017 #undef SETERRQ3
6018 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
6019 #undef SETERRQ
6020 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
6021 
6022 #if defined(PETSC_HAVE_FORTRAN_CAPS)
6023 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
6024 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
6025 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
6026 #else
6027 #endif
6028 PETSC_EXTERN void matsetvaluesmpiaij_(Mat *mmat,PetscInt *mm,const PetscInt im[],PetscInt *mn,const PetscInt in[],const PetscScalar v[],InsertMode *maddv,PetscErrorCode *_ierr)
6029 {
6030   Mat            mat  = *mmat;
6031   PetscInt       m    = *mm, n = *mn;
6032   InsertMode     addv = *maddv;
6033   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
6034   PetscScalar    value;
6035   PetscErrorCode ierr;
6036 
6037   MatCheckPreallocated(mat,1);
6038   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
6039 
6040 #if defined(PETSC_USE_DEBUG)
6041   else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
6042 #endif
6043   {
6044     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
6045     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
6046     PetscBool roworiented = aij->roworiented;
6047 
6048     /* Some Variables required in the macro */
6049     Mat        A                    = aij->A;
6050     Mat_SeqAIJ *a                   = (Mat_SeqAIJ*)A->data;
6051     PetscInt   *aimax               = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
6052     MatScalar  *aa                  = a->a;
6053     PetscBool  ignorezeroentries    = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
6054     Mat        B                    = aij->B;
6055     Mat_SeqAIJ *b                   = (Mat_SeqAIJ*)B->data;
6056     PetscInt   *bimax               = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
6057     MatScalar  *ba                  = b->a;
6058     /* This variable below is only for the PETSC_HAVE_VIENNACL or PETSC_HAVE_CUDA cases, but we define it in all cases because we
6059      * cannot use "#if defined" inside a macro. */
6060     PETSC_UNUSED PetscBool inserted = PETSC_FALSE;
6061 
6062     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
6063     PetscInt  nonew = a->nonew;
6064     MatScalar *ap1,*ap2;
6065 
6066     PetscFunctionBegin;
6067     for (i=0; i<m; i++) {
6068       if (im[i] < 0) continue;
6069 #if defined(PETSC_USE_DEBUG)
6070       if (im[i] >= mat->rmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %D max %D",im[i],mat->rmap->N-1);
6071 #endif
6072       if (im[i] >= rstart && im[i] < rend) {
6073         row      = im[i] - rstart;
6074         lastcol1 = -1;
6075         rp1      = aj + ai[row];
6076         ap1      = aa + ai[row];
6077         rmax1    = aimax[row];
6078         nrow1    = ailen[row];
6079         low1     = 0;
6080         high1    = nrow1;
6081         lastcol2 = -1;
6082         rp2      = bj + bi[row];
6083         ap2      = ba + bi[row];
6084         rmax2    = bimax[row];
6085         nrow2    = bilen[row];
6086         low2     = 0;
6087         high2    = nrow2;
6088 
6089         for (j=0; j<n; j++) {
6090           if (roworiented) value = v[i*n+j];
6091           else value = v[i+j*m];
6092           if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && im[i] != in[j]) continue;
6093           if (in[j] >= cstart && in[j] < cend) {
6094             col = in[j] - cstart;
6095             MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
6096 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
6097             if (A->offloadmask != PETSC_OFFLOAD_UNALLOCATED && inserted) A->offloadmask = PETSC_OFFLOAD_CPU;
6098 #endif
6099           } else if (in[j] < 0) continue;
6100 #if defined(PETSC_USE_DEBUG)
6101           /* extra brace on SETERRQ2() is required for --with-errorchecking=0 - due to the next 'else' clause */
6102           else if (in[j] >= mat->cmap->N) {SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %D max %D",in[j],mat->cmap->N-1);}
6103 #endif
6104           else {
6105             if (mat->was_assembled) {
6106               if (!aij->colmap) {
6107                 ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
6108               }
6109 #if defined(PETSC_USE_CTABLE)
6110               ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
6111               col--;
6112 #else
6113               col = aij->colmap[in[j]] - 1;
6114 #endif
6115               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
6116                 ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
6117                 col  =  in[j];
6118                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
6119                 B        = aij->B;
6120                 b        = (Mat_SeqAIJ*)B->data;
6121                 bimax    = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
6122                 rp2      = bj + bi[row];
6123                 ap2      = ba + bi[row];
6124                 rmax2    = bimax[row];
6125                 nrow2    = bilen[row];
6126                 low2     = 0;
6127                 high2    = nrow2;
6128                 bm       = aij->B->rmap->n;
6129                 ba       = b->a;
6130                 inserted = PETSC_FALSE;
6131               }
6132             } else col = in[j];
6133             MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
6134 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
6135             if (B->offloadmask != PETSC_OFFLOAD_UNALLOCATED && inserted) B->offloadmask = PETSC_OFFLOAD_CPU;
6136 #endif
6137           }
6138         }
6139       } else if (!aij->donotstash) {
6140         if (roworiented) {
6141           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
6142         } else {
6143           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
6144         }
6145       }
6146     }
6147   }
6148   PetscFunctionReturnVoid();
6149 }
6150