xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision 94ef8dde638caef1d0cd84a7dc8a2db65fcda8b6)
1 
2 
3 #include <../src/mat/impls/aij/mpi/mpiaij.h>   /*I "petscmat.h" I*/
4 #include <petsc/private/vecimpl.h>
5 #include <petsc/private/isimpl.h>
6 #include <petscblaslapack.h>
7 #include <petscsf.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: Subclasses include MATAIJCUSP, MATAIJCUSPARSE, MATAIJPERM, MATAIJCRL, and also automatically switches over to use inodes when
22    enough exist.
23 
24   Level: beginner
25 
26 .seealso: MatCreateAIJ(), MatCreateSeqAIJ(), MATSEQAIJ, MATMPIAIJ
27 M*/
28 
29 /*MC
30    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.
31 
32    This matrix type is identical to MATSEQAIJCRL when constructed with a single process communicator,
33    and MATMPIAIJCRL otherwise.  As a result, for single process communicators,
34    MatSeqAIJSetPreallocation() is supported, and similarly MatMPIAIJSetPreallocation() is supported
35   for communicators controlling multiple processes.  It is recommended that you call both of
36   the above preallocation routines for simplicity.
37 
38    Options Database Keys:
39 . -mat_type aijcrl - sets the matrix type to "aijcrl" during a call to MatSetFromOptions()
40 
41   Level: beginner
42 
43 .seealso: MatCreateMPIAIJCRL,MATSEQAIJCRL,MATMPIAIJCRL, MATSEQAIJCRL, MATMPIAIJCRL
44 M*/
45 
46 PetscErrorCode MatSetBlockSizes_MPIAIJ(Mat M, PetscInt rbs, PetscInt cbs)
47 {
48   PetscErrorCode ierr;
49   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)M->data;
50 
51   PetscFunctionBegin;
52   if (mat->A) {
53     ierr = MatSetBlockSizes(mat->A,rbs,cbs);CHKERRQ(ierr);
54     ierr = MatSetBlockSizes(mat->B,rbs,1);CHKERRQ(ierr);
55   }
56   PetscFunctionReturn(0);
57 }
58 
59 PetscErrorCode MatFindNonzeroRows_MPIAIJ(Mat M,IS *keptrows)
60 {
61   PetscErrorCode  ierr;
62   Mat_MPIAIJ      *mat = (Mat_MPIAIJ*)M->data;
63   Mat_SeqAIJ      *a   = (Mat_SeqAIJ*)mat->A->data;
64   Mat_SeqAIJ      *b   = (Mat_SeqAIJ*)mat->B->data;
65   const PetscInt  *ia,*ib;
66   const MatScalar *aa,*bb;
67   PetscInt        na,nb,i,j,*rows,cnt=0,n0rows;
68   PetscInt        m = M->rmap->n,rstart = M->rmap->rstart;
69 
70   PetscFunctionBegin;
71   *keptrows = 0;
72   ia        = a->i;
73   ib        = b->i;
74   for (i=0; i<m; i++) {
75     na = ia[i+1] - ia[i];
76     nb = ib[i+1] - ib[i];
77     if (!na && !nb) {
78       cnt++;
79       goto ok1;
80     }
81     aa = a->a + ia[i];
82     for (j=0; j<na; j++) {
83       if (aa[j] != 0.0) goto ok1;
84     }
85     bb = b->a + ib[i];
86     for (j=0; j <nb; j++) {
87       if (bb[j] != 0.0) goto ok1;
88     }
89     cnt++;
90 ok1:;
91   }
92   ierr = MPIU_Allreduce(&cnt,&n0rows,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)M));CHKERRQ(ierr);
93   if (!n0rows) PetscFunctionReturn(0);
94   ierr = PetscMalloc1(M->rmap->n-cnt,&rows);CHKERRQ(ierr);
95   cnt  = 0;
96   for (i=0; i<m; i++) {
97     na = ia[i+1] - ia[i];
98     nb = ib[i+1] - ib[i];
99     if (!na && !nb) continue;
100     aa = a->a + ia[i];
101     for (j=0; j<na;j++) {
102       if (aa[j] != 0.0) {
103         rows[cnt++] = rstart + i;
104         goto ok2;
105       }
106     }
107     bb = b->a + ib[i];
108     for (j=0; j<nb; j++) {
109       if (bb[j] != 0.0) {
110         rows[cnt++] = rstart + i;
111         goto ok2;
112       }
113     }
114 ok2:;
115   }
116   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)M),cnt,rows,PETSC_OWN_POINTER,keptrows);CHKERRQ(ierr);
117   PetscFunctionReturn(0);
118 }
119 
120 PetscErrorCode  MatDiagonalSet_MPIAIJ(Mat Y,Vec D,InsertMode is)
121 {
122   PetscErrorCode    ierr;
123   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*) Y->data;
124 
125   PetscFunctionBegin;
126   if (Y->assembled && Y->rmap->rstart == Y->cmap->rstart && Y->rmap->rend == Y->cmap->rend) {
127     ierr = MatDiagonalSet(aij->A,D,is);CHKERRQ(ierr);
128   } else {
129     ierr = MatDiagonalSet_Default(Y,D,is);CHKERRQ(ierr);
130   }
131   PetscFunctionReturn(0);
132 }
133 
134 
135 PetscErrorCode MatFindZeroDiagonals_MPIAIJ(Mat M,IS *zrows)
136 {
137   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)M->data;
138   PetscErrorCode ierr;
139   PetscInt       i,rstart,nrows,*rows;
140 
141   PetscFunctionBegin;
142   *zrows = NULL;
143   ierr   = MatFindZeroDiagonals_SeqAIJ_Private(aij->A,&nrows,&rows);CHKERRQ(ierr);
144   ierr   = MatGetOwnershipRange(M,&rstart,NULL);CHKERRQ(ierr);
145   for (i=0; i<nrows; i++) rows[i] += rstart;
146   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)M),nrows,rows,PETSC_OWN_POINTER,zrows);CHKERRQ(ierr);
147   PetscFunctionReturn(0);
148 }
149 
150 PetscErrorCode MatGetColumnNorms_MPIAIJ(Mat A,NormType type,PetscReal *norms)
151 {
152   PetscErrorCode ierr;
153   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)A->data;
154   PetscInt       i,n,*garray = aij->garray;
155   Mat_SeqAIJ     *a_aij = (Mat_SeqAIJ*) aij->A->data;
156   Mat_SeqAIJ     *b_aij = (Mat_SeqAIJ*) aij->B->data;
157   PetscReal      *work;
158 
159   PetscFunctionBegin;
160   ierr = MatGetSize(A,NULL,&n);CHKERRQ(ierr);
161   ierr = PetscCalloc1(n,&work);CHKERRQ(ierr);
162   if (type == NORM_2) {
163     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
164       work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i]*a_aij->a[i]);
165     }
166     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
167       work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]*b_aij->a[i]);
168     }
169   } else if (type == NORM_1) {
170     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
171       work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i]);
172     }
173     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
174       work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]);
175     }
176   } else if (type == NORM_INFINITY) {
177     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
178       work[A->cmap->rstart + a_aij->j[i]] = PetscMax(PetscAbsScalar(a_aij->a[i]), work[A->cmap->rstart + a_aij->j[i]]);
179     }
180     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
181       work[garray[b_aij->j[i]]] = PetscMax(PetscAbsScalar(b_aij->a[i]),work[garray[b_aij->j[i]]]);
182     }
183 
184   } else SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Unknown NormType");
185   if (type == NORM_INFINITY) {
186     ierr = MPIU_Allreduce(work,norms,n,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
187   } else {
188     ierr = MPIU_Allreduce(work,norms,n,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
189   }
190   ierr = PetscFree(work);CHKERRQ(ierr);
191   if (type == NORM_2) {
192     for (i=0; i<n; i++) norms[i] = PetscSqrtReal(norms[i]);
193   }
194   PetscFunctionReturn(0);
195 }
196 
197 PetscErrorCode MatFindOffBlockDiagonalEntries_MPIAIJ(Mat A,IS *is)
198 {
199   Mat_MPIAIJ      *a  = (Mat_MPIAIJ*)A->data;
200   IS              sis,gis;
201   PetscErrorCode  ierr;
202   const PetscInt  *isis,*igis;
203   PetscInt        n,*iis,nsis,ngis,rstart,i;
204 
205   PetscFunctionBegin;
206   ierr = MatFindOffBlockDiagonalEntries(a->A,&sis);CHKERRQ(ierr);
207   ierr = MatFindNonzeroRows(a->B,&gis);CHKERRQ(ierr);
208   ierr = ISGetSize(gis,&ngis);CHKERRQ(ierr);
209   ierr = ISGetSize(sis,&nsis);CHKERRQ(ierr);
210   ierr = ISGetIndices(sis,&isis);CHKERRQ(ierr);
211   ierr = ISGetIndices(gis,&igis);CHKERRQ(ierr);
212 
213   ierr = PetscMalloc1(ngis+nsis,&iis);CHKERRQ(ierr);
214   ierr = PetscMemcpy(iis,igis,ngis*sizeof(PetscInt));CHKERRQ(ierr);
215   ierr = PetscMemcpy(iis+ngis,isis,nsis*sizeof(PetscInt));CHKERRQ(ierr);
216   n    = ngis + nsis;
217   ierr = PetscSortRemoveDupsInt(&n,iis);CHKERRQ(ierr);
218   ierr = MatGetOwnershipRange(A,&rstart,NULL);CHKERRQ(ierr);
219   for (i=0; i<n; i++) iis[i] += rstart;
220   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)A),n,iis,PETSC_OWN_POINTER,is);CHKERRQ(ierr);
221 
222   ierr = ISRestoreIndices(sis,&isis);CHKERRQ(ierr);
223   ierr = ISRestoreIndices(gis,&igis);CHKERRQ(ierr);
224   ierr = ISDestroy(&sis);CHKERRQ(ierr);
225   ierr = ISDestroy(&gis);CHKERRQ(ierr);
226   PetscFunctionReturn(0);
227 }
228 
229 /*
230     Distributes a SeqAIJ matrix across a set of processes. Code stolen from
231     MatLoad_MPIAIJ(). Horrible lack of reuse. Should be a routine for each matrix type.
232 
233     Only for square matrices
234 
235     Used by a preconditioner, hence PETSC_EXTERN
236 */
237 PETSC_EXTERN PetscErrorCode MatDistribute_MPIAIJ(MPI_Comm comm,Mat gmat,PetscInt m,MatReuse reuse,Mat *inmat)
238 {
239   PetscMPIInt    rank,size;
240   PetscInt       *rowners,*dlens,*olens,i,rstart,rend,j,jj,nz = 0,*gmataj,cnt,row,*ld,bses[2];
241   PetscErrorCode ierr;
242   Mat            mat;
243   Mat_SeqAIJ     *gmata;
244   PetscMPIInt    tag;
245   MPI_Status     status;
246   PetscBool      aij;
247   MatScalar      *gmataa,*ao,*ad,*gmataarestore=0;
248 
249   PetscFunctionBegin;
250   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
251   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
252   if (!rank) {
253     ierr = PetscObjectTypeCompare((PetscObject)gmat,MATSEQAIJ,&aij);CHKERRQ(ierr);
254     if (!aij) SETERRQ1(PetscObjectComm((PetscObject)gmat),PETSC_ERR_SUP,"Currently no support for input matrix of type %s\n",((PetscObject)gmat)->type_name);
255   }
256   if (reuse == MAT_INITIAL_MATRIX) {
257     ierr = MatCreate(comm,&mat);CHKERRQ(ierr);
258     ierr = MatSetSizes(mat,m,m,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
259     ierr = MatGetBlockSizes(gmat,&bses[0],&bses[1]);CHKERRQ(ierr);
260     ierr = MPI_Bcast(bses,2,MPIU_INT,0,comm);CHKERRQ(ierr);
261     ierr = MatSetBlockSizes(mat,bses[0],bses[1]);CHKERRQ(ierr);
262     ierr = MatSetType(mat,MATAIJ);CHKERRQ(ierr);
263     ierr = PetscMalloc1(size+1,&rowners);CHKERRQ(ierr);
264     ierr = PetscMalloc2(m,&dlens,m,&olens);CHKERRQ(ierr);
265     ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
266 
267     rowners[0] = 0;
268     for (i=2; i<=size; i++) rowners[i] += rowners[i-1];
269     rstart = rowners[rank];
270     rend   = rowners[rank+1];
271     ierr   = PetscObjectGetNewTag((PetscObject)mat,&tag);CHKERRQ(ierr);
272     if (!rank) {
273       gmata = (Mat_SeqAIJ*) gmat->data;
274       /* send row lengths to all processors */
275       for (i=0; i<m; i++) dlens[i] = gmata->ilen[i];
276       for (i=1; i<size; i++) {
277         ierr = MPI_Send(gmata->ilen + rowners[i],rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
278       }
279       /* determine number diagonal and off-diagonal counts */
280       ierr = PetscMemzero(olens,m*sizeof(PetscInt));CHKERRQ(ierr);
281       ierr = PetscCalloc1(m,&ld);CHKERRQ(ierr);
282       jj   = 0;
283       for (i=0; i<m; i++) {
284         for (j=0; j<dlens[i]; j++) {
285           if (gmata->j[jj] < rstart) ld[i]++;
286           if (gmata->j[jj] < rstart || gmata->j[jj] >= rend) olens[i]++;
287           jj++;
288         }
289       }
290       /* send column indices to other processes */
291       for (i=1; i<size; i++) {
292         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
293         ierr = MPI_Send(&nz,1,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
294         ierr = MPI_Send(gmata->j + gmata->i[rowners[i]],nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
295       }
296 
297       /* send numerical values to other processes */
298       for (i=1; i<size; i++) {
299         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
300         ierr = MPI_Send(gmata->a + gmata->i[rowners[i]],nz,MPIU_SCALAR,i,tag,comm);CHKERRQ(ierr);
301       }
302       gmataa = gmata->a;
303       gmataj = gmata->j;
304 
305     } else {
306       /* receive row lengths */
307       ierr = MPI_Recv(dlens,m,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
308       /* receive column indices */
309       ierr = MPI_Recv(&nz,1,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
310       ierr = PetscMalloc2(nz,&gmataa,nz,&gmataj);CHKERRQ(ierr);
311       ierr = MPI_Recv(gmataj,nz,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
312       /* determine number diagonal and off-diagonal counts */
313       ierr = PetscMemzero(olens,m*sizeof(PetscInt));CHKERRQ(ierr);
314       ierr = PetscCalloc1(m,&ld);CHKERRQ(ierr);
315       jj   = 0;
316       for (i=0; i<m; i++) {
317         for (j=0; j<dlens[i]; j++) {
318           if (gmataj[jj] < rstart) ld[i]++;
319           if (gmataj[jj] < rstart || gmataj[jj] >= rend) olens[i]++;
320           jj++;
321         }
322       }
323       /* receive numerical values */
324       ierr = PetscMemzero(gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr);
325       ierr = MPI_Recv(gmataa,nz,MPIU_SCALAR,0,tag,comm,&status);CHKERRQ(ierr);
326     }
327     /* set preallocation */
328     for (i=0; i<m; i++) {
329       dlens[i] -= olens[i];
330     }
331     ierr = MatSeqAIJSetPreallocation(mat,0,dlens);CHKERRQ(ierr);
332     ierr = MatMPIAIJSetPreallocation(mat,0,dlens,0,olens);CHKERRQ(ierr);
333 
334     for (i=0; i<m; i++) {
335       dlens[i] += olens[i];
336     }
337     cnt = 0;
338     for (i=0; i<m; i++) {
339       row  = rstart + i;
340       ierr = MatSetValues(mat,1,&row,dlens[i],gmataj+cnt,gmataa+cnt,INSERT_VALUES);CHKERRQ(ierr);
341       cnt += dlens[i];
342     }
343     if (rank) {
344       ierr = PetscFree2(gmataa,gmataj);CHKERRQ(ierr);
345     }
346     ierr = PetscFree2(dlens,olens);CHKERRQ(ierr);
347     ierr = PetscFree(rowners);CHKERRQ(ierr);
348 
349     ((Mat_MPIAIJ*)(mat->data))->ld = ld;
350 
351     *inmat = mat;
352   } else {   /* column indices are already set; only need to move over numerical values from process 0 */
353     Mat_SeqAIJ *Ad = (Mat_SeqAIJ*)((Mat_MPIAIJ*)((*inmat)->data))->A->data;
354     Mat_SeqAIJ *Ao = (Mat_SeqAIJ*)((Mat_MPIAIJ*)((*inmat)->data))->B->data;
355     mat  = *inmat;
356     ierr = PetscObjectGetNewTag((PetscObject)mat,&tag);CHKERRQ(ierr);
357     if (!rank) {
358       /* send numerical values to other processes */
359       gmata  = (Mat_SeqAIJ*) gmat->data;
360       ierr   = MatGetOwnershipRanges(mat,(const PetscInt**)&rowners);CHKERRQ(ierr);
361       gmataa = gmata->a;
362       for (i=1; i<size; i++) {
363         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
364         ierr = MPI_Send(gmataa + gmata->i[rowners[i]],nz,MPIU_SCALAR,i,tag,comm);CHKERRQ(ierr);
365       }
366       nz = gmata->i[rowners[1]]-gmata->i[rowners[0]];
367     } else {
368       /* receive numerical values from process 0*/
369       nz   = Ad->nz + Ao->nz;
370       ierr = PetscMalloc1(nz,&gmataa);CHKERRQ(ierr); gmataarestore = gmataa;
371       ierr = MPI_Recv(gmataa,nz,MPIU_SCALAR,0,tag,comm,&status);CHKERRQ(ierr);
372     }
373     /* transfer numerical values into the diagonal A and off diagonal B parts of mat */
374     ld = ((Mat_MPIAIJ*)(mat->data))->ld;
375     ad = Ad->a;
376     ao = Ao->a;
377     if (mat->rmap->n) {
378       i  = 0;
379       nz = ld[i];                                   ierr = PetscMemcpy(ao,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ao += nz; gmataa += nz;
380       nz = Ad->i[i+1] - Ad->i[i];                   ierr = PetscMemcpy(ad,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ad += nz; gmataa += nz;
381     }
382     for (i=1; i<mat->rmap->n; i++) {
383       nz = Ao->i[i] - Ao->i[i-1] - ld[i-1] + ld[i]; ierr = PetscMemcpy(ao,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ao += nz; gmataa += nz;
384       nz = Ad->i[i+1] - Ad->i[i];                   ierr = PetscMemcpy(ad,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ad += nz; gmataa += nz;
385     }
386     i--;
387     if (mat->rmap->n) {
388       nz = Ao->i[i+1] - Ao->i[i] - ld[i];           ierr = PetscMemcpy(ao,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr);
389     }
390     if (rank) {
391       ierr = PetscFree(gmataarestore);CHKERRQ(ierr);
392     }
393   }
394   ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
395   ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
396   PetscFunctionReturn(0);
397 }
398 
399 /*
400   Local utility routine that creates a mapping from the global column
401 number to the local number in the off-diagonal part of the local
402 storage of the matrix.  When PETSC_USE_CTABLE is used this is scalable at
403 a slightly higher hash table cost; without it it is not scalable (each processor
404 has an order N integer array but is fast to acess.
405 */
406 PetscErrorCode MatCreateColmap_MPIAIJ_Private(Mat mat)
407 {
408   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
409   PetscErrorCode ierr;
410   PetscInt       n = aij->B->cmap->n,i;
411 
412   PetscFunctionBegin;
413   if (!aij->garray) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"MPIAIJ Matrix was assembled but is missing garray");
414 #if defined(PETSC_USE_CTABLE)
415   ierr = PetscTableCreate(n,mat->cmap->N+1,&aij->colmap);CHKERRQ(ierr);
416   for (i=0; i<n; i++) {
417     ierr = PetscTableAdd(aij->colmap,aij->garray[i]+1,i+1,INSERT_VALUES);CHKERRQ(ierr);
418   }
419 #else
420   ierr = PetscCalloc1(mat->cmap->N+1,&aij->colmap);CHKERRQ(ierr);
421   ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N+1)*sizeof(PetscInt));CHKERRQ(ierr);
422   for (i=0; i<n; i++) aij->colmap[aij->garray[i]] = i+1;
423 #endif
424   PetscFunctionReturn(0);
425 }
426 
427 #define MatSetValues_SeqAIJ_A_Private(row,col,value,addv,orow,ocol)     \
428 { \
429     if (col <= lastcol1)  low1 = 0;     \
430     else                 high1 = nrow1; \
431     lastcol1 = col;\
432     while (high1-low1 > 5) { \
433       t = (low1+high1)/2; \
434       if (rp1[t] > col) high1 = t; \
435       else              low1  = t; \
436     } \
437       for (_i=low1; _i<high1; _i++) { \
438         if (rp1[_i] > col) break; \
439         if (rp1[_i] == col) { \
440           if (addv == ADD_VALUES) ap1[_i] += value;   \
441           else                    ap1[_i] = value; \
442           goto a_noinsert; \
443         } \
444       }  \
445       if (value == 0.0 && ignorezeroentries && row != col) {low1 = 0; high1 = nrow1;goto a_noinsert;} \
446       if (nonew == 1) {low1 = 0; high1 = nrow1; goto a_noinsert;}                \
447       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); \
448       MatSeqXAIJReallocateAIJ(A,am,1,nrow1,row,col,rmax1,aa,ai,aj,rp1,ap1,aimax,nonew,MatScalar); \
449       N = nrow1++ - 1; a->nz++; high1++; \
450       /* shift up all the later entries in this row */ \
451       for (ii=N; ii>=_i; ii--) { \
452         rp1[ii+1] = rp1[ii]; \
453         ap1[ii+1] = ap1[ii]; \
454       } \
455       rp1[_i] = col;  \
456       ap1[_i] = value;  \
457       A->nonzerostate++;\
458       a_noinsert: ; \
459       ailen[row] = nrow1; \
460 }
461 
462 
463 #define MatSetValues_SeqAIJ_B_Private(row,col,value,addv,orow,ocol) \
464   { \
465     if (col <= lastcol2) low2 = 0;                        \
466     else high2 = nrow2;                                   \
467     lastcol2 = col;                                       \
468     while (high2-low2 > 5) {                              \
469       t = (low2+high2)/2;                                 \
470       if (rp2[t] > col) high2 = t;                        \
471       else             low2  = t;                         \
472     }                                                     \
473     for (_i=low2; _i<high2; _i++) {                       \
474       if (rp2[_i] > col) break;                           \
475       if (rp2[_i] == col) {                               \
476         if (addv == ADD_VALUES) ap2[_i] += value;         \
477         else                    ap2[_i] = value;          \
478         goto b_noinsert;                                  \
479       }                                                   \
480     }                                                     \
481     if (value == 0.0 && ignorezeroentries) {low2 = 0; high2 = nrow2; goto b_noinsert;} \
482     if (nonew == 1) {low2 = 0; high2 = nrow2; goto b_noinsert;}                        \
483     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); \
484     MatSeqXAIJReallocateAIJ(B,bm,1,nrow2,row,col,rmax2,ba,bi,bj,rp2,ap2,bimax,nonew,MatScalar); \
485     N = nrow2++ - 1; b->nz++; high2++;                    \
486     /* shift up all the later entries in this row */      \
487     for (ii=N; ii>=_i; ii--) {                            \
488       rp2[ii+1] = rp2[ii];                                \
489       ap2[ii+1] = ap2[ii];                                \
490     }                                                     \
491     rp2[_i] = col;                                        \
492     ap2[_i] = value;                                      \
493     B->nonzerostate++;                                    \
494     b_noinsert: ;                                         \
495     bilen[row] = nrow2;                                   \
496   }
497 
498 PetscErrorCode MatSetValuesRow_MPIAIJ(Mat A,PetscInt row,const PetscScalar v[])
499 {
500   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)A->data;
501   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)mat->A->data,*b = (Mat_SeqAIJ*)mat->B->data;
502   PetscErrorCode ierr;
503   PetscInt       l,*garray = mat->garray,diag;
504 
505   PetscFunctionBegin;
506   /* code only works for square matrices A */
507 
508   /* find size of row to the left of the diagonal part */
509   ierr = MatGetOwnershipRange(A,&diag,0);CHKERRQ(ierr);
510   row  = row - diag;
511   for (l=0; l<b->i[row+1]-b->i[row]; l++) {
512     if (garray[b->j[b->i[row]+l]] > diag) break;
513   }
514   ierr = PetscMemcpy(b->a+b->i[row],v,l*sizeof(PetscScalar));CHKERRQ(ierr);
515 
516   /* diagonal part */
517   ierr = PetscMemcpy(a->a+a->i[row],v+l,(a->i[row+1]-a->i[row])*sizeof(PetscScalar));CHKERRQ(ierr);
518 
519   /* right of diagonal part */
520   ierr = PetscMemcpy(b->a+b->i[row]+l,v+l+a->i[row+1]-a->i[row],(b->i[row+1]-b->i[row]-l)*sizeof(PetscScalar));CHKERRQ(ierr);
521   PetscFunctionReturn(0);
522 }
523 
524 PetscErrorCode MatSetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode addv)
525 {
526   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
527   PetscScalar    value;
528   PetscErrorCode ierr;
529   PetscInt       i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
530   PetscInt       cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
531   PetscBool      roworiented = aij->roworiented;
532 
533   /* Some Variables required in the macro */
534   Mat        A                 = aij->A;
535   Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
536   PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
537   MatScalar  *aa               = a->a;
538   PetscBool  ignorezeroentries = a->ignorezeroentries;
539   Mat        B                 = aij->B;
540   Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
541   PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
542   MatScalar  *ba               = b->a;
543 
544   PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
545   PetscInt  nonew;
546   MatScalar *ap1,*ap2;
547 
548   PetscFunctionBegin;
549   for (i=0; i<m; i++) {
550     if (im[i] < 0) continue;
551 #if defined(PETSC_USE_DEBUG)
552     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);
553 #endif
554     if (im[i] >= rstart && im[i] < rend) {
555       row      = im[i] - rstart;
556       lastcol1 = -1;
557       rp1      = aj + ai[row];
558       ap1      = aa + ai[row];
559       rmax1    = aimax[row];
560       nrow1    = ailen[row];
561       low1     = 0;
562       high1    = nrow1;
563       lastcol2 = -1;
564       rp2      = bj + bi[row];
565       ap2      = ba + bi[row];
566       rmax2    = bimax[row];
567       nrow2    = bilen[row];
568       low2     = 0;
569       high2    = nrow2;
570 
571       for (j=0; j<n; j++) {
572         if (roworiented) value = v[i*n+j];
573         else             value = v[i+j*m];
574         if (in[j] >= cstart && in[j] < cend) {
575           col   = in[j] - cstart;
576           nonew = a->nonew;
577           if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
578           MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
579         } else if (in[j] < 0) continue;
580 #if defined(PETSC_USE_DEBUG)
581         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);
582 #endif
583         else {
584           if (mat->was_assembled) {
585             if (!aij->colmap) {
586               ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
587             }
588 #if defined(PETSC_USE_CTABLE)
589             ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
590             col--;
591 #else
592             col = aij->colmap[in[j]] - 1;
593 #endif
594             if (col < 0 && !((Mat_SeqAIJ*)(aij->B->data))->nonew) {
595               ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
596               col  =  in[j];
597               /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
598               B     = aij->B;
599               b     = (Mat_SeqAIJ*)B->data;
600               bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j; ba = b->a;
601               rp2   = bj + bi[row];
602               ap2   = ba + bi[row];
603               rmax2 = bimax[row];
604               nrow2 = bilen[row];
605               low2  = 0;
606               high2 = nrow2;
607               bm    = aij->B->rmap->n;
608               ba    = b->a;
609             } else if (col < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at global row/column (%D, %D) into matrix", im[i], in[j]);
610           } else col = in[j];
611           nonew = b->nonew;
612           MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
613         }
614       }
615     } else {
616       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]);
617       if (!aij->donotstash) {
618         mat->assembled = PETSC_FALSE;
619         if (roworiented) {
620           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
621         } else {
622           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
623         }
624       }
625     }
626   }
627   PetscFunctionReturn(0);
628 }
629 
630 PetscErrorCode MatGetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],PetscScalar v[])
631 {
632   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
633   PetscErrorCode ierr;
634   PetscInt       i,j,rstart = mat->rmap->rstart,rend = mat->rmap->rend;
635   PetscInt       cstart = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
636 
637   PetscFunctionBegin;
638   for (i=0; i<m; i++) {
639     if (idxm[i] < 0) continue; /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative row: %D",idxm[i]);*/
640     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);
641     if (idxm[i] >= rstart && idxm[i] < rend) {
642       row = idxm[i] - rstart;
643       for (j=0; j<n; j++) {
644         if (idxn[j] < 0) continue; /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column: %D",idxn[j]); */
645         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);
646         if (idxn[j] >= cstart && idxn[j] < cend) {
647           col  = idxn[j] - cstart;
648           ierr = MatGetValues(aij->A,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
649         } else {
650           if (!aij->colmap) {
651             ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
652           }
653 #if defined(PETSC_USE_CTABLE)
654           ierr = PetscTableFind(aij->colmap,idxn[j]+1,&col);CHKERRQ(ierr);
655           col--;
656 #else
657           col = aij->colmap[idxn[j]] - 1;
658 #endif
659           if ((col < 0) || (aij->garray[col] != idxn[j])) *(v+i*n+j) = 0.0;
660           else {
661             ierr = MatGetValues(aij->B,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
662           }
663         }
664       }
665     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only local values currently supported");
666   }
667   PetscFunctionReturn(0);
668 }
669 
670 extern PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat,Vec,Vec);
671 
672 PetscErrorCode MatAssemblyBegin_MPIAIJ(Mat mat,MatAssemblyType mode)
673 {
674   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
675   PetscErrorCode ierr;
676   PetscInt       nstash,reallocs;
677 
678   PetscFunctionBegin;
679   if (aij->donotstash || mat->nooffprocentries) PetscFunctionReturn(0);
680 
681   ierr = MatStashScatterBegin_Private(mat,&mat->stash,mat->rmap->range);CHKERRQ(ierr);
682   ierr = MatStashGetInfo_Private(&mat->stash,&nstash,&reallocs);CHKERRQ(ierr);
683   ierr = PetscInfo2(aij->A,"Stash has %D entries, uses %D mallocs.\n",nstash,reallocs);CHKERRQ(ierr);
684   PetscFunctionReturn(0);
685 }
686 
687 PetscErrorCode MatAssemblyEnd_MPIAIJ(Mat mat,MatAssemblyType mode)
688 {
689   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
690   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)aij->A->data;
691   PetscErrorCode ierr;
692   PetscMPIInt    n;
693   PetscInt       i,j,rstart,ncols,flg;
694   PetscInt       *row,*col;
695   PetscBool      other_disassembled;
696   PetscScalar    *val;
697 
698   /* do not use 'b = (Mat_SeqAIJ*)aij->B->data' as B can be reset in disassembly */
699 
700   PetscFunctionBegin;
701   if (!aij->donotstash && !mat->nooffprocentries) {
702     while (1) {
703       ierr = MatStashScatterGetMesg_Private(&mat->stash,&n,&row,&col,&val,&flg);CHKERRQ(ierr);
704       if (!flg) break;
705 
706       for (i=0; i<n; ) {
707         /* Now identify the consecutive vals belonging to the same row */
708         for (j=i,rstart=row[j]; j<n; j++) {
709           if (row[j] != rstart) break;
710         }
711         if (j < n) ncols = j-i;
712         else       ncols = n-i;
713         /* Now assemble all these values with a single function call */
714         ierr = MatSetValues_MPIAIJ(mat,1,row+i,ncols,col+i,val+i,mat->insertmode);CHKERRQ(ierr);
715 
716         i = j;
717       }
718     }
719     ierr = MatStashScatterEnd_Private(&mat->stash);CHKERRQ(ierr);
720   }
721   ierr = MatAssemblyBegin(aij->A,mode);CHKERRQ(ierr);
722   ierr = MatAssemblyEnd(aij->A,mode);CHKERRQ(ierr);
723 
724   /* determine if any processor has disassembled, if so we must
725      also disassemble ourselfs, in order that we may reassemble. */
726   /*
727      if nonzero structure of submatrix B cannot change then we know that
728      no processor disassembled thus we can skip this stuff
729   */
730   if (!((Mat_SeqAIJ*)aij->B->data)->nonew) {
731     ierr = MPIU_Allreduce(&mat->was_assembled,&other_disassembled,1,MPIU_BOOL,MPI_PROD,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
732     if (mat->was_assembled && !other_disassembled) {
733       ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
734     }
735   }
736   if (!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) {
737     ierr = MatSetUpMultiply_MPIAIJ(mat);CHKERRQ(ierr);
738   }
739   ierr = MatSetOption(aij->B,MAT_USE_INODES,PETSC_FALSE);CHKERRQ(ierr);
740   ierr = MatAssemblyBegin(aij->B,mode);CHKERRQ(ierr);
741   ierr = MatAssemblyEnd(aij->B,mode);CHKERRQ(ierr);
742 
743   ierr = PetscFree2(aij->rowvalues,aij->rowindices);CHKERRQ(ierr);
744 
745   aij->rowvalues = 0;
746 
747   ierr = VecDestroy(&aij->diag);CHKERRQ(ierr);
748   if (a->inode.size) mat->ops->multdiagonalblock = MatMultDiagonalBlock_MPIAIJ;
749 
750   /* if no new nonzero locations are allowed in matrix then only set the matrix state the first time through */
751   if ((!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) || !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
752     PetscObjectState state = aij->A->nonzerostate + aij->B->nonzerostate;
753     ierr = MPIU_Allreduce(&state,&mat->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
754   }
755   PetscFunctionReturn(0);
756 }
757 
758 PetscErrorCode MatZeroEntries_MPIAIJ(Mat A)
759 {
760   Mat_MPIAIJ     *l = (Mat_MPIAIJ*)A->data;
761   PetscErrorCode ierr;
762 
763   PetscFunctionBegin;
764   ierr = MatZeroEntries(l->A);CHKERRQ(ierr);
765   ierr = MatZeroEntries(l->B);CHKERRQ(ierr);
766   PetscFunctionReturn(0);
767 }
768 
769 PetscErrorCode MatZeroRows_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
770 {
771   Mat_MPIAIJ    *mat    = (Mat_MPIAIJ *) A->data;
772   PetscInt      *lrows;
773   PetscInt       r, len;
774   PetscErrorCode ierr;
775 
776   PetscFunctionBegin;
777   /* get locally owned rows */
778   ierr = MatZeroRowsMapLocal_Private(A,N,rows,&len,&lrows);CHKERRQ(ierr);
779   /* fix right hand side if needed */
780   if (x && b) {
781     const PetscScalar *xx;
782     PetscScalar       *bb;
783 
784     ierr = VecGetArrayRead(x, &xx);CHKERRQ(ierr);
785     ierr = VecGetArray(b, &bb);CHKERRQ(ierr);
786     for (r = 0; r < len; ++r) bb[lrows[r]] = diag*xx[lrows[r]];
787     ierr = VecRestoreArrayRead(x, &xx);CHKERRQ(ierr);
788     ierr = VecRestoreArray(b, &bb);CHKERRQ(ierr);
789   }
790   /* Must zero l->B before l->A because the (diag) case below may put values into l->B*/
791   ierr = MatZeroRows(mat->B, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
792   if (A->congruentlayouts == -1) { /* first time we compare rows and cols layouts */
793     PetscBool cong;
794     ierr = PetscLayoutCompare(A->rmap,A->cmap,&cong);CHKERRQ(ierr);
795     if (cong) A->congruentlayouts = 1;
796     else      A->congruentlayouts = 0;
797   }
798   if ((diag != 0.0) && A->congruentlayouts) {
799     ierr = MatZeroRows(mat->A, len, lrows, diag, NULL, NULL);CHKERRQ(ierr);
800   } else if (diag != 0.0) {
801     ierr = MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
802     if (((Mat_SeqAIJ *) mat->A->data)->nonew) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatZeroRows() on rectangular matrices cannot be used with the Mat options\nMAT_NEW_NONZERO_LOCATIONS,MAT_NEW_NONZERO_LOCATION_ERR,MAT_NEW_NONZERO_ALLOCATION_ERR");
803     for (r = 0; r < len; ++r) {
804       const PetscInt row = lrows[r] + A->rmap->rstart;
805       ierr = MatSetValues(A, 1, &row, 1, &row, &diag, INSERT_VALUES);CHKERRQ(ierr);
806     }
807     ierr = MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
808     ierr = MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
809   } else {
810     ierr = MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
811   }
812   ierr = PetscFree(lrows);CHKERRQ(ierr);
813 
814   /* only change matrix nonzero state if pattern was allowed to be changed */
815   if (!((Mat_SeqAIJ*)(mat->A->data))->keepnonzeropattern) {
816     PetscObjectState state = mat->A->nonzerostate + mat->B->nonzerostate;
817     ierr = MPIU_Allreduce(&state,&A->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
818   }
819   PetscFunctionReturn(0);
820 }
821 
822 PetscErrorCode MatZeroRowsColumns_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
823 {
824   Mat_MPIAIJ        *l = (Mat_MPIAIJ*)A->data;
825   PetscErrorCode    ierr;
826   PetscMPIInt       n = A->rmap->n;
827   PetscInt          i,j,r,m,p = 0,len = 0;
828   PetscInt          *lrows,*owners = A->rmap->range;
829   PetscSFNode       *rrows;
830   PetscSF           sf;
831   const PetscScalar *xx;
832   PetscScalar       *bb,*mask;
833   Vec               xmask,lmask;
834   Mat_SeqAIJ        *aij = (Mat_SeqAIJ*)l->B->data;
835   const PetscInt    *aj, *ii,*ridx;
836   PetscScalar       *aa;
837 
838   PetscFunctionBegin;
839   /* Create SF where leaves are input rows and roots are owned rows */
840   ierr = PetscMalloc1(n, &lrows);CHKERRQ(ierr);
841   for (r = 0; r < n; ++r) lrows[r] = -1;
842   ierr = PetscMalloc1(N, &rrows);CHKERRQ(ierr);
843   for (r = 0; r < N; ++r) {
844     const PetscInt idx   = rows[r];
845     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);
846     if (idx < owners[p] || owners[p+1] <= idx) { /* short-circuit the search if the last p owns this row too */
847       ierr = PetscLayoutFindOwner(A->rmap,idx,&p);CHKERRQ(ierr);
848     }
849     rrows[r].rank  = p;
850     rrows[r].index = rows[r] - owners[p];
851   }
852   ierr = PetscSFCreate(PetscObjectComm((PetscObject) A), &sf);CHKERRQ(ierr);
853   ierr = PetscSFSetGraph(sf, n, N, NULL, PETSC_OWN_POINTER, rrows, PETSC_OWN_POINTER);CHKERRQ(ierr);
854   /* Collect flags for rows to be zeroed */
855   ierr = PetscSFReduceBegin(sf, MPIU_INT, (PetscInt *) rows, lrows, MPI_LOR);CHKERRQ(ierr);
856   ierr = PetscSFReduceEnd(sf, MPIU_INT, (PetscInt *) rows, lrows, MPI_LOR);CHKERRQ(ierr);
857   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
858   /* Compress and put in row numbers */
859   for (r = 0; r < n; ++r) if (lrows[r] >= 0) lrows[len++] = r;
860   /* zero diagonal part of matrix */
861   ierr = MatZeroRowsColumns(l->A,len,lrows,diag,x,b);CHKERRQ(ierr);
862   /* handle off diagonal part of matrix */
863   ierr = MatCreateVecs(A,&xmask,NULL);CHKERRQ(ierr);
864   ierr = VecDuplicate(l->lvec,&lmask);CHKERRQ(ierr);
865   ierr = VecGetArray(xmask,&bb);CHKERRQ(ierr);
866   for (i=0; i<len; i++) bb[lrows[i]] = 1;
867   ierr = VecRestoreArray(xmask,&bb);CHKERRQ(ierr);
868   ierr = VecScatterBegin(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
869   ierr = VecScatterEnd(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
870   ierr = VecDestroy(&xmask);CHKERRQ(ierr);
871   if (x) {
872     ierr = VecScatterBegin(l->Mvctx,x,l->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
873     ierr = VecScatterEnd(l->Mvctx,x,l->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
874     ierr = VecGetArrayRead(l->lvec,&xx);CHKERRQ(ierr);
875     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
876   }
877   ierr = VecGetArray(lmask,&mask);CHKERRQ(ierr);
878   /* remove zeroed rows of off diagonal matrix */
879   ii = aij->i;
880   for (i=0; i<len; i++) {
881     ierr = PetscMemzero(aij->a + ii[lrows[i]],(ii[lrows[i]+1] - ii[lrows[i]])*sizeof(PetscScalar));CHKERRQ(ierr);
882   }
883   /* loop over all elements of off process part of matrix zeroing removed columns*/
884   if (aij->compressedrow.use) {
885     m    = aij->compressedrow.nrows;
886     ii   = aij->compressedrow.i;
887     ridx = aij->compressedrow.rindex;
888     for (i=0; i<m; i++) {
889       n  = ii[i+1] - ii[i];
890       aj = aij->j + ii[i];
891       aa = aij->a + ii[i];
892 
893       for (j=0; j<n; j++) {
894         if (PetscAbsScalar(mask[*aj])) {
895           if (b) bb[*ridx] -= *aa*xx[*aj];
896           *aa = 0.0;
897         }
898         aa++;
899         aj++;
900       }
901       ridx++;
902     }
903   } else { /* do not use compressed row format */
904     m = l->B->rmap->n;
905     for (i=0; i<m; i++) {
906       n  = ii[i+1] - ii[i];
907       aj = aij->j + ii[i];
908       aa = aij->a + ii[i];
909       for (j=0; j<n; j++) {
910         if (PetscAbsScalar(mask[*aj])) {
911           if (b) bb[i] -= *aa*xx[*aj];
912           *aa = 0.0;
913         }
914         aa++;
915         aj++;
916       }
917     }
918   }
919   if (x) {
920     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
921     ierr = VecRestoreArrayRead(l->lvec,&xx);CHKERRQ(ierr);
922   }
923   ierr = VecRestoreArray(lmask,&mask);CHKERRQ(ierr);
924   ierr = VecDestroy(&lmask);CHKERRQ(ierr);
925   ierr = PetscFree(lrows);CHKERRQ(ierr);
926 
927   /* only change matrix nonzero state if pattern was allowed to be changed */
928   if (!((Mat_SeqAIJ*)(l->A->data))->keepnonzeropattern) {
929     PetscObjectState state = l->A->nonzerostate + l->B->nonzerostate;
930     ierr = MPIU_Allreduce(&state,&A->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
931   }
932   PetscFunctionReturn(0);
933 }
934 
935 PetscErrorCode MatMult_MPIAIJ(Mat A,Vec xx,Vec yy)
936 {
937   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
938   PetscErrorCode ierr;
939   PetscInt       nt;
940 
941   PetscFunctionBegin;
942   ierr = VecGetLocalSize(xx,&nt);CHKERRQ(ierr);
943   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);
944   ierr = VecScatterBegin(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
945   ierr = (*a->A->ops->mult)(a->A,xx,yy);CHKERRQ(ierr);
946   ierr = VecScatterEnd(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
947   ierr = (*a->B->ops->multadd)(a->B,a->lvec,yy,yy);CHKERRQ(ierr);
948   PetscFunctionReturn(0);
949 }
950 
951 PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat A,Vec bb,Vec xx)
952 {
953   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
954   PetscErrorCode ierr;
955 
956   PetscFunctionBegin;
957   ierr = MatMultDiagonalBlock(a->A,bb,xx);CHKERRQ(ierr);
958   PetscFunctionReturn(0);
959 }
960 
961 PetscErrorCode MatMultAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
962 {
963   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
964   PetscErrorCode ierr;
965 
966   PetscFunctionBegin;
967   ierr = VecScatterBegin(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
968   ierr = (*a->A->ops->multadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
969   ierr = VecScatterEnd(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
970   ierr = (*a->B->ops->multadd)(a->B,a->lvec,zz,zz);CHKERRQ(ierr);
971   PetscFunctionReturn(0);
972 }
973 
974 PetscErrorCode MatMultTranspose_MPIAIJ(Mat A,Vec xx,Vec yy)
975 {
976   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
977   PetscErrorCode ierr;
978   PetscBool      merged;
979 
980   PetscFunctionBegin;
981   ierr = VecScatterGetMerged(a->Mvctx,&merged);CHKERRQ(ierr);
982   /* do nondiagonal part */
983   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
984   if (!merged) {
985     /* send it on its way */
986     ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
987     /* do local part */
988     ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
989     /* receive remote parts: note this assumes the values are not actually */
990     /* added in yy until the next line, */
991     ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
992   } else {
993     /* do local part */
994     ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
995     /* send it on its way */
996     ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
997     /* values actually were received in the Begin() but we need to call this nop */
998     ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
999   }
1000   PetscFunctionReturn(0);
1001 }
1002 
1003 PetscErrorCode  MatIsTranspose_MPIAIJ(Mat Amat,Mat Bmat,PetscReal tol,PetscBool  *f)
1004 {
1005   MPI_Comm       comm;
1006   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ*) Amat->data, *Bij;
1007   Mat            Adia = Aij->A, Bdia, Aoff,Boff,*Aoffs,*Boffs;
1008   IS             Me,Notme;
1009   PetscErrorCode ierr;
1010   PetscInt       M,N,first,last,*notme,i;
1011   PetscMPIInt    size;
1012 
1013   PetscFunctionBegin;
1014   /* Easy test: symmetric diagonal block */
1015   Bij  = (Mat_MPIAIJ*) Bmat->data; Bdia = Bij->A;
1016   ierr = MatIsTranspose(Adia,Bdia,tol,f);CHKERRQ(ierr);
1017   if (!*f) PetscFunctionReturn(0);
1018   ierr = PetscObjectGetComm((PetscObject)Amat,&comm);CHKERRQ(ierr);
1019   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1020   if (size == 1) PetscFunctionReturn(0);
1021 
1022   /* Hard test: off-diagonal block. This takes a MatCreateSubMatrix. */
1023   ierr = MatGetSize(Amat,&M,&N);CHKERRQ(ierr);
1024   ierr = MatGetOwnershipRange(Amat,&first,&last);CHKERRQ(ierr);
1025   ierr = PetscMalloc1(N-last+first,&notme);CHKERRQ(ierr);
1026   for (i=0; i<first; i++) notme[i] = i;
1027   for (i=last; i<M; i++) notme[i-last+first] = i;
1028   ierr = ISCreateGeneral(MPI_COMM_SELF,N-last+first,notme,PETSC_COPY_VALUES,&Notme);CHKERRQ(ierr);
1029   ierr = ISCreateStride(MPI_COMM_SELF,last-first,first,1,&Me);CHKERRQ(ierr);
1030   ierr = MatCreateSubMatrices(Amat,1,&Me,&Notme,MAT_INITIAL_MATRIX,&Aoffs);CHKERRQ(ierr);
1031   Aoff = Aoffs[0];
1032   ierr = MatCreateSubMatrices(Bmat,1,&Notme,&Me,MAT_INITIAL_MATRIX,&Boffs);CHKERRQ(ierr);
1033   Boff = Boffs[0];
1034   ierr = MatIsTranspose(Aoff,Boff,tol,f);CHKERRQ(ierr);
1035   ierr = MatDestroyMatrices(1,&Aoffs);CHKERRQ(ierr);
1036   ierr = MatDestroyMatrices(1,&Boffs);CHKERRQ(ierr);
1037   ierr = ISDestroy(&Me);CHKERRQ(ierr);
1038   ierr = ISDestroy(&Notme);CHKERRQ(ierr);
1039   ierr = PetscFree(notme);CHKERRQ(ierr);
1040   PetscFunctionReturn(0);
1041 }
1042 
1043 PetscErrorCode MatMultTransposeAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1044 {
1045   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1046   PetscErrorCode ierr;
1047 
1048   PetscFunctionBegin;
1049   /* do nondiagonal part */
1050   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
1051   /* send it on its way */
1052   ierr = VecScatterBegin(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1053   /* do local part */
1054   ierr = (*a->A->ops->multtransposeadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
1055   /* receive remote parts */
1056   ierr = VecScatterEnd(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1057   PetscFunctionReturn(0);
1058 }
1059 
1060 /*
1061   This only works correctly for square matrices where the subblock A->A is the
1062    diagonal block
1063 */
1064 PetscErrorCode MatGetDiagonal_MPIAIJ(Mat A,Vec v)
1065 {
1066   PetscErrorCode ierr;
1067   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1068 
1069   PetscFunctionBegin;
1070   if (A->rmap->N != A->cmap->N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Supports only square matrix where A->A is diag block");
1071   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");
1072   ierr = MatGetDiagonal(a->A,v);CHKERRQ(ierr);
1073   PetscFunctionReturn(0);
1074 }
1075 
1076 PetscErrorCode MatScale_MPIAIJ(Mat A,PetscScalar aa)
1077 {
1078   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1079   PetscErrorCode ierr;
1080 
1081   PetscFunctionBegin;
1082   ierr = MatScale(a->A,aa);CHKERRQ(ierr);
1083   ierr = MatScale(a->B,aa);CHKERRQ(ierr);
1084   PetscFunctionReturn(0);
1085 }
1086 
1087 PetscErrorCode MatDestroy_MPIAIJ(Mat mat)
1088 {
1089   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1090   PetscErrorCode ierr;
1091 
1092   PetscFunctionBegin;
1093 #if defined(PETSC_USE_LOG)
1094   PetscLogObjectState((PetscObject)mat,"Rows=%D, Cols=%D",mat->rmap->N,mat->cmap->N);
1095 #endif
1096   ierr = MatStashDestroy_Private(&mat->stash);CHKERRQ(ierr);
1097   ierr = VecDestroy(&aij->diag);CHKERRQ(ierr);
1098   ierr = MatDestroy(&aij->A);CHKERRQ(ierr);
1099   ierr = MatDestroy(&aij->B);CHKERRQ(ierr);
1100 #if defined(PETSC_USE_CTABLE)
1101   ierr = PetscTableDestroy(&aij->colmap);CHKERRQ(ierr);
1102 #else
1103   ierr = PetscFree(aij->colmap);CHKERRQ(ierr);
1104 #endif
1105   ierr = PetscFree(aij->garray);CHKERRQ(ierr);
1106   ierr = VecDestroy(&aij->lvec);CHKERRQ(ierr);
1107   ierr = VecScatterDestroy(&aij->Mvctx);CHKERRQ(ierr);
1108   ierr = PetscFree2(aij->rowvalues,aij->rowindices);CHKERRQ(ierr);
1109   ierr = PetscFree(aij->ld);CHKERRQ(ierr);
1110   ierr = PetscFree(mat->data);CHKERRQ(ierr);
1111 
1112   ierr = PetscObjectChangeTypeName((PetscObject)mat,0);CHKERRQ(ierr);
1113   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatStoreValues_C",NULL);CHKERRQ(ierr);
1114   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatRetrieveValues_C",NULL);CHKERRQ(ierr);
1115   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatIsTranspose_C",NULL);CHKERRQ(ierr);
1116   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocation_C",NULL);CHKERRQ(ierr);
1117   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocationCSR_C",NULL);CHKERRQ(ierr);
1118   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDiagonalScaleLocal_C",NULL);CHKERRQ(ierr);
1119   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_mpisbaij_C",NULL);CHKERRQ(ierr);
1120 #if defined(PETSC_HAVE_ELEMENTAL)
1121   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_elemental_C",NULL);CHKERRQ(ierr);
1122 #endif
1123 #if defined(PETSC_HAVE_HYPRE)
1124   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_hypre_C",NULL);CHKERRQ(ierr);
1125   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMatMatMult_transpose_mpiaij_mpiaij_C",NULL);CHKERRQ(ierr);
1126 #endif
1127   PetscFunctionReturn(0);
1128 }
1129 
1130 PetscErrorCode MatView_MPIAIJ_Binary(Mat mat,PetscViewer viewer)
1131 {
1132   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1133   Mat_SeqAIJ     *A   = (Mat_SeqAIJ*)aij->A->data;
1134   Mat_SeqAIJ     *B   = (Mat_SeqAIJ*)aij->B->data;
1135   PetscErrorCode ierr;
1136   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
1137   int            fd;
1138   PetscInt       nz,header[4],*row_lengths,*range=0,rlen,i;
1139   PetscInt       nzmax,*column_indices,j,k,col,*garray = aij->garray,cnt,cstart = mat->cmap->rstart,rnz = 0;
1140   PetscScalar    *column_values;
1141   PetscInt       message_count,flowcontrolcount;
1142   FILE           *file;
1143 
1144   PetscFunctionBegin;
1145   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
1146   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);CHKERRQ(ierr);
1147   nz   = A->nz + B->nz;
1148   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
1149   if (!rank) {
1150     header[0] = MAT_FILE_CLASSID;
1151     header[1] = mat->rmap->N;
1152     header[2] = mat->cmap->N;
1153 
1154     ierr = MPI_Reduce(&nz,&header[3],1,MPIU_INT,MPI_SUM,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1155     ierr = PetscBinaryWrite(fd,header,4,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1156     /* get largest number of rows any processor has */
1157     rlen  = mat->rmap->n;
1158     range = mat->rmap->range;
1159     for (i=1; i<size; i++) rlen = PetscMax(rlen,range[i+1] - range[i]);
1160   } else {
1161     ierr = MPI_Reduce(&nz,0,1,MPIU_INT,MPI_SUM,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1162     rlen = mat->rmap->n;
1163   }
1164 
1165   /* load up the local row counts */
1166   ierr = PetscMalloc1(rlen+1,&row_lengths);CHKERRQ(ierr);
1167   for (i=0; i<mat->rmap->n; i++) row_lengths[i] = A->i[i+1] - A->i[i] + B->i[i+1] - B->i[i];
1168 
1169   /* store the row lengths to the file */
1170   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1171   if (!rank) {
1172     ierr = PetscBinaryWrite(fd,row_lengths,mat->rmap->n,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1173     for (i=1; i<size; i++) {
1174       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1175       rlen = range[i+1] - range[i];
1176       ierr = MPIULong_Recv(row_lengths,rlen,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1177       ierr = PetscBinaryWrite(fd,row_lengths,rlen,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1178     }
1179     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1180   } else {
1181     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1182     ierr = MPIULong_Send(row_lengths,mat->rmap->n,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1183     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1184   }
1185   ierr = PetscFree(row_lengths);CHKERRQ(ierr);
1186 
1187   /* load up the local column indices */
1188   nzmax = nz; /* th processor needs space a largest processor needs */
1189   ierr  = MPI_Reduce(&nz,&nzmax,1,MPIU_INT,MPI_MAX,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1190   ierr  = PetscMalloc1(nzmax+1,&column_indices);CHKERRQ(ierr);
1191   cnt   = 0;
1192   for (i=0; i<mat->rmap->n; i++) {
1193     for (j=B->i[i]; j<B->i[i+1]; j++) {
1194       if ((col = garray[B->j[j]]) > cstart) break;
1195       column_indices[cnt++] = col;
1196     }
1197     for (k=A->i[i]; k<A->i[i+1]; k++) column_indices[cnt++] = A->j[k] + cstart;
1198     for (; j<B->i[i+1]; j++) column_indices[cnt++] = garray[B->j[j]];
1199   }
1200   if (cnt != A->nz + B->nz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: cnt = %D nz = %D",cnt,A->nz+B->nz);
1201 
1202   /* store the column indices to the file */
1203   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1204   if (!rank) {
1205     MPI_Status status;
1206     ierr = PetscBinaryWrite(fd,column_indices,nz,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1207     for (i=1; i<size; i++) {
1208       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1209       ierr = MPI_Recv(&rnz,1,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat),&status);CHKERRQ(ierr);
1210       if (rnz > nzmax) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: nz = %D nzmax = %D",nz,nzmax);
1211       ierr = MPIULong_Recv(column_indices,rnz,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1212       ierr = PetscBinaryWrite(fd,column_indices,rnz,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1213     }
1214     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1215   } else {
1216     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1217     ierr = MPI_Send(&nz,1,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1218     ierr = MPIULong_Send(column_indices,nz,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1219     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1220   }
1221   ierr = PetscFree(column_indices);CHKERRQ(ierr);
1222 
1223   /* load up the local column values */
1224   ierr = PetscMalloc1(nzmax+1,&column_values);CHKERRQ(ierr);
1225   cnt  = 0;
1226   for (i=0; i<mat->rmap->n; i++) {
1227     for (j=B->i[i]; j<B->i[i+1]; j++) {
1228       if (garray[B->j[j]] > cstart) break;
1229       column_values[cnt++] = B->a[j];
1230     }
1231     for (k=A->i[i]; k<A->i[i+1]; k++) column_values[cnt++] = A->a[k];
1232     for (; j<B->i[i+1]; j++) column_values[cnt++] = B->a[j];
1233   }
1234   if (cnt != A->nz + B->nz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Internal PETSc error: cnt = %D nz = %D",cnt,A->nz+B->nz);
1235 
1236   /* store the column values to the file */
1237   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1238   if (!rank) {
1239     MPI_Status status;
1240     ierr = PetscBinaryWrite(fd,column_values,nz,PETSC_SCALAR,PETSC_TRUE);CHKERRQ(ierr);
1241     for (i=1; i<size; i++) {
1242       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1243       ierr = MPI_Recv(&rnz,1,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat),&status);CHKERRQ(ierr);
1244       if (rnz > nzmax) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: nz = %D nzmax = %D",nz,nzmax);
1245       ierr = MPIULong_Recv(column_values,rnz,MPIU_SCALAR,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1246       ierr = PetscBinaryWrite(fd,column_values,rnz,PETSC_SCALAR,PETSC_TRUE);CHKERRQ(ierr);
1247     }
1248     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1249   } else {
1250     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1251     ierr = MPI_Send(&nz,1,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1252     ierr = MPIULong_Send(column_values,nz,MPIU_SCALAR,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1253     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1254   }
1255   ierr = PetscFree(column_values);CHKERRQ(ierr);
1256 
1257   ierr = PetscViewerBinaryGetInfoPointer(viewer,&file);CHKERRQ(ierr);
1258   if (file) fprintf(file,"-matload_block_size %d\n",(int)PetscAbs(mat->rmap->bs));
1259   PetscFunctionReturn(0);
1260 }
1261 
1262 #include <petscdraw.h>
1263 PetscErrorCode MatView_MPIAIJ_ASCIIorDraworSocket(Mat mat,PetscViewer viewer)
1264 {
1265   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)mat->data;
1266   PetscErrorCode    ierr;
1267   PetscMPIInt       rank = aij->rank,size = aij->size;
1268   PetscBool         isdraw,iascii,isbinary;
1269   PetscViewer       sviewer;
1270   PetscViewerFormat format;
1271 
1272   PetscFunctionBegin;
1273   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1274   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1275   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1276   if (iascii) {
1277     ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
1278     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
1279       MatInfo   info;
1280       PetscBool inodes;
1281 
1282       ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
1283       ierr = MatGetInfo(mat,MAT_LOCAL,&info);CHKERRQ(ierr);
1284       ierr = MatInodeGetInodeSizes(aij->A,NULL,(PetscInt**)&inodes,NULL);CHKERRQ(ierr);
1285       ierr = PetscViewerASCIIPushSynchronized(viewer);CHKERRQ(ierr);
1286       if (!inodes) {
1287         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %D nz %D nz alloced %D mem %D, not using I-node routines\n",
1288                                                   rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
1289       } else {
1290         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %D nz %D nz alloced %D mem %D, using I-node routines\n",
1291                                                   rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
1292       }
1293       ierr = MatGetInfo(aij->A,MAT_LOCAL,&info);CHKERRQ(ierr);
1294       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] on-diagonal part: nz %D \n",rank,(PetscInt)info.nz_used);CHKERRQ(ierr);
1295       ierr = MatGetInfo(aij->B,MAT_LOCAL,&info);CHKERRQ(ierr);
1296       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] off-diagonal part: nz %D \n",rank,(PetscInt)info.nz_used);CHKERRQ(ierr);
1297       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1298       ierr = PetscViewerASCIIPopSynchronized(viewer);CHKERRQ(ierr);
1299       ierr = PetscViewerASCIIPrintf(viewer,"Information on VecScatter used in matrix-vector product: \n");CHKERRQ(ierr);
1300       ierr = VecScatterView(aij->Mvctx,viewer);CHKERRQ(ierr);
1301       PetscFunctionReturn(0);
1302     } else if (format == PETSC_VIEWER_ASCII_INFO) {
1303       PetscInt inodecount,inodelimit,*inodes;
1304       ierr = MatInodeGetInodeSizes(aij->A,&inodecount,&inodes,&inodelimit);CHKERRQ(ierr);
1305       if (inodes) {
1306         ierr = PetscViewerASCIIPrintf(viewer,"using I-node (on process 0) routines: found %D nodes, limit used is %D\n",inodecount,inodelimit);CHKERRQ(ierr);
1307       } else {
1308         ierr = PetscViewerASCIIPrintf(viewer,"not using I-node (on process 0) routines\n");CHKERRQ(ierr);
1309       }
1310       PetscFunctionReturn(0);
1311     } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO) {
1312       PetscFunctionReturn(0);
1313     }
1314   } else if (isbinary) {
1315     if (size == 1) {
1316       ierr = PetscObjectSetName((PetscObject)aij->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1317       ierr = MatView(aij->A,viewer);CHKERRQ(ierr);
1318     } else {
1319       ierr = MatView_MPIAIJ_Binary(mat,viewer);CHKERRQ(ierr);
1320     }
1321     PetscFunctionReturn(0);
1322   } else if (isdraw) {
1323     PetscDraw draw;
1324     PetscBool isnull;
1325     ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
1326     ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr);
1327     if (isnull) PetscFunctionReturn(0);
1328   }
1329 
1330   {
1331     /* assemble the entire matrix onto first processor. */
1332     Mat        A;
1333     Mat_SeqAIJ *Aloc;
1334     PetscInt   M = mat->rmap->N,N = mat->cmap->N,m,*ai,*aj,row,*cols,i,*ct;
1335     MatScalar  *a;
1336 
1337     ierr = MatCreate(PetscObjectComm((PetscObject)mat),&A);CHKERRQ(ierr);
1338     if (!rank) {
1339       ierr = MatSetSizes(A,M,N,M,N);CHKERRQ(ierr);
1340     } else {
1341       ierr = MatSetSizes(A,0,0,M,N);CHKERRQ(ierr);
1342     }
1343     /* This is just a temporary matrix, so explicitly using MATMPIAIJ is probably best */
1344     ierr = MatSetType(A,MATMPIAIJ);CHKERRQ(ierr);
1345     ierr = MatMPIAIJSetPreallocation(A,0,NULL,0,NULL);CHKERRQ(ierr);
1346     ierr = MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
1347     ierr = PetscLogObjectParent((PetscObject)mat,(PetscObject)A);CHKERRQ(ierr);
1348 
1349     /* copy over the A part */
1350     Aloc = (Mat_SeqAIJ*)aij->A->data;
1351     m    = aij->A->rmap->n; ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
1352     row  = mat->rmap->rstart;
1353     for (i=0; i<ai[m]; i++) aj[i] += mat->cmap->rstart;
1354     for (i=0; i<m; i++) {
1355       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],aj,a,INSERT_VALUES);CHKERRQ(ierr);
1356       row++;
1357       a += ai[i+1]-ai[i]; aj += ai[i+1]-ai[i];
1358     }
1359     aj = Aloc->j;
1360     for (i=0; i<ai[m]; i++) aj[i] -= mat->cmap->rstart;
1361 
1362     /* copy over the B part */
1363     Aloc = (Mat_SeqAIJ*)aij->B->data;
1364     m    = aij->B->rmap->n;  ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
1365     row  = mat->rmap->rstart;
1366     ierr = PetscMalloc1(ai[m]+1,&cols);CHKERRQ(ierr);
1367     ct   = cols;
1368     for (i=0; i<ai[m]; i++) cols[i] = aij->garray[aj[i]];
1369     for (i=0; i<m; i++) {
1370       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],cols,a,INSERT_VALUES);CHKERRQ(ierr);
1371       row++;
1372       a += ai[i+1]-ai[i]; cols += ai[i+1]-ai[i];
1373     }
1374     ierr = PetscFree(ct);CHKERRQ(ierr);
1375     ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1376     ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1377     /*
1378        Everyone has to call to draw the matrix since the graphics waits are
1379        synchronized across all processors that share the PetscDraw object
1380     */
1381     ierr = PetscViewerGetSubViewer(viewer,PETSC_COMM_SELF,&sviewer);CHKERRQ(ierr);
1382     if (!rank) {
1383       ierr = PetscObjectSetName((PetscObject)((Mat_MPIAIJ*)(A->data))->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1384       ierr = MatView_SeqAIJ(((Mat_MPIAIJ*)(A->data))->A,sviewer);CHKERRQ(ierr);
1385     }
1386     ierr = PetscViewerRestoreSubViewer(viewer,PETSC_COMM_SELF,&sviewer);CHKERRQ(ierr);
1387     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1388     ierr = MatDestroy(&A);CHKERRQ(ierr);
1389   }
1390   PetscFunctionReturn(0);
1391 }
1392 
1393 PetscErrorCode MatView_MPIAIJ(Mat mat,PetscViewer viewer)
1394 {
1395   PetscErrorCode ierr;
1396   PetscBool      iascii,isdraw,issocket,isbinary;
1397 
1398   PetscFunctionBegin;
1399   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1400   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1401   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1402   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSOCKET,&issocket);CHKERRQ(ierr);
1403   if (iascii || isdraw || isbinary || issocket) {
1404     ierr = MatView_MPIAIJ_ASCIIorDraworSocket(mat,viewer);CHKERRQ(ierr);
1405   }
1406   PetscFunctionReturn(0);
1407 }
1408 
1409 PetscErrorCode MatSOR_MPIAIJ(Mat matin,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
1410 {
1411   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1412   PetscErrorCode ierr;
1413   Vec            bb1 = 0;
1414   PetscBool      hasop;
1415 
1416   PetscFunctionBegin;
1417   if (flag == SOR_APPLY_UPPER) {
1418     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1419     PetscFunctionReturn(0);
1420   }
1421 
1422   if (its > 1 || ~flag & SOR_ZERO_INITIAL_GUESS || flag & SOR_EISENSTAT) {
1423     ierr = VecDuplicate(bb,&bb1);CHKERRQ(ierr);
1424   }
1425 
1426   if ((flag & SOR_LOCAL_SYMMETRIC_SWEEP) == SOR_LOCAL_SYMMETRIC_SWEEP) {
1427     if (flag & SOR_ZERO_INITIAL_GUESS) {
1428       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1429       its--;
1430     }
1431 
1432     while (its--) {
1433       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1434       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1435 
1436       /* update rhs: bb1 = bb - B*x */
1437       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1438       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1439 
1440       /* local sweep */
1441       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_SYMMETRIC_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1442     }
1443   } else if (flag & SOR_LOCAL_FORWARD_SWEEP) {
1444     if (flag & SOR_ZERO_INITIAL_GUESS) {
1445       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1446       its--;
1447     }
1448     while (its--) {
1449       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1450       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1451 
1452       /* update rhs: bb1 = bb - B*x */
1453       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1454       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1455 
1456       /* local sweep */
1457       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_FORWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1458     }
1459   } else if (flag & SOR_LOCAL_BACKWARD_SWEEP) {
1460     if (flag & SOR_ZERO_INITIAL_GUESS) {
1461       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1462       its--;
1463     }
1464     while (its--) {
1465       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1466       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1467 
1468       /* update rhs: bb1 = bb - B*x */
1469       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1470       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1471 
1472       /* local sweep */
1473       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_BACKWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1474     }
1475   } else if (flag & SOR_EISENSTAT) {
1476     Vec xx1;
1477 
1478     ierr = VecDuplicate(bb,&xx1);CHKERRQ(ierr);
1479     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_BACKWARD_SWEEP),fshift,lits,1,xx);CHKERRQ(ierr);
1480 
1481     ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1482     ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1483     if (!mat->diag) {
1484       ierr = MatCreateVecs(matin,&mat->diag,NULL);CHKERRQ(ierr);
1485       ierr = MatGetDiagonal(matin,mat->diag);CHKERRQ(ierr);
1486     }
1487     ierr = MatHasOperation(matin,MATOP_MULT_DIAGONAL_BLOCK,&hasop);CHKERRQ(ierr);
1488     if (hasop) {
1489       ierr = MatMultDiagonalBlock(matin,xx,bb1);CHKERRQ(ierr);
1490     } else {
1491       ierr = VecPointwiseMult(bb1,mat->diag,xx);CHKERRQ(ierr);
1492     }
1493     ierr = VecAYPX(bb1,(omega-2.0)/omega,bb);CHKERRQ(ierr);
1494 
1495     ierr = MatMultAdd(mat->B,mat->lvec,bb1,bb1);CHKERRQ(ierr);
1496 
1497     /* local sweep */
1498     ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_FORWARD_SWEEP),fshift,lits,1,xx1);CHKERRQ(ierr);
1499     ierr = VecAXPY(xx,1.0,xx1);CHKERRQ(ierr);
1500     ierr = VecDestroy(&xx1);CHKERRQ(ierr);
1501   } else SETERRQ(PetscObjectComm((PetscObject)matin),PETSC_ERR_SUP,"Parallel SOR not supported");
1502 
1503   ierr = VecDestroy(&bb1);CHKERRQ(ierr);
1504 
1505   matin->factorerrortype = mat->A->factorerrortype;
1506   PetscFunctionReturn(0);
1507 }
1508 
1509 PetscErrorCode MatPermute_MPIAIJ(Mat A,IS rowp,IS colp,Mat *B)
1510 {
1511   Mat            aA,aB,Aperm;
1512   const PetscInt *rwant,*cwant,*gcols,*ai,*bi,*aj,*bj;
1513   PetscScalar    *aa,*ba;
1514   PetscInt       i,j,m,n,ng,anz,bnz,*dnnz,*onnz,*tdnnz,*tonnz,*rdest,*cdest,*work,*gcdest;
1515   PetscSF        rowsf,sf;
1516   IS             parcolp = NULL;
1517   PetscBool      done;
1518   PetscErrorCode ierr;
1519 
1520   PetscFunctionBegin;
1521   ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
1522   ierr = ISGetIndices(rowp,&rwant);CHKERRQ(ierr);
1523   ierr = ISGetIndices(colp,&cwant);CHKERRQ(ierr);
1524   ierr = PetscMalloc3(PetscMax(m,n),&work,m,&rdest,n,&cdest);CHKERRQ(ierr);
1525 
1526   /* Invert row permutation to find out where my rows should go */
1527   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&rowsf);CHKERRQ(ierr);
1528   ierr = PetscSFSetGraphLayout(rowsf,A->rmap,A->rmap->n,NULL,PETSC_OWN_POINTER,rwant);CHKERRQ(ierr);
1529   ierr = PetscSFSetFromOptions(rowsf);CHKERRQ(ierr);
1530   for (i=0; i<m; i++) work[i] = A->rmap->rstart + i;
1531   ierr = PetscSFReduceBegin(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1532   ierr = PetscSFReduceEnd(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1533 
1534   /* Invert column permutation to find out where my columns should go */
1535   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1536   ierr = PetscSFSetGraphLayout(sf,A->cmap,A->cmap->n,NULL,PETSC_OWN_POINTER,cwant);CHKERRQ(ierr);
1537   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1538   for (i=0; i<n; i++) work[i] = A->cmap->rstart + i;
1539   ierr = PetscSFReduceBegin(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1540   ierr = PetscSFReduceEnd(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1541   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1542 
1543   ierr = ISRestoreIndices(rowp,&rwant);CHKERRQ(ierr);
1544   ierr = ISRestoreIndices(colp,&cwant);CHKERRQ(ierr);
1545   ierr = MatMPIAIJGetSeqAIJ(A,&aA,&aB,&gcols);CHKERRQ(ierr);
1546 
1547   /* Find out where my gcols should go */
1548   ierr = MatGetSize(aB,NULL,&ng);CHKERRQ(ierr);
1549   ierr = PetscMalloc1(ng,&gcdest);CHKERRQ(ierr);
1550   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1551   ierr = PetscSFSetGraphLayout(sf,A->cmap,ng,NULL,PETSC_OWN_POINTER,gcols);CHKERRQ(ierr);
1552   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1553   ierr = PetscSFBcastBegin(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1554   ierr = PetscSFBcastEnd(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1555   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1556 
1557   ierr = PetscCalloc4(m,&dnnz,m,&onnz,m,&tdnnz,m,&tonnz);CHKERRQ(ierr);
1558   ierr = MatGetRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1559   ierr = MatGetRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1560   for (i=0; i<m; i++) {
1561     PetscInt row = rdest[i],rowner;
1562     ierr = PetscLayoutFindOwner(A->rmap,row,&rowner);CHKERRQ(ierr);
1563     for (j=ai[i]; j<ai[i+1]; j++) {
1564       PetscInt cowner,col = cdest[aj[j]];
1565       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr); /* Could build an index for the columns to eliminate this search */
1566       if (rowner == cowner) dnnz[i]++;
1567       else onnz[i]++;
1568     }
1569     for (j=bi[i]; j<bi[i+1]; j++) {
1570       PetscInt cowner,col = gcdest[bj[j]];
1571       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr);
1572       if (rowner == cowner) dnnz[i]++;
1573       else onnz[i]++;
1574     }
1575   }
1576   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1577   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1578   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1579   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1580   ierr = PetscSFDestroy(&rowsf);CHKERRQ(ierr);
1581 
1582   ierr = MatCreateAIJ(PetscObjectComm((PetscObject)A),A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N,0,tdnnz,0,tonnz,&Aperm);CHKERRQ(ierr);
1583   ierr = MatSeqAIJGetArray(aA,&aa);CHKERRQ(ierr);
1584   ierr = MatSeqAIJGetArray(aB,&ba);CHKERRQ(ierr);
1585   for (i=0; i<m; i++) {
1586     PetscInt *acols = dnnz,*bcols = onnz; /* Repurpose now-unneeded arrays */
1587     PetscInt j0,rowlen;
1588     rowlen = ai[i+1] - ai[i];
1589     for (j0=j=0; j<rowlen; j0=j) { /* rowlen could be larger than number of rows m, so sum in batches */
1590       for ( ; j<PetscMin(rowlen,j0+m); j++) acols[j-j0] = cdest[aj[ai[i]+j]];
1591       ierr = MatSetValues(Aperm,1,&rdest[i],j-j0,acols,aa+ai[i]+j0,INSERT_VALUES);CHKERRQ(ierr);
1592     }
1593     rowlen = bi[i+1] - bi[i];
1594     for (j0=j=0; j<rowlen; j0=j) {
1595       for ( ; j<PetscMin(rowlen,j0+m); j++) bcols[j-j0] = gcdest[bj[bi[i]+j]];
1596       ierr = MatSetValues(Aperm,1,&rdest[i],j-j0,bcols,ba+bi[i]+j0,INSERT_VALUES);CHKERRQ(ierr);
1597     }
1598   }
1599   ierr = MatAssemblyBegin(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1600   ierr = MatAssemblyEnd(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1601   ierr = MatRestoreRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1602   ierr = MatRestoreRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1603   ierr = MatSeqAIJRestoreArray(aA,&aa);CHKERRQ(ierr);
1604   ierr = MatSeqAIJRestoreArray(aB,&ba);CHKERRQ(ierr);
1605   ierr = PetscFree4(dnnz,onnz,tdnnz,tonnz);CHKERRQ(ierr);
1606   ierr = PetscFree3(work,rdest,cdest);CHKERRQ(ierr);
1607   ierr = PetscFree(gcdest);CHKERRQ(ierr);
1608   if (parcolp) {ierr = ISDestroy(&colp);CHKERRQ(ierr);}
1609   *B = Aperm;
1610   PetscFunctionReturn(0);
1611 }
1612 
1613 PetscErrorCode  MatGetGhosts_MPIAIJ(Mat mat,PetscInt *nghosts,const PetscInt *ghosts[])
1614 {
1615   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1616   PetscErrorCode ierr;
1617 
1618   PetscFunctionBegin;
1619   ierr = MatGetSize(aij->B,NULL,nghosts);CHKERRQ(ierr);
1620   if (ghosts) *ghosts = aij->garray;
1621   PetscFunctionReturn(0);
1622 }
1623 
1624 PetscErrorCode MatGetInfo_MPIAIJ(Mat matin,MatInfoType flag,MatInfo *info)
1625 {
1626   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1627   Mat            A    = mat->A,B = mat->B;
1628   PetscErrorCode ierr;
1629   PetscReal      isend[5],irecv[5];
1630 
1631   PetscFunctionBegin;
1632   info->block_size = 1.0;
1633   ierr             = MatGetInfo(A,MAT_LOCAL,info);CHKERRQ(ierr);
1634 
1635   isend[0] = info->nz_used; isend[1] = info->nz_allocated; isend[2] = info->nz_unneeded;
1636   isend[3] = info->memory;  isend[4] = info->mallocs;
1637 
1638   ierr = MatGetInfo(B,MAT_LOCAL,info);CHKERRQ(ierr);
1639 
1640   isend[0] += info->nz_used; isend[1] += info->nz_allocated; isend[2] += info->nz_unneeded;
1641   isend[3] += info->memory;  isend[4] += info->mallocs;
1642   if (flag == MAT_LOCAL) {
1643     info->nz_used      = isend[0];
1644     info->nz_allocated = isend[1];
1645     info->nz_unneeded  = isend[2];
1646     info->memory       = isend[3];
1647     info->mallocs      = isend[4];
1648   } else if (flag == MAT_GLOBAL_MAX) {
1649     ierr = MPIU_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1650 
1651     info->nz_used      = irecv[0];
1652     info->nz_allocated = irecv[1];
1653     info->nz_unneeded  = irecv[2];
1654     info->memory       = irecv[3];
1655     info->mallocs      = irecv[4];
1656   } else if (flag == MAT_GLOBAL_SUM) {
1657     ierr = MPIU_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1658 
1659     info->nz_used      = irecv[0];
1660     info->nz_allocated = irecv[1];
1661     info->nz_unneeded  = irecv[2];
1662     info->memory       = irecv[3];
1663     info->mallocs      = irecv[4];
1664   }
1665   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
1666   info->fill_ratio_needed = 0;
1667   info->factor_mallocs    = 0;
1668   PetscFunctionReturn(0);
1669 }
1670 
1671 PetscErrorCode MatSetOption_MPIAIJ(Mat A,MatOption op,PetscBool flg)
1672 {
1673   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1674   PetscErrorCode ierr;
1675 
1676   PetscFunctionBegin;
1677   switch (op) {
1678   case MAT_NEW_NONZERO_LOCATIONS:
1679   case MAT_NEW_NONZERO_ALLOCATION_ERR:
1680   case MAT_UNUSED_NONZERO_LOCATION_ERR:
1681   case MAT_KEEP_NONZERO_PATTERN:
1682   case MAT_NEW_NONZERO_LOCATION_ERR:
1683   case MAT_USE_INODES:
1684   case MAT_IGNORE_ZERO_ENTRIES:
1685     MatCheckPreallocated(A,1);
1686     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1687     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1688     break;
1689   case MAT_ROW_ORIENTED:
1690     MatCheckPreallocated(A,1);
1691     a->roworiented = flg;
1692 
1693     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1694     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1695     break;
1696   case MAT_NEW_DIAGONALS:
1697     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
1698     break;
1699   case MAT_IGNORE_OFF_PROC_ENTRIES:
1700     a->donotstash = flg;
1701     break;
1702   case MAT_SPD:
1703     A->spd_set = PETSC_TRUE;
1704     A->spd     = flg;
1705     if (flg) {
1706       A->symmetric                  = PETSC_TRUE;
1707       A->structurally_symmetric     = PETSC_TRUE;
1708       A->symmetric_set              = PETSC_TRUE;
1709       A->structurally_symmetric_set = PETSC_TRUE;
1710     }
1711     break;
1712   case MAT_SYMMETRIC:
1713     MatCheckPreallocated(A,1);
1714     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1715     break;
1716   case MAT_STRUCTURALLY_SYMMETRIC:
1717     MatCheckPreallocated(A,1);
1718     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1719     break;
1720   case MAT_HERMITIAN:
1721     MatCheckPreallocated(A,1);
1722     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1723     break;
1724   case MAT_SYMMETRY_ETERNAL:
1725     MatCheckPreallocated(A,1);
1726     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1727     break;
1728   case MAT_SUBMAT_SINGLEIS:
1729     A->submat_singleis = flg;
1730     break;
1731   default:
1732     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %d",op);
1733   }
1734   PetscFunctionReturn(0);
1735 }
1736 
1737 PetscErrorCode MatGetRow_MPIAIJ(Mat matin,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1738 {
1739   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1740   PetscScalar    *vworkA,*vworkB,**pvA,**pvB,*v_p;
1741   PetscErrorCode ierr;
1742   PetscInt       i,*cworkA,*cworkB,**pcA,**pcB,cstart = matin->cmap->rstart;
1743   PetscInt       nztot,nzA,nzB,lrow,rstart = matin->rmap->rstart,rend = matin->rmap->rend;
1744   PetscInt       *cmap,*idx_p;
1745 
1746   PetscFunctionBegin;
1747   if (mat->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Already active");
1748   mat->getrowactive = PETSC_TRUE;
1749 
1750   if (!mat->rowvalues && (idx || v)) {
1751     /*
1752         allocate enough space to hold information from the longest row.
1753     */
1754     Mat_SeqAIJ *Aa = (Mat_SeqAIJ*)mat->A->data,*Ba = (Mat_SeqAIJ*)mat->B->data;
1755     PetscInt   max = 1,tmp;
1756     for (i=0; i<matin->rmap->n; i++) {
1757       tmp = Aa->i[i+1] - Aa->i[i] + Ba->i[i+1] - Ba->i[i];
1758       if (max < tmp) max = tmp;
1759     }
1760     ierr = PetscMalloc2(max,&mat->rowvalues,max,&mat->rowindices);CHKERRQ(ierr);
1761   }
1762 
1763   if (row < rstart || row >= rend) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Only local rows");
1764   lrow = row - rstart;
1765 
1766   pvA = &vworkA; pcA = &cworkA; pvB = &vworkB; pcB = &cworkB;
1767   if (!v)   {pvA = 0; pvB = 0;}
1768   if (!idx) {pcA = 0; if (!v) pcB = 0;}
1769   ierr  = (*mat->A->ops->getrow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1770   ierr  = (*mat->B->ops->getrow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1771   nztot = nzA + nzB;
1772 
1773   cmap = mat->garray;
1774   if (v  || idx) {
1775     if (nztot) {
1776       /* Sort by increasing column numbers, assuming A and B already sorted */
1777       PetscInt imark = -1;
1778       if (v) {
1779         *v = v_p = mat->rowvalues;
1780         for (i=0; i<nzB; i++) {
1781           if (cmap[cworkB[i]] < cstart) v_p[i] = vworkB[i];
1782           else break;
1783         }
1784         imark = i;
1785         for (i=0; i<nzA; i++)     v_p[imark+i] = vworkA[i];
1786         for (i=imark; i<nzB; i++) v_p[nzA+i]   = vworkB[i];
1787       }
1788       if (idx) {
1789         *idx = idx_p = mat->rowindices;
1790         if (imark > -1) {
1791           for (i=0; i<imark; i++) {
1792             idx_p[i] = cmap[cworkB[i]];
1793           }
1794         } else {
1795           for (i=0; i<nzB; i++) {
1796             if (cmap[cworkB[i]] < cstart) idx_p[i] = cmap[cworkB[i]];
1797             else break;
1798           }
1799           imark = i;
1800         }
1801         for (i=0; i<nzA; i++)     idx_p[imark+i] = cstart + cworkA[i];
1802         for (i=imark; i<nzB; i++) idx_p[nzA+i]   = cmap[cworkB[i]];
1803       }
1804     } else {
1805       if (idx) *idx = 0;
1806       if (v)   *v   = 0;
1807     }
1808   }
1809   *nz  = nztot;
1810   ierr = (*mat->A->ops->restorerow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1811   ierr = (*mat->B->ops->restorerow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1812   PetscFunctionReturn(0);
1813 }
1814 
1815 PetscErrorCode MatRestoreRow_MPIAIJ(Mat mat,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1816 {
1817   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1818 
1819   PetscFunctionBegin;
1820   if (!aij->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"MatGetRow() must be called first");
1821   aij->getrowactive = PETSC_FALSE;
1822   PetscFunctionReturn(0);
1823 }
1824 
1825 PetscErrorCode MatNorm_MPIAIJ(Mat mat,NormType type,PetscReal *norm)
1826 {
1827   Mat_MPIAIJ     *aij  = (Mat_MPIAIJ*)mat->data;
1828   Mat_SeqAIJ     *amat = (Mat_SeqAIJ*)aij->A->data,*bmat = (Mat_SeqAIJ*)aij->B->data;
1829   PetscErrorCode ierr;
1830   PetscInt       i,j,cstart = mat->cmap->rstart;
1831   PetscReal      sum = 0.0;
1832   MatScalar      *v;
1833 
1834   PetscFunctionBegin;
1835   if (aij->size == 1) {
1836     ierr =  MatNorm(aij->A,type,norm);CHKERRQ(ierr);
1837   } else {
1838     if (type == NORM_FROBENIUS) {
1839       v = amat->a;
1840       for (i=0; i<amat->nz; i++) {
1841         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1842       }
1843       v = bmat->a;
1844       for (i=0; i<bmat->nz; i++) {
1845         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1846       }
1847       ierr  = MPIU_Allreduce(&sum,norm,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1848       *norm = PetscSqrtReal(*norm);
1849       ierr = PetscLogFlops(2*amat->nz+2*bmat->nz);CHKERRQ(ierr);
1850     } else if (type == NORM_1) { /* max column norm */
1851       PetscReal *tmp,*tmp2;
1852       PetscInt  *jj,*garray = aij->garray;
1853       ierr  = PetscCalloc1(mat->cmap->N+1,&tmp);CHKERRQ(ierr);
1854       ierr  = PetscMalloc1(mat->cmap->N+1,&tmp2);CHKERRQ(ierr);
1855       *norm = 0.0;
1856       v     = amat->a; jj = amat->j;
1857       for (j=0; j<amat->nz; j++) {
1858         tmp[cstart + *jj++] += PetscAbsScalar(*v);  v++;
1859       }
1860       v = bmat->a; jj = bmat->j;
1861       for (j=0; j<bmat->nz; j++) {
1862         tmp[garray[*jj++]] += PetscAbsScalar(*v); v++;
1863       }
1864       ierr = MPIU_Allreduce(tmp,tmp2,mat->cmap->N,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1865       for (j=0; j<mat->cmap->N; j++) {
1866         if (tmp2[j] > *norm) *norm = tmp2[j];
1867       }
1868       ierr = PetscFree(tmp);CHKERRQ(ierr);
1869       ierr = PetscFree(tmp2);CHKERRQ(ierr);
1870       ierr = PetscLogFlops(PetscMax(amat->nz+bmat->nz-1,0));CHKERRQ(ierr);
1871     } else if (type == NORM_INFINITY) { /* max row norm */
1872       PetscReal ntemp = 0.0;
1873       for (j=0; j<aij->A->rmap->n; j++) {
1874         v   = amat->a + amat->i[j];
1875         sum = 0.0;
1876         for (i=0; i<amat->i[j+1]-amat->i[j]; i++) {
1877           sum += PetscAbsScalar(*v); v++;
1878         }
1879         v = bmat->a + bmat->i[j];
1880         for (i=0; i<bmat->i[j+1]-bmat->i[j]; i++) {
1881           sum += PetscAbsScalar(*v); v++;
1882         }
1883         if (sum > ntemp) ntemp = sum;
1884       }
1885       ierr = MPIU_Allreduce(&ntemp,norm,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1886       ierr = PetscLogFlops(PetscMax(amat->nz+bmat->nz-1,0));CHKERRQ(ierr);
1887     } else SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"No support for two norm");
1888   }
1889   PetscFunctionReturn(0);
1890 }
1891 
1892 PetscErrorCode MatTranspose_MPIAIJ(Mat A,MatReuse reuse,Mat *matout)
1893 {
1894   Mat_MPIAIJ     *a   = (Mat_MPIAIJ*)A->data;
1895   Mat_SeqAIJ     *Aloc=(Mat_SeqAIJ*)a->A->data,*Bloc=(Mat_SeqAIJ*)a->B->data;
1896   PetscErrorCode ierr;
1897   PetscInt       M      = A->rmap->N,N = A->cmap->N,ma,na,mb,nb,*ai,*aj,*bi,*bj,row,*cols,*cols_tmp,i;
1898   PetscInt       cstart = A->cmap->rstart,ncol;
1899   Mat            B;
1900   MatScalar      *array;
1901 
1902   PetscFunctionBegin;
1903   if (reuse == MAT_INPLACE_MATRIX && M != N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Square matrix only for in-place");
1904 
1905   ma = A->rmap->n; na = A->cmap->n; mb = a->B->rmap->n; nb = a->B->cmap->n;
1906   ai = Aloc->i; aj = Aloc->j;
1907   bi = Bloc->i; bj = Bloc->j;
1908   if (reuse == MAT_INITIAL_MATRIX || *matout == A) {
1909     PetscInt             *d_nnz,*g_nnz,*o_nnz;
1910     PetscSFNode          *oloc;
1911     PETSC_UNUSED PetscSF sf;
1912 
1913     ierr = PetscMalloc4(na,&d_nnz,na,&o_nnz,nb,&g_nnz,nb,&oloc);CHKERRQ(ierr);
1914     /* compute d_nnz for preallocation */
1915     ierr = PetscMemzero(d_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1916     for (i=0; i<ai[ma]; i++) {
1917       d_nnz[aj[i]]++;
1918       aj[i] += cstart; /* global col index to be used by MatSetValues() */
1919     }
1920     /* compute local off-diagonal contributions */
1921     ierr = PetscMemzero(g_nnz,nb*sizeof(PetscInt));CHKERRQ(ierr);
1922     for (i=0; i<bi[ma]; i++) g_nnz[bj[i]]++;
1923     /* map those to global */
1924     ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1925     ierr = PetscSFSetGraphLayout(sf,A->cmap,nb,NULL,PETSC_USE_POINTER,a->garray);CHKERRQ(ierr);
1926     ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1927     ierr = PetscMemzero(o_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1928     ierr = PetscSFReduceBegin(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
1929     ierr = PetscSFReduceEnd(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
1930     ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1931 
1932     ierr = MatCreate(PetscObjectComm((PetscObject)A),&B);CHKERRQ(ierr);
1933     ierr = MatSetSizes(B,A->cmap->n,A->rmap->n,N,M);CHKERRQ(ierr);
1934     ierr = MatSetBlockSizes(B,PetscAbs(A->cmap->bs),PetscAbs(A->rmap->bs));CHKERRQ(ierr);
1935     ierr = MatSetType(B,((PetscObject)A)->type_name);CHKERRQ(ierr);
1936     ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
1937     ierr = PetscFree4(d_nnz,o_nnz,g_nnz,oloc);CHKERRQ(ierr);
1938   } else {
1939     B    = *matout;
1940     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
1941     for (i=0; i<ai[ma]; i++) aj[i] += cstart; /* global col index to be used by MatSetValues() */
1942   }
1943 
1944   /* copy over the A part */
1945   array = Aloc->a;
1946   row   = A->rmap->rstart;
1947   for (i=0; i<ma; i++) {
1948     ncol = ai[i+1]-ai[i];
1949     ierr = MatSetValues(B,ncol,aj,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
1950     row++;
1951     array += ncol; aj += ncol;
1952   }
1953   aj = Aloc->j;
1954   for (i=0; i<ai[ma]; i++) aj[i] -= cstart; /* resume local col index */
1955 
1956   /* copy over the B part */
1957   ierr  = PetscCalloc1(bi[mb],&cols);CHKERRQ(ierr);
1958   array = Bloc->a;
1959   row   = A->rmap->rstart;
1960   for (i=0; i<bi[mb]; i++) cols[i] = a->garray[bj[i]];
1961   cols_tmp = cols;
1962   for (i=0; i<mb; i++) {
1963     ncol = bi[i+1]-bi[i];
1964     ierr = MatSetValues(B,ncol,cols_tmp,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
1965     row++;
1966     array += ncol; cols_tmp += ncol;
1967   }
1968   ierr = PetscFree(cols);CHKERRQ(ierr);
1969 
1970   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1971   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1972   if (reuse == MAT_INITIAL_MATRIX || reuse == MAT_REUSE_MATRIX) {
1973     *matout = B;
1974   } else {
1975     ierr = MatHeaderMerge(A,&B);CHKERRQ(ierr);
1976   }
1977   PetscFunctionReturn(0);
1978 }
1979 
1980 PetscErrorCode MatDiagonalScale_MPIAIJ(Mat mat,Vec ll,Vec rr)
1981 {
1982   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1983   Mat            a    = aij->A,b = aij->B;
1984   PetscErrorCode ierr;
1985   PetscInt       s1,s2,s3;
1986 
1987   PetscFunctionBegin;
1988   ierr = MatGetLocalSize(mat,&s2,&s3);CHKERRQ(ierr);
1989   if (rr) {
1990     ierr = VecGetLocalSize(rr,&s1);CHKERRQ(ierr);
1991     if (s1!=s3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"right vector non-conforming local size");
1992     /* Overlap communication with computation. */
1993     ierr = VecScatterBegin(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1994   }
1995   if (ll) {
1996     ierr = VecGetLocalSize(ll,&s1);CHKERRQ(ierr);
1997     if (s1!=s2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"left vector non-conforming local size");
1998     ierr = (*b->ops->diagonalscale)(b,ll,0);CHKERRQ(ierr);
1999   }
2000   /* scale  the diagonal block */
2001   ierr = (*a->ops->diagonalscale)(a,ll,rr);CHKERRQ(ierr);
2002 
2003   if (rr) {
2004     /* Do a scatter end and then right scale the off-diagonal block */
2005     ierr = VecScatterEnd(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2006     ierr = (*b->ops->diagonalscale)(b,0,aij->lvec);CHKERRQ(ierr);
2007   }
2008   PetscFunctionReturn(0);
2009 }
2010 
2011 PetscErrorCode MatSetUnfactored_MPIAIJ(Mat A)
2012 {
2013   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2014   PetscErrorCode ierr;
2015 
2016   PetscFunctionBegin;
2017   ierr = MatSetUnfactored(a->A);CHKERRQ(ierr);
2018   PetscFunctionReturn(0);
2019 }
2020 
2021 PetscErrorCode MatEqual_MPIAIJ(Mat A,Mat B,PetscBool  *flag)
2022 {
2023   Mat_MPIAIJ     *matB = (Mat_MPIAIJ*)B->data,*matA = (Mat_MPIAIJ*)A->data;
2024   Mat            a,b,c,d;
2025   PetscBool      flg;
2026   PetscErrorCode ierr;
2027 
2028   PetscFunctionBegin;
2029   a = matA->A; b = matA->B;
2030   c = matB->A; d = matB->B;
2031 
2032   ierr = MatEqual(a,c,&flg);CHKERRQ(ierr);
2033   if (flg) {
2034     ierr = MatEqual(b,d,&flg);CHKERRQ(ierr);
2035   }
2036   ierr = MPIU_Allreduce(&flg,flag,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
2037   PetscFunctionReturn(0);
2038 }
2039 
2040 PetscErrorCode MatCopy_MPIAIJ(Mat A,Mat B,MatStructure str)
2041 {
2042   PetscErrorCode ierr;
2043   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2044   Mat_MPIAIJ     *b = (Mat_MPIAIJ*)B->data;
2045 
2046   PetscFunctionBegin;
2047   /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
2048   if ((str != SAME_NONZERO_PATTERN) || (A->ops->copy != B->ops->copy)) {
2049     /* because of the column compression in the off-processor part of the matrix a->B,
2050        the number of columns in a->B and b->B may be different, hence we cannot call
2051        the MatCopy() directly on the two parts. If need be, we can provide a more
2052        efficient copy than the MatCopy_Basic() by first uncompressing the a->B matrices
2053        then copying the submatrices */
2054     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
2055   } else {
2056     ierr = MatCopy(a->A,b->A,str);CHKERRQ(ierr);
2057     ierr = MatCopy(a->B,b->B,str);CHKERRQ(ierr);
2058   }
2059   PetscFunctionReturn(0);
2060 }
2061 
2062 PetscErrorCode MatSetUp_MPIAIJ(Mat A)
2063 {
2064   PetscErrorCode ierr;
2065 
2066   PetscFunctionBegin;
2067   ierr =  MatMPIAIJSetPreallocation(A,PETSC_DEFAULT,0,PETSC_DEFAULT,0);CHKERRQ(ierr);
2068   PetscFunctionReturn(0);
2069 }
2070 
2071 /*
2072    Computes the number of nonzeros per row needed for preallocation when X and Y
2073    have different nonzero structure.
2074 */
2075 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)
2076 {
2077   PetscInt       i,j,k,nzx,nzy;
2078 
2079   PetscFunctionBegin;
2080   /* Set the number of nonzeros in the new matrix */
2081   for (i=0; i<m; i++) {
2082     const PetscInt *xjj = xj+xi[i],*yjj = yj+yi[i];
2083     nzx = xi[i+1] - xi[i];
2084     nzy = yi[i+1] - yi[i];
2085     nnz[i] = 0;
2086     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2087       for (; k<nzy && yltog[yjj[k]]<xltog[xjj[j]]; k++) nnz[i]++; /* Catch up to X */
2088       if (k<nzy && yltog[yjj[k]]==xltog[xjj[j]]) k++;             /* Skip duplicate */
2089       nnz[i]++;
2090     }
2091     for (; k<nzy; k++) nnz[i]++;
2092   }
2093   PetscFunctionReturn(0);
2094 }
2095 
2096 /* This is the same as MatAXPYGetPreallocation_SeqAIJ, except that the local-to-global map is provided */
2097 static PetscErrorCode MatAXPYGetPreallocation_MPIAIJ(Mat Y,const PetscInt *yltog,Mat X,const PetscInt *xltog,PetscInt *nnz)
2098 {
2099   PetscErrorCode ierr;
2100   PetscInt       m = Y->rmap->N;
2101   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data;
2102   Mat_SeqAIJ     *y = (Mat_SeqAIJ*)Y->data;
2103 
2104   PetscFunctionBegin;
2105   ierr = MatAXPYGetPreallocation_MPIX_private(m,x->i,x->j,xltog,y->i,y->j,yltog,nnz);CHKERRQ(ierr);
2106   PetscFunctionReturn(0);
2107 }
2108 
2109 PetscErrorCode MatAXPY_MPIAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
2110 {
2111   PetscErrorCode ierr;
2112   Mat_MPIAIJ     *xx = (Mat_MPIAIJ*)X->data,*yy = (Mat_MPIAIJ*)Y->data;
2113   PetscBLASInt   bnz,one=1;
2114   Mat_SeqAIJ     *x,*y;
2115 
2116   PetscFunctionBegin;
2117   if (str == SAME_NONZERO_PATTERN) {
2118     PetscScalar alpha = a;
2119     x    = (Mat_SeqAIJ*)xx->A->data;
2120     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2121     y    = (Mat_SeqAIJ*)yy->A->data;
2122     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2123     x    = (Mat_SeqAIJ*)xx->B->data;
2124     y    = (Mat_SeqAIJ*)yy->B->data;
2125     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2126     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2127     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
2128   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
2129     ierr = MatAXPY_Basic(Y,a,X,str);CHKERRQ(ierr);
2130   } else {
2131     Mat      B;
2132     PetscInt *nnz_d,*nnz_o;
2133     ierr = PetscMalloc1(yy->A->rmap->N,&nnz_d);CHKERRQ(ierr);
2134     ierr = PetscMalloc1(yy->B->rmap->N,&nnz_o);CHKERRQ(ierr);
2135     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
2136     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
2137     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
2138     ierr = MatSetBlockSizesFromMats(B,Y,Y);CHKERRQ(ierr);
2139     ierr = MatSetType(B,MATMPIAIJ);CHKERRQ(ierr);
2140     ierr = MatAXPYGetPreallocation_SeqAIJ(yy->A,xx->A,nnz_d);CHKERRQ(ierr);
2141     ierr = MatAXPYGetPreallocation_MPIAIJ(yy->B,yy->garray,xx->B,xx->garray,nnz_o);CHKERRQ(ierr);
2142     ierr = MatMPIAIJSetPreallocation(B,0,nnz_d,0,nnz_o);CHKERRQ(ierr);
2143     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
2144     ierr = MatHeaderReplace(Y,&B);CHKERRQ(ierr);
2145     ierr = PetscFree(nnz_d);CHKERRQ(ierr);
2146     ierr = PetscFree(nnz_o);CHKERRQ(ierr);
2147   }
2148   PetscFunctionReturn(0);
2149 }
2150 
2151 extern PetscErrorCode  MatConjugate_SeqAIJ(Mat);
2152 
2153 PetscErrorCode  MatConjugate_MPIAIJ(Mat mat)
2154 {
2155 #if defined(PETSC_USE_COMPLEX)
2156   PetscErrorCode ierr;
2157   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2158 
2159   PetscFunctionBegin;
2160   ierr = MatConjugate_SeqAIJ(aij->A);CHKERRQ(ierr);
2161   ierr = MatConjugate_SeqAIJ(aij->B);CHKERRQ(ierr);
2162 #else
2163   PetscFunctionBegin;
2164 #endif
2165   PetscFunctionReturn(0);
2166 }
2167 
2168 PetscErrorCode MatRealPart_MPIAIJ(Mat A)
2169 {
2170   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2171   PetscErrorCode ierr;
2172 
2173   PetscFunctionBegin;
2174   ierr = MatRealPart(a->A);CHKERRQ(ierr);
2175   ierr = MatRealPart(a->B);CHKERRQ(ierr);
2176   PetscFunctionReturn(0);
2177 }
2178 
2179 PetscErrorCode MatImaginaryPart_MPIAIJ(Mat A)
2180 {
2181   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2182   PetscErrorCode ierr;
2183 
2184   PetscFunctionBegin;
2185   ierr = MatImaginaryPart(a->A);CHKERRQ(ierr);
2186   ierr = MatImaginaryPart(a->B);CHKERRQ(ierr);
2187   PetscFunctionReturn(0);
2188 }
2189 
2190 PetscErrorCode MatGetRowMaxAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2191 {
2192   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2193   PetscErrorCode ierr;
2194   PetscInt       i,*idxb = 0;
2195   PetscScalar    *va,*vb;
2196   Vec            vtmp;
2197 
2198   PetscFunctionBegin;
2199   ierr = MatGetRowMaxAbs(a->A,v,idx);CHKERRQ(ierr);
2200   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2201   if (idx) {
2202     for (i=0; i<A->rmap->n; i++) {
2203       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2204     }
2205   }
2206 
2207   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2208   if (idx) {
2209     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2210   }
2211   ierr = MatGetRowMaxAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2212   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2213 
2214   for (i=0; i<A->rmap->n; i++) {
2215     if (PetscAbsScalar(va[i]) < PetscAbsScalar(vb[i])) {
2216       va[i] = vb[i];
2217       if (idx) idx[i] = a->garray[idxb[i]];
2218     }
2219   }
2220 
2221   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2222   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2223   ierr = PetscFree(idxb);CHKERRQ(ierr);
2224   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2225   PetscFunctionReturn(0);
2226 }
2227 
2228 PetscErrorCode MatGetRowMinAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2229 {
2230   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2231   PetscErrorCode ierr;
2232   PetscInt       i,*idxb = 0;
2233   PetscScalar    *va,*vb;
2234   Vec            vtmp;
2235 
2236   PetscFunctionBegin;
2237   ierr = MatGetRowMinAbs(a->A,v,idx);CHKERRQ(ierr);
2238   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2239   if (idx) {
2240     for (i=0; i<A->cmap->n; i++) {
2241       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2242     }
2243   }
2244 
2245   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2246   if (idx) {
2247     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2248   }
2249   ierr = MatGetRowMinAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2250   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2251 
2252   for (i=0; i<A->rmap->n; i++) {
2253     if (PetscAbsScalar(va[i]) > PetscAbsScalar(vb[i])) {
2254       va[i] = vb[i];
2255       if (idx) idx[i] = a->garray[idxb[i]];
2256     }
2257   }
2258 
2259   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2260   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2261   ierr = PetscFree(idxb);CHKERRQ(ierr);
2262   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2263   PetscFunctionReturn(0);
2264 }
2265 
2266 PetscErrorCode MatGetRowMin_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2267 {
2268   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2269   PetscInt       n      = A->rmap->n;
2270   PetscInt       cstart = A->cmap->rstart;
2271   PetscInt       *cmap  = mat->garray;
2272   PetscInt       *diagIdx, *offdiagIdx;
2273   Vec            diagV, offdiagV;
2274   PetscScalar    *a, *diagA, *offdiagA;
2275   PetscInt       r;
2276   PetscErrorCode ierr;
2277 
2278   PetscFunctionBegin;
2279   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2280   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &diagV);CHKERRQ(ierr);
2281   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &offdiagV);CHKERRQ(ierr);
2282   ierr = MatGetRowMin(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2283   ierr = MatGetRowMin(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2284   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2285   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2286   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2287   for (r = 0; r < n; ++r) {
2288     if (PetscAbsScalar(diagA[r]) <= PetscAbsScalar(offdiagA[r])) {
2289       a[r]   = diagA[r];
2290       idx[r] = cstart + diagIdx[r];
2291     } else {
2292       a[r]   = offdiagA[r];
2293       idx[r] = cmap[offdiagIdx[r]];
2294     }
2295   }
2296   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2297   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2298   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2299   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2300   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2301   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2302   PetscFunctionReturn(0);
2303 }
2304 
2305 PetscErrorCode MatGetRowMax_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2306 {
2307   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2308   PetscInt       n      = A->rmap->n;
2309   PetscInt       cstart = A->cmap->rstart;
2310   PetscInt       *cmap  = mat->garray;
2311   PetscInt       *diagIdx, *offdiagIdx;
2312   Vec            diagV, offdiagV;
2313   PetscScalar    *a, *diagA, *offdiagA;
2314   PetscInt       r;
2315   PetscErrorCode ierr;
2316 
2317   PetscFunctionBegin;
2318   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2319   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &diagV);CHKERRQ(ierr);
2320   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &offdiagV);CHKERRQ(ierr);
2321   ierr = MatGetRowMax(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2322   ierr = MatGetRowMax(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2323   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2324   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2325   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2326   for (r = 0; r < n; ++r) {
2327     if (PetscAbsScalar(diagA[r]) >= PetscAbsScalar(offdiagA[r])) {
2328       a[r]   = diagA[r];
2329       idx[r] = cstart + diagIdx[r];
2330     } else {
2331       a[r]   = offdiagA[r];
2332       idx[r] = cmap[offdiagIdx[r]];
2333     }
2334   }
2335   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2336   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2337   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2338   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2339   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2340   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2341   PetscFunctionReturn(0);
2342 }
2343 
2344 PetscErrorCode MatGetSeqNonzeroStructure_MPIAIJ(Mat mat,Mat *newmat)
2345 {
2346   PetscErrorCode ierr;
2347   Mat            *dummy;
2348 
2349   PetscFunctionBegin;
2350   ierr    = MatCreateSubMatrix_MPIAIJ_All(mat,MAT_DO_NOT_GET_VALUES,MAT_INITIAL_MATRIX,&dummy);CHKERRQ(ierr);
2351   *newmat = *dummy;
2352   ierr    = PetscFree(dummy);CHKERRQ(ierr);
2353   PetscFunctionReturn(0);
2354 }
2355 
2356 PetscErrorCode  MatInvertBlockDiagonal_MPIAIJ(Mat A,const PetscScalar **values)
2357 {
2358   Mat_MPIAIJ     *a = (Mat_MPIAIJ*) A->data;
2359   PetscErrorCode ierr;
2360 
2361   PetscFunctionBegin;
2362   ierr = MatInvertBlockDiagonal(a->A,values);CHKERRQ(ierr);
2363   A->factorerrortype = a->A->factorerrortype;
2364   PetscFunctionReturn(0);
2365 }
2366 
2367 static PetscErrorCode  MatSetRandom_MPIAIJ(Mat x,PetscRandom rctx)
2368 {
2369   PetscErrorCode ierr;
2370   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)x->data;
2371 
2372   PetscFunctionBegin;
2373   ierr = MatSetRandom(aij->A,rctx);CHKERRQ(ierr);
2374   ierr = MatSetRandom(aij->B,rctx);CHKERRQ(ierr);
2375   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2376   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2377   PetscFunctionReturn(0);
2378 }
2379 
2380 PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ(Mat A,PetscBool sc)
2381 {
2382   PetscFunctionBegin;
2383   if (sc) A->ops->increaseoverlap = MatIncreaseOverlap_MPIAIJ_Scalable;
2384   else A->ops->increaseoverlap    = MatIncreaseOverlap_MPIAIJ;
2385   PetscFunctionReturn(0);
2386 }
2387 
2388 /*@
2389    MatMPIAIJSetUseScalableIncreaseOverlap - Determine if the matrix uses a scalable algorithm to compute the overlap
2390 
2391    Collective on Mat
2392 
2393    Input Parameters:
2394 +    A - the matrix
2395 -    sc - PETSC_TRUE indicates use the scalable algorithm (default is not to use the scalable algorithm)
2396 
2397  Level: advanced
2398 
2399 @*/
2400 PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap(Mat A,PetscBool sc)
2401 {
2402   PetscErrorCode       ierr;
2403 
2404   PetscFunctionBegin;
2405   ierr = PetscTryMethod(A,"MatMPIAIJSetUseScalableIncreaseOverlap_C",(Mat,PetscBool),(A,sc));CHKERRQ(ierr);
2406   PetscFunctionReturn(0);
2407 }
2408 
2409 PetscErrorCode MatSetFromOptions_MPIAIJ(PetscOptionItems *PetscOptionsObject,Mat A)
2410 {
2411   PetscErrorCode       ierr;
2412   PetscBool            sc = PETSC_FALSE,flg;
2413 
2414   PetscFunctionBegin;
2415   ierr = PetscOptionsHead(PetscOptionsObject,"MPIAIJ options");CHKERRQ(ierr);
2416   ierr = PetscObjectOptionsBegin((PetscObject)A);
2417     if (A->ops->increaseoverlap == MatIncreaseOverlap_MPIAIJ_Scalable) sc = PETSC_TRUE;
2418     ierr = PetscOptionsBool("-mat_increase_overlap_scalable","Use a scalable algorithm to compute the overlap","MatIncreaseOverlap",sc,&sc,&flg);CHKERRQ(ierr);
2419     if (flg) {
2420       ierr = MatMPIAIJSetUseScalableIncreaseOverlap(A,sc);CHKERRQ(ierr);
2421     }
2422   ierr = PetscOptionsEnd();CHKERRQ(ierr);
2423   PetscFunctionReturn(0);
2424 }
2425 
2426 PetscErrorCode MatShift_MPIAIJ(Mat Y,PetscScalar a)
2427 {
2428   PetscErrorCode ierr;
2429   Mat_MPIAIJ     *maij = (Mat_MPIAIJ*)Y->data;
2430   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)maij->A->data;
2431 
2432   PetscFunctionBegin;
2433   if (!Y->preallocated) {
2434     ierr = MatMPIAIJSetPreallocation(Y,1,NULL,0,NULL);CHKERRQ(ierr);
2435   } else if (!aij->nz) {
2436     PetscInt nonew = aij->nonew;
2437     ierr = MatSeqAIJSetPreallocation(maij->A,1,NULL);CHKERRQ(ierr);
2438     aij->nonew = nonew;
2439   }
2440   ierr = MatShift_Basic(Y,a);CHKERRQ(ierr);
2441   PetscFunctionReturn(0);
2442 }
2443 
2444 PetscErrorCode MatMissingDiagonal_MPIAIJ(Mat A,PetscBool  *missing,PetscInt *d)
2445 {
2446   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2447   PetscErrorCode ierr;
2448 
2449   PetscFunctionBegin;
2450   if (A->rmap->n != A->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only works for square matrices");
2451   ierr = MatMissingDiagonal(a->A,missing,d);CHKERRQ(ierr);
2452   if (d) {
2453     PetscInt rstart;
2454     ierr = MatGetOwnershipRange(A,&rstart,NULL);CHKERRQ(ierr);
2455     *d += rstart;
2456 
2457   }
2458   PetscFunctionReturn(0);
2459 }
2460 
2461 
2462 /* -------------------------------------------------------------------*/
2463 static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
2464                                        MatGetRow_MPIAIJ,
2465                                        MatRestoreRow_MPIAIJ,
2466                                        MatMult_MPIAIJ,
2467                                 /* 4*/ MatMultAdd_MPIAIJ,
2468                                        MatMultTranspose_MPIAIJ,
2469                                        MatMultTransposeAdd_MPIAIJ,
2470                                        0,
2471                                        0,
2472                                        0,
2473                                 /*10*/ 0,
2474                                        0,
2475                                        0,
2476                                        MatSOR_MPIAIJ,
2477                                        MatTranspose_MPIAIJ,
2478                                 /*15*/ MatGetInfo_MPIAIJ,
2479                                        MatEqual_MPIAIJ,
2480                                        MatGetDiagonal_MPIAIJ,
2481                                        MatDiagonalScale_MPIAIJ,
2482                                        MatNorm_MPIAIJ,
2483                                 /*20*/ MatAssemblyBegin_MPIAIJ,
2484                                        MatAssemblyEnd_MPIAIJ,
2485                                        MatSetOption_MPIAIJ,
2486                                        MatZeroEntries_MPIAIJ,
2487                                 /*24*/ MatZeroRows_MPIAIJ,
2488                                        0,
2489                                        0,
2490                                        0,
2491                                        0,
2492                                 /*29*/ MatSetUp_MPIAIJ,
2493                                        0,
2494                                        0,
2495                                        MatGetDiagonalBlock_MPIAIJ,
2496                                        0,
2497                                 /*34*/ MatDuplicate_MPIAIJ,
2498                                        0,
2499                                        0,
2500                                        0,
2501                                        0,
2502                                 /*39*/ MatAXPY_MPIAIJ,
2503                                        MatCreateSubMatrices_MPIAIJ,
2504                                        MatIncreaseOverlap_MPIAIJ,
2505                                        MatGetValues_MPIAIJ,
2506                                        MatCopy_MPIAIJ,
2507                                 /*44*/ MatGetRowMax_MPIAIJ,
2508                                        MatScale_MPIAIJ,
2509                                        MatShift_MPIAIJ,
2510                                        MatDiagonalSet_MPIAIJ,
2511                                        MatZeroRowsColumns_MPIAIJ,
2512                                 /*49*/ MatSetRandom_MPIAIJ,
2513                                        0,
2514                                        0,
2515                                        0,
2516                                        0,
2517                                 /*54*/ MatFDColoringCreate_MPIXAIJ,
2518                                        0,
2519                                        MatSetUnfactored_MPIAIJ,
2520                                        MatPermute_MPIAIJ,
2521                                        0,
2522                                 /*59*/ MatCreateSubMatrix_MPIAIJ,
2523                                        MatDestroy_MPIAIJ,
2524                                        MatView_MPIAIJ,
2525                                        0,
2526                                        MatMatMatMult_MPIAIJ_MPIAIJ_MPIAIJ,
2527                                 /*64*/ MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ,
2528                                        MatMatMatMultNumeric_MPIAIJ_MPIAIJ_MPIAIJ,
2529                                        0,
2530                                        0,
2531                                        0,
2532                                 /*69*/ MatGetRowMaxAbs_MPIAIJ,
2533                                        MatGetRowMinAbs_MPIAIJ,
2534                                        0,
2535                                        0,
2536                                        0,
2537                                        0,
2538                                 /*75*/ MatFDColoringApply_AIJ,
2539                                        MatSetFromOptions_MPIAIJ,
2540                                        0,
2541                                        0,
2542                                        MatFindZeroDiagonals_MPIAIJ,
2543                                 /*80*/ 0,
2544                                        0,
2545                                        0,
2546                                 /*83*/ MatLoad_MPIAIJ,
2547                                        0,
2548                                        0,
2549                                        0,
2550                                        0,
2551                                        0,
2552                                 /*89*/ MatMatMult_MPIAIJ_MPIAIJ,
2553                                        MatMatMultSymbolic_MPIAIJ_MPIAIJ,
2554                                        MatMatMultNumeric_MPIAIJ_MPIAIJ,
2555                                        MatPtAP_MPIAIJ_MPIAIJ,
2556                                        MatPtAPSymbolic_MPIAIJ_MPIAIJ,
2557                                 /*94*/ MatPtAPNumeric_MPIAIJ_MPIAIJ,
2558                                        0,
2559                                        0,
2560                                        0,
2561                                        0,
2562                                 /*99*/ 0,
2563                                        0,
2564                                        0,
2565                                        MatConjugate_MPIAIJ,
2566                                        0,
2567                                 /*104*/MatSetValuesRow_MPIAIJ,
2568                                        MatRealPart_MPIAIJ,
2569                                        MatImaginaryPart_MPIAIJ,
2570                                        0,
2571                                        0,
2572                                 /*109*/0,
2573                                        0,
2574                                        MatGetRowMin_MPIAIJ,
2575                                        0,
2576                                        MatMissingDiagonal_MPIAIJ,
2577                                 /*114*/MatGetSeqNonzeroStructure_MPIAIJ,
2578                                        0,
2579                                        MatGetGhosts_MPIAIJ,
2580                                        0,
2581                                        0,
2582                                 /*119*/0,
2583                                        0,
2584                                        0,
2585                                        0,
2586                                        MatGetMultiProcBlock_MPIAIJ,
2587                                 /*124*/MatFindNonzeroRows_MPIAIJ,
2588                                        MatGetColumnNorms_MPIAIJ,
2589                                        MatInvertBlockDiagonal_MPIAIJ,
2590                                        0,
2591                                        MatCreateSubMatricesMPI_MPIAIJ,
2592                                 /*129*/0,
2593                                        MatTransposeMatMult_MPIAIJ_MPIAIJ,
2594                                        MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ,
2595                                        MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ,
2596                                        0,
2597                                 /*134*/0,
2598                                        0,
2599                                        0,
2600                                        0,
2601                                        0,
2602                                 /*139*/MatSetBlockSizes_MPIAIJ,
2603                                        0,
2604                                        0,
2605                                        MatFDColoringSetUp_MPIXAIJ,
2606                                        MatFindOffBlockDiagonalEntries_MPIAIJ,
2607                                 /*144*/MatCreateMPIMatConcatenateSeqMat_MPIAIJ
2608 };
2609 
2610 /* ----------------------------------------------------------------------------------------*/
2611 
2612 PetscErrorCode  MatStoreValues_MPIAIJ(Mat mat)
2613 {
2614   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2615   PetscErrorCode ierr;
2616 
2617   PetscFunctionBegin;
2618   ierr = MatStoreValues(aij->A);CHKERRQ(ierr);
2619   ierr = MatStoreValues(aij->B);CHKERRQ(ierr);
2620   PetscFunctionReturn(0);
2621 }
2622 
2623 PetscErrorCode  MatRetrieveValues_MPIAIJ(Mat mat)
2624 {
2625   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2626   PetscErrorCode ierr;
2627 
2628   PetscFunctionBegin;
2629   ierr = MatRetrieveValues(aij->A);CHKERRQ(ierr);
2630   ierr = MatRetrieveValues(aij->B);CHKERRQ(ierr);
2631   PetscFunctionReturn(0);
2632 }
2633 
2634 PetscErrorCode  MatMPIAIJSetPreallocation_MPIAIJ(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
2635 {
2636   Mat_MPIAIJ     *b;
2637   PetscErrorCode ierr;
2638 
2639   PetscFunctionBegin;
2640   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
2641   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
2642   b = (Mat_MPIAIJ*)B->data;
2643 
2644 #if defined(PETSC_USE_CTABLE)
2645   ierr = PetscTableDestroy(&b->colmap);CHKERRQ(ierr);
2646 #else
2647   ierr = PetscFree(b->colmap);CHKERRQ(ierr);
2648 #endif
2649   ierr = PetscFree(b->garray);CHKERRQ(ierr);
2650   ierr = VecDestroy(&b->lvec);CHKERRQ(ierr);
2651   ierr = VecScatterDestroy(&b->Mvctx);CHKERRQ(ierr);
2652 
2653   /* Because the B will have been resized we simply destroy it and create a new one each time */
2654   ierr = MatDestroy(&b->B);CHKERRQ(ierr);
2655   ierr = MatCreate(PETSC_COMM_SELF,&b->B);CHKERRQ(ierr);
2656   ierr = MatSetSizes(b->B,B->rmap->n,B->cmap->N,B->rmap->n,B->cmap->N);CHKERRQ(ierr);
2657   ierr = MatSetBlockSizesFromMats(b->B,B,B);CHKERRQ(ierr);
2658   ierr = MatSetType(b->B,MATSEQAIJ);CHKERRQ(ierr);
2659   ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->B);CHKERRQ(ierr);
2660 
2661   if (!B->preallocated) {
2662     ierr = MatCreate(PETSC_COMM_SELF,&b->A);CHKERRQ(ierr);
2663     ierr = MatSetSizes(b->A,B->rmap->n,B->cmap->n,B->rmap->n,B->cmap->n);CHKERRQ(ierr);
2664     ierr = MatSetBlockSizesFromMats(b->A,B,B);CHKERRQ(ierr);
2665     ierr = MatSetType(b->A,MATSEQAIJ);CHKERRQ(ierr);
2666     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->A);CHKERRQ(ierr);
2667   }
2668 
2669   ierr = MatSeqAIJSetPreallocation(b->A,d_nz,d_nnz);CHKERRQ(ierr);
2670   ierr = MatSeqAIJSetPreallocation(b->B,o_nz,o_nnz);CHKERRQ(ierr);
2671   B->preallocated  = PETSC_TRUE;
2672   B->was_assembled = PETSC_FALSE;
2673   B->assembled     = PETSC_FALSE;;
2674   PetscFunctionReturn(0);
2675 }
2676 
2677 PetscErrorCode MatDuplicate_MPIAIJ(Mat matin,MatDuplicateOption cpvalues,Mat *newmat)
2678 {
2679   Mat            mat;
2680   Mat_MPIAIJ     *a,*oldmat = (Mat_MPIAIJ*)matin->data;
2681   PetscErrorCode ierr;
2682 
2683   PetscFunctionBegin;
2684   *newmat = 0;
2685   ierr    = MatCreate(PetscObjectComm((PetscObject)matin),&mat);CHKERRQ(ierr);
2686   ierr    = MatSetSizes(mat,matin->rmap->n,matin->cmap->n,matin->rmap->N,matin->cmap->N);CHKERRQ(ierr);
2687   ierr    = MatSetBlockSizesFromMats(mat,matin,matin);CHKERRQ(ierr);
2688   ierr    = MatSetType(mat,((PetscObject)matin)->type_name);CHKERRQ(ierr);
2689   ierr    = PetscMemcpy(mat->ops,matin->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
2690   a       = (Mat_MPIAIJ*)mat->data;
2691 
2692   mat->factortype   = matin->factortype;
2693   mat->assembled    = PETSC_TRUE;
2694   mat->insertmode   = NOT_SET_VALUES;
2695   mat->preallocated = PETSC_TRUE;
2696 
2697   a->size         = oldmat->size;
2698   a->rank         = oldmat->rank;
2699   a->donotstash   = oldmat->donotstash;
2700   a->roworiented  = oldmat->roworiented;
2701   a->rowindices   = 0;
2702   a->rowvalues    = 0;
2703   a->getrowactive = PETSC_FALSE;
2704 
2705   ierr = PetscLayoutReference(matin->rmap,&mat->rmap);CHKERRQ(ierr);
2706   ierr = PetscLayoutReference(matin->cmap,&mat->cmap);CHKERRQ(ierr);
2707 
2708   if (oldmat->colmap) {
2709 #if defined(PETSC_USE_CTABLE)
2710     ierr = PetscTableCreateCopy(oldmat->colmap,&a->colmap);CHKERRQ(ierr);
2711 #else
2712     ierr = PetscMalloc1(mat->cmap->N,&a->colmap);CHKERRQ(ierr);
2713     ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2714     ierr = PetscMemcpy(a->colmap,oldmat->colmap,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2715 #endif
2716   } else a->colmap = 0;
2717   if (oldmat->garray) {
2718     PetscInt len;
2719     len  = oldmat->B->cmap->n;
2720     ierr = PetscMalloc1(len+1,&a->garray);CHKERRQ(ierr);
2721     ierr = PetscLogObjectMemory((PetscObject)mat,len*sizeof(PetscInt));CHKERRQ(ierr);
2722     if (len) { ierr = PetscMemcpy(a->garray,oldmat->garray,len*sizeof(PetscInt));CHKERRQ(ierr); }
2723   } else a->garray = 0;
2724 
2725   ierr    = VecDuplicate(oldmat->lvec,&a->lvec);CHKERRQ(ierr);
2726   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->lvec);CHKERRQ(ierr);
2727   ierr    = VecScatterCopy(oldmat->Mvctx,&a->Mvctx);CHKERRQ(ierr);
2728   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->Mvctx);CHKERRQ(ierr);
2729   ierr    = MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
2730   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->A);CHKERRQ(ierr);
2731   ierr    = MatDuplicate(oldmat->B,cpvalues,&a->B);CHKERRQ(ierr);
2732   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->B);CHKERRQ(ierr);
2733   ierr    = PetscFunctionListDuplicate(((PetscObject)matin)->qlist,&((PetscObject)mat)->qlist);CHKERRQ(ierr);
2734   *newmat = mat;
2735   PetscFunctionReturn(0);
2736 }
2737 
2738 
2739 
2740 PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
2741 {
2742   PetscScalar    *vals,*svals;
2743   MPI_Comm       comm;
2744   PetscErrorCode ierr;
2745   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
2746   PetscInt       i,nz,j,rstart,rend,mmax,maxnz = 0;
2747   PetscInt       header[4],*rowlengths = 0,M,N,m,*cols;
2748   PetscInt       *ourlens = NULL,*procsnz = NULL,*offlens = NULL,jj,*mycols,*smycols;
2749   PetscInt       cend,cstart,n,*rowners;
2750   int            fd;
2751   PetscInt       bs = newMat->rmap->bs;
2752 
2753   PetscFunctionBegin;
2754   /* force binary viewer to load .info file if it has not yet done so */
2755   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
2756   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
2757   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2758   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2759   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
2760   if (!rank) {
2761     ierr = PetscBinaryRead(fd,(char*)header,4,PETSC_INT);CHKERRQ(ierr);
2762     if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
2763     if (header[3] < 0) SETERRQ(PetscObjectComm((PetscObject)newMat),PETSC_ERR_FILE_UNEXPECTED,"Matrix stored in special format on disk,cannot load as MATMPIAIJ");
2764   }
2765 
2766   ierr = PetscOptionsBegin(comm,NULL,"Options for loading MATMPIAIJ matrix","Mat");CHKERRQ(ierr);
2767   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
2768   ierr = PetscOptionsEnd();CHKERRQ(ierr);
2769   if (bs < 0) bs = 1;
2770 
2771   ierr = MPI_Bcast(header+1,3,MPIU_INT,0,comm);CHKERRQ(ierr);
2772   M    = header[1]; N = header[2];
2773 
2774   /* If global sizes are set, check if they are consistent with that given in the file */
2775   if (newMat->rmap->N >= 0 && newMat->rmap->N != M) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Inconsistent # of rows:Matrix in file has (%D) and input matrix has (%D)",newMat->rmap->N,M);
2776   if (newMat->cmap->N >=0 && newMat->cmap->N != N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Inconsistent # of cols:Matrix in file has (%D) and input matrix has (%D)",newMat->cmap->N,N);
2777 
2778   /* determine ownership of all (block) rows */
2779   if (M%bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Inconsistent # of rows (%d) and block size (%d)",M,bs);
2780   if (newMat->rmap->n < 0) m = bs*((M/bs)/size + (((M/bs) % size) > rank));    /* PETSC_DECIDE */
2781   else m = newMat->rmap->n; /* Set by user */
2782 
2783   ierr = PetscMalloc1(size+1,&rowners);CHKERRQ(ierr);
2784   ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
2785 
2786   /* First process needs enough room for process with most rows */
2787   if (!rank) {
2788     mmax = rowners[1];
2789     for (i=2; i<=size; i++) {
2790       mmax = PetscMax(mmax, rowners[i]);
2791     }
2792   } else mmax = -1;             /* unused, but compilers complain */
2793 
2794   rowners[0] = 0;
2795   for (i=2; i<=size; i++) {
2796     rowners[i] += rowners[i-1];
2797   }
2798   rstart = rowners[rank];
2799   rend   = rowners[rank+1];
2800 
2801   /* distribute row lengths to all processors */
2802   ierr = PetscMalloc2(m,&ourlens,m,&offlens);CHKERRQ(ierr);
2803   if (!rank) {
2804     ierr = PetscBinaryRead(fd,ourlens,m,PETSC_INT);CHKERRQ(ierr);
2805     ierr = PetscMalloc1(mmax,&rowlengths);CHKERRQ(ierr);
2806     ierr = PetscCalloc1(size,&procsnz);CHKERRQ(ierr);
2807     for (j=0; j<m; j++) {
2808       procsnz[0] += ourlens[j];
2809     }
2810     for (i=1; i<size; i++) {
2811       ierr = PetscBinaryRead(fd,rowlengths,rowners[i+1]-rowners[i],PETSC_INT);CHKERRQ(ierr);
2812       /* calculate the number of nonzeros on each processor */
2813       for (j=0; j<rowners[i+1]-rowners[i]; j++) {
2814         procsnz[i] += rowlengths[j];
2815       }
2816       ierr = MPIULong_Send(rowlengths,rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2817     }
2818     ierr = PetscFree(rowlengths);CHKERRQ(ierr);
2819   } else {
2820     ierr = MPIULong_Recv(ourlens,m,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2821   }
2822 
2823   if (!rank) {
2824     /* determine max buffer needed and allocate it */
2825     maxnz = 0;
2826     for (i=0; i<size; i++) {
2827       maxnz = PetscMax(maxnz,procsnz[i]);
2828     }
2829     ierr = PetscMalloc1(maxnz,&cols);CHKERRQ(ierr);
2830 
2831     /* read in my part of the matrix column indices  */
2832     nz   = procsnz[0];
2833     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2834     ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);
2835 
2836     /* read in every one elses and ship off */
2837     for (i=1; i<size; i++) {
2838       nz   = procsnz[i];
2839       ierr = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
2840       ierr = MPIULong_Send(cols,nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2841     }
2842     ierr = PetscFree(cols);CHKERRQ(ierr);
2843   } else {
2844     /* determine buffer space needed for message */
2845     nz = 0;
2846     for (i=0; i<m; i++) {
2847       nz += ourlens[i];
2848     }
2849     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2850 
2851     /* receive message of column indices*/
2852     ierr = MPIULong_Recv(mycols,nz,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2853   }
2854 
2855   /* determine column ownership if matrix is not square */
2856   if (N != M) {
2857     if (newMat->cmap->n < 0) n = N/size + ((N % size) > rank);
2858     else n = newMat->cmap->n;
2859     ierr   = MPI_Scan(&n,&cend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
2860     cstart = cend - n;
2861   } else {
2862     cstart = rstart;
2863     cend   = rend;
2864     n      = cend - cstart;
2865   }
2866 
2867   /* loop over local rows, determining number of off diagonal entries */
2868   ierr = PetscMemzero(offlens,m*sizeof(PetscInt));CHKERRQ(ierr);
2869   jj   = 0;
2870   for (i=0; i<m; i++) {
2871     for (j=0; j<ourlens[i]; j++) {
2872       if (mycols[jj] < cstart || mycols[jj] >= cend) offlens[i]++;
2873       jj++;
2874     }
2875   }
2876 
2877   for (i=0; i<m; i++) {
2878     ourlens[i] -= offlens[i];
2879   }
2880   ierr = MatSetSizes(newMat,m,n,M,N);CHKERRQ(ierr);
2881 
2882   if (bs > 1) {ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);}
2883 
2884   ierr = MatMPIAIJSetPreallocation(newMat,0,ourlens,0,offlens);CHKERRQ(ierr);
2885 
2886   for (i=0; i<m; i++) {
2887     ourlens[i] += offlens[i];
2888   }
2889 
2890   if (!rank) {
2891     ierr = PetscMalloc1(maxnz+1,&vals);CHKERRQ(ierr);
2892 
2893     /* read in my part of the matrix numerical values  */
2894     nz   = procsnz[0];
2895     ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
2896 
2897     /* insert into matrix */
2898     jj      = rstart;
2899     smycols = mycols;
2900     svals   = vals;
2901     for (i=0; i<m; i++) {
2902       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
2903       smycols += ourlens[i];
2904       svals   += ourlens[i];
2905       jj++;
2906     }
2907 
2908     /* read in other processors and ship out */
2909     for (i=1; i<size; i++) {
2910       nz   = procsnz[i];
2911       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
2912       ierr = MPIULong_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
2913     }
2914     ierr = PetscFree(procsnz);CHKERRQ(ierr);
2915   } else {
2916     /* receive numeric values */
2917     ierr = PetscMalloc1(nz+1,&vals);CHKERRQ(ierr);
2918 
2919     /* receive message of values*/
2920     ierr = MPIULong_Recv(vals,nz,MPIU_SCALAR,0,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
2921 
2922     /* insert into matrix */
2923     jj      = rstart;
2924     smycols = mycols;
2925     svals   = vals;
2926     for (i=0; i<m; i++) {
2927       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
2928       smycols += ourlens[i];
2929       svals   += ourlens[i];
2930       jj++;
2931     }
2932   }
2933   ierr = PetscFree2(ourlens,offlens);CHKERRQ(ierr);
2934   ierr = PetscFree(vals);CHKERRQ(ierr);
2935   ierr = PetscFree(mycols);CHKERRQ(ierr);
2936   ierr = PetscFree(rowners);CHKERRQ(ierr);
2937   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2938   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2939   PetscFunctionReturn(0);
2940 }
2941 
2942 /* TODO: Not scalable because of ISAllGather() unless getting all columns. */
2943 PetscErrorCode MatCreateSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
2944 {
2945   PetscErrorCode ierr;
2946   IS             iscol_local;
2947   PetscInt       csize;
2948 
2949   PetscFunctionBegin;
2950   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
2951   if (call == MAT_REUSE_MATRIX) {
2952     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
2953     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
2954   } else {
2955     /* check if we are grabbing all columns*/
2956     PetscBool    isstride;
2957     PetscMPIInt  lisstride = 0,gisstride;
2958     ierr = PetscObjectTypeCompare((PetscObject)iscol,ISSTRIDE,&isstride);CHKERRQ(ierr);
2959     if (isstride) {
2960       PetscInt  start,len,mstart,mlen;
2961       ierr = ISStrideGetInfo(iscol,&start,NULL);CHKERRQ(ierr);
2962       ierr = ISGetLocalSize(iscol,&len);CHKERRQ(ierr);
2963       ierr = MatGetOwnershipRangeColumn(mat,&mstart,&mlen);CHKERRQ(ierr);
2964       if (mstart == start && mlen-mstart == len) lisstride = 1;
2965     }
2966     ierr = MPIU_Allreduce(&lisstride,&gisstride,1,MPI_INT,MPI_MIN,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
2967     if (gisstride) {
2968       PetscInt N;
2969       ierr = MatGetSize(mat,NULL,&N);CHKERRQ(ierr);
2970       ierr = ISCreateStride(PetscObjectComm((PetscObject)mat),N,0,1,&iscol_local);CHKERRQ(ierr);
2971       ierr = ISSetIdentity(iscol_local);CHKERRQ(ierr);
2972       ierr = PetscInfo(mat,"Optimizing for obtaining all columns of the matrix; skipping ISAllGather()\n");CHKERRQ(ierr);
2973     } else {
2974       PetscInt cbs;
2975       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
2976       ierr = ISAllGather(iscol,&iscol_local);CHKERRQ(ierr);
2977       ierr = ISSetBlockSize(iscol_local,cbs);CHKERRQ(ierr);
2978     }
2979   }
2980   ierr = MatCreateSubMatrix_MPIAIJ_Private(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
2981   if (call == MAT_INITIAL_MATRIX) {
2982     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
2983     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
2984   }
2985   PetscFunctionReturn(0);
2986 }
2987 
2988 extern PetscErrorCode MatCreateSubMatrices_MPIAIJ_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,Mat*);
2989 /*
2990     Not great since it makes two copies of the submatrix, first an SeqAIJ
2991   in local and then by concatenating the local matrices the end result.
2992   Writing it directly would be much like MatCreateSubMatrices_MPIAIJ()
2993 
2994   Note: This requires a sequential iscol with all indices.
2995 */
2996 PetscErrorCode MatCreateSubMatrix_MPIAIJ_Private(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
2997 {
2998   PetscErrorCode ierr;
2999   PetscMPIInt    rank,size;
3000   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3001   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
3002   Mat            M,Mreuse;
3003   MatScalar      *vwork,*aa;
3004   MPI_Comm       comm;
3005   Mat_SeqAIJ     *aij;
3006 
3007   PetscFunctionBegin;
3008   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3009   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3010   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3011 
3012   if (call ==  MAT_REUSE_MATRIX) {
3013     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3014     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3015     ierr = MatCreateSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,&Mreuse);CHKERRQ(ierr);
3016   } else {
3017     ierr = MatCreateSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&Mreuse);CHKERRQ(ierr);
3018   }
3019 
3020   /*
3021       m - number of local rows
3022       n - number of columns (same on all processors)
3023       rstart - first row in new global matrix generated
3024   */
3025   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3026   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3027   if (call == MAT_INITIAL_MATRIX) {
3028     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3029     ii  = aij->i;
3030     jj  = aij->j;
3031 
3032     /*
3033         Determine the number of non-zeros in the diagonal and off-diagonal
3034         portions of the matrix in order to do correct preallocation
3035     */
3036 
3037     /* first get start and end of "diagonal" columns */
3038     if (csize == PETSC_DECIDE) {
3039       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3040       if (mglobal == n) { /* square matrix */
3041         nlocal = m;
3042       } else {
3043         nlocal = n/size + ((n % size) > rank);
3044       }
3045     } else {
3046       nlocal = csize;
3047     }
3048     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3049     rstart = rend - nlocal;
3050     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);
3051 
3052     /* next, compute all the lengths */
3053     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3054     olens = dlens + m;
3055     for (i=0; i<m; i++) {
3056       jend = ii[i+1] - ii[i];
3057       olen = 0;
3058       dlen = 0;
3059       for (j=0; j<jend; j++) {
3060         if (*jj < rstart || *jj >= rend) olen++;
3061         else dlen++;
3062         jj++;
3063       }
3064       olens[i] = olen;
3065       dlens[i] = dlen;
3066     }
3067     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3068     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3069     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3070     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3071     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3072     ierr = PetscFree(dlens);CHKERRQ(ierr);
3073   } else {
3074     PetscInt ml,nl;
3075 
3076     M    = *newmat;
3077     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3078     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3079     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3080     /*
3081          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3082        rather than the slower MatSetValues().
3083     */
3084     M->was_assembled = PETSC_TRUE;
3085     M->assembled     = PETSC_FALSE;
3086   }
3087   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3088   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3089   ii   = aij->i;
3090   jj   = aij->j;
3091   aa   = aij->a;
3092   for (i=0; i<m; i++) {
3093     row   = rstart + i;
3094     nz    = ii[i+1] - ii[i];
3095     cwork = jj;     jj += nz;
3096     vwork = aa;     aa += nz;
3097     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3098   }
3099 
3100   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3101   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3102   *newmat = M;
3103 
3104   /* save submatrix used in processor for next request */
3105   if (call ==  MAT_INITIAL_MATRIX) {
3106     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3107     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3108   }
3109   PetscFunctionReturn(0);
3110 }
3111 
3112 PetscErrorCode  MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3113 {
3114   PetscInt       m,cstart, cend,j,nnz,i,d;
3115   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3116   const PetscInt *JJ;
3117   PetscScalar    *values;
3118   PetscErrorCode ierr;
3119   PetscBool      nooffprocentries;
3120 
3121   PetscFunctionBegin;
3122   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3123 
3124   ierr   = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3125   ierr   = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3126   m      = B->rmap->n;
3127   cstart = B->cmap->rstart;
3128   cend   = B->cmap->rend;
3129   rstart = B->rmap->rstart;
3130 
3131   ierr = PetscMalloc2(m,&d_nnz,m,&o_nnz);CHKERRQ(ierr);
3132 
3133 #if defined(PETSC_USE_DEBUGGING)
3134   for (i=0; i<m; i++) {
3135     nnz = Ii[i+1]- Ii[i];
3136     JJ  = J + Ii[i];
3137     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3138     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3139     if (nnz && (JJ[nnz-1] >= B->cmap->N) SETERRRQ3(PETSC_ERR_ARG_WRONGSTATE,"Row %D ends with too large a column index %D (max allowed %D)",i,JJ[nnz-1],B->cmap->N);
3140   }
3141 #endif
3142 
3143   for (i=0; i<m; i++) {
3144     nnz     = Ii[i+1]- Ii[i];
3145     JJ      = J + Ii[i];
3146     nnz_max = PetscMax(nnz_max,nnz);
3147     d       = 0;
3148     for (j=0; j<nnz; j++) {
3149       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3150     }
3151     d_nnz[i] = d;
3152     o_nnz[i] = nnz - d;
3153   }
3154   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3155   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3156 
3157   if (v) values = (PetscScalar*)v;
3158   else {
3159     ierr = PetscCalloc1(nnz_max+1,&values);CHKERRQ(ierr);
3160   }
3161 
3162   for (i=0; i<m; i++) {
3163     ii   = i + rstart;
3164     nnz  = Ii[i+1]- Ii[i];
3165     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3166   }
3167   nooffprocentries    = B->nooffprocentries;
3168   B->nooffprocentries = PETSC_TRUE;
3169   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3170   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3171   B->nooffprocentries = nooffprocentries;
3172 
3173   if (!v) {
3174     ierr = PetscFree(values);CHKERRQ(ierr);
3175   }
3176   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3177   PetscFunctionReturn(0);
3178 }
3179 
3180 /*@
3181    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3182    (the default parallel PETSc format).
3183 
3184    Collective on MPI_Comm
3185 
3186    Input Parameters:
3187 +  B - the matrix
3188 .  i - the indices into j for the start of each local row (starts with zero)
3189 .  j - the column indices for each local row (starts with zero)
3190 -  v - optional values in the matrix
3191 
3192    Level: developer
3193 
3194    Notes:
3195        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3196      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3197      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3198 
3199        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3200 
3201        The format which is used for the sparse matrix input, is equivalent to a
3202     row-major ordering.. i.e for the following matrix, the input data expected is
3203     as shown
3204 
3205 $        1 0 0
3206 $        2 0 3     P0
3207 $       -------
3208 $        4 5 6     P1
3209 $
3210 $     Process0 [P0]: rows_owned=[0,1]
3211 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3212 $        j =  {0,0,2}  [size = 3]
3213 $        v =  {1,2,3}  [size = 3]
3214 $
3215 $     Process1 [P1]: rows_owned=[2]
3216 $        i =  {0,3}    [size = nrow+1  = 1+1]
3217 $        j =  {0,1,2}  [size = 3]
3218 $        v =  {4,5,6}  [size = 3]
3219 
3220 .keywords: matrix, aij, compressed row, sparse, parallel
3221 
3222 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MATMPIAIJ,
3223           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3224 @*/
3225 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3226 {
3227   PetscErrorCode ierr;
3228 
3229   PetscFunctionBegin;
3230   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3231   PetscFunctionReturn(0);
3232 }
3233 
3234 /*@C
3235    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3236    (the default parallel PETSc format).  For good matrix assembly performance
3237    the user should preallocate the matrix storage by setting the parameters
3238    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3239    performance can be increased by more than a factor of 50.
3240 
3241    Collective on MPI_Comm
3242 
3243    Input Parameters:
3244 +  B - the matrix
3245 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3246            (same value is used for all local rows)
3247 .  d_nnz - array containing the number of nonzeros in the various rows of the
3248            DIAGONAL portion of the local submatrix (possibly different for each row)
3249            or NULL (PETSC_NULL_INTEGER in Fortran), if d_nz is used to specify the nonzero structure.
3250            The size of this array is equal to the number of local rows, i.e 'm'.
3251            For matrices that will be factored, you must leave room for (and set)
3252            the diagonal entry even if it is zero.
3253 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3254            submatrix (same value is used for all local rows).
3255 -  o_nnz - array containing the number of nonzeros in the various rows of the
3256            OFF-DIAGONAL portion of the local submatrix (possibly different for
3257            each row) or NULL (PETSC_NULL_INTEGER in Fortran), if o_nz is used to specify the nonzero
3258            structure. The size of this array is equal to the number
3259            of local rows, i.e 'm'.
3260 
3261    If the *_nnz parameter is given then the *_nz parameter is ignored
3262 
3263    The AIJ format (also called the Yale sparse matrix format or
3264    compressed row storage (CSR)), is fully compatible with standard Fortran 77
3265    storage.  The stored row and column indices begin with zero.
3266    See Users-Manual: ch_mat for details.
3267 
3268    The parallel matrix is partitioned such that the first m0 rows belong to
3269    process 0, the next m1 rows belong to process 1, the next m2 rows belong
3270    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
3271 
3272    The DIAGONAL portion of the local submatrix of a processor can be defined
3273    as the submatrix which is obtained by extraction the part corresponding to
3274    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
3275    first row that belongs to the processor, r2 is the last row belonging to
3276    the this processor, and c1-c2 is range of indices of the local part of a
3277    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
3278    common case of a square matrix, the row and column ranges are the same and
3279    the DIAGONAL part is also square. The remaining portion of the local
3280    submatrix (mxN) constitute the OFF-DIAGONAL portion.
3281 
3282    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3283 
3284    You can call MatGetInfo() to get information on how effective the preallocation was;
3285    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3286    You can also run with the option -info and look for messages with the string
3287    malloc in them to see if additional memory allocation was needed.
3288 
3289    Example usage:
3290 
3291    Consider the following 8x8 matrix with 34 non-zero values, that is
3292    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3293    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3294    as follows:
3295 
3296 .vb
3297             1  2  0  |  0  3  0  |  0  4
3298     Proc0   0  5  6  |  7  0  0  |  8  0
3299             9  0 10  | 11  0  0  | 12  0
3300     -------------------------------------
3301            13  0 14  | 15 16 17  |  0  0
3302     Proc1   0 18  0  | 19 20 21  |  0  0
3303             0  0  0  | 22 23  0  | 24  0
3304     -------------------------------------
3305     Proc2  25 26 27  |  0  0 28  | 29  0
3306            30  0  0  | 31 32 33  |  0 34
3307 .ve
3308 
3309    This can be represented as a collection of submatrices as:
3310 
3311 .vb
3312       A B C
3313       D E F
3314       G H I
3315 .ve
3316 
3317    Where the submatrices A,B,C are owned by proc0, D,E,F are
3318    owned by proc1, G,H,I are owned by proc2.
3319 
3320    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3321    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3322    The 'M','N' parameters are 8,8, and have the same values on all procs.
3323 
3324    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3325    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3326    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3327    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3328    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3329    matrix, ans [DF] as another SeqAIJ matrix.
3330 
3331    When d_nz, o_nz parameters are specified, d_nz storage elements are
3332    allocated for every row of the local diagonal submatrix, and o_nz
3333    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3334    One way to choose d_nz and o_nz is to use the max nonzerors per local
3335    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3336    In this case, the values of d_nz,o_nz are:
3337 .vb
3338      proc0 : dnz = 2, o_nz = 2
3339      proc1 : dnz = 3, o_nz = 2
3340      proc2 : dnz = 1, o_nz = 4
3341 .ve
3342    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3343    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3344    for proc3. i.e we are using 12+15+10=37 storage locations to store
3345    34 values.
3346 
3347    When d_nnz, o_nnz parameters are specified, the storage is specified
3348    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3349    In the above case the values for d_nnz,o_nnz are:
3350 .vb
3351      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3352      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3353      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3354 .ve
3355    Here the space allocated is sum of all the above values i.e 34, and
3356    hence pre-allocation is perfect.
3357 
3358    Level: intermediate
3359 
3360 .keywords: matrix, aij, compressed row, sparse, parallel
3361 
3362 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
3363           MATMPIAIJ, MatGetInfo(), PetscSplitOwnership()
3364 @*/
3365 PetscErrorCode  MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3366 {
3367   PetscErrorCode ierr;
3368 
3369   PetscFunctionBegin;
3370   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3371   PetscValidType(B,1);
3372   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
3373   PetscFunctionReturn(0);
3374 }
3375 
3376 /*@
3377      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
3378          CSR format the local rows.
3379 
3380    Collective on MPI_Comm
3381 
3382    Input Parameters:
3383 +  comm - MPI communicator
3384 .  m - number of local rows (Cannot be PETSC_DECIDE)
3385 .  n - This value should be the same as the local size used in creating the
3386        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3387        calculated if N is given) For square matrices n is almost always m.
3388 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3389 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3390 .   i - row indices
3391 .   j - column indices
3392 -   a - matrix values
3393 
3394    Output Parameter:
3395 .   mat - the matrix
3396 
3397    Level: intermediate
3398 
3399    Notes:
3400        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3401      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3402      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3403 
3404        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3405 
3406        The format which is used for the sparse matrix input, is equivalent to a
3407     row-major ordering.. i.e for the following matrix, the input data expected is
3408     as shown
3409 
3410 $        1 0 0
3411 $        2 0 3     P0
3412 $       -------
3413 $        4 5 6     P1
3414 $
3415 $     Process0 [P0]: rows_owned=[0,1]
3416 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3417 $        j =  {0,0,2}  [size = 3]
3418 $        v =  {1,2,3}  [size = 3]
3419 $
3420 $     Process1 [P1]: rows_owned=[2]
3421 $        i =  {0,3}    [size = nrow+1  = 1+1]
3422 $        j =  {0,1,2}  [size = 3]
3423 $        v =  {4,5,6}  [size = 3]
3424 
3425 .keywords: matrix, aij, compressed row, sparse, parallel
3426 
3427 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3428           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
3429 @*/
3430 PetscErrorCode  MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
3431 {
3432   PetscErrorCode ierr;
3433 
3434   PetscFunctionBegin;
3435   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
3436   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
3437   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
3438   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
3439   /* ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr); */
3440   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
3441   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
3442   PetscFunctionReturn(0);
3443 }
3444 
3445 /*@C
3446    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
3447    (the default parallel PETSc format).  For good matrix assembly performance
3448    the user should preallocate the matrix storage by setting the parameters
3449    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3450    performance can be increased by more than a factor of 50.
3451 
3452    Collective on MPI_Comm
3453 
3454    Input Parameters:
3455 +  comm - MPI communicator
3456 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
3457            This value should be the same as the local size used in creating the
3458            y vector for the matrix-vector product y = Ax.
3459 .  n - This value should be the same as the local size used in creating the
3460        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3461        calculated if N is given) For square matrices n is almost always m.
3462 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3463 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3464 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3465            (same value is used for all local rows)
3466 .  d_nnz - array containing the number of nonzeros in the various rows of the
3467            DIAGONAL portion of the local submatrix (possibly different for each row)
3468            or NULL, if d_nz is used to specify the nonzero structure.
3469            The size of this array is equal to the number of local rows, i.e 'm'.
3470 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3471            submatrix (same value is used for all local rows).
3472 -  o_nnz - array containing the number of nonzeros in the various rows of the
3473            OFF-DIAGONAL portion of the local submatrix (possibly different for
3474            each row) or NULL, if o_nz is used to specify the nonzero
3475            structure. The size of this array is equal to the number
3476            of local rows, i.e 'm'.
3477 
3478    Output Parameter:
3479 .  A - the matrix
3480 
3481    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3482    MatXXXXSetPreallocation() paradgm instead of this routine directly.
3483    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3484 
3485    Notes:
3486    If the *_nnz parameter is given then the *_nz parameter is ignored
3487 
3488    m,n,M,N parameters specify the size of the matrix, and its partitioning across
3489    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
3490    storage requirements for this matrix.
3491 
3492    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
3493    processor than it must be used on all processors that share the object for
3494    that argument.
3495 
3496    The user MUST specify either the local or global matrix dimensions
3497    (possibly both).
3498 
3499    The parallel matrix is partitioned across processors such that the
3500    first m0 rows belong to process 0, the next m1 rows belong to
3501    process 1, the next m2 rows belong to process 2 etc.. where
3502    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
3503    values corresponding to [m x N] submatrix.
3504 
3505    The columns are logically partitioned with the n0 columns belonging
3506    to 0th partition, the next n1 columns belonging to the next
3507    partition etc.. where n0,n1,n2... are the input parameter 'n'.
3508 
3509    The DIAGONAL portion of the local submatrix on any given processor
3510    is the submatrix corresponding to the rows and columns m,n
3511    corresponding to the given processor. i.e diagonal matrix on
3512    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
3513    etc. The remaining portion of the local submatrix [m x (N-n)]
3514    constitute the OFF-DIAGONAL portion. The example below better
3515    illustrates this concept.
3516 
3517    For a square global matrix we define each processor's diagonal portion
3518    to be its local rows and the corresponding columns (a square submatrix);
3519    each processor's off-diagonal portion encompasses the remainder of the
3520    local matrix (a rectangular submatrix).
3521 
3522    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3523 
3524    When calling this routine with a single process communicator, a matrix of
3525    type SEQAIJ is returned.  If a matrix of type MATMPIAIJ is desired for this
3526    type of communicator, use the construction mechanism:
3527      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
3528 
3529    By default, this format uses inodes (identical nodes) when possible.
3530    We search for consecutive rows with the same nonzero structure, thereby
3531    reusing matrix information to achieve increased efficiency.
3532 
3533    Options Database Keys:
3534 +  -mat_no_inode  - Do not use inodes
3535 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3536 -  -mat_aij_oneindex - Internally use indexing starting at 1
3537         rather than 0.  Note that when calling MatSetValues(),
3538         the user still MUST index entries starting at 0!
3539 
3540 
3541    Example usage:
3542 
3543    Consider the following 8x8 matrix with 34 non-zero values, that is
3544    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3545    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3546    as follows:
3547 
3548 .vb
3549             1  2  0  |  0  3  0  |  0  4
3550     Proc0   0  5  6  |  7  0  0  |  8  0
3551             9  0 10  | 11  0  0  | 12  0
3552     -------------------------------------
3553            13  0 14  | 15 16 17  |  0  0
3554     Proc1   0 18  0  | 19 20 21  |  0  0
3555             0  0  0  | 22 23  0  | 24  0
3556     -------------------------------------
3557     Proc2  25 26 27  |  0  0 28  | 29  0
3558            30  0  0  | 31 32 33  |  0 34
3559 .ve
3560 
3561    This can be represented as a collection of submatrices as:
3562 
3563 .vb
3564       A B C
3565       D E F
3566       G H I
3567 .ve
3568 
3569    Where the submatrices A,B,C are owned by proc0, D,E,F are
3570    owned by proc1, G,H,I are owned by proc2.
3571 
3572    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3573    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3574    The 'M','N' parameters are 8,8, and have the same values on all procs.
3575 
3576    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3577    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3578    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3579    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3580    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3581    matrix, ans [DF] as another SeqAIJ matrix.
3582 
3583    When d_nz, o_nz parameters are specified, d_nz storage elements are
3584    allocated for every row of the local diagonal submatrix, and o_nz
3585    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3586    One way to choose d_nz and o_nz is to use the max nonzerors per local
3587    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3588    In this case, the values of d_nz,o_nz are:
3589 .vb
3590      proc0 : dnz = 2, o_nz = 2
3591      proc1 : dnz = 3, o_nz = 2
3592      proc2 : dnz = 1, o_nz = 4
3593 .ve
3594    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3595    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3596    for proc3. i.e we are using 12+15+10=37 storage locations to store
3597    34 values.
3598 
3599    When d_nnz, o_nnz parameters are specified, the storage is specified
3600    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3601    In the above case the values for d_nnz,o_nnz are:
3602 .vb
3603      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3604      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3605      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3606 .ve
3607    Here the space allocated is sum of all the above values i.e 34, and
3608    hence pre-allocation is perfect.
3609 
3610    Level: intermediate
3611 
3612 .keywords: matrix, aij, compressed row, sparse, parallel
3613 
3614 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3615           MATMPIAIJ, MatCreateMPIAIJWithArrays()
3616 @*/
3617 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)
3618 {
3619   PetscErrorCode ierr;
3620   PetscMPIInt    size;
3621 
3622   PetscFunctionBegin;
3623   ierr = MatCreate(comm,A);CHKERRQ(ierr);
3624   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
3625   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3626   if (size > 1) {
3627     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
3628     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
3629   } else {
3630     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
3631     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
3632   }
3633   PetscFunctionReturn(0);
3634 }
3635 
3636 PetscErrorCode  MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
3637 {
3638   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3639   PetscBool      flg;
3640   PetscErrorCode ierr;
3641 
3642   PetscFunctionBegin;
3643   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&flg);CHKERRQ(ierr);
3644   if (!flg) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"This function requires a MATMPIAIJ matrix as input");
3645   if (Ad)     *Ad     = a->A;
3646   if (Ao)     *Ao     = a->B;
3647   if (colmap) *colmap = a->garray;
3648   PetscFunctionReturn(0);
3649 }
3650 
3651 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
3652 {
3653   PetscErrorCode ierr;
3654   PetscInt       m,N,i,rstart,nnz,Ii;
3655   PetscInt       *indx;
3656   PetscScalar    *values;
3657 
3658   PetscFunctionBegin;
3659   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
3660   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
3661     PetscInt       *dnz,*onz,sum,bs,cbs;
3662 
3663     if (n == PETSC_DECIDE) {
3664       ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
3665     }
3666     /* Check sum(n) = N */
3667     ierr = MPIU_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3668     if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
3669 
3670     ierr    = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3671     rstart -= m;
3672 
3673     ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
3674     for (i=0; i<m; i++) {
3675       ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3676       ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
3677       ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3678     }
3679 
3680     ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
3681     ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
3682     ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
3683     ierr = MatSetBlockSizes(*outmat,bs,cbs);CHKERRQ(ierr);
3684     ierr = MatSetType(*outmat,MATAIJ);CHKERRQ(ierr);
3685     ierr = MatSeqAIJSetPreallocation(*outmat,0,dnz);CHKERRQ(ierr);
3686     ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
3687     ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
3688   }
3689 
3690   /* numeric phase */
3691   ierr = MatGetOwnershipRange(*outmat,&rstart,NULL);CHKERRQ(ierr);
3692   for (i=0; i<m; i++) {
3693     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3694     Ii   = i + rstart;
3695     ierr = MatSetValues(*outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3696     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3697   }
3698   ierr = MatAssemblyBegin(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3699   ierr = MatAssemblyEnd(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3700   PetscFunctionReturn(0);
3701 }
3702 
3703 PetscErrorCode MatFileSplit(Mat A,char *outfile)
3704 {
3705   PetscErrorCode    ierr;
3706   PetscMPIInt       rank;
3707   PetscInt          m,N,i,rstart,nnz;
3708   size_t            len;
3709   const PetscInt    *indx;
3710   PetscViewer       out;
3711   char              *name;
3712   Mat               B;
3713   const PetscScalar *values;
3714 
3715   PetscFunctionBegin;
3716   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
3717   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
3718   /* Should this be the type of the diagonal block of A? */
3719   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
3720   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
3721   ierr = MatSetBlockSizesFromMats(B,A,A);CHKERRQ(ierr);
3722   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
3723   ierr = MatSeqAIJSetPreallocation(B,0,NULL);CHKERRQ(ierr);
3724   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
3725   for (i=0; i<m; i++) {
3726     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3727     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3728     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3729   }
3730   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3731   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3732 
3733   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
3734   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
3735   ierr = PetscMalloc1(len+5,&name);CHKERRQ(ierr);
3736   sprintf(name,"%s.%d",outfile,rank);
3737   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
3738   ierr = PetscFree(name);CHKERRQ(ierr);
3739   ierr = MatView(B,out);CHKERRQ(ierr);
3740   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
3741   ierr = MatDestroy(&B);CHKERRQ(ierr);
3742   PetscFunctionReturn(0);
3743 }
3744 
3745 PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
3746 {
3747   PetscErrorCode      ierr;
3748   Mat_Merge_SeqsToMPI *merge;
3749   PetscContainer      container;
3750 
3751   PetscFunctionBegin;
3752   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
3753   if (container) {
3754     ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
3755     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
3756     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
3757     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
3758     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
3759     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
3760     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
3761     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
3762     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
3763     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
3764     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
3765     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
3766     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
3767     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
3768     ierr = PetscFree(merge);CHKERRQ(ierr);
3769     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
3770   }
3771   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
3772   PetscFunctionReturn(0);
3773 }
3774 
3775 #include <../src/mat/utils/freespace.h>
3776 #include <petscbt.h>
3777 
3778 PetscErrorCode  MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
3779 {
3780   PetscErrorCode      ierr;
3781   MPI_Comm            comm;
3782   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
3783   PetscMPIInt         size,rank,taga,*len_s;
3784   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
3785   PetscInt            proc,m;
3786   PetscInt            **buf_ri,**buf_rj;
3787   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
3788   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
3789   MPI_Request         *s_waits,*r_waits;
3790   MPI_Status          *status;
3791   MatScalar           *aa=a->a;
3792   MatScalar           **abuf_r,*ba_i;
3793   Mat_Merge_SeqsToMPI *merge;
3794   PetscContainer      container;
3795 
3796   PetscFunctionBegin;
3797   ierr = PetscObjectGetComm((PetscObject)mpimat,&comm);CHKERRQ(ierr);
3798   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
3799 
3800   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3801   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3802 
3803   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
3804   ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
3805 
3806   bi     = merge->bi;
3807   bj     = merge->bj;
3808   buf_ri = merge->buf_ri;
3809   buf_rj = merge->buf_rj;
3810 
3811   ierr   = PetscMalloc1(size,&status);CHKERRQ(ierr);
3812   owners = merge->rowmap->range;
3813   len_s  = merge->len_s;
3814 
3815   /* send and recv matrix values */
3816   /*-----------------------------*/
3817   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
3818   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
3819 
3820   ierr = PetscMalloc1(merge->nsend+1,&s_waits);CHKERRQ(ierr);
3821   for (proc=0,k=0; proc<size; proc++) {
3822     if (!len_s[proc]) continue;
3823     i    = owners[proc];
3824     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
3825     k++;
3826   }
3827 
3828   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
3829   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
3830   ierr = PetscFree(status);CHKERRQ(ierr);
3831 
3832   ierr = PetscFree(s_waits);CHKERRQ(ierr);
3833   ierr = PetscFree(r_waits);CHKERRQ(ierr);
3834 
3835   /* insert mat values of mpimat */
3836   /*----------------------------*/
3837   ierr = PetscMalloc1(N,&ba_i);CHKERRQ(ierr);
3838   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
3839 
3840   for (k=0; k<merge->nrecv; k++) {
3841     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
3842     nrows       = *(buf_ri_k[k]);
3843     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
3844     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
3845   }
3846 
3847   /* set values of ba */
3848   m = merge->rowmap->n;
3849   for (i=0; i<m; i++) {
3850     arow = owners[rank] + i;
3851     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
3852     bnzi = bi[i+1] - bi[i];
3853     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
3854 
3855     /* add local non-zero vals of this proc's seqmat into ba */
3856     anzi   = ai[arow+1] - ai[arow];
3857     aj     = a->j + ai[arow];
3858     aa     = a->a + ai[arow];
3859     nextaj = 0;
3860     for (j=0; nextaj<anzi; j++) {
3861       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
3862         ba_i[j] += aa[nextaj++];
3863       }
3864     }
3865 
3866     /* add received vals into ba */
3867     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
3868       /* i-th row */
3869       if (i == *nextrow[k]) {
3870         anzi   = *(nextai[k]+1) - *nextai[k];
3871         aj     = buf_rj[k] + *(nextai[k]);
3872         aa     = abuf_r[k] + *(nextai[k]);
3873         nextaj = 0;
3874         for (j=0; nextaj<anzi; j++) {
3875           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
3876             ba_i[j] += aa[nextaj++];
3877           }
3878         }
3879         nextrow[k]++; nextai[k]++;
3880       }
3881     }
3882     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
3883   }
3884   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3885   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3886 
3887   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
3888   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
3889   ierr = PetscFree(ba_i);CHKERRQ(ierr);
3890   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
3891   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
3892   PetscFunctionReturn(0);
3893 }
3894 
3895 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
3896 {
3897   PetscErrorCode      ierr;
3898   Mat                 B_mpi;
3899   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
3900   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
3901   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
3902   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
3903   PetscInt            len,proc,*dnz,*onz,bs,cbs;
3904   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
3905   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
3906   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
3907   MPI_Status          *status;
3908   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
3909   PetscBT             lnkbt;
3910   Mat_Merge_SeqsToMPI *merge;
3911   PetscContainer      container;
3912 
3913   PetscFunctionBegin;
3914   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
3915 
3916   /* make sure it is a PETSc comm */
3917   ierr = PetscCommDuplicate(comm,&comm,NULL);CHKERRQ(ierr);
3918   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3919   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3920 
3921   ierr = PetscNew(&merge);CHKERRQ(ierr);
3922   ierr = PetscMalloc1(size,&status);CHKERRQ(ierr);
3923 
3924   /* determine row ownership */
3925   /*---------------------------------------------------------*/
3926   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
3927   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
3928   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
3929   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
3930   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
3931   ierr = PetscMalloc1(size,&len_si);CHKERRQ(ierr);
3932   ierr = PetscMalloc1(size,&merge->len_s);CHKERRQ(ierr);
3933 
3934   m      = merge->rowmap->n;
3935   owners = merge->rowmap->range;
3936 
3937   /* determine the number of messages to send, their lengths */
3938   /*---------------------------------------------------------*/
3939   len_s = merge->len_s;
3940 
3941   len          = 0; /* length of buf_si[] */
3942   merge->nsend = 0;
3943   for (proc=0; proc<size; proc++) {
3944     len_si[proc] = 0;
3945     if (proc == rank) {
3946       len_s[proc] = 0;
3947     } else {
3948       len_si[proc] = owners[proc+1] - owners[proc] + 1;
3949       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
3950     }
3951     if (len_s[proc]) {
3952       merge->nsend++;
3953       nrows = 0;
3954       for (i=owners[proc]; i<owners[proc+1]; i++) {
3955         if (ai[i+1] > ai[i]) nrows++;
3956       }
3957       len_si[proc] = 2*(nrows+1);
3958       len         += len_si[proc];
3959     }
3960   }
3961 
3962   /* determine the number and length of messages to receive for ij-structure */
3963   /*-------------------------------------------------------------------------*/
3964   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
3965   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
3966 
3967   /* post the Irecv of j-structure */
3968   /*-------------------------------*/
3969   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
3970   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
3971 
3972   /* post the Isend of j-structure */
3973   /*--------------------------------*/
3974   ierr = PetscMalloc2(merge->nsend,&si_waits,merge->nsend,&sj_waits);CHKERRQ(ierr);
3975 
3976   for (proc=0, k=0; proc<size; proc++) {
3977     if (!len_s[proc]) continue;
3978     i    = owners[proc];
3979     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
3980     k++;
3981   }
3982 
3983   /* receives and sends of j-structure are complete */
3984   /*------------------------------------------------*/
3985   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
3986   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
3987 
3988   /* send and recv i-structure */
3989   /*---------------------------*/
3990   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
3991   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
3992 
3993   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
3994   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
3995   for (proc=0,k=0; proc<size; proc++) {
3996     if (!len_s[proc]) continue;
3997     /* form outgoing message for i-structure:
3998          buf_si[0]:                 nrows to be sent
3999                [1:nrows]:           row index (global)
4000                [nrows+1:2*nrows+1]: i-structure index
4001     */
4002     /*-------------------------------------------*/
4003     nrows       = len_si[proc]/2 - 1;
4004     buf_si_i    = buf_si + nrows+1;
4005     buf_si[0]   = nrows;
4006     buf_si_i[0] = 0;
4007     nrows       = 0;
4008     for (i=owners[proc]; i<owners[proc+1]; i++) {
4009       anzi = ai[i+1] - ai[i];
4010       if (anzi) {
4011         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4012         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4013         nrows++;
4014       }
4015     }
4016     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4017     k++;
4018     buf_si += len_si[proc];
4019   }
4020 
4021   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4022   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4023 
4024   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4025   for (i=0; i<merge->nrecv; i++) {
4026     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);
4027   }
4028 
4029   ierr = PetscFree(len_si);CHKERRQ(ierr);
4030   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4031   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4032   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4033   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4034   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4035   ierr = PetscFree(status);CHKERRQ(ierr);
4036 
4037   /* compute a local seq matrix in each processor */
4038   /*----------------------------------------------*/
4039   /* allocate bi array and free space for accumulating nonzero column info */
4040   ierr  = PetscMalloc1(m+1,&bi);CHKERRQ(ierr);
4041   bi[0] = 0;
4042 
4043   /* create and initialize a linked list */
4044   nlnk = N+1;
4045   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4046 
4047   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4048   len  = ai[owners[rank+1]] - ai[owners[rank]];
4049   ierr = PetscFreeSpaceGet(PetscIntMultTruncate(2,len)+1,&free_space);CHKERRQ(ierr);
4050 
4051   current_space = free_space;
4052 
4053   /* determine symbolic info for each local row */
4054   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4055 
4056   for (k=0; k<merge->nrecv; k++) {
4057     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4058     nrows       = *buf_ri_k[k];
4059     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4060     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4061   }
4062 
4063   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4064   len  = 0;
4065   for (i=0; i<m; i++) {
4066     bnzi = 0;
4067     /* add local non-zero cols of this proc's seqmat into lnk */
4068     arow  = owners[rank] + i;
4069     anzi  = ai[arow+1] - ai[arow];
4070     aj    = a->j + ai[arow];
4071     ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4072     bnzi += nlnk;
4073     /* add received col data into lnk */
4074     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4075       if (i == *nextrow[k]) { /* i-th row */
4076         anzi  = *(nextai[k]+1) - *nextai[k];
4077         aj    = buf_rj[k] + *nextai[k];
4078         ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4079         bnzi += nlnk;
4080         nextrow[k]++; nextai[k]++;
4081       }
4082     }
4083     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4084 
4085     /* if free space is not available, make more free space */
4086     if (current_space->local_remaining<bnzi) {
4087       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(bnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
4088       nspacedouble++;
4089     }
4090     /* copy data into free space, then initialize lnk */
4091     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4092     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
4093 
4094     current_space->array           += bnzi;
4095     current_space->local_used      += bnzi;
4096     current_space->local_remaining -= bnzi;
4097 
4098     bi[i+1] = bi[i] + bnzi;
4099   }
4100 
4101   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4102 
4103   ierr = PetscMalloc1(bi[m]+1,&bj);CHKERRQ(ierr);
4104   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
4105   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4106 
4107   /* create symbolic parallel matrix B_mpi */
4108   /*---------------------------------------*/
4109   ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
4110   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
4111   if (n==PETSC_DECIDE) {
4112     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
4113   } else {
4114     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4115   }
4116   ierr = MatSetBlockSizes(B_mpi,bs,cbs);CHKERRQ(ierr);
4117   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
4118   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
4119   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4120   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
4121 
4122   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4123   B_mpi->assembled    = PETSC_FALSE;
4124   B_mpi->ops->destroy = MatDestroy_MPIAIJ_SeqsToMPI;
4125   merge->bi           = bi;
4126   merge->bj           = bj;
4127   merge->buf_ri       = buf_ri;
4128   merge->buf_rj       = buf_rj;
4129   merge->coi          = NULL;
4130   merge->coj          = NULL;
4131   merge->owners_co    = NULL;
4132 
4133   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
4134 
4135   /* attach the supporting struct to B_mpi for reuse */
4136   ierr    = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
4137   ierr    = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
4138   ierr    = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
4139   ierr    = PetscContainerDestroy(&container);CHKERRQ(ierr);
4140   *mpimat = B_mpi;
4141 
4142   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4143   PetscFunctionReturn(0);
4144 }
4145 
4146 /*@C
4147       MatCreateMPIAIJSumSeqAIJ - Creates a MATMPIAIJ matrix by adding sequential
4148                  matrices from each processor
4149 
4150     Collective on MPI_Comm
4151 
4152    Input Parameters:
4153 +    comm - the communicators the parallel matrix will live on
4154 .    seqmat - the input sequential matrices
4155 .    m - number of local rows (or PETSC_DECIDE)
4156 .    n - number of local columns (or PETSC_DECIDE)
4157 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4158 
4159    Output Parameter:
4160 .    mpimat - the parallel matrix generated
4161 
4162     Level: advanced
4163 
4164    Notes:
4165      The dimensions of the sequential matrix in each processor MUST be the same.
4166      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
4167      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
4168 @*/
4169 PetscErrorCode  MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
4170 {
4171   PetscErrorCode ierr;
4172   PetscMPIInt    size;
4173 
4174   PetscFunctionBegin;
4175   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4176   if (size == 1) {
4177     ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4178     if (scall == MAT_INITIAL_MATRIX) {
4179       ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
4180     } else {
4181       ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4182     }
4183     ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4184     PetscFunctionReturn(0);
4185   }
4186   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4187   if (scall == MAT_INITIAL_MATRIX) {
4188     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
4189   }
4190   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
4191   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4192   PetscFunctionReturn(0);
4193 }
4194 
4195 /*@
4196      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MATMPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
4197           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
4198           with MatGetSize()
4199 
4200     Not Collective
4201 
4202    Input Parameters:
4203 +    A - the matrix
4204 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4205 
4206    Output Parameter:
4207 .    A_loc - the local sequential matrix generated
4208 
4209     Level: developer
4210 
4211 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
4212 
4213 @*/
4214 PetscErrorCode  MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
4215 {
4216   PetscErrorCode ierr;
4217   Mat_MPIAIJ     *mpimat=(Mat_MPIAIJ*)A->data;
4218   Mat_SeqAIJ     *mat,*a,*b;
4219   PetscInt       *ai,*aj,*bi,*bj,*cmap=mpimat->garray;
4220   MatScalar      *aa,*ba,*cam;
4221   PetscScalar    *ca;
4222   PetscInt       am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
4223   PetscInt       *ci,*cj,col,ncols_d,ncols_o,jo;
4224   PetscBool      match;
4225   MPI_Comm       comm;
4226   PetscMPIInt    size;
4227 
4228   PetscFunctionBegin;
4229   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4230   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
4231   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4232   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4233   if (size == 1 && scall == MAT_REUSE_MATRIX) PetscFunctionReturn(0);
4234 
4235   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4236   a = (Mat_SeqAIJ*)(mpimat->A)->data;
4237   b = (Mat_SeqAIJ*)(mpimat->B)->data;
4238   ai = a->i; aj = a->j; bi = b->i; bj = b->j;
4239   aa = a->a; ba = b->a;
4240   if (scall == MAT_INITIAL_MATRIX) {
4241     if (size == 1) {
4242       ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ai,aj,aa,A_loc);CHKERRQ(ierr);
4243       PetscFunctionReturn(0);
4244     }
4245 
4246     ierr  = PetscMalloc1(1+am,&ci);CHKERRQ(ierr);
4247     ci[0] = 0;
4248     for (i=0; i<am; i++) {
4249       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
4250     }
4251     ierr = PetscMalloc1(1+ci[am],&cj);CHKERRQ(ierr);
4252     ierr = PetscMalloc1(1+ci[am],&ca);CHKERRQ(ierr);
4253     k    = 0;
4254     for (i=0; i<am; i++) {
4255       ncols_o = bi[i+1] - bi[i];
4256       ncols_d = ai[i+1] - ai[i];
4257       /* off-diagonal portion of A */
4258       for (jo=0; jo<ncols_o; jo++) {
4259         col = cmap[*bj];
4260         if (col >= cstart) break;
4261         cj[k]   = col; bj++;
4262         ca[k++] = *ba++;
4263       }
4264       /* diagonal portion of A */
4265       for (j=0; j<ncols_d; j++) {
4266         cj[k]   = cstart + *aj++;
4267         ca[k++] = *aa++;
4268       }
4269       /* off-diagonal portion of A */
4270       for (j=jo; j<ncols_o; j++) {
4271         cj[k]   = cmap[*bj++];
4272         ca[k++] = *ba++;
4273       }
4274     }
4275     /* put together the new matrix */
4276     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
4277     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4278     /* Since these are PETSc arrays, change flags to free them as necessary. */
4279     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
4280     mat->free_a  = PETSC_TRUE;
4281     mat->free_ij = PETSC_TRUE;
4282     mat->nonew   = 0;
4283   } else if (scall == MAT_REUSE_MATRIX) {
4284     mat=(Mat_SeqAIJ*)(*A_loc)->data;
4285     ci = mat->i; cj = mat->j; cam = mat->a;
4286     for (i=0; i<am; i++) {
4287       /* off-diagonal portion of A */
4288       ncols_o = bi[i+1] - bi[i];
4289       for (jo=0; jo<ncols_o; jo++) {
4290         col = cmap[*bj];
4291         if (col >= cstart) break;
4292         *cam++ = *ba++; bj++;
4293       }
4294       /* diagonal portion of A */
4295       ncols_d = ai[i+1] - ai[i];
4296       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
4297       /* off-diagonal portion of A */
4298       for (j=jo; j<ncols_o; j++) {
4299         *cam++ = *ba++; bj++;
4300       }
4301     }
4302   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
4303   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4304   PetscFunctionReturn(0);
4305 }
4306 
4307 /*@C
4308      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MATMPIAIJ matrix by taking all its local rows and NON-ZERO columns
4309 
4310     Not Collective
4311 
4312    Input Parameters:
4313 +    A - the matrix
4314 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4315 -    row, col - index sets of rows and columns to extract (or NULL)
4316 
4317    Output Parameter:
4318 .    A_loc - the local sequential matrix generated
4319 
4320     Level: developer
4321 
4322 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
4323 
4324 @*/
4325 PetscErrorCode  MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
4326 {
4327   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4328   PetscErrorCode ierr;
4329   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
4330   IS             isrowa,iscola;
4331   Mat            *aloc;
4332   PetscBool      match;
4333 
4334   PetscFunctionBegin;
4335   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4336   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
4337   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4338   if (!row) {
4339     start = A->rmap->rstart; end = A->rmap->rend;
4340     ierr  = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
4341   } else {
4342     isrowa = *row;
4343   }
4344   if (!col) {
4345     start = A->cmap->rstart;
4346     cmap  = a->garray;
4347     nzA   = a->A->cmap->n;
4348     nzB   = a->B->cmap->n;
4349     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4350     ncols = 0;
4351     for (i=0; i<nzB; i++) {
4352       if (cmap[i] < start) idx[ncols++] = cmap[i];
4353       else break;
4354     }
4355     imark = i;
4356     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
4357     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
4358     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
4359   } else {
4360     iscola = *col;
4361   }
4362   if (scall != MAT_INITIAL_MATRIX) {
4363     ierr    = PetscMalloc1(1,&aloc);CHKERRQ(ierr);
4364     aloc[0] = *A_loc;
4365   }
4366   ierr   = MatCreateSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
4367   *A_loc = aloc[0];
4368   ierr   = PetscFree(aloc);CHKERRQ(ierr);
4369   if (!row) {
4370     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
4371   }
4372   if (!col) {
4373     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
4374   }
4375   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4376   PetscFunctionReturn(0);
4377 }
4378 
4379 /*@C
4380     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
4381 
4382     Collective on Mat
4383 
4384    Input Parameters:
4385 +    A,B - the matrices in mpiaij format
4386 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4387 -    rowb, colb - index sets of rows and columns of B to extract (or NULL)
4388 
4389    Output Parameter:
4390 +    rowb, colb - index sets of rows and columns of B to extract
4391 -    B_seq - the sequential matrix generated
4392 
4393     Level: developer
4394 
4395 @*/
4396 PetscErrorCode  MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
4397 {
4398   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4399   PetscErrorCode ierr;
4400   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
4401   IS             isrowb,iscolb;
4402   Mat            *bseq=NULL;
4403 
4404   PetscFunctionBegin;
4405   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4406     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);
4407   }
4408   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4409 
4410   if (scall == MAT_INITIAL_MATRIX) {
4411     start = A->cmap->rstart;
4412     cmap  = a->garray;
4413     nzA   = a->A->cmap->n;
4414     nzB   = a->B->cmap->n;
4415     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4416     ncols = 0;
4417     for (i=0; i<nzB; i++) {  /* row < local row index */
4418       if (cmap[i] < start) idx[ncols++] = cmap[i];
4419       else break;
4420     }
4421     imark = i;
4422     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
4423     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
4424     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
4425     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
4426   } else {
4427     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
4428     isrowb  = *rowb; iscolb = *colb;
4429     ierr    = PetscMalloc1(1,&bseq);CHKERRQ(ierr);
4430     bseq[0] = *B_seq;
4431   }
4432   ierr   = MatCreateSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
4433   *B_seq = bseq[0];
4434   ierr   = PetscFree(bseq);CHKERRQ(ierr);
4435   if (!rowb) {
4436     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
4437   } else {
4438     *rowb = isrowb;
4439   }
4440   if (!colb) {
4441     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
4442   } else {
4443     *colb = iscolb;
4444   }
4445   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4446   PetscFunctionReturn(0);
4447 }
4448 
4449 /*
4450     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
4451     of the OFF-DIAGONAL portion of local A
4452 
4453     Collective on Mat
4454 
4455    Input Parameters:
4456 +    A,B - the matrices in mpiaij format
4457 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4458 
4459    Output Parameter:
4460 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
4461 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
4462 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
4463 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
4464 
4465     Level: developer
4466 
4467 */
4468 PetscErrorCode  MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
4469 {
4470   VecScatter_MPI_General *gen_to,*gen_from;
4471   PetscErrorCode         ierr;
4472   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
4473   Mat_SeqAIJ             *b_oth;
4474   VecScatter             ctx =a->Mvctx;
4475   MPI_Comm               comm;
4476   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
4477   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
4478   PetscInt               *rvalues,*svalues;
4479   MatScalar              *b_otha,*bufa,*bufA;
4480   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
4481   MPI_Request            *rwaits = NULL,*swaits = NULL;
4482   MPI_Status             *sstatus,rstatus;
4483   PetscMPIInt            jj,size;
4484   PetscInt               *cols,sbs,rbs;
4485   PetscScalar            *vals;
4486 
4487   PetscFunctionBegin;
4488   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4489   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4490 
4491   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4492     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);
4493   }
4494   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4495   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4496 
4497   gen_to   = (VecScatter_MPI_General*)ctx->todata;
4498   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
4499   nrecvs   = gen_from->n;
4500   nsends   = gen_to->n;
4501 
4502   ierr    = PetscMalloc2(nrecvs,&rwaits,nsends,&swaits);CHKERRQ(ierr);
4503   srow    = gen_to->indices;    /* local row index to be sent */
4504   sstarts = gen_to->starts;
4505   sprocs  = gen_to->procs;
4506   sstatus = gen_to->sstatus;
4507   sbs     = gen_to->bs;
4508   rstarts = gen_from->starts;
4509   rprocs  = gen_from->procs;
4510   rbs     = gen_from->bs;
4511 
4512   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
4513   if (scall == MAT_INITIAL_MATRIX) {
4514     /* i-array */
4515     /*---------*/
4516     /*  post receives */
4517     ierr = PetscMalloc1(rbs*(rstarts[nrecvs] - rstarts[0]),&rvalues);CHKERRQ(ierr);
4518     for (i=0; i<nrecvs; i++) {
4519       rowlen = rvalues + rstarts[i]*rbs;
4520       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
4521       ierr   = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4522     }
4523 
4524     /* pack the outgoing message */
4525     ierr = PetscMalloc2(nsends+1,&sstartsj,nrecvs+1,&rstartsj);CHKERRQ(ierr);
4526 
4527     sstartsj[0] = 0;
4528     rstartsj[0] = 0;
4529     len         = 0; /* total length of j or a array to be sent */
4530     k           = 0;
4531     ierr = PetscMalloc1(sbs*(sstarts[nsends] - sstarts[0]),&svalues);CHKERRQ(ierr);
4532     for (i=0; i<nsends; i++) {
4533       rowlen = svalues + sstarts[i]*sbs;
4534       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
4535       for (j=0; j<nrows; j++) {
4536         row = srow[k] + B->rmap->range[rank]; /* global row idx */
4537         for (l=0; l<sbs; l++) {
4538           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr); /* rowlength */
4539 
4540           rowlen[j*sbs+l] = ncols;
4541 
4542           len += ncols;
4543           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr);
4544         }
4545         k++;
4546       }
4547       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4548 
4549       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
4550     }
4551     /* recvs and sends of i-array are completed */
4552     i = nrecvs;
4553     while (i--) {
4554       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4555     }
4556     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4557     ierr = PetscFree(svalues);CHKERRQ(ierr);
4558 
4559     /* allocate buffers for sending j and a arrays */
4560     ierr = PetscMalloc1(len+1,&bufj);CHKERRQ(ierr);
4561     ierr = PetscMalloc1(len+1,&bufa);CHKERRQ(ierr);
4562 
4563     /* create i-array of B_oth */
4564     ierr = PetscMalloc1(aBn+2,&b_othi);CHKERRQ(ierr);
4565 
4566     b_othi[0] = 0;
4567     len       = 0; /* total length of j or a array to be received */
4568     k         = 0;
4569     for (i=0; i<nrecvs; i++) {
4570       rowlen = rvalues + rstarts[i]*rbs;
4571       nrows  = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be received */
4572       for (j=0; j<nrows; j++) {
4573         b_othi[k+1] = b_othi[k] + rowlen[j];
4574         ierr = PetscIntSumError(rowlen[j],len,&len);CHKERRQ(ierr);
4575         k++;
4576       }
4577       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
4578     }
4579     ierr = PetscFree(rvalues);CHKERRQ(ierr);
4580 
4581     /* allocate space for j and a arrrays of B_oth */
4582     ierr = PetscMalloc1(b_othi[aBn]+1,&b_othj);CHKERRQ(ierr);
4583     ierr = PetscMalloc1(b_othi[aBn]+1,&b_otha);CHKERRQ(ierr);
4584 
4585     /* j-array */
4586     /*---------*/
4587     /*  post receives of j-array */
4588     for (i=0; i<nrecvs; i++) {
4589       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4590       ierr  = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4591     }
4592 
4593     /* pack the outgoing message j-array */
4594     k = 0;
4595     for (i=0; i<nsends; i++) {
4596       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4597       bufJ  = bufj+sstartsj[i];
4598       for (j=0; j<nrows; j++) {
4599         row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4600         for (ll=0; ll<sbs; ll++) {
4601           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4602           for (l=0; l<ncols; l++) {
4603             *bufJ++ = cols[l];
4604           }
4605           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4606         }
4607       }
4608       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4609     }
4610 
4611     /* recvs and sends of j-array are completed */
4612     i = nrecvs;
4613     while (i--) {
4614       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4615     }
4616     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4617   } else if (scall == MAT_REUSE_MATRIX) {
4618     sstartsj = *startsj_s;
4619     rstartsj = *startsj_r;
4620     bufa     = *bufa_ptr;
4621     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
4622     b_otha   = b_oth->a;
4623   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
4624 
4625   /* a-array */
4626   /*---------*/
4627   /*  post receives of a-array */
4628   for (i=0; i<nrecvs; i++) {
4629     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4630     ierr  = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4631   }
4632 
4633   /* pack the outgoing message a-array */
4634   k = 0;
4635   for (i=0; i<nsends; i++) {
4636     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4637     bufA  = bufa+sstartsj[i];
4638     for (j=0; j<nrows; j++) {
4639       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4640       for (ll=0; ll<sbs; ll++) {
4641         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4642         for (l=0; l<ncols; l++) {
4643           *bufA++ = vals[l];
4644         }
4645         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4646       }
4647     }
4648     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4649   }
4650   /* recvs and sends of a-array are completed */
4651   i = nrecvs;
4652   while (i--) {
4653     ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4654   }
4655   if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4656   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
4657 
4658   if (scall == MAT_INITIAL_MATRIX) {
4659     /* put together the new matrix */
4660     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
4661 
4662     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4663     /* Since these are PETSc arrays, change flags to free them as necessary. */
4664     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
4665     b_oth->free_a  = PETSC_TRUE;
4666     b_oth->free_ij = PETSC_TRUE;
4667     b_oth->nonew   = 0;
4668 
4669     ierr = PetscFree(bufj);CHKERRQ(ierr);
4670     if (!startsj_s || !bufa_ptr) {
4671       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
4672       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
4673     } else {
4674       *startsj_s = sstartsj;
4675       *startsj_r = rstartsj;
4676       *bufa_ptr  = bufa;
4677     }
4678   }
4679   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4680   PetscFunctionReturn(0);
4681 }
4682 
4683 /*@C
4684   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
4685 
4686   Not Collective
4687 
4688   Input Parameters:
4689 . A - The matrix in mpiaij format
4690 
4691   Output Parameter:
4692 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
4693 . colmap - A map from global column index to local index into lvec
4694 - multScatter - A scatter from the argument of a matrix-vector product to lvec
4695 
4696   Level: developer
4697 
4698 @*/
4699 #if defined(PETSC_USE_CTABLE)
4700 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
4701 #else
4702 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
4703 #endif
4704 {
4705   Mat_MPIAIJ *a;
4706 
4707   PetscFunctionBegin;
4708   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4709   PetscValidPointer(lvec, 2);
4710   PetscValidPointer(colmap, 3);
4711   PetscValidPointer(multScatter, 4);
4712   a = (Mat_MPIAIJ*) A->data;
4713   if (lvec) *lvec = a->lvec;
4714   if (colmap) *colmap = a->colmap;
4715   if (multScatter) *multScatter = a->Mvctx;
4716   PetscFunctionReturn(0);
4717 }
4718 
4719 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
4720 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
4721 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
4722 #if defined(PETSC_HAVE_ELEMENTAL)
4723 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
4724 #endif
4725 #if defined(PETSC_HAVE_HYPRE)
4726 PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat,MatType,MatReuse,Mat*);
4727 PETSC_INTERN PetscErrorCode MatMatMatMult_Transpose_AIJ_AIJ(Mat,Mat,Mat,MatReuse,PetscReal,Mat*);
4728 #endif
4729 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_IS(Mat,MatType,MatReuse,Mat*);
4730 
4731 /*
4732     Computes (B'*A')' since computing B*A directly is untenable
4733 
4734                n                       p                          p
4735         (              )       (              )         (                  )
4736       m (      A       )  *  n (       B      )   =   m (         C        )
4737         (              )       (              )         (                  )
4738 
4739 */
4740 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
4741 {
4742   PetscErrorCode ierr;
4743   Mat            At,Bt,Ct;
4744 
4745   PetscFunctionBegin;
4746   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
4747   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
4748   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
4749   ierr = MatDestroy(&At);CHKERRQ(ierr);
4750   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
4751   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
4752   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
4753   PetscFunctionReturn(0);
4754 }
4755 
4756 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
4757 {
4758   PetscErrorCode ierr;
4759   PetscInt       m=A->rmap->n,n=B->cmap->n;
4760   Mat            Cmat;
4761 
4762   PetscFunctionBegin;
4763   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);
4764   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
4765   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4766   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
4767   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
4768   ierr = MatMPIDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
4769   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4770   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4771 
4772   Cmat->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
4773 
4774   *C = Cmat;
4775   PetscFunctionReturn(0);
4776 }
4777 
4778 /* ----------------------------------------------------------------*/
4779 PETSC_INTERN PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
4780 {
4781   PetscErrorCode ierr;
4782 
4783   PetscFunctionBegin;
4784   if (scall == MAT_INITIAL_MATRIX) {
4785     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
4786     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
4787     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
4788   }
4789   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
4790   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
4791   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
4792   PetscFunctionReturn(0);
4793 }
4794 
4795 /*MC
4796    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
4797 
4798    Options Database Keys:
4799 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
4800 
4801   Level: beginner
4802 
4803 .seealso: MatCreateAIJ()
4804 M*/
4805 
4806 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
4807 {
4808   Mat_MPIAIJ     *b;
4809   PetscErrorCode ierr;
4810   PetscMPIInt    size;
4811 
4812   PetscFunctionBegin;
4813   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
4814 
4815   ierr          = PetscNewLog(B,&b);CHKERRQ(ierr);
4816   B->data       = (void*)b;
4817   ierr          = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
4818   B->assembled  = PETSC_FALSE;
4819   B->insertmode = NOT_SET_VALUES;
4820   b->size       = size;
4821 
4822   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank);CHKERRQ(ierr);
4823 
4824   /* build cache for off array entries formed */
4825   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash);CHKERRQ(ierr);
4826 
4827   b->donotstash  = PETSC_FALSE;
4828   b->colmap      = 0;
4829   b->garray      = 0;
4830   b->roworiented = PETSC_TRUE;
4831 
4832   /* stuff used for matrix vector multiply */
4833   b->lvec  = NULL;
4834   b->Mvctx = NULL;
4835 
4836   /* stuff for MatGetRow() */
4837   b->rowindices   = 0;
4838   b->rowvalues    = 0;
4839   b->getrowactive = PETSC_FALSE;
4840 
4841   /* flexible pointer used in CUSP/CUSPARSE classes */
4842   b->spptr = NULL;
4843 
4844   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetUseScalableIncreaseOverlap_C",MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ);CHKERRQ(ierr);
4845   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ);CHKERRQ(ierr);
4846   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
4847   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
4848   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
4849   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
4850   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
4851   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
4852   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
4853   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
4854 #if defined(PETSC_HAVE_ELEMENTAL)
4855   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_elemental_C",MatConvert_MPIAIJ_Elemental);CHKERRQ(ierr);
4856 #endif
4857 #if defined(PETSC_HAVE_HYPRE)
4858   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_hypre_C",MatConvert_AIJ_HYPRE);CHKERRQ(ierr);
4859 #endif
4860   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_is_C",MatConvert_MPIAIJ_IS);CHKERRQ(ierr);
4861   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
4862   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
4863   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
4864 #if defined(PETSC_HAVE_HYPRE)
4865   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMatMult_transpose_mpiaij_mpiaij_C",MatMatMatMult_Transpose_AIJ_AIJ);CHKERRQ(ierr);
4866 #endif
4867   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
4868   PetscFunctionReturn(0);
4869 }
4870 
4871 /*@C
4872      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
4873          and "off-diagonal" part of the matrix in CSR format.
4874 
4875    Collective on MPI_Comm
4876 
4877    Input Parameters:
4878 +  comm - MPI communicator
4879 .  m - number of local rows (Cannot be PETSC_DECIDE)
4880 .  n - This value should be the same as the local size used in creating the
4881        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
4882        calculated if N is given) For square matrices n is almost always m.
4883 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
4884 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
4885 .   i - row indices for "diagonal" portion of matrix
4886 .   j - column indices
4887 .   a - matrix values
4888 .   oi - row indices for "off-diagonal" portion of matrix
4889 .   oj - column indices
4890 -   oa - matrix values
4891 
4892    Output Parameter:
4893 .   mat - the matrix
4894 
4895    Level: advanced
4896 
4897    Notes:
4898        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
4899        must free the arrays once the matrix has been destroyed and not before.
4900 
4901        The i and j indices are 0 based
4902 
4903        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
4904 
4905        This sets local rows and cannot be used to set off-processor values.
4906 
4907        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
4908        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
4909        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
4910        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
4911        keep track of the underlying array. Use MatSetOption(A,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
4912        communication if it is known that only local entries will be set.
4913 
4914 .keywords: matrix, aij, compressed row, sparse, parallel
4915 
4916 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
4917           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
4918 @*/
4919 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)
4920 {
4921   PetscErrorCode ierr;
4922   Mat_MPIAIJ     *maij;
4923 
4924   PetscFunctionBegin;
4925   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
4926   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
4927   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
4928   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4929   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
4930   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
4931   maij = (Mat_MPIAIJ*) (*mat)->data;
4932 
4933   (*mat)->preallocated = PETSC_TRUE;
4934 
4935   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
4936   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
4937 
4938   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
4939   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
4940 
4941   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4942   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4943   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4944   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4945 
4946   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
4947   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4948   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4949   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_FALSE);CHKERRQ(ierr);
4950   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
4951   PetscFunctionReturn(0);
4952 }
4953 
4954 /*
4955     Special version for direct calls from Fortran
4956 */
4957 #include <petsc/private/fortranimpl.h>
4958 
4959 /* Change these macros so can be used in void function */
4960 #undef CHKERRQ
4961 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
4962 #undef SETERRQ2
4963 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
4964 #undef SETERRQ3
4965 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
4966 #undef SETERRQ
4967 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
4968 
4969 #if defined(PETSC_HAVE_FORTRAN_CAPS)
4970 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
4971 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
4972 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
4973 #else
4974 #endif
4975 PETSC_EXTERN void PETSC_STDCALL matsetvaluesmpiaij_(Mat *mmat,PetscInt *mm,const PetscInt im[],PetscInt *mn,const PetscInt in[],const PetscScalar v[],InsertMode *maddv,PetscErrorCode *_ierr)
4976 {
4977   Mat            mat  = *mmat;
4978   PetscInt       m    = *mm, n = *mn;
4979   InsertMode     addv = *maddv;
4980   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
4981   PetscScalar    value;
4982   PetscErrorCode ierr;
4983 
4984   MatCheckPreallocated(mat,1);
4985   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
4986 
4987 #if defined(PETSC_USE_DEBUG)
4988   else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
4989 #endif
4990   {
4991     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
4992     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
4993     PetscBool roworiented = aij->roworiented;
4994 
4995     /* Some Variables required in the macro */
4996     Mat        A                 = aij->A;
4997     Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
4998     PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
4999     MatScalar  *aa               = a->a;
5000     PetscBool  ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
5001     Mat        B                 = aij->B;
5002     Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
5003     PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5004     MatScalar  *ba               = b->a;
5005 
5006     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5007     PetscInt  nonew = a->nonew;
5008     MatScalar *ap1,*ap2;
5009 
5010     PetscFunctionBegin;
5011     for (i=0; i<m; i++) {
5012       if (im[i] < 0) continue;
5013 #if defined(PETSC_USE_DEBUG)
5014       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);
5015 #endif
5016       if (im[i] >= rstart && im[i] < rend) {
5017         row      = im[i] - rstart;
5018         lastcol1 = -1;
5019         rp1      = aj + ai[row];
5020         ap1      = aa + ai[row];
5021         rmax1    = aimax[row];
5022         nrow1    = ailen[row];
5023         low1     = 0;
5024         high1    = nrow1;
5025         lastcol2 = -1;
5026         rp2      = bj + bi[row];
5027         ap2      = ba + bi[row];
5028         rmax2    = bimax[row];
5029         nrow2    = bilen[row];
5030         low2     = 0;
5031         high2    = nrow2;
5032 
5033         for (j=0; j<n; j++) {
5034           if (roworiented) value = v[i*n+j];
5035           else value = v[i+j*m];
5036           if (in[j] >= cstart && in[j] < cend) {
5037             col = in[j] - cstart;
5038             if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
5039             MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
5040           } else if (in[j] < 0) continue;
5041 #if defined(PETSC_USE_DEBUG)
5042           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);
5043 #endif
5044           else {
5045             if (mat->was_assembled) {
5046               if (!aij->colmap) {
5047                 ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5048               }
5049 #if defined(PETSC_USE_CTABLE)
5050               ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5051               col--;
5052 #else
5053               col = aij->colmap[in[j]] - 1;
5054 #endif
5055               if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
5056               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5057                 ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5058                 col  =  in[j];
5059                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5060                 B     = aij->B;
5061                 b     = (Mat_SeqAIJ*)B->data;
5062                 bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5063                 rp2   = bj + bi[row];
5064                 ap2   = ba + bi[row];
5065                 rmax2 = bimax[row];
5066                 nrow2 = bilen[row];
5067                 low2  = 0;
5068                 high2 = nrow2;
5069                 bm    = aij->B->rmap->n;
5070                 ba    = b->a;
5071               }
5072             } else col = in[j];
5073             MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
5074           }
5075         }
5076       } else if (!aij->donotstash) {
5077         if (roworiented) {
5078           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5079         } else {
5080           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5081         }
5082       }
5083     }
5084   }
5085   PetscFunctionReturnVoid();
5086 }
5087 
5088