xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision ef5145865fe2b3e7ccc5a94f2cf2a99b672211a9)
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_SingleIS_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool,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   PetscBool      colflag,allcolumns=PETSC_FALSE;
3007 
3008   PetscFunctionBegin;
3009   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3010   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3011   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3012 
3013   /* Check for special case: each processor gets entire matrix columns */
3014   ierr = ISIdentity(iscol,&colflag);CHKERRQ(ierr);
3015   ierr = ISGetLocalSize(iscol,&nlocal);CHKERRQ(ierr);
3016   if (colflag && nlocal == mat->cmap->N) allcolumns = PETSC_TRUE;
3017 
3018   if (call ==  MAT_REUSE_MATRIX) {
3019     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3020     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3021     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,allcolumns,&Mreuse);CHKERRQ(ierr);
3022   } else {
3023     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,allcolumns,&Mreuse);CHKERRQ(ierr);
3024   }
3025 
3026   /*
3027       m - number of local rows
3028       n - number of columns (same on all processors)
3029       rstart - first row in new global matrix generated
3030   */
3031   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3032   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3033   if (call == MAT_INITIAL_MATRIX) {
3034     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3035     ii  = aij->i;
3036     jj  = aij->j;
3037 
3038     /*
3039         Determine the number of non-zeros in the diagonal and off-diagonal
3040         portions of the matrix in order to do correct preallocation
3041     */
3042 
3043     /* first get start and end of "diagonal" columns */
3044     if (csize == PETSC_DECIDE) {
3045       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3046       if (mglobal == n) { /* square matrix */
3047         nlocal = m;
3048       } else {
3049         nlocal = n/size + ((n % size) > rank);
3050       }
3051     } else {
3052       nlocal = csize;
3053     }
3054     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3055     rstart = rend - nlocal;
3056     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);
3057 
3058     /* next, compute all the lengths */
3059     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3060     olens = dlens + m;
3061     for (i=0; i<m; i++) {
3062       jend = ii[i+1] - ii[i];
3063       olen = 0;
3064       dlen = 0;
3065       for (j=0; j<jend; j++) {
3066         if (*jj < rstart || *jj >= rend) olen++;
3067         else dlen++;
3068         jj++;
3069       }
3070       olens[i] = olen;
3071       dlens[i] = dlen;
3072     }
3073     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3074     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3075     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3076     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3077     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3078     ierr = PetscFree(dlens);CHKERRQ(ierr);
3079   } else {
3080     PetscInt ml,nl;
3081 
3082     M    = *newmat;
3083     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3084     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3085     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3086     /*
3087          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3088        rather than the slower MatSetValues().
3089     */
3090     M->was_assembled = PETSC_TRUE;
3091     M->assembled     = PETSC_FALSE;
3092   }
3093   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3094   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3095   ii   = aij->i;
3096   jj   = aij->j;
3097   aa   = aij->a;
3098   for (i=0; i<m; i++) {
3099     row   = rstart + i;
3100     nz    = ii[i+1] - ii[i];
3101     cwork = jj;     jj += nz;
3102     vwork = aa;     aa += nz;
3103     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3104   }
3105 
3106   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3107   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3108   *newmat = M;
3109 
3110   /* save submatrix used in processor for next request */
3111   if (call ==  MAT_INITIAL_MATRIX) {
3112     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3113     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3114   }
3115   PetscFunctionReturn(0);
3116 }
3117 
3118 PetscErrorCode  MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3119 {
3120   PetscInt       m,cstart, cend,j,nnz,i,d;
3121   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3122   const PetscInt *JJ;
3123   PetscScalar    *values;
3124   PetscErrorCode ierr;
3125   PetscBool      nooffprocentries;
3126 
3127   PetscFunctionBegin;
3128   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3129 
3130   ierr   = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3131   ierr   = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3132   m      = B->rmap->n;
3133   cstart = B->cmap->rstart;
3134   cend   = B->cmap->rend;
3135   rstart = B->rmap->rstart;
3136 
3137   ierr = PetscMalloc2(m,&d_nnz,m,&o_nnz);CHKERRQ(ierr);
3138 
3139 #if defined(PETSC_USE_DEBUGGING)
3140   for (i=0; i<m; i++) {
3141     nnz = Ii[i+1]- Ii[i];
3142     JJ  = J + Ii[i];
3143     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3144     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3145     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);
3146   }
3147 #endif
3148 
3149   for (i=0; i<m; i++) {
3150     nnz     = Ii[i+1]- Ii[i];
3151     JJ      = J + Ii[i];
3152     nnz_max = PetscMax(nnz_max,nnz);
3153     d       = 0;
3154     for (j=0; j<nnz; j++) {
3155       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3156     }
3157     d_nnz[i] = d;
3158     o_nnz[i] = nnz - d;
3159   }
3160   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3161   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3162 
3163   if (v) values = (PetscScalar*)v;
3164   else {
3165     ierr = PetscCalloc1(nnz_max+1,&values);CHKERRQ(ierr);
3166   }
3167 
3168   for (i=0; i<m; i++) {
3169     ii   = i + rstart;
3170     nnz  = Ii[i+1]- Ii[i];
3171     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3172   }
3173   nooffprocentries    = B->nooffprocentries;
3174   B->nooffprocentries = PETSC_TRUE;
3175   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3176   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3177   B->nooffprocentries = nooffprocentries;
3178 
3179   if (!v) {
3180     ierr = PetscFree(values);CHKERRQ(ierr);
3181   }
3182   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3183   PetscFunctionReturn(0);
3184 }
3185 
3186 /*@
3187    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3188    (the default parallel PETSc format).
3189 
3190    Collective on MPI_Comm
3191 
3192    Input Parameters:
3193 +  B - the matrix
3194 .  i - the indices into j for the start of each local row (starts with zero)
3195 .  j - the column indices for each local row (starts with zero)
3196 -  v - optional values in the matrix
3197 
3198    Level: developer
3199 
3200    Notes:
3201        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3202      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3203      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3204 
3205        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3206 
3207        The format which is used for the sparse matrix input, is equivalent to a
3208     row-major ordering.. i.e for the following matrix, the input data expected is
3209     as shown
3210 
3211 $        1 0 0
3212 $        2 0 3     P0
3213 $       -------
3214 $        4 5 6     P1
3215 $
3216 $     Process0 [P0]: rows_owned=[0,1]
3217 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3218 $        j =  {0,0,2}  [size = 3]
3219 $        v =  {1,2,3}  [size = 3]
3220 $
3221 $     Process1 [P1]: rows_owned=[2]
3222 $        i =  {0,3}    [size = nrow+1  = 1+1]
3223 $        j =  {0,1,2}  [size = 3]
3224 $        v =  {4,5,6}  [size = 3]
3225 
3226 .keywords: matrix, aij, compressed row, sparse, parallel
3227 
3228 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MATMPIAIJ,
3229           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3230 @*/
3231 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3232 {
3233   PetscErrorCode ierr;
3234 
3235   PetscFunctionBegin;
3236   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3237   PetscFunctionReturn(0);
3238 }
3239 
3240 /*@C
3241    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3242    (the default parallel PETSc format).  For good matrix assembly performance
3243    the user should preallocate the matrix storage by setting the parameters
3244    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3245    performance can be increased by more than a factor of 50.
3246 
3247    Collective on MPI_Comm
3248 
3249    Input Parameters:
3250 +  B - the matrix
3251 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3252            (same value is used for all local rows)
3253 .  d_nnz - array containing the number of nonzeros in the various rows of the
3254            DIAGONAL portion of the local submatrix (possibly different for each row)
3255            or NULL (PETSC_NULL_INTEGER in Fortran), if d_nz is used to specify the nonzero structure.
3256            The size of this array is equal to the number of local rows, i.e 'm'.
3257            For matrices that will be factored, you must leave room for (and set)
3258            the diagonal entry even if it is zero.
3259 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3260            submatrix (same value is used for all local rows).
3261 -  o_nnz - array containing the number of nonzeros in the various rows of the
3262            OFF-DIAGONAL portion of the local submatrix (possibly different for
3263            each row) or NULL (PETSC_NULL_INTEGER in Fortran), if o_nz is used to specify the nonzero
3264            structure. The size of this array is equal to the number
3265            of local rows, i.e 'm'.
3266 
3267    If the *_nnz parameter is given then the *_nz parameter is ignored
3268 
3269    The AIJ format (also called the Yale sparse matrix format or
3270    compressed row storage (CSR)), is fully compatible with standard Fortran 77
3271    storage.  The stored row and column indices begin with zero.
3272    See Users-Manual: ch_mat for details.
3273 
3274    The parallel matrix is partitioned such that the first m0 rows belong to
3275    process 0, the next m1 rows belong to process 1, the next m2 rows belong
3276    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
3277 
3278    The DIAGONAL portion of the local submatrix of a processor can be defined
3279    as the submatrix which is obtained by extraction the part corresponding to
3280    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
3281    first row that belongs to the processor, r2 is the last row belonging to
3282    the this processor, and c1-c2 is range of indices of the local part of a
3283    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
3284    common case of a square matrix, the row and column ranges are the same and
3285    the DIAGONAL part is also square. The remaining portion of the local
3286    submatrix (mxN) constitute the OFF-DIAGONAL portion.
3287 
3288    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3289 
3290    You can call MatGetInfo() to get information on how effective the preallocation was;
3291    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3292    You can also run with the option -info and look for messages with the string
3293    malloc in them to see if additional memory allocation was needed.
3294 
3295    Example usage:
3296 
3297    Consider the following 8x8 matrix with 34 non-zero values, that is
3298    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3299    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3300    as follows:
3301 
3302 .vb
3303             1  2  0  |  0  3  0  |  0  4
3304     Proc0   0  5  6  |  7  0  0  |  8  0
3305             9  0 10  | 11  0  0  | 12  0
3306     -------------------------------------
3307            13  0 14  | 15 16 17  |  0  0
3308     Proc1   0 18  0  | 19 20 21  |  0  0
3309             0  0  0  | 22 23  0  | 24  0
3310     -------------------------------------
3311     Proc2  25 26 27  |  0  0 28  | 29  0
3312            30  0  0  | 31 32 33  |  0 34
3313 .ve
3314 
3315    This can be represented as a collection of submatrices as:
3316 
3317 .vb
3318       A B C
3319       D E F
3320       G H I
3321 .ve
3322 
3323    Where the submatrices A,B,C are owned by proc0, D,E,F are
3324    owned by proc1, G,H,I are owned by proc2.
3325 
3326    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3327    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3328    The 'M','N' parameters are 8,8, and have the same values on all procs.
3329 
3330    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3331    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3332    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3333    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3334    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3335    matrix, ans [DF] as another SeqAIJ matrix.
3336 
3337    When d_nz, o_nz parameters are specified, d_nz storage elements are
3338    allocated for every row of the local diagonal submatrix, and o_nz
3339    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3340    One way to choose d_nz and o_nz is to use the max nonzerors per local
3341    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3342    In this case, the values of d_nz,o_nz are:
3343 .vb
3344      proc0 : dnz = 2, o_nz = 2
3345      proc1 : dnz = 3, o_nz = 2
3346      proc2 : dnz = 1, o_nz = 4
3347 .ve
3348    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3349    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3350    for proc3. i.e we are using 12+15+10=37 storage locations to store
3351    34 values.
3352 
3353    When d_nnz, o_nnz parameters are specified, the storage is specified
3354    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3355    In the above case the values for d_nnz,o_nnz are:
3356 .vb
3357      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3358      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3359      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3360 .ve
3361    Here the space allocated is sum of all the above values i.e 34, and
3362    hence pre-allocation is perfect.
3363 
3364    Level: intermediate
3365 
3366 .keywords: matrix, aij, compressed row, sparse, parallel
3367 
3368 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
3369           MATMPIAIJ, MatGetInfo(), PetscSplitOwnership()
3370 @*/
3371 PetscErrorCode  MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3372 {
3373   PetscErrorCode ierr;
3374 
3375   PetscFunctionBegin;
3376   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3377   PetscValidType(B,1);
3378   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
3379   PetscFunctionReturn(0);
3380 }
3381 
3382 /*@
3383      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
3384          CSR format the local rows.
3385 
3386    Collective on MPI_Comm
3387 
3388    Input Parameters:
3389 +  comm - MPI communicator
3390 .  m - number of local rows (Cannot be PETSC_DECIDE)
3391 .  n - This value should be the same as the local size used in creating the
3392        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3393        calculated if N is given) For square matrices n is almost always m.
3394 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3395 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3396 .   i - row indices
3397 .   j - column indices
3398 -   a - matrix values
3399 
3400    Output Parameter:
3401 .   mat - the matrix
3402 
3403    Level: intermediate
3404 
3405    Notes:
3406        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3407      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3408      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3409 
3410        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3411 
3412        The format which is used for the sparse matrix input, is equivalent to a
3413     row-major ordering.. i.e for the following matrix, the input data expected is
3414     as shown
3415 
3416 $        1 0 0
3417 $        2 0 3     P0
3418 $       -------
3419 $        4 5 6     P1
3420 $
3421 $     Process0 [P0]: rows_owned=[0,1]
3422 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3423 $        j =  {0,0,2}  [size = 3]
3424 $        v =  {1,2,3}  [size = 3]
3425 $
3426 $     Process1 [P1]: rows_owned=[2]
3427 $        i =  {0,3}    [size = nrow+1  = 1+1]
3428 $        j =  {0,1,2}  [size = 3]
3429 $        v =  {4,5,6}  [size = 3]
3430 
3431 .keywords: matrix, aij, compressed row, sparse, parallel
3432 
3433 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3434           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
3435 @*/
3436 PetscErrorCode  MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
3437 {
3438   PetscErrorCode ierr;
3439 
3440   PetscFunctionBegin;
3441   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
3442   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
3443   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
3444   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
3445   /* ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr); */
3446   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
3447   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
3448   PetscFunctionReturn(0);
3449 }
3450 
3451 /*@C
3452    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
3453    (the default parallel PETSc format).  For good matrix assembly performance
3454    the user should preallocate the matrix storage by setting the parameters
3455    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3456    performance can be increased by more than a factor of 50.
3457 
3458    Collective on MPI_Comm
3459 
3460    Input Parameters:
3461 +  comm - MPI communicator
3462 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
3463            This value should be the same as the local size used in creating the
3464            y vector for the matrix-vector product y = Ax.
3465 .  n - This value should be the same as the local size used in creating the
3466        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3467        calculated if N is given) For square matrices n is almost always m.
3468 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3469 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3470 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3471            (same value is used for all local rows)
3472 .  d_nnz - array containing the number of nonzeros in the various rows of the
3473            DIAGONAL portion of the local submatrix (possibly different for each row)
3474            or NULL, if d_nz is used to specify the nonzero structure.
3475            The size of this array is equal to the number of local rows, i.e 'm'.
3476 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3477            submatrix (same value is used for all local rows).
3478 -  o_nnz - array containing the number of nonzeros in the various rows of the
3479            OFF-DIAGONAL portion of the local submatrix (possibly different for
3480            each row) or NULL, if o_nz is used to specify the nonzero
3481            structure. The size of this array is equal to the number
3482            of local rows, i.e 'm'.
3483 
3484    Output Parameter:
3485 .  A - the matrix
3486 
3487    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3488    MatXXXXSetPreallocation() paradgm instead of this routine directly.
3489    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3490 
3491    Notes:
3492    If the *_nnz parameter is given then the *_nz parameter is ignored
3493 
3494    m,n,M,N parameters specify the size of the matrix, and its partitioning across
3495    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
3496    storage requirements for this matrix.
3497 
3498    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
3499    processor than it must be used on all processors that share the object for
3500    that argument.
3501 
3502    The user MUST specify either the local or global matrix dimensions
3503    (possibly both).
3504 
3505    The parallel matrix is partitioned across processors such that the
3506    first m0 rows belong to process 0, the next m1 rows belong to
3507    process 1, the next m2 rows belong to process 2 etc.. where
3508    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
3509    values corresponding to [m x N] submatrix.
3510 
3511    The columns are logically partitioned with the n0 columns belonging
3512    to 0th partition, the next n1 columns belonging to the next
3513    partition etc.. where n0,n1,n2... are the input parameter 'n'.
3514 
3515    The DIAGONAL portion of the local submatrix on any given processor
3516    is the submatrix corresponding to the rows and columns m,n
3517    corresponding to the given processor. i.e diagonal matrix on
3518    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
3519    etc. The remaining portion of the local submatrix [m x (N-n)]
3520    constitute the OFF-DIAGONAL portion. The example below better
3521    illustrates this concept.
3522 
3523    For a square global matrix we define each processor's diagonal portion
3524    to be its local rows and the corresponding columns (a square submatrix);
3525    each processor's off-diagonal portion encompasses the remainder of the
3526    local matrix (a rectangular submatrix).
3527 
3528    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3529 
3530    When calling this routine with a single process communicator, a matrix of
3531    type SEQAIJ is returned.  If a matrix of type MATMPIAIJ is desired for this
3532    type of communicator, use the construction mechanism:
3533      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
3534 
3535    By default, this format uses inodes (identical nodes) when possible.
3536    We search for consecutive rows with the same nonzero structure, thereby
3537    reusing matrix information to achieve increased efficiency.
3538 
3539    Options Database Keys:
3540 +  -mat_no_inode  - Do not use inodes
3541 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3542 -  -mat_aij_oneindex - Internally use indexing starting at 1
3543         rather than 0.  Note that when calling MatSetValues(),
3544         the user still MUST index entries starting at 0!
3545 
3546 
3547    Example usage:
3548 
3549    Consider the following 8x8 matrix with 34 non-zero values, that is
3550    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3551    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3552    as follows:
3553 
3554 .vb
3555             1  2  0  |  0  3  0  |  0  4
3556     Proc0   0  5  6  |  7  0  0  |  8  0
3557             9  0 10  | 11  0  0  | 12  0
3558     -------------------------------------
3559            13  0 14  | 15 16 17  |  0  0
3560     Proc1   0 18  0  | 19 20 21  |  0  0
3561             0  0  0  | 22 23  0  | 24  0
3562     -------------------------------------
3563     Proc2  25 26 27  |  0  0 28  | 29  0
3564            30  0  0  | 31 32 33  |  0 34
3565 .ve
3566 
3567    This can be represented as a collection of submatrices as:
3568 
3569 .vb
3570       A B C
3571       D E F
3572       G H I
3573 .ve
3574 
3575    Where the submatrices A,B,C are owned by proc0, D,E,F are
3576    owned by proc1, G,H,I are owned by proc2.
3577 
3578    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3579    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3580    The 'M','N' parameters are 8,8, and have the same values on all procs.
3581 
3582    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3583    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3584    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3585    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3586    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3587    matrix, ans [DF] as another SeqAIJ matrix.
3588 
3589    When d_nz, o_nz parameters are specified, d_nz storage elements are
3590    allocated for every row of the local diagonal submatrix, and o_nz
3591    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3592    One way to choose d_nz and o_nz is to use the max nonzerors per local
3593    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3594    In this case, the values of d_nz,o_nz are:
3595 .vb
3596      proc0 : dnz = 2, o_nz = 2
3597      proc1 : dnz = 3, o_nz = 2
3598      proc2 : dnz = 1, o_nz = 4
3599 .ve
3600    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3601    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3602    for proc3. i.e we are using 12+15+10=37 storage locations to store
3603    34 values.
3604 
3605    When d_nnz, o_nnz parameters are specified, the storage is specified
3606    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3607    In the above case the values for d_nnz,o_nnz are:
3608 .vb
3609      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3610      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3611      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3612 .ve
3613    Here the space allocated is sum of all the above values i.e 34, and
3614    hence pre-allocation is perfect.
3615 
3616    Level: intermediate
3617 
3618 .keywords: matrix, aij, compressed row, sparse, parallel
3619 
3620 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3621           MATMPIAIJ, MatCreateMPIAIJWithArrays()
3622 @*/
3623 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)
3624 {
3625   PetscErrorCode ierr;
3626   PetscMPIInt    size;
3627 
3628   PetscFunctionBegin;
3629   ierr = MatCreate(comm,A);CHKERRQ(ierr);
3630   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
3631   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3632   if (size > 1) {
3633     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
3634     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
3635   } else {
3636     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
3637     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
3638   }
3639   PetscFunctionReturn(0);
3640 }
3641 
3642 PetscErrorCode  MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
3643 {
3644   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3645   PetscBool      flg;
3646   PetscErrorCode ierr;
3647 
3648   PetscFunctionBegin;
3649   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&flg);CHKERRQ(ierr);
3650   if (!flg) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"This function requires a MATMPIAIJ matrix as input");
3651   if (Ad)     *Ad     = a->A;
3652   if (Ao)     *Ao     = a->B;
3653   if (colmap) *colmap = a->garray;
3654   PetscFunctionReturn(0);
3655 }
3656 
3657 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
3658 {
3659   PetscErrorCode ierr;
3660   PetscInt       m,N,i,rstart,nnz,Ii;
3661   PetscInt       *indx;
3662   PetscScalar    *values;
3663 
3664   PetscFunctionBegin;
3665   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
3666   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
3667     PetscInt       *dnz,*onz,sum,bs,cbs;
3668 
3669     if (n == PETSC_DECIDE) {
3670       ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
3671     }
3672     /* Check sum(n) = N */
3673     ierr = MPIU_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3674     if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
3675 
3676     ierr    = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3677     rstart -= m;
3678 
3679     ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
3680     for (i=0; i<m; i++) {
3681       ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3682       ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
3683       ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3684     }
3685 
3686     ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
3687     ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
3688     ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
3689     ierr = MatSetBlockSizes(*outmat,bs,cbs);CHKERRQ(ierr);
3690     ierr = MatSetType(*outmat,MATAIJ);CHKERRQ(ierr);
3691     ierr = MatSeqAIJSetPreallocation(*outmat,0,dnz);CHKERRQ(ierr);
3692     ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
3693     ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
3694   }
3695 
3696   /* numeric phase */
3697   ierr = MatGetOwnershipRange(*outmat,&rstart,NULL);CHKERRQ(ierr);
3698   for (i=0; i<m; i++) {
3699     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3700     Ii   = i + rstart;
3701     ierr = MatSetValues(*outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3702     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3703   }
3704   ierr = MatAssemblyBegin(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3705   ierr = MatAssemblyEnd(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3706   PetscFunctionReturn(0);
3707 }
3708 
3709 PetscErrorCode MatFileSplit(Mat A,char *outfile)
3710 {
3711   PetscErrorCode    ierr;
3712   PetscMPIInt       rank;
3713   PetscInt          m,N,i,rstart,nnz;
3714   size_t            len;
3715   const PetscInt    *indx;
3716   PetscViewer       out;
3717   char              *name;
3718   Mat               B;
3719   const PetscScalar *values;
3720 
3721   PetscFunctionBegin;
3722   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
3723   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
3724   /* Should this be the type of the diagonal block of A? */
3725   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
3726   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
3727   ierr = MatSetBlockSizesFromMats(B,A,A);CHKERRQ(ierr);
3728   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
3729   ierr = MatSeqAIJSetPreallocation(B,0,NULL);CHKERRQ(ierr);
3730   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
3731   for (i=0; i<m; i++) {
3732     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3733     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3734     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3735   }
3736   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3737   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3738 
3739   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
3740   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
3741   ierr = PetscMalloc1(len+5,&name);CHKERRQ(ierr);
3742   sprintf(name,"%s.%d",outfile,rank);
3743   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
3744   ierr = PetscFree(name);CHKERRQ(ierr);
3745   ierr = MatView(B,out);CHKERRQ(ierr);
3746   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
3747   ierr = MatDestroy(&B);CHKERRQ(ierr);
3748   PetscFunctionReturn(0);
3749 }
3750 
3751 PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
3752 {
3753   PetscErrorCode      ierr;
3754   Mat_Merge_SeqsToMPI *merge;
3755   PetscContainer      container;
3756 
3757   PetscFunctionBegin;
3758   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
3759   if (container) {
3760     ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
3761     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
3762     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
3763     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
3764     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
3765     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
3766     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
3767     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
3768     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
3769     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
3770     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
3771     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
3772     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
3773     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
3774     ierr = PetscFree(merge);CHKERRQ(ierr);
3775     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
3776   }
3777   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
3778   PetscFunctionReturn(0);
3779 }
3780 
3781 #include <../src/mat/utils/freespace.h>
3782 #include <petscbt.h>
3783 
3784 PetscErrorCode  MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
3785 {
3786   PetscErrorCode      ierr;
3787   MPI_Comm            comm;
3788   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
3789   PetscMPIInt         size,rank,taga,*len_s;
3790   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
3791   PetscInt            proc,m;
3792   PetscInt            **buf_ri,**buf_rj;
3793   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
3794   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
3795   MPI_Request         *s_waits,*r_waits;
3796   MPI_Status          *status;
3797   MatScalar           *aa=a->a;
3798   MatScalar           **abuf_r,*ba_i;
3799   Mat_Merge_SeqsToMPI *merge;
3800   PetscContainer      container;
3801 
3802   PetscFunctionBegin;
3803   ierr = PetscObjectGetComm((PetscObject)mpimat,&comm);CHKERRQ(ierr);
3804   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
3805 
3806   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3807   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3808 
3809   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
3810   ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
3811 
3812   bi     = merge->bi;
3813   bj     = merge->bj;
3814   buf_ri = merge->buf_ri;
3815   buf_rj = merge->buf_rj;
3816 
3817   ierr   = PetscMalloc1(size,&status);CHKERRQ(ierr);
3818   owners = merge->rowmap->range;
3819   len_s  = merge->len_s;
3820 
3821   /* send and recv matrix values */
3822   /*-----------------------------*/
3823   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
3824   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
3825 
3826   ierr = PetscMalloc1(merge->nsend+1,&s_waits);CHKERRQ(ierr);
3827   for (proc=0,k=0; proc<size; proc++) {
3828     if (!len_s[proc]) continue;
3829     i    = owners[proc];
3830     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
3831     k++;
3832   }
3833 
3834   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
3835   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
3836   ierr = PetscFree(status);CHKERRQ(ierr);
3837 
3838   ierr = PetscFree(s_waits);CHKERRQ(ierr);
3839   ierr = PetscFree(r_waits);CHKERRQ(ierr);
3840 
3841   /* insert mat values of mpimat */
3842   /*----------------------------*/
3843   ierr = PetscMalloc1(N,&ba_i);CHKERRQ(ierr);
3844   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
3845 
3846   for (k=0; k<merge->nrecv; k++) {
3847     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
3848     nrows       = *(buf_ri_k[k]);
3849     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
3850     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
3851   }
3852 
3853   /* set values of ba */
3854   m = merge->rowmap->n;
3855   for (i=0; i<m; i++) {
3856     arow = owners[rank] + i;
3857     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
3858     bnzi = bi[i+1] - bi[i];
3859     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
3860 
3861     /* add local non-zero vals of this proc's seqmat into ba */
3862     anzi   = ai[arow+1] - ai[arow];
3863     aj     = a->j + ai[arow];
3864     aa     = a->a + ai[arow];
3865     nextaj = 0;
3866     for (j=0; nextaj<anzi; j++) {
3867       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
3868         ba_i[j] += aa[nextaj++];
3869       }
3870     }
3871 
3872     /* add received vals into ba */
3873     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
3874       /* i-th row */
3875       if (i == *nextrow[k]) {
3876         anzi   = *(nextai[k]+1) - *nextai[k];
3877         aj     = buf_rj[k] + *(nextai[k]);
3878         aa     = abuf_r[k] + *(nextai[k]);
3879         nextaj = 0;
3880         for (j=0; nextaj<anzi; j++) {
3881           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
3882             ba_i[j] += aa[nextaj++];
3883           }
3884         }
3885         nextrow[k]++; nextai[k]++;
3886       }
3887     }
3888     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
3889   }
3890   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3891   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3892 
3893   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
3894   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
3895   ierr = PetscFree(ba_i);CHKERRQ(ierr);
3896   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
3897   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
3898   PetscFunctionReturn(0);
3899 }
3900 
3901 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
3902 {
3903   PetscErrorCode      ierr;
3904   Mat                 B_mpi;
3905   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
3906   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
3907   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
3908   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
3909   PetscInt            len,proc,*dnz,*onz,bs,cbs;
3910   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
3911   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
3912   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
3913   MPI_Status          *status;
3914   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
3915   PetscBT             lnkbt;
3916   Mat_Merge_SeqsToMPI *merge;
3917   PetscContainer      container;
3918 
3919   PetscFunctionBegin;
3920   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
3921 
3922   /* make sure it is a PETSc comm */
3923   ierr = PetscCommDuplicate(comm,&comm,NULL);CHKERRQ(ierr);
3924   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3925   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3926 
3927   ierr = PetscNew(&merge);CHKERRQ(ierr);
3928   ierr = PetscMalloc1(size,&status);CHKERRQ(ierr);
3929 
3930   /* determine row ownership */
3931   /*---------------------------------------------------------*/
3932   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
3933   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
3934   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
3935   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
3936   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
3937   ierr = PetscMalloc1(size,&len_si);CHKERRQ(ierr);
3938   ierr = PetscMalloc1(size,&merge->len_s);CHKERRQ(ierr);
3939 
3940   m      = merge->rowmap->n;
3941   owners = merge->rowmap->range;
3942 
3943   /* determine the number of messages to send, their lengths */
3944   /*---------------------------------------------------------*/
3945   len_s = merge->len_s;
3946 
3947   len          = 0; /* length of buf_si[] */
3948   merge->nsend = 0;
3949   for (proc=0; proc<size; proc++) {
3950     len_si[proc] = 0;
3951     if (proc == rank) {
3952       len_s[proc] = 0;
3953     } else {
3954       len_si[proc] = owners[proc+1] - owners[proc] + 1;
3955       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
3956     }
3957     if (len_s[proc]) {
3958       merge->nsend++;
3959       nrows = 0;
3960       for (i=owners[proc]; i<owners[proc+1]; i++) {
3961         if (ai[i+1] > ai[i]) nrows++;
3962       }
3963       len_si[proc] = 2*(nrows+1);
3964       len         += len_si[proc];
3965     }
3966   }
3967 
3968   /* determine the number and length of messages to receive for ij-structure */
3969   /*-------------------------------------------------------------------------*/
3970   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
3971   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
3972 
3973   /* post the Irecv of j-structure */
3974   /*-------------------------------*/
3975   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
3976   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
3977 
3978   /* post the Isend of j-structure */
3979   /*--------------------------------*/
3980   ierr = PetscMalloc2(merge->nsend,&si_waits,merge->nsend,&sj_waits);CHKERRQ(ierr);
3981 
3982   for (proc=0, k=0; proc<size; proc++) {
3983     if (!len_s[proc]) continue;
3984     i    = owners[proc];
3985     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
3986     k++;
3987   }
3988 
3989   /* receives and sends of j-structure are complete */
3990   /*------------------------------------------------*/
3991   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
3992   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
3993 
3994   /* send and recv i-structure */
3995   /*---------------------------*/
3996   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
3997   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
3998 
3999   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
4000   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4001   for (proc=0,k=0; proc<size; proc++) {
4002     if (!len_s[proc]) continue;
4003     /* form outgoing message for i-structure:
4004          buf_si[0]:                 nrows to be sent
4005                [1:nrows]:           row index (global)
4006                [nrows+1:2*nrows+1]: i-structure index
4007     */
4008     /*-------------------------------------------*/
4009     nrows       = len_si[proc]/2 - 1;
4010     buf_si_i    = buf_si + nrows+1;
4011     buf_si[0]   = nrows;
4012     buf_si_i[0] = 0;
4013     nrows       = 0;
4014     for (i=owners[proc]; i<owners[proc+1]; i++) {
4015       anzi = ai[i+1] - ai[i];
4016       if (anzi) {
4017         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4018         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4019         nrows++;
4020       }
4021     }
4022     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4023     k++;
4024     buf_si += len_si[proc];
4025   }
4026 
4027   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4028   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4029 
4030   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4031   for (i=0; i<merge->nrecv; i++) {
4032     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);
4033   }
4034 
4035   ierr = PetscFree(len_si);CHKERRQ(ierr);
4036   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4037   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4038   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4039   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4040   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4041   ierr = PetscFree(status);CHKERRQ(ierr);
4042 
4043   /* compute a local seq matrix in each processor */
4044   /*----------------------------------------------*/
4045   /* allocate bi array and free space for accumulating nonzero column info */
4046   ierr  = PetscMalloc1(m+1,&bi);CHKERRQ(ierr);
4047   bi[0] = 0;
4048 
4049   /* create and initialize a linked list */
4050   nlnk = N+1;
4051   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4052 
4053   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4054   len  = ai[owners[rank+1]] - ai[owners[rank]];
4055   ierr = PetscFreeSpaceGet(PetscIntMultTruncate(2,len)+1,&free_space);CHKERRQ(ierr);
4056 
4057   current_space = free_space;
4058 
4059   /* determine symbolic info for each local row */
4060   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4061 
4062   for (k=0; k<merge->nrecv; k++) {
4063     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4064     nrows       = *buf_ri_k[k];
4065     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4066     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4067   }
4068 
4069   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4070   len  = 0;
4071   for (i=0; i<m; i++) {
4072     bnzi = 0;
4073     /* add local non-zero cols of this proc's seqmat into lnk */
4074     arow  = owners[rank] + i;
4075     anzi  = ai[arow+1] - ai[arow];
4076     aj    = a->j + ai[arow];
4077     ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4078     bnzi += nlnk;
4079     /* add received col data into lnk */
4080     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4081       if (i == *nextrow[k]) { /* i-th row */
4082         anzi  = *(nextai[k]+1) - *nextai[k];
4083         aj    = buf_rj[k] + *nextai[k];
4084         ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4085         bnzi += nlnk;
4086         nextrow[k]++; nextai[k]++;
4087       }
4088     }
4089     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4090 
4091     /* if free space is not available, make more free space */
4092     if (current_space->local_remaining<bnzi) {
4093       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(bnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
4094       nspacedouble++;
4095     }
4096     /* copy data into free space, then initialize lnk */
4097     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4098     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
4099 
4100     current_space->array           += bnzi;
4101     current_space->local_used      += bnzi;
4102     current_space->local_remaining -= bnzi;
4103 
4104     bi[i+1] = bi[i] + bnzi;
4105   }
4106 
4107   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4108 
4109   ierr = PetscMalloc1(bi[m]+1,&bj);CHKERRQ(ierr);
4110   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
4111   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4112 
4113   /* create symbolic parallel matrix B_mpi */
4114   /*---------------------------------------*/
4115   ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
4116   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
4117   if (n==PETSC_DECIDE) {
4118     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
4119   } else {
4120     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4121   }
4122   ierr = MatSetBlockSizes(B_mpi,bs,cbs);CHKERRQ(ierr);
4123   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
4124   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
4125   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4126   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
4127 
4128   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4129   B_mpi->assembled    = PETSC_FALSE;
4130   B_mpi->ops->destroy = MatDestroy_MPIAIJ_SeqsToMPI;
4131   merge->bi           = bi;
4132   merge->bj           = bj;
4133   merge->buf_ri       = buf_ri;
4134   merge->buf_rj       = buf_rj;
4135   merge->coi          = NULL;
4136   merge->coj          = NULL;
4137   merge->owners_co    = NULL;
4138 
4139   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
4140 
4141   /* attach the supporting struct to B_mpi for reuse */
4142   ierr    = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
4143   ierr    = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
4144   ierr    = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
4145   ierr    = PetscContainerDestroy(&container);CHKERRQ(ierr);
4146   *mpimat = B_mpi;
4147 
4148   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4149   PetscFunctionReturn(0);
4150 }
4151 
4152 /*@C
4153       MatCreateMPIAIJSumSeqAIJ - Creates a MATMPIAIJ matrix by adding sequential
4154                  matrices from each processor
4155 
4156     Collective on MPI_Comm
4157 
4158    Input Parameters:
4159 +    comm - the communicators the parallel matrix will live on
4160 .    seqmat - the input sequential matrices
4161 .    m - number of local rows (or PETSC_DECIDE)
4162 .    n - number of local columns (or PETSC_DECIDE)
4163 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4164 
4165    Output Parameter:
4166 .    mpimat - the parallel matrix generated
4167 
4168     Level: advanced
4169 
4170    Notes:
4171      The dimensions of the sequential matrix in each processor MUST be the same.
4172      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
4173      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
4174 @*/
4175 PetscErrorCode  MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
4176 {
4177   PetscErrorCode ierr;
4178   PetscMPIInt    size;
4179 
4180   PetscFunctionBegin;
4181   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4182   if (size == 1) {
4183     ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4184     if (scall == MAT_INITIAL_MATRIX) {
4185       ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
4186     } else {
4187       ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4188     }
4189     ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4190     PetscFunctionReturn(0);
4191   }
4192   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4193   if (scall == MAT_INITIAL_MATRIX) {
4194     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
4195   }
4196   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
4197   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4198   PetscFunctionReturn(0);
4199 }
4200 
4201 /*@
4202      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MATMPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
4203           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
4204           with MatGetSize()
4205 
4206     Not Collective
4207 
4208    Input Parameters:
4209 +    A - the matrix
4210 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4211 
4212    Output Parameter:
4213 .    A_loc - the local sequential matrix generated
4214 
4215     Level: developer
4216 
4217 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
4218 
4219 @*/
4220 PetscErrorCode  MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
4221 {
4222   PetscErrorCode ierr;
4223   Mat_MPIAIJ     *mpimat=(Mat_MPIAIJ*)A->data;
4224   Mat_SeqAIJ     *mat,*a,*b;
4225   PetscInt       *ai,*aj,*bi,*bj,*cmap=mpimat->garray;
4226   MatScalar      *aa,*ba,*cam;
4227   PetscScalar    *ca;
4228   PetscInt       am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
4229   PetscInt       *ci,*cj,col,ncols_d,ncols_o,jo;
4230   PetscBool      match;
4231   MPI_Comm       comm;
4232   PetscMPIInt    size;
4233 
4234   PetscFunctionBegin;
4235   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4236   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
4237   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4238   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4239   if (size == 1 && scall == MAT_REUSE_MATRIX) PetscFunctionReturn(0);
4240 
4241   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4242   a = (Mat_SeqAIJ*)(mpimat->A)->data;
4243   b = (Mat_SeqAIJ*)(mpimat->B)->data;
4244   ai = a->i; aj = a->j; bi = b->i; bj = b->j;
4245   aa = a->a; ba = b->a;
4246   if (scall == MAT_INITIAL_MATRIX) {
4247     if (size == 1) {
4248       ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ai,aj,aa,A_loc);CHKERRQ(ierr);
4249       PetscFunctionReturn(0);
4250     }
4251 
4252     ierr  = PetscMalloc1(1+am,&ci);CHKERRQ(ierr);
4253     ci[0] = 0;
4254     for (i=0; i<am; i++) {
4255       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
4256     }
4257     ierr = PetscMalloc1(1+ci[am],&cj);CHKERRQ(ierr);
4258     ierr = PetscMalloc1(1+ci[am],&ca);CHKERRQ(ierr);
4259     k    = 0;
4260     for (i=0; i<am; i++) {
4261       ncols_o = bi[i+1] - bi[i];
4262       ncols_d = ai[i+1] - ai[i];
4263       /* off-diagonal portion of A */
4264       for (jo=0; jo<ncols_o; jo++) {
4265         col = cmap[*bj];
4266         if (col >= cstart) break;
4267         cj[k]   = col; bj++;
4268         ca[k++] = *ba++;
4269       }
4270       /* diagonal portion of A */
4271       for (j=0; j<ncols_d; j++) {
4272         cj[k]   = cstart + *aj++;
4273         ca[k++] = *aa++;
4274       }
4275       /* off-diagonal portion of A */
4276       for (j=jo; j<ncols_o; j++) {
4277         cj[k]   = cmap[*bj++];
4278         ca[k++] = *ba++;
4279       }
4280     }
4281     /* put together the new matrix */
4282     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
4283     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4284     /* Since these are PETSc arrays, change flags to free them as necessary. */
4285     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
4286     mat->free_a  = PETSC_TRUE;
4287     mat->free_ij = PETSC_TRUE;
4288     mat->nonew   = 0;
4289   } else if (scall == MAT_REUSE_MATRIX) {
4290     mat=(Mat_SeqAIJ*)(*A_loc)->data;
4291     ci = mat->i; cj = mat->j; cam = mat->a;
4292     for (i=0; i<am; i++) {
4293       /* off-diagonal portion of A */
4294       ncols_o = bi[i+1] - bi[i];
4295       for (jo=0; jo<ncols_o; jo++) {
4296         col = cmap[*bj];
4297         if (col >= cstart) break;
4298         *cam++ = *ba++; bj++;
4299       }
4300       /* diagonal portion of A */
4301       ncols_d = ai[i+1] - ai[i];
4302       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
4303       /* off-diagonal portion of A */
4304       for (j=jo; j<ncols_o; j++) {
4305         *cam++ = *ba++; bj++;
4306       }
4307     }
4308   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
4309   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4310   PetscFunctionReturn(0);
4311 }
4312 
4313 /*@C
4314      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MATMPIAIJ matrix by taking all its local rows and NON-ZERO columns
4315 
4316     Not Collective
4317 
4318    Input Parameters:
4319 +    A - the matrix
4320 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4321 -    row, col - index sets of rows and columns to extract (or NULL)
4322 
4323    Output Parameter:
4324 .    A_loc - the local sequential matrix generated
4325 
4326     Level: developer
4327 
4328 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
4329 
4330 @*/
4331 PetscErrorCode  MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
4332 {
4333   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4334   PetscErrorCode ierr;
4335   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
4336   IS             isrowa,iscola;
4337   Mat            *aloc;
4338   PetscBool      match;
4339 
4340   PetscFunctionBegin;
4341   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4342   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
4343   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4344   if (!row) {
4345     start = A->rmap->rstart; end = A->rmap->rend;
4346     ierr  = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
4347   } else {
4348     isrowa = *row;
4349   }
4350   if (!col) {
4351     start = A->cmap->rstart;
4352     cmap  = a->garray;
4353     nzA   = a->A->cmap->n;
4354     nzB   = a->B->cmap->n;
4355     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4356     ncols = 0;
4357     for (i=0; i<nzB; i++) {
4358       if (cmap[i] < start) idx[ncols++] = cmap[i];
4359       else break;
4360     }
4361     imark = i;
4362     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
4363     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
4364     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
4365   } else {
4366     iscola = *col;
4367   }
4368   if (scall != MAT_INITIAL_MATRIX) {
4369     ierr    = PetscMalloc1(1,&aloc);CHKERRQ(ierr);
4370     aloc[0] = *A_loc;
4371   }
4372   ierr   = MatCreateSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
4373   *A_loc = aloc[0];
4374   ierr   = PetscFree(aloc);CHKERRQ(ierr);
4375   if (!row) {
4376     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
4377   }
4378   if (!col) {
4379     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
4380   }
4381   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4382   PetscFunctionReturn(0);
4383 }
4384 
4385 /*@C
4386     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
4387 
4388     Collective on Mat
4389 
4390    Input Parameters:
4391 +    A,B - the matrices in mpiaij format
4392 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4393 -    rowb, colb - index sets of rows and columns of B to extract (or NULL)
4394 
4395    Output Parameter:
4396 +    rowb, colb - index sets of rows and columns of B to extract
4397 -    B_seq - the sequential matrix generated
4398 
4399     Level: developer
4400 
4401 @*/
4402 PetscErrorCode  MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
4403 {
4404   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4405   PetscErrorCode ierr;
4406   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
4407   IS             isrowb,iscolb;
4408   Mat            *bseq=NULL;
4409 
4410   PetscFunctionBegin;
4411   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4412     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);
4413   }
4414   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4415 
4416   if (scall == MAT_INITIAL_MATRIX) {
4417     start = A->cmap->rstart;
4418     cmap  = a->garray;
4419     nzA   = a->A->cmap->n;
4420     nzB   = a->B->cmap->n;
4421     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4422     ncols = 0;
4423     for (i=0; i<nzB; i++) {  /* row < local row index */
4424       if (cmap[i] < start) idx[ncols++] = cmap[i];
4425       else break;
4426     }
4427     imark = i;
4428     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
4429     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
4430     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
4431     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
4432   } else {
4433     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
4434     isrowb  = *rowb; iscolb = *colb;
4435     ierr    = PetscMalloc1(1,&bseq);CHKERRQ(ierr);
4436     bseq[0] = *B_seq;
4437   }
4438   ierr   = MatCreateSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
4439   *B_seq = bseq[0];
4440   ierr   = PetscFree(bseq);CHKERRQ(ierr);
4441   if (!rowb) {
4442     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
4443   } else {
4444     *rowb = isrowb;
4445   }
4446   if (!colb) {
4447     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
4448   } else {
4449     *colb = iscolb;
4450   }
4451   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4452   PetscFunctionReturn(0);
4453 }
4454 
4455 /*
4456     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
4457     of the OFF-DIAGONAL portion of local A
4458 
4459     Collective on Mat
4460 
4461    Input Parameters:
4462 +    A,B - the matrices in mpiaij format
4463 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4464 
4465    Output Parameter:
4466 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
4467 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
4468 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
4469 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
4470 
4471     Level: developer
4472 
4473 */
4474 PetscErrorCode  MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
4475 {
4476   VecScatter_MPI_General *gen_to,*gen_from;
4477   PetscErrorCode         ierr;
4478   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
4479   Mat_SeqAIJ             *b_oth;
4480   VecScatter             ctx =a->Mvctx;
4481   MPI_Comm               comm;
4482   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
4483   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
4484   PetscInt               *rvalues,*svalues;
4485   MatScalar              *b_otha,*bufa,*bufA;
4486   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
4487   MPI_Request            *rwaits = NULL,*swaits = NULL;
4488   MPI_Status             *sstatus,rstatus;
4489   PetscMPIInt            jj,size;
4490   PetscInt               *cols,sbs,rbs;
4491   PetscScalar            *vals;
4492 
4493   PetscFunctionBegin;
4494   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4495   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4496 
4497   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4498     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);
4499   }
4500   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4501   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4502 
4503   if (size == 1) {
4504     startsj_s = NULL;
4505     bufa_ptr  = NULL;
4506     *B_oth    = NULL;
4507     PetscFunctionReturn(0);
4508   }
4509 
4510   gen_to   = (VecScatter_MPI_General*)ctx->todata;
4511   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
4512   nrecvs   = gen_from->n;
4513   nsends   = gen_to->n;
4514 
4515   ierr    = PetscMalloc2(nrecvs,&rwaits,nsends,&swaits);CHKERRQ(ierr);
4516   srow    = gen_to->indices;    /* local row index to be sent */
4517   sstarts = gen_to->starts;
4518   sprocs  = gen_to->procs;
4519   sstatus = gen_to->sstatus;
4520   sbs     = gen_to->bs;
4521   rstarts = gen_from->starts;
4522   rprocs  = gen_from->procs;
4523   rbs     = gen_from->bs;
4524 
4525   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
4526   if (scall == MAT_INITIAL_MATRIX) {
4527     /* i-array */
4528     /*---------*/
4529     /*  post receives */
4530     ierr = PetscMalloc1(rbs*(rstarts[nrecvs] - rstarts[0]),&rvalues);CHKERRQ(ierr);
4531     for (i=0; i<nrecvs; i++) {
4532       rowlen = rvalues + rstarts[i]*rbs;
4533       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
4534       ierr   = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4535     }
4536 
4537     /* pack the outgoing message */
4538     ierr = PetscMalloc2(nsends+1,&sstartsj,nrecvs+1,&rstartsj);CHKERRQ(ierr);
4539 
4540     sstartsj[0] = 0;
4541     rstartsj[0] = 0;
4542     len         = 0; /* total length of j or a array to be sent */
4543     k           = 0;
4544     ierr = PetscMalloc1(sbs*(sstarts[nsends] - sstarts[0]),&svalues);CHKERRQ(ierr);
4545     for (i=0; i<nsends; i++) {
4546       rowlen = svalues + sstarts[i]*sbs;
4547       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
4548       for (j=0; j<nrows; j++) {
4549         row = srow[k] + B->rmap->range[rank]; /* global row idx */
4550         for (l=0; l<sbs; l++) {
4551           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr); /* rowlength */
4552 
4553           rowlen[j*sbs+l] = ncols;
4554 
4555           len += ncols;
4556           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr);
4557         }
4558         k++;
4559       }
4560       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4561 
4562       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
4563     }
4564     /* recvs and sends of i-array are completed */
4565     i = nrecvs;
4566     while (i--) {
4567       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4568     }
4569     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4570     ierr = PetscFree(svalues);CHKERRQ(ierr);
4571 
4572     /* allocate buffers for sending j and a arrays */
4573     ierr = PetscMalloc1(len+1,&bufj);CHKERRQ(ierr);
4574     ierr = PetscMalloc1(len+1,&bufa);CHKERRQ(ierr);
4575 
4576     /* create i-array of B_oth */
4577     ierr = PetscMalloc1(aBn+2,&b_othi);CHKERRQ(ierr);
4578 
4579     b_othi[0] = 0;
4580     len       = 0; /* total length of j or a array to be received */
4581     k         = 0;
4582     for (i=0; i<nrecvs; i++) {
4583       rowlen = rvalues + rstarts[i]*rbs;
4584       nrows  = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be received */
4585       for (j=0; j<nrows; j++) {
4586         b_othi[k+1] = b_othi[k] + rowlen[j];
4587         ierr = PetscIntSumError(rowlen[j],len,&len);CHKERRQ(ierr);
4588         k++;
4589       }
4590       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
4591     }
4592     ierr = PetscFree(rvalues);CHKERRQ(ierr);
4593 
4594     /* allocate space for j and a arrrays of B_oth */
4595     ierr = PetscMalloc1(b_othi[aBn]+1,&b_othj);CHKERRQ(ierr);
4596     ierr = PetscMalloc1(b_othi[aBn]+1,&b_otha);CHKERRQ(ierr);
4597 
4598     /* j-array */
4599     /*---------*/
4600     /*  post receives of j-array */
4601     for (i=0; i<nrecvs; i++) {
4602       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4603       ierr  = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4604     }
4605 
4606     /* pack the outgoing message j-array */
4607     k = 0;
4608     for (i=0; i<nsends; i++) {
4609       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4610       bufJ  = bufj+sstartsj[i];
4611       for (j=0; j<nrows; j++) {
4612         row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4613         for (ll=0; ll<sbs; ll++) {
4614           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4615           for (l=0; l<ncols; l++) {
4616             *bufJ++ = cols[l];
4617           }
4618           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4619         }
4620       }
4621       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4622     }
4623 
4624     /* recvs and sends of j-array are completed */
4625     i = nrecvs;
4626     while (i--) {
4627       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4628     }
4629     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4630   } else if (scall == MAT_REUSE_MATRIX) {
4631     sstartsj = *startsj_s;
4632     rstartsj = *startsj_r;
4633     bufa     = *bufa_ptr;
4634     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
4635     b_otha   = b_oth->a;
4636   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
4637 
4638   /* a-array */
4639   /*---------*/
4640   /*  post receives of a-array */
4641   for (i=0; i<nrecvs; i++) {
4642     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4643     ierr  = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4644   }
4645 
4646   /* pack the outgoing message a-array */
4647   k = 0;
4648   for (i=0; i<nsends; i++) {
4649     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4650     bufA  = bufa+sstartsj[i];
4651     for (j=0; j<nrows; j++) {
4652       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4653       for (ll=0; ll<sbs; ll++) {
4654         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4655         for (l=0; l<ncols; l++) {
4656           *bufA++ = vals[l];
4657         }
4658         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4659       }
4660     }
4661     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4662   }
4663   /* recvs and sends of a-array are completed */
4664   i = nrecvs;
4665   while (i--) {
4666     ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4667   }
4668   if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4669   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
4670 
4671   if (scall == MAT_INITIAL_MATRIX) {
4672     /* put together the new matrix */
4673     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
4674 
4675     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4676     /* Since these are PETSc arrays, change flags to free them as necessary. */
4677     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
4678     b_oth->free_a  = PETSC_TRUE;
4679     b_oth->free_ij = PETSC_TRUE;
4680     b_oth->nonew   = 0;
4681 
4682     ierr = PetscFree(bufj);CHKERRQ(ierr);
4683     if (!startsj_s || !bufa_ptr) {
4684       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
4685       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
4686     } else {
4687       *startsj_s = sstartsj;
4688       *startsj_r = rstartsj;
4689       *bufa_ptr  = bufa;
4690     }
4691   }
4692   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4693   PetscFunctionReturn(0);
4694 }
4695 
4696 /*@C
4697   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
4698 
4699   Not Collective
4700 
4701   Input Parameters:
4702 . A - The matrix in mpiaij format
4703 
4704   Output Parameter:
4705 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
4706 . colmap - A map from global column index to local index into lvec
4707 - multScatter - A scatter from the argument of a matrix-vector product to lvec
4708 
4709   Level: developer
4710 
4711 @*/
4712 #if defined(PETSC_USE_CTABLE)
4713 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
4714 #else
4715 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
4716 #endif
4717 {
4718   Mat_MPIAIJ *a;
4719 
4720   PetscFunctionBegin;
4721   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4722   PetscValidPointer(lvec, 2);
4723   PetscValidPointer(colmap, 3);
4724   PetscValidPointer(multScatter, 4);
4725   a = (Mat_MPIAIJ*) A->data;
4726   if (lvec) *lvec = a->lvec;
4727   if (colmap) *colmap = a->colmap;
4728   if (multScatter) *multScatter = a->Mvctx;
4729   PetscFunctionReturn(0);
4730 }
4731 
4732 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
4733 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
4734 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
4735 #if defined(PETSC_HAVE_ELEMENTAL)
4736 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
4737 #endif
4738 #if defined(PETSC_HAVE_HYPRE)
4739 PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat,MatType,MatReuse,Mat*);
4740 PETSC_INTERN PetscErrorCode MatMatMatMult_Transpose_AIJ_AIJ(Mat,Mat,Mat,MatReuse,PetscReal,Mat*);
4741 #endif
4742 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_IS(Mat,MatType,MatReuse,Mat*);
4743 
4744 /*
4745     Computes (B'*A')' since computing B*A directly is untenable
4746 
4747                n                       p                          p
4748         (              )       (              )         (                  )
4749       m (      A       )  *  n (       B      )   =   m (         C        )
4750         (              )       (              )         (                  )
4751 
4752 */
4753 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
4754 {
4755   PetscErrorCode ierr;
4756   Mat            At,Bt,Ct;
4757 
4758   PetscFunctionBegin;
4759   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
4760   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
4761   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
4762   ierr = MatDestroy(&At);CHKERRQ(ierr);
4763   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
4764   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
4765   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
4766   PetscFunctionReturn(0);
4767 }
4768 
4769 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
4770 {
4771   PetscErrorCode ierr;
4772   PetscInt       m=A->rmap->n,n=B->cmap->n;
4773   Mat            Cmat;
4774 
4775   PetscFunctionBegin;
4776   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);
4777   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
4778   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4779   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
4780   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
4781   ierr = MatMPIDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
4782   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4783   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4784 
4785   Cmat->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
4786 
4787   *C = Cmat;
4788   PetscFunctionReturn(0);
4789 }
4790 
4791 /* ----------------------------------------------------------------*/
4792 PETSC_INTERN PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
4793 {
4794   PetscErrorCode ierr;
4795 
4796   PetscFunctionBegin;
4797   if (scall == MAT_INITIAL_MATRIX) {
4798     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
4799     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
4800     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
4801   }
4802   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
4803   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
4804   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
4805   PetscFunctionReturn(0);
4806 }
4807 
4808 /*MC
4809    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
4810 
4811    Options Database Keys:
4812 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
4813 
4814   Level: beginner
4815 
4816 .seealso: MatCreateAIJ()
4817 M*/
4818 
4819 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
4820 {
4821   Mat_MPIAIJ     *b;
4822   PetscErrorCode ierr;
4823   PetscMPIInt    size;
4824 
4825   PetscFunctionBegin;
4826   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
4827 
4828   ierr          = PetscNewLog(B,&b);CHKERRQ(ierr);
4829   B->data       = (void*)b;
4830   ierr          = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
4831   B->assembled  = PETSC_FALSE;
4832   B->insertmode = NOT_SET_VALUES;
4833   b->size       = size;
4834 
4835   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank);CHKERRQ(ierr);
4836 
4837   /* build cache for off array entries formed */
4838   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash);CHKERRQ(ierr);
4839 
4840   b->donotstash  = PETSC_FALSE;
4841   b->colmap      = 0;
4842   b->garray      = 0;
4843   b->roworiented = PETSC_TRUE;
4844 
4845   /* stuff used for matrix vector multiply */
4846   b->lvec  = NULL;
4847   b->Mvctx = NULL;
4848 
4849   /* stuff for MatGetRow() */
4850   b->rowindices   = 0;
4851   b->rowvalues    = 0;
4852   b->getrowactive = PETSC_FALSE;
4853 
4854   /* flexible pointer used in CUSP/CUSPARSE classes */
4855   b->spptr = NULL;
4856 
4857   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetUseScalableIncreaseOverlap_C",MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ);CHKERRQ(ierr);
4858   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ);CHKERRQ(ierr);
4859   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
4860   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
4861   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
4862   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
4863   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
4864   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
4865   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
4866   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
4867 #if defined(PETSC_HAVE_ELEMENTAL)
4868   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_elemental_C",MatConvert_MPIAIJ_Elemental);CHKERRQ(ierr);
4869 #endif
4870 #if defined(PETSC_HAVE_HYPRE)
4871   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_hypre_C",MatConvert_AIJ_HYPRE);CHKERRQ(ierr);
4872 #endif
4873   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_is_C",MatConvert_MPIAIJ_IS);CHKERRQ(ierr);
4874   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
4875   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
4876   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
4877 #if defined(PETSC_HAVE_HYPRE)
4878   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMatMult_transpose_mpiaij_mpiaij_C",MatMatMatMult_Transpose_AIJ_AIJ);CHKERRQ(ierr);
4879 #endif
4880   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
4881   PetscFunctionReturn(0);
4882 }
4883 
4884 /*@C
4885      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
4886          and "off-diagonal" part of the matrix in CSR format.
4887 
4888    Collective on MPI_Comm
4889 
4890    Input Parameters:
4891 +  comm - MPI communicator
4892 .  m - number of local rows (Cannot be PETSC_DECIDE)
4893 .  n - This value should be the same as the local size used in creating the
4894        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
4895        calculated if N is given) For square matrices n is almost always m.
4896 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
4897 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
4898 .   i - row indices for "diagonal" portion of matrix
4899 .   j - column indices
4900 .   a - matrix values
4901 .   oi - row indices for "off-diagonal" portion of matrix
4902 .   oj - column indices
4903 -   oa - matrix values
4904 
4905    Output Parameter:
4906 .   mat - the matrix
4907 
4908    Level: advanced
4909 
4910    Notes:
4911        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
4912        must free the arrays once the matrix has been destroyed and not before.
4913 
4914        The i and j indices are 0 based
4915 
4916        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
4917 
4918        This sets local rows and cannot be used to set off-processor values.
4919 
4920        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
4921        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
4922        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
4923        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
4924        keep track of the underlying array. Use MatSetOption(A,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
4925        communication if it is known that only local entries will be set.
4926 
4927 .keywords: matrix, aij, compressed row, sparse, parallel
4928 
4929 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
4930           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
4931 @*/
4932 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)
4933 {
4934   PetscErrorCode ierr;
4935   Mat_MPIAIJ     *maij;
4936 
4937   PetscFunctionBegin;
4938   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
4939   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
4940   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
4941   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4942   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
4943   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
4944   maij = (Mat_MPIAIJ*) (*mat)->data;
4945 
4946   (*mat)->preallocated = PETSC_TRUE;
4947 
4948   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
4949   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
4950 
4951   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
4952   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
4953 
4954   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4955   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4956   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4957   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4958 
4959   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
4960   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4961   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4962   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_FALSE);CHKERRQ(ierr);
4963   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
4964   PetscFunctionReturn(0);
4965 }
4966 
4967 /*
4968     Special version for direct calls from Fortran
4969 */
4970 #include <petsc/private/fortranimpl.h>
4971 
4972 /* Change these macros so can be used in void function */
4973 #undef CHKERRQ
4974 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
4975 #undef SETERRQ2
4976 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
4977 #undef SETERRQ3
4978 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
4979 #undef SETERRQ
4980 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
4981 
4982 #if defined(PETSC_HAVE_FORTRAN_CAPS)
4983 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
4984 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
4985 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
4986 #else
4987 #endif
4988 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)
4989 {
4990   Mat            mat  = *mmat;
4991   PetscInt       m    = *mm, n = *mn;
4992   InsertMode     addv = *maddv;
4993   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
4994   PetscScalar    value;
4995   PetscErrorCode ierr;
4996 
4997   MatCheckPreallocated(mat,1);
4998   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
4999 
5000 #if defined(PETSC_USE_DEBUG)
5001   else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
5002 #endif
5003   {
5004     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
5005     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
5006     PetscBool roworiented = aij->roworiented;
5007 
5008     /* Some Variables required in the macro */
5009     Mat        A                 = aij->A;
5010     Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
5011     PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
5012     MatScalar  *aa               = a->a;
5013     PetscBool  ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
5014     Mat        B                 = aij->B;
5015     Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
5016     PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5017     MatScalar  *ba               = b->a;
5018 
5019     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5020     PetscInt  nonew = a->nonew;
5021     MatScalar *ap1,*ap2;
5022 
5023     PetscFunctionBegin;
5024     for (i=0; i<m; i++) {
5025       if (im[i] < 0) continue;
5026 #if defined(PETSC_USE_DEBUG)
5027       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);
5028 #endif
5029       if (im[i] >= rstart && im[i] < rend) {
5030         row      = im[i] - rstart;
5031         lastcol1 = -1;
5032         rp1      = aj + ai[row];
5033         ap1      = aa + ai[row];
5034         rmax1    = aimax[row];
5035         nrow1    = ailen[row];
5036         low1     = 0;
5037         high1    = nrow1;
5038         lastcol2 = -1;
5039         rp2      = bj + bi[row];
5040         ap2      = ba + bi[row];
5041         rmax2    = bimax[row];
5042         nrow2    = bilen[row];
5043         low2     = 0;
5044         high2    = nrow2;
5045 
5046         for (j=0; j<n; j++) {
5047           if (roworiented) value = v[i*n+j];
5048           else value = v[i+j*m];
5049           if (in[j] >= cstart && in[j] < cend) {
5050             col = in[j] - cstart;
5051             if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
5052             MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
5053           } else if (in[j] < 0) continue;
5054 #if defined(PETSC_USE_DEBUG)
5055           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);
5056 #endif
5057           else {
5058             if (mat->was_assembled) {
5059               if (!aij->colmap) {
5060                 ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5061               }
5062 #if defined(PETSC_USE_CTABLE)
5063               ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5064               col--;
5065 #else
5066               col = aij->colmap[in[j]] - 1;
5067 #endif
5068               if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
5069               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5070                 ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5071                 col  =  in[j];
5072                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5073                 B     = aij->B;
5074                 b     = (Mat_SeqAIJ*)B->data;
5075                 bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5076                 rp2   = bj + bi[row];
5077                 ap2   = ba + bi[row];
5078                 rmax2 = bimax[row];
5079                 nrow2 = bilen[row];
5080                 low2  = 0;
5081                 high2 = nrow2;
5082                 bm    = aij->B->rmap->n;
5083                 ba    = b->a;
5084               }
5085             } else col = in[j];
5086             MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
5087           }
5088         }
5089       } else if (!aij->donotstash) {
5090         if (roworiented) {
5091           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5092         } else {
5093           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5094         }
5095       }
5096     }
5097   }
5098   PetscFunctionReturnVoid();
5099 }
5100 
5101