xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision 64efcef9d2eba943a6e74289e62f4147c6ae5ef4)
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 /* Not scalable because of ISAllGather() unless getting all columns. */
2943 PetscErrorCode ISGetSeqIS_Private(Mat mat,IS iscol,IS *isseq)
2944 {
2945   PetscErrorCode ierr;
2946   IS             iscol_local;
2947   PetscBool      isstride;
2948   PetscMPIInt    lisstride=0,gisstride;
2949 
2950   PetscFunctionBegin;
2951   /* check if we are grabbing all columns*/
2952   ierr = PetscObjectTypeCompare((PetscObject)iscol,ISSTRIDE,&isstride);CHKERRQ(ierr);
2953 
2954   if (isstride) {
2955     PetscInt  start,len,mstart,mlen;
2956     ierr = ISStrideGetInfo(iscol,&start,NULL);CHKERRQ(ierr);
2957     ierr = ISGetLocalSize(iscol,&len);CHKERRQ(ierr);
2958     ierr = MatGetOwnershipRangeColumn(mat,&mstart,&mlen);CHKERRQ(ierr);
2959     if (mstart == start && mlen-mstart == len) lisstride = 1;
2960   }
2961 
2962   ierr = MPIU_Allreduce(&lisstride,&gisstride,1,MPI_INT,MPI_MIN,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
2963   if (gisstride) {
2964     PetscInt N;
2965     ierr = MatGetSize(mat,NULL,&N);CHKERRQ(ierr);
2966     ierr = ISCreateStride(PetscObjectComm((PetscObject)mat),N,0,1,&iscol_local);CHKERRQ(ierr);
2967     ierr = ISSetIdentity(iscol_local);CHKERRQ(ierr);
2968     ierr = PetscInfo(mat,"Optimizing for obtaining all columns of the matrix; skipping ISAllGather()\n");CHKERRQ(ierr);
2969   } else {
2970     PetscInt cbs;
2971     ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
2972     ierr = ISAllGather(iscol,&iscol_local);CHKERRQ(ierr);
2973     ierr = ISSetBlockSize(iscol_local,cbs);CHKERRQ(ierr);
2974   }
2975 
2976   *isseq = iscol_local;
2977   PetscFunctionReturn(0);
2978 }
2979 
2980 extern PetscErrorCode MatCreateSubMatrix_MPIAIJ_Private_SameDist(Mat,IS,IS,PetscInt,MatReuse,Mat*);
2981 
2982 /* isrow has same processor distribution as mat, avoid iscol_local which uses O(mat->cmap->N) ctable */
2983 PetscErrorCode MatCreateSubMatrix_MPIAIJ_SameDist(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
2984 {
2985   PetscErrorCode ierr;
2986   IS             iscol_local;
2987   PetscInt       csize;
2988   MPI_Comm       comm;
2989   PetscMPIInt    rank;
2990   PetscBool      sorted,sameDist = PETSC_FALSE,tsameDist;
2991   PetscInt       n,i,j,cstart,cend,N;
2992 
2993   PetscFunctionBegin;
2994   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
2995   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2996   //ierr = ISView(iscol,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
2997 
2998   /* If iscol has same processor distribution as mat, then use a scalable routine */
2999   ierr = ISSorted(iscol,&sorted);CHKERRQ(ierr); //must be locally sorted???
3000   if (!sorted) printf("[%d] iscol !sorted\n",rank);
3001 
3002   ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr);
3003   ierr = ISGetSize(iscol,&N);CHKERRQ(ierr);
3004   if (!n) {
3005     sameDist = PETSC_TRUE;
3006   } else {
3007     ierr = ISGetMinMax(isrow,&i,&j);CHKERRQ(ierr);
3008     ierr = MatGetOwnershipRangeColumn(mat,&cstart,&cend);CHKERRQ(ierr);
3009     if (i >= cstart && j < cend) sameDist = PETSC_TRUE;
3010   }
3011   ierr = MPIU_Allreduce(&sameDist,&tsameDist,1,MPIU_BOOL,MPI_LAND,comm);CHKERRQ(ierr);
3012   if (!rank) printf("[%d]..SubMatrix_MPIAIJ_SameDist ...reuse %d, sameDist for column %d \n",rank,call,tsameDist);
3013 
3014   if (tsameDist) { /* get iscol_sub without calling ISAllGather() */
3015     Vec            x,cmap;
3016     const PetscInt *is_idx;
3017     PetscScalar    *xarray,*cmaparray;
3018     PetscInt       isstart;
3019 
3020     /* find isstart */
3021     ierr = MPI_Scan(&n,&isstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3022     isstart -= n;
3023     //printf("[%d] n %d, isstart %d\n",rank,n,isstart);
3024 
3025     /* (1) iscol is a sub-vector of mat, pad it with '-1.' to form a full vector x */
3026     ierr = MatCreateVecs(mat,&x,NULL);CHKERRQ(ierr);
3027     ierr = VecSet(x,-1.0);CHKERRQ(ierr);
3028 
3029     ierr = MatCreateVecs(mat,&cmap,NULL);CHKERRQ(ierr);
3030     ierr = VecSet(cmap,-1.0);CHKERRQ(ierr);
3031 
3032     ierr = ISGetIndices(iscol,&is_idx);CHKERRQ(ierr);
3033     ierr = VecGetArray(x,&xarray);CHKERRQ(ierr);
3034     ierr = VecGetArray(cmap,&cmaparray);CHKERRQ(ierr);
3035     for (i=0; i<n; i++) {
3036       xarray[is_idx[i]-cstart]    = (PetscScalar)is_idx[i];
3037       cmaparray[is_idx[i]-cstart] = i + isstart;
3038     }
3039     ierr = VecRestoreArray(x,&xarray);CHKERRQ(ierr);
3040     ierr = VecRestoreArray(cmap,&cmaparray);CHKERRQ(ierr);
3041     ierr = ISRestoreIndices(iscol,&is_idx);CHKERRQ(ierr);
3042     //ierr = VecView(x,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
3043     //ierr = VecView(cmap,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
3044 
3045     /* (2) scatter x using aij->Mvctx to get off-process portion of x (see MatMult_MPIAIJ) */
3046     Mat_MPIAIJ     *a=(Mat_MPIAIJ*)mat->data;
3047     Mat            B=a->B;
3048     Vec            lvec = a->lvec,lcmap;
3049     PetscInt       Bn=B->cmap->N;
3050     PetscInt       *garray = a->garray;
3051 
3052     ierr = VecDuplicate(lvec,&lcmap);CHKERRQ(ierr);
3053 
3054     ierr = VecScatterBegin(a->Mvctx,x,lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3055     ierr = VecScatterEnd(a->Mvctx,x,lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3056 
3057     ierr = VecScatterBegin(a->Mvctx,cmap,lcmap,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3058     ierr = VecScatterEnd(a->Mvctx,cmap,lcmap,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3059 
3060     //printf("[%d] n(lvec) %d, Bn %d\n",rank,a->lvec->map->n,Bn);
3061     if (lvec->map->n != Bn) SETERRQ2(PETSC_COMM_SELF,0,"n(lvec) %d != Bn %d",lvec->map->n,Bn);
3062     if (rank == -1) {
3063       printf("[%d] lvec:\n",rank);
3064       ierr = VecView(lvec,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
3065     }
3066 
3067     /* create scalable iscol_sub (a subset of iscol) and iscmap */
3068     PetscInt *idx,*cmap1,count;
3069 
3070     ierr = PetscMalloc2(n+Bn,&idx,n+Bn,&cmap1);CHKERRQ(ierr);
3071     count = 0;
3072 
3073     /* A part */
3074     ierr = ISGetIndices(iscol,&is_idx);CHKERRQ(ierr);
3075     j = cstart;
3076     for (i=0; i<n; i++) {
3077       if (j >= cend) break;
3078       if (is_idx[i] == j) {
3079         idx[count]  = j;
3080         cmap1[count] = i + isstart; /* column index in submat */
3081         count++; j++;
3082       } else if (is_idx[i] > j) {
3083         while (is_idx[i] > j && j < cend-1) j++;
3084         if (is_idx[i] == j) {
3085           idx[count]  = j;
3086           cmap1[count] = i + isstart; /* column index in submat */
3087           count++; j++;
3088         }
3089       }
3090     }
3091     ierr = ISRestoreIndices(iscol,&is_idx);CHKERRQ(ierr);
3092 
3093     /* B part */
3094     ierr = VecGetArray(lvec,&xarray);CHKERRQ(ierr);
3095     ierr = VecGetArray(lcmap,&cmaparray);CHKERRQ(ierr);
3096     j = 0;
3097     for (i=0; i<Bn; i++) {
3098       if (j >= Bn) break;
3099       if ((PetscInt)xarray[i] == garray[j]) {
3100         idx[count]  = garray[j];
3101         cmap1[count] = cmaparray[i];  /* column index in submat */
3102         count++; j++;
3103       } else if ((PetscInt)xarray[i] > garray[j]) {
3104         while ((PetscInt)xarray[i] > garray[j] && j < Bn-1) j++;
3105         if ((PetscInt)xarray[i] == garray[j]) {
3106           idx[count]  = garray[j];
3107           cmap1[count] = cmaparray[i]; /* column index in submat */
3108           count++; j++;
3109         }
3110       }
3111     }
3112     ierr = VecRestoreArray(lvec,&xarray);CHKERRQ(ierr);
3113     ierr = VecRestoreArray(lcmap,&cmaparray);CHKERRQ(ierr);
3114     //printf("[%d] n %d + Bn %d = %d; count %d, isN %d, matN %d\n",rank,n,Bn,n+Bn,count,N,mat->cmap->N);
3115 
3116     IS iscol_sub,iscmap;
3117     ierr = PetscSortInt(count,idx);CHKERRQ(ierr);
3118     ierr = PetscSortInt(count,cmap1);CHKERRQ(ierr);
3119 
3120     ierr = ISCreateGeneral(PETSC_COMM_SELF,count,idx,PETSC_COPY_VALUES,&iscol_sub);CHKERRQ(ierr);
3121     ierr = ISCreateGeneral(PETSC_COMM_SELF,count,cmap1,PETSC_COPY_VALUES,&iscmap);CHKERRQ(ierr);
3122 
3123     if (rank == -1) {
3124       printf("[%d] iscmap:\n",rank);
3125       ierr = ISView(iscmap,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
3126     }
3127 
3128     ierr = ISDestroy(&iscol_sub);CHKERRQ(ierr);
3129     ierr = ISDestroy(&iscmap);CHKERRQ(ierr);
3130     ierr = PetscFree2(idx,cmap1);CHKERRQ(ierr);
3131     ierr = VecDestroy(&x);CHKERRQ(ierr);
3132     ierr = VecDestroy(&cmap);CHKERRQ(ierr);
3133     ierr = VecDestroy(&lcmap);CHKERRQ(ierr);
3134   }
3135   //-----------------------------------------------
3136 
3137   /* Get nonscalable iscol_local -- will replace it with iscol_sub! */
3138   if (call == MAT_REUSE_MATRIX) {
3139     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3140     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3141   } else {
3142     ierr = ISGetSeqIS_Private(mat,iscol,&iscol_local);CHKERRQ(ierr);
3143     PetscBool      sorted;
3144     ierr = ISSorted(iscol_local,&sorted);CHKERRQ(ierr);
3145     if (!sorted) printf("[%d] iscol_local !sorted\n",rank);
3146   }
3147 
3148   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3149   ierr = MatCreateSubMatrix_MPIAIJ_Private_SameDist(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
3150 
3151   if (call == MAT_INITIAL_MATRIX) {
3152     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3153     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3154   }
3155   PetscFunctionReturn(0);
3156 }
3157 
3158 PetscErrorCode MatCreateSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3159 {
3160   PetscErrorCode ierr;
3161   IS             iscol_local;
3162   PetscInt       csize;
3163   PetscInt       n,i,j,rstart,rend;
3164   PetscBool      sameDist=PETSC_FALSE,tsameDist;
3165   MPI_Comm       comm;
3166 
3167   PetscFunctionBegin;
3168   /* If isrow has same processor distribution as mat, then use a scalable routine */
3169   if (call == MAT_REUSE_MATRIX) {
3170     ierr = PetscObjectQuery((PetscObject)*newmat,"SubIScol",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3171     if (iscol_local) tsameDist = PETSC_TRUE;
3172   } else {
3173     ierr = ISGetLocalSize(isrow,&n);CHKERRQ(ierr);
3174     if (!n) {
3175       sameDist = PETSC_TRUE;
3176     } else {
3177       ierr = ISGetMinMax(isrow,&i,&j);CHKERRQ(ierr);
3178       ierr = MatGetOwnershipRange(mat,&rstart,&rend);CHKERRQ(ierr);
3179       if (i >= rstart && j < rend) sameDist = PETSC_TRUE;
3180     }
3181     ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3182     ierr = MPIU_Allreduce(&sameDist,&tsameDist,1,MPIU_BOOL,MPI_LAND,comm);CHKERRQ(ierr);
3183   }
3184 
3185   if (tsameDist) {
3186     ierr = MatCreateSubMatrix_MPIAIJ_SameDist(mat,isrow,iscol,call,newmat);CHKERRQ(ierr);
3187     PetscFunctionReturn(0);
3188   }
3189 
3190   /* General case                            */
3191   /* --------------------------------------- */
3192   if (call == MAT_REUSE_MATRIX) {
3193     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3194     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3195   } else {
3196     ierr = ISGetSeqIS_Private(mat,iscol,&iscol_local);CHKERRQ(ierr);
3197   }
3198 
3199   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3200   ierr = MatCreateSubMatrix_MPIAIJ_Private(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
3201 
3202   if (call == MAT_INITIAL_MATRIX) {
3203     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3204     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3205   }
3206   PetscFunctionReturn(0);
3207 }
3208 
3209 extern PetscErrorCode MatCreateSubMatrices_MPIAIJ_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,Mat*);
3210 extern PetscErrorCode MatCreateSubMatrices_MPIAIJ_SingleIS_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool,Mat*);
3211 
3212 PetscErrorCode MatCreateSubMatrix_MPIAIJ_Private_SameDist(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3213 {
3214   PetscErrorCode ierr;
3215   PetscInt       i,m,n,rstart,row,rend,nz,j,bs,cbs;
3216   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
3217   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)mat->data;
3218   Mat            M,Msub,B=a->B;
3219   MatScalar      *aa;
3220   Mat_SeqAIJ     *aij;
3221   PetscInt       *garray = a->garray,*colsub;
3222   PetscInt       count,Bn=B->cmap->N,cstart=mat->cmap->rstart,cend=mat->cmap->rend;
3223   IS             iscol_sub,iscmap;
3224   const PetscInt *is_idx,*cmap;
3225 
3226   PetscFunctionBegin;
3227   MPI_Comm       comm;
3228   PetscMPIInt    rank;
3229   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3230   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3231   //printf("SubMatrix_MPIAIJ_Private_SameDist ...\n");
3232   ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr); /* iscol should be sequential */
3233 
3234   if (call == MAT_INITIAL_MATRIX) {
3235     /* create scalable iscol_sub (a subset of iscol) */
3236     PetscInt *idx,*cmap1;
3237 
3238     PetscBool      sorted;
3239     ierr = ISSorted(iscol,&sorted);CHKERRQ(ierr);
3240     if (!sorted) printf("iscol_local !sorted\n");
3241 
3242     ierr = PetscMalloc2(n,&idx,n,&cmap1);CHKERRQ(ierr);
3243     ierr = ISGetIndices(iscol,&is_idx);CHKERRQ(ierr);
3244     count = 0;
3245 
3246     /* A part */
3247     j = cstart;
3248     for (i=0; i<n; i++) {
3249       if (j >= cend) break;
3250       if (is_idx[i] == j) {
3251         idx[count]  = j;
3252         cmap1[count] = i; /* column index in submat */
3253         count++; j++;
3254       } else if (is_idx[i] > j) {
3255         while (is_idx[i] > j && j < cend-1) j++;
3256         if (is_idx[i] == j) {
3257           idx[count]  = j;
3258           cmap1[count] = i; /* column index in submat */
3259           count++; j++;
3260         }
3261       }
3262     }
3263 
3264     /* B part */
3265     j = 0;
3266     for (i=0; i<n; i++) {
3267       if (j >= Bn) break;
3268       if (is_idx[i] == garray[j]) {
3269         idx[count]  = garray[j];
3270         cmap1[count] = i;  /* column index in submat */
3271         count++; j++;
3272       } else if (is_idx[i] > garray[j]) {
3273         while (is_idx[i] > garray[j] && j < Bn-1) j++;
3274         if (is_idx[i] == garray[j]) {
3275           idx[count]  = garray[j];
3276           cmap1[count] = i; /* column index in submat */
3277           count++; j++;
3278         }
3279       }
3280     }
3281     ierr = PetscSortInt(count,cmap1);CHKERRQ(ierr);
3282     ierr = ISRestoreIndices(iscol,&is_idx);CHKERRQ(ierr);
3283 
3284     ierr = ISCreateGeneral(PetscObjectComm((PetscObject)iscol),count,idx,PETSC_COPY_VALUES,&iscol_sub);CHKERRQ(ierr);
3285     ierr = ISSort(iscol_sub);CHKERRQ(ierr);
3286 
3287     ierr = ISCreateGeneral(PetscObjectComm((PetscObject)iscol),count,cmap1,PETSC_COPY_VALUES,&iscmap);CHKERRQ(ierr);
3288     ierr = PetscFree2(idx,cmap1);CHKERRQ(ierr);
3289 
3290     //printf("\n[%d] old count %d, isN %d, matN %d\n",rank,count,n,mat->cmap->N);
3291     if (rank == -1) {
3292       printf("[%d] old iscmap:\n",rank);
3293       ierr = ISView(iscmap,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
3294     }
3295 
3296     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol_sub,MAT_INITIAL_MATRIX,PETSC_FALSE,&Msub);CHKERRQ(ierr);
3297 
3298   } else { /* call ==  MAT_REUSE_MATRIX */
3299     ierr = PetscObjectQuery((PetscObject)*newmat,"SubIScol",(PetscObject*)&iscol_sub);CHKERRQ(ierr);
3300     if (!iscol_sub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"SubIScol passed in was not used before, cannot reuse");
3301     ierr = ISGetLocalSize(iscol_sub,&count);CHKERRQ(ierr);
3302 
3303     ierr = PetscObjectQuery((PetscObject)*newmat,"Subcmap",(PetscObject*)&iscmap);CHKERRQ(ierr);
3304     if (!iscmap) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Subcmap passed in was not used before, cannot reuse");
3305 
3306     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Msub);CHKERRQ(ierr);
3307     if (!Msub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3308 
3309     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol_sub,MAT_REUSE_MATRIX,PETSC_FALSE,&Msub);CHKERRQ(ierr);
3310   }
3311 
3312   aij = (Mat_SeqAIJ*)(Msub)->data;
3313   ii  = aij->i;
3314   ierr = ISGetIndices(iscmap,&cmap);CHKERRQ(ierr);
3315 
3316   /*
3317       m - number of local rows
3318       n - number of columns (same on all processors)
3319       rstart - first row in new global matrix generated
3320   */
3321   ierr = MatGetSize(Msub,&m,NULL);CHKERRQ(ierr);
3322 
3323   if (call == MAT_INITIAL_MATRIX) {
3324     MPI_Comm       comm;
3325     PetscMPIInt    rank,size;
3326 
3327     ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3328     ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3329     ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3330 
3331     /*
3332         Determine the number of non-zeros in the diagonal and off-diagonal
3333         portions of the matrix in order to do correct preallocation
3334     */
3335 
3336     /* first get start and end of "diagonal" columns */
3337     if (csize == PETSC_DECIDE) {
3338       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3339       if (mglobal == n) { /* square matrix */
3340         nlocal = m;
3341       } else {
3342         nlocal = n/size + ((n % size) > rank);
3343       }
3344     } else {
3345       nlocal = csize;
3346     }
3347     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3348     rstart = rend - nlocal;
3349     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);
3350 
3351     /* next, compute all the lengths */
3352     jj    = aij->j;
3353     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3354     olens = dlens + m;
3355     for (i=0; i<m; i++) {
3356       jend = ii[i+1] - ii[i];
3357       olen = 0;
3358       dlen = 0;
3359       for (j=0; j<jend; j++) {
3360         if (cmap[*jj] < rstart || cmap[*jj] >= rend) olen++;
3361         else dlen++;
3362         jj++;
3363       }
3364       olens[i] = olen;
3365       dlens[i] = dlen;
3366     }
3367     ierr = MatGetBlockSizes(Msub,&bs,&cbs);CHKERRQ(ierr);
3368 
3369     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3370     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3371     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3372     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3373     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3374     ierr = PetscFree(dlens);CHKERRQ(ierr);
3375   } else {
3376     M    = *newmat;
3377     ierr = MatGetLocalSize(M,&i,NULL);CHKERRQ(ierr);
3378     if (i != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3379     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3380     /*
3381          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3382        rather than the slower MatSetValues().
3383     */
3384     M->was_assembled = PETSC_TRUE;
3385     M->assembled     = PETSC_FALSE;
3386   }
3387 
3388   /* set values of Msub to *newmat */
3389   ierr = PetscMalloc1(count,&colsub);CHKERRQ(ierr);
3390   ierr = MatGetOwnershipRange(M,&rstart,NULL);CHKERRQ(ierr);
3391 
3392   jj   = aij->j;
3393   aa   = aij->a;
3394   for (i=0; i<m; i++) {
3395     row = rstart + i;
3396     nz  = ii[i+1] - ii[i];
3397     for (j=0; j<nz; j++) colsub[j] = cmap[jj[j]];
3398     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,colsub,aa,INSERT_VALUES);CHKERRQ(ierr);
3399     jj += nz; aa += nz;
3400   }
3401   ierr = ISRestoreIndices(iscmap,&cmap);CHKERRQ(ierr);
3402 
3403   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3404   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3405   *newmat = M;
3406 
3407   ierr = PetscFree(colsub);CHKERRQ(ierr);
3408 
3409   /* save Msub, iscol_sub and iscmap used in processor for next request */
3410   if (call ==  MAT_INITIAL_MATRIX) {
3411     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Msub);CHKERRQ(ierr);
3412     ierr = MatDestroy(&Msub);CHKERRQ(ierr);
3413 
3414     ierr = PetscObjectCompose((PetscObject)M,"SubIScol",(PetscObject)iscol_sub);CHKERRQ(ierr);
3415     ierr = ISDestroy(&iscol_sub);CHKERRQ(ierr);
3416 
3417     ierr = PetscObjectCompose((PetscObject)M,"Subcmap",(PetscObject)iscmap);CHKERRQ(ierr);
3418     ierr = ISDestroy(&iscmap);CHKERRQ(ierr);
3419   }
3420   PetscFunctionReturn(0);
3421 }
3422 
3423 /*
3424     Not great since it makes two copies of the submatrix, first an SeqAIJ
3425   in local and then by concatenating the local matrices the end result.
3426   Writing it directly would be much like MatCreateSubMatrices_MPIAIJ()
3427 
3428   Note: This requires a sequential iscol with all indices.
3429 */
3430 PetscErrorCode MatCreateSubMatrix_MPIAIJ_Private(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3431 {
3432   PetscErrorCode ierr;
3433   PetscMPIInt    rank,size;
3434   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3435   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
3436   Mat            M,Mreuse;
3437   MatScalar      *aa,*vwork;
3438   MPI_Comm       comm;
3439   Mat_SeqAIJ     *aij;
3440   //PetscBool      sameDist=PETSC_FALSE,tsameDist;
3441 
3442   PetscFunctionBegin;
3443   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3444   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3445   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3446 #if 0
3447   /* If isrow has same processor distribution as mat, then use a scalable routine */
3448   ierr = ISGetLocalSize(isrow,&n);CHKERRQ(ierr);
3449   if (!n) {
3450     sameDist=PETSC_TRUE;
3451   } else {
3452     ierr = ISGetMinMax(isrow,&i,&j);CHKERRQ(ierr);
3453     ierr = MatGetOwnershipRange(mat,&rstart,&rend);CHKERRQ(ierr);
3454     if (i >= rstart && j < rend) sameDist=PETSC_TRUE;
3455   }
3456   ierr = MPIU_Allreduce(&sameDist,&tsameDist,1,MPIU_BOOL,MPI_LAND,comm);CHKERRQ(ierr);
3457   if (tsameDist) {
3458     ierr = MatCreateSubMatrix_MPIAIJ_Private_SameDist(mat,isrow,iscol,csize,call,newmat);CHKERRQ(ierr);
3459     PetscFunctionReturn(0);
3460   }
3461 #endif
3462 
3463   if (call ==  MAT_REUSE_MATRIX) {
3464     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3465     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3466     ierr = MatCreateSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,&Mreuse);CHKERRQ(ierr);
3467   } else {
3468     ierr = MatCreateSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&Mreuse);CHKERRQ(ierr);
3469   }
3470 
3471   /*
3472       m - number of local rows
3473       n - number of columns (same on all processors)
3474       rstart - first row in new global matrix generated
3475   */
3476   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3477   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3478   if (call == MAT_INITIAL_MATRIX) {
3479     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3480     ii  = aij->i;
3481     jj  = aij->j;
3482 
3483     /*
3484         Determine the number of non-zeros in the diagonal and off-diagonal
3485         portions of the matrix in order to do correct preallocation
3486     */
3487 
3488     /* first get start and end of "diagonal" columns */
3489     if (csize == PETSC_DECIDE) {
3490       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3491       if (mglobal == n) { /* square matrix */
3492         nlocal = m;
3493       } else {
3494         nlocal = n/size + ((n % size) > rank);
3495       }
3496     } else {
3497       nlocal = csize;
3498     }
3499     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3500     rstart = rend - nlocal;
3501     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);
3502 
3503     /* next, compute all the lengths */
3504     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3505     olens = dlens + m;
3506     for (i=0; i<m; i++) {
3507       jend = ii[i+1] - ii[i];
3508       olen = 0;
3509       dlen = 0;
3510       for (j=0; j<jend; j++) {
3511         if (*jj < rstart || *jj >= rend) olen++;
3512         else dlen++;
3513         jj++;
3514       }
3515       olens[i] = olen;
3516       dlens[i] = dlen;
3517     }
3518     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3519     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3520     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3521     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3522     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3523     ierr = PetscFree(dlens);CHKERRQ(ierr);
3524   } else {
3525     PetscInt ml,nl;
3526 
3527     M    = *newmat;
3528     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3529     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3530     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3531     /*
3532          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3533        rather than the slower MatSetValues().
3534     */
3535     M->was_assembled = PETSC_TRUE;
3536     M->assembled     = PETSC_FALSE;
3537   }
3538   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3539   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3540   ii   = aij->i;
3541   jj   = aij->j;
3542   aa   = aij->a;
3543   for (i=0; i<m; i++) {
3544     row   = rstart + i;
3545     nz    = ii[i+1] - ii[i];
3546     cwork = jj;     jj += nz;
3547     vwork = aa;     aa += nz;
3548     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3549   }
3550 
3551   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3552   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3553   *newmat = M;
3554 
3555   /* save submatrix used in processor for next request */
3556   if (call ==  MAT_INITIAL_MATRIX) {
3557     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3558     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3559   }
3560   PetscFunctionReturn(0);
3561 }
3562 
3563 PetscErrorCode  MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3564 {
3565   PetscInt       m,cstart, cend,j,nnz,i,d;
3566   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3567   const PetscInt *JJ;
3568   PetscScalar    *values;
3569   PetscErrorCode ierr;
3570   PetscBool      nooffprocentries;
3571 
3572   PetscFunctionBegin;
3573   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3574 
3575   ierr   = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3576   ierr   = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3577   m      = B->rmap->n;
3578   cstart = B->cmap->rstart;
3579   cend   = B->cmap->rend;
3580   rstart = B->rmap->rstart;
3581 
3582   ierr = PetscMalloc2(m,&d_nnz,m,&o_nnz);CHKERRQ(ierr);
3583 
3584 #if defined(PETSC_USE_DEBUGGING)
3585   for (i=0; i<m; i++) {
3586     nnz = Ii[i+1]- Ii[i];
3587     JJ  = J + Ii[i];
3588     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3589     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3590     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);
3591   }
3592 #endif
3593 
3594   for (i=0; i<m; i++) {
3595     nnz     = Ii[i+1]- Ii[i];
3596     JJ      = J + Ii[i];
3597     nnz_max = PetscMax(nnz_max,nnz);
3598     d       = 0;
3599     for (j=0; j<nnz; j++) {
3600       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3601     }
3602     d_nnz[i] = d;
3603     o_nnz[i] = nnz - d;
3604   }
3605   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3606   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3607 
3608   if (v) values = (PetscScalar*)v;
3609   else {
3610     ierr = PetscCalloc1(nnz_max+1,&values);CHKERRQ(ierr);
3611   }
3612 
3613   for (i=0; i<m; i++) {
3614     ii   = i + rstart;
3615     nnz  = Ii[i+1]- Ii[i];
3616     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3617   }
3618   nooffprocentries    = B->nooffprocentries;
3619   B->nooffprocentries = PETSC_TRUE;
3620   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3621   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3622   B->nooffprocentries = nooffprocentries;
3623 
3624   if (!v) {
3625     ierr = PetscFree(values);CHKERRQ(ierr);
3626   }
3627   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3628   PetscFunctionReturn(0);
3629 }
3630 
3631 /*@
3632    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3633    (the default parallel PETSc format).
3634 
3635    Collective on MPI_Comm
3636 
3637    Input Parameters:
3638 +  B - the matrix
3639 .  i - the indices into j for the start of each local row (starts with zero)
3640 .  j - the column indices for each local row (starts with zero)
3641 -  v - optional values in the matrix
3642 
3643    Level: developer
3644 
3645    Notes:
3646        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3647      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3648      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3649 
3650        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3651 
3652        The format which is used for the sparse matrix input, is equivalent to a
3653     row-major ordering.. i.e for the following matrix, the input data expected is
3654     as shown
3655 
3656 $        1 0 0
3657 $        2 0 3     P0
3658 $       -------
3659 $        4 5 6     P1
3660 $
3661 $     Process0 [P0]: rows_owned=[0,1]
3662 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3663 $        j =  {0,0,2}  [size = 3]
3664 $        v =  {1,2,3}  [size = 3]
3665 $
3666 $     Process1 [P1]: rows_owned=[2]
3667 $        i =  {0,3}    [size = nrow+1  = 1+1]
3668 $        j =  {0,1,2}  [size = 3]
3669 $        v =  {4,5,6}  [size = 3]
3670 
3671 .keywords: matrix, aij, compressed row, sparse, parallel
3672 
3673 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MATMPIAIJ,
3674           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3675 @*/
3676 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3677 {
3678   PetscErrorCode ierr;
3679 
3680   PetscFunctionBegin;
3681   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3682   PetscFunctionReturn(0);
3683 }
3684 
3685 /*@C
3686    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3687    (the default parallel PETSc format).  For good matrix assembly performance
3688    the user should preallocate the matrix storage by setting the parameters
3689    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3690    performance can be increased by more than a factor of 50.
3691 
3692    Collective on MPI_Comm
3693 
3694    Input Parameters:
3695 +  B - the matrix
3696 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3697            (same value is used for all local rows)
3698 .  d_nnz - array containing the number of nonzeros in the various rows of the
3699            DIAGONAL portion of the local submatrix (possibly different for each row)
3700            or NULL (PETSC_NULL_INTEGER in Fortran), if d_nz is used to specify the nonzero structure.
3701            The size of this array is equal to the number of local rows, i.e 'm'.
3702            For matrices that will be factored, you must leave room for (and set)
3703            the diagonal entry even if it is zero.
3704 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3705            submatrix (same value is used for all local rows).
3706 -  o_nnz - array containing the number of nonzeros in the various rows of the
3707            OFF-DIAGONAL portion of the local submatrix (possibly different for
3708            each row) or NULL (PETSC_NULL_INTEGER in Fortran), if o_nz is used to specify the nonzero
3709            structure. The size of this array is equal to the number
3710            of local rows, i.e 'm'.
3711 
3712    If the *_nnz parameter is given then the *_nz parameter is ignored
3713 
3714    The AIJ format (also called the Yale sparse matrix format or
3715    compressed row storage (CSR)), is fully compatible with standard Fortran 77
3716    storage.  The stored row and column indices begin with zero.
3717    See Users-Manual: ch_mat for details.
3718 
3719    The parallel matrix is partitioned such that the first m0 rows belong to
3720    process 0, the next m1 rows belong to process 1, the next m2 rows belong
3721    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
3722 
3723    The DIAGONAL portion of the local submatrix of a processor can be defined
3724    as the submatrix which is obtained by extraction the part corresponding to
3725    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
3726    first row that belongs to the processor, r2 is the last row belonging to
3727    the this processor, and c1-c2 is range of indices of the local part of a
3728    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
3729    common case of a square matrix, the row and column ranges are the same and
3730    the DIAGONAL part is also square. The remaining portion of the local
3731    submatrix (mxN) constitute the OFF-DIAGONAL portion.
3732 
3733    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3734 
3735    You can call MatGetInfo() to get information on how effective the preallocation was;
3736    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3737    You can also run with the option -info and look for messages with the string
3738    malloc in them to see if additional memory allocation was needed.
3739 
3740    Example usage:
3741 
3742    Consider the following 8x8 matrix with 34 non-zero values, that is
3743    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3744    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3745    as follows:
3746 
3747 .vb
3748             1  2  0  |  0  3  0  |  0  4
3749     Proc0   0  5  6  |  7  0  0  |  8  0
3750             9  0 10  | 11  0  0  | 12  0
3751     -------------------------------------
3752            13  0 14  | 15 16 17  |  0  0
3753     Proc1   0 18  0  | 19 20 21  |  0  0
3754             0  0  0  | 22 23  0  | 24  0
3755     -------------------------------------
3756     Proc2  25 26 27  |  0  0 28  | 29  0
3757            30  0  0  | 31 32 33  |  0 34
3758 .ve
3759 
3760    This can be represented as a collection of submatrices as:
3761 
3762 .vb
3763       A B C
3764       D E F
3765       G H I
3766 .ve
3767 
3768    Where the submatrices A,B,C are owned by proc0, D,E,F are
3769    owned by proc1, G,H,I are owned by proc2.
3770 
3771    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3772    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3773    The 'M','N' parameters are 8,8, and have the same values on all procs.
3774 
3775    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3776    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3777    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3778    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3779    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3780    matrix, ans [DF] as another SeqAIJ matrix.
3781 
3782    When d_nz, o_nz parameters are specified, d_nz storage elements are
3783    allocated for every row of the local diagonal submatrix, and o_nz
3784    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3785    One way to choose d_nz and o_nz is to use the max nonzerors per local
3786    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3787    In this case, the values of d_nz,o_nz are:
3788 .vb
3789      proc0 : dnz = 2, o_nz = 2
3790      proc1 : dnz = 3, o_nz = 2
3791      proc2 : dnz = 1, o_nz = 4
3792 .ve
3793    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3794    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3795    for proc3. i.e we are using 12+15+10=37 storage locations to store
3796    34 values.
3797 
3798    When d_nnz, o_nnz parameters are specified, the storage is specified
3799    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3800    In the above case the values for d_nnz,o_nnz are:
3801 .vb
3802      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3803      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3804      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3805 .ve
3806    Here the space allocated is sum of all the above values i.e 34, and
3807    hence pre-allocation is perfect.
3808 
3809    Level: intermediate
3810 
3811 .keywords: matrix, aij, compressed row, sparse, parallel
3812 
3813 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
3814           MATMPIAIJ, MatGetInfo(), PetscSplitOwnership()
3815 @*/
3816 PetscErrorCode  MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3817 {
3818   PetscErrorCode ierr;
3819 
3820   PetscFunctionBegin;
3821   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3822   PetscValidType(B,1);
3823   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
3824   PetscFunctionReturn(0);
3825 }
3826 
3827 /*@
3828      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
3829          CSR format the local rows.
3830 
3831    Collective on MPI_Comm
3832 
3833    Input Parameters:
3834 +  comm - MPI communicator
3835 .  m - number of local rows (Cannot be PETSC_DECIDE)
3836 .  n - This value should be the same as the local size used in creating the
3837        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3838        calculated if N is given) For square matrices n is almost always m.
3839 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3840 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3841 .   i - row indices
3842 .   j - column indices
3843 -   a - matrix values
3844 
3845    Output Parameter:
3846 .   mat - the matrix
3847 
3848    Level: intermediate
3849 
3850    Notes:
3851        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3852      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3853      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3854 
3855        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3856 
3857        The format which is used for the sparse matrix input, is equivalent to a
3858     row-major ordering.. i.e for the following matrix, the input data expected is
3859     as shown
3860 
3861 $        1 0 0
3862 $        2 0 3     P0
3863 $       -------
3864 $        4 5 6     P1
3865 $
3866 $     Process0 [P0]: rows_owned=[0,1]
3867 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3868 $        j =  {0,0,2}  [size = 3]
3869 $        v =  {1,2,3}  [size = 3]
3870 $
3871 $     Process1 [P1]: rows_owned=[2]
3872 $        i =  {0,3}    [size = nrow+1  = 1+1]
3873 $        j =  {0,1,2}  [size = 3]
3874 $        v =  {4,5,6}  [size = 3]
3875 
3876 .keywords: matrix, aij, compressed row, sparse, parallel
3877 
3878 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3879           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
3880 @*/
3881 PetscErrorCode  MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
3882 {
3883   PetscErrorCode ierr;
3884 
3885   PetscFunctionBegin;
3886   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
3887   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
3888   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
3889   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
3890   /* ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr); */
3891   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
3892   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
3893   PetscFunctionReturn(0);
3894 }
3895 
3896 /*@C
3897    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
3898    (the default parallel PETSc format).  For good matrix assembly performance
3899    the user should preallocate the matrix storage by setting the parameters
3900    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3901    performance can be increased by more than a factor of 50.
3902 
3903    Collective on MPI_Comm
3904 
3905    Input Parameters:
3906 +  comm - MPI communicator
3907 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
3908            This value should be the same as the local size used in creating the
3909            y vector for the matrix-vector product y = Ax.
3910 .  n - This value should be the same as the local size used in creating the
3911        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3912        calculated if N is given) For square matrices n is almost always m.
3913 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3914 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3915 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3916            (same value is used for all local rows)
3917 .  d_nnz - array containing the number of nonzeros in the various rows of the
3918            DIAGONAL portion of the local submatrix (possibly different for each row)
3919            or NULL, if d_nz is used to specify the nonzero structure.
3920            The size of this array is equal to the number of local rows, i.e 'm'.
3921 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3922            submatrix (same value is used for all local rows).
3923 -  o_nnz - array containing the number of nonzeros in the various rows of the
3924            OFF-DIAGONAL portion of the local submatrix (possibly different for
3925            each row) or NULL, if o_nz is used to specify the nonzero
3926            structure. The size of this array is equal to the number
3927            of local rows, i.e 'm'.
3928 
3929    Output Parameter:
3930 .  A - the matrix
3931 
3932    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3933    MatXXXXSetPreallocation() paradgm instead of this routine directly.
3934    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3935 
3936    Notes:
3937    If the *_nnz parameter is given then the *_nz parameter is ignored
3938 
3939    m,n,M,N parameters specify the size of the matrix, and its partitioning across
3940    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
3941    storage requirements for this matrix.
3942 
3943    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
3944    processor than it must be used on all processors that share the object for
3945    that argument.
3946 
3947    The user MUST specify either the local or global matrix dimensions
3948    (possibly both).
3949 
3950    The parallel matrix is partitioned across processors such that the
3951    first m0 rows belong to process 0, the next m1 rows belong to
3952    process 1, the next m2 rows belong to process 2 etc.. where
3953    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
3954    values corresponding to [m x N] submatrix.
3955 
3956    The columns are logically partitioned with the n0 columns belonging
3957    to 0th partition, the next n1 columns belonging to the next
3958    partition etc.. where n0,n1,n2... are the input parameter 'n'.
3959 
3960    The DIAGONAL portion of the local submatrix on any given processor
3961    is the submatrix corresponding to the rows and columns m,n
3962    corresponding to the given processor. i.e diagonal matrix on
3963    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
3964    etc. The remaining portion of the local submatrix [m x (N-n)]
3965    constitute the OFF-DIAGONAL portion. The example below better
3966    illustrates this concept.
3967 
3968    For a square global matrix we define each processor's diagonal portion
3969    to be its local rows and the corresponding columns (a square submatrix);
3970    each processor's off-diagonal portion encompasses the remainder of the
3971    local matrix (a rectangular submatrix).
3972 
3973    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3974 
3975    When calling this routine with a single process communicator, a matrix of
3976    type SEQAIJ is returned.  If a matrix of type MATMPIAIJ is desired for this
3977    type of communicator, use the construction mechanism:
3978      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
3979 
3980    By default, this format uses inodes (identical nodes) when possible.
3981    We search for consecutive rows with the same nonzero structure, thereby
3982    reusing matrix information to achieve increased efficiency.
3983 
3984    Options Database Keys:
3985 +  -mat_no_inode  - Do not use inodes
3986 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3987 -  -mat_aij_oneindex - Internally use indexing starting at 1
3988         rather than 0.  Note that when calling MatSetValues(),
3989         the user still MUST index entries starting at 0!
3990 
3991 
3992    Example usage:
3993 
3994    Consider the following 8x8 matrix with 34 non-zero values, that is
3995    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3996    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3997    as follows:
3998 
3999 .vb
4000             1  2  0  |  0  3  0  |  0  4
4001     Proc0   0  5  6  |  7  0  0  |  8  0
4002             9  0 10  | 11  0  0  | 12  0
4003     -------------------------------------
4004            13  0 14  | 15 16 17  |  0  0
4005     Proc1   0 18  0  | 19 20 21  |  0  0
4006             0  0  0  | 22 23  0  | 24  0
4007     -------------------------------------
4008     Proc2  25 26 27  |  0  0 28  | 29  0
4009            30  0  0  | 31 32 33  |  0 34
4010 .ve
4011 
4012    This can be represented as a collection of submatrices as:
4013 
4014 .vb
4015       A B C
4016       D E F
4017       G H I
4018 .ve
4019 
4020    Where the submatrices A,B,C are owned by proc0, D,E,F are
4021    owned by proc1, G,H,I are owned by proc2.
4022 
4023    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4024    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4025    The 'M','N' parameters are 8,8, and have the same values on all procs.
4026 
4027    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
4028    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
4029    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
4030    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
4031    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
4032    matrix, ans [DF] as another SeqAIJ matrix.
4033 
4034    When d_nz, o_nz parameters are specified, d_nz storage elements are
4035    allocated for every row of the local diagonal submatrix, and o_nz
4036    storage locations are allocated for every row of the OFF-DIAGONAL submat.
4037    One way to choose d_nz and o_nz is to use the max nonzerors per local
4038    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
4039    In this case, the values of d_nz,o_nz are:
4040 .vb
4041      proc0 : dnz = 2, o_nz = 2
4042      proc1 : dnz = 3, o_nz = 2
4043      proc2 : dnz = 1, o_nz = 4
4044 .ve
4045    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
4046    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
4047    for proc3. i.e we are using 12+15+10=37 storage locations to store
4048    34 values.
4049 
4050    When d_nnz, o_nnz parameters are specified, the storage is specified
4051    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
4052    In the above case the values for d_nnz,o_nnz are:
4053 .vb
4054      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
4055      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
4056      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
4057 .ve
4058    Here the space allocated is sum of all the above values i.e 34, and
4059    hence pre-allocation is perfect.
4060 
4061    Level: intermediate
4062 
4063 .keywords: matrix, aij, compressed row, sparse, parallel
4064 
4065 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
4066           MATMPIAIJ, MatCreateMPIAIJWithArrays()
4067 @*/
4068 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)
4069 {
4070   PetscErrorCode ierr;
4071   PetscMPIInt    size;
4072 
4073   PetscFunctionBegin;
4074   ierr = MatCreate(comm,A);CHKERRQ(ierr);
4075   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
4076   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4077   if (size > 1) {
4078     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
4079     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
4080   } else {
4081     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
4082     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
4083   }
4084   PetscFunctionReturn(0);
4085 }
4086 
4087 PetscErrorCode  MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
4088 {
4089   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
4090   PetscBool      flg;
4091   PetscErrorCode ierr;
4092 
4093   PetscFunctionBegin;
4094   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&flg);CHKERRQ(ierr);
4095   if (!flg) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"This function requires a MATMPIAIJ matrix as input");
4096   if (Ad)     *Ad     = a->A;
4097   if (Ao)     *Ao     = a->B;
4098   if (colmap) *colmap = a->garray;
4099   PetscFunctionReturn(0);
4100 }
4101 
4102 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
4103 {
4104   PetscErrorCode ierr;
4105   PetscInt       m,N,i,rstart,nnz,Ii;
4106   PetscInt       *indx;
4107   PetscScalar    *values;
4108 
4109   PetscFunctionBegin;
4110   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
4111   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
4112     PetscInt       *dnz,*onz,sum,bs,cbs;
4113 
4114     if (n == PETSC_DECIDE) {
4115       ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
4116     }
4117     /* Check sum(n) = N */
4118     ierr = MPIU_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4119     if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
4120 
4121     ierr    = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4122     rstart -= m;
4123 
4124     ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4125     for (i=0; i<m; i++) {
4126       ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
4127       ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
4128       ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
4129     }
4130 
4131     ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
4132     ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4133     ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
4134     ierr = MatSetBlockSizes(*outmat,bs,cbs);CHKERRQ(ierr);
4135     ierr = MatSetType(*outmat,MATAIJ);CHKERRQ(ierr);
4136     ierr = MatSeqAIJSetPreallocation(*outmat,0,dnz);CHKERRQ(ierr);
4137     ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
4138     ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4139   }
4140 
4141   /* numeric phase */
4142   ierr = MatGetOwnershipRange(*outmat,&rstart,NULL);CHKERRQ(ierr);
4143   for (i=0; i<m; i++) {
4144     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4145     Ii   = i + rstart;
4146     ierr = MatSetValues(*outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4147     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4148   }
4149   ierr = MatAssemblyBegin(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4150   ierr = MatAssemblyEnd(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4151   PetscFunctionReturn(0);
4152 }
4153 
4154 PetscErrorCode MatFileSplit(Mat A,char *outfile)
4155 {
4156   PetscErrorCode    ierr;
4157   PetscMPIInt       rank;
4158   PetscInt          m,N,i,rstart,nnz;
4159   size_t            len;
4160   const PetscInt    *indx;
4161   PetscViewer       out;
4162   char              *name;
4163   Mat               B;
4164   const PetscScalar *values;
4165 
4166   PetscFunctionBegin;
4167   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
4168   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
4169   /* Should this be the type of the diagonal block of A? */
4170   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
4171   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
4172   ierr = MatSetBlockSizesFromMats(B,A,A);CHKERRQ(ierr);
4173   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
4174   ierr = MatSeqAIJSetPreallocation(B,0,NULL);CHKERRQ(ierr);
4175   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
4176   for (i=0; i<m; i++) {
4177     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4178     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4179     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4180   }
4181   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4182   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4183 
4184   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
4185   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
4186   ierr = PetscMalloc1(len+5,&name);CHKERRQ(ierr);
4187   sprintf(name,"%s.%d",outfile,rank);
4188   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
4189   ierr = PetscFree(name);CHKERRQ(ierr);
4190   ierr = MatView(B,out);CHKERRQ(ierr);
4191   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
4192   ierr = MatDestroy(&B);CHKERRQ(ierr);
4193   PetscFunctionReturn(0);
4194 }
4195 
4196 PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
4197 {
4198   PetscErrorCode      ierr;
4199   Mat_Merge_SeqsToMPI *merge;
4200   PetscContainer      container;
4201 
4202   PetscFunctionBegin;
4203   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4204   if (container) {
4205     ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4206     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
4207     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
4208     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
4209     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
4210     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
4211     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
4212     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
4213     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
4214     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
4215     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
4216     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
4217     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
4218     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
4219     ierr = PetscFree(merge);CHKERRQ(ierr);
4220     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
4221   }
4222   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
4223   PetscFunctionReturn(0);
4224 }
4225 
4226 #include <../src/mat/utils/freespace.h>
4227 #include <petscbt.h>
4228 
4229 PetscErrorCode  MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
4230 {
4231   PetscErrorCode      ierr;
4232   MPI_Comm            comm;
4233   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
4234   PetscMPIInt         size,rank,taga,*len_s;
4235   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
4236   PetscInt            proc,m;
4237   PetscInt            **buf_ri,**buf_rj;
4238   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
4239   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
4240   MPI_Request         *s_waits,*r_waits;
4241   MPI_Status          *status;
4242   MatScalar           *aa=a->a;
4243   MatScalar           **abuf_r,*ba_i;
4244   Mat_Merge_SeqsToMPI *merge;
4245   PetscContainer      container;
4246 
4247   PetscFunctionBegin;
4248   ierr = PetscObjectGetComm((PetscObject)mpimat,&comm);CHKERRQ(ierr);
4249   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4250 
4251   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4252   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4253 
4254   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4255   ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4256 
4257   bi     = merge->bi;
4258   bj     = merge->bj;
4259   buf_ri = merge->buf_ri;
4260   buf_rj = merge->buf_rj;
4261 
4262   ierr   = PetscMalloc1(size,&status);CHKERRQ(ierr);
4263   owners = merge->rowmap->range;
4264   len_s  = merge->len_s;
4265 
4266   /* send and recv matrix values */
4267   /*-----------------------------*/
4268   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
4269   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
4270 
4271   ierr = PetscMalloc1(merge->nsend+1,&s_waits);CHKERRQ(ierr);
4272   for (proc=0,k=0; proc<size; proc++) {
4273     if (!len_s[proc]) continue;
4274     i    = owners[proc];
4275     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
4276     k++;
4277   }
4278 
4279   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
4280   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
4281   ierr = PetscFree(status);CHKERRQ(ierr);
4282 
4283   ierr = PetscFree(s_waits);CHKERRQ(ierr);
4284   ierr = PetscFree(r_waits);CHKERRQ(ierr);
4285 
4286   /* insert mat values of mpimat */
4287   /*----------------------------*/
4288   ierr = PetscMalloc1(N,&ba_i);CHKERRQ(ierr);
4289   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4290 
4291   for (k=0; k<merge->nrecv; k++) {
4292     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4293     nrows       = *(buf_ri_k[k]);
4294     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
4295     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4296   }
4297 
4298   /* set values of ba */
4299   m = merge->rowmap->n;
4300   for (i=0; i<m; i++) {
4301     arow = owners[rank] + i;
4302     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
4303     bnzi = bi[i+1] - bi[i];
4304     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
4305 
4306     /* add local non-zero vals of this proc's seqmat into ba */
4307     anzi   = ai[arow+1] - ai[arow];
4308     aj     = a->j + ai[arow];
4309     aa     = a->a + ai[arow];
4310     nextaj = 0;
4311     for (j=0; nextaj<anzi; j++) {
4312       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4313         ba_i[j] += aa[nextaj++];
4314       }
4315     }
4316 
4317     /* add received vals into ba */
4318     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4319       /* i-th row */
4320       if (i == *nextrow[k]) {
4321         anzi   = *(nextai[k]+1) - *nextai[k];
4322         aj     = buf_rj[k] + *(nextai[k]);
4323         aa     = abuf_r[k] + *(nextai[k]);
4324         nextaj = 0;
4325         for (j=0; nextaj<anzi; j++) {
4326           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4327             ba_i[j] += aa[nextaj++];
4328           }
4329         }
4330         nextrow[k]++; nextai[k]++;
4331       }
4332     }
4333     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
4334   }
4335   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4336   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4337 
4338   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
4339   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
4340   ierr = PetscFree(ba_i);CHKERRQ(ierr);
4341   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4342   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4343   PetscFunctionReturn(0);
4344 }
4345 
4346 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4347 {
4348   PetscErrorCode      ierr;
4349   Mat                 B_mpi;
4350   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
4351   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4352   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
4353   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4354   PetscInt            len,proc,*dnz,*onz,bs,cbs;
4355   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4356   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4357   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
4358   MPI_Status          *status;
4359   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
4360   PetscBT             lnkbt;
4361   Mat_Merge_SeqsToMPI *merge;
4362   PetscContainer      container;
4363 
4364   PetscFunctionBegin;
4365   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4366 
4367   /* make sure it is a PETSc comm */
4368   ierr = PetscCommDuplicate(comm,&comm,NULL);CHKERRQ(ierr);
4369   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4370   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4371 
4372   ierr = PetscNew(&merge);CHKERRQ(ierr);
4373   ierr = PetscMalloc1(size,&status);CHKERRQ(ierr);
4374 
4375   /* determine row ownership */
4376   /*---------------------------------------------------------*/
4377   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
4378   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
4379   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
4380   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
4381   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
4382   ierr = PetscMalloc1(size,&len_si);CHKERRQ(ierr);
4383   ierr = PetscMalloc1(size,&merge->len_s);CHKERRQ(ierr);
4384 
4385   m      = merge->rowmap->n;
4386   owners = merge->rowmap->range;
4387 
4388   /* determine the number of messages to send, their lengths */
4389   /*---------------------------------------------------------*/
4390   len_s = merge->len_s;
4391 
4392   len          = 0; /* length of buf_si[] */
4393   merge->nsend = 0;
4394   for (proc=0; proc<size; proc++) {
4395     len_si[proc] = 0;
4396     if (proc == rank) {
4397       len_s[proc] = 0;
4398     } else {
4399       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4400       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4401     }
4402     if (len_s[proc]) {
4403       merge->nsend++;
4404       nrows = 0;
4405       for (i=owners[proc]; i<owners[proc+1]; i++) {
4406         if (ai[i+1] > ai[i]) nrows++;
4407       }
4408       len_si[proc] = 2*(nrows+1);
4409       len         += len_si[proc];
4410     }
4411   }
4412 
4413   /* determine the number and length of messages to receive for ij-structure */
4414   /*-------------------------------------------------------------------------*/
4415   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
4416   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
4417 
4418   /* post the Irecv of j-structure */
4419   /*-------------------------------*/
4420   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
4421   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
4422 
4423   /* post the Isend of j-structure */
4424   /*--------------------------------*/
4425   ierr = PetscMalloc2(merge->nsend,&si_waits,merge->nsend,&sj_waits);CHKERRQ(ierr);
4426 
4427   for (proc=0, k=0; proc<size; proc++) {
4428     if (!len_s[proc]) continue;
4429     i    = owners[proc];
4430     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
4431     k++;
4432   }
4433 
4434   /* receives and sends of j-structure are complete */
4435   /*------------------------------------------------*/
4436   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
4437   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
4438 
4439   /* send and recv i-structure */
4440   /*---------------------------*/
4441   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
4442   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
4443 
4444   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
4445   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4446   for (proc=0,k=0; proc<size; proc++) {
4447     if (!len_s[proc]) continue;
4448     /* form outgoing message for i-structure:
4449          buf_si[0]:                 nrows to be sent
4450                [1:nrows]:           row index (global)
4451                [nrows+1:2*nrows+1]: i-structure index
4452     */
4453     /*-------------------------------------------*/
4454     nrows       = len_si[proc]/2 - 1;
4455     buf_si_i    = buf_si + nrows+1;
4456     buf_si[0]   = nrows;
4457     buf_si_i[0] = 0;
4458     nrows       = 0;
4459     for (i=owners[proc]; i<owners[proc+1]; i++) {
4460       anzi = ai[i+1] - ai[i];
4461       if (anzi) {
4462         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4463         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4464         nrows++;
4465       }
4466     }
4467     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4468     k++;
4469     buf_si += len_si[proc];
4470   }
4471 
4472   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4473   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4474 
4475   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4476   for (i=0; i<merge->nrecv; i++) {
4477     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);
4478   }
4479 
4480   ierr = PetscFree(len_si);CHKERRQ(ierr);
4481   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4482   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4483   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4484   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4485   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4486   ierr = PetscFree(status);CHKERRQ(ierr);
4487 
4488   /* compute a local seq matrix in each processor */
4489   /*----------------------------------------------*/
4490   /* allocate bi array and free space for accumulating nonzero column info */
4491   ierr  = PetscMalloc1(m+1,&bi);CHKERRQ(ierr);
4492   bi[0] = 0;
4493 
4494   /* create and initialize a linked list */
4495   nlnk = N+1;
4496   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4497 
4498   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4499   len  = ai[owners[rank+1]] - ai[owners[rank]];
4500   ierr = PetscFreeSpaceGet(PetscIntMultTruncate(2,len)+1,&free_space);CHKERRQ(ierr);
4501 
4502   current_space = free_space;
4503 
4504   /* determine symbolic info for each local row */
4505   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4506 
4507   for (k=0; k<merge->nrecv; k++) {
4508     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4509     nrows       = *buf_ri_k[k];
4510     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4511     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4512   }
4513 
4514   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4515   len  = 0;
4516   for (i=0; i<m; i++) {
4517     bnzi = 0;
4518     /* add local non-zero cols of this proc's seqmat into lnk */
4519     arow  = owners[rank] + i;
4520     anzi  = ai[arow+1] - ai[arow];
4521     aj    = a->j + ai[arow];
4522     ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4523     bnzi += nlnk;
4524     /* add received col data into lnk */
4525     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4526       if (i == *nextrow[k]) { /* i-th row */
4527         anzi  = *(nextai[k]+1) - *nextai[k];
4528         aj    = buf_rj[k] + *nextai[k];
4529         ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4530         bnzi += nlnk;
4531         nextrow[k]++; nextai[k]++;
4532       }
4533     }
4534     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4535 
4536     /* if free space is not available, make more free space */
4537     if (current_space->local_remaining<bnzi) {
4538       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(bnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
4539       nspacedouble++;
4540     }
4541     /* copy data into free space, then initialize lnk */
4542     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4543     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
4544 
4545     current_space->array           += bnzi;
4546     current_space->local_used      += bnzi;
4547     current_space->local_remaining -= bnzi;
4548 
4549     bi[i+1] = bi[i] + bnzi;
4550   }
4551 
4552   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4553 
4554   ierr = PetscMalloc1(bi[m]+1,&bj);CHKERRQ(ierr);
4555   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
4556   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4557 
4558   /* create symbolic parallel matrix B_mpi */
4559   /*---------------------------------------*/
4560   ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
4561   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
4562   if (n==PETSC_DECIDE) {
4563     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
4564   } else {
4565     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4566   }
4567   ierr = MatSetBlockSizes(B_mpi,bs,cbs);CHKERRQ(ierr);
4568   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
4569   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
4570   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4571   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
4572 
4573   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4574   B_mpi->assembled    = PETSC_FALSE;
4575   B_mpi->ops->destroy = MatDestroy_MPIAIJ_SeqsToMPI;
4576   merge->bi           = bi;
4577   merge->bj           = bj;
4578   merge->buf_ri       = buf_ri;
4579   merge->buf_rj       = buf_rj;
4580   merge->coi          = NULL;
4581   merge->coj          = NULL;
4582   merge->owners_co    = NULL;
4583 
4584   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
4585 
4586   /* attach the supporting struct to B_mpi for reuse */
4587   ierr    = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
4588   ierr    = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
4589   ierr    = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
4590   ierr    = PetscContainerDestroy(&container);CHKERRQ(ierr);
4591   *mpimat = B_mpi;
4592 
4593   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4594   PetscFunctionReturn(0);
4595 }
4596 
4597 /*@C
4598       MatCreateMPIAIJSumSeqAIJ - Creates a MATMPIAIJ matrix by adding sequential
4599                  matrices from each processor
4600 
4601     Collective on MPI_Comm
4602 
4603    Input Parameters:
4604 +    comm - the communicators the parallel matrix will live on
4605 .    seqmat - the input sequential matrices
4606 .    m - number of local rows (or PETSC_DECIDE)
4607 .    n - number of local columns (or PETSC_DECIDE)
4608 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4609 
4610    Output Parameter:
4611 .    mpimat - the parallel matrix generated
4612 
4613     Level: advanced
4614 
4615    Notes:
4616      The dimensions of the sequential matrix in each processor MUST be the same.
4617      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
4618      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
4619 @*/
4620 PetscErrorCode  MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
4621 {
4622   PetscErrorCode ierr;
4623   PetscMPIInt    size;
4624 
4625   PetscFunctionBegin;
4626   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4627   if (size == 1) {
4628     ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4629     if (scall == MAT_INITIAL_MATRIX) {
4630       ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
4631     } else {
4632       ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4633     }
4634     ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4635     PetscFunctionReturn(0);
4636   }
4637   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4638   if (scall == MAT_INITIAL_MATRIX) {
4639     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
4640   }
4641   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
4642   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4643   PetscFunctionReturn(0);
4644 }
4645 
4646 /*@
4647      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MATMPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
4648           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
4649           with MatGetSize()
4650 
4651     Not Collective
4652 
4653    Input Parameters:
4654 +    A - the matrix
4655 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4656 
4657    Output Parameter:
4658 .    A_loc - the local sequential matrix generated
4659 
4660     Level: developer
4661 
4662 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
4663 
4664 @*/
4665 PetscErrorCode  MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
4666 {
4667   PetscErrorCode ierr;
4668   Mat_MPIAIJ     *mpimat=(Mat_MPIAIJ*)A->data;
4669   Mat_SeqAIJ     *mat,*a,*b;
4670   PetscInt       *ai,*aj,*bi,*bj,*cmap=mpimat->garray;
4671   MatScalar      *aa,*ba,*cam;
4672   PetscScalar    *ca;
4673   PetscInt       am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
4674   PetscInt       *ci,*cj,col,ncols_d,ncols_o,jo;
4675   PetscBool      match;
4676   MPI_Comm       comm;
4677   PetscMPIInt    size;
4678 
4679   PetscFunctionBegin;
4680   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4681   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
4682   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4683   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4684   if (size == 1 && scall == MAT_REUSE_MATRIX) PetscFunctionReturn(0);
4685 
4686   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4687   a = (Mat_SeqAIJ*)(mpimat->A)->data;
4688   b = (Mat_SeqAIJ*)(mpimat->B)->data;
4689   ai = a->i; aj = a->j; bi = b->i; bj = b->j;
4690   aa = a->a; ba = b->a;
4691   if (scall == MAT_INITIAL_MATRIX) {
4692     if (size == 1) {
4693       ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ai,aj,aa,A_loc);CHKERRQ(ierr);
4694       PetscFunctionReturn(0);
4695     }
4696 
4697     ierr  = PetscMalloc1(1+am,&ci);CHKERRQ(ierr);
4698     ci[0] = 0;
4699     for (i=0; i<am; i++) {
4700       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
4701     }
4702     ierr = PetscMalloc1(1+ci[am],&cj);CHKERRQ(ierr);
4703     ierr = PetscMalloc1(1+ci[am],&ca);CHKERRQ(ierr);
4704     k    = 0;
4705     for (i=0; i<am; i++) {
4706       ncols_o = bi[i+1] - bi[i];
4707       ncols_d = ai[i+1] - ai[i];
4708       /* off-diagonal portion of A */
4709       for (jo=0; jo<ncols_o; jo++) {
4710         col = cmap[*bj];
4711         if (col >= cstart) break;
4712         cj[k]   = col; bj++;
4713         ca[k++] = *ba++;
4714       }
4715       /* diagonal portion of A */
4716       for (j=0; j<ncols_d; j++) {
4717         cj[k]   = cstart + *aj++;
4718         ca[k++] = *aa++;
4719       }
4720       /* off-diagonal portion of A */
4721       for (j=jo; j<ncols_o; j++) {
4722         cj[k]   = cmap[*bj++];
4723         ca[k++] = *ba++;
4724       }
4725     }
4726     /* put together the new matrix */
4727     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
4728     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4729     /* Since these are PETSc arrays, change flags to free them as necessary. */
4730     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
4731     mat->free_a  = PETSC_TRUE;
4732     mat->free_ij = PETSC_TRUE;
4733     mat->nonew   = 0;
4734   } else if (scall == MAT_REUSE_MATRIX) {
4735     mat=(Mat_SeqAIJ*)(*A_loc)->data;
4736     ci = mat->i; cj = mat->j; cam = mat->a;
4737     for (i=0; i<am; i++) {
4738       /* off-diagonal portion of A */
4739       ncols_o = bi[i+1] - bi[i];
4740       for (jo=0; jo<ncols_o; jo++) {
4741         col = cmap[*bj];
4742         if (col >= cstart) break;
4743         *cam++ = *ba++; bj++;
4744       }
4745       /* diagonal portion of A */
4746       ncols_d = ai[i+1] - ai[i];
4747       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
4748       /* off-diagonal portion of A */
4749       for (j=jo; j<ncols_o; j++) {
4750         *cam++ = *ba++; bj++;
4751       }
4752     }
4753   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
4754   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4755   PetscFunctionReturn(0);
4756 }
4757 
4758 /*@C
4759      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MATMPIAIJ matrix by taking all its local rows and NON-ZERO columns
4760 
4761     Not Collective
4762 
4763    Input Parameters:
4764 +    A - the matrix
4765 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4766 -    row, col - index sets of rows and columns to extract (or NULL)
4767 
4768    Output Parameter:
4769 .    A_loc - the local sequential matrix generated
4770 
4771     Level: developer
4772 
4773 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
4774 
4775 @*/
4776 PetscErrorCode  MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
4777 {
4778   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4779   PetscErrorCode ierr;
4780   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
4781   IS             isrowa,iscola;
4782   Mat            *aloc;
4783   PetscBool      match;
4784 
4785   PetscFunctionBegin;
4786   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4787   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
4788   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4789   if (!row) {
4790     start = A->rmap->rstart; end = A->rmap->rend;
4791     ierr  = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
4792   } else {
4793     isrowa = *row;
4794   }
4795   if (!col) {
4796     start = A->cmap->rstart;
4797     cmap  = a->garray;
4798     nzA   = a->A->cmap->n;
4799     nzB   = a->B->cmap->n;
4800     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4801     ncols = 0;
4802     for (i=0; i<nzB; i++) {
4803       if (cmap[i] < start) idx[ncols++] = cmap[i];
4804       else break;
4805     }
4806     imark = i;
4807     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
4808     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
4809     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
4810   } else {
4811     iscola = *col;
4812   }
4813   if (scall != MAT_INITIAL_MATRIX) {
4814     ierr    = PetscMalloc1(1,&aloc);CHKERRQ(ierr);
4815     aloc[0] = *A_loc;
4816   }
4817   ierr   = MatCreateSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
4818   *A_loc = aloc[0];
4819   ierr   = PetscFree(aloc);CHKERRQ(ierr);
4820   if (!row) {
4821     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
4822   }
4823   if (!col) {
4824     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
4825   }
4826   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4827   PetscFunctionReturn(0);
4828 }
4829 
4830 /*@C
4831     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
4832 
4833     Collective on Mat
4834 
4835    Input Parameters:
4836 +    A,B - the matrices in mpiaij format
4837 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4838 -    rowb, colb - index sets of rows and columns of B to extract (or NULL)
4839 
4840    Output Parameter:
4841 +    rowb, colb - index sets of rows and columns of B to extract
4842 -    B_seq - the sequential matrix generated
4843 
4844     Level: developer
4845 
4846 @*/
4847 PetscErrorCode  MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
4848 {
4849   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4850   PetscErrorCode ierr;
4851   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
4852   IS             isrowb,iscolb;
4853   Mat            *bseq=NULL;
4854 
4855   PetscFunctionBegin;
4856   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4857     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);
4858   }
4859   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4860 
4861   if (scall == MAT_INITIAL_MATRIX) {
4862     start = A->cmap->rstart;
4863     cmap  = a->garray;
4864     nzA   = a->A->cmap->n;
4865     nzB   = a->B->cmap->n;
4866     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4867     ncols = 0;
4868     for (i=0; i<nzB; i++) {  /* row < local row index */
4869       if (cmap[i] < start) idx[ncols++] = cmap[i];
4870       else break;
4871     }
4872     imark = i;
4873     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
4874     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
4875     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
4876     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
4877   } else {
4878     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
4879     isrowb  = *rowb; iscolb = *colb;
4880     ierr    = PetscMalloc1(1,&bseq);CHKERRQ(ierr);
4881     bseq[0] = *B_seq;
4882   }
4883   ierr   = MatCreateSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
4884   *B_seq = bseq[0];
4885   ierr   = PetscFree(bseq);CHKERRQ(ierr);
4886   if (!rowb) {
4887     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
4888   } else {
4889     *rowb = isrowb;
4890   }
4891   if (!colb) {
4892     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
4893   } else {
4894     *colb = iscolb;
4895   }
4896   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4897   PetscFunctionReturn(0);
4898 }
4899 
4900 /*
4901     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
4902     of the OFF-DIAGONAL portion of local A
4903 
4904     Collective on Mat
4905 
4906    Input Parameters:
4907 +    A,B - the matrices in mpiaij format
4908 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4909 
4910    Output Parameter:
4911 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
4912 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
4913 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
4914 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
4915 
4916     Level: developer
4917 
4918 */
4919 PetscErrorCode  MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
4920 {
4921   VecScatter_MPI_General *gen_to,*gen_from;
4922   PetscErrorCode         ierr;
4923   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
4924   Mat_SeqAIJ             *b_oth;
4925   VecScatter             ctx =a->Mvctx;
4926   MPI_Comm               comm;
4927   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
4928   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
4929   PetscInt               *rvalues,*svalues;
4930   MatScalar              *b_otha,*bufa,*bufA;
4931   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
4932   MPI_Request            *rwaits = NULL,*swaits = NULL;
4933   MPI_Status             *sstatus,rstatus;
4934   PetscMPIInt            jj,size;
4935   PetscInt               *cols,sbs,rbs;
4936   PetscScalar            *vals;
4937 
4938   PetscFunctionBegin;
4939   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4940   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4941 
4942   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4943     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);
4944   }
4945   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4946   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4947 
4948   if (size == 1) {
4949     startsj_s = NULL;
4950     bufa_ptr  = NULL;
4951     *B_oth    = NULL;
4952     PetscFunctionReturn(0);
4953   }
4954 
4955   gen_to   = (VecScatter_MPI_General*)ctx->todata;
4956   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
4957   nrecvs   = gen_from->n;
4958   nsends   = gen_to->n;
4959 
4960   ierr    = PetscMalloc2(nrecvs,&rwaits,nsends,&swaits);CHKERRQ(ierr);
4961   srow    = gen_to->indices;    /* local row index to be sent */
4962   sstarts = gen_to->starts;
4963   sprocs  = gen_to->procs;
4964   sstatus = gen_to->sstatus;
4965   sbs     = gen_to->bs;
4966   rstarts = gen_from->starts;
4967   rprocs  = gen_from->procs;
4968   rbs     = gen_from->bs;
4969 
4970   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
4971   if (scall == MAT_INITIAL_MATRIX) {
4972     /* i-array */
4973     /*---------*/
4974     /*  post receives */
4975     ierr = PetscMalloc1(rbs*(rstarts[nrecvs] - rstarts[0]),&rvalues);CHKERRQ(ierr);
4976     for (i=0; i<nrecvs; i++) {
4977       rowlen = rvalues + rstarts[i]*rbs;
4978       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
4979       ierr   = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4980     }
4981 
4982     /* pack the outgoing message */
4983     ierr = PetscMalloc2(nsends+1,&sstartsj,nrecvs+1,&rstartsj);CHKERRQ(ierr);
4984 
4985     sstartsj[0] = 0;
4986     rstartsj[0] = 0;
4987     len         = 0; /* total length of j or a array to be sent */
4988     k           = 0;
4989     ierr = PetscMalloc1(sbs*(sstarts[nsends] - sstarts[0]),&svalues);CHKERRQ(ierr);
4990     for (i=0; i<nsends; i++) {
4991       rowlen = svalues + sstarts[i]*sbs;
4992       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
4993       for (j=0; j<nrows; j++) {
4994         row = srow[k] + B->rmap->range[rank]; /* global row idx */
4995         for (l=0; l<sbs; l++) {
4996           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr); /* rowlength */
4997 
4998           rowlen[j*sbs+l] = ncols;
4999 
5000           len += ncols;
5001           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr);
5002         }
5003         k++;
5004       }
5005       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5006 
5007       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
5008     }
5009     /* recvs and sends of i-array are completed */
5010     i = nrecvs;
5011     while (i--) {
5012       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5013     }
5014     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5015     ierr = PetscFree(svalues);CHKERRQ(ierr);
5016 
5017     /* allocate buffers for sending j and a arrays */
5018     ierr = PetscMalloc1(len+1,&bufj);CHKERRQ(ierr);
5019     ierr = PetscMalloc1(len+1,&bufa);CHKERRQ(ierr);
5020 
5021     /* create i-array of B_oth */
5022     ierr = PetscMalloc1(aBn+2,&b_othi);CHKERRQ(ierr);
5023 
5024     b_othi[0] = 0;
5025     len       = 0; /* total length of j or a array to be received */
5026     k         = 0;
5027     for (i=0; i<nrecvs; i++) {
5028       rowlen = rvalues + rstarts[i]*rbs;
5029       nrows  = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be received */
5030       for (j=0; j<nrows; j++) {
5031         b_othi[k+1] = b_othi[k] + rowlen[j];
5032         ierr = PetscIntSumError(rowlen[j],len,&len);CHKERRQ(ierr);
5033         k++;
5034       }
5035       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
5036     }
5037     ierr = PetscFree(rvalues);CHKERRQ(ierr);
5038 
5039     /* allocate space for j and a arrrays of B_oth */
5040     ierr = PetscMalloc1(b_othi[aBn]+1,&b_othj);CHKERRQ(ierr);
5041     ierr = PetscMalloc1(b_othi[aBn]+1,&b_otha);CHKERRQ(ierr);
5042 
5043     /* j-array */
5044     /*---------*/
5045     /*  post receives of j-array */
5046     for (i=0; i<nrecvs; i++) {
5047       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5048       ierr  = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5049     }
5050 
5051     /* pack the outgoing message j-array */
5052     k = 0;
5053     for (i=0; i<nsends; i++) {
5054       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5055       bufJ  = bufj+sstartsj[i];
5056       for (j=0; j<nrows; j++) {
5057         row = srow[k++] + B->rmap->range[rank];  /* global row idx */
5058         for (ll=0; ll<sbs; ll++) {
5059           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
5060           for (l=0; l<ncols; l++) {
5061             *bufJ++ = cols[l];
5062           }
5063           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
5064         }
5065       }
5066       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5067     }
5068 
5069     /* recvs and sends of j-array are completed */
5070     i = nrecvs;
5071     while (i--) {
5072       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5073     }
5074     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5075   } else if (scall == MAT_REUSE_MATRIX) {
5076     sstartsj = *startsj_s;
5077     rstartsj = *startsj_r;
5078     bufa     = *bufa_ptr;
5079     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
5080     b_otha   = b_oth->a;
5081   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
5082 
5083   /* a-array */
5084   /*---------*/
5085   /*  post receives of a-array */
5086   for (i=0; i<nrecvs; i++) {
5087     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5088     ierr  = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5089   }
5090 
5091   /* pack the outgoing message a-array */
5092   k = 0;
5093   for (i=0; i<nsends; i++) {
5094     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5095     bufA  = bufa+sstartsj[i];
5096     for (j=0; j<nrows; j++) {
5097       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
5098       for (ll=0; ll<sbs; ll++) {
5099         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
5100         for (l=0; l<ncols; l++) {
5101           *bufA++ = vals[l];
5102         }
5103         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
5104       }
5105     }
5106     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5107   }
5108   /* recvs and sends of a-array are completed */
5109   i = nrecvs;
5110   while (i--) {
5111     ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5112   }
5113   if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5114   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
5115 
5116   if (scall == MAT_INITIAL_MATRIX) {
5117     /* put together the new matrix */
5118     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
5119 
5120     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
5121     /* Since these are PETSc arrays, change flags to free them as necessary. */
5122     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
5123     b_oth->free_a  = PETSC_TRUE;
5124     b_oth->free_ij = PETSC_TRUE;
5125     b_oth->nonew   = 0;
5126 
5127     ierr = PetscFree(bufj);CHKERRQ(ierr);
5128     if (!startsj_s || !bufa_ptr) {
5129       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
5130       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
5131     } else {
5132       *startsj_s = sstartsj;
5133       *startsj_r = rstartsj;
5134       *bufa_ptr  = bufa;
5135     }
5136   }
5137   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5138   PetscFunctionReturn(0);
5139 }
5140 
5141 /*@C
5142   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
5143 
5144   Not Collective
5145 
5146   Input Parameters:
5147 . A - The matrix in mpiaij format
5148 
5149   Output Parameter:
5150 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
5151 . colmap - A map from global column index to local index into lvec
5152 - multScatter - A scatter from the argument of a matrix-vector product to lvec
5153 
5154   Level: developer
5155 
5156 @*/
5157 #if defined(PETSC_USE_CTABLE)
5158 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
5159 #else
5160 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
5161 #endif
5162 {
5163   Mat_MPIAIJ *a;
5164 
5165   PetscFunctionBegin;
5166   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
5167   PetscValidPointer(lvec, 2);
5168   PetscValidPointer(colmap, 3);
5169   PetscValidPointer(multScatter, 4);
5170   a = (Mat_MPIAIJ*) A->data;
5171   if (lvec) *lvec = a->lvec;
5172   if (colmap) *colmap = a->colmap;
5173   if (multScatter) *multScatter = a->Mvctx;
5174   PetscFunctionReturn(0);
5175 }
5176 
5177 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
5178 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
5179 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
5180 #if defined(PETSC_HAVE_ELEMENTAL)
5181 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
5182 #endif
5183 #if defined(PETSC_HAVE_HYPRE)
5184 PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat,MatType,MatReuse,Mat*);
5185 PETSC_INTERN PetscErrorCode MatMatMatMult_Transpose_AIJ_AIJ(Mat,Mat,Mat,MatReuse,PetscReal,Mat*);
5186 #endif
5187 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_IS(Mat,MatType,MatReuse,Mat*);
5188 
5189 /*
5190     Computes (B'*A')' since computing B*A directly is untenable
5191 
5192                n                       p                          p
5193         (              )       (              )         (                  )
5194       m (      A       )  *  n (       B      )   =   m (         C        )
5195         (              )       (              )         (                  )
5196 
5197 */
5198 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
5199 {
5200   PetscErrorCode ierr;
5201   Mat            At,Bt,Ct;
5202 
5203   PetscFunctionBegin;
5204   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
5205   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
5206   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
5207   ierr = MatDestroy(&At);CHKERRQ(ierr);
5208   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
5209   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
5210   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
5211   PetscFunctionReturn(0);
5212 }
5213 
5214 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
5215 {
5216   PetscErrorCode ierr;
5217   PetscInt       m=A->rmap->n,n=B->cmap->n;
5218   Mat            Cmat;
5219 
5220   PetscFunctionBegin;
5221   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);
5222   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
5223   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
5224   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
5225   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
5226   ierr = MatMPIDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
5227   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5228   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5229 
5230   Cmat->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
5231 
5232   *C = Cmat;
5233   PetscFunctionReturn(0);
5234 }
5235 
5236 /* ----------------------------------------------------------------*/
5237 PETSC_INTERN PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
5238 {
5239   PetscErrorCode ierr;
5240 
5241   PetscFunctionBegin;
5242   if (scall == MAT_INITIAL_MATRIX) {
5243     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5244     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
5245     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5246   }
5247   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5248   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
5249   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5250   PetscFunctionReturn(0);
5251 }
5252 
5253 /*MC
5254    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
5255 
5256    Options Database Keys:
5257 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
5258 
5259   Level: beginner
5260 
5261 .seealso: MatCreateAIJ()
5262 M*/
5263 
5264 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
5265 {
5266   Mat_MPIAIJ     *b;
5267   PetscErrorCode ierr;
5268   PetscMPIInt    size;
5269 
5270   PetscFunctionBegin;
5271   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
5272 
5273   ierr          = PetscNewLog(B,&b);CHKERRQ(ierr);
5274   B->data       = (void*)b;
5275   ierr          = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
5276   B->assembled  = PETSC_FALSE;
5277   B->insertmode = NOT_SET_VALUES;
5278   b->size       = size;
5279 
5280   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank);CHKERRQ(ierr);
5281 
5282   /* build cache for off array entries formed */
5283   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash);CHKERRQ(ierr);
5284 
5285   b->donotstash  = PETSC_FALSE;
5286   b->colmap      = 0;
5287   b->garray      = 0;
5288   b->roworiented = PETSC_TRUE;
5289 
5290   /* stuff used for matrix vector multiply */
5291   b->lvec  = NULL;
5292   b->Mvctx = NULL;
5293 
5294   /* stuff for MatGetRow() */
5295   b->rowindices   = 0;
5296   b->rowvalues    = 0;
5297   b->getrowactive = PETSC_FALSE;
5298 
5299   /* flexible pointer used in CUSP/CUSPARSE classes */
5300   b->spptr = NULL;
5301 
5302   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetUseScalableIncreaseOverlap_C",MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ);CHKERRQ(ierr);
5303   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ);CHKERRQ(ierr);
5304   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
5305   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
5306   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
5307   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
5308   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
5309   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
5310   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
5311   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
5312 #if defined(PETSC_HAVE_ELEMENTAL)
5313   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_elemental_C",MatConvert_MPIAIJ_Elemental);CHKERRQ(ierr);
5314 #endif
5315 #if defined(PETSC_HAVE_HYPRE)
5316   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_hypre_C",MatConvert_AIJ_HYPRE);CHKERRQ(ierr);
5317 #endif
5318   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_is_C",MatConvert_MPIAIJ_IS);CHKERRQ(ierr);
5319   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
5320   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
5321   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
5322 #if defined(PETSC_HAVE_HYPRE)
5323   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMatMult_transpose_mpiaij_mpiaij_C",MatMatMatMult_Transpose_AIJ_AIJ);CHKERRQ(ierr);
5324 #endif
5325   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
5326   PetscFunctionReturn(0);
5327 }
5328 
5329 /*@C
5330      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
5331          and "off-diagonal" part of the matrix in CSR format.
5332 
5333    Collective on MPI_Comm
5334 
5335    Input Parameters:
5336 +  comm - MPI communicator
5337 .  m - number of local rows (Cannot be PETSC_DECIDE)
5338 .  n - This value should be the same as the local size used in creating the
5339        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
5340        calculated if N is given) For square matrices n is almost always m.
5341 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
5342 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
5343 .   i - row indices for "diagonal" portion of matrix
5344 .   j - column indices
5345 .   a - matrix values
5346 .   oi - row indices for "off-diagonal" portion of matrix
5347 .   oj - column indices
5348 -   oa - matrix values
5349 
5350    Output Parameter:
5351 .   mat - the matrix
5352 
5353    Level: advanced
5354 
5355    Notes:
5356        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
5357        must free the arrays once the matrix has been destroyed and not before.
5358 
5359        The i and j indices are 0 based
5360 
5361        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
5362 
5363        This sets local rows and cannot be used to set off-processor values.
5364 
5365        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
5366        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
5367        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
5368        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
5369        keep track of the underlying array. Use MatSetOption(A,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
5370        communication if it is known that only local entries will be set.
5371 
5372 .keywords: matrix, aij, compressed row, sparse, parallel
5373 
5374 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
5375           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
5376 @*/
5377 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)
5378 {
5379   PetscErrorCode ierr;
5380   Mat_MPIAIJ     *maij;
5381 
5382   PetscFunctionBegin;
5383   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
5384   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
5385   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
5386   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
5387   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
5388   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
5389   maij = (Mat_MPIAIJ*) (*mat)->data;
5390 
5391   (*mat)->preallocated = PETSC_TRUE;
5392 
5393   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
5394   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
5395 
5396   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
5397   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
5398 
5399   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5400   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5401   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5402   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5403 
5404   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
5405   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5406   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5407   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_FALSE);CHKERRQ(ierr);
5408   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
5409   PetscFunctionReturn(0);
5410 }
5411 
5412 /*
5413     Special version for direct calls from Fortran
5414 */
5415 #include <petsc/private/fortranimpl.h>
5416 
5417 /* Change these macros so can be used in void function */
5418 #undef CHKERRQ
5419 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
5420 #undef SETERRQ2
5421 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5422 #undef SETERRQ3
5423 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5424 #undef SETERRQ
5425 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
5426 
5427 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5428 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
5429 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5430 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
5431 #else
5432 #endif
5433 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)
5434 {
5435   Mat            mat  = *mmat;
5436   PetscInt       m    = *mm, n = *mn;
5437   InsertMode     addv = *maddv;
5438   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
5439   PetscScalar    value;
5440   PetscErrorCode ierr;
5441 
5442   MatCheckPreallocated(mat,1);
5443   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
5444 
5445 #if defined(PETSC_USE_DEBUG)
5446   else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
5447 #endif
5448   {
5449     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
5450     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
5451     PetscBool roworiented = aij->roworiented;
5452 
5453     /* Some Variables required in the macro */
5454     Mat        A                 = aij->A;
5455     Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
5456     PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
5457     MatScalar  *aa               = a->a;
5458     PetscBool  ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
5459     Mat        B                 = aij->B;
5460     Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
5461     PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5462     MatScalar  *ba               = b->a;
5463 
5464     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5465     PetscInt  nonew = a->nonew;
5466     MatScalar *ap1,*ap2;
5467 
5468     PetscFunctionBegin;
5469     for (i=0; i<m; i++) {
5470       if (im[i] < 0) continue;
5471 #if defined(PETSC_USE_DEBUG)
5472       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);
5473 #endif
5474       if (im[i] >= rstart && im[i] < rend) {
5475         row      = im[i] - rstart;
5476         lastcol1 = -1;
5477         rp1      = aj + ai[row];
5478         ap1      = aa + ai[row];
5479         rmax1    = aimax[row];
5480         nrow1    = ailen[row];
5481         low1     = 0;
5482         high1    = nrow1;
5483         lastcol2 = -1;
5484         rp2      = bj + bi[row];
5485         ap2      = ba + bi[row];
5486         rmax2    = bimax[row];
5487         nrow2    = bilen[row];
5488         low2     = 0;
5489         high2    = nrow2;
5490 
5491         for (j=0; j<n; j++) {
5492           if (roworiented) value = v[i*n+j];
5493           else value = v[i+j*m];
5494           if (in[j] >= cstart && in[j] < cend) {
5495             col = in[j] - cstart;
5496             if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
5497             MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
5498           } else if (in[j] < 0) continue;
5499 #if defined(PETSC_USE_DEBUG)
5500           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);
5501 #endif
5502           else {
5503             if (mat->was_assembled) {
5504               if (!aij->colmap) {
5505                 ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5506               }
5507 #if defined(PETSC_USE_CTABLE)
5508               ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5509               col--;
5510 #else
5511               col = aij->colmap[in[j]] - 1;
5512 #endif
5513               if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
5514               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5515                 ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5516                 col  =  in[j];
5517                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5518                 B     = aij->B;
5519                 b     = (Mat_SeqAIJ*)B->data;
5520                 bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5521                 rp2   = bj + bi[row];
5522                 ap2   = ba + bi[row];
5523                 rmax2 = bimax[row];
5524                 nrow2 = bilen[row];
5525                 low2  = 0;
5526                 high2 = nrow2;
5527                 bm    = aij->B->rmap->n;
5528                 ba    = b->a;
5529               }
5530             } else col = in[j];
5531             MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
5532           }
5533         }
5534       } else if (!aij->donotstash) {
5535         if (roworiented) {
5536           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5537         } else {
5538           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5539         }
5540       }
5541     }
5542   }
5543   PetscFunctionReturnVoid();
5544 }
5545 
5546