xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision 62be2347f956eb6f11f7d113b8c78061fece4430)
1 
2 
3 #include <../src/mat/impls/aij/mpi/mpiaij.h>   /*I "petscmat.h" I*/
4 #include <petsc/private/vecimpl.h>
5 #include <petsc/private/isimpl.h>
6 #include <petscblaslapack.h>
7 #include <petscsf.h>
8 
9 /*MC
10    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.
11 
12    This matrix type is identical to MATSEQAIJ when constructed with a single process communicator,
13    and MATMPIAIJ otherwise.  As a result, for single process communicators,
14   MatSeqAIJSetPreallocation is supported, and similarly MatMPIAIJSetPreallocation is supported
15   for communicators controlling multiple processes.  It is recommended that you call both of
16   the above preallocation routines for simplicity.
17 
18    Options Database Keys:
19 . -mat_type aij - sets the matrix type to "aij" during a call to MatSetFromOptions()
20 
21   Developer Notes: Subclasses include MATAIJCUSP, MATAIJCUSPARSE, MATAIJPERM, MATAIJCRL, and also automatically switches over to use inodes when
22    enough exist.
23 
24   Level: beginner
25 
26 .seealso: MatCreateAIJ(), MatCreateSeqAIJ(), MATSEQAIJ, MATMPIAIJ
27 M*/
28 
29 /*MC
30    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.
31 
32    This matrix type is identical to MATSEQAIJCRL when constructed with a single process communicator,
33    and MATMPIAIJCRL otherwise.  As a result, for single process communicators,
34    MatSeqAIJSetPreallocation() is supported, and similarly MatMPIAIJSetPreallocation() is supported
35   for communicators controlling multiple processes.  It is recommended that you call both of
36   the above preallocation routines for simplicity.
37 
38    Options Database Keys:
39 . -mat_type aijcrl - sets the matrix type to "aijcrl" during a call to MatSetFromOptions()
40 
41   Level: beginner
42 
43 .seealso: MatCreateMPIAIJCRL,MATSEQAIJCRL,MATMPIAIJCRL, MATSEQAIJCRL, MATMPIAIJCRL
44 M*/
45 
46 PetscErrorCode MatSetBlockSizes_MPIAIJ(Mat M, PetscInt rbs, PetscInt cbs)
47 {
48   PetscErrorCode ierr;
49   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)M->data;
50 
51   PetscFunctionBegin;
52   if (mat->A) {
53     ierr = MatSetBlockSizes(mat->A,rbs,cbs);CHKERRQ(ierr);
54     ierr = MatSetBlockSizes(mat->B,rbs,1);CHKERRQ(ierr);
55   }
56   PetscFunctionReturn(0);
57 }
58 
59 PetscErrorCode MatFindNonzeroRows_MPIAIJ(Mat M,IS *keptrows)
60 {
61   PetscErrorCode  ierr;
62   Mat_MPIAIJ      *mat = (Mat_MPIAIJ*)M->data;
63   Mat_SeqAIJ      *a   = (Mat_SeqAIJ*)mat->A->data;
64   Mat_SeqAIJ      *b   = (Mat_SeqAIJ*)mat->B->data;
65   const PetscInt  *ia,*ib;
66   const MatScalar *aa,*bb;
67   PetscInt        na,nb,i,j,*rows,cnt=0,n0rows;
68   PetscInt        m = M->rmap->n,rstart = M->rmap->rstart;
69 
70   PetscFunctionBegin;
71   *keptrows = 0;
72   ia        = a->i;
73   ib        = b->i;
74   for (i=0; i<m; i++) {
75     na = ia[i+1] - ia[i];
76     nb = ib[i+1] - ib[i];
77     if (!na && !nb) {
78       cnt++;
79       goto ok1;
80     }
81     aa = a->a + ia[i];
82     for (j=0; j<na; j++) {
83       if (aa[j] != 0.0) goto ok1;
84     }
85     bb = b->a + ib[i];
86     for (j=0; j <nb; j++) {
87       if (bb[j] != 0.0) goto ok1;
88     }
89     cnt++;
90 ok1:;
91   }
92   ierr = MPIU_Allreduce(&cnt,&n0rows,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)M));CHKERRQ(ierr);
93   if (!n0rows) PetscFunctionReturn(0);
94   ierr = PetscMalloc1(M->rmap->n-cnt,&rows);CHKERRQ(ierr);
95   cnt  = 0;
96   for (i=0; i<m; i++) {
97     na = ia[i+1] - ia[i];
98     nb = ib[i+1] - ib[i];
99     if (!na && !nb) continue;
100     aa = a->a + ia[i];
101     for (j=0; j<na;j++) {
102       if (aa[j] != 0.0) {
103         rows[cnt++] = rstart + i;
104         goto ok2;
105       }
106     }
107     bb = b->a + ib[i];
108     for (j=0; j<nb; j++) {
109       if (bb[j] != 0.0) {
110         rows[cnt++] = rstart + i;
111         goto ok2;
112       }
113     }
114 ok2:;
115   }
116   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)M),cnt,rows,PETSC_OWN_POINTER,keptrows);CHKERRQ(ierr);
117   PetscFunctionReturn(0);
118 }
119 
120 PetscErrorCode  MatDiagonalSet_MPIAIJ(Mat Y,Vec D,InsertMode is)
121 {
122   PetscErrorCode    ierr;
123   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*) Y->data;
124 
125   PetscFunctionBegin;
126   if (Y->assembled && Y->rmap->rstart == Y->cmap->rstart && Y->rmap->rend == Y->cmap->rend) {
127     ierr = MatDiagonalSet(aij->A,D,is);CHKERRQ(ierr);
128   } else {
129     ierr = MatDiagonalSet_Default(Y,D,is);CHKERRQ(ierr);
130   }
131   PetscFunctionReturn(0);
132 }
133 
134 
135 PetscErrorCode MatFindZeroDiagonals_MPIAIJ(Mat M,IS *zrows)
136 {
137   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)M->data;
138   PetscErrorCode ierr;
139   PetscInt       i,rstart,nrows,*rows;
140 
141   PetscFunctionBegin;
142   *zrows = NULL;
143   ierr   = MatFindZeroDiagonals_SeqAIJ_Private(aij->A,&nrows,&rows);CHKERRQ(ierr);
144   ierr   = MatGetOwnershipRange(M,&rstart,NULL);CHKERRQ(ierr);
145   for (i=0; i<nrows; i++) rows[i] += rstart;
146   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)M),nrows,rows,PETSC_OWN_POINTER,zrows);CHKERRQ(ierr);
147   PetscFunctionReturn(0);
148 }
149 
150 PetscErrorCode MatGetColumnNorms_MPIAIJ(Mat A,NormType type,PetscReal *norms)
151 {
152   PetscErrorCode ierr;
153   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)A->data;
154   PetscInt       i,n,*garray = aij->garray;
155   Mat_SeqAIJ     *a_aij = (Mat_SeqAIJ*) aij->A->data;
156   Mat_SeqAIJ     *b_aij = (Mat_SeqAIJ*) aij->B->data;
157   PetscReal      *work;
158 
159   PetscFunctionBegin;
160   ierr = MatGetSize(A,NULL,&n);CHKERRQ(ierr);
161   ierr = PetscCalloc1(n,&work);CHKERRQ(ierr);
162   if (type == NORM_2) {
163     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
164       work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i]*a_aij->a[i]);
165     }
166     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
167       work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]*b_aij->a[i]);
168     }
169   } else if (type == NORM_1) {
170     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
171       work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i]);
172     }
173     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
174       work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]);
175     }
176   } else if (type == NORM_INFINITY) {
177     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
178       work[A->cmap->rstart + a_aij->j[i]] = PetscMax(PetscAbsScalar(a_aij->a[i]), work[A->cmap->rstart + a_aij->j[i]]);
179     }
180     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
181       work[garray[b_aij->j[i]]] = PetscMax(PetscAbsScalar(b_aij->a[i]),work[garray[b_aij->j[i]]]);
182     }
183 
184   } else SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Unknown NormType");
185   if (type == NORM_INFINITY) {
186     ierr = MPIU_Allreduce(work,norms,n,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
187   } else {
188     ierr = MPIU_Allreduce(work,norms,n,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
189   }
190   ierr = PetscFree(work);CHKERRQ(ierr);
191   if (type == NORM_2) {
192     for (i=0; i<n; i++) norms[i] = PetscSqrtReal(norms[i]);
193   }
194   PetscFunctionReturn(0);
195 }
196 
197 PetscErrorCode MatFindOffBlockDiagonalEntries_MPIAIJ(Mat A,IS *is)
198 {
199   Mat_MPIAIJ      *a  = (Mat_MPIAIJ*)A->data;
200   IS              sis,gis;
201   PetscErrorCode  ierr;
202   const PetscInt  *isis,*igis;
203   PetscInt        n,*iis,nsis,ngis,rstart,i;
204 
205   PetscFunctionBegin;
206   ierr = MatFindOffBlockDiagonalEntries(a->A,&sis);CHKERRQ(ierr);
207   ierr = MatFindNonzeroRows(a->B,&gis);CHKERRQ(ierr);
208   ierr = ISGetSize(gis,&ngis);CHKERRQ(ierr);
209   ierr = ISGetSize(sis,&nsis);CHKERRQ(ierr);
210   ierr = ISGetIndices(sis,&isis);CHKERRQ(ierr);
211   ierr = ISGetIndices(gis,&igis);CHKERRQ(ierr);
212 
213   ierr = PetscMalloc1(ngis+nsis,&iis);CHKERRQ(ierr);
214   ierr = PetscMemcpy(iis,igis,ngis*sizeof(PetscInt));CHKERRQ(ierr);
215   ierr = PetscMemcpy(iis+ngis,isis,nsis*sizeof(PetscInt));CHKERRQ(ierr);
216   n    = ngis + nsis;
217   ierr = PetscSortRemoveDupsInt(&n,iis);CHKERRQ(ierr);
218   ierr = MatGetOwnershipRange(A,&rstart,NULL);CHKERRQ(ierr);
219   for (i=0; i<n; i++) iis[i] += rstart;
220   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)A),n,iis,PETSC_OWN_POINTER,is);CHKERRQ(ierr);
221 
222   ierr = ISRestoreIndices(sis,&isis);CHKERRQ(ierr);
223   ierr = ISRestoreIndices(gis,&igis);CHKERRQ(ierr);
224   ierr = ISDestroy(&sis);CHKERRQ(ierr);
225   ierr = ISDestroy(&gis);CHKERRQ(ierr);
226   PetscFunctionReturn(0);
227 }
228 
229 /*
230     Distributes a SeqAIJ matrix across a set of processes. Code stolen from
231     MatLoad_MPIAIJ(). Horrible lack of reuse. Should be a routine for each matrix type.
232 
233     Only for square matrices
234 
235     Used by a preconditioner, hence PETSC_EXTERN
236 */
237 PETSC_EXTERN PetscErrorCode MatDistribute_MPIAIJ(MPI_Comm comm,Mat gmat,PetscInt m,MatReuse reuse,Mat *inmat)
238 {
239   PetscMPIInt    rank,size;
240   PetscInt       *rowners,*dlens,*olens,i,rstart,rend,j,jj,nz = 0,*gmataj,cnt,row,*ld,bses[2];
241   PetscErrorCode ierr;
242   Mat            mat;
243   Mat_SeqAIJ     *gmata;
244   PetscMPIInt    tag;
245   MPI_Status     status;
246   PetscBool      aij;
247   MatScalar      *gmataa,*ao,*ad,*gmataarestore=0;
248 
249   PetscFunctionBegin;
250   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
251   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
252   if (!rank) {
253     ierr = PetscObjectTypeCompare((PetscObject)gmat,MATSEQAIJ,&aij);CHKERRQ(ierr);
254     if (!aij) SETERRQ1(PetscObjectComm((PetscObject)gmat),PETSC_ERR_SUP,"Currently no support for input matrix of type %s\n",((PetscObject)gmat)->type_name);
255   }
256   if (reuse == MAT_INITIAL_MATRIX) {
257     ierr = MatCreate(comm,&mat);CHKERRQ(ierr);
258     ierr = MatSetSizes(mat,m,m,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
259     ierr = MatGetBlockSizes(gmat,&bses[0],&bses[1]);CHKERRQ(ierr);
260     ierr = MPI_Bcast(bses,2,MPIU_INT,0,comm);CHKERRQ(ierr);
261     ierr = MatSetBlockSizes(mat,bses[0],bses[1]);CHKERRQ(ierr);
262     ierr = MatSetType(mat,MATAIJ);CHKERRQ(ierr);
263     ierr = PetscMalloc1(size+1,&rowners);CHKERRQ(ierr);
264     ierr = PetscMalloc2(m,&dlens,m,&olens);CHKERRQ(ierr);
265     ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
266 
267     rowners[0] = 0;
268     for (i=2; i<=size; i++) rowners[i] += rowners[i-1];
269     rstart = rowners[rank];
270     rend   = rowners[rank+1];
271     ierr   = PetscObjectGetNewTag((PetscObject)mat,&tag);CHKERRQ(ierr);
272     if (!rank) {
273       gmata = (Mat_SeqAIJ*) gmat->data;
274       /* send row lengths to all processors */
275       for (i=0; i<m; i++) dlens[i] = gmata->ilen[i];
276       for (i=1; i<size; i++) {
277         ierr = MPI_Send(gmata->ilen + rowners[i],rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
278       }
279       /* determine number diagonal and off-diagonal counts */
280       ierr = PetscMemzero(olens,m*sizeof(PetscInt));CHKERRQ(ierr);
281       ierr = PetscCalloc1(m,&ld);CHKERRQ(ierr);
282       jj   = 0;
283       for (i=0; i<m; i++) {
284         for (j=0; j<dlens[i]; j++) {
285           if (gmata->j[jj] < rstart) ld[i]++;
286           if (gmata->j[jj] < rstart || gmata->j[jj] >= rend) olens[i]++;
287           jj++;
288         }
289       }
290       /* send column indices to other processes */
291       for (i=1; i<size; i++) {
292         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
293         ierr = MPI_Send(&nz,1,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
294         ierr = MPI_Send(gmata->j + gmata->i[rowners[i]],nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
295       }
296 
297       /* send numerical values to other processes */
298       for (i=1; i<size; i++) {
299         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
300         ierr = MPI_Send(gmata->a + gmata->i[rowners[i]],nz,MPIU_SCALAR,i,tag,comm);CHKERRQ(ierr);
301       }
302       gmataa = gmata->a;
303       gmataj = gmata->j;
304 
305     } else {
306       /* receive row lengths */
307       ierr = MPI_Recv(dlens,m,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
308       /* receive column indices */
309       ierr = MPI_Recv(&nz,1,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
310       ierr = PetscMalloc2(nz,&gmataa,nz,&gmataj);CHKERRQ(ierr);
311       ierr = MPI_Recv(gmataj,nz,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
312       /* determine number diagonal and off-diagonal counts */
313       ierr = PetscMemzero(olens,m*sizeof(PetscInt));CHKERRQ(ierr);
314       ierr = PetscCalloc1(m,&ld);CHKERRQ(ierr);
315       jj   = 0;
316       for (i=0; i<m; i++) {
317         for (j=0; j<dlens[i]; j++) {
318           if (gmataj[jj] < rstart) ld[i]++;
319           if (gmataj[jj] < rstart || gmataj[jj] >= rend) olens[i]++;
320           jj++;
321         }
322       }
323       /* receive numerical values */
324       ierr = PetscMemzero(gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr);
325       ierr = MPI_Recv(gmataa,nz,MPIU_SCALAR,0,tag,comm,&status);CHKERRQ(ierr);
326     }
327     /* set preallocation */
328     for (i=0; i<m; i++) {
329       dlens[i] -= olens[i];
330     }
331     ierr = MatSeqAIJSetPreallocation(mat,0,dlens);CHKERRQ(ierr);
332     ierr = MatMPIAIJSetPreallocation(mat,0,dlens,0,olens);CHKERRQ(ierr);
333 
334     for (i=0; i<m; i++) {
335       dlens[i] += olens[i];
336     }
337     cnt = 0;
338     for (i=0; i<m; i++) {
339       row  = rstart + i;
340       ierr = MatSetValues(mat,1,&row,dlens[i],gmataj+cnt,gmataa+cnt,INSERT_VALUES);CHKERRQ(ierr);
341       cnt += dlens[i];
342     }
343     if (rank) {
344       ierr = PetscFree2(gmataa,gmataj);CHKERRQ(ierr);
345     }
346     ierr = PetscFree2(dlens,olens);CHKERRQ(ierr);
347     ierr = PetscFree(rowners);CHKERRQ(ierr);
348 
349     ((Mat_MPIAIJ*)(mat->data))->ld = ld;
350 
351     *inmat = mat;
352   } else {   /* column indices are already set; only need to move over numerical values from process 0 */
353     Mat_SeqAIJ *Ad = (Mat_SeqAIJ*)((Mat_MPIAIJ*)((*inmat)->data))->A->data;
354     Mat_SeqAIJ *Ao = (Mat_SeqAIJ*)((Mat_MPIAIJ*)((*inmat)->data))->B->data;
355     mat  = *inmat;
356     ierr = PetscObjectGetNewTag((PetscObject)mat,&tag);CHKERRQ(ierr);
357     if (!rank) {
358       /* send numerical values to other processes */
359       gmata  = (Mat_SeqAIJ*) gmat->data;
360       ierr   = MatGetOwnershipRanges(mat,(const PetscInt**)&rowners);CHKERRQ(ierr);
361       gmataa = gmata->a;
362       for (i=1; i<size; i++) {
363         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
364         ierr = MPI_Send(gmataa + gmata->i[rowners[i]],nz,MPIU_SCALAR,i,tag,comm);CHKERRQ(ierr);
365       }
366       nz = gmata->i[rowners[1]]-gmata->i[rowners[0]];
367     } else {
368       /* receive numerical values from process 0*/
369       nz   = Ad->nz + Ao->nz;
370       ierr = PetscMalloc1(nz,&gmataa);CHKERRQ(ierr); gmataarestore = gmataa;
371       ierr = MPI_Recv(gmataa,nz,MPIU_SCALAR,0,tag,comm,&status);CHKERRQ(ierr);
372     }
373     /* transfer numerical values into the diagonal A and off diagonal B parts of mat */
374     ld = ((Mat_MPIAIJ*)(mat->data))->ld;
375     ad = Ad->a;
376     ao = Ao->a;
377     if (mat->rmap->n) {
378       i  = 0;
379       nz = ld[i];                                   ierr = PetscMemcpy(ao,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ao += nz; gmataa += nz;
380       nz = Ad->i[i+1] - Ad->i[i];                   ierr = PetscMemcpy(ad,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ad += nz; gmataa += nz;
381     }
382     for (i=1; i<mat->rmap->n; i++) {
383       nz = Ao->i[i] - Ao->i[i-1] - ld[i-1] + ld[i]; ierr = PetscMemcpy(ao,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ao += nz; gmataa += nz;
384       nz = Ad->i[i+1] - Ad->i[i];                   ierr = PetscMemcpy(ad,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ad += nz; gmataa += nz;
385     }
386     i--;
387     if (mat->rmap->n) {
388       nz = Ao->i[i+1] - Ao->i[i] - ld[i];           ierr = PetscMemcpy(ao,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr);
389     }
390     if (rank) {
391       ierr = PetscFree(gmataarestore);CHKERRQ(ierr);
392     }
393   }
394   ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
395   ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
396   PetscFunctionReturn(0);
397 }
398 
399 /*
400   Local utility routine that creates a mapping from the global column
401 number to the local number in the off-diagonal part of the local
402 storage of the matrix.  When PETSC_USE_CTABLE is used this is scalable at
403 a slightly higher hash table cost; without it it is not scalable (each processor
404 has an order N integer array but is fast to acess.
405 */
406 PetscErrorCode MatCreateColmap_MPIAIJ_Private(Mat mat)
407 {
408   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
409   PetscErrorCode ierr;
410   PetscInt       n = aij->B->cmap->n,i;
411 
412   PetscFunctionBegin;
413   if (!aij->garray) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"MPIAIJ Matrix was assembled but is missing garray");
414 #if defined(PETSC_USE_CTABLE)
415   ierr = PetscTableCreate(n,mat->cmap->N+1,&aij->colmap);CHKERRQ(ierr);
416   for (i=0; i<n; i++) {
417     ierr = PetscTableAdd(aij->colmap,aij->garray[i]+1,i+1,INSERT_VALUES);CHKERRQ(ierr);
418   }
419 #else
420   ierr = PetscCalloc1(mat->cmap->N+1,&aij->colmap);CHKERRQ(ierr);
421   ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N+1)*sizeof(PetscInt));CHKERRQ(ierr);
422   for (i=0; i<n; i++) aij->colmap[aij->garray[i]] = i+1;
423 #endif
424   PetscFunctionReturn(0);
425 }
426 
427 #define MatSetValues_SeqAIJ_A_Private(row,col,value,addv,orow,ocol)     \
428 { \
429     if (col <= lastcol1)  low1 = 0;     \
430     else                 high1 = nrow1; \
431     lastcol1 = col;\
432     while (high1-low1 > 5) { \
433       t = (low1+high1)/2; \
434       if (rp1[t] > col) high1 = t; \
435       else              low1  = t; \
436     } \
437       for (_i=low1; _i<high1; _i++) { \
438         if (rp1[_i] > col) break; \
439         if (rp1[_i] == col) { \
440           if (addv == ADD_VALUES) ap1[_i] += value;   \
441           else                    ap1[_i] = value; \
442           goto a_noinsert; \
443         } \
444       }  \
445       if (value == 0.0 && ignorezeroentries && row != col) {low1 = 0; high1 = nrow1;goto a_noinsert;} \
446       if (nonew == 1) {low1 = 0; high1 = nrow1; goto a_noinsert;}                \
447       if (nonew == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at global row/column (%D, %D) into matrix", orow, ocol); \
448       MatSeqXAIJReallocateAIJ(A,am,1,nrow1,row,col,rmax1,aa,ai,aj,rp1,ap1,aimax,nonew,MatScalar); \
449       N = nrow1++ - 1; a->nz++; high1++; \
450       /* shift up all the later entries in this row */ \
451       for (ii=N; ii>=_i; ii--) { \
452         rp1[ii+1] = rp1[ii]; \
453         ap1[ii+1] = ap1[ii]; \
454       } \
455       rp1[_i] = col;  \
456       ap1[_i] = value;  \
457       A->nonzerostate++;\
458       a_noinsert: ; \
459       ailen[row] = nrow1; \
460 }
461 
462 
463 #define MatSetValues_SeqAIJ_B_Private(row,col,value,addv,orow,ocol) \
464   { \
465     if (col <= lastcol2) low2 = 0;                        \
466     else high2 = nrow2;                                   \
467     lastcol2 = col;                                       \
468     while (high2-low2 > 5) {                              \
469       t = (low2+high2)/2;                                 \
470       if (rp2[t] > col) high2 = t;                        \
471       else             low2  = t;                         \
472     }                                                     \
473     for (_i=low2; _i<high2; _i++) {                       \
474       if (rp2[_i] > col) break;                           \
475       if (rp2[_i] == col) {                               \
476         if (addv == ADD_VALUES) ap2[_i] += value;         \
477         else                    ap2[_i] = value;          \
478         goto b_noinsert;                                  \
479       }                                                   \
480     }                                                     \
481     if (value == 0.0 && ignorezeroentries) {low2 = 0; high2 = nrow2; goto b_noinsert;} \
482     if (nonew == 1) {low2 = 0; high2 = nrow2; goto b_noinsert;}                        \
483     if (nonew == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at global row/column (%D, %D) into matrix", orow, ocol); \
484     MatSeqXAIJReallocateAIJ(B,bm,1,nrow2,row,col,rmax2,ba,bi,bj,rp2,ap2,bimax,nonew,MatScalar); \
485     N = nrow2++ - 1; b->nz++; high2++;                    \
486     /* shift up all the later entries in this row */      \
487     for (ii=N; ii>=_i; ii--) {                            \
488       rp2[ii+1] = rp2[ii];                                \
489       ap2[ii+1] = ap2[ii];                                \
490     }                                                     \
491     rp2[_i] = col;                                        \
492     ap2[_i] = value;                                      \
493     B->nonzerostate++;                                    \
494     b_noinsert: ;                                         \
495     bilen[row] = nrow2;                                   \
496   }
497 
498 PetscErrorCode MatSetValuesRow_MPIAIJ(Mat A,PetscInt row,const PetscScalar v[])
499 {
500   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)A->data;
501   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)mat->A->data,*b = (Mat_SeqAIJ*)mat->B->data;
502   PetscErrorCode ierr;
503   PetscInt       l,*garray = mat->garray,diag;
504 
505   PetscFunctionBegin;
506   /* code only works for square matrices A */
507 
508   /* find size of row to the left of the diagonal part */
509   ierr = MatGetOwnershipRange(A,&diag,0);CHKERRQ(ierr);
510   row  = row - diag;
511   for (l=0; l<b->i[row+1]-b->i[row]; l++) {
512     if (garray[b->j[b->i[row]+l]] > diag) break;
513   }
514   ierr = PetscMemcpy(b->a+b->i[row],v,l*sizeof(PetscScalar));CHKERRQ(ierr);
515 
516   /* diagonal part */
517   ierr = PetscMemcpy(a->a+a->i[row],v+l,(a->i[row+1]-a->i[row])*sizeof(PetscScalar));CHKERRQ(ierr);
518 
519   /* right of diagonal part */
520   ierr = PetscMemcpy(b->a+b->i[row]+l,v+l+a->i[row+1]-a->i[row],(b->i[row+1]-b->i[row]-l)*sizeof(PetscScalar));CHKERRQ(ierr);
521   PetscFunctionReturn(0);
522 }
523 
524 PetscErrorCode MatSetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode addv)
525 {
526   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
527   PetscScalar    value;
528   PetscErrorCode ierr;
529   PetscInt       i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
530   PetscInt       cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
531   PetscBool      roworiented = aij->roworiented;
532 
533   /* Some Variables required in the macro */
534   Mat        A                 = aij->A;
535   Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
536   PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
537   MatScalar  *aa               = a->a;
538   PetscBool  ignorezeroentries = a->ignorezeroentries;
539   Mat        B                 = aij->B;
540   Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
541   PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
542   MatScalar  *ba               = b->a;
543 
544   PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
545   PetscInt  nonew;
546   MatScalar *ap1,*ap2;
547 
548   PetscFunctionBegin;
549   for (i=0; i<m; i++) {
550     if (im[i] < 0) continue;
551 #if defined(PETSC_USE_DEBUG)
552     if (im[i] >= mat->rmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %D max %D",im[i],mat->rmap->N-1);
553 #endif
554     if (im[i] >= rstart && im[i] < rend) {
555       row      = im[i] - rstart;
556       lastcol1 = -1;
557       rp1      = aj + ai[row];
558       ap1      = aa + ai[row];
559       rmax1    = aimax[row];
560       nrow1    = ailen[row];
561       low1     = 0;
562       high1    = nrow1;
563       lastcol2 = -1;
564       rp2      = bj + bi[row];
565       ap2      = ba + bi[row];
566       rmax2    = bimax[row];
567       nrow2    = bilen[row];
568       low2     = 0;
569       high2    = nrow2;
570 
571       for (j=0; j<n; j++) {
572         if (roworiented) value = v[i*n+j];
573         else             value = v[i+j*m];
574         if (in[j] >= cstart && in[j] < cend) {
575           col   = in[j] - cstart;
576           nonew = a->nonew;
577           if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
578           MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
579         } else if (in[j] < 0) continue;
580 #if defined(PETSC_USE_DEBUG)
581         else if (in[j] >= mat->cmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %D max %D",in[j],mat->cmap->N-1);
582 #endif
583         else {
584           if (mat->was_assembled) {
585             if (!aij->colmap) {
586               ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
587             }
588 #if defined(PETSC_USE_CTABLE)
589             ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
590             col--;
591 #else
592             col = aij->colmap[in[j]] - 1;
593 #endif
594             if (col < 0 && !((Mat_SeqAIJ*)(aij->B->data))->nonew) {
595               ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
596               col  =  in[j];
597               /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
598               B     = aij->B;
599               b     = (Mat_SeqAIJ*)B->data;
600               bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j; ba = b->a;
601               rp2   = bj + bi[row];
602               ap2   = ba + bi[row];
603               rmax2 = bimax[row];
604               nrow2 = bilen[row];
605               low2  = 0;
606               high2 = nrow2;
607               bm    = aij->B->rmap->n;
608               ba    = b->a;
609             } else if (col < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at global row/column (%D, %D) into matrix", im[i], in[j]);
610           } else col = in[j];
611           nonew = b->nonew;
612           MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
613         }
614       }
615     } else {
616       if (mat->nooffprocentries) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Setting off process row %D even though MatSetOption(,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) was set",im[i]);
617       if (!aij->donotstash) {
618         mat->assembled = PETSC_FALSE;
619         if (roworiented) {
620           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
621         } else {
622           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
623         }
624       }
625     }
626   }
627   PetscFunctionReturn(0);
628 }
629 
630 PetscErrorCode MatGetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],PetscScalar v[])
631 {
632   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
633   PetscErrorCode ierr;
634   PetscInt       i,j,rstart = mat->rmap->rstart,rend = mat->rmap->rend;
635   PetscInt       cstart = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
636 
637   PetscFunctionBegin;
638   for (i=0; i<m; i++) {
639     if (idxm[i] < 0) continue; /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative row: %D",idxm[i]);*/
640     if (idxm[i] >= mat->rmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %D max %D",idxm[i],mat->rmap->N-1);
641     if (idxm[i] >= rstart && idxm[i] < rend) {
642       row = idxm[i] - rstart;
643       for (j=0; j<n; j++) {
644         if (idxn[j] < 0) continue; /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column: %D",idxn[j]); */
645         if (idxn[j] >= mat->cmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %D max %D",idxn[j],mat->cmap->N-1);
646         if (idxn[j] >= cstart && idxn[j] < cend) {
647           col  = idxn[j] - cstart;
648           ierr = MatGetValues(aij->A,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
649         } else {
650           if (!aij->colmap) {
651             ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
652           }
653 #if defined(PETSC_USE_CTABLE)
654           ierr = PetscTableFind(aij->colmap,idxn[j]+1,&col);CHKERRQ(ierr);
655           col--;
656 #else
657           col = aij->colmap[idxn[j]] - 1;
658 #endif
659           if ((col < 0) || (aij->garray[col] != idxn[j])) *(v+i*n+j) = 0.0;
660           else {
661             ierr = MatGetValues(aij->B,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
662           }
663         }
664       }
665     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only local values currently supported");
666   }
667   PetscFunctionReturn(0);
668 }
669 
670 extern PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat,Vec,Vec);
671 
672 PetscErrorCode MatAssemblyBegin_MPIAIJ(Mat mat,MatAssemblyType mode)
673 {
674   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
675   PetscErrorCode ierr;
676   PetscInt       nstash,reallocs;
677 
678   PetscFunctionBegin;
679   if (aij->donotstash || mat->nooffprocentries) PetscFunctionReturn(0);
680 
681   ierr = MatStashScatterBegin_Private(mat,&mat->stash,mat->rmap->range);CHKERRQ(ierr);
682   ierr = MatStashGetInfo_Private(&mat->stash,&nstash,&reallocs);CHKERRQ(ierr);
683   ierr = PetscInfo2(aij->A,"Stash has %D entries, uses %D mallocs.\n",nstash,reallocs);CHKERRQ(ierr);
684   PetscFunctionReturn(0);
685 }
686 
687 PetscErrorCode MatAssemblyEnd_MPIAIJ(Mat mat,MatAssemblyType mode)
688 {
689   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
690   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)aij->A->data;
691   PetscErrorCode ierr;
692   PetscMPIInt    n;
693   PetscInt       i,j,rstart,ncols,flg;
694   PetscInt       *row,*col;
695   PetscBool      other_disassembled;
696   PetscScalar    *val;
697 
698   /* do not use 'b = (Mat_SeqAIJ*)aij->B->data' as B can be reset in disassembly */
699 
700   PetscFunctionBegin;
701   if (!aij->donotstash && !mat->nooffprocentries) {
702     while (1) {
703       ierr = MatStashScatterGetMesg_Private(&mat->stash,&n,&row,&col,&val,&flg);CHKERRQ(ierr);
704       if (!flg) break;
705 
706       for (i=0; i<n; ) {
707         /* Now identify the consecutive vals belonging to the same row */
708         for (j=i,rstart=row[j]; j<n; j++) {
709           if (row[j] != rstart) break;
710         }
711         if (j < n) ncols = j-i;
712         else       ncols = n-i;
713         /* Now assemble all these values with a single function call */
714         ierr = MatSetValues_MPIAIJ(mat,1,row+i,ncols,col+i,val+i,mat->insertmode);CHKERRQ(ierr);
715 
716         i = j;
717       }
718     }
719     ierr = MatStashScatterEnd_Private(&mat->stash);CHKERRQ(ierr);
720   }
721   ierr = MatAssemblyBegin(aij->A,mode);CHKERRQ(ierr);
722   ierr = MatAssemblyEnd(aij->A,mode);CHKERRQ(ierr);
723 
724   /* determine if any processor has disassembled, if so we must
725      also disassemble ourselfs, in order that we may reassemble. */
726   /*
727      if nonzero structure of submatrix B cannot change then we know that
728      no processor disassembled thus we can skip this stuff
729   */
730   if (!((Mat_SeqAIJ*)aij->B->data)->nonew) {
731     ierr = MPIU_Allreduce(&mat->was_assembled,&other_disassembled,1,MPIU_BOOL,MPI_PROD,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
732     if (mat->was_assembled && !other_disassembled) {
733       ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
734     }
735   }
736   if (!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) {
737     ierr = MatSetUpMultiply_MPIAIJ(mat);CHKERRQ(ierr);
738   }
739   ierr = MatSetOption(aij->B,MAT_USE_INODES,PETSC_FALSE);CHKERRQ(ierr);
740   ierr = MatAssemblyBegin(aij->B,mode);CHKERRQ(ierr);
741   ierr = MatAssemblyEnd(aij->B,mode);CHKERRQ(ierr);
742 
743   ierr = PetscFree2(aij->rowvalues,aij->rowindices);CHKERRQ(ierr);
744 
745   aij->rowvalues = 0;
746 
747   ierr = VecDestroy(&aij->diag);CHKERRQ(ierr);
748   if (a->inode.size) mat->ops->multdiagonalblock = MatMultDiagonalBlock_MPIAIJ;
749 
750   /* if no new nonzero locations are allowed in matrix then only set the matrix state the first time through */
751   if ((!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) || !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
752     PetscObjectState state = aij->A->nonzerostate + aij->B->nonzerostate;
753     ierr = MPIU_Allreduce(&state,&mat->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
754   }
755   PetscFunctionReturn(0);
756 }
757 
758 PetscErrorCode MatZeroEntries_MPIAIJ(Mat A)
759 {
760   Mat_MPIAIJ     *l = (Mat_MPIAIJ*)A->data;
761   PetscErrorCode ierr;
762 
763   PetscFunctionBegin;
764   ierr = MatZeroEntries(l->A);CHKERRQ(ierr);
765   ierr = MatZeroEntries(l->B);CHKERRQ(ierr);
766   PetscFunctionReturn(0);
767 }
768 
769 PetscErrorCode MatZeroRows_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
770 {
771   Mat_MPIAIJ    *mat    = (Mat_MPIAIJ *) A->data;
772   PetscInt      *lrows;
773   PetscInt       r, len;
774   PetscErrorCode ierr;
775 
776   PetscFunctionBegin;
777   /* get locally owned rows */
778   ierr = MatZeroRowsMapLocal_Private(A,N,rows,&len,&lrows);CHKERRQ(ierr);
779   /* fix right hand side if needed */
780   if (x && b) {
781     const PetscScalar *xx;
782     PetscScalar       *bb;
783 
784     ierr = VecGetArrayRead(x, &xx);CHKERRQ(ierr);
785     ierr = VecGetArray(b, &bb);CHKERRQ(ierr);
786     for (r = 0; r < len; ++r) bb[lrows[r]] = diag*xx[lrows[r]];
787     ierr = VecRestoreArrayRead(x, &xx);CHKERRQ(ierr);
788     ierr = VecRestoreArray(b, &bb);CHKERRQ(ierr);
789   }
790   /* Must zero l->B before l->A because the (diag) case below may put values into l->B*/
791   ierr = MatZeroRows(mat->B, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
792   if (A->congruentlayouts == -1) { /* first time we compare rows and cols layouts */
793     PetscBool cong;
794     ierr = PetscLayoutCompare(A->rmap,A->cmap,&cong);CHKERRQ(ierr);
795     if (cong) A->congruentlayouts = 1;
796     else      A->congruentlayouts = 0;
797   }
798   if ((diag != 0.0) && A->congruentlayouts) {
799     ierr = MatZeroRows(mat->A, len, lrows, diag, NULL, NULL);CHKERRQ(ierr);
800   } else if (diag != 0.0) {
801     ierr = MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
802     if (((Mat_SeqAIJ *) mat->A->data)->nonew) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatZeroRows() on rectangular matrices cannot be used with the Mat options\nMAT_NEW_NONZERO_LOCATIONS,MAT_NEW_NONZERO_LOCATION_ERR,MAT_NEW_NONZERO_ALLOCATION_ERR");
803     for (r = 0; r < len; ++r) {
804       const PetscInt row = lrows[r] + A->rmap->rstart;
805       ierr = MatSetValues(A, 1, &row, 1, &row, &diag, INSERT_VALUES);CHKERRQ(ierr);
806     }
807     ierr = MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
808     ierr = MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
809   } else {
810     ierr = MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
811   }
812   ierr = PetscFree(lrows);CHKERRQ(ierr);
813 
814   /* only change matrix nonzero state if pattern was allowed to be changed */
815   if (!((Mat_SeqAIJ*)(mat->A->data))->keepnonzeropattern) {
816     PetscObjectState state = mat->A->nonzerostate + mat->B->nonzerostate;
817     ierr = MPIU_Allreduce(&state,&A->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
818   }
819   PetscFunctionReturn(0);
820 }
821 
822 PetscErrorCode MatZeroRowsColumns_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
823 {
824   Mat_MPIAIJ        *l = (Mat_MPIAIJ*)A->data;
825   PetscErrorCode    ierr;
826   PetscMPIInt       n = A->rmap->n;
827   PetscInt          i,j,r,m,p = 0,len = 0;
828   PetscInt          *lrows,*owners = A->rmap->range;
829   PetscSFNode       *rrows;
830   PetscSF           sf;
831   const PetscScalar *xx;
832   PetscScalar       *bb,*mask;
833   Vec               xmask,lmask;
834   Mat_SeqAIJ        *aij = (Mat_SeqAIJ*)l->B->data;
835   const PetscInt    *aj, *ii,*ridx;
836   PetscScalar       *aa;
837 
838   PetscFunctionBegin;
839   /* Create SF where leaves are input rows and roots are owned rows */
840   ierr = PetscMalloc1(n, &lrows);CHKERRQ(ierr);
841   for (r = 0; r < n; ++r) lrows[r] = -1;
842   ierr = PetscMalloc1(N, &rrows);CHKERRQ(ierr);
843   for (r = 0; r < N; ++r) {
844     const PetscInt idx   = rows[r];
845     if (idx < 0 || A->rmap->N <= idx) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row %D out of range [0,%D)",idx,A->rmap->N);
846     if (idx < owners[p] || owners[p+1] <= idx) { /* short-circuit the search if the last p owns this row too */
847       ierr = PetscLayoutFindOwner(A->rmap,idx,&p);CHKERRQ(ierr);
848     }
849     rrows[r].rank  = p;
850     rrows[r].index = rows[r] - owners[p];
851   }
852   ierr = PetscSFCreate(PetscObjectComm((PetscObject) A), &sf);CHKERRQ(ierr);
853   ierr = PetscSFSetGraph(sf, n, N, NULL, PETSC_OWN_POINTER, rrows, PETSC_OWN_POINTER);CHKERRQ(ierr);
854   /* Collect flags for rows to be zeroed */
855   ierr = PetscSFReduceBegin(sf, MPIU_INT, (PetscInt *) rows, lrows, MPI_LOR);CHKERRQ(ierr);
856   ierr = PetscSFReduceEnd(sf, MPIU_INT, (PetscInt *) rows, lrows, MPI_LOR);CHKERRQ(ierr);
857   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
858   /* Compress and put in row numbers */
859   for (r = 0; r < n; ++r) if (lrows[r] >= 0) lrows[len++] = r;
860   /* zero diagonal part of matrix */
861   ierr = MatZeroRowsColumns(l->A,len,lrows,diag,x,b);CHKERRQ(ierr);
862   /* handle off diagonal part of matrix */
863   ierr = MatCreateVecs(A,&xmask,NULL);CHKERRQ(ierr);
864   ierr = VecDuplicate(l->lvec,&lmask);CHKERRQ(ierr);
865   ierr = VecGetArray(xmask,&bb);CHKERRQ(ierr);
866   for (i=0; i<len; i++) bb[lrows[i]] = 1;
867   ierr = VecRestoreArray(xmask,&bb);CHKERRQ(ierr);
868   ierr = VecScatterBegin(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
869   ierr = VecScatterEnd(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
870   ierr = VecDestroy(&xmask);CHKERRQ(ierr);
871   if (x) {
872     ierr = VecScatterBegin(l->Mvctx,x,l->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
873     ierr = VecScatterEnd(l->Mvctx,x,l->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
874     ierr = VecGetArrayRead(l->lvec,&xx);CHKERRQ(ierr);
875     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
876   }
877   ierr = VecGetArray(lmask,&mask);CHKERRQ(ierr);
878   /* remove zeroed rows of off diagonal matrix */
879   ii = aij->i;
880   for (i=0; i<len; i++) {
881     ierr = PetscMemzero(aij->a + ii[lrows[i]],(ii[lrows[i]+1] - ii[lrows[i]])*sizeof(PetscScalar));CHKERRQ(ierr);
882   }
883   /* loop over all elements of off process part of matrix zeroing removed columns*/
884   if (aij->compressedrow.use) {
885     m    = aij->compressedrow.nrows;
886     ii   = aij->compressedrow.i;
887     ridx = aij->compressedrow.rindex;
888     for (i=0; i<m; i++) {
889       n  = ii[i+1] - ii[i];
890       aj = aij->j + ii[i];
891       aa = aij->a + ii[i];
892 
893       for (j=0; j<n; j++) {
894         if (PetscAbsScalar(mask[*aj])) {
895           if (b) bb[*ridx] -= *aa*xx[*aj];
896           *aa = 0.0;
897         }
898         aa++;
899         aj++;
900       }
901       ridx++;
902     }
903   } else { /* do not use compressed row format */
904     m = l->B->rmap->n;
905     for (i=0; i<m; i++) {
906       n  = ii[i+1] - ii[i];
907       aj = aij->j + ii[i];
908       aa = aij->a + ii[i];
909       for (j=0; j<n; j++) {
910         if (PetscAbsScalar(mask[*aj])) {
911           if (b) bb[i] -= *aa*xx[*aj];
912           *aa = 0.0;
913         }
914         aa++;
915         aj++;
916       }
917     }
918   }
919   if (x) {
920     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
921     ierr = VecRestoreArrayRead(l->lvec,&xx);CHKERRQ(ierr);
922   }
923   ierr = VecRestoreArray(lmask,&mask);CHKERRQ(ierr);
924   ierr = VecDestroy(&lmask);CHKERRQ(ierr);
925   ierr = PetscFree(lrows);CHKERRQ(ierr);
926 
927   /* only change matrix nonzero state if pattern was allowed to be changed */
928   if (!((Mat_SeqAIJ*)(l->A->data))->keepnonzeropattern) {
929     PetscObjectState state = l->A->nonzerostate + l->B->nonzerostate;
930     ierr = MPIU_Allreduce(&state,&A->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
931   }
932   PetscFunctionReturn(0);
933 }
934 
935 PetscErrorCode MatMult_MPIAIJ(Mat A,Vec xx,Vec yy)
936 {
937   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
938   PetscErrorCode ierr;
939   PetscInt       nt;
940 
941   PetscFunctionBegin;
942   ierr = VecGetLocalSize(xx,&nt);CHKERRQ(ierr);
943   if (nt != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Incompatible partition of A (%D) and xx (%D)",A->cmap->n,nt);
944   ierr = VecScatterBegin(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
945   ierr = (*a->A->ops->mult)(a->A,xx,yy);CHKERRQ(ierr);
946   ierr = VecScatterEnd(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
947   ierr = (*a->B->ops->multadd)(a->B,a->lvec,yy,yy);CHKERRQ(ierr);
948   PetscFunctionReturn(0);
949 }
950 
951 PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat A,Vec bb,Vec xx)
952 {
953   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
954   PetscErrorCode ierr;
955 
956   PetscFunctionBegin;
957   ierr = MatMultDiagonalBlock(a->A,bb,xx);CHKERRQ(ierr);
958   PetscFunctionReturn(0);
959 }
960 
961 PetscErrorCode MatMultAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
962 {
963   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
964   PetscErrorCode ierr;
965 
966   PetscFunctionBegin;
967   ierr = VecScatterBegin(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
968   ierr = (*a->A->ops->multadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
969   ierr = VecScatterEnd(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
970   ierr = (*a->B->ops->multadd)(a->B,a->lvec,zz,zz);CHKERRQ(ierr);
971   PetscFunctionReturn(0);
972 }
973 
974 PetscErrorCode MatMultTranspose_MPIAIJ(Mat A,Vec xx,Vec yy)
975 {
976   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
977   PetscErrorCode ierr;
978   PetscBool      merged;
979 
980   PetscFunctionBegin;
981   ierr = VecScatterGetMerged(a->Mvctx,&merged);CHKERRQ(ierr);
982   /* do nondiagonal part */
983   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
984   if (!merged) {
985     /* send it on its way */
986     ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
987     /* do local part */
988     ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
989     /* receive remote parts: note this assumes the values are not actually */
990     /* added in yy until the next line, */
991     ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
992   } else {
993     /* do local part */
994     ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
995     /* send it on its way */
996     ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
997     /* values actually were received in the Begin() but we need to call this nop */
998     ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
999   }
1000   PetscFunctionReturn(0);
1001 }
1002 
1003 PetscErrorCode  MatIsTranspose_MPIAIJ(Mat Amat,Mat Bmat,PetscReal tol,PetscBool  *f)
1004 {
1005   MPI_Comm       comm;
1006   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ*) Amat->data, *Bij;
1007   Mat            Adia = Aij->A, Bdia, Aoff,Boff,*Aoffs,*Boffs;
1008   IS             Me,Notme;
1009   PetscErrorCode ierr;
1010   PetscInt       M,N,first,last,*notme,i;
1011   PetscMPIInt    size;
1012 
1013   PetscFunctionBegin;
1014   /* Easy test: symmetric diagonal block */
1015   Bij  = (Mat_MPIAIJ*) Bmat->data; Bdia = Bij->A;
1016   ierr = MatIsTranspose(Adia,Bdia,tol,f);CHKERRQ(ierr);
1017   if (!*f) PetscFunctionReturn(0);
1018   ierr = PetscObjectGetComm((PetscObject)Amat,&comm);CHKERRQ(ierr);
1019   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1020   if (size == 1) PetscFunctionReturn(0);
1021 
1022   /* Hard test: off-diagonal block. This takes a MatCreateSubMatrix. */
1023   ierr = MatGetSize(Amat,&M,&N);CHKERRQ(ierr);
1024   ierr = MatGetOwnershipRange(Amat,&first,&last);CHKERRQ(ierr);
1025   ierr = PetscMalloc1(N-last+first,&notme);CHKERRQ(ierr);
1026   for (i=0; i<first; i++) notme[i] = i;
1027   for (i=last; i<M; i++) notme[i-last+first] = i;
1028   ierr = ISCreateGeneral(MPI_COMM_SELF,N-last+first,notme,PETSC_COPY_VALUES,&Notme);CHKERRQ(ierr);
1029   ierr = ISCreateStride(MPI_COMM_SELF,last-first,first,1,&Me);CHKERRQ(ierr);
1030   ierr = MatCreateSubMatrices(Amat,1,&Me,&Notme,MAT_INITIAL_MATRIX,&Aoffs);CHKERRQ(ierr);
1031   Aoff = Aoffs[0];
1032   ierr = MatCreateSubMatrices(Bmat,1,&Notme,&Me,MAT_INITIAL_MATRIX,&Boffs);CHKERRQ(ierr);
1033   Boff = Boffs[0];
1034   ierr = MatIsTranspose(Aoff,Boff,tol,f);CHKERRQ(ierr);
1035   ierr = MatDestroyMatrices(1,&Aoffs);CHKERRQ(ierr);
1036   ierr = MatDestroyMatrices(1,&Boffs);CHKERRQ(ierr);
1037   ierr = ISDestroy(&Me);CHKERRQ(ierr);
1038   ierr = ISDestroy(&Notme);CHKERRQ(ierr);
1039   ierr = PetscFree(notme);CHKERRQ(ierr);
1040   PetscFunctionReturn(0);
1041 }
1042 
1043 PetscErrorCode MatMultTransposeAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1044 {
1045   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1046   PetscErrorCode ierr;
1047 
1048   PetscFunctionBegin;
1049   /* do nondiagonal part */
1050   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
1051   /* send it on its way */
1052   ierr = VecScatterBegin(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1053   /* do local part */
1054   ierr = (*a->A->ops->multtransposeadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
1055   /* receive remote parts */
1056   ierr = VecScatterEnd(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1057   PetscFunctionReturn(0);
1058 }
1059 
1060 /*
1061   This only works correctly for square matrices where the subblock A->A is the
1062    diagonal block
1063 */
1064 PetscErrorCode MatGetDiagonal_MPIAIJ(Mat A,Vec v)
1065 {
1066   PetscErrorCode ierr;
1067   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1068 
1069   PetscFunctionBegin;
1070   if (A->rmap->N != A->cmap->N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Supports only square matrix where A->A is diag block");
1071   if (A->rmap->rstart != A->cmap->rstart || A->rmap->rend != A->cmap->rend) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"row partition must equal col partition");
1072   ierr = MatGetDiagonal(a->A,v);CHKERRQ(ierr);
1073   PetscFunctionReturn(0);
1074 }
1075 
1076 PetscErrorCode MatScale_MPIAIJ(Mat A,PetscScalar aa)
1077 {
1078   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1079   PetscErrorCode ierr;
1080 
1081   PetscFunctionBegin;
1082   ierr = MatScale(a->A,aa);CHKERRQ(ierr);
1083   ierr = MatScale(a->B,aa);CHKERRQ(ierr);
1084   PetscFunctionReturn(0);
1085 }
1086 
1087 PetscErrorCode MatDestroy_MPIAIJ(Mat mat)
1088 {
1089   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1090   PetscErrorCode ierr;
1091 
1092   PetscFunctionBegin;
1093 #if defined(PETSC_USE_LOG)
1094   PetscLogObjectState((PetscObject)mat,"Rows=%D, Cols=%D",mat->rmap->N,mat->cmap->N);
1095 #endif
1096   ierr = MatStashDestroy_Private(&mat->stash);CHKERRQ(ierr);
1097   ierr = VecDestroy(&aij->diag);CHKERRQ(ierr);
1098   ierr = MatDestroy(&aij->A);CHKERRQ(ierr);
1099   ierr = MatDestroy(&aij->B);CHKERRQ(ierr);
1100 #if defined(PETSC_USE_CTABLE)
1101   ierr = PetscTableDestroy(&aij->colmap);CHKERRQ(ierr);
1102 #else
1103   ierr = PetscFree(aij->colmap);CHKERRQ(ierr);
1104 #endif
1105   ierr = PetscFree(aij->garray);CHKERRQ(ierr);
1106   ierr = VecDestroy(&aij->lvec);CHKERRQ(ierr);
1107   ierr = VecScatterDestroy(&aij->Mvctx);CHKERRQ(ierr);
1108   ierr = PetscFree2(aij->rowvalues,aij->rowindices);CHKERRQ(ierr);
1109   ierr = PetscFree(aij->ld);CHKERRQ(ierr);
1110   ierr = PetscFree(mat->data);CHKERRQ(ierr);
1111 
1112   ierr = PetscObjectChangeTypeName((PetscObject)mat,0);CHKERRQ(ierr);
1113   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatStoreValues_C",NULL);CHKERRQ(ierr);
1114   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatRetrieveValues_C",NULL);CHKERRQ(ierr);
1115   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatIsTranspose_C",NULL);CHKERRQ(ierr);
1116   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocation_C",NULL);CHKERRQ(ierr);
1117   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocationCSR_C",NULL);CHKERRQ(ierr);
1118   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDiagonalScaleLocal_C",NULL);CHKERRQ(ierr);
1119   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_mpisbaij_C",NULL);CHKERRQ(ierr);
1120 #if defined(PETSC_HAVE_ELEMENTAL)
1121   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_elemental_C",NULL);CHKERRQ(ierr);
1122 #endif
1123 #if defined(PETSC_HAVE_HYPRE)
1124   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_hypre_C",NULL);CHKERRQ(ierr);
1125   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMatMatMult_transpose_mpiaij_mpiaij_C",NULL);CHKERRQ(ierr);
1126 #endif
1127   PetscFunctionReturn(0);
1128 }
1129 
1130 PetscErrorCode MatView_MPIAIJ_Binary(Mat mat,PetscViewer viewer)
1131 {
1132   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1133   Mat_SeqAIJ     *A   = (Mat_SeqAIJ*)aij->A->data;
1134   Mat_SeqAIJ     *B   = (Mat_SeqAIJ*)aij->B->data;
1135   PetscErrorCode ierr;
1136   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
1137   int            fd;
1138   PetscInt       nz,header[4],*row_lengths,*range=0,rlen,i;
1139   PetscInt       nzmax,*column_indices,j,k,col,*garray = aij->garray,cnt,cstart = mat->cmap->rstart,rnz = 0;
1140   PetscScalar    *column_values;
1141   PetscInt       message_count,flowcontrolcount;
1142   FILE           *file;
1143 
1144   PetscFunctionBegin;
1145   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
1146   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);CHKERRQ(ierr);
1147   nz   = A->nz + B->nz;
1148   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
1149   if (!rank) {
1150     header[0] = MAT_FILE_CLASSID;
1151     header[1] = mat->rmap->N;
1152     header[2] = mat->cmap->N;
1153 
1154     ierr = MPI_Reduce(&nz,&header[3],1,MPIU_INT,MPI_SUM,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1155     ierr = PetscBinaryWrite(fd,header,4,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1156     /* get largest number of rows any processor has */
1157     rlen  = mat->rmap->n;
1158     range = mat->rmap->range;
1159     for (i=1; i<size; i++) rlen = PetscMax(rlen,range[i+1] - range[i]);
1160   } else {
1161     ierr = MPI_Reduce(&nz,0,1,MPIU_INT,MPI_SUM,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1162     rlen = mat->rmap->n;
1163   }
1164 
1165   /* load up the local row counts */
1166   ierr = PetscMalloc1(rlen+1,&row_lengths);CHKERRQ(ierr);
1167   for (i=0; i<mat->rmap->n; i++) row_lengths[i] = A->i[i+1] - A->i[i] + B->i[i+1] - B->i[i];
1168 
1169   /* store the row lengths to the file */
1170   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1171   if (!rank) {
1172     ierr = PetscBinaryWrite(fd,row_lengths,mat->rmap->n,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1173     for (i=1; i<size; i++) {
1174       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1175       rlen = range[i+1] - range[i];
1176       ierr = MPIULong_Recv(row_lengths,rlen,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1177       ierr = PetscBinaryWrite(fd,row_lengths,rlen,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1178     }
1179     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1180   } else {
1181     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1182     ierr = MPIULong_Send(row_lengths,mat->rmap->n,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1183     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1184   }
1185   ierr = PetscFree(row_lengths);CHKERRQ(ierr);
1186 
1187   /* load up the local column indices */
1188   nzmax = nz; /* th processor needs space a largest processor needs */
1189   ierr  = MPI_Reduce(&nz,&nzmax,1,MPIU_INT,MPI_MAX,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1190   ierr  = PetscMalloc1(nzmax+1,&column_indices);CHKERRQ(ierr);
1191   cnt   = 0;
1192   for (i=0; i<mat->rmap->n; i++) {
1193     for (j=B->i[i]; j<B->i[i+1]; j++) {
1194       if ((col = garray[B->j[j]]) > cstart) break;
1195       column_indices[cnt++] = col;
1196     }
1197     for (k=A->i[i]; k<A->i[i+1]; k++) column_indices[cnt++] = A->j[k] + cstart;
1198     for (; j<B->i[i+1]; j++) column_indices[cnt++] = garray[B->j[j]];
1199   }
1200   if (cnt != A->nz + B->nz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: cnt = %D nz = %D",cnt,A->nz+B->nz);
1201 
1202   /* store the column indices to the file */
1203   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1204   if (!rank) {
1205     MPI_Status status;
1206     ierr = PetscBinaryWrite(fd,column_indices,nz,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1207     for (i=1; i<size; i++) {
1208       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1209       ierr = MPI_Recv(&rnz,1,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat),&status);CHKERRQ(ierr);
1210       if (rnz > nzmax) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: nz = %D nzmax = %D",nz,nzmax);
1211       ierr = MPIULong_Recv(column_indices,rnz,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1212       ierr = PetscBinaryWrite(fd,column_indices,rnz,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1213     }
1214     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1215   } else {
1216     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1217     ierr = MPI_Send(&nz,1,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1218     ierr = MPIULong_Send(column_indices,nz,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1219     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1220   }
1221   ierr = PetscFree(column_indices);CHKERRQ(ierr);
1222 
1223   /* load up the local column values */
1224   ierr = PetscMalloc1(nzmax+1,&column_values);CHKERRQ(ierr);
1225   cnt  = 0;
1226   for (i=0; i<mat->rmap->n; i++) {
1227     for (j=B->i[i]; j<B->i[i+1]; j++) {
1228       if (garray[B->j[j]] > cstart) break;
1229       column_values[cnt++] = B->a[j];
1230     }
1231     for (k=A->i[i]; k<A->i[i+1]; k++) column_values[cnt++] = A->a[k];
1232     for (; j<B->i[i+1]; j++) column_values[cnt++] = B->a[j];
1233   }
1234   if (cnt != A->nz + B->nz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Internal PETSc error: cnt = %D nz = %D",cnt,A->nz+B->nz);
1235 
1236   /* store the column values to the file */
1237   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1238   if (!rank) {
1239     MPI_Status status;
1240     ierr = PetscBinaryWrite(fd,column_values,nz,PETSC_SCALAR,PETSC_TRUE);CHKERRQ(ierr);
1241     for (i=1; i<size; i++) {
1242       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1243       ierr = MPI_Recv(&rnz,1,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat),&status);CHKERRQ(ierr);
1244       if (rnz > nzmax) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: nz = %D nzmax = %D",nz,nzmax);
1245       ierr = MPIULong_Recv(column_values,rnz,MPIU_SCALAR,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1246       ierr = PetscBinaryWrite(fd,column_values,rnz,PETSC_SCALAR,PETSC_TRUE);CHKERRQ(ierr);
1247     }
1248     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1249   } else {
1250     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1251     ierr = MPI_Send(&nz,1,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1252     ierr = MPIULong_Send(column_values,nz,MPIU_SCALAR,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1253     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1254   }
1255   ierr = PetscFree(column_values);CHKERRQ(ierr);
1256 
1257   ierr = PetscViewerBinaryGetInfoPointer(viewer,&file);CHKERRQ(ierr);
1258   if (file) fprintf(file,"-matload_block_size %d\n",(int)PetscAbs(mat->rmap->bs));
1259   PetscFunctionReturn(0);
1260 }
1261 
1262 #include <petscdraw.h>
1263 PetscErrorCode MatView_MPIAIJ_ASCIIorDraworSocket(Mat mat,PetscViewer viewer)
1264 {
1265   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)mat->data;
1266   PetscErrorCode    ierr;
1267   PetscMPIInt       rank = aij->rank,size = aij->size;
1268   PetscBool         isdraw,iascii,isbinary;
1269   PetscViewer       sviewer;
1270   PetscViewerFormat format;
1271 
1272   PetscFunctionBegin;
1273   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1274   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1275   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1276   if (iascii) {
1277     ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
1278     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
1279       MatInfo   info;
1280       PetscBool inodes;
1281 
1282       ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
1283       ierr = MatGetInfo(mat,MAT_LOCAL,&info);CHKERRQ(ierr);
1284       ierr = MatInodeGetInodeSizes(aij->A,NULL,(PetscInt**)&inodes,NULL);CHKERRQ(ierr);
1285       ierr = PetscViewerASCIIPushSynchronized(viewer);CHKERRQ(ierr);
1286       if (!inodes) {
1287         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %D nz %D nz alloced %D mem %D, not using I-node routines\n",
1288                                                   rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
1289       } else {
1290         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %D nz %D nz alloced %D mem %D, using I-node routines\n",
1291                                                   rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
1292       }
1293       ierr = MatGetInfo(aij->A,MAT_LOCAL,&info);CHKERRQ(ierr);
1294       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] on-diagonal part: nz %D \n",rank,(PetscInt)info.nz_used);CHKERRQ(ierr);
1295       ierr = MatGetInfo(aij->B,MAT_LOCAL,&info);CHKERRQ(ierr);
1296       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] off-diagonal part: nz %D \n",rank,(PetscInt)info.nz_used);CHKERRQ(ierr);
1297       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1298       ierr = PetscViewerASCIIPopSynchronized(viewer);CHKERRQ(ierr);
1299       ierr = PetscViewerASCIIPrintf(viewer,"Information on VecScatter used in matrix-vector product: \n");CHKERRQ(ierr);
1300       ierr = VecScatterView(aij->Mvctx,viewer);CHKERRQ(ierr);
1301       PetscFunctionReturn(0);
1302     } else if (format == PETSC_VIEWER_ASCII_INFO) {
1303       PetscInt inodecount,inodelimit,*inodes;
1304       ierr = MatInodeGetInodeSizes(aij->A,&inodecount,&inodes,&inodelimit);CHKERRQ(ierr);
1305       if (inodes) {
1306         ierr = PetscViewerASCIIPrintf(viewer,"using I-node (on process 0) routines: found %D nodes, limit used is %D\n",inodecount,inodelimit);CHKERRQ(ierr);
1307       } else {
1308         ierr = PetscViewerASCIIPrintf(viewer,"not using I-node (on process 0) routines\n");CHKERRQ(ierr);
1309       }
1310       PetscFunctionReturn(0);
1311     } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO) {
1312       PetscFunctionReturn(0);
1313     }
1314   } else if (isbinary) {
1315     if (size == 1) {
1316       ierr = PetscObjectSetName((PetscObject)aij->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1317       ierr = MatView(aij->A,viewer);CHKERRQ(ierr);
1318     } else {
1319       ierr = MatView_MPIAIJ_Binary(mat,viewer);CHKERRQ(ierr);
1320     }
1321     PetscFunctionReturn(0);
1322   } else if (isdraw) {
1323     PetscDraw draw;
1324     PetscBool isnull;
1325     ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
1326     ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr);
1327     if (isnull) PetscFunctionReturn(0);
1328   }
1329 
1330   {
1331     /* assemble the entire matrix onto first processor. */
1332     Mat        A;
1333     Mat_SeqAIJ *Aloc;
1334     PetscInt   M = mat->rmap->N,N = mat->cmap->N,m,*ai,*aj,row,*cols,i,*ct;
1335     MatScalar  *a;
1336 
1337     ierr = MatCreate(PetscObjectComm((PetscObject)mat),&A);CHKERRQ(ierr);
1338     if (!rank) {
1339       ierr = MatSetSizes(A,M,N,M,N);CHKERRQ(ierr);
1340     } else {
1341       ierr = MatSetSizes(A,0,0,M,N);CHKERRQ(ierr);
1342     }
1343     /* This is just a temporary matrix, so explicitly using MATMPIAIJ is probably best */
1344     ierr = MatSetType(A,MATMPIAIJ);CHKERRQ(ierr);
1345     ierr = MatMPIAIJSetPreallocation(A,0,NULL,0,NULL);CHKERRQ(ierr);
1346     ierr = MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
1347     ierr = PetscLogObjectParent((PetscObject)mat,(PetscObject)A);CHKERRQ(ierr);
1348 
1349     /* copy over the A part */
1350     Aloc = (Mat_SeqAIJ*)aij->A->data;
1351     m    = aij->A->rmap->n; ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
1352     row  = mat->rmap->rstart;
1353     for (i=0; i<ai[m]; i++) aj[i] += mat->cmap->rstart;
1354     for (i=0; i<m; i++) {
1355       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],aj,a,INSERT_VALUES);CHKERRQ(ierr);
1356       row++;
1357       a += ai[i+1]-ai[i]; aj += ai[i+1]-ai[i];
1358     }
1359     aj = Aloc->j;
1360     for (i=0; i<ai[m]; i++) aj[i] -= mat->cmap->rstart;
1361 
1362     /* copy over the B part */
1363     Aloc = (Mat_SeqAIJ*)aij->B->data;
1364     m    = aij->B->rmap->n;  ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
1365     row  = mat->rmap->rstart;
1366     ierr = PetscMalloc1(ai[m]+1,&cols);CHKERRQ(ierr);
1367     ct   = cols;
1368     for (i=0; i<ai[m]; i++) cols[i] = aij->garray[aj[i]];
1369     for (i=0; i<m; i++) {
1370       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],cols,a,INSERT_VALUES);CHKERRQ(ierr);
1371       row++;
1372       a += ai[i+1]-ai[i]; cols += ai[i+1]-ai[i];
1373     }
1374     ierr = PetscFree(ct);CHKERRQ(ierr);
1375     ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1376     ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1377     /*
1378        Everyone has to call to draw the matrix since the graphics waits are
1379        synchronized across all processors that share the PetscDraw object
1380     */
1381     ierr = PetscViewerGetSubViewer(viewer,PETSC_COMM_SELF,&sviewer);CHKERRQ(ierr);
1382     if (!rank) {
1383       ierr = PetscObjectSetName((PetscObject)((Mat_MPIAIJ*)(A->data))->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1384       ierr = MatView_SeqAIJ(((Mat_MPIAIJ*)(A->data))->A,sviewer);CHKERRQ(ierr);
1385     }
1386     ierr = PetscViewerRestoreSubViewer(viewer,PETSC_COMM_SELF,&sviewer);CHKERRQ(ierr);
1387     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1388     ierr = MatDestroy(&A);CHKERRQ(ierr);
1389   }
1390   PetscFunctionReturn(0);
1391 }
1392 
1393 PetscErrorCode MatView_MPIAIJ(Mat mat,PetscViewer viewer)
1394 {
1395   PetscErrorCode ierr;
1396   PetscBool      iascii,isdraw,issocket,isbinary;
1397 
1398   PetscFunctionBegin;
1399   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1400   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1401   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1402   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSOCKET,&issocket);CHKERRQ(ierr);
1403   if (iascii || isdraw || isbinary || issocket) {
1404     ierr = MatView_MPIAIJ_ASCIIorDraworSocket(mat,viewer);CHKERRQ(ierr);
1405   }
1406   PetscFunctionReturn(0);
1407 }
1408 
1409 PetscErrorCode MatSOR_MPIAIJ(Mat matin,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
1410 {
1411   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1412   PetscErrorCode ierr;
1413   Vec            bb1 = 0;
1414   PetscBool      hasop;
1415 
1416   PetscFunctionBegin;
1417   if (flag == SOR_APPLY_UPPER) {
1418     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1419     PetscFunctionReturn(0);
1420   }
1421 
1422   if (its > 1 || ~flag & SOR_ZERO_INITIAL_GUESS || flag & SOR_EISENSTAT) {
1423     ierr = VecDuplicate(bb,&bb1);CHKERRQ(ierr);
1424   }
1425 
1426   if ((flag & SOR_LOCAL_SYMMETRIC_SWEEP) == SOR_LOCAL_SYMMETRIC_SWEEP) {
1427     if (flag & SOR_ZERO_INITIAL_GUESS) {
1428       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1429       its--;
1430     }
1431 
1432     while (its--) {
1433       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1434       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1435 
1436       /* update rhs: bb1 = bb - B*x */
1437       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1438       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1439 
1440       /* local sweep */
1441       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_SYMMETRIC_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1442     }
1443   } else if (flag & SOR_LOCAL_FORWARD_SWEEP) {
1444     if (flag & SOR_ZERO_INITIAL_GUESS) {
1445       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1446       its--;
1447     }
1448     while (its--) {
1449       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1450       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1451 
1452       /* update rhs: bb1 = bb - B*x */
1453       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1454       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1455 
1456       /* local sweep */
1457       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_FORWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1458     }
1459   } else if (flag & SOR_LOCAL_BACKWARD_SWEEP) {
1460     if (flag & SOR_ZERO_INITIAL_GUESS) {
1461       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1462       its--;
1463     }
1464     while (its--) {
1465       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1466       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1467 
1468       /* update rhs: bb1 = bb - B*x */
1469       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1470       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1471 
1472       /* local sweep */
1473       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_BACKWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1474     }
1475   } else if (flag & SOR_EISENSTAT) {
1476     Vec xx1;
1477 
1478     ierr = VecDuplicate(bb,&xx1);CHKERRQ(ierr);
1479     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_BACKWARD_SWEEP),fshift,lits,1,xx);CHKERRQ(ierr);
1480 
1481     ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1482     ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1483     if (!mat->diag) {
1484       ierr = MatCreateVecs(matin,&mat->diag,NULL);CHKERRQ(ierr);
1485       ierr = MatGetDiagonal(matin,mat->diag);CHKERRQ(ierr);
1486     }
1487     ierr = MatHasOperation(matin,MATOP_MULT_DIAGONAL_BLOCK,&hasop);CHKERRQ(ierr);
1488     if (hasop) {
1489       ierr = MatMultDiagonalBlock(matin,xx,bb1);CHKERRQ(ierr);
1490     } else {
1491       ierr = VecPointwiseMult(bb1,mat->diag,xx);CHKERRQ(ierr);
1492     }
1493     ierr = VecAYPX(bb1,(omega-2.0)/omega,bb);CHKERRQ(ierr);
1494 
1495     ierr = MatMultAdd(mat->B,mat->lvec,bb1,bb1);CHKERRQ(ierr);
1496 
1497     /* local sweep */
1498     ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_FORWARD_SWEEP),fshift,lits,1,xx1);CHKERRQ(ierr);
1499     ierr = VecAXPY(xx,1.0,xx1);CHKERRQ(ierr);
1500     ierr = VecDestroy(&xx1);CHKERRQ(ierr);
1501   } else SETERRQ(PetscObjectComm((PetscObject)matin),PETSC_ERR_SUP,"Parallel SOR not supported");
1502 
1503   ierr = VecDestroy(&bb1);CHKERRQ(ierr);
1504 
1505   matin->factorerrortype = mat->A->factorerrortype;
1506   PetscFunctionReturn(0);
1507 }
1508 
1509 PetscErrorCode MatPermute_MPIAIJ(Mat A,IS rowp,IS colp,Mat *B)
1510 {
1511   Mat            aA,aB,Aperm;
1512   const PetscInt *rwant,*cwant,*gcols,*ai,*bi,*aj,*bj;
1513   PetscScalar    *aa,*ba;
1514   PetscInt       i,j,m,n,ng,anz,bnz,*dnnz,*onnz,*tdnnz,*tonnz,*rdest,*cdest,*work,*gcdest;
1515   PetscSF        rowsf,sf;
1516   IS             parcolp = NULL;
1517   PetscBool      done;
1518   PetscErrorCode ierr;
1519 
1520   PetscFunctionBegin;
1521   ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
1522   ierr = ISGetIndices(rowp,&rwant);CHKERRQ(ierr);
1523   ierr = ISGetIndices(colp,&cwant);CHKERRQ(ierr);
1524   ierr = PetscMalloc3(PetscMax(m,n),&work,m,&rdest,n,&cdest);CHKERRQ(ierr);
1525 
1526   /* Invert row permutation to find out where my rows should go */
1527   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&rowsf);CHKERRQ(ierr);
1528   ierr = PetscSFSetGraphLayout(rowsf,A->rmap,A->rmap->n,NULL,PETSC_OWN_POINTER,rwant);CHKERRQ(ierr);
1529   ierr = PetscSFSetFromOptions(rowsf);CHKERRQ(ierr);
1530   for (i=0; i<m; i++) work[i] = A->rmap->rstart + i;
1531   ierr = PetscSFReduceBegin(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1532   ierr = PetscSFReduceEnd(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1533 
1534   /* Invert column permutation to find out where my columns should go */
1535   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1536   ierr = PetscSFSetGraphLayout(sf,A->cmap,A->cmap->n,NULL,PETSC_OWN_POINTER,cwant);CHKERRQ(ierr);
1537   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1538   for (i=0; i<n; i++) work[i] = A->cmap->rstart + i;
1539   ierr = PetscSFReduceBegin(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1540   ierr = PetscSFReduceEnd(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1541   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1542 
1543   ierr = ISRestoreIndices(rowp,&rwant);CHKERRQ(ierr);
1544   ierr = ISRestoreIndices(colp,&cwant);CHKERRQ(ierr);
1545   ierr = MatMPIAIJGetSeqAIJ(A,&aA,&aB,&gcols);CHKERRQ(ierr);
1546 
1547   /* Find out where my gcols should go */
1548   ierr = MatGetSize(aB,NULL,&ng);CHKERRQ(ierr);
1549   ierr = PetscMalloc1(ng,&gcdest);CHKERRQ(ierr);
1550   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1551   ierr = PetscSFSetGraphLayout(sf,A->cmap,ng,NULL,PETSC_OWN_POINTER,gcols);CHKERRQ(ierr);
1552   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1553   ierr = PetscSFBcastBegin(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1554   ierr = PetscSFBcastEnd(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1555   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1556 
1557   ierr = PetscCalloc4(m,&dnnz,m,&onnz,m,&tdnnz,m,&tonnz);CHKERRQ(ierr);
1558   ierr = MatGetRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1559   ierr = MatGetRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1560   for (i=0; i<m; i++) {
1561     PetscInt row = rdest[i],rowner;
1562     ierr = PetscLayoutFindOwner(A->rmap,row,&rowner);CHKERRQ(ierr);
1563     for (j=ai[i]; j<ai[i+1]; j++) {
1564       PetscInt cowner,col = cdest[aj[j]];
1565       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr); /* Could build an index for the columns to eliminate this search */
1566       if (rowner == cowner) dnnz[i]++;
1567       else onnz[i]++;
1568     }
1569     for (j=bi[i]; j<bi[i+1]; j++) {
1570       PetscInt cowner,col = gcdest[bj[j]];
1571       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr);
1572       if (rowner == cowner) dnnz[i]++;
1573       else onnz[i]++;
1574     }
1575   }
1576   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1577   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1578   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1579   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1580   ierr = PetscSFDestroy(&rowsf);CHKERRQ(ierr);
1581 
1582   ierr = MatCreateAIJ(PetscObjectComm((PetscObject)A),A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N,0,tdnnz,0,tonnz,&Aperm);CHKERRQ(ierr);
1583   ierr = MatSeqAIJGetArray(aA,&aa);CHKERRQ(ierr);
1584   ierr = MatSeqAIJGetArray(aB,&ba);CHKERRQ(ierr);
1585   for (i=0; i<m; i++) {
1586     PetscInt *acols = dnnz,*bcols = onnz; /* Repurpose now-unneeded arrays */
1587     PetscInt j0,rowlen;
1588     rowlen = ai[i+1] - ai[i];
1589     for (j0=j=0; j<rowlen; j0=j) { /* rowlen could be larger than number of rows m, so sum in batches */
1590       for ( ; j<PetscMin(rowlen,j0+m); j++) acols[j-j0] = cdest[aj[ai[i]+j]];
1591       ierr = MatSetValues(Aperm,1,&rdest[i],j-j0,acols,aa+ai[i]+j0,INSERT_VALUES);CHKERRQ(ierr);
1592     }
1593     rowlen = bi[i+1] - bi[i];
1594     for (j0=j=0; j<rowlen; j0=j) {
1595       for ( ; j<PetscMin(rowlen,j0+m); j++) bcols[j-j0] = gcdest[bj[bi[i]+j]];
1596       ierr = MatSetValues(Aperm,1,&rdest[i],j-j0,bcols,ba+bi[i]+j0,INSERT_VALUES);CHKERRQ(ierr);
1597     }
1598   }
1599   ierr = MatAssemblyBegin(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1600   ierr = MatAssemblyEnd(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1601   ierr = MatRestoreRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1602   ierr = MatRestoreRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1603   ierr = MatSeqAIJRestoreArray(aA,&aa);CHKERRQ(ierr);
1604   ierr = MatSeqAIJRestoreArray(aB,&ba);CHKERRQ(ierr);
1605   ierr = PetscFree4(dnnz,onnz,tdnnz,tonnz);CHKERRQ(ierr);
1606   ierr = PetscFree3(work,rdest,cdest);CHKERRQ(ierr);
1607   ierr = PetscFree(gcdest);CHKERRQ(ierr);
1608   if (parcolp) {ierr = ISDestroy(&colp);CHKERRQ(ierr);}
1609   *B = Aperm;
1610   PetscFunctionReturn(0);
1611 }
1612 
1613 PetscErrorCode  MatGetGhosts_MPIAIJ(Mat mat,PetscInt *nghosts,const PetscInt *ghosts[])
1614 {
1615   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1616   PetscErrorCode ierr;
1617 
1618   PetscFunctionBegin;
1619   ierr = MatGetSize(aij->B,NULL,nghosts);CHKERRQ(ierr);
1620   if (ghosts) *ghosts = aij->garray;
1621   PetscFunctionReturn(0);
1622 }
1623 
1624 PetscErrorCode MatGetInfo_MPIAIJ(Mat matin,MatInfoType flag,MatInfo *info)
1625 {
1626   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1627   Mat            A    = mat->A,B = mat->B;
1628   PetscErrorCode ierr;
1629   PetscReal      isend[5],irecv[5];
1630 
1631   PetscFunctionBegin;
1632   info->block_size = 1.0;
1633   ierr             = MatGetInfo(A,MAT_LOCAL,info);CHKERRQ(ierr);
1634 
1635   isend[0] = info->nz_used; isend[1] = info->nz_allocated; isend[2] = info->nz_unneeded;
1636   isend[3] = info->memory;  isend[4] = info->mallocs;
1637 
1638   ierr = MatGetInfo(B,MAT_LOCAL,info);CHKERRQ(ierr);
1639 
1640   isend[0] += info->nz_used; isend[1] += info->nz_allocated; isend[2] += info->nz_unneeded;
1641   isend[3] += info->memory;  isend[4] += info->mallocs;
1642   if (flag == MAT_LOCAL) {
1643     info->nz_used      = isend[0];
1644     info->nz_allocated = isend[1];
1645     info->nz_unneeded  = isend[2];
1646     info->memory       = isend[3];
1647     info->mallocs      = isend[4];
1648   } else if (flag == MAT_GLOBAL_MAX) {
1649     ierr = MPIU_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1650 
1651     info->nz_used      = irecv[0];
1652     info->nz_allocated = irecv[1];
1653     info->nz_unneeded  = irecv[2];
1654     info->memory       = irecv[3];
1655     info->mallocs      = irecv[4];
1656   } else if (flag == MAT_GLOBAL_SUM) {
1657     ierr = MPIU_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1658 
1659     info->nz_used      = irecv[0];
1660     info->nz_allocated = irecv[1];
1661     info->nz_unneeded  = irecv[2];
1662     info->memory       = irecv[3];
1663     info->mallocs      = irecv[4];
1664   }
1665   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
1666   info->fill_ratio_needed = 0;
1667   info->factor_mallocs    = 0;
1668   PetscFunctionReturn(0);
1669 }
1670 
1671 PetscErrorCode MatSetOption_MPIAIJ(Mat A,MatOption op,PetscBool flg)
1672 {
1673   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1674   PetscErrorCode ierr;
1675 
1676   PetscFunctionBegin;
1677   switch (op) {
1678   case MAT_NEW_NONZERO_LOCATIONS:
1679   case MAT_NEW_NONZERO_ALLOCATION_ERR:
1680   case MAT_UNUSED_NONZERO_LOCATION_ERR:
1681   case MAT_KEEP_NONZERO_PATTERN:
1682   case MAT_NEW_NONZERO_LOCATION_ERR:
1683   case MAT_USE_INODES:
1684   case MAT_IGNORE_ZERO_ENTRIES:
1685     MatCheckPreallocated(A,1);
1686     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1687     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1688     break;
1689   case MAT_ROW_ORIENTED:
1690     MatCheckPreallocated(A,1);
1691     a->roworiented = flg;
1692 
1693     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1694     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1695     break;
1696   case MAT_NEW_DIAGONALS:
1697     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
1698     break;
1699   case MAT_IGNORE_OFF_PROC_ENTRIES:
1700     a->donotstash = flg;
1701     break;
1702   case MAT_SPD:
1703     A->spd_set = PETSC_TRUE;
1704     A->spd     = flg;
1705     if (flg) {
1706       A->symmetric                  = PETSC_TRUE;
1707       A->structurally_symmetric     = PETSC_TRUE;
1708       A->symmetric_set              = PETSC_TRUE;
1709       A->structurally_symmetric_set = PETSC_TRUE;
1710     }
1711     break;
1712   case MAT_SYMMETRIC:
1713     MatCheckPreallocated(A,1);
1714     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1715     break;
1716   case MAT_STRUCTURALLY_SYMMETRIC:
1717     MatCheckPreallocated(A,1);
1718     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1719     break;
1720   case MAT_HERMITIAN:
1721     MatCheckPreallocated(A,1);
1722     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1723     break;
1724   case MAT_SYMMETRY_ETERNAL:
1725     MatCheckPreallocated(A,1);
1726     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1727     break;
1728   case MAT_SUBMAT_SINGLEIS:
1729     A->submat_singleis = flg;
1730     break;
1731   default:
1732     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %d",op);
1733   }
1734   PetscFunctionReturn(0);
1735 }
1736 
1737 PetscErrorCode MatGetRow_MPIAIJ(Mat matin,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1738 {
1739   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1740   PetscScalar    *vworkA,*vworkB,**pvA,**pvB,*v_p;
1741   PetscErrorCode ierr;
1742   PetscInt       i,*cworkA,*cworkB,**pcA,**pcB,cstart = matin->cmap->rstart;
1743   PetscInt       nztot,nzA,nzB,lrow,rstart = matin->rmap->rstart,rend = matin->rmap->rend;
1744   PetscInt       *cmap,*idx_p;
1745 
1746   PetscFunctionBegin;
1747   if (mat->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Already active");
1748   mat->getrowactive = PETSC_TRUE;
1749 
1750   if (!mat->rowvalues && (idx || v)) {
1751     /*
1752         allocate enough space to hold information from the longest row.
1753     */
1754     Mat_SeqAIJ *Aa = (Mat_SeqAIJ*)mat->A->data,*Ba = (Mat_SeqAIJ*)mat->B->data;
1755     PetscInt   max = 1,tmp;
1756     for (i=0; i<matin->rmap->n; i++) {
1757       tmp = Aa->i[i+1] - Aa->i[i] + Ba->i[i+1] - Ba->i[i];
1758       if (max < tmp) max = tmp;
1759     }
1760     ierr = PetscMalloc2(max,&mat->rowvalues,max,&mat->rowindices);CHKERRQ(ierr);
1761   }
1762 
1763   if (row < rstart || row >= rend) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Only local rows");
1764   lrow = row - rstart;
1765 
1766   pvA = &vworkA; pcA = &cworkA; pvB = &vworkB; pcB = &cworkB;
1767   if (!v)   {pvA = 0; pvB = 0;}
1768   if (!idx) {pcA = 0; if (!v) pcB = 0;}
1769   ierr  = (*mat->A->ops->getrow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1770   ierr  = (*mat->B->ops->getrow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1771   nztot = nzA + nzB;
1772 
1773   cmap = mat->garray;
1774   if (v  || idx) {
1775     if (nztot) {
1776       /* Sort by increasing column numbers, assuming A and B already sorted */
1777       PetscInt imark = -1;
1778       if (v) {
1779         *v = v_p = mat->rowvalues;
1780         for (i=0; i<nzB; i++) {
1781           if (cmap[cworkB[i]] < cstart) v_p[i] = vworkB[i];
1782           else break;
1783         }
1784         imark = i;
1785         for (i=0; i<nzA; i++)     v_p[imark+i] = vworkA[i];
1786         for (i=imark; i<nzB; i++) v_p[nzA+i]   = vworkB[i];
1787       }
1788       if (idx) {
1789         *idx = idx_p = mat->rowindices;
1790         if (imark > -1) {
1791           for (i=0; i<imark; i++) {
1792             idx_p[i] = cmap[cworkB[i]];
1793           }
1794         } else {
1795           for (i=0; i<nzB; i++) {
1796             if (cmap[cworkB[i]] < cstart) idx_p[i] = cmap[cworkB[i]];
1797             else break;
1798           }
1799           imark = i;
1800         }
1801         for (i=0; i<nzA; i++)     idx_p[imark+i] = cstart + cworkA[i];
1802         for (i=imark; i<nzB; i++) idx_p[nzA+i]   = cmap[cworkB[i]];
1803       }
1804     } else {
1805       if (idx) *idx = 0;
1806       if (v)   *v   = 0;
1807     }
1808   }
1809   *nz  = nztot;
1810   ierr = (*mat->A->ops->restorerow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1811   ierr = (*mat->B->ops->restorerow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1812   PetscFunctionReturn(0);
1813 }
1814 
1815 PetscErrorCode MatRestoreRow_MPIAIJ(Mat mat,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1816 {
1817   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1818 
1819   PetscFunctionBegin;
1820   if (!aij->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"MatGetRow() must be called first");
1821   aij->getrowactive = PETSC_FALSE;
1822   PetscFunctionReturn(0);
1823 }
1824 
1825 PetscErrorCode MatNorm_MPIAIJ(Mat mat,NormType type,PetscReal *norm)
1826 {
1827   Mat_MPIAIJ     *aij  = (Mat_MPIAIJ*)mat->data;
1828   Mat_SeqAIJ     *amat = (Mat_SeqAIJ*)aij->A->data,*bmat = (Mat_SeqAIJ*)aij->B->data;
1829   PetscErrorCode ierr;
1830   PetscInt       i,j,cstart = mat->cmap->rstart;
1831   PetscReal      sum = 0.0;
1832   MatScalar      *v;
1833 
1834   PetscFunctionBegin;
1835   if (aij->size == 1) {
1836     ierr =  MatNorm(aij->A,type,norm);CHKERRQ(ierr);
1837   } else {
1838     if (type == NORM_FROBENIUS) {
1839       v = amat->a;
1840       for (i=0; i<amat->nz; i++) {
1841         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1842       }
1843       v = bmat->a;
1844       for (i=0; i<bmat->nz; i++) {
1845         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1846       }
1847       ierr  = MPIU_Allreduce(&sum,norm,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1848       *norm = PetscSqrtReal(*norm);
1849       ierr = PetscLogFlops(2*amat->nz+2*bmat->nz);CHKERRQ(ierr);
1850     } else if (type == NORM_1) { /* max column norm */
1851       PetscReal *tmp,*tmp2;
1852       PetscInt  *jj,*garray = aij->garray;
1853       ierr  = PetscCalloc1(mat->cmap->N+1,&tmp);CHKERRQ(ierr);
1854       ierr  = PetscMalloc1(mat->cmap->N+1,&tmp2);CHKERRQ(ierr);
1855       *norm = 0.0;
1856       v     = amat->a; jj = amat->j;
1857       for (j=0; j<amat->nz; j++) {
1858         tmp[cstart + *jj++] += PetscAbsScalar(*v);  v++;
1859       }
1860       v = bmat->a; jj = bmat->j;
1861       for (j=0; j<bmat->nz; j++) {
1862         tmp[garray[*jj++]] += PetscAbsScalar(*v); v++;
1863       }
1864       ierr = MPIU_Allreduce(tmp,tmp2,mat->cmap->N,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1865       for (j=0; j<mat->cmap->N; j++) {
1866         if (tmp2[j] > *norm) *norm = tmp2[j];
1867       }
1868       ierr = PetscFree(tmp);CHKERRQ(ierr);
1869       ierr = PetscFree(tmp2);CHKERRQ(ierr);
1870       ierr = PetscLogFlops(PetscMax(amat->nz+bmat->nz-1,0));CHKERRQ(ierr);
1871     } else if (type == NORM_INFINITY) { /* max row norm */
1872       PetscReal ntemp = 0.0;
1873       for (j=0; j<aij->A->rmap->n; j++) {
1874         v   = amat->a + amat->i[j];
1875         sum = 0.0;
1876         for (i=0; i<amat->i[j+1]-amat->i[j]; i++) {
1877           sum += PetscAbsScalar(*v); v++;
1878         }
1879         v = bmat->a + bmat->i[j];
1880         for (i=0; i<bmat->i[j+1]-bmat->i[j]; i++) {
1881           sum += PetscAbsScalar(*v); v++;
1882         }
1883         if (sum > ntemp) ntemp = sum;
1884       }
1885       ierr = MPIU_Allreduce(&ntemp,norm,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1886       ierr = PetscLogFlops(PetscMax(amat->nz+bmat->nz-1,0));CHKERRQ(ierr);
1887     } else SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"No support for two norm");
1888   }
1889   PetscFunctionReturn(0);
1890 }
1891 
1892 PetscErrorCode MatTranspose_MPIAIJ(Mat A,MatReuse reuse,Mat *matout)
1893 {
1894   Mat_MPIAIJ     *a   = (Mat_MPIAIJ*)A->data;
1895   Mat_SeqAIJ     *Aloc=(Mat_SeqAIJ*)a->A->data,*Bloc=(Mat_SeqAIJ*)a->B->data;
1896   PetscErrorCode ierr;
1897   PetscInt       M      = A->rmap->N,N = A->cmap->N,ma,na,mb,nb,*ai,*aj,*bi,*bj,row,*cols,*cols_tmp,i;
1898   PetscInt       cstart = A->cmap->rstart,ncol;
1899   Mat            B;
1900   MatScalar      *array;
1901 
1902   PetscFunctionBegin;
1903   if (reuse == MAT_INPLACE_MATRIX && M != N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Square matrix only for in-place");
1904 
1905   ma = A->rmap->n; na = A->cmap->n; mb = a->B->rmap->n; nb = a->B->cmap->n;
1906   ai = Aloc->i; aj = Aloc->j;
1907   bi = Bloc->i; bj = Bloc->j;
1908   if (reuse == MAT_INITIAL_MATRIX || *matout == A) {
1909     PetscInt             *d_nnz,*g_nnz,*o_nnz;
1910     PetscSFNode          *oloc;
1911     PETSC_UNUSED PetscSF sf;
1912 
1913     ierr = PetscMalloc4(na,&d_nnz,na,&o_nnz,nb,&g_nnz,nb,&oloc);CHKERRQ(ierr);
1914     /* compute d_nnz for preallocation */
1915     ierr = PetscMemzero(d_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1916     for (i=0; i<ai[ma]; i++) {
1917       d_nnz[aj[i]]++;
1918       aj[i] += cstart; /* global col index to be used by MatSetValues() */
1919     }
1920     /* compute local off-diagonal contributions */
1921     ierr = PetscMemzero(g_nnz,nb*sizeof(PetscInt));CHKERRQ(ierr);
1922     for (i=0; i<bi[ma]; i++) g_nnz[bj[i]]++;
1923     /* map those to global */
1924     ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1925     ierr = PetscSFSetGraphLayout(sf,A->cmap,nb,NULL,PETSC_USE_POINTER,a->garray);CHKERRQ(ierr);
1926     ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1927     ierr = PetscMemzero(o_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1928     ierr = PetscSFReduceBegin(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
1929     ierr = PetscSFReduceEnd(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
1930     ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1931 
1932     ierr = MatCreate(PetscObjectComm((PetscObject)A),&B);CHKERRQ(ierr);
1933     ierr = MatSetSizes(B,A->cmap->n,A->rmap->n,N,M);CHKERRQ(ierr);
1934     ierr = MatSetBlockSizes(B,PetscAbs(A->cmap->bs),PetscAbs(A->rmap->bs));CHKERRQ(ierr);
1935     ierr = MatSetType(B,((PetscObject)A)->type_name);CHKERRQ(ierr);
1936     ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
1937     ierr = PetscFree4(d_nnz,o_nnz,g_nnz,oloc);CHKERRQ(ierr);
1938   } else {
1939     B    = *matout;
1940     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
1941     for (i=0; i<ai[ma]; i++) aj[i] += cstart; /* global col index to be used by MatSetValues() */
1942   }
1943 
1944   /* copy over the A part */
1945   array = Aloc->a;
1946   row   = A->rmap->rstart;
1947   for (i=0; i<ma; i++) {
1948     ncol = ai[i+1]-ai[i];
1949     ierr = MatSetValues(B,ncol,aj,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
1950     row++;
1951     array += ncol; aj += ncol;
1952   }
1953   aj = Aloc->j;
1954   for (i=0; i<ai[ma]; i++) aj[i] -= cstart; /* resume local col index */
1955 
1956   /* copy over the B part */
1957   ierr  = PetscCalloc1(bi[mb],&cols);CHKERRQ(ierr);
1958   array = Bloc->a;
1959   row   = A->rmap->rstart;
1960   for (i=0; i<bi[mb]; i++) cols[i] = a->garray[bj[i]];
1961   cols_tmp = cols;
1962   for (i=0; i<mb; i++) {
1963     ncol = bi[i+1]-bi[i];
1964     ierr = MatSetValues(B,ncol,cols_tmp,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
1965     row++;
1966     array += ncol; cols_tmp += ncol;
1967   }
1968   ierr = PetscFree(cols);CHKERRQ(ierr);
1969 
1970   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1971   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1972   if (reuse == MAT_INITIAL_MATRIX || reuse == MAT_REUSE_MATRIX) {
1973     *matout = B;
1974   } else {
1975     ierr = MatHeaderMerge(A,&B);CHKERRQ(ierr);
1976   }
1977   PetscFunctionReturn(0);
1978 }
1979 
1980 PetscErrorCode MatDiagonalScale_MPIAIJ(Mat mat,Vec ll,Vec rr)
1981 {
1982   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1983   Mat            a    = aij->A,b = aij->B;
1984   PetscErrorCode ierr;
1985   PetscInt       s1,s2,s3;
1986 
1987   PetscFunctionBegin;
1988   ierr = MatGetLocalSize(mat,&s2,&s3);CHKERRQ(ierr);
1989   if (rr) {
1990     ierr = VecGetLocalSize(rr,&s1);CHKERRQ(ierr);
1991     if (s1!=s3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"right vector non-conforming local size");
1992     /* Overlap communication with computation. */
1993     ierr = VecScatterBegin(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1994   }
1995   if (ll) {
1996     ierr = VecGetLocalSize(ll,&s1);CHKERRQ(ierr);
1997     if (s1!=s2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"left vector non-conforming local size");
1998     ierr = (*b->ops->diagonalscale)(b,ll,0);CHKERRQ(ierr);
1999   }
2000   /* scale  the diagonal block */
2001   ierr = (*a->ops->diagonalscale)(a,ll,rr);CHKERRQ(ierr);
2002 
2003   if (rr) {
2004     /* Do a scatter end and then right scale the off-diagonal block */
2005     ierr = VecScatterEnd(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2006     ierr = (*b->ops->diagonalscale)(b,0,aij->lvec);CHKERRQ(ierr);
2007   }
2008   PetscFunctionReturn(0);
2009 }
2010 
2011 PetscErrorCode MatSetUnfactored_MPIAIJ(Mat A)
2012 {
2013   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2014   PetscErrorCode ierr;
2015 
2016   PetscFunctionBegin;
2017   ierr = MatSetUnfactored(a->A);CHKERRQ(ierr);
2018   PetscFunctionReturn(0);
2019 }
2020 
2021 PetscErrorCode MatEqual_MPIAIJ(Mat A,Mat B,PetscBool  *flag)
2022 {
2023   Mat_MPIAIJ     *matB = (Mat_MPIAIJ*)B->data,*matA = (Mat_MPIAIJ*)A->data;
2024   Mat            a,b,c,d;
2025   PetscBool      flg;
2026   PetscErrorCode ierr;
2027 
2028   PetscFunctionBegin;
2029   a = matA->A; b = matA->B;
2030   c = matB->A; d = matB->B;
2031 
2032   ierr = MatEqual(a,c,&flg);CHKERRQ(ierr);
2033   if (flg) {
2034     ierr = MatEqual(b,d,&flg);CHKERRQ(ierr);
2035   }
2036   ierr = MPIU_Allreduce(&flg,flag,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
2037   PetscFunctionReturn(0);
2038 }
2039 
2040 PetscErrorCode MatCopy_MPIAIJ(Mat A,Mat B,MatStructure str)
2041 {
2042   PetscErrorCode ierr;
2043   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2044   Mat_MPIAIJ     *b = (Mat_MPIAIJ*)B->data;
2045 
2046   PetscFunctionBegin;
2047   /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
2048   if ((str != SAME_NONZERO_PATTERN) || (A->ops->copy != B->ops->copy)) {
2049     /* because of the column compression in the off-processor part of the matrix a->B,
2050        the number of columns in a->B and b->B may be different, hence we cannot call
2051        the MatCopy() directly on the two parts. If need be, we can provide a more
2052        efficient copy than the MatCopy_Basic() by first uncompressing the a->B matrices
2053        then copying the submatrices */
2054     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
2055   } else {
2056     ierr = MatCopy(a->A,b->A,str);CHKERRQ(ierr);
2057     ierr = MatCopy(a->B,b->B,str);CHKERRQ(ierr);
2058   }
2059   PetscFunctionReturn(0);
2060 }
2061 
2062 PetscErrorCode MatSetUp_MPIAIJ(Mat A)
2063 {
2064   PetscErrorCode ierr;
2065 
2066   PetscFunctionBegin;
2067   ierr =  MatMPIAIJSetPreallocation(A,PETSC_DEFAULT,0,PETSC_DEFAULT,0);CHKERRQ(ierr);
2068   PetscFunctionReturn(0);
2069 }
2070 
2071 /*
2072    Computes the number of nonzeros per row needed for preallocation when X and Y
2073    have different nonzero structure.
2074 */
2075 PetscErrorCode MatAXPYGetPreallocation_MPIX_private(PetscInt m,const PetscInt *xi,const PetscInt *xj,const PetscInt *xltog,const PetscInt *yi,const PetscInt *yj,const PetscInt *yltog,PetscInt *nnz)
2076 {
2077   PetscInt       i,j,k,nzx,nzy;
2078 
2079   PetscFunctionBegin;
2080   /* Set the number of nonzeros in the new matrix */
2081   for (i=0; i<m; i++) {
2082     const PetscInt *xjj = xj+xi[i],*yjj = yj+yi[i];
2083     nzx = xi[i+1] - xi[i];
2084     nzy = yi[i+1] - yi[i];
2085     nnz[i] = 0;
2086     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2087       for (; k<nzy && yltog[yjj[k]]<xltog[xjj[j]]; k++) nnz[i]++; /* Catch up to X */
2088       if (k<nzy && yltog[yjj[k]]==xltog[xjj[j]]) k++;             /* Skip duplicate */
2089       nnz[i]++;
2090     }
2091     for (; k<nzy; k++) nnz[i]++;
2092   }
2093   PetscFunctionReturn(0);
2094 }
2095 
2096 /* This is the same as MatAXPYGetPreallocation_SeqAIJ, except that the local-to-global map is provided */
2097 static PetscErrorCode MatAXPYGetPreallocation_MPIAIJ(Mat Y,const PetscInt *yltog,Mat X,const PetscInt *xltog,PetscInt *nnz)
2098 {
2099   PetscErrorCode ierr;
2100   PetscInt       m = Y->rmap->N;
2101   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data;
2102   Mat_SeqAIJ     *y = (Mat_SeqAIJ*)Y->data;
2103 
2104   PetscFunctionBegin;
2105   ierr = MatAXPYGetPreallocation_MPIX_private(m,x->i,x->j,xltog,y->i,y->j,yltog,nnz);CHKERRQ(ierr);
2106   PetscFunctionReturn(0);
2107 }
2108 
2109 PetscErrorCode MatAXPY_MPIAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
2110 {
2111   PetscErrorCode ierr;
2112   Mat_MPIAIJ     *xx = (Mat_MPIAIJ*)X->data,*yy = (Mat_MPIAIJ*)Y->data;
2113   PetscBLASInt   bnz,one=1;
2114   Mat_SeqAIJ     *x,*y;
2115 
2116   PetscFunctionBegin;
2117   if (str == SAME_NONZERO_PATTERN) {
2118     PetscScalar alpha = a;
2119     x    = (Mat_SeqAIJ*)xx->A->data;
2120     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2121     y    = (Mat_SeqAIJ*)yy->A->data;
2122     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2123     x    = (Mat_SeqAIJ*)xx->B->data;
2124     y    = (Mat_SeqAIJ*)yy->B->data;
2125     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2126     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2127     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
2128   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
2129     ierr = MatAXPY_Basic(Y,a,X,str);CHKERRQ(ierr);
2130   } else {
2131     Mat      B;
2132     PetscInt *nnz_d,*nnz_o;
2133     ierr = PetscMalloc1(yy->A->rmap->N,&nnz_d);CHKERRQ(ierr);
2134     ierr = PetscMalloc1(yy->B->rmap->N,&nnz_o);CHKERRQ(ierr);
2135     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
2136     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
2137     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
2138     ierr = MatSetBlockSizesFromMats(B,Y,Y);CHKERRQ(ierr);
2139     ierr = MatSetType(B,MATMPIAIJ);CHKERRQ(ierr);
2140     ierr = MatAXPYGetPreallocation_SeqAIJ(yy->A,xx->A,nnz_d);CHKERRQ(ierr);
2141     ierr = MatAXPYGetPreallocation_MPIAIJ(yy->B,yy->garray,xx->B,xx->garray,nnz_o);CHKERRQ(ierr);
2142     ierr = MatMPIAIJSetPreallocation(B,0,nnz_d,0,nnz_o);CHKERRQ(ierr);
2143     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
2144     ierr = MatHeaderReplace(Y,&B);CHKERRQ(ierr);
2145     ierr = PetscFree(nnz_d);CHKERRQ(ierr);
2146     ierr = PetscFree(nnz_o);CHKERRQ(ierr);
2147   }
2148   PetscFunctionReturn(0);
2149 }
2150 
2151 extern PetscErrorCode  MatConjugate_SeqAIJ(Mat);
2152 
2153 PetscErrorCode  MatConjugate_MPIAIJ(Mat mat)
2154 {
2155 #if defined(PETSC_USE_COMPLEX)
2156   PetscErrorCode ierr;
2157   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2158 
2159   PetscFunctionBegin;
2160   ierr = MatConjugate_SeqAIJ(aij->A);CHKERRQ(ierr);
2161   ierr = MatConjugate_SeqAIJ(aij->B);CHKERRQ(ierr);
2162 #else
2163   PetscFunctionBegin;
2164 #endif
2165   PetscFunctionReturn(0);
2166 }
2167 
2168 PetscErrorCode MatRealPart_MPIAIJ(Mat A)
2169 {
2170   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2171   PetscErrorCode ierr;
2172 
2173   PetscFunctionBegin;
2174   ierr = MatRealPart(a->A);CHKERRQ(ierr);
2175   ierr = MatRealPart(a->B);CHKERRQ(ierr);
2176   PetscFunctionReturn(0);
2177 }
2178 
2179 PetscErrorCode MatImaginaryPart_MPIAIJ(Mat A)
2180 {
2181   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2182   PetscErrorCode ierr;
2183 
2184   PetscFunctionBegin;
2185   ierr = MatImaginaryPart(a->A);CHKERRQ(ierr);
2186   ierr = MatImaginaryPart(a->B);CHKERRQ(ierr);
2187   PetscFunctionReturn(0);
2188 }
2189 
2190 PetscErrorCode MatGetRowMaxAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2191 {
2192   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2193   PetscErrorCode ierr;
2194   PetscInt       i,*idxb = 0;
2195   PetscScalar    *va,*vb;
2196   Vec            vtmp;
2197 
2198   PetscFunctionBegin;
2199   ierr = MatGetRowMaxAbs(a->A,v,idx);CHKERRQ(ierr);
2200   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2201   if (idx) {
2202     for (i=0; i<A->rmap->n; i++) {
2203       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2204     }
2205   }
2206 
2207   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2208   if (idx) {
2209     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2210   }
2211   ierr = MatGetRowMaxAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2212   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2213 
2214   for (i=0; i<A->rmap->n; i++) {
2215     if (PetscAbsScalar(va[i]) < PetscAbsScalar(vb[i])) {
2216       va[i] = vb[i];
2217       if (idx) idx[i] = a->garray[idxb[i]];
2218     }
2219   }
2220 
2221   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2222   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2223   ierr = PetscFree(idxb);CHKERRQ(ierr);
2224   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2225   PetscFunctionReturn(0);
2226 }
2227 
2228 PetscErrorCode MatGetRowMinAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2229 {
2230   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2231   PetscErrorCode ierr;
2232   PetscInt       i,*idxb = 0;
2233   PetscScalar    *va,*vb;
2234   Vec            vtmp;
2235 
2236   PetscFunctionBegin;
2237   ierr = MatGetRowMinAbs(a->A,v,idx);CHKERRQ(ierr);
2238   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2239   if (idx) {
2240     for (i=0; i<A->cmap->n; i++) {
2241       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2242     }
2243   }
2244 
2245   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2246   if (idx) {
2247     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2248   }
2249   ierr = MatGetRowMinAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2250   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2251 
2252   for (i=0; i<A->rmap->n; i++) {
2253     if (PetscAbsScalar(va[i]) > PetscAbsScalar(vb[i])) {
2254       va[i] = vb[i];
2255       if (idx) idx[i] = a->garray[idxb[i]];
2256     }
2257   }
2258 
2259   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2260   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2261   ierr = PetscFree(idxb);CHKERRQ(ierr);
2262   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2263   PetscFunctionReturn(0);
2264 }
2265 
2266 PetscErrorCode MatGetRowMin_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2267 {
2268   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2269   PetscInt       n      = A->rmap->n;
2270   PetscInt       cstart = A->cmap->rstart;
2271   PetscInt       *cmap  = mat->garray;
2272   PetscInt       *diagIdx, *offdiagIdx;
2273   Vec            diagV, offdiagV;
2274   PetscScalar    *a, *diagA, *offdiagA;
2275   PetscInt       r;
2276   PetscErrorCode ierr;
2277 
2278   PetscFunctionBegin;
2279   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2280   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &diagV);CHKERRQ(ierr);
2281   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &offdiagV);CHKERRQ(ierr);
2282   ierr = MatGetRowMin(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2283   ierr = MatGetRowMin(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2284   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2285   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2286   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2287   for (r = 0; r < n; ++r) {
2288     if (PetscAbsScalar(diagA[r]) <= PetscAbsScalar(offdiagA[r])) {
2289       a[r]   = diagA[r];
2290       idx[r] = cstart + diagIdx[r];
2291     } else {
2292       a[r]   = offdiagA[r];
2293       idx[r] = cmap[offdiagIdx[r]];
2294     }
2295   }
2296   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2297   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2298   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2299   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2300   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2301   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2302   PetscFunctionReturn(0);
2303 }
2304 
2305 PetscErrorCode MatGetRowMax_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2306 {
2307   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2308   PetscInt       n      = A->rmap->n;
2309   PetscInt       cstart = A->cmap->rstart;
2310   PetscInt       *cmap  = mat->garray;
2311   PetscInt       *diagIdx, *offdiagIdx;
2312   Vec            diagV, offdiagV;
2313   PetscScalar    *a, *diagA, *offdiagA;
2314   PetscInt       r;
2315   PetscErrorCode ierr;
2316 
2317   PetscFunctionBegin;
2318   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2319   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &diagV);CHKERRQ(ierr);
2320   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &offdiagV);CHKERRQ(ierr);
2321   ierr = MatGetRowMax(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2322   ierr = MatGetRowMax(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2323   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2324   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2325   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2326   for (r = 0; r < n; ++r) {
2327     if (PetscAbsScalar(diagA[r]) >= PetscAbsScalar(offdiagA[r])) {
2328       a[r]   = diagA[r];
2329       idx[r] = cstart + diagIdx[r];
2330     } else {
2331       a[r]   = offdiagA[r];
2332       idx[r] = cmap[offdiagIdx[r]];
2333     }
2334   }
2335   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2336   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2337   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2338   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2339   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2340   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2341   PetscFunctionReturn(0);
2342 }
2343 
2344 PetscErrorCode MatGetSeqNonzeroStructure_MPIAIJ(Mat mat,Mat *newmat)
2345 {
2346   PetscErrorCode ierr;
2347   Mat            *dummy;
2348 
2349   PetscFunctionBegin;
2350   ierr    = MatCreateSubMatrix_MPIAIJ_All(mat,MAT_DO_NOT_GET_VALUES,MAT_INITIAL_MATRIX,&dummy);CHKERRQ(ierr);
2351   *newmat = *dummy;
2352   ierr    = PetscFree(dummy);CHKERRQ(ierr);
2353   PetscFunctionReturn(0);
2354 }
2355 
2356 PetscErrorCode  MatInvertBlockDiagonal_MPIAIJ(Mat A,const PetscScalar **values)
2357 {
2358   Mat_MPIAIJ     *a = (Mat_MPIAIJ*) A->data;
2359   PetscErrorCode ierr;
2360 
2361   PetscFunctionBegin;
2362   ierr = MatInvertBlockDiagonal(a->A,values);CHKERRQ(ierr);
2363   A->factorerrortype = a->A->factorerrortype;
2364   PetscFunctionReturn(0);
2365 }
2366 
2367 static PetscErrorCode  MatSetRandom_MPIAIJ(Mat x,PetscRandom rctx)
2368 {
2369   PetscErrorCode ierr;
2370   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)x->data;
2371 
2372   PetscFunctionBegin;
2373   ierr = MatSetRandom(aij->A,rctx);CHKERRQ(ierr);
2374   ierr = MatSetRandom(aij->B,rctx);CHKERRQ(ierr);
2375   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2376   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2377   PetscFunctionReturn(0);
2378 }
2379 
2380 PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ(Mat A,PetscBool sc)
2381 {
2382   PetscFunctionBegin;
2383   if (sc) A->ops->increaseoverlap = MatIncreaseOverlap_MPIAIJ_Scalable;
2384   else A->ops->increaseoverlap    = MatIncreaseOverlap_MPIAIJ;
2385   PetscFunctionReturn(0);
2386 }
2387 
2388 /*@
2389    MatMPIAIJSetUseScalableIncreaseOverlap - Determine if the matrix uses a scalable algorithm to compute the overlap
2390 
2391    Collective on Mat
2392 
2393    Input Parameters:
2394 +    A - the matrix
2395 -    sc - PETSC_TRUE indicates use the scalable algorithm (default is not to use the scalable algorithm)
2396 
2397  Level: advanced
2398 
2399 @*/
2400 PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap(Mat A,PetscBool sc)
2401 {
2402   PetscErrorCode       ierr;
2403 
2404   PetscFunctionBegin;
2405   ierr = PetscTryMethod(A,"MatMPIAIJSetUseScalableIncreaseOverlap_C",(Mat,PetscBool),(A,sc));CHKERRQ(ierr);
2406   PetscFunctionReturn(0);
2407 }
2408 
2409 PetscErrorCode MatSetFromOptions_MPIAIJ(PetscOptionItems *PetscOptionsObject,Mat A)
2410 {
2411   PetscErrorCode       ierr;
2412   PetscBool            sc = PETSC_FALSE,flg;
2413 
2414   PetscFunctionBegin;
2415   ierr = PetscOptionsHead(PetscOptionsObject,"MPIAIJ options");CHKERRQ(ierr);
2416   ierr = PetscObjectOptionsBegin((PetscObject)A);
2417     if (A->ops->increaseoverlap == MatIncreaseOverlap_MPIAIJ_Scalable) sc = PETSC_TRUE;
2418     ierr = PetscOptionsBool("-mat_increase_overlap_scalable","Use a scalable algorithm to compute the overlap","MatIncreaseOverlap",sc,&sc,&flg);CHKERRQ(ierr);
2419     if (flg) {
2420       ierr = MatMPIAIJSetUseScalableIncreaseOverlap(A,sc);CHKERRQ(ierr);
2421     }
2422   ierr = PetscOptionsEnd();CHKERRQ(ierr);
2423   PetscFunctionReturn(0);
2424 }
2425 
2426 PetscErrorCode MatShift_MPIAIJ(Mat Y,PetscScalar a)
2427 {
2428   PetscErrorCode ierr;
2429   Mat_MPIAIJ     *maij = (Mat_MPIAIJ*)Y->data;
2430   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)maij->A->data;
2431 
2432   PetscFunctionBegin;
2433   if (!Y->preallocated) {
2434     ierr = MatMPIAIJSetPreallocation(Y,1,NULL,0,NULL);CHKERRQ(ierr);
2435   } else if (!aij->nz) {
2436     PetscInt nonew = aij->nonew;
2437     ierr = MatSeqAIJSetPreallocation(maij->A,1,NULL);CHKERRQ(ierr);
2438     aij->nonew = nonew;
2439   }
2440   ierr = MatShift_Basic(Y,a);CHKERRQ(ierr);
2441   PetscFunctionReturn(0);
2442 }
2443 
2444 PetscErrorCode MatMissingDiagonal_MPIAIJ(Mat A,PetscBool  *missing,PetscInt *d)
2445 {
2446   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2447   PetscErrorCode ierr;
2448 
2449   PetscFunctionBegin;
2450   if (A->rmap->n != A->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only works for square matrices");
2451   ierr = MatMissingDiagonal(a->A,missing,d);CHKERRQ(ierr);
2452   if (d) {
2453     PetscInt rstart;
2454     ierr = MatGetOwnershipRange(A,&rstart,NULL);CHKERRQ(ierr);
2455     *d += rstart;
2456 
2457   }
2458   PetscFunctionReturn(0);
2459 }
2460 
2461 
2462 /* -------------------------------------------------------------------*/
2463 static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
2464                                        MatGetRow_MPIAIJ,
2465                                        MatRestoreRow_MPIAIJ,
2466                                        MatMult_MPIAIJ,
2467                                 /* 4*/ MatMultAdd_MPIAIJ,
2468                                        MatMultTranspose_MPIAIJ,
2469                                        MatMultTransposeAdd_MPIAIJ,
2470                                        0,
2471                                        0,
2472                                        0,
2473                                 /*10*/ 0,
2474                                        0,
2475                                        0,
2476                                        MatSOR_MPIAIJ,
2477                                        MatTranspose_MPIAIJ,
2478                                 /*15*/ MatGetInfo_MPIAIJ,
2479                                        MatEqual_MPIAIJ,
2480                                        MatGetDiagonal_MPIAIJ,
2481                                        MatDiagonalScale_MPIAIJ,
2482                                        MatNorm_MPIAIJ,
2483                                 /*20*/ MatAssemblyBegin_MPIAIJ,
2484                                        MatAssemblyEnd_MPIAIJ,
2485                                        MatSetOption_MPIAIJ,
2486                                        MatZeroEntries_MPIAIJ,
2487                                 /*24*/ MatZeroRows_MPIAIJ,
2488                                        0,
2489                                        0,
2490                                        0,
2491                                        0,
2492                                 /*29*/ MatSetUp_MPIAIJ,
2493                                        0,
2494                                        0,
2495                                        MatGetDiagonalBlock_MPIAIJ,
2496                                        0,
2497                                 /*34*/ MatDuplicate_MPIAIJ,
2498                                        0,
2499                                        0,
2500                                        0,
2501                                        0,
2502                                 /*39*/ MatAXPY_MPIAIJ,
2503                                        MatCreateSubMatrices_MPIAIJ,
2504                                        MatIncreaseOverlap_MPIAIJ,
2505                                        MatGetValues_MPIAIJ,
2506                                        MatCopy_MPIAIJ,
2507                                 /*44*/ MatGetRowMax_MPIAIJ,
2508                                        MatScale_MPIAIJ,
2509                                        MatShift_MPIAIJ,
2510                                        MatDiagonalSet_MPIAIJ,
2511                                        MatZeroRowsColumns_MPIAIJ,
2512                                 /*49*/ MatSetRandom_MPIAIJ,
2513                                        0,
2514                                        0,
2515                                        0,
2516                                        0,
2517                                 /*54*/ MatFDColoringCreate_MPIXAIJ,
2518                                        0,
2519                                        MatSetUnfactored_MPIAIJ,
2520                                        MatPermute_MPIAIJ,
2521                                        0,
2522                                 /*59*/ MatCreateSubMatrix_MPIAIJ,
2523                                        MatDestroy_MPIAIJ,
2524                                        MatView_MPIAIJ,
2525                                        0,
2526                                        MatMatMatMult_MPIAIJ_MPIAIJ_MPIAIJ,
2527                                 /*64*/ MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ,
2528                                        MatMatMatMultNumeric_MPIAIJ_MPIAIJ_MPIAIJ,
2529                                        0,
2530                                        0,
2531                                        0,
2532                                 /*69*/ MatGetRowMaxAbs_MPIAIJ,
2533                                        MatGetRowMinAbs_MPIAIJ,
2534                                        0,
2535                                        0,
2536                                        0,
2537                                        0,
2538                                 /*75*/ MatFDColoringApply_AIJ,
2539                                        MatSetFromOptions_MPIAIJ,
2540                                        0,
2541                                        0,
2542                                        MatFindZeroDiagonals_MPIAIJ,
2543                                 /*80*/ 0,
2544                                        0,
2545                                        0,
2546                                 /*83*/ MatLoad_MPIAIJ,
2547                                        0,
2548                                        0,
2549                                        0,
2550                                        0,
2551                                        0,
2552                                 /*89*/ MatMatMult_MPIAIJ_MPIAIJ,
2553                                        MatMatMultSymbolic_MPIAIJ_MPIAIJ,
2554                                        MatMatMultNumeric_MPIAIJ_MPIAIJ,
2555                                        MatPtAP_MPIAIJ_MPIAIJ,
2556                                        MatPtAPSymbolic_MPIAIJ_MPIAIJ,
2557                                 /*94*/ MatPtAPNumeric_MPIAIJ_MPIAIJ,
2558                                        0,
2559                                        0,
2560                                        0,
2561                                        0,
2562                                 /*99*/ 0,
2563                                        0,
2564                                        0,
2565                                        MatConjugate_MPIAIJ,
2566                                        0,
2567                                 /*104*/MatSetValuesRow_MPIAIJ,
2568                                        MatRealPart_MPIAIJ,
2569                                        MatImaginaryPart_MPIAIJ,
2570                                        0,
2571                                        0,
2572                                 /*109*/0,
2573                                        0,
2574                                        MatGetRowMin_MPIAIJ,
2575                                        0,
2576                                        MatMissingDiagonal_MPIAIJ,
2577                                 /*114*/MatGetSeqNonzeroStructure_MPIAIJ,
2578                                        0,
2579                                        MatGetGhosts_MPIAIJ,
2580                                        0,
2581                                        0,
2582                                 /*119*/0,
2583                                        0,
2584                                        0,
2585                                        0,
2586                                        MatGetMultiProcBlock_MPIAIJ,
2587                                 /*124*/MatFindNonzeroRows_MPIAIJ,
2588                                        MatGetColumnNorms_MPIAIJ,
2589                                        MatInvertBlockDiagonal_MPIAIJ,
2590                                        0,
2591                                        MatCreateSubMatricesMPI_MPIAIJ,
2592                                 /*129*/0,
2593                                        MatTransposeMatMult_MPIAIJ_MPIAIJ,
2594                                        MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ,
2595                                        MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ,
2596                                        0,
2597                                 /*134*/0,
2598                                        0,
2599                                        0,
2600                                        0,
2601                                        0,
2602                                 /*139*/MatSetBlockSizes_MPIAIJ,
2603                                        0,
2604                                        0,
2605                                        MatFDColoringSetUp_MPIXAIJ,
2606                                        MatFindOffBlockDiagonalEntries_MPIAIJ,
2607                                 /*144*/MatCreateMPIMatConcatenateSeqMat_MPIAIJ
2608 };
2609 
2610 /* ----------------------------------------------------------------------------------------*/
2611 
2612 PetscErrorCode  MatStoreValues_MPIAIJ(Mat mat)
2613 {
2614   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2615   PetscErrorCode ierr;
2616 
2617   PetscFunctionBegin;
2618   ierr = MatStoreValues(aij->A);CHKERRQ(ierr);
2619   ierr = MatStoreValues(aij->B);CHKERRQ(ierr);
2620   PetscFunctionReturn(0);
2621 }
2622 
2623 PetscErrorCode  MatRetrieveValues_MPIAIJ(Mat mat)
2624 {
2625   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2626   PetscErrorCode ierr;
2627 
2628   PetscFunctionBegin;
2629   ierr = MatRetrieveValues(aij->A);CHKERRQ(ierr);
2630   ierr = MatRetrieveValues(aij->B);CHKERRQ(ierr);
2631   PetscFunctionReturn(0);
2632 }
2633 
2634 PetscErrorCode  MatMPIAIJSetPreallocation_MPIAIJ(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
2635 {
2636   Mat_MPIAIJ     *b;
2637   PetscErrorCode ierr;
2638 
2639   PetscFunctionBegin;
2640   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
2641   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
2642   b = (Mat_MPIAIJ*)B->data;
2643 
2644 #if defined(PETSC_USE_CTABLE)
2645   ierr = PetscTableDestroy(&b->colmap);CHKERRQ(ierr);
2646 #else
2647   ierr = PetscFree(b->colmap);CHKERRQ(ierr);
2648 #endif
2649   ierr = PetscFree(b->garray);CHKERRQ(ierr);
2650   ierr = VecDestroy(&b->lvec);CHKERRQ(ierr);
2651   ierr = VecScatterDestroy(&b->Mvctx);CHKERRQ(ierr);
2652 
2653   /* Because the B will have been resized we simply destroy it and create a new one each time */
2654   ierr = MatDestroy(&b->B);CHKERRQ(ierr);
2655   ierr = MatCreate(PETSC_COMM_SELF,&b->B);CHKERRQ(ierr);
2656   ierr = MatSetSizes(b->B,B->rmap->n,B->cmap->N,B->rmap->n,B->cmap->N);CHKERRQ(ierr);
2657   ierr = MatSetBlockSizesFromMats(b->B,B,B);CHKERRQ(ierr);
2658   ierr = MatSetType(b->B,MATSEQAIJ);CHKERRQ(ierr);
2659   ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->B);CHKERRQ(ierr);
2660 
2661   if (!B->preallocated) {
2662     ierr = MatCreate(PETSC_COMM_SELF,&b->A);CHKERRQ(ierr);
2663     ierr = MatSetSizes(b->A,B->rmap->n,B->cmap->n,B->rmap->n,B->cmap->n);CHKERRQ(ierr);
2664     ierr = MatSetBlockSizesFromMats(b->A,B,B);CHKERRQ(ierr);
2665     ierr = MatSetType(b->A,MATSEQAIJ);CHKERRQ(ierr);
2666     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->A);CHKERRQ(ierr);
2667   }
2668 
2669   ierr = MatSeqAIJSetPreallocation(b->A,d_nz,d_nnz);CHKERRQ(ierr);
2670   ierr = MatSeqAIJSetPreallocation(b->B,o_nz,o_nnz);CHKERRQ(ierr);
2671   B->preallocated  = PETSC_TRUE;
2672   B->was_assembled = PETSC_FALSE;
2673   B->assembled     = PETSC_FALSE;;
2674   PetscFunctionReturn(0);
2675 }
2676 
2677 PetscErrorCode MatDuplicate_MPIAIJ(Mat matin,MatDuplicateOption cpvalues,Mat *newmat)
2678 {
2679   Mat            mat;
2680   Mat_MPIAIJ     *a,*oldmat = (Mat_MPIAIJ*)matin->data;
2681   PetscErrorCode ierr;
2682 
2683   PetscFunctionBegin;
2684   *newmat = 0;
2685   ierr    = MatCreate(PetscObjectComm((PetscObject)matin),&mat);CHKERRQ(ierr);
2686   ierr    = MatSetSizes(mat,matin->rmap->n,matin->cmap->n,matin->rmap->N,matin->cmap->N);CHKERRQ(ierr);
2687   ierr    = MatSetBlockSizesFromMats(mat,matin,matin);CHKERRQ(ierr);
2688   ierr    = MatSetType(mat,((PetscObject)matin)->type_name);CHKERRQ(ierr);
2689   ierr    = PetscMemcpy(mat->ops,matin->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
2690   a       = (Mat_MPIAIJ*)mat->data;
2691 
2692   mat->factortype   = matin->factortype;
2693   mat->assembled    = PETSC_TRUE;
2694   mat->insertmode   = NOT_SET_VALUES;
2695   mat->preallocated = PETSC_TRUE;
2696 
2697   a->size         = oldmat->size;
2698   a->rank         = oldmat->rank;
2699   a->donotstash   = oldmat->donotstash;
2700   a->roworiented  = oldmat->roworiented;
2701   a->rowindices   = 0;
2702   a->rowvalues    = 0;
2703   a->getrowactive = PETSC_FALSE;
2704 
2705   ierr = PetscLayoutReference(matin->rmap,&mat->rmap);CHKERRQ(ierr);
2706   ierr = PetscLayoutReference(matin->cmap,&mat->cmap);CHKERRQ(ierr);
2707 
2708   if (oldmat->colmap) {
2709 #if defined(PETSC_USE_CTABLE)
2710     ierr = PetscTableCreateCopy(oldmat->colmap,&a->colmap);CHKERRQ(ierr);
2711 #else
2712     ierr = PetscMalloc1(mat->cmap->N,&a->colmap);CHKERRQ(ierr);
2713     ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2714     ierr = PetscMemcpy(a->colmap,oldmat->colmap,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2715 #endif
2716   } else a->colmap = 0;
2717   if (oldmat->garray) {
2718     PetscInt len;
2719     len  = oldmat->B->cmap->n;
2720     ierr = PetscMalloc1(len+1,&a->garray);CHKERRQ(ierr);
2721     ierr = PetscLogObjectMemory((PetscObject)mat,len*sizeof(PetscInt));CHKERRQ(ierr);
2722     if (len) { ierr = PetscMemcpy(a->garray,oldmat->garray,len*sizeof(PetscInt));CHKERRQ(ierr); }
2723   } else a->garray = 0;
2724 
2725   ierr    = VecDuplicate(oldmat->lvec,&a->lvec);CHKERRQ(ierr);
2726   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->lvec);CHKERRQ(ierr);
2727   ierr    = VecScatterCopy(oldmat->Mvctx,&a->Mvctx);CHKERRQ(ierr);
2728   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->Mvctx);CHKERRQ(ierr);
2729   ierr    = MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
2730   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->A);CHKERRQ(ierr);
2731   ierr    = MatDuplicate(oldmat->B,cpvalues,&a->B);CHKERRQ(ierr);
2732   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->B);CHKERRQ(ierr);
2733   ierr    = PetscFunctionListDuplicate(((PetscObject)matin)->qlist,&((PetscObject)mat)->qlist);CHKERRQ(ierr);
2734   *newmat = mat;
2735   PetscFunctionReturn(0);
2736 }
2737 
2738 
2739 
2740 PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
2741 {
2742   PetscScalar    *vals,*svals;
2743   MPI_Comm       comm;
2744   PetscErrorCode ierr;
2745   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
2746   PetscInt       i,nz,j,rstart,rend,mmax,maxnz = 0;
2747   PetscInt       header[4],*rowlengths = 0,M,N,m,*cols;
2748   PetscInt       *ourlens = NULL,*procsnz = NULL,*offlens = NULL,jj,*mycols,*smycols;
2749   PetscInt       cend,cstart,n,*rowners;
2750   int            fd;
2751   PetscInt       bs = newMat->rmap->bs;
2752 
2753   PetscFunctionBegin;
2754   /* force binary viewer to load .info file if it has not yet done so */
2755   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
2756   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
2757   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2758   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2759   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
2760   if (!rank) {
2761     ierr = PetscBinaryRead(fd,(char*)header,4,PETSC_INT);CHKERRQ(ierr);
2762     if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
2763     if (header[3] < 0) SETERRQ(PetscObjectComm((PetscObject)newMat),PETSC_ERR_FILE_UNEXPECTED,"Matrix stored in special format on disk,cannot load as MATMPIAIJ");
2764   }
2765 
2766   ierr = PetscOptionsBegin(comm,NULL,"Options for loading MATMPIAIJ matrix","Mat");CHKERRQ(ierr);
2767   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
2768   ierr = PetscOptionsEnd();CHKERRQ(ierr);
2769   if (bs < 0) bs = 1;
2770 
2771   ierr = MPI_Bcast(header+1,3,MPIU_INT,0,comm);CHKERRQ(ierr);
2772   M    = header[1]; N = header[2];
2773 
2774   /* If global sizes are set, check if they are consistent with that given in the file */
2775   if (newMat->rmap->N >= 0 && newMat->rmap->N != M) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Inconsistent # of rows:Matrix in file has (%D) and input matrix has (%D)",newMat->rmap->N,M);
2776   if (newMat->cmap->N >=0 && newMat->cmap->N != N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Inconsistent # of cols:Matrix in file has (%D) and input matrix has (%D)",newMat->cmap->N,N);
2777 
2778   /* determine ownership of all (block) rows */
2779   if (M%bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Inconsistent # of rows (%d) and block size (%d)",M,bs);
2780   if (newMat->rmap->n < 0) m = bs*((M/bs)/size + (((M/bs) % size) > rank));    /* PETSC_DECIDE */
2781   else m = newMat->rmap->n; /* Set by user */
2782 
2783   ierr = PetscMalloc1(size+1,&rowners);CHKERRQ(ierr);
2784   ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
2785 
2786   /* First process needs enough room for process with most rows */
2787   if (!rank) {
2788     mmax = rowners[1];
2789     for (i=2; i<=size; i++) {
2790       mmax = PetscMax(mmax, rowners[i]);
2791     }
2792   } else mmax = -1;             /* unused, but compilers complain */
2793 
2794   rowners[0] = 0;
2795   for (i=2; i<=size; i++) {
2796     rowners[i] += rowners[i-1];
2797   }
2798   rstart = rowners[rank];
2799   rend   = rowners[rank+1];
2800 
2801   /* distribute row lengths to all processors */
2802   ierr = PetscMalloc2(m,&ourlens,m,&offlens);CHKERRQ(ierr);
2803   if (!rank) {
2804     ierr = PetscBinaryRead(fd,ourlens,m,PETSC_INT);CHKERRQ(ierr);
2805     ierr = PetscMalloc1(mmax,&rowlengths);CHKERRQ(ierr);
2806     ierr = PetscCalloc1(size,&procsnz);CHKERRQ(ierr);
2807     for (j=0; j<m; j++) {
2808       procsnz[0] += ourlens[j];
2809     }
2810     for (i=1; i<size; i++) {
2811       ierr = PetscBinaryRead(fd,rowlengths,rowners[i+1]-rowners[i],PETSC_INT);CHKERRQ(ierr);
2812       /* calculate the number of nonzeros on each processor */
2813       for (j=0; j<rowners[i+1]-rowners[i]; j++) {
2814         procsnz[i] += rowlengths[j];
2815       }
2816       ierr = MPIULong_Send(rowlengths,rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2817     }
2818     ierr = PetscFree(rowlengths);CHKERRQ(ierr);
2819   } else {
2820     ierr = MPIULong_Recv(ourlens,m,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2821   }
2822 
2823   if (!rank) {
2824     /* determine max buffer needed and allocate it */
2825     maxnz = 0;
2826     for (i=0; i<size; i++) {
2827       maxnz = PetscMax(maxnz,procsnz[i]);
2828     }
2829     ierr = PetscMalloc1(maxnz,&cols);CHKERRQ(ierr);
2830 
2831     /* read in my part of the matrix column indices  */
2832     nz   = procsnz[0];
2833     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2834     ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);
2835 
2836     /* read in every one elses and ship off */
2837     for (i=1; i<size; i++) {
2838       nz   = procsnz[i];
2839       ierr = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
2840       ierr = MPIULong_Send(cols,nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2841     }
2842     ierr = PetscFree(cols);CHKERRQ(ierr);
2843   } else {
2844     /* determine buffer space needed for message */
2845     nz = 0;
2846     for (i=0; i<m; i++) {
2847       nz += ourlens[i];
2848     }
2849     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2850 
2851     /* receive message of column indices*/
2852     ierr = MPIULong_Recv(mycols,nz,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2853   }
2854 
2855   /* determine column ownership if matrix is not square */
2856   if (N != M) {
2857     if (newMat->cmap->n < 0) n = N/size + ((N % size) > rank);
2858     else n = newMat->cmap->n;
2859     ierr   = MPI_Scan(&n,&cend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
2860     cstart = cend - n;
2861   } else {
2862     cstart = rstart;
2863     cend   = rend;
2864     n      = cend - cstart;
2865   }
2866 
2867   /* loop over local rows, determining number of off diagonal entries */
2868   ierr = PetscMemzero(offlens,m*sizeof(PetscInt));CHKERRQ(ierr);
2869   jj   = 0;
2870   for (i=0; i<m; i++) {
2871     for (j=0; j<ourlens[i]; j++) {
2872       if (mycols[jj] < cstart || mycols[jj] >= cend) offlens[i]++;
2873       jj++;
2874     }
2875   }
2876 
2877   for (i=0; i<m; i++) {
2878     ourlens[i] -= offlens[i];
2879   }
2880   ierr = MatSetSizes(newMat,m,n,M,N);CHKERRQ(ierr);
2881 
2882   if (bs > 1) {ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);}
2883 
2884   ierr = MatMPIAIJSetPreallocation(newMat,0,ourlens,0,offlens);CHKERRQ(ierr);
2885 
2886   for (i=0; i<m; i++) {
2887     ourlens[i] += offlens[i];
2888   }
2889 
2890   if (!rank) {
2891     ierr = PetscMalloc1(maxnz+1,&vals);CHKERRQ(ierr);
2892 
2893     /* read in my part of the matrix numerical values  */
2894     nz   = procsnz[0];
2895     ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
2896 
2897     /* insert into matrix */
2898     jj      = rstart;
2899     smycols = mycols;
2900     svals   = vals;
2901     for (i=0; i<m; i++) {
2902       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
2903       smycols += ourlens[i];
2904       svals   += ourlens[i];
2905       jj++;
2906     }
2907 
2908     /* read in other processors and ship out */
2909     for (i=1; i<size; i++) {
2910       nz   = procsnz[i];
2911       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
2912       ierr = MPIULong_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
2913     }
2914     ierr = PetscFree(procsnz);CHKERRQ(ierr);
2915   } else {
2916     /* receive numeric values */
2917     ierr = PetscMalloc1(nz+1,&vals);CHKERRQ(ierr);
2918 
2919     /* receive message of values*/
2920     ierr = MPIULong_Recv(vals,nz,MPIU_SCALAR,0,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
2921 
2922     /* insert into matrix */
2923     jj      = rstart;
2924     smycols = mycols;
2925     svals   = vals;
2926     for (i=0; i<m; i++) {
2927       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
2928       smycols += ourlens[i];
2929       svals   += ourlens[i];
2930       jj++;
2931     }
2932   }
2933   ierr = PetscFree2(ourlens,offlens);CHKERRQ(ierr);
2934   ierr = PetscFree(vals);CHKERRQ(ierr);
2935   ierr = PetscFree(mycols);CHKERRQ(ierr);
2936   ierr = PetscFree(rowners);CHKERRQ(ierr);
2937   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2938   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2939   PetscFunctionReturn(0);
2940 }
2941 
2942 /* TODO: Not scalable because of ISAllGather() unless getting all columns. */
2943 PetscErrorCode MatCreateSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
2944 {
2945   PetscErrorCode ierr;
2946   IS             iscol_local;
2947   PetscInt       csize;
2948 
2949   PetscFunctionBegin;
2950   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
2951   if (call == MAT_REUSE_MATRIX) {
2952     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
2953     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
2954   } else {
2955     /* check if we are grabbing all columns*/
2956     PetscBool    isstride;
2957     PetscMPIInt  lisstride = 0,gisstride;
2958     ierr = PetscObjectTypeCompare((PetscObject)iscol,ISSTRIDE,&isstride);CHKERRQ(ierr);
2959     if (isstride) {
2960       PetscInt  start,len,mstart,mlen;
2961       ierr = ISStrideGetInfo(iscol,&start,NULL);CHKERRQ(ierr);
2962       ierr = ISGetLocalSize(iscol,&len);CHKERRQ(ierr);
2963       ierr = MatGetOwnershipRangeColumn(mat,&mstart,&mlen);CHKERRQ(ierr);
2964       if (mstart == start && mlen-mstart == len) lisstride = 1;
2965     }
2966     ierr = MPIU_Allreduce(&lisstride,&gisstride,1,MPI_INT,MPI_MIN,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
2967     if (gisstride) {
2968       PetscInt N;
2969       ierr = MatGetSize(mat,NULL,&N);CHKERRQ(ierr);
2970       ierr = ISCreateStride(PetscObjectComm((PetscObject)mat),N,0,1,&iscol_local);CHKERRQ(ierr);
2971       ierr = ISSetIdentity(iscol_local);CHKERRQ(ierr);
2972       ierr = PetscInfo(mat,"Optimizing for obtaining all columns of the matrix; skipping ISAllGather()\n");CHKERRQ(ierr);
2973     } else {
2974       PetscInt cbs;
2975       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
2976       ierr = ISAllGather(iscol,&iscol_local);CHKERRQ(ierr);
2977       ierr = ISSetBlockSize(iscol_local,cbs);CHKERRQ(ierr);
2978     }
2979   }
2980 
2981   ierr = MatCreateSubMatrix_MPIAIJ_Private(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
2982   if (call == MAT_INITIAL_MATRIX) {
2983     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
2984     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
2985   }
2986   PetscFunctionReturn(0);
2987 }
2988 
2989 extern PetscErrorCode MatCreateSubMatrices_MPIAIJ_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,Mat*);
2990 extern PetscErrorCode MatCreateSubMatrices_MPIAIJ_SingleIS_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool,Mat*);
2991 
2992 PetscErrorCode MatCreateSubMatrix_MPIAIJ_Private_SameDist(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
2993 {
2994   PetscErrorCode ierr;
2995   PetscMPIInt    rank,size;
2996   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
2997   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
2998   Mat            M,Mreuse;
2999   MatScalar      *vwork,*aa;
3000   MPI_Comm       comm;
3001   Mat_SeqAIJ     *aij;
3002   //PetscBool      colflag,allcolumns=PETSC_FALSE;
3003 
3004   PetscFunctionBegin;
3005   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3006   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3007   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3008   if (!rank) printf("MatCreateSubMatrix_MPIAIJ_Private_SameDist...\n");
3009 
3010   //ierr = ISView(isrow,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
3011   //ierr = ISSorted(iscol,&colflag);CHKERRQ(ierr);
3012   //if (!colflag) printf("[%d] iscol is not sorted!\n",rank);
3013 
3014   /* Check for special case: each processor gets entire matrix columns */
3015   //ierr = ISIdentity(iscol,&colflag);CHKERRQ(ierr);
3016   ierr = ISGetLocalSize(iscol,&nlocal);CHKERRQ(ierr);
3017   //if (colflag && nlocal == mat->cmap->N) allcolumns = PETSC_TRUE; //not working yet!!!
3018 
3019   //==================== new ====================
3020   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)mat->data;
3021   Mat            A = a->A,B = a->B;
3022   PetscInt       *garray = a->garray;
3023   PetscInt       count = 0,An=A->cmap->N,Bn=B->cmap->N,cstart=mat->cmap->rstart,cend=mat->cmap->rend;
3024   const PetscInt *is_idx;
3025   IS             iscol_local = iscol;
3026 
3027   if (rank==-1) {
3028     printf("[%d] iscol_local:\n",rank);
3029     ierr = ISView(iscol_local,0);CHKERRQ(ierr);
3030   }
3031 
3032   //printf("[%d] cstart/end: %d - %d; cstart/end: %d - %d; nlocal %d; mat: %d %d\n",rank,mat->rmap->n,mat->cmap->n,cstart,cend,nlocal,mat->rmap->N,mat->cmap->N);
3033   ierr = ISGetIndices(iscol_local,&is_idx);CHKERRQ(ierr);
3034 
3035   /* (1) create a reduced scalable iscol_loc */
3036   IS       iscol_loc;
3037   PetscInt idx[nlocal],cmap[nlocal];
3038   count = 0;
3039 
3040   /* A part */
3041   j = cstart;
3042   for (i=0; i<nlocal; i++) {
3043     if (j >= cend) break;
3044     if (is_idx[i] == j) {
3045       idx[count]  = j;
3046       cmap[count] = i; /* column index in submat */
3047       count++; j++;
3048     } else if (is_idx[i] > j) {
3049       while (is_idx[i] > j && j < cend-1) j++;
3050       if (is_idx[i] == j) {
3051         idx[count]  = j;
3052         cmap[count] = i; /* column index in submat */
3053         count++; j++;
3054       }
3055     }
3056   }
3057 
3058   /* B part */
3059   j = 0;
3060   for (i=0; i<nlocal; i++) {
3061     if (j >= Bn) break;
3062     if (is_idx[i] == garray[j]) {
3063       idx[count]  = garray[j];
3064       cmap[count] = i; /* column index in submat */
3065       count++; j++;
3066     } else if (is_idx[i] > garray[j]) {
3067       while (is_idx[i] > garray[j] && j < Bn-1) j++;
3068       if (is_idx[i] == garray[j]) {
3069         idx[count]  = garray[j];
3070         cmap[count] = i; /* column index in submat */
3071         count++; j++;
3072       }
3073     }
3074   }
3075   ierr = ISRestoreIndices(iscol_local,&is_idx);CHKERRQ(ierr);
3076   //printf("[%d] nlocal %d, N %d, Bn %d + An %d = %d, count %d\n",rank,nlocal,mat->cmap->N,Bn,An,Bn+An,count);
3077 
3078   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)iscol_local),count,idx,PETSC_COPY_VALUES,&iscol_loc);CHKERRQ(ierr);
3079   ierr = ISSort(iscol_loc);CHKERRQ(ierr);
3080   ierr = PetscSortInt(count,cmap);CHKERRQ(ierr);
3081   if (rank==-1) {
3082     printf("[%d] iscol_loc:\n",rank);
3083     ierr = ISView(iscol_loc,0);CHKERRQ(ierr);
3084     for (i=0; i<count; i++) printf("cmap[%d] = %d\n",i,cmap[i]);
3085   }
3086 
3087   Mat Msub;
3088   ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol_loc,MAT_INITIAL_MATRIX,PETSC_FALSE,&Msub);CHKERRQ(ierr);
3089   if (rank==-1) {
3090     printf("[%d] Msub: %d %d \n",rank,Msub->rmap->N,Msub->cmap->N);
3091     ierr = MatView(Msub,0);CHKERRQ(ierr);
3092   }
3093   ierr = ISDestroy(&iscol_loc);CHKERRQ(ierr);
3094   //==========================================================
3095 
3096   if (call ==  MAT_REUSE_MATRIX) {
3097     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3098     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3099     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,PETSC_FALSE,&Mreuse);CHKERRQ(ierr);
3100   } else {
3101     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,PETSC_FALSE,&Mreuse);CHKERRQ(ierr);
3102     if (rank==-11) {
3103       printf("[%d] Msub: %d %d \n",rank,Msub->rmap->N,Msub->cmap->N);
3104       ierr = MatView(Mreuse,0);CHKERRQ(ierr);
3105     }
3106   }
3107 
3108   /*
3109       m - number of local rows
3110       n - number of columns (same on all processors)
3111       rstart - first row in new global matrix generated
3112   */
3113   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3114   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3115   if (call == MAT_INITIAL_MATRIX) {
3116     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3117     ii  = aij->i;
3118     jj  = aij->j;
3119 
3120     /*
3121         Determine the number of non-zeros in the diagonal and off-diagonal
3122         portions of the matrix in order to do correct preallocation
3123     */
3124 
3125     /* first get start and end of "diagonal" columns */
3126     if (csize == PETSC_DECIDE) {
3127       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3128       if (mglobal == n) { /* square matrix */
3129         nlocal = m;
3130       } else {
3131         nlocal = n/size + ((n % size) > rank);
3132       }
3133     } else {
3134       nlocal = csize;
3135     }
3136     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3137     rstart = rend - nlocal;
3138     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);
3139 
3140     /* next, compute all the lengths */
3141     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3142     olens = dlens + m;
3143     for (i=0; i<m; i++) {
3144       jend = ii[i+1] - ii[i];
3145       olen = 0;
3146       dlen = 0;
3147       for (j=0; j<jend; j++) {
3148         if (*jj < rstart || *jj >= rend) olen++;
3149         else dlen++;
3150         jj++;
3151       }
3152       olens[i] = olen;
3153       dlens[i] = dlen;
3154     }
3155     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3156     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3157     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3158     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3159     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3160     ierr = PetscFree(dlens);CHKERRQ(ierr);
3161   } else {
3162     PetscInt ml,nl;
3163 
3164     M    = *newmat;
3165     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3166     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3167     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3168     /*
3169          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3170        rather than the slower MatSetValues().
3171     */
3172     M->was_assembled = PETSC_TRUE;
3173     M->assembled     = PETSC_FALSE;
3174   }
3175 
3176   //==========================
3177   Mat_SeqAIJ  *aijsub = (Mat_SeqAIJ*)(Msub)->data;
3178   PetscInt    *iisub  = aijsub->i,*jjsub = aijsub->j,nzsub,colsub[count];
3179   //===========================
3180 
3181   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3182   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3183   ii   = aij->i;
3184   jj   = aij->j;
3185   aa   = aijsub->a;
3186   for (i=0; i<m; i++) {
3187     row   = rstart + i;
3188     nz    = ii[i+1] - ii[i];
3189     cwork = jj;     jj += nz;
3190     vwork = aa;     aa += nz;
3191 
3192     nzsub = iisub[i+1] - iisub[i];
3193     if (nzsub != nz) printf(" nzsub != nz\n");
3194 
3195     for (j=0; j<nz; j++) {
3196       colsub[j] = cmap[jjsub[iisub[i]+j]];
3197       if (colsub[j] != cwork[j])  {
3198         printf("[%d] row %d, colsub %d != %d\n",rank,i,colsub[j],cwork[j]);
3199       }
3200     }
3201 
3202     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,colsub,vwork,INSERT_VALUES);CHKERRQ(ierr);
3203   }
3204 
3205   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3206   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3207   *newmat = M;
3208   //ierr = MatView(M,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
3209 
3210   /* save submatrix used in processor for next request */
3211   if (call ==  MAT_INITIAL_MATRIX) {
3212     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3213     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3214   }
3215 
3216   ierr = MatDestroy(&Msub);CHKERRQ(ierr);
3217   PetscFunctionReturn(0);
3218 }
3219 
3220 /*
3221     Not great since it makes two copies of the submatrix, first an SeqAIJ
3222   in local and then by concatenating the local matrices the end result.
3223   Writing it directly would be much like MatCreateSubMatrices_MPIAIJ()
3224 
3225   Note: This requires a sequential iscol with all indices.
3226 */
3227 PetscErrorCode MatCreateSubMatrix_MPIAIJ_Private(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3228 {
3229   PetscErrorCode ierr;
3230   PetscMPIInt    rank,size;
3231   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3232   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
3233   Mat            M,Mreuse;
3234   MatScalar      *vwork,*aa;
3235   MPI_Comm       comm;
3236   Mat_SeqAIJ     *aij;
3237   PetscBool      sameDist=PETSC_FALSE,tsameDist;
3238 
3239   PetscFunctionBegin;
3240   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3241   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3242   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3243 
3244   /* If isrow has same processor distribution as mat, then use a scalable routine */
3245   ierr = ISGetLocalSize(isrow,&n);CHKERRQ(ierr);
3246   if (!n) {
3247     sameDist=PETSC_TRUE;
3248   } else {
3249     ierr = ISGetMinMax(isrow,&i,&j);CHKERRQ(ierr);
3250     ierr = MatGetOwnershipRange(mat,&rstart,&rend);CHKERRQ(ierr);
3251     if (i >= rstart && j < rend) sameDist=PETSC_TRUE;
3252   }
3253   ierr = MPIU_Allreduce(&sameDist,&tsameDist,1,MPIU_BOOL,MPI_LAND,comm);CHKERRQ(ierr);
3254   if (tsameDist) {
3255     ierr = MatCreateSubMatrix_MPIAIJ_Private_SameDist(mat,isrow,iscol,csize,call,newmat);CHKERRQ(ierr);
3256     PetscFunctionReturn(0);
3257   }
3258 
3259   if (call ==  MAT_REUSE_MATRIX) {
3260     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3261     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3262     ierr = MatCreateSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,&Mreuse);CHKERRQ(ierr);
3263   } else {
3264     ierr = MatCreateSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&Mreuse);CHKERRQ(ierr);
3265   }
3266 
3267   /*
3268       m - number of local rows
3269       n - number of columns (same on all processors)
3270       rstart - first row in new global matrix generated
3271   */
3272   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3273   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3274   if (call == MAT_INITIAL_MATRIX) {
3275     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3276     ii  = aij->i;
3277     jj  = aij->j;
3278 
3279     /*
3280         Determine the number of non-zeros in the diagonal and off-diagonal
3281         portions of the matrix in order to do correct preallocation
3282     */
3283 
3284     /* first get start and end of "diagonal" columns */
3285     if (csize == PETSC_DECIDE) {
3286       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3287       if (mglobal == n) { /* square matrix */
3288         nlocal = m;
3289       } else {
3290         nlocal = n/size + ((n % size) > rank);
3291       }
3292     } else {
3293       nlocal = csize;
3294     }
3295     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3296     rstart = rend - nlocal;
3297     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);
3298 
3299     /* next, compute all the lengths */
3300     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3301     olens = dlens + m;
3302     for (i=0; i<m; i++) {
3303       jend = ii[i+1] - ii[i];
3304       olen = 0;
3305       dlen = 0;
3306       for (j=0; j<jend; j++) {
3307         if (*jj < rstart || *jj >= rend) olen++;
3308         else dlen++;
3309         jj++;
3310       }
3311       olens[i] = olen;
3312       dlens[i] = dlen;
3313     }
3314     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3315     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3316     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3317     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3318     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3319     ierr = PetscFree(dlens);CHKERRQ(ierr);
3320   } else {
3321     PetscInt ml,nl;
3322 
3323     M    = *newmat;
3324     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3325     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3326     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3327     /*
3328          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3329        rather than the slower MatSetValues().
3330     */
3331     M->was_assembled = PETSC_TRUE;
3332     M->assembled     = PETSC_FALSE;
3333   }
3334   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3335   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3336   ii   = aij->i;
3337   jj   = aij->j;
3338   aa   = aij->a;
3339   for (i=0; i<m; i++) {
3340     row   = rstart + i;
3341     nz    = ii[i+1] - ii[i];
3342     cwork = jj;     jj += nz;
3343     vwork = aa;     aa += nz;
3344     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3345   }
3346 
3347   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3348   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3349   *newmat = M;
3350 
3351   /* save submatrix used in processor for next request */
3352   if (call ==  MAT_INITIAL_MATRIX) {
3353     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3354     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3355   }
3356   PetscFunctionReturn(0);
3357 }
3358 
3359 PetscErrorCode  MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3360 {
3361   PetscInt       m,cstart, cend,j,nnz,i,d;
3362   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3363   const PetscInt *JJ;
3364   PetscScalar    *values;
3365   PetscErrorCode ierr;
3366   PetscBool      nooffprocentries;
3367 
3368   PetscFunctionBegin;
3369   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3370 
3371   ierr   = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3372   ierr   = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3373   m      = B->rmap->n;
3374   cstart = B->cmap->rstart;
3375   cend   = B->cmap->rend;
3376   rstart = B->rmap->rstart;
3377 
3378   ierr = PetscMalloc2(m,&d_nnz,m,&o_nnz);CHKERRQ(ierr);
3379 
3380 #if defined(PETSC_USE_DEBUGGING)
3381   for (i=0; i<m; i++) {
3382     nnz = Ii[i+1]- Ii[i];
3383     JJ  = J + Ii[i];
3384     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3385     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3386     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);
3387   }
3388 #endif
3389 
3390   for (i=0; i<m; i++) {
3391     nnz     = Ii[i+1]- Ii[i];
3392     JJ      = J + Ii[i];
3393     nnz_max = PetscMax(nnz_max,nnz);
3394     d       = 0;
3395     for (j=0; j<nnz; j++) {
3396       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3397     }
3398     d_nnz[i] = d;
3399     o_nnz[i] = nnz - d;
3400   }
3401   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3402   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3403 
3404   if (v) values = (PetscScalar*)v;
3405   else {
3406     ierr = PetscCalloc1(nnz_max+1,&values);CHKERRQ(ierr);
3407   }
3408 
3409   for (i=0; i<m; i++) {
3410     ii   = i + rstart;
3411     nnz  = Ii[i+1]- Ii[i];
3412     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3413   }
3414   nooffprocentries    = B->nooffprocentries;
3415   B->nooffprocentries = PETSC_TRUE;
3416   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3417   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3418   B->nooffprocentries = nooffprocentries;
3419 
3420   if (!v) {
3421     ierr = PetscFree(values);CHKERRQ(ierr);
3422   }
3423   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3424   PetscFunctionReturn(0);
3425 }
3426 
3427 /*@
3428    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3429    (the default parallel PETSc format).
3430 
3431    Collective on MPI_Comm
3432 
3433    Input Parameters:
3434 +  B - the matrix
3435 .  i - the indices into j for the start of each local row (starts with zero)
3436 .  j - the column indices for each local row (starts with zero)
3437 -  v - optional values in the matrix
3438 
3439    Level: developer
3440 
3441    Notes:
3442        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3443      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3444      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3445 
3446        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3447 
3448        The format which is used for the sparse matrix input, is equivalent to a
3449     row-major ordering.. i.e for the following matrix, the input data expected is
3450     as shown
3451 
3452 $        1 0 0
3453 $        2 0 3     P0
3454 $       -------
3455 $        4 5 6     P1
3456 $
3457 $     Process0 [P0]: rows_owned=[0,1]
3458 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3459 $        j =  {0,0,2}  [size = 3]
3460 $        v =  {1,2,3}  [size = 3]
3461 $
3462 $     Process1 [P1]: rows_owned=[2]
3463 $        i =  {0,3}    [size = nrow+1  = 1+1]
3464 $        j =  {0,1,2}  [size = 3]
3465 $        v =  {4,5,6}  [size = 3]
3466 
3467 .keywords: matrix, aij, compressed row, sparse, parallel
3468 
3469 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MATMPIAIJ,
3470           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3471 @*/
3472 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3473 {
3474   PetscErrorCode ierr;
3475 
3476   PetscFunctionBegin;
3477   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3478   PetscFunctionReturn(0);
3479 }
3480 
3481 /*@C
3482    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3483    (the default parallel PETSc format).  For good matrix assembly performance
3484    the user should preallocate the matrix storage by setting the parameters
3485    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3486    performance can be increased by more than a factor of 50.
3487 
3488    Collective on MPI_Comm
3489 
3490    Input Parameters:
3491 +  B - the matrix
3492 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3493            (same value is used for all local rows)
3494 .  d_nnz - array containing the number of nonzeros in the various rows of the
3495            DIAGONAL portion of the local submatrix (possibly different for each row)
3496            or NULL (PETSC_NULL_INTEGER in Fortran), if d_nz is used to specify the nonzero structure.
3497            The size of this array is equal to the number of local rows, i.e 'm'.
3498            For matrices that will be factored, you must leave room for (and set)
3499            the diagonal entry even if it is zero.
3500 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3501            submatrix (same value is used for all local rows).
3502 -  o_nnz - array containing the number of nonzeros in the various rows of the
3503            OFF-DIAGONAL portion of the local submatrix (possibly different for
3504            each row) or NULL (PETSC_NULL_INTEGER in Fortran), if o_nz is used to specify the nonzero
3505            structure. The size of this array is equal to the number
3506            of local rows, i.e 'm'.
3507 
3508    If the *_nnz parameter is given then the *_nz parameter is ignored
3509 
3510    The AIJ format (also called the Yale sparse matrix format or
3511    compressed row storage (CSR)), is fully compatible with standard Fortran 77
3512    storage.  The stored row and column indices begin with zero.
3513    See Users-Manual: ch_mat for details.
3514 
3515    The parallel matrix is partitioned such that the first m0 rows belong to
3516    process 0, the next m1 rows belong to process 1, the next m2 rows belong
3517    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
3518 
3519    The DIAGONAL portion of the local submatrix of a processor can be defined
3520    as the submatrix which is obtained by extraction the part corresponding to
3521    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
3522    first row that belongs to the processor, r2 is the last row belonging to
3523    the this processor, and c1-c2 is range of indices of the local part of a
3524    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
3525    common case of a square matrix, the row and column ranges are the same and
3526    the DIAGONAL part is also square. The remaining portion of the local
3527    submatrix (mxN) constitute the OFF-DIAGONAL portion.
3528 
3529    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3530 
3531    You can call MatGetInfo() to get information on how effective the preallocation was;
3532    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3533    You can also run with the option -info and look for messages with the string
3534    malloc in them to see if additional memory allocation was needed.
3535 
3536    Example usage:
3537 
3538    Consider the following 8x8 matrix with 34 non-zero values, that is
3539    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3540    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3541    as follows:
3542 
3543 .vb
3544             1  2  0  |  0  3  0  |  0  4
3545     Proc0   0  5  6  |  7  0  0  |  8  0
3546             9  0 10  | 11  0  0  | 12  0
3547     -------------------------------------
3548            13  0 14  | 15 16 17  |  0  0
3549     Proc1   0 18  0  | 19 20 21  |  0  0
3550             0  0  0  | 22 23  0  | 24  0
3551     -------------------------------------
3552     Proc2  25 26 27  |  0  0 28  | 29  0
3553            30  0  0  | 31 32 33  |  0 34
3554 .ve
3555 
3556    This can be represented as a collection of submatrices as:
3557 
3558 .vb
3559       A B C
3560       D E F
3561       G H I
3562 .ve
3563 
3564    Where the submatrices A,B,C are owned by proc0, D,E,F are
3565    owned by proc1, G,H,I are owned by proc2.
3566 
3567    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3568    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3569    The 'M','N' parameters are 8,8, and have the same values on all procs.
3570 
3571    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3572    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3573    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3574    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3575    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3576    matrix, ans [DF] as another SeqAIJ matrix.
3577 
3578    When d_nz, o_nz parameters are specified, d_nz storage elements are
3579    allocated for every row of the local diagonal submatrix, and o_nz
3580    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3581    One way to choose d_nz and o_nz is to use the max nonzerors per local
3582    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3583    In this case, the values of d_nz,o_nz are:
3584 .vb
3585      proc0 : dnz = 2, o_nz = 2
3586      proc1 : dnz = 3, o_nz = 2
3587      proc2 : dnz = 1, o_nz = 4
3588 .ve
3589    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3590    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3591    for proc3. i.e we are using 12+15+10=37 storage locations to store
3592    34 values.
3593 
3594    When d_nnz, o_nnz parameters are specified, the storage is specified
3595    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3596    In the above case the values for d_nnz,o_nnz are:
3597 .vb
3598      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3599      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3600      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3601 .ve
3602    Here the space allocated is sum of all the above values i.e 34, and
3603    hence pre-allocation is perfect.
3604 
3605    Level: intermediate
3606 
3607 .keywords: matrix, aij, compressed row, sparse, parallel
3608 
3609 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
3610           MATMPIAIJ, MatGetInfo(), PetscSplitOwnership()
3611 @*/
3612 PetscErrorCode  MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3613 {
3614   PetscErrorCode ierr;
3615 
3616   PetscFunctionBegin;
3617   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3618   PetscValidType(B,1);
3619   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
3620   PetscFunctionReturn(0);
3621 }
3622 
3623 /*@
3624      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
3625          CSR format the local rows.
3626 
3627    Collective on MPI_Comm
3628 
3629    Input Parameters:
3630 +  comm - MPI communicator
3631 .  m - number of local rows (Cannot be PETSC_DECIDE)
3632 .  n - This value should be the same as the local size used in creating the
3633        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3634        calculated if N is given) For square matrices n is almost always m.
3635 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3636 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3637 .   i - row indices
3638 .   j - column indices
3639 -   a - matrix values
3640 
3641    Output Parameter:
3642 .   mat - the matrix
3643 
3644    Level: intermediate
3645 
3646    Notes:
3647        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3648      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3649      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3650 
3651        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3652 
3653        The format which is used for the sparse matrix input, is equivalent to a
3654     row-major ordering.. i.e for the following matrix, the input data expected is
3655     as shown
3656 
3657 $        1 0 0
3658 $        2 0 3     P0
3659 $       -------
3660 $        4 5 6     P1
3661 $
3662 $     Process0 [P0]: rows_owned=[0,1]
3663 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3664 $        j =  {0,0,2}  [size = 3]
3665 $        v =  {1,2,3}  [size = 3]
3666 $
3667 $     Process1 [P1]: rows_owned=[2]
3668 $        i =  {0,3}    [size = nrow+1  = 1+1]
3669 $        j =  {0,1,2}  [size = 3]
3670 $        v =  {4,5,6}  [size = 3]
3671 
3672 .keywords: matrix, aij, compressed row, sparse, parallel
3673 
3674 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3675           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
3676 @*/
3677 PetscErrorCode  MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
3678 {
3679   PetscErrorCode ierr;
3680 
3681   PetscFunctionBegin;
3682   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
3683   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
3684   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
3685   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
3686   /* ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr); */
3687   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
3688   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
3689   PetscFunctionReturn(0);
3690 }
3691 
3692 /*@C
3693    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
3694    (the default parallel PETSc format).  For good matrix assembly performance
3695    the user should preallocate the matrix storage by setting the parameters
3696    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3697    performance can be increased by more than a factor of 50.
3698 
3699    Collective on MPI_Comm
3700 
3701    Input Parameters:
3702 +  comm - MPI communicator
3703 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
3704            This value should be the same as the local size used in creating the
3705            y vector for the matrix-vector product y = Ax.
3706 .  n - This value should be the same as the local size used in creating the
3707        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3708        calculated if N is given) For square matrices n is almost always m.
3709 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3710 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3711 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3712            (same value is used for all local rows)
3713 .  d_nnz - array containing the number of nonzeros in the various rows of the
3714            DIAGONAL portion of the local submatrix (possibly different for each row)
3715            or NULL, if d_nz is used to specify the nonzero structure.
3716            The size of this array is equal to the number of local rows, i.e 'm'.
3717 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3718            submatrix (same value is used for all local rows).
3719 -  o_nnz - array containing the number of nonzeros in the various rows of the
3720            OFF-DIAGONAL portion of the local submatrix (possibly different for
3721            each row) or NULL, if o_nz is used to specify the nonzero
3722            structure. The size of this array is equal to the number
3723            of local rows, i.e 'm'.
3724 
3725    Output Parameter:
3726 .  A - the matrix
3727 
3728    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3729    MatXXXXSetPreallocation() paradgm instead of this routine directly.
3730    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3731 
3732    Notes:
3733    If the *_nnz parameter is given then the *_nz parameter is ignored
3734 
3735    m,n,M,N parameters specify the size of the matrix, and its partitioning across
3736    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
3737    storage requirements for this matrix.
3738 
3739    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
3740    processor than it must be used on all processors that share the object for
3741    that argument.
3742 
3743    The user MUST specify either the local or global matrix dimensions
3744    (possibly both).
3745 
3746    The parallel matrix is partitioned across processors such that the
3747    first m0 rows belong to process 0, the next m1 rows belong to
3748    process 1, the next m2 rows belong to process 2 etc.. where
3749    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
3750    values corresponding to [m x N] submatrix.
3751 
3752    The columns are logically partitioned with the n0 columns belonging
3753    to 0th partition, the next n1 columns belonging to the next
3754    partition etc.. where n0,n1,n2... are the input parameter 'n'.
3755 
3756    The DIAGONAL portion of the local submatrix on any given processor
3757    is the submatrix corresponding to the rows and columns m,n
3758    corresponding to the given processor. i.e diagonal matrix on
3759    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
3760    etc. The remaining portion of the local submatrix [m x (N-n)]
3761    constitute the OFF-DIAGONAL portion. The example below better
3762    illustrates this concept.
3763 
3764    For a square global matrix we define each processor's diagonal portion
3765    to be its local rows and the corresponding columns (a square submatrix);
3766    each processor's off-diagonal portion encompasses the remainder of the
3767    local matrix (a rectangular submatrix).
3768 
3769    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3770 
3771    When calling this routine with a single process communicator, a matrix of
3772    type SEQAIJ is returned.  If a matrix of type MATMPIAIJ is desired for this
3773    type of communicator, use the construction mechanism:
3774      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
3775 
3776    By default, this format uses inodes (identical nodes) when possible.
3777    We search for consecutive rows with the same nonzero structure, thereby
3778    reusing matrix information to achieve increased efficiency.
3779 
3780    Options Database Keys:
3781 +  -mat_no_inode  - Do not use inodes
3782 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3783 -  -mat_aij_oneindex - Internally use indexing starting at 1
3784         rather than 0.  Note that when calling MatSetValues(),
3785         the user still MUST index entries starting at 0!
3786 
3787 
3788    Example usage:
3789 
3790    Consider the following 8x8 matrix with 34 non-zero values, that is
3791    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3792    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3793    as follows:
3794 
3795 .vb
3796             1  2  0  |  0  3  0  |  0  4
3797     Proc0   0  5  6  |  7  0  0  |  8  0
3798             9  0 10  | 11  0  0  | 12  0
3799     -------------------------------------
3800            13  0 14  | 15 16 17  |  0  0
3801     Proc1   0 18  0  | 19 20 21  |  0  0
3802             0  0  0  | 22 23  0  | 24  0
3803     -------------------------------------
3804     Proc2  25 26 27  |  0  0 28  | 29  0
3805            30  0  0  | 31 32 33  |  0 34
3806 .ve
3807 
3808    This can be represented as a collection of submatrices as:
3809 
3810 .vb
3811       A B C
3812       D E F
3813       G H I
3814 .ve
3815 
3816    Where the submatrices A,B,C are owned by proc0, D,E,F are
3817    owned by proc1, G,H,I are owned by proc2.
3818 
3819    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3820    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3821    The 'M','N' parameters are 8,8, and have the same values on all procs.
3822 
3823    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3824    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3825    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3826    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3827    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3828    matrix, ans [DF] as another SeqAIJ matrix.
3829 
3830    When d_nz, o_nz parameters are specified, d_nz storage elements are
3831    allocated for every row of the local diagonal submatrix, and o_nz
3832    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3833    One way to choose d_nz and o_nz is to use the max nonzerors per local
3834    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3835    In this case, the values of d_nz,o_nz are:
3836 .vb
3837      proc0 : dnz = 2, o_nz = 2
3838      proc1 : dnz = 3, o_nz = 2
3839      proc2 : dnz = 1, o_nz = 4
3840 .ve
3841    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3842    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3843    for proc3. i.e we are using 12+15+10=37 storage locations to store
3844    34 values.
3845 
3846    When d_nnz, o_nnz parameters are specified, the storage is specified
3847    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3848    In the above case the values for d_nnz,o_nnz are:
3849 .vb
3850      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3851      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3852      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3853 .ve
3854    Here the space allocated is sum of all the above values i.e 34, and
3855    hence pre-allocation is perfect.
3856 
3857    Level: intermediate
3858 
3859 .keywords: matrix, aij, compressed row, sparse, parallel
3860 
3861 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3862           MATMPIAIJ, MatCreateMPIAIJWithArrays()
3863 @*/
3864 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)
3865 {
3866   PetscErrorCode ierr;
3867   PetscMPIInt    size;
3868 
3869   PetscFunctionBegin;
3870   ierr = MatCreate(comm,A);CHKERRQ(ierr);
3871   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
3872   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3873   if (size > 1) {
3874     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
3875     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
3876   } else {
3877     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
3878     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
3879   }
3880   PetscFunctionReturn(0);
3881 }
3882 
3883 PetscErrorCode  MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
3884 {
3885   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3886   PetscBool      flg;
3887   PetscErrorCode ierr;
3888 
3889   PetscFunctionBegin;
3890   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&flg);CHKERRQ(ierr);
3891   if (!flg) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"This function requires a MATMPIAIJ matrix as input");
3892   if (Ad)     *Ad     = a->A;
3893   if (Ao)     *Ao     = a->B;
3894   if (colmap) *colmap = a->garray;
3895   PetscFunctionReturn(0);
3896 }
3897 
3898 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
3899 {
3900   PetscErrorCode ierr;
3901   PetscInt       m,N,i,rstart,nnz,Ii;
3902   PetscInt       *indx;
3903   PetscScalar    *values;
3904 
3905   PetscFunctionBegin;
3906   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
3907   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
3908     PetscInt       *dnz,*onz,sum,bs,cbs;
3909 
3910     if (n == PETSC_DECIDE) {
3911       ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
3912     }
3913     /* Check sum(n) = N */
3914     ierr = MPIU_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3915     if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
3916 
3917     ierr    = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3918     rstart -= m;
3919 
3920     ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
3921     for (i=0; i<m; i++) {
3922       ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3923       ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
3924       ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3925     }
3926 
3927     ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
3928     ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
3929     ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
3930     ierr = MatSetBlockSizes(*outmat,bs,cbs);CHKERRQ(ierr);
3931     ierr = MatSetType(*outmat,MATAIJ);CHKERRQ(ierr);
3932     ierr = MatSeqAIJSetPreallocation(*outmat,0,dnz);CHKERRQ(ierr);
3933     ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
3934     ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
3935   }
3936 
3937   /* numeric phase */
3938   ierr = MatGetOwnershipRange(*outmat,&rstart,NULL);CHKERRQ(ierr);
3939   for (i=0; i<m; i++) {
3940     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3941     Ii   = i + rstart;
3942     ierr = MatSetValues(*outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3943     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3944   }
3945   ierr = MatAssemblyBegin(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3946   ierr = MatAssemblyEnd(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3947   PetscFunctionReturn(0);
3948 }
3949 
3950 PetscErrorCode MatFileSplit(Mat A,char *outfile)
3951 {
3952   PetscErrorCode    ierr;
3953   PetscMPIInt       rank;
3954   PetscInt          m,N,i,rstart,nnz;
3955   size_t            len;
3956   const PetscInt    *indx;
3957   PetscViewer       out;
3958   char              *name;
3959   Mat               B;
3960   const PetscScalar *values;
3961 
3962   PetscFunctionBegin;
3963   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
3964   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
3965   /* Should this be the type of the diagonal block of A? */
3966   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
3967   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
3968   ierr = MatSetBlockSizesFromMats(B,A,A);CHKERRQ(ierr);
3969   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
3970   ierr = MatSeqAIJSetPreallocation(B,0,NULL);CHKERRQ(ierr);
3971   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
3972   for (i=0; i<m; i++) {
3973     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3974     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3975     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3976   }
3977   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3978   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3979 
3980   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
3981   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
3982   ierr = PetscMalloc1(len+5,&name);CHKERRQ(ierr);
3983   sprintf(name,"%s.%d",outfile,rank);
3984   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
3985   ierr = PetscFree(name);CHKERRQ(ierr);
3986   ierr = MatView(B,out);CHKERRQ(ierr);
3987   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
3988   ierr = MatDestroy(&B);CHKERRQ(ierr);
3989   PetscFunctionReturn(0);
3990 }
3991 
3992 PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
3993 {
3994   PetscErrorCode      ierr;
3995   Mat_Merge_SeqsToMPI *merge;
3996   PetscContainer      container;
3997 
3998   PetscFunctionBegin;
3999   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4000   if (container) {
4001     ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4002     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
4003     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
4004     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
4005     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
4006     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
4007     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
4008     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
4009     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
4010     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
4011     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
4012     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
4013     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
4014     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
4015     ierr = PetscFree(merge);CHKERRQ(ierr);
4016     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
4017   }
4018   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
4019   PetscFunctionReturn(0);
4020 }
4021 
4022 #include <../src/mat/utils/freespace.h>
4023 #include <petscbt.h>
4024 
4025 PetscErrorCode  MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
4026 {
4027   PetscErrorCode      ierr;
4028   MPI_Comm            comm;
4029   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
4030   PetscMPIInt         size,rank,taga,*len_s;
4031   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
4032   PetscInt            proc,m;
4033   PetscInt            **buf_ri,**buf_rj;
4034   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
4035   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
4036   MPI_Request         *s_waits,*r_waits;
4037   MPI_Status          *status;
4038   MatScalar           *aa=a->a;
4039   MatScalar           **abuf_r,*ba_i;
4040   Mat_Merge_SeqsToMPI *merge;
4041   PetscContainer      container;
4042 
4043   PetscFunctionBegin;
4044   ierr = PetscObjectGetComm((PetscObject)mpimat,&comm);CHKERRQ(ierr);
4045   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4046 
4047   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4048   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4049 
4050   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4051   ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4052 
4053   bi     = merge->bi;
4054   bj     = merge->bj;
4055   buf_ri = merge->buf_ri;
4056   buf_rj = merge->buf_rj;
4057 
4058   ierr   = PetscMalloc1(size,&status);CHKERRQ(ierr);
4059   owners = merge->rowmap->range;
4060   len_s  = merge->len_s;
4061 
4062   /* send and recv matrix values */
4063   /*-----------------------------*/
4064   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
4065   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
4066 
4067   ierr = PetscMalloc1(merge->nsend+1,&s_waits);CHKERRQ(ierr);
4068   for (proc=0,k=0; proc<size; proc++) {
4069     if (!len_s[proc]) continue;
4070     i    = owners[proc];
4071     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
4072     k++;
4073   }
4074 
4075   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
4076   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
4077   ierr = PetscFree(status);CHKERRQ(ierr);
4078 
4079   ierr = PetscFree(s_waits);CHKERRQ(ierr);
4080   ierr = PetscFree(r_waits);CHKERRQ(ierr);
4081 
4082   /* insert mat values of mpimat */
4083   /*----------------------------*/
4084   ierr = PetscMalloc1(N,&ba_i);CHKERRQ(ierr);
4085   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4086 
4087   for (k=0; k<merge->nrecv; k++) {
4088     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4089     nrows       = *(buf_ri_k[k]);
4090     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
4091     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4092   }
4093 
4094   /* set values of ba */
4095   m = merge->rowmap->n;
4096   for (i=0; i<m; i++) {
4097     arow = owners[rank] + i;
4098     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
4099     bnzi = bi[i+1] - bi[i];
4100     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
4101 
4102     /* add local non-zero vals of this proc's seqmat into ba */
4103     anzi   = ai[arow+1] - ai[arow];
4104     aj     = a->j + ai[arow];
4105     aa     = a->a + ai[arow];
4106     nextaj = 0;
4107     for (j=0; nextaj<anzi; j++) {
4108       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4109         ba_i[j] += aa[nextaj++];
4110       }
4111     }
4112 
4113     /* add received vals into ba */
4114     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4115       /* i-th row */
4116       if (i == *nextrow[k]) {
4117         anzi   = *(nextai[k]+1) - *nextai[k];
4118         aj     = buf_rj[k] + *(nextai[k]);
4119         aa     = abuf_r[k] + *(nextai[k]);
4120         nextaj = 0;
4121         for (j=0; nextaj<anzi; j++) {
4122           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4123             ba_i[j] += aa[nextaj++];
4124           }
4125         }
4126         nextrow[k]++; nextai[k]++;
4127       }
4128     }
4129     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
4130   }
4131   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4132   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4133 
4134   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
4135   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
4136   ierr = PetscFree(ba_i);CHKERRQ(ierr);
4137   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4138   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4139   PetscFunctionReturn(0);
4140 }
4141 
4142 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4143 {
4144   PetscErrorCode      ierr;
4145   Mat                 B_mpi;
4146   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
4147   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4148   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
4149   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4150   PetscInt            len,proc,*dnz,*onz,bs,cbs;
4151   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4152   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4153   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
4154   MPI_Status          *status;
4155   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
4156   PetscBT             lnkbt;
4157   Mat_Merge_SeqsToMPI *merge;
4158   PetscContainer      container;
4159 
4160   PetscFunctionBegin;
4161   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4162 
4163   /* make sure it is a PETSc comm */
4164   ierr = PetscCommDuplicate(comm,&comm,NULL);CHKERRQ(ierr);
4165   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4166   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4167 
4168   ierr = PetscNew(&merge);CHKERRQ(ierr);
4169   ierr = PetscMalloc1(size,&status);CHKERRQ(ierr);
4170 
4171   /* determine row ownership */
4172   /*---------------------------------------------------------*/
4173   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
4174   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
4175   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
4176   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
4177   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
4178   ierr = PetscMalloc1(size,&len_si);CHKERRQ(ierr);
4179   ierr = PetscMalloc1(size,&merge->len_s);CHKERRQ(ierr);
4180 
4181   m      = merge->rowmap->n;
4182   owners = merge->rowmap->range;
4183 
4184   /* determine the number of messages to send, their lengths */
4185   /*---------------------------------------------------------*/
4186   len_s = merge->len_s;
4187 
4188   len          = 0; /* length of buf_si[] */
4189   merge->nsend = 0;
4190   for (proc=0; proc<size; proc++) {
4191     len_si[proc] = 0;
4192     if (proc == rank) {
4193       len_s[proc] = 0;
4194     } else {
4195       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4196       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4197     }
4198     if (len_s[proc]) {
4199       merge->nsend++;
4200       nrows = 0;
4201       for (i=owners[proc]; i<owners[proc+1]; i++) {
4202         if (ai[i+1] > ai[i]) nrows++;
4203       }
4204       len_si[proc] = 2*(nrows+1);
4205       len         += len_si[proc];
4206     }
4207   }
4208 
4209   /* determine the number and length of messages to receive for ij-structure */
4210   /*-------------------------------------------------------------------------*/
4211   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
4212   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
4213 
4214   /* post the Irecv of j-structure */
4215   /*-------------------------------*/
4216   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
4217   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
4218 
4219   /* post the Isend of j-structure */
4220   /*--------------------------------*/
4221   ierr = PetscMalloc2(merge->nsend,&si_waits,merge->nsend,&sj_waits);CHKERRQ(ierr);
4222 
4223   for (proc=0, k=0; proc<size; proc++) {
4224     if (!len_s[proc]) continue;
4225     i    = owners[proc];
4226     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
4227     k++;
4228   }
4229 
4230   /* receives and sends of j-structure are complete */
4231   /*------------------------------------------------*/
4232   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
4233   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
4234 
4235   /* send and recv i-structure */
4236   /*---------------------------*/
4237   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
4238   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
4239 
4240   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
4241   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4242   for (proc=0,k=0; proc<size; proc++) {
4243     if (!len_s[proc]) continue;
4244     /* form outgoing message for i-structure:
4245          buf_si[0]:                 nrows to be sent
4246                [1:nrows]:           row index (global)
4247                [nrows+1:2*nrows+1]: i-structure index
4248     */
4249     /*-------------------------------------------*/
4250     nrows       = len_si[proc]/2 - 1;
4251     buf_si_i    = buf_si + nrows+1;
4252     buf_si[0]   = nrows;
4253     buf_si_i[0] = 0;
4254     nrows       = 0;
4255     for (i=owners[proc]; i<owners[proc+1]; i++) {
4256       anzi = ai[i+1] - ai[i];
4257       if (anzi) {
4258         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4259         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4260         nrows++;
4261       }
4262     }
4263     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4264     k++;
4265     buf_si += len_si[proc];
4266   }
4267 
4268   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4269   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4270 
4271   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4272   for (i=0; i<merge->nrecv; i++) {
4273     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);
4274   }
4275 
4276   ierr = PetscFree(len_si);CHKERRQ(ierr);
4277   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4278   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4279   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4280   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4281   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4282   ierr = PetscFree(status);CHKERRQ(ierr);
4283 
4284   /* compute a local seq matrix in each processor */
4285   /*----------------------------------------------*/
4286   /* allocate bi array and free space for accumulating nonzero column info */
4287   ierr  = PetscMalloc1(m+1,&bi);CHKERRQ(ierr);
4288   bi[0] = 0;
4289 
4290   /* create and initialize a linked list */
4291   nlnk = N+1;
4292   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4293 
4294   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4295   len  = ai[owners[rank+1]] - ai[owners[rank]];
4296   ierr = PetscFreeSpaceGet(PetscIntMultTruncate(2,len)+1,&free_space);CHKERRQ(ierr);
4297 
4298   current_space = free_space;
4299 
4300   /* determine symbolic info for each local row */
4301   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4302 
4303   for (k=0; k<merge->nrecv; k++) {
4304     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4305     nrows       = *buf_ri_k[k];
4306     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4307     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4308   }
4309 
4310   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4311   len  = 0;
4312   for (i=0; i<m; i++) {
4313     bnzi = 0;
4314     /* add local non-zero cols of this proc's seqmat into lnk */
4315     arow  = owners[rank] + i;
4316     anzi  = ai[arow+1] - ai[arow];
4317     aj    = a->j + ai[arow];
4318     ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4319     bnzi += nlnk;
4320     /* add received col data into lnk */
4321     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4322       if (i == *nextrow[k]) { /* i-th row */
4323         anzi  = *(nextai[k]+1) - *nextai[k];
4324         aj    = buf_rj[k] + *nextai[k];
4325         ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4326         bnzi += nlnk;
4327         nextrow[k]++; nextai[k]++;
4328       }
4329     }
4330     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4331 
4332     /* if free space is not available, make more free space */
4333     if (current_space->local_remaining<bnzi) {
4334       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(bnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
4335       nspacedouble++;
4336     }
4337     /* copy data into free space, then initialize lnk */
4338     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4339     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
4340 
4341     current_space->array           += bnzi;
4342     current_space->local_used      += bnzi;
4343     current_space->local_remaining -= bnzi;
4344 
4345     bi[i+1] = bi[i] + bnzi;
4346   }
4347 
4348   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4349 
4350   ierr = PetscMalloc1(bi[m]+1,&bj);CHKERRQ(ierr);
4351   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
4352   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4353 
4354   /* create symbolic parallel matrix B_mpi */
4355   /*---------------------------------------*/
4356   ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
4357   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
4358   if (n==PETSC_DECIDE) {
4359     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
4360   } else {
4361     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4362   }
4363   ierr = MatSetBlockSizes(B_mpi,bs,cbs);CHKERRQ(ierr);
4364   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
4365   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
4366   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4367   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
4368 
4369   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4370   B_mpi->assembled    = PETSC_FALSE;
4371   B_mpi->ops->destroy = MatDestroy_MPIAIJ_SeqsToMPI;
4372   merge->bi           = bi;
4373   merge->bj           = bj;
4374   merge->buf_ri       = buf_ri;
4375   merge->buf_rj       = buf_rj;
4376   merge->coi          = NULL;
4377   merge->coj          = NULL;
4378   merge->owners_co    = NULL;
4379 
4380   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
4381 
4382   /* attach the supporting struct to B_mpi for reuse */
4383   ierr    = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
4384   ierr    = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
4385   ierr    = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
4386   ierr    = PetscContainerDestroy(&container);CHKERRQ(ierr);
4387   *mpimat = B_mpi;
4388 
4389   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4390   PetscFunctionReturn(0);
4391 }
4392 
4393 /*@C
4394       MatCreateMPIAIJSumSeqAIJ - Creates a MATMPIAIJ matrix by adding sequential
4395                  matrices from each processor
4396 
4397     Collective on MPI_Comm
4398 
4399    Input Parameters:
4400 +    comm - the communicators the parallel matrix will live on
4401 .    seqmat - the input sequential matrices
4402 .    m - number of local rows (or PETSC_DECIDE)
4403 .    n - number of local columns (or PETSC_DECIDE)
4404 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4405 
4406    Output Parameter:
4407 .    mpimat - the parallel matrix generated
4408 
4409     Level: advanced
4410 
4411    Notes:
4412      The dimensions of the sequential matrix in each processor MUST be the same.
4413      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
4414      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
4415 @*/
4416 PetscErrorCode  MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
4417 {
4418   PetscErrorCode ierr;
4419   PetscMPIInt    size;
4420 
4421   PetscFunctionBegin;
4422   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4423   if (size == 1) {
4424     ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4425     if (scall == MAT_INITIAL_MATRIX) {
4426       ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
4427     } else {
4428       ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4429     }
4430     ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4431     PetscFunctionReturn(0);
4432   }
4433   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4434   if (scall == MAT_INITIAL_MATRIX) {
4435     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
4436   }
4437   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
4438   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4439   PetscFunctionReturn(0);
4440 }
4441 
4442 /*@
4443      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MATMPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
4444           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
4445           with MatGetSize()
4446 
4447     Not Collective
4448 
4449    Input Parameters:
4450 +    A - the matrix
4451 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4452 
4453    Output Parameter:
4454 .    A_loc - the local sequential matrix generated
4455 
4456     Level: developer
4457 
4458 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
4459 
4460 @*/
4461 PetscErrorCode  MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
4462 {
4463   PetscErrorCode ierr;
4464   Mat_MPIAIJ     *mpimat=(Mat_MPIAIJ*)A->data;
4465   Mat_SeqAIJ     *mat,*a,*b;
4466   PetscInt       *ai,*aj,*bi,*bj,*cmap=mpimat->garray;
4467   MatScalar      *aa,*ba,*cam;
4468   PetscScalar    *ca;
4469   PetscInt       am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
4470   PetscInt       *ci,*cj,col,ncols_d,ncols_o,jo;
4471   PetscBool      match;
4472   MPI_Comm       comm;
4473   PetscMPIInt    size;
4474 
4475   PetscFunctionBegin;
4476   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4477   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
4478   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4479   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4480   if (size == 1 && scall == MAT_REUSE_MATRIX) PetscFunctionReturn(0);
4481 
4482   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4483   a = (Mat_SeqAIJ*)(mpimat->A)->data;
4484   b = (Mat_SeqAIJ*)(mpimat->B)->data;
4485   ai = a->i; aj = a->j; bi = b->i; bj = b->j;
4486   aa = a->a; ba = b->a;
4487   if (scall == MAT_INITIAL_MATRIX) {
4488     if (size == 1) {
4489       ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ai,aj,aa,A_loc);CHKERRQ(ierr);
4490       PetscFunctionReturn(0);
4491     }
4492 
4493     ierr  = PetscMalloc1(1+am,&ci);CHKERRQ(ierr);
4494     ci[0] = 0;
4495     for (i=0; i<am; i++) {
4496       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
4497     }
4498     ierr = PetscMalloc1(1+ci[am],&cj);CHKERRQ(ierr);
4499     ierr = PetscMalloc1(1+ci[am],&ca);CHKERRQ(ierr);
4500     k    = 0;
4501     for (i=0; i<am; i++) {
4502       ncols_o = bi[i+1] - bi[i];
4503       ncols_d = ai[i+1] - ai[i];
4504       /* off-diagonal portion of A */
4505       for (jo=0; jo<ncols_o; jo++) {
4506         col = cmap[*bj];
4507         if (col >= cstart) break;
4508         cj[k]   = col; bj++;
4509         ca[k++] = *ba++;
4510       }
4511       /* diagonal portion of A */
4512       for (j=0; j<ncols_d; j++) {
4513         cj[k]   = cstart + *aj++;
4514         ca[k++] = *aa++;
4515       }
4516       /* off-diagonal portion of A */
4517       for (j=jo; j<ncols_o; j++) {
4518         cj[k]   = cmap[*bj++];
4519         ca[k++] = *ba++;
4520       }
4521     }
4522     /* put together the new matrix */
4523     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
4524     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4525     /* Since these are PETSc arrays, change flags to free them as necessary. */
4526     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
4527     mat->free_a  = PETSC_TRUE;
4528     mat->free_ij = PETSC_TRUE;
4529     mat->nonew   = 0;
4530   } else if (scall == MAT_REUSE_MATRIX) {
4531     mat=(Mat_SeqAIJ*)(*A_loc)->data;
4532     ci = mat->i; cj = mat->j; cam = mat->a;
4533     for (i=0; i<am; i++) {
4534       /* off-diagonal portion of A */
4535       ncols_o = bi[i+1] - bi[i];
4536       for (jo=0; jo<ncols_o; jo++) {
4537         col = cmap[*bj];
4538         if (col >= cstart) break;
4539         *cam++ = *ba++; bj++;
4540       }
4541       /* diagonal portion of A */
4542       ncols_d = ai[i+1] - ai[i];
4543       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
4544       /* off-diagonal portion of A */
4545       for (j=jo; j<ncols_o; j++) {
4546         *cam++ = *ba++; bj++;
4547       }
4548     }
4549   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
4550   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4551   PetscFunctionReturn(0);
4552 }
4553 
4554 /*@C
4555      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MATMPIAIJ matrix by taking all its local rows and NON-ZERO columns
4556 
4557     Not Collective
4558 
4559    Input Parameters:
4560 +    A - the matrix
4561 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4562 -    row, col - index sets of rows and columns to extract (or NULL)
4563 
4564    Output Parameter:
4565 .    A_loc - the local sequential matrix generated
4566 
4567     Level: developer
4568 
4569 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
4570 
4571 @*/
4572 PetscErrorCode  MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
4573 {
4574   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4575   PetscErrorCode ierr;
4576   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
4577   IS             isrowa,iscola;
4578   Mat            *aloc;
4579   PetscBool      match;
4580 
4581   PetscFunctionBegin;
4582   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4583   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
4584   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4585   if (!row) {
4586     start = A->rmap->rstart; end = A->rmap->rend;
4587     ierr  = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
4588   } else {
4589     isrowa = *row;
4590   }
4591   if (!col) {
4592     start = A->cmap->rstart;
4593     cmap  = a->garray;
4594     nzA   = a->A->cmap->n;
4595     nzB   = a->B->cmap->n;
4596     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4597     ncols = 0;
4598     for (i=0; i<nzB; i++) {
4599       if (cmap[i] < start) idx[ncols++] = cmap[i];
4600       else break;
4601     }
4602     imark = i;
4603     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
4604     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
4605     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
4606   } else {
4607     iscola = *col;
4608   }
4609   if (scall != MAT_INITIAL_MATRIX) {
4610     ierr    = PetscMalloc1(1,&aloc);CHKERRQ(ierr);
4611     aloc[0] = *A_loc;
4612   }
4613   ierr   = MatCreateSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
4614   *A_loc = aloc[0];
4615   ierr   = PetscFree(aloc);CHKERRQ(ierr);
4616   if (!row) {
4617     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
4618   }
4619   if (!col) {
4620     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
4621   }
4622   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4623   PetscFunctionReturn(0);
4624 }
4625 
4626 /*@C
4627     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
4628 
4629     Collective on Mat
4630 
4631    Input Parameters:
4632 +    A,B - the matrices in mpiaij format
4633 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4634 -    rowb, colb - index sets of rows and columns of B to extract (or NULL)
4635 
4636    Output Parameter:
4637 +    rowb, colb - index sets of rows and columns of B to extract
4638 -    B_seq - the sequential matrix generated
4639 
4640     Level: developer
4641 
4642 @*/
4643 PetscErrorCode  MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
4644 {
4645   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4646   PetscErrorCode ierr;
4647   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
4648   IS             isrowb,iscolb;
4649   Mat            *bseq=NULL;
4650 
4651   PetscFunctionBegin;
4652   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4653     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);
4654   }
4655   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4656 
4657   if (scall == MAT_INITIAL_MATRIX) {
4658     start = A->cmap->rstart;
4659     cmap  = a->garray;
4660     nzA   = a->A->cmap->n;
4661     nzB   = a->B->cmap->n;
4662     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4663     ncols = 0;
4664     for (i=0; i<nzB; i++) {  /* row < local row index */
4665       if (cmap[i] < start) idx[ncols++] = cmap[i];
4666       else break;
4667     }
4668     imark = i;
4669     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
4670     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
4671     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
4672     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
4673   } else {
4674     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
4675     isrowb  = *rowb; iscolb = *colb;
4676     ierr    = PetscMalloc1(1,&bseq);CHKERRQ(ierr);
4677     bseq[0] = *B_seq;
4678   }
4679   ierr   = MatCreateSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
4680   *B_seq = bseq[0];
4681   ierr   = PetscFree(bseq);CHKERRQ(ierr);
4682   if (!rowb) {
4683     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
4684   } else {
4685     *rowb = isrowb;
4686   }
4687   if (!colb) {
4688     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
4689   } else {
4690     *colb = iscolb;
4691   }
4692   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4693   PetscFunctionReturn(0);
4694 }
4695 
4696 /*
4697     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
4698     of the OFF-DIAGONAL portion of local A
4699 
4700     Collective on Mat
4701 
4702    Input Parameters:
4703 +    A,B - the matrices in mpiaij format
4704 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4705 
4706    Output Parameter:
4707 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
4708 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
4709 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
4710 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
4711 
4712     Level: developer
4713 
4714 */
4715 PetscErrorCode  MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
4716 {
4717   VecScatter_MPI_General *gen_to,*gen_from;
4718   PetscErrorCode         ierr;
4719   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
4720   Mat_SeqAIJ             *b_oth;
4721   VecScatter             ctx =a->Mvctx;
4722   MPI_Comm               comm;
4723   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
4724   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
4725   PetscInt               *rvalues,*svalues;
4726   MatScalar              *b_otha,*bufa,*bufA;
4727   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
4728   MPI_Request            *rwaits = NULL,*swaits = NULL;
4729   MPI_Status             *sstatus,rstatus;
4730   PetscMPIInt            jj,size;
4731   PetscInt               *cols,sbs,rbs;
4732   PetscScalar            *vals;
4733 
4734   PetscFunctionBegin;
4735   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4736   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4737 
4738   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4739     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);
4740   }
4741   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4742   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4743 
4744   if (size == 1) {
4745     startsj_s = NULL;
4746     bufa_ptr  = NULL;
4747     *B_oth    = NULL;
4748     PetscFunctionReturn(0);
4749   }
4750 
4751   gen_to   = (VecScatter_MPI_General*)ctx->todata;
4752   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
4753   nrecvs   = gen_from->n;
4754   nsends   = gen_to->n;
4755 
4756   ierr    = PetscMalloc2(nrecvs,&rwaits,nsends,&swaits);CHKERRQ(ierr);
4757   srow    = gen_to->indices;    /* local row index to be sent */
4758   sstarts = gen_to->starts;
4759   sprocs  = gen_to->procs;
4760   sstatus = gen_to->sstatus;
4761   sbs     = gen_to->bs;
4762   rstarts = gen_from->starts;
4763   rprocs  = gen_from->procs;
4764   rbs     = gen_from->bs;
4765 
4766   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
4767   if (scall == MAT_INITIAL_MATRIX) {
4768     /* i-array */
4769     /*---------*/
4770     /*  post receives */
4771     ierr = PetscMalloc1(rbs*(rstarts[nrecvs] - rstarts[0]),&rvalues);CHKERRQ(ierr);
4772     for (i=0; i<nrecvs; i++) {
4773       rowlen = rvalues + rstarts[i]*rbs;
4774       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
4775       ierr   = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4776     }
4777 
4778     /* pack the outgoing message */
4779     ierr = PetscMalloc2(nsends+1,&sstartsj,nrecvs+1,&rstartsj);CHKERRQ(ierr);
4780 
4781     sstartsj[0] = 0;
4782     rstartsj[0] = 0;
4783     len         = 0; /* total length of j or a array to be sent */
4784     k           = 0;
4785     ierr = PetscMalloc1(sbs*(sstarts[nsends] - sstarts[0]),&svalues);CHKERRQ(ierr);
4786     for (i=0; i<nsends; i++) {
4787       rowlen = svalues + sstarts[i]*sbs;
4788       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
4789       for (j=0; j<nrows; j++) {
4790         row = srow[k] + B->rmap->range[rank]; /* global row idx */
4791         for (l=0; l<sbs; l++) {
4792           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr); /* rowlength */
4793 
4794           rowlen[j*sbs+l] = ncols;
4795 
4796           len += ncols;
4797           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr);
4798         }
4799         k++;
4800       }
4801       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4802 
4803       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
4804     }
4805     /* recvs and sends of i-array are completed */
4806     i = nrecvs;
4807     while (i--) {
4808       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4809     }
4810     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4811     ierr = PetscFree(svalues);CHKERRQ(ierr);
4812 
4813     /* allocate buffers for sending j and a arrays */
4814     ierr = PetscMalloc1(len+1,&bufj);CHKERRQ(ierr);
4815     ierr = PetscMalloc1(len+1,&bufa);CHKERRQ(ierr);
4816 
4817     /* create i-array of B_oth */
4818     ierr = PetscMalloc1(aBn+2,&b_othi);CHKERRQ(ierr);
4819 
4820     b_othi[0] = 0;
4821     len       = 0; /* total length of j or a array to be received */
4822     k         = 0;
4823     for (i=0; i<nrecvs; i++) {
4824       rowlen = rvalues + rstarts[i]*rbs;
4825       nrows  = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be received */
4826       for (j=0; j<nrows; j++) {
4827         b_othi[k+1] = b_othi[k] + rowlen[j];
4828         ierr = PetscIntSumError(rowlen[j],len,&len);CHKERRQ(ierr);
4829         k++;
4830       }
4831       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
4832     }
4833     ierr = PetscFree(rvalues);CHKERRQ(ierr);
4834 
4835     /* allocate space for j and a arrrays of B_oth */
4836     ierr = PetscMalloc1(b_othi[aBn]+1,&b_othj);CHKERRQ(ierr);
4837     ierr = PetscMalloc1(b_othi[aBn]+1,&b_otha);CHKERRQ(ierr);
4838 
4839     /* j-array */
4840     /*---------*/
4841     /*  post receives of j-array */
4842     for (i=0; i<nrecvs; i++) {
4843       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4844       ierr  = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4845     }
4846 
4847     /* pack the outgoing message j-array */
4848     k = 0;
4849     for (i=0; i<nsends; i++) {
4850       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4851       bufJ  = bufj+sstartsj[i];
4852       for (j=0; j<nrows; j++) {
4853         row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4854         for (ll=0; ll<sbs; ll++) {
4855           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4856           for (l=0; l<ncols; l++) {
4857             *bufJ++ = cols[l];
4858           }
4859           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4860         }
4861       }
4862       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4863     }
4864 
4865     /* recvs and sends of j-array are completed */
4866     i = nrecvs;
4867     while (i--) {
4868       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4869     }
4870     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4871   } else if (scall == MAT_REUSE_MATRIX) {
4872     sstartsj = *startsj_s;
4873     rstartsj = *startsj_r;
4874     bufa     = *bufa_ptr;
4875     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
4876     b_otha   = b_oth->a;
4877   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
4878 
4879   /* a-array */
4880   /*---------*/
4881   /*  post receives of a-array */
4882   for (i=0; i<nrecvs; i++) {
4883     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4884     ierr  = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4885   }
4886 
4887   /* pack the outgoing message a-array */
4888   k = 0;
4889   for (i=0; i<nsends; i++) {
4890     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4891     bufA  = bufa+sstartsj[i];
4892     for (j=0; j<nrows; j++) {
4893       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4894       for (ll=0; ll<sbs; ll++) {
4895         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4896         for (l=0; l<ncols; l++) {
4897           *bufA++ = vals[l];
4898         }
4899         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4900       }
4901     }
4902     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4903   }
4904   /* recvs and sends of a-array are completed */
4905   i = nrecvs;
4906   while (i--) {
4907     ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4908   }
4909   if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4910   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
4911 
4912   if (scall == MAT_INITIAL_MATRIX) {
4913     /* put together the new matrix */
4914     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
4915 
4916     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4917     /* Since these are PETSc arrays, change flags to free them as necessary. */
4918     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
4919     b_oth->free_a  = PETSC_TRUE;
4920     b_oth->free_ij = PETSC_TRUE;
4921     b_oth->nonew   = 0;
4922 
4923     ierr = PetscFree(bufj);CHKERRQ(ierr);
4924     if (!startsj_s || !bufa_ptr) {
4925       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
4926       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
4927     } else {
4928       *startsj_s = sstartsj;
4929       *startsj_r = rstartsj;
4930       *bufa_ptr  = bufa;
4931     }
4932   }
4933   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4934   PetscFunctionReturn(0);
4935 }
4936 
4937 /*@C
4938   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
4939 
4940   Not Collective
4941 
4942   Input Parameters:
4943 . A - The matrix in mpiaij format
4944 
4945   Output Parameter:
4946 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
4947 . colmap - A map from global column index to local index into lvec
4948 - multScatter - A scatter from the argument of a matrix-vector product to lvec
4949 
4950   Level: developer
4951 
4952 @*/
4953 #if defined(PETSC_USE_CTABLE)
4954 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
4955 #else
4956 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
4957 #endif
4958 {
4959   Mat_MPIAIJ *a;
4960 
4961   PetscFunctionBegin;
4962   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4963   PetscValidPointer(lvec, 2);
4964   PetscValidPointer(colmap, 3);
4965   PetscValidPointer(multScatter, 4);
4966   a = (Mat_MPIAIJ*) A->data;
4967   if (lvec) *lvec = a->lvec;
4968   if (colmap) *colmap = a->colmap;
4969   if (multScatter) *multScatter = a->Mvctx;
4970   PetscFunctionReturn(0);
4971 }
4972 
4973 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
4974 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
4975 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
4976 #if defined(PETSC_HAVE_ELEMENTAL)
4977 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
4978 #endif
4979 #if defined(PETSC_HAVE_HYPRE)
4980 PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat,MatType,MatReuse,Mat*);
4981 PETSC_INTERN PetscErrorCode MatMatMatMult_Transpose_AIJ_AIJ(Mat,Mat,Mat,MatReuse,PetscReal,Mat*);
4982 #endif
4983 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_IS(Mat,MatType,MatReuse,Mat*);
4984 
4985 /*
4986     Computes (B'*A')' since computing B*A directly is untenable
4987 
4988                n                       p                          p
4989         (              )       (              )         (                  )
4990       m (      A       )  *  n (       B      )   =   m (         C        )
4991         (              )       (              )         (                  )
4992 
4993 */
4994 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
4995 {
4996   PetscErrorCode ierr;
4997   Mat            At,Bt,Ct;
4998 
4999   PetscFunctionBegin;
5000   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
5001   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
5002   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
5003   ierr = MatDestroy(&At);CHKERRQ(ierr);
5004   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
5005   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
5006   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
5007   PetscFunctionReturn(0);
5008 }
5009 
5010 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
5011 {
5012   PetscErrorCode ierr;
5013   PetscInt       m=A->rmap->n,n=B->cmap->n;
5014   Mat            Cmat;
5015 
5016   PetscFunctionBegin;
5017   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);
5018   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
5019   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
5020   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
5021   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
5022   ierr = MatMPIDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
5023   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5024   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5025 
5026   Cmat->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
5027 
5028   *C = Cmat;
5029   PetscFunctionReturn(0);
5030 }
5031 
5032 /* ----------------------------------------------------------------*/
5033 PETSC_INTERN PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
5034 {
5035   PetscErrorCode ierr;
5036 
5037   PetscFunctionBegin;
5038   if (scall == MAT_INITIAL_MATRIX) {
5039     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5040     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
5041     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5042   }
5043   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5044   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
5045   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5046   PetscFunctionReturn(0);
5047 }
5048 
5049 /*MC
5050    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
5051 
5052    Options Database Keys:
5053 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
5054 
5055   Level: beginner
5056 
5057 .seealso: MatCreateAIJ()
5058 M*/
5059 
5060 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
5061 {
5062   Mat_MPIAIJ     *b;
5063   PetscErrorCode ierr;
5064   PetscMPIInt    size;
5065 
5066   PetscFunctionBegin;
5067   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
5068 
5069   ierr          = PetscNewLog(B,&b);CHKERRQ(ierr);
5070   B->data       = (void*)b;
5071   ierr          = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
5072   B->assembled  = PETSC_FALSE;
5073   B->insertmode = NOT_SET_VALUES;
5074   b->size       = size;
5075 
5076   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank);CHKERRQ(ierr);
5077 
5078   /* build cache for off array entries formed */
5079   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash);CHKERRQ(ierr);
5080 
5081   b->donotstash  = PETSC_FALSE;
5082   b->colmap      = 0;
5083   b->garray      = 0;
5084   b->roworiented = PETSC_TRUE;
5085 
5086   /* stuff used for matrix vector multiply */
5087   b->lvec  = NULL;
5088   b->Mvctx = NULL;
5089 
5090   /* stuff for MatGetRow() */
5091   b->rowindices   = 0;
5092   b->rowvalues    = 0;
5093   b->getrowactive = PETSC_FALSE;
5094 
5095   /* flexible pointer used in CUSP/CUSPARSE classes */
5096   b->spptr = NULL;
5097 
5098   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetUseScalableIncreaseOverlap_C",MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ);CHKERRQ(ierr);
5099   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ);CHKERRQ(ierr);
5100   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
5101   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
5102   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
5103   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
5104   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
5105   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
5106   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
5107   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
5108 #if defined(PETSC_HAVE_ELEMENTAL)
5109   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_elemental_C",MatConvert_MPIAIJ_Elemental);CHKERRQ(ierr);
5110 #endif
5111 #if defined(PETSC_HAVE_HYPRE)
5112   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_hypre_C",MatConvert_AIJ_HYPRE);CHKERRQ(ierr);
5113 #endif
5114   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_is_C",MatConvert_MPIAIJ_IS);CHKERRQ(ierr);
5115   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
5116   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
5117   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
5118 #if defined(PETSC_HAVE_HYPRE)
5119   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMatMult_transpose_mpiaij_mpiaij_C",MatMatMatMult_Transpose_AIJ_AIJ);CHKERRQ(ierr);
5120 #endif
5121   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
5122   PetscFunctionReturn(0);
5123 }
5124 
5125 /*@C
5126      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
5127          and "off-diagonal" part of the matrix in CSR format.
5128 
5129    Collective on MPI_Comm
5130 
5131    Input Parameters:
5132 +  comm - MPI communicator
5133 .  m - number of local rows (Cannot be PETSC_DECIDE)
5134 .  n - This value should be the same as the local size used in creating the
5135        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
5136        calculated if N is given) For square matrices n is almost always m.
5137 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
5138 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
5139 .   i - row indices for "diagonal" portion of matrix
5140 .   j - column indices
5141 .   a - matrix values
5142 .   oi - row indices for "off-diagonal" portion of matrix
5143 .   oj - column indices
5144 -   oa - matrix values
5145 
5146    Output Parameter:
5147 .   mat - the matrix
5148 
5149    Level: advanced
5150 
5151    Notes:
5152        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
5153        must free the arrays once the matrix has been destroyed and not before.
5154 
5155        The i and j indices are 0 based
5156 
5157        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
5158 
5159        This sets local rows and cannot be used to set off-processor values.
5160 
5161        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
5162        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
5163        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
5164        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
5165        keep track of the underlying array. Use MatSetOption(A,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
5166        communication if it is known that only local entries will be set.
5167 
5168 .keywords: matrix, aij, compressed row, sparse, parallel
5169 
5170 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
5171           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
5172 @*/
5173 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)
5174 {
5175   PetscErrorCode ierr;
5176   Mat_MPIAIJ     *maij;
5177 
5178   PetscFunctionBegin;
5179   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
5180   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
5181   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
5182   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
5183   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
5184   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
5185   maij = (Mat_MPIAIJ*) (*mat)->data;
5186 
5187   (*mat)->preallocated = PETSC_TRUE;
5188 
5189   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
5190   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
5191 
5192   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
5193   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
5194 
5195   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5196   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5197   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5198   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5199 
5200   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
5201   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5202   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5203   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_FALSE);CHKERRQ(ierr);
5204   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
5205   PetscFunctionReturn(0);
5206 }
5207 
5208 /*
5209     Special version for direct calls from Fortran
5210 */
5211 #include <petsc/private/fortranimpl.h>
5212 
5213 /* Change these macros so can be used in void function */
5214 #undef CHKERRQ
5215 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
5216 #undef SETERRQ2
5217 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5218 #undef SETERRQ3
5219 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5220 #undef SETERRQ
5221 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
5222 
5223 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5224 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
5225 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5226 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
5227 #else
5228 #endif
5229 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)
5230 {
5231   Mat            mat  = *mmat;
5232   PetscInt       m    = *mm, n = *mn;
5233   InsertMode     addv = *maddv;
5234   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
5235   PetscScalar    value;
5236   PetscErrorCode ierr;
5237 
5238   MatCheckPreallocated(mat,1);
5239   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
5240 
5241 #if defined(PETSC_USE_DEBUG)
5242   else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
5243 #endif
5244   {
5245     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
5246     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
5247     PetscBool roworiented = aij->roworiented;
5248 
5249     /* Some Variables required in the macro */
5250     Mat        A                 = aij->A;
5251     Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
5252     PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
5253     MatScalar  *aa               = a->a;
5254     PetscBool  ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
5255     Mat        B                 = aij->B;
5256     Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
5257     PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5258     MatScalar  *ba               = b->a;
5259 
5260     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5261     PetscInt  nonew = a->nonew;
5262     MatScalar *ap1,*ap2;
5263 
5264     PetscFunctionBegin;
5265     for (i=0; i<m; i++) {
5266       if (im[i] < 0) continue;
5267 #if defined(PETSC_USE_DEBUG)
5268       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);
5269 #endif
5270       if (im[i] >= rstart && im[i] < rend) {
5271         row      = im[i] - rstart;
5272         lastcol1 = -1;
5273         rp1      = aj + ai[row];
5274         ap1      = aa + ai[row];
5275         rmax1    = aimax[row];
5276         nrow1    = ailen[row];
5277         low1     = 0;
5278         high1    = nrow1;
5279         lastcol2 = -1;
5280         rp2      = bj + bi[row];
5281         ap2      = ba + bi[row];
5282         rmax2    = bimax[row];
5283         nrow2    = bilen[row];
5284         low2     = 0;
5285         high2    = nrow2;
5286 
5287         for (j=0; j<n; j++) {
5288           if (roworiented) value = v[i*n+j];
5289           else value = v[i+j*m];
5290           if (in[j] >= cstart && in[j] < cend) {
5291             col = in[j] - cstart;
5292             if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
5293             MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
5294           } else if (in[j] < 0) continue;
5295 #if defined(PETSC_USE_DEBUG)
5296           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);
5297 #endif
5298           else {
5299             if (mat->was_assembled) {
5300               if (!aij->colmap) {
5301                 ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5302               }
5303 #if defined(PETSC_USE_CTABLE)
5304               ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5305               col--;
5306 #else
5307               col = aij->colmap[in[j]] - 1;
5308 #endif
5309               if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
5310               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5311                 ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5312                 col  =  in[j];
5313                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5314                 B     = aij->B;
5315                 b     = (Mat_SeqAIJ*)B->data;
5316                 bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5317                 rp2   = bj + bi[row];
5318                 ap2   = ba + bi[row];
5319                 rmax2 = bimax[row];
5320                 nrow2 = bilen[row];
5321                 low2  = 0;
5322                 high2 = nrow2;
5323                 bm    = aij->B->rmap->n;
5324                 ba    = b->a;
5325               }
5326             } else col = in[j];
5327             MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
5328           }
5329         }
5330       } else if (!aij->donotstash) {
5331         if (roworiented) {
5332           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5333         } else {
5334           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5335         }
5336       }
5337     }
5338   }
5339   PetscFunctionReturnVoid();
5340 }
5341 
5342