xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision 96f18dee9609738d9979dcd4b335173297a85859)
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 PetscErrorCode MatFindZeroDiagonals_MPIAIJ(Mat M,IS *zrows)
135 {
136   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)M->data;
137   PetscErrorCode ierr;
138   PetscInt       i,rstart,nrows,*rows;
139 
140   PetscFunctionBegin;
141   *zrows = NULL;
142   ierr   = MatFindZeroDiagonals_SeqAIJ_Private(aij->A,&nrows,&rows);CHKERRQ(ierr);
143   ierr   = MatGetOwnershipRange(M,&rstart,NULL);CHKERRQ(ierr);
144   for (i=0; i<nrows; i++) rows[i] += rstart;
145   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)M),nrows,rows,PETSC_OWN_POINTER,zrows);CHKERRQ(ierr);
146   PetscFunctionReturn(0);
147 }
148 
149 PetscErrorCode MatGetColumnNorms_MPIAIJ(Mat A,NormType type,PetscReal *norms)
150 {
151   PetscErrorCode ierr;
152   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)A->data;
153   PetscInt       i,n,*garray = aij->garray;
154   Mat_SeqAIJ     *a_aij = (Mat_SeqAIJ*) aij->A->data;
155   Mat_SeqAIJ     *b_aij = (Mat_SeqAIJ*) aij->B->data;
156   PetscReal      *work;
157 
158   PetscFunctionBegin;
159   ierr = MatGetSize(A,NULL,&n);CHKERRQ(ierr);
160   ierr = PetscCalloc1(n,&work);CHKERRQ(ierr);
161   if (type == NORM_2) {
162     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
163       work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i]*a_aij->a[i]);
164     }
165     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
166       work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]*b_aij->a[i]);
167     }
168   } else if (type == NORM_1) {
169     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
170       work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i]);
171     }
172     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
173       work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]);
174     }
175   } else if (type == NORM_INFINITY) {
176     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
177       work[A->cmap->rstart + a_aij->j[i]] = PetscMax(PetscAbsScalar(a_aij->a[i]), work[A->cmap->rstart + a_aij->j[i]]);
178     }
179     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
180       work[garray[b_aij->j[i]]] = PetscMax(PetscAbsScalar(b_aij->a[i]),work[garray[b_aij->j[i]]]);
181     }
182 
183   } else SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Unknown NormType");
184   if (type == NORM_INFINITY) {
185     ierr = MPIU_Allreduce(work,norms,n,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
186   } else {
187     ierr = MPIU_Allreduce(work,norms,n,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
188   }
189   ierr = PetscFree(work);CHKERRQ(ierr);
190   if (type == NORM_2) {
191     for (i=0; i<n; i++) norms[i] = PetscSqrtReal(norms[i]);
192   }
193   PetscFunctionReturn(0);
194 }
195 
196 PetscErrorCode MatFindOffBlockDiagonalEntries_MPIAIJ(Mat A,IS *is)
197 {
198   Mat_MPIAIJ      *a  = (Mat_MPIAIJ*)A->data;
199   IS              sis,gis;
200   PetscErrorCode  ierr;
201   const PetscInt  *isis,*igis;
202   PetscInt        n,*iis,nsis,ngis,rstart,i;
203 
204   PetscFunctionBegin;
205   ierr = MatFindOffBlockDiagonalEntries(a->A,&sis);CHKERRQ(ierr);
206   ierr = MatFindNonzeroRows(a->B,&gis);CHKERRQ(ierr);
207   ierr = ISGetSize(gis,&ngis);CHKERRQ(ierr);
208   ierr = ISGetSize(sis,&nsis);CHKERRQ(ierr);
209   ierr = ISGetIndices(sis,&isis);CHKERRQ(ierr);
210   ierr = ISGetIndices(gis,&igis);CHKERRQ(ierr);
211 
212   ierr = PetscMalloc1(ngis+nsis,&iis);CHKERRQ(ierr);
213   ierr = PetscMemcpy(iis,igis,ngis*sizeof(PetscInt));CHKERRQ(ierr);
214   ierr = PetscMemcpy(iis+ngis,isis,nsis*sizeof(PetscInt));CHKERRQ(ierr);
215   n    = ngis + nsis;
216   ierr = PetscSortRemoveDupsInt(&n,iis);CHKERRQ(ierr);
217   ierr = MatGetOwnershipRange(A,&rstart,NULL);CHKERRQ(ierr);
218   for (i=0; i<n; i++) iis[i] += rstart;
219   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)A),n,iis,PETSC_OWN_POINTER,is);CHKERRQ(ierr);
220 
221   ierr = ISRestoreIndices(sis,&isis);CHKERRQ(ierr);
222   ierr = ISRestoreIndices(gis,&igis);CHKERRQ(ierr);
223   ierr = ISDestroy(&sis);CHKERRQ(ierr);
224   ierr = ISDestroy(&gis);CHKERRQ(ierr);
225   PetscFunctionReturn(0);
226 }
227 
228 /*
229     Distributes a SeqAIJ matrix across a set of processes. Code stolen from
230     MatLoad_MPIAIJ(). Horrible lack of reuse. Should be a routine for each matrix type.
231 
232     Only for square matrices
233 
234     Used by a preconditioner, hence PETSC_EXTERN
235 */
236 PETSC_EXTERN PetscErrorCode MatDistribute_MPIAIJ(MPI_Comm comm,Mat gmat,PetscInt m,MatReuse reuse,Mat *inmat)
237 {
238   PetscMPIInt    rank,size;
239   PetscInt       *rowners,*dlens,*olens,i,rstart,rend,j,jj,nz = 0,*gmataj,cnt,row,*ld,bses[2];
240   PetscErrorCode ierr;
241   Mat            mat;
242   Mat_SeqAIJ     *gmata;
243   PetscMPIInt    tag;
244   MPI_Status     status;
245   PetscBool      aij;
246   MatScalar      *gmataa,*ao,*ad,*gmataarestore=0;
247 
248   PetscFunctionBegin;
249   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
250   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
251   if (!rank) {
252     ierr = PetscObjectTypeCompare((PetscObject)gmat,MATSEQAIJ,&aij);CHKERRQ(ierr);
253     if (!aij) SETERRQ1(PetscObjectComm((PetscObject)gmat),PETSC_ERR_SUP,"Currently no support for input matrix of type %s\n",((PetscObject)gmat)->type_name);
254   }
255   if (reuse == MAT_INITIAL_MATRIX) {
256     ierr = MatCreate(comm,&mat);CHKERRQ(ierr);
257     ierr = MatSetSizes(mat,m,m,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
258     ierr = MatGetBlockSizes(gmat,&bses[0],&bses[1]);CHKERRQ(ierr);
259     ierr = MPI_Bcast(bses,2,MPIU_INT,0,comm);CHKERRQ(ierr);
260     ierr = MatSetBlockSizes(mat,bses[0],bses[1]);CHKERRQ(ierr);
261     ierr = MatSetType(mat,MATAIJ);CHKERRQ(ierr);
262     ierr = PetscMalloc1(size+1,&rowners);CHKERRQ(ierr);
263     ierr = PetscMalloc2(m,&dlens,m,&olens);CHKERRQ(ierr);
264     ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
265 
266     rowners[0] = 0;
267     for (i=2; i<=size; i++) rowners[i] += rowners[i-1];
268     rstart = rowners[rank];
269     rend   = rowners[rank+1];
270     ierr   = PetscObjectGetNewTag((PetscObject)mat,&tag);CHKERRQ(ierr);
271     if (!rank) {
272       gmata = (Mat_SeqAIJ*) gmat->data;
273       /* send row lengths to all processors */
274       for (i=0; i<m; i++) dlens[i] = gmata->ilen[i];
275       for (i=1; i<size; i++) {
276         ierr = MPI_Send(gmata->ilen + rowners[i],rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
277       }
278       /* determine number diagonal and off-diagonal counts */
279       ierr = PetscMemzero(olens,m*sizeof(PetscInt));CHKERRQ(ierr);
280       ierr = PetscCalloc1(m,&ld);CHKERRQ(ierr);
281       jj   = 0;
282       for (i=0; i<m; i++) {
283         for (j=0; j<dlens[i]; j++) {
284           if (gmata->j[jj] < rstart) ld[i]++;
285           if (gmata->j[jj] < rstart || gmata->j[jj] >= rend) olens[i]++;
286           jj++;
287         }
288       }
289       /* send column indices to other processes */
290       for (i=1; i<size; i++) {
291         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
292         ierr = MPI_Send(&nz,1,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
293         ierr = MPI_Send(gmata->j + gmata->i[rowners[i]],nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
294       }
295 
296       /* send numerical values to other processes */
297       for (i=1; i<size; i++) {
298         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
299         ierr = MPI_Send(gmata->a + gmata->i[rowners[i]],nz,MPIU_SCALAR,i,tag,comm);CHKERRQ(ierr);
300       }
301       gmataa = gmata->a;
302       gmataj = gmata->j;
303 
304     } else {
305       /* receive row lengths */
306       ierr = MPI_Recv(dlens,m,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
307       /* receive column indices */
308       ierr = MPI_Recv(&nz,1,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
309       ierr = PetscMalloc2(nz,&gmataa,nz,&gmataj);CHKERRQ(ierr);
310       ierr = MPI_Recv(gmataj,nz,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
311       /* determine number diagonal and off-diagonal counts */
312       ierr = PetscMemzero(olens,m*sizeof(PetscInt));CHKERRQ(ierr);
313       ierr = PetscCalloc1(m,&ld);CHKERRQ(ierr);
314       jj   = 0;
315       for (i=0; i<m; i++) {
316         for (j=0; j<dlens[i]; j++) {
317           if (gmataj[jj] < rstart) ld[i]++;
318           if (gmataj[jj] < rstart || gmataj[jj] >= rend) olens[i]++;
319           jj++;
320         }
321       }
322       /* receive numerical values */
323       ierr = PetscMemzero(gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr);
324       ierr = MPI_Recv(gmataa,nz,MPIU_SCALAR,0,tag,comm,&status);CHKERRQ(ierr);
325     }
326     /* set preallocation */
327     for (i=0; i<m; i++) {
328       dlens[i] -= olens[i];
329     }
330     ierr = MatSeqAIJSetPreallocation(mat,0,dlens);CHKERRQ(ierr);
331     ierr = MatMPIAIJSetPreallocation(mat,0,dlens,0,olens);CHKERRQ(ierr);
332 
333     for (i=0; i<m; i++) {
334       dlens[i] += olens[i];
335     }
336     cnt = 0;
337     for (i=0; i<m; i++) {
338       row  = rstart + i;
339       ierr = MatSetValues(mat,1,&row,dlens[i],gmataj+cnt,gmataa+cnt,INSERT_VALUES);CHKERRQ(ierr);
340       cnt += dlens[i];
341     }
342     if (rank) {
343       ierr = PetscFree2(gmataa,gmataj);CHKERRQ(ierr);
344     }
345     ierr = PetscFree2(dlens,olens);CHKERRQ(ierr);
346     ierr = PetscFree(rowners);CHKERRQ(ierr);
347 
348     ((Mat_MPIAIJ*)(mat->data))->ld = ld;
349 
350     *inmat = mat;
351   } else {   /* column indices are already set; only need to move over numerical values from process 0 */
352     Mat_SeqAIJ *Ad = (Mat_SeqAIJ*)((Mat_MPIAIJ*)((*inmat)->data))->A->data;
353     Mat_SeqAIJ *Ao = (Mat_SeqAIJ*)((Mat_MPIAIJ*)((*inmat)->data))->B->data;
354     mat  = *inmat;
355     ierr = PetscObjectGetNewTag((PetscObject)mat,&tag);CHKERRQ(ierr);
356     if (!rank) {
357       /* send numerical values to other processes */
358       gmata  = (Mat_SeqAIJ*) gmat->data;
359       ierr   = MatGetOwnershipRanges(mat,(const PetscInt**)&rowners);CHKERRQ(ierr);
360       gmataa = gmata->a;
361       for (i=1; i<size; i++) {
362         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
363         ierr = MPI_Send(gmataa + gmata->i[rowners[i]],nz,MPIU_SCALAR,i,tag,comm);CHKERRQ(ierr);
364       }
365       nz = gmata->i[rowners[1]]-gmata->i[rowners[0]];
366     } else {
367       /* receive numerical values from process 0*/
368       nz   = Ad->nz + Ao->nz;
369       ierr = PetscMalloc1(nz,&gmataa);CHKERRQ(ierr); gmataarestore = gmataa;
370       ierr = MPI_Recv(gmataa,nz,MPIU_SCALAR,0,tag,comm,&status);CHKERRQ(ierr);
371     }
372     /* transfer numerical values into the diagonal A and off diagonal B parts of mat */
373     ld = ((Mat_MPIAIJ*)(mat->data))->ld;
374     ad = Ad->a;
375     ao = Ao->a;
376     if (mat->rmap->n) {
377       i  = 0;
378       nz = ld[i];                                   ierr = PetscMemcpy(ao,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ao += nz; gmataa += nz;
379       nz = Ad->i[i+1] - Ad->i[i];                   ierr = PetscMemcpy(ad,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ad += nz; gmataa += nz;
380     }
381     for (i=1; i<mat->rmap->n; i++) {
382       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;
383       nz = Ad->i[i+1] - Ad->i[i];                   ierr = PetscMemcpy(ad,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ad += nz; gmataa += nz;
384     }
385     i--;
386     if (mat->rmap->n) {
387       nz = Ao->i[i+1] - Ao->i[i] - ld[i];           ierr = PetscMemcpy(ao,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr);
388     }
389     if (rank) {
390       ierr = PetscFree(gmataarestore);CHKERRQ(ierr);
391     }
392   }
393   ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
394   ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
395   PetscFunctionReturn(0);
396 }
397 
398 /*
399   Local utility routine that creates a mapping from the global column
400 number to the local number in the off-diagonal part of the local
401 storage of the matrix.  When PETSC_USE_CTABLE is used this is scalable at
402 a slightly higher hash table cost; without it it is not scalable (each processor
403 has an order N integer array but is fast to acess.
404 */
405 PetscErrorCode MatCreateColmap_MPIAIJ_Private(Mat mat)
406 {
407   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
408   PetscErrorCode ierr;
409   PetscInt       n = aij->B->cmap->n,i;
410 
411   PetscFunctionBegin;
412   if (!aij->garray) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"MPIAIJ Matrix was assembled but is missing garray");
413 #if defined(PETSC_USE_CTABLE)
414   ierr = PetscTableCreate(n,mat->cmap->N+1,&aij->colmap);CHKERRQ(ierr);
415   for (i=0; i<n; i++) {
416     ierr = PetscTableAdd(aij->colmap,aij->garray[i]+1,i+1,INSERT_VALUES);CHKERRQ(ierr);
417   }
418 #else
419   ierr = PetscCalloc1(mat->cmap->N+1,&aij->colmap);CHKERRQ(ierr);
420   ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N+1)*sizeof(PetscInt));CHKERRQ(ierr);
421   for (i=0; i<n; i++) aij->colmap[aij->garray[i]] = i+1;
422 #endif
423   PetscFunctionReturn(0);
424 }
425 
426 #define MatSetValues_SeqAIJ_A_Private(row,col,value,addv,orow,ocol)     \
427 { \
428     if (col <= lastcol1)  low1 = 0;     \
429     else                 high1 = nrow1; \
430     lastcol1 = col;\
431     while (high1-low1 > 5) { \
432       t = (low1+high1)/2; \
433       if (rp1[t] > col) high1 = t; \
434       else              low1  = t; \
435     } \
436       for (_i=low1; _i<high1; _i++) { \
437         if (rp1[_i] > col) break; \
438         if (rp1[_i] == col) { \
439           if (addv == ADD_VALUES) ap1[_i] += value;   \
440           else                    ap1[_i] = value; \
441           goto a_noinsert; \
442         } \
443       }  \
444       if (value == 0.0 && ignorezeroentries && row != col) {low1 = 0; high1 = nrow1;goto a_noinsert;} \
445       if (nonew == 1) {low1 = 0; high1 = nrow1; goto a_noinsert;}                \
446       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); \
447       MatSeqXAIJReallocateAIJ(A,am,1,nrow1,row,col,rmax1,aa,ai,aj,rp1,ap1,aimax,nonew,MatScalar); \
448       N = nrow1++ - 1; a->nz++; high1++; \
449       /* shift up all the later entries in this row */ \
450       for (ii=N; ii>=_i; ii--) { \
451         rp1[ii+1] = rp1[ii]; \
452         ap1[ii+1] = ap1[ii]; \
453       } \
454       rp1[_i] = col;  \
455       ap1[_i] = value;  \
456       A->nonzerostate++;\
457       a_noinsert: ; \
458       ailen[row] = nrow1; \
459 }
460 
461 #define MatSetValues_SeqAIJ_B_Private(row,col,value,addv,orow,ocol) \
462   { \
463     if (col <= lastcol2) low2 = 0;                        \
464     else high2 = nrow2;                                   \
465     lastcol2 = col;                                       \
466     while (high2-low2 > 5) {                              \
467       t = (low2+high2)/2;                                 \
468       if (rp2[t] > col) high2 = t;                        \
469       else             low2  = t;                         \
470     }                                                     \
471     for (_i=low2; _i<high2; _i++) {                       \
472       if (rp2[_i] > col) break;                           \
473       if (rp2[_i] == col) {                               \
474         if (addv == ADD_VALUES) ap2[_i] += value;         \
475         else                    ap2[_i] = value;          \
476         goto b_noinsert;                                  \
477       }                                                   \
478     }                                                     \
479     if (value == 0.0 && ignorezeroentries) {low2 = 0; high2 = nrow2; goto b_noinsert;} \
480     if (nonew == 1) {low2 = 0; high2 = nrow2; goto b_noinsert;}                        \
481     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); \
482     MatSeqXAIJReallocateAIJ(B,bm,1,nrow2,row,col,rmax2,ba,bi,bj,rp2,ap2,bimax,nonew,MatScalar); \
483     N = nrow2++ - 1; b->nz++; high2++;                    \
484     /* shift up all the later entries in this row */      \
485     for (ii=N; ii>=_i; ii--) {                            \
486       rp2[ii+1] = rp2[ii];                                \
487       ap2[ii+1] = ap2[ii];                                \
488     }                                                     \
489     rp2[_i] = col;                                        \
490     ap2[_i] = value;                                      \
491     B->nonzerostate++;                                    \
492     b_noinsert: ;                                         \
493     bilen[row] = nrow2;                                   \
494   }
495 
496 PetscErrorCode MatSetValuesRow_MPIAIJ(Mat A,PetscInt row,const PetscScalar v[])
497 {
498   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)A->data;
499   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)mat->A->data,*b = (Mat_SeqAIJ*)mat->B->data;
500   PetscErrorCode ierr;
501   PetscInt       l,*garray = mat->garray,diag;
502 
503   PetscFunctionBegin;
504   /* code only works for square matrices A */
505 
506   /* find size of row to the left of the diagonal part */
507   ierr = MatGetOwnershipRange(A,&diag,0);CHKERRQ(ierr);
508   row  = row - diag;
509   for (l=0; l<b->i[row+1]-b->i[row]; l++) {
510     if (garray[b->j[b->i[row]+l]] > diag) break;
511   }
512   ierr = PetscMemcpy(b->a+b->i[row],v,l*sizeof(PetscScalar));CHKERRQ(ierr);
513 
514   /* diagonal part */
515   ierr = PetscMemcpy(a->a+a->i[row],v+l,(a->i[row+1]-a->i[row])*sizeof(PetscScalar));CHKERRQ(ierr);
516 
517   /* right of diagonal part */
518   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);
519   PetscFunctionReturn(0);
520 }
521 
522 PetscErrorCode MatSetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode addv)
523 {
524   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
525   PetscScalar    value;
526   PetscErrorCode ierr;
527   PetscInt       i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
528   PetscInt       cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
529   PetscBool      roworiented = aij->roworiented;
530 
531   /* Some Variables required in the macro */
532   Mat        A                 = aij->A;
533   Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
534   PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
535   MatScalar  *aa               = a->a;
536   PetscBool  ignorezeroentries = a->ignorezeroentries;
537   Mat        B                 = aij->B;
538   Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
539   PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
540   MatScalar  *ba               = b->a;
541 
542   PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
543   PetscInt  nonew;
544   MatScalar *ap1,*ap2;
545 
546   PetscFunctionBegin;
547   for (i=0; i<m; i++) {
548     if (im[i] < 0) continue;
549 #if defined(PETSC_USE_DEBUG)
550     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);
551 #endif
552     if (im[i] >= rstart && im[i] < rend) {
553       row      = im[i] - rstart;
554       lastcol1 = -1;
555       rp1      = aj + ai[row];
556       ap1      = aa + ai[row];
557       rmax1    = aimax[row];
558       nrow1    = ailen[row];
559       low1     = 0;
560       high1    = nrow1;
561       lastcol2 = -1;
562       rp2      = bj + bi[row];
563       ap2      = ba + bi[row];
564       rmax2    = bimax[row];
565       nrow2    = bilen[row];
566       low2     = 0;
567       high2    = nrow2;
568 
569       for (j=0; j<n; j++) {
570         if (roworiented) value = v[i*n+j];
571         else             value = v[i+j*m];
572         if (in[j] >= cstart && in[j] < cend) {
573           col   = in[j] - cstart;
574           nonew = a->nonew;
575           if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
576           MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
577         } else if (in[j] < 0) continue;
578 #if defined(PETSC_USE_DEBUG)
579         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);
580 #endif
581         else {
582           if (mat->was_assembled) {
583             if (!aij->colmap) {
584               ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
585             }
586 #if defined(PETSC_USE_CTABLE)
587             ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
588             col--;
589 #else
590             col = aij->colmap[in[j]] - 1;
591 #endif
592             if (col < 0 && !((Mat_SeqAIJ*)(aij->B->data))->nonew) {
593               ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
594               col  =  in[j];
595               /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
596               B     = aij->B;
597               b     = (Mat_SeqAIJ*)B->data;
598               bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j; ba = b->a;
599               rp2   = bj + bi[row];
600               ap2   = ba + bi[row];
601               rmax2 = bimax[row];
602               nrow2 = bilen[row];
603               low2  = 0;
604               high2 = nrow2;
605               bm    = aij->B->rmap->n;
606               ba    = b->a;
607             } 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]);
608           } else col = in[j];
609           nonew = b->nonew;
610           MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
611         }
612       }
613     } else {
614       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]);
615       if (!aij->donotstash) {
616         mat->assembled = PETSC_FALSE;
617         if (roworiented) {
618           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
619         } else {
620           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
621         }
622       }
623     }
624   }
625   PetscFunctionReturn(0);
626 }
627 
628 PetscErrorCode MatGetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],PetscScalar v[])
629 {
630   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
631   PetscErrorCode ierr;
632   PetscInt       i,j,rstart = mat->rmap->rstart,rend = mat->rmap->rend;
633   PetscInt       cstart = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
634 
635   PetscFunctionBegin;
636   for (i=0; i<m; i++) {
637     if (idxm[i] < 0) continue; /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative row: %D",idxm[i]);*/
638     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);
639     if (idxm[i] >= rstart && idxm[i] < rend) {
640       row = idxm[i] - rstart;
641       for (j=0; j<n; j++) {
642         if (idxn[j] < 0) continue; /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column: %D",idxn[j]); */
643         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);
644         if (idxn[j] >= cstart && idxn[j] < cend) {
645           col  = idxn[j] - cstart;
646           ierr = MatGetValues(aij->A,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
647         } else {
648           if (!aij->colmap) {
649             ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
650           }
651 #if defined(PETSC_USE_CTABLE)
652           ierr = PetscTableFind(aij->colmap,idxn[j]+1,&col);CHKERRQ(ierr);
653           col--;
654 #else
655           col = aij->colmap[idxn[j]] - 1;
656 #endif
657           if ((col < 0) || (aij->garray[col] != idxn[j])) *(v+i*n+j) = 0.0;
658           else {
659             ierr = MatGetValues(aij->B,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
660           }
661         }
662       }
663     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only local values currently supported");
664   }
665   PetscFunctionReturn(0);
666 }
667 
668 extern PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat,Vec,Vec);
669 
670 PetscErrorCode MatAssemblyBegin_MPIAIJ(Mat mat,MatAssemblyType mode)
671 {
672   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
673   PetscErrorCode ierr;
674   PetscInt       nstash,reallocs;
675 
676   PetscFunctionBegin;
677   if (aij->donotstash || mat->nooffprocentries) PetscFunctionReturn(0);
678 
679   ierr = MatStashScatterBegin_Private(mat,&mat->stash,mat->rmap->range);CHKERRQ(ierr);
680   ierr = MatStashGetInfo_Private(&mat->stash,&nstash,&reallocs);CHKERRQ(ierr);
681   ierr = PetscInfo2(aij->A,"Stash has %D entries, uses %D mallocs.\n",nstash,reallocs);CHKERRQ(ierr);
682   PetscFunctionReturn(0);
683 }
684 
685 PetscErrorCode MatAssemblyEnd_MPIAIJ(Mat mat,MatAssemblyType mode)
686 {
687   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
688   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)aij->A->data;
689   PetscErrorCode ierr;
690   PetscMPIInt    n;
691   PetscInt       i,j,rstart,ncols,flg;
692   PetscInt       *row,*col;
693   PetscBool      other_disassembled;
694   PetscScalar    *val;
695 
696   /* do not use 'b = (Mat_SeqAIJ*)aij->B->data' as B can be reset in disassembly */
697 
698   PetscFunctionBegin;
699   if (!aij->donotstash && !mat->nooffprocentries) {
700     while (1) {
701       ierr = MatStashScatterGetMesg_Private(&mat->stash,&n,&row,&col,&val,&flg);CHKERRQ(ierr);
702       if (!flg) break;
703 
704       for (i=0; i<n; ) {
705         /* Now identify the consecutive vals belonging to the same row */
706         for (j=i,rstart=row[j]; j<n; j++) {
707           if (row[j] != rstart) break;
708         }
709         if (j < n) ncols = j-i;
710         else       ncols = n-i;
711         /* Now assemble all these values with a single function call */
712         ierr = MatSetValues_MPIAIJ(mat,1,row+i,ncols,col+i,val+i,mat->insertmode);CHKERRQ(ierr);
713 
714         i = j;
715       }
716     }
717     ierr = MatStashScatterEnd_Private(&mat->stash);CHKERRQ(ierr);
718   }
719   ierr = MatAssemblyBegin(aij->A,mode);CHKERRQ(ierr);
720   ierr = MatAssemblyEnd(aij->A,mode);CHKERRQ(ierr);
721 
722   /* determine if any processor has disassembled, if so we must
723      also disassemble ourselfs, in order that we may reassemble. */
724   /*
725      if nonzero structure of submatrix B cannot change then we know that
726      no processor disassembled thus we can skip this stuff
727   */
728   if (!((Mat_SeqAIJ*)aij->B->data)->nonew) {
729     ierr = MPIU_Allreduce(&mat->was_assembled,&other_disassembled,1,MPIU_BOOL,MPI_PROD,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
730     if (mat->was_assembled && !other_disassembled) {
731       ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
732     }
733   }
734   if (!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) {
735     ierr = MatSetUpMultiply_MPIAIJ(mat);CHKERRQ(ierr);
736   }
737   ierr = MatSetOption(aij->B,MAT_USE_INODES,PETSC_FALSE);CHKERRQ(ierr);
738   ierr = MatAssemblyBegin(aij->B,mode);CHKERRQ(ierr);
739   ierr = MatAssemblyEnd(aij->B,mode);CHKERRQ(ierr);
740 
741   ierr = PetscFree2(aij->rowvalues,aij->rowindices);CHKERRQ(ierr);
742 
743   aij->rowvalues = 0;
744 
745   ierr = VecDestroy(&aij->diag);CHKERRQ(ierr);
746   if (a->inode.size) mat->ops->multdiagonalblock = MatMultDiagonalBlock_MPIAIJ;
747 
748   /* if no new nonzero locations are allowed in matrix then only set the matrix state the first time through */
749   if ((!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) || !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
750     PetscObjectState state = aij->A->nonzerostate + aij->B->nonzerostate;
751     ierr = MPIU_Allreduce(&state,&mat->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
752   }
753   PetscFunctionReturn(0);
754 }
755 
756 PetscErrorCode MatZeroEntries_MPIAIJ(Mat A)
757 {
758   Mat_MPIAIJ     *l = (Mat_MPIAIJ*)A->data;
759   PetscErrorCode ierr;
760 
761   PetscFunctionBegin;
762   ierr = MatZeroEntries(l->A);CHKERRQ(ierr);
763   ierr = MatZeroEntries(l->B);CHKERRQ(ierr);
764   PetscFunctionReturn(0);
765 }
766 
767 PetscErrorCode MatZeroRows_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
768 {
769   Mat_MPIAIJ    *mat    = (Mat_MPIAIJ *) A->data;
770   PetscInt      *lrows;
771   PetscInt       r, len;
772   PetscErrorCode ierr;
773 
774   PetscFunctionBegin;
775   /* get locally owned rows */
776   ierr = MatZeroRowsMapLocal_Private(A,N,rows,&len,&lrows);CHKERRQ(ierr);
777   /* fix right hand side if needed */
778   if (x && b) {
779     const PetscScalar *xx;
780     PetscScalar       *bb;
781 
782     ierr = VecGetArrayRead(x, &xx);CHKERRQ(ierr);
783     ierr = VecGetArray(b, &bb);CHKERRQ(ierr);
784     for (r = 0; r < len; ++r) bb[lrows[r]] = diag*xx[lrows[r]];
785     ierr = VecRestoreArrayRead(x, &xx);CHKERRQ(ierr);
786     ierr = VecRestoreArray(b, &bb);CHKERRQ(ierr);
787   }
788   /* Must zero l->B before l->A because the (diag) case below may put values into l->B*/
789   ierr = MatZeroRows(mat->B, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
790   if (A->congruentlayouts == -1) { /* first time we compare rows and cols layouts */
791     PetscBool cong;
792     ierr = PetscLayoutCompare(A->rmap,A->cmap,&cong);CHKERRQ(ierr);
793     if (cong) A->congruentlayouts = 1;
794     else      A->congruentlayouts = 0;
795   }
796   if ((diag != 0.0) && A->congruentlayouts) {
797     ierr = MatZeroRows(mat->A, len, lrows, diag, NULL, NULL);CHKERRQ(ierr);
798   } else if (diag != 0.0) {
799     ierr = MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
800     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");
801     for (r = 0; r < len; ++r) {
802       const PetscInt row = lrows[r] + A->rmap->rstart;
803       ierr = MatSetValues(A, 1, &row, 1, &row, &diag, INSERT_VALUES);CHKERRQ(ierr);
804     }
805     ierr = MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
806     ierr = MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
807   } else {
808     ierr = MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
809   }
810   ierr = PetscFree(lrows);CHKERRQ(ierr);
811 
812   /* only change matrix nonzero state if pattern was allowed to be changed */
813   if (!((Mat_SeqAIJ*)(mat->A->data))->keepnonzeropattern) {
814     PetscObjectState state = mat->A->nonzerostate + mat->B->nonzerostate;
815     ierr = MPIU_Allreduce(&state,&A->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
816   }
817   PetscFunctionReturn(0);
818 }
819 
820 PetscErrorCode MatZeroRowsColumns_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
821 {
822   Mat_MPIAIJ        *l = (Mat_MPIAIJ*)A->data;
823   PetscErrorCode    ierr;
824   PetscMPIInt       n = A->rmap->n;
825   PetscInt          i,j,r,m,p = 0,len = 0;
826   PetscInt          *lrows,*owners = A->rmap->range;
827   PetscSFNode       *rrows;
828   PetscSF           sf;
829   const PetscScalar *xx;
830   PetscScalar       *bb,*mask;
831   Vec               xmask,lmask;
832   Mat_SeqAIJ        *aij = (Mat_SeqAIJ*)l->B->data;
833   const PetscInt    *aj, *ii,*ridx;
834   PetscScalar       *aa;
835 
836   PetscFunctionBegin;
837   /* Create SF where leaves are input rows and roots are owned rows */
838   ierr = PetscMalloc1(n, &lrows);CHKERRQ(ierr);
839   for (r = 0; r < n; ++r) lrows[r] = -1;
840   ierr = PetscMalloc1(N, &rrows);CHKERRQ(ierr);
841   for (r = 0; r < N; ++r) {
842     const PetscInt idx   = rows[r];
843     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);
844     if (idx < owners[p] || owners[p+1] <= idx) { /* short-circuit the search if the last p owns this row too */
845       ierr = PetscLayoutFindOwner(A->rmap,idx,&p);CHKERRQ(ierr);
846     }
847     rrows[r].rank  = p;
848     rrows[r].index = rows[r] - owners[p];
849   }
850   ierr = PetscSFCreate(PetscObjectComm((PetscObject) A), &sf);CHKERRQ(ierr);
851   ierr = PetscSFSetGraph(sf, n, N, NULL, PETSC_OWN_POINTER, rrows, PETSC_OWN_POINTER);CHKERRQ(ierr);
852   /* Collect flags for rows to be zeroed */
853   ierr = PetscSFReduceBegin(sf, MPIU_INT, (PetscInt *) rows, lrows, MPI_LOR);CHKERRQ(ierr);
854   ierr = PetscSFReduceEnd(sf, MPIU_INT, (PetscInt *) rows, lrows, MPI_LOR);CHKERRQ(ierr);
855   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
856   /* Compress and put in row numbers */
857   for (r = 0; r < n; ++r) if (lrows[r] >= 0) lrows[len++] = r;
858   /* zero diagonal part of matrix */
859   ierr = MatZeroRowsColumns(l->A,len,lrows,diag,x,b);CHKERRQ(ierr);
860   /* handle off diagonal part of matrix */
861   ierr = MatCreateVecs(A,&xmask,NULL);CHKERRQ(ierr);
862   ierr = VecDuplicate(l->lvec,&lmask);CHKERRQ(ierr);
863   ierr = VecGetArray(xmask,&bb);CHKERRQ(ierr);
864   for (i=0; i<len; i++) bb[lrows[i]] = 1;
865   ierr = VecRestoreArray(xmask,&bb);CHKERRQ(ierr);
866   ierr = VecScatterBegin(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
867   ierr = VecScatterEnd(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
868   ierr = VecDestroy(&xmask);CHKERRQ(ierr);
869   if (x) {
870     ierr = VecScatterBegin(l->Mvctx,x,l->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
871     ierr = VecScatterEnd(l->Mvctx,x,l->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
872     ierr = VecGetArrayRead(l->lvec,&xx);CHKERRQ(ierr);
873     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
874   }
875   ierr = VecGetArray(lmask,&mask);CHKERRQ(ierr);
876   /* remove zeroed rows of off diagonal matrix */
877   ii = aij->i;
878   for (i=0; i<len; i++) {
879     ierr = PetscMemzero(aij->a + ii[lrows[i]],(ii[lrows[i]+1] - ii[lrows[i]])*sizeof(PetscScalar));CHKERRQ(ierr);
880   }
881   /* loop over all elements of off process part of matrix zeroing removed columns*/
882   if (aij->compressedrow.use) {
883     m    = aij->compressedrow.nrows;
884     ii   = aij->compressedrow.i;
885     ridx = aij->compressedrow.rindex;
886     for (i=0; i<m; i++) {
887       n  = ii[i+1] - ii[i];
888       aj = aij->j + ii[i];
889       aa = aij->a + ii[i];
890 
891       for (j=0; j<n; j++) {
892         if (PetscAbsScalar(mask[*aj])) {
893           if (b) bb[*ridx] -= *aa*xx[*aj];
894           *aa = 0.0;
895         }
896         aa++;
897         aj++;
898       }
899       ridx++;
900     }
901   } else { /* do not use compressed row format */
902     m = l->B->rmap->n;
903     for (i=0; i<m; i++) {
904       n  = ii[i+1] - ii[i];
905       aj = aij->j + ii[i];
906       aa = aij->a + ii[i];
907       for (j=0; j<n; j++) {
908         if (PetscAbsScalar(mask[*aj])) {
909           if (b) bb[i] -= *aa*xx[*aj];
910           *aa = 0.0;
911         }
912         aa++;
913         aj++;
914       }
915     }
916   }
917   if (x) {
918     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
919     ierr = VecRestoreArrayRead(l->lvec,&xx);CHKERRQ(ierr);
920   }
921   ierr = VecRestoreArray(lmask,&mask);CHKERRQ(ierr);
922   ierr = VecDestroy(&lmask);CHKERRQ(ierr);
923   ierr = PetscFree(lrows);CHKERRQ(ierr);
924 
925   /* only change matrix nonzero state if pattern was allowed to be changed */
926   if (!((Mat_SeqAIJ*)(l->A->data))->keepnonzeropattern) {
927     PetscObjectState state = l->A->nonzerostate + l->B->nonzerostate;
928     ierr = MPIU_Allreduce(&state,&A->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
929   }
930   PetscFunctionReturn(0);
931 }
932 
933 PetscErrorCode MatMult_MPIAIJ(Mat A,Vec xx,Vec yy)
934 {
935   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
936   PetscErrorCode ierr;
937   PetscInt       nt;
938 
939   PetscFunctionBegin;
940   ierr = VecGetLocalSize(xx,&nt);CHKERRQ(ierr);
941   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);
942   ierr = VecScatterBegin(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
943   ierr = (*a->A->ops->mult)(a->A,xx,yy);CHKERRQ(ierr);
944   ierr = VecScatterEnd(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
945   ierr = (*a->B->ops->multadd)(a->B,a->lvec,yy,yy);CHKERRQ(ierr);
946   PetscFunctionReturn(0);
947 }
948 
949 PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat A,Vec bb,Vec xx)
950 {
951   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
952   PetscErrorCode ierr;
953 
954   PetscFunctionBegin;
955   ierr = MatMultDiagonalBlock(a->A,bb,xx);CHKERRQ(ierr);
956   PetscFunctionReturn(0);
957 }
958 
959 PetscErrorCode MatMultAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
960 {
961   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
962   PetscErrorCode ierr;
963 
964   PetscFunctionBegin;
965   ierr = VecScatterBegin(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
966   ierr = (*a->A->ops->multadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
967   ierr = VecScatterEnd(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
968   ierr = (*a->B->ops->multadd)(a->B,a->lvec,zz,zz);CHKERRQ(ierr);
969   PetscFunctionReturn(0);
970 }
971 
972 PetscErrorCode MatMultTranspose_MPIAIJ(Mat A,Vec xx,Vec yy)
973 {
974   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
975   PetscErrorCode ierr;
976   PetscBool      merged;
977 
978   PetscFunctionBegin;
979   ierr = VecScatterGetMerged(a->Mvctx,&merged);CHKERRQ(ierr);
980   /* do nondiagonal part */
981   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
982   if (!merged) {
983     /* send it on its way */
984     ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
985     /* do local part */
986     ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
987     /* receive remote parts: note this assumes the values are not actually */
988     /* added in yy until the next line, */
989     ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
990   } else {
991     /* do local part */
992     ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
993     /* send it on its way */
994     ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
995     /* values actually were received in the Begin() but we need to call this nop */
996     ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
997   }
998   PetscFunctionReturn(0);
999 }
1000 
1001 PetscErrorCode MatIsTranspose_MPIAIJ(Mat Amat,Mat Bmat,PetscReal tol,PetscBool  *f)
1002 {
1003   MPI_Comm       comm;
1004   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ*) Amat->data, *Bij;
1005   Mat            Adia = Aij->A, Bdia, Aoff,Boff,*Aoffs,*Boffs;
1006   IS             Me,Notme;
1007   PetscErrorCode ierr;
1008   PetscInt       M,N,first,last,*notme,i;
1009   PetscMPIInt    size;
1010 
1011   PetscFunctionBegin;
1012   /* Easy test: symmetric diagonal block */
1013   Bij  = (Mat_MPIAIJ*) Bmat->data; Bdia = Bij->A;
1014   ierr = MatIsTranspose(Adia,Bdia,tol,f);CHKERRQ(ierr);
1015   if (!*f) PetscFunctionReturn(0);
1016   ierr = PetscObjectGetComm((PetscObject)Amat,&comm);CHKERRQ(ierr);
1017   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1018   if (size == 1) PetscFunctionReturn(0);
1019 
1020   /* Hard test: off-diagonal block. This takes a MatCreateSubMatrix. */
1021   ierr = MatGetSize(Amat,&M,&N);CHKERRQ(ierr);
1022   ierr = MatGetOwnershipRange(Amat,&first,&last);CHKERRQ(ierr);
1023   ierr = PetscMalloc1(N-last+first,&notme);CHKERRQ(ierr);
1024   for (i=0; i<first; i++) notme[i] = i;
1025   for (i=last; i<M; i++) notme[i-last+first] = i;
1026   ierr = ISCreateGeneral(MPI_COMM_SELF,N-last+first,notme,PETSC_COPY_VALUES,&Notme);CHKERRQ(ierr);
1027   ierr = ISCreateStride(MPI_COMM_SELF,last-first,first,1,&Me);CHKERRQ(ierr);
1028   ierr = MatCreateSubMatrices(Amat,1,&Me,&Notme,MAT_INITIAL_MATRIX,&Aoffs);CHKERRQ(ierr);
1029   Aoff = Aoffs[0];
1030   ierr = MatCreateSubMatrices(Bmat,1,&Notme,&Me,MAT_INITIAL_MATRIX,&Boffs);CHKERRQ(ierr);
1031   Boff = Boffs[0];
1032   ierr = MatIsTranspose(Aoff,Boff,tol,f);CHKERRQ(ierr);
1033   ierr = MatDestroyMatrices(1,&Aoffs);CHKERRQ(ierr);
1034   ierr = MatDestroyMatrices(1,&Boffs);CHKERRQ(ierr);
1035   ierr = ISDestroy(&Me);CHKERRQ(ierr);
1036   ierr = ISDestroy(&Notme);CHKERRQ(ierr);
1037   ierr = PetscFree(notme);CHKERRQ(ierr);
1038   PetscFunctionReturn(0);
1039 }
1040 
1041 PetscErrorCode MatMultTransposeAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1042 {
1043   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1044   PetscErrorCode ierr;
1045 
1046   PetscFunctionBegin;
1047   /* do nondiagonal part */
1048   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
1049   /* send it on its way */
1050   ierr = VecScatterBegin(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1051   /* do local part */
1052   ierr = (*a->A->ops->multtransposeadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
1053   /* receive remote parts */
1054   ierr = VecScatterEnd(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1055   PetscFunctionReturn(0);
1056 }
1057 
1058 /*
1059   This only works correctly for square matrices where the subblock A->A is the
1060    diagonal block
1061 */
1062 PetscErrorCode MatGetDiagonal_MPIAIJ(Mat A,Vec v)
1063 {
1064   PetscErrorCode ierr;
1065   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1066 
1067   PetscFunctionBegin;
1068   if (A->rmap->N != A->cmap->N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Supports only square matrix where A->A is diag block");
1069   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");
1070   ierr = MatGetDiagonal(a->A,v);CHKERRQ(ierr);
1071   PetscFunctionReturn(0);
1072 }
1073 
1074 PetscErrorCode MatScale_MPIAIJ(Mat A,PetscScalar aa)
1075 {
1076   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1077   PetscErrorCode ierr;
1078 
1079   PetscFunctionBegin;
1080   ierr = MatScale(a->A,aa);CHKERRQ(ierr);
1081   ierr = MatScale(a->B,aa);CHKERRQ(ierr);
1082   PetscFunctionReturn(0);
1083 }
1084 
1085 PetscErrorCode MatDestroy_MPIAIJ(Mat mat)
1086 {
1087   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1088   PetscErrorCode ierr;
1089 
1090   PetscFunctionBegin;
1091 #if defined(PETSC_USE_LOG)
1092   PetscLogObjectState((PetscObject)mat,"Rows=%D, Cols=%D",mat->rmap->N,mat->cmap->N);
1093 #endif
1094   ierr = MatStashDestroy_Private(&mat->stash);CHKERRQ(ierr);
1095   ierr = VecDestroy(&aij->diag);CHKERRQ(ierr);
1096   ierr = MatDestroy(&aij->A);CHKERRQ(ierr);
1097   ierr = MatDestroy(&aij->B);CHKERRQ(ierr);
1098 #if defined(PETSC_USE_CTABLE)
1099   ierr = PetscTableDestroy(&aij->colmap);CHKERRQ(ierr);
1100 #else
1101   ierr = PetscFree(aij->colmap);CHKERRQ(ierr);
1102 #endif
1103   ierr = PetscFree(aij->garray);CHKERRQ(ierr);
1104   ierr = VecDestroy(&aij->lvec);CHKERRQ(ierr);
1105   ierr = VecScatterDestroy(&aij->Mvctx);CHKERRQ(ierr);
1106   ierr = PetscFree2(aij->rowvalues,aij->rowindices);CHKERRQ(ierr);
1107   ierr = PetscFree(aij->ld);CHKERRQ(ierr);
1108   ierr = PetscFree(mat->data);CHKERRQ(ierr);
1109 
1110   ierr = PetscObjectChangeTypeName((PetscObject)mat,0);CHKERRQ(ierr);
1111   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatStoreValues_C",NULL);CHKERRQ(ierr);
1112   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatRetrieveValues_C",NULL);CHKERRQ(ierr);
1113   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatIsTranspose_C",NULL);CHKERRQ(ierr);
1114   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocation_C",NULL);CHKERRQ(ierr);
1115   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocationCSR_C",NULL);CHKERRQ(ierr);
1116   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDiagonalScaleLocal_C",NULL);CHKERRQ(ierr);
1117   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_mpisbaij_C",NULL);CHKERRQ(ierr);
1118 #if defined(PETSC_HAVE_ELEMENTAL)
1119   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_elemental_C",NULL);CHKERRQ(ierr);
1120 #endif
1121 #if defined(PETSC_HAVE_HYPRE)
1122   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_hypre_C",NULL);CHKERRQ(ierr);
1123   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMatMatMult_transpose_mpiaij_mpiaij_C",NULL);CHKERRQ(ierr);
1124 #endif
1125   PetscFunctionReturn(0);
1126 }
1127 
1128 PetscErrorCode MatView_MPIAIJ_Binary(Mat mat,PetscViewer viewer)
1129 {
1130   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1131   Mat_SeqAIJ     *A   = (Mat_SeqAIJ*)aij->A->data;
1132   Mat_SeqAIJ     *B   = (Mat_SeqAIJ*)aij->B->data;
1133   PetscErrorCode ierr;
1134   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
1135   int            fd;
1136   PetscInt       nz,header[4],*row_lengths,*range=0,rlen,i;
1137   PetscInt       nzmax,*column_indices,j,k,col,*garray = aij->garray,cnt,cstart = mat->cmap->rstart,rnz = 0;
1138   PetscScalar    *column_values;
1139   PetscInt       message_count,flowcontrolcount;
1140   FILE           *file;
1141 
1142   PetscFunctionBegin;
1143   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
1144   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);CHKERRQ(ierr);
1145   nz   = A->nz + B->nz;
1146   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
1147   if (!rank) {
1148     header[0] = MAT_FILE_CLASSID;
1149     header[1] = mat->rmap->N;
1150     header[2] = mat->cmap->N;
1151 
1152     ierr = MPI_Reduce(&nz,&header[3],1,MPIU_INT,MPI_SUM,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1153     ierr = PetscBinaryWrite(fd,header,4,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1154     /* get largest number of rows any processor has */
1155     rlen  = mat->rmap->n;
1156     range = mat->rmap->range;
1157     for (i=1; i<size; i++) rlen = PetscMax(rlen,range[i+1] - range[i]);
1158   } else {
1159     ierr = MPI_Reduce(&nz,0,1,MPIU_INT,MPI_SUM,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1160     rlen = mat->rmap->n;
1161   }
1162 
1163   /* load up the local row counts */
1164   ierr = PetscMalloc1(rlen+1,&row_lengths);CHKERRQ(ierr);
1165   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];
1166 
1167   /* store the row lengths to the file */
1168   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1169   if (!rank) {
1170     ierr = PetscBinaryWrite(fd,row_lengths,mat->rmap->n,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1171     for (i=1; i<size; i++) {
1172       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1173       rlen = range[i+1] - range[i];
1174       ierr = MPIULong_Recv(row_lengths,rlen,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1175       ierr = PetscBinaryWrite(fd,row_lengths,rlen,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1176     }
1177     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1178   } else {
1179     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1180     ierr = MPIULong_Send(row_lengths,mat->rmap->n,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1181     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1182   }
1183   ierr = PetscFree(row_lengths);CHKERRQ(ierr);
1184 
1185   /* load up the local column indices */
1186   nzmax = nz; /* th processor needs space a largest processor needs */
1187   ierr  = MPI_Reduce(&nz,&nzmax,1,MPIU_INT,MPI_MAX,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1188   ierr  = PetscMalloc1(nzmax+1,&column_indices);CHKERRQ(ierr);
1189   cnt   = 0;
1190   for (i=0; i<mat->rmap->n; i++) {
1191     for (j=B->i[i]; j<B->i[i+1]; j++) {
1192       if ((col = garray[B->j[j]]) > cstart) break;
1193       column_indices[cnt++] = col;
1194     }
1195     for (k=A->i[i]; k<A->i[i+1]; k++) column_indices[cnt++] = A->j[k] + cstart;
1196     for (; j<B->i[i+1]; j++) column_indices[cnt++] = garray[B->j[j]];
1197   }
1198   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);
1199 
1200   /* store the column indices to the file */
1201   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1202   if (!rank) {
1203     MPI_Status status;
1204     ierr = PetscBinaryWrite(fd,column_indices,nz,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1205     for (i=1; i<size; i++) {
1206       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1207       ierr = MPI_Recv(&rnz,1,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat),&status);CHKERRQ(ierr);
1208       if (rnz > nzmax) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: nz = %D nzmax = %D",nz,nzmax);
1209       ierr = MPIULong_Recv(column_indices,rnz,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1210       ierr = PetscBinaryWrite(fd,column_indices,rnz,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1211     }
1212     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1213   } else {
1214     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1215     ierr = MPI_Send(&nz,1,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1216     ierr = MPIULong_Send(column_indices,nz,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1217     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1218   }
1219   ierr = PetscFree(column_indices);CHKERRQ(ierr);
1220 
1221   /* load up the local column values */
1222   ierr = PetscMalloc1(nzmax+1,&column_values);CHKERRQ(ierr);
1223   cnt  = 0;
1224   for (i=0; i<mat->rmap->n; i++) {
1225     for (j=B->i[i]; j<B->i[i+1]; j++) {
1226       if (garray[B->j[j]] > cstart) break;
1227       column_values[cnt++] = B->a[j];
1228     }
1229     for (k=A->i[i]; k<A->i[i+1]; k++) column_values[cnt++] = A->a[k];
1230     for (; j<B->i[i+1]; j++) column_values[cnt++] = B->a[j];
1231   }
1232   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);
1233 
1234   /* store the column values to the file */
1235   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1236   if (!rank) {
1237     MPI_Status status;
1238     ierr = PetscBinaryWrite(fd,column_values,nz,PETSC_SCALAR,PETSC_TRUE);CHKERRQ(ierr);
1239     for (i=1; i<size; i++) {
1240       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1241       ierr = MPI_Recv(&rnz,1,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat),&status);CHKERRQ(ierr);
1242       if (rnz > nzmax) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: nz = %D nzmax = %D",nz,nzmax);
1243       ierr = MPIULong_Recv(column_values,rnz,MPIU_SCALAR,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1244       ierr = PetscBinaryWrite(fd,column_values,rnz,PETSC_SCALAR,PETSC_TRUE);CHKERRQ(ierr);
1245     }
1246     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1247   } else {
1248     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1249     ierr = MPI_Send(&nz,1,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1250     ierr = MPIULong_Send(column_values,nz,MPIU_SCALAR,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1251     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1252   }
1253   ierr = PetscFree(column_values);CHKERRQ(ierr);
1254 
1255   ierr = PetscViewerBinaryGetInfoPointer(viewer,&file);CHKERRQ(ierr);
1256   if (file) fprintf(file,"-matload_block_size %d\n",(int)PetscAbs(mat->rmap->bs));
1257   PetscFunctionReturn(0);
1258 }
1259 
1260 #include <petscdraw.h>
1261 PetscErrorCode MatView_MPIAIJ_ASCIIorDraworSocket(Mat mat,PetscViewer viewer)
1262 {
1263   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)mat->data;
1264   PetscErrorCode    ierr;
1265   PetscMPIInt       rank = aij->rank,size = aij->size;
1266   PetscBool         isdraw,iascii,isbinary;
1267   PetscViewer       sviewer;
1268   PetscViewerFormat format;
1269 
1270   PetscFunctionBegin;
1271   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1272   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1273   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1274   if (iascii) {
1275     ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
1276     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
1277       MatInfo   info;
1278       PetscBool inodes;
1279 
1280       ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
1281       ierr = MatGetInfo(mat,MAT_LOCAL,&info);CHKERRQ(ierr);
1282       ierr = MatInodeGetInodeSizes(aij->A,NULL,(PetscInt**)&inodes,NULL);CHKERRQ(ierr);
1283       ierr = PetscViewerASCIIPushSynchronized(viewer);CHKERRQ(ierr);
1284       if (!inodes) {
1285         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %D nz %D nz alloced %D mem %D, not using I-node routines\n",
1286                                                   rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
1287       } else {
1288         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %D nz %D nz alloced %D mem %D, using I-node routines\n",
1289                                                   rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
1290       }
1291       ierr = MatGetInfo(aij->A,MAT_LOCAL,&info);CHKERRQ(ierr);
1292       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] on-diagonal part: nz %D \n",rank,(PetscInt)info.nz_used);CHKERRQ(ierr);
1293       ierr = MatGetInfo(aij->B,MAT_LOCAL,&info);CHKERRQ(ierr);
1294       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] off-diagonal part: nz %D \n",rank,(PetscInt)info.nz_used);CHKERRQ(ierr);
1295       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1296       ierr = PetscViewerASCIIPopSynchronized(viewer);CHKERRQ(ierr);
1297       ierr = PetscViewerASCIIPrintf(viewer,"Information on VecScatter used in matrix-vector product: \n");CHKERRQ(ierr);
1298       ierr = VecScatterView(aij->Mvctx,viewer);CHKERRQ(ierr);
1299       PetscFunctionReturn(0);
1300     } else if (format == PETSC_VIEWER_ASCII_INFO) {
1301       PetscInt inodecount,inodelimit,*inodes;
1302       ierr = MatInodeGetInodeSizes(aij->A,&inodecount,&inodes,&inodelimit);CHKERRQ(ierr);
1303       if (inodes) {
1304         ierr = PetscViewerASCIIPrintf(viewer,"using I-node (on process 0) routines: found %D nodes, limit used is %D\n",inodecount,inodelimit);CHKERRQ(ierr);
1305       } else {
1306         ierr = PetscViewerASCIIPrintf(viewer,"not using I-node (on process 0) routines\n");CHKERRQ(ierr);
1307       }
1308       PetscFunctionReturn(0);
1309     } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO) {
1310       PetscFunctionReturn(0);
1311     }
1312   } else if (isbinary) {
1313     if (size == 1) {
1314       ierr = PetscObjectSetName((PetscObject)aij->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1315       ierr = MatView(aij->A,viewer);CHKERRQ(ierr);
1316     } else {
1317       ierr = MatView_MPIAIJ_Binary(mat,viewer);CHKERRQ(ierr);
1318     }
1319     PetscFunctionReturn(0);
1320   } else if (isdraw) {
1321     PetscDraw draw;
1322     PetscBool isnull;
1323     ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
1324     ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr);
1325     if (isnull) PetscFunctionReturn(0);
1326   }
1327 
1328   {
1329     /* assemble the entire matrix onto first processor. */
1330     Mat        A;
1331     Mat_SeqAIJ *Aloc;
1332     PetscInt   M = mat->rmap->N,N = mat->cmap->N,m,*ai,*aj,row,*cols,i,*ct;
1333     MatScalar  *a;
1334 
1335     ierr = MatCreate(PetscObjectComm((PetscObject)mat),&A);CHKERRQ(ierr);
1336     if (!rank) {
1337       ierr = MatSetSizes(A,M,N,M,N);CHKERRQ(ierr);
1338     } else {
1339       ierr = MatSetSizes(A,0,0,M,N);CHKERRQ(ierr);
1340     }
1341     /* This is just a temporary matrix, so explicitly using MATMPIAIJ is probably best */
1342     ierr = MatSetType(A,MATMPIAIJ);CHKERRQ(ierr);
1343     ierr = MatMPIAIJSetPreallocation(A,0,NULL,0,NULL);CHKERRQ(ierr);
1344     ierr = MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
1345     ierr = PetscLogObjectParent((PetscObject)mat,(PetscObject)A);CHKERRQ(ierr);
1346 
1347     /* copy over the A part */
1348     Aloc = (Mat_SeqAIJ*)aij->A->data;
1349     m    = aij->A->rmap->n; ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
1350     row  = mat->rmap->rstart;
1351     for (i=0; i<ai[m]; i++) aj[i] += mat->cmap->rstart;
1352     for (i=0; i<m; i++) {
1353       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],aj,a,INSERT_VALUES);CHKERRQ(ierr);
1354       row++;
1355       a += ai[i+1]-ai[i]; aj += ai[i+1]-ai[i];
1356     }
1357     aj = Aloc->j;
1358     for (i=0; i<ai[m]; i++) aj[i] -= mat->cmap->rstart;
1359 
1360     /* copy over the B part */
1361     Aloc = (Mat_SeqAIJ*)aij->B->data;
1362     m    = aij->B->rmap->n;  ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
1363     row  = mat->rmap->rstart;
1364     ierr = PetscMalloc1(ai[m]+1,&cols);CHKERRQ(ierr);
1365     ct   = cols;
1366     for (i=0; i<ai[m]; i++) cols[i] = aij->garray[aj[i]];
1367     for (i=0; i<m; i++) {
1368       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],cols,a,INSERT_VALUES);CHKERRQ(ierr);
1369       row++;
1370       a += ai[i+1]-ai[i]; cols += ai[i+1]-ai[i];
1371     }
1372     ierr = PetscFree(ct);CHKERRQ(ierr);
1373     ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1374     ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1375     /*
1376        Everyone has to call to draw the matrix since the graphics waits are
1377        synchronized across all processors that share the PetscDraw object
1378     */
1379     ierr = PetscViewerGetSubViewer(viewer,PETSC_COMM_SELF,&sviewer);CHKERRQ(ierr);
1380     if (!rank) {
1381       ierr = PetscObjectSetName((PetscObject)((Mat_MPIAIJ*)(A->data))->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1382       ierr = MatView_SeqAIJ(((Mat_MPIAIJ*)(A->data))->A,sviewer);CHKERRQ(ierr);
1383     }
1384     ierr = PetscViewerRestoreSubViewer(viewer,PETSC_COMM_SELF,&sviewer);CHKERRQ(ierr);
1385     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1386     ierr = MatDestroy(&A);CHKERRQ(ierr);
1387   }
1388   PetscFunctionReturn(0);
1389 }
1390 
1391 PetscErrorCode MatView_MPIAIJ(Mat mat,PetscViewer viewer)
1392 {
1393   PetscErrorCode ierr;
1394   PetscBool      iascii,isdraw,issocket,isbinary;
1395 
1396   PetscFunctionBegin;
1397   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1398   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1399   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1400   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSOCKET,&issocket);CHKERRQ(ierr);
1401   if (iascii || isdraw || isbinary || issocket) {
1402     ierr = MatView_MPIAIJ_ASCIIorDraworSocket(mat,viewer);CHKERRQ(ierr);
1403   }
1404   PetscFunctionReturn(0);
1405 }
1406 
1407 PetscErrorCode MatSOR_MPIAIJ(Mat matin,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
1408 {
1409   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1410   PetscErrorCode ierr;
1411   Vec            bb1 = 0;
1412   PetscBool      hasop;
1413 
1414   PetscFunctionBegin;
1415   if (flag == SOR_APPLY_UPPER) {
1416     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1417     PetscFunctionReturn(0);
1418   }
1419 
1420   if (its > 1 || ~flag & SOR_ZERO_INITIAL_GUESS || flag & SOR_EISENSTAT) {
1421     ierr = VecDuplicate(bb,&bb1);CHKERRQ(ierr);
1422   }
1423 
1424   if ((flag & SOR_LOCAL_SYMMETRIC_SWEEP) == SOR_LOCAL_SYMMETRIC_SWEEP) {
1425     if (flag & SOR_ZERO_INITIAL_GUESS) {
1426       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1427       its--;
1428     }
1429 
1430     while (its--) {
1431       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1432       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1433 
1434       /* update rhs: bb1 = bb - B*x */
1435       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1436       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1437 
1438       /* local sweep */
1439       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_SYMMETRIC_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1440     }
1441   } else if (flag & SOR_LOCAL_FORWARD_SWEEP) {
1442     if (flag & SOR_ZERO_INITIAL_GUESS) {
1443       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1444       its--;
1445     }
1446     while (its--) {
1447       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1448       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1449 
1450       /* update rhs: bb1 = bb - B*x */
1451       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1452       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1453 
1454       /* local sweep */
1455       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_FORWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1456     }
1457   } else if (flag & SOR_LOCAL_BACKWARD_SWEEP) {
1458     if (flag & SOR_ZERO_INITIAL_GUESS) {
1459       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1460       its--;
1461     }
1462     while (its--) {
1463       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1464       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1465 
1466       /* update rhs: bb1 = bb - B*x */
1467       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1468       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1469 
1470       /* local sweep */
1471       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_BACKWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1472     }
1473   } else if (flag & SOR_EISENSTAT) {
1474     Vec xx1;
1475 
1476     ierr = VecDuplicate(bb,&xx1);CHKERRQ(ierr);
1477     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_BACKWARD_SWEEP),fshift,lits,1,xx);CHKERRQ(ierr);
1478 
1479     ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1480     ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1481     if (!mat->diag) {
1482       ierr = MatCreateVecs(matin,&mat->diag,NULL);CHKERRQ(ierr);
1483       ierr = MatGetDiagonal(matin,mat->diag);CHKERRQ(ierr);
1484     }
1485     ierr = MatHasOperation(matin,MATOP_MULT_DIAGONAL_BLOCK,&hasop);CHKERRQ(ierr);
1486     if (hasop) {
1487       ierr = MatMultDiagonalBlock(matin,xx,bb1);CHKERRQ(ierr);
1488     } else {
1489       ierr = VecPointwiseMult(bb1,mat->diag,xx);CHKERRQ(ierr);
1490     }
1491     ierr = VecAYPX(bb1,(omega-2.0)/omega,bb);CHKERRQ(ierr);
1492 
1493     ierr = MatMultAdd(mat->B,mat->lvec,bb1,bb1);CHKERRQ(ierr);
1494 
1495     /* local sweep */
1496     ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_FORWARD_SWEEP),fshift,lits,1,xx1);CHKERRQ(ierr);
1497     ierr = VecAXPY(xx,1.0,xx1);CHKERRQ(ierr);
1498     ierr = VecDestroy(&xx1);CHKERRQ(ierr);
1499   } else SETERRQ(PetscObjectComm((PetscObject)matin),PETSC_ERR_SUP,"Parallel SOR not supported");
1500 
1501   ierr = VecDestroy(&bb1);CHKERRQ(ierr);
1502 
1503   matin->factorerrortype = mat->A->factorerrortype;
1504   PetscFunctionReturn(0);
1505 }
1506 
1507 PetscErrorCode MatPermute_MPIAIJ(Mat A,IS rowp,IS colp,Mat *B)
1508 {
1509   Mat            aA,aB,Aperm;
1510   const PetscInt *rwant,*cwant,*gcols,*ai,*bi,*aj,*bj;
1511   PetscScalar    *aa,*ba;
1512   PetscInt       i,j,m,n,ng,anz,bnz,*dnnz,*onnz,*tdnnz,*tonnz,*rdest,*cdest,*work,*gcdest;
1513   PetscSF        rowsf,sf;
1514   IS             parcolp = NULL;
1515   PetscBool      done;
1516   PetscErrorCode ierr;
1517 
1518   PetscFunctionBegin;
1519   ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
1520   ierr = ISGetIndices(rowp,&rwant);CHKERRQ(ierr);
1521   ierr = ISGetIndices(colp,&cwant);CHKERRQ(ierr);
1522   ierr = PetscMalloc3(PetscMax(m,n),&work,m,&rdest,n,&cdest);CHKERRQ(ierr);
1523 
1524   /* Invert row permutation to find out where my rows should go */
1525   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&rowsf);CHKERRQ(ierr);
1526   ierr = PetscSFSetGraphLayout(rowsf,A->rmap,A->rmap->n,NULL,PETSC_OWN_POINTER,rwant);CHKERRQ(ierr);
1527   ierr = PetscSFSetFromOptions(rowsf);CHKERRQ(ierr);
1528   for (i=0; i<m; i++) work[i] = A->rmap->rstart + i;
1529   ierr = PetscSFReduceBegin(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1530   ierr = PetscSFReduceEnd(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1531 
1532   /* Invert column permutation to find out where my columns should go */
1533   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1534   ierr = PetscSFSetGraphLayout(sf,A->cmap,A->cmap->n,NULL,PETSC_OWN_POINTER,cwant);CHKERRQ(ierr);
1535   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1536   for (i=0; i<n; i++) work[i] = A->cmap->rstart + i;
1537   ierr = PetscSFReduceBegin(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1538   ierr = PetscSFReduceEnd(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1539   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1540 
1541   ierr = ISRestoreIndices(rowp,&rwant);CHKERRQ(ierr);
1542   ierr = ISRestoreIndices(colp,&cwant);CHKERRQ(ierr);
1543   ierr = MatMPIAIJGetSeqAIJ(A,&aA,&aB,&gcols);CHKERRQ(ierr);
1544 
1545   /* Find out where my gcols should go */
1546   ierr = MatGetSize(aB,NULL,&ng);CHKERRQ(ierr);
1547   ierr = PetscMalloc1(ng,&gcdest);CHKERRQ(ierr);
1548   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1549   ierr = PetscSFSetGraphLayout(sf,A->cmap,ng,NULL,PETSC_OWN_POINTER,gcols);CHKERRQ(ierr);
1550   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1551   ierr = PetscSFBcastBegin(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1552   ierr = PetscSFBcastEnd(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1553   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1554 
1555   ierr = PetscCalloc4(m,&dnnz,m,&onnz,m,&tdnnz,m,&tonnz);CHKERRQ(ierr);
1556   ierr = MatGetRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1557   ierr = MatGetRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1558   for (i=0; i<m; i++) {
1559     PetscInt row = rdest[i],rowner;
1560     ierr = PetscLayoutFindOwner(A->rmap,row,&rowner);CHKERRQ(ierr);
1561     for (j=ai[i]; j<ai[i+1]; j++) {
1562       PetscInt cowner,col = cdest[aj[j]];
1563       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr); /* Could build an index for the columns to eliminate this search */
1564       if (rowner == cowner) dnnz[i]++;
1565       else onnz[i]++;
1566     }
1567     for (j=bi[i]; j<bi[i+1]; j++) {
1568       PetscInt cowner,col = gcdest[bj[j]];
1569       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr);
1570       if (rowner == cowner) dnnz[i]++;
1571       else onnz[i]++;
1572     }
1573   }
1574   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1575   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1576   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1577   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1578   ierr = PetscSFDestroy(&rowsf);CHKERRQ(ierr);
1579 
1580   ierr = MatCreateAIJ(PetscObjectComm((PetscObject)A),A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N,0,tdnnz,0,tonnz,&Aperm);CHKERRQ(ierr);
1581   ierr = MatSeqAIJGetArray(aA,&aa);CHKERRQ(ierr);
1582   ierr = MatSeqAIJGetArray(aB,&ba);CHKERRQ(ierr);
1583   for (i=0; i<m; i++) {
1584     PetscInt *acols = dnnz,*bcols = onnz; /* Repurpose now-unneeded arrays */
1585     PetscInt j0,rowlen;
1586     rowlen = ai[i+1] - ai[i];
1587     for (j0=j=0; j<rowlen; j0=j) { /* rowlen could be larger than number of rows m, so sum in batches */
1588       for ( ; j<PetscMin(rowlen,j0+m); j++) acols[j-j0] = cdest[aj[ai[i]+j]];
1589       ierr = MatSetValues(Aperm,1,&rdest[i],j-j0,acols,aa+ai[i]+j0,INSERT_VALUES);CHKERRQ(ierr);
1590     }
1591     rowlen = bi[i+1] - bi[i];
1592     for (j0=j=0; j<rowlen; j0=j) {
1593       for ( ; j<PetscMin(rowlen,j0+m); j++) bcols[j-j0] = gcdest[bj[bi[i]+j]];
1594       ierr = MatSetValues(Aperm,1,&rdest[i],j-j0,bcols,ba+bi[i]+j0,INSERT_VALUES);CHKERRQ(ierr);
1595     }
1596   }
1597   ierr = MatAssemblyBegin(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1598   ierr = MatAssemblyEnd(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1599   ierr = MatRestoreRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1600   ierr = MatRestoreRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1601   ierr = MatSeqAIJRestoreArray(aA,&aa);CHKERRQ(ierr);
1602   ierr = MatSeqAIJRestoreArray(aB,&ba);CHKERRQ(ierr);
1603   ierr = PetscFree4(dnnz,onnz,tdnnz,tonnz);CHKERRQ(ierr);
1604   ierr = PetscFree3(work,rdest,cdest);CHKERRQ(ierr);
1605   ierr = PetscFree(gcdest);CHKERRQ(ierr);
1606   if (parcolp) {ierr = ISDestroy(&colp);CHKERRQ(ierr);}
1607   *B = Aperm;
1608   PetscFunctionReturn(0);
1609 }
1610 
1611 PetscErrorCode  MatGetGhosts_MPIAIJ(Mat mat,PetscInt *nghosts,const PetscInt *ghosts[])
1612 {
1613   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1614   PetscErrorCode ierr;
1615 
1616   PetscFunctionBegin;
1617   ierr = MatGetSize(aij->B,NULL,nghosts);CHKERRQ(ierr);
1618   if (ghosts) *ghosts = aij->garray;
1619   PetscFunctionReturn(0);
1620 }
1621 
1622 PetscErrorCode MatGetInfo_MPIAIJ(Mat matin,MatInfoType flag,MatInfo *info)
1623 {
1624   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1625   Mat            A    = mat->A,B = mat->B;
1626   PetscErrorCode ierr;
1627   PetscReal      isend[5],irecv[5];
1628 
1629   PetscFunctionBegin;
1630   info->block_size = 1.0;
1631   ierr             = MatGetInfo(A,MAT_LOCAL,info);CHKERRQ(ierr);
1632 
1633   isend[0] = info->nz_used; isend[1] = info->nz_allocated; isend[2] = info->nz_unneeded;
1634   isend[3] = info->memory;  isend[4] = info->mallocs;
1635 
1636   ierr = MatGetInfo(B,MAT_LOCAL,info);CHKERRQ(ierr);
1637 
1638   isend[0] += info->nz_used; isend[1] += info->nz_allocated; isend[2] += info->nz_unneeded;
1639   isend[3] += info->memory;  isend[4] += info->mallocs;
1640   if (flag == MAT_LOCAL) {
1641     info->nz_used      = isend[0];
1642     info->nz_allocated = isend[1];
1643     info->nz_unneeded  = isend[2];
1644     info->memory       = isend[3];
1645     info->mallocs      = isend[4];
1646   } else if (flag == MAT_GLOBAL_MAX) {
1647     ierr = MPIU_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1648 
1649     info->nz_used      = irecv[0];
1650     info->nz_allocated = irecv[1];
1651     info->nz_unneeded  = irecv[2];
1652     info->memory       = irecv[3];
1653     info->mallocs      = irecv[4];
1654   } else if (flag == MAT_GLOBAL_SUM) {
1655     ierr = MPIU_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1656 
1657     info->nz_used      = irecv[0];
1658     info->nz_allocated = irecv[1];
1659     info->nz_unneeded  = irecv[2];
1660     info->memory       = irecv[3];
1661     info->mallocs      = irecv[4];
1662   }
1663   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
1664   info->fill_ratio_needed = 0;
1665   info->factor_mallocs    = 0;
1666   PetscFunctionReturn(0);
1667 }
1668 
1669 PetscErrorCode MatSetOption_MPIAIJ(Mat A,MatOption op,PetscBool flg)
1670 {
1671   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1672   PetscErrorCode ierr;
1673 
1674   PetscFunctionBegin;
1675   switch (op) {
1676   case MAT_NEW_NONZERO_LOCATIONS:
1677   case MAT_NEW_NONZERO_ALLOCATION_ERR:
1678   case MAT_UNUSED_NONZERO_LOCATION_ERR:
1679   case MAT_KEEP_NONZERO_PATTERN:
1680   case MAT_NEW_NONZERO_LOCATION_ERR:
1681   case MAT_USE_INODES:
1682   case MAT_IGNORE_ZERO_ENTRIES:
1683     MatCheckPreallocated(A,1);
1684     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1685     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1686     break;
1687   case MAT_ROW_ORIENTED:
1688     MatCheckPreallocated(A,1);
1689     a->roworiented = flg;
1690 
1691     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1692     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1693     break;
1694   case MAT_NEW_DIAGONALS:
1695     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
1696     break;
1697   case MAT_IGNORE_OFF_PROC_ENTRIES:
1698     a->donotstash = flg;
1699     break;
1700   case MAT_SPD:
1701     A->spd_set = PETSC_TRUE;
1702     A->spd     = flg;
1703     if (flg) {
1704       A->symmetric                  = PETSC_TRUE;
1705       A->structurally_symmetric     = PETSC_TRUE;
1706       A->symmetric_set              = PETSC_TRUE;
1707       A->structurally_symmetric_set = PETSC_TRUE;
1708     }
1709     break;
1710   case MAT_SYMMETRIC:
1711     MatCheckPreallocated(A,1);
1712     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1713     break;
1714   case MAT_STRUCTURALLY_SYMMETRIC:
1715     MatCheckPreallocated(A,1);
1716     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1717     break;
1718   case MAT_HERMITIAN:
1719     MatCheckPreallocated(A,1);
1720     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1721     break;
1722   case MAT_SYMMETRY_ETERNAL:
1723     MatCheckPreallocated(A,1);
1724     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1725     break;
1726   case MAT_SUBMAT_SINGLEIS:
1727     A->submat_singleis = flg;
1728     break;
1729   case MAT_STRUCTURE_ONLY:
1730     /* The option is handled directly by MatSetOption() */
1731     break;
1732   default:
1733     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %d",op);
1734   }
1735   PetscFunctionReturn(0);
1736 }
1737 
1738 PetscErrorCode MatGetRow_MPIAIJ(Mat matin,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1739 {
1740   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1741   PetscScalar    *vworkA,*vworkB,**pvA,**pvB,*v_p;
1742   PetscErrorCode ierr;
1743   PetscInt       i,*cworkA,*cworkB,**pcA,**pcB,cstart = matin->cmap->rstart;
1744   PetscInt       nztot,nzA,nzB,lrow,rstart = matin->rmap->rstart,rend = matin->rmap->rend;
1745   PetscInt       *cmap,*idx_p;
1746 
1747   PetscFunctionBegin;
1748   if (mat->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Already active");
1749   mat->getrowactive = PETSC_TRUE;
1750 
1751   if (!mat->rowvalues && (idx || v)) {
1752     /*
1753         allocate enough space to hold information from the longest row.
1754     */
1755     Mat_SeqAIJ *Aa = (Mat_SeqAIJ*)mat->A->data,*Ba = (Mat_SeqAIJ*)mat->B->data;
1756     PetscInt   max = 1,tmp;
1757     for (i=0; i<matin->rmap->n; i++) {
1758       tmp = Aa->i[i+1] - Aa->i[i] + Ba->i[i+1] - Ba->i[i];
1759       if (max < tmp) max = tmp;
1760     }
1761     ierr = PetscMalloc2(max,&mat->rowvalues,max,&mat->rowindices);CHKERRQ(ierr);
1762   }
1763 
1764   if (row < rstart || row >= rend) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Only local rows");
1765   lrow = row - rstart;
1766 
1767   pvA = &vworkA; pcA = &cworkA; pvB = &vworkB; pcB = &cworkB;
1768   if (!v)   {pvA = 0; pvB = 0;}
1769   if (!idx) {pcA = 0; if (!v) pcB = 0;}
1770   ierr  = (*mat->A->ops->getrow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1771   ierr  = (*mat->B->ops->getrow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1772   nztot = nzA + nzB;
1773 
1774   cmap = mat->garray;
1775   if (v  || idx) {
1776     if (nztot) {
1777       /* Sort by increasing column numbers, assuming A and B already sorted */
1778       PetscInt imark = -1;
1779       if (v) {
1780         *v = v_p = mat->rowvalues;
1781         for (i=0; i<nzB; i++) {
1782           if (cmap[cworkB[i]] < cstart) v_p[i] = vworkB[i];
1783           else break;
1784         }
1785         imark = i;
1786         for (i=0; i<nzA; i++)     v_p[imark+i] = vworkA[i];
1787         for (i=imark; i<nzB; i++) v_p[nzA+i]   = vworkB[i];
1788       }
1789       if (idx) {
1790         *idx = idx_p = mat->rowindices;
1791         if (imark > -1) {
1792           for (i=0; i<imark; i++) {
1793             idx_p[i] = cmap[cworkB[i]];
1794           }
1795         } else {
1796           for (i=0; i<nzB; i++) {
1797             if (cmap[cworkB[i]] < cstart) idx_p[i] = cmap[cworkB[i]];
1798             else break;
1799           }
1800           imark = i;
1801         }
1802         for (i=0; i<nzA; i++)     idx_p[imark+i] = cstart + cworkA[i];
1803         for (i=imark; i<nzB; i++) idx_p[nzA+i]   = cmap[cworkB[i]];
1804       }
1805     } else {
1806       if (idx) *idx = 0;
1807       if (v)   *v   = 0;
1808     }
1809   }
1810   *nz  = nztot;
1811   ierr = (*mat->A->ops->restorerow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1812   ierr = (*mat->B->ops->restorerow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1813   PetscFunctionReturn(0);
1814 }
1815 
1816 PetscErrorCode MatRestoreRow_MPIAIJ(Mat mat,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1817 {
1818   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1819 
1820   PetscFunctionBegin;
1821   if (!aij->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"MatGetRow() must be called first");
1822   aij->getrowactive = PETSC_FALSE;
1823   PetscFunctionReturn(0);
1824 }
1825 
1826 PetscErrorCode MatNorm_MPIAIJ(Mat mat,NormType type,PetscReal *norm)
1827 {
1828   Mat_MPIAIJ     *aij  = (Mat_MPIAIJ*)mat->data;
1829   Mat_SeqAIJ     *amat = (Mat_SeqAIJ*)aij->A->data,*bmat = (Mat_SeqAIJ*)aij->B->data;
1830   PetscErrorCode ierr;
1831   PetscInt       i,j,cstart = mat->cmap->rstart;
1832   PetscReal      sum = 0.0;
1833   MatScalar      *v;
1834 
1835   PetscFunctionBegin;
1836   if (aij->size == 1) {
1837     ierr =  MatNorm(aij->A,type,norm);CHKERRQ(ierr);
1838   } else {
1839     if (type == NORM_FROBENIUS) {
1840       v = amat->a;
1841       for (i=0; i<amat->nz; i++) {
1842         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1843       }
1844       v = bmat->a;
1845       for (i=0; i<bmat->nz; i++) {
1846         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1847       }
1848       ierr  = MPIU_Allreduce(&sum,norm,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1849       *norm = PetscSqrtReal(*norm);
1850       ierr = PetscLogFlops(2*amat->nz+2*bmat->nz);CHKERRQ(ierr);
1851     } else if (type == NORM_1) { /* max column norm */
1852       PetscReal *tmp,*tmp2;
1853       PetscInt  *jj,*garray = aij->garray;
1854       ierr  = PetscCalloc1(mat->cmap->N+1,&tmp);CHKERRQ(ierr);
1855       ierr  = PetscMalloc1(mat->cmap->N+1,&tmp2);CHKERRQ(ierr);
1856       *norm = 0.0;
1857       v     = amat->a; jj = amat->j;
1858       for (j=0; j<amat->nz; j++) {
1859         tmp[cstart + *jj++] += PetscAbsScalar(*v);  v++;
1860       }
1861       v = bmat->a; jj = bmat->j;
1862       for (j=0; j<bmat->nz; j++) {
1863         tmp[garray[*jj++]] += PetscAbsScalar(*v); v++;
1864       }
1865       ierr = MPIU_Allreduce(tmp,tmp2,mat->cmap->N,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1866       for (j=0; j<mat->cmap->N; j++) {
1867         if (tmp2[j] > *norm) *norm = tmp2[j];
1868       }
1869       ierr = PetscFree(tmp);CHKERRQ(ierr);
1870       ierr = PetscFree(tmp2);CHKERRQ(ierr);
1871       ierr = PetscLogFlops(PetscMax(amat->nz+bmat->nz-1,0));CHKERRQ(ierr);
1872     } else if (type == NORM_INFINITY) { /* max row norm */
1873       PetscReal ntemp = 0.0;
1874       for (j=0; j<aij->A->rmap->n; j++) {
1875         v   = amat->a + amat->i[j];
1876         sum = 0.0;
1877         for (i=0; i<amat->i[j+1]-amat->i[j]; i++) {
1878           sum += PetscAbsScalar(*v); v++;
1879         }
1880         v = bmat->a + bmat->i[j];
1881         for (i=0; i<bmat->i[j+1]-bmat->i[j]; i++) {
1882           sum += PetscAbsScalar(*v); v++;
1883         }
1884         if (sum > ntemp) ntemp = sum;
1885       }
1886       ierr = MPIU_Allreduce(&ntemp,norm,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1887       ierr = PetscLogFlops(PetscMax(amat->nz+bmat->nz-1,0));CHKERRQ(ierr);
1888     } else SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"No support for two norm");
1889   }
1890   PetscFunctionReturn(0);
1891 }
1892 
1893 PetscErrorCode MatTranspose_MPIAIJ(Mat A,MatReuse reuse,Mat *matout)
1894 {
1895   Mat_MPIAIJ     *a   = (Mat_MPIAIJ*)A->data;
1896   Mat_SeqAIJ     *Aloc=(Mat_SeqAIJ*)a->A->data,*Bloc=(Mat_SeqAIJ*)a->B->data;
1897   PetscErrorCode ierr;
1898   PetscInt       M      = A->rmap->N,N = A->cmap->N,ma,na,mb,nb,*ai,*aj,*bi,*bj,row,*cols,*cols_tmp,i;
1899   PetscInt       cstart = A->cmap->rstart,ncol;
1900   Mat            B;
1901   MatScalar      *array;
1902 
1903   PetscFunctionBegin;
1904   if (reuse == MAT_INPLACE_MATRIX && M != N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Square matrix only for in-place");
1905 
1906   ma = A->rmap->n; na = A->cmap->n; mb = a->B->rmap->n; nb = a->B->cmap->n;
1907   ai = Aloc->i; aj = Aloc->j;
1908   bi = Bloc->i; bj = Bloc->j;
1909   if (reuse == MAT_INITIAL_MATRIX || *matout == A) {
1910     PetscInt             *d_nnz,*g_nnz,*o_nnz;
1911     PetscSFNode          *oloc;
1912     PETSC_UNUSED PetscSF sf;
1913 
1914     ierr = PetscMalloc4(na,&d_nnz,na,&o_nnz,nb,&g_nnz,nb,&oloc);CHKERRQ(ierr);
1915     /* compute d_nnz for preallocation */
1916     ierr = PetscMemzero(d_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1917     for (i=0; i<ai[ma]; i++) {
1918       d_nnz[aj[i]]++;
1919       aj[i] += cstart; /* global col index to be used by MatSetValues() */
1920     }
1921     /* compute local off-diagonal contributions */
1922     ierr = PetscMemzero(g_nnz,nb*sizeof(PetscInt));CHKERRQ(ierr);
1923     for (i=0; i<bi[ma]; i++) g_nnz[bj[i]]++;
1924     /* map those to global */
1925     ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1926     ierr = PetscSFSetGraphLayout(sf,A->cmap,nb,NULL,PETSC_USE_POINTER,a->garray);CHKERRQ(ierr);
1927     ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1928     ierr = PetscMemzero(o_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1929     ierr = PetscSFReduceBegin(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
1930     ierr = PetscSFReduceEnd(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
1931     ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1932 
1933     ierr = MatCreate(PetscObjectComm((PetscObject)A),&B);CHKERRQ(ierr);
1934     ierr = MatSetSizes(B,A->cmap->n,A->rmap->n,N,M);CHKERRQ(ierr);
1935     ierr = MatSetBlockSizes(B,PetscAbs(A->cmap->bs),PetscAbs(A->rmap->bs));CHKERRQ(ierr);
1936     ierr = MatSetType(B,((PetscObject)A)->type_name);CHKERRQ(ierr);
1937     ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
1938     ierr = PetscFree4(d_nnz,o_nnz,g_nnz,oloc);CHKERRQ(ierr);
1939   } else {
1940     B    = *matout;
1941     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
1942     for (i=0; i<ai[ma]; i++) aj[i] += cstart; /* global col index to be used by MatSetValues() */
1943   }
1944 
1945   /* copy over the A part */
1946   array = Aloc->a;
1947   row   = A->rmap->rstart;
1948   for (i=0; i<ma; i++) {
1949     ncol = ai[i+1]-ai[i];
1950     ierr = MatSetValues(B,ncol,aj,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
1951     row++;
1952     array += ncol; aj += ncol;
1953   }
1954   aj = Aloc->j;
1955   for (i=0; i<ai[ma]; i++) aj[i] -= cstart; /* resume local col index */
1956 
1957   /* copy over the B part */
1958   ierr  = PetscCalloc1(bi[mb],&cols);CHKERRQ(ierr);
1959   array = Bloc->a;
1960   row   = A->rmap->rstart;
1961   for (i=0; i<bi[mb]; i++) cols[i] = a->garray[bj[i]];
1962   cols_tmp = cols;
1963   for (i=0; i<mb; i++) {
1964     ncol = bi[i+1]-bi[i];
1965     ierr = MatSetValues(B,ncol,cols_tmp,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
1966     row++;
1967     array += ncol; cols_tmp += ncol;
1968   }
1969   ierr = PetscFree(cols);CHKERRQ(ierr);
1970 
1971   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1972   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1973   if (reuse == MAT_INITIAL_MATRIX || reuse == MAT_REUSE_MATRIX) {
1974     *matout = B;
1975   } else {
1976     ierr = MatHeaderMerge(A,&B);CHKERRQ(ierr);
1977   }
1978   PetscFunctionReturn(0);
1979 }
1980 
1981 PetscErrorCode MatDiagonalScale_MPIAIJ(Mat mat,Vec ll,Vec rr)
1982 {
1983   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1984   Mat            a    = aij->A,b = aij->B;
1985   PetscErrorCode ierr;
1986   PetscInt       s1,s2,s3;
1987 
1988   PetscFunctionBegin;
1989   ierr = MatGetLocalSize(mat,&s2,&s3);CHKERRQ(ierr);
1990   if (rr) {
1991     ierr = VecGetLocalSize(rr,&s1);CHKERRQ(ierr);
1992     if (s1!=s3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"right vector non-conforming local size");
1993     /* Overlap communication with computation. */
1994     ierr = VecScatterBegin(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1995   }
1996   if (ll) {
1997     ierr = VecGetLocalSize(ll,&s1);CHKERRQ(ierr);
1998     if (s1!=s2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"left vector non-conforming local size");
1999     ierr = (*b->ops->diagonalscale)(b,ll,0);CHKERRQ(ierr);
2000   }
2001   /* scale  the diagonal block */
2002   ierr = (*a->ops->diagonalscale)(a,ll,rr);CHKERRQ(ierr);
2003 
2004   if (rr) {
2005     /* Do a scatter end and then right scale the off-diagonal block */
2006     ierr = VecScatterEnd(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2007     ierr = (*b->ops->diagonalscale)(b,0,aij->lvec);CHKERRQ(ierr);
2008   }
2009   PetscFunctionReturn(0);
2010 }
2011 
2012 PetscErrorCode MatSetUnfactored_MPIAIJ(Mat A)
2013 {
2014   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2015   PetscErrorCode ierr;
2016 
2017   PetscFunctionBegin;
2018   ierr = MatSetUnfactored(a->A);CHKERRQ(ierr);
2019   PetscFunctionReturn(0);
2020 }
2021 
2022 PetscErrorCode MatEqual_MPIAIJ(Mat A,Mat B,PetscBool  *flag)
2023 {
2024   Mat_MPIAIJ     *matB = (Mat_MPIAIJ*)B->data,*matA = (Mat_MPIAIJ*)A->data;
2025   Mat            a,b,c,d;
2026   PetscBool      flg;
2027   PetscErrorCode ierr;
2028 
2029   PetscFunctionBegin;
2030   a = matA->A; b = matA->B;
2031   c = matB->A; d = matB->B;
2032 
2033   ierr = MatEqual(a,c,&flg);CHKERRQ(ierr);
2034   if (flg) {
2035     ierr = MatEqual(b,d,&flg);CHKERRQ(ierr);
2036   }
2037   ierr = MPIU_Allreduce(&flg,flag,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
2038   PetscFunctionReturn(0);
2039 }
2040 
2041 PetscErrorCode MatCopy_MPIAIJ(Mat A,Mat B,MatStructure str)
2042 {
2043   PetscErrorCode ierr;
2044   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2045   Mat_MPIAIJ     *b = (Mat_MPIAIJ*)B->data;
2046 
2047   PetscFunctionBegin;
2048   /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
2049   if ((str != SAME_NONZERO_PATTERN) || (A->ops->copy != B->ops->copy)) {
2050     /* because of the column compression in the off-processor part of the matrix a->B,
2051        the number of columns in a->B and b->B may be different, hence we cannot call
2052        the MatCopy() directly on the two parts. If need be, we can provide a more
2053        efficient copy than the MatCopy_Basic() by first uncompressing the a->B matrices
2054        then copying the submatrices */
2055     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
2056   } else {
2057     ierr = MatCopy(a->A,b->A,str);CHKERRQ(ierr);
2058     ierr = MatCopy(a->B,b->B,str);CHKERRQ(ierr);
2059   }
2060   PetscFunctionReturn(0);
2061 }
2062 
2063 PetscErrorCode MatSetUp_MPIAIJ(Mat A)
2064 {
2065   PetscErrorCode ierr;
2066 
2067   PetscFunctionBegin;
2068   ierr =  MatMPIAIJSetPreallocation(A,PETSC_DEFAULT,0,PETSC_DEFAULT,0);CHKERRQ(ierr);
2069   PetscFunctionReturn(0);
2070 }
2071 
2072 /*
2073    Computes the number of nonzeros per row needed for preallocation when X and Y
2074    have different nonzero structure.
2075 */
2076 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)
2077 {
2078   PetscInt       i,j,k,nzx,nzy;
2079 
2080   PetscFunctionBegin;
2081   /* Set the number of nonzeros in the new matrix */
2082   for (i=0; i<m; i++) {
2083     const PetscInt *xjj = xj+xi[i],*yjj = yj+yi[i];
2084     nzx = xi[i+1] - xi[i];
2085     nzy = yi[i+1] - yi[i];
2086     nnz[i] = 0;
2087     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2088       for (; k<nzy && yltog[yjj[k]]<xltog[xjj[j]]; k++) nnz[i]++; /* Catch up to X */
2089       if (k<nzy && yltog[yjj[k]]==xltog[xjj[j]]) k++;             /* Skip duplicate */
2090       nnz[i]++;
2091     }
2092     for (; k<nzy; k++) nnz[i]++;
2093   }
2094   PetscFunctionReturn(0);
2095 }
2096 
2097 /* This is the same as MatAXPYGetPreallocation_SeqAIJ, except that the local-to-global map is provided */
2098 static PetscErrorCode MatAXPYGetPreallocation_MPIAIJ(Mat Y,const PetscInt *yltog,Mat X,const PetscInt *xltog,PetscInt *nnz)
2099 {
2100   PetscErrorCode ierr;
2101   PetscInt       m = Y->rmap->N;
2102   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data;
2103   Mat_SeqAIJ     *y = (Mat_SeqAIJ*)Y->data;
2104 
2105   PetscFunctionBegin;
2106   ierr = MatAXPYGetPreallocation_MPIX_private(m,x->i,x->j,xltog,y->i,y->j,yltog,nnz);CHKERRQ(ierr);
2107   PetscFunctionReturn(0);
2108 }
2109 
2110 PetscErrorCode MatAXPY_MPIAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
2111 {
2112   PetscErrorCode ierr;
2113   Mat_MPIAIJ     *xx = (Mat_MPIAIJ*)X->data,*yy = (Mat_MPIAIJ*)Y->data;
2114   PetscBLASInt   bnz,one=1;
2115   Mat_SeqAIJ     *x,*y;
2116 
2117   PetscFunctionBegin;
2118   if (str == SAME_NONZERO_PATTERN) {
2119     PetscScalar alpha = a;
2120     x    = (Mat_SeqAIJ*)xx->A->data;
2121     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2122     y    = (Mat_SeqAIJ*)yy->A->data;
2123     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2124     x    = (Mat_SeqAIJ*)xx->B->data;
2125     y    = (Mat_SeqAIJ*)yy->B->data;
2126     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2127     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2128     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
2129   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
2130     ierr = MatAXPY_Basic(Y,a,X,str);CHKERRQ(ierr);
2131   } else {
2132     Mat      B;
2133     PetscInt *nnz_d,*nnz_o;
2134     ierr = PetscMalloc1(yy->A->rmap->N,&nnz_d);CHKERRQ(ierr);
2135     ierr = PetscMalloc1(yy->B->rmap->N,&nnz_o);CHKERRQ(ierr);
2136     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
2137     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
2138     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
2139     ierr = MatSetBlockSizesFromMats(B,Y,Y);CHKERRQ(ierr);
2140     ierr = MatSetType(B,MATMPIAIJ);CHKERRQ(ierr);
2141     ierr = MatAXPYGetPreallocation_SeqAIJ(yy->A,xx->A,nnz_d);CHKERRQ(ierr);
2142     ierr = MatAXPYGetPreallocation_MPIAIJ(yy->B,yy->garray,xx->B,xx->garray,nnz_o);CHKERRQ(ierr);
2143     ierr = MatMPIAIJSetPreallocation(B,0,nnz_d,0,nnz_o);CHKERRQ(ierr);
2144     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
2145     ierr = MatHeaderReplace(Y,&B);CHKERRQ(ierr);
2146     ierr = PetscFree(nnz_d);CHKERRQ(ierr);
2147     ierr = PetscFree(nnz_o);CHKERRQ(ierr);
2148   }
2149   PetscFunctionReturn(0);
2150 }
2151 
2152 extern PetscErrorCode  MatConjugate_SeqAIJ(Mat);
2153 
2154 PetscErrorCode  MatConjugate_MPIAIJ(Mat mat)
2155 {
2156 #if defined(PETSC_USE_COMPLEX)
2157   PetscErrorCode ierr;
2158   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2159 
2160   PetscFunctionBegin;
2161   ierr = MatConjugate_SeqAIJ(aij->A);CHKERRQ(ierr);
2162   ierr = MatConjugate_SeqAIJ(aij->B);CHKERRQ(ierr);
2163 #else
2164   PetscFunctionBegin;
2165 #endif
2166   PetscFunctionReturn(0);
2167 }
2168 
2169 PetscErrorCode MatRealPart_MPIAIJ(Mat A)
2170 {
2171   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2172   PetscErrorCode ierr;
2173 
2174   PetscFunctionBegin;
2175   ierr = MatRealPart(a->A);CHKERRQ(ierr);
2176   ierr = MatRealPart(a->B);CHKERRQ(ierr);
2177   PetscFunctionReturn(0);
2178 }
2179 
2180 PetscErrorCode MatImaginaryPart_MPIAIJ(Mat A)
2181 {
2182   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2183   PetscErrorCode ierr;
2184 
2185   PetscFunctionBegin;
2186   ierr = MatImaginaryPart(a->A);CHKERRQ(ierr);
2187   ierr = MatImaginaryPart(a->B);CHKERRQ(ierr);
2188   PetscFunctionReturn(0);
2189 }
2190 
2191 PetscErrorCode MatGetRowMaxAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2192 {
2193   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2194   PetscErrorCode ierr;
2195   PetscInt       i,*idxb = 0;
2196   PetscScalar    *va,*vb;
2197   Vec            vtmp;
2198 
2199   PetscFunctionBegin;
2200   ierr = MatGetRowMaxAbs(a->A,v,idx);CHKERRQ(ierr);
2201   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2202   if (idx) {
2203     for (i=0; i<A->rmap->n; i++) {
2204       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2205     }
2206   }
2207 
2208   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2209   if (idx) {
2210     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2211   }
2212   ierr = MatGetRowMaxAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2213   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2214 
2215   for (i=0; i<A->rmap->n; i++) {
2216     if (PetscAbsScalar(va[i]) < PetscAbsScalar(vb[i])) {
2217       va[i] = vb[i];
2218       if (idx) idx[i] = a->garray[idxb[i]];
2219     }
2220   }
2221 
2222   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2223   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2224   ierr = PetscFree(idxb);CHKERRQ(ierr);
2225   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2226   PetscFunctionReturn(0);
2227 }
2228 
2229 PetscErrorCode MatGetRowMinAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2230 {
2231   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2232   PetscErrorCode ierr;
2233   PetscInt       i,*idxb = 0;
2234   PetscScalar    *va,*vb;
2235   Vec            vtmp;
2236 
2237   PetscFunctionBegin;
2238   ierr = MatGetRowMinAbs(a->A,v,idx);CHKERRQ(ierr);
2239   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2240   if (idx) {
2241     for (i=0; i<A->cmap->n; i++) {
2242       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2243     }
2244   }
2245 
2246   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2247   if (idx) {
2248     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2249   }
2250   ierr = MatGetRowMinAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2251   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2252 
2253   for (i=0; i<A->rmap->n; i++) {
2254     if (PetscAbsScalar(va[i]) > PetscAbsScalar(vb[i])) {
2255       va[i] = vb[i];
2256       if (idx) idx[i] = a->garray[idxb[i]];
2257     }
2258   }
2259 
2260   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2261   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2262   ierr = PetscFree(idxb);CHKERRQ(ierr);
2263   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2264   PetscFunctionReturn(0);
2265 }
2266 
2267 PetscErrorCode MatGetRowMin_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2268 {
2269   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2270   PetscInt       n      = A->rmap->n;
2271   PetscInt       cstart = A->cmap->rstart;
2272   PetscInt       *cmap  = mat->garray;
2273   PetscInt       *diagIdx, *offdiagIdx;
2274   Vec            diagV, offdiagV;
2275   PetscScalar    *a, *diagA, *offdiagA;
2276   PetscInt       r;
2277   PetscErrorCode ierr;
2278 
2279   PetscFunctionBegin;
2280   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2281   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &diagV);CHKERRQ(ierr);
2282   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &offdiagV);CHKERRQ(ierr);
2283   ierr = MatGetRowMin(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2284   ierr = MatGetRowMin(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2285   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2286   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2287   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2288   for (r = 0; r < n; ++r) {
2289     if (PetscAbsScalar(diagA[r]) <= PetscAbsScalar(offdiagA[r])) {
2290       a[r]   = diagA[r];
2291       idx[r] = cstart + diagIdx[r];
2292     } else {
2293       a[r]   = offdiagA[r];
2294       idx[r] = cmap[offdiagIdx[r]];
2295     }
2296   }
2297   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2298   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2299   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2300   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2301   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2302   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2303   PetscFunctionReturn(0);
2304 }
2305 
2306 PetscErrorCode MatGetRowMax_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2307 {
2308   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2309   PetscInt       n      = A->rmap->n;
2310   PetscInt       cstart = A->cmap->rstart;
2311   PetscInt       *cmap  = mat->garray;
2312   PetscInt       *diagIdx, *offdiagIdx;
2313   Vec            diagV, offdiagV;
2314   PetscScalar    *a, *diagA, *offdiagA;
2315   PetscInt       r;
2316   PetscErrorCode ierr;
2317 
2318   PetscFunctionBegin;
2319   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2320   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &diagV);CHKERRQ(ierr);
2321   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &offdiagV);CHKERRQ(ierr);
2322   ierr = MatGetRowMax(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2323   ierr = MatGetRowMax(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2324   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2325   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2326   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2327   for (r = 0; r < n; ++r) {
2328     if (PetscAbsScalar(diagA[r]) >= PetscAbsScalar(offdiagA[r])) {
2329       a[r]   = diagA[r];
2330       idx[r] = cstart + diagIdx[r];
2331     } else {
2332       a[r]   = offdiagA[r];
2333       idx[r] = cmap[offdiagIdx[r]];
2334     }
2335   }
2336   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2337   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2338   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2339   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2340   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2341   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2342   PetscFunctionReturn(0);
2343 }
2344 
2345 PetscErrorCode MatGetSeqNonzeroStructure_MPIAIJ(Mat mat,Mat *newmat)
2346 {
2347   PetscErrorCode ierr;
2348   Mat            *dummy;
2349 
2350   PetscFunctionBegin;
2351   ierr    = MatCreateSubMatrix_MPIAIJ_All(mat,MAT_DO_NOT_GET_VALUES,MAT_INITIAL_MATRIX,&dummy);CHKERRQ(ierr);
2352   *newmat = *dummy;
2353   ierr    = PetscFree(dummy);CHKERRQ(ierr);
2354   PetscFunctionReturn(0);
2355 }
2356 
2357 PetscErrorCode  MatInvertBlockDiagonal_MPIAIJ(Mat A,const PetscScalar **values)
2358 {
2359   Mat_MPIAIJ     *a = (Mat_MPIAIJ*) A->data;
2360   PetscErrorCode ierr;
2361 
2362   PetscFunctionBegin;
2363   ierr = MatInvertBlockDiagonal(a->A,values);CHKERRQ(ierr);
2364   A->factorerrortype = a->A->factorerrortype;
2365   PetscFunctionReturn(0);
2366 }
2367 
2368 static PetscErrorCode  MatSetRandom_MPIAIJ(Mat x,PetscRandom rctx)
2369 {
2370   PetscErrorCode ierr;
2371   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)x->data;
2372 
2373   PetscFunctionBegin;
2374   ierr = MatSetRandom(aij->A,rctx);CHKERRQ(ierr);
2375   ierr = MatSetRandom(aij->B,rctx);CHKERRQ(ierr);
2376   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2377   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2378   PetscFunctionReturn(0);
2379 }
2380 
2381 PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ(Mat A,PetscBool sc)
2382 {
2383   PetscFunctionBegin;
2384   if (sc) A->ops->increaseoverlap = MatIncreaseOverlap_MPIAIJ_Scalable;
2385   else A->ops->increaseoverlap    = MatIncreaseOverlap_MPIAIJ;
2386   PetscFunctionReturn(0);
2387 }
2388 
2389 /*@
2390    MatMPIAIJSetUseScalableIncreaseOverlap - Determine if the matrix uses a scalable algorithm to compute the overlap
2391 
2392    Collective on Mat
2393 
2394    Input Parameters:
2395 +    A - the matrix
2396 -    sc - PETSC_TRUE indicates use the scalable algorithm (default is not to use the scalable algorithm)
2397 
2398  Level: advanced
2399 
2400 @*/
2401 PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap(Mat A,PetscBool sc)
2402 {
2403   PetscErrorCode       ierr;
2404 
2405   PetscFunctionBegin;
2406   ierr = PetscTryMethod(A,"MatMPIAIJSetUseScalableIncreaseOverlap_C",(Mat,PetscBool),(A,sc));CHKERRQ(ierr);
2407   PetscFunctionReturn(0);
2408 }
2409 
2410 PetscErrorCode MatSetFromOptions_MPIAIJ(PetscOptionItems *PetscOptionsObject,Mat A)
2411 {
2412   PetscErrorCode       ierr;
2413   PetscBool            sc = PETSC_FALSE,flg;
2414 
2415   PetscFunctionBegin;
2416   ierr = PetscOptionsHead(PetscOptionsObject,"MPIAIJ options");CHKERRQ(ierr);
2417   ierr = PetscObjectOptionsBegin((PetscObject)A);
2418     if (A->ops->increaseoverlap == MatIncreaseOverlap_MPIAIJ_Scalable) sc = PETSC_TRUE;
2419     ierr = PetscOptionsBool("-mat_increase_overlap_scalable","Use a scalable algorithm to compute the overlap","MatIncreaseOverlap",sc,&sc,&flg);CHKERRQ(ierr);
2420     if (flg) {
2421       ierr = MatMPIAIJSetUseScalableIncreaseOverlap(A,sc);CHKERRQ(ierr);
2422     }
2423   ierr = PetscOptionsEnd();CHKERRQ(ierr);
2424   PetscFunctionReturn(0);
2425 }
2426 
2427 PetscErrorCode MatShift_MPIAIJ(Mat Y,PetscScalar a)
2428 {
2429   PetscErrorCode ierr;
2430   Mat_MPIAIJ     *maij = (Mat_MPIAIJ*)Y->data;
2431   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)maij->A->data;
2432 
2433   PetscFunctionBegin;
2434   if (!Y->preallocated) {
2435     ierr = MatMPIAIJSetPreallocation(Y,1,NULL,0,NULL);CHKERRQ(ierr);
2436   } else if (!aij->nz) {
2437     PetscInt nonew = aij->nonew;
2438     ierr = MatSeqAIJSetPreallocation(maij->A,1,NULL);CHKERRQ(ierr);
2439     aij->nonew = nonew;
2440   }
2441   ierr = MatShift_Basic(Y,a);CHKERRQ(ierr);
2442   PetscFunctionReturn(0);
2443 }
2444 
2445 PetscErrorCode MatMissingDiagonal_MPIAIJ(Mat A,PetscBool  *missing,PetscInt *d)
2446 {
2447   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2448   PetscErrorCode ierr;
2449 
2450   PetscFunctionBegin;
2451   if (A->rmap->n != A->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only works for square matrices");
2452   ierr = MatMissingDiagonal(a->A,missing,d);CHKERRQ(ierr);
2453   if (d) {
2454     PetscInt rstart;
2455     ierr = MatGetOwnershipRange(A,&rstart,NULL);CHKERRQ(ierr);
2456     *d += rstart;
2457 
2458   }
2459   PetscFunctionReturn(0);
2460 }
2461 
2462 
2463 /* -------------------------------------------------------------------*/
2464 static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
2465                                        MatGetRow_MPIAIJ,
2466                                        MatRestoreRow_MPIAIJ,
2467                                        MatMult_MPIAIJ,
2468                                 /* 4*/ MatMultAdd_MPIAIJ,
2469                                        MatMultTranspose_MPIAIJ,
2470                                        MatMultTransposeAdd_MPIAIJ,
2471                                        0,
2472                                        0,
2473                                        0,
2474                                 /*10*/ 0,
2475                                        0,
2476                                        0,
2477                                        MatSOR_MPIAIJ,
2478                                        MatTranspose_MPIAIJ,
2479                                 /*15*/ MatGetInfo_MPIAIJ,
2480                                        MatEqual_MPIAIJ,
2481                                        MatGetDiagonal_MPIAIJ,
2482                                        MatDiagonalScale_MPIAIJ,
2483                                        MatNorm_MPIAIJ,
2484                                 /*20*/ MatAssemblyBegin_MPIAIJ,
2485                                        MatAssemblyEnd_MPIAIJ,
2486                                        MatSetOption_MPIAIJ,
2487                                        MatZeroEntries_MPIAIJ,
2488                                 /*24*/ MatZeroRows_MPIAIJ,
2489                                        0,
2490                                        0,
2491                                        0,
2492                                        0,
2493                                 /*29*/ MatSetUp_MPIAIJ,
2494                                        0,
2495                                        0,
2496                                        MatGetDiagonalBlock_MPIAIJ,
2497                                        0,
2498                                 /*34*/ MatDuplicate_MPIAIJ,
2499                                        0,
2500                                        0,
2501                                        0,
2502                                        0,
2503                                 /*39*/ MatAXPY_MPIAIJ,
2504                                        MatCreateSubMatrices_MPIAIJ,
2505                                        MatIncreaseOverlap_MPIAIJ,
2506                                        MatGetValues_MPIAIJ,
2507                                        MatCopy_MPIAIJ,
2508                                 /*44*/ MatGetRowMax_MPIAIJ,
2509                                        MatScale_MPIAIJ,
2510                                        MatShift_MPIAIJ,
2511                                        MatDiagonalSet_MPIAIJ,
2512                                        MatZeroRowsColumns_MPIAIJ,
2513                                 /*49*/ MatSetRandom_MPIAIJ,
2514                                        0,
2515                                        0,
2516                                        0,
2517                                        0,
2518                                 /*54*/ MatFDColoringCreate_MPIXAIJ,
2519                                        0,
2520                                        MatSetUnfactored_MPIAIJ,
2521                                        MatPermute_MPIAIJ,
2522                                        0,
2523                                 /*59*/ MatCreateSubMatrix_MPIAIJ,
2524                                        MatDestroy_MPIAIJ,
2525                                        MatView_MPIAIJ,
2526                                        0,
2527                                        MatMatMatMult_MPIAIJ_MPIAIJ_MPIAIJ,
2528                                 /*64*/ MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ,
2529                                        MatMatMatMultNumeric_MPIAIJ_MPIAIJ_MPIAIJ,
2530                                        0,
2531                                        0,
2532                                        0,
2533                                 /*69*/ MatGetRowMaxAbs_MPIAIJ,
2534                                        MatGetRowMinAbs_MPIAIJ,
2535                                        0,
2536                                        0,
2537                                        0,
2538                                        0,
2539                                 /*75*/ MatFDColoringApply_AIJ,
2540                                        MatSetFromOptions_MPIAIJ,
2541                                        0,
2542                                        0,
2543                                        MatFindZeroDiagonals_MPIAIJ,
2544                                 /*80*/ 0,
2545                                        0,
2546                                        0,
2547                                 /*83*/ MatLoad_MPIAIJ,
2548                                        0,
2549                                        0,
2550                                        0,
2551                                        0,
2552                                        0,
2553                                 /*89*/ MatMatMult_MPIAIJ_MPIAIJ,
2554                                        MatMatMultSymbolic_MPIAIJ_MPIAIJ,
2555                                        MatMatMultNumeric_MPIAIJ_MPIAIJ,
2556                                        MatPtAP_MPIAIJ_MPIAIJ,
2557                                        MatPtAPSymbolic_MPIAIJ_MPIAIJ,
2558                                 /*94*/ MatPtAPNumeric_MPIAIJ_MPIAIJ,
2559                                        0,
2560                                        0,
2561                                        0,
2562                                        0,
2563                                 /*99*/ 0,
2564                                        0,
2565                                        0,
2566                                        MatConjugate_MPIAIJ,
2567                                        0,
2568                                 /*104*/MatSetValuesRow_MPIAIJ,
2569                                        MatRealPart_MPIAIJ,
2570                                        MatImaginaryPart_MPIAIJ,
2571                                        0,
2572                                        0,
2573                                 /*109*/0,
2574                                        0,
2575                                        MatGetRowMin_MPIAIJ,
2576                                        0,
2577                                        MatMissingDiagonal_MPIAIJ,
2578                                 /*114*/MatGetSeqNonzeroStructure_MPIAIJ,
2579                                        0,
2580                                        MatGetGhosts_MPIAIJ,
2581                                        0,
2582                                        0,
2583                                 /*119*/0,
2584                                        0,
2585                                        0,
2586                                        0,
2587                                        MatGetMultiProcBlock_MPIAIJ,
2588                                 /*124*/MatFindNonzeroRows_MPIAIJ,
2589                                        MatGetColumnNorms_MPIAIJ,
2590                                        MatInvertBlockDiagonal_MPIAIJ,
2591                                        0,
2592                                        MatCreateSubMatricesMPI_MPIAIJ,
2593                                 /*129*/0,
2594                                        MatTransposeMatMult_MPIAIJ_MPIAIJ,
2595                                        MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ,
2596                                        MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ,
2597                                        0,
2598                                 /*134*/0,
2599                                        0,
2600                                        0,
2601                                        0,
2602                                        0,
2603                                 /*139*/MatSetBlockSizes_MPIAIJ,
2604                                        0,
2605                                        0,
2606                                        MatFDColoringSetUp_MPIXAIJ,
2607                                        MatFindOffBlockDiagonalEntries_MPIAIJ,
2608                                 /*144*/MatCreateMPIMatConcatenateSeqMat_MPIAIJ
2609 };
2610 
2611 /* ----------------------------------------------------------------------------------------*/
2612 
2613 PetscErrorCode  MatStoreValues_MPIAIJ(Mat mat)
2614 {
2615   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2616   PetscErrorCode ierr;
2617 
2618   PetscFunctionBegin;
2619   ierr = MatStoreValues(aij->A);CHKERRQ(ierr);
2620   ierr = MatStoreValues(aij->B);CHKERRQ(ierr);
2621   PetscFunctionReturn(0);
2622 }
2623 
2624 PetscErrorCode  MatRetrieveValues_MPIAIJ(Mat mat)
2625 {
2626   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2627   PetscErrorCode ierr;
2628 
2629   PetscFunctionBegin;
2630   ierr = MatRetrieveValues(aij->A);CHKERRQ(ierr);
2631   ierr = MatRetrieveValues(aij->B);CHKERRQ(ierr);
2632   PetscFunctionReturn(0);
2633 }
2634 
2635 PetscErrorCode  MatMPIAIJSetPreallocation_MPIAIJ(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
2636 {
2637   Mat_MPIAIJ     *b;
2638   PetscErrorCode ierr;
2639 
2640   PetscFunctionBegin;
2641   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
2642   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
2643   b = (Mat_MPIAIJ*)B->data;
2644 
2645 #if defined(PETSC_USE_CTABLE)
2646   ierr = PetscTableDestroy(&b->colmap);CHKERRQ(ierr);
2647 #else
2648   ierr = PetscFree(b->colmap);CHKERRQ(ierr);
2649 #endif
2650   ierr = PetscFree(b->garray);CHKERRQ(ierr);
2651   ierr = VecDestroy(&b->lvec);CHKERRQ(ierr);
2652   ierr = VecScatterDestroy(&b->Mvctx);CHKERRQ(ierr);
2653 
2654   /* Because the B will have been resized we simply destroy it and create a new one each time */
2655   ierr = MatDestroy(&b->B);CHKERRQ(ierr);
2656   ierr = MatCreate(PETSC_COMM_SELF,&b->B);CHKERRQ(ierr);
2657   ierr = MatSetSizes(b->B,B->rmap->n,B->cmap->N,B->rmap->n,B->cmap->N);CHKERRQ(ierr);
2658   ierr = MatSetBlockSizesFromMats(b->B,B,B);CHKERRQ(ierr);
2659   ierr = MatSetType(b->B,MATSEQAIJ);CHKERRQ(ierr);
2660   ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->B);CHKERRQ(ierr);
2661 
2662   if (!B->preallocated) {
2663     ierr = MatCreate(PETSC_COMM_SELF,&b->A);CHKERRQ(ierr);
2664     ierr = MatSetSizes(b->A,B->rmap->n,B->cmap->n,B->rmap->n,B->cmap->n);CHKERRQ(ierr);
2665     ierr = MatSetBlockSizesFromMats(b->A,B,B);CHKERRQ(ierr);
2666     ierr = MatSetType(b->A,MATSEQAIJ);CHKERRQ(ierr);
2667     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->A);CHKERRQ(ierr);
2668   }
2669 
2670   ierr = MatSeqAIJSetPreallocation(b->A,d_nz,d_nnz);CHKERRQ(ierr);
2671   ierr = MatSeqAIJSetPreallocation(b->B,o_nz,o_nnz);CHKERRQ(ierr);
2672   B->preallocated  = PETSC_TRUE;
2673   B->was_assembled = PETSC_FALSE;
2674   B->assembled     = PETSC_FALSE;;
2675   PetscFunctionReturn(0);
2676 }
2677 
2678 PetscErrorCode MatDuplicate_MPIAIJ(Mat matin,MatDuplicateOption cpvalues,Mat *newmat)
2679 {
2680   Mat            mat;
2681   Mat_MPIAIJ     *a,*oldmat = (Mat_MPIAIJ*)matin->data;
2682   PetscErrorCode ierr;
2683 
2684   PetscFunctionBegin;
2685   *newmat = 0;
2686   ierr    = MatCreate(PetscObjectComm((PetscObject)matin),&mat);CHKERRQ(ierr);
2687   ierr    = MatSetSizes(mat,matin->rmap->n,matin->cmap->n,matin->rmap->N,matin->cmap->N);CHKERRQ(ierr);
2688   ierr    = MatSetBlockSizesFromMats(mat,matin,matin);CHKERRQ(ierr);
2689   ierr    = MatSetType(mat,((PetscObject)matin)->type_name);CHKERRQ(ierr);
2690   ierr    = PetscMemcpy(mat->ops,matin->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
2691   a       = (Mat_MPIAIJ*)mat->data;
2692 
2693   mat->factortype   = matin->factortype;
2694   mat->assembled    = PETSC_TRUE;
2695   mat->insertmode   = NOT_SET_VALUES;
2696   mat->preallocated = PETSC_TRUE;
2697 
2698   a->size         = oldmat->size;
2699   a->rank         = oldmat->rank;
2700   a->donotstash   = oldmat->donotstash;
2701   a->roworiented  = oldmat->roworiented;
2702   a->rowindices   = 0;
2703   a->rowvalues    = 0;
2704   a->getrowactive = PETSC_FALSE;
2705 
2706   ierr = PetscLayoutReference(matin->rmap,&mat->rmap);CHKERRQ(ierr);
2707   ierr = PetscLayoutReference(matin->cmap,&mat->cmap);CHKERRQ(ierr);
2708 
2709   if (oldmat->colmap) {
2710 #if defined(PETSC_USE_CTABLE)
2711     ierr = PetscTableCreateCopy(oldmat->colmap,&a->colmap);CHKERRQ(ierr);
2712 #else
2713     ierr = PetscMalloc1(mat->cmap->N,&a->colmap);CHKERRQ(ierr);
2714     ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2715     ierr = PetscMemcpy(a->colmap,oldmat->colmap,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2716 #endif
2717   } else a->colmap = 0;
2718   if (oldmat->garray) {
2719     PetscInt len;
2720     len  = oldmat->B->cmap->n;
2721     ierr = PetscMalloc1(len+1,&a->garray);CHKERRQ(ierr);
2722     ierr = PetscLogObjectMemory((PetscObject)mat,len*sizeof(PetscInt));CHKERRQ(ierr);
2723     if (len) { ierr = PetscMemcpy(a->garray,oldmat->garray,len*sizeof(PetscInt));CHKERRQ(ierr); }
2724   } else a->garray = 0;
2725 
2726   ierr    = VecDuplicate(oldmat->lvec,&a->lvec);CHKERRQ(ierr);
2727   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->lvec);CHKERRQ(ierr);
2728   ierr    = VecScatterCopy(oldmat->Mvctx,&a->Mvctx);CHKERRQ(ierr);
2729   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->Mvctx);CHKERRQ(ierr);
2730   ierr    = MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
2731   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->A);CHKERRQ(ierr);
2732   ierr    = MatDuplicate(oldmat->B,cpvalues,&a->B);CHKERRQ(ierr);
2733   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->B);CHKERRQ(ierr);
2734   ierr    = PetscFunctionListDuplicate(((PetscObject)matin)->qlist,&((PetscObject)mat)->qlist);CHKERRQ(ierr);
2735   *newmat = mat;
2736   PetscFunctionReturn(0);
2737 }
2738 
2739 PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
2740 {
2741   PetscScalar    *vals,*svals;
2742   MPI_Comm       comm;
2743   PetscErrorCode ierr;
2744   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
2745   PetscInt       i,nz,j,rstart,rend,mmax,maxnz = 0;
2746   PetscInt       header[4],*rowlengths = 0,M,N,m,*cols;
2747   PetscInt       *ourlens = NULL,*procsnz = NULL,*offlens = NULL,jj,*mycols,*smycols;
2748   PetscInt       cend,cstart,n,*rowners;
2749   int            fd;
2750   PetscInt       bs = newMat->rmap->bs;
2751 
2752   PetscFunctionBegin;
2753   /* force binary viewer to load .info file if it has not yet done so */
2754   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
2755   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
2756   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2757   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2758   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
2759   if (!rank) {
2760     ierr = PetscBinaryRead(fd,(char*)header,4,PETSC_INT);CHKERRQ(ierr);
2761     if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
2762     if (header[3] < 0) SETERRQ(PetscObjectComm((PetscObject)newMat),PETSC_ERR_FILE_UNEXPECTED,"Matrix stored in special format on disk,cannot load as MATMPIAIJ");
2763   }
2764 
2765   ierr = PetscOptionsBegin(comm,NULL,"Options for loading MATMPIAIJ matrix","Mat");CHKERRQ(ierr);
2766   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
2767   ierr = PetscOptionsEnd();CHKERRQ(ierr);
2768   if (bs < 0) bs = 1;
2769 
2770   ierr = MPI_Bcast(header+1,3,MPIU_INT,0,comm);CHKERRQ(ierr);
2771   M    = header[1]; N = header[2];
2772 
2773   /* If global sizes are set, check if they are consistent with that given in the file */
2774   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);
2775   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);
2776 
2777   /* determine ownership of all (block) rows */
2778   if (M%bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Inconsistent # of rows (%d) and block size (%d)",M,bs);
2779   if (newMat->rmap->n < 0) m = bs*((M/bs)/size + (((M/bs) % size) > rank));    /* PETSC_DECIDE */
2780   else m = newMat->rmap->n; /* Set by user */
2781 
2782   ierr = PetscMalloc1(size+1,&rowners);CHKERRQ(ierr);
2783   ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
2784 
2785   /* First process needs enough room for process with most rows */
2786   if (!rank) {
2787     mmax = rowners[1];
2788     for (i=2; i<=size; i++) {
2789       mmax = PetscMax(mmax, rowners[i]);
2790     }
2791   } else mmax = -1;             /* unused, but compilers complain */
2792 
2793   rowners[0] = 0;
2794   for (i=2; i<=size; i++) {
2795     rowners[i] += rowners[i-1];
2796   }
2797   rstart = rowners[rank];
2798   rend   = rowners[rank+1];
2799 
2800   /* distribute row lengths to all processors */
2801   ierr = PetscMalloc2(m,&ourlens,m,&offlens);CHKERRQ(ierr);
2802   if (!rank) {
2803     ierr = PetscBinaryRead(fd,ourlens,m,PETSC_INT);CHKERRQ(ierr);
2804     ierr = PetscMalloc1(mmax,&rowlengths);CHKERRQ(ierr);
2805     ierr = PetscCalloc1(size,&procsnz);CHKERRQ(ierr);
2806     for (j=0; j<m; j++) {
2807       procsnz[0] += ourlens[j];
2808     }
2809     for (i=1; i<size; i++) {
2810       ierr = PetscBinaryRead(fd,rowlengths,rowners[i+1]-rowners[i],PETSC_INT);CHKERRQ(ierr);
2811       /* calculate the number of nonzeros on each processor */
2812       for (j=0; j<rowners[i+1]-rowners[i]; j++) {
2813         procsnz[i] += rowlengths[j];
2814       }
2815       ierr = MPIULong_Send(rowlengths,rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2816     }
2817     ierr = PetscFree(rowlengths);CHKERRQ(ierr);
2818   } else {
2819     ierr = MPIULong_Recv(ourlens,m,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2820   }
2821 
2822   if (!rank) {
2823     /* determine max buffer needed and allocate it */
2824     maxnz = 0;
2825     for (i=0; i<size; i++) {
2826       maxnz = PetscMax(maxnz,procsnz[i]);
2827     }
2828     ierr = PetscMalloc1(maxnz,&cols);CHKERRQ(ierr);
2829 
2830     /* read in my part of the matrix column indices  */
2831     nz   = procsnz[0];
2832     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2833     ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);
2834 
2835     /* read in every one elses and ship off */
2836     for (i=1; i<size; i++) {
2837       nz   = procsnz[i];
2838       ierr = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
2839       ierr = MPIULong_Send(cols,nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2840     }
2841     ierr = PetscFree(cols);CHKERRQ(ierr);
2842   } else {
2843     /* determine buffer space needed for message */
2844     nz = 0;
2845     for (i=0; i<m; i++) {
2846       nz += ourlens[i];
2847     }
2848     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2849 
2850     /* receive message of column indices*/
2851     ierr = MPIULong_Recv(mycols,nz,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2852   }
2853 
2854   /* determine column ownership if matrix is not square */
2855   if (N != M) {
2856     if (newMat->cmap->n < 0) n = N/size + ((N % size) > rank);
2857     else n = newMat->cmap->n;
2858     ierr   = MPI_Scan(&n,&cend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
2859     cstart = cend - n;
2860   } else {
2861     cstart = rstart;
2862     cend   = rend;
2863     n      = cend - cstart;
2864   }
2865 
2866   /* loop over local rows, determining number of off diagonal entries */
2867   ierr = PetscMemzero(offlens,m*sizeof(PetscInt));CHKERRQ(ierr);
2868   jj   = 0;
2869   for (i=0; i<m; i++) {
2870     for (j=0; j<ourlens[i]; j++) {
2871       if (mycols[jj] < cstart || mycols[jj] >= cend) offlens[i]++;
2872       jj++;
2873     }
2874   }
2875 
2876   for (i=0; i<m; i++) {
2877     ourlens[i] -= offlens[i];
2878   }
2879   ierr = MatSetSizes(newMat,m,n,M,N);CHKERRQ(ierr);
2880 
2881   if (bs > 1) {ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);}
2882 
2883   ierr = MatMPIAIJSetPreallocation(newMat,0,ourlens,0,offlens);CHKERRQ(ierr);
2884 
2885   for (i=0; i<m; i++) {
2886     ourlens[i] += offlens[i];
2887   }
2888 
2889   if (!rank) {
2890     ierr = PetscMalloc1(maxnz+1,&vals);CHKERRQ(ierr);
2891 
2892     /* read in my part of the matrix numerical values  */
2893     nz   = procsnz[0];
2894     ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
2895 
2896     /* insert into matrix */
2897     jj      = rstart;
2898     smycols = mycols;
2899     svals   = vals;
2900     for (i=0; i<m; i++) {
2901       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
2902       smycols += ourlens[i];
2903       svals   += ourlens[i];
2904       jj++;
2905     }
2906 
2907     /* read in other processors and ship out */
2908     for (i=1; i<size; i++) {
2909       nz   = procsnz[i];
2910       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
2911       ierr = MPIULong_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
2912     }
2913     ierr = PetscFree(procsnz);CHKERRQ(ierr);
2914   } else {
2915     /* receive numeric values */
2916     ierr = PetscMalloc1(nz+1,&vals);CHKERRQ(ierr);
2917 
2918     /* receive message of values*/
2919     ierr = MPIULong_Recv(vals,nz,MPIU_SCALAR,0,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
2920 
2921     /* insert into matrix */
2922     jj      = rstart;
2923     smycols = mycols;
2924     svals   = vals;
2925     for (i=0; i<m; i++) {
2926       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
2927       smycols += ourlens[i];
2928       svals   += ourlens[i];
2929       jj++;
2930     }
2931   }
2932   ierr = PetscFree2(ourlens,offlens);CHKERRQ(ierr);
2933   ierr = PetscFree(vals);CHKERRQ(ierr);
2934   ierr = PetscFree(mycols);CHKERRQ(ierr);
2935   ierr = PetscFree(rowners);CHKERRQ(ierr);
2936   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2937   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2938   PetscFunctionReturn(0);
2939 }
2940 
2941 /* Not scalable because of ISAllGather() unless getting all columns. */
2942 PetscErrorCode ISGetSeqIS_Private(Mat mat,IS iscol,IS *isseq)
2943 {
2944   PetscErrorCode ierr;
2945   IS             iscol_local;
2946   PetscBool      isstride;
2947   PetscMPIInt    lisstride=0,gisstride;
2948 
2949   PetscFunctionBegin;
2950   /* check if we are grabbing all columns*/
2951   ierr = PetscObjectTypeCompare((PetscObject)iscol,ISSTRIDE,&isstride);CHKERRQ(ierr);
2952 
2953   if (isstride) {
2954     PetscInt  start,len,mstart,mlen;
2955     ierr = ISStrideGetInfo(iscol,&start,NULL);CHKERRQ(ierr);
2956     ierr = ISGetLocalSize(iscol,&len);CHKERRQ(ierr);
2957     ierr = MatGetOwnershipRangeColumn(mat,&mstart,&mlen);CHKERRQ(ierr);
2958     if (mstart == start && mlen-mstart == len) lisstride = 1;
2959   }
2960 
2961   ierr = MPIU_Allreduce(&lisstride,&gisstride,1,MPI_INT,MPI_MIN,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
2962   if (gisstride) {
2963     PetscInt N;
2964     ierr = MatGetSize(mat,NULL,&N);CHKERRQ(ierr);
2965     ierr = ISCreateStride(PetscObjectComm((PetscObject)mat),N,0,1,&iscol_local);CHKERRQ(ierr);
2966     ierr = ISSetIdentity(iscol_local);CHKERRQ(ierr);
2967     ierr = PetscInfo(mat,"Optimizing for obtaining all columns of the matrix; skipping ISAllGather()\n");CHKERRQ(ierr);
2968   } else {
2969     PetscInt cbs;
2970     ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
2971     ierr = ISAllGather(iscol,&iscol_local);CHKERRQ(ierr);
2972     ierr = ISSetBlockSize(iscol_local,cbs);CHKERRQ(ierr);
2973   }
2974 
2975   *isseq = iscol_local;
2976   PetscFunctionReturn(0);
2977 }
2978 
2979 /*
2980  Used by MatCreateSubMatrix_MPIAIJ_SameRowColDist() to avoid ISAllGather() and global size of iscol_local
2981  (see MatCreateSubMatrix_MPIAIJ_nonscalable)
2982 
2983  Input Parameters:
2984    mat - matrix
2985    isrow - parallel row index set; its local indices are a subset of local columns of mat,
2986            i.e., mat->rstart <= isrow[i] < mat->rend
2987    iscol - parallel column index set; its local indices are a subset of local columns of mat,
2988            i.e., mat->cstart <= iscol[i] < mat->cend
2989  Output Parameter:
2990    isrow_d,iscol_d - sequential row and column index sets for retrieving mat->A
2991    iscol_o - sequential column index set for retrieving mat->B
2992    garray - column map; garray[i] indicates global location of iscol_o[i] in iscol
2993  */
2994 PetscErrorCode ISGetSeqIS_SameColDist_Private(Mat mat,IS isrow,IS iscol,IS *isrow_d,IS *iscol_d,IS *iscol_o,const PetscInt *garray[])
2995 {
2996   PetscErrorCode ierr;
2997   Vec            x,cmap;
2998   const PetscInt *is_idx;
2999   PetscScalar    *xarray,*cmaparray;
3000   PetscInt       ncols,isstart,*idx,m,rstart,*cmap1,count;
3001   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)mat->data;
3002   Mat            B=a->B;
3003   Vec            lvec=a->lvec,lcmap;
3004   PetscInt       i,cstart,cend,Bn=B->cmap->N;
3005   MPI_Comm       comm;
3006 
3007   PetscFunctionBegin;
3008   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3009   ierr = ISGetLocalSize(iscol,&ncols);CHKERRQ(ierr);
3010 
3011   /* (1) iscol is a sub-column vector of mat, pad it with '-1.' to form a full vector x */
3012   ierr = MatCreateVecs(mat,&x,NULL);CHKERRQ(ierr);
3013   ierr = VecDuplicate(x,&cmap);CHKERRQ(ierr);
3014   ierr = VecSet(x,-1.0);CHKERRQ(ierr);
3015 
3016   /* Get start indices */
3017   ierr = MPI_Scan(&ncols,&isstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3018   isstart -= ncols;
3019   ierr = MatGetOwnershipRangeColumn(mat,&cstart,&cend);CHKERRQ(ierr);
3020 
3021   ierr = ISGetIndices(iscol,&is_idx);CHKERRQ(ierr);
3022   ierr = VecGetArray(x,&xarray);CHKERRQ(ierr);
3023   ierr = VecGetArray(cmap,&cmaparray);CHKERRQ(ierr);
3024   ierr = PetscMalloc1(ncols,&idx);CHKERRQ(ierr);
3025   for (i=0; i<ncols; i++) {
3026     xarray[is_idx[i]-cstart]    = (PetscScalar)is_idx[i];
3027     cmaparray[is_idx[i]-cstart] = i + isstart;      /* global index of iscol[i] */
3028     idx[i]                      = is_idx[i]-cstart; /* local index of iscol[i]  */
3029   }
3030   ierr = VecRestoreArray(x,&xarray);CHKERRQ(ierr);
3031   ierr = VecRestoreArray(cmap,&cmaparray);CHKERRQ(ierr);
3032   ierr = ISRestoreIndices(iscol,&is_idx);CHKERRQ(ierr);
3033 
3034   /* Get iscol_d */
3035   ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,iscol_d);CHKERRQ(ierr);
3036 
3037   /* Get isrow_d */
3038   ierr = ISGetLocalSize(isrow,&m);CHKERRQ(ierr);
3039   rstart = mat->rmap->rstart;
3040   ierr = PetscMalloc1(m,&idx);CHKERRQ(ierr);
3041   ierr = ISGetIndices(isrow,&is_idx);CHKERRQ(ierr);
3042   for (i=0; i<m; i++) idx[i] = is_idx[i]-rstart;
3043   ierr = ISRestoreIndices(isrow,&is_idx);CHKERRQ(ierr);
3044 
3045   ierr = ISCreateGeneral(PETSC_COMM_SELF,m,idx,PETSC_OWN_POINTER,isrow_d);CHKERRQ(ierr);
3046   ierr = ISGetBlockSize(isrow,&i);CHKERRQ(ierr);
3047   ierr = ISSetBlockSize(*isrow_d,i);CHKERRQ(ierr);
3048 
3049   /* (2) Scatter x and cmap using aij->Mvctx to get their off-process portions (see MatMult_MPIAIJ) */
3050   ierr = VecScatterBegin(a->Mvctx,x,lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3051 
3052   ierr = VecDuplicate(lvec,&lcmap);CHKERRQ(ierr);
3053 
3054   ierr = VecScatterEnd(a->Mvctx,x,lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3055   ierr = VecScatterBegin(a->Mvctx,cmap,lcmap,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3056   ierr = VecScatterEnd(a->Mvctx,cmap,lcmap,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3057 
3058   /* (3) create sequential iscol_o (a subset of iscol) and isgarray */
3059   /* off-process column indices */
3060   count = 0;
3061   ierr = PetscMalloc1(Bn,&idx);CHKERRQ(ierr);
3062   ierr = PetscMalloc1(Bn,&cmap1);CHKERRQ(ierr);
3063 
3064   ierr = VecGetArray(lvec,&xarray);CHKERRQ(ierr);
3065   ierr = VecGetArray(lcmap,&cmaparray);CHKERRQ(ierr);
3066   for (i=0; i<Bn; i++) {
3067     if (PetscRealPart(xarray[i]) > -1.0) {
3068       idx[count]     = i;                   /* local column index in off-diagonal part B */
3069       cmap1[count++] = (PetscInt)PetscRealPart(cmaparray[i]);  /* column index in submat */
3070     }
3071   }
3072   ierr = VecRestoreArray(lvec,&xarray);CHKERRQ(ierr);
3073   ierr = VecRestoreArray(lcmap,&cmaparray);CHKERRQ(ierr);
3074 
3075   ierr = ISCreateGeneral(PETSC_COMM_SELF,count,idx,PETSC_COPY_VALUES,iscol_o);CHKERRQ(ierr);
3076   ierr = PetscFree(idx);CHKERRQ(ierr);
3077 
3078   *garray = cmap1;
3079 
3080   ierr = VecDestroy(&x);CHKERRQ(ierr);
3081   ierr = VecDestroy(&cmap);CHKERRQ(ierr);
3082   ierr = VecDestroy(&lcmap);CHKERRQ(ierr);
3083   PetscFunctionReturn(0);
3084 }
3085 
3086 /* isrow and iscol have same processor distribution as mat, output *submat is a submatrix of local mat */
3087 PetscErrorCode MatCreateSubMatrix_MPIAIJ_SameRowColDist(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *submat)
3088 {
3089   PetscErrorCode ierr;
3090   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)mat->data,*asub;
3091   Mat            M = NULL;
3092   MPI_Comm       comm;
3093   IS             iscol_d,isrow_d,iscol_o;
3094   Mat            Asub = NULL,Bsub = NULL;
3095   PetscInt       n;
3096 
3097   PetscFunctionBegin;
3098   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3099 
3100   if (call == MAT_REUSE_MATRIX) {
3101     /* Retrieve isrow_d, iscol_d and iscol_o from submat */
3102     ierr = PetscObjectQuery((PetscObject)*submat,"isrow_d",(PetscObject*)&isrow_d);CHKERRQ(ierr);
3103     if (!isrow_d) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"isrow_d passed in was not used before, cannot reuse");
3104 
3105     ierr = PetscObjectQuery((PetscObject)*submat,"iscol_d",(PetscObject*)&iscol_d);CHKERRQ(ierr);
3106     if (!iscol_d) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"iscol_d passed in was not used before, cannot reuse");
3107 
3108     ierr = PetscObjectQuery((PetscObject)*submat,"iscol_o",(PetscObject*)&iscol_o);CHKERRQ(ierr);
3109     if (!iscol_o) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"iscol_o passed in was not used before, cannot reuse");
3110 
3111     /* Update diagonal and off-diagonal portions of submat */
3112     asub = (Mat_MPIAIJ*)(*submat)->data;
3113     ierr = MatCreateSubMatrix_SeqAIJ(a->A,isrow_d,iscol_d,PETSC_DECIDE,MAT_REUSE_MATRIX,&asub->A);CHKERRQ(ierr);
3114     ierr = ISGetLocalSize(iscol_o,&n);CHKERRQ(ierr);
3115     if (n) {
3116       ierr = MatCreateSubMatrix_SeqAIJ(a->B,isrow_d,iscol_o,PETSC_DECIDE,MAT_REUSE_MATRIX,&asub->B);CHKERRQ(ierr);
3117     }
3118     ierr = MatAssemblyBegin(*submat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3119     ierr = MatAssemblyEnd(*submat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3120 
3121   } else { /* call == MAT_INITIAL_MATRIX) */
3122     const PetscInt *garray;
3123     PetscInt        BsubN;
3124 
3125     /* Create isrow_d, iscol_d, iscol_o and isgarray (replace isgarray with array?) */
3126     ierr = ISGetSeqIS_SameColDist_Private(mat,isrow,iscol,&isrow_d,&iscol_d,&iscol_o,&garray);CHKERRQ(ierr);
3127 
3128     /* Create local submatrices Asub and Bsub */
3129     ierr = MatCreateSubMatrix_SeqAIJ(a->A,isrow_d,iscol_d,PETSC_DECIDE,MAT_INITIAL_MATRIX,&Asub);CHKERRQ(ierr);
3130     ierr = MatCreateSubMatrix_SeqAIJ(a->B,isrow_d,iscol_o,PETSC_DECIDE,MAT_INITIAL_MATRIX,&Bsub);CHKERRQ(ierr);
3131 
3132     /* Create submatrix M */
3133     ierr = MatCreateMPIAIJWithSeqAIJ(comm,Asub,Bsub,garray,&M);CHKERRQ(ierr);
3134 
3135     /* If Bsub has empty columns, compress iscol_o such that it will retrieve condensed Bsub from a->B during reuse */
3136     asub = (Mat_MPIAIJ*)M->data;
3137 
3138     ierr = ISGetLocalSize(iscol_o,&BsubN);CHKERRQ(ierr);
3139     n = asub->B->cmap->N;
3140     if (BsubN > n) {
3141       /* This case can be tested using ~petsc/src/tao/bound/examples/tutorials/runplate2_3 */
3142       const PetscInt *idx;
3143       PetscInt       i,j,*idx_new,*subgarray = asub->garray;
3144       ierr = PetscInfo2(M,"submatrix Bn %D != BsubN %D, update iscol_o\n",n,BsubN);CHKERRQ(ierr);
3145 
3146       ierr = PetscMalloc1(n,&idx_new);CHKERRQ(ierr);
3147       j = 0;
3148       ierr = ISGetIndices(iscol_o,&idx);CHKERRQ(ierr);
3149       for (i=0; i<n; i++) {
3150         if (j >= BsubN) break;
3151         while (subgarray[i] > garray[j]) j++;
3152 
3153         if (subgarray[i] == garray[j]) {
3154           idx_new[i] = idx[j++];
3155         } else SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"subgarray[%D]=%D cannot < garray[%D]=%D",i,subgarray[i],j,garray[j]);
3156       }
3157       ierr = ISRestoreIndices(iscol_o,&idx);CHKERRQ(ierr);
3158 
3159       ierr = ISDestroy(&iscol_o);CHKERRQ(ierr);
3160       ierr = ISCreateGeneral(PETSC_COMM_SELF,n,idx_new,PETSC_OWN_POINTER,&iscol_o);CHKERRQ(ierr);
3161 
3162     } else if (BsubN < n) {
3163       SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Columns of Bsub cannot be smaller than B's",BsubN,asub->B->cmap->N);
3164     }
3165 
3166     ierr = PetscFree(garray);CHKERRQ(ierr);
3167     *submat = M;
3168 
3169     /* Save isrow_d, iscol_d and iscol_o used in processor for next request */
3170     ierr = PetscObjectCompose((PetscObject)M,"isrow_d",(PetscObject)isrow_d);CHKERRQ(ierr);
3171     ierr = ISDestroy(&isrow_d);CHKERRQ(ierr);
3172 
3173     ierr = PetscObjectCompose((PetscObject)M,"iscol_d",(PetscObject)iscol_d);CHKERRQ(ierr);
3174     ierr = ISDestroy(&iscol_d);CHKERRQ(ierr);
3175 
3176     ierr = PetscObjectCompose((PetscObject)M,"iscol_o",(PetscObject)iscol_o);CHKERRQ(ierr);
3177     ierr = ISDestroy(&iscol_o);CHKERRQ(ierr);
3178   }
3179   PetscFunctionReturn(0);
3180 }
3181 
3182 PetscErrorCode MatCreateSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3183 {
3184   PetscErrorCode ierr;
3185   IS             iscol_local,isrow_d;
3186   PetscInt       csize;
3187   PetscInt       n,i,j,start,end;
3188   PetscBool      sameRowDist=PETSC_FALSE,sameDist[2],tsameDist[2];
3189   MPI_Comm       comm;
3190 
3191   PetscFunctionBegin;
3192   /* If isrow has same processor distribution as mat,
3193      call MatCreateSubMatrix_MPIAIJ_SameRowDist() to avoid using a hash table with global size of iscol */
3194   if (call == MAT_REUSE_MATRIX) {
3195     ierr = PetscObjectQuery((PetscObject)*newmat,"isrow_d",(PetscObject*)&isrow_d);CHKERRQ(ierr);
3196     if (isrow_d) {
3197       sameRowDist  = PETSC_TRUE;
3198       tsameDist[1] = PETSC_TRUE; /* sameColDist */
3199     } else {
3200       ierr = PetscObjectQuery((PetscObject)*newmat,"SubIScol",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3201       if (iscol_local) {
3202         sameRowDist  = PETSC_TRUE;
3203         tsameDist[1] = PETSC_FALSE; /* !sameColDist */
3204       }
3205     }
3206   } else {
3207     /* Check if isrow has same processor distribution as mat */
3208     sameDist[0] = PETSC_FALSE;
3209     ierr = ISGetLocalSize(isrow,&n);CHKERRQ(ierr);
3210     if (!n) {
3211       sameDist[0] = PETSC_TRUE;
3212     } else {
3213       ierr = ISGetMinMax(isrow,&i,&j);CHKERRQ(ierr);
3214       ierr = MatGetOwnershipRange(mat,&start,&end);CHKERRQ(ierr);
3215       if (i >= start && j < end) {
3216         sameDist[0] = PETSC_TRUE;
3217       }
3218     }
3219 
3220     /* Check if iscol has same processor distribution as mat */
3221     sameDist[1] = PETSC_FALSE;
3222     ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr);
3223     if (!n) {
3224       sameDist[1] = PETSC_TRUE;
3225     } else {
3226       ierr = ISGetMinMax(iscol,&i,&j);CHKERRQ(ierr);
3227       ierr = MatGetOwnershipRangeColumn(mat,&start,&end);CHKERRQ(ierr);
3228       if (i >= start && j < end) sameDist[1] = PETSC_TRUE;
3229     }
3230 
3231     ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3232     ierr = MPIU_Allreduce(&sameDist,&tsameDist,2,MPIU_BOOL,MPI_LAND,comm);CHKERRQ(ierr);
3233     sameRowDist = tsameDist[0];
3234   }
3235 
3236   if (sameRowDist) {
3237     if (tsameDist[1]) { /* sameRowDist & sameColDist */
3238       /* isrow and iscol have same processor distribution as mat */
3239       ierr = MatCreateSubMatrix_MPIAIJ_SameRowColDist(mat,isrow,iscol,call,newmat);CHKERRQ(ierr);
3240     } else { /* sameRowDist */
3241       /* isrow has same processor distribution as mat */
3242       ierr = MatCreateSubMatrix_MPIAIJ_SameRowDist(mat,isrow,iscol,call,newmat);CHKERRQ(ierr);
3243     }
3244     PetscFunctionReturn(0);
3245   }
3246 
3247   /* General case: iscol -> iscol_local which has global size of iscol */
3248   if (call == MAT_REUSE_MATRIX) {
3249     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3250     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3251   } else {
3252     ierr = ISGetSeqIS_Private(mat,iscol,&iscol_local);CHKERRQ(ierr);
3253   }
3254 
3255   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3256   ierr = MatCreateSubMatrix_MPIAIJ_nonscalable(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
3257 
3258   if (call == MAT_INITIAL_MATRIX) {
3259     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3260     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3261   }
3262   PetscFunctionReturn(0);
3263 }
3264 
3265 /*@C
3266      MatCreateMPIAIJWithSeqAIJ - creates a MPIAIJ matrix using SeqAIJ matrices that contain the "diagonal"
3267          and "off-diagonal" part of the matrix in CSR format.
3268 
3269    Collective on MPI_Comm
3270 
3271    Input Parameters:
3272 +  comm - MPI communicator
3273 .  A - "diagonal" portion of matrix
3274 .  B - "off-diagonal" portion of matrix, may have empty columns, will be destroyed by this routine
3275 -  garray - global index of B columns
3276 
3277    Output Parameter:
3278 .   mat - the matrix, with input A as its local diagonal matrix
3279    Level: advanced
3280 
3281    Notes:
3282        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix.
3283        A becomes part of output mat, B is destroyed by this routine. The user cannot use A and B anymore.
3284 
3285 .seealso: MatCreateMPIAIJWithSplitArrays()
3286 @*/
3287 PetscErrorCode MatCreateMPIAIJWithSeqAIJ(MPI_Comm comm,Mat A,Mat B,const PetscInt garray[],Mat *mat)
3288 {
3289   PetscErrorCode ierr;
3290   Mat_MPIAIJ     *maij;
3291   Mat_SeqAIJ     *b=(Mat_SeqAIJ*)B->data,*bnew;
3292   PetscInt       *oi=b->i,*oj=b->j,i,nz,col;
3293   PetscScalar    *oa=b->a;
3294   Mat            Bnew;
3295   PetscInt       m,n,N;
3296 
3297   PetscFunctionBegin;
3298   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
3299   ierr = MatGetSize(A,&m,&n);CHKERRQ(ierr);
3300   if (m != B->rmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Am %D != Bm %D",m,B->rmap->N);
3301   if (A->rmap->bs != B->rmap->bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"A row bs %D != B row bs %D",A->rmap->bs,B->rmap->bs);
3302   if (A->cmap->bs != B->cmap->bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"A column bs %D != B column bs %D",A->cmap->bs,B->cmap->bs);
3303 
3304   /* Get global columns of mat */
3305   ierr = MPIU_Allreduce(&n,&N,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3306 
3307   ierr = MatSetSizes(*mat,m,n,PETSC_DECIDE,N);CHKERRQ(ierr);
3308   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
3309   ierr = MatSetBlockSizes(*mat,A->rmap->bs,A->cmap->bs);CHKERRQ(ierr);
3310   maij = (Mat_MPIAIJ*)(*mat)->data;
3311 
3312   (*mat)->preallocated = PETSC_TRUE;
3313 
3314   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
3315   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
3316 
3317   /* Set A as diagonal portion of *mat */
3318   maij->A = A;
3319 
3320   nz = oi[m];
3321   for (i=0; i<nz; i++) {
3322     col   = oj[i];
3323     oj[i] = garray[col];
3324   }
3325 
3326    /* Set Bnew as off-diagonal portion of *mat */
3327   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,N,oi,oj,oa,&Bnew);CHKERRQ(ierr);
3328   bnew        = (Mat_SeqAIJ*)Bnew->data;
3329   bnew->maxnz = b->maxnz; /* allocated nonzeros of B */
3330   maij->B     = Bnew;
3331 
3332   if (B->rmap->N != Bnew->rmap->N) SETERRQ2(PETSC_COMM_SELF,0,"BN %d != BnewN %d",B->rmap->N,Bnew->rmap->N);
3333 
3334   b->singlemalloc = PETSC_FALSE; /* B arrays are shared by Bnew */
3335   b->free_a       = PETSC_FALSE;
3336   b->free_ij      = PETSC_FALSE;
3337   ierr = MatDestroy(&B);CHKERRQ(ierr);
3338 
3339   bnew->singlemalloc = PETSC_TRUE; /* arrays will be freed by MatDestroy(&Bnew) */
3340   bnew->free_a       = PETSC_TRUE;
3341   bnew->free_ij      = PETSC_TRUE;
3342 
3343   /* condense columns of maij->B */
3344   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
3345   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3346   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3347   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_FALSE);CHKERRQ(ierr);
3348   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3349   PetscFunctionReturn(0);
3350 }
3351 
3352 extern PetscErrorCode MatCreateSubMatrices_MPIAIJ_SingleIS_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool,Mat*);
3353 
3354 PetscErrorCode MatCreateSubMatrix_MPIAIJ_SameRowDist(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3355 {
3356   PetscErrorCode ierr;
3357   PetscInt       i,m,n,rstart,row,rend,nz,j,bs,cbs;
3358   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
3359   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)mat->data;
3360   Mat            M,Msub,B=a->B;
3361   MatScalar      *aa;
3362   Mat_SeqAIJ     *aij;
3363   PetscInt       *garray = a->garray,*colsub,Ncols;
3364   PetscInt       count,Bn=B->cmap->N,cstart=mat->cmap->rstart,cend=mat->cmap->rend;
3365   IS             iscol_sub,iscmap;
3366   const PetscInt *is_idx,*cmap;
3367   PetscBool      allcolumns=PETSC_FALSE;
3368   IS             iscol_local=NULL;
3369   MPI_Comm       comm;
3370 
3371   PetscFunctionBegin;
3372   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3373 
3374   if (call == MAT_REUSE_MATRIX) {
3375     ierr = PetscObjectQuery((PetscObject)*newmat,"SubIScol",(PetscObject*)&iscol_sub);CHKERRQ(ierr);
3376     if (!iscol_sub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"SubIScol passed in was not used before, cannot reuse");
3377     ierr = ISGetLocalSize(iscol_sub,&count);CHKERRQ(ierr);
3378 
3379     ierr = PetscObjectQuery((PetscObject)*newmat,"Subcmap",(PetscObject*)&iscmap);CHKERRQ(ierr);
3380     if (!iscmap) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Subcmap passed in was not used before, cannot reuse");
3381 
3382     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Msub);CHKERRQ(ierr);
3383     if (!Msub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3384 
3385     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol_sub,MAT_REUSE_MATRIX,PETSC_FALSE,&Msub);CHKERRQ(ierr);
3386 
3387   } else { /* call == MAT_INITIAL_MATRIX) */
3388     PetscBool flg;
3389 
3390     ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr);
3391     ierr = ISGetSize(iscol,&Ncols);CHKERRQ(ierr);
3392 
3393     /* (1) iscol -> nonscalable iscol_local */
3394     ierr = ISGetSeqIS_Private(mat,iscol,&iscol_local);CHKERRQ(ierr);
3395     ierr = ISGetLocalSize(iscol_local,&n);CHKERRQ(ierr); /* local size of iscol_local = global columns of newmat */
3396     if (n != Ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"n %d != Ncols %d",n,Ncols);
3397 
3398     /* Check for special case: each processor gets entire matrix columns */
3399     ierr = ISIdentity(iscol_local,&flg);CHKERRQ(ierr);
3400     if (flg && n == mat->cmap->N) allcolumns = PETSC_TRUE;
3401     if (allcolumns) {
3402       iscol_sub = iscol_local;
3403       ierr = PetscObjectReference((PetscObject)iscol_local);CHKERRQ(ierr);
3404       ierr = ISCreateStride(PETSC_COMM_SELF,n,0,1,&iscmap);CHKERRQ(ierr);
3405 
3406     } else {
3407       /* (2) iscol_local -> iscol_sub and iscmap */
3408       PetscInt *idx,*cmap1,k,cbs;
3409 
3410       /* implementation below requires iscol_local be sorted, it can have duplicate indices */
3411       ierr = ISSorted(iscol_local,&flg);CHKERRQ(ierr);
3412       if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"unsorted iscol_local is not implemented yet");
3413 
3414       ierr = PetscMalloc1(Ncols,&idx);CHKERRQ(ierr);
3415       ierr = PetscMalloc1(Ncols,&cmap1);CHKERRQ(ierr);
3416       ierr = ISGetIndices(iscol_local,&is_idx);CHKERRQ(ierr);
3417       count = 0;
3418       k     = 0;
3419       for (i=0; i<Ncols; i++) {
3420         j = is_idx[i];
3421         if (j >= cstart && j < cend) {
3422           /* diagonal part of mat */
3423           idx[count]     = j;
3424           cmap1[count++] = i; /* column index in submat */
3425         } else if (Bn) {
3426           /* off-diagonal part of mat */
3427           if (j == garray[k]) {
3428             idx[count]     = j;
3429             cmap1[count++] = i;  /* column index in submat */
3430           } else if (j > garray[k]) {
3431             while (j > garray[k] && k < Bn-1) k++;
3432             if (j == garray[k]) {
3433               idx[count]     = j;
3434               cmap1[count++] = i; /* column index in submat */
3435             }
3436           }
3437         }
3438       }
3439       ierr = ISRestoreIndices(iscol_local,&is_idx);CHKERRQ(ierr);
3440 
3441       ierr = ISCreateGeneral(PETSC_COMM_SELF,count,idx,PETSC_OWN_POINTER,&iscol_sub);CHKERRQ(ierr);
3442       ierr = ISCreateGeneral(PetscObjectComm((PetscObject)iscol_local),count,cmap1,PETSC_OWN_POINTER,&iscmap);CHKERRQ(ierr);
3443     }
3444 
3445     /* (3) Create sequential Msub */
3446     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol_sub,MAT_INITIAL_MATRIX,allcolumns,&Msub);CHKERRQ(ierr);
3447   }
3448 
3449   ierr = ISGetLocalSize(iscol_sub,&count);CHKERRQ(ierr);
3450   aij  = (Mat_SeqAIJ*)(Msub)->data;
3451   ii   = aij->i;
3452   ierr = ISGetIndices(iscmap,&cmap);CHKERRQ(ierr);
3453 
3454   /*
3455       m - number of local rows
3456       Ncols - number of columns (same on all processors)
3457       rstart - first row in new global matrix generated
3458   */
3459   ierr = MatGetSize(Msub,&m,NULL);CHKERRQ(ierr);
3460 
3461   if (call == MAT_INITIAL_MATRIX) {
3462     /* (4) Create parallel newmat */
3463     PetscMPIInt    rank,size;
3464     PetscInt       csize;
3465 
3466     ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3467     ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3468 
3469     /*
3470         Determine the number of non-zeros in the diagonal and off-diagonal
3471         portions of the matrix in order to do correct preallocation
3472     */
3473 
3474     /* first get start and end of "diagonal" columns */
3475     ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3476     if (csize == PETSC_DECIDE) {
3477       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3478       if (mglobal == Ncols) { /* square matrix */
3479         nlocal = m;
3480       } else {
3481         nlocal = Ncols/size + ((Ncols % size) > rank);
3482       }
3483     } else {
3484       nlocal = csize;
3485     }
3486     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3487     rstart = rend - nlocal;
3488     if (rank == size - 1 && rend != Ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local column sizes %D do not add up to total number of columns %D",rend,Ncols);
3489 
3490     /* next, compute all the lengths */
3491     jj    = aij->j;
3492     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3493     olens = dlens + m;
3494     for (i=0; i<m; i++) {
3495       jend = ii[i+1] - ii[i];
3496       olen = 0;
3497       dlen = 0;
3498       for (j=0; j<jend; j++) {
3499         if (cmap[*jj] < rstart || cmap[*jj] >= rend) olen++;
3500         else dlen++;
3501         jj++;
3502       }
3503       olens[i] = olen;
3504       dlens[i] = dlen;
3505     }
3506     ierr = MatGetBlockSizes(Msub,&bs,&cbs);CHKERRQ(ierr);
3507 
3508     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3509     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,Ncols);CHKERRQ(ierr);
3510     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3511     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3512     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3513     ierr = PetscFree(dlens);CHKERRQ(ierr);
3514 
3515   } else { /* call == MAT_REUSE_MATRIX */
3516     M    = *newmat;
3517     ierr = MatGetLocalSize(M,&i,NULL);CHKERRQ(ierr);
3518     if (i != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3519     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3520     /*
3521          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3522        rather than the slower MatSetValues().
3523     */
3524     M->was_assembled = PETSC_TRUE;
3525     M->assembled     = PETSC_FALSE;
3526   }
3527 
3528   /* (5) Set values of Msub to *newmat */
3529   ierr = PetscMalloc1(count,&colsub);CHKERRQ(ierr);
3530   ierr = MatGetOwnershipRange(M,&rstart,NULL);CHKERRQ(ierr);
3531 
3532   jj   = aij->j;
3533   aa   = aij->a;
3534   for (i=0; i<m; i++) {
3535     row = rstart + i;
3536     nz  = ii[i+1] - ii[i];
3537     for (j=0; j<nz; j++) colsub[j] = cmap[jj[j]];
3538     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,colsub,aa,INSERT_VALUES);CHKERRQ(ierr);
3539     jj += nz; aa += nz;
3540   }
3541   ierr = ISRestoreIndices(iscmap,&cmap);CHKERRQ(ierr);
3542 
3543   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3544   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3545 
3546   ierr = PetscFree(colsub);CHKERRQ(ierr);
3547 
3548   /* save Msub, iscol_sub and iscmap used in processor for next request */
3549   if (call ==  MAT_INITIAL_MATRIX) {
3550     *newmat = M;
3551     ierr = PetscObjectCompose((PetscObject)(*newmat),"SubMatrix",(PetscObject)Msub);CHKERRQ(ierr);
3552     ierr = MatDestroy(&Msub);CHKERRQ(ierr);
3553 
3554     ierr = PetscObjectCompose((PetscObject)(*newmat),"SubIScol",(PetscObject)iscol_sub);CHKERRQ(ierr);
3555     ierr = ISDestroy(&iscol_sub);CHKERRQ(ierr);
3556 
3557     ierr = PetscObjectCompose((PetscObject)(*newmat),"Subcmap",(PetscObject)iscmap);CHKERRQ(ierr);
3558     ierr = ISDestroy(&iscmap);CHKERRQ(ierr);
3559 
3560     if (iscol_local) {
3561       ierr = PetscObjectCompose((PetscObject)(*newmat),"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3562       ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3563     }
3564   }
3565   PetscFunctionReturn(0);
3566 }
3567 
3568 /*
3569     Not great since it makes two copies of the submatrix, first an SeqAIJ
3570   in local and then by concatenating the local matrices the end result.
3571   Writing it directly would be much like MatCreateSubMatrices_MPIAIJ()
3572 
3573   Note: This requires a sequential iscol with all indices.
3574 */
3575 PetscErrorCode MatCreateSubMatrix_MPIAIJ_nonscalable(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3576 {
3577   PetscErrorCode ierr;
3578   PetscMPIInt    rank,size;
3579   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3580   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
3581   Mat            M,Mreuse;
3582   MatScalar      *aa,*vwork;
3583   MPI_Comm       comm;
3584   Mat_SeqAIJ     *aij;
3585   PetscBool      colflag,allcolumns=PETSC_FALSE;
3586 
3587   PetscFunctionBegin;
3588   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3589   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3590   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3591 
3592   /* Check for special case: each processor gets entire matrix columns */
3593   ierr = ISIdentity(iscol,&colflag);CHKERRQ(ierr);
3594   ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr);
3595   if (colflag && n == mat->cmap->N) allcolumns = PETSC_TRUE;
3596 
3597   if (call ==  MAT_REUSE_MATRIX) {
3598     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3599     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3600     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,allcolumns,&Mreuse);CHKERRQ(ierr);
3601   } else {
3602     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,allcolumns,&Mreuse);CHKERRQ(ierr);
3603   }
3604 
3605   /*
3606       m - number of local rows
3607       n - number of columns (same on all processors)
3608       rstart - first row in new global matrix generated
3609   */
3610   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3611   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3612   if (call == MAT_INITIAL_MATRIX) {
3613     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3614     ii  = aij->i;
3615     jj  = aij->j;
3616 
3617     /*
3618         Determine the number of non-zeros in the diagonal and off-diagonal
3619         portions of the matrix in order to do correct preallocation
3620     */
3621 
3622     /* first get start and end of "diagonal" columns */
3623     if (csize == PETSC_DECIDE) {
3624       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3625       if (mglobal == n) { /* square matrix */
3626         nlocal = m;
3627       } else {
3628         nlocal = n/size + ((n % size) > rank);
3629       }
3630     } else {
3631       nlocal = csize;
3632     }
3633     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3634     rstart = rend - nlocal;
3635     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);
3636 
3637     /* next, compute all the lengths */
3638     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3639     olens = dlens + m;
3640     for (i=0; i<m; i++) {
3641       jend = ii[i+1] - ii[i];
3642       olen = 0;
3643       dlen = 0;
3644       for (j=0; j<jend; j++) {
3645         if (*jj < rstart || *jj >= rend) olen++;
3646         else dlen++;
3647         jj++;
3648       }
3649       olens[i] = olen;
3650       dlens[i] = dlen;
3651     }
3652     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3653     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3654     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3655     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3656     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3657     ierr = PetscFree(dlens);CHKERRQ(ierr);
3658   } else {
3659     PetscInt ml,nl;
3660 
3661     M    = *newmat;
3662     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3663     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3664     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3665     /*
3666          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3667        rather than the slower MatSetValues().
3668     */
3669     M->was_assembled = PETSC_TRUE;
3670     M->assembled     = PETSC_FALSE;
3671   }
3672   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3673   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3674   ii   = aij->i;
3675   jj   = aij->j;
3676   aa   = aij->a;
3677   for (i=0; i<m; i++) {
3678     row   = rstart + i;
3679     nz    = ii[i+1] - ii[i];
3680     cwork = jj;     jj += nz;
3681     vwork = aa;     aa += nz;
3682     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3683   }
3684 
3685   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3686   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3687   *newmat = M;
3688 
3689   /* save submatrix used in processor for next request */
3690   if (call ==  MAT_INITIAL_MATRIX) {
3691     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3692     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3693   }
3694   PetscFunctionReturn(0);
3695 }
3696 
3697 PetscErrorCode MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3698 {
3699   PetscInt       m,cstart, cend,j,nnz,i,d;
3700   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3701   const PetscInt *JJ;
3702   PetscScalar    *values;
3703   PetscErrorCode ierr;
3704   PetscBool      nooffprocentries;
3705 
3706   PetscFunctionBegin;
3707   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3708 
3709   ierr   = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3710   ierr   = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3711   m      = B->rmap->n;
3712   cstart = B->cmap->rstart;
3713   cend   = B->cmap->rend;
3714   rstart = B->rmap->rstart;
3715 
3716   ierr = PetscMalloc2(m,&d_nnz,m,&o_nnz);CHKERRQ(ierr);
3717 
3718 #if defined(PETSC_USE_DEBUGGING)
3719   for (i=0; i<m; i++) {
3720     nnz = Ii[i+1]- Ii[i];
3721     JJ  = J + Ii[i];
3722     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3723     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3724     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);
3725   }
3726 #endif
3727 
3728   for (i=0; i<m; i++) {
3729     nnz     = Ii[i+1]- Ii[i];
3730     JJ      = J + Ii[i];
3731     nnz_max = PetscMax(nnz_max,nnz);
3732     d       = 0;
3733     for (j=0; j<nnz; j++) {
3734       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3735     }
3736     d_nnz[i] = d;
3737     o_nnz[i] = nnz - d;
3738   }
3739   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3740   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3741 
3742   if (v) values = (PetscScalar*)v;
3743   else {
3744     ierr = PetscCalloc1(nnz_max+1,&values);CHKERRQ(ierr);
3745   }
3746 
3747   for (i=0; i<m; i++) {
3748     ii   = i + rstart;
3749     nnz  = Ii[i+1]- Ii[i];
3750     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3751   }
3752   nooffprocentries    = B->nooffprocentries;
3753   B->nooffprocentries = PETSC_TRUE;
3754   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3755   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3756   B->nooffprocentries = nooffprocentries;
3757 
3758   if (!v) {
3759     ierr = PetscFree(values);CHKERRQ(ierr);
3760   }
3761   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3762   PetscFunctionReturn(0);
3763 }
3764 
3765 /*@
3766    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3767    (the default parallel PETSc format).
3768 
3769    Collective on MPI_Comm
3770 
3771    Input Parameters:
3772 +  B - the matrix
3773 .  i - the indices into j for the start of each local row (starts with zero)
3774 .  j - the column indices for each local row (starts with zero)
3775 -  v - optional values in the matrix
3776 
3777    Level: developer
3778 
3779    Notes:
3780        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3781      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3782      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3783 
3784        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3785 
3786        The format which is used for the sparse matrix input, is equivalent to a
3787     row-major ordering.. i.e for the following matrix, the input data expected is
3788     as shown
3789 
3790 $        1 0 0
3791 $        2 0 3     P0
3792 $       -------
3793 $        4 5 6     P1
3794 $
3795 $     Process0 [P0]: rows_owned=[0,1]
3796 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3797 $        j =  {0,0,2}  [size = 3]
3798 $        v =  {1,2,3}  [size = 3]
3799 $
3800 $     Process1 [P1]: rows_owned=[2]
3801 $        i =  {0,3}    [size = nrow+1  = 1+1]
3802 $        j =  {0,1,2}  [size = 3]
3803 $        v =  {4,5,6}  [size = 3]
3804 
3805 .keywords: matrix, aij, compressed row, sparse, parallel
3806 
3807 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MATMPIAIJ,
3808           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3809 @*/
3810 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3811 {
3812   PetscErrorCode ierr;
3813 
3814   PetscFunctionBegin;
3815   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3816   PetscFunctionReturn(0);
3817 }
3818 
3819 /*@C
3820    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3821    (the default parallel PETSc format).  For good matrix assembly performance
3822    the user should preallocate the matrix storage by setting the parameters
3823    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3824    performance can be increased by more than a factor of 50.
3825 
3826    Collective on MPI_Comm
3827 
3828    Input Parameters:
3829 +  B - the matrix
3830 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3831            (same value is used for all local rows)
3832 .  d_nnz - array containing the number of nonzeros in the various rows of the
3833            DIAGONAL portion of the local submatrix (possibly different for each row)
3834            or NULL (PETSC_NULL_INTEGER in Fortran), if d_nz is used to specify the nonzero structure.
3835            The size of this array is equal to the number of local rows, i.e 'm'.
3836            For matrices that will be factored, you must leave room for (and set)
3837            the diagonal entry even if it is zero.
3838 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3839            submatrix (same value is used for all local rows).
3840 -  o_nnz - array containing the number of nonzeros in the various rows of the
3841            OFF-DIAGONAL portion of the local submatrix (possibly different for
3842            each row) or NULL (PETSC_NULL_INTEGER in Fortran), if o_nz is used to specify the nonzero
3843            structure. The size of this array is equal to the number
3844            of local rows, i.e 'm'.
3845 
3846    If the *_nnz parameter is given then the *_nz parameter is ignored
3847 
3848    The AIJ format (also called the Yale sparse matrix format or
3849    compressed row storage (CSR)), is fully compatible with standard Fortran 77
3850    storage.  The stored row and column indices begin with zero.
3851    See Users-Manual: ch_mat for details.
3852 
3853    The parallel matrix is partitioned such that the first m0 rows belong to
3854    process 0, the next m1 rows belong to process 1, the next m2 rows belong
3855    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
3856 
3857    The DIAGONAL portion of the local submatrix of a processor can be defined
3858    as the submatrix which is obtained by extraction the part corresponding to
3859    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
3860    first row that belongs to the processor, r2 is the last row belonging to
3861    the this processor, and c1-c2 is range of indices of the local part of a
3862    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
3863    common case of a square matrix, the row and column ranges are the same and
3864    the DIAGONAL part is also square. The remaining portion of the local
3865    submatrix (mxN) constitute the OFF-DIAGONAL portion.
3866 
3867    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3868 
3869    You can call MatGetInfo() to get information on how effective the preallocation was;
3870    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3871    You can also run with the option -info and look for messages with the string
3872    malloc in them to see if additional memory allocation was needed.
3873 
3874    Example usage:
3875 
3876    Consider the following 8x8 matrix with 34 non-zero values, that is
3877    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3878    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3879    as follows:
3880 
3881 .vb
3882             1  2  0  |  0  3  0  |  0  4
3883     Proc0   0  5  6  |  7  0  0  |  8  0
3884             9  0 10  | 11  0  0  | 12  0
3885     -------------------------------------
3886            13  0 14  | 15 16 17  |  0  0
3887     Proc1   0 18  0  | 19 20 21  |  0  0
3888             0  0  0  | 22 23  0  | 24  0
3889     -------------------------------------
3890     Proc2  25 26 27  |  0  0 28  | 29  0
3891            30  0  0  | 31 32 33  |  0 34
3892 .ve
3893 
3894    This can be represented as a collection of submatrices as:
3895 
3896 .vb
3897       A B C
3898       D E F
3899       G H I
3900 .ve
3901 
3902    Where the submatrices A,B,C are owned by proc0, D,E,F are
3903    owned by proc1, G,H,I are owned by proc2.
3904 
3905    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3906    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3907    The 'M','N' parameters are 8,8, and have the same values on all procs.
3908 
3909    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3910    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3911    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3912    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3913    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3914    matrix, ans [DF] as another SeqAIJ matrix.
3915 
3916    When d_nz, o_nz parameters are specified, d_nz storage elements are
3917    allocated for every row of the local diagonal submatrix, and o_nz
3918    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3919    One way to choose d_nz and o_nz is to use the max nonzerors per local
3920    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3921    In this case, the values of d_nz,o_nz are:
3922 .vb
3923      proc0 : dnz = 2, o_nz = 2
3924      proc1 : dnz = 3, o_nz = 2
3925      proc2 : dnz = 1, o_nz = 4
3926 .ve
3927    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3928    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3929    for proc3. i.e we are using 12+15+10=37 storage locations to store
3930    34 values.
3931 
3932    When d_nnz, o_nnz parameters are specified, the storage is specified
3933    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3934    In the above case the values for d_nnz,o_nnz are:
3935 .vb
3936      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3937      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3938      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3939 .ve
3940    Here the space allocated is sum of all the above values i.e 34, and
3941    hence pre-allocation is perfect.
3942 
3943    Level: intermediate
3944 
3945 .keywords: matrix, aij, compressed row, sparse, parallel
3946 
3947 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
3948           MATMPIAIJ, MatGetInfo(), PetscSplitOwnership()
3949 @*/
3950 PetscErrorCode MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3951 {
3952   PetscErrorCode ierr;
3953 
3954   PetscFunctionBegin;
3955   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3956   PetscValidType(B,1);
3957   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
3958   PetscFunctionReturn(0);
3959 }
3960 
3961 /*@
3962      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
3963          CSR format the local rows.
3964 
3965    Collective on MPI_Comm
3966 
3967    Input Parameters:
3968 +  comm - MPI communicator
3969 .  m - number of local rows (Cannot be PETSC_DECIDE)
3970 .  n - This value should be the same as the local size used in creating the
3971        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3972        calculated if N is given) For square matrices n is almost always m.
3973 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3974 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3975 .   i - row indices
3976 .   j - column indices
3977 -   a - matrix values
3978 
3979    Output Parameter:
3980 .   mat - the matrix
3981 
3982    Level: intermediate
3983 
3984    Notes:
3985        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3986      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3987      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3988 
3989        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3990 
3991        The format which is used for the sparse matrix input, is equivalent to a
3992     row-major ordering.. i.e for the following matrix, the input data expected is
3993     as shown
3994 
3995 $        1 0 0
3996 $        2 0 3     P0
3997 $       -------
3998 $        4 5 6     P1
3999 $
4000 $     Process0 [P0]: rows_owned=[0,1]
4001 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
4002 $        j =  {0,0,2}  [size = 3]
4003 $        v =  {1,2,3}  [size = 3]
4004 $
4005 $     Process1 [P1]: rows_owned=[2]
4006 $        i =  {0,3}    [size = nrow+1  = 1+1]
4007 $        j =  {0,1,2}  [size = 3]
4008 $        v =  {4,5,6}  [size = 3]
4009 
4010 .keywords: matrix, aij, compressed row, sparse, parallel
4011 
4012 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
4013           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
4014 @*/
4015 PetscErrorCode MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
4016 {
4017   PetscErrorCode ierr;
4018 
4019   PetscFunctionBegin;
4020   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
4021   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
4022   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4023   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
4024   /* ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr); */
4025   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
4026   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
4027   PetscFunctionReturn(0);
4028 }
4029 
4030 /*@C
4031    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
4032    (the default parallel PETSc format).  For good matrix assembly performance
4033    the user should preallocate the matrix storage by setting the parameters
4034    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
4035    performance can be increased by more than a factor of 50.
4036 
4037    Collective on MPI_Comm
4038 
4039    Input Parameters:
4040 +  comm - MPI communicator
4041 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
4042            This value should be the same as the local size used in creating the
4043            y vector for the matrix-vector product y = Ax.
4044 .  n - This value should be the same as the local size used in creating the
4045        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
4046        calculated if N is given) For square matrices n is almost always m.
4047 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
4048 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
4049 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
4050            (same value is used for all local rows)
4051 .  d_nnz - array containing the number of nonzeros in the various rows of the
4052            DIAGONAL portion of the local submatrix (possibly different for each row)
4053            or NULL, if d_nz is used to specify the nonzero structure.
4054            The size of this array is equal to the number of local rows, i.e 'm'.
4055 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
4056            submatrix (same value is used for all local rows).
4057 -  o_nnz - array containing the number of nonzeros in the various rows of the
4058            OFF-DIAGONAL portion of the local submatrix (possibly different for
4059            each row) or NULL, if o_nz is used to specify the nonzero
4060            structure. The size of this array is equal to the number
4061            of local rows, i.e 'm'.
4062 
4063    Output Parameter:
4064 .  A - the matrix
4065 
4066    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
4067    MatXXXXSetPreallocation() paradgm instead of this routine directly.
4068    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
4069 
4070    Notes:
4071    If the *_nnz parameter is given then the *_nz parameter is ignored
4072 
4073    m,n,M,N parameters specify the size of the matrix, and its partitioning across
4074    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
4075    storage requirements for this matrix.
4076 
4077    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
4078    processor than it must be used on all processors that share the object for
4079    that argument.
4080 
4081    The user MUST specify either the local or global matrix dimensions
4082    (possibly both).
4083 
4084    The parallel matrix is partitioned across processors such that the
4085    first m0 rows belong to process 0, the next m1 rows belong to
4086    process 1, the next m2 rows belong to process 2 etc.. where
4087    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
4088    values corresponding to [m x N] submatrix.
4089 
4090    The columns are logically partitioned with the n0 columns belonging
4091    to 0th partition, the next n1 columns belonging to the next
4092    partition etc.. where n0,n1,n2... are the input parameter 'n'.
4093 
4094    The DIAGONAL portion of the local submatrix on any given processor
4095    is the submatrix corresponding to the rows and columns m,n
4096    corresponding to the given processor. i.e diagonal matrix on
4097    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
4098    etc. The remaining portion of the local submatrix [m x (N-n)]
4099    constitute the OFF-DIAGONAL portion. The example below better
4100    illustrates this concept.
4101 
4102    For a square global matrix we define each processor's diagonal portion
4103    to be its local rows and the corresponding columns (a square submatrix);
4104    each processor's off-diagonal portion encompasses the remainder of the
4105    local matrix (a rectangular submatrix).
4106 
4107    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
4108 
4109    When calling this routine with a single process communicator, a matrix of
4110    type SEQAIJ is returned.  If a matrix of type MATMPIAIJ is desired for this
4111    type of communicator, use the construction mechanism:
4112      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
4113 
4114    By default, this format uses inodes (identical nodes) when possible.
4115    We search for consecutive rows with the same nonzero structure, thereby
4116    reusing matrix information to achieve increased efficiency.
4117 
4118    Options Database Keys:
4119 +  -mat_no_inode  - Do not use inodes
4120 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
4121 -  -mat_aij_oneindex - Internally use indexing starting at 1
4122         rather than 0.  Note that when calling MatSetValues(),
4123         the user still MUST index entries starting at 0!
4124 
4125 
4126    Example usage:
4127 
4128    Consider the following 8x8 matrix with 34 non-zero values, that is
4129    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
4130    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
4131    as follows:
4132 
4133 .vb
4134             1  2  0  |  0  3  0  |  0  4
4135     Proc0   0  5  6  |  7  0  0  |  8  0
4136             9  0 10  | 11  0  0  | 12  0
4137     -------------------------------------
4138            13  0 14  | 15 16 17  |  0  0
4139     Proc1   0 18  0  | 19 20 21  |  0  0
4140             0  0  0  | 22 23  0  | 24  0
4141     -------------------------------------
4142     Proc2  25 26 27  |  0  0 28  | 29  0
4143            30  0  0  | 31 32 33  |  0 34
4144 .ve
4145 
4146    This can be represented as a collection of submatrices as:
4147 
4148 .vb
4149       A B C
4150       D E F
4151       G H I
4152 .ve
4153 
4154    Where the submatrices A,B,C are owned by proc0, D,E,F are
4155    owned by proc1, G,H,I are owned by proc2.
4156 
4157    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4158    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4159    The 'M','N' parameters are 8,8, and have the same values on all procs.
4160 
4161    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
4162    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
4163    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
4164    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
4165    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
4166    matrix, ans [DF] as another SeqAIJ matrix.
4167 
4168    When d_nz, o_nz parameters are specified, d_nz storage elements are
4169    allocated for every row of the local diagonal submatrix, and o_nz
4170    storage locations are allocated for every row of the OFF-DIAGONAL submat.
4171    One way to choose d_nz and o_nz is to use the max nonzerors per local
4172    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
4173    In this case, the values of d_nz,o_nz are:
4174 .vb
4175      proc0 : dnz = 2, o_nz = 2
4176      proc1 : dnz = 3, o_nz = 2
4177      proc2 : dnz = 1, o_nz = 4
4178 .ve
4179    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
4180    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
4181    for proc3. i.e we are using 12+15+10=37 storage locations to store
4182    34 values.
4183 
4184    When d_nnz, o_nnz parameters are specified, the storage is specified
4185    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
4186    In the above case the values for d_nnz,o_nnz are:
4187 .vb
4188      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
4189      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
4190      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
4191 .ve
4192    Here the space allocated is sum of all the above values i.e 34, and
4193    hence pre-allocation is perfect.
4194 
4195    Level: intermediate
4196 
4197 .keywords: matrix, aij, compressed row, sparse, parallel
4198 
4199 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
4200           MATMPIAIJ, MatCreateMPIAIJWithArrays()
4201 @*/
4202 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)
4203 {
4204   PetscErrorCode ierr;
4205   PetscMPIInt    size;
4206 
4207   PetscFunctionBegin;
4208   ierr = MatCreate(comm,A);CHKERRQ(ierr);
4209   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
4210   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4211   if (size > 1) {
4212     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
4213     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
4214   } else {
4215     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
4216     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
4217   }
4218   PetscFunctionReturn(0);
4219 }
4220 
4221 PetscErrorCode MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
4222 {
4223   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
4224   PetscBool      flg;
4225   PetscErrorCode ierr;
4226 
4227   PetscFunctionBegin;
4228   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&flg);CHKERRQ(ierr);
4229   if (!flg) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"This function requires a MATMPIAIJ matrix as input");
4230   if (Ad)     *Ad     = a->A;
4231   if (Ao)     *Ao     = a->B;
4232   if (colmap) *colmap = a->garray;
4233   PetscFunctionReturn(0);
4234 }
4235 
4236 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
4237 {
4238   PetscErrorCode ierr;
4239   PetscInt       m,N,i,rstart,nnz,Ii;
4240   PetscInt       *indx;
4241   PetscScalar    *values;
4242 
4243   PetscFunctionBegin;
4244   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
4245   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
4246     PetscInt       *dnz,*onz,sum,bs,cbs;
4247 
4248     if (n == PETSC_DECIDE) {
4249       ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
4250     }
4251     /* Check sum(n) = N */
4252     ierr = MPIU_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4253     if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
4254 
4255     ierr    = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4256     rstart -= m;
4257 
4258     ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4259     for (i=0; i<m; i++) {
4260       ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
4261       ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
4262       ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
4263     }
4264 
4265     ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
4266     ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4267     ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
4268     ierr = MatSetBlockSizes(*outmat,bs,cbs);CHKERRQ(ierr);
4269     ierr = MatSetType(*outmat,MATAIJ);CHKERRQ(ierr);
4270     ierr = MatSeqAIJSetPreallocation(*outmat,0,dnz);CHKERRQ(ierr);
4271     ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
4272     ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4273   }
4274 
4275   /* numeric phase */
4276   ierr = MatGetOwnershipRange(*outmat,&rstart,NULL);CHKERRQ(ierr);
4277   for (i=0; i<m; i++) {
4278     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4279     Ii   = i + rstart;
4280     ierr = MatSetValues(*outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4281     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4282   }
4283   ierr = MatAssemblyBegin(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4284   ierr = MatAssemblyEnd(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4285   PetscFunctionReturn(0);
4286 }
4287 
4288 PetscErrorCode MatFileSplit(Mat A,char *outfile)
4289 {
4290   PetscErrorCode    ierr;
4291   PetscMPIInt       rank;
4292   PetscInt          m,N,i,rstart,nnz;
4293   size_t            len;
4294   const PetscInt    *indx;
4295   PetscViewer       out;
4296   char              *name;
4297   Mat               B;
4298   const PetscScalar *values;
4299 
4300   PetscFunctionBegin;
4301   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
4302   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
4303   /* Should this be the type of the diagonal block of A? */
4304   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
4305   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
4306   ierr = MatSetBlockSizesFromMats(B,A,A);CHKERRQ(ierr);
4307   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
4308   ierr = MatSeqAIJSetPreallocation(B,0,NULL);CHKERRQ(ierr);
4309   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
4310   for (i=0; i<m; i++) {
4311     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4312     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4313     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4314   }
4315   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4316   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4317 
4318   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
4319   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
4320   ierr = PetscMalloc1(len+5,&name);CHKERRQ(ierr);
4321   sprintf(name,"%s.%d",outfile,rank);
4322   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
4323   ierr = PetscFree(name);CHKERRQ(ierr);
4324   ierr = MatView(B,out);CHKERRQ(ierr);
4325   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
4326   ierr = MatDestroy(&B);CHKERRQ(ierr);
4327   PetscFunctionReturn(0);
4328 }
4329 
4330 PetscErrorCode MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
4331 {
4332   PetscErrorCode      ierr;
4333   Mat_Merge_SeqsToMPI *merge;
4334   PetscContainer      container;
4335 
4336   PetscFunctionBegin;
4337   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4338   if (container) {
4339     ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4340     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
4341     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
4342     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
4343     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
4344     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
4345     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
4346     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
4347     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
4348     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
4349     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
4350     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
4351     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
4352     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
4353     ierr = PetscFree(merge);CHKERRQ(ierr);
4354     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
4355   }
4356   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
4357   PetscFunctionReturn(0);
4358 }
4359 
4360 #include <../src/mat/utils/freespace.h>
4361 #include <petscbt.h>
4362 
4363 PetscErrorCode MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
4364 {
4365   PetscErrorCode      ierr;
4366   MPI_Comm            comm;
4367   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
4368   PetscMPIInt         size,rank,taga,*len_s;
4369   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
4370   PetscInt            proc,m;
4371   PetscInt            **buf_ri,**buf_rj;
4372   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
4373   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
4374   MPI_Request         *s_waits,*r_waits;
4375   MPI_Status          *status;
4376   MatScalar           *aa=a->a;
4377   MatScalar           **abuf_r,*ba_i;
4378   Mat_Merge_SeqsToMPI *merge;
4379   PetscContainer      container;
4380 
4381   PetscFunctionBegin;
4382   ierr = PetscObjectGetComm((PetscObject)mpimat,&comm);CHKERRQ(ierr);
4383   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4384 
4385   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4386   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4387 
4388   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4389   ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4390 
4391   bi     = merge->bi;
4392   bj     = merge->bj;
4393   buf_ri = merge->buf_ri;
4394   buf_rj = merge->buf_rj;
4395 
4396   ierr   = PetscMalloc1(size,&status);CHKERRQ(ierr);
4397   owners = merge->rowmap->range;
4398   len_s  = merge->len_s;
4399 
4400   /* send and recv matrix values */
4401   /*-----------------------------*/
4402   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
4403   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
4404 
4405   ierr = PetscMalloc1(merge->nsend+1,&s_waits);CHKERRQ(ierr);
4406   for (proc=0,k=0; proc<size; proc++) {
4407     if (!len_s[proc]) continue;
4408     i    = owners[proc];
4409     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
4410     k++;
4411   }
4412 
4413   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
4414   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
4415   ierr = PetscFree(status);CHKERRQ(ierr);
4416 
4417   ierr = PetscFree(s_waits);CHKERRQ(ierr);
4418   ierr = PetscFree(r_waits);CHKERRQ(ierr);
4419 
4420   /* insert mat values of mpimat */
4421   /*----------------------------*/
4422   ierr = PetscMalloc1(N,&ba_i);CHKERRQ(ierr);
4423   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4424 
4425   for (k=0; k<merge->nrecv; k++) {
4426     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4427     nrows       = *(buf_ri_k[k]);
4428     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
4429     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4430   }
4431 
4432   /* set values of ba */
4433   m = merge->rowmap->n;
4434   for (i=0; i<m; i++) {
4435     arow = owners[rank] + i;
4436     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
4437     bnzi = bi[i+1] - bi[i];
4438     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
4439 
4440     /* add local non-zero vals of this proc's seqmat into ba */
4441     anzi   = ai[arow+1] - ai[arow];
4442     aj     = a->j + ai[arow];
4443     aa     = a->a + ai[arow];
4444     nextaj = 0;
4445     for (j=0; nextaj<anzi; j++) {
4446       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4447         ba_i[j] += aa[nextaj++];
4448       }
4449     }
4450 
4451     /* add received vals into ba */
4452     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4453       /* i-th row */
4454       if (i == *nextrow[k]) {
4455         anzi   = *(nextai[k]+1) - *nextai[k];
4456         aj     = buf_rj[k] + *(nextai[k]);
4457         aa     = abuf_r[k] + *(nextai[k]);
4458         nextaj = 0;
4459         for (j=0; nextaj<anzi; j++) {
4460           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4461             ba_i[j] += aa[nextaj++];
4462           }
4463         }
4464         nextrow[k]++; nextai[k]++;
4465       }
4466     }
4467     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
4468   }
4469   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4470   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4471 
4472   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
4473   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
4474   ierr = PetscFree(ba_i);CHKERRQ(ierr);
4475   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4476   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4477   PetscFunctionReturn(0);
4478 }
4479 
4480 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4481 {
4482   PetscErrorCode      ierr;
4483   Mat                 B_mpi;
4484   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
4485   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4486   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
4487   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4488   PetscInt            len,proc,*dnz,*onz,bs,cbs;
4489   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4490   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4491   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
4492   MPI_Status          *status;
4493   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
4494   PetscBT             lnkbt;
4495   Mat_Merge_SeqsToMPI *merge;
4496   PetscContainer      container;
4497 
4498   PetscFunctionBegin;
4499   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4500 
4501   /* make sure it is a PETSc comm */
4502   ierr = PetscCommDuplicate(comm,&comm,NULL);CHKERRQ(ierr);
4503   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4504   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4505 
4506   ierr = PetscNew(&merge);CHKERRQ(ierr);
4507   ierr = PetscMalloc1(size,&status);CHKERRQ(ierr);
4508 
4509   /* determine row ownership */
4510   /*---------------------------------------------------------*/
4511   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
4512   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
4513   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
4514   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
4515   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
4516   ierr = PetscMalloc1(size,&len_si);CHKERRQ(ierr);
4517   ierr = PetscMalloc1(size,&merge->len_s);CHKERRQ(ierr);
4518 
4519   m      = merge->rowmap->n;
4520   owners = merge->rowmap->range;
4521 
4522   /* determine the number of messages to send, their lengths */
4523   /*---------------------------------------------------------*/
4524   len_s = merge->len_s;
4525 
4526   len          = 0; /* length of buf_si[] */
4527   merge->nsend = 0;
4528   for (proc=0; proc<size; proc++) {
4529     len_si[proc] = 0;
4530     if (proc == rank) {
4531       len_s[proc] = 0;
4532     } else {
4533       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4534       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4535     }
4536     if (len_s[proc]) {
4537       merge->nsend++;
4538       nrows = 0;
4539       for (i=owners[proc]; i<owners[proc+1]; i++) {
4540         if (ai[i+1] > ai[i]) nrows++;
4541       }
4542       len_si[proc] = 2*(nrows+1);
4543       len         += len_si[proc];
4544     }
4545   }
4546 
4547   /* determine the number and length of messages to receive for ij-structure */
4548   /*-------------------------------------------------------------------------*/
4549   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
4550   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
4551 
4552   /* post the Irecv of j-structure */
4553   /*-------------------------------*/
4554   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
4555   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
4556 
4557   /* post the Isend of j-structure */
4558   /*--------------------------------*/
4559   ierr = PetscMalloc2(merge->nsend,&si_waits,merge->nsend,&sj_waits);CHKERRQ(ierr);
4560 
4561   for (proc=0, k=0; proc<size; proc++) {
4562     if (!len_s[proc]) continue;
4563     i    = owners[proc];
4564     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
4565     k++;
4566   }
4567 
4568   /* receives and sends of j-structure are complete */
4569   /*------------------------------------------------*/
4570   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
4571   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
4572 
4573   /* send and recv i-structure */
4574   /*---------------------------*/
4575   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
4576   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
4577 
4578   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
4579   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4580   for (proc=0,k=0; proc<size; proc++) {
4581     if (!len_s[proc]) continue;
4582     /* form outgoing message for i-structure:
4583          buf_si[0]:                 nrows to be sent
4584                [1:nrows]:           row index (global)
4585                [nrows+1:2*nrows+1]: i-structure index
4586     */
4587     /*-------------------------------------------*/
4588     nrows       = len_si[proc]/2 - 1;
4589     buf_si_i    = buf_si + nrows+1;
4590     buf_si[0]   = nrows;
4591     buf_si_i[0] = 0;
4592     nrows       = 0;
4593     for (i=owners[proc]; i<owners[proc+1]; i++) {
4594       anzi = ai[i+1] - ai[i];
4595       if (anzi) {
4596         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4597         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4598         nrows++;
4599       }
4600     }
4601     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4602     k++;
4603     buf_si += len_si[proc];
4604   }
4605 
4606   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4607   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4608 
4609   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4610   for (i=0; i<merge->nrecv; i++) {
4611     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);
4612   }
4613 
4614   ierr = PetscFree(len_si);CHKERRQ(ierr);
4615   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4616   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4617   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4618   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4619   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4620   ierr = PetscFree(status);CHKERRQ(ierr);
4621 
4622   /* compute a local seq matrix in each processor */
4623   /*----------------------------------------------*/
4624   /* allocate bi array and free space for accumulating nonzero column info */
4625   ierr  = PetscMalloc1(m+1,&bi);CHKERRQ(ierr);
4626   bi[0] = 0;
4627 
4628   /* create and initialize a linked list */
4629   nlnk = N+1;
4630   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4631 
4632   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4633   len  = ai[owners[rank+1]] - ai[owners[rank]];
4634   ierr = PetscFreeSpaceGet(PetscIntMultTruncate(2,len)+1,&free_space);CHKERRQ(ierr);
4635 
4636   current_space = free_space;
4637 
4638   /* determine symbolic info for each local row */
4639   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4640 
4641   for (k=0; k<merge->nrecv; k++) {
4642     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4643     nrows       = *buf_ri_k[k];
4644     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4645     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4646   }
4647 
4648   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4649   len  = 0;
4650   for (i=0; i<m; i++) {
4651     bnzi = 0;
4652     /* add local non-zero cols of this proc's seqmat into lnk */
4653     arow  = owners[rank] + i;
4654     anzi  = ai[arow+1] - ai[arow];
4655     aj    = a->j + ai[arow];
4656     ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4657     bnzi += nlnk;
4658     /* add received col data into lnk */
4659     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4660       if (i == *nextrow[k]) { /* i-th row */
4661         anzi  = *(nextai[k]+1) - *nextai[k];
4662         aj    = buf_rj[k] + *nextai[k];
4663         ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4664         bnzi += nlnk;
4665         nextrow[k]++; nextai[k]++;
4666       }
4667     }
4668     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4669 
4670     /* if free space is not available, make more free space */
4671     if (current_space->local_remaining<bnzi) {
4672       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(bnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
4673       nspacedouble++;
4674     }
4675     /* copy data into free space, then initialize lnk */
4676     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4677     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
4678 
4679     current_space->array           += bnzi;
4680     current_space->local_used      += bnzi;
4681     current_space->local_remaining -= bnzi;
4682 
4683     bi[i+1] = bi[i] + bnzi;
4684   }
4685 
4686   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4687 
4688   ierr = PetscMalloc1(bi[m]+1,&bj);CHKERRQ(ierr);
4689   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
4690   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4691 
4692   /* create symbolic parallel matrix B_mpi */
4693   /*---------------------------------------*/
4694   ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
4695   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
4696   if (n==PETSC_DECIDE) {
4697     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
4698   } else {
4699     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4700   }
4701   ierr = MatSetBlockSizes(B_mpi,bs,cbs);CHKERRQ(ierr);
4702   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
4703   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
4704   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4705   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
4706 
4707   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4708   B_mpi->assembled    = PETSC_FALSE;
4709   B_mpi->ops->destroy = MatDestroy_MPIAIJ_SeqsToMPI;
4710   merge->bi           = bi;
4711   merge->bj           = bj;
4712   merge->buf_ri       = buf_ri;
4713   merge->buf_rj       = buf_rj;
4714   merge->coi          = NULL;
4715   merge->coj          = NULL;
4716   merge->owners_co    = NULL;
4717 
4718   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
4719 
4720   /* attach the supporting struct to B_mpi for reuse */
4721   ierr    = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
4722   ierr    = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
4723   ierr    = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
4724   ierr    = PetscContainerDestroy(&container);CHKERRQ(ierr);
4725   *mpimat = B_mpi;
4726 
4727   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4728   PetscFunctionReturn(0);
4729 }
4730 
4731 /*@C
4732       MatCreateMPIAIJSumSeqAIJ - Creates a MATMPIAIJ matrix by adding sequential
4733                  matrices from each processor
4734 
4735     Collective on MPI_Comm
4736 
4737    Input Parameters:
4738 +    comm - the communicators the parallel matrix will live on
4739 .    seqmat - the input sequential matrices
4740 .    m - number of local rows (or PETSC_DECIDE)
4741 .    n - number of local columns (or PETSC_DECIDE)
4742 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4743 
4744    Output Parameter:
4745 .    mpimat - the parallel matrix generated
4746 
4747     Level: advanced
4748 
4749    Notes:
4750      The dimensions of the sequential matrix in each processor MUST be the same.
4751      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
4752      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
4753 @*/
4754 PetscErrorCode MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
4755 {
4756   PetscErrorCode ierr;
4757   PetscMPIInt    size;
4758 
4759   PetscFunctionBegin;
4760   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4761   if (size == 1) {
4762     ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4763     if (scall == MAT_INITIAL_MATRIX) {
4764       ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
4765     } else {
4766       ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4767     }
4768     ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4769     PetscFunctionReturn(0);
4770   }
4771   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4772   if (scall == MAT_INITIAL_MATRIX) {
4773     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
4774   }
4775   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
4776   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4777   PetscFunctionReturn(0);
4778 }
4779 
4780 /*@
4781      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MATMPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
4782           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
4783           with MatGetSize()
4784 
4785     Not Collective
4786 
4787    Input Parameters:
4788 +    A - the matrix
4789 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4790 
4791    Output Parameter:
4792 .    A_loc - the local sequential matrix generated
4793 
4794     Level: developer
4795 
4796 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
4797 
4798 @*/
4799 PetscErrorCode MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
4800 {
4801   PetscErrorCode ierr;
4802   Mat_MPIAIJ     *mpimat=(Mat_MPIAIJ*)A->data;
4803   Mat_SeqAIJ     *mat,*a,*b;
4804   PetscInt       *ai,*aj,*bi,*bj,*cmap=mpimat->garray;
4805   MatScalar      *aa,*ba,*cam;
4806   PetscScalar    *ca;
4807   PetscInt       am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
4808   PetscInt       *ci,*cj,col,ncols_d,ncols_o,jo;
4809   PetscBool      match;
4810   MPI_Comm       comm;
4811   PetscMPIInt    size;
4812 
4813   PetscFunctionBegin;
4814   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4815   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
4816   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4817   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4818   if (size == 1 && scall == MAT_REUSE_MATRIX) PetscFunctionReturn(0);
4819 
4820   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4821   a = (Mat_SeqAIJ*)(mpimat->A)->data;
4822   b = (Mat_SeqAIJ*)(mpimat->B)->data;
4823   ai = a->i; aj = a->j; bi = b->i; bj = b->j;
4824   aa = a->a; ba = b->a;
4825   if (scall == MAT_INITIAL_MATRIX) {
4826     if (size == 1) {
4827       ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ai,aj,aa,A_loc);CHKERRQ(ierr);
4828       PetscFunctionReturn(0);
4829     }
4830 
4831     ierr  = PetscMalloc1(1+am,&ci);CHKERRQ(ierr);
4832     ci[0] = 0;
4833     for (i=0; i<am; i++) {
4834       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
4835     }
4836     ierr = PetscMalloc1(1+ci[am],&cj);CHKERRQ(ierr);
4837     ierr = PetscMalloc1(1+ci[am],&ca);CHKERRQ(ierr);
4838     k    = 0;
4839     for (i=0; i<am; i++) {
4840       ncols_o = bi[i+1] - bi[i];
4841       ncols_d = ai[i+1] - ai[i];
4842       /* off-diagonal portion of A */
4843       for (jo=0; jo<ncols_o; jo++) {
4844         col = cmap[*bj];
4845         if (col >= cstart) break;
4846         cj[k]   = col; bj++;
4847         ca[k++] = *ba++;
4848       }
4849       /* diagonal portion of A */
4850       for (j=0; j<ncols_d; j++) {
4851         cj[k]   = cstart + *aj++;
4852         ca[k++] = *aa++;
4853       }
4854       /* off-diagonal portion of A */
4855       for (j=jo; j<ncols_o; j++) {
4856         cj[k]   = cmap[*bj++];
4857         ca[k++] = *ba++;
4858       }
4859     }
4860     /* put together the new matrix */
4861     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
4862     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4863     /* Since these are PETSc arrays, change flags to free them as necessary. */
4864     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
4865     mat->free_a  = PETSC_TRUE;
4866     mat->free_ij = PETSC_TRUE;
4867     mat->nonew   = 0;
4868   } else if (scall == MAT_REUSE_MATRIX) {
4869     mat=(Mat_SeqAIJ*)(*A_loc)->data;
4870     ci = mat->i; cj = mat->j; cam = mat->a;
4871     for (i=0; i<am; i++) {
4872       /* off-diagonal portion of A */
4873       ncols_o = bi[i+1] - bi[i];
4874       for (jo=0; jo<ncols_o; jo++) {
4875         col = cmap[*bj];
4876         if (col >= cstart) break;
4877         *cam++ = *ba++; bj++;
4878       }
4879       /* diagonal portion of A */
4880       ncols_d = ai[i+1] - ai[i];
4881       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
4882       /* off-diagonal portion of A */
4883       for (j=jo; j<ncols_o; j++) {
4884         *cam++ = *ba++; bj++;
4885       }
4886     }
4887   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
4888   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4889   PetscFunctionReturn(0);
4890 }
4891 
4892 /*@C
4893      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MATMPIAIJ matrix by taking all its local rows and NON-ZERO columns
4894 
4895     Not Collective
4896 
4897    Input Parameters:
4898 +    A - the matrix
4899 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4900 -    row, col - index sets of rows and columns to extract (or NULL)
4901 
4902    Output Parameter:
4903 .    A_loc - the local sequential matrix generated
4904 
4905     Level: developer
4906 
4907 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
4908 
4909 @*/
4910 PetscErrorCode MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
4911 {
4912   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4913   PetscErrorCode ierr;
4914   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
4915   IS             isrowa,iscola;
4916   Mat            *aloc;
4917   PetscBool      match;
4918 
4919   PetscFunctionBegin;
4920   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4921   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
4922   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4923   if (!row) {
4924     start = A->rmap->rstart; end = A->rmap->rend;
4925     ierr  = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
4926   } else {
4927     isrowa = *row;
4928   }
4929   if (!col) {
4930     start = A->cmap->rstart;
4931     cmap  = a->garray;
4932     nzA   = a->A->cmap->n;
4933     nzB   = a->B->cmap->n;
4934     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4935     ncols = 0;
4936     for (i=0; i<nzB; i++) {
4937       if (cmap[i] < start) idx[ncols++] = cmap[i];
4938       else break;
4939     }
4940     imark = i;
4941     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
4942     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
4943     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
4944   } else {
4945     iscola = *col;
4946   }
4947   if (scall != MAT_INITIAL_MATRIX) {
4948     ierr    = PetscMalloc1(1,&aloc);CHKERRQ(ierr);
4949     aloc[0] = *A_loc;
4950   }
4951   ierr   = MatCreateSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
4952   *A_loc = aloc[0];
4953   ierr   = PetscFree(aloc);CHKERRQ(ierr);
4954   if (!row) {
4955     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
4956   }
4957   if (!col) {
4958     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
4959   }
4960   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4961   PetscFunctionReturn(0);
4962 }
4963 
4964 /*@C
4965     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
4966 
4967     Collective on Mat
4968 
4969    Input Parameters:
4970 +    A,B - the matrices in mpiaij format
4971 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4972 -    rowb, colb - index sets of rows and columns of B to extract (or NULL)
4973 
4974    Output Parameter:
4975 +    rowb, colb - index sets of rows and columns of B to extract
4976 -    B_seq - the sequential matrix generated
4977 
4978     Level: developer
4979 
4980 @*/
4981 PetscErrorCode MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
4982 {
4983   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4984   PetscErrorCode ierr;
4985   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
4986   IS             isrowb,iscolb;
4987   Mat            *bseq=NULL;
4988 
4989   PetscFunctionBegin;
4990   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4991     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);
4992   }
4993   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4994 
4995   if (scall == MAT_INITIAL_MATRIX) {
4996     start = A->cmap->rstart;
4997     cmap  = a->garray;
4998     nzA   = a->A->cmap->n;
4999     nzB   = a->B->cmap->n;
5000     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
5001     ncols = 0;
5002     for (i=0; i<nzB; i++) {  /* row < local row index */
5003       if (cmap[i] < start) idx[ncols++] = cmap[i];
5004       else break;
5005     }
5006     imark = i;
5007     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
5008     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
5009     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
5010     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
5011   } else {
5012     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
5013     isrowb  = *rowb; iscolb = *colb;
5014     ierr    = PetscMalloc1(1,&bseq);CHKERRQ(ierr);
5015     bseq[0] = *B_seq;
5016   }
5017   ierr   = MatCreateSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
5018   *B_seq = bseq[0];
5019   ierr   = PetscFree(bseq);CHKERRQ(ierr);
5020   if (!rowb) {
5021     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
5022   } else {
5023     *rowb = isrowb;
5024   }
5025   if (!colb) {
5026     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
5027   } else {
5028     *colb = iscolb;
5029   }
5030   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
5031   PetscFunctionReturn(0);
5032 }
5033 
5034 /*
5035     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
5036     of the OFF-DIAGONAL portion of local A
5037 
5038     Collective on Mat
5039 
5040    Input Parameters:
5041 +    A,B - the matrices in mpiaij format
5042 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5043 
5044    Output Parameter:
5045 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
5046 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
5047 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
5048 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
5049 
5050     Level: developer
5051 
5052 */
5053 PetscErrorCode MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
5054 {
5055   VecScatter_MPI_General *gen_to,*gen_from;
5056   PetscErrorCode         ierr;
5057   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
5058   Mat_SeqAIJ             *b_oth;
5059   VecScatter             ctx =a->Mvctx;
5060   MPI_Comm               comm;
5061   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
5062   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
5063   PetscInt               *rvalues,*svalues;
5064   MatScalar              *b_otha,*bufa,*bufA;
5065   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
5066   MPI_Request            *rwaits = NULL,*swaits = NULL;
5067   MPI_Status             *sstatus,rstatus;
5068   PetscMPIInt            jj,size;
5069   PetscInt               *cols,sbs,rbs;
5070   PetscScalar            *vals;
5071 
5072   PetscFunctionBegin;
5073   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
5074   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
5075 
5076   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
5077     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);
5078   }
5079   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5080   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
5081 
5082   if (size == 1) {
5083     startsj_s = NULL;
5084     bufa_ptr  = NULL;
5085     *B_oth    = NULL;
5086     PetscFunctionReturn(0);
5087   }
5088 
5089   gen_to   = (VecScatter_MPI_General*)ctx->todata;
5090   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
5091   nrecvs   = gen_from->n;
5092   nsends   = gen_to->n;
5093 
5094   ierr    = PetscMalloc2(nrecvs,&rwaits,nsends,&swaits);CHKERRQ(ierr);
5095   srow    = gen_to->indices;    /* local row index to be sent */
5096   sstarts = gen_to->starts;
5097   sprocs  = gen_to->procs;
5098   sstatus = gen_to->sstatus;
5099   sbs     = gen_to->bs;
5100   rstarts = gen_from->starts;
5101   rprocs  = gen_from->procs;
5102   rbs     = gen_from->bs;
5103 
5104   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
5105   if (scall == MAT_INITIAL_MATRIX) {
5106     /* i-array */
5107     /*---------*/
5108     /*  post receives */
5109     ierr = PetscMalloc1(rbs*(rstarts[nrecvs] - rstarts[0]),&rvalues);CHKERRQ(ierr);
5110     for (i=0; i<nrecvs; i++) {
5111       rowlen = rvalues + rstarts[i]*rbs;
5112       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
5113       ierr   = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5114     }
5115 
5116     /* pack the outgoing message */
5117     ierr = PetscMalloc2(nsends+1,&sstartsj,nrecvs+1,&rstartsj);CHKERRQ(ierr);
5118 
5119     sstartsj[0] = 0;
5120     rstartsj[0] = 0;
5121     len         = 0; /* total length of j or a array to be sent */
5122     k           = 0;
5123     ierr = PetscMalloc1(sbs*(sstarts[nsends] - sstarts[0]),&svalues);CHKERRQ(ierr);
5124     for (i=0; i<nsends; i++) {
5125       rowlen = svalues + sstarts[i]*sbs;
5126       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
5127       for (j=0; j<nrows; j++) {
5128         row = srow[k] + B->rmap->range[rank]; /* global row idx */
5129         for (l=0; l<sbs; l++) {
5130           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr); /* rowlength */
5131 
5132           rowlen[j*sbs+l] = ncols;
5133 
5134           len += ncols;
5135           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr);
5136         }
5137         k++;
5138       }
5139       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5140 
5141       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
5142     }
5143     /* recvs and sends of i-array are completed */
5144     i = nrecvs;
5145     while (i--) {
5146       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5147     }
5148     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5149     ierr = PetscFree(svalues);CHKERRQ(ierr);
5150 
5151     /* allocate buffers for sending j and a arrays */
5152     ierr = PetscMalloc1(len+1,&bufj);CHKERRQ(ierr);
5153     ierr = PetscMalloc1(len+1,&bufa);CHKERRQ(ierr);
5154 
5155     /* create i-array of B_oth */
5156     ierr = PetscMalloc1(aBn+2,&b_othi);CHKERRQ(ierr);
5157 
5158     b_othi[0] = 0;
5159     len       = 0; /* total length of j or a array to be received */
5160     k         = 0;
5161     for (i=0; i<nrecvs; i++) {
5162       rowlen = rvalues + rstarts[i]*rbs;
5163       nrows  = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be received */
5164       for (j=0; j<nrows; j++) {
5165         b_othi[k+1] = b_othi[k] + rowlen[j];
5166         ierr = PetscIntSumError(rowlen[j],len,&len);CHKERRQ(ierr);
5167         k++;
5168       }
5169       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
5170     }
5171     ierr = PetscFree(rvalues);CHKERRQ(ierr);
5172 
5173     /* allocate space for j and a arrrays of B_oth */
5174     ierr = PetscMalloc1(b_othi[aBn]+1,&b_othj);CHKERRQ(ierr);
5175     ierr = PetscMalloc1(b_othi[aBn]+1,&b_otha);CHKERRQ(ierr);
5176 
5177     /* j-array */
5178     /*---------*/
5179     /*  post receives of j-array */
5180     for (i=0; i<nrecvs; i++) {
5181       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5182       ierr  = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5183     }
5184 
5185     /* pack the outgoing message j-array */
5186     k = 0;
5187     for (i=0; i<nsends; i++) {
5188       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5189       bufJ  = bufj+sstartsj[i];
5190       for (j=0; j<nrows; j++) {
5191         row = srow[k++] + B->rmap->range[rank];  /* global row idx */
5192         for (ll=0; ll<sbs; ll++) {
5193           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
5194           for (l=0; l<ncols; l++) {
5195             *bufJ++ = cols[l];
5196           }
5197           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
5198         }
5199       }
5200       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5201     }
5202 
5203     /* recvs and sends of j-array are completed */
5204     i = nrecvs;
5205     while (i--) {
5206       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5207     }
5208     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5209   } else if (scall == MAT_REUSE_MATRIX) {
5210     sstartsj = *startsj_s;
5211     rstartsj = *startsj_r;
5212     bufa     = *bufa_ptr;
5213     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
5214     b_otha   = b_oth->a;
5215   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
5216 
5217   /* a-array */
5218   /*---------*/
5219   /*  post receives of a-array */
5220   for (i=0; i<nrecvs; i++) {
5221     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5222     ierr  = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5223   }
5224 
5225   /* pack the outgoing message a-array */
5226   k = 0;
5227   for (i=0; i<nsends; i++) {
5228     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5229     bufA  = bufa+sstartsj[i];
5230     for (j=0; j<nrows; j++) {
5231       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
5232       for (ll=0; ll<sbs; ll++) {
5233         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
5234         for (l=0; l<ncols; l++) {
5235           *bufA++ = vals[l];
5236         }
5237         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
5238       }
5239     }
5240     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5241   }
5242   /* recvs and sends of a-array are completed */
5243   i = nrecvs;
5244   while (i--) {
5245     ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5246   }
5247   if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5248   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
5249 
5250   if (scall == MAT_INITIAL_MATRIX) {
5251     /* put together the new matrix */
5252     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
5253 
5254     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
5255     /* Since these are PETSc arrays, change flags to free them as necessary. */
5256     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
5257     b_oth->free_a  = PETSC_TRUE;
5258     b_oth->free_ij = PETSC_TRUE;
5259     b_oth->nonew   = 0;
5260 
5261     ierr = PetscFree(bufj);CHKERRQ(ierr);
5262     if (!startsj_s || !bufa_ptr) {
5263       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
5264       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
5265     } else {
5266       *startsj_s = sstartsj;
5267       *startsj_r = rstartsj;
5268       *bufa_ptr  = bufa;
5269     }
5270   }
5271   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5272   PetscFunctionReturn(0);
5273 }
5274 
5275 /*@C
5276   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
5277 
5278   Not Collective
5279 
5280   Input Parameters:
5281 . A - The matrix in mpiaij format
5282 
5283   Output Parameter:
5284 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
5285 . colmap - A map from global column index to local index into lvec
5286 - multScatter - A scatter from the argument of a matrix-vector product to lvec
5287 
5288   Level: developer
5289 
5290 @*/
5291 #if defined(PETSC_USE_CTABLE)
5292 PetscErrorCode MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
5293 #else
5294 PetscErrorCode MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
5295 #endif
5296 {
5297   Mat_MPIAIJ *a;
5298 
5299   PetscFunctionBegin;
5300   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
5301   PetscValidPointer(lvec, 2);
5302   PetscValidPointer(colmap, 3);
5303   PetscValidPointer(multScatter, 4);
5304   a = (Mat_MPIAIJ*) A->data;
5305   if (lvec) *lvec = a->lvec;
5306   if (colmap) *colmap = a->colmap;
5307   if (multScatter) *multScatter = a->Mvctx;
5308   PetscFunctionReturn(0);
5309 }
5310 
5311 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
5312 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
5313 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
5314 #if defined(PETSC_HAVE_ELEMENTAL)
5315 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
5316 #endif
5317 #if defined(PETSC_HAVE_HYPRE)
5318 PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat,MatType,MatReuse,Mat*);
5319 PETSC_INTERN PetscErrorCode MatMatMatMult_Transpose_AIJ_AIJ(Mat,Mat,Mat,MatReuse,PetscReal,Mat*);
5320 #endif
5321 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_IS(Mat,MatType,MatReuse,Mat*);
5322 
5323 /*
5324     Computes (B'*A')' since computing B*A directly is untenable
5325 
5326                n                       p                          p
5327         (              )       (              )         (                  )
5328       m (      A       )  *  n (       B      )   =   m (         C        )
5329         (              )       (              )         (                  )
5330 
5331 */
5332 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
5333 {
5334   PetscErrorCode ierr;
5335   Mat            At,Bt,Ct;
5336 
5337   PetscFunctionBegin;
5338   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
5339   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
5340   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
5341   ierr = MatDestroy(&At);CHKERRQ(ierr);
5342   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
5343   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
5344   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
5345   PetscFunctionReturn(0);
5346 }
5347 
5348 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
5349 {
5350   PetscErrorCode ierr;
5351   PetscInt       m=A->rmap->n,n=B->cmap->n;
5352   Mat            Cmat;
5353 
5354   PetscFunctionBegin;
5355   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);
5356   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
5357   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
5358   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
5359   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
5360   ierr = MatMPIDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
5361   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5362   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5363 
5364   Cmat->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
5365 
5366   *C = Cmat;
5367   PetscFunctionReturn(0);
5368 }
5369 
5370 /* ----------------------------------------------------------------*/
5371 PETSC_INTERN PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
5372 {
5373   PetscErrorCode ierr;
5374 
5375   PetscFunctionBegin;
5376   if (scall == MAT_INITIAL_MATRIX) {
5377     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5378     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
5379     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5380   }
5381   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5382   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
5383   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5384   PetscFunctionReturn(0);
5385 }
5386 
5387 /*MC
5388    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
5389 
5390    Options Database Keys:
5391 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
5392 
5393   Level: beginner
5394 
5395 .seealso: MatCreateAIJ()
5396 M*/
5397 
5398 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
5399 {
5400   Mat_MPIAIJ     *b;
5401   PetscErrorCode ierr;
5402   PetscMPIInt    size;
5403 
5404   PetscFunctionBegin;
5405   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
5406 
5407   ierr          = PetscNewLog(B,&b);CHKERRQ(ierr);
5408   B->data       = (void*)b;
5409   ierr          = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
5410   B->assembled  = PETSC_FALSE;
5411   B->insertmode = NOT_SET_VALUES;
5412   b->size       = size;
5413 
5414   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank);CHKERRQ(ierr);
5415 
5416   /* build cache for off array entries formed */
5417   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash);CHKERRQ(ierr);
5418 
5419   b->donotstash  = PETSC_FALSE;
5420   b->colmap      = 0;
5421   b->garray      = 0;
5422   b->roworiented = PETSC_TRUE;
5423 
5424   /* stuff used for matrix vector multiply */
5425   b->lvec  = NULL;
5426   b->Mvctx = NULL;
5427 
5428   /* stuff for MatGetRow() */
5429   b->rowindices   = 0;
5430   b->rowvalues    = 0;
5431   b->getrowactive = PETSC_FALSE;
5432 
5433   /* flexible pointer used in CUSP/CUSPARSE classes */
5434   b->spptr = NULL;
5435 
5436   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetUseScalableIncreaseOverlap_C",MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ);CHKERRQ(ierr);
5437   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ);CHKERRQ(ierr);
5438   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
5439   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
5440   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
5441   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
5442   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
5443   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
5444   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
5445   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
5446 #if defined(PETSC_HAVE_ELEMENTAL)
5447   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_elemental_C",MatConvert_MPIAIJ_Elemental);CHKERRQ(ierr);
5448 #endif
5449 #if defined(PETSC_HAVE_HYPRE)
5450   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_hypre_C",MatConvert_AIJ_HYPRE);CHKERRQ(ierr);
5451 #endif
5452   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_is_C",MatConvert_MPIAIJ_IS);CHKERRQ(ierr);
5453   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
5454   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
5455   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
5456 #if defined(PETSC_HAVE_HYPRE)
5457   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMatMult_transpose_mpiaij_mpiaij_C",MatMatMatMult_Transpose_AIJ_AIJ);CHKERRQ(ierr);
5458 #endif
5459   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
5460   PetscFunctionReturn(0);
5461 }
5462 
5463 /*@C
5464      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
5465          and "off-diagonal" part of the matrix in CSR format.
5466 
5467    Collective on MPI_Comm
5468 
5469    Input Parameters:
5470 +  comm - MPI communicator
5471 .  m - number of local rows (Cannot be PETSC_DECIDE)
5472 .  n - This value should be the same as the local size used in creating the
5473        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
5474        calculated if N is given) For square matrices n is almost always m.
5475 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
5476 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
5477 .   i - row indices for "diagonal" portion of matrix
5478 .   j - column indices
5479 .   a - matrix values
5480 .   oi - row indices for "off-diagonal" portion of matrix
5481 .   oj - column indices
5482 -   oa - matrix values
5483 
5484    Output Parameter:
5485 .   mat - the matrix
5486 
5487    Level: advanced
5488 
5489    Notes:
5490        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
5491        must free the arrays once the matrix has been destroyed and not before.
5492 
5493        The i and j indices are 0 based
5494 
5495        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
5496 
5497        This sets local rows and cannot be used to set off-processor values.
5498 
5499        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
5500        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
5501        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
5502        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
5503        keep track of the underlying array. Use MatSetOption(A,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
5504        communication if it is known that only local entries will be set.
5505 
5506 .keywords: matrix, aij, compressed row, sparse, parallel
5507 
5508 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
5509           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
5510 @*/
5511 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)
5512 {
5513   PetscErrorCode ierr;
5514   Mat_MPIAIJ     *maij;
5515 
5516   PetscFunctionBegin;
5517   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
5518   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
5519   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
5520   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
5521   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
5522   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
5523   maij = (Mat_MPIAIJ*) (*mat)->data;
5524 
5525   (*mat)->preallocated = PETSC_TRUE;
5526 
5527   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
5528   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
5529 
5530   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
5531   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
5532 
5533   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5534   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5535   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5536   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5537 
5538   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
5539   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5540   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5541   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_FALSE);CHKERRQ(ierr);
5542   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
5543   PetscFunctionReturn(0);
5544 }
5545 
5546 /*
5547     Special version for direct calls from Fortran
5548 */
5549 #include <petsc/private/fortranimpl.h>
5550 
5551 /* Change these macros so can be used in void function */
5552 #undef CHKERRQ
5553 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
5554 #undef SETERRQ2
5555 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5556 #undef SETERRQ3
5557 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5558 #undef SETERRQ
5559 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
5560 
5561 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5562 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
5563 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5564 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
5565 #else
5566 #endif
5567 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)
5568 {
5569   Mat            mat  = *mmat;
5570   PetscInt       m    = *mm, n = *mn;
5571   InsertMode     addv = *maddv;
5572   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
5573   PetscScalar    value;
5574   PetscErrorCode ierr;
5575 
5576   MatCheckPreallocated(mat,1);
5577   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
5578 
5579 #if defined(PETSC_USE_DEBUG)
5580   else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
5581 #endif
5582   {
5583     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
5584     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
5585     PetscBool roworiented = aij->roworiented;
5586 
5587     /* Some Variables required in the macro */
5588     Mat        A                 = aij->A;
5589     Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
5590     PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
5591     MatScalar  *aa               = a->a;
5592     PetscBool  ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
5593     Mat        B                 = aij->B;
5594     Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
5595     PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5596     MatScalar  *ba               = b->a;
5597 
5598     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5599     PetscInt  nonew = a->nonew;
5600     MatScalar *ap1,*ap2;
5601 
5602     PetscFunctionBegin;
5603     for (i=0; i<m; i++) {
5604       if (im[i] < 0) continue;
5605 #if defined(PETSC_USE_DEBUG)
5606       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);
5607 #endif
5608       if (im[i] >= rstart && im[i] < rend) {
5609         row      = im[i] - rstart;
5610         lastcol1 = -1;
5611         rp1      = aj + ai[row];
5612         ap1      = aa + ai[row];
5613         rmax1    = aimax[row];
5614         nrow1    = ailen[row];
5615         low1     = 0;
5616         high1    = nrow1;
5617         lastcol2 = -1;
5618         rp2      = bj + bi[row];
5619         ap2      = ba + bi[row];
5620         rmax2    = bimax[row];
5621         nrow2    = bilen[row];
5622         low2     = 0;
5623         high2    = nrow2;
5624 
5625         for (j=0; j<n; j++) {
5626           if (roworiented) value = v[i*n+j];
5627           else value = v[i+j*m];
5628           if (in[j] >= cstart && in[j] < cend) {
5629             col = in[j] - cstart;
5630             if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
5631             MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
5632           } else if (in[j] < 0) continue;
5633 #if defined(PETSC_USE_DEBUG)
5634           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);
5635 #endif
5636           else {
5637             if (mat->was_assembled) {
5638               if (!aij->colmap) {
5639                 ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5640               }
5641 #if defined(PETSC_USE_CTABLE)
5642               ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5643               col--;
5644 #else
5645               col = aij->colmap[in[j]] - 1;
5646 #endif
5647               if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
5648               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5649                 ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5650                 col  =  in[j];
5651                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5652                 B     = aij->B;
5653                 b     = (Mat_SeqAIJ*)B->data;
5654                 bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5655                 rp2   = bj + bi[row];
5656                 ap2   = ba + bi[row];
5657                 rmax2 = bimax[row];
5658                 nrow2 = bilen[row];
5659                 low2  = 0;
5660                 high2 = nrow2;
5661                 bm    = aij->B->rmap->n;
5662                 ba    = b->a;
5663               }
5664             } else col = in[j];
5665             MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
5666           }
5667         }
5668       } else if (!aij->donotstash) {
5669         if (roworiented) {
5670           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5671         } else {
5672           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5673         }
5674       }
5675     }
5676   }
5677   PetscFunctionReturnVoid();
5678 }
5679 
5680