xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision d5761cda66b6da37d83eeb4a614ba8c0afcfdd5f)
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   default:
1730     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %d",op);
1731   }
1732   PetscFunctionReturn(0);
1733 }
1734 
1735 PetscErrorCode MatGetRow_MPIAIJ(Mat matin,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1736 {
1737   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1738   PetscScalar    *vworkA,*vworkB,**pvA,**pvB,*v_p;
1739   PetscErrorCode ierr;
1740   PetscInt       i,*cworkA,*cworkB,**pcA,**pcB,cstart = matin->cmap->rstart;
1741   PetscInt       nztot,nzA,nzB,lrow,rstart = matin->rmap->rstart,rend = matin->rmap->rend;
1742   PetscInt       *cmap,*idx_p;
1743 
1744   PetscFunctionBegin;
1745   if (mat->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Already active");
1746   mat->getrowactive = PETSC_TRUE;
1747 
1748   if (!mat->rowvalues && (idx || v)) {
1749     /*
1750         allocate enough space to hold information from the longest row.
1751     */
1752     Mat_SeqAIJ *Aa = (Mat_SeqAIJ*)mat->A->data,*Ba = (Mat_SeqAIJ*)mat->B->data;
1753     PetscInt   max = 1,tmp;
1754     for (i=0; i<matin->rmap->n; i++) {
1755       tmp = Aa->i[i+1] - Aa->i[i] + Ba->i[i+1] - Ba->i[i];
1756       if (max < tmp) max = tmp;
1757     }
1758     ierr = PetscMalloc2(max,&mat->rowvalues,max,&mat->rowindices);CHKERRQ(ierr);
1759   }
1760 
1761   if (row < rstart || row >= rend) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Only local rows");
1762   lrow = row - rstart;
1763 
1764   pvA = &vworkA; pcA = &cworkA; pvB = &vworkB; pcB = &cworkB;
1765   if (!v)   {pvA = 0; pvB = 0;}
1766   if (!idx) {pcA = 0; if (!v) pcB = 0;}
1767   ierr  = (*mat->A->ops->getrow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1768   ierr  = (*mat->B->ops->getrow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1769   nztot = nzA + nzB;
1770 
1771   cmap = mat->garray;
1772   if (v  || idx) {
1773     if (nztot) {
1774       /* Sort by increasing column numbers, assuming A and B already sorted */
1775       PetscInt imark = -1;
1776       if (v) {
1777         *v = v_p = mat->rowvalues;
1778         for (i=0; i<nzB; i++) {
1779           if (cmap[cworkB[i]] < cstart) v_p[i] = vworkB[i];
1780           else break;
1781         }
1782         imark = i;
1783         for (i=0; i<nzA; i++)     v_p[imark+i] = vworkA[i];
1784         for (i=imark; i<nzB; i++) v_p[nzA+i]   = vworkB[i];
1785       }
1786       if (idx) {
1787         *idx = idx_p = mat->rowindices;
1788         if (imark > -1) {
1789           for (i=0; i<imark; i++) {
1790             idx_p[i] = cmap[cworkB[i]];
1791           }
1792         } else {
1793           for (i=0; i<nzB; i++) {
1794             if (cmap[cworkB[i]] < cstart) idx_p[i] = cmap[cworkB[i]];
1795             else break;
1796           }
1797           imark = i;
1798         }
1799         for (i=0; i<nzA; i++)     idx_p[imark+i] = cstart + cworkA[i];
1800         for (i=imark; i<nzB; i++) idx_p[nzA+i]   = cmap[cworkB[i]];
1801       }
1802     } else {
1803       if (idx) *idx = 0;
1804       if (v)   *v   = 0;
1805     }
1806   }
1807   *nz  = nztot;
1808   ierr = (*mat->A->ops->restorerow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1809   ierr = (*mat->B->ops->restorerow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1810   PetscFunctionReturn(0);
1811 }
1812 
1813 PetscErrorCode MatRestoreRow_MPIAIJ(Mat mat,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1814 {
1815   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1816 
1817   PetscFunctionBegin;
1818   if (!aij->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"MatGetRow() must be called first");
1819   aij->getrowactive = PETSC_FALSE;
1820   PetscFunctionReturn(0);
1821 }
1822 
1823 PetscErrorCode MatNorm_MPIAIJ(Mat mat,NormType type,PetscReal *norm)
1824 {
1825   Mat_MPIAIJ     *aij  = (Mat_MPIAIJ*)mat->data;
1826   Mat_SeqAIJ     *amat = (Mat_SeqAIJ*)aij->A->data,*bmat = (Mat_SeqAIJ*)aij->B->data;
1827   PetscErrorCode ierr;
1828   PetscInt       i,j,cstart = mat->cmap->rstart;
1829   PetscReal      sum = 0.0;
1830   MatScalar      *v;
1831 
1832   PetscFunctionBegin;
1833   if (aij->size == 1) {
1834     ierr =  MatNorm(aij->A,type,norm);CHKERRQ(ierr);
1835   } else {
1836     if (type == NORM_FROBENIUS) {
1837       v = amat->a;
1838       for (i=0; i<amat->nz; i++) {
1839         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1840       }
1841       v = bmat->a;
1842       for (i=0; i<bmat->nz; i++) {
1843         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1844       }
1845       ierr  = MPIU_Allreduce(&sum,norm,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1846       *norm = PetscSqrtReal(*norm);
1847       ierr = PetscLogFlops(2*amat->nz+2*bmat->nz);CHKERRQ(ierr);
1848     } else if (type == NORM_1) { /* max column norm */
1849       PetscReal *tmp,*tmp2;
1850       PetscInt  *jj,*garray = aij->garray;
1851       ierr  = PetscCalloc1(mat->cmap->N+1,&tmp);CHKERRQ(ierr);
1852       ierr  = PetscMalloc1(mat->cmap->N+1,&tmp2);CHKERRQ(ierr);
1853       *norm = 0.0;
1854       v     = amat->a; jj = amat->j;
1855       for (j=0; j<amat->nz; j++) {
1856         tmp[cstart + *jj++] += PetscAbsScalar(*v);  v++;
1857       }
1858       v = bmat->a; jj = bmat->j;
1859       for (j=0; j<bmat->nz; j++) {
1860         tmp[garray[*jj++]] += PetscAbsScalar(*v); v++;
1861       }
1862       ierr = MPIU_Allreduce(tmp,tmp2,mat->cmap->N,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1863       for (j=0; j<mat->cmap->N; j++) {
1864         if (tmp2[j] > *norm) *norm = tmp2[j];
1865       }
1866       ierr = PetscFree(tmp);CHKERRQ(ierr);
1867       ierr = PetscFree(tmp2);CHKERRQ(ierr);
1868       ierr = PetscLogFlops(PetscMax(amat->nz+bmat->nz-1,0));CHKERRQ(ierr);
1869     } else if (type == NORM_INFINITY) { /* max row norm */
1870       PetscReal ntemp = 0.0;
1871       for (j=0; j<aij->A->rmap->n; j++) {
1872         v   = amat->a + amat->i[j];
1873         sum = 0.0;
1874         for (i=0; i<amat->i[j+1]-amat->i[j]; i++) {
1875           sum += PetscAbsScalar(*v); v++;
1876         }
1877         v = bmat->a + bmat->i[j];
1878         for (i=0; i<bmat->i[j+1]-bmat->i[j]; i++) {
1879           sum += PetscAbsScalar(*v); v++;
1880         }
1881         if (sum > ntemp) ntemp = sum;
1882       }
1883       ierr = MPIU_Allreduce(&ntemp,norm,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1884       ierr = PetscLogFlops(PetscMax(amat->nz+bmat->nz-1,0));CHKERRQ(ierr);
1885     } else SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"No support for two norm");
1886   }
1887   PetscFunctionReturn(0);
1888 }
1889 
1890 PetscErrorCode MatTranspose_MPIAIJ(Mat A,MatReuse reuse,Mat *matout)
1891 {
1892   Mat_MPIAIJ     *a   = (Mat_MPIAIJ*)A->data;
1893   Mat_SeqAIJ     *Aloc=(Mat_SeqAIJ*)a->A->data,*Bloc=(Mat_SeqAIJ*)a->B->data;
1894   PetscErrorCode ierr;
1895   PetscInt       M      = A->rmap->N,N = A->cmap->N,ma,na,mb,nb,*ai,*aj,*bi,*bj,row,*cols,*cols_tmp,i;
1896   PetscInt       cstart = A->cmap->rstart,ncol;
1897   Mat            B;
1898   MatScalar      *array;
1899 
1900   PetscFunctionBegin;
1901   if (reuse == MAT_INPLACE_MATRIX && M != N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Square matrix only for in-place");
1902 
1903   ma = A->rmap->n; na = A->cmap->n; mb = a->B->rmap->n; nb = a->B->cmap->n;
1904   ai = Aloc->i; aj = Aloc->j;
1905   bi = Bloc->i; bj = Bloc->j;
1906   if (reuse == MAT_INITIAL_MATRIX || *matout == A) {
1907     PetscInt             *d_nnz,*g_nnz,*o_nnz;
1908     PetscSFNode          *oloc;
1909     PETSC_UNUSED PetscSF sf;
1910 
1911     ierr = PetscMalloc4(na,&d_nnz,na,&o_nnz,nb,&g_nnz,nb,&oloc);CHKERRQ(ierr);
1912     /* compute d_nnz for preallocation */
1913     ierr = PetscMemzero(d_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1914     for (i=0; i<ai[ma]; i++) {
1915       d_nnz[aj[i]]++;
1916       aj[i] += cstart; /* global col index to be used by MatSetValues() */
1917     }
1918     /* compute local off-diagonal contributions */
1919     ierr = PetscMemzero(g_nnz,nb*sizeof(PetscInt));CHKERRQ(ierr);
1920     for (i=0; i<bi[ma]; i++) g_nnz[bj[i]]++;
1921     /* map those to global */
1922     ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1923     ierr = PetscSFSetGraphLayout(sf,A->cmap,nb,NULL,PETSC_USE_POINTER,a->garray);CHKERRQ(ierr);
1924     ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1925     ierr = PetscMemzero(o_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1926     ierr = PetscSFReduceBegin(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
1927     ierr = PetscSFReduceEnd(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
1928     ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1929 
1930     ierr = MatCreate(PetscObjectComm((PetscObject)A),&B);CHKERRQ(ierr);
1931     ierr = MatSetSizes(B,A->cmap->n,A->rmap->n,N,M);CHKERRQ(ierr);
1932     ierr = MatSetBlockSizes(B,PetscAbs(A->cmap->bs),PetscAbs(A->rmap->bs));CHKERRQ(ierr);
1933     ierr = MatSetType(B,((PetscObject)A)->type_name);CHKERRQ(ierr);
1934     ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
1935     ierr = PetscFree4(d_nnz,o_nnz,g_nnz,oloc);CHKERRQ(ierr);
1936   } else {
1937     B    = *matout;
1938     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
1939     for (i=0; i<ai[ma]; i++) aj[i] += cstart; /* global col index to be used by MatSetValues() */
1940   }
1941 
1942   /* copy over the A part */
1943   array = Aloc->a;
1944   row   = A->rmap->rstart;
1945   for (i=0; i<ma; i++) {
1946     ncol = ai[i+1]-ai[i];
1947     ierr = MatSetValues(B,ncol,aj,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
1948     row++;
1949     array += ncol; aj += ncol;
1950   }
1951   aj = Aloc->j;
1952   for (i=0; i<ai[ma]; i++) aj[i] -= cstart; /* resume local col index */
1953 
1954   /* copy over the B part */
1955   ierr  = PetscCalloc1(bi[mb],&cols);CHKERRQ(ierr);
1956   array = Bloc->a;
1957   row   = A->rmap->rstart;
1958   for (i=0; i<bi[mb]; i++) cols[i] = a->garray[bj[i]];
1959   cols_tmp = cols;
1960   for (i=0; i<mb; i++) {
1961     ncol = bi[i+1]-bi[i];
1962     ierr = MatSetValues(B,ncol,cols_tmp,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
1963     row++;
1964     array += ncol; cols_tmp += ncol;
1965   }
1966   ierr = PetscFree(cols);CHKERRQ(ierr);
1967 
1968   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1969   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1970   if (reuse == MAT_INITIAL_MATRIX || reuse == MAT_REUSE_MATRIX) {
1971     *matout = B;
1972   } else {
1973     ierr = MatHeaderMerge(A,&B);CHKERRQ(ierr);
1974   }
1975   PetscFunctionReturn(0);
1976 }
1977 
1978 PetscErrorCode MatDiagonalScale_MPIAIJ(Mat mat,Vec ll,Vec rr)
1979 {
1980   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1981   Mat            a    = aij->A,b = aij->B;
1982   PetscErrorCode ierr;
1983   PetscInt       s1,s2,s3;
1984 
1985   PetscFunctionBegin;
1986   ierr = MatGetLocalSize(mat,&s2,&s3);CHKERRQ(ierr);
1987   if (rr) {
1988     ierr = VecGetLocalSize(rr,&s1);CHKERRQ(ierr);
1989     if (s1!=s3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"right vector non-conforming local size");
1990     /* Overlap communication with computation. */
1991     ierr = VecScatterBegin(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1992   }
1993   if (ll) {
1994     ierr = VecGetLocalSize(ll,&s1);CHKERRQ(ierr);
1995     if (s1!=s2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"left vector non-conforming local size");
1996     ierr = (*b->ops->diagonalscale)(b,ll,0);CHKERRQ(ierr);
1997   }
1998   /* scale  the diagonal block */
1999   ierr = (*a->ops->diagonalscale)(a,ll,rr);CHKERRQ(ierr);
2000 
2001   if (rr) {
2002     /* Do a scatter end and then right scale the off-diagonal block */
2003     ierr = VecScatterEnd(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2004     ierr = (*b->ops->diagonalscale)(b,0,aij->lvec);CHKERRQ(ierr);
2005   }
2006   PetscFunctionReturn(0);
2007 }
2008 
2009 PetscErrorCode MatSetUnfactored_MPIAIJ(Mat A)
2010 {
2011   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2012   PetscErrorCode ierr;
2013 
2014   PetscFunctionBegin;
2015   ierr = MatSetUnfactored(a->A);CHKERRQ(ierr);
2016   PetscFunctionReturn(0);
2017 }
2018 
2019 PetscErrorCode MatEqual_MPIAIJ(Mat A,Mat B,PetscBool  *flag)
2020 {
2021   Mat_MPIAIJ     *matB = (Mat_MPIAIJ*)B->data,*matA = (Mat_MPIAIJ*)A->data;
2022   Mat            a,b,c,d;
2023   PetscBool      flg;
2024   PetscErrorCode ierr;
2025 
2026   PetscFunctionBegin;
2027   a = matA->A; b = matA->B;
2028   c = matB->A; d = matB->B;
2029 
2030   ierr = MatEqual(a,c,&flg);CHKERRQ(ierr);
2031   if (flg) {
2032     ierr = MatEqual(b,d,&flg);CHKERRQ(ierr);
2033   }
2034   ierr = MPIU_Allreduce(&flg,flag,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
2035   PetscFunctionReturn(0);
2036 }
2037 
2038 PetscErrorCode MatCopy_MPIAIJ(Mat A,Mat B,MatStructure str)
2039 {
2040   PetscErrorCode ierr;
2041   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2042   Mat_MPIAIJ     *b = (Mat_MPIAIJ*)B->data;
2043 
2044   PetscFunctionBegin;
2045   /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
2046   if ((str != SAME_NONZERO_PATTERN) || (A->ops->copy != B->ops->copy)) {
2047     /* because of the column compression in the off-processor part of the matrix a->B,
2048        the number of columns in a->B and b->B may be different, hence we cannot call
2049        the MatCopy() directly on the two parts. If need be, we can provide a more
2050        efficient copy than the MatCopy_Basic() by first uncompressing the a->B matrices
2051        then copying the submatrices */
2052     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
2053   } else {
2054     ierr = MatCopy(a->A,b->A,str);CHKERRQ(ierr);
2055     ierr = MatCopy(a->B,b->B,str);CHKERRQ(ierr);
2056   }
2057   PetscFunctionReturn(0);
2058 }
2059 
2060 PetscErrorCode MatSetUp_MPIAIJ(Mat A)
2061 {
2062   PetscErrorCode ierr;
2063 
2064   PetscFunctionBegin;
2065   ierr =  MatMPIAIJSetPreallocation(A,PETSC_DEFAULT,0,PETSC_DEFAULT,0);CHKERRQ(ierr);
2066   PetscFunctionReturn(0);
2067 }
2068 
2069 /*
2070    Computes the number of nonzeros per row needed for preallocation when X and Y
2071    have different nonzero structure.
2072 */
2073 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)
2074 {
2075   PetscInt       i,j,k,nzx,nzy;
2076 
2077   PetscFunctionBegin;
2078   /* Set the number of nonzeros in the new matrix */
2079   for (i=0; i<m; i++) {
2080     const PetscInt *xjj = xj+xi[i],*yjj = yj+yi[i];
2081     nzx = xi[i+1] - xi[i];
2082     nzy = yi[i+1] - yi[i];
2083     nnz[i] = 0;
2084     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2085       for (; k<nzy && yltog[yjj[k]]<xltog[xjj[j]]; k++) nnz[i]++; /* Catch up to X */
2086       if (k<nzy && yltog[yjj[k]]==xltog[xjj[j]]) k++;             /* Skip duplicate */
2087       nnz[i]++;
2088     }
2089     for (; k<nzy; k++) nnz[i]++;
2090   }
2091   PetscFunctionReturn(0);
2092 }
2093 
2094 /* This is the same as MatAXPYGetPreallocation_SeqAIJ, except that the local-to-global map is provided */
2095 static PetscErrorCode MatAXPYGetPreallocation_MPIAIJ(Mat Y,const PetscInt *yltog,Mat X,const PetscInt *xltog,PetscInt *nnz)
2096 {
2097   PetscErrorCode ierr;
2098   PetscInt       m = Y->rmap->N;
2099   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data;
2100   Mat_SeqAIJ     *y = (Mat_SeqAIJ*)Y->data;
2101 
2102   PetscFunctionBegin;
2103   ierr = MatAXPYGetPreallocation_MPIX_private(m,x->i,x->j,xltog,y->i,y->j,yltog,nnz);CHKERRQ(ierr);
2104   PetscFunctionReturn(0);
2105 }
2106 
2107 PetscErrorCode MatAXPY_MPIAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
2108 {
2109   PetscErrorCode ierr;
2110   Mat_MPIAIJ     *xx = (Mat_MPIAIJ*)X->data,*yy = (Mat_MPIAIJ*)Y->data;
2111   PetscBLASInt   bnz,one=1;
2112   Mat_SeqAIJ     *x,*y;
2113 
2114   PetscFunctionBegin;
2115   if (str == SAME_NONZERO_PATTERN) {
2116     PetscScalar alpha = a;
2117     x    = (Mat_SeqAIJ*)xx->A->data;
2118     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2119     y    = (Mat_SeqAIJ*)yy->A->data;
2120     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2121     x    = (Mat_SeqAIJ*)xx->B->data;
2122     y    = (Mat_SeqAIJ*)yy->B->data;
2123     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2124     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2125     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
2126   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
2127     ierr = MatAXPY_Basic(Y,a,X,str);CHKERRQ(ierr);
2128   } else {
2129     Mat      B;
2130     PetscInt *nnz_d,*nnz_o;
2131     ierr = PetscMalloc1(yy->A->rmap->N,&nnz_d);CHKERRQ(ierr);
2132     ierr = PetscMalloc1(yy->B->rmap->N,&nnz_o);CHKERRQ(ierr);
2133     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
2134     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
2135     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
2136     ierr = MatSetBlockSizesFromMats(B,Y,Y);CHKERRQ(ierr);
2137     ierr = MatSetType(B,MATMPIAIJ);CHKERRQ(ierr);
2138     ierr = MatAXPYGetPreallocation_SeqAIJ(yy->A,xx->A,nnz_d);CHKERRQ(ierr);
2139     ierr = MatAXPYGetPreallocation_MPIAIJ(yy->B,yy->garray,xx->B,xx->garray,nnz_o);CHKERRQ(ierr);
2140     ierr = MatMPIAIJSetPreallocation(B,0,nnz_d,0,nnz_o);CHKERRQ(ierr);
2141     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
2142     ierr = MatHeaderReplace(Y,&B);CHKERRQ(ierr);
2143     ierr = PetscFree(nnz_d);CHKERRQ(ierr);
2144     ierr = PetscFree(nnz_o);CHKERRQ(ierr);
2145   }
2146   PetscFunctionReturn(0);
2147 }
2148 
2149 extern PetscErrorCode  MatConjugate_SeqAIJ(Mat);
2150 
2151 PetscErrorCode  MatConjugate_MPIAIJ(Mat mat)
2152 {
2153 #if defined(PETSC_USE_COMPLEX)
2154   PetscErrorCode ierr;
2155   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2156 
2157   PetscFunctionBegin;
2158   ierr = MatConjugate_SeqAIJ(aij->A);CHKERRQ(ierr);
2159   ierr = MatConjugate_SeqAIJ(aij->B);CHKERRQ(ierr);
2160 #else
2161   PetscFunctionBegin;
2162 #endif
2163   PetscFunctionReturn(0);
2164 }
2165 
2166 PetscErrorCode MatRealPart_MPIAIJ(Mat A)
2167 {
2168   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2169   PetscErrorCode ierr;
2170 
2171   PetscFunctionBegin;
2172   ierr = MatRealPart(a->A);CHKERRQ(ierr);
2173   ierr = MatRealPart(a->B);CHKERRQ(ierr);
2174   PetscFunctionReturn(0);
2175 }
2176 
2177 PetscErrorCode MatImaginaryPart_MPIAIJ(Mat A)
2178 {
2179   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2180   PetscErrorCode ierr;
2181 
2182   PetscFunctionBegin;
2183   ierr = MatImaginaryPart(a->A);CHKERRQ(ierr);
2184   ierr = MatImaginaryPart(a->B);CHKERRQ(ierr);
2185   PetscFunctionReturn(0);
2186 }
2187 
2188 PetscErrorCode MatGetRowMaxAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2189 {
2190   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2191   PetscErrorCode ierr;
2192   PetscInt       i,*idxb = 0;
2193   PetscScalar    *va,*vb;
2194   Vec            vtmp;
2195 
2196   PetscFunctionBegin;
2197   ierr = MatGetRowMaxAbs(a->A,v,idx);CHKERRQ(ierr);
2198   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2199   if (idx) {
2200     for (i=0; i<A->rmap->n; i++) {
2201       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2202     }
2203   }
2204 
2205   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2206   if (idx) {
2207     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2208   }
2209   ierr = MatGetRowMaxAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2210   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2211 
2212   for (i=0; i<A->rmap->n; i++) {
2213     if (PetscAbsScalar(va[i]) < PetscAbsScalar(vb[i])) {
2214       va[i] = vb[i];
2215       if (idx) idx[i] = a->garray[idxb[i]];
2216     }
2217   }
2218 
2219   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2220   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2221   ierr = PetscFree(idxb);CHKERRQ(ierr);
2222   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2223   PetscFunctionReturn(0);
2224 }
2225 
2226 PetscErrorCode MatGetRowMinAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2227 {
2228   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2229   PetscErrorCode ierr;
2230   PetscInt       i,*idxb = 0;
2231   PetscScalar    *va,*vb;
2232   Vec            vtmp;
2233 
2234   PetscFunctionBegin;
2235   ierr = MatGetRowMinAbs(a->A,v,idx);CHKERRQ(ierr);
2236   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2237   if (idx) {
2238     for (i=0; i<A->cmap->n; i++) {
2239       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2240     }
2241   }
2242 
2243   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2244   if (idx) {
2245     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2246   }
2247   ierr = MatGetRowMinAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2248   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2249 
2250   for (i=0; i<A->rmap->n; i++) {
2251     if (PetscAbsScalar(va[i]) > PetscAbsScalar(vb[i])) {
2252       va[i] = vb[i];
2253       if (idx) idx[i] = a->garray[idxb[i]];
2254     }
2255   }
2256 
2257   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2258   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2259   ierr = PetscFree(idxb);CHKERRQ(ierr);
2260   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2261   PetscFunctionReturn(0);
2262 }
2263 
2264 PetscErrorCode MatGetRowMin_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2265 {
2266   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2267   PetscInt       n      = A->rmap->n;
2268   PetscInt       cstart = A->cmap->rstart;
2269   PetscInt       *cmap  = mat->garray;
2270   PetscInt       *diagIdx, *offdiagIdx;
2271   Vec            diagV, offdiagV;
2272   PetscScalar    *a, *diagA, *offdiagA;
2273   PetscInt       r;
2274   PetscErrorCode ierr;
2275 
2276   PetscFunctionBegin;
2277   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2278   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &diagV);CHKERRQ(ierr);
2279   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &offdiagV);CHKERRQ(ierr);
2280   ierr = MatGetRowMin(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2281   ierr = MatGetRowMin(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2282   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2283   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2284   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2285   for (r = 0; r < n; ++r) {
2286     if (PetscAbsScalar(diagA[r]) <= PetscAbsScalar(offdiagA[r])) {
2287       a[r]   = diagA[r];
2288       idx[r] = cstart + diagIdx[r];
2289     } else {
2290       a[r]   = offdiagA[r];
2291       idx[r] = cmap[offdiagIdx[r]];
2292     }
2293   }
2294   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2295   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2296   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2297   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2298   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2299   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2300   PetscFunctionReturn(0);
2301 }
2302 
2303 PetscErrorCode MatGetRowMax_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2304 {
2305   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2306   PetscInt       n      = A->rmap->n;
2307   PetscInt       cstart = A->cmap->rstart;
2308   PetscInt       *cmap  = mat->garray;
2309   PetscInt       *diagIdx, *offdiagIdx;
2310   Vec            diagV, offdiagV;
2311   PetscScalar    *a, *diagA, *offdiagA;
2312   PetscInt       r;
2313   PetscErrorCode ierr;
2314 
2315   PetscFunctionBegin;
2316   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2317   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &diagV);CHKERRQ(ierr);
2318   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &offdiagV);CHKERRQ(ierr);
2319   ierr = MatGetRowMax(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2320   ierr = MatGetRowMax(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2321   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2322   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2323   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2324   for (r = 0; r < n; ++r) {
2325     if (PetscAbsScalar(diagA[r]) >= PetscAbsScalar(offdiagA[r])) {
2326       a[r]   = diagA[r];
2327       idx[r] = cstart + diagIdx[r];
2328     } else {
2329       a[r]   = offdiagA[r];
2330       idx[r] = cmap[offdiagIdx[r]];
2331     }
2332   }
2333   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2334   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2335   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2336   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2337   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2338   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2339   PetscFunctionReturn(0);
2340 }
2341 
2342 PetscErrorCode MatGetSeqNonzeroStructure_MPIAIJ(Mat mat,Mat *newmat)
2343 {
2344   PetscErrorCode ierr;
2345   Mat            *dummy;
2346 
2347   PetscFunctionBegin;
2348   ierr    = MatCreateSubMatrix_MPIAIJ_All(mat,MAT_DO_NOT_GET_VALUES,MAT_INITIAL_MATRIX,&dummy);CHKERRQ(ierr);
2349   *newmat = *dummy;
2350   ierr    = PetscFree(dummy);CHKERRQ(ierr);
2351   PetscFunctionReturn(0);
2352 }
2353 
2354 PetscErrorCode  MatInvertBlockDiagonal_MPIAIJ(Mat A,const PetscScalar **values)
2355 {
2356   Mat_MPIAIJ     *a = (Mat_MPIAIJ*) A->data;
2357   PetscErrorCode ierr;
2358 
2359   PetscFunctionBegin;
2360   ierr = MatInvertBlockDiagonal(a->A,values);CHKERRQ(ierr);
2361   A->factorerrortype = a->A->factorerrortype;
2362   PetscFunctionReturn(0);
2363 }
2364 
2365 static PetscErrorCode  MatSetRandom_MPIAIJ(Mat x,PetscRandom rctx)
2366 {
2367   PetscErrorCode ierr;
2368   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)x->data;
2369 
2370   PetscFunctionBegin;
2371   ierr = MatSetRandom(aij->A,rctx);CHKERRQ(ierr);
2372   ierr = MatSetRandom(aij->B,rctx);CHKERRQ(ierr);
2373   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2374   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2375   PetscFunctionReturn(0);
2376 }
2377 
2378 PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ(Mat A,PetscBool sc)
2379 {
2380   PetscFunctionBegin;
2381   if (sc) A->ops->increaseoverlap = MatIncreaseOverlap_MPIAIJ_Scalable;
2382   else A->ops->increaseoverlap    = MatIncreaseOverlap_MPIAIJ;
2383   PetscFunctionReturn(0);
2384 }
2385 
2386 /*@
2387    MatMPIAIJSetUseScalableIncreaseOverlap - Determine if the matrix uses a scalable algorithm to compute the overlap
2388 
2389    Collective on Mat
2390 
2391    Input Parameters:
2392 +    A - the matrix
2393 -    sc - PETSC_TRUE indicates use the scalable algorithm (default is not to use the scalable algorithm)
2394 
2395  Level: advanced
2396 
2397 @*/
2398 PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap(Mat A,PetscBool sc)
2399 {
2400   PetscErrorCode       ierr;
2401 
2402   PetscFunctionBegin;
2403   ierr = PetscTryMethod(A,"MatMPIAIJSetUseScalableIncreaseOverlap_C",(Mat,PetscBool),(A,sc));CHKERRQ(ierr);
2404   PetscFunctionReturn(0);
2405 }
2406 
2407 PetscErrorCode MatSetFromOptions_MPIAIJ(PetscOptionItems *PetscOptionsObject,Mat A)
2408 {
2409   PetscErrorCode       ierr;
2410   PetscBool            sc = PETSC_FALSE,flg;
2411 
2412   PetscFunctionBegin;
2413   ierr = PetscOptionsHead(PetscOptionsObject,"MPIAIJ options");CHKERRQ(ierr);
2414   ierr = PetscObjectOptionsBegin((PetscObject)A);
2415     if (A->ops->increaseoverlap == MatIncreaseOverlap_MPIAIJ_Scalable) sc = PETSC_TRUE;
2416     ierr = PetscOptionsBool("-mat_increase_overlap_scalable","Use a scalable algorithm to compute the overlap","MatIncreaseOverlap",sc,&sc,&flg);CHKERRQ(ierr);
2417     if (flg) {
2418       ierr = MatMPIAIJSetUseScalableIncreaseOverlap(A,sc);CHKERRQ(ierr);
2419     }
2420   ierr = PetscOptionsEnd();CHKERRQ(ierr);
2421   PetscFunctionReturn(0);
2422 }
2423 
2424 PetscErrorCode MatShift_MPIAIJ(Mat Y,PetscScalar a)
2425 {
2426   PetscErrorCode ierr;
2427   Mat_MPIAIJ     *maij = (Mat_MPIAIJ*)Y->data;
2428   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)maij->A->data;
2429 
2430   PetscFunctionBegin;
2431   if (!Y->preallocated) {
2432     ierr = MatMPIAIJSetPreallocation(Y,1,NULL,0,NULL);CHKERRQ(ierr);
2433   } else if (!aij->nz) {
2434     PetscInt nonew = aij->nonew;
2435     ierr = MatSeqAIJSetPreallocation(maij->A,1,NULL);CHKERRQ(ierr);
2436     aij->nonew = nonew;
2437   }
2438   ierr = MatShift_Basic(Y,a);CHKERRQ(ierr);
2439   PetscFunctionReturn(0);
2440 }
2441 
2442 PetscErrorCode MatMissingDiagonal_MPIAIJ(Mat A,PetscBool  *missing,PetscInt *d)
2443 {
2444   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2445   PetscErrorCode ierr;
2446 
2447   PetscFunctionBegin;
2448   if (A->rmap->n != A->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only works for square matrices");
2449   ierr = MatMissingDiagonal(a->A,missing,d);CHKERRQ(ierr);
2450   if (d) {
2451     PetscInt rstart;
2452     ierr = MatGetOwnershipRange(A,&rstart,NULL);CHKERRQ(ierr);
2453     *d += rstart;
2454 
2455   }
2456   PetscFunctionReturn(0);
2457 }
2458 
2459 
2460 /* -------------------------------------------------------------------*/
2461 static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
2462                                        MatGetRow_MPIAIJ,
2463                                        MatRestoreRow_MPIAIJ,
2464                                        MatMult_MPIAIJ,
2465                                 /* 4*/ MatMultAdd_MPIAIJ,
2466                                        MatMultTranspose_MPIAIJ,
2467                                        MatMultTransposeAdd_MPIAIJ,
2468                                        0,
2469                                        0,
2470                                        0,
2471                                 /*10*/ 0,
2472                                        0,
2473                                        0,
2474                                        MatSOR_MPIAIJ,
2475                                        MatTranspose_MPIAIJ,
2476                                 /*15*/ MatGetInfo_MPIAIJ,
2477                                        MatEqual_MPIAIJ,
2478                                        MatGetDiagonal_MPIAIJ,
2479                                        MatDiagonalScale_MPIAIJ,
2480                                        MatNorm_MPIAIJ,
2481                                 /*20*/ MatAssemblyBegin_MPIAIJ,
2482                                        MatAssemblyEnd_MPIAIJ,
2483                                        MatSetOption_MPIAIJ,
2484                                        MatZeroEntries_MPIAIJ,
2485                                 /*24*/ MatZeroRows_MPIAIJ,
2486                                        0,
2487                                        0,
2488                                        0,
2489                                        0,
2490                                 /*29*/ MatSetUp_MPIAIJ,
2491                                        0,
2492                                        0,
2493                                        MatGetDiagonalBlock_MPIAIJ,
2494                                        0,
2495                                 /*34*/ MatDuplicate_MPIAIJ,
2496                                        0,
2497                                        0,
2498                                        0,
2499                                        0,
2500                                 /*39*/ MatAXPY_MPIAIJ,
2501                                        MatCreateSubMatrices_MPIAIJ,
2502                                        MatIncreaseOverlap_MPIAIJ,
2503                                        MatGetValues_MPIAIJ,
2504                                        MatCopy_MPIAIJ,
2505                                 /*44*/ MatGetRowMax_MPIAIJ,
2506                                        MatScale_MPIAIJ,
2507                                        MatShift_MPIAIJ,
2508                                        MatDiagonalSet_MPIAIJ,
2509                                        MatZeroRowsColumns_MPIAIJ,
2510                                 /*49*/ MatSetRandom_MPIAIJ,
2511                                        0,
2512                                        0,
2513                                        0,
2514                                        0,
2515                                 /*54*/ MatFDColoringCreate_MPIXAIJ,
2516                                        0,
2517                                        MatSetUnfactored_MPIAIJ,
2518                                        MatPermute_MPIAIJ,
2519                                        0,
2520                                 /*59*/ MatCreateSubMatrix_MPIAIJ,
2521                                        MatDestroy_MPIAIJ,
2522                                        MatView_MPIAIJ,
2523                                        0,
2524                                        MatMatMatMult_MPIAIJ_MPIAIJ_MPIAIJ,
2525                                 /*64*/ MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ,
2526                                        MatMatMatMultNumeric_MPIAIJ_MPIAIJ_MPIAIJ,
2527                                        0,
2528                                        0,
2529                                        0,
2530                                 /*69*/ MatGetRowMaxAbs_MPIAIJ,
2531                                        MatGetRowMinAbs_MPIAIJ,
2532                                        0,
2533                                        0,
2534                                        0,
2535                                        0,
2536                                 /*75*/ MatFDColoringApply_AIJ,
2537                                        MatSetFromOptions_MPIAIJ,
2538                                        0,
2539                                        0,
2540                                        MatFindZeroDiagonals_MPIAIJ,
2541                                 /*80*/ 0,
2542                                        0,
2543                                        0,
2544                                 /*83*/ MatLoad_MPIAIJ,
2545                                        0,
2546                                        0,
2547                                        0,
2548                                        0,
2549                                        0,
2550                                 /*89*/ MatMatMult_MPIAIJ_MPIAIJ,
2551                                        MatMatMultSymbolic_MPIAIJ_MPIAIJ,
2552                                        MatMatMultNumeric_MPIAIJ_MPIAIJ,
2553                                        MatPtAP_MPIAIJ_MPIAIJ,
2554                                        MatPtAPSymbolic_MPIAIJ_MPIAIJ,
2555                                 /*94*/ MatPtAPNumeric_MPIAIJ_MPIAIJ,
2556                                        0,
2557                                        0,
2558                                        0,
2559                                        0,
2560                                 /*99*/ 0,
2561                                        0,
2562                                        0,
2563                                        MatConjugate_MPIAIJ,
2564                                        0,
2565                                 /*104*/MatSetValuesRow_MPIAIJ,
2566                                        MatRealPart_MPIAIJ,
2567                                        MatImaginaryPart_MPIAIJ,
2568                                        0,
2569                                        0,
2570                                 /*109*/0,
2571                                        0,
2572                                        MatGetRowMin_MPIAIJ,
2573                                        0,
2574                                        MatMissingDiagonal_MPIAIJ,
2575                                 /*114*/MatGetSeqNonzeroStructure_MPIAIJ,
2576                                        0,
2577                                        MatGetGhosts_MPIAIJ,
2578                                        0,
2579                                        0,
2580                                 /*119*/0,
2581                                        0,
2582                                        0,
2583                                        0,
2584                                        MatGetMultiProcBlock_MPIAIJ,
2585                                 /*124*/MatFindNonzeroRows_MPIAIJ,
2586                                        MatGetColumnNorms_MPIAIJ,
2587                                        MatInvertBlockDiagonal_MPIAIJ,
2588                                        0,
2589                                        MatCreateSubMatricesMPI_MPIAIJ,
2590                                 /*129*/0,
2591                                        MatTransposeMatMult_MPIAIJ_MPIAIJ,
2592                                        MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ,
2593                                        MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ,
2594                                        0,
2595                                 /*134*/0,
2596                                        0,
2597                                        0,
2598                                        0,
2599                                        0,
2600                                 /*139*/MatSetBlockSizes_MPIAIJ,
2601                                        0,
2602                                        0,
2603                                        MatFDColoringSetUp_MPIXAIJ,
2604                                        MatFindOffBlockDiagonalEntries_MPIAIJ,
2605                                 /*144*/MatCreateMPIMatConcatenateSeqMat_MPIAIJ
2606 };
2607 
2608 /* ----------------------------------------------------------------------------------------*/
2609 
2610 PetscErrorCode  MatStoreValues_MPIAIJ(Mat mat)
2611 {
2612   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2613   PetscErrorCode ierr;
2614 
2615   PetscFunctionBegin;
2616   ierr = MatStoreValues(aij->A);CHKERRQ(ierr);
2617   ierr = MatStoreValues(aij->B);CHKERRQ(ierr);
2618   PetscFunctionReturn(0);
2619 }
2620 
2621 PetscErrorCode  MatRetrieveValues_MPIAIJ(Mat mat)
2622 {
2623   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2624   PetscErrorCode ierr;
2625 
2626   PetscFunctionBegin;
2627   ierr = MatRetrieveValues(aij->A);CHKERRQ(ierr);
2628   ierr = MatRetrieveValues(aij->B);CHKERRQ(ierr);
2629   PetscFunctionReturn(0);
2630 }
2631 
2632 PetscErrorCode  MatMPIAIJSetPreallocation_MPIAIJ(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
2633 {
2634   Mat_MPIAIJ     *b;
2635   PetscErrorCode ierr;
2636 
2637   PetscFunctionBegin;
2638   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
2639   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
2640   b = (Mat_MPIAIJ*)B->data;
2641 
2642 #if defined(PETSC_USE_CTABLE)
2643   ierr = PetscTableDestroy(&b->colmap);CHKERRQ(ierr);
2644 #else
2645   ierr = PetscFree(b->colmap);CHKERRQ(ierr);
2646 #endif
2647   ierr = PetscFree(b->garray);CHKERRQ(ierr);
2648   ierr = VecDestroy(&b->lvec);CHKERRQ(ierr);
2649   ierr = VecScatterDestroy(&b->Mvctx);CHKERRQ(ierr);
2650 
2651   /* Because the B will have been resized we simply destroy it and create a new one each time */
2652   ierr = MatDestroy(&b->B);CHKERRQ(ierr);
2653   ierr = MatCreate(PETSC_COMM_SELF,&b->B);CHKERRQ(ierr);
2654   ierr = MatSetSizes(b->B,B->rmap->n,B->cmap->N,B->rmap->n,B->cmap->N);CHKERRQ(ierr);
2655   ierr = MatSetBlockSizesFromMats(b->B,B,B);CHKERRQ(ierr);
2656   ierr = MatSetType(b->B,MATSEQAIJ);CHKERRQ(ierr);
2657   ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->B);CHKERRQ(ierr);
2658 
2659   if (!B->preallocated) {
2660     ierr = MatCreate(PETSC_COMM_SELF,&b->A);CHKERRQ(ierr);
2661     ierr = MatSetSizes(b->A,B->rmap->n,B->cmap->n,B->rmap->n,B->cmap->n);CHKERRQ(ierr);
2662     ierr = MatSetBlockSizesFromMats(b->A,B,B);CHKERRQ(ierr);
2663     ierr = MatSetType(b->A,MATSEQAIJ);CHKERRQ(ierr);
2664     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->A);CHKERRQ(ierr);
2665   }
2666 
2667   ierr = MatSeqAIJSetPreallocation(b->A,d_nz,d_nnz);CHKERRQ(ierr);
2668   ierr = MatSeqAIJSetPreallocation(b->B,o_nz,o_nnz);CHKERRQ(ierr);
2669   B->preallocated  = PETSC_TRUE;
2670   B->was_assembled = PETSC_FALSE;
2671   B->assembled     = PETSC_FALSE;;
2672   PetscFunctionReturn(0);
2673 }
2674 
2675 PetscErrorCode MatDuplicate_MPIAIJ(Mat matin,MatDuplicateOption cpvalues,Mat *newmat)
2676 {
2677   Mat            mat;
2678   Mat_MPIAIJ     *a,*oldmat = (Mat_MPIAIJ*)matin->data;
2679   PetscErrorCode ierr;
2680 
2681   PetscFunctionBegin;
2682   *newmat = 0;
2683   ierr    = MatCreate(PetscObjectComm((PetscObject)matin),&mat);CHKERRQ(ierr);
2684   ierr    = MatSetSizes(mat,matin->rmap->n,matin->cmap->n,matin->rmap->N,matin->cmap->N);CHKERRQ(ierr);
2685   ierr    = MatSetBlockSizesFromMats(mat,matin,matin);CHKERRQ(ierr);
2686   ierr    = MatSetType(mat,((PetscObject)matin)->type_name);CHKERRQ(ierr);
2687   ierr    = PetscMemcpy(mat->ops,matin->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
2688   a       = (Mat_MPIAIJ*)mat->data;
2689 
2690   mat->factortype   = matin->factortype;
2691   mat->assembled    = PETSC_TRUE;
2692   mat->insertmode   = NOT_SET_VALUES;
2693   mat->preallocated = PETSC_TRUE;
2694 
2695   a->size         = oldmat->size;
2696   a->rank         = oldmat->rank;
2697   a->donotstash   = oldmat->donotstash;
2698   a->roworiented  = oldmat->roworiented;
2699   a->rowindices   = 0;
2700   a->rowvalues    = 0;
2701   a->getrowactive = PETSC_FALSE;
2702 
2703   ierr = PetscLayoutReference(matin->rmap,&mat->rmap);CHKERRQ(ierr);
2704   ierr = PetscLayoutReference(matin->cmap,&mat->cmap);CHKERRQ(ierr);
2705 
2706   if (oldmat->colmap) {
2707 #if defined(PETSC_USE_CTABLE)
2708     ierr = PetscTableCreateCopy(oldmat->colmap,&a->colmap);CHKERRQ(ierr);
2709 #else
2710     ierr = PetscMalloc1(mat->cmap->N,&a->colmap);CHKERRQ(ierr);
2711     ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2712     ierr = PetscMemcpy(a->colmap,oldmat->colmap,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2713 #endif
2714   } else a->colmap = 0;
2715   if (oldmat->garray) {
2716     PetscInt len;
2717     len  = oldmat->B->cmap->n;
2718     ierr = PetscMalloc1(len+1,&a->garray);CHKERRQ(ierr);
2719     ierr = PetscLogObjectMemory((PetscObject)mat,len*sizeof(PetscInt));CHKERRQ(ierr);
2720     if (len) { ierr = PetscMemcpy(a->garray,oldmat->garray,len*sizeof(PetscInt));CHKERRQ(ierr); }
2721   } else a->garray = 0;
2722 
2723   ierr    = VecDuplicate(oldmat->lvec,&a->lvec);CHKERRQ(ierr);
2724   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->lvec);CHKERRQ(ierr);
2725   ierr    = VecScatterCopy(oldmat->Mvctx,&a->Mvctx);CHKERRQ(ierr);
2726   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->Mvctx);CHKERRQ(ierr);
2727   ierr    = MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
2728   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->A);CHKERRQ(ierr);
2729   ierr    = MatDuplicate(oldmat->B,cpvalues,&a->B);CHKERRQ(ierr);
2730   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->B);CHKERRQ(ierr);
2731   ierr    = PetscFunctionListDuplicate(((PetscObject)matin)->qlist,&((PetscObject)mat)->qlist);CHKERRQ(ierr);
2732   *newmat = mat;
2733   PetscFunctionReturn(0);
2734 }
2735 
2736 PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
2737 {
2738   PetscScalar    *vals,*svals;
2739   MPI_Comm       comm;
2740   PetscErrorCode ierr;
2741   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
2742   PetscInt       i,nz,j,rstart,rend,mmax,maxnz = 0;
2743   PetscInt       header[4],*rowlengths = 0,M,N,m,*cols;
2744   PetscInt       *ourlens = NULL,*procsnz = NULL,*offlens = NULL,jj,*mycols,*smycols;
2745   PetscInt       cend,cstart,n,*rowners;
2746   int            fd;
2747   PetscInt       bs = newMat->rmap->bs;
2748 
2749   PetscFunctionBegin;
2750   /* force binary viewer to load .info file if it has not yet done so */
2751   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
2752   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
2753   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2754   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2755   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
2756   if (!rank) {
2757     ierr = PetscBinaryRead(fd,(char*)header,4,PETSC_INT);CHKERRQ(ierr);
2758     if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
2759     if (header[3] < 0) SETERRQ(PetscObjectComm((PetscObject)newMat),PETSC_ERR_FILE_UNEXPECTED,"Matrix stored in special format on disk,cannot load as MATMPIAIJ");
2760   }
2761 
2762   ierr = PetscOptionsBegin(comm,NULL,"Options for loading MATMPIAIJ matrix","Mat");CHKERRQ(ierr);
2763   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
2764   ierr = PetscOptionsEnd();CHKERRQ(ierr);
2765   if (bs < 0) bs = 1;
2766 
2767   ierr = MPI_Bcast(header+1,3,MPIU_INT,0,comm);CHKERRQ(ierr);
2768   M    = header[1]; N = header[2];
2769 
2770   /* If global sizes are set, check if they are consistent with that given in the file */
2771   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);
2772   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);
2773 
2774   /* determine ownership of all (block) rows */
2775   if (M%bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Inconsistent # of rows (%d) and block size (%d)",M,bs);
2776   if (newMat->rmap->n < 0) m = bs*((M/bs)/size + (((M/bs) % size) > rank));    /* PETSC_DECIDE */
2777   else m = newMat->rmap->n; /* Set by user */
2778 
2779   ierr = PetscMalloc1(size+1,&rowners);CHKERRQ(ierr);
2780   ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
2781 
2782   /* First process needs enough room for process with most rows */
2783   if (!rank) {
2784     mmax = rowners[1];
2785     for (i=2; i<=size; i++) {
2786       mmax = PetscMax(mmax, rowners[i]);
2787     }
2788   } else mmax = -1;             /* unused, but compilers complain */
2789 
2790   rowners[0] = 0;
2791   for (i=2; i<=size; i++) {
2792     rowners[i] += rowners[i-1];
2793   }
2794   rstart = rowners[rank];
2795   rend   = rowners[rank+1];
2796 
2797   /* distribute row lengths to all processors */
2798   ierr = PetscMalloc2(m,&ourlens,m,&offlens);CHKERRQ(ierr);
2799   if (!rank) {
2800     ierr = PetscBinaryRead(fd,ourlens,m,PETSC_INT);CHKERRQ(ierr);
2801     ierr = PetscMalloc1(mmax,&rowlengths);CHKERRQ(ierr);
2802     ierr = PetscCalloc1(size,&procsnz);CHKERRQ(ierr);
2803     for (j=0; j<m; j++) {
2804       procsnz[0] += ourlens[j];
2805     }
2806     for (i=1; i<size; i++) {
2807       ierr = PetscBinaryRead(fd,rowlengths,rowners[i+1]-rowners[i],PETSC_INT);CHKERRQ(ierr);
2808       /* calculate the number of nonzeros on each processor */
2809       for (j=0; j<rowners[i+1]-rowners[i]; j++) {
2810         procsnz[i] += rowlengths[j];
2811       }
2812       ierr = MPIULong_Send(rowlengths,rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2813     }
2814     ierr = PetscFree(rowlengths);CHKERRQ(ierr);
2815   } else {
2816     ierr = MPIULong_Recv(ourlens,m,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2817   }
2818 
2819   if (!rank) {
2820     /* determine max buffer needed and allocate it */
2821     maxnz = 0;
2822     for (i=0; i<size; i++) {
2823       maxnz = PetscMax(maxnz,procsnz[i]);
2824     }
2825     ierr = PetscMalloc1(maxnz,&cols);CHKERRQ(ierr);
2826 
2827     /* read in my part of the matrix column indices  */
2828     nz   = procsnz[0];
2829     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2830     ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);
2831 
2832     /* read in every one elses and ship off */
2833     for (i=1; i<size; i++) {
2834       nz   = procsnz[i];
2835       ierr = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
2836       ierr = MPIULong_Send(cols,nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2837     }
2838     ierr = PetscFree(cols);CHKERRQ(ierr);
2839   } else {
2840     /* determine buffer space needed for message */
2841     nz = 0;
2842     for (i=0; i<m; i++) {
2843       nz += ourlens[i];
2844     }
2845     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2846 
2847     /* receive message of column indices*/
2848     ierr = MPIULong_Recv(mycols,nz,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2849   }
2850 
2851   /* determine column ownership if matrix is not square */
2852   if (N != M) {
2853     if (newMat->cmap->n < 0) n = N/size + ((N % size) > rank);
2854     else n = newMat->cmap->n;
2855     ierr   = MPI_Scan(&n,&cend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
2856     cstart = cend - n;
2857   } else {
2858     cstart = rstart;
2859     cend   = rend;
2860     n      = cend - cstart;
2861   }
2862 
2863   /* loop over local rows, determining number of off diagonal entries */
2864   ierr = PetscMemzero(offlens,m*sizeof(PetscInt));CHKERRQ(ierr);
2865   jj   = 0;
2866   for (i=0; i<m; i++) {
2867     for (j=0; j<ourlens[i]; j++) {
2868       if (mycols[jj] < cstart || mycols[jj] >= cend) offlens[i]++;
2869       jj++;
2870     }
2871   }
2872 
2873   for (i=0; i<m; i++) {
2874     ourlens[i] -= offlens[i];
2875   }
2876   ierr = MatSetSizes(newMat,m,n,M,N);CHKERRQ(ierr);
2877 
2878   if (bs > 1) {ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);}
2879 
2880   ierr = MatMPIAIJSetPreallocation(newMat,0,ourlens,0,offlens);CHKERRQ(ierr);
2881 
2882   for (i=0; i<m; i++) {
2883     ourlens[i] += offlens[i];
2884   }
2885 
2886   if (!rank) {
2887     ierr = PetscMalloc1(maxnz+1,&vals);CHKERRQ(ierr);
2888 
2889     /* read in my part of the matrix numerical values  */
2890     nz   = procsnz[0];
2891     ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
2892 
2893     /* insert into matrix */
2894     jj      = rstart;
2895     smycols = mycols;
2896     svals   = vals;
2897     for (i=0; i<m; i++) {
2898       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
2899       smycols += ourlens[i];
2900       svals   += ourlens[i];
2901       jj++;
2902     }
2903 
2904     /* read in other processors and ship out */
2905     for (i=1; i<size; i++) {
2906       nz   = procsnz[i];
2907       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
2908       ierr = MPIULong_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
2909     }
2910     ierr = PetscFree(procsnz);CHKERRQ(ierr);
2911   } else {
2912     /* receive numeric values */
2913     ierr = PetscMalloc1(nz+1,&vals);CHKERRQ(ierr);
2914 
2915     /* receive message of values*/
2916     ierr = MPIULong_Recv(vals,nz,MPIU_SCALAR,0,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
2917 
2918     /* insert into matrix */
2919     jj      = rstart;
2920     smycols = mycols;
2921     svals   = vals;
2922     for (i=0; i<m; i++) {
2923       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
2924       smycols += ourlens[i];
2925       svals   += ourlens[i];
2926       jj++;
2927     }
2928   }
2929   ierr = PetscFree2(ourlens,offlens);CHKERRQ(ierr);
2930   ierr = PetscFree(vals);CHKERRQ(ierr);
2931   ierr = PetscFree(mycols);CHKERRQ(ierr);
2932   ierr = PetscFree(rowners);CHKERRQ(ierr);
2933   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2934   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2935   PetscFunctionReturn(0);
2936 }
2937 
2938 /* Not scalable because of ISAllGather() unless getting all columns. */
2939 PetscErrorCode ISGetSeqIS_Private(Mat mat,IS iscol,IS *isseq)
2940 {
2941   PetscErrorCode ierr;
2942   IS             iscol_local;
2943   PetscBool      isstride;
2944   PetscMPIInt    lisstride=0,gisstride;
2945 
2946   PetscFunctionBegin;
2947   /* check if we are grabbing all columns*/
2948   ierr = PetscObjectTypeCompare((PetscObject)iscol,ISSTRIDE,&isstride);CHKERRQ(ierr);
2949 
2950   if (isstride) {
2951     PetscInt  start,len,mstart,mlen;
2952     ierr = ISStrideGetInfo(iscol,&start,NULL);CHKERRQ(ierr);
2953     ierr = ISGetLocalSize(iscol,&len);CHKERRQ(ierr);
2954     ierr = MatGetOwnershipRangeColumn(mat,&mstart,&mlen);CHKERRQ(ierr);
2955     if (mstart == start && mlen-mstart == len) lisstride = 1;
2956   }
2957 
2958   ierr = MPIU_Allreduce(&lisstride,&gisstride,1,MPI_INT,MPI_MIN,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
2959   if (gisstride) {
2960     PetscInt N;
2961     ierr = MatGetSize(mat,NULL,&N);CHKERRQ(ierr);
2962     ierr = ISCreateStride(PetscObjectComm((PetscObject)mat),N,0,1,&iscol_local);CHKERRQ(ierr);
2963     ierr = ISSetIdentity(iscol_local);CHKERRQ(ierr);
2964     ierr = PetscInfo(mat,"Optimizing for obtaining all columns of the matrix; skipping ISAllGather()\n");CHKERRQ(ierr);
2965   } else {
2966     PetscInt cbs;
2967     ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
2968     ierr = ISAllGather(iscol,&iscol_local);CHKERRQ(ierr);
2969     ierr = ISSetBlockSize(iscol_local,cbs);CHKERRQ(ierr);
2970   }
2971 
2972   *isseq = iscol_local;
2973   PetscFunctionReturn(0);
2974 }
2975 
2976 /*
2977  Used for avoiding ISAllGather() and global size of iscol_local (see MatCreateSubMatrix_MPIAIJ_nonscalable)
2978 
2979  Input Parameters:
2980    mat - matrix
2981    iscol - parallel column index set; its local indices are a subset of local columns of mat,
2982            i.e., mat->cstart <= iscol[i] < mat->cend
2983  Output Parameter:
2984    iscol_sub - sequential column index set, a subset of iscol
2985    iscmap - column map; iscmap[i] indicates global location of iscol_sub[i] in iscol
2986  */
2987 PetscErrorCode ISGetSeqIS_SameColDist_Private(Mat mat,IS isrow,IS iscol,IS *isrow_d,IS *iscol_d,IS *iscol_o,IS *isgarray)
2988 {
2989   PetscErrorCode ierr;
2990   Vec            x,cmap;
2991   const PetscInt *is_idx;
2992   PetscScalar    *xarray,*cmaparray;
2993   PetscInt       ncols,isstart,*idx,*camp,count,m,rstart;
2994   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)mat->data;
2995   Mat            B=a->B;
2996   Vec            lvec=a->lvec,lcmap;
2997   PetscInt       i,cstart,cend,Bn=B->cmap->N;
2998   MPI_Comm       comm;
2999 
3000   PetscFunctionBegin;
3001   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3002   PetscMPIInt rank;
3003   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3004   ierr = ISGetLocalSize(iscol,&ncols);CHKERRQ(ierr);
3005 
3006   /* (1) iscol is a sub-column vector of mat, pad it with '-1.' to form a full vector x */
3007   ierr = MatCreateVecs(mat,&x,NULL);CHKERRQ(ierr);
3008   ierr = VecDuplicate(x,&cmap);CHKERRQ(ierr);
3009   ierr = VecSet(x,-1.0);CHKERRQ(ierr);
3010 
3011   /* get start indices */
3012   ierr = MPI_Scan(&ncols,&isstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3013   isstart -= ncols;
3014   ierr = MatGetOwnershipRangeColumn(mat,&cstart,&cend);CHKERRQ(ierr);
3015 
3016   ierr = ISGetIndices(iscol,&is_idx);CHKERRQ(ierr);
3017   ierr = VecGetArray(x,&xarray);CHKERRQ(ierr);
3018   ierr = VecGetArray(cmap,&cmaparray);CHKERRQ(ierr);
3019   ierr = PetscMalloc1(ncols,&idx);CHKERRQ(ierr);
3020   for (i=0; i<ncols; i++) {
3021     xarray[is_idx[i]-cstart]    = (PetscScalar)is_idx[i];
3022     cmaparray[is_idx[i]-cstart] = i + isstart; /* global index of iscol[i] */
3023 
3024     idx[i]                      = is_idx[i]-cstart;
3025   }
3026   ierr = VecRestoreArray(x,&xarray);CHKERRQ(ierr);
3027   ierr = VecRestoreArray(cmap,&cmaparray);CHKERRQ(ierr);
3028   ierr = ISRestoreIndices(iscol,&is_idx);CHKERRQ(ierr);
3029 
3030   ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_COPY_VALUES,iscol_d);CHKERRQ(ierr);
3031   ierr = ISGetBlockSize(iscol,&i);CHKERRQ(ierr);
3032   ierr = ISSetBlockSize(*iscol_d,i);CHKERRQ(ierr);
3033   ierr = PetscFree(idx);CHKERRQ(ierr);
3034 
3035   ierr = ISGetLocalSize(isrow,&m);CHKERRQ(ierr);
3036   rstart = mat->rmap->rstart;
3037   ierr = PetscMalloc1(m,&idx);CHKERRQ(ierr);
3038   ierr = ISGetIndices(isrow,&is_idx);CHKERRQ(ierr);
3039   for (i=0; i<m; i++) {
3040     idx[i] = is_idx[i]-rstart;
3041   }
3042   ierr = ISRestoreIndices(isrow,&is_idx);CHKERRQ(ierr);
3043 
3044   ierr = ISCreateGeneral(PETSC_COMM_SELF,m,idx,PETSC_COPY_VALUES,isrow_d);CHKERRQ(ierr);
3045   ierr = ISGetBlockSize(isrow,&i);CHKERRQ(ierr);
3046   ierr = ISSetBlockSize(*isrow_d,i);CHKERRQ(ierr);
3047   ierr = PetscFree(idx);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 
3057   count = ncols + Bn;
3058   ierr  = PetscMalloc2(count,&idx,count,&camp);CHKERRQ(ierr);
3059 
3060   ierr = VecScatterEnd(a->Mvctx,cmap,lcmap,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3061 
3062   /* (3) create scalable iscol_sub (a subset of iscol) and iscmap */
3063   /* local column indices */
3064   ierr = ISGetIndices(iscol,&is_idx);CHKERRQ(ierr);
3065   for (i=0; i<ncols; i++) {
3066     idx[i]  = is_idx[i];
3067     camp[i] = i + isstart; /* global index of iscol = column index in submat */
3068   }
3069   ierr = ISRestoreIndices(iscol,&is_idx);CHKERRQ(ierr);
3070   count = ncols;
3071 
3072   /* off-process column indices */
3073   PetscInt *idx1,*cmap1,count1=0;
3074   ierr = PetscMalloc2(Bn,&idx1,Bn,&cmap1);CHKERRQ(ierr);
3075 
3076   ierr = VecGetArray(lvec,&xarray);CHKERRQ(ierr);
3077   ierr = VecGetArray(lcmap,&cmaparray);CHKERRQ(ierr);
3078   for (i=0; i<Bn; i++) {
3079     if (PetscRealPart(xarray[i]) > -1.0) {
3080       idx1[count1]    = i; /* local column index in off-diagonal part B */
3081       cmap1[count1++] = (PetscInt)PetscRealPart(cmaparray[i]);  /* column index in submat */
3082 
3083       idx[count]    = (PetscInt)PetscRealPart(xarray[i]);
3084       camp[count++] = (PetscInt)PetscRealPart(cmaparray[i]);  /* column index in submat */
3085     }
3086   }
3087   ierr = VecRestoreArray(lvec,&xarray);CHKERRQ(ierr);
3088   ierr = VecRestoreArray(lcmap,&cmaparray);CHKERRQ(ierr);
3089 
3090   ierr = PetscSortIntWithArray(count,camp,idx);CHKERRQ(ierr);
3091 
3092   ierr = ISCreateGeneral(PETSC_COMM_SELF,count1,idx1,PETSC_COPY_VALUES,iscol_o);CHKERRQ(ierr);
3093   ierr = ISCreateGeneral(PETSC_COMM_SELF,count1,cmap1,PETSC_COPY_VALUES,isgarray);CHKERRQ(ierr);
3094   ierr = ISGetBlockSize(iscol,&i);CHKERRQ(ierr);
3095   ierr = ISSetBlockSize(*iscol_o,i);CHKERRQ(ierr);
3096   ierr = PetscFree2(idx1,cmap1);CHKERRQ(ierr);
3097 
3098   ierr = PetscFree2(idx,camp);CHKERRQ(ierr);
3099   ierr = VecDestroy(&x);CHKERRQ(ierr);
3100   ierr = VecDestroy(&cmap);CHKERRQ(ierr);
3101   ierr = VecDestroy(&lcmap);CHKERRQ(ierr);
3102   PetscFunctionReturn(0);
3103 }
3104 
3105 PetscErrorCode MatCreateSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3106 {
3107   PetscErrorCode ierr;
3108   IS             iscol_local,isrow_d;
3109   PetscInt       csize;
3110   PetscInt       n,i,j,start,end;
3111   PetscBool      sameRowDist=PETSC_FALSE,sameDist[2],tsameDist[2];
3112   MPI_Comm       comm;
3113 
3114   PetscFunctionBegin;
3115   /* If isrow has same processor distribution as mat,
3116      call MatCreateSubMatrix_MPIAIJ_SameRowDist() to avoid using a hash table with global size of iscol */
3117   if (call == MAT_REUSE_MATRIX) {
3118     ierr = PetscObjectQuery((PetscObject)*newmat,"isrow_d",(PetscObject*)&isrow_d);CHKERRQ(ierr);
3119     if (isrow_d) {
3120       sameRowDist  = PETSC_TRUE;
3121       tsameDist[1] = PETSC_TRUE; /* sameColDist */
3122     } else {
3123       ierr = PetscObjectQuery((PetscObject)*newmat,"SubIScol",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3124       if (iscol_local) {
3125         sameRowDist  = PETSC_TRUE;
3126         tsameDist[1] = PETSC_FALSE; /* !sameColDist */
3127       }
3128     }
3129   } else {
3130     /* check if isrow has same processor distribution as mat */
3131     sameDist[0] = PETSC_FALSE;
3132     ierr = ISGetLocalSize(isrow,&n);CHKERRQ(ierr);
3133     if (!n) {
3134       sameDist[0] = PETSC_TRUE;
3135     } else {
3136       ierr = ISGetMinMax(isrow,&i,&j);CHKERRQ(ierr);
3137       ierr = MatGetOwnershipRange(mat,&start,&end);CHKERRQ(ierr);
3138       if (i >= start && j < end) {
3139         sameDist[0] = PETSC_TRUE;
3140       }
3141     }
3142 
3143     /* check if iscol has same processor distribution as mat */
3144     sameDist[1] = PETSC_FALSE;
3145     ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr);
3146     if (!n) {
3147       sameDist[1] = PETSC_TRUE;
3148     } else {
3149       ierr = ISGetMinMax(iscol,&i,&j);CHKERRQ(ierr);
3150       ierr = MatGetOwnershipRangeColumn(mat,&start,&end);CHKERRQ(ierr);
3151       if (i >= start && j < end) sameDist[1] = PETSC_TRUE;
3152     }
3153 
3154     ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3155     ierr = MPIU_Allreduce(&sameDist,&tsameDist,2,MPIU_BOOL,MPI_LAND,comm);CHKERRQ(ierr);
3156     sameRowDist = tsameDist[0];
3157   }
3158 
3159   if (sameRowDist) {
3160     ierr = MatCreateSubMatrix_MPIAIJ_SameRowDist(mat,isrow,iscol,call,tsameDist[1],newmat);CHKERRQ(ierr);
3161     PetscFunctionReturn(0);
3162   }
3163 
3164   /* General case: iscol -> iscol_local which has global size of iscol */
3165   if (call == MAT_REUSE_MATRIX) {
3166     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3167     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3168   } else {
3169     ierr = ISGetSeqIS_Private(mat,iscol,&iscol_local);CHKERRQ(ierr);
3170   }
3171 
3172   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3173   ierr = MatCreateSubMatrix_MPIAIJ_nonscalable(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
3174 
3175   if (call == MAT_INITIAL_MATRIX) {
3176     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3177     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3178   }
3179   PetscFunctionReturn(0);
3180 }
3181 
3182 /*@C
3183      MatCreateMPIAIJWithSeqAIJ - creates a MPIAIJ matrix using SeqAIJ matrices that contain the "diagonal"
3184          and "off-diagonal" part of the matrix in CSR format.
3185 
3186    Collective on MPI_Comm
3187 
3188    Input Parameters:
3189 +  comm - MPI communicator
3190 .  A - "diagonal" portion of matrix
3191 .  B - "off-diagonal" portion of matrix, destroyed by this routine
3192 -  garray - global index of B columns
3193 
3194    Output Parameter:
3195 .   mat - the matrix, with input A as its local diagonal matrix
3196    Level: advanced
3197 
3198    Notes:
3199        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix.
3200        A becomes part of output mat, B is destroyed by this routine. The user cannot use A and B anymore.
3201 
3202 .seealso: MatCreateMPIAIJWithSplitArrays()
3203 @*/
3204 PetscErrorCode MatCreateMPIAIJWithSeqAIJ(MPI_Comm comm,Mat A,Mat B,const PetscInt garray[],Mat *mat)
3205 {
3206   PetscErrorCode ierr;
3207   Mat_MPIAIJ     *maij;
3208   Mat_SeqAIJ     *b=(Mat_SeqAIJ*)B->data;
3209   PetscInt       *oi=b->i,*oj=b->j,i,nz,col;
3210   PetscScalar    *oa=b->a;
3211   Mat            Btmp;
3212   PetscInt       m,n,N;
3213 
3214   PetscFunctionBegin;
3215   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
3216   ierr = MatGetSize(A,&m,&n);CHKERRQ(ierr);
3217   if (m != B->rmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Am %d != Bm %d",m,B->rmap->N);
3218 
3219   /* get global columns of mat */
3220   ierr = MPIU_Allreduce(&n,&N,1,MPI_INT,MPI_SUM,comm);CHKERRQ(ierr);
3221 
3222   ierr = MatSetSizes(*mat,m,n,PETSC_DECIDE,N);CHKERRQ(ierr);
3223   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
3224   maij = (Mat_MPIAIJ*)(*mat)->data;
3225 
3226   (*mat)->preallocated = PETSC_TRUE;
3227 
3228   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
3229   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
3230 
3231   maij->A = A;
3232 
3233   nz = oi[m];
3234   for (i=0; i<nz; i++) {
3235     col   = oj[i];
3236     oj[i] = garray[col];
3237   }
3238 
3239   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,N,oi,oj,oa,&Btmp);CHKERRQ(ierr);
3240   maij->B         = Btmp;
3241 
3242   if (B->rmap->N != Btmp->rmap->N) SETERRQ2(PETSC_COMM_SELF,0,"BN %d != BtmpN %d",B->rmap->N,Btmp->rmap->N);
3243 
3244   b->singlemalloc = PETSC_FALSE; /* these arrays are shared by Btmp */
3245   b->free_a       = PETSC_FALSE;
3246   b->free_ij      = PETSC_FALSE;
3247   ierr = MatDestroy(&B);CHKERRQ(ierr);
3248 
3249   b = (Mat_SeqAIJ*)Btmp->data;
3250   b->singlemalloc = PETSC_TRUE; /* arrays will be freed by MatDestroy(&Btmp) */
3251   b->free_a       = PETSC_TRUE;
3252   b->free_ij      = PETSC_TRUE;
3253 
3254   /* condense columns of maij->B */
3255   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
3256   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3257   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3258   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_FALSE);CHKERRQ(ierr);
3259   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3260   PetscFunctionReturn(0);
3261 }
3262 
3263 extern PetscErrorCode MatCreateSubMatrices_MPIAIJ_SingleIS_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool,Mat*);
3264 
3265 PetscErrorCode MatCreateSubMatrix_MPIAIJ_SameRowDist(Mat mat,IS isrow,IS iscol,MatReuse call,PetscBool sameColDist,Mat *newmat)
3266 {
3267   PetscErrorCode ierr;
3268   PetscInt       i,m,n,rstart,row,rend,nz,j,bs,cbs;
3269   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
3270   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)mat->data;
3271   Mat            M,Msub,B=a->B,Mnew=NULL;
3272   MatScalar      *aa;
3273   Mat_SeqAIJ     *aij;
3274   PetscInt       *garray = a->garray,*colsub,Ncols;
3275   PetscInt       count,Bn=B->cmap->N,cstart=mat->cmap->rstart,cend=mat->cmap->rend;
3276   IS             iscol_sub,iscmap;
3277   const PetscInt *is_idx,*cmap;
3278   PetscBool      allcolumns=PETSC_FALSE;
3279   IS             iscol_local=NULL;
3280   MPI_Comm       comm;
3281   IS             iscol_d,isrow_d,iscol_o,isgarray;
3282   Mat            Asub=NULL,Bsub=NULL;
3283 
3284   PetscFunctionBegin;
3285   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3286   PetscMPIInt rank;
3287   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3288 
3289   if (call == MAT_REUSE_MATRIX) {
3290     if (sameColDist) {
3291       Mat_MPIAIJ *matsub=(Mat_MPIAIJ*)(*newmat)->data;
3292 
3293       ierr = PetscObjectQuery((PetscObject)*newmat,"isrow_d",(PetscObject*)&isrow_d);CHKERRQ(ierr);
3294       if (!isrow_d) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"isrow_d passed in was not used before, cannot reuse");
3295 
3296       ierr = PetscObjectQuery((PetscObject)*newmat,"iscol_d",(PetscObject*)&iscol_d);CHKERRQ(ierr);
3297       if (!iscol_d) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"iscol_d passed in was not used before, cannot reuse");
3298 
3299       ierr = PetscObjectQuery((PetscObject)*newmat,"iscol_o",(PetscObject*)&iscol_o);CHKERRQ(ierr);
3300       if (!iscol_o) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"iscol_o passed in was not used before, cannot reuse");
3301 
3302       ierr = MatCreateSubMatrix_SeqAIJ(a->A,isrow_d,iscol_d,PETSC_DECIDE,call,&matsub->A);CHKERRQ(ierr);
3303       ierr = MatCreateSubMatrix_SeqAIJ(a->B,isrow_d,iscol_o,PETSC_DECIDE,call,&matsub->B);CHKERRQ(ierr);
3304       ierr = MatAssemblyBegin(*newmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3305       ierr = MatAssemblyEnd(*newmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3306       PetscFunctionReturn(0);
3307 
3308     } else {
3309       SETERRQ(PETSC_COMM_SELF,0,"not done yet");
3310       //===============================
3311       ierr = PetscObjectQuery((PetscObject)*newmat,"SubIScol",(PetscObject*)&iscol_sub);CHKERRQ(ierr);
3312       if (!iscol_sub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"SubIScol passed in was not used before, cannot reuse");
3313       ierr = ISGetLocalSize(iscol_sub,&count);CHKERRQ(ierr);
3314 
3315       ierr = PetscObjectQuery((PetscObject)*newmat,"Subcmap",(PetscObject*)&iscmap);CHKERRQ(ierr);
3316       if (!iscmap) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Subcmap passed in was not used before, cannot reuse");
3317 
3318       ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Msub);CHKERRQ(ierr);
3319       if (!Msub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3320 
3321       ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol_sub,MAT_REUSE_MATRIX,PETSC_FALSE,&Msub);CHKERRQ(ierr);
3322     }
3323 
3324   } else { /* call == MAT_INITIAL_MATRIX) */
3325     ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr);
3326     ierr = ISGetSize(iscol,&Ncols);CHKERRQ(ierr);
3327 
3328     if (sameColDist) {
3329       /* iscol has same processor distribution as mat, *newmat is a submatrix of local mat */
3330       ierr = ISGetSeqIS_SameColDist_Private(mat,isrow,iscol,&isrow_d,&iscol_d,&iscol_o,&isgarray);CHKERRQ(ierr);
3331 
3332       ierr = MatCreateSubMatrix_SeqAIJ(a->A,isrow_d,iscol_d,PETSC_DECIDE,call,&Asub);CHKERRQ(ierr);
3333       ierr = MatCreateSubMatrix_SeqAIJ(a->B,isrow_d,iscol_o,PETSC_DECIDE,call,&Bsub);CHKERRQ(ierr);
3334 #if 0
3335       ierr = ISGetBlockSize(isrow,&bs);CHKERRQ(ierr);
3336       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
3337       ierr = MatSetBlockSizes(Asub,bs,cbs);CHKERRQ(ierr);
3338       printf("[%d] bs %d cbs %d Asub rbs %d, cbs %d\n",rank,bs,cbs,Asub->rmap->bs,Asub->cmap->bs);
3339 #endif
3340       const PetscInt *garray1;
3341       ierr = ISGetIndices(isgarray,&garray1);CHKERRQ(ierr);
3342       ierr = MatCreateMPIAIJWithSeqAIJ(comm,Asub,Bsub,garray1,&Mnew);CHKERRQ(ierr);
3343       ierr = ISRestoreIndices(isgarray,&garray1);CHKERRQ(ierr);
3344       //ierr = MatView(Mnew,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
3345 
3346       ierr = ISDestroy(&isgarray);CHKERRQ(ierr);
3347 
3348       /* save isrow_d, iscol_d and iscol_o used in processor for next request */
3349       ierr = PetscObjectCompose((PetscObject)Mnew,"isrow_d",(PetscObject)isrow_d);CHKERRQ(ierr);
3350       ierr = ISDestroy(&isrow_d);CHKERRQ(ierr);
3351 
3352       ierr = PetscObjectCompose((PetscObject)Mnew,"iscol_d",(PetscObject)iscol_d);CHKERRQ(ierr);
3353       ierr = ISDestroy(&iscol_d);CHKERRQ(ierr);
3354 
3355       ierr = PetscObjectCompose((PetscObject)Mnew,"iscol_o",(PetscObject)iscol_o);CHKERRQ(ierr);
3356       ierr = ISDestroy(&iscol_o);CHKERRQ(ierr);
3357 
3358       *newmat = Mnew;
3359       PetscFunctionReturn(0);
3360 
3361     } else { /* !sameColDist: iscol -> nonscalable iscol_local, then get scalable iscol_sub and iscmap */
3362       PetscBool flg;
3363 
3364       /* (1) Create scalable iscol_sub and iscmap */
3365       /* iscol -> nonscalable iscol_local */
3366       ierr = ISGetSeqIS_Private(mat,iscol,&iscol_local);CHKERRQ(ierr);
3367       ierr = ISGetLocalSize(iscol_local,&n);CHKERRQ(ierr); /* local size of iscol_local = global columns of newmat */
3368       if (n != Ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"n %d != Ncols %d",n,Ncols);
3369 
3370       /* Check for special case: each processor gets entire matrix columns */
3371       ierr = ISIdentity(iscol_local,&flg);CHKERRQ(ierr);
3372       if (flg && n == mat->cmap->N) allcolumns = PETSC_TRUE;
3373       if (allcolumns) {
3374         iscol_sub = iscol_local;
3375         ierr = PetscObjectReference((PetscObject)iscol_local);CHKERRQ(ierr);
3376         ierr = ISCreateStride(PETSC_COMM_SELF,n,0,1,&iscmap);CHKERRQ(ierr);
3377 
3378       } else { /* iscol_local -> iscol_sub and iscmap */
3379         PetscInt *idx,*cmap1,k,cbs;
3380 
3381         /* implementation below requires iscol_local be sorted, it can have duplicate indices */
3382         ierr = ISSorted(iscol_local,&flg);CHKERRQ(ierr);
3383         if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"unsorted iscol_local is not implemented yet");
3384 
3385         ierr = PetscMalloc2(Ncols,&idx,Ncols,&cmap1);CHKERRQ(ierr);
3386         ierr = ISGetIndices(iscol_local,&is_idx);CHKERRQ(ierr);
3387         count = 0;
3388         k     = 0;
3389         for (i=0; i<Ncols; i++) {
3390           j = is_idx[i];
3391           if (j >= cstart && j < cend) {
3392             /* diagonal part of mat */
3393             idx[count]     = j;
3394             cmap1[count++] = i; /* column index in submat */
3395           } else if (Bn) {
3396             /* off-diagonal part of mat */
3397             if (j == garray[k]) {
3398               idx[count]     = j;
3399               cmap1[count++] = i;  /* column index in submat */
3400             } else if (j > garray[k]) {
3401               while (j > garray[k] && k < Bn-1) k++;
3402               if (j == garray[k]) {
3403                 idx[count]     = j;
3404                 cmap1[count++] = i; /* column index in submat */
3405               }
3406             }
3407           }
3408         }
3409         ierr = ISRestoreIndices(iscol_local,&is_idx);CHKERRQ(ierr);
3410 
3411         ierr = ISCreateGeneral(PETSC_COMM_SELF,count,idx,PETSC_COPY_VALUES,&iscol_sub);CHKERRQ(ierr);
3412         ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
3413         ierr = ISSetBlockSize(iscol_sub,cbs);CHKERRQ(ierr);
3414 
3415         ierr = ISCreateGeneral(PetscObjectComm((PetscObject)iscol_local),count,cmap1,PETSC_COPY_VALUES,&iscmap);CHKERRQ(ierr);
3416         ierr = PetscFree2(idx,cmap1);CHKERRQ(ierr);
3417       }
3418 
3419       /* (2) Create sequential Msub */
3420       ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol_sub,MAT_INITIAL_MATRIX,allcolumns,&Msub);CHKERRQ(ierr);
3421     }
3422   }
3423 
3424   ierr = ISGetLocalSize(iscol_sub,&count);CHKERRQ(ierr);
3425   aij  = (Mat_SeqAIJ*)(Msub)->data;
3426   ii   = aij->i;
3427   ierr = ISGetIndices(iscmap,&cmap);CHKERRQ(ierr);
3428 
3429   /*
3430       m - number of local rows
3431       Ncols - number of columns (same on all processors)
3432       rstart - first row in new global matrix generated
3433   */
3434   ierr = MatGetSize(Msub,&m,NULL);CHKERRQ(ierr);
3435 
3436   if (call == MAT_INITIAL_MATRIX && !sameColDist) {
3437     /* (3) Create parallel newmat */
3438     PetscMPIInt    rank,size;
3439     PetscInt       csize;
3440 
3441     ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3442     ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3443 
3444     /*
3445         Determine the number of non-zeros in the diagonal and off-diagonal
3446         portions of the matrix in order to do correct preallocation
3447     */
3448 
3449     /* first get start and end of "diagonal" columns */
3450     ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3451     if (csize == PETSC_DECIDE) {
3452       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3453       if (mglobal == Ncols) { /* square matrix */
3454         nlocal = m;
3455       } else {
3456         nlocal = Ncols/size + ((Ncols % size) > rank);
3457       }
3458     } else {
3459       nlocal = csize;
3460     }
3461     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3462     rstart = rend - nlocal;
3463     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);
3464 
3465     /* next, compute all the lengths */
3466     jj    = aij->j;
3467     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3468     olens = dlens + m;
3469     for (i=0; i<m; i++) {
3470       jend = ii[i+1] - ii[i];
3471       olen = 0;
3472       dlen = 0;
3473       for (j=0; j<jend; j++) {
3474         if (cmap[*jj] < rstart || cmap[*jj] >= rend) olen++;
3475         else dlen++;
3476         jj++;
3477       }
3478       olens[i] = olen;
3479       dlens[i] = dlen;
3480     }
3481     ierr = MatGetBlockSizes(Msub,&bs,&cbs);CHKERRQ(ierr);
3482 
3483     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3484     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,Ncols);CHKERRQ(ierr);
3485     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3486     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3487     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3488     ierr = PetscFree(dlens);CHKERRQ(ierr);
3489 
3490   } else { /* call == MAT_REUSE_MATRIX */
3491     M    = *newmat;
3492     ierr = MatGetLocalSize(M,&i,NULL);CHKERRQ(ierr);
3493     if (i != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3494     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3495     /*
3496          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3497        rather than the slower MatSetValues().
3498     */
3499     M->was_assembled = PETSC_TRUE;
3500     M->assembled     = PETSC_FALSE;
3501   }
3502 
3503   /* (4) Set values of Msub to *newmat */
3504   ierr = PetscMalloc1(count,&colsub);CHKERRQ(ierr);
3505   ierr = MatGetOwnershipRange(M,&rstart,NULL);CHKERRQ(ierr);
3506 
3507   jj   = aij->j;
3508   aa   = aij->a;
3509   for (i=0; i<m; i++) {
3510     row = rstart + i;
3511     nz  = ii[i+1] - ii[i];
3512     for (j=0; j<nz; j++) colsub[j] = cmap[jj[j]];
3513     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,colsub,aa,INSERT_VALUES);CHKERRQ(ierr);
3514     jj += nz; aa += nz;
3515   }
3516   ierr = ISRestoreIndices(iscmap,&cmap);CHKERRQ(ierr);
3517 
3518   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3519   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3520 
3521   ierr = PetscFree(colsub);CHKERRQ(ierr);
3522 
3523   /* save Msub, iscol_sub and iscmap used in processor for next request */
3524   if (call ==  MAT_INITIAL_MATRIX) {
3525     if (!sameColDist) *newmat = M;
3526     ierr = PetscObjectCompose((PetscObject)(*newmat),"SubMatrix",(PetscObject)Msub);CHKERRQ(ierr);
3527     ierr = MatDestroy(&Msub);CHKERRQ(ierr);
3528 
3529     ierr = PetscObjectCompose((PetscObject)(*newmat),"SubIScol",(PetscObject)iscol_sub);CHKERRQ(ierr);
3530     ierr = ISDestroy(&iscol_sub);CHKERRQ(ierr);
3531 
3532     ierr = PetscObjectCompose((PetscObject)(*newmat),"Subcmap",(PetscObject)iscmap);CHKERRQ(ierr);
3533     ierr = ISDestroy(&iscmap);CHKERRQ(ierr);
3534 
3535     if (iscol_local) {
3536       ierr = PetscObjectCompose((PetscObject)(*newmat),"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3537       ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3538     }
3539 
3540     if (*newmat != M) {ierr = MatDestroy(&M);CHKERRQ(ierr);}
3541   }
3542   PetscFunctionReturn(0);
3543 }
3544 
3545 /*
3546     Not great since it makes two copies of the submatrix, first an SeqAIJ
3547   in local and then by concatenating the local matrices the end result.
3548   Writing it directly would be much like MatCreateSubMatrices_MPIAIJ()
3549 
3550   Note: This requires a sequential iscol with all indices.
3551 */
3552 PetscErrorCode MatCreateSubMatrix_MPIAIJ_nonscalable(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3553 {
3554   PetscErrorCode ierr;
3555   PetscMPIInt    rank,size;
3556   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3557   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
3558   Mat            M,Mreuse;
3559   MatScalar      *aa,*vwork;
3560   MPI_Comm       comm;
3561   Mat_SeqAIJ     *aij;
3562   PetscBool      colflag,allcolumns=PETSC_FALSE;
3563 
3564   PetscFunctionBegin;
3565   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3566   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3567   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3568 
3569   /* Check for special case: each processor gets entire matrix columns */
3570   ierr = ISIdentity(iscol,&colflag);CHKERRQ(ierr);
3571   ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr);
3572   if (colflag && n == mat->cmap->N) allcolumns = PETSC_TRUE;
3573 
3574   if (call ==  MAT_REUSE_MATRIX) {
3575     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3576     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3577     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,allcolumns,&Mreuse);CHKERRQ(ierr);
3578   } else {
3579     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,allcolumns,&Mreuse);CHKERRQ(ierr);
3580   }
3581 
3582   /*
3583       m - number of local rows
3584       n - number of columns (same on all processors)
3585       rstart - first row in new global matrix generated
3586   */
3587   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3588   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3589   if (call == MAT_INITIAL_MATRIX) {
3590     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3591     ii  = aij->i;
3592     jj  = aij->j;
3593 
3594     /*
3595         Determine the number of non-zeros in the diagonal and off-diagonal
3596         portions of the matrix in order to do correct preallocation
3597     */
3598 
3599     /* first get start and end of "diagonal" columns */
3600     if (csize == PETSC_DECIDE) {
3601       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3602       if (mglobal == n) { /* square matrix */
3603         nlocal = m;
3604       } else {
3605         nlocal = n/size + ((n % size) > rank);
3606       }
3607     } else {
3608       nlocal = csize;
3609     }
3610     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3611     rstart = rend - nlocal;
3612     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);
3613 
3614     /* next, compute all the lengths */
3615     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3616     olens = dlens + m;
3617     for (i=0; i<m; i++) {
3618       jend = ii[i+1] - ii[i];
3619       olen = 0;
3620       dlen = 0;
3621       for (j=0; j<jend; j++) {
3622         if (*jj < rstart || *jj >= rend) olen++;
3623         else dlen++;
3624         jj++;
3625       }
3626       olens[i] = olen;
3627       dlens[i] = dlen;
3628     }
3629     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3630     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3631     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3632     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3633     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3634     ierr = PetscFree(dlens);CHKERRQ(ierr);
3635   } else {
3636     PetscInt ml,nl;
3637 
3638     M    = *newmat;
3639     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3640     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3641     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3642     /*
3643          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3644        rather than the slower MatSetValues().
3645     */
3646     M->was_assembled = PETSC_TRUE;
3647     M->assembled     = PETSC_FALSE;
3648   }
3649   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3650   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3651   ii   = aij->i;
3652   jj   = aij->j;
3653   aa   = aij->a;
3654   for (i=0; i<m; i++) {
3655     row   = rstart + i;
3656     nz    = ii[i+1] - ii[i];
3657     cwork = jj;     jj += nz;
3658     vwork = aa;     aa += nz;
3659     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3660   }
3661 
3662   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3663   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3664   *newmat = M;
3665 
3666   /* save submatrix used in processor for next request */
3667   if (call ==  MAT_INITIAL_MATRIX) {
3668     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3669     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3670   }
3671   PetscFunctionReturn(0);
3672 }
3673 
3674 PetscErrorCode MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3675 {
3676   PetscInt       m,cstart, cend,j,nnz,i,d;
3677   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3678   const PetscInt *JJ;
3679   PetscScalar    *values;
3680   PetscErrorCode ierr;
3681   PetscBool      nooffprocentries;
3682 
3683   PetscFunctionBegin;
3684   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3685 
3686   ierr   = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3687   ierr   = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3688   m      = B->rmap->n;
3689   cstart = B->cmap->rstart;
3690   cend   = B->cmap->rend;
3691   rstart = B->rmap->rstart;
3692 
3693   ierr = PetscMalloc2(m,&d_nnz,m,&o_nnz);CHKERRQ(ierr);
3694 
3695 #if defined(PETSC_USE_DEBUGGING)
3696   for (i=0; i<m; i++) {
3697     nnz = Ii[i+1]- Ii[i];
3698     JJ  = J + Ii[i];
3699     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3700     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3701     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);
3702   }
3703 #endif
3704 
3705   for (i=0; i<m; i++) {
3706     nnz     = Ii[i+1]- Ii[i];
3707     JJ      = J + Ii[i];
3708     nnz_max = PetscMax(nnz_max,nnz);
3709     d       = 0;
3710     for (j=0; j<nnz; j++) {
3711       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3712     }
3713     d_nnz[i] = d;
3714     o_nnz[i] = nnz - d;
3715   }
3716   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3717   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3718 
3719   if (v) values = (PetscScalar*)v;
3720   else {
3721     ierr = PetscCalloc1(nnz_max+1,&values);CHKERRQ(ierr);
3722   }
3723 
3724   for (i=0; i<m; i++) {
3725     ii   = i + rstart;
3726     nnz  = Ii[i+1]- Ii[i];
3727     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3728   }
3729   nooffprocentries    = B->nooffprocentries;
3730   B->nooffprocentries = PETSC_TRUE;
3731   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3732   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3733   B->nooffprocentries = nooffprocentries;
3734 
3735   if (!v) {
3736     ierr = PetscFree(values);CHKERRQ(ierr);
3737   }
3738   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3739   PetscFunctionReturn(0);
3740 }
3741 
3742 /*@
3743    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3744    (the default parallel PETSc format).
3745 
3746    Collective on MPI_Comm
3747 
3748    Input Parameters:
3749 +  B - the matrix
3750 .  i - the indices into j for the start of each local row (starts with zero)
3751 .  j - the column indices for each local row (starts with zero)
3752 -  v - optional values in the matrix
3753 
3754    Level: developer
3755 
3756    Notes:
3757        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3758      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3759      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3760 
3761        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3762 
3763        The format which is used for the sparse matrix input, is equivalent to a
3764     row-major ordering.. i.e for the following matrix, the input data expected is
3765     as shown
3766 
3767 $        1 0 0
3768 $        2 0 3     P0
3769 $       -------
3770 $        4 5 6     P1
3771 $
3772 $     Process0 [P0]: rows_owned=[0,1]
3773 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3774 $        j =  {0,0,2}  [size = 3]
3775 $        v =  {1,2,3}  [size = 3]
3776 $
3777 $     Process1 [P1]: rows_owned=[2]
3778 $        i =  {0,3}    [size = nrow+1  = 1+1]
3779 $        j =  {0,1,2}  [size = 3]
3780 $        v =  {4,5,6}  [size = 3]
3781 
3782 .keywords: matrix, aij, compressed row, sparse, parallel
3783 
3784 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MATMPIAIJ,
3785           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3786 @*/
3787 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3788 {
3789   PetscErrorCode ierr;
3790 
3791   PetscFunctionBegin;
3792   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3793   PetscFunctionReturn(0);
3794 }
3795 
3796 /*@C
3797    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3798    (the default parallel PETSc format).  For good matrix assembly performance
3799    the user should preallocate the matrix storage by setting the parameters
3800    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3801    performance can be increased by more than a factor of 50.
3802 
3803    Collective on MPI_Comm
3804 
3805    Input Parameters:
3806 +  B - the matrix
3807 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3808            (same value is used for all local rows)
3809 .  d_nnz - array containing the number of nonzeros in the various rows of the
3810            DIAGONAL portion of the local submatrix (possibly different for each row)
3811            or NULL (PETSC_NULL_INTEGER in Fortran), if d_nz is used to specify the nonzero structure.
3812            The size of this array is equal to the number of local rows, i.e 'm'.
3813            For matrices that will be factored, you must leave room for (and set)
3814            the diagonal entry even if it is zero.
3815 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3816            submatrix (same value is used for all local rows).
3817 -  o_nnz - array containing the number of nonzeros in the various rows of the
3818            OFF-DIAGONAL portion of the local submatrix (possibly different for
3819            each row) or NULL (PETSC_NULL_INTEGER in Fortran), if o_nz is used to specify the nonzero
3820            structure. The size of this array is equal to the number
3821            of local rows, i.e 'm'.
3822 
3823    If the *_nnz parameter is given then the *_nz parameter is ignored
3824 
3825    The AIJ format (also called the Yale sparse matrix format or
3826    compressed row storage (CSR)), is fully compatible with standard Fortran 77
3827    storage.  The stored row and column indices begin with zero.
3828    See Users-Manual: ch_mat for details.
3829 
3830    The parallel matrix is partitioned such that the first m0 rows belong to
3831    process 0, the next m1 rows belong to process 1, the next m2 rows belong
3832    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
3833 
3834    The DIAGONAL portion of the local submatrix of a processor can be defined
3835    as the submatrix which is obtained by extraction the part corresponding to
3836    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
3837    first row that belongs to the processor, r2 is the last row belonging to
3838    the this processor, and c1-c2 is range of indices of the local part of a
3839    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
3840    common case of a square matrix, the row and column ranges are the same and
3841    the DIAGONAL part is also square. The remaining portion of the local
3842    submatrix (mxN) constitute the OFF-DIAGONAL portion.
3843 
3844    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3845 
3846    You can call MatGetInfo() to get information on how effective the preallocation was;
3847    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3848    You can also run with the option -info and look for messages with the string
3849    malloc in them to see if additional memory allocation was needed.
3850 
3851    Example usage:
3852 
3853    Consider the following 8x8 matrix with 34 non-zero values, that is
3854    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3855    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3856    as follows:
3857 
3858 .vb
3859             1  2  0  |  0  3  0  |  0  4
3860     Proc0   0  5  6  |  7  0  0  |  8  0
3861             9  0 10  | 11  0  0  | 12  0
3862     -------------------------------------
3863            13  0 14  | 15 16 17  |  0  0
3864     Proc1   0 18  0  | 19 20 21  |  0  0
3865             0  0  0  | 22 23  0  | 24  0
3866     -------------------------------------
3867     Proc2  25 26 27  |  0  0 28  | 29  0
3868            30  0  0  | 31 32 33  |  0 34
3869 .ve
3870 
3871    This can be represented as a collection of submatrices as:
3872 
3873 .vb
3874       A B C
3875       D E F
3876       G H I
3877 .ve
3878 
3879    Where the submatrices A,B,C are owned by proc0, D,E,F are
3880    owned by proc1, G,H,I are owned by proc2.
3881 
3882    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3883    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3884    The 'M','N' parameters are 8,8, and have the same values on all procs.
3885 
3886    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3887    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3888    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3889    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3890    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3891    matrix, ans [DF] as another SeqAIJ matrix.
3892 
3893    When d_nz, o_nz parameters are specified, d_nz storage elements are
3894    allocated for every row of the local diagonal submatrix, and o_nz
3895    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3896    One way to choose d_nz and o_nz is to use the max nonzerors per local
3897    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3898    In this case, the values of d_nz,o_nz are:
3899 .vb
3900      proc0 : dnz = 2, o_nz = 2
3901      proc1 : dnz = 3, o_nz = 2
3902      proc2 : dnz = 1, o_nz = 4
3903 .ve
3904    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3905    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3906    for proc3. i.e we are using 12+15+10=37 storage locations to store
3907    34 values.
3908 
3909    When d_nnz, o_nnz parameters are specified, the storage is specified
3910    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3911    In the above case the values for d_nnz,o_nnz are:
3912 .vb
3913      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3914      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3915      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3916 .ve
3917    Here the space allocated is sum of all the above values i.e 34, and
3918    hence pre-allocation is perfect.
3919 
3920    Level: intermediate
3921 
3922 .keywords: matrix, aij, compressed row, sparse, parallel
3923 
3924 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
3925           MATMPIAIJ, MatGetInfo(), PetscSplitOwnership()
3926 @*/
3927 PetscErrorCode MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3928 {
3929   PetscErrorCode ierr;
3930 
3931   PetscFunctionBegin;
3932   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3933   PetscValidType(B,1);
3934   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
3935   PetscFunctionReturn(0);
3936 }
3937 
3938 /*@
3939      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
3940          CSR format the local rows.
3941 
3942    Collective on MPI_Comm
3943 
3944    Input Parameters:
3945 +  comm - MPI communicator
3946 .  m - number of local rows (Cannot be PETSC_DECIDE)
3947 .  n - This value should be the same as the local size used in creating the
3948        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3949        calculated if N is given) For square matrices n is almost always m.
3950 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3951 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3952 .   i - row indices
3953 .   j - column indices
3954 -   a - matrix values
3955 
3956    Output Parameter:
3957 .   mat - the matrix
3958 
3959    Level: intermediate
3960 
3961    Notes:
3962        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3963      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3964      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3965 
3966        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3967 
3968        The format which is used for the sparse matrix input, is equivalent to a
3969     row-major ordering.. i.e for the following matrix, the input data expected is
3970     as shown
3971 
3972 $        1 0 0
3973 $        2 0 3     P0
3974 $       -------
3975 $        4 5 6     P1
3976 $
3977 $     Process0 [P0]: rows_owned=[0,1]
3978 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3979 $        j =  {0,0,2}  [size = 3]
3980 $        v =  {1,2,3}  [size = 3]
3981 $
3982 $     Process1 [P1]: rows_owned=[2]
3983 $        i =  {0,3}    [size = nrow+1  = 1+1]
3984 $        j =  {0,1,2}  [size = 3]
3985 $        v =  {4,5,6}  [size = 3]
3986 
3987 .keywords: matrix, aij, compressed row, sparse, parallel
3988 
3989 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3990           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
3991 @*/
3992 PetscErrorCode MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
3993 {
3994   PetscErrorCode ierr;
3995 
3996   PetscFunctionBegin;
3997   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
3998   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
3999   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4000   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
4001   /* ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr); */
4002   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
4003   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
4004   PetscFunctionReturn(0);
4005 }
4006 
4007 /*@C
4008    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
4009    (the default parallel PETSc format).  For good matrix assembly performance
4010    the user should preallocate the matrix storage by setting the parameters
4011    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
4012    performance can be increased by more than a factor of 50.
4013 
4014    Collective on MPI_Comm
4015 
4016    Input Parameters:
4017 +  comm - MPI communicator
4018 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
4019            This value should be the same as the local size used in creating the
4020            y vector for the matrix-vector product y = Ax.
4021 .  n - This value should be the same as the local size used in creating the
4022        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
4023        calculated if N is given) For square matrices n is almost always m.
4024 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
4025 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
4026 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
4027            (same value is used for all local rows)
4028 .  d_nnz - array containing the number of nonzeros in the various rows of the
4029            DIAGONAL portion of the local submatrix (possibly different for each row)
4030            or NULL, if d_nz is used to specify the nonzero structure.
4031            The size of this array is equal to the number of local rows, i.e 'm'.
4032 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
4033            submatrix (same value is used for all local rows).
4034 -  o_nnz - array containing the number of nonzeros in the various rows of the
4035            OFF-DIAGONAL portion of the local submatrix (possibly different for
4036            each row) or NULL, if o_nz is used to specify the nonzero
4037            structure. The size of this array is equal to the number
4038            of local rows, i.e 'm'.
4039 
4040    Output Parameter:
4041 .  A - the matrix
4042 
4043    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
4044    MatXXXXSetPreallocation() paradgm instead of this routine directly.
4045    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
4046 
4047    Notes:
4048    If the *_nnz parameter is given then the *_nz parameter is ignored
4049 
4050    m,n,M,N parameters specify the size of the matrix, and its partitioning across
4051    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
4052    storage requirements for this matrix.
4053 
4054    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
4055    processor than it must be used on all processors that share the object for
4056    that argument.
4057 
4058    The user MUST specify either the local or global matrix dimensions
4059    (possibly both).
4060 
4061    The parallel matrix is partitioned across processors such that the
4062    first m0 rows belong to process 0, the next m1 rows belong to
4063    process 1, the next m2 rows belong to process 2 etc.. where
4064    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
4065    values corresponding to [m x N] submatrix.
4066 
4067    The columns are logically partitioned with the n0 columns belonging
4068    to 0th partition, the next n1 columns belonging to the next
4069    partition etc.. where n0,n1,n2... are the input parameter 'n'.
4070 
4071    The DIAGONAL portion of the local submatrix on any given processor
4072    is the submatrix corresponding to the rows and columns m,n
4073    corresponding to the given processor. i.e diagonal matrix on
4074    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
4075    etc. The remaining portion of the local submatrix [m x (N-n)]
4076    constitute the OFF-DIAGONAL portion. The example below better
4077    illustrates this concept.
4078 
4079    For a square global matrix we define each processor's diagonal portion
4080    to be its local rows and the corresponding columns (a square submatrix);
4081    each processor's off-diagonal portion encompasses the remainder of the
4082    local matrix (a rectangular submatrix).
4083 
4084    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
4085 
4086    When calling this routine with a single process communicator, a matrix of
4087    type SEQAIJ is returned.  If a matrix of type MATMPIAIJ is desired for this
4088    type of communicator, use the construction mechanism:
4089      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
4090 
4091    By default, this format uses inodes (identical nodes) when possible.
4092    We search for consecutive rows with the same nonzero structure, thereby
4093    reusing matrix information to achieve increased efficiency.
4094 
4095    Options Database Keys:
4096 +  -mat_no_inode  - Do not use inodes
4097 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
4098 -  -mat_aij_oneindex - Internally use indexing starting at 1
4099         rather than 0.  Note that when calling MatSetValues(),
4100         the user still MUST index entries starting at 0!
4101 
4102 
4103    Example usage:
4104 
4105    Consider the following 8x8 matrix with 34 non-zero values, that is
4106    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
4107    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
4108    as follows:
4109 
4110 .vb
4111             1  2  0  |  0  3  0  |  0  4
4112     Proc0   0  5  6  |  7  0  0  |  8  0
4113             9  0 10  | 11  0  0  | 12  0
4114     -------------------------------------
4115            13  0 14  | 15 16 17  |  0  0
4116     Proc1   0 18  0  | 19 20 21  |  0  0
4117             0  0  0  | 22 23  0  | 24  0
4118     -------------------------------------
4119     Proc2  25 26 27  |  0  0 28  | 29  0
4120            30  0  0  | 31 32 33  |  0 34
4121 .ve
4122 
4123    This can be represented as a collection of submatrices as:
4124 
4125 .vb
4126       A B C
4127       D E F
4128       G H I
4129 .ve
4130 
4131    Where the submatrices A,B,C are owned by proc0, D,E,F are
4132    owned by proc1, G,H,I are owned by proc2.
4133 
4134    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4135    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4136    The 'M','N' parameters are 8,8, and have the same values on all procs.
4137 
4138    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
4139    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
4140    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
4141    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
4142    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
4143    matrix, ans [DF] as another SeqAIJ matrix.
4144 
4145    When d_nz, o_nz parameters are specified, d_nz storage elements are
4146    allocated for every row of the local diagonal submatrix, and o_nz
4147    storage locations are allocated for every row of the OFF-DIAGONAL submat.
4148    One way to choose d_nz and o_nz is to use the max nonzerors per local
4149    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
4150    In this case, the values of d_nz,o_nz are:
4151 .vb
4152      proc0 : dnz = 2, o_nz = 2
4153      proc1 : dnz = 3, o_nz = 2
4154      proc2 : dnz = 1, o_nz = 4
4155 .ve
4156    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
4157    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
4158    for proc3. i.e we are using 12+15+10=37 storage locations to store
4159    34 values.
4160 
4161    When d_nnz, o_nnz parameters are specified, the storage is specified
4162    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
4163    In the above case the values for d_nnz,o_nnz are:
4164 .vb
4165      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
4166      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
4167      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
4168 .ve
4169    Here the space allocated is sum of all the above values i.e 34, and
4170    hence pre-allocation is perfect.
4171 
4172    Level: intermediate
4173 
4174 .keywords: matrix, aij, compressed row, sparse, parallel
4175 
4176 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
4177           MATMPIAIJ, MatCreateMPIAIJWithArrays()
4178 @*/
4179 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)
4180 {
4181   PetscErrorCode ierr;
4182   PetscMPIInt    size;
4183 
4184   PetscFunctionBegin;
4185   ierr = MatCreate(comm,A);CHKERRQ(ierr);
4186   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
4187   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4188   if (size > 1) {
4189     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
4190     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
4191   } else {
4192     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
4193     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
4194   }
4195   PetscFunctionReturn(0);
4196 }
4197 
4198 PetscErrorCode MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
4199 {
4200   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
4201   PetscBool      flg;
4202   PetscErrorCode ierr;
4203 
4204   PetscFunctionBegin;
4205   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&flg);CHKERRQ(ierr);
4206   if (!flg) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"This function requires a MATMPIAIJ matrix as input");
4207   if (Ad)     *Ad     = a->A;
4208   if (Ao)     *Ao     = a->B;
4209   if (colmap) *colmap = a->garray;
4210   PetscFunctionReturn(0);
4211 }
4212 
4213 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
4214 {
4215   PetscErrorCode ierr;
4216   PetscInt       m,N,i,rstart,nnz,Ii;
4217   PetscInt       *indx;
4218   PetscScalar    *values;
4219 
4220   PetscFunctionBegin;
4221   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
4222   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
4223     PetscInt       *dnz,*onz,sum,bs,cbs;
4224 
4225     if (n == PETSC_DECIDE) {
4226       ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
4227     }
4228     /* Check sum(n) = N */
4229     ierr = MPIU_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4230     if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
4231 
4232     ierr    = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4233     rstart -= m;
4234 
4235     ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4236     for (i=0; i<m; i++) {
4237       ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
4238       ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
4239       ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
4240     }
4241 
4242     ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
4243     ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4244     ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
4245     ierr = MatSetBlockSizes(*outmat,bs,cbs);CHKERRQ(ierr);
4246     ierr = MatSetType(*outmat,MATAIJ);CHKERRQ(ierr);
4247     ierr = MatSeqAIJSetPreallocation(*outmat,0,dnz);CHKERRQ(ierr);
4248     ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
4249     ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4250   }
4251 
4252   /* numeric phase */
4253   ierr = MatGetOwnershipRange(*outmat,&rstart,NULL);CHKERRQ(ierr);
4254   for (i=0; i<m; i++) {
4255     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4256     Ii   = i + rstart;
4257     ierr = MatSetValues(*outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4258     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4259   }
4260   ierr = MatAssemblyBegin(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4261   ierr = MatAssemblyEnd(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4262   PetscFunctionReturn(0);
4263 }
4264 
4265 PetscErrorCode MatFileSplit(Mat A,char *outfile)
4266 {
4267   PetscErrorCode    ierr;
4268   PetscMPIInt       rank;
4269   PetscInt          m,N,i,rstart,nnz;
4270   size_t            len;
4271   const PetscInt    *indx;
4272   PetscViewer       out;
4273   char              *name;
4274   Mat               B;
4275   const PetscScalar *values;
4276 
4277   PetscFunctionBegin;
4278   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
4279   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
4280   /* Should this be the type of the diagonal block of A? */
4281   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
4282   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
4283   ierr = MatSetBlockSizesFromMats(B,A,A);CHKERRQ(ierr);
4284   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
4285   ierr = MatSeqAIJSetPreallocation(B,0,NULL);CHKERRQ(ierr);
4286   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
4287   for (i=0; i<m; i++) {
4288     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4289     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4290     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4291   }
4292   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4293   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4294 
4295   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
4296   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
4297   ierr = PetscMalloc1(len+5,&name);CHKERRQ(ierr);
4298   sprintf(name,"%s.%d",outfile,rank);
4299   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
4300   ierr = PetscFree(name);CHKERRQ(ierr);
4301   ierr = MatView(B,out);CHKERRQ(ierr);
4302   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
4303   ierr = MatDestroy(&B);CHKERRQ(ierr);
4304   PetscFunctionReturn(0);
4305 }
4306 
4307 PetscErrorCode MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
4308 {
4309   PetscErrorCode      ierr;
4310   Mat_Merge_SeqsToMPI *merge;
4311   PetscContainer      container;
4312 
4313   PetscFunctionBegin;
4314   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4315   if (container) {
4316     ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4317     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
4318     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
4319     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
4320     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
4321     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
4322     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
4323     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
4324     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
4325     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
4326     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
4327     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
4328     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
4329     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
4330     ierr = PetscFree(merge);CHKERRQ(ierr);
4331     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
4332   }
4333   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
4334   PetscFunctionReturn(0);
4335 }
4336 
4337 #include <../src/mat/utils/freespace.h>
4338 #include <petscbt.h>
4339 
4340 PetscErrorCode MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
4341 {
4342   PetscErrorCode      ierr;
4343   MPI_Comm            comm;
4344   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
4345   PetscMPIInt         size,rank,taga,*len_s;
4346   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
4347   PetscInt            proc,m;
4348   PetscInt            **buf_ri,**buf_rj;
4349   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
4350   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
4351   MPI_Request         *s_waits,*r_waits;
4352   MPI_Status          *status;
4353   MatScalar           *aa=a->a;
4354   MatScalar           **abuf_r,*ba_i;
4355   Mat_Merge_SeqsToMPI *merge;
4356   PetscContainer      container;
4357 
4358   PetscFunctionBegin;
4359   ierr = PetscObjectGetComm((PetscObject)mpimat,&comm);CHKERRQ(ierr);
4360   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4361 
4362   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4363   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4364 
4365   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4366   ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4367 
4368   bi     = merge->bi;
4369   bj     = merge->bj;
4370   buf_ri = merge->buf_ri;
4371   buf_rj = merge->buf_rj;
4372 
4373   ierr   = PetscMalloc1(size,&status);CHKERRQ(ierr);
4374   owners = merge->rowmap->range;
4375   len_s  = merge->len_s;
4376 
4377   /* send and recv matrix values */
4378   /*-----------------------------*/
4379   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
4380   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
4381 
4382   ierr = PetscMalloc1(merge->nsend+1,&s_waits);CHKERRQ(ierr);
4383   for (proc=0,k=0; proc<size; proc++) {
4384     if (!len_s[proc]) continue;
4385     i    = owners[proc];
4386     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
4387     k++;
4388   }
4389 
4390   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
4391   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
4392   ierr = PetscFree(status);CHKERRQ(ierr);
4393 
4394   ierr = PetscFree(s_waits);CHKERRQ(ierr);
4395   ierr = PetscFree(r_waits);CHKERRQ(ierr);
4396 
4397   /* insert mat values of mpimat */
4398   /*----------------------------*/
4399   ierr = PetscMalloc1(N,&ba_i);CHKERRQ(ierr);
4400   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4401 
4402   for (k=0; k<merge->nrecv; k++) {
4403     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4404     nrows       = *(buf_ri_k[k]);
4405     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
4406     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4407   }
4408 
4409   /* set values of ba */
4410   m = merge->rowmap->n;
4411   for (i=0; i<m; i++) {
4412     arow = owners[rank] + i;
4413     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
4414     bnzi = bi[i+1] - bi[i];
4415     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
4416 
4417     /* add local non-zero vals of this proc's seqmat into ba */
4418     anzi   = ai[arow+1] - ai[arow];
4419     aj     = a->j + ai[arow];
4420     aa     = a->a + ai[arow];
4421     nextaj = 0;
4422     for (j=0; nextaj<anzi; j++) {
4423       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4424         ba_i[j] += aa[nextaj++];
4425       }
4426     }
4427 
4428     /* add received vals into ba */
4429     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4430       /* i-th row */
4431       if (i == *nextrow[k]) {
4432         anzi   = *(nextai[k]+1) - *nextai[k];
4433         aj     = buf_rj[k] + *(nextai[k]);
4434         aa     = abuf_r[k] + *(nextai[k]);
4435         nextaj = 0;
4436         for (j=0; nextaj<anzi; j++) {
4437           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4438             ba_i[j] += aa[nextaj++];
4439           }
4440         }
4441         nextrow[k]++; nextai[k]++;
4442       }
4443     }
4444     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
4445   }
4446   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4447   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4448 
4449   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
4450   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
4451   ierr = PetscFree(ba_i);CHKERRQ(ierr);
4452   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4453   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4454   PetscFunctionReturn(0);
4455 }
4456 
4457 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4458 {
4459   PetscErrorCode      ierr;
4460   Mat                 B_mpi;
4461   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
4462   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4463   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
4464   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4465   PetscInt            len,proc,*dnz,*onz,bs,cbs;
4466   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4467   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4468   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
4469   MPI_Status          *status;
4470   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
4471   PetscBT             lnkbt;
4472   Mat_Merge_SeqsToMPI *merge;
4473   PetscContainer      container;
4474 
4475   PetscFunctionBegin;
4476   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4477 
4478   /* make sure it is a PETSc comm */
4479   ierr = PetscCommDuplicate(comm,&comm,NULL);CHKERRQ(ierr);
4480   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4481   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4482 
4483   ierr = PetscNew(&merge);CHKERRQ(ierr);
4484   ierr = PetscMalloc1(size,&status);CHKERRQ(ierr);
4485 
4486   /* determine row ownership */
4487   /*---------------------------------------------------------*/
4488   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
4489   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
4490   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
4491   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
4492   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
4493   ierr = PetscMalloc1(size,&len_si);CHKERRQ(ierr);
4494   ierr = PetscMalloc1(size,&merge->len_s);CHKERRQ(ierr);
4495 
4496   m      = merge->rowmap->n;
4497   owners = merge->rowmap->range;
4498 
4499   /* determine the number of messages to send, their lengths */
4500   /*---------------------------------------------------------*/
4501   len_s = merge->len_s;
4502 
4503   len          = 0; /* length of buf_si[] */
4504   merge->nsend = 0;
4505   for (proc=0; proc<size; proc++) {
4506     len_si[proc] = 0;
4507     if (proc == rank) {
4508       len_s[proc] = 0;
4509     } else {
4510       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4511       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4512     }
4513     if (len_s[proc]) {
4514       merge->nsend++;
4515       nrows = 0;
4516       for (i=owners[proc]; i<owners[proc+1]; i++) {
4517         if (ai[i+1] > ai[i]) nrows++;
4518       }
4519       len_si[proc] = 2*(nrows+1);
4520       len         += len_si[proc];
4521     }
4522   }
4523 
4524   /* determine the number and length of messages to receive for ij-structure */
4525   /*-------------------------------------------------------------------------*/
4526   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
4527   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
4528 
4529   /* post the Irecv of j-structure */
4530   /*-------------------------------*/
4531   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
4532   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
4533 
4534   /* post the Isend of j-structure */
4535   /*--------------------------------*/
4536   ierr = PetscMalloc2(merge->nsend,&si_waits,merge->nsend,&sj_waits);CHKERRQ(ierr);
4537 
4538   for (proc=0, k=0; proc<size; proc++) {
4539     if (!len_s[proc]) continue;
4540     i    = owners[proc];
4541     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
4542     k++;
4543   }
4544 
4545   /* receives and sends of j-structure are complete */
4546   /*------------------------------------------------*/
4547   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
4548   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
4549 
4550   /* send and recv i-structure */
4551   /*---------------------------*/
4552   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
4553   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
4554 
4555   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
4556   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4557   for (proc=0,k=0; proc<size; proc++) {
4558     if (!len_s[proc]) continue;
4559     /* form outgoing message for i-structure:
4560          buf_si[0]:                 nrows to be sent
4561                [1:nrows]:           row index (global)
4562                [nrows+1:2*nrows+1]: i-structure index
4563     */
4564     /*-------------------------------------------*/
4565     nrows       = len_si[proc]/2 - 1;
4566     buf_si_i    = buf_si + nrows+1;
4567     buf_si[0]   = nrows;
4568     buf_si_i[0] = 0;
4569     nrows       = 0;
4570     for (i=owners[proc]; i<owners[proc+1]; i++) {
4571       anzi = ai[i+1] - ai[i];
4572       if (anzi) {
4573         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4574         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4575         nrows++;
4576       }
4577     }
4578     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4579     k++;
4580     buf_si += len_si[proc];
4581   }
4582 
4583   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4584   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4585 
4586   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4587   for (i=0; i<merge->nrecv; i++) {
4588     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);
4589   }
4590 
4591   ierr = PetscFree(len_si);CHKERRQ(ierr);
4592   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4593   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4594   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4595   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4596   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4597   ierr = PetscFree(status);CHKERRQ(ierr);
4598 
4599   /* compute a local seq matrix in each processor */
4600   /*----------------------------------------------*/
4601   /* allocate bi array and free space for accumulating nonzero column info */
4602   ierr  = PetscMalloc1(m+1,&bi);CHKERRQ(ierr);
4603   bi[0] = 0;
4604 
4605   /* create and initialize a linked list */
4606   nlnk = N+1;
4607   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4608 
4609   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4610   len  = ai[owners[rank+1]] - ai[owners[rank]];
4611   ierr = PetscFreeSpaceGet(PetscIntMultTruncate(2,len)+1,&free_space);CHKERRQ(ierr);
4612 
4613   current_space = free_space;
4614 
4615   /* determine symbolic info for each local row */
4616   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4617 
4618   for (k=0; k<merge->nrecv; k++) {
4619     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4620     nrows       = *buf_ri_k[k];
4621     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4622     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4623   }
4624 
4625   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4626   len  = 0;
4627   for (i=0; i<m; i++) {
4628     bnzi = 0;
4629     /* add local non-zero cols of this proc's seqmat into lnk */
4630     arow  = owners[rank] + i;
4631     anzi  = ai[arow+1] - ai[arow];
4632     aj    = a->j + ai[arow];
4633     ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4634     bnzi += nlnk;
4635     /* add received col data into lnk */
4636     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4637       if (i == *nextrow[k]) { /* i-th row */
4638         anzi  = *(nextai[k]+1) - *nextai[k];
4639         aj    = buf_rj[k] + *nextai[k];
4640         ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4641         bnzi += nlnk;
4642         nextrow[k]++; nextai[k]++;
4643       }
4644     }
4645     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4646 
4647     /* if free space is not available, make more free space */
4648     if (current_space->local_remaining<bnzi) {
4649       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(bnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
4650       nspacedouble++;
4651     }
4652     /* copy data into free space, then initialize lnk */
4653     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4654     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
4655 
4656     current_space->array           += bnzi;
4657     current_space->local_used      += bnzi;
4658     current_space->local_remaining -= bnzi;
4659 
4660     bi[i+1] = bi[i] + bnzi;
4661   }
4662 
4663   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4664 
4665   ierr = PetscMalloc1(bi[m]+1,&bj);CHKERRQ(ierr);
4666   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
4667   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4668 
4669   /* create symbolic parallel matrix B_mpi */
4670   /*---------------------------------------*/
4671   ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
4672   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
4673   if (n==PETSC_DECIDE) {
4674     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
4675   } else {
4676     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4677   }
4678   ierr = MatSetBlockSizes(B_mpi,bs,cbs);CHKERRQ(ierr);
4679   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
4680   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
4681   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4682   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
4683 
4684   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4685   B_mpi->assembled    = PETSC_FALSE;
4686   B_mpi->ops->destroy = MatDestroy_MPIAIJ_SeqsToMPI;
4687   merge->bi           = bi;
4688   merge->bj           = bj;
4689   merge->buf_ri       = buf_ri;
4690   merge->buf_rj       = buf_rj;
4691   merge->coi          = NULL;
4692   merge->coj          = NULL;
4693   merge->owners_co    = NULL;
4694 
4695   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
4696 
4697   /* attach the supporting struct to B_mpi for reuse */
4698   ierr    = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
4699   ierr    = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
4700   ierr    = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
4701   ierr    = PetscContainerDestroy(&container);CHKERRQ(ierr);
4702   *mpimat = B_mpi;
4703 
4704   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4705   PetscFunctionReturn(0);
4706 }
4707 
4708 /*@C
4709       MatCreateMPIAIJSumSeqAIJ - Creates a MATMPIAIJ matrix by adding sequential
4710                  matrices from each processor
4711 
4712     Collective on MPI_Comm
4713 
4714    Input Parameters:
4715 +    comm - the communicators the parallel matrix will live on
4716 .    seqmat - the input sequential matrices
4717 .    m - number of local rows (or PETSC_DECIDE)
4718 .    n - number of local columns (or PETSC_DECIDE)
4719 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4720 
4721    Output Parameter:
4722 .    mpimat - the parallel matrix generated
4723 
4724     Level: advanced
4725 
4726    Notes:
4727      The dimensions of the sequential matrix in each processor MUST be the same.
4728      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
4729      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
4730 @*/
4731 PetscErrorCode MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
4732 {
4733   PetscErrorCode ierr;
4734   PetscMPIInt    size;
4735 
4736   PetscFunctionBegin;
4737   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4738   if (size == 1) {
4739     ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4740     if (scall == MAT_INITIAL_MATRIX) {
4741       ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
4742     } else {
4743       ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4744     }
4745     ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4746     PetscFunctionReturn(0);
4747   }
4748   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4749   if (scall == MAT_INITIAL_MATRIX) {
4750     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
4751   }
4752   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
4753   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4754   PetscFunctionReturn(0);
4755 }
4756 
4757 /*@
4758      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MATMPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
4759           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
4760           with MatGetSize()
4761 
4762     Not Collective
4763 
4764    Input Parameters:
4765 +    A - the matrix
4766 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4767 
4768    Output Parameter:
4769 .    A_loc - the local sequential matrix generated
4770 
4771     Level: developer
4772 
4773 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
4774 
4775 @*/
4776 PetscErrorCode MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
4777 {
4778   PetscErrorCode ierr;
4779   Mat_MPIAIJ     *mpimat=(Mat_MPIAIJ*)A->data;
4780   Mat_SeqAIJ     *mat,*a,*b;
4781   PetscInt       *ai,*aj,*bi,*bj,*cmap=mpimat->garray;
4782   MatScalar      *aa,*ba,*cam;
4783   PetscScalar    *ca;
4784   PetscInt       am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
4785   PetscInt       *ci,*cj,col,ncols_d,ncols_o,jo;
4786   PetscBool      match;
4787   MPI_Comm       comm;
4788   PetscMPIInt    size;
4789 
4790   PetscFunctionBegin;
4791   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4792   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
4793   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4794   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4795   if (size == 1 && scall == MAT_REUSE_MATRIX) PetscFunctionReturn(0);
4796 
4797   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4798   a = (Mat_SeqAIJ*)(mpimat->A)->data;
4799   b = (Mat_SeqAIJ*)(mpimat->B)->data;
4800   ai = a->i; aj = a->j; bi = b->i; bj = b->j;
4801   aa = a->a; ba = b->a;
4802   if (scall == MAT_INITIAL_MATRIX) {
4803     if (size == 1) {
4804       ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ai,aj,aa,A_loc);CHKERRQ(ierr);
4805       PetscFunctionReturn(0);
4806     }
4807 
4808     ierr  = PetscMalloc1(1+am,&ci);CHKERRQ(ierr);
4809     ci[0] = 0;
4810     for (i=0; i<am; i++) {
4811       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
4812     }
4813     ierr = PetscMalloc1(1+ci[am],&cj);CHKERRQ(ierr);
4814     ierr = PetscMalloc1(1+ci[am],&ca);CHKERRQ(ierr);
4815     k    = 0;
4816     for (i=0; i<am; i++) {
4817       ncols_o = bi[i+1] - bi[i];
4818       ncols_d = ai[i+1] - ai[i];
4819       /* off-diagonal portion of A */
4820       for (jo=0; jo<ncols_o; jo++) {
4821         col = cmap[*bj];
4822         if (col >= cstart) break;
4823         cj[k]   = col; bj++;
4824         ca[k++] = *ba++;
4825       }
4826       /* diagonal portion of A */
4827       for (j=0; j<ncols_d; j++) {
4828         cj[k]   = cstart + *aj++;
4829         ca[k++] = *aa++;
4830       }
4831       /* off-diagonal portion of A */
4832       for (j=jo; j<ncols_o; j++) {
4833         cj[k]   = cmap[*bj++];
4834         ca[k++] = *ba++;
4835       }
4836     }
4837     /* put together the new matrix */
4838     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
4839     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4840     /* Since these are PETSc arrays, change flags to free them as necessary. */
4841     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
4842     mat->free_a  = PETSC_TRUE;
4843     mat->free_ij = PETSC_TRUE;
4844     mat->nonew   = 0;
4845   } else if (scall == MAT_REUSE_MATRIX) {
4846     mat=(Mat_SeqAIJ*)(*A_loc)->data;
4847     ci = mat->i; cj = mat->j; cam = mat->a;
4848     for (i=0; i<am; i++) {
4849       /* off-diagonal portion of A */
4850       ncols_o = bi[i+1] - bi[i];
4851       for (jo=0; jo<ncols_o; jo++) {
4852         col = cmap[*bj];
4853         if (col >= cstart) break;
4854         *cam++ = *ba++; bj++;
4855       }
4856       /* diagonal portion of A */
4857       ncols_d = ai[i+1] - ai[i];
4858       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
4859       /* off-diagonal portion of A */
4860       for (j=jo; j<ncols_o; j++) {
4861         *cam++ = *ba++; bj++;
4862       }
4863     }
4864   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
4865   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4866   PetscFunctionReturn(0);
4867 }
4868 
4869 /*@C
4870      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MATMPIAIJ matrix by taking all its local rows and NON-ZERO columns
4871 
4872     Not Collective
4873 
4874    Input Parameters:
4875 +    A - the matrix
4876 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4877 -    row, col - index sets of rows and columns to extract (or NULL)
4878 
4879    Output Parameter:
4880 .    A_loc - the local sequential matrix generated
4881 
4882     Level: developer
4883 
4884 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
4885 
4886 @*/
4887 PetscErrorCode MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
4888 {
4889   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4890   PetscErrorCode ierr;
4891   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
4892   IS             isrowa,iscola;
4893   Mat            *aloc;
4894   PetscBool      match;
4895 
4896   PetscFunctionBegin;
4897   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4898   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
4899   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4900   if (!row) {
4901     start = A->rmap->rstart; end = A->rmap->rend;
4902     ierr  = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
4903   } else {
4904     isrowa = *row;
4905   }
4906   if (!col) {
4907     start = A->cmap->rstart;
4908     cmap  = a->garray;
4909     nzA   = a->A->cmap->n;
4910     nzB   = a->B->cmap->n;
4911     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4912     ncols = 0;
4913     for (i=0; i<nzB; i++) {
4914       if (cmap[i] < start) idx[ncols++] = cmap[i];
4915       else break;
4916     }
4917     imark = i;
4918     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
4919     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
4920     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
4921   } else {
4922     iscola = *col;
4923   }
4924   if (scall != MAT_INITIAL_MATRIX) {
4925     ierr    = PetscMalloc1(1,&aloc);CHKERRQ(ierr);
4926     aloc[0] = *A_loc;
4927   }
4928   ierr   = MatCreateSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
4929   *A_loc = aloc[0];
4930   ierr   = PetscFree(aloc);CHKERRQ(ierr);
4931   if (!row) {
4932     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
4933   }
4934   if (!col) {
4935     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
4936   }
4937   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4938   PetscFunctionReturn(0);
4939 }
4940 
4941 /*@C
4942     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
4943 
4944     Collective on Mat
4945 
4946    Input Parameters:
4947 +    A,B - the matrices in mpiaij format
4948 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4949 -    rowb, colb - index sets of rows and columns of B to extract (or NULL)
4950 
4951    Output Parameter:
4952 +    rowb, colb - index sets of rows and columns of B to extract
4953 -    B_seq - the sequential matrix generated
4954 
4955     Level: developer
4956 
4957 @*/
4958 PetscErrorCode MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
4959 {
4960   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4961   PetscErrorCode ierr;
4962   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
4963   IS             isrowb,iscolb;
4964   Mat            *bseq=NULL;
4965 
4966   PetscFunctionBegin;
4967   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4968     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);
4969   }
4970   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4971 
4972   if (scall == MAT_INITIAL_MATRIX) {
4973     start = A->cmap->rstart;
4974     cmap  = a->garray;
4975     nzA   = a->A->cmap->n;
4976     nzB   = a->B->cmap->n;
4977     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4978     ncols = 0;
4979     for (i=0; i<nzB; i++) {  /* row < local row index */
4980       if (cmap[i] < start) idx[ncols++] = cmap[i];
4981       else break;
4982     }
4983     imark = i;
4984     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
4985     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
4986     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
4987     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
4988   } else {
4989     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
4990     isrowb  = *rowb; iscolb = *colb;
4991     ierr    = PetscMalloc1(1,&bseq);CHKERRQ(ierr);
4992     bseq[0] = *B_seq;
4993   }
4994   ierr   = MatCreateSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
4995   *B_seq = bseq[0];
4996   ierr   = PetscFree(bseq);CHKERRQ(ierr);
4997   if (!rowb) {
4998     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
4999   } else {
5000     *rowb = isrowb;
5001   }
5002   if (!colb) {
5003     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
5004   } else {
5005     *colb = iscolb;
5006   }
5007   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
5008   PetscFunctionReturn(0);
5009 }
5010 
5011 /*
5012     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
5013     of the OFF-DIAGONAL portion of local A
5014 
5015     Collective on Mat
5016 
5017    Input Parameters:
5018 +    A,B - the matrices in mpiaij format
5019 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5020 
5021    Output Parameter:
5022 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
5023 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
5024 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
5025 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
5026 
5027     Level: developer
5028 
5029 */
5030 PetscErrorCode MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
5031 {
5032   VecScatter_MPI_General *gen_to,*gen_from;
5033   PetscErrorCode         ierr;
5034   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
5035   Mat_SeqAIJ             *b_oth;
5036   VecScatter             ctx =a->Mvctx;
5037   MPI_Comm               comm;
5038   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
5039   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
5040   PetscInt               *rvalues,*svalues;
5041   MatScalar              *b_otha,*bufa,*bufA;
5042   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
5043   MPI_Request            *rwaits = NULL,*swaits = NULL;
5044   MPI_Status             *sstatus,rstatus;
5045   PetscMPIInt            jj,size;
5046   PetscInt               *cols,sbs,rbs;
5047   PetscScalar            *vals;
5048 
5049   PetscFunctionBegin;
5050   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
5051   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
5052 
5053   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
5054     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);
5055   }
5056   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5057   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
5058 
5059   if (size == 1) {
5060     startsj_s = NULL;
5061     bufa_ptr  = NULL;
5062     *B_oth    = NULL;
5063     PetscFunctionReturn(0);
5064   }
5065 
5066   gen_to   = (VecScatter_MPI_General*)ctx->todata;
5067   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
5068   nrecvs   = gen_from->n;
5069   nsends   = gen_to->n;
5070 
5071   ierr    = PetscMalloc2(nrecvs,&rwaits,nsends,&swaits);CHKERRQ(ierr);
5072   srow    = gen_to->indices;    /* local row index to be sent */
5073   sstarts = gen_to->starts;
5074   sprocs  = gen_to->procs;
5075   sstatus = gen_to->sstatus;
5076   sbs     = gen_to->bs;
5077   rstarts = gen_from->starts;
5078   rprocs  = gen_from->procs;
5079   rbs     = gen_from->bs;
5080 
5081   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
5082   if (scall == MAT_INITIAL_MATRIX) {
5083     /* i-array */
5084     /*---------*/
5085     /*  post receives */
5086     ierr = PetscMalloc1(rbs*(rstarts[nrecvs] - rstarts[0]),&rvalues);CHKERRQ(ierr);
5087     for (i=0; i<nrecvs; i++) {
5088       rowlen = rvalues + rstarts[i]*rbs;
5089       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
5090       ierr   = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5091     }
5092 
5093     /* pack the outgoing message */
5094     ierr = PetscMalloc2(nsends+1,&sstartsj,nrecvs+1,&rstartsj);CHKERRQ(ierr);
5095 
5096     sstartsj[0] = 0;
5097     rstartsj[0] = 0;
5098     len         = 0; /* total length of j or a array to be sent */
5099     k           = 0;
5100     ierr = PetscMalloc1(sbs*(sstarts[nsends] - sstarts[0]),&svalues);CHKERRQ(ierr);
5101     for (i=0; i<nsends; i++) {
5102       rowlen = svalues + sstarts[i]*sbs;
5103       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
5104       for (j=0; j<nrows; j++) {
5105         row = srow[k] + B->rmap->range[rank]; /* global row idx */
5106         for (l=0; l<sbs; l++) {
5107           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr); /* rowlength */
5108 
5109           rowlen[j*sbs+l] = ncols;
5110 
5111           len += ncols;
5112           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr);
5113         }
5114         k++;
5115       }
5116       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5117 
5118       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
5119     }
5120     /* recvs and sends of i-array are completed */
5121     i = nrecvs;
5122     while (i--) {
5123       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5124     }
5125     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5126     ierr = PetscFree(svalues);CHKERRQ(ierr);
5127 
5128     /* allocate buffers for sending j and a arrays */
5129     ierr = PetscMalloc1(len+1,&bufj);CHKERRQ(ierr);
5130     ierr = PetscMalloc1(len+1,&bufa);CHKERRQ(ierr);
5131 
5132     /* create i-array of B_oth */
5133     ierr = PetscMalloc1(aBn+2,&b_othi);CHKERRQ(ierr);
5134 
5135     b_othi[0] = 0;
5136     len       = 0; /* total length of j or a array to be received */
5137     k         = 0;
5138     for (i=0; i<nrecvs; i++) {
5139       rowlen = rvalues + rstarts[i]*rbs;
5140       nrows  = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be received */
5141       for (j=0; j<nrows; j++) {
5142         b_othi[k+1] = b_othi[k] + rowlen[j];
5143         ierr = PetscIntSumError(rowlen[j],len,&len);CHKERRQ(ierr);
5144         k++;
5145       }
5146       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
5147     }
5148     ierr = PetscFree(rvalues);CHKERRQ(ierr);
5149 
5150     /* allocate space for j and a arrrays of B_oth */
5151     ierr = PetscMalloc1(b_othi[aBn]+1,&b_othj);CHKERRQ(ierr);
5152     ierr = PetscMalloc1(b_othi[aBn]+1,&b_otha);CHKERRQ(ierr);
5153 
5154     /* j-array */
5155     /*---------*/
5156     /*  post receives of j-array */
5157     for (i=0; i<nrecvs; i++) {
5158       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5159       ierr  = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5160     }
5161 
5162     /* pack the outgoing message j-array */
5163     k = 0;
5164     for (i=0; i<nsends; i++) {
5165       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5166       bufJ  = bufj+sstartsj[i];
5167       for (j=0; j<nrows; j++) {
5168         row = srow[k++] + B->rmap->range[rank];  /* global row idx */
5169         for (ll=0; ll<sbs; ll++) {
5170           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
5171           for (l=0; l<ncols; l++) {
5172             *bufJ++ = cols[l];
5173           }
5174           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
5175         }
5176       }
5177       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5178     }
5179 
5180     /* recvs and sends of j-array are completed */
5181     i = nrecvs;
5182     while (i--) {
5183       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5184     }
5185     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5186   } else if (scall == MAT_REUSE_MATRIX) {
5187     sstartsj = *startsj_s;
5188     rstartsj = *startsj_r;
5189     bufa     = *bufa_ptr;
5190     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
5191     b_otha   = b_oth->a;
5192   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
5193 
5194   /* a-array */
5195   /*---------*/
5196   /*  post receives of a-array */
5197   for (i=0; i<nrecvs; i++) {
5198     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5199     ierr  = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5200   }
5201 
5202   /* pack the outgoing message a-array */
5203   k = 0;
5204   for (i=0; i<nsends; i++) {
5205     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5206     bufA  = bufa+sstartsj[i];
5207     for (j=0; j<nrows; j++) {
5208       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
5209       for (ll=0; ll<sbs; ll++) {
5210         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
5211         for (l=0; l<ncols; l++) {
5212           *bufA++ = vals[l];
5213         }
5214         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
5215       }
5216     }
5217     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5218   }
5219   /* recvs and sends of a-array are completed */
5220   i = nrecvs;
5221   while (i--) {
5222     ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5223   }
5224   if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5225   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
5226 
5227   if (scall == MAT_INITIAL_MATRIX) {
5228     /* put together the new matrix */
5229     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
5230 
5231     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
5232     /* Since these are PETSc arrays, change flags to free them as necessary. */
5233     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
5234     b_oth->free_a  = PETSC_TRUE;
5235     b_oth->free_ij = PETSC_TRUE;
5236     b_oth->nonew   = 0;
5237 
5238     ierr = PetscFree(bufj);CHKERRQ(ierr);
5239     if (!startsj_s || !bufa_ptr) {
5240       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
5241       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
5242     } else {
5243       *startsj_s = sstartsj;
5244       *startsj_r = rstartsj;
5245       *bufa_ptr  = bufa;
5246     }
5247   }
5248   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5249   PetscFunctionReturn(0);
5250 }
5251 
5252 /*@C
5253   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
5254 
5255   Not Collective
5256 
5257   Input Parameters:
5258 . A - The matrix in mpiaij format
5259 
5260   Output Parameter:
5261 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
5262 . colmap - A map from global column index to local index into lvec
5263 - multScatter - A scatter from the argument of a matrix-vector product to lvec
5264 
5265   Level: developer
5266 
5267 @*/
5268 #if defined(PETSC_USE_CTABLE)
5269 PetscErrorCode MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
5270 #else
5271 PetscErrorCode MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
5272 #endif
5273 {
5274   Mat_MPIAIJ *a;
5275 
5276   PetscFunctionBegin;
5277   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
5278   PetscValidPointer(lvec, 2);
5279   PetscValidPointer(colmap, 3);
5280   PetscValidPointer(multScatter, 4);
5281   a = (Mat_MPIAIJ*) A->data;
5282   if (lvec) *lvec = a->lvec;
5283   if (colmap) *colmap = a->colmap;
5284   if (multScatter) *multScatter = a->Mvctx;
5285   PetscFunctionReturn(0);
5286 }
5287 
5288 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
5289 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
5290 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
5291 #if defined(PETSC_HAVE_ELEMENTAL)
5292 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
5293 #endif
5294 #if defined(PETSC_HAVE_HYPRE)
5295 PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat,MatType,MatReuse,Mat*);
5296 PETSC_INTERN PetscErrorCode MatMatMatMult_Transpose_AIJ_AIJ(Mat,Mat,Mat,MatReuse,PetscReal,Mat*);
5297 #endif
5298 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_IS(Mat,MatType,MatReuse,Mat*);
5299 
5300 /*
5301     Computes (B'*A')' since computing B*A directly is untenable
5302 
5303                n                       p                          p
5304         (              )       (              )         (                  )
5305       m (      A       )  *  n (       B      )   =   m (         C        )
5306         (              )       (              )         (                  )
5307 
5308 */
5309 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
5310 {
5311   PetscErrorCode ierr;
5312   Mat            At,Bt,Ct;
5313 
5314   PetscFunctionBegin;
5315   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
5316   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
5317   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
5318   ierr = MatDestroy(&At);CHKERRQ(ierr);
5319   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
5320   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
5321   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
5322   PetscFunctionReturn(0);
5323 }
5324 
5325 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
5326 {
5327   PetscErrorCode ierr;
5328   PetscInt       m=A->rmap->n,n=B->cmap->n;
5329   Mat            Cmat;
5330 
5331   PetscFunctionBegin;
5332   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);
5333   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
5334   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
5335   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
5336   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
5337   ierr = MatMPIDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
5338   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5339   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5340 
5341   Cmat->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
5342 
5343   *C = Cmat;
5344   PetscFunctionReturn(0);
5345 }
5346 
5347 /* ----------------------------------------------------------------*/
5348 PETSC_INTERN PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
5349 {
5350   PetscErrorCode ierr;
5351 
5352   PetscFunctionBegin;
5353   if (scall == MAT_INITIAL_MATRIX) {
5354     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5355     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
5356     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5357   }
5358   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5359   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
5360   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5361   PetscFunctionReturn(0);
5362 }
5363 
5364 /*MC
5365    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
5366 
5367    Options Database Keys:
5368 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
5369 
5370   Level: beginner
5371 
5372 .seealso: MatCreateAIJ()
5373 M*/
5374 
5375 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
5376 {
5377   Mat_MPIAIJ     *b;
5378   PetscErrorCode ierr;
5379   PetscMPIInt    size;
5380 
5381   PetscFunctionBegin;
5382   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
5383 
5384   ierr          = PetscNewLog(B,&b);CHKERRQ(ierr);
5385   B->data       = (void*)b;
5386   ierr          = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
5387   B->assembled  = PETSC_FALSE;
5388   B->insertmode = NOT_SET_VALUES;
5389   b->size       = size;
5390 
5391   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank);CHKERRQ(ierr);
5392 
5393   /* build cache for off array entries formed */
5394   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash);CHKERRQ(ierr);
5395 
5396   b->donotstash  = PETSC_FALSE;
5397   b->colmap      = 0;
5398   b->garray      = 0;
5399   b->roworiented = PETSC_TRUE;
5400 
5401   /* stuff used for matrix vector multiply */
5402   b->lvec  = NULL;
5403   b->Mvctx = NULL;
5404 
5405   /* stuff for MatGetRow() */
5406   b->rowindices   = 0;
5407   b->rowvalues    = 0;
5408   b->getrowactive = PETSC_FALSE;
5409 
5410   /* flexible pointer used in CUSP/CUSPARSE classes */
5411   b->spptr = NULL;
5412 
5413   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetUseScalableIncreaseOverlap_C",MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ);CHKERRQ(ierr);
5414   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ);CHKERRQ(ierr);
5415   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
5416   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
5417   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
5418   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
5419   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
5420   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
5421   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
5422   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
5423 #if defined(PETSC_HAVE_ELEMENTAL)
5424   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_elemental_C",MatConvert_MPIAIJ_Elemental);CHKERRQ(ierr);
5425 #endif
5426 #if defined(PETSC_HAVE_HYPRE)
5427   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_hypre_C",MatConvert_AIJ_HYPRE);CHKERRQ(ierr);
5428 #endif
5429   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_is_C",MatConvert_MPIAIJ_IS);CHKERRQ(ierr);
5430   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
5431   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
5432   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
5433 #if defined(PETSC_HAVE_HYPRE)
5434   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMatMult_transpose_mpiaij_mpiaij_C",MatMatMatMult_Transpose_AIJ_AIJ);CHKERRQ(ierr);
5435 #endif
5436   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
5437   PetscFunctionReturn(0);
5438 }
5439 
5440 /*@C
5441      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
5442          and "off-diagonal" part of the matrix in CSR format.
5443 
5444    Collective on MPI_Comm
5445 
5446    Input Parameters:
5447 +  comm - MPI communicator
5448 .  m - number of local rows (Cannot be PETSC_DECIDE)
5449 .  n - This value should be the same as the local size used in creating the
5450        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
5451        calculated if N is given) For square matrices n is almost always m.
5452 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
5453 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
5454 .   i - row indices for "diagonal" portion of matrix
5455 .   j - column indices
5456 .   a - matrix values
5457 .   oi - row indices for "off-diagonal" portion of matrix
5458 .   oj - column indices
5459 -   oa - matrix values
5460 
5461    Output Parameter:
5462 .   mat - the matrix
5463 
5464    Level: advanced
5465 
5466    Notes:
5467        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
5468        must free the arrays once the matrix has been destroyed and not before.
5469 
5470        The i and j indices are 0 based
5471 
5472        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
5473 
5474        This sets local rows and cannot be used to set off-processor values.
5475 
5476        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
5477        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
5478        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
5479        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
5480        keep track of the underlying array. Use MatSetOption(A,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
5481        communication if it is known that only local entries will be set.
5482 
5483 .keywords: matrix, aij, compressed row, sparse, parallel
5484 
5485 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
5486           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
5487 @*/
5488 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)
5489 {
5490   PetscErrorCode ierr;
5491   Mat_MPIAIJ     *maij;
5492 
5493   PetscFunctionBegin;
5494   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
5495   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
5496   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
5497   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
5498   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
5499   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
5500   maij = (Mat_MPIAIJ*) (*mat)->data;
5501 
5502   (*mat)->preallocated = PETSC_TRUE;
5503 
5504   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
5505   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
5506 
5507   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
5508   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
5509 
5510   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5511   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5512   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5513   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5514 
5515   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
5516   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5517   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5518   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_FALSE);CHKERRQ(ierr);
5519   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
5520   PetscFunctionReturn(0);
5521 }
5522 
5523 /*
5524     Special version for direct calls from Fortran
5525 */
5526 #include <petsc/private/fortranimpl.h>
5527 
5528 /* Change these macros so can be used in void function */
5529 #undef CHKERRQ
5530 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
5531 #undef SETERRQ2
5532 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5533 #undef SETERRQ3
5534 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5535 #undef SETERRQ
5536 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
5537 
5538 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5539 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
5540 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5541 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
5542 #else
5543 #endif
5544 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)
5545 {
5546   Mat            mat  = *mmat;
5547   PetscInt       m    = *mm, n = *mn;
5548   InsertMode     addv = *maddv;
5549   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
5550   PetscScalar    value;
5551   PetscErrorCode ierr;
5552 
5553   MatCheckPreallocated(mat,1);
5554   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
5555 
5556 #if defined(PETSC_USE_DEBUG)
5557   else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
5558 #endif
5559   {
5560     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
5561     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
5562     PetscBool roworiented = aij->roworiented;
5563 
5564     /* Some Variables required in the macro */
5565     Mat        A                 = aij->A;
5566     Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
5567     PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
5568     MatScalar  *aa               = a->a;
5569     PetscBool  ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
5570     Mat        B                 = aij->B;
5571     Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
5572     PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5573     MatScalar  *ba               = b->a;
5574 
5575     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5576     PetscInt  nonew = a->nonew;
5577     MatScalar *ap1,*ap2;
5578 
5579     PetscFunctionBegin;
5580     for (i=0; i<m; i++) {
5581       if (im[i] < 0) continue;
5582 #if defined(PETSC_USE_DEBUG)
5583       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);
5584 #endif
5585       if (im[i] >= rstart && im[i] < rend) {
5586         row      = im[i] - rstart;
5587         lastcol1 = -1;
5588         rp1      = aj + ai[row];
5589         ap1      = aa + ai[row];
5590         rmax1    = aimax[row];
5591         nrow1    = ailen[row];
5592         low1     = 0;
5593         high1    = nrow1;
5594         lastcol2 = -1;
5595         rp2      = bj + bi[row];
5596         ap2      = ba + bi[row];
5597         rmax2    = bimax[row];
5598         nrow2    = bilen[row];
5599         low2     = 0;
5600         high2    = nrow2;
5601 
5602         for (j=0; j<n; j++) {
5603           if (roworiented) value = v[i*n+j];
5604           else value = v[i+j*m];
5605           if (in[j] >= cstart && in[j] < cend) {
5606             col = in[j] - cstart;
5607             if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
5608             MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
5609           } else if (in[j] < 0) continue;
5610 #if defined(PETSC_USE_DEBUG)
5611           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);
5612 #endif
5613           else {
5614             if (mat->was_assembled) {
5615               if (!aij->colmap) {
5616                 ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5617               }
5618 #if defined(PETSC_USE_CTABLE)
5619               ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5620               col--;
5621 #else
5622               col = aij->colmap[in[j]] - 1;
5623 #endif
5624               if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
5625               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5626                 ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5627                 col  =  in[j];
5628                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5629                 B     = aij->B;
5630                 b     = (Mat_SeqAIJ*)B->data;
5631                 bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5632                 rp2   = bj + bi[row];
5633                 ap2   = ba + bi[row];
5634                 rmax2 = bimax[row];
5635                 nrow2 = bilen[row];
5636                 low2  = 0;
5637                 high2 = nrow2;
5638                 bm    = aij->B->rmap->n;
5639                 ba    = b->a;
5640               }
5641             } else col = in[j];
5642             MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
5643           }
5644         }
5645       } else if (!aij->donotstash) {
5646         if (roworiented) {
5647           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5648         } else {
5649           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5650         }
5651       }
5652     }
5653   }
5654   PetscFunctionReturnVoid();
5655 }
5656 
5657