xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision 6ccf5d5763ee3ff4fd455dfd2a4a28ab2072f039)
1 
2 #include <../src/mat/impls/aij/mpi/mpiaij.h>   /*I "petscmat.h" I*/
3 #include <petsc/private/vecimpl.h>
4 #include <petsc/private/isimpl.h>
5 #include <petscblaslapack.h>
6 #include <petscsf.h>
7 
8 /*MC
9    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.
10 
11    This matrix type is identical to MATSEQAIJ when constructed with a single process communicator,
12    and MATMPIAIJ otherwise.  As a result, for single process communicators,
13   MatSeqAIJSetPreallocation is supported, and similarly MatMPIAIJSetPreallocation is supported
14   for communicators controlling multiple processes.  It is recommended that you call both of
15   the above preallocation routines for simplicity.
16 
17    Options Database Keys:
18 . -mat_type aij - sets the matrix type to "aij" during a call to MatSetFromOptions()
19 
20   Developer Notes: Subclasses include MATAIJCUSP, MATAIJCUSPARSE, MATAIJPERM, MATAIJCRL, and also automatically switches over to use inodes when
21    enough exist.
22 
23   Level: beginner
24 
25 .seealso: MatCreateAIJ(), MatCreateSeqAIJ(), MATSEQAIJ,MATMPIAIJ
26 M*/
27 
28 /*MC
29    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.
30 
31    This matrix type is identical to MATSEQAIJCRL when constructed with a single process communicator,
32    and MATMPIAIJCRL otherwise.  As a result, for single process communicators,
33    MatSeqAIJSetPreallocation() is supported, and similarly MatMPIAIJSetPreallocation() is supported
34   for communicators controlling multiple processes.  It is recommended that you call both of
35   the above preallocation routines for simplicity.
36 
37    Options Database Keys:
38 . -mat_type aijcrl - sets the matrix type to "aijcrl" during a call to MatSetFromOptions()
39 
40   Level: beginner
41 
42 .seealso: MatCreateMPIAIJCRL,MATSEQAIJCRL,MATMPIAIJCRL, MATSEQAIJCRL, MATMPIAIJCRL
43 M*/
44 
45 #undef __FUNCT__
46 #define __FUNCT__ "MatFindNonzeroRows_MPIAIJ"
47 PetscErrorCode MatFindNonzeroRows_MPIAIJ(Mat M,IS *keptrows)
48 {
49   PetscErrorCode  ierr;
50   Mat_MPIAIJ      *mat = (Mat_MPIAIJ*)M->data;
51   Mat_SeqAIJ      *a   = (Mat_SeqAIJ*)mat->A->data;
52   Mat_SeqAIJ      *b   = (Mat_SeqAIJ*)mat->B->data;
53   const PetscInt  *ia,*ib;
54   const MatScalar *aa,*bb;
55   PetscInt        na,nb,i,j,*rows,cnt=0,n0rows;
56   PetscInt        m = M->rmap->n,rstart = M->rmap->rstart;
57 
58   PetscFunctionBegin;
59   *keptrows = 0;
60   ia        = a->i;
61   ib        = b->i;
62   for (i=0; i<m; i++) {
63     na = ia[i+1] - ia[i];
64     nb = ib[i+1] - ib[i];
65     if (!na && !nb) {
66       cnt++;
67       goto ok1;
68     }
69     aa = a->a + ia[i];
70     for (j=0; j<na; j++) {
71       if (aa[j] != 0.0) goto ok1;
72     }
73     bb = b->a + ib[i];
74     for (j=0; j <nb; j++) {
75       if (bb[j] != 0.0) goto ok1;
76     }
77     cnt++;
78 ok1:;
79   }
80   ierr = MPIU_Allreduce(&cnt,&n0rows,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)M));CHKERRQ(ierr);
81   if (!n0rows) PetscFunctionReturn(0);
82   ierr = PetscMalloc1(M->rmap->n-cnt,&rows);CHKERRQ(ierr);
83   cnt  = 0;
84   for (i=0; i<m; i++) {
85     na = ia[i+1] - ia[i];
86     nb = ib[i+1] - ib[i];
87     if (!na && !nb) continue;
88     aa = a->a + ia[i];
89     for (j=0; j<na;j++) {
90       if (aa[j] != 0.0) {
91         rows[cnt++] = rstart + i;
92         goto ok2;
93       }
94     }
95     bb = b->a + ib[i];
96     for (j=0; j<nb; j++) {
97       if (bb[j] != 0.0) {
98         rows[cnt++] = rstart + i;
99         goto ok2;
100       }
101     }
102 ok2:;
103   }
104   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)M),cnt,rows,PETSC_OWN_POINTER,keptrows);CHKERRQ(ierr);
105   PetscFunctionReturn(0);
106 }
107 
108 #undef __FUNCT__
109 #define __FUNCT__ "MatDiagonalSet_MPIAIJ"
110 PetscErrorCode  MatDiagonalSet_MPIAIJ(Mat Y,Vec D,InsertMode is)
111 {
112   PetscErrorCode    ierr;
113   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*) Y->data;
114 
115   PetscFunctionBegin;
116   if (Y->assembled && Y->rmap->rstart == Y->cmap->rstart && Y->rmap->rend == Y->cmap->rend) {
117     ierr = MatDiagonalSet(aij->A,D,is);CHKERRQ(ierr);
118   } else {
119     ierr = MatDiagonalSet_Default(Y,D,is);CHKERRQ(ierr);
120   }
121   PetscFunctionReturn(0);
122 }
123 
124 
125 #undef __FUNCT__
126 #define __FUNCT__ "MatFindZeroDiagonals_MPIAIJ"
127 PetscErrorCode MatFindZeroDiagonals_MPIAIJ(Mat M,IS *zrows)
128 {
129   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)M->data;
130   PetscErrorCode ierr;
131   PetscInt       i,rstart,nrows,*rows;
132 
133   PetscFunctionBegin;
134   *zrows = NULL;
135   ierr   = MatFindZeroDiagonals_SeqAIJ_Private(aij->A,&nrows,&rows);CHKERRQ(ierr);
136   ierr   = MatGetOwnershipRange(M,&rstart,NULL);CHKERRQ(ierr);
137   for (i=0; i<nrows; i++) rows[i] += rstart;
138   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)M),nrows,rows,PETSC_OWN_POINTER,zrows);CHKERRQ(ierr);
139   PetscFunctionReturn(0);
140 }
141 
142 #undef __FUNCT__
143 #define __FUNCT__ "MatGetColumnNorms_MPIAIJ"
144 PetscErrorCode MatGetColumnNorms_MPIAIJ(Mat A,NormType type,PetscReal *norms)
145 {
146   PetscErrorCode ierr;
147   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)A->data;
148   PetscInt       i,n,*garray = aij->garray;
149   Mat_SeqAIJ     *a_aij = (Mat_SeqAIJ*) aij->A->data;
150   Mat_SeqAIJ     *b_aij = (Mat_SeqAIJ*) aij->B->data;
151   PetscReal      *work;
152 
153   PetscFunctionBegin;
154   ierr = MatGetSize(A,NULL,&n);CHKERRQ(ierr);
155   ierr = PetscCalloc1(n,&work);CHKERRQ(ierr);
156   if (type == NORM_2) {
157     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
158       work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i]*a_aij->a[i]);
159     }
160     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
161       work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]*b_aij->a[i]);
162     }
163   } else if (type == NORM_1) {
164     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
165       work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i]);
166     }
167     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
168       work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]);
169     }
170   } else if (type == NORM_INFINITY) {
171     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
172       work[A->cmap->rstart + a_aij->j[i]] = PetscMax(PetscAbsScalar(a_aij->a[i]), work[A->cmap->rstart + a_aij->j[i]]);
173     }
174     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
175       work[garray[b_aij->j[i]]] = PetscMax(PetscAbsScalar(b_aij->a[i]),work[garray[b_aij->j[i]]]);
176     }
177 
178   } else SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Unknown NormType");
179   if (type == NORM_INFINITY) {
180     ierr = MPIU_Allreduce(work,norms,n,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
181   } else {
182     ierr = MPIU_Allreduce(work,norms,n,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
183   }
184   ierr = PetscFree(work);CHKERRQ(ierr);
185   if (type == NORM_2) {
186     for (i=0; i<n; i++) norms[i] = PetscSqrtReal(norms[i]);
187   }
188   PetscFunctionReturn(0);
189 }
190 
191 #undef __FUNCT__
192 #define __FUNCT__ "MatFindOffBlockDiagonalEntries_MPIAIJ"
193 PetscErrorCode MatFindOffBlockDiagonalEntries_MPIAIJ(Mat A,IS *is)
194 {
195   Mat_MPIAIJ      *a  = (Mat_MPIAIJ*)A->data;
196   IS              sis,gis;
197   PetscErrorCode  ierr;
198   const PetscInt  *isis,*igis;
199   PetscInt        n,*iis,nsis,ngis,rstart,i;
200 
201   PetscFunctionBegin;
202   ierr = MatFindOffBlockDiagonalEntries(a->A,&sis);CHKERRQ(ierr);
203   ierr = MatFindNonzeroRows(a->B,&gis);CHKERRQ(ierr);
204   ierr = ISGetSize(gis,&ngis);CHKERRQ(ierr);
205   ierr = ISGetSize(sis,&nsis);CHKERRQ(ierr);
206   ierr = ISGetIndices(sis,&isis);CHKERRQ(ierr);
207   ierr = ISGetIndices(gis,&igis);CHKERRQ(ierr);
208 
209   ierr = PetscMalloc1(ngis+nsis,&iis);CHKERRQ(ierr);
210   ierr = PetscMemcpy(iis,igis,ngis*sizeof(PetscInt));CHKERRQ(ierr);
211   ierr = PetscMemcpy(iis+ngis,isis,nsis*sizeof(PetscInt));CHKERRQ(ierr);
212   n    = ngis + nsis;
213   ierr = PetscSortRemoveDupsInt(&n,iis);CHKERRQ(ierr);
214   ierr = MatGetOwnershipRange(A,&rstart,NULL);CHKERRQ(ierr);
215   for (i=0; i<n; i++) iis[i] += rstart;
216   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)A),n,iis,PETSC_OWN_POINTER,is);CHKERRQ(ierr);
217 
218   ierr = ISRestoreIndices(sis,&isis);CHKERRQ(ierr);
219   ierr = ISRestoreIndices(gis,&igis);CHKERRQ(ierr);
220   ierr = ISDestroy(&sis);CHKERRQ(ierr);
221   ierr = ISDestroy(&gis);CHKERRQ(ierr);
222   PetscFunctionReturn(0);
223 }
224 
225 #undef __FUNCT__
226 #define __FUNCT__ "MatDistribute_MPIAIJ"
227 /*
228     Distributes a SeqAIJ matrix across a set of processes. Code stolen from
229     MatLoad_MPIAIJ(). Horrible lack of reuse. Should be a routine for each matrix type.
230 
231     Only for square matrices
232 
233     Used by a preconditioner, hence PETSC_EXTERN
234 */
235 PETSC_EXTERN PetscErrorCode MatDistribute_MPIAIJ(MPI_Comm comm,Mat gmat,PetscInt m,MatReuse reuse,Mat *inmat)
236 {
237   PetscMPIInt    rank,size;
238   PetscInt       *rowners,*dlens,*olens,i,rstart,rend,j,jj,nz = 0,*gmataj,cnt,row,*ld,bses[2];
239   PetscErrorCode ierr;
240   Mat            mat;
241   Mat_SeqAIJ     *gmata;
242   PetscMPIInt    tag;
243   MPI_Status     status;
244   PetscBool      aij;
245   MatScalar      *gmataa,*ao,*ad,*gmataarestore=0;
246 
247   PetscFunctionBegin;
248   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
249   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
250   if (!rank) {
251     ierr = PetscObjectTypeCompare((PetscObject)gmat,MATSEQAIJ,&aij);CHKERRQ(ierr);
252     if (!aij) SETERRQ1(PetscObjectComm((PetscObject)gmat),PETSC_ERR_SUP,"Currently no support for input matrix of type %s\n",((PetscObject)gmat)->type_name);
253   }
254   if (reuse == MAT_INITIAL_MATRIX) {
255     ierr = MatCreate(comm,&mat);CHKERRQ(ierr);
256     ierr = MatSetSizes(mat,m,m,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
257     ierr = MatGetBlockSizes(gmat,&bses[0],&bses[1]);CHKERRQ(ierr);
258     ierr = MPI_Bcast(bses,2,MPIU_INT,0,comm);CHKERRQ(ierr);
259     ierr = MatSetBlockSizes(mat,bses[0],bses[1]);CHKERRQ(ierr);
260     ierr = MatSetType(mat,MATAIJ);CHKERRQ(ierr);
261     ierr = PetscMalloc1(size+1,&rowners);CHKERRQ(ierr);
262     ierr = PetscMalloc2(m,&dlens,m,&olens);CHKERRQ(ierr);
263     ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
264 
265     rowners[0] = 0;
266     for (i=2; i<=size; i++) rowners[i] += rowners[i-1];
267     rstart = rowners[rank];
268     rend   = rowners[rank+1];
269     ierr   = PetscObjectGetNewTag((PetscObject)mat,&tag);CHKERRQ(ierr);
270     if (!rank) {
271       gmata = (Mat_SeqAIJ*) gmat->data;
272       /* send row lengths to all processors */
273       for (i=0; i<m; i++) dlens[i] = gmata->ilen[i];
274       for (i=1; i<size; i++) {
275         ierr = MPI_Send(gmata->ilen + rowners[i],rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
276       }
277       /* determine number diagonal and off-diagonal counts */
278       ierr = PetscMemzero(olens,m*sizeof(PetscInt));CHKERRQ(ierr);
279       ierr = PetscCalloc1(m,&ld);CHKERRQ(ierr);
280       jj   = 0;
281       for (i=0; i<m; i++) {
282         for (j=0; j<dlens[i]; j++) {
283           if (gmata->j[jj] < rstart) ld[i]++;
284           if (gmata->j[jj] < rstart || gmata->j[jj] >= rend) olens[i]++;
285           jj++;
286         }
287       }
288       /* send column indices to other processes */
289       for (i=1; i<size; i++) {
290         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
291         ierr = MPI_Send(&nz,1,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
292         ierr = MPI_Send(gmata->j + gmata->i[rowners[i]],nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
293       }
294 
295       /* send numerical values to other processes */
296       for (i=1; i<size; i++) {
297         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
298         ierr = MPI_Send(gmata->a + gmata->i[rowners[i]],nz,MPIU_SCALAR,i,tag,comm);CHKERRQ(ierr);
299       }
300       gmataa = gmata->a;
301       gmataj = gmata->j;
302 
303     } else {
304       /* receive row lengths */
305       ierr = MPI_Recv(dlens,m,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
306       /* receive column indices */
307       ierr = MPI_Recv(&nz,1,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
308       ierr = PetscMalloc2(nz,&gmataa,nz,&gmataj);CHKERRQ(ierr);
309       ierr = MPI_Recv(gmataj,nz,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
310       /* determine number diagonal and off-diagonal counts */
311       ierr = PetscMemzero(olens,m*sizeof(PetscInt));CHKERRQ(ierr);
312       ierr = PetscCalloc1(m,&ld);CHKERRQ(ierr);
313       jj   = 0;
314       for (i=0; i<m; i++) {
315         for (j=0; j<dlens[i]; j++) {
316           if (gmataj[jj] < rstart) ld[i]++;
317           if (gmataj[jj] < rstart || gmataj[jj] >= rend) olens[i]++;
318           jj++;
319         }
320       }
321       /* receive numerical values */
322       ierr = PetscMemzero(gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr);
323       ierr = MPI_Recv(gmataa,nz,MPIU_SCALAR,0,tag,comm,&status);CHKERRQ(ierr);
324     }
325     /* set preallocation */
326     for (i=0; i<m; i++) {
327       dlens[i] -= olens[i];
328     }
329     ierr = MatSeqAIJSetPreallocation(mat,0,dlens);CHKERRQ(ierr);
330     ierr = MatMPIAIJSetPreallocation(mat,0,dlens,0,olens);CHKERRQ(ierr);
331 
332     for (i=0; i<m; i++) {
333       dlens[i] += olens[i];
334     }
335     cnt = 0;
336     for (i=0; i<m; i++) {
337       row  = rstart + i;
338       ierr = MatSetValues(mat,1,&row,dlens[i],gmataj+cnt,gmataa+cnt,INSERT_VALUES);CHKERRQ(ierr);
339       cnt += dlens[i];
340     }
341     if (rank) {
342       ierr = PetscFree2(gmataa,gmataj);CHKERRQ(ierr);
343     }
344     ierr = PetscFree2(dlens,olens);CHKERRQ(ierr);
345     ierr = PetscFree(rowners);CHKERRQ(ierr);
346 
347     ((Mat_MPIAIJ*)(mat->data))->ld = ld;
348 
349     *inmat = mat;
350   } else {   /* column indices are already set; only need to move over numerical values from process 0 */
351     Mat_SeqAIJ *Ad = (Mat_SeqAIJ*)((Mat_MPIAIJ*)((*inmat)->data))->A->data;
352     Mat_SeqAIJ *Ao = (Mat_SeqAIJ*)((Mat_MPIAIJ*)((*inmat)->data))->B->data;
353     mat  = *inmat;
354     ierr = PetscObjectGetNewTag((PetscObject)mat,&tag);CHKERRQ(ierr);
355     if (!rank) {
356       /* send numerical values to other processes */
357       gmata  = (Mat_SeqAIJ*) gmat->data;
358       ierr   = MatGetOwnershipRanges(mat,(const PetscInt**)&rowners);CHKERRQ(ierr);
359       gmataa = gmata->a;
360       for (i=1; i<size; i++) {
361         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
362         ierr = MPI_Send(gmataa + gmata->i[rowners[i]],nz,MPIU_SCALAR,i,tag,comm);CHKERRQ(ierr);
363       }
364       nz = gmata->i[rowners[1]]-gmata->i[rowners[0]];
365     } else {
366       /* receive numerical values from process 0*/
367       nz   = Ad->nz + Ao->nz;
368       ierr = PetscMalloc1(nz,&gmataa);CHKERRQ(ierr); gmataarestore = gmataa;
369       ierr = MPI_Recv(gmataa,nz,MPIU_SCALAR,0,tag,comm,&status);CHKERRQ(ierr);
370     }
371     /* transfer numerical values into the diagonal A and off diagonal B parts of mat */
372     ld = ((Mat_MPIAIJ*)(mat->data))->ld;
373     ad = Ad->a;
374     ao = Ao->a;
375     if (mat->rmap->n) {
376       i  = 0;
377       nz = ld[i];                                   ierr = PetscMemcpy(ao,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ao += nz; gmataa += nz;
378       nz = Ad->i[i+1] - Ad->i[i];                   ierr = PetscMemcpy(ad,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ad += nz; gmataa += nz;
379     }
380     for (i=1; i<mat->rmap->n; i++) {
381       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;
382       nz = Ad->i[i+1] - Ad->i[i];                   ierr = PetscMemcpy(ad,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ad += nz; gmataa += nz;
383     }
384     i--;
385     if (mat->rmap->n) {
386       nz = Ao->i[i+1] - Ao->i[i] - ld[i];           ierr = PetscMemcpy(ao,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr);
387     }
388     if (rank) {
389       ierr = PetscFree(gmataarestore);CHKERRQ(ierr);
390     }
391   }
392   ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
393   ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
394   PetscFunctionReturn(0);
395 }
396 
397 /*
398   Local utility routine that creates a mapping from the global column
399 number to the local number in the off-diagonal part of the local
400 storage of the matrix.  When PETSC_USE_CTABLE is used this is scalable at
401 a slightly higher hash table cost; without it it is not scalable (each processor
402 has an order N integer array but is fast to acess.
403 */
404 #undef __FUNCT__
405 #define __FUNCT__ "MatCreateColmap_MPIAIJ_Private"
406 PetscErrorCode MatCreateColmap_MPIAIJ_Private(Mat mat)
407 {
408   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
409   PetscErrorCode ierr;
410   PetscInt       n = aij->B->cmap->n,i;
411 
412   PetscFunctionBegin;
413   if (!aij->garray) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"MPIAIJ Matrix was assembled but is missing garray");
414 #if defined(PETSC_USE_CTABLE)
415   ierr = PetscTableCreate(n,mat->cmap->N+1,&aij->colmap);CHKERRQ(ierr);
416   for (i=0; i<n; i++) {
417     ierr = PetscTableAdd(aij->colmap,aij->garray[i]+1,i+1,INSERT_VALUES);CHKERRQ(ierr);
418   }
419 #else
420   ierr = PetscCalloc1(mat->cmap->N+1,&aij->colmap);CHKERRQ(ierr);
421   ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N+1)*sizeof(PetscInt));CHKERRQ(ierr);
422   for (i=0; i<n; i++) aij->colmap[aij->garray[i]] = i+1;
423 #endif
424   PetscFunctionReturn(0);
425 }
426 
427 #define MatSetValues_SeqAIJ_A_Private(row,col,value,addv,orow,ocol)     \
428 { \
429     if (col <= lastcol1)  low1 = 0;     \
430     else                 high1 = nrow1; \
431     lastcol1 = col;\
432     while (high1-low1 > 5) { \
433       t = (low1+high1)/2; \
434       if (rp1[t] > col) high1 = t; \
435       else              low1  = t; \
436     } \
437       for (_i=low1; _i<high1; _i++) { \
438         if (rp1[_i] > col) break; \
439         if (rp1[_i] == col) { \
440           if (addv == ADD_VALUES) ap1[_i] += value;   \
441           else                    ap1[_i] = value; \
442           goto a_noinsert; \
443         } \
444       }  \
445       if (value == 0.0 && ignorezeroentries) {low1 = 0; high1 = nrow1;goto a_noinsert;} \
446       if (nonew == 1) {low1 = 0; high1 = nrow1; goto a_noinsert;}                \
447       if (nonew == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at global row/column (%D, %D) into matrix", orow, ocol); \
448       MatSeqXAIJReallocateAIJ(A,am,1,nrow1,row,col,rmax1,aa,ai,aj,rp1,ap1,aimax,nonew,MatScalar); \
449       N = nrow1++ - 1; a->nz++; high1++; \
450       /* shift up all the later entries in this row */ \
451       for (ii=N; ii>=_i; ii--) { \
452         rp1[ii+1] = rp1[ii]; \
453         ap1[ii+1] = ap1[ii]; \
454       } \
455       rp1[_i] = col;  \
456       ap1[_i] = value;  \
457       A->nonzerostate++;\
458       a_noinsert: ; \
459       ailen[row] = nrow1; \
460 }
461 
462 
463 #define MatSetValues_SeqAIJ_B_Private(row,col,value,addv,orow,ocol) \
464   { \
465     if (col <= lastcol2) low2 = 0;                        \
466     else high2 = nrow2;                                   \
467     lastcol2 = col;                                       \
468     while (high2-low2 > 5) {                              \
469       t = (low2+high2)/2;                                 \
470       if (rp2[t] > col) high2 = t;                        \
471       else             low2  = t;                         \
472     }                                                     \
473     for (_i=low2; _i<high2; _i++) {                       \
474       if (rp2[_i] > col) break;                           \
475       if (rp2[_i] == col) {                               \
476         if (addv == ADD_VALUES) ap2[_i] += value;         \
477         else                    ap2[_i] = value;          \
478         goto b_noinsert;                                  \
479       }                                                   \
480     }                                                     \
481     if (value == 0.0 && ignorezeroentries) {low2 = 0; high2 = nrow2; goto b_noinsert;} \
482     if (nonew == 1) {low2 = 0; high2 = nrow2; goto b_noinsert;}                        \
483     if (nonew == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at global row/column (%D, %D) into matrix", orow, ocol); \
484     MatSeqXAIJReallocateAIJ(B,bm,1,nrow2,row,col,rmax2,ba,bi,bj,rp2,ap2,bimax,nonew,MatScalar); \
485     N = nrow2++ - 1; b->nz++; high2++;                    \
486     /* shift up all the later entries in this row */      \
487     for (ii=N; ii>=_i; ii--) {                            \
488       rp2[ii+1] = rp2[ii];                                \
489       ap2[ii+1] = ap2[ii];                                \
490     }                                                     \
491     rp2[_i] = col;                                        \
492     ap2[_i] = value;                                      \
493     B->nonzerostate++;                                    \
494     b_noinsert: ;                                         \
495     bilen[row] = nrow2;                                   \
496   }
497 
498 #undef __FUNCT__
499 #define __FUNCT__ "MatSetValuesRow_MPIAIJ"
500 PetscErrorCode MatSetValuesRow_MPIAIJ(Mat A,PetscInt row,const PetscScalar v[])
501 {
502   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)A->data;
503   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)mat->A->data,*b = (Mat_SeqAIJ*)mat->B->data;
504   PetscErrorCode ierr;
505   PetscInt       l,*garray = mat->garray,diag;
506 
507   PetscFunctionBegin;
508   /* code only works for square matrices A */
509 
510   /* find size of row to the left of the diagonal part */
511   ierr = MatGetOwnershipRange(A,&diag,0);CHKERRQ(ierr);
512   row  = row - diag;
513   for (l=0; l<b->i[row+1]-b->i[row]; l++) {
514     if (garray[b->j[b->i[row]+l]] > diag) break;
515   }
516   ierr = PetscMemcpy(b->a+b->i[row],v,l*sizeof(PetscScalar));CHKERRQ(ierr);
517 
518   /* diagonal part */
519   ierr = PetscMemcpy(a->a+a->i[row],v+l,(a->i[row+1]-a->i[row])*sizeof(PetscScalar));CHKERRQ(ierr);
520 
521   /* right of diagonal part */
522   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);
523   PetscFunctionReturn(0);
524 }
525 
526 #undef __FUNCT__
527 #define __FUNCT__ "MatSetValues_MPIAIJ"
528 PetscErrorCode MatSetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode addv)
529 {
530   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
531   PetscScalar    value;
532   PetscErrorCode ierr;
533   PetscInt       i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
534   PetscInt       cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
535   PetscBool      roworiented = aij->roworiented;
536 
537   /* Some Variables required in the macro */
538   Mat        A                 = aij->A;
539   Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
540   PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
541   MatScalar  *aa               = a->a;
542   PetscBool  ignorezeroentries = a->ignorezeroentries;
543   Mat        B                 = aij->B;
544   Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
545   PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
546   MatScalar  *ba               = b->a;
547 
548   PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
549   PetscInt  nonew;
550   MatScalar *ap1,*ap2;
551 
552   PetscFunctionBegin;
553   for (i=0; i<m; i++) {
554     if (im[i] < 0) continue;
555 #if defined(PETSC_USE_DEBUG)
556     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);
557 #endif
558     if (im[i] >= rstart && im[i] < rend) {
559       row      = im[i] - rstart;
560       lastcol1 = -1;
561       rp1      = aj + ai[row];
562       ap1      = aa + ai[row];
563       rmax1    = aimax[row];
564       nrow1    = ailen[row];
565       low1     = 0;
566       high1    = nrow1;
567       lastcol2 = -1;
568       rp2      = bj + bi[row];
569       ap2      = ba + bi[row];
570       rmax2    = bimax[row];
571       nrow2    = bilen[row];
572       low2     = 0;
573       high2    = nrow2;
574 
575       for (j=0; j<n; j++) {
576         if (roworiented) value = v[i*n+j];
577         else             value = v[i+j*m];
578         if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES)) continue;
579         if (in[j] >= cstart && in[j] < cend) {
580           col   = in[j] - cstart;
581           nonew = a->nonew;
582           MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
583         } else if (in[j] < 0) continue;
584 #if defined(PETSC_USE_DEBUG)
585         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);
586 #endif
587         else {
588           if (mat->was_assembled) {
589             if (!aij->colmap) {
590               ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
591             }
592 #if defined(PETSC_USE_CTABLE)
593             ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
594             col--;
595 #else
596             col = aij->colmap[in[j]] - 1;
597 #endif
598             if (col < 0 && !((Mat_SeqAIJ*)(aij->B->data))->nonew) {
599               ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
600               col  =  in[j];
601               /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
602               B     = aij->B;
603               b     = (Mat_SeqAIJ*)B->data;
604               bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j; ba = b->a;
605               rp2   = bj + bi[row];
606               ap2   = ba + bi[row];
607               rmax2 = bimax[row];
608               nrow2 = bilen[row];
609               low2  = 0;
610               high2 = nrow2;
611               bm    = aij->B->rmap->n;
612               ba    = b->a;
613             } 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]);
614           } else col = in[j];
615           nonew = b->nonew;
616           MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
617         }
618       }
619     } else {
620       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]);
621       if (!aij->donotstash) {
622         mat->assembled = PETSC_FALSE;
623         if (roworiented) {
624           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
625         } else {
626           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
627         }
628       }
629     }
630   }
631   PetscFunctionReturn(0);
632 }
633 
634 #undef __FUNCT__
635 #define __FUNCT__ "MatGetValues_MPIAIJ"
636 PetscErrorCode MatGetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],PetscScalar v[])
637 {
638   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
639   PetscErrorCode ierr;
640   PetscInt       i,j,rstart = mat->rmap->rstart,rend = mat->rmap->rend;
641   PetscInt       cstart = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
642 
643   PetscFunctionBegin;
644   for (i=0; i<m; i++) {
645     if (idxm[i] < 0) continue; /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative row: %D",idxm[i]);*/
646     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);
647     if (idxm[i] >= rstart && idxm[i] < rend) {
648       row = idxm[i] - rstart;
649       for (j=0; j<n; j++) {
650         if (idxn[j] < 0) continue; /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column: %D",idxn[j]); */
651         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);
652         if (idxn[j] >= cstart && idxn[j] < cend) {
653           col  = idxn[j] - cstart;
654           ierr = MatGetValues(aij->A,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
655         } else {
656           if (!aij->colmap) {
657             ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
658           }
659 #if defined(PETSC_USE_CTABLE)
660           ierr = PetscTableFind(aij->colmap,idxn[j]+1,&col);CHKERRQ(ierr);
661           col--;
662 #else
663           col = aij->colmap[idxn[j]] - 1;
664 #endif
665           if ((col < 0) || (aij->garray[col] != idxn[j])) *(v+i*n+j) = 0.0;
666           else {
667             ierr = MatGetValues(aij->B,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
668           }
669         }
670       }
671     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only local values currently supported");
672   }
673   PetscFunctionReturn(0);
674 }
675 
676 extern PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat,Vec,Vec);
677 
678 #undef __FUNCT__
679 #define __FUNCT__ "MatAssemblyBegin_MPIAIJ"
680 PetscErrorCode MatAssemblyBegin_MPIAIJ(Mat mat,MatAssemblyType mode)
681 {
682   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
683   PetscErrorCode ierr;
684   PetscInt       nstash,reallocs;
685 
686   PetscFunctionBegin;
687   if (aij->donotstash || mat->nooffprocentries) PetscFunctionReturn(0);
688 
689   ierr = MatStashScatterBegin_Private(mat,&mat->stash,mat->rmap->range);CHKERRQ(ierr);
690   ierr = MatStashGetInfo_Private(&mat->stash,&nstash,&reallocs);CHKERRQ(ierr);
691   ierr = PetscInfo2(aij->A,"Stash has %D entries, uses %D mallocs.\n",nstash,reallocs);CHKERRQ(ierr);
692   PetscFunctionReturn(0);
693 }
694 
695 #undef __FUNCT__
696 #define __FUNCT__ "MatAssemblyEnd_MPIAIJ"
697 PetscErrorCode MatAssemblyEnd_MPIAIJ(Mat mat,MatAssemblyType mode)
698 {
699   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
700   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)aij->A->data;
701   PetscErrorCode ierr;
702   PetscMPIInt    n;
703   PetscInt       i,j,rstart,ncols,flg;
704   PetscInt       *row,*col;
705   PetscBool      other_disassembled;
706   PetscScalar    *val;
707 
708   /* do not use 'b = (Mat_SeqAIJ*)aij->B->data' as B can be reset in disassembly */
709 
710   PetscFunctionBegin;
711   if (!aij->donotstash && !mat->nooffprocentries) {
712     while (1) {
713       ierr = MatStashScatterGetMesg_Private(&mat->stash,&n,&row,&col,&val,&flg);CHKERRQ(ierr);
714       if (!flg) break;
715 
716       for (i=0; i<n; ) {
717         /* Now identify the consecutive vals belonging to the same row */
718         for (j=i,rstart=row[j]; j<n; j++) {
719           if (row[j] != rstart) break;
720         }
721         if (j < n) ncols = j-i;
722         else       ncols = n-i;
723         /* Now assemble all these values with a single function call */
724         ierr = MatSetValues_MPIAIJ(mat,1,row+i,ncols,col+i,val+i,mat->insertmode);CHKERRQ(ierr);
725 
726         i = j;
727       }
728     }
729     ierr = MatStashScatterEnd_Private(&mat->stash);CHKERRQ(ierr);
730   }
731   ierr = MatAssemblyBegin(aij->A,mode);CHKERRQ(ierr);
732   ierr = MatAssemblyEnd(aij->A,mode);CHKERRQ(ierr);
733 
734   /* determine if any processor has disassembled, if so we must
735      also disassemble ourselfs, in order that we may reassemble. */
736   /*
737      if nonzero structure of submatrix B cannot change then we know that
738      no processor disassembled thus we can skip this stuff
739   */
740   if (!((Mat_SeqAIJ*)aij->B->data)->nonew) {
741     ierr = MPIU_Allreduce(&mat->was_assembled,&other_disassembled,1,MPIU_BOOL,MPI_PROD,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
742     if (mat->was_assembled && !other_disassembled) {
743       ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
744     }
745   }
746   if (!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) {
747     ierr = MatSetUpMultiply_MPIAIJ(mat);CHKERRQ(ierr);
748   }
749   ierr = MatSetOption(aij->B,MAT_USE_INODES,PETSC_FALSE);CHKERRQ(ierr);
750   ierr = MatAssemblyBegin(aij->B,mode);CHKERRQ(ierr);
751   ierr = MatAssemblyEnd(aij->B,mode);CHKERRQ(ierr);
752 
753   ierr = PetscFree2(aij->rowvalues,aij->rowindices);CHKERRQ(ierr);
754 
755   aij->rowvalues = 0;
756 
757   ierr = VecDestroy(&aij->diag);CHKERRQ(ierr);
758   if (a->inode.size) mat->ops->multdiagonalblock = MatMultDiagonalBlock_MPIAIJ;
759 
760   /* if no new nonzero locations are allowed in matrix then only set the matrix state the first time through */
761   if ((!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) || !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
762     PetscObjectState state = aij->A->nonzerostate + aij->B->nonzerostate;
763     ierr = MPIU_Allreduce(&state,&mat->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
764   }
765   PetscFunctionReturn(0);
766 }
767 
768 #undef __FUNCT__
769 #define __FUNCT__ "MatZeroEntries_MPIAIJ"
770 PetscErrorCode MatZeroEntries_MPIAIJ(Mat A)
771 {
772   Mat_MPIAIJ     *l = (Mat_MPIAIJ*)A->data;
773   PetscErrorCode ierr;
774 
775   PetscFunctionBegin;
776   ierr = MatZeroEntries(l->A);CHKERRQ(ierr);
777   ierr = MatZeroEntries(l->B);CHKERRQ(ierr);
778   PetscFunctionReturn(0);
779 }
780 
781 #undef __FUNCT__
782 #define __FUNCT__ "MatZeroRows_MPIAIJ"
783 PetscErrorCode MatZeroRows_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
784 {
785   Mat_MPIAIJ    *mat    = (Mat_MPIAIJ *) A->data;
786   PetscInt      *owners = A->rmap->range;
787   PetscInt       n      = A->rmap->n;
788   PetscSF        sf;
789   PetscInt      *lrows;
790   PetscSFNode   *rrows;
791   PetscInt       r, p = 0, len = 0;
792   PetscErrorCode ierr;
793 
794   PetscFunctionBegin;
795   /* Create SF where leaves are input rows and roots are owned rows */
796   ierr = PetscMalloc1(n, &lrows);CHKERRQ(ierr);
797   for (r = 0; r < n; ++r) lrows[r] = -1;
798   if (!A->nooffproczerorows) {ierr = PetscMalloc1(N, &rrows);CHKERRQ(ierr);}
799   for (r = 0; r < N; ++r) {
800     const PetscInt idx   = rows[r];
801     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);
802     if (idx < owners[p] || owners[p+1] <= idx) { /* short-circuit the search if the last p owns this row too */
803       ierr = PetscLayoutFindOwner(A->rmap,idx,&p);CHKERRQ(ierr);
804     }
805     if (A->nooffproczerorows) {
806       if (p != mat->rank) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"MAT_NO_OFF_PROC_ZERO_ROWS set, but row %D is not owned by rank %d",idx,mat->rank);
807       lrows[len++] = idx - owners[p];
808     } else {
809       rrows[r].rank = p;
810       rrows[r].index = rows[r] - owners[p];
811     }
812   }
813   if (!A->nooffproczerorows) {
814     ierr = PetscSFCreate(PetscObjectComm((PetscObject) A), &sf);CHKERRQ(ierr);
815     ierr = PetscSFSetGraph(sf, n, N, NULL, PETSC_OWN_POINTER, rrows, PETSC_OWN_POINTER);CHKERRQ(ierr);
816     /* Collect flags for rows to be zeroed */
817     ierr = PetscSFReduceBegin(sf, MPIU_INT, (PetscInt*)rows, lrows, MPI_LOR);CHKERRQ(ierr);
818     ierr = PetscSFReduceEnd(sf, MPIU_INT, (PetscInt*)rows, lrows, MPI_LOR);CHKERRQ(ierr);
819     ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
820     /* Compress and put in row numbers */
821     for (r = 0; r < n; ++r) if (lrows[r] >= 0) lrows[len++] = r;
822   }
823   /* fix right hand side if needed */
824   if (x && b) {
825     const PetscScalar *xx;
826     PetscScalar       *bb;
827 
828     ierr = VecGetArrayRead(x, &xx);CHKERRQ(ierr);
829     ierr = VecGetArray(b, &bb);CHKERRQ(ierr);
830     for (r = 0; r < len; ++r) bb[lrows[r]] = diag*xx[lrows[r]];
831     ierr = VecRestoreArrayRead(x, &xx);CHKERRQ(ierr);
832     ierr = VecRestoreArray(b, &bb);CHKERRQ(ierr);
833   }
834   /* Must zero l->B before l->A because the (diag) case below may put values into l->B*/
835   ierr = MatZeroRows(mat->B, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
836   if ((diag != 0.0) && (mat->A->rmap->N == mat->A->cmap->N)) {
837     ierr = MatZeroRows(mat->A, len, lrows, diag, NULL, NULL);CHKERRQ(ierr);
838   } else if (diag != 0.0) {
839     ierr = MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
840     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");
841     for (r = 0; r < len; ++r) {
842       const PetscInt row = lrows[r] + A->rmap->rstart;
843       ierr = MatSetValues(A, 1, &row, 1, &row, &diag, INSERT_VALUES);CHKERRQ(ierr);
844     }
845     ierr = MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
846     ierr = MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
847   } else {
848     ierr = MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
849   }
850   ierr = PetscFree(lrows);CHKERRQ(ierr);
851 
852   /* only change matrix nonzero state if pattern was allowed to be changed */
853   if (!((Mat_SeqAIJ*)(mat->A->data))->keepnonzeropattern) {
854     PetscObjectState state = mat->A->nonzerostate + mat->B->nonzerostate;
855     ierr = MPIU_Allreduce(&state,&A->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
856   }
857   PetscFunctionReturn(0);
858 }
859 
860 #undef __FUNCT__
861 #define __FUNCT__ "MatZeroRowsColumns_MPIAIJ"
862 PetscErrorCode MatZeroRowsColumns_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
863 {
864   Mat_MPIAIJ        *l = (Mat_MPIAIJ*)A->data;
865   PetscErrorCode    ierr;
866   PetscMPIInt       n = A->rmap->n;
867   PetscInt          i,j,r,m,p = 0,len = 0;
868   PetscInt          *lrows,*owners = A->rmap->range;
869   PetscSFNode       *rrows;
870   PetscSF           sf;
871   const PetscScalar *xx;
872   PetscScalar       *bb,*mask;
873   Vec               xmask,lmask;
874   Mat_SeqAIJ        *aij = (Mat_SeqAIJ*)l->B->data;
875   const PetscInt    *aj, *ii,*ridx;
876   PetscScalar       *aa;
877 
878   PetscFunctionBegin;
879   /* Create SF where leaves are input rows and roots are owned rows */
880   ierr = PetscMalloc1(n, &lrows);CHKERRQ(ierr);
881   for (r = 0; r < n; ++r) lrows[r] = -1;
882   ierr = PetscMalloc1(N, &rrows);CHKERRQ(ierr);
883   for (r = 0; r < N; ++r) {
884     const PetscInt idx   = rows[r];
885     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);
886     if (idx < owners[p] || owners[p+1] <= idx) { /* short-circuit the search if the last p owns this row too */
887       ierr = PetscLayoutFindOwner(A->rmap,idx,&p);CHKERRQ(ierr);
888     }
889     rrows[r].rank  = p;
890     rrows[r].index = rows[r] - owners[p];
891   }
892   ierr = PetscSFCreate(PetscObjectComm((PetscObject) A), &sf);CHKERRQ(ierr);
893   ierr = PetscSFSetGraph(sf, n, N, NULL, PETSC_OWN_POINTER, rrows, PETSC_OWN_POINTER);CHKERRQ(ierr);
894   /* Collect flags for rows to be zeroed */
895   ierr = PetscSFReduceBegin(sf, MPIU_INT, (PetscInt *) rows, lrows, MPI_LOR);CHKERRQ(ierr);
896   ierr = PetscSFReduceEnd(sf, MPIU_INT, (PetscInt *) rows, lrows, MPI_LOR);CHKERRQ(ierr);
897   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
898   /* Compress and put in row numbers */
899   for (r = 0; r < n; ++r) if (lrows[r] >= 0) lrows[len++] = r;
900   /* zero diagonal part of matrix */
901   ierr = MatZeroRowsColumns(l->A,len,lrows,diag,x,b);CHKERRQ(ierr);
902   /* handle off diagonal part of matrix */
903   ierr = MatCreateVecs(A,&xmask,NULL);CHKERRQ(ierr);
904   ierr = VecDuplicate(l->lvec,&lmask);CHKERRQ(ierr);
905   ierr = VecGetArray(xmask,&bb);CHKERRQ(ierr);
906   for (i=0; i<len; i++) bb[lrows[i]] = 1;
907   ierr = VecRestoreArray(xmask,&bb);CHKERRQ(ierr);
908   ierr = VecScatterBegin(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
909   ierr = VecScatterEnd(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
910   ierr = VecDestroy(&xmask);CHKERRQ(ierr);
911   if (x) {
912     ierr = VecScatterBegin(l->Mvctx,x,l->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
913     ierr = VecScatterEnd(l->Mvctx,x,l->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
914     ierr = VecGetArrayRead(l->lvec,&xx);CHKERRQ(ierr);
915     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
916   }
917   ierr = VecGetArray(lmask,&mask);CHKERRQ(ierr);
918   /* remove zeroed rows of off diagonal matrix */
919   ii = aij->i;
920   for (i=0; i<len; i++) {
921     ierr = PetscMemzero(aij->a + ii[lrows[i]],(ii[lrows[i]+1] - ii[lrows[i]])*sizeof(PetscScalar));CHKERRQ(ierr);
922   }
923   /* loop over all elements of off process part of matrix zeroing removed columns*/
924   if (aij->compressedrow.use) {
925     m    = aij->compressedrow.nrows;
926     ii   = aij->compressedrow.i;
927     ridx = aij->compressedrow.rindex;
928     for (i=0; i<m; i++) {
929       n  = ii[i+1] - ii[i];
930       aj = aij->j + ii[i];
931       aa = aij->a + ii[i];
932 
933       for (j=0; j<n; j++) {
934         if (PetscAbsScalar(mask[*aj])) {
935           if (b) bb[*ridx] -= *aa*xx[*aj];
936           *aa = 0.0;
937         }
938         aa++;
939         aj++;
940       }
941       ridx++;
942     }
943   } else { /* do not use compressed row format */
944     m = l->B->rmap->n;
945     for (i=0; i<m; i++) {
946       n  = ii[i+1] - ii[i];
947       aj = aij->j + ii[i];
948       aa = aij->a + ii[i];
949       for (j=0; j<n; j++) {
950         if (PetscAbsScalar(mask[*aj])) {
951           if (b) bb[i] -= *aa*xx[*aj];
952           *aa = 0.0;
953         }
954         aa++;
955         aj++;
956       }
957     }
958   }
959   if (x) {
960     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
961     ierr = VecRestoreArrayRead(l->lvec,&xx);CHKERRQ(ierr);
962   }
963   ierr = VecRestoreArray(lmask,&mask);CHKERRQ(ierr);
964   ierr = VecDestroy(&lmask);CHKERRQ(ierr);
965   ierr = PetscFree(lrows);CHKERRQ(ierr);
966 
967   /* only change matrix nonzero state if pattern was allowed to be changed */
968   if (!((Mat_SeqAIJ*)(l->A->data))->keepnonzeropattern) {
969     PetscObjectState state = l->A->nonzerostate + l->B->nonzerostate;
970     ierr = MPIU_Allreduce(&state,&A->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
971   }
972   PetscFunctionReturn(0);
973 }
974 
975 #undef __FUNCT__
976 #define __FUNCT__ "MatMult_MPIAIJ"
977 PetscErrorCode MatMult_MPIAIJ(Mat A,Vec xx,Vec yy)
978 {
979   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
980   PetscErrorCode ierr;
981   PetscInt       nt;
982 
983   PetscFunctionBegin;
984   ierr = VecGetLocalSize(xx,&nt);CHKERRQ(ierr);
985   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);
986   ierr = VecScatterBegin(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
987   ierr = (*a->A->ops->mult)(a->A,xx,yy);CHKERRQ(ierr);
988   ierr = VecScatterEnd(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
989   ierr = (*a->B->ops->multadd)(a->B,a->lvec,yy,yy);CHKERRQ(ierr);
990   PetscFunctionReturn(0);
991 }
992 
993 #undef __FUNCT__
994 #define __FUNCT__ "MatMultDiagonalBlock_MPIAIJ"
995 PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat A,Vec bb,Vec xx)
996 {
997   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
998   PetscErrorCode ierr;
999 
1000   PetscFunctionBegin;
1001   ierr = MatMultDiagonalBlock(a->A,bb,xx);CHKERRQ(ierr);
1002   PetscFunctionReturn(0);
1003 }
1004 
1005 #undef __FUNCT__
1006 #define __FUNCT__ "MatMultAdd_MPIAIJ"
1007 PetscErrorCode MatMultAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1008 {
1009   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1010   PetscErrorCode ierr;
1011 
1012   PetscFunctionBegin;
1013   ierr = VecScatterBegin(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1014   ierr = (*a->A->ops->multadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
1015   ierr = VecScatterEnd(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1016   ierr = (*a->B->ops->multadd)(a->B,a->lvec,zz,zz);CHKERRQ(ierr);
1017   PetscFunctionReturn(0);
1018 }
1019 
1020 #undef __FUNCT__
1021 #define __FUNCT__ "MatMultTranspose_MPIAIJ"
1022 PetscErrorCode MatMultTranspose_MPIAIJ(Mat A,Vec xx,Vec yy)
1023 {
1024   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1025   PetscErrorCode ierr;
1026   PetscBool      merged;
1027 
1028   PetscFunctionBegin;
1029   ierr = VecScatterGetMerged(a->Mvctx,&merged);CHKERRQ(ierr);
1030   /* do nondiagonal part */
1031   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
1032   if (!merged) {
1033     /* send it on its way */
1034     ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1035     /* do local part */
1036     ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
1037     /* receive remote parts: note this assumes the values are not actually */
1038     /* added in yy until the next line, */
1039     ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1040   } else {
1041     /* do local part */
1042     ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
1043     /* send it on its way */
1044     ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1045     /* values actually were received in the Begin() but we need to call this nop */
1046     ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1047   }
1048   PetscFunctionReturn(0);
1049 }
1050 
1051 #undef __FUNCT__
1052 #define __FUNCT__ "MatIsTranspose_MPIAIJ"
1053 PetscErrorCode  MatIsTranspose_MPIAIJ(Mat Amat,Mat Bmat,PetscReal tol,PetscBool  *f)
1054 {
1055   MPI_Comm       comm;
1056   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ*) Amat->data, *Bij;
1057   Mat            Adia = Aij->A, Bdia, Aoff,Boff,*Aoffs,*Boffs;
1058   IS             Me,Notme;
1059   PetscErrorCode ierr;
1060   PetscInt       M,N,first,last,*notme,i;
1061   PetscMPIInt    size;
1062 
1063   PetscFunctionBegin;
1064   /* Easy test: symmetric diagonal block */
1065   Bij  = (Mat_MPIAIJ*) Bmat->data; Bdia = Bij->A;
1066   ierr = MatIsTranspose(Adia,Bdia,tol,f);CHKERRQ(ierr);
1067   if (!*f) PetscFunctionReturn(0);
1068   ierr = PetscObjectGetComm((PetscObject)Amat,&comm);CHKERRQ(ierr);
1069   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1070   if (size == 1) PetscFunctionReturn(0);
1071 
1072   /* Hard test: off-diagonal block. This takes a MatGetSubMatrix. */
1073   ierr = MatGetSize(Amat,&M,&N);CHKERRQ(ierr);
1074   ierr = MatGetOwnershipRange(Amat,&first,&last);CHKERRQ(ierr);
1075   ierr = PetscMalloc1(N-last+first,&notme);CHKERRQ(ierr);
1076   for (i=0; i<first; i++) notme[i] = i;
1077   for (i=last; i<M; i++) notme[i-last+first] = i;
1078   ierr = ISCreateGeneral(MPI_COMM_SELF,N-last+first,notme,PETSC_COPY_VALUES,&Notme);CHKERRQ(ierr);
1079   ierr = ISCreateStride(MPI_COMM_SELF,last-first,first,1,&Me);CHKERRQ(ierr);
1080   ierr = MatGetSubMatrices(Amat,1,&Me,&Notme,MAT_INITIAL_MATRIX,&Aoffs);CHKERRQ(ierr);
1081   Aoff = Aoffs[0];
1082   ierr = MatGetSubMatrices(Bmat,1,&Notme,&Me,MAT_INITIAL_MATRIX,&Boffs);CHKERRQ(ierr);
1083   Boff = Boffs[0];
1084   ierr = MatIsTranspose(Aoff,Boff,tol,f);CHKERRQ(ierr);
1085   ierr = MatDestroyMatrices(1,&Aoffs);CHKERRQ(ierr);
1086   ierr = MatDestroyMatrices(1,&Boffs);CHKERRQ(ierr);
1087   ierr = ISDestroy(&Me);CHKERRQ(ierr);
1088   ierr = ISDestroy(&Notme);CHKERRQ(ierr);
1089   ierr = PetscFree(notme);CHKERRQ(ierr);
1090   PetscFunctionReturn(0);
1091 }
1092 
1093 #undef __FUNCT__
1094 #define __FUNCT__ "MatMultTransposeAdd_MPIAIJ"
1095 PetscErrorCode MatMultTransposeAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1096 {
1097   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1098   PetscErrorCode ierr;
1099 
1100   PetscFunctionBegin;
1101   /* do nondiagonal part */
1102   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
1103   /* send it on its way */
1104   ierr = VecScatterBegin(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1105   /* do local part */
1106   ierr = (*a->A->ops->multtransposeadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
1107   /* receive remote parts */
1108   ierr = VecScatterEnd(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1109   PetscFunctionReturn(0);
1110 }
1111 
1112 /*
1113   This only works correctly for square matrices where the subblock A->A is the
1114    diagonal block
1115 */
1116 #undef __FUNCT__
1117 #define __FUNCT__ "MatGetDiagonal_MPIAIJ"
1118 PetscErrorCode MatGetDiagonal_MPIAIJ(Mat A,Vec v)
1119 {
1120   PetscErrorCode ierr;
1121   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1122 
1123   PetscFunctionBegin;
1124   if (A->rmap->N != A->cmap->N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Supports only square matrix where A->A is diag block");
1125   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");
1126   ierr = MatGetDiagonal(a->A,v);CHKERRQ(ierr);
1127   PetscFunctionReturn(0);
1128 }
1129 
1130 #undef __FUNCT__
1131 #define __FUNCT__ "MatScale_MPIAIJ"
1132 PetscErrorCode MatScale_MPIAIJ(Mat A,PetscScalar aa)
1133 {
1134   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1135   PetscErrorCode ierr;
1136 
1137   PetscFunctionBegin;
1138   ierr = MatScale(a->A,aa);CHKERRQ(ierr);
1139   ierr = MatScale(a->B,aa);CHKERRQ(ierr);
1140   PetscFunctionReturn(0);
1141 }
1142 
1143 #undef __FUNCT__
1144 #define __FUNCT__ "MatDestroy_MPIAIJ"
1145 PetscErrorCode MatDestroy_MPIAIJ(Mat mat)
1146 {
1147   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1148   PetscErrorCode ierr;
1149 
1150   PetscFunctionBegin;
1151 #if defined(PETSC_USE_LOG)
1152   PetscLogObjectState((PetscObject)mat,"Rows=%D, Cols=%D",mat->rmap->N,mat->cmap->N);
1153 #endif
1154   ierr = MatStashDestroy_Private(&mat->stash);CHKERRQ(ierr);
1155   ierr = VecDestroy(&aij->diag);CHKERRQ(ierr);
1156   ierr = MatDestroy(&aij->A);CHKERRQ(ierr);
1157   ierr = MatDestroy(&aij->B);CHKERRQ(ierr);
1158 #if defined(PETSC_USE_CTABLE)
1159   ierr = PetscTableDestroy(&aij->colmap);CHKERRQ(ierr);
1160 #else
1161   ierr = PetscFree(aij->colmap);CHKERRQ(ierr);
1162 #endif
1163   ierr = PetscFree(aij->garray);CHKERRQ(ierr);
1164   ierr = VecDestroy(&aij->lvec);CHKERRQ(ierr);
1165   ierr = VecScatterDestroy(&aij->Mvctx);CHKERRQ(ierr);
1166   ierr = PetscFree2(aij->rowvalues,aij->rowindices);CHKERRQ(ierr);
1167   ierr = PetscFree(aij->ld);CHKERRQ(ierr);
1168   ierr = PetscFree(mat->data);CHKERRQ(ierr);
1169 
1170   ierr = PetscObjectChangeTypeName((PetscObject)mat,0);CHKERRQ(ierr);
1171   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatStoreValues_C",NULL);CHKERRQ(ierr);
1172   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatRetrieveValues_C",NULL);CHKERRQ(ierr);
1173   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatGetDiagonalBlock_C",NULL);CHKERRQ(ierr);
1174   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatIsTranspose_C",NULL);CHKERRQ(ierr);
1175   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocation_C",NULL);CHKERRQ(ierr);
1176   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocationCSR_C",NULL);CHKERRQ(ierr);
1177   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDiagonalScaleLocal_C",NULL);CHKERRQ(ierr);
1178   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_mpisbaij_C",NULL);CHKERRQ(ierr);
1179 #if defined(PETSC_HAVE_ELEMENTAL)
1180   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_elemental_C",NULL);CHKERRQ(ierr);
1181 #endif
1182   PetscFunctionReturn(0);
1183 }
1184 
1185 #undef __FUNCT__
1186 #define __FUNCT__ "MatView_MPIAIJ_Binary"
1187 PetscErrorCode MatView_MPIAIJ_Binary(Mat mat,PetscViewer viewer)
1188 {
1189   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1190   Mat_SeqAIJ     *A   = (Mat_SeqAIJ*)aij->A->data;
1191   Mat_SeqAIJ     *B   = (Mat_SeqAIJ*)aij->B->data;
1192   PetscErrorCode ierr;
1193   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
1194   int            fd;
1195   PetscInt       nz,header[4],*row_lengths,*range=0,rlen,i;
1196   PetscInt       nzmax,*column_indices,j,k,col,*garray = aij->garray,cnt,cstart = mat->cmap->rstart,rnz = 0;
1197   PetscScalar    *column_values;
1198   PetscInt       message_count,flowcontrolcount;
1199   FILE           *file;
1200 
1201   PetscFunctionBegin;
1202   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
1203   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);CHKERRQ(ierr);
1204   nz   = A->nz + B->nz;
1205   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
1206   if (!rank) {
1207     header[0] = MAT_FILE_CLASSID;
1208     header[1] = mat->rmap->N;
1209     header[2] = mat->cmap->N;
1210 
1211     ierr = MPI_Reduce(&nz,&header[3],1,MPIU_INT,MPI_SUM,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1212     ierr = PetscBinaryWrite(fd,header,4,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1213     /* get largest number of rows any processor has */
1214     rlen  = mat->rmap->n;
1215     range = mat->rmap->range;
1216     for (i=1; i<size; i++) rlen = PetscMax(rlen,range[i+1] - range[i]);
1217   } else {
1218     ierr = MPI_Reduce(&nz,0,1,MPIU_INT,MPI_SUM,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1219     rlen = mat->rmap->n;
1220   }
1221 
1222   /* load up the local row counts */
1223   ierr = PetscMalloc1(rlen+1,&row_lengths);CHKERRQ(ierr);
1224   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];
1225 
1226   /* store the row lengths to the file */
1227   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1228   if (!rank) {
1229     ierr = PetscBinaryWrite(fd,row_lengths,mat->rmap->n,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1230     for (i=1; i<size; i++) {
1231       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1232       rlen = range[i+1] - range[i];
1233       ierr = MPIULong_Recv(row_lengths,rlen,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1234       ierr = PetscBinaryWrite(fd,row_lengths,rlen,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1235     }
1236     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1237   } else {
1238     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1239     ierr = MPIULong_Send(row_lengths,mat->rmap->n,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1240     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1241   }
1242   ierr = PetscFree(row_lengths);CHKERRQ(ierr);
1243 
1244   /* load up the local column indices */
1245   nzmax = nz; /* th processor needs space a largest processor needs */
1246   ierr  = MPI_Reduce(&nz,&nzmax,1,MPIU_INT,MPI_MAX,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1247   ierr  = PetscMalloc1(nzmax+1,&column_indices);CHKERRQ(ierr);
1248   cnt   = 0;
1249   for (i=0; i<mat->rmap->n; i++) {
1250     for (j=B->i[i]; j<B->i[i+1]; j++) {
1251       if ((col = garray[B->j[j]]) > cstart) break;
1252       column_indices[cnt++] = col;
1253     }
1254     for (k=A->i[i]; k<A->i[i+1]; k++) column_indices[cnt++] = A->j[k] + cstart;
1255     for (; j<B->i[i+1]; j++) column_indices[cnt++] = garray[B->j[j]];
1256   }
1257   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);
1258 
1259   /* store the column indices to the file */
1260   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1261   if (!rank) {
1262     MPI_Status status;
1263     ierr = PetscBinaryWrite(fd,column_indices,nz,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1264     for (i=1; i<size; i++) {
1265       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1266       ierr = MPI_Recv(&rnz,1,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat),&status);CHKERRQ(ierr);
1267       if (rnz > nzmax) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: nz = %D nzmax = %D",nz,nzmax);
1268       ierr = MPIULong_Recv(column_indices,rnz,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1269       ierr = PetscBinaryWrite(fd,column_indices,rnz,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1270     }
1271     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1272   } else {
1273     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1274     ierr = MPI_Send(&nz,1,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1275     ierr = MPIULong_Send(column_indices,nz,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1276     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1277   }
1278   ierr = PetscFree(column_indices);CHKERRQ(ierr);
1279 
1280   /* load up the local column values */
1281   ierr = PetscMalloc1(nzmax+1,&column_values);CHKERRQ(ierr);
1282   cnt  = 0;
1283   for (i=0; i<mat->rmap->n; i++) {
1284     for (j=B->i[i]; j<B->i[i+1]; j++) {
1285       if (garray[B->j[j]] > cstart) break;
1286       column_values[cnt++] = B->a[j];
1287     }
1288     for (k=A->i[i]; k<A->i[i+1]; k++) column_values[cnt++] = A->a[k];
1289     for (; j<B->i[i+1]; j++) column_values[cnt++] = B->a[j];
1290   }
1291   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);
1292 
1293   /* store the column values to the file */
1294   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1295   if (!rank) {
1296     MPI_Status status;
1297     ierr = PetscBinaryWrite(fd,column_values,nz,PETSC_SCALAR,PETSC_TRUE);CHKERRQ(ierr);
1298     for (i=1; i<size; i++) {
1299       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1300       ierr = MPI_Recv(&rnz,1,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat),&status);CHKERRQ(ierr);
1301       if (rnz > nzmax) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: nz = %D nzmax = %D",nz,nzmax);
1302       ierr = MPIULong_Recv(column_values,rnz,MPIU_SCALAR,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1303       ierr = PetscBinaryWrite(fd,column_values,rnz,PETSC_SCALAR,PETSC_TRUE);CHKERRQ(ierr);
1304     }
1305     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1306   } else {
1307     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1308     ierr = MPI_Send(&nz,1,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1309     ierr = MPIULong_Send(column_values,nz,MPIU_SCALAR,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1310     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1311   }
1312   ierr = PetscFree(column_values);CHKERRQ(ierr);
1313 
1314   ierr = PetscViewerBinaryGetInfoPointer(viewer,&file);CHKERRQ(ierr);
1315   if (file) fprintf(file,"-matload_block_size %d\n",(int)PetscAbs(mat->rmap->bs));
1316   PetscFunctionReturn(0);
1317 }
1318 
1319 #include <petscdraw.h>
1320 #undef __FUNCT__
1321 #define __FUNCT__ "MatView_MPIAIJ_ASCIIorDraworSocket"
1322 PetscErrorCode MatView_MPIAIJ_ASCIIorDraworSocket(Mat mat,PetscViewer viewer)
1323 {
1324   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)mat->data;
1325   PetscErrorCode    ierr;
1326   PetscMPIInt       rank = aij->rank,size = aij->size;
1327   PetscBool         isdraw,iascii,isbinary;
1328   PetscViewer       sviewer;
1329   PetscViewerFormat format;
1330 
1331   PetscFunctionBegin;
1332   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1333   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1334   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1335   if (iascii) {
1336     ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
1337     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
1338       MatInfo   info;
1339       PetscBool inodes;
1340 
1341       ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
1342       ierr = MatGetInfo(mat,MAT_LOCAL,&info);CHKERRQ(ierr);
1343       ierr = MatInodeGetInodeSizes(aij->A,NULL,(PetscInt**)&inodes,NULL);CHKERRQ(ierr);
1344       ierr = PetscViewerASCIIPushSynchronized(viewer);CHKERRQ(ierr);
1345       if (!inodes) {
1346         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %D nz %D nz alloced %D mem %D, not using I-node routines\n",
1347                                                   rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
1348       } else {
1349         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %D nz %D nz alloced %D mem %D, using I-node routines\n",
1350                                                   rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
1351       }
1352       ierr = MatGetInfo(aij->A,MAT_LOCAL,&info);CHKERRQ(ierr);
1353       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] on-diagonal part: nz %D \n",rank,(PetscInt)info.nz_used);CHKERRQ(ierr);
1354       ierr = MatGetInfo(aij->B,MAT_LOCAL,&info);CHKERRQ(ierr);
1355       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] off-diagonal part: nz %D \n",rank,(PetscInt)info.nz_used);CHKERRQ(ierr);
1356       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1357       ierr = PetscViewerASCIIPopSynchronized(viewer);CHKERRQ(ierr);
1358       ierr = PetscViewerASCIIPrintf(viewer,"Information on VecScatter used in matrix-vector product: \n");CHKERRQ(ierr);
1359       ierr = VecScatterView(aij->Mvctx,viewer);CHKERRQ(ierr);
1360       PetscFunctionReturn(0);
1361     } else if (format == PETSC_VIEWER_ASCII_INFO) {
1362       PetscInt inodecount,inodelimit,*inodes;
1363       ierr = MatInodeGetInodeSizes(aij->A,&inodecount,&inodes,&inodelimit);CHKERRQ(ierr);
1364       if (inodes) {
1365         ierr = PetscViewerASCIIPrintf(viewer,"using I-node (on process 0) routines: found %D nodes, limit used is %D\n",inodecount,inodelimit);CHKERRQ(ierr);
1366       } else {
1367         ierr = PetscViewerASCIIPrintf(viewer,"not using I-node (on process 0) routines\n");CHKERRQ(ierr);
1368       }
1369       PetscFunctionReturn(0);
1370     } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO) {
1371       PetscFunctionReturn(0);
1372     }
1373   } else if (isbinary) {
1374     if (size == 1) {
1375       ierr = PetscObjectSetName((PetscObject)aij->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1376       ierr = MatView(aij->A,viewer);CHKERRQ(ierr);
1377     } else {
1378       ierr = MatView_MPIAIJ_Binary(mat,viewer);CHKERRQ(ierr);
1379     }
1380     PetscFunctionReturn(0);
1381   } else if (isdraw) {
1382     PetscDraw draw;
1383     PetscBool isnull;
1384     ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
1385     ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr);
1386     if (isnull) PetscFunctionReturn(0);
1387   }
1388 
1389   {
1390     /* assemble the entire matrix onto first processor. */
1391     Mat        A;
1392     Mat_SeqAIJ *Aloc;
1393     PetscInt   M = mat->rmap->N,N = mat->cmap->N,m,*ai,*aj,row,*cols,i,*ct;
1394     MatScalar  *a;
1395 
1396     ierr = MatCreate(PetscObjectComm((PetscObject)mat),&A);CHKERRQ(ierr);
1397     if (!rank) {
1398       ierr = MatSetSizes(A,M,N,M,N);CHKERRQ(ierr);
1399     } else {
1400       ierr = MatSetSizes(A,0,0,M,N);CHKERRQ(ierr);
1401     }
1402     /* This is just a temporary matrix, so explicitly using MATMPIAIJ is probably best */
1403     ierr = MatSetType(A,MATMPIAIJ);CHKERRQ(ierr);
1404     ierr = MatMPIAIJSetPreallocation(A,0,NULL,0,NULL);CHKERRQ(ierr);
1405     ierr = MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
1406     ierr = PetscLogObjectParent((PetscObject)mat,(PetscObject)A);CHKERRQ(ierr);
1407 
1408     /* copy over the A part */
1409     Aloc = (Mat_SeqAIJ*)aij->A->data;
1410     m    = aij->A->rmap->n; ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
1411     row  = mat->rmap->rstart;
1412     for (i=0; i<ai[m]; i++) aj[i] += mat->cmap->rstart;
1413     for (i=0; i<m; i++) {
1414       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],aj,a,INSERT_VALUES);CHKERRQ(ierr);
1415       row++;
1416       a += ai[i+1]-ai[i]; aj += ai[i+1]-ai[i];
1417     }
1418     aj = Aloc->j;
1419     for (i=0; i<ai[m]; i++) aj[i] -= mat->cmap->rstart;
1420 
1421     /* copy over the B part */
1422     Aloc = (Mat_SeqAIJ*)aij->B->data;
1423     m    = aij->B->rmap->n;  ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
1424     row  = mat->rmap->rstart;
1425     ierr = PetscMalloc1(ai[m]+1,&cols);CHKERRQ(ierr);
1426     ct   = cols;
1427     for (i=0; i<ai[m]; i++) cols[i] = aij->garray[aj[i]];
1428     for (i=0; i<m; i++) {
1429       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],cols,a,INSERT_VALUES);CHKERRQ(ierr);
1430       row++;
1431       a += ai[i+1]-ai[i]; cols += ai[i+1]-ai[i];
1432     }
1433     ierr = PetscFree(ct);CHKERRQ(ierr);
1434     ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1435     ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1436     /*
1437        Everyone has to call to draw the matrix since the graphics waits are
1438        synchronized across all processors that share the PetscDraw object
1439     */
1440     ierr = PetscViewerGetSubViewer(viewer,PETSC_COMM_SELF,&sviewer);CHKERRQ(ierr);
1441     if (!rank) {
1442       ierr = PetscObjectSetName((PetscObject)((Mat_MPIAIJ*)(A->data))->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1443       ierr = MatView_SeqAIJ(((Mat_MPIAIJ*)(A->data))->A,sviewer);CHKERRQ(ierr);
1444     }
1445     ierr = PetscViewerRestoreSubViewer(viewer,PETSC_COMM_SELF,&sviewer);CHKERRQ(ierr);
1446     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1447     ierr = MatDestroy(&A);CHKERRQ(ierr);
1448   }
1449   PetscFunctionReturn(0);
1450 }
1451 
1452 #undef __FUNCT__
1453 #define __FUNCT__ "MatView_MPIAIJ"
1454 PetscErrorCode MatView_MPIAIJ(Mat mat,PetscViewer viewer)
1455 {
1456   PetscErrorCode ierr;
1457   PetscBool      iascii,isdraw,issocket,isbinary;
1458 
1459   PetscFunctionBegin;
1460   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1461   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1462   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1463   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSOCKET,&issocket);CHKERRQ(ierr);
1464   if (iascii || isdraw || isbinary || issocket) {
1465     ierr = MatView_MPIAIJ_ASCIIorDraworSocket(mat,viewer);CHKERRQ(ierr);
1466   }
1467   PetscFunctionReturn(0);
1468 }
1469 
1470 #undef __FUNCT__
1471 #define __FUNCT__ "MatSOR_MPIAIJ"
1472 PetscErrorCode MatSOR_MPIAIJ(Mat matin,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
1473 {
1474   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1475   PetscErrorCode ierr;
1476   Vec            bb1 = 0;
1477   PetscBool      hasop;
1478 
1479   PetscFunctionBegin;
1480   if (flag == SOR_APPLY_UPPER) {
1481     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1482     PetscFunctionReturn(0);
1483   }
1484 
1485   if (its > 1 || ~flag & SOR_ZERO_INITIAL_GUESS || flag & SOR_EISENSTAT) {
1486     ierr = VecDuplicate(bb,&bb1);CHKERRQ(ierr);
1487   }
1488 
1489   if ((flag & SOR_LOCAL_SYMMETRIC_SWEEP) == SOR_LOCAL_SYMMETRIC_SWEEP) {
1490     if (flag & SOR_ZERO_INITIAL_GUESS) {
1491       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1492       its--;
1493     }
1494 
1495     while (its--) {
1496       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1497       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1498 
1499       /* update rhs: bb1 = bb - B*x */
1500       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1501       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1502 
1503       /* local sweep */
1504       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_SYMMETRIC_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1505     }
1506   } else if (flag & SOR_LOCAL_FORWARD_SWEEP) {
1507     if (flag & SOR_ZERO_INITIAL_GUESS) {
1508       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1509       its--;
1510     }
1511     while (its--) {
1512       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1513       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1514 
1515       /* update rhs: bb1 = bb - B*x */
1516       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1517       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1518 
1519       /* local sweep */
1520       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_FORWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1521     }
1522   } else if (flag & SOR_LOCAL_BACKWARD_SWEEP) {
1523     if (flag & SOR_ZERO_INITIAL_GUESS) {
1524       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1525       its--;
1526     }
1527     while (its--) {
1528       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1529       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1530 
1531       /* update rhs: bb1 = bb - B*x */
1532       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1533       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1534 
1535       /* local sweep */
1536       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_BACKWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1537     }
1538   } else if (flag & SOR_EISENSTAT) {
1539     Vec xx1;
1540 
1541     ierr = VecDuplicate(bb,&xx1);CHKERRQ(ierr);
1542     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_BACKWARD_SWEEP),fshift,lits,1,xx);CHKERRQ(ierr);
1543 
1544     ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1545     ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1546     if (!mat->diag) {
1547       ierr = MatCreateVecs(matin,&mat->diag,NULL);CHKERRQ(ierr);
1548       ierr = MatGetDiagonal(matin,mat->diag);CHKERRQ(ierr);
1549     }
1550     ierr = MatHasOperation(matin,MATOP_MULT_DIAGONAL_BLOCK,&hasop);CHKERRQ(ierr);
1551     if (hasop) {
1552       ierr = MatMultDiagonalBlock(matin,xx,bb1);CHKERRQ(ierr);
1553     } else {
1554       ierr = VecPointwiseMult(bb1,mat->diag,xx);CHKERRQ(ierr);
1555     }
1556     ierr = VecAYPX(bb1,(omega-2.0)/omega,bb);CHKERRQ(ierr);
1557 
1558     ierr = MatMultAdd(mat->B,mat->lvec,bb1,bb1);CHKERRQ(ierr);
1559 
1560     /* local sweep */
1561     ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_FORWARD_SWEEP),fshift,lits,1,xx1);CHKERRQ(ierr);
1562     ierr = VecAXPY(xx,1.0,xx1);CHKERRQ(ierr);
1563     ierr = VecDestroy(&xx1);CHKERRQ(ierr);
1564   } else SETERRQ(PetscObjectComm((PetscObject)matin),PETSC_ERR_SUP,"Parallel SOR not supported");
1565 
1566   ierr = VecDestroy(&bb1);CHKERRQ(ierr);
1567 
1568   matin->errortype = mat->A->errortype;
1569   PetscFunctionReturn(0);
1570 }
1571 
1572 #undef __FUNCT__
1573 #define __FUNCT__ "MatPermute_MPIAIJ"
1574 PetscErrorCode MatPermute_MPIAIJ(Mat A,IS rowp,IS colp,Mat *B)
1575 {
1576   Mat            aA,aB,Aperm;
1577   const PetscInt *rwant,*cwant,*gcols,*ai,*bi,*aj,*bj;
1578   PetscScalar    *aa,*ba;
1579   PetscInt       i,j,m,n,ng,anz,bnz,*dnnz,*onnz,*tdnnz,*tonnz,*rdest,*cdest,*work,*gcdest;
1580   PetscSF        rowsf,sf;
1581   IS             parcolp = NULL;
1582   PetscBool      done;
1583   PetscErrorCode ierr;
1584 
1585   PetscFunctionBegin;
1586   ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
1587   ierr = ISGetIndices(rowp,&rwant);CHKERRQ(ierr);
1588   ierr = ISGetIndices(colp,&cwant);CHKERRQ(ierr);
1589   ierr = PetscMalloc3(PetscMax(m,n),&work,m,&rdest,n,&cdest);CHKERRQ(ierr);
1590 
1591   /* Invert row permutation to find out where my rows should go */
1592   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&rowsf);CHKERRQ(ierr);
1593   ierr = PetscSFSetGraphLayout(rowsf,A->rmap,A->rmap->n,NULL,PETSC_OWN_POINTER,rwant);CHKERRQ(ierr);
1594   ierr = PetscSFSetFromOptions(rowsf);CHKERRQ(ierr);
1595   for (i=0; i<m; i++) work[i] = A->rmap->rstart + i;
1596   ierr = PetscSFReduceBegin(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1597   ierr = PetscSFReduceEnd(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1598 
1599   /* Invert column permutation to find out where my columns should go */
1600   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1601   ierr = PetscSFSetGraphLayout(sf,A->cmap,A->cmap->n,NULL,PETSC_OWN_POINTER,cwant);CHKERRQ(ierr);
1602   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1603   for (i=0; i<n; i++) work[i] = A->cmap->rstart + i;
1604   ierr = PetscSFReduceBegin(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1605   ierr = PetscSFReduceEnd(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1606   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1607 
1608   ierr = ISRestoreIndices(rowp,&rwant);CHKERRQ(ierr);
1609   ierr = ISRestoreIndices(colp,&cwant);CHKERRQ(ierr);
1610   ierr = MatMPIAIJGetSeqAIJ(A,&aA,&aB,&gcols);CHKERRQ(ierr);
1611 
1612   /* Find out where my gcols should go */
1613   ierr = MatGetSize(aB,NULL,&ng);CHKERRQ(ierr);
1614   ierr = PetscMalloc1(ng,&gcdest);CHKERRQ(ierr);
1615   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1616   ierr = PetscSFSetGraphLayout(sf,A->cmap,ng,NULL,PETSC_OWN_POINTER,gcols);CHKERRQ(ierr);
1617   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1618   ierr = PetscSFBcastBegin(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1619   ierr = PetscSFBcastEnd(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1620   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1621 
1622   ierr = PetscCalloc4(m,&dnnz,m,&onnz,m,&tdnnz,m,&tonnz);CHKERRQ(ierr);
1623   ierr = MatGetRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1624   ierr = MatGetRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1625   for (i=0; i<m; i++) {
1626     PetscInt row = rdest[i],rowner;
1627     ierr = PetscLayoutFindOwner(A->rmap,row,&rowner);CHKERRQ(ierr);
1628     for (j=ai[i]; j<ai[i+1]; j++) {
1629       PetscInt cowner,col = cdest[aj[j]];
1630       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr); /* Could build an index for the columns to eliminate this search */
1631       if (rowner == cowner) dnnz[i]++;
1632       else onnz[i]++;
1633     }
1634     for (j=bi[i]; j<bi[i+1]; j++) {
1635       PetscInt cowner,col = gcdest[bj[j]];
1636       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr);
1637       if (rowner == cowner) dnnz[i]++;
1638       else onnz[i]++;
1639     }
1640   }
1641   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1642   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1643   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1644   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1645   ierr = PetscSFDestroy(&rowsf);CHKERRQ(ierr);
1646 
1647   ierr = MatCreateAIJ(PetscObjectComm((PetscObject)A),A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N,0,tdnnz,0,tonnz,&Aperm);CHKERRQ(ierr);
1648   ierr = MatSeqAIJGetArray(aA,&aa);CHKERRQ(ierr);
1649   ierr = MatSeqAIJGetArray(aB,&ba);CHKERRQ(ierr);
1650   for (i=0; i<m; i++) {
1651     PetscInt *acols = dnnz,*bcols = onnz; /* Repurpose now-unneeded arrays */
1652     PetscInt j0,rowlen;
1653     rowlen = ai[i+1] - ai[i];
1654     for (j0=j=0; j<rowlen; j0=j) { /* rowlen could be larger than number of rows m, so sum in batches */
1655       for ( ; j<PetscMin(rowlen,j0+m); j++) acols[j-j0] = cdest[aj[ai[i]+j]];
1656       ierr = MatSetValues(Aperm,1,&rdest[i],j-j0,acols,aa+ai[i]+j0,INSERT_VALUES);CHKERRQ(ierr);
1657     }
1658     rowlen = bi[i+1] - bi[i];
1659     for (j0=j=0; j<rowlen; j0=j) {
1660       for ( ; j<PetscMin(rowlen,j0+m); j++) bcols[j-j0] = gcdest[bj[bi[i]+j]];
1661       ierr = MatSetValues(Aperm,1,&rdest[i],j-j0,bcols,ba+bi[i]+j0,INSERT_VALUES);CHKERRQ(ierr);
1662     }
1663   }
1664   ierr = MatAssemblyBegin(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1665   ierr = MatAssemblyEnd(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1666   ierr = MatRestoreRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1667   ierr = MatRestoreRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1668   ierr = MatSeqAIJRestoreArray(aA,&aa);CHKERRQ(ierr);
1669   ierr = MatSeqAIJRestoreArray(aB,&ba);CHKERRQ(ierr);
1670   ierr = PetscFree4(dnnz,onnz,tdnnz,tonnz);CHKERRQ(ierr);
1671   ierr = PetscFree3(work,rdest,cdest);CHKERRQ(ierr);
1672   ierr = PetscFree(gcdest);CHKERRQ(ierr);
1673   if (parcolp) {ierr = ISDestroy(&colp);CHKERRQ(ierr);}
1674   *B = Aperm;
1675   PetscFunctionReturn(0);
1676 }
1677 
1678 #undef __FUNCT__
1679 #define __FUNCT__ "MatGetGhosts_MPIAIJ"
1680 PetscErrorCode  MatGetGhosts_MPIAIJ(Mat mat,PetscInt *nghosts,const PetscInt *ghosts[])
1681 {
1682   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1683   PetscErrorCode ierr;
1684 
1685   PetscFunctionBegin;
1686   ierr = MatGetSize(aij->B,NULL,nghosts);CHKERRQ(ierr);
1687   if (ghosts) *ghosts = aij->garray;
1688   PetscFunctionReturn(0);
1689 }
1690 
1691 #undef __FUNCT__
1692 #define __FUNCT__ "MatGetInfo_MPIAIJ"
1693 PetscErrorCode MatGetInfo_MPIAIJ(Mat matin,MatInfoType flag,MatInfo *info)
1694 {
1695   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1696   Mat            A    = mat->A,B = mat->B;
1697   PetscErrorCode ierr;
1698   PetscReal      isend[5],irecv[5];
1699 
1700   PetscFunctionBegin;
1701   info->block_size = 1.0;
1702   ierr             = MatGetInfo(A,MAT_LOCAL,info);CHKERRQ(ierr);
1703 
1704   isend[0] = info->nz_used; isend[1] = info->nz_allocated; isend[2] = info->nz_unneeded;
1705   isend[3] = info->memory;  isend[4] = info->mallocs;
1706 
1707   ierr = MatGetInfo(B,MAT_LOCAL,info);CHKERRQ(ierr);
1708 
1709   isend[0] += info->nz_used; isend[1] += info->nz_allocated; isend[2] += info->nz_unneeded;
1710   isend[3] += info->memory;  isend[4] += info->mallocs;
1711   if (flag == MAT_LOCAL) {
1712     info->nz_used      = isend[0];
1713     info->nz_allocated = isend[1];
1714     info->nz_unneeded  = isend[2];
1715     info->memory       = isend[3];
1716     info->mallocs      = isend[4];
1717   } else if (flag == MAT_GLOBAL_MAX) {
1718     ierr = MPIU_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1719 
1720     info->nz_used      = irecv[0];
1721     info->nz_allocated = irecv[1];
1722     info->nz_unneeded  = irecv[2];
1723     info->memory       = irecv[3];
1724     info->mallocs      = irecv[4];
1725   } else if (flag == MAT_GLOBAL_SUM) {
1726     ierr = MPIU_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1727 
1728     info->nz_used      = irecv[0];
1729     info->nz_allocated = irecv[1];
1730     info->nz_unneeded  = irecv[2];
1731     info->memory       = irecv[3];
1732     info->mallocs      = irecv[4];
1733   }
1734   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
1735   info->fill_ratio_needed = 0;
1736   info->factor_mallocs    = 0;
1737   PetscFunctionReturn(0);
1738 }
1739 
1740 #undef __FUNCT__
1741 #define __FUNCT__ "MatSetOption_MPIAIJ"
1742 PetscErrorCode MatSetOption_MPIAIJ(Mat A,MatOption op,PetscBool flg)
1743 {
1744   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1745   PetscErrorCode ierr;
1746 
1747   PetscFunctionBegin;
1748   switch (op) {
1749   case MAT_NEW_NONZERO_LOCATIONS:
1750   case MAT_NEW_NONZERO_ALLOCATION_ERR:
1751   case MAT_UNUSED_NONZERO_LOCATION_ERR:
1752   case MAT_KEEP_NONZERO_PATTERN:
1753   case MAT_NEW_NONZERO_LOCATION_ERR:
1754   case MAT_USE_INODES:
1755   case MAT_IGNORE_ZERO_ENTRIES:
1756     MatCheckPreallocated(A,1);
1757     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1758     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1759     break;
1760   case MAT_ROW_ORIENTED:
1761     MatCheckPreallocated(A,1);
1762     a->roworiented = flg;
1763 
1764     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1765     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1766     break;
1767   case MAT_NEW_DIAGONALS:
1768     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
1769     break;
1770   case MAT_IGNORE_OFF_PROC_ENTRIES:
1771     a->donotstash = flg;
1772     break;
1773   case MAT_SPD:
1774     A->spd_set = PETSC_TRUE;
1775     A->spd     = flg;
1776     if (flg) {
1777       A->symmetric                  = PETSC_TRUE;
1778       A->structurally_symmetric     = PETSC_TRUE;
1779       A->symmetric_set              = PETSC_TRUE;
1780       A->structurally_symmetric_set = PETSC_TRUE;
1781     }
1782     break;
1783   case MAT_SYMMETRIC:
1784     MatCheckPreallocated(A,1);
1785     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1786     break;
1787   case MAT_STRUCTURALLY_SYMMETRIC:
1788     MatCheckPreallocated(A,1);
1789     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1790     break;
1791   case MAT_HERMITIAN:
1792     MatCheckPreallocated(A,1);
1793     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1794     break;
1795   case MAT_SYMMETRY_ETERNAL:
1796     MatCheckPreallocated(A,1);
1797     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1798     break;
1799   default:
1800     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %d",op);
1801   }
1802   PetscFunctionReturn(0);
1803 }
1804 
1805 #undef __FUNCT__
1806 #define __FUNCT__ "MatGetRow_MPIAIJ"
1807 PetscErrorCode MatGetRow_MPIAIJ(Mat matin,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1808 {
1809   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1810   PetscScalar    *vworkA,*vworkB,**pvA,**pvB,*v_p;
1811   PetscErrorCode ierr;
1812   PetscInt       i,*cworkA,*cworkB,**pcA,**pcB,cstart = matin->cmap->rstart;
1813   PetscInt       nztot,nzA,nzB,lrow,rstart = matin->rmap->rstart,rend = matin->rmap->rend;
1814   PetscInt       *cmap,*idx_p;
1815 
1816   PetscFunctionBegin;
1817   if (mat->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Already active");
1818   mat->getrowactive = PETSC_TRUE;
1819 
1820   if (!mat->rowvalues && (idx || v)) {
1821     /*
1822         allocate enough space to hold information from the longest row.
1823     */
1824     Mat_SeqAIJ *Aa = (Mat_SeqAIJ*)mat->A->data,*Ba = (Mat_SeqAIJ*)mat->B->data;
1825     PetscInt   max = 1,tmp;
1826     for (i=0; i<matin->rmap->n; i++) {
1827       tmp = Aa->i[i+1] - Aa->i[i] + Ba->i[i+1] - Ba->i[i];
1828       if (max < tmp) max = tmp;
1829     }
1830     ierr = PetscMalloc2(max,&mat->rowvalues,max,&mat->rowindices);CHKERRQ(ierr);
1831   }
1832 
1833   if (row < rstart || row >= rend) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Only local rows");
1834   lrow = row - rstart;
1835 
1836   pvA = &vworkA; pcA = &cworkA; pvB = &vworkB; pcB = &cworkB;
1837   if (!v)   {pvA = 0; pvB = 0;}
1838   if (!idx) {pcA = 0; if (!v) pcB = 0;}
1839   ierr  = (*mat->A->ops->getrow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1840   ierr  = (*mat->B->ops->getrow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1841   nztot = nzA + nzB;
1842 
1843   cmap = mat->garray;
1844   if (v  || idx) {
1845     if (nztot) {
1846       /* Sort by increasing column numbers, assuming A and B already sorted */
1847       PetscInt imark = -1;
1848       if (v) {
1849         *v = v_p = mat->rowvalues;
1850         for (i=0; i<nzB; i++) {
1851           if (cmap[cworkB[i]] < cstart) v_p[i] = vworkB[i];
1852           else break;
1853         }
1854         imark = i;
1855         for (i=0; i<nzA; i++)     v_p[imark+i] = vworkA[i];
1856         for (i=imark; i<nzB; i++) v_p[nzA+i]   = vworkB[i];
1857       }
1858       if (idx) {
1859         *idx = idx_p = mat->rowindices;
1860         if (imark > -1) {
1861           for (i=0; i<imark; i++) {
1862             idx_p[i] = cmap[cworkB[i]];
1863           }
1864         } else {
1865           for (i=0; i<nzB; i++) {
1866             if (cmap[cworkB[i]] < cstart) idx_p[i] = cmap[cworkB[i]];
1867             else break;
1868           }
1869           imark = i;
1870         }
1871         for (i=0; i<nzA; i++)     idx_p[imark+i] = cstart + cworkA[i];
1872         for (i=imark; i<nzB; i++) idx_p[nzA+i]   = cmap[cworkB[i]];
1873       }
1874     } else {
1875       if (idx) *idx = 0;
1876       if (v)   *v   = 0;
1877     }
1878   }
1879   *nz  = nztot;
1880   ierr = (*mat->A->ops->restorerow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1881   ierr = (*mat->B->ops->restorerow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1882   PetscFunctionReturn(0);
1883 }
1884 
1885 #undef __FUNCT__
1886 #define __FUNCT__ "MatRestoreRow_MPIAIJ"
1887 PetscErrorCode MatRestoreRow_MPIAIJ(Mat mat,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1888 {
1889   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1890 
1891   PetscFunctionBegin;
1892   if (!aij->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"MatGetRow() must be called first");
1893   aij->getrowactive = PETSC_FALSE;
1894   PetscFunctionReturn(0);
1895 }
1896 
1897 #undef __FUNCT__
1898 #define __FUNCT__ "MatNorm_MPIAIJ"
1899 PetscErrorCode MatNorm_MPIAIJ(Mat mat,NormType type,PetscReal *norm)
1900 {
1901   Mat_MPIAIJ     *aij  = (Mat_MPIAIJ*)mat->data;
1902   Mat_SeqAIJ     *amat = (Mat_SeqAIJ*)aij->A->data,*bmat = (Mat_SeqAIJ*)aij->B->data;
1903   PetscErrorCode ierr;
1904   PetscInt       i,j,cstart = mat->cmap->rstart;
1905   PetscReal      sum = 0.0;
1906   MatScalar      *v;
1907 
1908   PetscFunctionBegin;
1909   if (aij->size == 1) {
1910     ierr =  MatNorm(aij->A,type,norm);CHKERRQ(ierr);
1911   } else {
1912     if (type == NORM_FROBENIUS) {
1913       v = amat->a;
1914       for (i=0; i<amat->nz; i++) {
1915         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1916       }
1917       v = bmat->a;
1918       for (i=0; i<bmat->nz; i++) {
1919         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1920       }
1921       ierr  = MPIU_Allreduce(&sum,norm,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1922       *norm = PetscSqrtReal(*norm);
1923       ierr = PetscLogFlops(2*amat->nz+2*bmat->nz);CHKERRQ(ierr);
1924     } else if (type == NORM_1) { /* max column norm */
1925       PetscReal *tmp,*tmp2;
1926       PetscInt  *jj,*garray = aij->garray;
1927       ierr  = PetscCalloc1(mat->cmap->N+1,&tmp);CHKERRQ(ierr);
1928       ierr  = PetscMalloc1(mat->cmap->N+1,&tmp2);CHKERRQ(ierr);
1929       *norm = 0.0;
1930       v     = amat->a; jj = amat->j;
1931       for (j=0; j<amat->nz; j++) {
1932         tmp[cstart + *jj++] += PetscAbsScalar(*v);  v++;
1933       }
1934       v = bmat->a; jj = bmat->j;
1935       for (j=0; j<bmat->nz; j++) {
1936         tmp[garray[*jj++]] += PetscAbsScalar(*v); v++;
1937       }
1938       ierr = MPIU_Allreduce(tmp,tmp2,mat->cmap->N,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1939       for (j=0; j<mat->cmap->N; j++) {
1940         if (tmp2[j] > *norm) *norm = tmp2[j];
1941       }
1942       ierr = PetscFree(tmp);CHKERRQ(ierr);
1943       ierr = PetscFree(tmp2);CHKERRQ(ierr);
1944       ierr = PetscLogFlops(PetscMax(amat->nz+bmat->nz-1,0));CHKERRQ(ierr);
1945     } else if (type == NORM_INFINITY) { /* max row norm */
1946       PetscReal ntemp = 0.0;
1947       for (j=0; j<aij->A->rmap->n; j++) {
1948         v   = amat->a + amat->i[j];
1949         sum = 0.0;
1950         for (i=0; i<amat->i[j+1]-amat->i[j]; i++) {
1951           sum += PetscAbsScalar(*v); v++;
1952         }
1953         v = bmat->a + bmat->i[j];
1954         for (i=0; i<bmat->i[j+1]-bmat->i[j]; i++) {
1955           sum += PetscAbsScalar(*v); v++;
1956         }
1957         if (sum > ntemp) ntemp = sum;
1958       }
1959       ierr = MPIU_Allreduce(&ntemp,norm,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1960       ierr = PetscLogFlops(PetscMax(amat->nz+bmat->nz-1,0));CHKERRQ(ierr);
1961     } else SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"No support for two norm");
1962   }
1963   PetscFunctionReturn(0);
1964 }
1965 
1966 #undef __FUNCT__
1967 #define __FUNCT__ "MatTranspose_MPIAIJ"
1968 PetscErrorCode MatTranspose_MPIAIJ(Mat A,MatReuse reuse,Mat *matout)
1969 {
1970   Mat_MPIAIJ     *a   = (Mat_MPIAIJ*)A->data;
1971   Mat_SeqAIJ     *Aloc=(Mat_SeqAIJ*)a->A->data,*Bloc=(Mat_SeqAIJ*)a->B->data;
1972   PetscErrorCode ierr;
1973   PetscInt       M      = A->rmap->N,N = A->cmap->N,ma,na,mb,nb,*ai,*aj,*bi,*bj,row,*cols,*cols_tmp,i;
1974   PetscInt       cstart = A->cmap->rstart,ncol;
1975   Mat            B;
1976   MatScalar      *array;
1977 
1978   PetscFunctionBegin;
1979   if (reuse == MAT_REUSE_MATRIX && A == *matout && M != N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Square matrix only for in-place");
1980 
1981   ma = A->rmap->n; na = A->cmap->n; mb = a->B->rmap->n; nb = a->B->cmap->n;
1982   ai = Aloc->i; aj = Aloc->j;
1983   bi = Bloc->i; bj = Bloc->j;
1984   if (reuse == MAT_INITIAL_MATRIX || *matout == A) {
1985     PetscInt             *d_nnz,*g_nnz,*o_nnz;
1986     PetscSFNode          *oloc;
1987     PETSC_UNUSED PetscSF sf;
1988 
1989     ierr = PetscMalloc4(na,&d_nnz,na,&o_nnz,nb,&g_nnz,nb,&oloc);CHKERRQ(ierr);
1990     /* compute d_nnz for preallocation */
1991     ierr = PetscMemzero(d_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1992     for (i=0; i<ai[ma]; i++) {
1993       d_nnz[aj[i]]++;
1994       aj[i] += cstart; /* global col index to be used by MatSetValues() */
1995     }
1996     /* compute local off-diagonal contributions */
1997     ierr = PetscMemzero(g_nnz,nb*sizeof(PetscInt));CHKERRQ(ierr);
1998     for (i=0; i<bi[ma]; i++) g_nnz[bj[i]]++;
1999     /* map those to global */
2000     ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
2001     ierr = PetscSFSetGraphLayout(sf,A->cmap,nb,NULL,PETSC_USE_POINTER,a->garray);CHKERRQ(ierr);
2002     ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
2003     ierr = PetscMemzero(o_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
2004     ierr = PetscSFReduceBegin(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
2005     ierr = PetscSFReduceEnd(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
2006     ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
2007 
2008     ierr = MatCreate(PetscObjectComm((PetscObject)A),&B);CHKERRQ(ierr);
2009     ierr = MatSetSizes(B,A->cmap->n,A->rmap->n,N,M);CHKERRQ(ierr);
2010     ierr = MatSetBlockSizes(B,PetscAbs(A->cmap->bs),PetscAbs(A->rmap->bs));CHKERRQ(ierr);
2011     ierr = MatSetType(B,((PetscObject)A)->type_name);CHKERRQ(ierr);
2012     ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
2013     ierr = PetscFree4(d_nnz,o_nnz,g_nnz,oloc);CHKERRQ(ierr);
2014   } else {
2015     B    = *matout;
2016     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
2017     for (i=0; i<ai[ma]; i++) aj[i] += cstart; /* global col index to be used by MatSetValues() */
2018   }
2019 
2020   /* copy over the A part */
2021   array = Aloc->a;
2022   row   = A->rmap->rstart;
2023   for (i=0; i<ma; i++) {
2024     ncol = ai[i+1]-ai[i];
2025     ierr = MatSetValues(B,ncol,aj,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
2026     row++;
2027     array += ncol; aj += ncol;
2028   }
2029   aj = Aloc->j;
2030   for (i=0; i<ai[ma]; i++) aj[i] -= cstart; /* resume local col index */
2031 
2032   /* copy over the B part */
2033   ierr  = PetscCalloc1(bi[mb],&cols);CHKERRQ(ierr);
2034   array = Bloc->a;
2035   row   = A->rmap->rstart;
2036   for (i=0; i<bi[mb]; i++) cols[i] = a->garray[bj[i]];
2037   cols_tmp = cols;
2038   for (i=0; i<mb; i++) {
2039     ncol = bi[i+1]-bi[i];
2040     ierr = MatSetValues(B,ncol,cols_tmp,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
2041     row++;
2042     array += ncol; cols_tmp += ncol;
2043   }
2044   ierr = PetscFree(cols);CHKERRQ(ierr);
2045 
2046   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2047   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2048   if (reuse == MAT_INITIAL_MATRIX || *matout != A) {
2049     *matout = B;
2050   } else {
2051     ierr = MatHeaderMerge(A,&B);CHKERRQ(ierr);
2052   }
2053   PetscFunctionReturn(0);
2054 }
2055 
2056 #undef __FUNCT__
2057 #define __FUNCT__ "MatDiagonalScale_MPIAIJ"
2058 PetscErrorCode MatDiagonalScale_MPIAIJ(Mat mat,Vec ll,Vec rr)
2059 {
2060   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2061   Mat            a    = aij->A,b = aij->B;
2062   PetscErrorCode ierr;
2063   PetscInt       s1,s2,s3;
2064 
2065   PetscFunctionBegin;
2066   ierr = MatGetLocalSize(mat,&s2,&s3);CHKERRQ(ierr);
2067   if (rr) {
2068     ierr = VecGetLocalSize(rr,&s1);CHKERRQ(ierr);
2069     if (s1!=s3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"right vector non-conforming local size");
2070     /* Overlap communication with computation. */
2071     ierr = VecScatterBegin(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2072   }
2073   if (ll) {
2074     ierr = VecGetLocalSize(ll,&s1);CHKERRQ(ierr);
2075     if (s1!=s2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"left vector non-conforming local size");
2076     ierr = (*b->ops->diagonalscale)(b,ll,0);CHKERRQ(ierr);
2077   }
2078   /* scale  the diagonal block */
2079   ierr = (*a->ops->diagonalscale)(a,ll,rr);CHKERRQ(ierr);
2080 
2081   if (rr) {
2082     /* Do a scatter end and then right scale the off-diagonal block */
2083     ierr = VecScatterEnd(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2084     ierr = (*b->ops->diagonalscale)(b,0,aij->lvec);CHKERRQ(ierr);
2085   }
2086   PetscFunctionReturn(0);
2087 }
2088 
2089 #undef __FUNCT__
2090 #define __FUNCT__ "MatSetUnfactored_MPIAIJ"
2091 PetscErrorCode MatSetUnfactored_MPIAIJ(Mat A)
2092 {
2093   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2094   PetscErrorCode ierr;
2095 
2096   PetscFunctionBegin;
2097   ierr = MatSetUnfactored(a->A);CHKERRQ(ierr);
2098   PetscFunctionReturn(0);
2099 }
2100 
2101 #undef __FUNCT__
2102 #define __FUNCT__ "MatEqual_MPIAIJ"
2103 PetscErrorCode MatEqual_MPIAIJ(Mat A,Mat B,PetscBool  *flag)
2104 {
2105   Mat_MPIAIJ     *matB = (Mat_MPIAIJ*)B->data,*matA = (Mat_MPIAIJ*)A->data;
2106   Mat            a,b,c,d;
2107   PetscBool      flg;
2108   PetscErrorCode ierr;
2109 
2110   PetscFunctionBegin;
2111   a = matA->A; b = matA->B;
2112   c = matB->A; d = matB->B;
2113 
2114   ierr = MatEqual(a,c,&flg);CHKERRQ(ierr);
2115   if (flg) {
2116     ierr = MatEqual(b,d,&flg);CHKERRQ(ierr);
2117   }
2118   ierr = MPIU_Allreduce(&flg,flag,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
2119   PetscFunctionReturn(0);
2120 }
2121 
2122 #undef __FUNCT__
2123 #define __FUNCT__ "MatCopy_MPIAIJ"
2124 PetscErrorCode MatCopy_MPIAIJ(Mat A,Mat B,MatStructure str)
2125 {
2126   PetscErrorCode ierr;
2127   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2128   Mat_MPIAIJ     *b = (Mat_MPIAIJ*)B->data;
2129 
2130   PetscFunctionBegin;
2131   /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
2132   if ((str != SAME_NONZERO_PATTERN) || (A->ops->copy != B->ops->copy)) {
2133     /* because of the column compression in the off-processor part of the matrix a->B,
2134        the number of columns in a->B and b->B may be different, hence we cannot call
2135        the MatCopy() directly on the two parts. If need be, we can provide a more
2136        efficient copy than the MatCopy_Basic() by first uncompressing the a->B matrices
2137        then copying the submatrices */
2138     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
2139   } else {
2140     ierr = MatCopy(a->A,b->A,str);CHKERRQ(ierr);
2141     ierr = MatCopy(a->B,b->B,str);CHKERRQ(ierr);
2142   }
2143   PetscFunctionReturn(0);
2144 }
2145 
2146 #undef __FUNCT__
2147 #define __FUNCT__ "MatSetUp_MPIAIJ"
2148 PetscErrorCode MatSetUp_MPIAIJ(Mat A)
2149 {
2150   PetscErrorCode ierr;
2151 
2152   PetscFunctionBegin;
2153   ierr =  MatMPIAIJSetPreallocation(A,PETSC_DEFAULT,0,PETSC_DEFAULT,0);CHKERRQ(ierr);
2154   PetscFunctionReturn(0);
2155 }
2156 
2157 /*
2158    Computes the number of nonzeros per row needed for preallocation when X and Y
2159    have different nonzero structure.
2160 */
2161 #undef __FUNCT__
2162 #define __FUNCT__ "MatAXPYGetPreallocation_MPIX_private"
2163 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)
2164 {
2165   PetscInt       i,j,k,nzx,nzy;
2166 
2167   PetscFunctionBegin;
2168   /* Set the number of nonzeros in the new matrix */
2169   for (i=0; i<m; i++) {
2170     const PetscInt *xjj = xj+xi[i],*yjj = yj+yi[i];
2171     nzx = xi[i+1] - xi[i];
2172     nzy = yi[i+1] - yi[i];
2173     nnz[i] = 0;
2174     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2175       for (; k<nzy && yltog[yjj[k]]<xltog[xjj[j]]; k++) nnz[i]++; /* Catch up to X */
2176       if (k<nzy && yltog[yjj[k]]==xltog[xjj[j]]) k++;             /* Skip duplicate */
2177       nnz[i]++;
2178     }
2179     for (; k<nzy; k++) nnz[i]++;
2180   }
2181   PetscFunctionReturn(0);
2182 }
2183 
2184 /* This is the same as MatAXPYGetPreallocation_SeqAIJ, except that the local-to-global map is provided */
2185 #undef __FUNCT__
2186 #define __FUNCT__ "MatAXPYGetPreallocation_MPIAIJ"
2187 static PetscErrorCode MatAXPYGetPreallocation_MPIAIJ(Mat Y,const PetscInt *yltog,Mat X,const PetscInt *xltog,PetscInt *nnz)
2188 {
2189   PetscErrorCode ierr;
2190   PetscInt       m = Y->rmap->N;
2191   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data;
2192   Mat_SeqAIJ     *y = (Mat_SeqAIJ*)Y->data;
2193 
2194   PetscFunctionBegin;
2195   ierr = MatAXPYGetPreallocation_MPIX_private(m,x->i,x->j,xltog,y->i,y->j,yltog,nnz);CHKERRQ(ierr);
2196   PetscFunctionReturn(0);
2197 }
2198 
2199 #undef __FUNCT__
2200 #define __FUNCT__ "MatAXPY_MPIAIJ"
2201 PetscErrorCode MatAXPY_MPIAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
2202 {
2203   PetscErrorCode ierr;
2204   Mat_MPIAIJ     *xx = (Mat_MPIAIJ*)X->data,*yy = (Mat_MPIAIJ*)Y->data;
2205   PetscBLASInt   bnz,one=1;
2206   Mat_SeqAIJ     *x,*y;
2207 
2208   PetscFunctionBegin;
2209   if (str == SAME_NONZERO_PATTERN) {
2210     PetscScalar alpha = a;
2211     x    = (Mat_SeqAIJ*)xx->A->data;
2212     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2213     y    = (Mat_SeqAIJ*)yy->A->data;
2214     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2215     x    = (Mat_SeqAIJ*)xx->B->data;
2216     y    = (Mat_SeqAIJ*)yy->B->data;
2217     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2218     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2219     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
2220   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
2221     ierr = MatAXPY_Basic(Y,a,X,str);CHKERRQ(ierr);
2222   } else {
2223     Mat      B;
2224     PetscInt *nnz_d,*nnz_o;
2225     ierr = PetscMalloc1(yy->A->rmap->N,&nnz_d);CHKERRQ(ierr);
2226     ierr = PetscMalloc1(yy->B->rmap->N,&nnz_o);CHKERRQ(ierr);
2227     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
2228     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
2229     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
2230     ierr = MatSetBlockSizesFromMats(B,Y,Y);CHKERRQ(ierr);
2231     ierr = MatSetType(B,MATMPIAIJ);CHKERRQ(ierr);
2232     ierr = MatAXPYGetPreallocation_SeqAIJ(yy->A,xx->A,nnz_d);CHKERRQ(ierr);
2233     ierr = MatAXPYGetPreallocation_MPIAIJ(yy->B,yy->garray,xx->B,xx->garray,nnz_o);CHKERRQ(ierr);
2234     ierr = MatMPIAIJSetPreallocation(B,0,nnz_d,0,nnz_o);CHKERRQ(ierr);
2235     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
2236     ierr = MatHeaderReplace(Y,&B);CHKERRQ(ierr);
2237     ierr = PetscFree(nnz_d);CHKERRQ(ierr);
2238     ierr = PetscFree(nnz_o);CHKERRQ(ierr);
2239   }
2240   PetscFunctionReturn(0);
2241 }
2242 
2243 extern PetscErrorCode  MatConjugate_SeqAIJ(Mat);
2244 
2245 #undef __FUNCT__
2246 #define __FUNCT__ "MatConjugate_MPIAIJ"
2247 PetscErrorCode  MatConjugate_MPIAIJ(Mat mat)
2248 {
2249 #if defined(PETSC_USE_COMPLEX)
2250   PetscErrorCode ierr;
2251   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2252 
2253   PetscFunctionBegin;
2254   ierr = MatConjugate_SeqAIJ(aij->A);CHKERRQ(ierr);
2255   ierr = MatConjugate_SeqAIJ(aij->B);CHKERRQ(ierr);
2256 #else
2257   PetscFunctionBegin;
2258 #endif
2259   PetscFunctionReturn(0);
2260 }
2261 
2262 #undef __FUNCT__
2263 #define __FUNCT__ "MatRealPart_MPIAIJ"
2264 PetscErrorCode MatRealPart_MPIAIJ(Mat A)
2265 {
2266   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2267   PetscErrorCode ierr;
2268 
2269   PetscFunctionBegin;
2270   ierr = MatRealPart(a->A);CHKERRQ(ierr);
2271   ierr = MatRealPart(a->B);CHKERRQ(ierr);
2272   PetscFunctionReturn(0);
2273 }
2274 
2275 #undef __FUNCT__
2276 #define __FUNCT__ "MatImaginaryPart_MPIAIJ"
2277 PetscErrorCode MatImaginaryPart_MPIAIJ(Mat A)
2278 {
2279   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2280   PetscErrorCode ierr;
2281 
2282   PetscFunctionBegin;
2283   ierr = MatImaginaryPart(a->A);CHKERRQ(ierr);
2284   ierr = MatImaginaryPart(a->B);CHKERRQ(ierr);
2285   PetscFunctionReturn(0);
2286 }
2287 
2288 #undef __FUNCT__
2289 #define __FUNCT__ "MatGetRowMaxAbs_MPIAIJ"
2290 PetscErrorCode MatGetRowMaxAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2291 {
2292   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2293   PetscErrorCode ierr;
2294   PetscInt       i,*idxb = 0;
2295   PetscScalar    *va,*vb;
2296   Vec            vtmp;
2297 
2298   PetscFunctionBegin;
2299   ierr = MatGetRowMaxAbs(a->A,v,idx);CHKERRQ(ierr);
2300   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2301   if (idx) {
2302     for (i=0; i<A->rmap->n; i++) {
2303       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2304     }
2305   }
2306 
2307   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2308   if (idx) {
2309     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2310   }
2311   ierr = MatGetRowMaxAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2312   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2313 
2314   for (i=0; i<A->rmap->n; i++) {
2315     if (PetscAbsScalar(va[i]) < PetscAbsScalar(vb[i])) {
2316       va[i] = vb[i];
2317       if (idx) idx[i] = a->garray[idxb[i]];
2318     }
2319   }
2320 
2321   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2322   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2323   ierr = PetscFree(idxb);CHKERRQ(ierr);
2324   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2325   PetscFunctionReturn(0);
2326 }
2327 
2328 #undef __FUNCT__
2329 #define __FUNCT__ "MatGetRowMinAbs_MPIAIJ"
2330 PetscErrorCode MatGetRowMinAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2331 {
2332   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2333   PetscErrorCode ierr;
2334   PetscInt       i,*idxb = 0;
2335   PetscScalar    *va,*vb;
2336   Vec            vtmp;
2337 
2338   PetscFunctionBegin;
2339   ierr = MatGetRowMinAbs(a->A,v,idx);CHKERRQ(ierr);
2340   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2341   if (idx) {
2342     for (i=0; i<A->cmap->n; i++) {
2343       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2344     }
2345   }
2346 
2347   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2348   if (idx) {
2349     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2350   }
2351   ierr = MatGetRowMinAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2352   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2353 
2354   for (i=0; i<A->rmap->n; i++) {
2355     if (PetscAbsScalar(va[i]) > PetscAbsScalar(vb[i])) {
2356       va[i] = vb[i];
2357       if (idx) idx[i] = a->garray[idxb[i]];
2358     }
2359   }
2360 
2361   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2362   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2363   ierr = PetscFree(idxb);CHKERRQ(ierr);
2364   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2365   PetscFunctionReturn(0);
2366 }
2367 
2368 #undef __FUNCT__
2369 #define __FUNCT__ "MatGetRowMin_MPIAIJ"
2370 PetscErrorCode MatGetRowMin_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2371 {
2372   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2373   PetscInt       n      = A->rmap->n;
2374   PetscInt       cstart = A->cmap->rstart;
2375   PetscInt       *cmap  = mat->garray;
2376   PetscInt       *diagIdx, *offdiagIdx;
2377   Vec            diagV, offdiagV;
2378   PetscScalar    *a, *diagA, *offdiagA;
2379   PetscInt       r;
2380   PetscErrorCode ierr;
2381 
2382   PetscFunctionBegin;
2383   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2384   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &diagV);CHKERRQ(ierr);
2385   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &offdiagV);CHKERRQ(ierr);
2386   ierr = MatGetRowMin(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2387   ierr = MatGetRowMin(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2388   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2389   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2390   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2391   for (r = 0; r < n; ++r) {
2392     if (PetscAbsScalar(diagA[r]) <= PetscAbsScalar(offdiagA[r])) {
2393       a[r]   = diagA[r];
2394       idx[r] = cstart + diagIdx[r];
2395     } else {
2396       a[r]   = offdiagA[r];
2397       idx[r] = cmap[offdiagIdx[r]];
2398     }
2399   }
2400   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2401   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2402   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2403   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2404   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2405   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2406   PetscFunctionReturn(0);
2407 }
2408 
2409 #undef __FUNCT__
2410 #define __FUNCT__ "MatGetRowMax_MPIAIJ"
2411 PetscErrorCode MatGetRowMax_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2412 {
2413   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2414   PetscInt       n      = A->rmap->n;
2415   PetscInt       cstart = A->cmap->rstart;
2416   PetscInt       *cmap  = mat->garray;
2417   PetscInt       *diagIdx, *offdiagIdx;
2418   Vec            diagV, offdiagV;
2419   PetscScalar    *a, *diagA, *offdiagA;
2420   PetscInt       r;
2421   PetscErrorCode ierr;
2422 
2423   PetscFunctionBegin;
2424   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2425   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &diagV);CHKERRQ(ierr);
2426   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &offdiagV);CHKERRQ(ierr);
2427   ierr = MatGetRowMax(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2428   ierr = MatGetRowMax(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2429   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2430   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2431   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2432   for (r = 0; r < n; ++r) {
2433     if (PetscAbsScalar(diagA[r]) >= PetscAbsScalar(offdiagA[r])) {
2434       a[r]   = diagA[r];
2435       idx[r] = cstart + diagIdx[r];
2436     } else {
2437       a[r]   = offdiagA[r];
2438       idx[r] = cmap[offdiagIdx[r]];
2439     }
2440   }
2441   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2442   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2443   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2444   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2445   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2446   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2447   PetscFunctionReturn(0);
2448 }
2449 
2450 #undef __FUNCT__
2451 #define __FUNCT__ "MatGetSeqNonzeroStructure_MPIAIJ"
2452 PetscErrorCode MatGetSeqNonzeroStructure_MPIAIJ(Mat mat,Mat *newmat)
2453 {
2454   PetscErrorCode ierr;
2455   Mat            *dummy;
2456 
2457   PetscFunctionBegin;
2458   ierr    = MatGetSubMatrix_MPIAIJ_All(mat,MAT_DO_NOT_GET_VALUES,MAT_INITIAL_MATRIX,&dummy);CHKERRQ(ierr);
2459   *newmat = *dummy;
2460   ierr    = PetscFree(dummy);CHKERRQ(ierr);
2461   PetscFunctionReturn(0);
2462 }
2463 
2464 #undef __FUNCT__
2465 #define __FUNCT__ "MatInvertBlockDiagonal_MPIAIJ"
2466 PetscErrorCode  MatInvertBlockDiagonal_MPIAIJ(Mat A,const PetscScalar **values)
2467 {
2468   Mat_MPIAIJ     *a = (Mat_MPIAIJ*) A->data;
2469   PetscErrorCode ierr;
2470 
2471   PetscFunctionBegin;
2472   ierr = MatInvertBlockDiagonal(a->A,values);CHKERRQ(ierr);
2473   A->errortype = a->A->errortype;
2474   PetscFunctionReturn(0);
2475 }
2476 
2477 #undef __FUNCT__
2478 #define __FUNCT__ "MatSetRandom_MPIAIJ"
2479 static PetscErrorCode  MatSetRandom_MPIAIJ(Mat x,PetscRandom rctx)
2480 {
2481   PetscErrorCode ierr;
2482   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)x->data;
2483 
2484   PetscFunctionBegin;
2485   ierr = MatSetRandom(aij->A,rctx);CHKERRQ(ierr);
2486   ierr = MatSetRandom(aij->B,rctx);CHKERRQ(ierr);
2487   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2488   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2489   PetscFunctionReturn(0);
2490 }
2491 
2492 #undef __FUNCT__
2493 #define __FUNCT__ "MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ"
2494 PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ(Mat A,PetscBool sc)
2495 {
2496   PetscFunctionBegin;
2497   if (sc) A->ops->increaseoverlap = MatIncreaseOverlap_MPIAIJ_Scalable;
2498   else A->ops->increaseoverlap    = MatIncreaseOverlap_MPIAIJ;
2499   PetscFunctionReturn(0);
2500 }
2501 
2502 #undef __FUNCT__
2503 #define __FUNCT__ "MatMPIAIJSetUseScalableIncreaseOverlap"
2504 /*@
2505    MatMPIAIJSetUseScalableIncreaseOverlap - Determine if the matrix uses a scalable algorithm to compute the overlap
2506 
2507    Collective on Mat
2508 
2509    Input Parameters:
2510 +    A - the matrix
2511 -    sc - PETSC_TRUE indicates use the scalable algorithm (default is not to use the scalable algorithm)
2512 
2513  Level: advanced
2514 
2515 @*/
2516 PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap(Mat A,PetscBool sc)
2517 {
2518   PetscErrorCode       ierr;
2519 
2520   PetscFunctionBegin;
2521   ierr = PetscTryMethod(A,"MatMPIAIJSetUseScalableIncreaseOverlap_C",(Mat,PetscBool),(A,sc));CHKERRQ(ierr);
2522   PetscFunctionReturn(0);
2523 }
2524 
2525 #undef __FUNCT__
2526 #define __FUNCT__ "MatSetFromOptions_MPIAIJ"
2527 PetscErrorCode MatSetFromOptions_MPIAIJ(PetscOptionItems *PetscOptionsObject,Mat A)
2528 {
2529   PetscErrorCode       ierr;
2530   PetscBool            sc = PETSC_FALSE,flg;
2531 
2532   PetscFunctionBegin;
2533   ierr = PetscOptionsHead(PetscOptionsObject,"MPIAIJ options");CHKERRQ(ierr);
2534   ierr = PetscObjectOptionsBegin((PetscObject)A);
2535     if (A->ops->increaseoverlap == MatIncreaseOverlap_MPIAIJ_Scalable) sc = PETSC_TRUE;
2536     ierr = PetscOptionsBool("-mat_increase_overlap_scalable","Use a scalable algorithm to compute the overlap","MatIncreaseOverlap",sc,&sc,&flg);CHKERRQ(ierr);
2537     if (flg) {
2538       ierr = MatMPIAIJSetUseScalableIncreaseOverlap(A,sc);CHKERRQ(ierr);
2539     }
2540   ierr = PetscOptionsEnd();CHKERRQ(ierr);
2541   PetscFunctionReturn(0);
2542 }
2543 
2544 #undef __FUNCT__
2545 #define __FUNCT__ "MatShift_MPIAIJ"
2546 PetscErrorCode MatShift_MPIAIJ(Mat Y,PetscScalar a)
2547 {
2548   PetscErrorCode ierr;
2549   Mat_MPIAIJ     *maij = (Mat_MPIAIJ*)Y->data;
2550   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)maij->A->data;
2551 
2552   PetscFunctionBegin;
2553   if (!Y->preallocated) {
2554     ierr = MatMPIAIJSetPreallocation(Y,1,NULL,0,NULL);CHKERRQ(ierr);
2555   } else if (!aij->nz) {
2556     PetscInt nonew = aij->nonew;
2557     ierr = MatSeqAIJSetPreallocation(maij->A,1,NULL);CHKERRQ(ierr);
2558     aij->nonew = nonew;
2559   }
2560   ierr = MatShift_Basic(Y,a);CHKERRQ(ierr);
2561   PetscFunctionReturn(0);
2562 }
2563 
2564 #undef __FUNCT__
2565 #define __FUNCT__ "MatMissingDiagonal_MPIAIJ"
2566 PetscErrorCode MatMissingDiagonal_MPIAIJ(Mat A,PetscBool  *missing,PetscInt *d)
2567 {
2568   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2569   PetscErrorCode ierr;
2570 
2571   PetscFunctionBegin;
2572   if (A->rmap->n != A->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only works for square matrices");
2573   ierr = MatMissingDiagonal(a->A,missing,d);CHKERRQ(ierr);
2574   if (d) {
2575     PetscInt rstart;
2576     ierr = MatGetOwnershipRange(A,&rstart,NULL);CHKERRQ(ierr);
2577     *d += rstart;
2578 
2579   }
2580   PetscFunctionReturn(0);
2581 }
2582 
2583 
2584 /* -------------------------------------------------------------------*/
2585 static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
2586                                        MatGetRow_MPIAIJ,
2587                                        MatRestoreRow_MPIAIJ,
2588                                        MatMult_MPIAIJ,
2589                                 /* 4*/ MatMultAdd_MPIAIJ,
2590                                        MatMultTranspose_MPIAIJ,
2591                                        MatMultTransposeAdd_MPIAIJ,
2592                                        0,
2593                                        0,
2594                                        0,
2595                                 /*10*/ 0,
2596                                        0,
2597                                        0,
2598                                        MatSOR_MPIAIJ,
2599                                        MatTranspose_MPIAIJ,
2600                                 /*15*/ MatGetInfo_MPIAIJ,
2601                                        MatEqual_MPIAIJ,
2602                                        MatGetDiagonal_MPIAIJ,
2603                                        MatDiagonalScale_MPIAIJ,
2604                                        MatNorm_MPIAIJ,
2605                                 /*20*/ MatAssemblyBegin_MPIAIJ,
2606                                        MatAssemblyEnd_MPIAIJ,
2607                                        MatSetOption_MPIAIJ,
2608                                        MatZeroEntries_MPIAIJ,
2609                                 /*24*/ MatZeroRows_MPIAIJ,
2610                                        0,
2611                                        0,
2612                                        0,
2613                                        0,
2614                                 /*29*/ MatSetUp_MPIAIJ,
2615                                        0,
2616                                        0,
2617                                        0,
2618                                        0,
2619                                 /*34*/ MatDuplicate_MPIAIJ,
2620                                        0,
2621                                        0,
2622                                        0,
2623                                        0,
2624                                 /*39*/ MatAXPY_MPIAIJ,
2625                                        MatGetSubMatrices_MPIAIJ,
2626                                        MatIncreaseOverlap_MPIAIJ,
2627                                        MatGetValues_MPIAIJ,
2628                                        MatCopy_MPIAIJ,
2629                                 /*44*/ MatGetRowMax_MPIAIJ,
2630                                        MatScale_MPIAIJ,
2631                                        MatShift_MPIAIJ,
2632                                        MatDiagonalSet_MPIAIJ,
2633                                        MatZeroRowsColumns_MPIAIJ,
2634                                 /*49*/ MatSetRandom_MPIAIJ,
2635                                        0,
2636                                        0,
2637                                        0,
2638                                        0,
2639                                 /*54*/ MatFDColoringCreate_MPIXAIJ,
2640                                        0,
2641                                        MatSetUnfactored_MPIAIJ,
2642                                        MatPermute_MPIAIJ,
2643                                        0,
2644                                 /*59*/ MatGetSubMatrix_MPIAIJ,
2645                                        MatDestroy_MPIAIJ,
2646                                        MatView_MPIAIJ,
2647                                        0,
2648                                        MatMatMatMult_MPIAIJ_MPIAIJ_MPIAIJ,
2649                                 /*64*/ MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ,
2650                                        MatMatMatMultNumeric_MPIAIJ_MPIAIJ_MPIAIJ,
2651                                        0,
2652                                        0,
2653                                        0,
2654                                 /*69*/ MatGetRowMaxAbs_MPIAIJ,
2655                                        MatGetRowMinAbs_MPIAIJ,
2656                                        0,
2657                                        MatSetColoring_MPIAIJ,
2658                                        0,
2659                                        MatSetValuesAdifor_MPIAIJ,
2660                                 /*75*/ MatFDColoringApply_AIJ,
2661                                        MatSetFromOptions_MPIAIJ,
2662                                        0,
2663                                        0,
2664                                        MatFindZeroDiagonals_MPIAIJ,
2665                                 /*80*/ 0,
2666                                        0,
2667                                        0,
2668                                 /*83*/ MatLoad_MPIAIJ,
2669                                        0,
2670                                        0,
2671                                        0,
2672                                        0,
2673                                        0,
2674                                 /*89*/ MatMatMult_MPIAIJ_MPIAIJ,
2675                                        MatMatMultSymbolic_MPIAIJ_MPIAIJ,
2676                                        MatMatMultNumeric_MPIAIJ_MPIAIJ,
2677                                        MatPtAP_MPIAIJ_MPIAIJ,
2678                                        MatPtAPSymbolic_MPIAIJ_MPIAIJ,
2679                                 /*94*/ MatPtAPNumeric_MPIAIJ_MPIAIJ,
2680                                        0,
2681                                        0,
2682                                        0,
2683                                        0,
2684                                 /*99*/ 0,
2685                                        0,
2686                                        0,
2687                                        MatConjugate_MPIAIJ,
2688                                        0,
2689                                 /*104*/MatSetValuesRow_MPIAIJ,
2690                                        MatRealPart_MPIAIJ,
2691                                        MatImaginaryPart_MPIAIJ,
2692                                        0,
2693                                        0,
2694                                 /*109*/0,
2695                                        0,
2696                                        MatGetRowMin_MPIAIJ,
2697                                        0,
2698                                        MatMissingDiagonal_MPIAIJ,
2699                                 /*114*/MatGetSeqNonzeroStructure_MPIAIJ,
2700                                        0,
2701                                        MatGetGhosts_MPIAIJ,
2702                                        0,
2703                                        0,
2704                                 /*119*/0,
2705                                        0,
2706                                        0,
2707                                        0,
2708                                        MatGetMultiProcBlock_MPIAIJ,
2709                                 /*124*/MatFindNonzeroRows_MPIAIJ,
2710                                        MatGetColumnNorms_MPIAIJ,
2711                                        MatInvertBlockDiagonal_MPIAIJ,
2712                                        0,
2713                                        MatGetSubMatricesMPI_MPIAIJ,
2714                                 /*129*/0,
2715                                        MatTransposeMatMult_MPIAIJ_MPIAIJ,
2716                                        MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ,
2717                                        MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ,
2718                                        0,
2719                                 /*134*/0,
2720                                        0,
2721                                        0,
2722                                        0,
2723                                        0,
2724                                 /*139*/0,
2725                                        0,
2726                                        0,
2727                                        MatFDColoringSetUp_MPIXAIJ,
2728                                        MatFindOffBlockDiagonalEntries_MPIAIJ,
2729                                 /*144*/MatCreateMPIMatConcatenateSeqMat_MPIAIJ
2730 };
2731 
2732 /* ----------------------------------------------------------------------------------------*/
2733 
2734 #undef __FUNCT__
2735 #define __FUNCT__ "MatStoreValues_MPIAIJ"
2736 PetscErrorCode  MatStoreValues_MPIAIJ(Mat mat)
2737 {
2738   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2739   PetscErrorCode ierr;
2740 
2741   PetscFunctionBegin;
2742   ierr = MatStoreValues(aij->A);CHKERRQ(ierr);
2743   ierr = MatStoreValues(aij->B);CHKERRQ(ierr);
2744   PetscFunctionReturn(0);
2745 }
2746 
2747 #undef __FUNCT__
2748 #define __FUNCT__ "MatRetrieveValues_MPIAIJ"
2749 PetscErrorCode  MatRetrieveValues_MPIAIJ(Mat mat)
2750 {
2751   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2752   PetscErrorCode ierr;
2753 
2754   PetscFunctionBegin;
2755   ierr = MatRetrieveValues(aij->A);CHKERRQ(ierr);
2756   ierr = MatRetrieveValues(aij->B);CHKERRQ(ierr);
2757   PetscFunctionReturn(0);
2758 }
2759 
2760 #undef __FUNCT__
2761 #define __FUNCT__ "MatMPIAIJSetPreallocation_MPIAIJ"
2762 PetscErrorCode  MatMPIAIJSetPreallocation_MPIAIJ(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
2763 {
2764   Mat_MPIAIJ     *b;
2765   PetscErrorCode ierr;
2766 
2767   PetscFunctionBegin;
2768   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
2769   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
2770   b = (Mat_MPIAIJ*)B->data;
2771 
2772   if (!B->preallocated) {
2773     /* Explicitly create 2 MATSEQAIJ matrices. */
2774     ierr = MatCreate(PETSC_COMM_SELF,&b->A);CHKERRQ(ierr);
2775     ierr = MatSetSizes(b->A,B->rmap->n,B->cmap->n,B->rmap->n,B->cmap->n);CHKERRQ(ierr);
2776     ierr = MatSetBlockSizesFromMats(b->A,B,B);CHKERRQ(ierr);
2777     ierr = MatSetType(b->A,MATSEQAIJ);CHKERRQ(ierr);
2778     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->A);CHKERRQ(ierr);
2779     ierr = MatCreate(PETSC_COMM_SELF,&b->B);CHKERRQ(ierr);
2780     ierr = MatSetSizes(b->B,B->rmap->n,B->cmap->N,B->rmap->n,B->cmap->N);CHKERRQ(ierr);
2781     ierr = MatSetBlockSizesFromMats(b->B,B,B);CHKERRQ(ierr);
2782     ierr = MatSetType(b->B,MATSEQAIJ);CHKERRQ(ierr);
2783     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->B);CHKERRQ(ierr);
2784   }
2785 
2786   ierr = MatSeqAIJSetPreallocation(b->A,d_nz,d_nnz);CHKERRQ(ierr);
2787   ierr = MatSeqAIJSetPreallocation(b->B,o_nz,o_nnz);CHKERRQ(ierr);
2788   B->preallocated = PETSC_TRUE;
2789   PetscFunctionReturn(0);
2790 }
2791 
2792 #undef __FUNCT__
2793 #define __FUNCT__ "MatDuplicate_MPIAIJ"
2794 PetscErrorCode MatDuplicate_MPIAIJ(Mat matin,MatDuplicateOption cpvalues,Mat *newmat)
2795 {
2796   Mat            mat;
2797   Mat_MPIAIJ     *a,*oldmat = (Mat_MPIAIJ*)matin->data;
2798   PetscErrorCode ierr;
2799 
2800   PetscFunctionBegin;
2801   *newmat = 0;
2802   ierr    = MatCreate(PetscObjectComm((PetscObject)matin),&mat);CHKERRQ(ierr);
2803   ierr    = MatSetSizes(mat,matin->rmap->n,matin->cmap->n,matin->rmap->N,matin->cmap->N);CHKERRQ(ierr);
2804   ierr    = MatSetBlockSizesFromMats(mat,matin,matin);CHKERRQ(ierr);
2805   ierr    = MatSetType(mat,((PetscObject)matin)->type_name);CHKERRQ(ierr);
2806   ierr    = PetscMemcpy(mat->ops,matin->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
2807   a       = (Mat_MPIAIJ*)mat->data;
2808 
2809   mat->factortype   = matin->factortype;
2810   mat->assembled    = PETSC_TRUE;
2811   mat->insertmode   = NOT_SET_VALUES;
2812   mat->preallocated = PETSC_TRUE;
2813 
2814   a->size         = oldmat->size;
2815   a->rank         = oldmat->rank;
2816   a->donotstash   = oldmat->donotstash;
2817   a->roworiented  = oldmat->roworiented;
2818   a->rowindices   = 0;
2819   a->rowvalues    = 0;
2820   a->getrowactive = PETSC_FALSE;
2821 
2822   ierr = PetscLayoutReference(matin->rmap,&mat->rmap);CHKERRQ(ierr);
2823   ierr = PetscLayoutReference(matin->cmap,&mat->cmap);CHKERRQ(ierr);
2824 
2825   if (oldmat->colmap) {
2826 #if defined(PETSC_USE_CTABLE)
2827     ierr = PetscTableCreateCopy(oldmat->colmap,&a->colmap);CHKERRQ(ierr);
2828 #else
2829     ierr = PetscMalloc1(mat->cmap->N,&a->colmap);CHKERRQ(ierr);
2830     ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2831     ierr = PetscMemcpy(a->colmap,oldmat->colmap,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2832 #endif
2833   } else a->colmap = 0;
2834   if (oldmat->garray) {
2835     PetscInt len;
2836     len  = oldmat->B->cmap->n;
2837     ierr = PetscMalloc1(len+1,&a->garray);CHKERRQ(ierr);
2838     ierr = PetscLogObjectMemory((PetscObject)mat,len*sizeof(PetscInt));CHKERRQ(ierr);
2839     if (len) { ierr = PetscMemcpy(a->garray,oldmat->garray,len*sizeof(PetscInt));CHKERRQ(ierr); }
2840   } else a->garray = 0;
2841 
2842   ierr    = VecDuplicate(oldmat->lvec,&a->lvec);CHKERRQ(ierr);
2843   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->lvec);CHKERRQ(ierr);
2844   ierr    = VecScatterCopy(oldmat->Mvctx,&a->Mvctx);CHKERRQ(ierr);
2845   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->Mvctx);CHKERRQ(ierr);
2846   ierr    = MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
2847   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->A);CHKERRQ(ierr);
2848   ierr    = MatDuplicate(oldmat->B,cpvalues,&a->B);CHKERRQ(ierr);
2849   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->B);CHKERRQ(ierr);
2850   ierr    = PetscFunctionListDuplicate(((PetscObject)matin)->qlist,&((PetscObject)mat)->qlist);CHKERRQ(ierr);
2851   *newmat = mat;
2852   PetscFunctionReturn(0);
2853 }
2854 
2855 
2856 
2857 #undef __FUNCT__
2858 #define __FUNCT__ "MatLoad_MPIAIJ"
2859 PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
2860 {
2861   PetscScalar    *vals,*svals;
2862   MPI_Comm       comm;
2863   PetscErrorCode ierr;
2864   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
2865   PetscInt       i,nz,j,rstart,rend,mmax,maxnz = 0;
2866   PetscInt       header[4],*rowlengths = 0,M,N,m,*cols;
2867   PetscInt       *ourlens = NULL,*procsnz = NULL,*offlens = NULL,jj,*mycols,*smycols;
2868   PetscInt       cend,cstart,n,*rowners;
2869   int            fd;
2870   PetscInt       bs = newMat->rmap->bs;
2871 
2872   PetscFunctionBegin;
2873   /* force binary viewer to load .info file if it has not yet done so */
2874   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
2875   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
2876   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2877   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2878   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
2879   if (!rank) {
2880     ierr = PetscBinaryRead(fd,(char*)header,4,PETSC_INT);CHKERRQ(ierr);
2881     if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
2882     if (header[3] < 0) SETERRQ(PetscObjectComm((PetscObject)newMat),PETSC_ERR_FILE_UNEXPECTED,"Matrix stored in special format on disk,cannot load as MPIAIJ");
2883   }
2884 
2885   ierr = PetscOptionsBegin(comm,NULL,"Options for loading MPIAIJ matrix","Mat");CHKERRQ(ierr);
2886   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
2887   ierr = PetscOptionsEnd();CHKERRQ(ierr);
2888   if (bs < 0) bs = 1;
2889 
2890   ierr = MPI_Bcast(header+1,3,MPIU_INT,0,comm);CHKERRQ(ierr);
2891   M    = header[1]; N = header[2];
2892 
2893   /* If global sizes are set, check if they are consistent with that given in the file */
2894   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);
2895   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);
2896 
2897   /* determine ownership of all (block) rows */
2898   if (M%bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Inconsistent # of rows (%d) and block size (%d)",M,bs);
2899   if (newMat->rmap->n < 0) m = bs*((M/bs)/size + (((M/bs) % size) > rank));    /* PETSC_DECIDE */
2900   else m = newMat->rmap->n; /* Set by user */
2901 
2902   ierr = PetscMalloc1(size+1,&rowners);CHKERRQ(ierr);
2903   ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
2904 
2905   /* First process needs enough room for process with most rows */
2906   if (!rank) {
2907     mmax = rowners[1];
2908     for (i=2; i<=size; i++) {
2909       mmax = PetscMax(mmax, rowners[i]);
2910     }
2911   } else mmax = -1;             /* unused, but compilers complain */
2912 
2913   rowners[0] = 0;
2914   for (i=2; i<=size; i++) {
2915     rowners[i] += rowners[i-1];
2916   }
2917   rstart = rowners[rank];
2918   rend   = rowners[rank+1];
2919 
2920   /* distribute row lengths to all processors */
2921   ierr = PetscMalloc2(m,&ourlens,m,&offlens);CHKERRQ(ierr);
2922   if (!rank) {
2923     ierr = PetscBinaryRead(fd,ourlens,m,PETSC_INT);CHKERRQ(ierr);
2924     ierr = PetscMalloc1(mmax,&rowlengths);CHKERRQ(ierr);
2925     ierr = PetscCalloc1(size,&procsnz);CHKERRQ(ierr);
2926     for (j=0; j<m; j++) {
2927       procsnz[0] += ourlens[j];
2928     }
2929     for (i=1; i<size; i++) {
2930       ierr = PetscBinaryRead(fd,rowlengths,rowners[i+1]-rowners[i],PETSC_INT);CHKERRQ(ierr);
2931       /* calculate the number of nonzeros on each processor */
2932       for (j=0; j<rowners[i+1]-rowners[i]; j++) {
2933         procsnz[i] += rowlengths[j];
2934       }
2935       ierr = MPIULong_Send(rowlengths,rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2936     }
2937     ierr = PetscFree(rowlengths);CHKERRQ(ierr);
2938   } else {
2939     ierr = MPIULong_Recv(ourlens,m,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2940   }
2941 
2942   if (!rank) {
2943     /* determine max buffer needed and allocate it */
2944     maxnz = 0;
2945     for (i=0; i<size; i++) {
2946       maxnz = PetscMax(maxnz,procsnz[i]);
2947     }
2948     ierr = PetscMalloc1(maxnz,&cols);CHKERRQ(ierr);
2949 
2950     /* read in my part of the matrix column indices  */
2951     nz   = procsnz[0];
2952     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2953     ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);
2954 
2955     /* read in every one elses and ship off */
2956     for (i=1; i<size; i++) {
2957       nz   = procsnz[i];
2958       ierr = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
2959       ierr = MPIULong_Send(cols,nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2960     }
2961     ierr = PetscFree(cols);CHKERRQ(ierr);
2962   } else {
2963     /* determine buffer space needed for message */
2964     nz = 0;
2965     for (i=0; i<m; i++) {
2966       nz += ourlens[i];
2967     }
2968     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2969 
2970     /* receive message of column indices*/
2971     ierr = MPIULong_Recv(mycols,nz,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2972   }
2973 
2974   /* determine column ownership if matrix is not square */
2975   if (N != M) {
2976     if (newMat->cmap->n < 0) n = N/size + ((N % size) > rank);
2977     else n = newMat->cmap->n;
2978     ierr   = MPI_Scan(&n,&cend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
2979     cstart = cend - n;
2980   } else {
2981     cstart = rstart;
2982     cend   = rend;
2983     n      = cend - cstart;
2984   }
2985 
2986   /* loop over local rows, determining number of off diagonal entries */
2987   ierr = PetscMemzero(offlens,m*sizeof(PetscInt));CHKERRQ(ierr);
2988   jj   = 0;
2989   for (i=0; i<m; i++) {
2990     for (j=0; j<ourlens[i]; j++) {
2991       if (mycols[jj] < cstart || mycols[jj] >= cend) offlens[i]++;
2992       jj++;
2993     }
2994   }
2995 
2996   for (i=0; i<m; i++) {
2997     ourlens[i] -= offlens[i];
2998   }
2999   ierr = MatSetSizes(newMat,m,n,M,N);CHKERRQ(ierr);
3000 
3001   if (bs > 1) {ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);}
3002 
3003   ierr = MatMPIAIJSetPreallocation(newMat,0,ourlens,0,offlens);CHKERRQ(ierr);
3004 
3005   for (i=0; i<m; i++) {
3006     ourlens[i] += offlens[i];
3007   }
3008 
3009   if (!rank) {
3010     ierr = PetscMalloc1(maxnz+1,&vals);CHKERRQ(ierr);
3011 
3012     /* read in my part of the matrix numerical values  */
3013     nz   = procsnz[0];
3014     ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
3015 
3016     /* insert into matrix */
3017     jj      = rstart;
3018     smycols = mycols;
3019     svals   = vals;
3020     for (i=0; i<m; i++) {
3021       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
3022       smycols += ourlens[i];
3023       svals   += ourlens[i];
3024       jj++;
3025     }
3026 
3027     /* read in other processors and ship out */
3028     for (i=1; i<size; i++) {
3029       nz   = procsnz[i];
3030       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
3031       ierr = MPIULong_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
3032     }
3033     ierr = PetscFree(procsnz);CHKERRQ(ierr);
3034   } else {
3035     /* receive numeric values */
3036     ierr = PetscMalloc1(nz+1,&vals);CHKERRQ(ierr);
3037 
3038     /* receive message of values*/
3039     ierr = MPIULong_Recv(vals,nz,MPIU_SCALAR,0,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
3040 
3041     /* insert into matrix */
3042     jj      = rstart;
3043     smycols = mycols;
3044     svals   = vals;
3045     for (i=0; i<m; i++) {
3046       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
3047       smycols += ourlens[i];
3048       svals   += ourlens[i];
3049       jj++;
3050     }
3051   }
3052   ierr = PetscFree2(ourlens,offlens);CHKERRQ(ierr);
3053   ierr = PetscFree(vals);CHKERRQ(ierr);
3054   ierr = PetscFree(mycols);CHKERRQ(ierr);
3055   ierr = PetscFree(rowners);CHKERRQ(ierr);
3056   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3057   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3058   PetscFunctionReturn(0);
3059 }
3060 
3061 #undef __FUNCT__
3062 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ"
3063 /* TODO: Not scalable because of ISAllGather() unless getting all columns. */
3064 PetscErrorCode MatGetSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3065 {
3066   PetscErrorCode ierr;
3067   IS             iscol_local;
3068   PetscInt       csize;
3069 
3070   PetscFunctionBegin;
3071   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3072   if (call == MAT_REUSE_MATRIX) {
3073     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3074     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3075   } else {
3076     /* check if we are grabbing all columns*/
3077     PetscBool    isstride;
3078     PetscMPIInt  lisstride = 0,gisstride;
3079     ierr = PetscObjectTypeCompare((PetscObject)iscol,ISSTRIDE,&isstride);CHKERRQ(ierr);
3080     if (isstride) {
3081       PetscInt  start,len,mstart,mlen;
3082       ierr = ISStrideGetInfo(iscol,&start,NULL);CHKERRQ(ierr);
3083       ierr = ISGetLocalSize(iscol,&len);CHKERRQ(ierr);
3084       ierr = MatGetOwnershipRangeColumn(mat,&mstart,&mlen);CHKERRQ(ierr);
3085       if (mstart == start && mlen-mstart == len) lisstride = 1;
3086     }
3087     ierr = MPIU_Allreduce(&lisstride,&gisstride,1,MPI_INT,MPI_MIN,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
3088     if (gisstride) {
3089       PetscInt N;
3090       ierr = MatGetSize(mat,NULL,&N);CHKERRQ(ierr);
3091       ierr = ISCreateStride(PetscObjectComm((PetscObject)mat),N,0,1,&iscol_local);CHKERRQ(ierr);
3092       ierr = ISSetIdentity(iscol_local);CHKERRQ(ierr);
3093       ierr = PetscInfo(mat,"Optimizing for obtaining all columns of the matrix; skipping ISAllGather()\n");CHKERRQ(ierr);
3094     } else {
3095       PetscInt cbs;
3096       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
3097       ierr = ISAllGather(iscol,&iscol_local);CHKERRQ(ierr);
3098       ierr = ISSetBlockSize(iscol_local,cbs);CHKERRQ(ierr);
3099     }
3100   }
3101   ierr = MatGetSubMatrix_MPIAIJ_Private(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
3102   if (call == MAT_INITIAL_MATRIX) {
3103     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3104     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3105   }
3106   PetscFunctionReturn(0);
3107 }
3108 
3109 extern PetscErrorCode MatGetSubMatrices_MPIAIJ_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool*,Mat*);
3110 #undef __FUNCT__
3111 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ_Private"
3112 /*
3113     Not great since it makes two copies of the submatrix, first an SeqAIJ
3114   in local and then by concatenating the local matrices the end result.
3115   Writing it directly would be much like MatGetSubMatrices_MPIAIJ()
3116 
3117   Note: This requires a sequential iscol with all indices.
3118 */
3119 PetscErrorCode MatGetSubMatrix_MPIAIJ_Private(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3120 {
3121   PetscErrorCode ierr;
3122   PetscMPIInt    rank,size;
3123   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3124   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal,ncol;
3125   PetscBool      allcolumns, colflag;
3126   Mat            M,Mreuse;
3127   MatScalar      *vwork,*aa;
3128   MPI_Comm       comm;
3129   Mat_SeqAIJ     *aij;
3130 
3131   PetscFunctionBegin;
3132   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3133   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3134   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3135 
3136   ierr = ISIdentity(iscol,&colflag);CHKERRQ(ierr);
3137   ierr = ISGetLocalSize(iscol,&ncol);CHKERRQ(ierr);
3138   if (colflag && ncol == mat->cmap->N) {
3139     allcolumns = PETSC_TRUE;
3140     ierr = PetscInfo(mat,"Optimizing for obtaining all columns of the matrix\n");CHKERRQ(ierr);
3141   } else {
3142     allcolumns = PETSC_FALSE;
3143   }
3144   if (call ==  MAT_REUSE_MATRIX) {
3145     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3146     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3147     ierr = MatGetSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,&allcolumns,&Mreuse);CHKERRQ(ierr);
3148   } else {
3149     ierr = MatGetSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&allcolumns,&Mreuse);CHKERRQ(ierr);
3150   }
3151 
3152   /*
3153       m - number of local rows
3154       n - number of columns (same on all processors)
3155       rstart - first row in new global matrix generated
3156   */
3157   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3158   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3159   if (call == MAT_INITIAL_MATRIX) {
3160     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3161     ii  = aij->i;
3162     jj  = aij->j;
3163 
3164     /*
3165         Determine the number of non-zeros in the diagonal and off-diagonal
3166         portions of the matrix in order to do correct preallocation
3167     */
3168 
3169     /* first get start and end of "diagonal" columns */
3170     if (csize == PETSC_DECIDE) {
3171       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3172       if (mglobal == n) { /* square matrix */
3173         nlocal = m;
3174       } else {
3175         nlocal = n/size + ((n % size) > rank);
3176       }
3177     } else {
3178       nlocal = csize;
3179     }
3180     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3181     rstart = rend - nlocal;
3182     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);
3183 
3184     /* next, compute all the lengths */
3185     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3186     olens = dlens + m;
3187     for (i=0; i<m; i++) {
3188       jend = ii[i+1] - ii[i];
3189       olen = 0;
3190       dlen = 0;
3191       for (j=0; j<jend; j++) {
3192         if (*jj < rstart || *jj >= rend) olen++;
3193         else dlen++;
3194         jj++;
3195       }
3196       olens[i] = olen;
3197       dlens[i] = dlen;
3198     }
3199     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3200     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3201     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3202     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3203     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3204     ierr = PetscFree(dlens);CHKERRQ(ierr);
3205   } else {
3206     PetscInt ml,nl;
3207 
3208     M    = *newmat;
3209     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3210     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3211     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3212     /*
3213          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3214        rather than the slower MatSetValues().
3215     */
3216     M->was_assembled = PETSC_TRUE;
3217     M->assembled     = PETSC_FALSE;
3218   }
3219   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3220   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3221   ii   = aij->i;
3222   jj   = aij->j;
3223   aa   = aij->a;
3224   for (i=0; i<m; i++) {
3225     row   = rstart + i;
3226     nz    = ii[i+1] - ii[i];
3227     cwork = jj;     jj += nz;
3228     vwork = aa;     aa += nz;
3229     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3230   }
3231 
3232   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3233   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3234   *newmat = M;
3235 
3236   /* save submatrix used in processor for next request */
3237   if (call ==  MAT_INITIAL_MATRIX) {
3238     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3239     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3240   }
3241   PetscFunctionReturn(0);
3242 }
3243 
3244 #undef __FUNCT__
3245 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR_MPIAIJ"
3246 PetscErrorCode  MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3247 {
3248   PetscInt       m,cstart, cend,j,nnz,i,d;
3249   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3250   const PetscInt *JJ;
3251   PetscScalar    *values;
3252   PetscErrorCode ierr;
3253 
3254   PetscFunctionBegin;
3255   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3256 
3257   ierr   = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3258   ierr   = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3259   m      = B->rmap->n;
3260   cstart = B->cmap->rstart;
3261   cend   = B->cmap->rend;
3262   rstart = B->rmap->rstart;
3263 
3264   ierr = PetscMalloc2(m,&d_nnz,m,&o_nnz);CHKERRQ(ierr);
3265 
3266 #if defined(PETSC_USE_DEBUGGING)
3267   for (i=0; i<m; i++) {
3268     nnz = Ii[i+1]- Ii[i];
3269     JJ  = J + Ii[i];
3270     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3271     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3272     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);
3273   }
3274 #endif
3275 
3276   for (i=0; i<m; i++) {
3277     nnz     = Ii[i+1]- Ii[i];
3278     JJ      = J + Ii[i];
3279     nnz_max = PetscMax(nnz_max,nnz);
3280     d       = 0;
3281     for (j=0; j<nnz; j++) {
3282       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3283     }
3284     d_nnz[i] = d;
3285     o_nnz[i] = nnz - d;
3286   }
3287   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3288   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3289 
3290   if (v) values = (PetscScalar*)v;
3291   else {
3292     ierr = PetscCalloc1(nnz_max+1,&values);CHKERRQ(ierr);
3293   }
3294 
3295   for (i=0; i<m; i++) {
3296     ii   = i + rstart;
3297     nnz  = Ii[i+1]- Ii[i];
3298     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3299   }
3300   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3301   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3302 
3303   if (!v) {
3304     ierr = PetscFree(values);CHKERRQ(ierr);
3305   }
3306   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3307   PetscFunctionReturn(0);
3308 }
3309 
3310 #undef __FUNCT__
3311 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR"
3312 /*@
3313    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3314    (the default parallel PETSc format).
3315 
3316    Collective on MPI_Comm
3317 
3318    Input Parameters:
3319 +  B - the matrix
3320 .  i - the indices into j for the start of each local row (starts with zero)
3321 .  j - the column indices for each local row (starts with zero)
3322 -  v - optional values in the matrix
3323 
3324    Level: developer
3325 
3326    Notes:
3327        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3328      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3329      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3330 
3331        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3332 
3333        The format which is used for the sparse matrix input, is equivalent to a
3334     row-major ordering.. i.e for the following matrix, the input data expected is
3335     as shown
3336 
3337 $        1 0 0
3338 $        2 0 3     P0
3339 $       -------
3340 $        4 5 6     P1
3341 $
3342 $     Process0 [P0]: rows_owned=[0,1]
3343 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3344 $        j =  {0,0,2}  [size = 3]
3345 $        v =  {1,2,3}  [size = 3]
3346 $
3347 $     Process1 [P1]: rows_owned=[2]
3348 $        i =  {0,3}    [size = nrow+1  = 1+1]
3349 $        j =  {0,1,2}  [size = 3]
3350 $        v =  {4,5,6}  [size = 3]
3351 
3352 .keywords: matrix, aij, compressed row, sparse, parallel
3353 
3354 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MPIAIJ,
3355           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3356 @*/
3357 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3358 {
3359   PetscErrorCode ierr;
3360 
3361   PetscFunctionBegin;
3362   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3363   PetscFunctionReturn(0);
3364 }
3365 
3366 #undef __FUNCT__
3367 #define __FUNCT__ "MatMPIAIJSetPreallocation"
3368 /*@C
3369    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3370    (the default parallel PETSc format).  For good matrix assembly performance
3371    the user should preallocate the matrix storage by setting the parameters
3372    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3373    performance can be increased by more than a factor of 50.
3374 
3375    Collective on MPI_Comm
3376 
3377    Input Parameters:
3378 +  B - the matrix
3379 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3380            (same value is used for all local rows)
3381 .  d_nnz - array containing the number of nonzeros in the various rows of the
3382            DIAGONAL portion of the local submatrix (possibly different for each row)
3383            or NULL (PETSC_NULL_INTEGER in Fortran), if d_nz is used to specify the nonzero structure.
3384            The size of this array is equal to the number of local rows, i.e 'm'.
3385            For matrices that will be factored, you must leave room for (and set)
3386            the diagonal entry even if it is zero.
3387 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3388            submatrix (same value is used for all local rows).
3389 -  o_nnz - array containing the number of nonzeros in the various rows of the
3390            OFF-DIAGONAL portion of the local submatrix (possibly different for
3391            each row) or NULL (PETSC_NULL_INTEGER in Fortran), if o_nz is used to specify the nonzero
3392            structure. The size of this array is equal to the number
3393            of local rows, i.e 'm'.
3394 
3395    If the *_nnz parameter is given then the *_nz parameter is ignored
3396 
3397    The AIJ format (also called the Yale sparse matrix format or
3398    compressed row storage (CSR)), is fully compatible with standard Fortran 77
3399    storage.  The stored row and column indices begin with zero.
3400    See Users-Manual: ch_mat for details.
3401 
3402    The parallel matrix is partitioned such that the first m0 rows belong to
3403    process 0, the next m1 rows belong to process 1, the next m2 rows belong
3404    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
3405 
3406    The DIAGONAL portion of the local submatrix of a processor can be defined
3407    as the submatrix which is obtained by extraction the part corresponding to
3408    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
3409    first row that belongs to the processor, r2 is the last row belonging to
3410    the this processor, and c1-c2 is range of indices of the local part of a
3411    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
3412    common case of a square matrix, the row and column ranges are the same and
3413    the DIAGONAL part is also square. The remaining portion of the local
3414    submatrix (mxN) constitute the OFF-DIAGONAL portion.
3415 
3416    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3417 
3418    You can call MatGetInfo() to get information on how effective the preallocation was;
3419    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3420    You can also run with the option -info and look for messages with the string
3421    malloc in them to see if additional memory allocation was needed.
3422 
3423    Example usage:
3424 
3425    Consider the following 8x8 matrix with 34 non-zero values, that is
3426    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3427    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3428    as follows:
3429 
3430 .vb
3431             1  2  0  |  0  3  0  |  0  4
3432     Proc0   0  5  6  |  7  0  0  |  8  0
3433             9  0 10  | 11  0  0  | 12  0
3434     -------------------------------------
3435            13  0 14  | 15 16 17  |  0  0
3436     Proc1   0 18  0  | 19 20 21  |  0  0
3437             0  0  0  | 22 23  0  | 24  0
3438     -------------------------------------
3439     Proc2  25 26 27  |  0  0 28  | 29  0
3440            30  0  0  | 31 32 33  |  0 34
3441 .ve
3442 
3443    This can be represented as a collection of submatrices as:
3444 
3445 .vb
3446       A B C
3447       D E F
3448       G H I
3449 .ve
3450 
3451    Where the submatrices A,B,C are owned by proc0, D,E,F are
3452    owned by proc1, G,H,I are owned by proc2.
3453 
3454    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3455    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3456    The 'M','N' parameters are 8,8, and have the same values on all procs.
3457 
3458    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3459    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3460    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3461    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3462    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3463    matrix, ans [DF] as another SeqAIJ matrix.
3464 
3465    When d_nz, o_nz parameters are specified, d_nz storage elements are
3466    allocated for every row of the local diagonal submatrix, and o_nz
3467    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3468    One way to choose d_nz and o_nz is to use the max nonzerors per local
3469    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3470    In this case, the values of d_nz,o_nz are:
3471 .vb
3472      proc0 : dnz = 2, o_nz = 2
3473      proc1 : dnz = 3, o_nz = 2
3474      proc2 : dnz = 1, o_nz = 4
3475 .ve
3476    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3477    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3478    for proc3. i.e we are using 12+15+10=37 storage locations to store
3479    34 values.
3480 
3481    When d_nnz, o_nnz parameters are specified, the storage is specified
3482    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3483    In the above case the values for d_nnz,o_nnz are:
3484 .vb
3485      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3486      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3487      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3488 .ve
3489    Here the space allocated is sum of all the above values i.e 34, and
3490    hence pre-allocation is perfect.
3491 
3492    Level: intermediate
3493 
3494 .keywords: matrix, aij, compressed row, sparse, parallel
3495 
3496 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
3497           MPIAIJ, MatGetInfo(), PetscSplitOwnership()
3498 @*/
3499 PetscErrorCode  MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3500 {
3501   PetscErrorCode ierr;
3502 
3503   PetscFunctionBegin;
3504   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3505   PetscValidType(B,1);
3506   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
3507   PetscFunctionReturn(0);
3508 }
3509 
3510 #undef __FUNCT__
3511 #define __FUNCT__ "MatCreateMPIAIJWithArrays"
3512 /*@
3513      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
3514          CSR format the local rows.
3515 
3516    Collective on MPI_Comm
3517 
3518    Input Parameters:
3519 +  comm - MPI communicator
3520 .  m - number of local rows (Cannot be PETSC_DECIDE)
3521 .  n - This value should be the same as the local size used in creating the
3522        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3523        calculated if N is given) For square matrices n is almost always m.
3524 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3525 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3526 .   i - row indices
3527 .   j - column indices
3528 -   a - matrix values
3529 
3530    Output Parameter:
3531 .   mat - the matrix
3532 
3533    Level: intermediate
3534 
3535    Notes:
3536        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3537      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3538      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3539 
3540        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3541 
3542        The format which is used for the sparse matrix input, is equivalent to a
3543     row-major ordering.. i.e for the following matrix, the input data expected is
3544     as shown
3545 
3546 $        1 0 0
3547 $        2 0 3     P0
3548 $       -------
3549 $        4 5 6     P1
3550 $
3551 $     Process0 [P0]: rows_owned=[0,1]
3552 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3553 $        j =  {0,0,2}  [size = 3]
3554 $        v =  {1,2,3}  [size = 3]
3555 $
3556 $     Process1 [P1]: rows_owned=[2]
3557 $        i =  {0,3}    [size = nrow+1  = 1+1]
3558 $        j =  {0,1,2}  [size = 3]
3559 $        v =  {4,5,6}  [size = 3]
3560 
3561 .keywords: matrix, aij, compressed row, sparse, parallel
3562 
3563 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3564           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
3565 @*/
3566 PetscErrorCode  MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
3567 {
3568   PetscErrorCode ierr;
3569 
3570   PetscFunctionBegin;
3571   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
3572   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
3573   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
3574   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
3575   /* ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr); */
3576   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
3577   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
3578   PetscFunctionReturn(0);
3579 }
3580 
3581 #undef __FUNCT__
3582 #define __FUNCT__ "MatCreateAIJ"
3583 /*@C
3584    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
3585    (the default parallel PETSc format).  For good matrix assembly performance
3586    the user should preallocate the matrix storage by setting the parameters
3587    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3588    performance can be increased by more than a factor of 50.
3589 
3590    Collective on MPI_Comm
3591 
3592    Input Parameters:
3593 +  comm - MPI communicator
3594 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
3595            This value should be the same as the local size used in creating the
3596            y vector for the matrix-vector product y = Ax.
3597 .  n - This value should be the same as the local size used in creating the
3598        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3599        calculated if N is given) For square matrices n is almost always m.
3600 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3601 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3602 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3603            (same value is used for all local rows)
3604 .  d_nnz - array containing the number of nonzeros in the various rows of the
3605            DIAGONAL portion of the local submatrix (possibly different for each row)
3606            or NULL, if d_nz is used to specify the nonzero structure.
3607            The size of this array is equal to the number of local rows, i.e 'm'.
3608 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3609            submatrix (same value is used for all local rows).
3610 -  o_nnz - array containing the number of nonzeros in the various rows of the
3611            OFF-DIAGONAL portion of the local submatrix (possibly different for
3612            each row) or NULL, if o_nz is used to specify the nonzero
3613            structure. The size of this array is equal to the number
3614            of local rows, i.e 'm'.
3615 
3616    Output Parameter:
3617 .  A - the matrix
3618 
3619    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3620    MatXXXXSetPreallocation() paradgm instead of this routine directly.
3621    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3622 
3623    Notes:
3624    If the *_nnz parameter is given then the *_nz parameter is ignored
3625 
3626    m,n,M,N parameters specify the size of the matrix, and its partitioning across
3627    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
3628    storage requirements for this matrix.
3629 
3630    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
3631    processor than it must be used on all processors that share the object for
3632    that argument.
3633 
3634    The user MUST specify either the local or global matrix dimensions
3635    (possibly both).
3636 
3637    The parallel matrix is partitioned across processors such that the
3638    first m0 rows belong to process 0, the next m1 rows belong to
3639    process 1, the next m2 rows belong to process 2 etc.. where
3640    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
3641    values corresponding to [m x N] submatrix.
3642 
3643    The columns are logically partitioned with the n0 columns belonging
3644    to 0th partition, the next n1 columns belonging to the next
3645    partition etc.. where n0,n1,n2... are the input parameter 'n'.
3646 
3647    The DIAGONAL portion of the local submatrix on any given processor
3648    is the submatrix corresponding to the rows and columns m,n
3649    corresponding to the given processor. i.e diagonal matrix on
3650    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
3651    etc. The remaining portion of the local submatrix [m x (N-n)]
3652    constitute the OFF-DIAGONAL portion. The example below better
3653    illustrates this concept.
3654 
3655    For a square global matrix we define each processor's diagonal portion
3656    to be its local rows and the corresponding columns (a square submatrix);
3657    each processor's off-diagonal portion encompasses the remainder of the
3658    local matrix (a rectangular submatrix).
3659 
3660    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3661 
3662    When calling this routine with a single process communicator, a matrix of
3663    type SEQAIJ is returned.  If a matrix of type MPIAIJ is desired for this
3664    type of communicator, use the construction mechanism:
3665      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
3666 
3667    By default, this format uses inodes (identical nodes) when possible.
3668    We search for consecutive rows with the same nonzero structure, thereby
3669    reusing matrix information to achieve increased efficiency.
3670 
3671    Options Database Keys:
3672 +  -mat_no_inode  - Do not use inodes
3673 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3674 -  -mat_aij_oneindex - Internally use indexing starting at 1
3675         rather than 0.  Note that when calling MatSetValues(),
3676         the user still MUST index entries starting at 0!
3677 
3678 
3679    Example usage:
3680 
3681    Consider the following 8x8 matrix with 34 non-zero values, that is
3682    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3683    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3684    as follows:
3685 
3686 .vb
3687             1  2  0  |  0  3  0  |  0  4
3688     Proc0   0  5  6  |  7  0  0  |  8  0
3689             9  0 10  | 11  0  0  | 12  0
3690     -------------------------------------
3691            13  0 14  | 15 16 17  |  0  0
3692     Proc1   0 18  0  | 19 20 21  |  0  0
3693             0  0  0  | 22 23  0  | 24  0
3694     -------------------------------------
3695     Proc2  25 26 27  |  0  0 28  | 29  0
3696            30  0  0  | 31 32 33  |  0 34
3697 .ve
3698 
3699    This can be represented as a collection of submatrices as:
3700 
3701 .vb
3702       A B C
3703       D E F
3704       G H I
3705 .ve
3706 
3707    Where the submatrices A,B,C are owned by proc0, D,E,F are
3708    owned by proc1, G,H,I are owned by proc2.
3709 
3710    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3711    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3712    The 'M','N' parameters are 8,8, and have the same values on all procs.
3713 
3714    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3715    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3716    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3717    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3718    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3719    matrix, ans [DF] as another SeqAIJ matrix.
3720 
3721    When d_nz, o_nz parameters are specified, d_nz storage elements are
3722    allocated for every row of the local diagonal submatrix, and o_nz
3723    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3724    One way to choose d_nz and o_nz is to use the max nonzerors per local
3725    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3726    In this case, the values of d_nz,o_nz are:
3727 .vb
3728      proc0 : dnz = 2, o_nz = 2
3729      proc1 : dnz = 3, o_nz = 2
3730      proc2 : dnz = 1, o_nz = 4
3731 .ve
3732    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3733    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3734    for proc3. i.e we are using 12+15+10=37 storage locations to store
3735    34 values.
3736 
3737    When d_nnz, o_nnz parameters are specified, the storage is specified
3738    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3739    In the above case the values for d_nnz,o_nnz are:
3740 .vb
3741      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3742      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3743      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3744 .ve
3745    Here the space allocated is sum of all the above values i.e 34, and
3746    hence pre-allocation is perfect.
3747 
3748    Level: intermediate
3749 
3750 .keywords: matrix, aij, compressed row, sparse, parallel
3751 
3752 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3753           MPIAIJ, MatCreateMPIAIJWithArrays()
3754 @*/
3755 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)
3756 {
3757   PetscErrorCode ierr;
3758   PetscMPIInt    size;
3759 
3760   PetscFunctionBegin;
3761   ierr = MatCreate(comm,A);CHKERRQ(ierr);
3762   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
3763   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3764   if (size > 1) {
3765     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
3766     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
3767   } else {
3768     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
3769     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
3770   }
3771   PetscFunctionReturn(0);
3772 }
3773 
3774 #undef __FUNCT__
3775 #define __FUNCT__ "MatMPIAIJGetSeqAIJ"
3776 PetscErrorCode  MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
3777 {
3778   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3779   PetscBool      flg;
3780   PetscErrorCode ierr;
3781 
3782   PetscFunctionBegin;
3783   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&flg);CHKERRQ(ierr);
3784   if (!flg) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"This function requires a MPIAIJ matrix as input");
3785   if (Ad)     *Ad     = a->A;
3786   if (Ao)     *Ao     = a->B;
3787   if (colmap) *colmap = a->garray;
3788   PetscFunctionReturn(0);
3789 }
3790 
3791 #undef __FUNCT__
3792 #define __FUNCT__ "MatSetColoring_MPIAIJ"
3793 PetscErrorCode MatSetColoring_MPIAIJ(Mat A,ISColoring coloring)
3794 {
3795   PetscErrorCode ierr;
3796   PetscInt       i;
3797   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3798 
3799   PetscFunctionBegin;
3800   if (coloring->ctype == IS_COLORING_GLOBAL) {
3801     ISColoringValue *allcolors,*colors;
3802     ISColoring      ocoloring;
3803 
3804     /* set coloring for diagonal portion */
3805     ierr = MatSetColoring_SeqAIJ(a->A,coloring);CHKERRQ(ierr);
3806 
3807     /* set coloring for off-diagonal portion */
3808     ierr = ISAllGatherColors(PetscObjectComm((PetscObject)A),coloring->n,coloring->colors,NULL,&allcolors);CHKERRQ(ierr);
3809     ierr = PetscMalloc1(a->B->cmap->n+1,&colors);CHKERRQ(ierr);
3810     for (i=0; i<a->B->cmap->n; i++) {
3811       colors[i] = allcolors[a->garray[i]];
3812     }
3813     ierr = PetscFree(allcolors);CHKERRQ(ierr);
3814     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3815     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
3816     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3817   } else if (coloring->ctype == IS_COLORING_GHOSTED) {
3818     ISColoringValue *colors;
3819     PetscInt        *larray;
3820     ISColoring      ocoloring;
3821 
3822     /* set coloring for diagonal portion */
3823     ierr = PetscMalloc1(a->A->cmap->n+1,&larray);CHKERRQ(ierr);
3824     for (i=0; i<a->A->cmap->n; i++) {
3825       larray[i] = i + A->cmap->rstart;
3826     }
3827     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->A->cmap->n,larray,NULL,larray);CHKERRQ(ierr);
3828     ierr = PetscMalloc1(a->A->cmap->n+1,&colors);CHKERRQ(ierr);
3829     for (i=0; i<a->A->cmap->n; i++) {
3830       colors[i] = coloring->colors[larray[i]];
3831     }
3832     ierr = PetscFree(larray);CHKERRQ(ierr);
3833     ierr = ISColoringCreate(PETSC_COMM_SELF,coloring->n,a->A->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3834     ierr = MatSetColoring_SeqAIJ(a->A,ocoloring);CHKERRQ(ierr);
3835     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3836 
3837     /* set coloring for off-diagonal portion */
3838     ierr = PetscMalloc1(a->B->cmap->n+1,&larray);CHKERRQ(ierr);
3839     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->B->cmap->n,a->garray,NULL,larray);CHKERRQ(ierr);
3840     ierr = PetscMalloc1(a->B->cmap->n+1,&colors);CHKERRQ(ierr);
3841     for (i=0; i<a->B->cmap->n; i++) {
3842       colors[i] = coloring->colors[larray[i]];
3843     }
3844     ierr = PetscFree(larray);CHKERRQ(ierr);
3845     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3846     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
3847     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3848   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support ISColoringType %d",(int)coloring->ctype);
3849   PetscFunctionReturn(0);
3850 }
3851 
3852 #undef __FUNCT__
3853 #define __FUNCT__ "MatSetValuesAdifor_MPIAIJ"
3854 PetscErrorCode MatSetValuesAdifor_MPIAIJ(Mat A,PetscInt nl,void *advalues)
3855 {
3856   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3857   PetscErrorCode ierr;
3858 
3859   PetscFunctionBegin;
3860   ierr = MatSetValuesAdifor_SeqAIJ(a->A,nl,advalues);CHKERRQ(ierr);
3861   ierr = MatSetValuesAdifor_SeqAIJ(a->B,nl,advalues);CHKERRQ(ierr);
3862   PetscFunctionReturn(0);
3863 }
3864 
3865 #undef __FUNCT__
3866 #define __FUNCT__ "MatCreateMPIMatConcatenateSeqMat_MPIAIJ"
3867 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
3868 {
3869   PetscErrorCode ierr;
3870   PetscInt       m,N,i,rstart,nnz,Ii;
3871   PetscInt       *indx;
3872   PetscScalar    *values;
3873 
3874   PetscFunctionBegin;
3875   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
3876   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
3877     PetscInt       *dnz,*onz,sum,bs,cbs;
3878 
3879     if (n == PETSC_DECIDE) {
3880       ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
3881     }
3882     /* Check sum(n) = N */
3883     ierr = MPIU_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3884     if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
3885 
3886     ierr    = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3887     rstart -= m;
3888 
3889     ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
3890     for (i=0; i<m; i++) {
3891       ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3892       ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
3893       ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3894     }
3895 
3896     ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
3897     ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
3898     ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
3899     ierr = MatSetBlockSizes(*outmat,bs,cbs);CHKERRQ(ierr);
3900     ierr = MatSetType(*outmat,MATMPIAIJ);CHKERRQ(ierr);
3901     ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
3902     ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
3903   }
3904 
3905   /* numeric phase */
3906   ierr = MatGetOwnershipRange(*outmat,&rstart,NULL);CHKERRQ(ierr);
3907   for (i=0; i<m; i++) {
3908     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3909     Ii   = i + rstart;
3910     ierr = MatSetValues(*outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3911     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3912   }
3913   ierr = MatAssemblyBegin(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3914   ierr = MatAssemblyEnd(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3915   PetscFunctionReturn(0);
3916 }
3917 
3918 #undef __FUNCT__
3919 #define __FUNCT__ "MatFileSplit"
3920 PetscErrorCode MatFileSplit(Mat A,char *outfile)
3921 {
3922   PetscErrorCode    ierr;
3923   PetscMPIInt       rank;
3924   PetscInt          m,N,i,rstart,nnz;
3925   size_t            len;
3926   const PetscInt    *indx;
3927   PetscViewer       out;
3928   char              *name;
3929   Mat               B;
3930   const PetscScalar *values;
3931 
3932   PetscFunctionBegin;
3933   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
3934   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
3935   /* Should this be the type of the diagonal block of A? */
3936   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
3937   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
3938   ierr = MatSetBlockSizesFromMats(B,A,A);CHKERRQ(ierr);
3939   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
3940   ierr = MatSeqAIJSetPreallocation(B,0,NULL);CHKERRQ(ierr);
3941   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
3942   for (i=0; i<m; i++) {
3943     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3944     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3945     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3946   }
3947   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3948   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3949 
3950   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
3951   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
3952   ierr = PetscMalloc1(len+5,&name);CHKERRQ(ierr);
3953   sprintf(name,"%s.%d",outfile,rank);
3954   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
3955   ierr = PetscFree(name);CHKERRQ(ierr);
3956   ierr = MatView(B,out);CHKERRQ(ierr);
3957   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
3958   ierr = MatDestroy(&B);CHKERRQ(ierr);
3959   PetscFunctionReturn(0);
3960 }
3961 
3962 extern PetscErrorCode MatDestroy_MPIAIJ(Mat);
3963 #undef __FUNCT__
3964 #define __FUNCT__ "MatDestroy_MPIAIJ_SeqsToMPI"
3965 PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
3966 {
3967   PetscErrorCode      ierr;
3968   Mat_Merge_SeqsToMPI *merge;
3969   PetscContainer      container;
3970 
3971   PetscFunctionBegin;
3972   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
3973   if (container) {
3974     ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
3975     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
3976     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
3977     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
3978     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
3979     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
3980     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
3981     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
3982     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
3983     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
3984     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
3985     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
3986     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
3987     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
3988     ierr = PetscFree(merge);CHKERRQ(ierr);
3989     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
3990   }
3991   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
3992   PetscFunctionReturn(0);
3993 }
3994 
3995 #include <../src/mat/utils/freespace.h>
3996 #include <petscbt.h>
3997 
3998 #undef __FUNCT__
3999 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJNumeric"
4000 PetscErrorCode  MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
4001 {
4002   PetscErrorCode      ierr;
4003   MPI_Comm            comm;
4004   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
4005   PetscMPIInt         size,rank,taga,*len_s;
4006   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
4007   PetscInt            proc,m;
4008   PetscInt            **buf_ri,**buf_rj;
4009   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
4010   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
4011   MPI_Request         *s_waits,*r_waits;
4012   MPI_Status          *status;
4013   MatScalar           *aa=a->a;
4014   MatScalar           **abuf_r,*ba_i;
4015   Mat_Merge_SeqsToMPI *merge;
4016   PetscContainer      container;
4017 
4018   PetscFunctionBegin;
4019   ierr = PetscObjectGetComm((PetscObject)mpimat,&comm);CHKERRQ(ierr);
4020   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4021 
4022   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4023   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4024 
4025   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4026   ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4027 
4028   bi     = merge->bi;
4029   bj     = merge->bj;
4030   buf_ri = merge->buf_ri;
4031   buf_rj = merge->buf_rj;
4032 
4033   ierr   = PetscMalloc1(size,&status);CHKERRQ(ierr);
4034   owners = merge->rowmap->range;
4035   len_s  = merge->len_s;
4036 
4037   /* send and recv matrix values */
4038   /*-----------------------------*/
4039   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
4040   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
4041 
4042   ierr = PetscMalloc1(merge->nsend+1,&s_waits);CHKERRQ(ierr);
4043   for (proc=0,k=0; proc<size; proc++) {
4044     if (!len_s[proc]) continue;
4045     i    = owners[proc];
4046     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
4047     k++;
4048   }
4049 
4050   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
4051   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
4052   ierr = PetscFree(status);CHKERRQ(ierr);
4053 
4054   ierr = PetscFree(s_waits);CHKERRQ(ierr);
4055   ierr = PetscFree(r_waits);CHKERRQ(ierr);
4056 
4057   /* insert mat values of mpimat */
4058   /*----------------------------*/
4059   ierr = PetscMalloc1(N,&ba_i);CHKERRQ(ierr);
4060   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4061 
4062   for (k=0; k<merge->nrecv; k++) {
4063     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4064     nrows       = *(buf_ri_k[k]);
4065     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
4066     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4067   }
4068 
4069   /* set values of ba */
4070   m = merge->rowmap->n;
4071   for (i=0; i<m; i++) {
4072     arow = owners[rank] + i;
4073     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
4074     bnzi = bi[i+1] - bi[i];
4075     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
4076 
4077     /* add local non-zero vals of this proc's seqmat into ba */
4078     anzi   = ai[arow+1] - ai[arow];
4079     aj     = a->j + ai[arow];
4080     aa     = a->a + ai[arow];
4081     nextaj = 0;
4082     for (j=0; nextaj<anzi; j++) {
4083       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4084         ba_i[j] += aa[nextaj++];
4085       }
4086     }
4087 
4088     /* add received vals into ba */
4089     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4090       /* i-th row */
4091       if (i == *nextrow[k]) {
4092         anzi   = *(nextai[k]+1) - *nextai[k];
4093         aj     = buf_rj[k] + *(nextai[k]);
4094         aa     = abuf_r[k] + *(nextai[k]);
4095         nextaj = 0;
4096         for (j=0; nextaj<anzi; j++) {
4097           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4098             ba_i[j] += aa[nextaj++];
4099           }
4100         }
4101         nextrow[k]++; nextai[k]++;
4102       }
4103     }
4104     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
4105   }
4106   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4107   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4108 
4109   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
4110   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
4111   ierr = PetscFree(ba_i);CHKERRQ(ierr);
4112   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4113   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4114   PetscFunctionReturn(0);
4115 }
4116 
4117 extern PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat);
4118 
4119 #undef __FUNCT__
4120 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJSymbolic"
4121 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4122 {
4123   PetscErrorCode      ierr;
4124   Mat                 B_mpi;
4125   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
4126   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4127   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
4128   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4129   PetscInt            len,proc,*dnz,*onz,bs,cbs;
4130   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4131   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4132   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
4133   MPI_Status          *status;
4134   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
4135   PetscBT             lnkbt;
4136   Mat_Merge_SeqsToMPI *merge;
4137   PetscContainer      container;
4138 
4139   PetscFunctionBegin;
4140   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4141 
4142   /* make sure it is a PETSc comm */
4143   ierr = PetscCommDuplicate(comm,&comm,NULL);CHKERRQ(ierr);
4144   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4145   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4146 
4147   ierr = PetscNew(&merge);CHKERRQ(ierr);
4148   ierr = PetscMalloc1(size,&status);CHKERRQ(ierr);
4149 
4150   /* determine row ownership */
4151   /*---------------------------------------------------------*/
4152   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
4153   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
4154   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
4155   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
4156   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
4157   ierr = PetscMalloc1(size,&len_si);CHKERRQ(ierr);
4158   ierr = PetscMalloc1(size,&merge->len_s);CHKERRQ(ierr);
4159 
4160   m      = merge->rowmap->n;
4161   owners = merge->rowmap->range;
4162 
4163   /* determine the number of messages to send, their lengths */
4164   /*---------------------------------------------------------*/
4165   len_s = merge->len_s;
4166 
4167   len          = 0; /* length of buf_si[] */
4168   merge->nsend = 0;
4169   for (proc=0; proc<size; proc++) {
4170     len_si[proc] = 0;
4171     if (proc == rank) {
4172       len_s[proc] = 0;
4173     } else {
4174       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4175       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4176     }
4177     if (len_s[proc]) {
4178       merge->nsend++;
4179       nrows = 0;
4180       for (i=owners[proc]; i<owners[proc+1]; i++) {
4181         if (ai[i+1] > ai[i]) nrows++;
4182       }
4183       len_si[proc] = 2*(nrows+1);
4184       len         += len_si[proc];
4185     }
4186   }
4187 
4188   /* determine the number and length of messages to receive for ij-structure */
4189   /*-------------------------------------------------------------------------*/
4190   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
4191   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
4192 
4193   /* post the Irecv of j-structure */
4194   /*-------------------------------*/
4195   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
4196   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
4197 
4198   /* post the Isend of j-structure */
4199   /*--------------------------------*/
4200   ierr = PetscMalloc2(merge->nsend,&si_waits,merge->nsend,&sj_waits);CHKERRQ(ierr);
4201 
4202   for (proc=0, k=0; proc<size; proc++) {
4203     if (!len_s[proc]) continue;
4204     i    = owners[proc];
4205     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
4206     k++;
4207   }
4208 
4209   /* receives and sends of j-structure are complete */
4210   /*------------------------------------------------*/
4211   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
4212   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
4213 
4214   /* send and recv i-structure */
4215   /*---------------------------*/
4216   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
4217   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
4218 
4219   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
4220   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4221   for (proc=0,k=0; proc<size; proc++) {
4222     if (!len_s[proc]) continue;
4223     /* form outgoing message for i-structure:
4224          buf_si[0]:                 nrows to be sent
4225                [1:nrows]:           row index (global)
4226                [nrows+1:2*nrows+1]: i-structure index
4227     */
4228     /*-------------------------------------------*/
4229     nrows       = len_si[proc]/2 - 1;
4230     buf_si_i    = buf_si + nrows+1;
4231     buf_si[0]   = nrows;
4232     buf_si_i[0] = 0;
4233     nrows       = 0;
4234     for (i=owners[proc]; i<owners[proc+1]; i++) {
4235       anzi = ai[i+1] - ai[i];
4236       if (anzi) {
4237         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4238         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4239         nrows++;
4240       }
4241     }
4242     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4243     k++;
4244     buf_si += len_si[proc];
4245   }
4246 
4247   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4248   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4249 
4250   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4251   for (i=0; i<merge->nrecv; i++) {
4252     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);
4253   }
4254 
4255   ierr = PetscFree(len_si);CHKERRQ(ierr);
4256   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4257   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4258   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4259   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4260   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4261   ierr = PetscFree(status);CHKERRQ(ierr);
4262 
4263   /* compute a local seq matrix in each processor */
4264   /*----------------------------------------------*/
4265   /* allocate bi array and free space for accumulating nonzero column info */
4266   ierr  = PetscMalloc1(m+1,&bi);CHKERRQ(ierr);
4267   bi[0] = 0;
4268 
4269   /* create and initialize a linked list */
4270   nlnk = N+1;
4271   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4272 
4273   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4274   len  = ai[owners[rank+1]] - ai[owners[rank]];
4275   ierr = PetscFreeSpaceGet(PetscIntMultTruncate(2,len)+1,&free_space);CHKERRQ(ierr);
4276 
4277   current_space = free_space;
4278 
4279   /* determine symbolic info for each local row */
4280   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4281 
4282   for (k=0; k<merge->nrecv; k++) {
4283     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4284     nrows       = *buf_ri_k[k];
4285     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4286     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4287   }
4288 
4289   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4290   len  = 0;
4291   for (i=0; i<m; i++) {
4292     bnzi = 0;
4293     /* add local non-zero cols of this proc's seqmat into lnk */
4294     arow  = owners[rank] + i;
4295     anzi  = ai[arow+1] - ai[arow];
4296     aj    = a->j + ai[arow];
4297     ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4298     bnzi += nlnk;
4299     /* add received col data into lnk */
4300     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4301       if (i == *nextrow[k]) { /* i-th row */
4302         anzi  = *(nextai[k]+1) - *nextai[k];
4303         aj    = buf_rj[k] + *nextai[k];
4304         ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4305         bnzi += nlnk;
4306         nextrow[k]++; nextai[k]++;
4307       }
4308     }
4309     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4310 
4311     /* if free space is not available, make more free space */
4312     if (current_space->local_remaining<bnzi) {
4313       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(bnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
4314       nspacedouble++;
4315     }
4316     /* copy data into free space, then initialize lnk */
4317     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4318     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
4319 
4320     current_space->array           += bnzi;
4321     current_space->local_used      += bnzi;
4322     current_space->local_remaining -= bnzi;
4323 
4324     bi[i+1] = bi[i] + bnzi;
4325   }
4326 
4327   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4328 
4329   ierr = PetscMalloc1(bi[m]+1,&bj);CHKERRQ(ierr);
4330   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
4331   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4332 
4333   /* create symbolic parallel matrix B_mpi */
4334   /*---------------------------------------*/
4335   ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
4336   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
4337   if (n==PETSC_DECIDE) {
4338     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
4339   } else {
4340     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4341   }
4342   ierr = MatSetBlockSizes(B_mpi,bs,cbs);CHKERRQ(ierr);
4343   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
4344   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
4345   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4346   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
4347 
4348   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4349   B_mpi->assembled    = PETSC_FALSE;
4350   B_mpi->ops->destroy = MatDestroy_MPIAIJ_SeqsToMPI;
4351   merge->bi           = bi;
4352   merge->bj           = bj;
4353   merge->buf_ri       = buf_ri;
4354   merge->buf_rj       = buf_rj;
4355   merge->coi          = NULL;
4356   merge->coj          = NULL;
4357   merge->owners_co    = NULL;
4358 
4359   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
4360 
4361   /* attach the supporting struct to B_mpi for reuse */
4362   ierr    = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
4363   ierr    = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
4364   ierr    = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
4365   ierr    = PetscContainerDestroy(&container);CHKERRQ(ierr);
4366   *mpimat = B_mpi;
4367 
4368   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4369   PetscFunctionReturn(0);
4370 }
4371 
4372 #undef __FUNCT__
4373 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJ"
4374 /*@C
4375       MatCreateMPIAIJSumSeqAIJ - Creates a MPIAIJ matrix by adding sequential
4376                  matrices from each processor
4377 
4378     Collective on MPI_Comm
4379 
4380    Input Parameters:
4381 +    comm - the communicators the parallel matrix will live on
4382 .    seqmat - the input sequential matrices
4383 .    m - number of local rows (or PETSC_DECIDE)
4384 .    n - number of local columns (or PETSC_DECIDE)
4385 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4386 
4387    Output Parameter:
4388 .    mpimat - the parallel matrix generated
4389 
4390     Level: advanced
4391 
4392    Notes:
4393      The dimensions of the sequential matrix in each processor MUST be the same.
4394      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
4395      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
4396 @*/
4397 PetscErrorCode  MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
4398 {
4399   PetscErrorCode ierr;
4400   PetscMPIInt    size;
4401 
4402   PetscFunctionBegin;
4403   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4404   if (size == 1) {
4405     ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4406     if (scall == MAT_INITIAL_MATRIX) {
4407       ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
4408     } else {
4409       ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4410     }
4411     ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4412     PetscFunctionReturn(0);
4413   }
4414   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4415   if (scall == MAT_INITIAL_MATRIX) {
4416     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
4417   }
4418   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
4419   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4420   PetscFunctionReturn(0);
4421 }
4422 
4423 #undef __FUNCT__
4424 #define __FUNCT__ "MatMPIAIJGetLocalMat"
4425 /*@
4426      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
4427           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
4428           with MatGetSize()
4429 
4430     Not Collective
4431 
4432    Input Parameters:
4433 +    A - the matrix
4434 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4435 
4436    Output Parameter:
4437 .    A_loc - the local sequential matrix generated
4438 
4439     Level: developer
4440 
4441 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
4442 
4443 @*/
4444 PetscErrorCode  MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
4445 {
4446   PetscErrorCode ierr;
4447   Mat_MPIAIJ     *mpimat=(Mat_MPIAIJ*)A->data;
4448   Mat_SeqAIJ     *mat,*a,*b;
4449   PetscInt       *ai,*aj,*bi,*bj,*cmap=mpimat->garray;
4450   MatScalar      *aa,*ba,*cam;
4451   PetscScalar    *ca;
4452   PetscInt       am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
4453   PetscInt       *ci,*cj,col,ncols_d,ncols_o,jo;
4454   PetscBool      match;
4455   MPI_Comm       comm;
4456   PetscMPIInt    size;
4457 
4458   PetscFunctionBegin;
4459   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4460   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
4461   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4462   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4463   if (size == 1 && scall == MAT_REUSE_MATRIX) PetscFunctionReturn(0);
4464 
4465   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4466   a = (Mat_SeqAIJ*)(mpimat->A)->data;
4467   b = (Mat_SeqAIJ*)(mpimat->B)->data;
4468   ai = a->i; aj = a->j; bi = b->i; bj = b->j;
4469   aa = a->a; ba = b->a;
4470   if (scall == MAT_INITIAL_MATRIX) {
4471     if (size == 1) {
4472       ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ai,aj,aa,A_loc);CHKERRQ(ierr);
4473       PetscFunctionReturn(0);
4474     }
4475 
4476     ierr  = PetscMalloc1(1+am,&ci);CHKERRQ(ierr);
4477     ci[0] = 0;
4478     for (i=0; i<am; i++) {
4479       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
4480     }
4481     ierr = PetscMalloc1(1+ci[am],&cj);CHKERRQ(ierr);
4482     ierr = PetscMalloc1(1+ci[am],&ca);CHKERRQ(ierr);
4483     k    = 0;
4484     for (i=0; i<am; i++) {
4485       ncols_o = bi[i+1] - bi[i];
4486       ncols_d = ai[i+1] - ai[i];
4487       /* off-diagonal portion of A */
4488       for (jo=0; jo<ncols_o; jo++) {
4489         col = cmap[*bj];
4490         if (col >= cstart) break;
4491         cj[k]   = col; bj++;
4492         ca[k++] = *ba++;
4493       }
4494       /* diagonal portion of A */
4495       for (j=0; j<ncols_d; j++) {
4496         cj[k]   = cstart + *aj++;
4497         ca[k++] = *aa++;
4498       }
4499       /* off-diagonal portion of A */
4500       for (j=jo; j<ncols_o; j++) {
4501         cj[k]   = cmap[*bj++];
4502         ca[k++] = *ba++;
4503       }
4504     }
4505     /* put together the new matrix */
4506     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
4507     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4508     /* Since these are PETSc arrays, change flags to free them as necessary. */
4509     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
4510     mat->free_a  = PETSC_TRUE;
4511     mat->free_ij = PETSC_TRUE;
4512     mat->nonew   = 0;
4513   } else if (scall == MAT_REUSE_MATRIX) {
4514     mat=(Mat_SeqAIJ*)(*A_loc)->data;
4515     ci = mat->i; cj = mat->j; cam = mat->a;
4516     for (i=0; i<am; i++) {
4517       /* off-diagonal portion of A */
4518       ncols_o = bi[i+1] - bi[i];
4519       for (jo=0; jo<ncols_o; jo++) {
4520         col = cmap[*bj];
4521         if (col >= cstart) break;
4522         *cam++ = *ba++; bj++;
4523       }
4524       /* diagonal portion of A */
4525       ncols_d = ai[i+1] - ai[i];
4526       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
4527       /* off-diagonal portion of A */
4528       for (j=jo; j<ncols_o; j++) {
4529         *cam++ = *ba++; bj++;
4530       }
4531     }
4532   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
4533   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4534   PetscFunctionReturn(0);
4535 }
4536 
4537 #undef __FUNCT__
4538 #define __FUNCT__ "MatMPIAIJGetLocalMatCondensed"
4539 /*@C
4540      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MPIAIJ matrix by taking all its local rows and NON-ZERO columns
4541 
4542     Not Collective
4543 
4544    Input Parameters:
4545 +    A - the matrix
4546 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4547 -    row, col - index sets of rows and columns to extract (or NULL)
4548 
4549    Output Parameter:
4550 .    A_loc - the local sequential matrix generated
4551 
4552     Level: developer
4553 
4554 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
4555 
4556 @*/
4557 PetscErrorCode  MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
4558 {
4559   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4560   PetscErrorCode ierr;
4561   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
4562   IS             isrowa,iscola;
4563   Mat            *aloc;
4564   PetscBool      match;
4565 
4566   PetscFunctionBegin;
4567   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4568   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
4569   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4570   if (!row) {
4571     start = A->rmap->rstart; end = A->rmap->rend;
4572     ierr  = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
4573   } else {
4574     isrowa = *row;
4575   }
4576   if (!col) {
4577     start = A->cmap->rstart;
4578     cmap  = a->garray;
4579     nzA   = a->A->cmap->n;
4580     nzB   = a->B->cmap->n;
4581     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4582     ncols = 0;
4583     for (i=0; i<nzB; i++) {
4584       if (cmap[i] < start) idx[ncols++] = cmap[i];
4585       else break;
4586     }
4587     imark = i;
4588     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
4589     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
4590     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
4591   } else {
4592     iscola = *col;
4593   }
4594   if (scall != MAT_INITIAL_MATRIX) {
4595     ierr    = PetscMalloc1(1,&aloc);CHKERRQ(ierr);
4596     aloc[0] = *A_loc;
4597   }
4598   ierr   = MatGetSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
4599   *A_loc = aloc[0];
4600   ierr   = PetscFree(aloc);CHKERRQ(ierr);
4601   if (!row) {
4602     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
4603   }
4604   if (!col) {
4605     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
4606   }
4607   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4608   PetscFunctionReturn(0);
4609 }
4610 
4611 #undef __FUNCT__
4612 #define __FUNCT__ "MatGetBrowsOfAcols"
4613 /*@C
4614     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
4615 
4616     Collective on Mat
4617 
4618    Input Parameters:
4619 +    A,B - the matrices in mpiaij format
4620 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4621 -    rowb, colb - index sets of rows and columns of B to extract (or NULL)
4622 
4623    Output Parameter:
4624 +    rowb, colb - index sets of rows and columns of B to extract
4625 -    B_seq - the sequential matrix generated
4626 
4627     Level: developer
4628 
4629 @*/
4630 PetscErrorCode  MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
4631 {
4632   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4633   PetscErrorCode ierr;
4634   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
4635   IS             isrowb,iscolb;
4636   Mat            *bseq=NULL;
4637 
4638   PetscFunctionBegin;
4639   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4640     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);
4641   }
4642   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4643 
4644   if (scall == MAT_INITIAL_MATRIX) {
4645     start = A->cmap->rstart;
4646     cmap  = a->garray;
4647     nzA   = a->A->cmap->n;
4648     nzB   = a->B->cmap->n;
4649     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4650     ncols = 0;
4651     for (i=0; i<nzB; i++) {  /* row < local row index */
4652       if (cmap[i] < start) idx[ncols++] = cmap[i];
4653       else break;
4654     }
4655     imark = i;
4656     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
4657     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
4658     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
4659     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
4660   } else {
4661     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
4662     isrowb  = *rowb; iscolb = *colb;
4663     ierr    = PetscMalloc1(1,&bseq);CHKERRQ(ierr);
4664     bseq[0] = *B_seq;
4665   }
4666   ierr   = MatGetSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
4667   *B_seq = bseq[0];
4668   ierr   = PetscFree(bseq);CHKERRQ(ierr);
4669   if (!rowb) {
4670     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
4671   } else {
4672     *rowb = isrowb;
4673   }
4674   if (!colb) {
4675     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
4676   } else {
4677     *colb = iscolb;
4678   }
4679   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4680   PetscFunctionReturn(0);
4681 }
4682 
4683 #undef __FUNCT__
4684 #define __FUNCT__ "MatGetBrowsOfAoCols_MPIAIJ"
4685 /*
4686     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
4687     of the OFF-DIAGONAL portion of local A
4688 
4689     Collective on Mat
4690 
4691    Input Parameters:
4692 +    A,B - the matrices in mpiaij format
4693 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4694 
4695    Output Parameter:
4696 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
4697 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
4698 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
4699 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
4700 
4701     Level: developer
4702 
4703 */
4704 PetscErrorCode  MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
4705 {
4706   VecScatter_MPI_General *gen_to,*gen_from;
4707   PetscErrorCode         ierr;
4708   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
4709   Mat_SeqAIJ             *b_oth;
4710   VecScatter             ctx =a->Mvctx;
4711   MPI_Comm               comm;
4712   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
4713   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
4714   PetscScalar            *rvalues,*svalues;
4715   MatScalar              *b_otha,*bufa,*bufA;
4716   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
4717   MPI_Request            *rwaits = NULL,*swaits = NULL;
4718   MPI_Status             *sstatus,rstatus;
4719   PetscMPIInt            jj,size;
4720   PetscInt               *cols,sbs,rbs;
4721   PetscScalar            *vals;
4722 
4723   PetscFunctionBegin;
4724   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4725   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4726 
4727   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4728     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);
4729   }
4730   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4731   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4732 
4733   gen_to   = (VecScatter_MPI_General*)ctx->todata;
4734   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
4735   rvalues  = gen_from->values; /* holds the length of receiving row */
4736   svalues  = gen_to->values;   /* holds the length of sending row */
4737   nrecvs   = gen_from->n;
4738   nsends   = gen_to->n;
4739 
4740   ierr    = PetscMalloc2(nrecvs,&rwaits,nsends,&swaits);CHKERRQ(ierr);
4741   srow    = gen_to->indices;    /* local row index to be sent */
4742   sstarts = gen_to->starts;
4743   sprocs  = gen_to->procs;
4744   sstatus = gen_to->sstatus;
4745   sbs     = gen_to->bs;
4746   rstarts = gen_from->starts;
4747   rprocs  = gen_from->procs;
4748   rbs     = gen_from->bs;
4749 
4750   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
4751   if (scall == MAT_INITIAL_MATRIX) {
4752     /* i-array */
4753     /*---------*/
4754     /*  post receives */
4755     for (i=0; i<nrecvs; i++) {
4756       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
4757       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
4758       ierr   = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4759     }
4760 
4761     /* pack the outgoing message */
4762     ierr = PetscMalloc2(nsends+1,&sstartsj,nrecvs+1,&rstartsj);CHKERRQ(ierr);
4763 
4764     sstartsj[0] = 0;
4765     rstartsj[0] = 0;
4766     len         = 0; /* total length of j or a array to be sent */
4767     k           = 0;
4768     for (i=0; i<nsends; i++) {
4769       rowlen = (PetscInt*)svalues + sstarts[i]*sbs;
4770       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
4771       for (j=0; j<nrows; j++) {
4772         row = srow[k] + B->rmap->range[rank]; /* global row idx */
4773         for (l=0; l<sbs; l++) {
4774           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr); /* rowlength */
4775 
4776           rowlen[j*sbs+l] = ncols;
4777 
4778           len += ncols;
4779           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr);
4780         }
4781         k++;
4782       }
4783       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4784 
4785       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
4786     }
4787     /* recvs and sends of i-array are completed */
4788     i = nrecvs;
4789     while (i--) {
4790       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4791     }
4792     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4793 
4794     /* allocate buffers for sending j and a arrays */
4795     ierr = PetscMalloc1(len+1,&bufj);CHKERRQ(ierr);
4796     ierr = PetscMalloc1(len+1,&bufa);CHKERRQ(ierr);
4797 
4798     /* create i-array of B_oth */
4799     ierr = PetscMalloc1(aBn+2,&b_othi);CHKERRQ(ierr);
4800 
4801     b_othi[0] = 0;
4802     len       = 0; /* total length of j or a array to be received */
4803     k         = 0;
4804     for (i=0; i<nrecvs; i++) {
4805       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
4806       nrows  = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be received */
4807       for (j=0; j<nrows; j++) {
4808         b_othi[k+1] = b_othi[k] + rowlen[j];
4809         ierr = PetscIntSumError(rowlen[j],len,&len);CHKERRQ(ierr);
4810         k++;
4811       }
4812       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
4813     }
4814 
4815     /* allocate space for j and a arrrays of B_oth */
4816     ierr = PetscMalloc1(b_othi[aBn]+1,&b_othj);CHKERRQ(ierr);
4817     ierr = PetscMalloc1(b_othi[aBn]+1,&b_otha);CHKERRQ(ierr);
4818 
4819     /* j-array */
4820     /*---------*/
4821     /*  post receives of j-array */
4822     for (i=0; i<nrecvs; i++) {
4823       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4824       ierr  = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4825     }
4826 
4827     /* pack the outgoing message j-array */
4828     k = 0;
4829     for (i=0; i<nsends; i++) {
4830       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4831       bufJ  = bufj+sstartsj[i];
4832       for (j=0; j<nrows; j++) {
4833         row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4834         for (ll=0; ll<sbs; ll++) {
4835           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4836           for (l=0; l<ncols; l++) {
4837             *bufJ++ = cols[l];
4838           }
4839           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4840         }
4841       }
4842       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4843     }
4844 
4845     /* recvs and sends of j-array are completed */
4846     i = nrecvs;
4847     while (i--) {
4848       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4849     }
4850     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4851   } else if (scall == MAT_REUSE_MATRIX) {
4852     sstartsj = *startsj_s;
4853     rstartsj = *startsj_r;
4854     bufa     = *bufa_ptr;
4855     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
4856     b_otha   = b_oth->a;
4857   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
4858 
4859   /* a-array */
4860   /*---------*/
4861   /*  post receives of a-array */
4862   for (i=0; i<nrecvs; i++) {
4863     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4864     ierr  = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4865   }
4866 
4867   /* pack the outgoing message a-array */
4868   k = 0;
4869   for (i=0; i<nsends; i++) {
4870     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4871     bufA  = bufa+sstartsj[i];
4872     for (j=0; j<nrows; j++) {
4873       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4874       for (ll=0; ll<sbs; ll++) {
4875         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4876         for (l=0; l<ncols; l++) {
4877           *bufA++ = vals[l];
4878         }
4879         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4880       }
4881     }
4882     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4883   }
4884   /* recvs and sends of a-array are completed */
4885   i = nrecvs;
4886   while (i--) {
4887     ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4888   }
4889   if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4890   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
4891 
4892   if (scall == MAT_INITIAL_MATRIX) {
4893     /* put together the new matrix */
4894     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
4895 
4896     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4897     /* Since these are PETSc arrays, change flags to free them as necessary. */
4898     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
4899     b_oth->free_a  = PETSC_TRUE;
4900     b_oth->free_ij = PETSC_TRUE;
4901     b_oth->nonew   = 0;
4902 
4903     ierr = PetscFree(bufj);CHKERRQ(ierr);
4904     if (!startsj_s || !bufa_ptr) {
4905       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
4906       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
4907     } else {
4908       *startsj_s = sstartsj;
4909       *startsj_r = rstartsj;
4910       *bufa_ptr  = bufa;
4911     }
4912   }
4913   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4914   PetscFunctionReturn(0);
4915 }
4916 
4917 #undef __FUNCT__
4918 #define __FUNCT__ "MatGetCommunicationStructs"
4919 /*@C
4920   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
4921 
4922   Not Collective
4923 
4924   Input Parameters:
4925 . A - The matrix in mpiaij format
4926 
4927   Output Parameter:
4928 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
4929 . colmap - A map from global column index to local index into lvec
4930 - multScatter - A scatter from the argument of a matrix-vector product to lvec
4931 
4932   Level: developer
4933 
4934 @*/
4935 #if defined(PETSC_USE_CTABLE)
4936 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
4937 #else
4938 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
4939 #endif
4940 {
4941   Mat_MPIAIJ *a;
4942 
4943   PetscFunctionBegin;
4944   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4945   PetscValidPointer(lvec, 2);
4946   PetscValidPointer(colmap, 3);
4947   PetscValidPointer(multScatter, 4);
4948   a = (Mat_MPIAIJ*) A->data;
4949   if (lvec) *lvec = a->lvec;
4950   if (colmap) *colmap = a->colmap;
4951   if (multScatter) *multScatter = a->Mvctx;
4952   PetscFunctionReturn(0);
4953 }
4954 
4955 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
4956 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
4957 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
4958 #if defined(PETSC_HAVE_ELEMENTAL)
4959 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
4960 #endif
4961 
4962 #undef __FUNCT__
4963 #define __FUNCT__ "MatMatMultNumeric_MPIDense_MPIAIJ"
4964 /*
4965     Computes (B'*A')' since computing B*A directly is untenable
4966 
4967                n                       p                          p
4968         (              )       (              )         (                  )
4969       m (      A       )  *  n (       B      )   =   m (         C        )
4970         (              )       (              )         (                  )
4971 
4972 */
4973 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
4974 {
4975   PetscErrorCode ierr;
4976   Mat            At,Bt,Ct;
4977 
4978   PetscFunctionBegin;
4979   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
4980   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
4981   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
4982   ierr = MatDestroy(&At);CHKERRQ(ierr);
4983   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
4984   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
4985   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
4986   PetscFunctionReturn(0);
4987 }
4988 
4989 #undef __FUNCT__
4990 #define __FUNCT__ "MatMatMultSymbolic_MPIDense_MPIAIJ"
4991 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
4992 {
4993   PetscErrorCode ierr;
4994   PetscInt       m=A->rmap->n,n=B->cmap->n;
4995   Mat            Cmat;
4996 
4997   PetscFunctionBegin;
4998   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);
4999   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
5000   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
5001   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
5002   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
5003   ierr = MatMPIDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
5004   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5005   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5006 
5007   Cmat->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
5008 
5009   *C = Cmat;
5010   PetscFunctionReturn(0);
5011 }
5012 
5013 /* ----------------------------------------------------------------*/
5014 #undef __FUNCT__
5015 #define __FUNCT__ "MatMatMult_MPIDense_MPIAIJ"
5016 PETSC_INTERN PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
5017 {
5018   PetscErrorCode ierr;
5019 
5020   PetscFunctionBegin;
5021   if (scall == MAT_INITIAL_MATRIX) {
5022     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5023     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
5024     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5025   }
5026   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5027   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
5028   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5029   PetscFunctionReturn(0);
5030 }
5031 
5032 /*MC
5033    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
5034 
5035    Options Database Keys:
5036 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
5037 
5038   Level: beginner
5039 
5040 .seealso: MatCreateAIJ()
5041 M*/
5042 
5043 #undef __FUNCT__
5044 #define __FUNCT__ "MatCreate_MPIAIJ"
5045 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
5046 {
5047   Mat_MPIAIJ     *b;
5048   PetscErrorCode ierr;
5049   PetscMPIInt    size;
5050 
5051   PetscFunctionBegin;
5052   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
5053 
5054   ierr          = PetscNewLog(B,&b);CHKERRQ(ierr);
5055   B->data       = (void*)b;
5056   ierr          = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
5057   B->assembled  = PETSC_FALSE;
5058   B->insertmode = NOT_SET_VALUES;
5059   b->size       = size;
5060 
5061   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank);CHKERRQ(ierr);
5062 
5063   /* build cache for off array entries formed */
5064   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash);CHKERRQ(ierr);
5065 
5066   b->donotstash  = PETSC_FALSE;
5067   b->colmap      = 0;
5068   b->garray      = 0;
5069   b->roworiented = PETSC_TRUE;
5070 
5071   /* stuff used for matrix vector multiply */
5072   b->lvec  = NULL;
5073   b->Mvctx = NULL;
5074 
5075   /* stuff for MatGetRow() */
5076   b->rowindices   = 0;
5077   b->rowvalues    = 0;
5078   b->getrowactive = PETSC_FALSE;
5079 
5080   /* flexible pointer used in CUSP/CUSPARSE classes */
5081   b->spptr = NULL;
5082 
5083   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetUseScalableIncreaseOverlap_C",MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ);CHKERRQ(ierr);
5084   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ);CHKERRQ(ierr);
5085   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
5086   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetDiagonalBlock_C",MatGetDiagonalBlock_MPIAIJ);CHKERRQ(ierr);
5087   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
5088   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
5089   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
5090   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
5091   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
5092   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
5093   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
5094 #if defined(PETSC_HAVE_ELEMENTAL)
5095   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_elemental_C",MatConvert_MPIAIJ_Elemental);CHKERRQ(ierr);
5096 #endif
5097   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
5098   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
5099   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
5100   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
5101   PetscFunctionReturn(0);
5102 }
5103 
5104 #undef __FUNCT__
5105 #define __FUNCT__ "MatCreateMPIAIJWithSplitArrays"
5106 /*@C
5107      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
5108          and "off-diagonal" part of the matrix in CSR format.
5109 
5110    Collective on MPI_Comm
5111 
5112    Input Parameters:
5113 +  comm - MPI communicator
5114 .  m - number of local rows (Cannot be PETSC_DECIDE)
5115 .  n - This value should be the same as the local size used in creating the
5116        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
5117        calculated if N is given) For square matrices n is almost always m.
5118 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
5119 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
5120 .   i - row indices for "diagonal" portion of matrix
5121 .   j - column indices
5122 .   a - matrix values
5123 .   oi - row indices for "off-diagonal" portion of matrix
5124 .   oj - column indices
5125 -   oa - matrix values
5126 
5127    Output Parameter:
5128 .   mat - the matrix
5129 
5130    Level: advanced
5131 
5132    Notes:
5133        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
5134        must free the arrays once the matrix has been destroyed and not before.
5135 
5136        The i and j indices are 0 based
5137 
5138        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
5139 
5140        This sets local rows and cannot be used to set off-processor values.
5141 
5142        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
5143        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
5144        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
5145        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
5146        keep track of the underlying array. Use MatSetOption(A,MAT_IGNORE_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
5147        communication if it is known that only local entries will be set.
5148 
5149 .keywords: matrix, aij, compressed row, sparse, parallel
5150 
5151 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
5152           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
5153 @*/
5154 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)
5155 {
5156   PetscErrorCode ierr;
5157   Mat_MPIAIJ     *maij;
5158 
5159   PetscFunctionBegin;
5160   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
5161   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
5162   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
5163   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
5164   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
5165   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
5166   maij = (Mat_MPIAIJ*) (*mat)->data;
5167 
5168   (*mat)->preallocated = PETSC_TRUE;
5169 
5170   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
5171   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
5172 
5173   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
5174   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
5175 
5176   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5177   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5178   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5179   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5180 
5181   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5182   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5183   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
5184   PetscFunctionReturn(0);
5185 }
5186 
5187 /*
5188     Special version for direct calls from Fortran
5189 */
5190 #include <petsc/private/fortranimpl.h>
5191 
5192 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5193 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
5194 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5195 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
5196 #endif
5197 
5198 /* Change these macros so can be used in void function */
5199 #undef CHKERRQ
5200 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
5201 #undef SETERRQ2
5202 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5203 #undef SETERRQ3
5204 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5205 #undef SETERRQ
5206 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
5207 
5208 #undef __FUNCT__
5209 #define __FUNCT__ "matsetvaluesmpiaij_"
5210 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)
5211 {
5212   Mat            mat  = *mmat;
5213   PetscInt       m    = *mm, n = *mn;
5214   InsertMode     addv = *maddv;
5215   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
5216   PetscScalar    value;
5217   PetscErrorCode ierr;
5218 
5219   MatCheckPreallocated(mat,1);
5220   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
5221 
5222 #if defined(PETSC_USE_DEBUG)
5223   else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
5224 #endif
5225   {
5226     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
5227     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
5228     PetscBool roworiented = aij->roworiented;
5229 
5230     /* Some Variables required in the macro */
5231     Mat        A                 = aij->A;
5232     Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
5233     PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
5234     MatScalar  *aa               = a->a;
5235     PetscBool  ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
5236     Mat        B                 = aij->B;
5237     Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
5238     PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5239     MatScalar  *ba               = b->a;
5240 
5241     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5242     PetscInt  nonew = a->nonew;
5243     MatScalar *ap1,*ap2;
5244 
5245     PetscFunctionBegin;
5246     for (i=0; i<m; i++) {
5247       if (im[i] < 0) continue;
5248 #if defined(PETSC_USE_DEBUG)
5249       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);
5250 #endif
5251       if (im[i] >= rstart && im[i] < rend) {
5252         row      = im[i] - rstart;
5253         lastcol1 = -1;
5254         rp1      = aj + ai[row];
5255         ap1      = aa + ai[row];
5256         rmax1    = aimax[row];
5257         nrow1    = ailen[row];
5258         low1     = 0;
5259         high1    = nrow1;
5260         lastcol2 = -1;
5261         rp2      = bj + bi[row];
5262         ap2      = ba + bi[row];
5263         rmax2    = bimax[row];
5264         nrow2    = bilen[row];
5265         low2     = 0;
5266         high2    = nrow2;
5267 
5268         for (j=0; j<n; j++) {
5269           if (roworiented) value = v[i*n+j];
5270           else value = v[i+j*m];
5271           if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES)) continue;
5272           if (in[j] >= cstart && in[j] < cend) {
5273             col = in[j] - cstart;
5274             MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
5275           } else if (in[j] < 0) continue;
5276 #if defined(PETSC_USE_DEBUG)
5277           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);
5278 #endif
5279           else {
5280             if (mat->was_assembled) {
5281               if (!aij->colmap) {
5282                 ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5283               }
5284 #if defined(PETSC_USE_CTABLE)
5285               ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5286               col--;
5287 #else
5288               col = aij->colmap[in[j]] - 1;
5289 #endif
5290               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5291                 ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5292                 col  =  in[j];
5293                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5294                 B     = aij->B;
5295                 b     = (Mat_SeqAIJ*)B->data;
5296                 bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5297                 rp2   = bj + bi[row];
5298                 ap2   = ba + bi[row];
5299                 rmax2 = bimax[row];
5300                 nrow2 = bilen[row];
5301                 low2  = 0;
5302                 high2 = nrow2;
5303                 bm    = aij->B->rmap->n;
5304                 ba    = b->a;
5305               }
5306             } else col = in[j];
5307             MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
5308           }
5309         }
5310       } else if (!aij->donotstash) {
5311         if (roworiented) {
5312           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5313         } else {
5314           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5315         }
5316       }
5317     }
5318   }
5319   PetscFunctionReturnVoid();
5320 }
5321 
5322