xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision 3b49f96a08d19738f4d6d5931585bcc3c1253d7a)
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 = MPI_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 = MPI_Allreduce(work,norms,n,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
181   } else {
182     ierr = MPI_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 = MPI_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 = MPI_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 = MPI_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 = MPI_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); if (isnull) PetscFunctionReturn(0);
1386   }
1387 
1388   {
1389     /* assemble the entire matrix onto first processor. */
1390     Mat        A;
1391     Mat_SeqAIJ *Aloc;
1392     PetscInt   M = mat->rmap->N,N = mat->cmap->N,m,*ai,*aj,row,*cols,i,*ct;
1393     MatScalar  *a;
1394 
1395     ierr = MatCreate(PetscObjectComm((PetscObject)mat),&A);CHKERRQ(ierr);
1396     if (!rank) {
1397       ierr = MatSetSizes(A,M,N,M,N);CHKERRQ(ierr);
1398     } else {
1399       ierr = MatSetSizes(A,0,0,M,N);CHKERRQ(ierr);
1400     }
1401     /* This is just a temporary matrix, so explicitly using MATMPIAIJ is probably best */
1402     ierr = MatSetType(A,MATMPIAIJ);CHKERRQ(ierr);
1403     ierr = MatMPIAIJSetPreallocation(A,0,NULL,0,NULL);CHKERRQ(ierr);
1404     ierr = MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
1405     ierr = PetscLogObjectParent((PetscObject)mat,(PetscObject)A);CHKERRQ(ierr);
1406 
1407     /* copy over the A part */
1408     Aloc = (Mat_SeqAIJ*)aij->A->data;
1409     m    = aij->A->rmap->n; ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
1410     row  = mat->rmap->rstart;
1411     for (i=0; i<ai[m]; i++) aj[i] += mat->cmap->rstart;
1412     for (i=0; i<m; i++) {
1413       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],aj,a,INSERT_VALUES);CHKERRQ(ierr);
1414       row++;
1415       a += ai[i+1]-ai[i]; aj += ai[i+1]-ai[i];
1416     }
1417     aj = Aloc->j;
1418     for (i=0; i<ai[m]; i++) aj[i] -= mat->cmap->rstart;
1419 
1420     /* copy over the B part */
1421     Aloc = (Mat_SeqAIJ*)aij->B->data;
1422     m    = aij->B->rmap->n;  ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
1423     row  = mat->rmap->rstart;
1424     ierr = PetscMalloc1(ai[m]+1,&cols);CHKERRQ(ierr);
1425     ct   = cols;
1426     for (i=0; i<ai[m]; i++) cols[i] = aij->garray[aj[i]];
1427     for (i=0; i<m; i++) {
1428       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],cols,a,INSERT_VALUES);CHKERRQ(ierr);
1429       row++;
1430       a += ai[i+1]-ai[i]; cols += ai[i+1]-ai[i];
1431     }
1432     ierr = PetscFree(ct);CHKERRQ(ierr);
1433     ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1434     ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1435     /*
1436        Everyone has to call to draw the matrix since the graphics waits are
1437        synchronized across all processors that share the PetscDraw object
1438     */
1439     ierr = PetscViewerGetSubViewer(viewer,PETSC_COMM_SELF,&sviewer);CHKERRQ(ierr);
1440     if (!rank) {
1441       ierr = PetscObjectSetName((PetscObject)((Mat_MPIAIJ*)(A->data))->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1442       ierr = MatView_SeqAIJ(((Mat_MPIAIJ*)(A->data))->A,sviewer);CHKERRQ(ierr);
1443     }
1444     ierr = PetscViewerRestoreSubViewer(viewer,PETSC_COMM_SELF,&sviewer);CHKERRQ(ierr);
1445     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1446     ierr = MatDestroy(&A);CHKERRQ(ierr);
1447   }
1448   PetscFunctionReturn(0);
1449 }
1450 
1451 #undef __FUNCT__
1452 #define __FUNCT__ "MatView_MPIAIJ"
1453 PetscErrorCode MatView_MPIAIJ(Mat mat,PetscViewer viewer)
1454 {
1455   PetscErrorCode ierr;
1456   PetscBool      iascii,isdraw,issocket,isbinary;
1457 
1458   PetscFunctionBegin;
1459   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1460   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1461   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1462   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSOCKET,&issocket);CHKERRQ(ierr);
1463   if (iascii || isdraw || isbinary || issocket) {
1464     ierr = MatView_MPIAIJ_ASCIIorDraworSocket(mat,viewer);CHKERRQ(ierr);
1465   }
1466   PetscFunctionReturn(0);
1467 }
1468 
1469 #undef __FUNCT__
1470 #define __FUNCT__ "MatSOR_MPIAIJ"
1471 PetscErrorCode MatSOR_MPIAIJ(Mat matin,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
1472 {
1473   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1474   PetscErrorCode ierr;
1475   Vec            bb1 = 0;
1476   PetscBool      hasop;
1477 
1478   PetscFunctionBegin;
1479   if (flag == SOR_APPLY_UPPER) {
1480     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1481     PetscFunctionReturn(0);
1482   }
1483 
1484   if (its > 1 || ~flag & SOR_ZERO_INITIAL_GUESS || flag & SOR_EISENSTAT) {
1485     ierr = VecDuplicate(bb,&bb1);CHKERRQ(ierr);
1486   }
1487 
1488   if ((flag & SOR_LOCAL_SYMMETRIC_SWEEP) == SOR_LOCAL_SYMMETRIC_SWEEP) {
1489     if (flag & SOR_ZERO_INITIAL_GUESS) {
1490       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1491       its--;
1492     }
1493 
1494     while (its--) {
1495       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1496       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1497 
1498       /* update rhs: bb1 = bb - B*x */
1499       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1500       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1501 
1502       /* local sweep */
1503       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_SYMMETRIC_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1504     }
1505   } else if (flag & SOR_LOCAL_FORWARD_SWEEP) {
1506     if (flag & SOR_ZERO_INITIAL_GUESS) {
1507       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1508       its--;
1509     }
1510     while (its--) {
1511       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1512       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1513 
1514       /* update rhs: bb1 = bb - B*x */
1515       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1516       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1517 
1518       /* local sweep */
1519       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_FORWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1520     }
1521   } else if (flag & SOR_LOCAL_BACKWARD_SWEEP) {
1522     if (flag & SOR_ZERO_INITIAL_GUESS) {
1523       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1524       its--;
1525     }
1526     while (its--) {
1527       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1528       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1529 
1530       /* update rhs: bb1 = bb - B*x */
1531       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1532       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1533 
1534       /* local sweep */
1535       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_BACKWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1536     }
1537   } else if (flag & SOR_EISENSTAT) {
1538     Vec xx1;
1539 
1540     ierr = VecDuplicate(bb,&xx1);CHKERRQ(ierr);
1541     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_BACKWARD_SWEEP),fshift,lits,1,xx);CHKERRQ(ierr);
1542 
1543     ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1544     ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1545     if (!mat->diag) {
1546       ierr = MatCreateVecs(matin,&mat->diag,NULL);CHKERRQ(ierr);
1547       ierr = MatGetDiagonal(matin,mat->diag);CHKERRQ(ierr);
1548     }
1549     ierr = MatHasOperation(matin,MATOP_MULT_DIAGONAL_BLOCK,&hasop);CHKERRQ(ierr);
1550     if (hasop) {
1551       ierr = MatMultDiagonalBlock(matin,xx,bb1);CHKERRQ(ierr);
1552     } else {
1553       ierr = VecPointwiseMult(bb1,mat->diag,xx);CHKERRQ(ierr);
1554     }
1555     ierr = VecAYPX(bb1,(omega-2.0)/omega,bb);CHKERRQ(ierr);
1556 
1557     ierr = MatMultAdd(mat->B,mat->lvec,bb1,bb1);CHKERRQ(ierr);
1558 
1559     /* local sweep */
1560     ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_FORWARD_SWEEP),fshift,lits,1,xx1);CHKERRQ(ierr);
1561     ierr = VecAXPY(xx,1.0,xx1);CHKERRQ(ierr);
1562     ierr = VecDestroy(&xx1);CHKERRQ(ierr);
1563   } else SETERRQ(PetscObjectComm((PetscObject)matin),PETSC_ERR_SUP,"Parallel SOR not supported");
1564 
1565   ierr = VecDestroy(&bb1);CHKERRQ(ierr);
1566   PetscFunctionReturn(0);
1567 }
1568 
1569 #undef __FUNCT__
1570 #define __FUNCT__ "MatPermute_MPIAIJ"
1571 PetscErrorCode MatPermute_MPIAIJ(Mat A,IS rowp,IS colp,Mat *B)
1572 {
1573   Mat            aA,aB,Aperm;
1574   const PetscInt *rwant,*cwant,*gcols,*ai,*bi,*aj,*bj;
1575   PetscScalar    *aa,*ba;
1576   PetscInt       i,j,m,n,ng,anz,bnz,*dnnz,*onnz,*tdnnz,*tonnz,*rdest,*cdest,*work,*gcdest;
1577   PetscSF        rowsf,sf;
1578   IS             parcolp = NULL;
1579   PetscBool      done;
1580   PetscErrorCode ierr;
1581 
1582   PetscFunctionBegin;
1583   ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
1584   ierr = ISGetIndices(rowp,&rwant);CHKERRQ(ierr);
1585   ierr = ISGetIndices(colp,&cwant);CHKERRQ(ierr);
1586   ierr = PetscMalloc3(PetscMax(m,n),&work,m,&rdest,n,&cdest);CHKERRQ(ierr);
1587 
1588   /* Invert row permutation to find out where my rows should go */
1589   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&rowsf);CHKERRQ(ierr);
1590   ierr = PetscSFSetGraphLayout(rowsf,A->rmap,A->rmap->n,NULL,PETSC_OWN_POINTER,rwant);CHKERRQ(ierr);
1591   ierr = PetscSFSetFromOptions(rowsf);CHKERRQ(ierr);
1592   for (i=0; i<m; i++) work[i] = A->rmap->rstart + i;
1593   ierr = PetscSFReduceBegin(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1594   ierr = PetscSFReduceEnd(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1595 
1596   /* Invert column permutation to find out where my columns should go */
1597   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1598   ierr = PetscSFSetGraphLayout(sf,A->cmap,A->cmap->n,NULL,PETSC_OWN_POINTER,cwant);CHKERRQ(ierr);
1599   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1600   for (i=0; i<n; i++) work[i] = A->cmap->rstart + i;
1601   ierr = PetscSFReduceBegin(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1602   ierr = PetscSFReduceEnd(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1603   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1604 
1605   ierr = ISRestoreIndices(rowp,&rwant);CHKERRQ(ierr);
1606   ierr = ISRestoreIndices(colp,&cwant);CHKERRQ(ierr);
1607   ierr = MatMPIAIJGetSeqAIJ(A,&aA,&aB,&gcols);CHKERRQ(ierr);
1608 
1609   /* Find out where my gcols should go */
1610   ierr = MatGetSize(aB,NULL,&ng);CHKERRQ(ierr);
1611   ierr = PetscMalloc1(ng,&gcdest);CHKERRQ(ierr);
1612   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1613   ierr = PetscSFSetGraphLayout(sf,A->cmap,ng,NULL,PETSC_OWN_POINTER,gcols);CHKERRQ(ierr);
1614   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1615   ierr = PetscSFBcastBegin(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1616   ierr = PetscSFBcastEnd(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1617   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1618 
1619   ierr = PetscCalloc4(m,&dnnz,m,&onnz,m,&tdnnz,m,&tonnz);CHKERRQ(ierr);
1620   ierr = MatGetRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1621   ierr = MatGetRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1622   for (i=0; i<m; i++) {
1623     PetscInt row = rdest[i],rowner;
1624     ierr = PetscLayoutFindOwner(A->rmap,row,&rowner);CHKERRQ(ierr);
1625     for (j=ai[i]; j<ai[i+1]; j++) {
1626       PetscInt cowner,col = cdest[aj[j]];
1627       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr); /* Could build an index for the columns to eliminate this search */
1628       if (rowner == cowner) dnnz[i]++;
1629       else onnz[i]++;
1630     }
1631     for (j=bi[i]; j<bi[i+1]; j++) {
1632       PetscInt cowner,col = gcdest[bj[j]];
1633       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr);
1634       if (rowner == cowner) dnnz[i]++;
1635       else onnz[i]++;
1636     }
1637   }
1638   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1639   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1640   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1641   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1642   ierr = PetscSFDestroy(&rowsf);CHKERRQ(ierr);
1643 
1644   ierr = MatCreateAIJ(PetscObjectComm((PetscObject)A),A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N,0,tdnnz,0,tonnz,&Aperm);CHKERRQ(ierr);
1645   ierr = MatSeqAIJGetArray(aA,&aa);CHKERRQ(ierr);
1646   ierr = MatSeqAIJGetArray(aB,&ba);CHKERRQ(ierr);
1647   for (i=0; i<m; i++) {
1648     PetscInt *acols = dnnz,*bcols = onnz; /* Repurpose now-unneeded arrays */
1649     PetscInt j0,rowlen;
1650     rowlen = ai[i+1] - ai[i];
1651     for (j0=j=0; j<rowlen; j0=j) { /* rowlen could be larger than number of rows m, so sum in batches */
1652       for ( ; j<PetscMin(rowlen,j0+m); j++) acols[j-j0] = cdest[aj[ai[i]+j]];
1653       ierr = MatSetValues(Aperm,1,&rdest[i],j-j0,acols,aa+ai[i]+j0,INSERT_VALUES);CHKERRQ(ierr);
1654     }
1655     rowlen = bi[i+1] - bi[i];
1656     for (j0=j=0; j<rowlen; j0=j) {
1657       for ( ; j<PetscMin(rowlen,j0+m); j++) bcols[j-j0] = gcdest[bj[bi[i]+j]];
1658       ierr = MatSetValues(Aperm,1,&rdest[i],j-j0,bcols,ba+bi[i]+j0,INSERT_VALUES);CHKERRQ(ierr);
1659     }
1660   }
1661   ierr = MatAssemblyBegin(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1662   ierr = MatAssemblyEnd(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1663   ierr = MatRestoreRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1664   ierr = MatRestoreRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1665   ierr = MatSeqAIJRestoreArray(aA,&aa);CHKERRQ(ierr);
1666   ierr = MatSeqAIJRestoreArray(aB,&ba);CHKERRQ(ierr);
1667   ierr = PetscFree4(dnnz,onnz,tdnnz,tonnz);CHKERRQ(ierr);
1668   ierr = PetscFree3(work,rdest,cdest);CHKERRQ(ierr);
1669   ierr = PetscFree(gcdest);CHKERRQ(ierr);
1670   if (parcolp) {ierr = ISDestroy(&colp);CHKERRQ(ierr);}
1671   *B = Aperm;
1672   PetscFunctionReturn(0);
1673 }
1674 
1675 #undef __FUNCT__
1676 #define __FUNCT__ "MatGetGhosts_MPIAIJ"
1677 PetscErrorCode  MatGetGhosts_MPIAIJ(Mat mat,PetscInt *nghosts,const PetscInt *ghosts[])
1678 {
1679   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1680   PetscErrorCode ierr;
1681 
1682   PetscFunctionBegin;
1683   ierr = MatGetSize(aij->B,NULL,nghosts);CHKERRQ(ierr);
1684   if (ghosts) *ghosts = aij->garray;
1685   PetscFunctionReturn(0);
1686 }
1687 
1688 #undef __FUNCT__
1689 #define __FUNCT__ "MatGetInfo_MPIAIJ"
1690 PetscErrorCode MatGetInfo_MPIAIJ(Mat matin,MatInfoType flag,MatInfo *info)
1691 {
1692   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1693   Mat            A    = mat->A,B = mat->B;
1694   PetscErrorCode ierr;
1695   PetscReal      isend[5],irecv[5];
1696 
1697   PetscFunctionBegin;
1698   info->block_size = 1.0;
1699   ierr             = MatGetInfo(A,MAT_LOCAL,info);CHKERRQ(ierr);
1700 
1701   isend[0] = info->nz_used; isend[1] = info->nz_allocated; isend[2] = info->nz_unneeded;
1702   isend[3] = info->memory;  isend[4] = info->mallocs;
1703 
1704   ierr = MatGetInfo(B,MAT_LOCAL,info);CHKERRQ(ierr);
1705 
1706   isend[0] += info->nz_used; isend[1] += info->nz_allocated; isend[2] += info->nz_unneeded;
1707   isend[3] += info->memory;  isend[4] += info->mallocs;
1708   if (flag == MAT_LOCAL) {
1709     info->nz_used      = isend[0];
1710     info->nz_allocated = isend[1];
1711     info->nz_unneeded  = isend[2];
1712     info->memory       = isend[3];
1713     info->mallocs      = isend[4];
1714   } else if (flag == MAT_GLOBAL_MAX) {
1715     ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1716 
1717     info->nz_used      = irecv[0];
1718     info->nz_allocated = irecv[1];
1719     info->nz_unneeded  = irecv[2];
1720     info->memory       = irecv[3];
1721     info->mallocs      = irecv[4];
1722   } else if (flag == MAT_GLOBAL_SUM) {
1723     ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1724 
1725     info->nz_used      = irecv[0];
1726     info->nz_allocated = irecv[1];
1727     info->nz_unneeded  = irecv[2];
1728     info->memory       = irecv[3];
1729     info->mallocs      = irecv[4];
1730   }
1731   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
1732   info->fill_ratio_needed = 0;
1733   info->factor_mallocs    = 0;
1734   PetscFunctionReturn(0);
1735 }
1736 
1737 #undef __FUNCT__
1738 #define __FUNCT__ "MatSetOption_MPIAIJ"
1739 PetscErrorCode MatSetOption_MPIAIJ(Mat A,MatOption op,PetscBool flg)
1740 {
1741   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1742   PetscErrorCode ierr;
1743 
1744   PetscFunctionBegin;
1745   switch (op) {
1746   case MAT_NEW_NONZERO_LOCATIONS:
1747   case MAT_NEW_NONZERO_ALLOCATION_ERR:
1748   case MAT_UNUSED_NONZERO_LOCATION_ERR:
1749   case MAT_KEEP_NONZERO_PATTERN:
1750   case MAT_NEW_NONZERO_LOCATION_ERR:
1751   case MAT_USE_INODES:
1752   case MAT_IGNORE_ZERO_ENTRIES:
1753     MatCheckPreallocated(A,1);
1754     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1755     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1756     break;
1757   case MAT_ROW_ORIENTED:
1758     a->roworiented = flg;
1759 
1760     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1761     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1762     break;
1763   case MAT_NEW_DIAGONALS:
1764     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
1765     break;
1766   case MAT_IGNORE_OFF_PROC_ENTRIES:
1767     a->donotstash = flg;
1768     break;
1769   case MAT_SPD:
1770     A->spd_set = PETSC_TRUE;
1771     A->spd     = flg;
1772     if (flg) {
1773       A->symmetric                  = PETSC_TRUE;
1774       A->structurally_symmetric     = PETSC_TRUE;
1775       A->symmetric_set              = PETSC_TRUE;
1776       A->structurally_symmetric_set = PETSC_TRUE;
1777     }
1778     break;
1779   case MAT_SYMMETRIC:
1780     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1781     break;
1782   case MAT_STRUCTURALLY_SYMMETRIC:
1783     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1784     break;
1785   case MAT_HERMITIAN:
1786     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1787     break;
1788   case MAT_SYMMETRY_ETERNAL:
1789     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1790     break;
1791   default:
1792     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %d",op);
1793   }
1794   PetscFunctionReturn(0);
1795 }
1796 
1797 #undef __FUNCT__
1798 #define __FUNCT__ "MatGetRow_MPIAIJ"
1799 PetscErrorCode MatGetRow_MPIAIJ(Mat matin,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1800 {
1801   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1802   PetscScalar    *vworkA,*vworkB,**pvA,**pvB,*v_p;
1803   PetscErrorCode ierr;
1804   PetscInt       i,*cworkA,*cworkB,**pcA,**pcB,cstart = matin->cmap->rstart;
1805   PetscInt       nztot,nzA,nzB,lrow,rstart = matin->rmap->rstart,rend = matin->rmap->rend;
1806   PetscInt       *cmap,*idx_p;
1807 
1808   PetscFunctionBegin;
1809   if (mat->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Already active");
1810   mat->getrowactive = PETSC_TRUE;
1811 
1812   if (!mat->rowvalues && (idx || v)) {
1813     /*
1814         allocate enough space to hold information from the longest row.
1815     */
1816     Mat_SeqAIJ *Aa = (Mat_SeqAIJ*)mat->A->data,*Ba = (Mat_SeqAIJ*)mat->B->data;
1817     PetscInt   max = 1,tmp;
1818     for (i=0; i<matin->rmap->n; i++) {
1819       tmp = Aa->i[i+1] - Aa->i[i] + Ba->i[i+1] - Ba->i[i];
1820       if (max < tmp) max = tmp;
1821     }
1822     ierr = PetscMalloc2(max,&mat->rowvalues,max,&mat->rowindices);CHKERRQ(ierr);
1823   }
1824 
1825   if (row < rstart || row >= rend) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Only local rows");
1826   lrow = row - rstart;
1827 
1828   pvA = &vworkA; pcA = &cworkA; pvB = &vworkB; pcB = &cworkB;
1829   if (!v)   {pvA = 0; pvB = 0;}
1830   if (!idx) {pcA = 0; if (!v) pcB = 0;}
1831   ierr  = (*mat->A->ops->getrow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1832   ierr  = (*mat->B->ops->getrow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1833   nztot = nzA + nzB;
1834 
1835   cmap = mat->garray;
1836   if (v  || idx) {
1837     if (nztot) {
1838       /* Sort by increasing column numbers, assuming A and B already sorted */
1839       PetscInt imark = -1;
1840       if (v) {
1841         *v = v_p = mat->rowvalues;
1842         for (i=0; i<nzB; i++) {
1843           if (cmap[cworkB[i]] < cstart) v_p[i] = vworkB[i];
1844           else break;
1845         }
1846         imark = i;
1847         for (i=0; i<nzA; i++)     v_p[imark+i] = vworkA[i];
1848         for (i=imark; i<nzB; i++) v_p[nzA+i]   = vworkB[i];
1849       }
1850       if (idx) {
1851         *idx = idx_p = mat->rowindices;
1852         if (imark > -1) {
1853           for (i=0; i<imark; i++) {
1854             idx_p[i] = cmap[cworkB[i]];
1855           }
1856         } else {
1857           for (i=0; i<nzB; i++) {
1858             if (cmap[cworkB[i]] < cstart) idx_p[i] = cmap[cworkB[i]];
1859             else break;
1860           }
1861           imark = i;
1862         }
1863         for (i=0; i<nzA; i++)     idx_p[imark+i] = cstart + cworkA[i];
1864         for (i=imark; i<nzB; i++) idx_p[nzA+i]   = cmap[cworkB[i]];
1865       }
1866     } else {
1867       if (idx) *idx = 0;
1868       if (v)   *v   = 0;
1869     }
1870   }
1871   *nz  = nztot;
1872   ierr = (*mat->A->ops->restorerow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1873   ierr = (*mat->B->ops->restorerow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1874   PetscFunctionReturn(0);
1875 }
1876 
1877 #undef __FUNCT__
1878 #define __FUNCT__ "MatRestoreRow_MPIAIJ"
1879 PetscErrorCode MatRestoreRow_MPIAIJ(Mat mat,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1880 {
1881   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1882 
1883   PetscFunctionBegin;
1884   if (!aij->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"MatGetRow() must be called first");
1885   aij->getrowactive = PETSC_FALSE;
1886   PetscFunctionReturn(0);
1887 }
1888 
1889 #undef __FUNCT__
1890 #define __FUNCT__ "MatNorm_MPIAIJ"
1891 PetscErrorCode MatNorm_MPIAIJ(Mat mat,NormType type,PetscReal *norm)
1892 {
1893   Mat_MPIAIJ     *aij  = (Mat_MPIAIJ*)mat->data;
1894   Mat_SeqAIJ     *amat = (Mat_SeqAIJ*)aij->A->data,*bmat = (Mat_SeqAIJ*)aij->B->data;
1895   PetscErrorCode ierr;
1896   PetscInt       i,j,cstart = mat->cmap->rstart;
1897   PetscReal      sum = 0.0;
1898   MatScalar      *v;
1899 
1900   PetscFunctionBegin;
1901   if (aij->size == 1) {
1902     ierr =  MatNorm(aij->A,type,norm);CHKERRQ(ierr);
1903   } else {
1904     if (type == NORM_FROBENIUS) {
1905       v = amat->a;
1906       for (i=0; i<amat->nz; i++) {
1907         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1908       }
1909       v = bmat->a;
1910       for (i=0; i<bmat->nz; i++) {
1911         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1912       }
1913       ierr  = MPI_Allreduce(&sum,norm,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1914       *norm = PetscSqrtReal(*norm);
1915     } else if (type == NORM_1) { /* max column norm */
1916       PetscReal *tmp,*tmp2;
1917       PetscInt  *jj,*garray = aij->garray;
1918       ierr  = PetscCalloc1(mat->cmap->N+1,&tmp);CHKERRQ(ierr);
1919       ierr  = PetscMalloc1(mat->cmap->N+1,&tmp2);CHKERRQ(ierr);
1920       *norm = 0.0;
1921       v     = amat->a; jj = amat->j;
1922       for (j=0; j<amat->nz; j++) {
1923         tmp[cstart + *jj++] += PetscAbsScalar(*v);  v++;
1924       }
1925       v = bmat->a; jj = bmat->j;
1926       for (j=0; j<bmat->nz; j++) {
1927         tmp[garray[*jj++]] += PetscAbsScalar(*v); v++;
1928       }
1929       ierr = MPI_Allreduce(tmp,tmp2,mat->cmap->N,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1930       for (j=0; j<mat->cmap->N; j++) {
1931         if (tmp2[j] > *norm) *norm = tmp2[j];
1932       }
1933       ierr = PetscFree(tmp);CHKERRQ(ierr);
1934       ierr = PetscFree(tmp2);CHKERRQ(ierr);
1935     } else if (type == NORM_INFINITY) { /* max row norm */
1936       PetscReal ntemp = 0.0;
1937       for (j=0; j<aij->A->rmap->n; j++) {
1938         v   = amat->a + amat->i[j];
1939         sum = 0.0;
1940         for (i=0; i<amat->i[j+1]-amat->i[j]; i++) {
1941           sum += PetscAbsScalar(*v); v++;
1942         }
1943         v = bmat->a + bmat->i[j];
1944         for (i=0; i<bmat->i[j+1]-bmat->i[j]; i++) {
1945           sum += PetscAbsScalar(*v); v++;
1946         }
1947         if (sum > ntemp) ntemp = sum;
1948       }
1949       ierr = MPI_Allreduce(&ntemp,norm,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1950     } else SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"No support for two norm");
1951   }
1952   PetscFunctionReturn(0);
1953 }
1954 
1955 #undef __FUNCT__
1956 #define __FUNCT__ "MatTranspose_MPIAIJ"
1957 PetscErrorCode MatTranspose_MPIAIJ(Mat A,MatReuse reuse,Mat *matout)
1958 {
1959   Mat_MPIAIJ     *a   = (Mat_MPIAIJ*)A->data;
1960   Mat_SeqAIJ     *Aloc=(Mat_SeqAIJ*)a->A->data,*Bloc=(Mat_SeqAIJ*)a->B->data;
1961   PetscErrorCode ierr;
1962   PetscInt       M      = A->rmap->N,N = A->cmap->N,ma,na,mb,nb,*ai,*aj,*bi,*bj,row,*cols,*cols_tmp,i;
1963   PetscInt       cstart = A->cmap->rstart,ncol;
1964   Mat            B;
1965   MatScalar      *array;
1966 
1967   PetscFunctionBegin;
1968   if (reuse == MAT_REUSE_MATRIX && A == *matout && M != N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Square matrix only for in-place");
1969 
1970   ma = A->rmap->n; na = A->cmap->n; mb = a->B->rmap->n; nb = a->B->cmap->n;
1971   ai = Aloc->i; aj = Aloc->j;
1972   bi = Bloc->i; bj = Bloc->j;
1973   if (reuse == MAT_INITIAL_MATRIX || *matout == A) {
1974     PetscInt             *d_nnz,*g_nnz,*o_nnz;
1975     PetscSFNode          *oloc;
1976     PETSC_UNUSED PetscSF sf;
1977 
1978     ierr = PetscMalloc4(na,&d_nnz,na,&o_nnz,nb,&g_nnz,nb,&oloc);CHKERRQ(ierr);
1979     /* compute d_nnz for preallocation */
1980     ierr = PetscMemzero(d_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1981     for (i=0; i<ai[ma]; i++) {
1982       d_nnz[aj[i]]++;
1983       aj[i] += cstart; /* global col index to be used by MatSetValues() */
1984     }
1985     /* compute local off-diagonal contributions */
1986     ierr = PetscMemzero(g_nnz,nb*sizeof(PetscInt));CHKERRQ(ierr);
1987     for (i=0; i<bi[ma]; i++) g_nnz[bj[i]]++;
1988     /* map those to global */
1989     ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1990     ierr = PetscSFSetGraphLayout(sf,A->cmap,nb,NULL,PETSC_USE_POINTER,a->garray);CHKERRQ(ierr);
1991     ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1992     ierr = PetscMemzero(o_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1993     ierr = PetscSFReduceBegin(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
1994     ierr = PetscSFReduceEnd(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
1995     ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1996 
1997     ierr = MatCreate(PetscObjectComm((PetscObject)A),&B);CHKERRQ(ierr);
1998     ierr = MatSetSizes(B,A->cmap->n,A->rmap->n,N,M);CHKERRQ(ierr);
1999     ierr = MatSetBlockSizes(B,PetscAbs(A->cmap->bs),PetscAbs(A->rmap->bs));CHKERRQ(ierr);
2000     ierr = MatSetType(B,((PetscObject)A)->type_name);CHKERRQ(ierr);
2001     ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
2002     ierr = PetscFree4(d_nnz,o_nnz,g_nnz,oloc);CHKERRQ(ierr);
2003   } else {
2004     B    = *matout;
2005     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
2006     for (i=0; i<ai[ma]; i++) aj[i] += cstart; /* global col index to be used by MatSetValues() */
2007   }
2008 
2009   /* copy over the A part */
2010   array = Aloc->a;
2011   row   = A->rmap->rstart;
2012   for (i=0; i<ma; i++) {
2013     ncol = ai[i+1]-ai[i];
2014     ierr = MatSetValues(B,ncol,aj,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
2015     row++;
2016     array += ncol; aj += ncol;
2017   }
2018   aj = Aloc->j;
2019   for (i=0; i<ai[ma]; i++) aj[i] -= cstart; /* resume local col index */
2020 
2021   /* copy over the B part */
2022   ierr  = PetscCalloc1(bi[mb],&cols);CHKERRQ(ierr);
2023   array = Bloc->a;
2024   row   = A->rmap->rstart;
2025   for (i=0; i<bi[mb]; i++) cols[i] = a->garray[bj[i]];
2026   cols_tmp = cols;
2027   for (i=0; i<mb; i++) {
2028     ncol = bi[i+1]-bi[i];
2029     ierr = MatSetValues(B,ncol,cols_tmp,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
2030     row++;
2031     array += ncol; cols_tmp += ncol;
2032   }
2033   ierr = PetscFree(cols);CHKERRQ(ierr);
2034 
2035   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2036   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2037   if (reuse == MAT_INITIAL_MATRIX || *matout != A) {
2038     *matout = B;
2039   } else {
2040     ierr = MatHeaderMerge(A,&B);CHKERRQ(ierr);
2041   }
2042   PetscFunctionReturn(0);
2043 }
2044 
2045 #undef __FUNCT__
2046 #define __FUNCT__ "MatDiagonalScale_MPIAIJ"
2047 PetscErrorCode MatDiagonalScale_MPIAIJ(Mat mat,Vec ll,Vec rr)
2048 {
2049   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2050   Mat            a    = aij->A,b = aij->B;
2051   PetscErrorCode ierr;
2052   PetscInt       s1,s2,s3;
2053 
2054   PetscFunctionBegin;
2055   ierr = MatGetLocalSize(mat,&s2,&s3);CHKERRQ(ierr);
2056   if (rr) {
2057     ierr = VecGetLocalSize(rr,&s1);CHKERRQ(ierr);
2058     if (s1!=s3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"right vector non-conforming local size");
2059     /* Overlap communication with computation. */
2060     ierr = VecScatterBegin(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2061   }
2062   if (ll) {
2063     ierr = VecGetLocalSize(ll,&s1);CHKERRQ(ierr);
2064     if (s1!=s2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"left vector non-conforming local size");
2065     ierr = (*b->ops->diagonalscale)(b,ll,0);CHKERRQ(ierr);
2066   }
2067   /* scale  the diagonal block */
2068   ierr = (*a->ops->diagonalscale)(a,ll,rr);CHKERRQ(ierr);
2069 
2070   if (rr) {
2071     /* Do a scatter end and then right scale the off-diagonal block */
2072     ierr = VecScatterEnd(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2073     ierr = (*b->ops->diagonalscale)(b,0,aij->lvec);CHKERRQ(ierr);
2074   }
2075   PetscFunctionReturn(0);
2076 }
2077 
2078 #undef __FUNCT__
2079 #define __FUNCT__ "MatSetUnfactored_MPIAIJ"
2080 PetscErrorCode MatSetUnfactored_MPIAIJ(Mat A)
2081 {
2082   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2083   PetscErrorCode ierr;
2084 
2085   PetscFunctionBegin;
2086   ierr = MatSetUnfactored(a->A);CHKERRQ(ierr);
2087   PetscFunctionReturn(0);
2088 }
2089 
2090 #undef __FUNCT__
2091 #define __FUNCT__ "MatEqual_MPIAIJ"
2092 PetscErrorCode MatEqual_MPIAIJ(Mat A,Mat B,PetscBool  *flag)
2093 {
2094   Mat_MPIAIJ     *matB = (Mat_MPIAIJ*)B->data,*matA = (Mat_MPIAIJ*)A->data;
2095   Mat            a,b,c,d;
2096   PetscBool      flg;
2097   PetscErrorCode ierr;
2098 
2099   PetscFunctionBegin;
2100   a = matA->A; b = matA->B;
2101   c = matB->A; d = matB->B;
2102 
2103   ierr = MatEqual(a,c,&flg);CHKERRQ(ierr);
2104   if (flg) {
2105     ierr = MatEqual(b,d,&flg);CHKERRQ(ierr);
2106   }
2107   ierr = MPI_Allreduce(&flg,flag,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
2108   PetscFunctionReturn(0);
2109 }
2110 
2111 #undef __FUNCT__
2112 #define __FUNCT__ "MatCopy_MPIAIJ"
2113 PetscErrorCode MatCopy_MPIAIJ(Mat A,Mat B,MatStructure str)
2114 {
2115   PetscErrorCode ierr;
2116   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2117   Mat_MPIAIJ     *b = (Mat_MPIAIJ*)B->data;
2118 
2119   PetscFunctionBegin;
2120   /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
2121   if ((str != SAME_NONZERO_PATTERN) || (A->ops->copy != B->ops->copy)) {
2122     /* because of the column compression in the off-processor part of the matrix a->B,
2123        the number of columns in a->B and b->B may be different, hence we cannot call
2124        the MatCopy() directly on the two parts. If need be, we can provide a more
2125        efficient copy than the MatCopy_Basic() by first uncompressing the a->B matrices
2126        then copying the submatrices */
2127     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
2128   } else {
2129     ierr = MatCopy(a->A,b->A,str);CHKERRQ(ierr);
2130     ierr = MatCopy(a->B,b->B,str);CHKERRQ(ierr);
2131   }
2132   PetscFunctionReturn(0);
2133 }
2134 
2135 #undef __FUNCT__
2136 #define __FUNCT__ "MatSetUp_MPIAIJ"
2137 PetscErrorCode MatSetUp_MPIAIJ(Mat A)
2138 {
2139   PetscErrorCode ierr;
2140 
2141   PetscFunctionBegin;
2142   ierr =  MatMPIAIJSetPreallocation(A,PETSC_DEFAULT,0,PETSC_DEFAULT,0);CHKERRQ(ierr);
2143   PetscFunctionReturn(0);
2144 }
2145 
2146 /*
2147    Computes the number of nonzeros per row needed for preallocation when X and Y
2148    have different nonzero structure.
2149 */
2150 #undef __FUNCT__
2151 #define __FUNCT__ "MatAXPYGetPreallocation_MPIX_private"
2152 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)
2153 {
2154   PetscInt       i,j,k,nzx,nzy;
2155 
2156   PetscFunctionBegin;
2157   /* Set the number of nonzeros in the new matrix */
2158   for (i=0; i<m; i++) {
2159     const PetscInt *xjj = xj+xi[i],*yjj = yj+yi[i];
2160     nzx = xi[i+1] - xi[i];
2161     nzy = yi[i+1] - yi[i];
2162     nnz[i] = 0;
2163     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2164       for (; k<nzy && yltog[yjj[k]]<xltog[xjj[j]]; k++) nnz[i]++; /* Catch up to X */
2165       if (k<nzy && yltog[yjj[k]]==xltog[xjj[j]]) k++;             /* Skip duplicate */
2166       nnz[i]++;
2167     }
2168     for (; k<nzy; k++) nnz[i]++;
2169   }
2170   PetscFunctionReturn(0);
2171 }
2172 
2173 /* This is the same as MatAXPYGetPreallocation_SeqAIJ, except that the local-to-global map is provided */
2174 #undef __FUNCT__
2175 #define __FUNCT__ "MatAXPYGetPreallocation_MPIAIJ"
2176 static PetscErrorCode MatAXPYGetPreallocation_MPIAIJ(Mat Y,const PetscInt *yltog,Mat X,const PetscInt *xltog,PetscInt *nnz)
2177 {
2178   PetscErrorCode ierr;
2179   PetscInt       m = Y->rmap->N;
2180   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data;
2181   Mat_SeqAIJ     *y = (Mat_SeqAIJ*)Y->data;
2182 
2183   PetscFunctionBegin;
2184   ierr = MatAXPYGetPreallocation_MPIX_private(m,x->i,x->j,xltog,y->i,y->j,yltog,nnz);CHKERRQ(ierr);
2185   PetscFunctionReturn(0);
2186 }
2187 
2188 #undef __FUNCT__
2189 #define __FUNCT__ "MatAXPY_MPIAIJ"
2190 PetscErrorCode MatAXPY_MPIAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
2191 {
2192   PetscErrorCode ierr;
2193   Mat_MPIAIJ     *xx = (Mat_MPIAIJ*)X->data,*yy = (Mat_MPIAIJ*)Y->data;
2194   PetscBLASInt   bnz,one=1;
2195   Mat_SeqAIJ     *x,*y;
2196 
2197   PetscFunctionBegin;
2198   if (str == SAME_NONZERO_PATTERN) {
2199     PetscScalar alpha = a;
2200     x    = (Mat_SeqAIJ*)xx->A->data;
2201     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2202     y    = (Mat_SeqAIJ*)yy->A->data;
2203     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2204     x    = (Mat_SeqAIJ*)xx->B->data;
2205     y    = (Mat_SeqAIJ*)yy->B->data;
2206     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2207     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2208     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
2209   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
2210     ierr = MatAXPY_Basic(Y,a,X,str);CHKERRQ(ierr);
2211   } else {
2212     Mat      B;
2213     PetscInt *nnz_d,*nnz_o;
2214     ierr = PetscMalloc1(yy->A->rmap->N,&nnz_d);CHKERRQ(ierr);
2215     ierr = PetscMalloc1(yy->B->rmap->N,&nnz_o);CHKERRQ(ierr);
2216     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
2217     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
2218     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
2219     ierr = MatSetBlockSizesFromMats(B,Y,Y);CHKERRQ(ierr);
2220     ierr = MatSetType(B,MATMPIAIJ);CHKERRQ(ierr);
2221     ierr = MatAXPYGetPreallocation_SeqAIJ(yy->A,xx->A,nnz_d);CHKERRQ(ierr);
2222     ierr = MatAXPYGetPreallocation_MPIAIJ(yy->B,yy->garray,xx->B,xx->garray,nnz_o);CHKERRQ(ierr);
2223     ierr = MatMPIAIJSetPreallocation(B,0,nnz_d,0,nnz_o);CHKERRQ(ierr);
2224     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
2225     ierr = MatHeaderReplace(Y,&B);CHKERRQ(ierr);
2226     ierr = PetscFree(nnz_d);CHKERRQ(ierr);
2227     ierr = PetscFree(nnz_o);CHKERRQ(ierr);
2228   }
2229   PetscFunctionReturn(0);
2230 }
2231 
2232 extern PetscErrorCode  MatConjugate_SeqAIJ(Mat);
2233 
2234 #undef __FUNCT__
2235 #define __FUNCT__ "MatConjugate_MPIAIJ"
2236 PetscErrorCode  MatConjugate_MPIAIJ(Mat mat)
2237 {
2238 #if defined(PETSC_USE_COMPLEX)
2239   PetscErrorCode ierr;
2240   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2241 
2242   PetscFunctionBegin;
2243   ierr = MatConjugate_SeqAIJ(aij->A);CHKERRQ(ierr);
2244   ierr = MatConjugate_SeqAIJ(aij->B);CHKERRQ(ierr);
2245 #else
2246   PetscFunctionBegin;
2247 #endif
2248   PetscFunctionReturn(0);
2249 }
2250 
2251 #undef __FUNCT__
2252 #define __FUNCT__ "MatRealPart_MPIAIJ"
2253 PetscErrorCode MatRealPart_MPIAIJ(Mat A)
2254 {
2255   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2256   PetscErrorCode ierr;
2257 
2258   PetscFunctionBegin;
2259   ierr = MatRealPart(a->A);CHKERRQ(ierr);
2260   ierr = MatRealPart(a->B);CHKERRQ(ierr);
2261   PetscFunctionReturn(0);
2262 }
2263 
2264 #undef __FUNCT__
2265 #define __FUNCT__ "MatImaginaryPart_MPIAIJ"
2266 PetscErrorCode MatImaginaryPart_MPIAIJ(Mat A)
2267 {
2268   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2269   PetscErrorCode ierr;
2270 
2271   PetscFunctionBegin;
2272   ierr = MatImaginaryPart(a->A);CHKERRQ(ierr);
2273   ierr = MatImaginaryPart(a->B);CHKERRQ(ierr);
2274   PetscFunctionReturn(0);
2275 }
2276 
2277 #undef __FUNCT__
2278 #define __FUNCT__ "MatGetRowMaxAbs_MPIAIJ"
2279 PetscErrorCode MatGetRowMaxAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2280 {
2281   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2282   PetscErrorCode ierr;
2283   PetscInt       i,*idxb = 0;
2284   PetscScalar    *va,*vb;
2285   Vec            vtmp;
2286 
2287   PetscFunctionBegin;
2288   ierr = MatGetRowMaxAbs(a->A,v,idx);CHKERRQ(ierr);
2289   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2290   if (idx) {
2291     for (i=0; i<A->rmap->n; i++) {
2292       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2293     }
2294   }
2295 
2296   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2297   if (idx) {
2298     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2299   }
2300   ierr = MatGetRowMaxAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2301   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2302 
2303   for (i=0; i<A->rmap->n; i++) {
2304     if (PetscAbsScalar(va[i]) < PetscAbsScalar(vb[i])) {
2305       va[i] = vb[i];
2306       if (idx) idx[i] = a->garray[idxb[i]];
2307     }
2308   }
2309 
2310   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2311   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2312   ierr = PetscFree(idxb);CHKERRQ(ierr);
2313   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2314   PetscFunctionReturn(0);
2315 }
2316 
2317 #undef __FUNCT__
2318 #define __FUNCT__ "MatGetRowMinAbs_MPIAIJ"
2319 PetscErrorCode MatGetRowMinAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2320 {
2321   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2322   PetscErrorCode ierr;
2323   PetscInt       i,*idxb = 0;
2324   PetscScalar    *va,*vb;
2325   Vec            vtmp;
2326 
2327   PetscFunctionBegin;
2328   ierr = MatGetRowMinAbs(a->A,v,idx);CHKERRQ(ierr);
2329   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2330   if (idx) {
2331     for (i=0; i<A->cmap->n; i++) {
2332       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2333     }
2334   }
2335 
2336   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2337   if (idx) {
2338     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2339   }
2340   ierr = MatGetRowMinAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2341   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2342 
2343   for (i=0; i<A->rmap->n; i++) {
2344     if (PetscAbsScalar(va[i]) > PetscAbsScalar(vb[i])) {
2345       va[i] = vb[i];
2346       if (idx) idx[i] = a->garray[idxb[i]];
2347     }
2348   }
2349 
2350   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2351   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2352   ierr = PetscFree(idxb);CHKERRQ(ierr);
2353   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2354   PetscFunctionReturn(0);
2355 }
2356 
2357 #undef __FUNCT__
2358 #define __FUNCT__ "MatGetRowMin_MPIAIJ"
2359 PetscErrorCode MatGetRowMin_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2360 {
2361   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2362   PetscInt       n      = A->rmap->n;
2363   PetscInt       cstart = A->cmap->rstart;
2364   PetscInt       *cmap  = mat->garray;
2365   PetscInt       *diagIdx, *offdiagIdx;
2366   Vec            diagV, offdiagV;
2367   PetscScalar    *a, *diagA, *offdiagA;
2368   PetscInt       r;
2369   PetscErrorCode ierr;
2370 
2371   PetscFunctionBegin;
2372   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2373   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &diagV);CHKERRQ(ierr);
2374   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &offdiagV);CHKERRQ(ierr);
2375   ierr = MatGetRowMin(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2376   ierr = MatGetRowMin(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2377   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2378   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2379   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2380   for (r = 0; r < n; ++r) {
2381     if (PetscAbsScalar(diagA[r]) <= PetscAbsScalar(offdiagA[r])) {
2382       a[r]   = diagA[r];
2383       idx[r] = cstart + diagIdx[r];
2384     } else {
2385       a[r]   = offdiagA[r];
2386       idx[r] = cmap[offdiagIdx[r]];
2387     }
2388   }
2389   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2390   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2391   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2392   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2393   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2394   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2395   PetscFunctionReturn(0);
2396 }
2397 
2398 #undef __FUNCT__
2399 #define __FUNCT__ "MatGetRowMax_MPIAIJ"
2400 PetscErrorCode MatGetRowMax_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2401 {
2402   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2403   PetscInt       n      = A->rmap->n;
2404   PetscInt       cstart = A->cmap->rstart;
2405   PetscInt       *cmap  = mat->garray;
2406   PetscInt       *diagIdx, *offdiagIdx;
2407   Vec            diagV, offdiagV;
2408   PetscScalar    *a, *diagA, *offdiagA;
2409   PetscInt       r;
2410   PetscErrorCode ierr;
2411 
2412   PetscFunctionBegin;
2413   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2414   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &diagV);CHKERRQ(ierr);
2415   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &offdiagV);CHKERRQ(ierr);
2416   ierr = MatGetRowMax(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2417   ierr = MatGetRowMax(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2418   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2419   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2420   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2421   for (r = 0; r < n; ++r) {
2422     if (PetscAbsScalar(diagA[r]) >= PetscAbsScalar(offdiagA[r])) {
2423       a[r]   = diagA[r];
2424       idx[r] = cstart + diagIdx[r];
2425     } else {
2426       a[r]   = offdiagA[r];
2427       idx[r] = cmap[offdiagIdx[r]];
2428     }
2429   }
2430   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2431   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2432   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2433   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2434   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2435   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2436   PetscFunctionReturn(0);
2437 }
2438 
2439 #undef __FUNCT__
2440 #define __FUNCT__ "MatGetSeqNonzeroStructure_MPIAIJ"
2441 PetscErrorCode MatGetSeqNonzeroStructure_MPIAIJ(Mat mat,Mat *newmat)
2442 {
2443   PetscErrorCode ierr;
2444   Mat            *dummy;
2445 
2446   PetscFunctionBegin;
2447   ierr    = MatGetSubMatrix_MPIAIJ_All(mat,MAT_DO_NOT_GET_VALUES,MAT_INITIAL_MATRIX,&dummy);CHKERRQ(ierr);
2448   *newmat = *dummy;
2449   ierr    = PetscFree(dummy);CHKERRQ(ierr);
2450   PetscFunctionReturn(0);
2451 }
2452 
2453 #undef __FUNCT__
2454 #define __FUNCT__ "MatInvertBlockDiagonal_MPIAIJ"
2455 PetscErrorCode  MatInvertBlockDiagonal_MPIAIJ(Mat A,const PetscScalar **values)
2456 {
2457   Mat_MPIAIJ     *a = (Mat_MPIAIJ*) A->data;
2458   PetscErrorCode ierr;
2459 
2460   PetscFunctionBegin;
2461   ierr = MatInvertBlockDiagonal(a->A,values);CHKERRQ(ierr);
2462   PetscFunctionReturn(0);
2463 }
2464 
2465 #undef __FUNCT__
2466 #define __FUNCT__ "MatSetRandom_MPIAIJ"
2467 static PetscErrorCode  MatSetRandom_MPIAIJ(Mat x,PetscRandom rctx)
2468 {
2469   PetscErrorCode ierr;
2470   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)x->data;
2471 
2472   PetscFunctionBegin;
2473   ierr = MatSetRandom(aij->A,rctx);CHKERRQ(ierr);
2474   ierr = MatSetRandom(aij->B,rctx);CHKERRQ(ierr);
2475   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2476   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2477   PetscFunctionReturn(0);
2478 }
2479 
2480 #undef __FUNCT__
2481 #define __FUNCT__ "MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ"
2482 PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ(Mat A,PetscBool sc)
2483 {
2484   PetscFunctionBegin;
2485   if (sc) A->ops->increaseoverlap = MatIncreaseOverlap_MPIAIJ_Scalable;
2486   else A->ops->increaseoverlap    = MatIncreaseOverlap_MPIAIJ;
2487   PetscFunctionReturn(0);
2488 }
2489 
2490 #undef __FUNCT__
2491 #define __FUNCT__ "MatMPIAIJSetUseScalableIncreaseOverlap"
2492 /*@
2493    MatMPIAIJSetUseScalableIncreaseOverlap - Determine if the matrix uses a scalable algorithm to compute the overlap
2494 
2495    Collective on Mat
2496 
2497    Input Parameters:
2498 +    A - the matrix
2499 -    sc - PETSC_TRUE indicates use the scalable algorithm (default is not to use the scalable algorithm)
2500 
2501 @*/
2502 PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap(Mat A,PetscBool sc)
2503 {
2504   PetscErrorCode       ierr;
2505 
2506   PetscFunctionBegin;
2507   ierr = PetscTryMethod(A,"MatMPIAIJSetUseScalableIncreaseOverlap_C",(Mat,PetscBool),(A,sc));CHKERRQ(ierr);
2508   PetscFunctionReturn(0);
2509 }
2510 
2511 #undef __FUNCT__
2512 #define __FUNCT__ "MatSetFromOptions_MPIAIJ"
2513 PetscErrorCode MatSetFromOptions_MPIAIJ(PetscOptions *PetscOptionsObject,Mat A)
2514 {
2515   PetscErrorCode       ierr;
2516   PetscBool            sc = PETSC_FALSE,flg;
2517 
2518   PetscFunctionBegin;
2519   ierr = PetscOptionsHead(PetscOptionsObject,"MPIAIJ options");CHKERRQ(ierr);
2520   ierr = PetscObjectOptionsBegin((PetscObject)A);
2521     if (A->ops->increaseoverlap == MatIncreaseOverlap_MPIAIJ_Scalable) sc = PETSC_TRUE;
2522     ierr = PetscOptionsBool("-mat_increase_overlap_scalable","Use a scalable algorithm to compute the overlap","MatIncreaseOverlap",sc,&sc,&flg);CHKERRQ(ierr);
2523     if (flg) {
2524       ierr = MatMPIAIJSetUseScalableIncreaseOverlap(A,sc);CHKERRQ(ierr);
2525     }
2526   ierr = PetscOptionsEnd();CHKERRQ(ierr);
2527   PetscFunctionReturn(0);
2528 }
2529 
2530 #undef __FUNCT__
2531 #define __FUNCT__ "MatShift_MPIAIJ"
2532 PetscErrorCode MatShift_MPIAIJ(Mat Y,PetscScalar a)
2533 {
2534   PetscErrorCode ierr;
2535   Mat_MPIAIJ     *maij = (Mat_MPIAIJ*)Y->data;
2536   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)maij->A->data;
2537 
2538   PetscFunctionBegin;
2539   if (!Y->preallocated) {
2540     ierr = MatMPIAIJSetPreallocation(Y,1,NULL,0,NULL);CHKERRQ(ierr);
2541   } else if (!aij->nz) {
2542     ierr = MatSeqAIJSetPreallocation(maij->A,1,NULL);CHKERRQ(ierr);
2543   }
2544   ierr = MatShift_Basic(Y,a);CHKERRQ(ierr);
2545   PetscFunctionReturn(0);
2546 }
2547 
2548 #undef __FUNCT__
2549 #define __FUNCT__ "MatMissingDiagonal_MPIAIJ"
2550 PetscErrorCode MatMissingDiagonal_MPIAIJ(Mat A,PetscBool  *missing,PetscInt *d)
2551 {
2552   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2553   PetscErrorCode ierr;
2554 
2555   PetscFunctionBegin;
2556   if (A->rmap->n != A->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only works for square matrices");
2557   ierr = MatMissingDiagonal(a->A,missing,d);CHKERRQ(ierr);
2558   if (d) {
2559     PetscInt rstart;
2560     ierr = MatGetOwnershipRange(A,&rstart,NULL);CHKERRQ(ierr);
2561     *d += rstart;
2562 
2563   }
2564   PetscFunctionReturn(0);
2565 }
2566 
2567 
2568 /* -------------------------------------------------------------------*/
2569 static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
2570                                        MatGetRow_MPIAIJ,
2571                                        MatRestoreRow_MPIAIJ,
2572                                        MatMult_MPIAIJ,
2573                                 /* 4*/ MatMultAdd_MPIAIJ,
2574                                        MatMultTranspose_MPIAIJ,
2575                                        MatMultTransposeAdd_MPIAIJ,
2576                                        0,
2577                                        0,
2578                                        0,
2579                                 /*10*/ 0,
2580                                        0,
2581                                        0,
2582                                        MatSOR_MPIAIJ,
2583                                        MatTranspose_MPIAIJ,
2584                                 /*15*/ MatGetInfo_MPIAIJ,
2585                                        MatEqual_MPIAIJ,
2586                                        MatGetDiagonal_MPIAIJ,
2587                                        MatDiagonalScale_MPIAIJ,
2588                                        MatNorm_MPIAIJ,
2589                                 /*20*/ MatAssemblyBegin_MPIAIJ,
2590                                        MatAssemblyEnd_MPIAIJ,
2591                                        MatSetOption_MPIAIJ,
2592                                        MatZeroEntries_MPIAIJ,
2593                                 /*24*/ MatZeroRows_MPIAIJ,
2594                                        0,
2595                                        0,
2596                                        0,
2597                                        0,
2598                                 /*29*/ MatSetUp_MPIAIJ,
2599                                        0,
2600                                        0,
2601                                        0,
2602                                        0,
2603                                 /*34*/ MatDuplicate_MPIAIJ,
2604                                        0,
2605                                        0,
2606                                        0,
2607                                        0,
2608                                 /*39*/ MatAXPY_MPIAIJ,
2609                                        MatGetSubMatrices_MPIAIJ,
2610                                        MatIncreaseOverlap_MPIAIJ,
2611                                        MatGetValues_MPIAIJ,
2612                                        MatCopy_MPIAIJ,
2613                                 /*44*/ MatGetRowMax_MPIAIJ,
2614                                        MatScale_MPIAIJ,
2615                                        MatShift_MPIAIJ,
2616                                        MatDiagonalSet_MPIAIJ,
2617                                        MatZeroRowsColumns_MPIAIJ,
2618                                 /*49*/ MatSetRandom_MPIAIJ,
2619                                        0,
2620                                        0,
2621                                        0,
2622                                        0,
2623                                 /*54*/ MatFDColoringCreate_MPIXAIJ,
2624                                        0,
2625                                        MatSetUnfactored_MPIAIJ,
2626                                        MatPermute_MPIAIJ,
2627                                        0,
2628                                 /*59*/ MatGetSubMatrix_MPIAIJ,
2629                                        MatDestroy_MPIAIJ,
2630                                        MatView_MPIAIJ,
2631                                        0,
2632                                        MatMatMatMult_MPIAIJ_MPIAIJ_MPIAIJ,
2633                                 /*64*/ MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ,
2634                                        MatMatMatMultNumeric_MPIAIJ_MPIAIJ_MPIAIJ,
2635                                        0,
2636                                        0,
2637                                        0,
2638                                 /*69*/ MatGetRowMaxAbs_MPIAIJ,
2639                                        MatGetRowMinAbs_MPIAIJ,
2640                                        0,
2641                                        MatSetColoring_MPIAIJ,
2642                                        0,
2643                                        MatSetValuesAdifor_MPIAIJ,
2644                                 /*75*/ MatFDColoringApply_AIJ,
2645                                        MatSetFromOptions_MPIAIJ,
2646                                        0,
2647                                        0,
2648                                        MatFindZeroDiagonals_MPIAIJ,
2649                                 /*80*/ 0,
2650                                        0,
2651                                        0,
2652                                 /*83*/ MatLoad_MPIAIJ,
2653                                        0,
2654                                        0,
2655                                        0,
2656                                        0,
2657                                        0,
2658                                 /*89*/ MatMatMult_MPIAIJ_MPIAIJ,
2659                                        MatMatMultSymbolic_MPIAIJ_MPIAIJ,
2660                                        MatMatMultNumeric_MPIAIJ_MPIAIJ,
2661                                        MatPtAP_MPIAIJ_MPIAIJ,
2662                                        MatPtAPSymbolic_MPIAIJ_MPIAIJ,
2663                                 /*94*/ MatPtAPNumeric_MPIAIJ_MPIAIJ,
2664                                        0,
2665                                        0,
2666                                        0,
2667                                        0,
2668                                 /*99*/ 0,
2669                                        0,
2670                                        0,
2671                                        MatConjugate_MPIAIJ,
2672                                        0,
2673                                 /*104*/MatSetValuesRow_MPIAIJ,
2674                                        MatRealPart_MPIAIJ,
2675                                        MatImaginaryPart_MPIAIJ,
2676                                        0,
2677                                        0,
2678                                 /*109*/0,
2679                                        0,
2680                                        MatGetRowMin_MPIAIJ,
2681                                        0,
2682                                        MatMissingDiagonal_MPIAIJ,
2683                                 /*114*/MatGetSeqNonzeroStructure_MPIAIJ,
2684                                        0,
2685                                        MatGetGhosts_MPIAIJ,
2686                                        0,
2687                                        0,
2688                                 /*119*/0,
2689                                        0,
2690                                        0,
2691                                        0,
2692                                        MatGetMultiProcBlock_MPIAIJ,
2693                                 /*124*/MatFindNonzeroRows_MPIAIJ,
2694                                        MatGetColumnNorms_MPIAIJ,
2695                                        MatInvertBlockDiagonal_MPIAIJ,
2696                                        0,
2697                                        MatGetSubMatricesMPI_MPIAIJ,
2698                                 /*129*/0,
2699                                        MatTransposeMatMult_MPIAIJ_MPIAIJ,
2700                                        MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ,
2701                                        MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ,
2702                                        0,
2703                                 /*134*/0,
2704                                        0,
2705                                        0,
2706                                        0,
2707                                        0,
2708                                 /*139*/0,
2709                                        0,
2710                                        0,
2711                                        MatFDColoringSetUp_MPIXAIJ,
2712                                        MatFindOffBlockDiagonalEntries_MPIAIJ,
2713                                 /*144*/MatCreateMPIMatConcatenateSeqMat_MPIAIJ
2714 };
2715 
2716 /* ----------------------------------------------------------------------------------------*/
2717 
2718 #undef __FUNCT__
2719 #define __FUNCT__ "MatStoreValues_MPIAIJ"
2720 PetscErrorCode  MatStoreValues_MPIAIJ(Mat mat)
2721 {
2722   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2723   PetscErrorCode ierr;
2724 
2725   PetscFunctionBegin;
2726   ierr = MatStoreValues(aij->A);CHKERRQ(ierr);
2727   ierr = MatStoreValues(aij->B);CHKERRQ(ierr);
2728   PetscFunctionReturn(0);
2729 }
2730 
2731 #undef __FUNCT__
2732 #define __FUNCT__ "MatRetrieveValues_MPIAIJ"
2733 PetscErrorCode  MatRetrieveValues_MPIAIJ(Mat mat)
2734 {
2735   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2736   PetscErrorCode ierr;
2737 
2738   PetscFunctionBegin;
2739   ierr = MatRetrieveValues(aij->A);CHKERRQ(ierr);
2740   ierr = MatRetrieveValues(aij->B);CHKERRQ(ierr);
2741   PetscFunctionReturn(0);
2742 }
2743 
2744 #undef __FUNCT__
2745 #define __FUNCT__ "MatMPIAIJSetPreallocation_MPIAIJ"
2746 PetscErrorCode  MatMPIAIJSetPreallocation_MPIAIJ(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
2747 {
2748   Mat_MPIAIJ     *b;
2749   PetscErrorCode ierr;
2750 
2751   PetscFunctionBegin;
2752   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
2753   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
2754   b = (Mat_MPIAIJ*)B->data;
2755 
2756   if (!B->preallocated) {
2757     /* Explicitly create 2 MATSEQAIJ matrices. */
2758     ierr = MatCreate(PETSC_COMM_SELF,&b->A);CHKERRQ(ierr);
2759     ierr = MatSetSizes(b->A,B->rmap->n,B->cmap->n,B->rmap->n,B->cmap->n);CHKERRQ(ierr);
2760     ierr = MatSetBlockSizesFromMats(b->A,B,B);CHKERRQ(ierr);
2761     ierr = MatSetType(b->A,MATSEQAIJ);CHKERRQ(ierr);
2762     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->A);CHKERRQ(ierr);
2763     ierr = MatCreate(PETSC_COMM_SELF,&b->B);CHKERRQ(ierr);
2764     ierr = MatSetSizes(b->B,B->rmap->n,B->cmap->N,B->rmap->n,B->cmap->N);CHKERRQ(ierr);
2765     ierr = MatSetBlockSizesFromMats(b->B,B,B);CHKERRQ(ierr);
2766     ierr = MatSetType(b->B,MATSEQAIJ);CHKERRQ(ierr);
2767     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->B);CHKERRQ(ierr);
2768   }
2769 
2770   ierr = MatSeqAIJSetPreallocation(b->A,d_nz,d_nnz);CHKERRQ(ierr);
2771   ierr = MatSeqAIJSetPreallocation(b->B,o_nz,o_nnz);CHKERRQ(ierr);
2772   B->preallocated = PETSC_TRUE;
2773   PetscFunctionReturn(0);
2774 }
2775 
2776 #undef __FUNCT__
2777 #define __FUNCT__ "MatDuplicate_MPIAIJ"
2778 PetscErrorCode MatDuplicate_MPIAIJ(Mat matin,MatDuplicateOption cpvalues,Mat *newmat)
2779 {
2780   Mat            mat;
2781   Mat_MPIAIJ     *a,*oldmat = (Mat_MPIAIJ*)matin->data;
2782   PetscErrorCode ierr;
2783 
2784   PetscFunctionBegin;
2785   *newmat = 0;
2786   ierr    = MatCreate(PetscObjectComm((PetscObject)matin),&mat);CHKERRQ(ierr);
2787   ierr    = MatSetSizes(mat,matin->rmap->n,matin->cmap->n,matin->rmap->N,matin->cmap->N);CHKERRQ(ierr);
2788   ierr    = MatSetBlockSizesFromMats(mat,matin,matin);CHKERRQ(ierr);
2789   ierr    = MatSetType(mat,((PetscObject)matin)->type_name);CHKERRQ(ierr);
2790   ierr    = PetscMemcpy(mat->ops,matin->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
2791   a       = (Mat_MPIAIJ*)mat->data;
2792 
2793   mat->factortype   = matin->factortype;
2794   mat->assembled    = PETSC_TRUE;
2795   mat->insertmode   = NOT_SET_VALUES;
2796   mat->preallocated = PETSC_TRUE;
2797 
2798   a->size         = oldmat->size;
2799   a->rank         = oldmat->rank;
2800   a->donotstash   = oldmat->donotstash;
2801   a->roworiented  = oldmat->roworiented;
2802   a->rowindices   = 0;
2803   a->rowvalues    = 0;
2804   a->getrowactive = PETSC_FALSE;
2805 
2806   ierr = PetscLayoutReference(matin->rmap,&mat->rmap);CHKERRQ(ierr);
2807   ierr = PetscLayoutReference(matin->cmap,&mat->cmap);CHKERRQ(ierr);
2808 
2809   if (oldmat->colmap) {
2810 #if defined(PETSC_USE_CTABLE)
2811     ierr = PetscTableCreateCopy(oldmat->colmap,&a->colmap);CHKERRQ(ierr);
2812 #else
2813     ierr = PetscMalloc1(mat->cmap->N,&a->colmap);CHKERRQ(ierr);
2814     ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2815     ierr = PetscMemcpy(a->colmap,oldmat->colmap,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2816 #endif
2817   } else a->colmap = 0;
2818   if (oldmat->garray) {
2819     PetscInt len;
2820     len  = oldmat->B->cmap->n;
2821     ierr = PetscMalloc1(len+1,&a->garray);CHKERRQ(ierr);
2822     ierr = PetscLogObjectMemory((PetscObject)mat,len*sizeof(PetscInt));CHKERRQ(ierr);
2823     if (len) { ierr = PetscMemcpy(a->garray,oldmat->garray,len*sizeof(PetscInt));CHKERRQ(ierr); }
2824   } else a->garray = 0;
2825 
2826   ierr    = VecDuplicate(oldmat->lvec,&a->lvec);CHKERRQ(ierr);
2827   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->lvec);CHKERRQ(ierr);
2828   ierr    = VecScatterCopy(oldmat->Mvctx,&a->Mvctx);CHKERRQ(ierr);
2829   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->Mvctx);CHKERRQ(ierr);
2830   ierr    = MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
2831   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->A);CHKERRQ(ierr);
2832   ierr    = MatDuplicate(oldmat->B,cpvalues,&a->B);CHKERRQ(ierr);
2833   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->B);CHKERRQ(ierr);
2834   ierr    = PetscFunctionListDuplicate(((PetscObject)matin)->qlist,&((PetscObject)mat)->qlist);CHKERRQ(ierr);
2835   *newmat = mat;
2836   PetscFunctionReturn(0);
2837 }
2838 
2839 
2840 
2841 #undef __FUNCT__
2842 #define __FUNCT__ "MatLoad_MPIAIJ"
2843 PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
2844 {
2845   PetscScalar    *vals,*svals;
2846   MPI_Comm       comm;
2847   PetscErrorCode ierr;
2848   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
2849   PetscInt       i,nz,j,rstart,rend,mmax,maxnz = 0;
2850   PetscInt       header[4],*rowlengths = 0,M,N,m,*cols;
2851   PetscInt       *ourlens = NULL,*procsnz = NULL,*offlens = NULL,jj,*mycols,*smycols;
2852   PetscInt       cend,cstart,n,*rowners;
2853   int            fd;
2854   PetscInt       bs = newMat->rmap->bs;
2855 
2856   PetscFunctionBegin;
2857   /* force binary viewer to load .info file if it has not yet done so */
2858   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
2859   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
2860   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2861   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2862   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
2863   if (!rank) {
2864     ierr = PetscBinaryRead(fd,(char*)header,4,PETSC_INT);CHKERRQ(ierr);
2865     if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
2866   }
2867 
2868   ierr = PetscOptionsBegin(comm,NULL,"Options for loading MPIAIJ matrix","Mat");CHKERRQ(ierr);
2869   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
2870   ierr = PetscOptionsEnd();CHKERRQ(ierr);
2871   if (bs < 0) bs = 1;
2872 
2873   ierr = MPI_Bcast(header+1,3,MPIU_INT,0,comm);CHKERRQ(ierr);
2874   M    = header[1]; N = header[2];
2875 
2876   /* If global sizes are set, check if they are consistent with that given in the file */
2877   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);
2878   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);
2879 
2880   /* determine ownership of all (block) rows */
2881   if (M%bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Inconsistent # of rows (%d) and block size (%d)",M,bs);
2882   if (newMat->rmap->n < 0) m = bs*((M/bs)/size + (((M/bs) % size) > rank));    /* PETSC_DECIDE */
2883   else m = newMat->rmap->n; /* Set by user */
2884 
2885   ierr = PetscMalloc1(size+1,&rowners);CHKERRQ(ierr);
2886   ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
2887 
2888   /* First process needs enough room for process with most rows */
2889   if (!rank) {
2890     mmax = rowners[1];
2891     for (i=2; i<=size; i++) {
2892       mmax = PetscMax(mmax, rowners[i]);
2893     }
2894   } else mmax = -1;             /* unused, but compilers complain */
2895 
2896   rowners[0] = 0;
2897   for (i=2; i<=size; i++) {
2898     rowners[i] += rowners[i-1];
2899   }
2900   rstart = rowners[rank];
2901   rend   = rowners[rank+1];
2902 
2903   /* distribute row lengths to all processors */
2904   ierr = PetscMalloc2(m,&ourlens,m,&offlens);CHKERRQ(ierr);
2905   if (!rank) {
2906     ierr = PetscBinaryRead(fd,ourlens,m,PETSC_INT);CHKERRQ(ierr);
2907     ierr = PetscMalloc1(mmax,&rowlengths);CHKERRQ(ierr);
2908     ierr = PetscCalloc1(size,&procsnz);CHKERRQ(ierr);
2909     for (j=0; j<m; j++) {
2910       procsnz[0] += ourlens[j];
2911     }
2912     for (i=1; i<size; i++) {
2913       ierr = PetscBinaryRead(fd,rowlengths,rowners[i+1]-rowners[i],PETSC_INT);CHKERRQ(ierr);
2914       /* calculate the number of nonzeros on each processor */
2915       for (j=0; j<rowners[i+1]-rowners[i]; j++) {
2916         procsnz[i] += rowlengths[j];
2917       }
2918       ierr = MPIULong_Send(rowlengths,rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2919     }
2920     ierr = PetscFree(rowlengths);CHKERRQ(ierr);
2921   } else {
2922     ierr = MPIULong_Recv(ourlens,m,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2923   }
2924 
2925   if (!rank) {
2926     /* determine max buffer needed and allocate it */
2927     maxnz = 0;
2928     for (i=0; i<size; i++) {
2929       maxnz = PetscMax(maxnz,procsnz[i]);
2930     }
2931     ierr = PetscMalloc1(maxnz,&cols);CHKERRQ(ierr);
2932 
2933     /* read in my part of the matrix column indices  */
2934     nz   = procsnz[0];
2935     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2936     ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);
2937 
2938     /* read in every one elses and ship off */
2939     for (i=1; i<size; i++) {
2940       nz   = procsnz[i];
2941       ierr = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
2942       ierr = MPIULong_Send(cols,nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2943     }
2944     ierr = PetscFree(cols);CHKERRQ(ierr);
2945   } else {
2946     /* determine buffer space needed for message */
2947     nz = 0;
2948     for (i=0; i<m; i++) {
2949       nz += ourlens[i];
2950     }
2951     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2952 
2953     /* receive message of column indices*/
2954     ierr = MPIULong_Recv(mycols,nz,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2955   }
2956 
2957   /* determine column ownership if matrix is not square */
2958   if (N != M) {
2959     if (newMat->cmap->n < 0) n = N/size + ((N % size) > rank);
2960     else n = newMat->cmap->n;
2961     ierr   = MPI_Scan(&n,&cend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
2962     cstart = cend - n;
2963   } else {
2964     cstart = rstart;
2965     cend   = rend;
2966     n      = cend - cstart;
2967   }
2968 
2969   /* loop over local rows, determining number of off diagonal entries */
2970   ierr = PetscMemzero(offlens,m*sizeof(PetscInt));CHKERRQ(ierr);
2971   jj   = 0;
2972   for (i=0; i<m; i++) {
2973     for (j=0; j<ourlens[i]; j++) {
2974       if (mycols[jj] < cstart || mycols[jj] >= cend) offlens[i]++;
2975       jj++;
2976     }
2977   }
2978 
2979   for (i=0; i<m; i++) {
2980     ourlens[i] -= offlens[i];
2981   }
2982   ierr = MatSetSizes(newMat,m,n,M,N);CHKERRQ(ierr);
2983 
2984   if (bs > 1) {ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);}
2985 
2986   ierr = MatMPIAIJSetPreallocation(newMat,0,ourlens,0,offlens);CHKERRQ(ierr);
2987 
2988   for (i=0; i<m; i++) {
2989     ourlens[i] += offlens[i];
2990   }
2991 
2992   if (!rank) {
2993     ierr = PetscMalloc1(maxnz+1,&vals);CHKERRQ(ierr);
2994 
2995     /* read in my part of the matrix numerical values  */
2996     nz   = procsnz[0];
2997     ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
2998 
2999     /* insert into matrix */
3000     jj      = rstart;
3001     smycols = mycols;
3002     svals   = vals;
3003     for (i=0; i<m; i++) {
3004       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
3005       smycols += ourlens[i];
3006       svals   += ourlens[i];
3007       jj++;
3008     }
3009 
3010     /* read in other processors and ship out */
3011     for (i=1; i<size; i++) {
3012       nz   = procsnz[i];
3013       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
3014       ierr = MPIULong_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
3015     }
3016     ierr = PetscFree(procsnz);CHKERRQ(ierr);
3017   } else {
3018     /* receive numeric values */
3019     ierr = PetscMalloc1(nz+1,&vals);CHKERRQ(ierr);
3020 
3021     /* receive message of values*/
3022     ierr = MPIULong_Recv(vals,nz,MPIU_SCALAR,0,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
3023 
3024     /* insert into matrix */
3025     jj      = rstart;
3026     smycols = mycols;
3027     svals   = vals;
3028     for (i=0; i<m; i++) {
3029       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
3030       smycols += ourlens[i];
3031       svals   += ourlens[i];
3032       jj++;
3033     }
3034   }
3035   ierr = PetscFree2(ourlens,offlens);CHKERRQ(ierr);
3036   ierr = PetscFree(vals);CHKERRQ(ierr);
3037   ierr = PetscFree(mycols);CHKERRQ(ierr);
3038   ierr = PetscFree(rowners);CHKERRQ(ierr);
3039   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3040   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3041   PetscFunctionReturn(0);
3042 }
3043 
3044 #undef __FUNCT__
3045 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ"
3046 /* TODO: Not scalable because of ISAllGather() unless getting all columns. */
3047 PetscErrorCode MatGetSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3048 {
3049   PetscErrorCode ierr;
3050   IS             iscol_local;
3051   PetscInt       csize;
3052 
3053   PetscFunctionBegin;
3054   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3055   if (call == MAT_REUSE_MATRIX) {
3056     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3057     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3058   } else {
3059     /* check if we are grabbing all columns*/
3060     PetscBool    isstride;
3061     PetscMPIInt  lisstride = 0,gisstride;
3062     ierr = PetscObjectTypeCompare((PetscObject)iscol,ISSTRIDE,&isstride);CHKERRQ(ierr);
3063     if (isstride) {
3064       PetscInt  start,len,mstart,mlen;
3065       ierr = ISStrideGetInfo(iscol,&start,NULL);CHKERRQ(ierr);
3066       ierr = ISGetLocalSize(iscol,&len);CHKERRQ(ierr);
3067       ierr = MatGetOwnershipRangeColumn(mat,&mstart,&mlen);CHKERRQ(ierr);
3068       if (mstart == start && mlen-mstart == len) lisstride = 1;
3069     }
3070     ierr = MPI_Allreduce(&lisstride,&gisstride,1,MPI_INT,MPI_MIN,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
3071     if (gisstride) {
3072       PetscInt N;
3073       ierr = MatGetSize(mat,NULL,&N);CHKERRQ(ierr);
3074       ierr = ISCreateStride(PetscObjectComm((PetscObject)mat),N,0,1,&iscol_local);CHKERRQ(ierr);
3075       ierr = ISSetIdentity(iscol_local);CHKERRQ(ierr);
3076       ierr = PetscInfo(mat,"Optimizing for obtaining all columns of the matrix; skipping ISAllGather()\n");CHKERRQ(ierr);
3077     } else {
3078       PetscInt cbs;
3079       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
3080       ierr = ISAllGather(iscol,&iscol_local);CHKERRQ(ierr);
3081       ierr = ISSetBlockSize(iscol_local,cbs);CHKERRQ(ierr);
3082     }
3083   }
3084   ierr = MatGetSubMatrix_MPIAIJ_Private(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
3085   if (call == MAT_INITIAL_MATRIX) {
3086     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3087     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3088   }
3089   PetscFunctionReturn(0);
3090 }
3091 
3092 extern PetscErrorCode MatGetSubMatrices_MPIAIJ_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool*,Mat*);
3093 #undef __FUNCT__
3094 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ_Private"
3095 /*
3096     Not great since it makes two copies of the submatrix, first an SeqAIJ
3097   in local and then by concatenating the local matrices the end result.
3098   Writing it directly would be much like MatGetSubMatrices_MPIAIJ()
3099 
3100   Note: This requires a sequential iscol with all indices.
3101 */
3102 PetscErrorCode MatGetSubMatrix_MPIAIJ_Private(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3103 {
3104   PetscErrorCode ierr;
3105   PetscMPIInt    rank,size;
3106   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3107   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal,ncol;
3108   PetscBool      allcolumns, colflag;
3109   Mat            M,Mreuse;
3110   MatScalar      *vwork,*aa;
3111   MPI_Comm       comm;
3112   Mat_SeqAIJ     *aij;
3113 
3114   PetscFunctionBegin;
3115   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3116   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3117   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3118 
3119   ierr = ISIdentity(iscol,&colflag);CHKERRQ(ierr);
3120   ierr = ISGetLocalSize(iscol,&ncol);CHKERRQ(ierr);
3121   if (colflag && ncol == mat->cmap->N) {
3122     allcolumns = PETSC_TRUE;
3123     ierr = PetscInfo(mat,"Optimizing for obtaining all columns of the matrix\n");CHKERRQ(ierr);
3124   } else {
3125     allcolumns = PETSC_FALSE;
3126   }
3127   if (call ==  MAT_REUSE_MATRIX) {
3128     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3129     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3130     ierr = MatGetSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,&allcolumns,&Mreuse);CHKERRQ(ierr);
3131   } else {
3132     ierr = MatGetSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&allcolumns,&Mreuse);CHKERRQ(ierr);
3133   }
3134 
3135   /*
3136       m - number of local rows
3137       n - number of columns (same on all processors)
3138       rstart - first row in new global matrix generated
3139   */
3140   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3141   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3142   if (call == MAT_INITIAL_MATRIX) {
3143     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3144     ii  = aij->i;
3145     jj  = aij->j;
3146 
3147     /*
3148         Determine the number of non-zeros in the diagonal and off-diagonal
3149         portions of the matrix in order to do correct preallocation
3150     */
3151 
3152     /* first get start and end of "diagonal" columns */
3153     if (csize == PETSC_DECIDE) {
3154       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3155       if (mglobal == n) { /* square matrix */
3156         nlocal = m;
3157       } else {
3158         nlocal = n/size + ((n % size) > rank);
3159       }
3160     } else {
3161       nlocal = csize;
3162     }
3163     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3164     rstart = rend - nlocal;
3165     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);
3166 
3167     /* next, compute all the lengths */
3168     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3169     olens = dlens + m;
3170     for (i=0; i<m; i++) {
3171       jend = ii[i+1] - ii[i];
3172       olen = 0;
3173       dlen = 0;
3174       for (j=0; j<jend; j++) {
3175         if (*jj < rstart || *jj >= rend) olen++;
3176         else dlen++;
3177         jj++;
3178       }
3179       olens[i] = olen;
3180       dlens[i] = dlen;
3181     }
3182     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3183     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3184     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3185     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3186     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3187     ierr = PetscFree(dlens);CHKERRQ(ierr);
3188   } else {
3189     PetscInt ml,nl;
3190 
3191     M    = *newmat;
3192     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3193     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3194     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3195     /*
3196          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3197        rather than the slower MatSetValues().
3198     */
3199     M->was_assembled = PETSC_TRUE;
3200     M->assembled     = PETSC_FALSE;
3201   }
3202   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3203   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3204   ii   = aij->i;
3205   jj   = aij->j;
3206   aa   = aij->a;
3207   for (i=0; i<m; i++) {
3208     row   = rstart + i;
3209     nz    = ii[i+1] - ii[i];
3210     cwork = jj;     jj += nz;
3211     vwork = aa;     aa += nz;
3212     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3213   }
3214 
3215   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3216   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3217   *newmat = M;
3218 
3219   /* save submatrix used in processor for next request */
3220   if (call ==  MAT_INITIAL_MATRIX) {
3221     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3222     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3223   }
3224   PetscFunctionReturn(0);
3225 }
3226 
3227 #undef __FUNCT__
3228 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR_MPIAIJ"
3229 PetscErrorCode  MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3230 {
3231   PetscInt       m,cstart, cend,j,nnz,i,d;
3232   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3233   const PetscInt *JJ;
3234   PetscScalar    *values;
3235   PetscErrorCode ierr;
3236 
3237   PetscFunctionBegin;
3238   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3239 
3240   ierr   = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3241   ierr   = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3242   m      = B->rmap->n;
3243   cstart = B->cmap->rstart;
3244   cend   = B->cmap->rend;
3245   rstart = B->rmap->rstart;
3246 
3247   ierr = PetscMalloc2(m,&d_nnz,m,&o_nnz);CHKERRQ(ierr);
3248 
3249 #if defined(PETSC_USE_DEBUGGING)
3250   for (i=0; i<m; i++) {
3251     nnz = Ii[i+1]- Ii[i];
3252     JJ  = J + Ii[i];
3253     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3254     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3255     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);
3256   }
3257 #endif
3258 
3259   for (i=0; i<m; i++) {
3260     nnz     = Ii[i+1]- Ii[i];
3261     JJ      = J + Ii[i];
3262     nnz_max = PetscMax(nnz_max,nnz);
3263     d       = 0;
3264     for (j=0; j<nnz; j++) {
3265       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3266     }
3267     d_nnz[i] = d;
3268     o_nnz[i] = nnz - d;
3269   }
3270   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3271   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3272 
3273   if (v) values = (PetscScalar*)v;
3274   else {
3275     ierr = PetscCalloc1(nnz_max+1,&values);CHKERRQ(ierr);
3276   }
3277 
3278   for (i=0; i<m; i++) {
3279     ii   = i + rstart;
3280     nnz  = Ii[i+1]- Ii[i];
3281     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3282   }
3283   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3284   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3285 
3286   if (!v) {
3287     ierr = PetscFree(values);CHKERRQ(ierr);
3288   }
3289   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3290   PetscFunctionReturn(0);
3291 }
3292 
3293 #undef __FUNCT__
3294 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR"
3295 /*@
3296    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3297    (the default parallel PETSc format).
3298 
3299    Collective on MPI_Comm
3300 
3301    Input Parameters:
3302 +  B - the matrix
3303 .  i - the indices into j for the start of each local row (starts with zero)
3304 .  j - the column indices for each local row (starts with zero)
3305 -  v - optional values in the matrix
3306 
3307    Level: developer
3308 
3309    Notes:
3310        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3311      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3312      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3313 
3314        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3315 
3316        The format which is used for the sparse matrix input, is equivalent to a
3317     row-major ordering.. i.e for the following matrix, the input data expected is
3318     as shown
3319 
3320 $        1 0 0
3321 $        2 0 3     P0
3322 $       -------
3323 $        4 5 6     P1
3324 $
3325 $     Process0 [P0]: rows_owned=[0,1]
3326 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3327 $        j =  {0,0,2}  [size = 3]
3328 $        v =  {1,2,3}  [size = 3]
3329 $
3330 $     Process1 [P1]: rows_owned=[2]
3331 $        i =  {0,3}    [size = nrow+1  = 1+1]
3332 $        j =  {0,1,2}  [size = 3]
3333 $        v =  {4,5,6}  [size = 3]
3334 
3335 .keywords: matrix, aij, compressed row, sparse, parallel
3336 
3337 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MPIAIJ,
3338           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3339 @*/
3340 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3341 {
3342   PetscErrorCode ierr;
3343 
3344   PetscFunctionBegin;
3345   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3346   PetscFunctionReturn(0);
3347 }
3348 
3349 #undef __FUNCT__
3350 #define __FUNCT__ "MatMPIAIJSetPreallocation"
3351 /*@C
3352    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3353    (the default parallel PETSc format).  For good matrix assembly performance
3354    the user should preallocate the matrix storage by setting the parameters
3355    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3356    performance can be increased by more than a factor of 50.
3357 
3358    Collective on MPI_Comm
3359 
3360    Input Parameters:
3361 +  B - the matrix
3362 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3363            (same value is used for all local rows)
3364 .  d_nnz - array containing the number of nonzeros in the various rows of the
3365            DIAGONAL portion of the local submatrix (possibly different for each row)
3366            or NULL (PETSC_NULL_INTEGER in Fortran), if d_nz is used to specify the nonzero structure.
3367            The size of this array is equal to the number of local rows, i.e 'm'.
3368            For matrices that will be factored, you must leave room for (and set)
3369            the diagonal entry even if it is zero.
3370 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3371            submatrix (same value is used for all local rows).
3372 -  o_nnz - array containing the number of nonzeros in the various rows of the
3373            OFF-DIAGONAL portion of the local submatrix (possibly different for
3374            each row) or NULL (PETSC_NULL_INTEGER in Fortran), if o_nz is used to specify the nonzero
3375            structure. The size of this array is equal to the number
3376            of local rows, i.e 'm'.
3377 
3378    If the *_nnz parameter is given then the *_nz parameter is ignored
3379 
3380    The AIJ format (also called the Yale sparse matrix format or
3381    compressed row storage (CSR)), is fully compatible with standard Fortran 77
3382    storage.  The stored row and column indices begin with zero.
3383    See Users-Manual: ch_mat for details.
3384 
3385    The parallel matrix is partitioned such that the first m0 rows belong to
3386    process 0, the next m1 rows belong to process 1, the next m2 rows belong
3387    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
3388 
3389    The DIAGONAL portion of the local submatrix of a processor can be defined
3390    as the submatrix which is obtained by extraction the part corresponding to
3391    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
3392    first row that belongs to the processor, r2 is the last row belonging to
3393    the this processor, and c1-c2 is range of indices of the local part of a
3394    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
3395    common case of a square matrix, the row and column ranges are the same and
3396    the DIAGONAL part is also square. The remaining portion of the local
3397    submatrix (mxN) constitute the OFF-DIAGONAL portion.
3398 
3399    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3400 
3401    You can call MatGetInfo() to get information on how effective the preallocation was;
3402    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3403    You can also run with the option -info and look for messages with the string
3404    malloc in them to see if additional memory allocation was needed.
3405 
3406    Example usage:
3407 
3408    Consider the following 8x8 matrix with 34 non-zero values, that is
3409    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3410    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3411    as follows:
3412 
3413 .vb
3414             1  2  0  |  0  3  0  |  0  4
3415     Proc0   0  5  6  |  7  0  0  |  8  0
3416             9  0 10  | 11  0  0  | 12  0
3417     -------------------------------------
3418            13  0 14  | 15 16 17  |  0  0
3419     Proc1   0 18  0  | 19 20 21  |  0  0
3420             0  0  0  | 22 23  0  | 24  0
3421     -------------------------------------
3422     Proc2  25 26 27  |  0  0 28  | 29  0
3423            30  0  0  | 31 32 33  |  0 34
3424 .ve
3425 
3426    This can be represented as a collection of submatrices as:
3427 
3428 .vb
3429       A B C
3430       D E F
3431       G H I
3432 .ve
3433 
3434    Where the submatrices A,B,C are owned by proc0, D,E,F are
3435    owned by proc1, G,H,I are owned by proc2.
3436 
3437    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3438    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3439    The 'M','N' parameters are 8,8, and have the same values on all procs.
3440 
3441    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3442    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3443    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3444    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3445    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3446    matrix, ans [DF] as another SeqAIJ matrix.
3447 
3448    When d_nz, o_nz parameters are specified, d_nz storage elements are
3449    allocated for every row of the local diagonal submatrix, and o_nz
3450    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3451    One way to choose d_nz and o_nz is to use the max nonzerors per local
3452    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3453    In this case, the values of d_nz,o_nz are:
3454 .vb
3455      proc0 : dnz = 2, o_nz = 2
3456      proc1 : dnz = 3, o_nz = 2
3457      proc2 : dnz = 1, o_nz = 4
3458 .ve
3459    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3460    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3461    for proc3. i.e we are using 12+15+10=37 storage locations to store
3462    34 values.
3463 
3464    When d_nnz, o_nnz parameters are specified, the storage is specified
3465    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3466    In the above case the values for d_nnz,o_nnz are:
3467 .vb
3468      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3469      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3470      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3471 .ve
3472    Here the space allocated is sum of all the above values i.e 34, and
3473    hence pre-allocation is perfect.
3474 
3475    Level: intermediate
3476 
3477 .keywords: matrix, aij, compressed row, sparse, parallel
3478 
3479 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
3480           MPIAIJ, MatGetInfo(), PetscSplitOwnership()
3481 @*/
3482 PetscErrorCode  MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3483 {
3484   PetscErrorCode ierr;
3485 
3486   PetscFunctionBegin;
3487   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3488   PetscValidType(B,1);
3489   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
3490   PetscFunctionReturn(0);
3491 }
3492 
3493 #undef __FUNCT__
3494 #define __FUNCT__ "MatCreateMPIAIJWithArrays"
3495 /*@
3496      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
3497          CSR format the local rows.
3498 
3499    Collective on MPI_Comm
3500 
3501    Input Parameters:
3502 +  comm - MPI communicator
3503 .  m - number of local rows (Cannot be PETSC_DECIDE)
3504 .  n - This value should be the same as the local size used in creating the
3505        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3506        calculated if N is given) For square matrices n is almost always m.
3507 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3508 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3509 .   i - row indices
3510 .   j - column indices
3511 -   a - matrix values
3512 
3513    Output Parameter:
3514 .   mat - the matrix
3515 
3516    Level: intermediate
3517 
3518    Notes:
3519        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3520      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3521      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3522 
3523        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3524 
3525        The format which is used for the sparse matrix input, is equivalent to a
3526     row-major ordering.. i.e for the following matrix, the input data expected is
3527     as shown
3528 
3529 $        1 0 0
3530 $        2 0 3     P0
3531 $       -------
3532 $        4 5 6     P1
3533 $
3534 $     Process0 [P0]: rows_owned=[0,1]
3535 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3536 $        j =  {0,0,2}  [size = 3]
3537 $        v =  {1,2,3}  [size = 3]
3538 $
3539 $     Process1 [P1]: rows_owned=[2]
3540 $        i =  {0,3}    [size = nrow+1  = 1+1]
3541 $        j =  {0,1,2}  [size = 3]
3542 $        v =  {4,5,6}  [size = 3]
3543 
3544 .keywords: matrix, aij, compressed row, sparse, parallel
3545 
3546 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3547           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
3548 @*/
3549 PetscErrorCode  MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
3550 {
3551   PetscErrorCode ierr;
3552 
3553   PetscFunctionBegin;
3554   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
3555   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
3556   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
3557   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
3558   /* ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr); */
3559   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
3560   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
3561   PetscFunctionReturn(0);
3562 }
3563 
3564 #undef __FUNCT__
3565 #define __FUNCT__ "MatCreateAIJ"
3566 /*@C
3567    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
3568    (the default parallel PETSc format).  For good matrix assembly performance
3569    the user should preallocate the matrix storage by setting the parameters
3570    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3571    performance can be increased by more than a factor of 50.
3572 
3573    Collective on MPI_Comm
3574 
3575    Input Parameters:
3576 +  comm - MPI communicator
3577 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
3578            This value should be the same as the local size used in creating the
3579            y vector for the matrix-vector product y = Ax.
3580 .  n - This value should be the same as the local size used in creating the
3581        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3582        calculated if N is given) For square matrices n is almost always m.
3583 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3584 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3585 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3586            (same value is used for all local rows)
3587 .  d_nnz - array containing the number of nonzeros in the various rows of the
3588            DIAGONAL portion of the local submatrix (possibly different for each row)
3589            or NULL, if d_nz is used to specify the nonzero structure.
3590            The size of this array is equal to the number of local rows, i.e 'm'.
3591 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3592            submatrix (same value is used for all local rows).
3593 -  o_nnz - array containing the number of nonzeros in the various rows of the
3594            OFF-DIAGONAL portion of the local submatrix (possibly different for
3595            each row) or NULL, if o_nz is used to specify the nonzero
3596            structure. The size of this array is equal to the number
3597            of local rows, i.e 'm'.
3598 
3599    Output Parameter:
3600 .  A - the matrix
3601 
3602    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3603    MatXXXXSetPreallocation() paradgm instead of this routine directly.
3604    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3605 
3606    Notes:
3607    If the *_nnz parameter is given then the *_nz parameter is ignored
3608 
3609    m,n,M,N parameters specify the size of the matrix, and its partitioning across
3610    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
3611    storage requirements for this matrix.
3612 
3613    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
3614    processor than it must be used on all processors that share the object for
3615    that argument.
3616 
3617    The user MUST specify either the local or global matrix dimensions
3618    (possibly both).
3619 
3620    The parallel matrix is partitioned across processors such that the
3621    first m0 rows belong to process 0, the next m1 rows belong to
3622    process 1, the next m2 rows belong to process 2 etc.. where
3623    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
3624    values corresponding to [m x N] submatrix.
3625 
3626    The columns are logically partitioned with the n0 columns belonging
3627    to 0th partition, the next n1 columns belonging to the next
3628    partition etc.. where n0,n1,n2... are the input parameter 'n'.
3629 
3630    The DIAGONAL portion of the local submatrix on any given processor
3631    is the submatrix corresponding to the rows and columns m,n
3632    corresponding to the given processor. i.e diagonal matrix on
3633    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
3634    etc. The remaining portion of the local submatrix [m x (N-n)]
3635    constitute the OFF-DIAGONAL portion. The example below better
3636    illustrates this concept.
3637 
3638    For a square global matrix we define each processor's diagonal portion
3639    to be its local rows and the corresponding columns (a square submatrix);
3640    each processor's off-diagonal portion encompasses the remainder of the
3641    local matrix (a rectangular submatrix).
3642 
3643    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3644 
3645    When calling this routine with a single process communicator, a matrix of
3646    type SEQAIJ is returned.  If a matrix of type MPIAIJ is desired for this
3647    type of communicator, use the construction mechanism:
3648      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
3649 
3650    By default, this format uses inodes (identical nodes) when possible.
3651    We search for consecutive rows with the same nonzero structure, thereby
3652    reusing matrix information to achieve increased efficiency.
3653 
3654    Options Database Keys:
3655 +  -mat_no_inode  - Do not use inodes
3656 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3657 -  -mat_aij_oneindex - Internally use indexing starting at 1
3658         rather than 0.  Note that when calling MatSetValues(),
3659         the user still MUST index entries starting at 0!
3660 
3661 
3662    Example usage:
3663 
3664    Consider the following 8x8 matrix with 34 non-zero values, that is
3665    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3666    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3667    as follows:
3668 
3669 .vb
3670             1  2  0  |  0  3  0  |  0  4
3671     Proc0   0  5  6  |  7  0  0  |  8  0
3672             9  0 10  | 11  0  0  | 12  0
3673     -------------------------------------
3674            13  0 14  | 15 16 17  |  0  0
3675     Proc1   0 18  0  | 19 20 21  |  0  0
3676             0  0  0  | 22 23  0  | 24  0
3677     -------------------------------------
3678     Proc2  25 26 27  |  0  0 28  | 29  0
3679            30  0  0  | 31 32 33  |  0 34
3680 .ve
3681 
3682    This can be represented as a collection of submatrices as:
3683 
3684 .vb
3685       A B C
3686       D E F
3687       G H I
3688 .ve
3689 
3690    Where the submatrices A,B,C are owned by proc0, D,E,F are
3691    owned by proc1, G,H,I are owned by proc2.
3692 
3693    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3694    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3695    The 'M','N' parameters are 8,8, and have the same values on all procs.
3696 
3697    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3698    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3699    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3700    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3701    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3702    matrix, ans [DF] as another SeqAIJ matrix.
3703 
3704    When d_nz, o_nz parameters are specified, d_nz storage elements are
3705    allocated for every row of the local diagonal submatrix, and o_nz
3706    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3707    One way to choose d_nz and o_nz is to use the max nonzerors per local
3708    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3709    In this case, the values of d_nz,o_nz are:
3710 .vb
3711      proc0 : dnz = 2, o_nz = 2
3712      proc1 : dnz = 3, o_nz = 2
3713      proc2 : dnz = 1, o_nz = 4
3714 .ve
3715    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3716    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3717    for proc3. i.e we are using 12+15+10=37 storage locations to store
3718    34 values.
3719 
3720    When d_nnz, o_nnz parameters are specified, the storage is specified
3721    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3722    In the above case the values for d_nnz,o_nnz are:
3723 .vb
3724      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3725      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3726      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3727 .ve
3728    Here the space allocated is sum of all the above values i.e 34, and
3729    hence pre-allocation is perfect.
3730 
3731    Level: intermediate
3732 
3733 .keywords: matrix, aij, compressed row, sparse, parallel
3734 
3735 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3736           MPIAIJ, MatCreateMPIAIJWithArrays()
3737 @*/
3738 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)
3739 {
3740   PetscErrorCode ierr;
3741   PetscMPIInt    size;
3742 
3743   PetscFunctionBegin;
3744   ierr = MatCreate(comm,A);CHKERRQ(ierr);
3745   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
3746   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3747   if (size > 1) {
3748     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
3749     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
3750   } else {
3751     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
3752     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
3753   }
3754   PetscFunctionReturn(0);
3755 }
3756 
3757 #undef __FUNCT__
3758 #define __FUNCT__ "MatMPIAIJGetSeqAIJ"
3759 PetscErrorCode  MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
3760 {
3761   Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
3762 
3763   PetscFunctionBegin;
3764   if (Ad)     *Ad     = a->A;
3765   if (Ao)     *Ao     = a->B;
3766   if (colmap) *colmap = a->garray;
3767   PetscFunctionReturn(0);
3768 }
3769 
3770 #undef __FUNCT__
3771 #define __FUNCT__ "MatSetColoring_MPIAIJ"
3772 PetscErrorCode MatSetColoring_MPIAIJ(Mat A,ISColoring coloring)
3773 {
3774   PetscErrorCode ierr;
3775   PetscInt       i;
3776   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3777 
3778   PetscFunctionBegin;
3779   if (coloring->ctype == IS_COLORING_GLOBAL) {
3780     ISColoringValue *allcolors,*colors;
3781     ISColoring      ocoloring;
3782 
3783     /* set coloring for diagonal portion */
3784     ierr = MatSetColoring_SeqAIJ(a->A,coloring);CHKERRQ(ierr);
3785 
3786     /* set coloring for off-diagonal portion */
3787     ierr = ISAllGatherColors(PetscObjectComm((PetscObject)A),coloring->n,coloring->colors,NULL,&allcolors);CHKERRQ(ierr);
3788     ierr = PetscMalloc1(a->B->cmap->n+1,&colors);CHKERRQ(ierr);
3789     for (i=0; i<a->B->cmap->n; i++) {
3790       colors[i] = allcolors[a->garray[i]];
3791     }
3792     ierr = PetscFree(allcolors);CHKERRQ(ierr);
3793     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3794     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
3795     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3796   } else if (coloring->ctype == IS_COLORING_GHOSTED) {
3797     ISColoringValue *colors;
3798     PetscInt        *larray;
3799     ISColoring      ocoloring;
3800 
3801     /* set coloring for diagonal portion */
3802     ierr = PetscMalloc1(a->A->cmap->n+1,&larray);CHKERRQ(ierr);
3803     for (i=0; i<a->A->cmap->n; i++) {
3804       larray[i] = i + A->cmap->rstart;
3805     }
3806     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->A->cmap->n,larray,NULL,larray);CHKERRQ(ierr);
3807     ierr = PetscMalloc1(a->A->cmap->n+1,&colors);CHKERRQ(ierr);
3808     for (i=0; i<a->A->cmap->n; i++) {
3809       colors[i] = coloring->colors[larray[i]];
3810     }
3811     ierr = PetscFree(larray);CHKERRQ(ierr);
3812     ierr = ISColoringCreate(PETSC_COMM_SELF,coloring->n,a->A->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3813     ierr = MatSetColoring_SeqAIJ(a->A,ocoloring);CHKERRQ(ierr);
3814     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3815 
3816     /* set coloring for off-diagonal portion */
3817     ierr = PetscMalloc1(a->B->cmap->n+1,&larray);CHKERRQ(ierr);
3818     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->B->cmap->n,a->garray,NULL,larray);CHKERRQ(ierr);
3819     ierr = PetscMalloc1(a->B->cmap->n+1,&colors);CHKERRQ(ierr);
3820     for (i=0; i<a->B->cmap->n; i++) {
3821       colors[i] = coloring->colors[larray[i]];
3822     }
3823     ierr = PetscFree(larray);CHKERRQ(ierr);
3824     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3825     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
3826     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3827   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support ISColoringType %d",(int)coloring->ctype);
3828   PetscFunctionReturn(0);
3829 }
3830 
3831 #undef __FUNCT__
3832 #define __FUNCT__ "MatSetValuesAdifor_MPIAIJ"
3833 PetscErrorCode MatSetValuesAdifor_MPIAIJ(Mat A,PetscInt nl,void *advalues)
3834 {
3835   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3836   PetscErrorCode ierr;
3837 
3838   PetscFunctionBegin;
3839   ierr = MatSetValuesAdifor_SeqAIJ(a->A,nl,advalues);CHKERRQ(ierr);
3840   ierr = MatSetValuesAdifor_SeqAIJ(a->B,nl,advalues);CHKERRQ(ierr);
3841   PetscFunctionReturn(0);
3842 }
3843 
3844 #undef __FUNCT__
3845 #define __FUNCT__ "MatCreateMPIMatConcatenateSeqMat_MPIAIJ"
3846 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
3847 {
3848   PetscErrorCode ierr;
3849   PetscInt       m,N,i,rstart,nnz,Ii;
3850   PetscInt       *indx;
3851   PetscScalar    *values;
3852 
3853   PetscFunctionBegin;
3854   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
3855   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
3856     PetscInt       *dnz,*onz,sum,bs,cbs;
3857 
3858     if (n == PETSC_DECIDE) {
3859       ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
3860     }
3861     /* Check sum(n) = N */
3862     ierr = MPI_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3863     if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
3864 
3865     ierr    = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3866     rstart -= m;
3867 
3868     ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
3869     for (i=0; i<m; i++) {
3870       ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3871       ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
3872       ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3873     }
3874 
3875     ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
3876     ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
3877     ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
3878     ierr = MatSetBlockSizes(*outmat,bs,cbs);CHKERRQ(ierr);
3879     ierr = MatSetType(*outmat,MATMPIAIJ);CHKERRQ(ierr);
3880     ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
3881     ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
3882   }
3883 
3884   /* numeric phase */
3885   ierr = MatGetOwnershipRange(*outmat,&rstart,NULL);CHKERRQ(ierr);
3886   for (i=0; i<m; i++) {
3887     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3888     Ii   = i + rstart;
3889     ierr = MatSetValues(*outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3890     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3891   }
3892   ierr = MatAssemblyBegin(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3893   ierr = MatAssemblyEnd(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3894   PetscFunctionReturn(0);
3895 }
3896 
3897 #undef __FUNCT__
3898 #define __FUNCT__ "MatFileSplit"
3899 PetscErrorCode MatFileSplit(Mat A,char *outfile)
3900 {
3901   PetscErrorCode    ierr;
3902   PetscMPIInt       rank;
3903   PetscInt          m,N,i,rstart,nnz;
3904   size_t            len;
3905   const PetscInt    *indx;
3906   PetscViewer       out;
3907   char              *name;
3908   Mat               B;
3909   const PetscScalar *values;
3910 
3911   PetscFunctionBegin;
3912   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
3913   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
3914   /* Should this be the type of the diagonal block of A? */
3915   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
3916   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
3917   ierr = MatSetBlockSizesFromMats(B,A,A);CHKERRQ(ierr);
3918   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
3919   ierr = MatSeqAIJSetPreallocation(B,0,NULL);CHKERRQ(ierr);
3920   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
3921   for (i=0; i<m; i++) {
3922     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3923     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3924     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3925   }
3926   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3927   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3928 
3929   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
3930   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
3931   ierr = PetscMalloc1(len+5,&name);CHKERRQ(ierr);
3932   sprintf(name,"%s.%d",outfile,rank);
3933   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
3934   ierr = PetscFree(name);CHKERRQ(ierr);
3935   ierr = MatView(B,out);CHKERRQ(ierr);
3936   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
3937   ierr = MatDestroy(&B);CHKERRQ(ierr);
3938   PetscFunctionReturn(0);
3939 }
3940 
3941 extern PetscErrorCode MatDestroy_MPIAIJ(Mat);
3942 #undef __FUNCT__
3943 #define __FUNCT__ "MatDestroy_MPIAIJ_SeqsToMPI"
3944 PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
3945 {
3946   PetscErrorCode      ierr;
3947   Mat_Merge_SeqsToMPI *merge;
3948   PetscContainer      container;
3949 
3950   PetscFunctionBegin;
3951   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
3952   if (container) {
3953     ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
3954     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
3955     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
3956     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
3957     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
3958     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
3959     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
3960     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
3961     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
3962     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
3963     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
3964     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
3965     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
3966     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
3967     ierr = PetscFree(merge);CHKERRQ(ierr);
3968     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
3969   }
3970   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
3971   PetscFunctionReturn(0);
3972 }
3973 
3974 #include <../src/mat/utils/freespace.h>
3975 #include <petscbt.h>
3976 
3977 #undef __FUNCT__
3978 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJNumeric"
3979 PetscErrorCode  MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
3980 {
3981   PetscErrorCode      ierr;
3982   MPI_Comm            comm;
3983   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
3984   PetscMPIInt         size,rank,taga,*len_s;
3985   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
3986   PetscInt            proc,m;
3987   PetscInt            **buf_ri,**buf_rj;
3988   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
3989   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
3990   MPI_Request         *s_waits,*r_waits;
3991   MPI_Status          *status;
3992   MatScalar           *aa=a->a;
3993   MatScalar           **abuf_r,*ba_i;
3994   Mat_Merge_SeqsToMPI *merge;
3995   PetscContainer      container;
3996 
3997   PetscFunctionBegin;
3998   ierr = PetscObjectGetComm((PetscObject)mpimat,&comm);CHKERRQ(ierr);
3999   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4000 
4001   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4002   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4003 
4004   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4005   ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4006 
4007   bi     = merge->bi;
4008   bj     = merge->bj;
4009   buf_ri = merge->buf_ri;
4010   buf_rj = merge->buf_rj;
4011 
4012   ierr   = PetscMalloc1(size,&status);CHKERRQ(ierr);
4013   owners = merge->rowmap->range;
4014   len_s  = merge->len_s;
4015 
4016   /* send and recv matrix values */
4017   /*-----------------------------*/
4018   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
4019   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
4020 
4021   ierr = PetscMalloc1(merge->nsend+1,&s_waits);CHKERRQ(ierr);
4022   for (proc=0,k=0; proc<size; proc++) {
4023     if (!len_s[proc]) continue;
4024     i    = owners[proc];
4025     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
4026     k++;
4027   }
4028 
4029   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
4030   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
4031   ierr = PetscFree(status);CHKERRQ(ierr);
4032 
4033   ierr = PetscFree(s_waits);CHKERRQ(ierr);
4034   ierr = PetscFree(r_waits);CHKERRQ(ierr);
4035 
4036   /* insert mat values of mpimat */
4037   /*----------------------------*/
4038   ierr = PetscMalloc1(N,&ba_i);CHKERRQ(ierr);
4039   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4040 
4041   for (k=0; k<merge->nrecv; k++) {
4042     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4043     nrows       = *(buf_ri_k[k]);
4044     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
4045     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4046   }
4047 
4048   /* set values of ba */
4049   m = merge->rowmap->n;
4050   for (i=0; i<m; i++) {
4051     arow = owners[rank] + i;
4052     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
4053     bnzi = bi[i+1] - bi[i];
4054     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
4055 
4056     /* add local non-zero vals of this proc's seqmat into ba */
4057     anzi   = ai[arow+1] - ai[arow];
4058     aj     = a->j + ai[arow];
4059     aa     = a->a + ai[arow];
4060     nextaj = 0;
4061     for (j=0; nextaj<anzi; j++) {
4062       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4063         ba_i[j] += aa[nextaj++];
4064       }
4065     }
4066 
4067     /* add received vals into ba */
4068     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4069       /* i-th row */
4070       if (i == *nextrow[k]) {
4071         anzi   = *(nextai[k]+1) - *nextai[k];
4072         aj     = buf_rj[k] + *(nextai[k]);
4073         aa     = abuf_r[k] + *(nextai[k]);
4074         nextaj = 0;
4075         for (j=0; nextaj<anzi; j++) {
4076           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4077             ba_i[j] += aa[nextaj++];
4078           }
4079         }
4080         nextrow[k]++; nextai[k]++;
4081       }
4082     }
4083     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
4084   }
4085   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4086   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4087 
4088   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
4089   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
4090   ierr = PetscFree(ba_i);CHKERRQ(ierr);
4091   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4092   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4093   PetscFunctionReturn(0);
4094 }
4095 
4096 extern PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat);
4097 
4098 #undef __FUNCT__
4099 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJSymbolic"
4100 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4101 {
4102   PetscErrorCode      ierr;
4103   Mat                 B_mpi;
4104   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
4105   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4106   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
4107   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4108   PetscInt            len,proc,*dnz,*onz,bs,cbs;
4109   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4110   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4111   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
4112   MPI_Status          *status;
4113   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
4114   PetscBT             lnkbt;
4115   Mat_Merge_SeqsToMPI *merge;
4116   PetscContainer      container;
4117 
4118   PetscFunctionBegin;
4119   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4120 
4121   /* make sure it is a PETSc comm */
4122   ierr = PetscCommDuplicate(comm,&comm,NULL);CHKERRQ(ierr);
4123   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4124   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4125 
4126   ierr = PetscNew(&merge);CHKERRQ(ierr);
4127   ierr = PetscMalloc1(size,&status);CHKERRQ(ierr);
4128 
4129   /* determine row ownership */
4130   /*---------------------------------------------------------*/
4131   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
4132   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
4133   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
4134   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
4135   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
4136   ierr = PetscMalloc1(size,&len_si);CHKERRQ(ierr);
4137   ierr = PetscMalloc1(size,&merge->len_s);CHKERRQ(ierr);
4138 
4139   m      = merge->rowmap->n;
4140   owners = merge->rowmap->range;
4141 
4142   /* determine the number of messages to send, their lengths */
4143   /*---------------------------------------------------------*/
4144   len_s = merge->len_s;
4145 
4146   len          = 0; /* length of buf_si[] */
4147   merge->nsend = 0;
4148   for (proc=0; proc<size; proc++) {
4149     len_si[proc] = 0;
4150     if (proc == rank) {
4151       len_s[proc] = 0;
4152     } else {
4153       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4154       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4155     }
4156     if (len_s[proc]) {
4157       merge->nsend++;
4158       nrows = 0;
4159       for (i=owners[proc]; i<owners[proc+1]; i++) {
4160         if (ai[i+1] > ai[i]) nrows++;
4161       }
4162       len_si[proc] = 2*(nrows+1);
4163       len         += len_si[proc];
4164     }
4165   }
4166 
4167   /* determine the number and length of messages to receive for ij-structure */
4168   /*-------------------------------------------------------------------------*/
4169   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
4170   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
4171 
4172   /* post the Irecv of j-structure */
4173   /*-------------------------------*/
4174   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
4175   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
4176 
4177   /* post the Isend of j-structure */
4178   /*--------------------------------*/
4179   ierr = PetscMalloc2(merge->nsend,&si_waits,merge->nsend,&sj_waits);CHKERRQ(ierr);
4180 
4181   for (proc=0, k=0; proc<size; proc++) {
4182     if (!len_s[proc]) continue;
4183     i    = owners[proc];
4184     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
4185     k++;
4186   }
4187 
4188   /* receives and sends of j-structure are complete */
4189   /*------------------------------------------------*/
4190   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
4191   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
4192 
4193   /* send and recv i-structure */
4194   /*---------------------------*/
4195   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
4196   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
4197 
4198   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
4199   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4200   for (proc=0,k=0; proc<size; proc++) {
4201     if (!len_s[proc]) continue;
4202     /* form outgoing message for i-structure:
4203          buf_si[0]:                 nrows to be sent
4204                [1:nrows]:           row index (global)
4205                [nrows+1:2*nrows+1]: i-structure index
4206     */
4207     /*-------------------------------------------*/
4208     nrows       = len_si[proc]/2 - 1;
4209     buf_si_i    = buf_si + nrows+1;
4210     buf_si[0]   = nrows;
4211     buf_si_i[0] = 0;
4212     nrows       = 0;
4213     for (i=owners[proc]; i<owners[proc+1]; i++) {
4214       anzi = ai[i+1] - ai[i];
4215       if (anzi) {
4216         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4217         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4218         nrows++;
4219       }
4220     }
4221     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4222     k++;
4223     buf_si += len_si[proc];
4224   }
4225 
4226   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4227   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4228 
4229   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4230   for (i=0; i<merge->nrecv; i++) {
4231     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);
4232   }
4233 
4234   ierr = PetscFree(len_si);CHKERRQ(ierr);
4235   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4236   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4237   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4238   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4239   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4240   ierr = PetscFree(status);CHKERRQ(ierr);
4241 
4242   /* compute a local seq matrix in each processor */
4243   /*----------------------------------------------*/
4244   /* allocate bi array and free space for accumulating nonzero column info */
4245   ierr  = PetscMalloc1(m+1,&bi);CHKERRQ(ierr);
4246   bi[0] = 0;
4247 
4248   /* create and initialize a linked list */
4249   nlnk = N+1;
4250   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4251 
4252   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4253   len  = ai[owners[rank+1]] - ai[owners[rank]];
4254   ierr = PetscFreeSpaceGet((PetscInt)(2*len+1),&free_space);CHKERRQ(ierr);
4255 
4256   current_space = free_space;
4257 
4258   /* determine symbolic info for each local row */
4259   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4260 
4261   for (k=0; k<merge->nrecv; k++) {
4262     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4263     nrows       = *buf_ri_k[k];
4264     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4265     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4266   }
4267 
4268   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4269   len  = 0;
4270   for (i=0; i<m; i++) {
4271     bnzi = 0;
4272     /* add local non-zero cols of this proc's seqmat into lnk */
4273     arow  = owners[rank] + i;
4274     anzi  = ai[arow+1] - ai[arow];
4275     aj    = a->j + ai[arow];
4276     ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4277     bnzi += nlnk;
4278     /* add received col data into lnk */
4279     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4280       if (i == *nextrow[k]) { /* i-th row */
4281         anzi  = *(nextai[k]+1) - *nextai[k];
4282         aj    = buf_rj[k] + *nextai[k];
4283         ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4284         bnzi += nlnk;
4285         nextrow[k]++; nextai[k]++;
4286       }
4287     }
4288     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4289 
4290     /* if free space is not available, make more free space */
4291     if (current_space->local_remaining<bnzi) {
4292       ierr = PetscFreeSpaceGet(bnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
4293       nspacedouble++;
4294     }
4295     /* copy data into free space, then initialize lnk */
4296     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4297     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
4298 
4299     current_space->array           += bnzi;
4300     current_space->local_used      += bnzi;
4301     current_space->local_remaining -= bnzi;
4302 
4303     bi[i+1] = bi[i] + bnzi;
4304   }
4305 
4306   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4307 
4308   ierr = PetscMalloc1(bi[m]+1,&bj);CHKERRQ(ierr);
4309   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
4310   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4311 
4312   /* create symbolic parallel matrix B_mpi */
4313   /*---------------------------------------*/
4314   ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
4315   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
4316   if (n==PETSC_DECIDE) {
4317     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
4318   } else {
4319     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4320   }
4321   ierr = MatSetBlockSizes(B_mpi,bs,cbs);CHKERRQ(ierr);
4322   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
4323   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
4324   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4325   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
4326 
4327   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4328   B_mpi->assembled    = PETSC_FALSE;
4329   B_mpi->ops->destroy = MatDestroy_MPIAIJ_SeqsToMPI;
4330   merge->bi           = bi;
4331   merge->bj           = bj;
4332   merge->buf_ri       = buf_ri;
4333   merge->buf_rj       = buf_rj;
4334   merge->coi          = NULL;
4335   merge->coj          = NULL;
4336   merge->owners_co    = NULL;
4337 
4338   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
4339 
4340   /* attach the supporting struct to B_mpi for reuse */
4341   ierr    = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
4342   ierr    = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
4343   ierr    = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
4344   ierr    = PetscContainerDestroy(&container);CHKERRQ(ierr);
4345   *mpimat = B_mpi;
4346 
4347   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4348   PetscFunctionReturn(0);
4349 }
4350 
4351 #undef __FUNCT__
4352 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJ"
4353 /*@C
4354       MatCreateMPIAIJSumSeqAIJ - Creates a MPIAIJ matrix by adding sequential
4355                  matrices from each processor
4356 
4357     Collective on MPI_Comm
4358 
4359    Input Parameters:
4360 +    comm - the communicators the parallel matrix will live on
4361 .    seqmat - the input sequential matrices
4362 .    m - number of local rows (or PETSC_DECIDE)
4363 .    n - number of local columns (or PETSC_DECIDE)
4364 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4365 
4366    Output Parameter:
4367 .    mpimat - the parallel matrix generated
4368 
4369     Level: advanced
4370 
4371    Notes:
4372      The dimensions of the sequential matrix in each processor MUST be the same.
4373      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
4374      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
4375 @*/
4376 PetscErrorCode  MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
4377 {
4378   PetscErrorCode ierr;
4379   PetscMPIInt    size;
4380 
4381   PetscFunctionBegin;
4382   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4383   if (size == 1) {
4384     ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4385     if (scall == MAT_INITIAL_MATRIX) {
4386       ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
4387     } else {
4388       ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4389     }
4390     ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4391     PetscFunctionReturn(0);
4392   }
4393   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4394   if (scall == MAT_INITIAL_MATRIX) {
4395     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
4396   }
4397   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
4398   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4399   PetscFunctionReturn(0);
4400 }
4401 
4402 #undef __FUNCT__
4403 #define __FUNCT__ "MatMPIAIJGetLocalMat"
4404 /*@
4405      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
4406           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
4407           with MatGetSize()
4408 
4409     Not Collective
4410 
4411    Input Parameters:
4412 +    A - the matrix
4413 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4414 
4415    Output Parameter:
4416 .    A_loc - the local sequential matrix generated
4417 
4418     Level: developer
4419 
4420 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
4421 
4422 @*/
4423 PetscErrorCode  MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
4424 {
4425   PetscErrorCode ierr;
4426   Mat_MPIAIJ     *mpimat=(Mat_MPIAIJ*)A->data;
4427   Mat_SeqAIJ     *mat,*a,*b;
4428   PetscInt       *ai,*aj,*bi,*bj,*cmap=mpimat->garray;
4429   MatScalar      *aa,*ba,*cam;
4430   PetscScalar    *ca;
4431   PetscInt       am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
4432   PetscInt       *ci,*cj,col,ncols_d,ncols_o,jo;
4433   PetscBool      match;
4434   MPI_Comm       comm;
4435   PetscMPIInt    size;
4436 
4437   PetscFunctionBegin;
4438   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4439   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
4440   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4441   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4442   if (size == 1 && scall == MAT_REUSE_MATRIX) PetscFunctionReturn(0);
4443 
4444   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4445   a = (Mat_SeqAIJ*)(mpimat->A)->data;
4446   b = (Mat_SeqAIJ*)(mpimat->B)->data;
4447   ai = a->i; aj = a->j; bi = b->i; bj = b->j;
4448   aa = a->a; ba = b->a;
4449   if (scall == MAT_INITIAL_MATRIX) {
4450     if (size == 1) {
4451       ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ai,aj,aa,A_loc);CHKERRQ(ierr);
4452       PetscFunctionReturn(0);
4453     }
4454 
4455     ierr  = PetscMalloc1(1+am,&ci);CHKERRQ(ierr);
4456     ci[0] = 0;
4457     for (i=0; i<am; i++) {
4458       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
4459     }
4460     ierr = PetscMalloc1(1+ci[am],&cj);CHKERRQ(ierr);
4461     ierr = PetscMalloc1(1+ci[am],&ca);CHKERRQ(ierr);
4462     k    = 0;
4463     for (i=0; i<am; i++) {
4464       ncols_o = bi[i+1] - bi[i];
4465       ncols_d = ai[i+1] - ai[i];
4466       /* off-diagonal portion of A */
4467       for (jo=0; jo<ncols_o; jo++) {
4468         col = cmap[*bj];
4469         if (col >= cstart) break;
4470         cj[k]   = col; bj++;
4471         ca[k++] = *ba++;
4472       }
4473       /* diagonal portion of A */
4474       for (j=0; j<ncols_d; j++) {
4475         cj[k]   = cstart + *aj++;
4476         ca[k++] = *aa++;
4477       }
4478       /* off-diagonal portion of A */
4479       for (j=jo; j<ncols_o; j++) {
4480         cj[k]   = cmap[*bj++];
4481         ca[k++] = *ba++;
4482       }
4483     }
4484     /* put together the new matrix */
4485     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
4486     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4487     /* Since these are PETSc arrays, change flags to free them as necessary. */
4488     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
4489     mat->free_a  = PETSC_TRUE;
4490     mat->free_ij = PETSC_TRUE;
4491     mat->nonew   = 0;
4492   } else if (scall == MAT_REUSE_MATRIX) {
4493     mat=(Mat_SeqAIJ*)(*A_loc)->data;
4494     ci = mat->i; cj = mat->j; cam = mat->a;
4495     for (i=0; i<am; i++) {
4496       /* off-diagonal portion of A */
4497       ncols_o = bi[i+1] - bi[i];
4498       for (jo=0; jo<ncols_o; jo++) {
4499         col = cmap[*bj];
4500         if (col >= cstart) break;
4501         *cam++ = *ba++; bj++;
4502       }
4503       /* diagonal portion of A */
4504       ncols_d = ai[i+1] - ai[i];
4505       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
4506       /* off-diagonal portion of A */
4507       for (j=jo; j<ncols_o; j++) {
4508         *cam++ = *ba++; bj++;
4509       }
4510     }
4511   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
4512   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4513   PetscFunctionReturn(0);
4514 }
4515 
4516 #undef __FUNCT__
4517 #define __FUNCT__ "MatMPIAIJGetLocalMatCondensed"
4518 /*@C
4519      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MPIAIJ matrix by taking all its local rows and NON-ZERO columns
4520 
4521     Not Collective
4522 
4523    Input Parameters:
4524 +    A - the matrix
4525 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4526 -    row, col - index sets of rows and columns to extract (or NULL)
4527 
4528    Output Parameter:
4529 .    A_loc - the local sequential matrix generated
4530 
4531     Level: developer
4532 
4533 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
4534 
4535 @*/
4536 PetscErrorCode  MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
4537 {
4538   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4539   PetscErrorCode ierr;
4540   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
4541   IS             isrowa,iscola;
4542   Mat            *aloc;
4543   PetscBool      match;
4544 
4545   PetscFunctionBegin;
4546   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4547   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
4548   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4549   if (!row) {
4550     start = A->rmap->rstart; end = A->rmap->rend;
4551     ierr  = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
4552   } else {
4553     isrowa = *row;
4554   }
4555   if (!col) {
4556     start = A->cmap->rstart;
4557     cmap  = a->garray;
4558     nzA   = a->A->cmap->n;
4559     nzB   = a->B->cmap->n;
4560     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4561     ncols = 0;
4562     for (i=0; i<nzB; i++) {
4563       if (cmap[i] < start) idx[ncols++] = cmap[i];
4564       else break;
4565     }
4566     imark = i;
4567     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
4568     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
4569     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
4570   } else {
4571     iscola = *col;
4572   }
4573   if (scall != MAT_INITIAL_MATRIX) {
4574     ierr    = PetscMalloc1(1,&aloc);CHKERRQ(ierr);
4575     aloc[0] = *A_loc;
4576   }
4577   ierr   = MatGetSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
4578   *A_loc = aloc[0];
4579   ierr   = PetscFree(aloc);CHKERRQ(ierr);
4580   if (!row) {
4581     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
4582   }
4583   if (!col) {
4584     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
4585   }
4586   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4587   PetscFunctionReturn(0);
4588 }
4589 
4590 #undef __FUNCT__
4591 #define __FUNCT__ "MatGetBrowsOfAcols"
4592 /*@C
4593     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
4594 
4595     Collective on Mat
4596 
4597    Input Parameters:
4598 +    A,B - the matrices in mpiaij format
4599 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4600 -    rowb, colb - index sets of rows and columns of B to extract (or NULL)
4601 
4602    Output Parameter:
4603 +    rowb, colb - index sets of rows and columns of B to extract
4604 -    B_seq - the sequential matrix generated
4605 
4606     Level: developer
4607 
4608 @*/
4609 PetscErrorCode  MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
4610 {
4611   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4612   PetscErrorCode ierr;
4613   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
4614   IS             isrowb,iscolb;
4615   Mat            *bseq=NULL;
4616 
4617   PetscFunctionBegin;
4618   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4619     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);
4620   }
4621   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4622 
4623   if (scall == MAT_INITIAL_MATRIX) {
4624     start = A->cmap->rstart;
4625     cmap  = a->garray;
4626     nzA   = a->A->cmap->n;
4627     nzB   = a->B->cmap->n;
4628     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4629     ncols = 0;
4630     for (i=0; i<nzB; i++) {  /* row < local row index */
4631       if (cmap[i] < start) idx[ncols++] = cmap[i];
4632       else break;
4633     }
4634     imark = i;
4635     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
4636     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
4637     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
4638     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
4639   } else {
4640     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
4641     isrowb  = *rowb; iscolb = *colb;
4642     ierr    = PetscMalloc1(1,&bseq);CHKERRQ(ierr);
4643     bseq[0] = *B_seq;
4644   }
4645   ierr   = MatGetSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
4646   *B_seq = bseq[0];
4647   ierr   = PetscFree(bseq);CHKERRQ(ierr);
4648   if (!rowb) {
4649     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
4650   } else {
4651     *rowb = isrowb;
4652   }
4653   if (!colb) {
4654     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
4655   } else {
4656     *colb = iscolb;
4657   }
4658   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4659   PetscFunctionReturn(0);
4660 }
4661 
4662 #undef __FUNCT__
4663 #define __FUNCT__ "MatGetBrowsOfAoCols_MPIAIJ"
4664 /*
4665     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
4666     of the OFF-DIAGONAL portion of local A
4667 
4668     Collective on Mat
4669 
4670    Input Parameters:
4671 +    A,B - the matrices in mpiaij format
4672 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4673 
4674    Output Parameter:
4675 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
4676 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
4677 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
4678 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
4679 
4680     Level: developer
4681 
4682 */
4683 PetscErrorCode  MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
4684 {
4685   VecScatter_MPI_General *gen_to,*gen_from;
4686   PetscErrorCode         ierr;
4687   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
4688   Mat_SeqAIJ             *b_oth;
4689   VecScatter             ctx =a->Mvctx;
4690   MPI_Comm               comm;
4691   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
4692   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
4693   PetscScalar            *rvalues,*svalues;
4694   MatScalar              *b_otha,*bufa,*bufA;
4695   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
4696   MPI_Request            *rwaits = NULL,*swaits = NULL;
4697   MPI_Status             *sstatus,rstatus;
4698   PetscMPIInt            jj,size;
4699   PetscInt               *cols,sbs,rbs;
4700   PetscScalar            *vals;
4701 
4702   PetscFunctionBegin;
4703   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4704   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4705 
4706   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4707     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);
4708   }
4709   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4710   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4711 
4712   gen_to   = (VecScatter_MPI_General*)ctx->todata;
4713   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
4714   rvalues  = gen_from->values; /* holds the length of receiving row */
4715   svalues  = gen_to->values;   /* holds the length of sending row */
4716   nrecvs   = gen_from->n;
4717   nsends   = gen_to->n;
4718 
4719   ierr    = PetscMalloc2(nrecvs,&rwaits,nsends,&swaits);CHKERRQ(ierr);
4720   srow    = gen_to->indices;    /* local row index to be sent */
4721   sstarts = gen_to->starts;
4722   sprocs  = gen_to->procs;
4723   sstatus = gen_to->sstatus;
4724   sbs     = gen_to->bs;
4725   rstarts = gen_from->starts;
4726   rprocs  = gen_from->procs;
4727   rbs     = gen_from->bs;
4728 
4729   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
4730   if (scall == MAT_INITIAL_MATRIX) {
4731     /* i-array */
4732     /*---------*/
4733     /*  post receives */
4734     for (i=0; i<nrecvs; i++) {
4735       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
4736       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
4737       ierr   = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4738     }
4739 
4740     /* pack the outgoing message */
4741     ierr = PetscMalloc2(nsends+1,&sstartsj,nrecvs+1,&rstartsj);CHKERRQ(ierr);
4742 
4743     sstartsj[0] = 0;
4744     rstartsj[0] = 0;
4745     len         = 0; /* total length of j or a array to be sent */
4746     k           = 0;
4747     for (i=0; i<nsends; i++) {
4748       rowlen = (PetscInt*)svalues + sstarts[i]*sbs;
4749       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
4750       for (j=0; j<nrows; j++) {
4751         row = srow[k] + B->rmap->range[rank]; /* global row idx */
4752         for (l=0; l<sbs; l++) {
4753           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr); /* rowlength */
4754 
4755           rowlen[j*sbs+l] = ncols;
4756 
4757           len += ncols;
4758           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr);
4759         }
4760         k++;
4761       }
4762       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4763 
4764       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
4765     }
4766     /* recvs and sends of i-array are completed */
4767     i = nrecvs;
4768     while (i--) {
4769       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4770     }
4771     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4772 
4773     /* allocate buffers for sending j and a arrays */
4774     ierr = PetscMalloc1(len+1,&bufj);CHKERRQ(ierr);
4775     ierr = PetscMalloc1(len+1,&bufa);CHKERRQ(ierr);
4776 
4777     /* create i-array of B_oth */
4778     ierr = PetscMalloc1(aBn+2,&b_othi);CHKERRQ(ierr);
4779 
4780     b_othi[0] = 0;
4781     len       = 0; /* total length of j or a array to be received */
4782     k         = 0;
4783     for (i=0; i<nrecvs; i++) {
4784       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
4785       nrows  = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be recieved */
4786       for (j=0; j<nrows; j++) {
4787         b_othi[k+1] = b_othi[k] + rowlen[j];
4788         len        += rowlen[j]; k++;
4789       }
4790       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
4791     }
4792 
4793     /* allocate space for j and a arrrays of B_oth */
4794     ierr = PetscMalloc1(b_othi[aBn]+1,&b_othj);CHKERRQ(ierr);
4795     ierr = PetscMalloc1(b_othi[aBn]+1,&b_otha);CHKERRQ(ierr);
4796 
4797     /* j-array */
4798     /*---------*/
4799     /*  post receives of j-array */
4800     for (i=0; i<nrecvs; i++) {
4801       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4802       ierr  = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4803     }
4804 
4805     /* pack the outgoing message j-array */
4806     k = 0;
4807     for (i=0; i<nsends; i++) {
4808       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4809       bufJ  = bufj+sstartsj[i];
4810       for (j=0; j<nrows; j++) {
4811         row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4812         for (ll=0; ll<sbs; ll++) {
4813           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4814           for (l=0; l<ncols; l++) {
4815             *bufJ++ = cols[l];
4816           }
4817           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4818         }
4819       }
4820       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4821     }
4822 
4823     /* recvs and sends of j-array are completed */
4824     i = nrecvs;
4825     while (i--) {
4826       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4827     }
4828     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4829   } else if (scall == MAT_REUSE_MATRIX) {
4830     sstartsj = *startsj_s;
4831     rstartsj = *startsj_r;
4832     bufa     = *bufa_ptr;
4833     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
4834     b_otha   = b_oth->a;
4835   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
4836 
4837   /* a-array */
4838   /*---------*/
4839   /*  post receives of a-array */
4840   for (i=0; i<nrecvs; i++) {
4841     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4842     ierr  = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4843   }
4844 
4845   /* pack the outgoing message a-array */
4846   k = 0;
4847   for (i=0; i<nsends; i++) {
4848     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4849     bufA  = bufa+sstartsj[i];
4850     for (j=0; j<nrows; j++) {
4851       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4852       for (ll=0; ll<sbs; ll++) {
4853         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4854         for (l=0; l<ncols; l++) {
4855           *bufA++ = vals[l];
4856         }
4857         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4858       }
4859     }
4860     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4861   }
4862   /* recvs and sends of a-array are completed */
4863   i = nrecvs;
4864   while (i--) {
4865     ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4866   }
4867   if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4868   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
4869 
4870   if (scall == MAT_INITIAL_MATRIX) {
4871     /* put together the new matrix */
4872     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
4873 
4874     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4875     /* Since these are PETSc arrays, change flags to free them as necessary. */
4876     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
4877     b_oth->free_a  = PETSC_TRUE;
4878     b_oth->free_ij = PETSC_TRUE;
4879     b_oth->nonew   = 0;
4880 
4881     ierr = PetscFree(bufj);CHKERRQ(ierr);
4882     if (!startsj_s || !bufa_ptr) {
4883       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
4884       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
4885     } else {
4886       *startsj_s = sstartsj;
4887       *startsj_r = rstartsj;
4888       *bufa_ptr  = bufa;
4889     }
4890   }
4891   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4892   PetscFunctionReturn(0);
4893 }
4894 
4895 #undef __FUNCT__
4896 #define __FUNCT__ "MatGetCommunicationStructs"
4897 /*@C
4898   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
4899 
4900   Not Collective
4901 
4902   Input Parameters:
4903 . A - The matrix in mpiaij format
4904 
4905   Output Parameter:
4906 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
4907 . colmap - A map from global column index to local index into lvec
4908 - multScatter - A scatter from the argument of a matrix-vector product to lvec
4909 
4910   Level: developer
4911 
4912 @*/
4913 #if defined(PETSC_USE_CTABLE)
4914 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
4915 #else
4916 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
4917 #endif
4918 {
4919   Mat_MPIAIJ *a;
4920 
4921   PetscFunctionBegin;
4922   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4923   PetscValidPointer(lvec, 2);
4924   PetscValidPointer(colmap, 3);
4925   PetscValidPointer(multScatter, 4);
4926   a = (Mat_MPIAIJ*) A->data;
4927   if (lvec) *lvec = a->lvec;
4928   if (colmap) *colmap = a->colmap;
4929   if (multScatter) *multScatter = a->Mvctx;
4930   PetscFunctionReturn(0);
4931 }
4932 
4933 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
4934 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
4935 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
4936 #if defined(PETSC_HAVE_ELEMENTAL)
4937 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
4938 #endif
4939 
4940 #undef __FUNCT__
4941 #define __FUNCT__ "MatMatMultNumeric_MPIDense_MPIAIJ"
4942 /*
4943     Computes (B'*A')' since computing B*A directly is untenable
4944 
4945                n                       p                          p
4946         (              )       (              )         (                  )
4947       m (      A       )  *  n (       B      )   =   m (         C        )
4948         (              )       (              )         (                  )
4949 
4950 */
4951 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
4952 {
4953   PetscErrorCode ierr;
4954   Mat            At,Bt,Ct;
4955 
4956   PetscFunctionBegin;
4957   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
4958   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
4959   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
4960   ierr = MatDestroy(&At);CHKERRQ(ierr);
4961   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
4962   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
4963   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
4964   PetscFunctionReturn(0);
4965 }
4966 
4967 #undef __FUNCT__
4968 #define __FUNCT__ "MatMatMultSymbolic_MPIDense_MPIAIJ"
4969 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
4970 {
4971   PetscErrorCode ierr;
4972   PetscInt       m=A->rmap->n,n=B->cmap->n;
4973   Mat            Cmat;
4974 
4975   PetscFunctionBegin;
4976   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);
4977   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
4978   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4979   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
4980   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
4981   ierr = MatMPIDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
4982   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4983   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4984 
4985   Cmat->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
4986 
4987   *C = Cmat;
4988   PetscFunctionReturn(0);
4989 }
4990 
4991 /* ----------------------------------------------------------------*/
4992 #undef __FUNCT__
4993 #define __FUNCT__ "MatMatMult_MPIDense_MPIAIJ"
4994 PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
4995 {
4996   PetscErrorCode ierr;
4997 
4998   PetscFunctionBegin;
4999   if (scall == MAT_INITIAL_MATRIX) {
5000     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5001     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
5002     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5003   }
5004   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5005   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
5006   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5007   PetscFunctionReturn(0);
5008 }
5009 
5010 /*MC
5011    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
5012 
5013    Options Database Keys:
5014 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
5015 
5016   Level: beginner
5017 
5018 .seealso: MatCreateAIJ()
5019 M*/
5020 
5021 #undef __FUNCT__
5022 #define __FUNCT__ "MatCreate_MPIAIJ"
5023 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
5024 {
5025   Mat_MPIAIJ     *b;
5026   PetscErrorCode ierr;
5027   PetscMPIInt    size;
5028 
5029   PetscFunctionBegin;
5030   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
5031 
5032   ierr          = PetscNewLog(B,&b);CHKERRQ(ierr);
5033   B->data       = (void*)b;
5034   ierr          = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
5035   B->assembled  = PETSC_FALSE;
5036   B->insertmode = NOT_SET_VALUES;
5037   b->size       = size;
5038 
5039   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank);CHKERRQ(ierr);
5040 
5041   /* build cache for off array entries formed */
5042   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash);CHKERRQ(ierr);
5043 
5044   b->donotstash  = PETSC_FALSE;
5045   b->colmap      = 0;
5046   b->garray      = 0;
5047   b->roworiented = PETSC_TRUE;
5048 
5049   /* stuff used for matrix vector multiply */
5050   b->lvec  = NULL;
5051   b->Mvctx = NULL;
5052 
5053   /* stuff for MatGetRow() */
5054   b->rowindices   = 0;
5055   b->rowvalues    = 0;
5056   b->getrowactive = PETSC_FALSE;
5057 
5058   /* flexible pointer used in CUSP/CUSPARSE classes */
5059   b->spptr = NULL;
5060 
5061   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetUseScalableIncreaseOverlap_C",MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ);CHKERRQ(ierr);
5062   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ);CHKERRQ(ierr);
5063   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
5064   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetDiagonalBlock_C",MatGetDiagonalBlock_MPIAIJ);CHKERRQ(ierr);
5065   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
5066   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
5067   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
5068   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
5069   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
5070   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
5071   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
5072 #if defined(PETSC_HAVE_ELEMENTAL)
5073   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_elemental_C",MatConvert_MPIAIJ_Elemental);CHKERRQ(ierr);
5074 #endif
5075   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
5076   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
5077   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
5078   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
5079   PetscFunctionReturn(0);
5080 }
5081 
5082 #undef __FUNCT__
5083 #define __FUNCT__ "MatCreateMPIAIJWithSplitArrays"
5084 /*@C
5085      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
5086          and "off-diagonal" part of the matrix in CSR format.
5087 
5088    Collective on MPI_Comm
5089 
5090    Input Parameters:
5091 +  comm - MPI communicator
5092 .  m - number of local rows (Cannot be PETSC_DECIDE)
5093 .  n - This value should be the same as the local size used in creating the
5094        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
5095        calculated if N is given) For square matrices n is almost always m.
5096 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
5097 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
5098 .   i - row indices for "diagonal" portion of matrix
5099 .   j - column indices
5100 .   a - matrix values
5101 .   oi - row indices for "off-diagonal" portion of matrix
5102 .   oj - column indices
5103 -   oa - matrix values
5104 
5105    Output Parameter:
5106 .   mat - the matrix
5107 
5108    Level: advanced
5109 
5110    Notes:
5111        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
5112        must free the arrays once the matrix has been destroyed and not before.
5113 
5114        The i and j indices are 0 based
5115 
5116        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
5117 
5118        This sets local rows and cannot be used to set off-processor values.
5119 
5120        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
5121        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
5122        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
5123        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
5124        keep track of the underlying array. Use MatSetOption(A,MAT_IGNORE_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
5125        communication if it is known that only local entries will be set.
5126 
5127 .keywords: matrix, aij, compressed row, sparse, parallel
5128 
5129 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
5130           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
5131 @*/
5132 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)
5133 {
5134   PetscErrorCode ierr;
5135   Mat_MPIAIJ     *maij;
5136 
5137   PetscFunctionBegin;
5138   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
5139   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
5140   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
5141   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
5142   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
5143   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
5144   maij = (Mat_MPIAIJ*) (*mat)->data;
5145 
5146   (*mat)->preallocated = PETSC_TRUE;
5147 
5148   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
5149   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
5150 
5151   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
5152   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
5153 
5154   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5155   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5156   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5157   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5158 
5159   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5160   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5161   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
5162   PetscFunctionReturn(0);
5163 }
5164 
5165 /*
5166     Special version for direct calls from Fortran
5167 */
5168 #include <petsc/private/fortranimpl.h>
5169 
5170 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5171 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
5172 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5173 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
5174 #endif
5175 
5176 /* Change these macros so can be used in void function */
5177 #undef CHKERRQ
5178 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
5179 #undef SETERRQ2
5180 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5181 #undef SETERRQ3
5182 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5183 #undef SETERRQ
5184 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
5185 
5186 #undef __FUNCT__
5187 #define __FUNCT__ "matsetvaluesmpiaij_"
5188 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)
5189 {
5190   Mat            mat  = *mmat;
5191   PetscInt       m    = *mm, n = *mn;
5192   InsertMode     addv = *maddv;
5193   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
5194   PetscScalar    value;
5195   PetscErrorCode ierr;
5196 
5197   MatCheckPreallocated(mat,1);
5198   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
5199 
5200 #if defined(PETSC_USE_DEBUG)
5201   else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
5202 #endif
5203   {
5204     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
5205     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
5206     PetscBool roworiented = aij->roworiented;
5207 
5208     /* Some Variables required in the macro */
5209     Mat        A                 = aij->A;
5210     Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
5211     PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
5212     MatScalar  *aa               = a->a;
5213     PetscBool  ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
5214     Mat        B                 = aij->B;
5215     Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
5216     PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5217     MatScalar  *ba               = b->a;
5218 
5219     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5220     PetscInt  nonew = a->nonew;
5221     MatScalar *ap1,*ap2;
5222 
5223     PetscFunctionBegin;
5224     for (i=0; i<m; i++) {
5225       if (im[i] < 0) continue;
5226 #if defined(PETSC_USE_DEBUG)
5227       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);
5228 #endif
5229       if (im[i] >= rstart && im[i] < rend) {
5230         row      = im[i] - rstart;
5231         lastcol1 = -1;
5232         rp1      = aj + ai[row];
5233         ap1      = aa + ai[row];
5234         rmax1    = aimax[row];
5235         nrow1    = ailen[row];
5236         low1     = 0;
5237         high1    = nrow1;
5238         lastcol2 = -1;
5239         rp2      = bj + bi[row];
5240         ap2      = ba + bi[row];
5241         rmax2    = bimax[row];
5242         nrow2    = bilen[row];
5243         low2     = 0;
5244         high2    = nrow2;
5245 
5246         for (j=0; j<n; j++) {
5247           if (roworiented) value = v[i*n+j];
5248           else value = v[i+j*m];
5249           if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES)) continue;
5250           if (in[j] >= cstart && in[j] < cend) {
5251             col = in[j] - cstart;
5252             MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
5253           } else if (in[j] < 0) continue;
5254 #if defined(PETSC_USE_DEBUG)
5255           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);
5256 #endif
5257           else {
5258             if (mat->was_assembled) {
5259               if (!aij->colmap) {
5260                 ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5261               }
5262 #if defined(PETSC_USE_CTABLE)
5263               ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5264               col--;
5265 #else
5266               col = aij->colmap[in[j]] - 1;
5267 #endif
5268               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5269                 ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5270                 col  =  in[j];
5271                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5272                 B     = aij->B;
5273                 b     = (Mat_SeqAIJ*)B->data;
5274                 bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5275                 rp2   = bj + bi[row];
5276                 ap2   = ba + bi[row];
5277                 rmax2 = bimax[row];
5278                 nrow2 = bilen[row];
5279                 low2  = 0;
5280                 high2 = nrow2;
5281                 bm    = aij->B->rmap->n;
5282                 ba    = b->a;
5283               }
5284             } else col = in[j];
5285             MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
5286           }
5287         }
5288       } else if (!aij->donotstash) {
5289         if (roworiented) {
5290           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5291         } else {
5292           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5293         }
5294       }
5295     }
5296   }
5297   PetscFunctionReturnVoid();
5298 }
5299 
5300