xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision 3646cfeb797400a3e4541320631fb1502714bdc9)
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 /* -------------------------------------------------------------------*/
2549 static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
2550                                        MatGetRow_MPIAIJ,
2551                                        MatRestoreRow_MPIAIJ,
2552                                        MatMult_MPIAIJ,
2553                                 /* 4*/ MatMultAdd_MPIAIJ,
2554                                        MatMultTranspose_MPIAIJ,
2555                                        MatMultTransposeAdd_MPIAIJ,
2556                                        0,
2557                                        0,
2558                                        0,
2559                                 /*10*/ 0,
2560                                        0,
2561                                        0,
2562                                        MatSOR_MPIAIJ,
2563                                        MatTranspose_MPIAIJ,
2564                                 /*15*/ MatGetInfo_MPIAIJ,
2565                                        MatEqual_MPIAIJ,
2566                                        MatGetDiagonal_MPIAIJ,
2567                                        MatDiagonalScale_MPIAIJ,
2568                                        MatNorm_MPIAIJ,
2569                                 /*20*/ MatAssemblyBegin_MPIAIJ,
2570                                        MatAssemblyEnd_MPIAIJ,
2571                                        MatSetOption_MPIAIJ,
2572                                        MatZeroEntries_MPIAIJ,
2573                                 /*24*/ MatZeroRows_MPIAIJ,
2574                                        0,
2575                                        0,
2576                                        0,
2577                                        0,
2578                                 /*29*/ MatSetUp_MPIAIJ,
2579                                        0,
2580                                        0,
2581                                        0,
2582                                        0,
2583                                 /*34*/ MatDuplicate_MPIAIJ,
2584                                        0,
2585                                        0,
2586                                        0,
2587                                        0,
2588                                 /*39*/ MatAXPY_MPIAIJ,
2589                                        MatGetSubMatrices_MPIAIJ,
2590                                        MatIncreaseOverlap_MPIAIJ,
2591                                        MatGetValues_MPIAIJ,
2592                                        MatCopy_MPIAIJ,
2593                                 /*44*/ MatGetRowMax_MPIAIJ,
2594                                        MatScale_MPIAIJ,
2595                                        MatShift_MPIAIJ,
2596                                        MatDiagonalSet_MPIAIJ,
2597                                        MatZeroRowsColumns_MPIAIJ,
2598                                 /*49*/ MatSetRandom_MPIAIJ,
2599                                        0,
2600                                        0,
2601                                        0,
2602                                        0,
2603                                 /*54*/ MatFDColoringCreate_MPIXAIJ,
2604                                        0,
2605                                        MatSetUnfactored_MPIAIJ,
2606                                        MatPermute_MPIAIJ,
2607                                        0,
2608                                 /*59*/ MatGetSubMatrix_MPIAIJ,
2609                                        MatDestroy_MPIAIJ,
2610                                        MatView_MPIAIJ,
2611                                        0,
2612                                        MatMatMatMult_MPIAIJ_MPIAIJ_MPIAIJ,
2613                                 /*64*/ MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ,
2614                                        MatMatMatMultNumeric_MPIAIJ_MPIAIJ_MPIAIJ,
2615                                        0,
2616                                        0,
2617                                        0,
2618                                 /*69*/ MatGetRowMaxAbs_MPIAIJ,
2619                                        MatGetRowMinAbs_MPIAIJ,
2620                                        0,
2621                                        MatSetColoring_MPIAIJ,
2622                                        0,
2623                                        MatSetValuesAdifor_MPIAIJ,
2624                                 /*75*/ MatFDColoringApply_AIJ,
2625                                        MatSetFromOptions_MPIAIJ,
2626                                        0,
2627                                        0,
2628                                        MatFindZeroDiagonals_MPIAIJ,
2629                                 /*80*/ 0,
2630                                        0,
2631                                        0,
2632                                 /*83*/ MatLoad_MPIAIJ,
2633                                        0,
2634                                        0,
2635                                        0,
2636                                        0,
2637                                        0,
2638                                 /*89*/ MatMatMult_MPIAIJ_MPIAIJ,
2639                                        MatMatMultSymbolic_MPIAIJ_MPIAIJ,
2640                                        MatMatMultNumeric_MPIAIJ_MPIAIJ,
2641                                        MatPtAP_MPIAIJ_MPIAIJ,
2642                                        MatPtAPSymbolic_MPIAIJ_MPIAIJ,
2643                                 /*94*/ MatPtAPNumeric_MPIAIJ_MPIAIJ,
2644                                        0,
2645                                        0,
2646                                        0,
2647                                        0,
2648                                 /*99*/ 0,
2649                                        0,
2650                                        0,
2651                                        MatConjugate_MPIAIJ,
2652                                        0,
2653                                 /*104*/MatSetValuesRow_MPIAIJ,
2654                                        MatRealPart_MPIAIJ,
2655                                        MatImaginaryPart_MPIAIJ,
2656                                        0,
2657                                        0,
2658                                 /*109*/0,
2659                                        0,
2660                                        MatGetRowMin_MPIAIJ,
2661                                        0,
2662                                        0,
2663                                 /*114*/MatGetSeqNonzeroStructure_MPIAIJ,
2664                                        0,
2665                                        MatGetGhosts_MPIAIJ,
2666                                        0,
2667                                        0,
2668                                 /*119*/0,
2669                                        0,
2670                                        0,
2671                                        0,
2672                                        MatGetMultiProcBlock_MPIAIJ,
2673                                 /*124*/MatFindNonzeroRows_MPIAIJ,
2674                                        MatGetColumnNorms_MPIAIJ,
2675                                        MatInvertBlockDiagonal_MPIAIJ,
2676                                        0,
2677                                        MatGetSubMatricesMPI_MPIAIJ,
2678                                 /*129*/0,
2679                                        MatTransposeMatMult_MPIAIJ_MPIAIJ,
2680                                        MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ,
2681                                        MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ,
2682                                        0,
2683                                 /*134*/0,
2684                                        0,
2685                                        0,
2686                                        0,
2687                                        0,
2688                                 /*139*/0,
2689                                        0,
2690                                        0,
2691                                        MatFDColoringSetUp_MPIXAIJ,
2692                                        MatFindOffBlockDiagonalEntries_MPIAIJ,
2693                                 /*144*/MatCreateMPIMatConcatenateSeqMat_MPIAIJ
2694 };
2695 
2696 /* ----------------------------------------------------------------------------------------*/
2697 
2698 #undef __FUNCT__
2699 #define __FUNCT__ "MatStoreValues_MPIAIJ"
2700 PetscErrorCode  MatStoreValues_MPIAIJ(Mat mat)
2701 {
2702   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2703   PetscErrorCode ierr;
2704 
2705   PetscFunctionBegin;
2706   ierr = MatStoreValues(aij->A);CHKERRQ(ierr);
2707   ierr = MatStoreValues(aij->B);CHKERRQ(ierr);
2708   PetscFunctionReturn(0);
2709 }
2710 
2711 #undef __FUNCT__
2712 #define __FUNCT__ "MatRetrieveValues_MPIAIJ"
2713 PetscErrorCode  MatRetrieveValues_MPIAIJ(Mat mat)
2714 {
2715   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2716   PetscErrorCode ierr;
2717 
2718   PetscFunctionBegin;
2719   ierr = MatRetrieveValues(aij->A);CHKERRQ(ierr);
2720   ierr = MatRetrieveValues(aij->B);CHKERRQ(ierr);
2721   PetscFunctionReturn(0);
2722 }
2723 
2724 #undef __FUNCT__
2725 #define __FUNCT__ "MatMPIAIJSetPreallocation_MPIAIJ"
2726 PetscErrorCode  MatMPIAIJSetPreallocation_MPIAIJ(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
2727 {
2728   Mat_MPIAIJ     *b;
2729   PetscErrorCode ierr;
2730 
2731   PetscFunctionBegin;
2732   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
2733   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
2734   b = (Mat_MPIAIJ*)B->data;
2735 
2736   if (!B->preallocated) {
2737     /* Explicitly create 2 MATSEQAIJ matrices. */
2738     ierr = MatCreate(PETSC_COMM_SELF,&b->A);CHKERRQ(ierr);
2739     ierr = MatSetSizes(b->A,B->rmap->n,B->cmap->n,B->rmap->n,B->cmap->n);CHKERRQ(ierr);
2740     ierr = MatSetBlockSizesFromMats(b->A,B,B);CHKERRQ(ierr);
2741     ierr = MatSetType(b->A,MATSEQAIJ);CHKERRQ(ierr);
2742     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->A);CHKERRQ(ierr);
2743     ierr = MatCreate(PETSC_COMM_SELF,&b->B);CHKERRQ(ierr);
2744     ierr = MatSetSizes(b->B,B->rmap->n,B->cmap->N,B->rmap->n,B->cmap->N);CHKERRQ(ierr);
2745     ierr = MatSetBlockSizesFromMats(b->B,B,B);CHKERRQ(ierr);
2746     ierr = MatSetType(b->B,MATSEQAIJ);CHKERRQ(ierr);
2747     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->B);CHKERRQ(ierr);
2748   }
2749 
2750   ierr = MatSeqAIJSetPreallocation(b->A,d_nz,d_nnz);CHKERRQ(ierr);
2751   ierr = MatSeqAIJSetPreallocation(b->B,o_nz,o_nnz);CHKERRQ(ierr);
2752   B->preallocated = PETSC_TRUE;
2753   PetscFunctionReturn(0);
2754 }
2755 
2756 #undef __FUNCT__
2757 #define __FUNCT__ "MatDuplicate_MPIAIJ"
2758 PetscErrorCode MatDuplicate_MPIAIJ(Mat matin,MatDuplicateOption cpvalues,Mat *newmat)
2759 {
2760   Mat            mat;
2761   Mat_MPIAIJ     *a,*oldmat = (Mat_MPIAIJ*)matin->data;
2762   PetscErrorCode ierr;
2763 
2764   PetscFunctionBegin;
2765   *newmat = 0;
2766   ierr    = MatCreate(PetscObjectComm((PetscObject)matin),&mat);CHKERRQ(ierr);
2767   ierr    = MatSetSizes(mat,matin->rmap->n,matin->cmap->n,matin->rmap->N,matin->cmap->N);CHKERRQ(ierr);
2768   ierr    = MatSetBlockSizesFromMats(mat,matin,matin);CHKERRQ(ierr);
2769   ierr    = MatSetType(mat,((PetscObject)matin)->type_name);CHKERRQ(ierr);
2770   ierr    = PetscMemcpy(mat->ops,matin->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
2771   a       = (Mat_MPIAIJ*)mat->data;
2772 
2773   mat->factortype   = matin->factortype;
2774   mat->assembled    = PETSC_TRUE;
2775   mat->insertmode   = NOT_SET_VALUES;
2776   mat->preallocated = PETSC_TRUE;
2777 
2778   a->size         = oldmat->size;
2779   a->rank         = oldmat->rank;
2780   a->donotstash   = oldmat->donotstash;
2781   a->roworiented  = oldmat->roworiented;
2782   a->rowindices   = 0;
2783   a->rowvalues    = 0;
2784   a->getrowactive = PETSC_FALSE;
2785 
2786   ierr = PetscLayoutReference(matin->rmap,&mat->rmap);CHKERRQ(ierr);
2787   ierr = PetscLayoutReference(matin->cmap,&mat->cmap);CHKERRQ(ierr);
2788 
2789   if (oldmat->colmap) {
2790 #if defined(PETSC_USE_CTABLE)
2791     ierr = PetscTableCreateCopy(oldmat->colmap,&a->colmap);CHKERRQ(ierr);
2792 #else
2793     ierr = PetscMalloc1(mat->cmap->N,&a->colmap);CHKERRQ(ierr);
2794     ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2795     ierr = PetscMemcpy(a->colmap,oldmat->colmap,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2796 #endif
2797   } else a->colmap = 0;
2798   if (oldmat->garray) {
2799     PetscInt len;
2800     len  = oldmat->B->cmap->n;
2801     ierr = PetscMalloc1(len+1,&a->garray);CHKERRQ(ierr);
2802     ierr = PetscLogObjectMemory((PetscObject)mat,len*sizeof(PetscInt));CHKERRQ(ierr);
2803     if (len) { ierr = PetscMemcpy(a->garray,oldmat->garray,len*sizeof(PetscInt));CHKERRQ(ierr); }
2804   } else a->garray = 0;
2805 
2806   ierr    = VecDuplicate(oldmat->lvec,&a->lvec);CHKERRQ(ierr);
2807   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->lvec);CHKERRQ(ierr);
2808   ierr    = VecScatterCopy(oldmat->Mvctx,&a->Mvctx);CHKERRQ(ierr);
2809   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->Mvctx);CHKERRQ(ierr);
2810   ierr    = MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
2811   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->A);CHKERRQ(ierr);
2812   ierr    = MatDuplicate(oldmat->B,cpvalues,&a->B);CHKERRQ(ierr);
2813   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->B);CHKERRQ(ierr);
2814   ierr    = PetscFunctionListDuplicate(((PetscObject)matin)->qlist,&((PetscObject)mat)->qlist);CHKERRQ(ierr);
2815   *newmat = mat;
2816   PetscFunctionReturn(0);
2817 }
2818 
2819 
2820 
2821 #undef __FUNCT__
2822 #define __FUNCT__ "MatLoad_MPIAIJ"
2823 PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
2824 {
2825   PetscScalar    *vals,*svals;
2826   MPI_Comm       comm;
2827   PetscErrorCode ierr;
2828   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
2829   PetscInt       i,nz,j,rstart,rend,mmax,maxnz = 0;
2830   PetscInt       header[4],*rowlengths = 0,M,N,m,*cols;
2831   PetscInt       *ourlens = NULL,*procsnz = NULL,*offlens = NULL,jj,*mycols,*smycols;
2832   PetscInt       cend,cstart,n,*rowners;
2833   int            fd;
2834   PetscInt       bs = newMat->rmap->bs;
2835 
2836   PetscFunctionBegin;
2837   /* force binary viewer to load .info file if it has not yet done so */
2838   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
2839   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
2840   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2841   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2842   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
2843   if (!rank) {
2844     ierr = PetscBinaryRead(fd,(char*)header,4,PETSC_INT);CHKERRQ(ierr);
2845     if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
2846   }
2847 
2848   ierr = PetscOptionsBegin(comm,NULL,"Options for loading MPIAIJ matrix","Mat");CHKERRQ(ierr);
2849   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
2850   ierr = PetscOptionsEnd();CHKERRQ(ierr);
2851   if (bs < 0) bs = 1;
2852 
2853   ierr = MPI_Bcast(header+1,3,MPIU_INT,0,comm);CHKERRQ(ierr);
2854   M    = header[1]; N = header[2];
2855 
2856   /* If global sizes are set, check if they are consistent with that given in the file */
2857   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);
2858   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);
2859 
2860   /* determine ownership of all (block) rows */
2861   if (M%bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Inconsistent # of rows (%d) and block size (%d)",M,bs);
2862   if (newMat->rmap->n < 0) m = bs*((M/bs)/size + (((M/bs) % size) > rank));    /* PETSC_DECIDE */
2863   else m = newMat->rmap->n; /* Set by user */
2864 
2865   ierr = PetscMalloc1(size+1,&rowners);CHKERRQ(ierr);
2866   ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
2867 
2868   /* First process needs enough room for process with most rows */
2869   if (!rank) {
2870     mmax = rowners[1];
2871     for (i=2; i<=size; i++) {
2872       mmax = PetscMax(mmax, rowners[i]);
2873     }
2874   } else mmax = -1;             /* unused, but compilers complain */
2875 
2876   rowners[0] = 0;
2877   for (i=2; i<=size; i++) {
2878     rowners[i] += rowners[i-1];
2879   }
2880   rstart = rowners[rank];
2881   rend   = rowners[rank+1];
2882 
2883   /* distribute row lengths to all processors */
2884   ierr = PetscMalloc2(m,&ourlens,m,&offlens);CHKERRQ(ierr);
2885   if (!rank) {
2886     ierr = PetscBinaryRead(fd,ourlens,m,PETSC_INT);CHKERRQ(ierr);
2887     ierr = PetscMalloc1(mmax,&rowlengths);CHKERRQ(ierr);
2888     ierr = PetscCalloc1(size,&procsnz);CHKERRQ(ierr);
2889     for (j=0; j<m; j++) {
2890       procsnz[0] += ourlens[j];
2891     }
2892     for (i=1; i<size; i++) {
2893       ierr = PetscBinaryRead(fd,rowlengths,rowners[i+1]-rowners[i],PETSC_INT);CHKERRQ(ierr);
2894       /* calculate the number of nonzeros on each processor */
2895       for (j=0; j<rowners[i+1]-rowners[i]; j++) {
2896         procsnz[i] += rowlengths[j];
2897       }
2898       ierr = MPIULong_Send(rowlengths,rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2899     }
2900     ierr = PetscFree(rowlengths);CHKERRQ(ierr);
2901   } else {
2902     ierr = MPIULong_Recv(ourlens,m,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2903   }
2904 
2905   if (!rank) {
2906     /* determine max buffer needed and allocate it */
2907     maxnz = 0;
2908     for (i=0; i<size; i++) {
2909       maxnz = PetscMax(maxnz,procsnz[i]);
2910     }
2911     ierr = PetscMalloc1(maxnz,&cols);CHKERRQ(ierr);
2912 
2913     /* read in my part of the matrix column indices  */
2914     nz   = procsnz[0];
2915     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2916     ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);
2917 
2918     /* read in every one elses and ship off */
2919     for (i=1; i<size; i++) {
2920       nz   = procsnz[i];
2921       ierr = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
2922       ierr = MPIULong_Send(cols,nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2923     }
2924     ierr = PetscFree(cols);CHKERRQ(ierr);
2925   } else {
2926     /* determine buffer space needed for message */
2927     nz = 0;
2928     for (i=0; i<m; i++) {
2929       nz += ourlens[i];
2930     }
2931     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2932 
2933     /* receive message of column indices*/
2934     ierr = MPIULong_Recv(mycols,nz,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2935   }
2936 
2937   /* determine column ownership if matrix is not square */
2938   if (N != M) {
2939     if (newMat->cmap->n < 0) n = N/size + ((N % size) > rank);
2940     else n = newMat->cmap->n;
2941     ierr   = MPI_Scan(&n,&cend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
2942     cstart = cend - n;
2943   } else {
2944     cstart = rstart;
2945     cend   = rend;
2946     n      = cend - cstart;
2947   }
2948 
2949   /* loop over local rows, determining number of off diagonal entries */
2950   ierr = PetscMemzero(offlens,m*sizeof(PetscInt));CHKERRQ(ierr);
2951   jj   = 0;
2952   for (i=0; i<m; i++) {
2953     for (j=0; j<ourlens[i]; j++) {
2954       if (mycols[jj] < cstart || mycols[jj] >= cend) offlens[i]++;
2955       jj++;
2956     }
2957   }
2958 
2959   for (i=0; i<m; i++) {
2960     ourlens[i] -= offlens[i];
2961   }
2962   ierr = MatSetSizes(newMat,m,n,M,N);CHKERRQ(ierr);
2963 
2964   if (bs > 1) {ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);}
2965 
2966   ierr = MatMPIAIJSetPreallocation(newMat,0,ourlens,0,offlens);CHKERRQ(ierr);
2967 
2968   for (i=0; i<m; i++) {
2969     ourlens[i] += offlens[i];
2970   }
2971 
2972   if (!rank) {
2973     ierr = PetscMalloc1(maxnz+1,&vals);CHKERRQ(ierr);
2974 
2975     /* read in my part of the matrix numerical values  */
2976     nz   = procsnz[0];
2977     ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
2978 
2979     /* insert into matrix */
2980     jj      = rstart;
2981     smycols = mycols;
2982     svals   = vals;
2983     for (i=0; i<m; i++) {
2984       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
2985       smycols += ourlens[i];
2986       svals   += ourlens[i];
2987       jj++;
2988     }
2989 
2990     /* read in other processors and ship out */
2991     for (i=1; i<size; i++) {
2992       nz   = procsnz[i];
2993       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
2994       ierr = MPIULong_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
2995     }
2996     ierr = PetscFree(procsnz);CHKERRQ(ierr);
2997   } else {
2998     /* receive numeric values */
2999     ierr = PetscMalloc1(nz+1,&vals);CHKERRQ(ierr);
3000 
3001     /* receive message of values*/
3002     ierr = MPIULong_Recv(vals,nz,MPIU_SCALAR,0,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
3003 
3004     /* insert into matrix */
3005     jj      = rstart;
3006     smycols = mycols;
3007     svals   = vals;
3008     for (i=0; i<m; i++) {
3009       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
3010       smycols += ourlens[i];
3011       svals   += ourlens[i];
3012       jj++;
3013     }
3014   }
3015   ierr = PetscFree2(ourlens,offlens);CHKERRQ(ierr);
3016   ierr = PetscFree(vals);CHKERRQ(ierr);
3017   ierr = PetscFree(mycols);CHKERRQ(ierr);
3018   ierr = PetscFree(rowners);CHKERRQ(ierr);
3019   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3020   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3021   PetscFunctionReturn(0);
3022 }
3023 
3024 #undef __FUNCT__
3025 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ"
3026 /* TODO: Not scalable because of ISAllGather() unless getting all columns. */
3027 PetscErrorCode MatGetSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3028 {
3029   PetscErrorCode ierr;
3030   IS             iscol_local;
3031   PetscInt       csize;
3032 
3033   PetscFunctionBegin;
3034   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3035   if (call == MAT_REUSE_MATRIX) {
3036     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3037     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3038   } else {
3039     /* check if we are grabbing all columns*/
3040     PetscBool    isstride;
3041     PetscMPIInt  lisstride = 0,gisstride;
3042     ierr = PetscObjectTypeCompare((PetscObject)iscol,ISSTRIDE,&isstride);CHKERRQ(ierr);
3043     if (isstride) {
3044       PetscInt  start,len,mstart,mlen;
3045       ierr = ISStrideGetInfo(iscol,&start,&len);CHKERRQ(ierr);
3046       ierr = MatGetOwnershipRangeColumn(mat,&mstart,&mlen);CHKERRQ(ierr);
3047       if (mstart == start && mlen == len) lisstride = 1;
3048     }
3049     ierr = MPI_Allreduce(&lisstride,&gisstride,1,MPI_INT,MPI_MIN,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
3050     if (gisstride) {
3051       PetscInt N;
3052       ierr = MatGetSize(mat,NULL,&N);CHKERRQ(ierr);
3053       ierr = ISCreateStride(PetscObjectComm((PetscObject)mat),N,0,1,&iscol_local);CHKERRQ(ierr);
3054       ierr = ISSetIdentity(iscol_local);CHKERRQ(ierr);
3055       ierr = PetscInfo(mat,"Optimizing for obtaining all columns of the matrix; skipping ISAllGather()\n");CHKERRQ(ierr);
3056     } else {
3057       PetscInt cbs;
3058       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
3059       ierr = ISAllGather(iscol,&iscol_local);CHKERRQ(ierr);
3060       ierr = ISSetBlockSize(iscol_local,cbs);CHKERRQ(ierr);
3061     }
3062   }
3063   ierr = MatGetSubMatrix_MPIAIJ_Private(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
3064   if (call == MAT_INITIAL_MATRIX) {
3065     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3066     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3067   }
3068   PetscFunctionReturn(0);
3069 }
3070 
3071 extern PetscErrorCode MatGetSubMatrices_MPIAIJ_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool*,Mat*);
3072 #undef __FUNCT__
3073 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ_Private"
3074 /*
3075     Not great since it makes two copies of the submatrix, first an SeqAIJ
3076   in local and then by concatenating the local matrices the end result.
3077   Writing it directly would be much like MatGetSubMatrices_MPIAIJ()
3078 
3079   Note: This requires a sequential iscol with all indices.
3080 */
3081 PetscErrorCode MatGetSubMatrix_MPIAIJ_Private(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3082 {
3083   PetscErrorCode ierr;
3084   PetscMPIInt    rank,size;
3085   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3086   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal,ncol;
3087   PetscBool      allcolumns, colflag;
3088   Mat            M,Mreuse;
3089   MatScalar      *vwork,*aa;
3090   MPI_Comm       comm;
3091   Mat_SeqAIJ     *aij;
3092 
3093   PetscFunctionBegin;
3094   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3095   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3096   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3097 
3098   ierr = ISIdentity(iscol,&colflag);CHKERRQ(ierr);
3099   ierr = ISGetLocalSize(iscol,&ncol);CHKERRQ(ierr);
3100   if (colflag && ncol == mat->cmap->N) {
3101     allcolumns = PETSC_TRUE;
3102     ierr = PetscInfo(mat,"Optimizing for obtaining all columns of the matrix\n");CHKERRQ(ierr);
3103   } else {
3104     allcolumns = PETSC_FALSE;
3105   }
3106   if (call ==  MAT_REUSE_MATRIX) {
3107     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3108     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3109     ierr = MatGetSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,&allcolumns,&Mreuse);CHKERRQ(ierr);
3110   } else {
3111     ierr = MatGetSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&allcolumns,&Mreuse);CHKERRQ(ierr);
3112   }
3113 
3114   /*
3115       m - number of local rows
3116       n - number of columns (same on all processors)
3117       rstart - first row in new global matrix generated
3118   */
3119   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3120   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3121   if (call == MAT_INITIAL_MATRIX) {
3122     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3123     ii  = aij->i;
3124     jj  = aij->j;
3125 
3126     /*
3127         Determine the number of non-zeros in the diagonal and off-diagonal
3128         portions of the matrix in order to do correct preallocation
3129     */
3130 
3131     /* first get start and end of "diagonal" columns */
3132     if (csize == PETSC_DECIDE) {
3133       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3134       if (mglobal == n) { /* square matrix */
3135         nlocal = m;
3136       } else {
3137         nlocal = n/size + ((n % size) > rank);
3138       }
3139     } else {
3140       nlocal = csize;
3141     }
3142     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3143     rstart = rend - nlocal;
3144     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);
3145 
3146     /* next, compute all the lengths */
3147     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3148     olens = dlens + m;
3149     for (i=0; i<m; i++) {
3150       jend = ii[i+1] - ii[i];
3151       olen = 0;
3152       dlen = 0;
3153       for (j=0; j<jend; j++) {
3154         if (*jj < rstart || *jj >= rend) olen++;
3155         else dlen++;
3156         jj++;
3157       }
3158       olens[i] = olen;
3159       dlens[i] = dlen;
3160     }
3161     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3162     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3163     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3164     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3165     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3166     ierr = PetscFree(dlens);CHKERRQ(ierr);
3167   } else {
3168     PetscInt ml,nl;
3169 
3170     M    = *newmat;
3171     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3172     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3173     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3174     /*
3175          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3176        rather than the slower MatSetValues().
3177     */
3178     M->was_assembled = PETSC_TRUE;
3179     M->assembled     = PETSC_FALSE;
3180   }
3181   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3182   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3183   ii   = aij->i;
3184   jj   = aij->j;
3185   aa   = aij->a;
3186   for (i=0; i<m; i++) {
3187     row   = rstart + i;
3188     nz    = ii[i+1] - ii[i];
3189     cwork = jj;     jj += nz;
3190     vwork = aa;     aa += nz;
3191     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3192   }
3193 
3194   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3195   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3196   *newmat = M;
3197 
3198   /* save submatrix used in processor for next request */
3199   if (call ==  MAT_INITIAL_MATRIX) {
3200     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3201     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3202   }
3203   PetscFunctionReturn(0);
3204 }
3205 
3206 #undef __FUNCT__
3207 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR_MPIAIJ"
3208 PetscErrorCode  MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3209 {
3210   PetscInt       m,cstart, cend,j,nnz,i,d;
3211   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3212   const PetscInt *JJ;
3213   PetscScalar    *values;
3214   PetscErrorCode ierr;
3215 
3216   PetscFunctionBegin;
3217   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3218 
3219   ierr   = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3220   ierr   = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3221   m      = B->rmap->n;
3222   cstart = B->cmap->rstart;
3223   cend   = B->cmap->rend;
3224   rstart = B->rmap->rstart;
3225 
3226   ierr = PetscMalloc2(m,&d_nnz,m,&o_nnz);CHKERRQ(ierr);
3227 
3228 #if defined(PETSC_USE_DEBUGGING)
3229   for (i=0; i<m; i++) {
3230     nnz = Ii[i+1]- Ii[i];
3231     JJ  = J + Ii[i];
3232     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3233     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3234     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);
3235   }
3236 #endif
3237 
3238   for (i=0; i<m; i++) {
3239     nnz     = Ii[i+1]- Ii[i];
3240     JJ      = J + Ii[i];
3241     nnz_max = PetscMax(nnz_max,nnz);
3242     d       = 0;
3243     for (j=0; j<nnz; j++) {
3244       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3245     }
3246     d_nnz[i] = d;
3247     o_nnz[i] = nnz - d;
3248   }
3249   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3250   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3251 
3252   if (v) values = (PetscScalar*)v;
3253   else {
3254     ierr = PetscCalloc1(nnz_max+1,&values);CHKERRQ(ierr);
3255   }
3256 
3257   for (i=0; i<m; i++) {
3258     ii   = i + rstart;
3259     nnz  = Ii[i+1]- Ii[i];
3260     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3261   }
3262   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3263   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3264 
3265   if (!v) {
3266     ierr = PetscFree(values);CHKERRQ(ierr);
3267   }
3268   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3269   PetscFunctionReturn(0);
3270 }
3271 
3272 #undef __FUNCT__
3273 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR"
3274 /*@
3275    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3276    (the default parallel PETSc format).
3277 
3278    Collective on MPI_Comm
3279 
3280    Input Parameters:
3281 +  B - the matrix
3282 .  i - the indices into j for the start of each local row (starts with zero)
3283 .  j - the column indices for each local row (starts with zero)
3284 -  v - optional values in the matrix
3285 
3286    Level: developer
3287 
3288    Notes:
3289        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3290      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3291      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3292 
3293        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3294 
3295        The format which is used for the sparse matrix input, is equivalent to a
3296     row-major ordering.. i.e for the following matrix, the input data expected is
3297     as shown
3298 
3299 $        1 0 0
3300 $        2 0 3     P0
3301 $       -------
3302 $        4 5 6     P1
3303 $
3304 $     Process0 [P0]: rows_owned=[0,1]
3305 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3306 $        j =  {0,0,2}  [size = 3]
3307 $        v =  {1,2,3}  [size = 3]
3308 $
3309 $     Process1 [P1]: rows_owned=[2]
3310 $        i =  {0,3}    [size = nrow+1  = 1+1]
3311 $        j =  {0,1,2}  [size = 3]
3312 $        v =  {4,5,6}  [size = 3]
3313 
3314 .keywords: matrix, aij, compressed row, sparse, parallel
3315 
3316 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MPIAIJ,
3317           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3318 @*/
3319 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3320 {
3321   PetscErrorCode ierr;
3322 
3323   PetscFunctionBegin;
3324   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3325   PetscFunctionReturn(0);
3326 }
3327 
3328 #undef __FUNCT__
3329 #define __FUNCT__ "MatMPIAIJSetPreallocation"
3330 /*@C
3331    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3332    (the default parallel PETSc format).  For good matrix assembly performance
3333    the user should preallocate the matrix storage by setting the parameters
3334    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3335    performance can be increased by more than a factor of 50.
3336 
3337    Collective on MPI_Comm
3338 
3339    Input Parameters:
3340 +  B - the matrix
3341 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3342            (same value is used for all local rows)
3343 .  d_nnz - array containing the number of nonzeros in the various rows of the
3344            DIAGONAL portion of the local submatrix (possibly different for each row)
3345            or NULL (PETSC_NULL_INTEGER in Fortran), if d_nz is used to specify the nonzero structure.
3346            The size of this array is equal to the number of local rows, i.e 'm'.
3347            For matrices that will be factored, you must leave room for (and set)
3348            the diagonal entry even if it is zero.
3349 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3350            submatrix (same value is used for all local rows).
3351 -  o_nnz - array containing the number of nonzeros in the various rows of the
3352            OFF-DIAGONAL portion of the local submatrix (possibly different for
3353            each row) or NULL (PETSC_NULL_INTEGER in Fortran), if o_nz is used to specify the nonzero
3354            structure. The size of this array is equal to the number
3355            of local rows, i.e 'm'.
3356 
3357    If the *_nnz parameter is given then the *_nz parameter is ignored
3358 
3359    The AIJ format (also called the Yale sparse matrix format or
3360    compressed row storage (CSR)), is fully compatible with standard Fortran 77
3361    storage.  The stored row and column indices begin with zero.
3362    See Users-Manual: ch_mat for details.
3363 
3364    The parallel matrix is partitioned such that the first m0 rows belong to
3365    process 0, the next m1 rows belong to process 1, the next m2 rows belong
3366    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
3367 
3368    The DIAGONAL portion of the local submatrix of a processor can be defined
3369    as the submatrix which is obtained by extraction the part corresponding to
3370    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
3371    first row that belongs to the processor, r2 is the last row belonging to
3372    the this processor, and c1-c2 is range of indices of the local part of a
3373    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
3374    common case of a square matrix, the row and column ranges are the same and
3375    the DIAGONAL part is also square. The remaining portion of the local
3376    submatrix (mxN) constitute the OFF-DIAGONAL portion.
3377 
3378    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3379 
3380    You can call MatGetInfo() to get information on how effective the preallocation was;
3381    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3382    You can also run with the option -info and look for messages with the string
3383    malloc in them to see if additional memory allocation was needed.
3384 
3385    Example usage:
3386 
3387    Consider the following 8x8 matrix with 34 non-zero values, that is
3388    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3389    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3390    as follows:
3391 
3392 .vb
3393             1  2  0  |  0  3  0  |  0  4
3394     Proc0   0  5  6  |  7  0  0  |  8  0
3395             9  0 10  | 11  0  0  | 12  0
3396     -------------------------------------
3397            13  0 14  | 15 16 17  |  0  0
3398     Proc1   0 18  0  | 19 20 21  |  0  0
3399             0  0  0  | 22 23  0  | 24  0
3400     -------------------------------------
3401     Proc2  25 26 27  |  0  0 28  | 29  0
3402            30  0  0  | 31 32 33  |  0 34
3403 .ve
3404 
3405    This can be represented as a collection of submatrices as:
3406 
3407 .vb
3408       A B C
3409       D E F
3410       G H I
3411 .ve
3412 
3413    Where the submatrices A,B,C are owned by proc0, D,E,F are
3414    owned by proc1, G,H,I are owned by proc2.
3415 
3416    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3417    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3418    The 'M','N' parameters are 8,8, and have the same values on all procs.
3419 
3420    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3421    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3422    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3423    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3424    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3425    matrix, ans [DF] as another SeqAIJ matrix.
3426 
3427    When d_nz, o_nz parameters are specified, d_nz storage elements are
3428    allocated for every row of the local diagonal submatrix, and o_nz
3429    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3430    One way to choose d_nz and o_nz is to use the max nonzerors per local
3431    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3432    In this case, the values of d_nz,o_nz are:
3433 .vb
3434      proc0 : dnz = 2, o_nz = 2
3435      proc1 : dnz = 3, o_nz = 2
3436      proc2 : dnz = 1, o_nz = 4
3437 .ve
3438    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3439    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3440    for proc3. i.e we are using 12+15+10=37 storage locations to store
3441    34 values.
3442 
3443    When d_nnz, o_nnz parameters are specified, the storage is specified
3444    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3445    In the above case the values for d_nnz,o_nnz are:
3446 .vb
3447      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3448      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3449      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3450 .ve
3451    Here the space allocated is sum of all the above values i.e 34, and
3452    hence pre-allocation is perfect.
3453 
3454    Level: intermediate
3455 
3456 .keywords: matrix, aij, compressed row, sparse, parallel
3457 
3458 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
3459           MPIAIJ, MatGetInfo(), PetscSplitOwnership()
3460 @*/
3461 PetscErrorCode  MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3462 {
3463   PetscErrorCode ierr;
3464 
3465   PetscFunctionBegin;
3466   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3467   PetscValidType(B,1);
3468   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
3469   PetscFunctionReturn(0);
3470 }
3471 
3472 #undef __FUNCT__
3473 #define __FUNCT__ "MatCreateMPIAIJWithArrays"
3474 /*@
3475      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
3476          CSR format the local rows.
3477 
3478    Collective on MPI_Comm
3479 
3480    Input Parameters:
3481 +  comm - MPI communicator
3482 .  m - number of local rows (Cannot be PETSC_DECIDE)
3483 .  n - This value should be the same as the local size used in creating the
3484        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3485        calculated if N is given) For square matrices n is almost always m.
3486 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3487 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3488 .   i - row indices
3489 .   j - column indices
3490 -   a - matrix values
3491 
3492    Output Parameter:
3493 .   mat - the matrix
3494 
3495    Level: intermediate
3496 
3497    Notes:
3498        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3499      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3500      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3501 
3502        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3503 
3504        The format which is used for the sparse matrix input, is equivalent to a
3505     row-major ordering.. i.e for the following matrix, the input data expected is
3506     as shown
3507 
3508 $        1 0 0
3509 $        2 0 3     P0
3510 $       -------
3511 $        4 5 6     P1
3512 $
3513 $     Process0 [P0]: rows_owned=[0,1]
3514 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3515 $        j =  {0,0,2}  [size = 3]
3516 $        v =  {1,2,3}  [size = 3]
3517 $
3518 $     Process1 [P1]: rows_owned=[2]
3519 $        i =  {0,3}    [size = nrow+1  = 1+1]
3520 $        j =  {0,1,2}  [size = 3]
3521 $        v =  {4,5,6}  [size = 3]
3522 
3523 .keywords: matrix, aij, compressed row, sparse, parallel
3524 
3525 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3526           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
3527 @*/
3528 PetscErrorCode  MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
3529 {
3530   PetscErrorCode ierr;
3531 
3532   PetscFunctionBegin;
3533   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
3534   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
3535   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
3536   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
3537   /* ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr); */
3538   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
3539   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
3540   PetscFunctionReturn(0);
3541 }
3542 
3543 #undef __FUNCT__
3544 #define __FUNCT__ "MatCreateAIJ"
3545 /*@C
3546    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
3547    (the default parallel PETSc format).  For good matrix assembly performance
3548    the user should preallocate the matrix storage by setting the parameters
3549    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3550    performance can be increased by more than a factor of 50.
3551 
3552    Collective on MPI_Comm
3553 
3554    Input Parameters:
3555 +  comm - MPI communicator
3556 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
3557            This value should be the same as the local size used in creating the
3558            y vector for the matrix-vector product y = Ax.
3559 .  n - This value should be the same as the local size used in creating the
3560        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3561        calculated if N is given) For square matrices n is almost always m.
3562 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3563 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3564 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3565            (same value is used for all local rows)
3566 .  d_nnz - array containing the number of nonzeros in the various rows of the
3567            DIAGONAL portion of the local submatrix (possibly different for each row)
3568            or NULL, if d_nz is used to specify the nonzero structure.
3569            The size of this array is equal to the number of local rows, i.e 'm'.
3570 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3571            submatrix (same value is used for all local rows).
3572 -  o_nnz - array containing the number of nonzeros in the various rows of the
3573            OFF-DIAGONAL portion of the local submatrix (possibly different for
3574            each row) or NULL, if o_nz is used to specify the nonzero
3575            structure. The size of this array is equal to the number
3576            of local rows, i.e 'm'.
3577 
3578    Output Parameter:
3579 .  A - the matrix
3580 
3581    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3582    MatXXXXSetPreallocation() paradgm instead of this routine directly.
3583    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3584 
3585    Notes:
3586    If the *_nnz parameter is given then the *_nz parameter is ignored
3587 
3588    m,n,M,N parameters specify the size of the matrix, and its partitioning across
3589    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
3590    storage requirements for this matrix.
3591 
3592    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
3593    processor than it must be used on all processors that share the object for
3594    that argument.
3595 
3596    The user MUST specify either the local or global matrix dimensions
3597    (possibly both).
3598 
3599    The parallel matrix is partitioned across processors such that the
3600    first m0 rows belong to process 0, the next m1 rows belong to
3601    process 1, the next m2 rows belong to process 2 etc.. where
3602    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
3603    values corresponding to [m x N] submatrix.
3604 
3605    The columns are logically partitioned with the n0 columns belonging
3606    to 0th partition, the next n1 columns belonging to the next
3607    partition etc.. where n0,n1,n2... are the input parameter 'n'.
3608 
3609    The DIAGONAL portion of the local submatrix on any given processor
3610    is the submatrix corresponding to the rows and columns m,n
3611    corresponding to the given processor. i.e diagonal matrix on
3612    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
3613    etc. The remaining portion of the local submatrix [m x (N-n)]
3614    constitute the OFF-DIAGONAL portion. The example below better
3615    illustrates this concept.
3616 
3617    For a square global matrix we define each processor's diagonal portion
3618    to be its local rows and the corresponding columns (a square submatrix);
3619    each processor's off-diagonal portion encompasses the remainder of the
3620    local matrix (a rectangular submatrix).
3621 
3622    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3623 
3624    When calling this routine with a single process communicator, a matrix of
3625    type SEQAIJ is returned.  If a matrix of type MPIAIJ is desired for this
3626    type of communicator, use the construction mechanism:
3627      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
3628 
3629    By default, this format uses inodes (identical nodes) when possible.
3630    We search for consecutive rows with the same nonzero structure, thereby
3631    reusing matrix information to achieve increased efficiency.
3632 
3633    Options Database Keys:
3634 +  -mat_no_inode  - Do not use inodes
3635 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3636 -  -mat_aij_oneindex - Internally use indexing starting at 1
3637         rather than 0.  Note that when calling MatSetValues(),
3638         the user still MUST index entries starting at 0!
3639 
3640 
3641    Example usage:
3642 
3643    Consider the following 8x8 matrix with 34 non-zero values, that is
3644    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3645    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3646    as follows:
3647 
3648 .vb
3649             1  2  0  |  0  3  0  |  0  4
3650     Proc0   0  5  6  |  7  0  0  |  8  0
3651             9  0 10  | 11  0  0  | 12  0
3652     -------------------------------------
3653            13  0 14  | 15 16 17  |  0  0
3654     Proc1   0 18  0  | 19 20 21  |  0  0
3655             0  0  0  | 22 23  0  | 24  0
3656     -------------------------------------
3657     Proc2  25 26 27  |  0  0 28  | 29  0
3658            30  0  0  | 31 32 33  |  0 34
3659 .ve
3660 
3661    This can be represented as a collection of submatrices as:
3662 
3663 .vb
3664       A B C
3665       D E F
3666       G H I
3667 .ve
3668 
3669    Where the submatrices A,B,C are owned by proc0, D,E,F are
3670    owned by proc1, G,H,I are owned by proc2.
3671 
3672    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3673    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3674    The 'M','N' parameters are 8,8, and have the same values on all procs.
3675 
3676    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3677    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3678    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3679    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3680    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3681    matrix, ans [DF] as another SeqAIJ matrix.
3682 
3683    When d_nz, o_nz parameters are specified, d_nz storage elements are
3684    allocated for every row of the local diagonal submatrix, and o_nz
3685    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3686    One way to choose d_nz and o_nz is to use the max nonzerors per local
3687    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3688    In this case, the values of d_nz,o_nz are:
3689 .vb
3690      proc0 : dnz = 2, o_nz = 2
3691      proc1 : dnz = 3, o_nz = 2
3692      proc2 : dnz = 1, o_nz = 4
3693 .ve
3694    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3695    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3696    for proc3. i.e we are using 12+15+10=37 storage locations to store
3697    34 values.
3698 
3699    When d_nnz, o_nnz parameters are specified, the storage is specified
3700    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3701    In the above case the values for d_nnz,o_nnz are:
3702 .vb
3703      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3704      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3705      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3706 .ve
3707    Here the space allocated is sum of all the above values i.e 34, and
3708    hence pre-allocation is perfect.
3709 
3710    Level: intermediate
3711 
3712 .keywords: matrix, aij, compressed row, sparse, parallel
3713 
3714 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3715           MPIAIJ, MatCreateMPIAIJWithArrays()
3716 @*/
3717 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)
3718 {
3719   PetscErrorCode ierr;
3720   PetscMPIInt    size;
3721 
3722   PetscFunctionBegin;
3723   ierr = MatCreate(comm,A);CHKERRQ(ierr);
3724   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
3725   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3726   if (size > 1) {
3727     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
3728     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
3729   } else {
3730     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
3731     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
3732   }
3733   PetscFunctionReturn(0);
3734 }
3735 
3736 #undef __FUNCT__
3737 #define __FUNCT__ "MatMPIAIJGetSeqAIJ"
3738 PetscErrorCode  MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
3739 {
3740   Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
3741 
3742   PetscFunctionBegin;
3743   if (Ad)     *Ad     = a->A;
3744   if (Ao)     *Ao     = a->B;
3745   if (colmap) *colmap = a->garray;
3746   PetscFunctionReturn(0);
3747 }
3748 
3749 #undef __FUNCT__
3750 #define __FUNCT__ "MatSetColoring_MPIAIJ"
3751 PetscErrorCode MatSetColoring_MPIAIJ(Mat A,ISColoring coloring)
3752 {
3753   PetscErrorCode ierr;
3754   PetscInt       i;
3755   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3756 
3757   PetscFunctionBegin;
3758   if (coloring->ctype == IS_COLORING_GLOBAL) {
3759     ISColoringValue *allcolors,*colors;
3760     ISColoring      ocoloring;
3761 
3762     /* set coloring for diagonal portion */
3763     ierr = MatSetColoring_SeqAIJ(a->A,coloring);CHKERRQ(ierr);
3764 
3765     /* set coloring for off-diagonal portion */
3766     ierr = ISAllGatherColors(PetscObjectComm((PetscObject)A),coloring->n,coloring->colors,NULL,&allcolors);CHKERRQ(ierr);
3767     ierr = PetscMalloc1(a->B->cmap->n+1,&colors);CHKERRQ(ierr);
3768     for (i=0; i<a->B->cmap->n; i++) {
3769       colors[i] = allcolors[a->garray[i]];
3770     }
3771     ierr = PetscFree(allcolors);CHKERRQ(ierr);
3772     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3773     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
3774     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3775   } else if (coloring->ctype == IS_COLORING_GHOSTED) {
3776     ISColoringValue *colors;
3777     PetscInt        *larray;
3778     ISColoring      ocoloring;
3779 
3780     /* set coloring for diagonal portion */
3781     ierr = PetscMalloc1(a->A->cmap->n+1,&larray);CHKERRQ(ierr);
3782     for (i=0; i<a->A->cmap->n; i++) {
3783       larray[i] = i + A->cmap->rstart;
3784     }
3785     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->A->cmap->n,larray,NULL,larray);CHKERRQ(ierr);
3786     ierr = PetscMalloc1(a->A->cmap->n+1,&colors);CHKERRQ(ierr);
3787     for (i=0; i<a->A->cmap->n; i++) {
3788       colors[i] = coloring->colors[larray[i]];
3789     }
3790     ierr = PetscFree(larray);CHKERRQ(ierr);
3791     ierr = ISColoringCreate(PETSC_COMM_SELF,coloring->n,a->A->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3792     ierr = MatSetColoring_SeqAIJ(a->A,ocoloring);CHKERRQ(ierr);
3793     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3794 
3795     /* set coloring for off-diagonal portion */
3796     ierr = PetscMalloc1(a->B->cmap->n+1,&larray);CHKERRQ(ierr);
3797     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->B->cmap->n,a->garray,NULL,larray);CHKERRQ(ierr);
3798     ierr = PetscMalloc1(a->B->cmap->n+1,&colors);CHKERRQ(ierr);
3799     for (i=0; i<a->B->cmap->n; i++) {
3800       colors[i] = coloring->colors[larray[i]];
3801     }
3802     ierr = PetscFree(larray);CHKERRQ(ierr);
3803     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3804     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
3805     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3806   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support ISColoringType %d",(int)coloring->ctype);
3807   PetscFunctionReturn(0);
3808 }
3809 
3810 #undef __FUNCT__
3811 #define __FUNCT__ "MatSetValuesAdifor_MPIAIJ"
3812 PetscErrorCode MatSetValuesAdifor_MPIAIJ(Mat A,PetscInt nl,void *advalues)
3813 {
3814   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3815   PetscErrorCode ierr;
3816 
3817   PetscFunctionBegin;
3818   ierr = MatSetValuesAdifor_SeqAIJ(a->A,nl,advalues);CHKERRQ(ierr);
3819   ierr = MatSetValuesAdifor_SeqAIJ(a->B,nl,advalues);CHKERRQ(ierr);
3820   PetscFunctionReturn(0);
3821 }
3822 
3823 #undef __FUNCT__
3824 #define __FUNCT__ "MatCreateMPIMatConcatenateSeqMat_MPIAIJ"
3825 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
3826 {
3827   PetscErrorCode ierr;
3828   PetscInt       m,N,i,rstart,nnz,Ii;
3829   PetscInt       *indx;
3830   PetscScalar    *values;
3831 
3832   PetscFunctionBegin;
3833   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
3834   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
3835     PetscInt       *dnz,*onz,sum,bs,cbs;
3836 
3837     if (n == PETSC_DECIDE) {
3838       ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
3839     }
3840     /* Check sum(n) = N */
3841     ierr = MPI_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3842     if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
3843 
3844     ierr    = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3845     rstart -= m;
3846 
3847     ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
3848     for (i=0; i<m; i++) {
3849       ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3850       ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
3851       ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3852     }
3853 
3854     ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
3855     ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
3856     ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
3857     ierr = MatSetBlockSizes(*outmat,bs,cbs);CHKERRQ(ierr);
3858     ierr = MatSetType(*outmat,MATMPIAIJ);CHKERRQ(ierr);
3859     ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
3860     ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
3861   }
3862 
3863   /* numeric phase */
3864   ierr = MatGetOwnershipRange(*outmat,&rstart,NULL);CHKERRQ(ierr);
3865   for (i=0; i<m; i++) {
3866     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3867     Ii   = i + rstart;
3868     ierr = MatSetValues(*outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3869     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3870   }
3871   ierr = MatAssemblyBegin(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3872   ierr = MatAssemblyEnd(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3873   PetscFunctionReturn(0);
3874 }
3875 
3876 #undef __FUNCT__
3877 #define __FUNCT__ "MatFileSplit"
3878 PetscErrorCode MatFileSplit(Mat A,char *outfile)
3879 {
3880   PetscErrorCode    ierr;
3881   PetscMPIInt       rank;
3882   PetscInt          m,N,i,rstart,nnz;
3883   size_t            len;
3884   const PetscInt    *indx;
3885   PetscViewer       out;
3886   char              *name;
3887   Mat               B;
3888   const PetscScalar *values;
3889 
3890   PetscFunctionBegin;
3891   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
3892   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
3893   /* Should this be the type of the diagonal block of A? */
3894   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
3895   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
3896   ierr = MatSetBlockSizesFromMats(B,A,A);CHKERRQ(ierr);
3897   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
3898   ierr = MatSeqAIJSetPreallocation(B,0,NULL);CHKERRQ(ierr);
3899   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
3900   for (i=0; i<m; i++) {
3901     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3902     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3903     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3904   }
3905   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3906   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3907 
3908   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
3909   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
3910   ierr = PetscMalloc1(len+5,&name);CHKERRQ(ierr);
3911   sprintf(name,"%s.%d",outfile,rank);
3912   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
3913   ierr = PetscFree(name);CHKERRQ(ierr);
3914   ierr = MatView(B,out);CHKERRQ(ierr);
3915   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
3916   ierr = MatDestroy(&B);CHKERRQ(ierr);
3917   PetscFunctionReturn(0);
3918 }
3919 
3920 extern PetscErrorCode MatDestroy_MPIAIJ(Mat);
3921 #undef __FUNCT__
3922 #define __FUNCT__ "MatDestroy_MPIAIJ_SeqsToMPI"
3923 PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
3924 {
3925   PetscErrorCode      ierr;
3926   Mat_Merge_SeqsToMPI *merge;
3927   PetscContainer      container;
3928 
3929   PetscFunctionBegin;
3930   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
3931   if (container) {
3932     ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
3933     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
3934     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
3935     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
3936     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
3937     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
3938     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
3939     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
3940     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
3941     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
3942     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
3943     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
3944     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
3945     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
3946     ierr = PetscFree(merge);CHKERRQ(ierr);
3947     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
3948   }
3949   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
3950   PetscFunctionReturn(0);
3951 }
3952 
3953 #include <../src/mat/utils/freespace.h>
3954 #include <petscbt.h>
3955 
3956 #undef __FUNCT__
3957 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJNumeric"
3958 PetscErrorCode  MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
3959 {
3960   PetscErrorCode      ierr;
3961   MPI_Comm            comm;
3962   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
3963   PetscMPIInt         size,rank,taga,*len_s;
3964   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
3965   PetscInt            proc,m;
3966   PetscInt            **buf_ri,**buf_rj;
3967   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
3968   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
3969   MPI_Request         *s_waits,*r_waits;
3970   MPI_Status          *status;
3971   MatScalar           *aa=a->a;
3972   MatScalar           **abuf_r,*ba_i;
3973   Mat_Merge_SeqsToMPI *merge;
3974   PetscContainer      container;
3975 
3976   PetscFunctionBegin;
3977   ierr = PetscObjectGetComm((PetscObject)mpimat,&comm);CHKERRQ(ierr);
3978   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
3979 
3980   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3981   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3982 
3983   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
3984   ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
3985 
3986   bi     = merge->bi;
3987   bj     = merge->bj;
3988   buf_ri = merge->buf_ri;
3989   buf_rj = merge->buf_rj;
3990 
3991   ierr   = PetscMalloc1(size,&status);CHKERRQ(ierr);
3992   owners = merge->rowmap->range;
3993   len_s  = merge->len_s;
3994 
3995   /* send and recv matrix values */
3996   /*-----------------------------*/
3997   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
3998   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
3999 
4000   ierr = PetscMalloc1(merge->nsend+1,&s_waits);CHKERRQ(ierr);
4001   for (proc=0,k=0; proc<size; proc++) {
4002     if (!len_s[proc]) continue;
4003     i    = owners[proc];
4004     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
4005     k++;
4006   }
4007 
4008   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
4009   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
4010   ierr = PetscFree(status);CHKERRQ(ierr);
4011 
4012   ierr = PetscFree(s_waits);CHKERRQ(ierr);
4013   ierr = PetscFree(r_waits);CHKERRQ(ierr);
4014 
4015   /* insert mat values of mpimat */
4016   /*----------------------------*/
4017   ierr = PetscMalloc1(N,&ba_i);CHKERRQ(ierr);
4018   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4019 
4020   for (k=0; k<merge->nrecv; k++) {
4021     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4022     nrows       = *(buf_ri_k[k]);
4023     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
4024     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4025   }
4026 
4027   /* set values of ba */
4028   m = merge->rowmap->n;
4029   for (i=0; i<m; i++) {
4030     arow = owners[rank] + i;
4031     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
4032     bnzi = bi[i+1] - bi[i];
4033     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
4034 
4035     /* add local non-zero vals of this proc's seqmat into ba */
4036     anzi   = ai[arow+1] - ai[arow];
4037     aj     = a->j + ai[arow];
4038     aa     = a->a + ai[arow];
4039     nextaj = 0;
4040     for (j=0; nextaj<anzi; j++) {
4041       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4042         ba_i[j] += aa[nextaj++];
4043       }
4044     }
4045 
4046     /* add received vals into ba */
4047     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4048       /* i-th row */
4049       if (i == *nextrow[k]) {
4050         anzi   = *(nextai[k]+1) - *nextai[k];
4051         aj     = buf_rj[k] + *(nextai[k]);
4052         aa     = abuf_r[k] + *(nextai[k]);
4053         nextaj = 0;
4054         for (j=0; nextaj<anzi; j++) {
4055           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4056             ba_i[j] += aa[nextaj++];
4057           }
4058         }
4059         nextrow[k]++; nextai[k]++;
4060       }
4061     }
4062     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
4063   }
4064   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4065   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4066 
4067   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
4068   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
4069   ierr = PetscFree(ba_i);CHKERRQ(ierr);
4070   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4071   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4072   PetscFunctionReturn(0);
4073 }
4074 
4075 extern PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat);
4076 
4077 #undef __FUNCT__
4078 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJSymbolic"
4079 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4080 {
4081   PetscErrorCode      ierr;
4082   Mat                 B_mpi;
4083   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
4084   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4085   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
4086   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4087   PetscInt            len,proc,*dnz,*onz,bs,cbs;
4088   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4089   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4090   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
4091   MPI_Status          *status;
4092   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
4093   PetscBT             lnkbt;
4094   Mat_Merge_SeqsToMPI *merge;
4095   PetscContainer      container;
4096 
4097   PetscFunctionBegin;
4098   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4099 
4100   /* make sure it is a PETSc comm */
4101   ierr = PetscCommDuplicate(comm,&comm,NULL);CHKERRQ(ierr);
4102   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4103   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4104 
4105   ierr = PetscNew(&merge);CHKERRQ(ierr);
4106   ierr = PetscMalloc1(size,&status);CHKERRQ(ierr);
4107 
4108   /* determine row ownership */
4109   /*---------------------------------------------------------*/
4110   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
4111   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
4112   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
4113   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
4114   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
4115   ierr = PetscMalloc1(size,&len_si);CHKERRQ(ierr);
4116   ierr = PetscMalloc1(size,&merge->len_s);CHKERRQ(ierr);
4117 
4118   m      = merge->rowmap->n;
4119   owners = merge->rowmap->range;
4120 
4121   /* determine the number of messages to send, their lengths */
4122   /*---------------------------------------------------------*/
4123   len_s = merge->len_s;
4124 
4125   len          = 0; /* length of buf_si[] */
4126   merge->nsend = 0;
4127   for (proc=0; proc<size; proc++) {
4128     len_si[proc] = 0;
4129     if (proc == rank) {
4130       len_s[proc] = 0;
4131     } else {
4132       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4133       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4134     }
4135     if (len_s[proc]) {
4136       merge->nsend++;
4137       nrows = 0;
4138       for (i=owners[proc]; i<owners[proc+1]; i++) {
4139         if (ai[i+1] > ai[i]) nrows++;
4140       }
4141       len_si[proc] = 2*(nrows+1);
4142       len         += len_si[proc];
4143     }
4144   }
4145 
4146   /* determine the number and length of messages to receive for ij-structure */
4147   /*-------------------------------------------------------------------------*/
4148   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
4149   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
4150 
4151   /* post the Irecv of j-structure */
4152   /*-------------------------------*/
4153   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
4154   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
4155 
4156   /* post the Isend of j-structure */
4157   /*--------------------------------*/
4158   ierr = PetscMalloc2(merge->nsend,&si_waits,merge->nsend,&sj_waits);CHKERRQ(ierr);
4159 
4160   for (proc=0, k=0; proc<size; proc++) {
4161     if (!len_s[proc]) continue;
4162     i    = owners[proc];
4163     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
4164     k++;
4165   }
4166 
4167   /* receives and sends of j-structure are complete */
4168   /*------------------------------------------------*/
4169   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
4170   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
4171 
4172   /* send and recv i-structure */
4173   /*---------------------------*/
4174   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
4175   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
4176 
4177   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
4178   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4179   for (proc=0,k=0; proc<size; proc++) {
4180     if (!len_s[proc]) continue;
4181     /* form outgoing message for i-structure:
4182          buf_si[0]:                 nrows to be sent
4183                [1:nrows]:           row index (global)
4184                [nrows+1:2*nrows+1]: i-structure index
4185     */
4186     /*-------------------------------------------*/
4187     nrows       = len_si[proc]/2 - 1;
4188     buf_si_i    = buf_si + nrows+1;
4189     buf_si[0]   = nrows;
4190     buf_si_i[0] = 0;
4191     nrows       = 0;
4192     for (i=owners[proc]; i<owners[proc+1]; i++) {
4193       anzi = ai[i+1] - ai[i];
4194       if (anzi) {
4195         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4196         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4197         nrows++;
4198       }
4199     }
4200     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4201     k++;
4202     buf_si += len_si[proc];
4203   }
4204 
4205   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4206   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4207 
4208   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4209   for (i=0; i<merge->nrecv; i++) {
4210     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);
4211   }
4212 
4213   ierr = PetscFree(len_si);CHKERRQ(ierr);
4214   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4215   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4216   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4217   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4218   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4219   ierr = PetscFree(status);CHKERRQ(ierr);
4220 
4221   /* compute a local seq matrix in each processor */
4222   /*----------------------------------------------*/
4223   /* allocate bi array and free space for accumulating nonzero column info */
4224   ierr  = PetscMalloc1(m+1,&bi);CHKERRQ(ierr);
4225   bi[0] = 0;
4226 
4227   /* create and initialize a linked list */
4228   nlnk = N+1;
4229   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4230 
4231   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4232   len  = ai[owners[rank+1]] - ai[owners[rank]];
4233   ierr = PetscFreeSpaceGet((PetscInt)(2*len+1),&free_space);CHKERRQ(ierr);
4234 
4235   current_space = free_space;
4236 
4237   /* determine symbolic info for each local row */
4238   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4239 
4240   for (k=0; k<merge->nrecv; k++) {
4241     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4242     nrows       = *buf_ri_k[k];
4243     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4244     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4245   }
4246 
4247   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4248   len  = 0;
4249   for (i=0; i<m; i++) {
4250     bnzi = 0;
4251     /* add local non-zero cols of this proc's seqmat into lnk */
4252     arow  = owners[rank] + i;
4253     anzi  = ai[arow+1] - ai[arow];
4254     aj    = a->j + ai[arow];
4255     ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4256     bnzi += nlnk;
4257     /* add received col data into lnk */
4258     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4259       if (i == *nextrow[k]) { /* i-th row */
4260         anzi  = *(nextai[k]+1) - *nextai[k];
4261         aj    = buf_rj[k] + *nextai[k];
4262         ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4263         bnzi += nlnk;
4264         nextrow[k]++; nextai[k]++;
4265       }
4266     }
4267     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4268 
4269     /* if free space is not available, make more free space */
4270     if (current_space->local_remaining<bnzi) {
4271       ierr = PetscFreeSpaceGet(bnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
4272       nspacedouble++;
4273     }
4274     /* copy data into free space, then initialize lnk */
4275     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4276     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
4277 
4278     current_space->array           += bnzi;
4279     current_space->local_used      += bnzi;
4280     current_space->local_remaining -= bnzi;
4281 
4282     bi[i+1] = bi[i] + bnzi;
4283   }
4284 
4285   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4286 
4287   ierr = PetscMalloc1(bi[m]+1,&bj);CHKERRQ(ierr);
4288   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
4289   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4290 
4291   /* create symbolic parallel matrix B_mpi */
4292   /*---------------------------------------*/
4293   ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
4294   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
4295   if (n==PETSC_DECIDE) {
4296     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
4297   } else {
4298     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4299   }
4300   ierr = MatSetBlockSizes(B_mpi,bs,cbs);CHKERRQ(ierr);
4301   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
4302   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
4303   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4304   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
4305 
4306   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4307   B_mpi->assembled    = PETSC_FALSE;
4308   B_mpi->ops->destroy = MatDestroy_MPIAIJ_SeqsToMPI;
4309   merge->bi           = bi;
4310   merge->bj           = bj;
4311   merge->buf_ri       = buf_ri;
4312   merge->buf_rj       = buf_rj;
4313   merge->coi          = NULL;
4314   merge->coj          = NULL;
4315   merge->owners_co    = NULL;
4316 
4317   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
4318 
4319   /* attach the supporting struct to B_mpi for reuse */
4320   ierr    = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
4321   ierr    = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
4322   ierr    = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
4323   ierr    = PetscContainerDestroy(&container);CHKERRQ(ierr);
4324   *mpimat = B_mpi;
4325 
4326   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4327   PetscFunctionReturn(0);
4328 }
4329 
4330 #undef __FUNCT__
4331 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJ"
4332 /*@C
4333       MatCreateMPIAIJSumSeqAIJ - Creates a MPIAIJ matrix by adding sequential
4334                  matrices from each processor
4335 
4336     Collective on MPI_Comm
4337 
4338    Input Parameters:
4339 +    comm - the communicators the parallel matrix will live on
4340 .    seqmat - the input sequential matrices
4341 .    m - number of local rows (or PETSC_DECIDE)
4342 .    n - number of local columns (or PETSC_DECIDE)
4343 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4344 
4345    Output Parameter:
4346 .    mpimat - the parallel matrix generated
4347 
4348     Level: advanced
4349 
4350    Notes:
4351      The dimensions of the sequential matrix in each processor MUST be the same.
4352      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
4353      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
4354 @*/
4355 PetscErrorCode  MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
4356 {
4357   PetscErrorCode ierr;
4358   PetscMPIInt    size;
4359 
4360   PetscFunctionBegin;
4361   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4362   if (size == 1) {
4363     ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4364     if (scall == MAT_INITIAL_MATRIX) {
4365       ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
4366     } else {
4367       ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4368     }
4369     ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4370     PetscFunctionReturn(0);
4371   }
4372   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4373   if (scall == MAT_INITIAL_MATRIX) {
4374     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
4375   }
4376   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
4377   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4378   PetscFunctionReturn(0);
4379 }
4380 
4381 #undef __FUNCT__
4382 #define __FUNCT__ "MatMPIAIJGetLocalMat"
4383 /*@
4384      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
4385           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
4386           with MatGetSize()
4387 
4388     Not Collective
4389 
4390    Input Parameters:
4391 +    A - the matrix
4392 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4393 
4394    Output Parameter:
4395 .    A_loc - the local sequential matrix generated
4396 
4397     Level: developer
4398 
4399 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
4400 
4401 @*/
4402 PetscErrorCode  MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
4403 {
4404   PetscErrorCode ierr;
4405   Mat_MPIAIJ     *mpimat=(Mat_MPIAIJ*)A->data;
4406   Mat_SeqAIJ     *mat,*a,*b;
4407   PetscInt       *ai,*aj,*bi,*bj,*cmap=mpimat->garray;
4408   MatScalar      *aa,*ba,*cam;
4409   PetscScalar    *ca;
4410   PetscInt       am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
4411   PetscInt       *ci,*cj,col,ncols_d,ncols_o,jo;
4412   PetscBool      match;
4413   MPI_Comm       comm;
4414   PetscMPIInt    size;
4415 
4416   PetscFunctionBegin;
4417   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4418   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
4419   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4420   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4421   if (size == 1 && scall == MAT_REUSE_MATRIX) PetscFunctionReturn(0);
4422 
4423   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4424   a = (Mat_SeqAIJ*)(mpimat->A)->data;
4425   b = (Mat_SeqAIJ*)(mpimat->B)->data;
4426   ai = a->i; aj = a->j; bi = b->i; bj = b->j;
4427   aa = a->a; ba = b->a;
4428   if (scall == MAT_INITIAL_MATRIX) {
4429     if (size == 1) {
4430       ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ai,aj,aa,A_loc);CHKERRQ(ierr);
4431       PetscFunctionReturn(0);
4432     }
4433 
4434     ierr  = PetscMalloc1(1+am,&ci);CHKERRQ(ierr);
4435     ci[0] = 0;
4436     for (i=0; i<am; i++) {
4437       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
4438     }
4439     ierr = PetscMalloc1(1+ci[am],&cj);CHKERRQ(ierr);
4440     ierr = PetscMalloc1(1+ci[am],&ca);CHKERRQ(ierr);
4441     k    = 0;
4442     for (i=0; i<am; i++) {
4443       ncols_o = bi[i+1] - bi[i];
4444       ncols_d = ai[i+1] - ai[i];
4445       /* off-diagonal portion of A */
4446       for (jo=0; jo<ncols_o; jo++) {
4447         col = cmap[*bj];
4448         if (col >= cstart) break;
4449         cj[k]   = col; bj++;
4450         ca[k++] = *ba++;
4451       }
4452       /* diagonal portion of A */
4453       for (j=0; j<ncols_d; j++) {
4454         cj[k]   = cstart + *aj++;
4455         ca[k++] = *aa++;
4456       }
4457       /* off-diagonal portion of A */
4458       for (j=jo; j<ncols_o; j++) {
4459         cj[k]   = cmap[*bj++];
4460         ca[k++] = *ba++;
4461       }
4462     }
4463     /* put together the new matrix */
4464     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
4465     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4466     /* Since these are PETSc arrays, change flags to free them as necessary. */
4467     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
4468     mat->free_a  = PETSC_TRUE;
4469     mat->free_ij = PETSC_TRUE;
4470     mat->nonew   = 0;
4471   } else if (scall == MAT_REUSE_MATRIX) {
4472     mat=(Mat_SeqAIJ*)(*A_loc)->data;
4473     ci = mat->i; cj = mat->j; cam = mat->a;
4474     for (i=0; i<am; i++) {
4475       /* off-diagonal portion of A */
4476       ncols_o = bi[i+1] - bi[i];
4477       for (jo=0; jo<ncols_o; jo++) {
4478         col = cmap[*bj];
4479         if (col >= cstart) break;
4480         *cam++ = *ba++; bj++;
4481       }
4482       /* diagonal portion of A */
4483       ncols_d = ai[i+1] - ai[i];
4484       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
4485       /* off-diagonal portion of A */
4486       for (j=jo; j<ncols_o; j++) {
4487         *cam++ = *ba++; bj++;
4488       }
4489     }
4490   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
4491   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4492   PetscFunctionReturn(0);
4493 }
4494 
4495 #undef __FUNCT__
4496 #define __FUNCT__ "MatMPIAIJGetLocalMatCondensed"
4497 /*@C
4498      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MPIAIJ matrix by taking all its local rows and NON-ZERO columns
4499 
4500     Not Collective
4501 
4502    Input Parameters:
4503 +    A - the matrix
4504 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4505 -    row, col - index sets of rows and columns to extract (or NULL)
4506 
4507    Output Parameter:
4508 .    A_loc - the local sequential matrix generated
4509 
4510     Level: developer
4511 
4512 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
4513 
4514 @*/
4515 PetscErrorCode  MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
4516 {
4517   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4518   PetscErrorCode ierr;
4519   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
4520   IS             isrowa,iscola;
4521   Mat            *aloc;
4522   PetscBool      match;
4523 
4524   PetscFunctionBegin;
4525   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4526   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
4527   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4528   if (!row) {
4529     start = A->rmap->rstart; end = A->rmap->rend;
4530     ierr  = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
4531   } else {
4532     isrowa = *row;
4533   }
4534   if (!col) {
4535     start = A->cmap->rstart;
4536     cmap  = a->garray;
4537     nzA   = a->A->cmap->n;
4538     nzB   = a->B->cmap->n;
4539     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4540     ncols = 0;
4541     for (i=0; i<nzB; i++) {
4542       if (cmap[i] < start) idx[ncols++] = cmap[i];
4543       else break;
4544     }
4545     imark = i;
4546     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
4547     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
4548     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
4549   } else {
4550     iscola = *col;
4551   }
4552   if (scall != MAT_INITIAL_MATRIX) {
4553     ierr    = PetscMalloc1(1,&aloc);CHKERRQ(ierr);
4554     aloc[0] = *A_loc;
4555   }
4556   ierr   = MatGetSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
4557   *A_loc = aloc[0];
4558   ierr   = PetscFree(aloc);CHKERRQ(ierr);
4559   if (!row) {
4560     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
4561   }
4562   if (!col) {
4563     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
4564   }
4565   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4566   PetscFunctionReturn(0);
4567 }
4568 
4569 #undef __FUNCT__
4570 #define __FUNCT__ "MatGetBrowsOfAcols"
4571 /*@C
4572     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
4573 
4574     Collective on Mat
4575 
4576    Input Parameters:
4577 +    A,B - the matrices in mpiaij format
4578 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4579 -    rowb, colb - index sets of rows and columns of B to extract (or NULL)
4580 
4581    Output Parameter:
4582 +    rowb, colb - index sets of rows and columns of B to extract
4583 -    B_seq - the sequential matrix generated
4584 
4585     Level: developer
4586 
4587 @*/
4588 PetscErrorCode  MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
4589 {
4590   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4591   PetscErrorCode ierr;
4592   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
4593   IS             isrowb,iscolb;
4594   Mat            *bseq=NULL;
4595 
4596   PetscFunctionBegin;
4597   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4598     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);
4599   }
4600   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4601 
4602   if (scall == MAT_INITIAL_MATRIX) {
4603     start = A->cmap->rstart;
4604     cmap  = a->garray;
4605     nzA   = a->A->cmap->n;
4606     nzB   = a->B->cmap->n;
4607     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4608     ncols = 0;
4609     for (i=0; i<nzB; i++) {  /* row < local row index */
4610       if (cmap[i] < start) idx[ncols++] = cmap[i];
4611       else break;
4612     }
4613     imark = i;
4614     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
4615     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
4616     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
4617     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
4618   } else {
4619     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
4620     isrowb  = *rowb; iscolb = *colb;
4621     ierr    = PetscMalloc1(1,&bseq);CHKERRQ(ierr);
4622     bseq[0] = *B_seq;
4623   }
4624   ierr   = MatGetSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
4625   *B_seq = bseq[0];
4626   ierr   = PetscFree(bseq);CHKERRQ(ierr);
4627   if (!rowb) {
4628     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
4629   } else {
4630     *rowb = isrowb;
4631   }
4632   if (!colb) {
4633     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
4634   } else {
4635     *colb = iscolb;
4636   }
4637   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4638   PetscFunctionReturn(0);
4639 }
4640 
4641 #undef __FUNCT__
4642 #define __FUNCT__ "MatGetBrowsOfAoCols_MPIAIJ"
4643 /*
4644     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
4645     of the OFF-DIAGONAL portion of local A
4646 
4647     Collective on Mat
4648 
4649    Input Parameters:
4650 +    A,B - the matrices in mpiaij format
4651 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4652 
4653    Output Parameter:
4654 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
4655 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
4656 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
4657 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
4658 
4659     Level: developer
4660 
4661 */
4662 PetscErrorCode  MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
4663 {
4664   VecScatter_MPI_General *gen_to,*gen_from;
4665   PetscErrorCode         ierr;
4666   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
4667   Mat_SeqAIJ             *b_oth;
4668   VecScatter             ctx =a->Mvctx;
4669   MPI_Comm               comm;
4670   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
4671   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
4672   PetscScalar            *rvalues,*svalues;
4673   MatScalar              *b_otha,*bufa,*bufA;
4674   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
4675   MPI_Request            *rwaits = NULL,*swaits = NULL;
4676   MPI_Status             *sstatus,rstatus;
4677   PetscMPIInt            jj,size;
4678   PetscInt               *cols,sbs,rbs;
4679   PetscScalar            *vals;
4680 
4681   PetscFunctionBegin;
4682   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4683   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4684 
4685   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4686     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);
4687   }
4688   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4689   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4690 
4691   gen_to   = (VecScatter_MPI_General*)ctx->todata;
4692   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
4693   rvalues  = gen_from->values; /* holds the length of receiving row */
4694   svalues  = gen_to->values;   /* holds the length of sending row */
4695   nrecvs   = gen_from->n;
4696   nsends   = gen_to->n;
4697 
4698   ierr    = PetscMalloc2(nrecvs,&rwaits,nsends,&swaits);CHKERRQ(ierr);
4699   srow    = gen_to->indices;    /* local row index to be sent */
4700   sstarts = gen_to->starts;
4701   sprocs  = gen_to->procs;
4702   sstatus = gen_to->sstatus;
4703   sbs     = gen_to->bs;
4704   rstarts = gen_from->starts;
4705   rprocs  = gen_from->procs;
4706   rbs     = gen_from->bs;
4707 
4708   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
4709   if (scall == MAT_INITIAL_MATRIX) {
4710     /* i-array */
4711     /*---------*/
4712     /*  post receives */
4713     for (i=0; i<nrecvs; i++) {
4714       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
4715       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
4716       ierr   = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4717     }
4718 
4719     /* pack the outgoing message */
4720     ierr = PetscMalloc2(nsends+1,&sstartsj,nrecvs+1,&rstartsj);CHKERRQ(ierr);
4721 
4722     sstartsj[0] = 0;
4723     rstartsj[0] = 0;
4724     len         = 0; /* total length of j or a array to be sent */
4725     k           = 0;
4726     for (i=0; i<nsends; i++) {
4727       rowlen = (PetscInt*)svalues + sstarts[i]*sbs;
4728       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
4729       for (j=0; j<nrows; j++) {
4730         row = srow[k] + B->rmap->range[rank]; /* global row idx */
4731         for (l=0; l<sbs; l++) {
4732           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr); /* rowlength */
4733 
4734           rowlen[j*sbs+l] = ncols;
4735 
4736           len += ncols;
4737           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr);
4738         }
4739         k++;
4740       }
4741       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4742 
4743       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
4744     }
4745     /* recvs and sends of i-array are completed */
4746     i = nrecvs;
4747     while (i--) {
4748       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4749     }
4750     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4751 
4752     /* allocate buffers for sending j and a arrays */
4753     ierr = PetscMalloc1(len+1,&bufj);CHKERRQ(ierr);
4754     ierr = PetscMalloc1(len+1,&bufa);CHKERRQ(ierr);
4755 
4756     /* create i-array of B_oth */
4757     ierr = PetscMalloc1(aBn+2,&b_othi);CHKERRQ(ierr);
4758 
4759     b_othi[0] = 0;
4760     len       = 0; /* total length of j or a array to be received */
4761     k         = 0;
4762     for (i=0; i<nrecvs; i++) {
4763       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
4764       nrows  = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be recieved */
4765       for (j=0; j<nrows; j++) {
4766         b_othi[k+1] = b_othi[k] + rowlen[j];
4767         len        += rowlen[j]; k++;
4768       }
4769       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
4770     }
4771 
4772     /* allocate space for j and a arrrays of B_oth */
4773     ierr = PetscMalloc1(b_othi[aBn]+1,&b_othj);CHKERRQ(ierr);
4774     ierr = PetscMalloc1(b_othi[aBn]+1,&b_otha);CHKERRQ(ierr);
4775 
4776     /* j-array */
4777     /*---------*/
4778     /*  post receives of j-array */
4779     for (i=0; i<nrecvs; i++) {
4780       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4781       ierr  = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4782     }
4783 
4784     /* pack the outgoing message j-array */
4785     k = 0;
4786     for (i=0; i<nsends; i++) {
4787       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4788       bufJ  = bufj+sstartsj[i];
4789       for (j=0; j<nrows; j++) {
4790         row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4791         for (ll=0; ll<sbs; ll++) {
4792           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4793           for (l=0; l<ncols; l++) {
4794             *bufJ++ = cols[l];
4795           }
4796           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4797         }
4798       }
4799       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4800     }
4801 
4802     /* recvs and sends of j-array are completed */
4803     i = nrecvs;
4804     while (i--) {
4805       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4806     }
4807     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4808   } else if (scall == MAT_REUSE_MATRIX) {
4809     sstartsj = *startsj_s;
4810     rstartsj = *startsj_r;
4811     bufa     = *bufa_ptr;
4812     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
4813     b_otha   = b_oth->a;
4814   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
4815 
4816   /* a-array */
4817   /*---------*/
4818   /*  post receives of a-array */
4819   for (i=0; i<nrecvs; i++) {
4820     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4821     ierr  = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4822   }
4823 
4824   /* pack the outgoing message a-array */
4825   k = 0;
4826   for (i=0; i<nsends; i++) {
4827     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4828     bufA  = bufa+sstartsj[i];
4829     for (j=0; j<nrows; j++) {
4830       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4831       for (ll=0; ll<sbs; ll++) {
4832         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4833         for (l=0; l<ncols; l++) {
4834           *bufA++ = vals[l];
4835         }
4836         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4837       }
4838     }
4839     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4840   }
4841   /* recvs and sends of a-array are completed */
4842   i = nrecvs;
4843   while (i--) {
4844     ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4845   }
4846   if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4847   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
4848 
4849   if (scall == MAT_INITIAL_MATRIX) {
4850     /* put together the new matrix */
4851     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
4852 
4853     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4854     /* Since these are PETSc arrays, change flags to free them as necessary. */
4855     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
4856     b_oth->free_a  = PETSC_TRUE;
4857     b_oth->free_ij = PETSC_TRUE;
4858     b_oth->nonew   = 0;
4859 
4860     ierr = PetscFree(bufj);CHKERRQ(ierr);
4861     if (!startsj_s || !bufa_ptr) {
4862       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
4863       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
4864     } else {
4865       *startsj_s = sstartsj;
4866       *startsj_r = rstartsj;
4867       *bufa_ptr  = bufa;
4868     }
4869   }
4870   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4871   PetscFunctionReturn(0);
4872 }
4873 
4874 #undef __FUNCT__
4875 #define __FUNCT__ "MatGetCommunicationStructs"
4876 /*@C
4877   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
4878 
4879   Not Collective
4880 
4881   Input Parameters:
4882 . A - The matrix in mpiaij format
4883 
4884   Output Parameter:
4885 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
4886 . colmap - A map from global column index to local index into lvec
4887 - multScatter - A scatter from the argument of a matrix-vector product to lvec
4888 
4889   Level: developer
4890 
4891 @*/
4892 #if defined(PETSC_USE_CTABLE)
4893 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
4894 #else
4895 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
4896 #endif
4897 {
4898   Mat_MPIAIJ *a;
4899 
4900   PetscFunctionBegin;
4901   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4902   PetscValidPointer(lvec, 2);
4903   PetscValidPointer(colmap, 3);
4904   PetscValidPointer(multScatter, 4);
4905   a = (Mat_MPIAIJ*) A->data;
4906   if (lvec) *lvec = a->lvec;
4907   if (colmap) *colmap = a->colmap;
4908   if (multScatter) *multScatter = a->Mvctx;
4909   PetscFunctionReturn(0);
4910 }
4911 
4912 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
4913 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
4914 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
4915 #if defined(PETSC_HAVE_ELEMENTAL)
4916 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
4917 #endif
4918 
4919 #undef __FUNCT__
4920 #define __FUNCT__ "MatMatMultNumeric_MPIDense_MPIAIJ"
4921 /*
4922     Computes (B'*A')' since computing B*A directly is untenable
4923 
4924                n                       p                          p
4925         (              )       (              )         (                  )
4926       m (      A       )  *  n (       B      )   =   m (         C        )
4927         (              )       (              )         (                  )
4928 
4929 */
4930 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
4931 {
4932   PetscErrorCode ierr;
4933   Mat            At,Bt,Ct;
4934 
4935   PetscFunctionBegin;
4936   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
4937   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
4938   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
4939   ierr = MatDestroy(&At);CHKERRQ(ierr);
4940   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
4941   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
4942   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
4943   PetscFunctionReturn(0);
4944 }
4945 
4946 #undef __FUNCT__
4947 #define __FUNCT__ "MatMatMultSymbolic_MPIDense_MPIAIJ"
4948 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
4949 {
4950   PetscErrorCode ierr;
4951   PetscInt       m=A->rmap->n,n=B->cmap->n;
4952   Mat            Cmat;
4953 
4954   PetscFunctionBegin;
4955   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);
4956   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
4957   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4958   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
4959   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
4960   ierr = MatMPIDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
4961   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4962   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4963 
4964   Cmat->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
4965 
4966   *C = Cmat;
4967   PetscFunctionReturn(0);
4968 }
4969 
4970 /* ----------------------------------------------------------------*/
4971 #undef __FUNCT__
4972 #define __FUNCT__ "MatMatMult_MPIDense_MPIAIJ"
4973 PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
4974 {
4975   PetscErrorCode ierr;
4976 
4977   PetscFunctionBegin;
4978   if (scall == MAT_INITIAL_MATRIX) {
4979     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
4980     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
4981     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
4982   }
4983   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
4984   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
4985   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
4986   PetscFunctionReturn(0);
4987 }
4988 
4989 /*MC
4990    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
4991 
4992    Options Database Keys:
4993 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
4994 
4995   Level: beginner
4996 
4997 .seealso: MatCreateAIJ()
4998 M*/
4999 
5000 #undef __FUNCT__
5001 #define __FUNCT__ "MatCreate_MPIAIJ"
5002 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
5003 {
5004   Mat_MPIAIJ     *b;
5005   PetscErrorCode ierr;
5006   PetscMPIInt    size;
5007 
5008   PetscFunctionBegin;
5009   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
5010 
5011   ierr          = PetscNewLog(B,&b);CHKERRQ(ierr);
5012   B->data       = (void*)b;
5013   ierr          = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
5014   B->assembled  = PETSC_FALSE;
5015   B->insertmode = NOT_SET_VALUES;
5016   b->size       = size;
5017 
5018   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank);CHKERRQ(ierr);
5019 
5020   /* build cache for off array entries formed */
5021   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash);CHKERRQ(ierr);
5022 
5023   b->donotstash  = PETSC_FALSE;
5024   b->colmap      = 0;
5025   b->garray      = 0;
5026   b->roworiented = PETSC_TRUE;
5027 
5028   /* stuff used for matrix vector multiply */
5029   b->lvec  = NULL;
5030   b->Mvctx = NULL;
5031 
5032   /* stuff for MatGetRow() */
5033   b->rowindices   = 0;
5034   b->rowvalues    = 0;
5035   b->getrowactive = PETSC_FALSE;
5036 
5037   /* flexible pointer used in CUSP/CUSPARSE classes */
5038   b->spptr = NULL;
5039 
5040   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetUseScalableIncreaseOverlap_C",MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ);CHKERRQ(ierr);
5041   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ);CHKERRQ(ierr);
5042   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
5043   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetDiagonalBlock_C",MatGetDiagonalBlock_MPIAIJ);CHKERRQ(ierr);
5044   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
5045   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
5046   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
5047   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
5048   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
5049   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
5050   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
5051 #if defined(PETSC_HAVE_ELEMENTAL)
5052   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_elemental_C",MatConvert_MPIAIJ_Elemental);CHKERRQ(ierr);
5053 #endif
5054   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
5055   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
5056   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
5057   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
5058   PetscFunctionReturn(0);
5059 }
5060 
5061 #undef __FUNCT__
5062 #define __FUNCT__ "MatCreateMPIAIJWithSplitArrays"
5063 /*@C
5064      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
5065          and "off-diagonal" part of the matrix in CSR format.
5066 
5067    Collective on MPI_Comm
5068 
5069    Input Parameters:
5070 +  comm - MPI communicator
5071 .  m - number of local rows (Cannot be PETSC_DECIDE)
5072 .  n - This value should be the same as the local size used in creating the
5073        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
5074        calculated if N is given) For square matrices n is almost always m.
5075 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
5076 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
5077 .   i - row indices for "diagonal" portion of matrix
5078 .   j - column indices
5079 .   a - matrix values
5080 .   oi - row indices for "off-diagonal" portion of matrix
5081 .   oj - column indices
5082 -   oa - matrix values
5083 
5084    Output Parameter:
5085 .   mat - the matrix
5086 
5087    Level: advanced
5088 
5089    Notes:
5090        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
5091        must free the arrays once the matrix has been destroyed and not before.
5092 
5093        The i and j indices are 0 based
5094 
5095        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
5096 
5097        This sets local rows and cannot be used to set off-processor values.
5098 
5099        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
5100        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
5101        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
5102        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
5103        keep track of the underlying array. Use MatSetOption(A,MAT_IGNORE_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
5104        communication if it is known that only local entries will be set.
5105 
5106 .keywords: matrix, aij, compressed row, sparse, parallel
5107 
5108 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
5109           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
5110 @*/
5111 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)
5112 {
5113   PetscErrorCode ierr;
5114   Mat_MPIAIJ     *maij;
5115 
5116   PetscFunctionBegin;
5117   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
5118   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
5119   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
5120   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
5121   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
5122   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
5123   maij = (Mat_MPIAIJ*) (*mat)->data;
5124 
5125   (*mat)->preallocated = PETSC_TRUE;
5126 
5127   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
5128   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
5129 
5130   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
5131   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
5132 
5133   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5134   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5135   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5136   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5137 
5138   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5139   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5140   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
5141   PetscFunctionReturn(0);
5142 }
5143 
5144 /*
5145     Special version for direct calls from Fortran
5146 */
5147 #include <petsc/private/fortranimpl.h>
5148 
5149 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5150 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
5151 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5152 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
5153 #endif
5154 
5155 /* Change these macros so can be used in void function */
5156 #undef CHKERRQ
5157 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
5158 #undef SETERRQ2
5159 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5160 #undef SETERRQ3
5161 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5162 #undef SETERRQ
5163 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
5164 
5165 #undef __FUNCT__
5166 #define __FUNCT__ "matsetvaluesmpiaij_"
5167 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)
5168 {
5169   Mat            mat  = *mmat;
5170   PetscInt       m    = *mm, n = *mn;
5171   InsertMode     addv = *maddv;
5172   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
5173   PetscScalar    value;
5174   PetscErrorCode ierr;
5175 
5176   MatCheckPreallocated(mat,1);
5177   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
5178 
5179 #if defined(PETSC_USE_DEBUG)
5180   else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
5181 #endif
5182   {
5183     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
5184     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
5185     PetscBool roworiented = aij->roworiented;
5186 
5187     /* Some Variables required in the macro */
5188     Mat        A                 = aij->A;
5189     Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
5190     PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
5191     MatScalar  *aa               = a->a;
5192     PetscBool  ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
5193     Mat        B                 = aij->B;
5194     Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
5195     PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5196     MatScalar  *ba               = b->a;
5197 
5198     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5199     PetscInt  nonew = a->nonew;
5200     MatScalar *ap1,*ap2;
5201 
5202     PetscFunctionBegin;
5203     for (i=0; i<m; i++) {
5204       if (im[i] < 0) continue;
5205 #if defined(PETSC_USE_DEBUG)
5206       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);
5207 #endif
5208       if (im[i] >= rstart && im[i] < rend) {
5209         row      = im[i] - rstart;
5210         lastcol1 = -1;
5211         rp1      = aj + ai[row];
5212         ap1      = aa + ai[row];
5213         rmax1    = aimax[row];
5214         nrow1    = ailen[row];
5215         low1     = 0;
5216         high1    = nrow1;
5217         lastcol2 = -1;
5218         rp2      = bj + bi[row];
5219         ap2      = ba + bi[row];
5220         rmax2    = bimax[row];
5221         nrow2    = bilen[row];
5222         low2     = 0;
5223         high2    = nrow2;
5224 
5225         for (j=0; j<n; j++) {
5226           if (roworiented) value = v[i*n+j];
5227           else value = v[i+j*m];
5228           if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES)) continue;
5229           if (in[j] >= cstart && in[j] < cend) {
5230             col = in[j] - cstart;
5231             MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
5232           } else if (in[j] < 0) continue;
5233 #if defined(PETSC_USE_DEBUG)
5234           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);
5235 #endif
5236           else {
5237             if (mat->was_assembled) {
5238               if (!aij->colmap) {
5239                 ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5240               }
5241 #if defined(PETSC_USE_CTABLE)
5242               ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5243               col--;
5244 #else
5245               col = aij->colmap[in[j]] - 1;
5246 #endif
5247               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5248                 ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5249                 col  =  in[j];
5250                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5251                 B     = aij->B;
5252                 b     = (Mat_SeqAIJ*)B->data;
5253                 bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5254                 rp2   = bj + bi[row];
5255                 ap2   = ba + bi[row];
5256                 rmax2 = bimax[row];
5257                 nrow2 = bilen[row];
5258                 low2  = 0;
5259                 high2 = nrow2;
5260                 bm    = aij->B->rmap->n;
5261                 ba    = b->a;
5262               }
5263             } else col = in[j];
5264             MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
5265           }
5266         }
5267       } else if (!aij->donotstash) {
5268         if (roworiented) {
5269           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5270         } else {
5271           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5272         }
5273       }
5274     }
5275   }
5276   PetscFunctionReturnVoid();
5277 }
5278 
5279