xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision e6e36fe83a92e0b59a33046d72bc05a51845f521)
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   InsertMode     addv;
686 
687   PetscFunctionBegin;
688   if (aij->donotstash || mat->nooffprocentries) PetscFunctionReturn(0);
689 
690   /* make sure all processors are either in INSERTMODE or ADDMODE */
691   ierr = MPI_Allreduce((PetscEnum*)&mat->insertmode,(PetscEnum*)&addv,1,MPIU_ENUM,MPI_BOR,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
692   if (addv == (ADD_VALUES|INSERT_VALUES)) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Some processors inserted others added");
693   mat->insertmode = addv; /* in case this processor had no cache */
694 
695   ierr = MatStashScatterBegin_Private(mat,&mat->stash,mat->rmap->range);CHKERRQ(ierr);
696   ierr = MatStashGetInfo_Private(&mat->stash,&nstash,&reallocs);CHKERRQ(ierr);
697   ierr = PetscInfo2(aij->A,"Stash has %D entries, uses %D mallocs.\n",nstash,reallocs);CHKERRQ(ierr);
698   PetscFunctionReturn(0);
699 }
700 
701 #undef __FUNCT__
702 #define __FUNCT__ "MatAssemblyEnd_MPIAIJ"
703 PetscErrorCode MatAssemblyEnd_MPIAIJ(Mat mat,MatAssemblyType mode)
704 {
705   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
706   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)aij->A->data;
707   PetscErrorCode ierr;
708   PetscMPIInt    n;
709   PetscInt       i,j,rstart,ncols,flg;
710   PetscInt       *row,*col;
711   PetscBool      other_disassembled;
712   PetscScalar    *val;
713   InsertMode     addv = mat->insertmode;
714 
715   /* do not use 'b = (Mat_SeqAIJ*)aij->B->data' as B can be reset in disassembly */
716 
717   PetscFunctionBegin;
718   if (!aij->donotstash && !mat->nooffprocentries) {
719     while (1) {
720       ierr = MatStashScatterGetMesg_Private(&mat->stash,&n,&row,&col,&val,&flg);CHKERRQ(ierr);
721       if (!flg) break;
722 
723       for (i=0; i<n; ) {
724         /* Now identify the consecutive vals belonging to the same row */
725         for (j=i,rstart=row[j]; j<n; j++) {
726           if (row[j] != rstart) break;
727         }
728         if (j < n) ncols = j-i;
729         else       ncols = n-i;
730         /* Now assemble all these values with a single function call */
731         ierr = MatSetValues_MPIAIJ(mat,1,row+i,ncols,col+i,val+i,addv);CHKERRQ(ierr);
732 
733         i = j;
734       }
735     }
736     ierr = MatStashScatterEnd_Private(&mat->stash);CHKERRQ(ierr);
737   }
738   ierr = MatAssemblyBegin(aij->A,mode);CHKERRQ(ierr);
739   ierr = MatAssemblyEnd(aij->A,mode);CHKERRQ(ierr);
740 
741   /* determine if any processor has disassembled, if so we must
742      also disassemble ourselfs, in order that we may reassemble. */
743   /*
744      if nonzero structure of submatrix B cannot change then we know that
745      no processor disassembled thus we can skip this stuff
746   */
747   if (!((Mat_SeqAIJ*)aij->B->data)->nonew) {
748     ierr = MPI_Allreduce(&mat->was_assembled,&other_disassembled,1,MPIU_BOOL,MPI_PROD,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
749     if (mat->was_assembled && !other_disassembled) {
750       ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
751     }
752   }
753   if (!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) {
754     ierr = MatSetUpMultiply_MPIAIJ(mat);CHKERRQ(ierr);
755   }
756   ierr = MatSetOption(aij->B,MAT_USE_INODES,PETSC_FALSE);CHKERRQ(ierr);
757   ierr = MatAssemblyBegin(aij->B,mode);CHKERRQ(ierr);
758   ierr = MatAssemblyEnd(aij->B,mode);CHKERRQ(ierr);
759 
760   ierr = PetscFree2(aij->rowvalues,aij->rowindices);CHKERRQ(ierr);
761 
762   aij->rowvalues = 0;
763 
764   ierr = VecDestroy(&aij->diag);CHKERRQ(ierr);
765   if (a->inode.size) mat->ops->multdiagonalblock = MatMultDiagonalBlock_MPIAIJ;
766 
767   /* if no new nonzero locations are allowed in matrix then only set the matrix state the first time through */
768   if ((!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) || !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
769     PetscObjectState state = aij->A->nonzerostate + aij->B->nonzerostate;
770     ierr = MPI_Allreduce(&state,&mat->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
771   }
772   PetscFunctionReturn(0);
773 }
774 
775 #undef __FUNCT__
776 #define __FUNCT__ "MatZeroEntries_MPIAIJ"
777 PetscErrorCode MatZeroEntries_MPIAIJ(Mat A)
778 {
779   Mat_MPIAIJ     *l = (Mat_MPIAIJ*)A->data;
780   PetscErrorCode ierr;
781 
782   PetscFunctionBegin;
783   ierr = MatZeroEntries(l->A);CHKERRQ(ierr);
784   ierr = MatZeroEntries(l->B);CHKERRQ(ierr);
785   PetscFunctionReturn(0);
786 }
787 
788 #undef __FUNCT__
789 #define __FUNCT__ "MatZeroRows_MPIAIJ"
790 PetscErrorCode MatZeroRows_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
791 {
792   Mat_MPIAIJ    *mat    = (Mat_MPIAIJ *) A->data;
793   PetscInt      *owners = A->rmap->range;
794   PetscInt       n      = A->rmap->n;
795   PetscSF        sf;
796   PetscInt      *lrows;
797   PetscSFNode   *rrows;
798   PetscInt       r, p = 0, len = 0;
799   PetscErrorCode ierr;
800 
801   PetscFunctionBegin;
802   /* Create SF where leaves are input rows and roots are owned rows */
803   ierr = PetscMalloc1(n, &lrows);CHKERRQ(ierr);
804   for (r = 0; r < n; ++r) lrows[r] = -1;
805   if (!A->nooffproczerorows) {ierr = PetscMalloc1(N, &rrows);CHKERRQ(ierr);}
806   for (r = 0; r < N; ++r) {
807     const PetscInt idx   = rows[r];
808     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);
809     if (idx < owners[p] || owners[p+1] <= idx) { /* short-circuit the search if the last p owns this row too */
810       ierr = PetscLayoutFindOwner(A->rmap,idx,&p);CHKERRQ(ierr);
811     }
812     if (A->nooffproczerorows) {
813       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);
814       lrows[len++] = idx - owners[p];
815     } else {
816       rrows[r].rank = p;
817       rrows[r].index = rows[r] - owners[p];
818     }
819   }
820   if (!A->nooffproczerorows) {
821     ierr = PetscSFCreate(PetscObjectComm((PetscObject) A), &sf);CHKERRQ(ierr);
822     ierr = PetscSFSetGraph(sf, n, N, NULL, PETSC_OWN_POINTER, rrows, PETSC_OWN_POINTER);CHKERRQ(ierr);
823     /* Collect flags for rows to be zeroed */
824     ierr = PetscSFReduceBegin(sf, MPIU_INT, (PetscInt*)rows, lrows, MPI_LOR);CHKERRQ(ierr);
825     ierr = PetscSFReduceEnd(sf, MPIU_INT, (PetscInt*)rows, lrows, MPI_LOR);CHKERRQ(ierr);
826     ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
827     /* Compress and put in row numbers */
828     for (r = 0; r < n; ++r) if (lrows[r] >= 0) lrows[len++] = r;
829   }
830   /* fix right hand side if needed */
831   if (x && b) {
832     const PetscScalar *xx;
833     PetscScalar       *bb;
834 
835     ierr = VecGetArrayRead(x, &xx);CHKERRQ(ierr);
836     ierr = VecGetArray(b, &bb);CHKERRQ(ierr);
837     for (r = 0; r < len; ++r) bb[lrows[r]] = diag*xx[lrows[r]];
838     ierr = VecRestoreArrayRead(x, &xx);CHKERRQ(ierr);
839     ierr = VecRestoreArray(b, &bb);CHKERRQ(ierr);
840   }
841   /* Must zero l->B before l->A because the (diag) case below may put values into l->B*/
842   ierr = MatZeroRows(mat->B, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
843   if ((diag != 0.0) && (mat->A->rmap->N == mat->A->cmap->N)) {
844     ierr = MatZeroRows(mat->A, len, lrows, diag, NULL, NULL);CHKERRQ(ierr);
845   } else if (diag != 0.0) {
846     ierr = MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
847     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");
848     for (r = 0; r < len; ++r) {
849       const PetscInt row = lrows[r] + A->rmap->rstart;
850       ierr = MatSetValues(A, 1, &row, 1, &row, &diag, INSERT_VALUES);CHKERRQ(ierr);
851     }
852     ierr = MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
853     ierr = MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
854   } else {
855     ierr = MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
856   }
857   ierr = PetscFree(lrows);CHKERRQ(ierr);
858 
859   /* only change matrix nonzero state if pattern was allowed to be changed */
860   if (!((Mat_SeqAIJ*)(mat->A->data))->keepnonzeropattern) {
861     PetscObjectState state = mat->A->nonzerostate + mat->B->nonzerostate;
862     ierr = MPI_Allreduce(&state,&A->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
863   }
864   PetscFunctionReturn(0);
865 }
866 
867 #undef __FUNCT__
868 #define __FUNCT__ "MatZeroRowsColumns_MPIAIJ"
869 PetscErrorCode MatZeroRowsColumns_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
870 {
871   Mat_MPIAIJ        *l = (Mat_MPIAIJ*)A->data;
872   PetscErrorCode    ierr;
873   PetscMPIInt       n = A->rmap->n;
874   PetscInt          i,j,r,m,p = 0,len = 0;
875   PetscInt          *lrows,*owners = A->rmap->range;
876   PetscSFNode       *rrows;
877   PetscSF           sf;
878   const PetscScalar *xx;
879   PetscScalar       *bb,*mask;
880   Vec               xmask,lmask;
881   Mat_SeqAIJ        *aij = (Mat_SeqAIJ*)l->B->data;
882   const PetscInt    *aj, *ii,*ridx;
883   PetscScalar       *aa;
884 
885   PetscFunctionBegin;
886   /* Create SF where leaves are input rows and roots are owned rows */
887   ierr = PetscMalloc1(n, &lrows);CHKERRQ(ierr);
888   for (r = 0; r < n; ++r) lrows[r] = -1;
889   ierr = PetscMalloc1(N, &rrows);CHKERRQ(ierr);
890   for (r = 0; r < N; ++r) {
891     const PetscInt idx   = rows[r];
892     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);
893     if (idx < owners[p] || owners[p+1] <= idx) { /* short-circuit the search if the last p owns this row too */
894       ierr = PetscLayoutFindOwner(A->rmap,idx,&p);CHKERRQ(ierr);
895     }
896     rrows[r].rank  = p;
897     rrows[r].index = rows[r] - owners[p];
898   }
899   ierr = PetscSFCreate(PetscObjectComm((PetscObject) A), &sf);CHKERRQ(ierr);
900   ierr = PetscSFSetGraph(sf, n, N, NULL, PETSC_OWN_POINTER, rrows, PETSC_OWN_POINTER);CHKERRQ(ierr);
901   /* Collect flags for rows to be zeroed */
902   ierr = PetscSFReduceBegin(sf, MPIU_INT, (PetscInt *) rows, lrows, MPI_LOR);CHKERRQ(ierr);
903   ierr = PetscSFReduceEnd(sf, MPIU_INT, (PetscInt *) rows, lrows, MPI_LOR);CHKERRQ(ierr);
904   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
905   /* Compress and put in row numbers */
906   for (r = 0; r < n; ++r) if (lrows[r] >= 0) lrows[len++] = r;
907   /* zero diagonal part of matrix */
908   ierr = MatZeroRowsColumns(l->A,len,lrows,diag,x,b);CHKERRQ(ierr);
909   /* handle off diagonal part of matrix */
910   ierr = MatCreateVecs(A,&xmask,NULL);CHKERRQ(ierr);
911   ierr = VecDuplicate(l->lvec,&lmask);CHKERRQ(ierr);
912   ierr = VecGetArray(xmask,&bb);CHKERRQ(ierr);
913   for (i=0; i<len; i++) bb[lrows[i]] = 1;
914   ierr = VecRestoreArray(xmask,&bb);CHKERRQ(ierr);
915   ierr = VecScatterBegin(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
916   ierr = VecScatterEnd(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
917   ierr = VecDestroy(&xmask);CHKERRQ(ierr);
918   if (x) {
919     ierr = VecScatterBegin(l->Mvctx,x,l->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
920     ierr = VecScatterEnd(l->Mvctx,x,l->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
921     ierr = VecGetArrayRead(l->lvec,&xx);CHKERRQ(ierr);
922     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
923   }
924   ierr = VecGetArray(lmask,&mask);CHKERRQ(ierr);
925   /* remove zeroed rows of off diagonal matrix */
926   ii = aij->i;
927   for (i=0; i<len; i++) {
928     ierr = PetscMemzero(aij->a + ii[lrows[i]],(ii[lrows[i]+1] - ii[lrows[i]])*sizeof(PetscScalar));CHKERRQ(ierr);
929   }
930   /* loop over all elements of off process part of matrix zeroing removed columns*/
931   if (aij->compressedrow.use) {
932     m    = aij->compressedrow.nrows;
933     ii   = aij->compressedrow.i;
934     ridx = aij->compressedrow.rindex;
935     for (i=0; i<m; i++) {
936       n  = ii[i+1] - ii[i];
937       aj = aij->j + ii[i];
938       aa = aij->a + ii[i];
939 
940       for (j=0; j<n; j++) {
941         if (PetscAbsScalar(mask[*aj])) {
942           if (b) bb[*ridx] -= *aa*xx[*aj];
943           *aa = 0.0;
944         }
945         aa++;
946         aj++;
947       }
948       ridx++;
949     }
950   } else { /* do not use compressed row format */
951     m = l->B->rmap->n;
952     for (i=0; i<m; i++) {
953       n  = ii[i+1] - ii[i];
954       aj = aij->j + ii[i];
955       aa = aij->a + ii[i];
956       for (j=0; j<n; j++) {
957         if (PetscAbsScalar(mask[*aj])) {
958           if (b) bb[i] -= *aa*xx[*aj];
959           *aa = 0.0;
960         }
961         aa++;
962         aj++;
963       }
964     }
965   }
966   if (x) {
967     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
968     ierr = VecRestoreArrayRead(l->lvec,&xx);CHKERRQ(ierr);
969   }
970   ierr = VecRestoreArray(lmask,&mask);CHKERRQ(ierr);
971   ierr = VecDestroy(&lmask);CHKERRQ(ierr);
972   ierr = PetscFree(lrows);CHKERRQ(ierr);
973 
974   /* only change matrix nonzero state if pattern was allowed to be changed */
975   if (!((Mat_SeqAIJ*)(l->A->data))->keepnonzeropattern) {
976     PetscObjectState state = l->A->nonzerostate + l->B->nonzerostate;
977     ierr = MPI_Allreduce(&state,&A->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
978   }
979   PetscFunctionReturn(0);
980 }
981 
982 #undef __FUNCT__
983 #define __FUNCT__ "MatMult_MPIAIJ"
984 PetscErrorCode MatMult_MPIAIJ(Mat A,Vec xx,Vec yy)
985 {
986   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
987   PetscErrorCode ierr;
988   PetscInt       nt;
989 
990   PetscFunctionBegin;
991   ierr = VecGetLocalSize(xx,&nt);CHKERRQ(ierr);
992   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);
993   ierr = VecScatterBegin(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
994   ierr = (*a->A->ops->mult)(a->A,xx,yy);CHKERRQ(ierr);
995   ierr = VecScatterEnd(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
996   ierr = (*a->B->ops->multadd)(a->B,a->lvec,yy,yy);CHKERRQ(ierr);
997   PetscFunctionReturn(0);
998 }
999 
1000 #undef __FUNCT__
1001 #define __FUNCT__ "MatMultDiagonalBlock_MPIAIJ"
1002 PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat A,Vec bb,Vec xx)
1003 {
1004   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1005   PetscErrorCode ierr;
1006 
1007   PetscFunctionBegin;
1008   ierr = MatMultDiagonalBlock(a->A,bb,xx);CHKERRQ(ierr);
1009   PetscFunctionReturn(0);
1010 }
1011 
1012 #undef __FUNCT__
1013 #define __FUNCT__ "MatMultAdd_MPIAIJ"
1014 PetscErrorCode MatMultAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1015 {
1016   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1017   PetscErrorCode ierr;
1018 
1019   PetscFunctionBegin;
1020   ierr = VecScatterBegin(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1021   ierr = (*a->A->ops->multadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
1022   ierr = VecScatterEnd(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1023   ierr = (*a->B->ops->multadd)(a->B,a->lvec,zz,zz);CHKERRQ(ierr);
1024   PetscFunctionReturn(0);
1025 }
1026 
1027 #undef __FUNCT__
1028 #define __FUNCT__ "MatMultTranspose_MPIAIJ"
1029 PetscErrorCode MatMultTranspose_MPIAIJ(Mat A,Vec xx,Vec yy)
1030 {
1031   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1032   PetscErrorCode ierr;
1033   PetscBool      merged;
1034 
1035   PetscFunctionBegin;
1036   ierr = VecScatterGetMerged(a->Mvctx,&merged);CHKERRQ(ierr);
1037   /* do nondiagonal part */
1038   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
1039   if (!merged) {
1040     /* send it on its way */
1041     ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1042     /* do local part */
1043     ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
1044     /* receive remote parts: note this assumes the values are not actually */
1045     /* added in yy until the next line, */
1046     ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1047   } else {
1048     /* do local part */
1049     ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
1050     /* send it on its way */
1051     ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1052     /* values actually were received in the Begin() but we need to call this nop */
1053     ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1054   }
1055   PetscFunctionReturn(0);
1056 }
1057 
1058 #undef __FUNCT__
1059 #define __FUNCT__ "MatIsTranspose_MPIAIJ"
1060 PetscErrorCode  MatIsTranspose_MPIAIJ(Mat Amat,Mat Bmat,PetscReal tol,PetscBool  *f)
1061 {
1062   MPI_Comm       comm;
1063   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ*) Amat->data, *Bij;
1064   Mat            Adia = Aij->A, Bdia, Aoff,Boff,*Aoffs,*Boffs;
1065   IS             Me,Notme;
1066   PetscErrorCode ierr;
1067   PetscInt       M,N,first,last,*notme,i;
1068   PetscMPIInt    size;
1069 
1070   PetscFunctionBegin;
1071   /* Easy test: symmetric diagonal block */
1072   Bij  = (Mat_MPIAIJ*) Bmat->data; Bdia = Bij->A;
1073   ierr = MatIsTranspose(Adia,Bdia,tol,f);CHKERRQ(ierr);
1074   if (!*f) PetscFunctionReturn(0);
1075   ierr = PetscObjectGetComm((PetscObject)Amat,&comm);CHKERRQ(ierr);
1076   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1077   if (size == 1) PetscFunctionReturn(0);
1078 
1079   /* Hard test: off-diagonal block. This takes a MatGetSubMatrix. */
1080   ierr = MatGetSize(Amat,&M,&N);CHKERRQ(ierr);
1081   ierr = MatGetOwnershipRange(Amat,&first,&last);CHKERRQ(ierr);
1082   ierr = PetscMalloc1(N-last+first,&notme);CHKERRQ(ierr);
1083   for (i=0; i<first; i++) notme[i] = i;
1084   for (i=last; i<M; i++) notme[i-last+first] = i;
1085   ierr = ISCreateGeneral(MPI_COMM_SELF,N-last+first,notme,PETSC_COPY_VALUES,&Notme);CHKERRQ(ierr);
1086   ierr = ISCreateStride(MPI_COMM_SELF,last-first,first,1,&Me);CHKERRQ(ierr);
1087   ierr = MatGetSubMatrices(Amat,1,&Me,&Notme,MAT_INITIAL_MATRIX,&Aoffs);CHKERRQ(ierr);
1088   Aoff = Aoffs[0];
1089   ierr = MatGetSubMatrices(Bmat,1,&Notme,&Me,MAT_INITIAL_MATRIX,&Boffs);CHKERRQ(ierr);
1090   Boff = Boffs[0];
1091   ierr = MatIsTranspose(Aoff,Boff,tol,f);CHKERRQ(ierr);
1092   ierr = MatDestroyMatrices(1,&Aoffs);CHKERRQ(ierr);
1093   ierr = MatDestroyMatrices(1,&Boffs);CHKERRQ(ierr);
1094   ierr = ISDestroy(&Me);CHKERRQ(ierr);
1095   ierr = ISDestroy(&Notme);CHKERRQ(ierr);
1096   ierr = PetscFree(notme);CHKERRQ(ierr);
1097   PetscFunctionReturn(0);
1098 }
1099 
1100 #undef __FUNCT__
1101 #define __FUNCT__ "MatMultTransposeAdd_MPIAIJ"
1102 PetscErrorCode MatMultTransposeAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1103 {
1104   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1105   PetscErrorCode ierr;
1106 
1107   PetscFunctionBegin;
1108   /* do nondiagonal part */
1109   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
1110   /* send it on its way */
1111   ierr = VecScatterBegin(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1112   /* do local part */
1113   ierr = (*a->A->ops->multtransposeadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
1114   /* receive remote parts */
1115   ierr = VecScatterEnd(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1116   PetscFunctionReturn(0);
1117 }
1118 
1119 /*
1120   This only works correctly for square matrices where the subblock A->A is the
1121    diagonal block
1122 */
1123 #undef __FUNCT__
1124 #define __FUNCT__ "MatGetDiagonal_MPIAIJ"
1125 PetscErrorCode MatGetDiagonal_MPIAIJ(Mat A,Vec v)
1126 {
1127   PetscErrorCode ierr;
1128   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1129 
1130   PetscFunctionBegin;
1131   if (A->rmap->N != A->cmap->N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Supports only square matrix where A->A is diag block");
1132   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");
1133   ierr = MatGetDiagonal(a->A,v);CHKERRQ(ierr);
1134   PetscFunctionReturn(0);
1135 }
1136 
1137 #undef __FUNCT__
1138 #define __FUNCT__ "MatScale_MPIAIJ"
1139 PetscErrorCode MatScale_MPIAIJ(Mat A,PetscScalar aa)
1140 {
1141   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1142   PetscErrorCode ierr;
1143 
1144   PetscFunctionBegin;
1145   ierr = MatScale(a->A,aa);CHKERRQ(ierr);
1146   ierr = MatScale(a->B,aa);CHKERRQ(ierr);
1147   PetscFunctionReturn(0);
1148 }
1149 
1150 #undef __FUNCT__
1151 #define __FUNCT__ "MatDestroy_MPIAIJ"
1152 PetscErrorCode MatDestroy_MPIAIJ(Mat mat)
1153 {
1154   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1155   PetscErrorCode ierr;
1156 
1157   PetscFunctionBegin;
1158 #if defined(PETSC_USE_LOG)
1159   PetscLogObjectState((PetscObject)mat,"Rows=%D, Cols=%D",mat->rmap->N,mat->cmap->N);
1160 #endif
1161   ierr = MatStashDestroy_Private(&mat->stash);CHKERRQ(ierr);
1162   ierr = VecDestroy(&aij->diag);CHKERRQ(ierr);
1163   ierr = MatDestroy(&aij->A);CHKERRQ(ierr);
1164   ierr = MatDestroy(&aij->B);CHKERRQ(ierr);
1165 #if defined(PETSC_USE_CTABLE)
1166   ierr = PetscTableDestroy(&aij->colmap);CHKERRQ(ierr);
1167 #else
1168   ierr = PetscFree(aij->colmap);CHKERRQ(ierr);
1169 #endif
1170   ierr = PetscFree(aij->garray);CHKERRQ(ierr);
1171   ierr = VecDestroy(&aij->lvec);CHKERRQ(ierr);
1172   ierr = VecScatterDestroy(&aij->Mvctx);CHKERRQ(ierr);
1173   ierr = PetscFree2(aij->rowvalues,aij->rowindices);CHKERRQ(ierr);
1174   ierr = PetscFree(aij->ld);CHKERRQ(ierr);
1175   ierr = PetscFree(mat->data);CHKERRQ(ierr);
1176 
1177   ierr = PetscObjectChangeTypeName((PetscObject)mat,0);CHKERRQ(ierr);
1178   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatStoreValues_C",NULL);CHKERRQ(ierr);
1179   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatRetrieveValues_C",NULL);CHKERRQ(ierr);
1180   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatGetDiagonalBlock_C",NULL);CHKERRQ(ierr);
1181   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatIsTranspose_C",NULL);CHKERRQ(ierr);
1182   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocation_C",NULL);CHKERRQ(ierr);
1183   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocationCSR_C",NULL);CHKERRQ(ierr);
1184   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDiagonalScaleLocal_C",NULL);CHKERRQ(ierr);
1185   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_mpisbaij_C",NULL);CHKERRQ(ierr);
1186 #if defined(PETSC_HAVE_ELEMENTAL)
1187   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_elemental_C",NULL);CHKERRQ(ierr);
1188 #endif
1189   PetscFunctionReturn(0);
1190 }
1191 
1192 #undef __FUNCT__
1193 #define __FUNCT__ "MatView_MPIAIJ_Binary"
1194 PetscErrorCode MatView_MPIAIJ_Binary(Mat mat,PetscViewer viewer)
1195 {
1196   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1197   Mat_SeqAIJ     *A   = (Mat_SeqAIJ*)aij->A->data;
1198   Mat_SeqAIJ     *B   = (Mat_SeqAIJ*)aij->B->data;
1199   PetscErrorCode ierr;
1200   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
1201   int            fd;
1202   PetscInt       nz,header[4],*row_lengths,*range=0,rlen,i;
1203   PetscInt       nzmax,*column_indices,j,k,col,*garray = aij->garray,cnt,cstart = mat->cmap->rstart,rnz = 0;
1204   PetscScalar    *column_values;
1205   PetscInt       message_count,flowcontrolcount;
1206   FILE           *file;
1207 
1208   PetscFunctionBegin;
1209   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
1210   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);CHKERRQ(ierr);
1211   nz   = A->nz + B->nz;
1212   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
1213   if (!rank) {
1214     header[0] = MAT_FILE_CLASSID;
1215     header[1] = mat->rmap->N;
1216     header[2] = mat->cmap->N;
1217 
1218     ierr = MPI_Reduce(&nz,&header[3],1,MPIU_INT,MPI_SUM,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1219     ierr = PetscBinaryWrite(fd,header,4,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1220     /* get largest number of rows any processor has */
1221     rlen  = mat->rmap->n;
1222     range = mat->rmap->range;
1223     for (i=1; i<size; i++) rlen = PetscMax(rlen,range[i+1] - range[i]);
1224   } else {
1225     ierr = MPI_Reduce(&nz,0,1,MPIU_INT,MPI_SUM,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1226     rlen = mat->rmap->n;
1227   }
1228 
1229   /* load up the local row counts */
1230   ierr = PetscMalloc1(rlen+1,&row_lengths);CHKERRQ(ierr);
1231   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];
1232 
1233   /* store the row lengths to the file */
1234   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1235   if (!rank) {
1236     ierr = PetscBinaryWrite(fd,row_lengths,mat->rmap->n,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1237     for (i=1; i<size; i++) {
1238       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1239       rlen = range[i+1] - range[i];
1240       ierr = MPIULong_Recv(row_lengths,rlen,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1241       ierr = PetscBinaryWrite(fd,row_lengths,rlen,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1242     }
1243     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1244   } else {
1245     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1246     ierr = MPIULong_Send(row_lengths,mat->rmap->n,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1247     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1248   }
1249   ierr = PetscFree(row_lengths);CHKERRQ(ierr);
1250 
1251   /* load up the local column indices */
1252   nzmax = nz; /* th processor needs space a largest processor needs */
1253   ierr  = MPI_Reduce(&nz,&nzmax,1,MPIU_INT,MPI_MAX,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1254   ierr  = PetscMalloc1(nzmax+1,&column_indices);CHKERRQ(ierr);
1255   cnt   = 0;
1256   for (i=0; i<mat->rmap->n; i++) {
1257     for (j=B->i[i]; j<B->i[i+1]; j++) {
1258       if ((col = garray[B->j[j]]) > cstart) break;
1259       column_indices[cnt++] = col;
1260     }
1261     for (k=A->i[i]; k<A->i[i+1]; k++) column_indices[cnt++] = A->j[k] + cstart;
1262     for (; j<B->i[i+1]; j++) column_indices[cnt++] = garray[B->j[j]];
1263   }
1264   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);
1265 
1266   /* store the column indices to the file */
1267   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1268   if (!rank) {
1269     MPI_Status status;
1270     ierr = PetscBinaryWrite(fd,column_indices,nz,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1271     for (i=1; i<size; i++) {
1272       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1273       ierr = MPI_Recv(&rnz,1,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat),&status);CHKERRQ(ierr);
1274       if (rnz > nzmax) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: nz = %D nzmax = %D",nz,nzmax);
1275       ierr = MPIULong_Recv(column_indices,rnz,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1276       ierr = PetscBinaryWrite(fd,column_indices,rnz,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1277     }
1278     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1279   } else {
1280     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1281     ierr = MPI_Send(&nz,1,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1282     ierr = MPIULong_Send(column_indices,nz,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1283     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1284   }
1285   ierr = PetscFree(column_indices);CHKERRQ(ierr);
1286 
1287   /* load up the local column values */
1288   ierr = PetscMalloc1(nzmax+1,&column_values);CHKERRQ(ierr);
1289   cnt  = 0;
1290   for (i=0; i<mat->rmap->n; i++) {
1291     for (j=B->i[i]; j<B->i[i+1]; j++) {
1292       if (garray[B->j[j]] > cstart) break;
1293       column_values[cnt++] = B->a[j];
1294     }
1295     for (k=A->i[i]; k<A->i[i+1]; k++) column_values[cnt++] = A->a[k];
1296     for (; j<B->i[i+1]; j++) column_values[cnt++] = B->a[j];
1297   }
1298   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);
1299 
1300   /* store the column values to the file */
1301   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1302   if (!rank) {
1303     MPI_Status status;
1304     ierr = PetscBinaryWrite(fd,column_values,nz,PETSC_SCALAR,PETSC_TRUE);CHKERRQ(ierr);
1305     for (i=1; i<size; i++) {
1306       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1307       ierr = MPI_Recv(&rnz,1,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat),&status);CHKERRQ(ierr);
1308       if (rnz > nzmax) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: nz = %D nzmax = %D",nz,nzmax);
1309       ierr = MPIULong_Recv(column_values,rnz,MPIU_SCALAR,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1310       ierr = PetscBinaryWrite(fd,column_values,rnz,PETSC_SCALAR,PETSC_TRUE);CHKERRQ(ierr);
1311     }
1312     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1313   } else {
1314     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1315     ierr = MPI_Send(&nz,1,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1316     ierr = MPIULong_Send(column_values,nz,MPIU_SCALAR,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1317     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1318   }
1319   ierr = PetscFree(column_values);CHKERRQ(ierr);
1320 
1321   ierr = PetscViewerBinaryGetInfoPointer(viewer,&file);CHKERRQ(ierr);
1322   if (file) fprintf(file,"-matload_block_size %d\n",(int)PetscAbs(mat->rmap->bs));
1323   PetscFunctionReturn(0);
1324 }
1325 
1326 #include <petscdraw.h>
1327 #undef __FUNCT__
1328 #define __FUNCT__ "MatView_MPIAIJ_ASCIIorDraworSocket"
1329 PetscErrorCode MatView_MPIAIJ_ASCIIorDraworSocket(Mat mat,PetscViewer viewer)
1330 {
1331   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)mat->data;
1332   PetscErrorCode    ierr;
1333   PetscMPIInt       rank = aij->rank,size = aij->size;
1334   PetscBool         isdraw,iascii,isbinary;
1335   PetscViewer       sviewer;
1336   PetscViewerFormat format;
1337 
1338   PetscFunctionBegin;
1339   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1340   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1341   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1342   if (iascii) {
1343     ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
1344     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
1345       MatInfo   info;
1346       PetscBool inodes;
1347 
1348       ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
1349       ierr = MatGetInfo(mat,MAT_LOCAL,&info);CHKERRQ(ierr);
1350       ierr = MatInodeGetInodeSizes(aij->A,NULL,(PetscInt**)&inodes,NULL);CHKERRQ(ierr);
1351       ierr = PetscViewerASCIISynchronizedAllow(viewer,PETSC_TRUE);CHKERRQ(ierr);
1352       if (!inodes) {
1353         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %D nz %D nz alloced %D mem %D, not using I-node routines\n",
1354                                                   rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
1355       } else {
1356         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %D nz %D nz alloced %D mem %D, using I-node routines\n",
1357                                                   rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
1358       }
1359       ierr = MatGetInfo(aij->A,MAT_LOCAL,&info);CHKERRQ(ierr);
1360       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] on-diagonal part: nz %D \n",rank,(PetscInt)info.nz_used);CHKERRQ(ierr);
1361       ierr = MatGetInfo(aij->B,MAT_LOCAL,&info);CHKERRQ(ierr);
1362       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] off-diagonal part: nz %D \n",rank,(PetscInt)info.nz_used);CHKERRQ(ierr);
1363       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1364       ierr = PetscViewerASCIISynchronizedAllow(viewer,PETSC_FALSE);CHKERRQ(ierr);
1365       ierr = PetscViewerASCIIPrintf(viewer,"Information on VecScatter used in matrix-vector product: \n");CHKERRQ(ierr);
1366       ierr = VecScatterView(aij->Mvctx,viewer);CHKERRQ(ierr);
1367       PetscFunctionReturn(0);
1368     } else if (format == PETSC_VIEWER_ASCII_INFO) {
1369       PetscInt inodecount,inodelimit,*inodes;
1370       ierr = MatInodeGetInodeSizes(aij->A,&inodecount,&inodes,&inodelimit);CHKERRQ(ierr);
1371       if (inodes) {
1372         ierr = PetscViewerASCIIPrintf(viewer,"using I-node (on process 0) routines: found %D nodes, limit used is %D\n",inodecount,inodelimit);CHKERRQ(ierr);
1373       } else {
1374         ierr = PetscViewerASCIIPrintf(viewer,"not using I-node (on process 0) routines\n");CHKERRQ(ierr);
1375       }
1376       PetscFunctionReturn(0);
1377     } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO) {
1378       PetscFunctionReturn(0);
1379     }
1380   } else if (isbinary) {
1381     if (size == 1) {
1382       ierr = PetscObjectSetName((PetscObject)aij->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1383       ierr = MatView(aij->A,viewer);CHKERRQ(ierr);
1384     } else {
1385       ierr = MatView_MPIAIJ_Binary(mat,viewer);CHKERRQ(ierr);
1386     }
1387     PetscFunctionReturn(0);
1388   } else if (isdraw) {
1389     PetscDraw draw;
1390     PetscBool isnull;
1391     ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
1392     ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr); if (isnull) PetscFunctionReturn(0);
1393   }
1394 
1395   {
1396     /* assemble the entire matrix onto first processor. */
1397     Mat        A;
1398     Mat_SeqAIJ *Aloc;
1399     PetscInt   M = mat->rmap->N,N = mat->cmap->N,m,*ai,*aj,row,*cols,i,*ct;
1400     MatScalar  *a;
1401 
1402     ierr = MatCreate(PetscObjectComm((PetscObject)mat),&A);CHKERRQ(ierr);
1403     if (!rank) {
1404       ierr = MatSetSizes(A,M,N,M,N);CHKERRQ(ierr);
1405     } else {
1406       ierr = MatSetSizes(A,0,0,M,N);CHKERRQ(ierr);
1407     }
1408     /* This is just a temporary matrix, so explicitly using MATMPIAIJ is probably best */
1409     ierr = MatSetType(A,MATMPIAIJ);CHKERRQ(ierr);
1410     ierr = MatMPIAIJSetPreallocation(A,0,NULL,0,NULL);CHKERRQ(ierr);
1411     ierr = MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
1412     ierr = PetscLogObjectParent((PetscObject)mat,(PetscObject)A);CHKERRQ(ierr);
1413 
1414     /* copy over the A part */
1415     Aloc = (Mat_SeqAIJ*)aij->A->data;
1416     m    = aij->A->rmap->n; ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
1417     row  = mat->rmap->rstart;
1418     for (i=0; i<ai[m]; i++) aj[i] += mat->cmap->rstart;
1419     for (i=0; i<m; i++) {
1420       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],aj,a,INSERT_VALUES);CHKERRQ(ierr);
1421       row++;
1422       a += ai[i+1]-ai[i]; aj += ai[i+1]-ai[i];
1423     }
1424     aj = Aloc->j;
1425     for (i=0; i<ai[m]; i++) aj[i] -= mat->cmap->rstart;
1426 
1427     /* copy over the B part */
1428     Aloc = (Mat_SeqAIJ*)aij->B->data;
1429     m    = aij->B->rmap->n;  ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
1430     row  = mat->rmap->rstart;
1431     ierr = PetscMalloc1(ai[m]+1,&cols);CHKERRQ(ierr);
1432     ct   = cols;
1433     for (i=0; i<ai[m]; i++) cols[i] = aij->garray[aj[i]];
1434     for (i=0; i<m; i++) {
1435       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],cols,a,INSERT_VALUES);CHKERRQ(ierr);
1436       row++;
1437       a += ai[i+1]-ai[i]; cols += ai[i+1]-ai[i];
1438     }
1439     ierr = PetscFree(ct);CHKERRQ(ierr);
1440     ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1441     ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1442     /*
1443        Everyone has to call to draw the matrix since the graphics waits are
1444        synchronized across all processors that share the PetscDraw object
1445     */
1446     ierr = PetscViewerGetSingleton(viewer,&sviewer);CHKERRQ(ierr);
1447     if (!rank) {
1448       ierr = PetscObjectSetName((PetscObject)((Mat_MPIAIJ*)(A->data))->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1449       ierr = MatView_SeqAIJ(((Mat_MPIAIJ*)(A->data))->A,sviewer);CHKERRQ(ierr);
1450     }
1451     ierr = PetscViewerRestoreSingleton(viewer,&sviewer);CHKERRQ(ierr);
1452     ierr = MatDestroy(&A);CHKERRQ(ierr);
1453   }
1454   PetscFunctionReturn(0);
1455 }
1456 
1457 #undef __FUNCT__
1458 #define __FUNCT__ "MatView_MPIAIJ"
1459 PetscErrorCode MatView_MPIAIJ(Mat mat,PetscViewer viewer)
1460 {
1461   PetscErrorCode ierr;
1462   PetscBool      iascii,isdraw,issocket,isbinary;
1463 
1464   PetscFunctionBegin;
1465   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1466   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1467   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1468   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSOCKET,&issocket);CHKERRQ(ierr);
1469   if (iascii || isdraw || isbinary || issocket) {
1470     ierr = MatView_MPIAIJ_ASCIIorDraworSocket(mat,viewer);CHKERRQ(ierr);
1471   }
1472   PetscFunctionReturn(0);
1473 }
1474 
1475 #undef __FUNCT__
1476 #define __FUNCT__ "MatSOR_MPIAIJ"
1477 PetscErrorCode MatSOR_MPIAIJ(Mat matin,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
1478 {
1479   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1480   PetscErrorCode ierr;
1481   Vec            bb1 = 0;
1482   PetscBool      hasop;
1483 
1484   PetscFunctionBegin;
1485   if (flag == SOR_APPLY_UPPER) {
1486     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1487     PetscFunctionReturn(0);
1488   }
1489 
1490   if (its > 1 || ~flag & SOR_ZERO_INITIAL_GUESS || flag & SOR_EISENSTAT) {
1491     ierr = VecDuplicate(bb,&bb1);CHKERRQ(ierr);
1492   }
1493 
1494   if ((flag & SOR_LOCAL_SYMMETRIC_SWEEP) == SOR_LOCAL_SYMMETRIC_SWEEP) {
1495     if (flag & SOR_ZERO_INITIAL_GUESS) {
1496       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1497       its--;
1498     }
1499 
1500     while (its--) {
1501       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1502       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1503 
1504       /* update rhs: bb1 = bb - B*x */
1505       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1506       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1507 
1508       /* local sweep */
1509       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_SYMMETRIC_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1510     }
1511   } else if (flag & SOR_LOCAL_FORWARD_SWEEP) {
1512     if (flag & SOR_ZERO_INITIAL_GUESS) {
1513       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1514       its--;
1515     }
1516     while (its--) {
1517       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1518       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1519 
1520       /* update rhs: bb1 = bb - B*x */
1521       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1522       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1523 
1524       /* local sweep */
1525       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_FORWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1526     }
1527   } else if (flag & SOR_LOCAL_BACKWARD_SWEEP) {
1528     if (flag & SOR_ZERO_INITIAL_GUESS) {
1529       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1530       its--;
1531     }
1532     while (its--) {
1533       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1534       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1535 
1536       /* update rhs: bb1 = bb - B*x */
1537       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1538       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1539 
1540       /* local sweep */
1541       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_BACKWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1542     }
1543   } else if (flag & SOR_EISENSTAT) {
1544     Vec xx1;
1545 
1546     ierr = VecDuplicate(bb,&xx1);CHKERRQ(ierr);
1547     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_BACKWARD_SWEEP),fshift,lits,1,xx);CHKERRQ(ierr);
1548 
1549     ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1550     ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1551     if (!mat->diag) {
1552       ierr = MatCreateVecs(matin,&mat->diag,NULL);CHKERRQ(ierr);
1553       ierr = MatGetDiagonal(matin,mat->diag);CHKERRQ(ierr);
1554     }
1555     ierr = MatHasOperation(matin,MATOP_MULT_DIAGONAL_BLOCK,&hasop);CHKERRQ(ierr);
1556     if (hasop) {
1557       ierr = MatMultDiagonalBlock(matin,xx,bb1);CHKERRQ(ierr);
1558     } else {
1559       ierr = VecPointwiseMult(bb1,mat->diag,xx);CHKERRQ(ierr);
1560     }
1561     ierr = VecAYPX(bb1,(omega-2.0)/omega,bb);CHKERRQ(ierr);
1562 
1563     ierr = MatMultAdd(mat->B,mat->lvec,bb1,bb1);CHKERRQ(ierr);
1564 
1565     /* local sweep */
1566     ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_FORWARD_SWEEP),fshift,lits,1,xx1);CHKERRQ(ierr);
1567     ierr = VecAXPY(xx,1.0,xx1);CHKERRQ(ierr);
1568     ierr = VecDestroy(&xx1);CHKERRQ(ierr);
1569   } else SETERRQ(PetscObjectComm((PetscObject)matin),PETSC_ERR_SUP,"Parallel SOR not supported");
1570 
1571   ierr = VecDestroy(&bb1);CHKERRQ(ierr);
1572   PetscFunctionReturn(0);
1573 }
1574 
1575 #undef __FUNCT__
1576 #define __FUNCT__ "MatPermute_MPIAIJ"
1577 PetscErrorCode MatPermute_MPIAIJ(Mat A,IS rowp,IS colp,Mat *B)
1578 {
1579   Mat            aA,aB,Aperm;
1580   const PetscInt *rwant,*cwant,*gcols,*ai,*bi,*aj,*bj;
1581   PetscScalar    *aa,*ba;
1582   PetscInt       i,j,m,n,ng,anz,bnz,*dnnz,*onnz,*tdnnz,*tonnz,*rdest,*cdest,*work,*gcdest;
1583   PetscSF        rowsf,sf;
1584   IS             parcolp = NULL;
1585   PetscBool      done;
1586   PetscErrorCode ierr;
1587 
1588   PetscFunctionBegin;
1589   ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
1590   ierr = ISGetIndices(rowp,&rwant);CHKERRQ(ierr);
1591   ierr = ISGetIndices(colp,&cwant);CHKERRQ(ierr);
1592   ierr = PetscMalloc3(PetscMax(m,n),&work,m,&rdest,n,&cdest);CHKERRQ(ierr);
1593 
1594   /* Invert row permutation to find out where my rows should go */
1595   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&rowsf);CHKERRQ(ierr);
1596   ierr = PetscSFSetGraphLayout(rowsf,A->rmap,A->rmap->n,NULL,PETSC_OWN_POINTER,rwant);CHKERRQ(ierr);
1597   ierr = PetscSFSetFromOptions(rowsf);CHKERRQ(ierr);
1598   for (i=0; i<m; i++) work[i] = A->rmap->rstart + i;
1599   ierr = PetscSFReduceBegin(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1600   ierr = PetscSFReduceEnd(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1601 
1602   /* Invert column permutation to find out where my columns should go */
1603   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1604   ierr = PetscSFSetGraphLayout(sf,A->cmap,A->cmap->n,NULL,PETSC_OWN_POINTER,cwant);CHKERRQ(ierr);
1605   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1606   for (i=0; i<n; i++) work[i] = A->cmap->rstart + i;
1607   ierr = PetscSFReduceBegin(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1608   ierr = PetscSFReduceEnd(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1609   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1610 
1611   ierr = ISRestoreIndices(rowp,&rwant);CHKERRQ(ierr);
1612   ierr = ISRestoreIndices(colp,&cwant);CHKERRQ(ierr);
1613   ierr = MatMPIAIJGetSeqAIJ(A,&aA,&aB,&gcols);CHKERRQ(ierr);
1614 
1615   /* Find out where my gcols should go */
1616   ierr = MatGetSize(aB,NULL,&ng);CHKERRQ(ierr);
1617   ierr = PetscMalloc1(ng,&gcdest);CHKERRQ(ierr);
1618   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1619   ierr = PetscSFSetGraphLayout(sf,A->cmap,ng,NULL,PETSC_OWN_POINTER,gcols);CHKERRQ(ierr);
1620   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1621   ierr = PetscSFBcastBegin(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1622   ierr = PetscSFBcastEnd(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1623   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1624 
1625   ierr = PetscCalloc4(m,&dnnz,m,&onnz,m,&tdnnz,m,&tonnz);CHKERRQ(ierr);
1626   ierr = MatGetRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1627   ierr = MatGetRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1628   for (i=0; i<m; i++) {
1629     PetscInt row = rdest[i],rowner;
1630     ierr = PetscLayoutFindOwner(A->rmap,row,&rowner);CHKERRQ(ierr);
1631     for (j=ai[i]; j<ai[i+1]; j++) {
1632       PetscInt cowner,col = cdest[aj[j]];
1633       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr); /* Could build an index for the columns to eliminate this search */
1634       if (rowner == cowner) dnnz[i]++;
1635       else onnz[i]++;
1636     }
1637     for (j=bi[i]; j<bi[i+1]; j++) {
1638       PetscInt cowner,col = gcdest[bj[j]];
1639       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr);
1640       if (rowner == cowner) dnnz[i]++;
1641       else onnz[i]++;
1642     }
1643   }
1644   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1645   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1646   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1647   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1648   ierr = PetscSFDestroy(&rowsf);CHKERRQ(ierr);
1649 
1650   ierr = MatCreateAIJ(PetscObjectComm((PetscObject)A),A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N,0,tdnnz,0,tonnz,&Aperm);CHKERRQ(ierr);
1651   ierr = MatSeqAIJGetArray(aA,&aa);CHKERRQ(ierr);
1652   ierr = MatSeqAIJGetArray(aB,&ba);CHKERRQ(ierr);
1653   for (i=0; i<m; i++) {
1654     PetscInt *acols = dnnz,*bcols = onnz; /* Repurpose now-unneeded arrays */
1655     PetscInt j0,rowlen;
1656     rowlen = ai[i+1] - ai[i];
1657     for (j0=j=0; j<rowlen; j0=j) { /* rowlen could be larger than number of rows m, so sum in batches */
1658       for ( ; j<PetscMin(rowlen,j0+m); j++) acols[j-j0] = cdest[aj[ai[i]+j]];
1659       ierr = MatSetValues(Aperm,1,&rdest[i],j-j0,acols,aa+ai[i]+j0,INSERT_VALUES);CHKERRQ(ierr);
1660     }
1661     rowlen = bi[i+1] - bi[i];
1662     for (j0=j=0; j<rowlen; j0=j) {
1663       for ( ; j<PetscMin(rowlen,j0+m); j++) bcols[j-j0] = gcdest[bj[bi[i]+j]];
1664       ierr = MatSetValues(Aperm,1,&rdest[i],j-j0,bcols,ba+bi[i]+j0,INSERT_VALUES);CHKERRQ(ierr);
1665     }
1666   }
1667   ierr = MatAssemblyBegin(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1668   ierr = MatAssemblyEnd(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1669   ierr = MatRestoreRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1670   ierr = MatRestoreRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1671   ierr = MatSeqAIJRestoreArray(aA,&aa);CHKERRQ(ierr);
1672   ierr = MatSeqAIJRestoreArray(aB,&ba);CHKERRQ(ierr);
1673   ierr = PetscFree4(dnnz,onnz,tdnnz,tonnz);CHKERRQ(ierr);
1674   ierr = PetscFree3(work,rdest,cdest);CHKERRQ(ierr);
1675   ierr = PetscFree(gcdest);CHKERRQ(ierr);
1676   if (parcolp) {ierr = ISDestroy(&colp);CHKERRQ(ierr);}
1677   *B = Aperm;
1678   PetscFunctionReturn(0);
1679 }
1680 
1681 #undef __FUNCT__
1682 #define __FUNCT__ "MatGetGhosts_MPIAIJ"
1683 PetscErrorCode  MatGetGhosts_MPIAIJ(Mat mat,PetscInt *nghosts,const PetscInt *ghosts[])
1684 {
1685   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1686   PetscErrorCode ierr;
1687 
1688   PetscFunctionBegin;
1689   ierr = MatGetSize(aij->B,NULL,nghosts);CHKERRQ(ierr);
1690   if (ghosts) *ghosts = aij->garray;
1691   PetscFunctionReturn(0);
1692 }
1693 
1694 #undef __FUNCT__
1695 #define __FUNCT__ "MatGetInfo_MPIAIJ"
1696 PetscErrorCode MatGetInfo_MPIAIJ(Mat matin,MatInfoType flag,MatInfo *info)
1697 {
1698   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1699   Mat            A    = mat->A,B = mat->B;
1700   PetscErrorCode ierr;
1701   PetscReal      isend[5],irecv[5];
1702 
1703   PetscFunctionBegin;
1704   info->block_size = 1.0;
1705   ierr             = MatGetInfo(A,MAT_LOCAL,info);CHKERRQ(ierr);
1706 
1707   isend[0] = info->nz_used; isend[1] = info->nz_allocated; isend[2] = info->nz_unneeded;
1708   isend[3] = info->memory;  isend[4] = info->mallocs;
1709 
1710   ierr = MatGetInfo(B,MAT_LOCAL,info);CHKERRQ(ierr);
1711 
1712   isend[0] += info->nz_used; isend[1] += info->nz_allocated; isend[2] += info->nz_unneeded;
1713   isend[3] += info->memory;  isend[4] += info->mallocs;
1714   if (flag == MAT_LOCAL) {
1715     info->nz_used      = isend[0];
1716     info->nz_allocated = isend[1];
1717     info->nz_unneeded  = isend[2];
1718     info->memory       = isend[3];
1719     info->mallocs      = isend[4];
1720   } else if (flag == MAT_GLOBAL_MAX) {
1721     ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1722 
1723     info->nz_used      = irecv[0];
1724     info->nz_allocated = irecv[1];
1725     info->nz_unneeded  = irecv[2];
1726     info->memory       = irecv[3];
1727     info->mallocs      = irecv[4];
1728   } else if (flag == MAT_GLOBAL_SUM) {
1729     ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1730 
1731     info->nz_used      = irecv[0];
1732     info->nz_allocated = irecv[1];
1733     info->nz_unneeded  = irecv[2];
1734     info->memory       = irecv[3];
1735     info->mallocs      = irecv[4];
1736   }
1737   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
1738   info->fill_ratio_needed = 0;
1739   info->factor_mallocs    = 0;
1740   PetscFunctionReturn(0);
1741 }
1742 
1743 #undef __FUNCT__
1744 #define __FUNCT__ "MatSetOption_MPIAIJ"
1745 PetscErrorCode MatSetOption_MPIAIJ(Mat A,MatOption op,PetscBool flg)
1746 {
1747   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1748   PetscErrorCode ierr;
1749 
1750   PetscFunctionBegin;
1751   switch (op) {
1752   case MAT_NEW_NONZERO_LOCATIONS:
1753   case MAT_NEW_NONZERO_ALLOCATION_ERR:
1754   case MAT_UNUSED_NONZERO_LOCATION_ERR:
1755   case MAT_KEEP_NONZERO_PATTERN:
1756   case MAT_NEW_NONZERO_LOCATION_ERR:
1757   case MAT_USE_INODES:
1758   case MAT_IGNORE_ZERO_ENTRIES:
1759     MatCheckPreallocated(A,1);
1760     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1761     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1762     break;
1763   case MAT_ROW_ORIENTED:
1764     a->roworiented = flg;
1765 
1766     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1767     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1768     break;
1769   case MAT_NEW_DIAGONALS:
1770     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
1771     break;
1772   case MAT_IGNORE_OFF_PROC_ENTRIES:
1773     a->donotstash = flg;
1774     break;
1775   case MAT_SPD:
1776     A->spd_set = PETSC_TRUE;
1777     A->spd     = flg;
1778     if (flg) {
1779       A->symmetric                  = PETSC_TRUE;
1780       A->structurally_symmetric     = PETSC_TRUE;
1781       A->symmetric_set              = PETSC_TRUE;
1782       A->structurally_symmetric_set = PETSC_TRUE;
1783     }
1784     break;
1785   case MAT_SYMMETRIC:
1786     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1787     break;
1788   case MAT_STRUCTURALLY_SYMMETRIC:
1789     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1790     break;
1791   case MAT_HERMITIAN:
1792     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1793     break;
1794   case MAT_SYMMETRY_ETERNAL:
1795     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1796     break;
1797   default:
1798     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %d",op);
1799   }
1800   PetscFunctionReturn(0);
1801 }
1802 
1803 #undef __FUNCT__
1804 #define __FUNCT__ "MatGetRow_MPIAIJ"
1805 PetscErrorCode MatGetRow_MPIAIJ(Mat matin,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1806 {
1807   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1808   PetscScalar    *vworkA,*vworkB,**pvA,**pvB,*v_p;
1809   PetscErrorCode ierr;
1810   PetscInt       i,*cworkA,*cworkB,**pcA,**pcB,cstart = matin->cmap->rstart;
1811   PetscInt       nztot,nzA,nzB,lrow,rstart = matin->rmap->rstart,rend = matin->rmap->rend;
1812   PetscInt       *cmap,*idx_p;
1813 
1814   PetscFunctionBegin;
1815   if (mat->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Already active");
1816   mat->getrowactive = PETSC_TRUE;
1817 
1818   if (!mat->rowvalues && (idx || v)) {
1819     /*
1820         allocate enough space to hold information from the longest row.
1821     */
1822     Mat_SeqAIJ *Aa = (Mat_SeqAIJ*)mat->A->data,*Ba = (Mat_SeqAIJ*)mat->B->data;
1823     PetscInt   max = 1,tmp;
1824     for (i=0; i<matin->rmap->n; i++) {
1825       tmp = Aa->i[i+1] - Aa->i[i] + Ba->i[i+1] - Ba->i[i];
1826       if (max < tmp) max = tmp;
1827     }
1828     ierr = PetscMalloc2(max,&mat->rowvalues,max,&mat->rowindices);CHKERRQ(ierr);
1829   }
1830 
1831   if (row < rstart || row >= rend) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Only local rows");
1832   lrow = row - rstart;
1833 
1834   pvA = &vworkA; pcA = &cworkA; pvB = &vworkB; pcB = &cworkB;
1835   if (!v)   {pvA = 0; pvB = 0;}
1836   if (!idx) {pcA = 0; if (!v) pcB = 0;}
1837   ierr  = (*mat->A->ops->getrow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1838   ierr  = (*mat->B->ops->getrow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1839   nztot = nzA + nzB;
1840 
1841   cmap = mat->garray;
1842   if (v  || idx) {
1843     if (nztot) {
1844       /* Sort by increasing column numbers, assuming A and B already sorted */
1845       PetscInt imark = -1;
1846       if (v) {
1847         *v = v_p = mat->rowvalues;
1848         for (i=0; i<nzB; i++) {
1849           if (cmap[cworkB[i]] < cstart) v_p[i] = vworkB[i];
1850           else break;
1851         }
1852         imark = i;
1853         for (i=0; i<nzA; i++)     v_p[imark+i] = vworkA[i];
1854         for (i=imark; i<nzB; i++) v_p[nzA+i]   = vworkB[i];
1855       }
1856       if (idx) {
1857         *idx = idx_p = mat->rowindices;
1858         if (imark > -1) {
1859           for (i=0; i<imark; i++) {
1860             idx_p[i] = cmap[cworkB[i]];
1861           }
1862         } else {
1863           for (i=0; i<nzB; i++) {
1864             if (cmap[cworkB[i]] < cstart) idx_p[i] = cmap[cworkB[i]];
1865             else break;
1866           }
1867           imark = i;
1868         }
1869         for (i=0; i<nzA; i++)     idx_p[imark+i] = cstart + cworkA[i];
1870         for (i=imark; i<nzB; i++) idx_p[nzA+i]   = cmap[cworkB[i]];
1871       }
1872     } else {
1873       if (idx) *idx = 0;
1874       if (v)   *v   = 0;
1875     }
1876   }
1877   *nz  = nztot;
1878   ierr = (*mat->A->ops->restorerow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1879   ierr = (*mat->B->ops->restorerow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1880   PetscFunctionReturn(0);
1881 }
1882 
1883 #undef __FUNCT__
1884 #define __FUNCT__ "MatRestoreRow_MPIAIJ"
1885 PetscErrorCode MatRestoreRow_MPIAIJ(Mat mat,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1886 {
1887   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1888 
1889   PetscFunctionBegin;
1890   if (!aij->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"MatGetRow() must be called first");
1891   aij->getrowactive = PETSC_FALSE;
1892   PetscFunctionReturn(0);
1893 }
1894 
1895 #undef __FUNCT__
1896 #define __FUNCT__ "MatNorm_MPIAIJ"
1897 PetscErrorCode MatNorm_MPIAIJ(Mat mat,NormType type,PetscReal *norm)
1898 {
1899   Mat_MPIAIJ     *aij  = (Mat_MPIAIJ*)mat->data;
1900   Mat_SeqAIJ     *amat = (Mat_SeqAIJ*)aij->A->data,*bmat = (Mat_SeqAIJ*)aij->B->data;
1901   PetscErrorCode ierr;
1902   PetscInt       i,j,cstart = mat->cmap->rstart;
1903   PetscReal      sum = 0.0;
1904   MatScalar      *v;
1905 
1906   PetscFunctionBegin;
1907   if (aij->size == 1) {
1908     ierr =  MatNorm(aij->A,type,norm);CHKERRQ(ierr);
1909   } else {
1910     if (type == NORM_FROBENIUS) {
1911       v = amat->a;
1912       for (i=0; i<amat->nz; i++) {
1913         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1914       }
1915       v = bmat->a;
1916       for (i=0; i<bmat->nz; i++) {
1917         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1918       }
1919       ierr  = MPI_Allreduce(&sum,norm,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1920       *norm = PetscSqrtReal(*norm);
1921     } else if (type == NORM_1) { /* max column norm */
1922       PetscReal *tmp,*tmp2;
1923       PetscInt  *jj,*garray = aij->garray;
1924       ierr  = PetscCalloc1(mat->cmap->N+1,&tmp);CHKERRQ(ierr);
1925       ierr  = PetscMalloc1(mat->cmap->N+1,&tmp2);CHKERRQ(ierr);
1926       *norm = 0.0;
1927       v     = amat->a; jj = amat->j;
1928       for (j=0; j<amat->nz; j++) {
1929         tmp[cstart + *jj++] += PetscAbsScalar(*v);  v++;
1930       }
1931       v = bmat->a; jj = bmat->j;
1932       for (j=0; j<bmat->nz; j++) {
1933         tmp[garray[*jj++]] += PetscAbsScalar(*v); v++;
1934       }
1935       ierr = MPI_Allreduce(tmp,tmp2,mat->cmap->N,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1936       for (j=0; j<mat->cmap->N; j++) {
1937         if (tmp2[j] > *norm) *norm = tmp2[j];
1938       }
1939       ierr = PetscFree(tmp);CHKERRQ(ierr);
1940       ierr = PetscFree(tmp2);CHKERRQ(ierr);
1941     } else if (type == NORM_INFINITY) { /* max row norm */
1942       PetscReal ntemp = 0.0;
1943       for (j=0; j<aij->A->rmap->n; j++) {
1944         v   = amat->a + amat->i[j];
1945         sum = 0.0;
1946         for (i=0; i<amat->i[j+1]-amat->i[j]; i++) {
1947           sum += PetscAbsScalar(*v); v++;
1948         }
1949         v = bmat->a + bmat->i[j];
1950         for (i=0; i<bmat->i[j+1]-bmat->i[j]; i++) {
1951           sum += PetscAbsScalar(*v); v++;
1952         }
1953         if (sum > ntemp) ntemp = sum;
1954       }
1955       ierr = MPI_Allreduce(&ntemp,norm,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1956     } else SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"No support for two norm");
1957   }
1958   PetscFunctionReturn(0);
1959 }
1960 
1961 #undef __FUNCT__
1962 #define __FUNCT__ "MatTranspose_MPIAIJ"
1963 PetscErrorCode MatTranspose_MPIAIJ(Mat A,MatReuse reuse,Mat *matout)
1964 {
1965   Mat_MPIAIJ     *a   = (Mat_MPIAIJ*)A->data;
1966   Mat_SeqAIJ     *Aloc=(Mat_SeqAIJ*)a->A->data,*Bloc=(Mat_SeqAIJ*)a->B->data;
1967   PetscErrorCode ierr;
1968   PetscInt       M      = A->rmap->N,N = A->cmap->N,ma,na,mb,nb,*ai,*aj,*bi,*bj,row,*cols,*cols_tmp,i;
1969   PetscInt       cstart = A->cmap->rstart,ncol;
1970   Mat            B;
1971   MatScalar      *array;
1972 
1973   PetscFunctionBegin;
1974   if (reuse == MAT_REUSE_MATRIX && A == *matout && M != N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Square matrix only for in-place");
1975 
1976   ma = A->rmap->n; na = A->cmap->n; mb = a->B->rmap->n; nb = a->B->cmap->n;
1977   ai = Aloc->i; aj = Aloc->j;
1978   bi = Bloc->i; bj = Bloc->j;
1979   if (reuse == MAT_INITIAL_MATRIX || *matout == A) {
1980     PetscInt             *d_nnz,*g_nnz,*o_nnz;
1981     PetscSFNode          *oloc;
1982     PETSC_UNUSED PetscSF sf;
1983 
1984     ierr = PetscMalloc4(na,&d_nnz,na,&o_nnz,nb,&g_nnz,nb,&oloc);CHKERRQ(ierr);
1985     /* compute d_nnz for preallocation */
1986     ierr = PetscMemzero(d_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1987     for (i=0; i<ai[ma]; i++) {
1988       d_nnz[aj[i]]++;
1989       aj[i] += cstart; /* global col index to be used by MatSetValues() */
1990     }
1991     /* compute local off-diagonal contributions */
1992     ierr = PetscMemzero(g_nnz,nb*sizeof(PetscInt));CHKERRQ(ierr);
1993     for (i=0; i<bi[ma]; i++) g_nnz[bj[i]]++;
1994     /* map those to global */
1995     ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1996     ierr = PetscSFSetGraphLayout(sf,A->cmap,nb,NULL,PETSC_USE_POINTER,a->garray);CHKERRQ(ierr);
1997     ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1998     ierr = PetscMemzero(o_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1999     ierr = PetscSFReduceBegin(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
2000     ierr = PetscSFReduceEnd(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
2001     ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
2002 
2003     ierr = MatCreate(PetscObjectComm((PetscObject)A),&B);CHKERRQ(ierr);
2004     ierr = MatSetSizes(B,A->cmap->n,A->rmap->n,N,M);CHKERRQ(ierr);
2005     ierr = MatSetBlockSizes(B,PetscAbs(A->cmap->bs),PetscAbs(A->rmap->bs));CHKERRQ(ierr);
2006     ierr = MatSetType(B,((PetscObject)A)->type_name);CHKERRQ(ierr);
2007     ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
2008     ierr = PetscFree4(d_nnz,o_nnz,g_nnz,oloc);CHKERRQ(ierr);
2009   } else {
2010     B    = *matout;
2011     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
2012     for (i=0; i<ai[ma]; i++) aj[i] += cstart; /* global col index to be used by MatSetValues() */
2013   }
2014 
2015   /* copy over the A part */
2016   array = Aloc->a;
2017   row   = A->rmap->rstart;
2018   for (i=0; i<ma; i++) {
2019     ncol = ai[i+1]-ai[i];
2020     ierr = MatSetValues(B,ncol,aj,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
2021     row++;
2022     array += ncol; aj += ncol;
2023   }
2024   aj = Aloc->j;
2025   for (i=0; i<ai[ma]; i++) aj[i] -= cstart; /* resume local col index */
2026 
2027   /* copy over the B part */
2028   ierr  = PetscCalloc1(bi[mb],&cols);CHKERRQ(ierr);
2029   array = Bloc->a;
2030   row   = A->rmap->rstart;
2031   for (i=0; i<bi[mb]; i++) cols[i] = a->garray[bj[i]];
2032   cols_tmp = cols;
2033   for (i=0; i<mb; i++) {
2034     ncol = bi[i+1]-bi[i];
2035     ierr = MatSetValues(B,ncol,cols_tmp,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
2036     row++;
2037     array += ncol; cols_tmp += ncol;
2038   }
2039   ierr = PetscFree(cols);CHKERRQ(ierr);
2040 
2041   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2042   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2043   if (reuse == MAT_INITIAL_MATRIX || *matout != A) {
2044     *matout = B;
2045   } else {
2046     ierr = MatHeaderMerge(A,B);CHKERRQ(ierr);
2047   }
2048   PetscFunctionReturn(0);
2049 }
2050 
2051 #undef __FUNCT__
2052 #define __FUNCT__ "MatDiagonalScale_MPIAIJ"
2053 PetscErrorCode MatDiagonalScale_MPIAIJ(Mat mat,Vec ll,Vec rr)
2054 {
2055   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2056   Mat            a    = aij->A,b = aij->B;
2057   PetscErrorCode ierr;
2058   PetscInt       s1,s2,s3;
2059 
2060   PetscFunctionBegin;
2061   ierr = MatGetLocalSize(mat,&s2,&s3);CHKERRQ(ierr);
2062   if (rr) {
2063     ierr = VecGetLocalSize(rr,&s1);CHKERRQ(ierr);
2064     if (s1!=s3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"right vector non-conforming local size");
2065     /* Overlap communication with computation. */
2066     ierr = VecScatterBegin(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2067   }
2068   if (ll) {
2069     ierr = VecGetLocalSize(ll,&s1);CHKERRQ(ierr);
2070     if (s1!=s2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"left vector non-conforming local size");
2071     ierr = (*b->ops->diagonalscale)(b,ll,0);CHKERRQ(ierr);
2072   }
2073   /* scale  the diagonal block */
2074   ierr = (*a->ops->diagonalscale)(a,ll,rr);CHKERRQ(ierr);
2075 
2076   if (rr) {
2077     /* Do a scatter end and then right scale the off-diagonal block */
2078     ierr = VecScatterEnd(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2079     ierr = (*b->ops->diagonalscale)(b,0,aij->lvec);CHKERRQ(ierr);
2080   }
2081   PetscFunctionReturn(0);
2082 }
2083 
2084 #undef __FUNCT__
2085 #define __FUNCT__ "MatSetUnfactored_MPIAIJ"
2086 PetscErrorCode MatSetUnfactored_MPIAIJ(Mat A)
2087 {
2088   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2089   PetscErrorCode ierr;
2090 
2091   PetscFunctionBegin;
2092   ierr = MatSetUnfactored(a->A);CHKERRQ(ierr);
2093   PetscFunctionReturn(0);
2094 }
2095 
2096 #undef __FUNCT__
2097 #define __FUNCT__ "MatEqual_MPIAIJ"
2098 PetscErrorCode MatEqual_MPIAIJ(Mat A,Mat B,PetscBool  *flag)
2099 {
2100   Mat_MPIAIJ     *matB = (Mat_MPIAIJ*)B->data,*matA = (Mat_MPIAIJ*)A->data;
2101   Mat            a,b,c,d;
2102   PetscBool      flg;
2103   PetscErrorCode ierr;
2104 
2105   PetscFunctionBegin;
2106   a = matA->A; b = matA->B;
2107   c = matB->A; d = matB->B;
2108 
2109   ierr = MatEqual(a,c,&flg);CHKERRQ(ierr);
2110   if (flg) {
2111     ierr = MatEqual(b,d,&flg);CHKERRQ(ierr);
2112   }
2113   ierr = MPI_Allreduce(&flg,flag,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
2114   PetscFunctionReturn(0);
2115 }
2116 
2117 #undef __FUNCT__
2118 #define __FUNCT__ "MatCopy_MPIAIJ"
2119 PetscErrorCode MatCopy_MPIAIJ(Mat A,Mat B,MatStructure str)
2120 {
2121   PetscErrorCode ierr;
2122   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2123   Mat_MPIAIJ     *b = (Mat_MPIAIJ*)B->data;
2124 
2125   PetscFunctionBegin;
2126   /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
2127   if ((str != SAME_NONZERO_PATTERN) || (A->ops->copy != B->ops->copy)) {
2128     /* because of the column compression in the off-processor part of the matrix a->B,
2129        the number of columns in a->B and b->B may be different, hence we cannot call
2130        the MatCopy() directly on the two parts. If need be, we can provide a more
2131        efficient copy than the MatCopy_Basic() by first uncompressing the a->B matrices
2132        then copying the submatrices */
2133     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
2134   } else {
2135     ierr = MatCopy(a->A,b->A,str);CHKERRQ(ierr);
2136     ierr = MatCopy(a->B,b->B,str);CHKERRQ(ierr);
2137   }
2138   PetscFunctionReturn(0);
2139 }
2140 
2141 #undef __FUNCT__
2142 #define __FUNCT__ "MatSetUp_MPIAIJ"
2143 PetscErrorCode MatSetUp_MPIAIJ(Mat A)
2144 {
2145   PetscErrorCode ierr;
2146 
2147   PetscFunctionBegin;
2148   ierr =  MatMPIAIJSetPreallocation(A,PETSC_DEFAULT,0,PETSC_DEFAULT,0);CHKERRQ(ierr);
2149   PetscFunctionReturn(0);
2150 }
2151 
2152 /*
2153    Computes the number of nonzeros per row needed for preallocation when X and Y
2154    have different nonzero structure.
2155 */
2156 #undef __FUNCT__
2157 #define __FUNCT__ "MatAXPYGetPreallocation_MPIX_private"
2158 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)
2159 {
2160   PetscInt       i,j,k,nzx,nzy;
2161 
2162   PetscFunctionBegin;
2163   /* Set the number of nonzeros in the new matrix */
2164   for (i=0; i<m; i++) {
2165     const PetscInt *xjj = xj+xi[i],*yjj = yj+yi[i];
2166     nzx = xi[i+1] - xi[i];
2167     nzy = yi[i+1] - yi[i];
2168     nnz[i] = 0;
2169     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2170       for (; k<nzy && yltog[yjj[k]]<xltog[xjj[j]]; k++) nnz[i]++; /* Catch up to X */
2171       if (k<nzy && yltog[yjj[k]]==xltog[xjj[j]]) k++;             /* Skip duplicate */
2172       nnz[i]++;
2173     }
2174     for (; k<nzy; k++) nnz[i]++;
2175   }
2176   PetscFunctionReturn(0);
2177 }
2178 
2179 /* This is the same as MatAXPYGetPreallocation_SeqAIJ, except that the local-to-global map is provided */
2180 #undef __FUNCT__
2181 #define __FUNCT__ "MatAXPYGetPreallocation_MPIAIJ"
2182 static PetscErrorCode MatAXPYGetPreallocation_MPIAIJ(Mat Y,const PetscInt *yltog,Mat X,const PetscInt *xltog,PetscInt *nnz)
2183 {
2184   PetscErrorCode ierr;
2185   PetscInt       m = Y->rmap->N;
2186   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data;
2187   Mat_SeqAIJ     *y = (Mat_SeqAIJ*)Y->data;
2188 
2189   PetscFunctionBegin;
2190   ierr = MatAXPYGetPreallocation_MPIX_private(m,x->i,x->j,xltog,y->i,y->j,yltog,nnz);CHKERRQ(ierr);
2191   PetscFunctionReturn(0);
2192 }
2193 
2194 #undef __FUNCT__
2195 #define __FUNCT__ "MatAXPY_MPIAIJ"
2196 PetscErrorCode MatAXPY_MPIAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
2197 {
2198   PetscErrorCode ierr;
2199   Mat_MPIAIJ     *xx = (Mat_MPIAIJ*)X->data,*yy = (Mat_MPIAIJ*)Y->data;
2200   PetscBLASInt   bnz,one=1;
2201   Mat_SeqAIJ     *x,*y;
2202 
2203   PetscFunctionBegin;
2204   if (str == SAME_NONZERO_PATTERN) {
2205     PetscScalar alpha = a;
2206     x    = (Mat_SeqAIJ*)xx->A->data;
2207     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2208     y    = (Mat_SeqAIJ*)yy->A->data;
2209     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2210     x    = (Mat_SeqAIJ*)xx->B->data;
2211     y    = (Mat_SeqAIJ*)yy->B->data;
2212     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2213     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2214     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
2215   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
2216     ierr = MatAXPY_Basic(Y,a,X,str);CHKERRQ(ierr);
2217   } else {
2218     Mat      B;
2219     PetscInt *nnz_d,*nnz_o;
2220     ierr = PetscMalloc1(yy->A->rmap->N,&nnz_d);CHKERRQ(ierr);
2221     ierr = PetscMalloc1(yy->B->rmap->N,&nnz_o);CHKERRQ(ierr);
2222     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
2223     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
2224     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
2225     ierr = MatSetBlockSizesFromMats(B,Y,Y);CHKERRQ(ierr);
2226     ierr = MatSetType(B,MATMPIAIJ);CHKERRQ(ierr);
2227     ierr = MatAXPYGetPreallocation_SeqAIJ(yy->A,xx->A,nnz_d);CHKERRQ(ierr);
2228     ierr = MatAXPYGetPreallocation_MPIAIJ(yy->B,yy->garray,xx->B,xx->garray,nnz_o);CHKERRQ(ierr);
2229     ierr = MatMPIAIJSetPreallocation(B,0,nnz_d,0,nnz_o);CHKERRQ(ierr);
2230     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
2231     ierr = MatHeaderReplace(Y,B);CHKERRQ(ierr);
2232     ierr = PetscFree(nnz_d);CHKERRQ(ierr);
2233     ierr = PetscFree(nnz_o);CHKERRQ(ierr);
2234   }
2235   PetscFunctionReturn(0);
2236 }
2237 
2238 extern PetscErrorCode  MatConjugate_SeqAIJ(Mat);
2239 
2240 #undef __FUNCT__
2241 #define __FUNCT__ "MatConjugate_MPIAIJ"
2242 PetscErrorCode  MatConjugate_MPIAIJ(Mat mat)
2243 {
2244 #if defined(PETSC_USE_COMPLEX)
2245   PetscErrorCode ierr;
2246   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2247 
2248   PetscFunctionBegin;
2249   ierr = MatConjugate_SeqAIJ(aij->A);CHKERRQ(ierr);
2250   ierr = MatConjugate_SeqAIJ(aij->B);CHKERRQ(ierr);
2251 #else
2252   PetscFunctionBegin;
2253 #endif
2254   PetscFunctionReturn(0);
2255 }
2256 
2257 #undef __FUNCT__
2258 #define __FUNCT__ "MatRealPart_MPIAIJ"
2259 PetscErrorCode MatRealPart_MPIAIJ(Mat A)
2260 {
2261   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2262   PetscErrorCode ierr;
2263 
2264   PetscFunctionBegin;
2265   ierr = MatRealPart(a->A);CHKERRQ(ierr);
2266   ierr = MatRealPart(a->B);CHKERRQ(ierr);
2267   PetscFunctionReturn(0);
2268 }
2269 
2270 #undef __FUNCT__
2271 #define __FUNCT__ "MatImaginaryPart_MPIAIJ"
2272 PetscErrorCode MatImaginaryPart_MPIAIJ(Mat A)
2273 {
2274   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2275   PetscErrorCode ierr;
2276 
2277   PetscFunctionBegin;
2278   ierr = MatImaginaryPart(a->A);CHKERRQ(ierr);
2279   ierr = MatImaginaryPart(a->B);CHKERRQ(ierr);
2280   PetscFunctionReturn(0);
2281 }
2282 
2283 #undef __FUNCT__
2284 #define __FUNCT__ "MatGetRowMaxAbs_MPIAIJ"
2285 PetscErrorCode MatGetRowMaxAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2286 {
2287   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2288   PetscErrorCode ierr;
2289   PetscInt       i,*idxb = 0;
2290   PetscScalar    *va,*vb;
2291   Vec            vtmp;
2292 
2293   PetscFunctionBegin;
2294   ierr = MatGetRowMaxAbs(a->A,v,idx);CHKERRQ(ierr);
2295   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2296   if (idx) {
2297     for (i=0; i<A->rmap->n; i++) {
2298       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2299     }
2300   }
2301 
2302   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2303   if (idx) {
2304     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2305   }
2306   ierr = MatGetRowMaxAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2307   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2308 
2309   for (i=0; i<A->rmap->n; i++) {
2310     if (PetscAbsScalar(va[i]) < PetscAbsScalar(vb[i])) {
2311       va[i] = vb[i];
2312       if (idx) idx[i] = a->garray[idxb[i]];
2313     }
2314   }
2315 
2316   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2317   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2318   ierr = PetscFree(idxb);CHKERRQ(ierr);
2319   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2320   PetscFunctionReturn(0);
2321 }
2322 
2323 #undef __FUNCT__
2324 #define __FUNCT__ "MatGetRowMinAbs_MPIAIJ"
2325 PetscErrorCode MatGetRowMinAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2326 {
2327   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2328   PetscErrorCode ierr;
2329   PetscInt       i,*idxb = 0;
2330   PetscScalar    *va,*vb;
2331   Vec            vtmp;
2332 
2333   PetscFunctionBegin;
2334   ierr = MatGetRowMinAbs(a->A,v,idx);CHKERRQ(ierr);
2335   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2336   if (idx) {
2337     for (i=0; i<A->cmap->n; i++) {
2338       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2339     }
2340   }
2341 
2342   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2343   if (idx) {
2344     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2345   }
2346   ierr = MatGetRowMinAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2347   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2348 
2349   for (i=0; i<A->rmap->n; i++) {
2350     if (PetscAbsScalar(va[i]) > PetscAbsScalar(vb[i])) {
2351       va[i] = vb[i];
2352       if (idx) idx[i] = a->garray[idxb[i]];
2353     }
2354   }
2355 
2356   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2357   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2358   ierr = PetscFree(idxb);CHKERRQ(ierr);
2359   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2360   PetscFunctionReturn(0);
2361 }
2362 
2363 #undef __FUNCT__
2364 #define __FUNCT__ "MatGetRowMin_MPIAIJ"
2365 PetscErrorCode MatGetRowMin_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2366 {
2367   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2368   PetscInt       n      = A->rmap->n;
2369   PetscInt       cstart = A->cmap->rstart;
2370   PetscInt       *cmap  = mat->garray;
2371   PetscInt       *diagIdx, *offdiagIdx;
2372   Vec            diagV, offdiagV;
2373   PetscScalar    *a, *diagA, *offdiagA;
2374   PetscInt       r;
2375   PetscErrorCode ierr;
2376 
2377   PetscFunctionBegin;
2378   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2379   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &diagV);CHKERRQ(ierr);
2380   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &offdiagV);CHKERRQ(ierr);
2381   ierr = MatGetRowMin(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2382   ierr = MatGetRowMin(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2383   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2384   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2385   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2386   for (r = 0; r < n; ++r) {
2387     if (PetscAbsScalar(diagA[r]) <= PetscAbsScalar(offdiagA[r])) {
2388       a[r]   = diagA[r];
2389       idx[r] = cstart + diagIdx[r];
2390     } else {
2391       a[r]   = offdiagA[r];
2392       idx[r] = cmap[offdiagIdx[r]];
2393     }
2394   }
2395   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2396   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2397   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2398   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2399   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2400   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2401   PetscFunctionReturn(0);
2402 }
2403 
2404 #undef __FUNCT__
2405 #define __FUNCT__ "MatGetRowMax_MPIAIJ"
2406 PetscErrorCode MatGetRowMax_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2407 {
2408   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2409   PetscInt       n      = A->rmap->n;
2410   PetscInt       cstart = A->cmap->rstart;
2411   PetscInt       *cmap  = mat->garray;
2412   PetscInt       *diagIdx, *offdiagIdx;
2413   Vec            diagV, offdiagV;
2414   PetscScalar    *a, *diagA, *offdiagA;
2415   PetscInt       r;
2416   PetscErrorCode ierr;
2417 
2418   PetscFunctionBegin;
2419   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2420   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &diagV);CHKERRQ(ierr);
2421   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &offdiagV);CHKERRQ(ierr);
2422   ierr = MatGetRowMax(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2423   ierr = MatGetRowMax(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2424   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2425   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2426   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2427   for (r = 0; r < n; ++r) {
2428     if (PetscAbsScalar(diagA[r]) >= PetscAbsScalar(offdiagA[r])) {
2429       a[r]   = diagA[r];
2430       idx[r] = cstart + diagIdx[r];
2431     } else {
2432       a[r]   = offdiagA[r];
2433       idx[r] = cmap[offdiagIdx[r]];
2434     }
2435   }
2436   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2437   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2438   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2439   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2440   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2441   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2442   PetscFunctionReturn(0);
2443 }
2444 
2445 #undef __FUNCT__
2446 #define __FUNCT__ "MatGetSeqNonzeroStructure_MPIAIJ"
2447 PetscErrorCode MatGetSeqNonzeroStructure_MPIAIJ(Mat mat,Mat *newmat)
2448 {
2449   PetscErrorCode ierr;
2450   Mat            *dummy;
2451 
2452   PetscFunctionBegin;
2453   ierr    = MatGetSubMatrix_MPIAIJ_All(mat,MAT_DO_NOT_GET_VALUES,MAT_INITIAL_MATRIX,&dummy);CHKERRQ(ierr);
2454   *newmat = *dummy;
2455   ierr    = PetscFree(dummy);CHKERRQ(ierr);
2456   PetscFunctionReturn(0);
2457 }
2458 
2459 #undef __FUNCT__
2460 #define __FUNCT__ "MatInvertBlockDiagonal_MPIAIJ"
2461 PetscErrorCode  MatInvertBlockDiagonal_MPIAIJ(Mat A,const PetscScalar **values)
2462 {
2463   Mat_MPIAIJ     *a = (Mat_MPIAIJ*) A->data;
2464   PetscErrorCode ierr;
2465 
2466   PetscFunctionBegin;
2467   ierr = MatInvertBlockDiagonal(a->A,values);CHKERRQ(ierr);
2468   PetscFunctionReturn(0);
2469 }
2470 
2471 #undef __FUNCT__
2472 #define __FUNCT__ "MatSetRandom_MPIAIJ"
2473 static PetscErrorCode  MatSetRandom_MPIAIJ(Mat x,PetscRandom rctx)
2474 {
2475   PetscErrorCode ierr;
2476   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)x->data;
2477 
2478   PetscFunctionBegin;
2479   ierr = MatSetRandom(aij->A,rctx);CHKERRQ(ierr);
2480   ierr = MatSetRandom(aij->B,rctx);CHKERRQ(ierr);
2481   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2482   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2483   PetscFunctionReturn(0);
2484 }
2485 
2486 #undef __FUNCT__
2487 #define __FUNCT__ "MatShift_MPIAIJ"
2488 PetscErrorCode MatShift_MPIAIJ(Mat Y,PetscScalar a)
2489 {
2490   PetscErrorCode ierr;
2491   Mat_MPIAIJ     *maij = (Mat_MPIAIJ*)Y->data;
2492   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)maij->A->data,*bij = (Mat_SeqAIJ*)maij->B->data;
2493 
2494   PetscFunctionBegin;
2495   if (!aij->nz && !bij->nz) {
2496     ierr = MatMPIAIJSetPreallocation(Y,1,NULL,0,NULL);CHKERRQ(ierr);
2497   }
2498   ierr = MatShift_Basic(Y,a);CHKERRQ(ierr);
2499   PetscFunctionReturn(0);
2500 }
2501 
2502 /* -------------------------------------------------------------------*/
2503 static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
2504                                        MatGetRow_MPIAIJ,
2505                                        MatRestoreRow_MPIAIJ,
2506                                        MatMult_MPIAIJ,
2507                                 /* 4*/ MatMultAdd_MPIAIJ,
2508                                        MatMultTranspose_MPIAIJ,
2509                                        MatMultTransposeAdd_MPIAIJ,
2510                                        0,
2511                                        0,
2512                                        0,
2513                                 /*10*/ 0,
2514                                        0,
2515                                        0,
2516                                        MatSOR_MPIAIJ,
2517                                        MatTranspose_MPIAIJ,
2518                                 /*15*/ MatGetInfo_MPIAIJ,
2519                                        MatEqual_MPIAIJ,
2520                                        MatGetDiagonal_MPIAIJ,
2521                                        MatDiagonalScale_MPIAIJ,
2522                                        MatNorm_MPIAIJ,
2523                                 /*20*/ MatAssemblyBegin_MPIAIJ,
2524                                        MatAssemblyEnd_MPIAIJ,
2525                                        MatSetOption_MPIAIJ,
2526                                        MatZeroEntries_MPIAIJ,
2527                                 /*24*/ MatZeroRows_MPIAIJ,
2528                                        0,
2529                                        0,
2530                                        0,
2531                                        0,
2532                                 /*29*/ MatSetUp_MPIAIJ,
2533                                        0,
2534                                        0,
2535                                        0,
2536                                        0,
2537                                 /*34*/ MatDuplicate_MPIAIJ,
2538                                        0,
2539                                        0,
2540                                        0,
2541                                        0,
2542                                 /*39*/ MatAXPY_MPIAIJ,
2543                                        MatGetSubMatrices_MPIAIJ,
2544                                        MatIncreaseOverlap_MPIAIJ,
2545                                        MatGetValues_MPIAIJ,
2546                                        MatCopy_MPIAIJ,
2547                                 /*44*/ MatGetRowMax_MPIAIJ,
2548                                        MatScale_MPIAIJ,
2549                                        MatShift_MPIAIJ,
2550                                        MatDiagonalSet_MPIAIJ,
2551                                        MatZeroRowsColumns_MPIAIJ,
2552                                 /*49*/ MatSetRandom_MPIAIJ,
2553                                        0,
2554                                        0,
2555                                        0,
2556                                        0,
2557                                 /*54*/ MatFDColoringCreate_MPIXAIJ,
2558                                        0,
2559                                        MatSetUnfactored_MPIAIJ,
2560                                        MatPermute_MPIAIJ,
2561                                        0,
2562                                 /*59*/ MatGetSubMatrix_MPIAIJ,
2563                                        MatDestroy_MPIAIJ,
2564                                        MatView_MPIAIJ,
2565                                        0,
2566                                        MatMatMatMult_MPIAIJ_MPIAIJ_MPIAIJ,
2567                                 /*64*/ MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ,
2568                                        MatMatMatMultNumeric_MPIAIJ_MPIAIJ_MPIAIJ,
2569                                        0,
2570                                        0,
2571                                        0,
2572                                 /*69*/ MatGetRowMaxAbs_MPIAIJ,
2573                                        MatGetRowMinAbs_MPIAIJ,
2574                                        0,
2575                                        MatSetColoring_MPIAIJ,
2576                                        0,
2577                                        MatSetValuesAdifor_MPIAIJ,
2578                                 /*75*/ MatFDColoringApply_AIJ,
2579                                        0,
2580                                        0,
2581                                        0,
2582                                        MatFindZeroDiagonals_MPIAIJ,
2583                                 /*80*/ 0,
2584                                        0,
2585                                        0,
2586                                 /*83*/ MatLoad_MPIAIJ,
2587                                        0,
2588                                        0,
2589                                        0,
2590                                        0,
2591                                        0,
2592                                 /*89*/ MatMatMult_MPIAIJ_MPIAIJ,
2593                                        MatMatMultSymbolic_MPIAIJ_MPIAIJ,
2594                                        MatMatMultNumeric_MPIAIJ_MPIAIJ,
2595                                        MatPtAP_MPIAIJ_MPIAIJ,
2596                                        MatPtAPSymbolic_MPIAIJ_MPIAIJ,
2597                                 /*94*/ MatPtAPNumeric_MPIAIJ_MPIAIJ,
2598                                        0,
2599                                        0,
2600                                        0,
2601                                        0,
2602                                 /*99*/ 0,
2603                                        0,
2604                                        0,
2605                                        MatConjugate_MPIAIJ,
2606                                        0,
2607                                 /*104*/MatSetValuesRow_MPIAIJ,
2608                                        MatRealPart_MPIAIJ,
2609                                        MatImaginaryPart_MPIAIJ,
2610                                        0,
2611                                        0,
2612                                 /*109*/0,
2613                                        0,
2614                                        MatGetRowMin_MPIAIJ,
2615                                        0,
2616                                        0,
2617                                 /*114*/MatGetSeqNonzeroStructure_MPIAIJ,
2618                                        0,
2619                                        MatGetGhosts_MPIAIJ,
2620                                        0,
2621                                        0,
2622                                 /*119*/0,
2623                                        0,
2624                                        0,
2625                                        0,
2626                                        MatGetMultiProcBlock_MPIAIJ,
2627                                 /*124*/MatFindNonzeroRows_MPIAIJ,
2628                                        MatGetColumnNorms_MPIAIJ,
2629                                        MatInvertBlockDiagonal_MPIAIJ,
2630                                        0,
2631                                        MatGetSubMatricesMPI_MPIAIJ,
2632                                 /*129*/0,
2633                                        MatTransposeMatMult_MPIAIJ_MPIAIJ,
2634                                        MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ,
2635                                        MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ,
2636                                        0,
2637                                 /*134*/0,
2638                                        0,
2639                                        0,
2640                                        0,
2641                                        0,
2642                                 /*139*/0,
2643                                        0,
2644                                        0,
2645                                        MatFDColoringSetUp_MPIXAIJ,
2646                                        MatFindOffBlockDiagonalEntries_MPIAIJ,
2647                                 /*144*/MatCreateMPIMatConcatenateSeqMat_MPIAIJ
2648 };
2649 
2650 /* ----------------------------------------------------------------------------------------*/
2651 
2652 #undef __FUNCT__
2653 #define __FUNCT__ "MatStoreValues_MPIAIJ"
2654 PetscErrorCode  MatStoreValues_MPIAIJ(Mat mat)
2655 {
2656   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2657   PetscErrorCode ierr;
2658 
2659   PetscFunctionBegin;
2660   ierr = MatStoreValues(aij->A);CHKERRQ(ierr);
2661   ierr = MatStoreValues(aij->B);CHKERRQ(ierr);
2662   PetscFunctionReturn(0);
2663 }
2664 
2665 #undef __FUNCT__
2666 #define __FUNCT__ "MatRetrieveValues_MPIAIJ"
2667 PetscErrorCode  MatRetrieveValues_MPIAIJ(Mat mat)
2668 {
2669   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2670   PetscErrorCode ierr;
2671 
2672   PetscFunctionBegin;
2673   ierr = MatRetrieveValues(aij->A);CHKERRQ(ierr);
2674   ierr = MatRetrieveValues(aij->B);CHKERRQ(ierr);
2675   PetscFunctionReturn(0);
2676 }
2677 
2678 #undef __FUNCT__
2679 #define __FUNCT__ "MatMPIAIJSetPreallocation_MPIAIJ"
2680 PetscErrorCode  MatMPIAIJSetPreallocation_MPIAIJ(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
2681 {
2682   Mat_MPIAIJ     *b;
2683   PetscErrorCode ierr;
2684 
2685   PetscFunctionBegin;
2686   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
2687   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
2688   b = (Mat_MPIAIJ*)B->data;
2689 
2690   if (!B->preallocated) {
2691     /* Explicitly create 2 MATSEQAIJ matrices. */
2692     ierr = MatCreate(PETSC_COMM_SELF,&b->A);CHKERRQ(ierr);
2693     ierr = MatSetSizes(b->A,B->rmap->n,B->cmap->n,B->rmap->n,B->cmap->n);CHKERRQ(ierr);
2694     ierr = MatSetBlockSizesFromMats(b->A,B,B);CHKERRQ(ierr);
2695     ierr = MatSetType(b->A,MATSEQAIJ);CHKERRQ(ierr);
2696     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->A);CHKERRQ(ierr);
2697     ierr = MatCreate(PETSC_COMM_SELF,&b->B);CHKERRQ(ierr);
2698     ierr = MatSetSizes(b->B,B->rmap->n,B->cmap->N,B->rmap->n,B->cmap->N);CHKERRQ(ierr);
2699     ierr = MatSetBlockSizesFromMats(b->B,B,B);CHKERRQ(ierr);
2700     ierr = MatSetType(b->B,MATSEQAIJ);CHKERRQ(ierr);
2701     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->B);CHKERRQ(ierr);
2702   }
2703 
2704   ierr = MatSeqAIJSetPreallocation(b->A,d_nz,d_nnz);CHKERRQ(ierr);
2705   ierr = MatSeqAIJSetPreallocation(b->B,o_nz,o_nnz);CHKERRQ(ierr);
2706   B->preallocated = PETSC_TRUE;
2707   PetscFunctionReturn(0);
2708 }
2709 
2710 #undef __FUNCT__
2711 #define __FUNCT__ "MatDuplicate_MPIAIJ"
2712 PetscErrorCode MatDuplicate_MPIAIJ(Mat matin,MatDuplicateOption cpvalues,Mat *newmat)
2713 {
2714   Mat            mat;
2715   Mat_MPIAIJ     *a,*oldmat = (Mat_MPIAIJ*)matin->data;
2716   PetscErrorCode ierr;
2717 
2718   PetscFunctionBegin;
2719   *newmat = 0;
2720   ierr    = MatCreate(PetscObjectComm((PetscObject)matin),&mat);CHKERRQ(ierr);
2721   ierr    = MatSetSizes(mat,matin->rmap->n,matin->cmap->n,matin->rmap->N,matin->cmap->N);CHKERRQ(ierr);
2722   ierr    = MatSetBlockSizesFromMats(mat,matin,matin);CHKERRQ(ierr);
2723   ierr    = MatSetType(mat,((PetscObject)matin)->type_name);CHKERRQ(ierr);
2724   ierr    = PetscMemcpy(mat->ops,matin->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
2725   a       = (Mat_MPIAIJ*)mat->data;
2726 
2727   mat->factortype   = matin->factortype;
2728   mat->assembled    = PETSC_TRUE;
2729   mat->insertmode   = NOT_SET_VALUES;
2730   mat->preallocated = PETSC_TRUE;
2731 
2732   a->size         = oldmat->size;
2733   a->rank         = oldmat->rank;
2734   a->donotstash   = oldmat->donotstash;
2735   a->roworiented  = oldmat->roworiented;
2736   a->rowindices   = 0;
2737   a->rowvalues    = 0;
2738   a->getrowactive = PETSC_FALSE;
2739 
2740   ierr = PetscLayoutReference(matin->rmap,&mat->rmap);CHKERRQ(ierr);
2741   ierr = PetscLayoutReference(matin->cmap,&mat->cmap);CHKERRQ(ierr);
2742 
2743   if (oldmat->colmap) {
2744 #if defined(PETSC_USE_CTABLE)
2745     ierr = PetscTableCreateCopy(oldmat->colmap,&a->colmap);CHKERRQ(ierr);
2746 #else
2747     ierr = PetscMalloc1(mat->cmap->N,&a->colmap);CHKERRQ(ierr);
2748     ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2749     ierr = PetscMemcpy(a->colmap,oldmat->colmap,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2750 #endif
2751   } else a->colmap = 0;
2752   if (oldmat->garray) {
2753     PetscInt len;
2754     len  = oldmat->B->cmap->n;
2755     ierr = PetscMalloc1(len+1,&a->garray);CHKERRQ(ierr);
2756     ierr = PetscLogObjectMemory((PetscObject)mat,len*sizeof(PetscInt));CHKERRQ(ierr);
2757     if (len) { ierr = PetscMemcpy(a->garray,oldmat->garray,len*sizeof(PetscInt));CHKERRQ(ierr); }
2758   } else a->garray = 0;
2759 
2760   ierr    = VecDuplicate(oldmat->lvec,&a->lvec);CHKERRQ(ierr);
2761   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->lvec);CHKERRQ(ierr);
2762   ierr    = VecScatterCopy(oldmat->Mvctx,&a->Mvctx);CHKERRQ(ierr);
2763   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->Mvctx);CHKERRQ(ierr);
2764   ierr    = MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
2765   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->A);CHKERRQ(ierr);
2766   ierr    = MatDuplicate(oldmat->B,cpvalues,&a->B);CHKERRQ(ierr);
2767   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->B);CHKERRQ(ierr);
2768   ierr    = PetscFunctionListDuplicate(((PetscObject)matin)->qlist,&((PetscObject)mat)->qlist);CHKERRQ(ierr);
2769   *newmat = mat;
2770   PetscFunctionReturn(0);
2771 }
2772 
2773 
2774 
2775 #undef __FUNCT__
2776 #define __FUNCT__ "MatLoad_MPIAIJ"
2777 PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
2778 {
2779   PetscScalar    *vals,*svals;
2780   MPI_Comm       comm;
2781   PetscErrorCode ierr;
2782   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
2783   PetscInt       i,nz,j,rstart,rend,mmax,maxnz = 0;
2784   PetscInt       header[4],*rowlengths = 0,M,N,m,*cols;
2785   PetscInt       *ourlens = NULL,*procsnz = NULL,*offlens = NULL,jj,*mycols,*smycols;
2786   PetscInt       cend,cstart,n,*rowners;
2787   int            fd;
2788   PetscInt       bs = newMat->rmap->bs;
2789 
2790   PetscFunctionBegin;
2791   /* force binary viewer to load .info file if it has not yet done so */
2792   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
2793   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
2794   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2795   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2796   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
2797   if (!rank) {
2798     ierr = PetscBinaryRead(fd,(char*)header,4,PETSC_INT);CHKERRQ(ierr);
2799     if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
2800   }
2801 
2802   ierr = PetscOptionsBegin(comm,NULL,"Options for loading MPIAIJ matrix","Mat");CHKERRQ(ierr);
2803   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
2804   ierr = PetscOptionsEnd();CHKERRQ(ierr);
2805   if (bs < 0) bs = 1;
2806 
2807   ierr = MPI_Bcast(header+1,3,MPIU_INT,0,comm);CHKERRQ(ierr);
2808   M    = header[1]; N = header[2];
2809 
2810   /* If global sizes are set, check if they are consistent with that given in the file */
2811   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);
2812   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);
2813 
2814   /* determine ownership of all (block) rows */
2815   if (M%bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Inconsistent # of rows (%d) and block size (%d)",M,bs);
2816   if (newMat->rmap->n < 0) m = bs*((M/bs)/size + (((M/bs) % size) > rank));    /* PETSC_DECIDE */
2817   else m = newMat->rmap->n; /* Set by user */
2818 
2819   ierr = PetscMalloc1(size+1,&rowners);CHKERRQ(ierr);
2820   ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
2821 
2822   /* First process needs enough room for process with most rows */
2823   if (!rank) {
2824     mmax = rowners[1];
2825     for (i=2; i<=size; i++) {
2826       mmax = PetscMax(mmax, rowners[i]);
2827     }
2828   } else mmax = -1;             /* unused, but compilers complain */
2829 
2830   rowners[0] = 0;
2831   for (i=2; i<=size; i++) {
2832     rowners[i] += rowners[i-1];
2833   }
2834   rstart = rowners[rank];
2835   rend   = rowners[rank+1];
2836 
2837   /* distribute row lengths to all processors */
2838   ierr = PetscMalloc2(m,&ourlens,m,&offlens);CHKERRQ(ierr);
2839   if (!rank) {
2840     ierr = PetscBinaryRead(fd,ourlens,m,PETSC_INT);CHKERRQ(ierr);
2841     ierr = PetscMalloc1(mmax,&rowlengths);CHKERRQ(ierr);
2842     ierr = PetscCalloc1(size,&procsnz);CHKERRQ(ierr);
2843     for (j=0; j<m; j++) {
2844       procsnz[0] += ourlens[j];
2845     }
2846     for (i=1; i<size; i++) {
2847       ierr = PetscBinaryRead(fd,rowlengths,rowners[i+1]-rowners[i],PETSC_INT);CHKERRQ(ierr);
2848       /* calculate the number of nonzeros on each processor */
2849       for (j=0; j<rowners[i+1]-rowners[i]; j++) {
2850         procsnz[i] += rowlengths[j];
2851       }
2852       ierr = MPIULong_Send(rowlengths,rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2853     }
2854     ierr = PetscFree(rowlengths);CHKERRQ(ierr);
2855   } else {
2856     ierr = MPIULong_Recv(ourlens,m,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2857   }
2858 
2859   if (!rank) {
2860     /* determine max buffer needed and allocate it */
2861     maxnz = 0;
2862     for (i=0; i<size; i++) {
2863       maxnz = PetscMax(maxnz,procsnz[i]);
2864     }
2865     ierr = PetscMalloc1(maxnz,&cols);CHKERRQ(ierr);
2866 
2867     /* read in my part of the matrix column indices  */
2868     nz   = procsnz[0];
2869     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2870     ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);
2871 
2872     /* read in every one elses and ship off */
2873     for (i=1; i<size; i++) {
2874       nz   = procsnz[i];
2875       ierr = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
2876       ierr = MPIULong_Send(cols,nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2877     }
2878     ierr = PetscFree(cols);CHKERRQ(ierr);
2879   } else {
2880     /* determine buffer space needed for message */
2881     nz = 0;
2882     for (i=0; i<m; i++) {
2883       nz += ourlens[i];
2884     }
2885     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2886 
2887     /* receive message of column indices*/
2888     ierr = MPIULong_Recv(mycols,nz,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2889   }
2890 
2891   /* determine column ownership if matrix is not square */
2892   if (N != M) {
2893     if (newMat->cmap->n < 0) n = N/size + ((N % size) > rank);
2894     else n = newMat->cmap->n;
2895     ierr   = MPI_Scan(&n,&cend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
2896     cstart = cend - n;
2897   } else {
2898     cstart = rstart;
2899     cend   = rend;
2900     n      = cend - cstart;
2901   }
2902 
2903   /* loop over local rows, determining number of off diagonal entries */
2904   ierr = PetscMemzero(offlens,m*sizeof(PetscInt));CHKERRQ(ierr);
2905   jj   = 0;
2906   for (i=0; i<m; i++) {
2907     for (j=0; j<ourlens[i]; j++) {
2908       if (mycols[jj] < cstart || mycols[jj] >= cend) offlens[i]++;
2909       jj++;
2910     }
2911   }
2912 
2913   for (i=0; i<m; i++) {
2914     ourlens[i] -= offlens[i];
2915   }
2916   ierr = MatSetSizes(newMat,m,n,M,N);CHKERRQ(ierr);
2917 
2918   if (bs > 1) {ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);}
2919 
2920   ierr = MatMPIAIJSetPreallocation(newMat,0,ourlens,0,offlens);CHKERRQ(ierr);
2921 
2922   for (i=0; i<m; i++) {
2923     ourlens[i] += offlens[i];
2924   }
2925 
2926   if (!rank) {
2927     ierr = PetscMalloc1(maxnz+1,&vals);CHKERRQ(ierr);
2928 
2929     /* read in my part of the matrix numerical values  */
2930     nz   = procsnz[0];
2931     ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
2932 
2933     /* insert into matrix */
2934     jj      = rstart;
2935     smycols = mycols;
2936     svals   = vals;
2937     for (i=0; i<m; i++) {
2938       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
2939       smycols += ourlens[i];
2940       svals   += ourlens[i];
2941       jj++;
2942     }
2943 
2944     /* read in other processors and ship out */
2945     for (i=1; i<size; i++) {
2946       nz   = procsnz[i];
2947       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
2948       ierr = MPIULong_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
2949     }
2950     ierr = PetscFree(procsnz);CHKERRQ(ierr);
2951   } else {
2952     /* receive numeric values */
2953     ierr = PetscMalloc1(nz+1,&vals);CHKERRQ(ierr);
2954 
2955     /* receive message of values*/
2956     ierr = MPIULong_Recv(vals,nz,MPIU_SCALAR,0,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
2957 
2958     /* insert into matrix */
2959     jj      = rstart;
2960     smycols = mycols;
2961     svals   = vals;
2962     for (i=0; i<m; i++) {
2963       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
2964       smycols += ourlens[i];
2965       svals   += ourlens[i];
2966       jj++;
2967     }
2968   }
2969   ierr = PetscFree2(ourlens,offlens);CHKERRQ(ierr);
2970   ierr = PetscFree(vals);CHKERRQ(ierr);
2971   ierr = PetscFree(mycols);CHKERRQ(ierr);
2972   ierr = PetscFree(rowners);CHKERRQ(ierr);
2973   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2974   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2975   PetscFunctionReturn(0);
2976 }
2977 
2978 #undef __FUNCT__
2979 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ"
2980 /* TODO: Not scalable because of ISAllGather(). */
2981 PetscErrorCode MatGetSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
2982 {
2983   PetscErrorCode ierr;
2984   IS             iscol_local;
2985   PetscInt       csize;
2986 
2987   PetscFunctionBegin;
2988   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
2989   if (call == MAT_REUSE_MATRIX) {
2990     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
2991     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
2992   } else {
2993     PetscInt cbs;
2994     ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
2995     ierr = ISAllGather(iscol,&iscol_local);CHKERRQ(ierr);
2996     ierr = ISSetBlockSize(iscol_local,cbs);CHKERRQ(ierr);
2997   }
2998   ierr = MatGetSubMatrix_MPIAIJ_Private(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
2999   if (call == MAT_INITIAL_MATRIX) {
3000     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3001     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3002   }
3003   PetscFunctionReturn(0);
3004 }
3005 
3006 extern PetscErrorCode MatGetSubMatrices_MPIAIJ_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool*,Mat*);
3007 #undef __FUNCT__
3008 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ_Private"
3009 /*
3010     Not great since it makes two copies of the submatrix, first an SeqAIJ
3011   in local and then by concatenating the local matrices the end result.
3012   Writing it directly would be much like MatGetSubMatrices_MPIAIJ()
3013 
3014   Note: This requires a sequential iscol with all indices.
3015 */
3016 PetscErrorCode MatGetSubMatrix_MPIAIJ_Private(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3017 {
3018   PetscErrorCode ierr;
3019   PetscMPIInt    rank,size;
3020   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3021   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal,ncol;
3022   PetscBool      allcolumns, colflag;
3023   Mat            M,Mreuse;
3024   MatScalar      *vwork,*aa;
3025   MPI_Comm       comm;
3026   Mat_SeqAIJ     *aij;
3027 
3028   PetscFunctionBegin;
3029   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3030   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3031   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3032 
3033   ierr = ISIdentity(iscol,&colflag);CHKERRQ(ierr);
3034   ierr = ISGetLocalSize(iscol,&ncol);CHKERRQ(ierr);
3035   if (colflag && ncol == mat->cmap->N) {
3036     allcolumns = PETSC_TRUE;
3037   } else {
3038     allcolumns = PETSC_FALSE;
3039   }
3040   if (call ==  MAT_REUSE_MATRIX) {
3041     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3042     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3043     ierr = MatGetSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,&allcolumns,&Mreuse);CHKERRQ(ierr);
3044   } else {
3045     ierr = MatGetSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&allcolumns,&Mreuse);CHKERRQ(ierr);
3046   }
3047 
3048   /*
3049       m - number of local rows
3050       n - number of columns (same on all processors)
3051       rstart - first row in new global matrix generated
3052   */
3053   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3054   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3055   if (call == MAT_INITIAL_MATRIX) {
3056     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3057     ii  = aij->i;
3058     jj  = aij->j;
3059 
3060     /*
3061         Determine the number of non-zeros in the diagonal and off-diagonal
3062         portions of the matrix in order to do correct preallocation
3063     */
3064 
3065     /* first get start and end of "diagonal" columns */
3066     if (csize == PETSC_DECIDE) {
3067       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3068       if (mglobal == n) { /* square matrix */
3069         nlocal = m;
3070       } else {
3071         nlocal = n/size + ((n % size) > rank);
3072       }
3073     } else {
3074       nlocal = csize;
3075     }
3076     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3077     rstart = rend - nlocal;
3078     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);
3079 
3080     /* next, compute all the lengths */
3081     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3082     olens = dlens + m;
3083     for (i=0; i<m; i++) {
3084       jend = ii[i+1] - ii[i];
3085       olen = 0;
3086       dlen = 0;
3087       for (j=0; j<jend; j++) {
3088         if (*jj < rstart || *jj >= rend) olen++;
3089         else dlen++;
3090         jj++;
3091       }
3092       olens[i] = olen;
3093       dlens[i] = dlen;
3094     }
3095     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3096     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3097     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3098     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3099     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3100     ierr = PetscFree(dlens);CHKERRQ(ierr);
3101   } else {
3102     PetscInt ml,nl;
3103 
3104     M    = *newmat;
3105     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3106     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3107     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3108     /*
3109          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3110        rather than the slower MatSetValues().
3111     */
3112     M->was_assembled = PETSC_TRUE;
3113     M->assembled     = PETSC_FALSE;
3114   }
3115   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3116   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3117   ii   = aij->i;
3118   jj   = aij->j;
3119   aa   = aij->a;
3120   for (i=0; i<m; i++) {
3121     row   = rstart + i;
3122     nz    = ii[i+1] - ii[i];
3123     cwork = jj;     jj += nz;
3124     vwork = aa;     aa += nz;
3125     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3126   }
3127 
3128   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3129   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3130   *newmat = M;
3131 
3132   /* save submatrix used in processor for next request */
3133   if (call ==  MAT_INITIAL_MATRIX) {
3134     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3135     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3136   }
3137   PetscFunctionReturn(0);
3138 }
3139 
3140 #undef __FUNCT__
3141 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR_MPIAIJ"
3142 PetscErrorCode  MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3143 {
3144   PetscInt       m,cstart, cend,j,nnz,i,d;
3145   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3146   const PetscInt *JJ;
3147   PetscScalar    *values;
3148   PetscErrorCode ierr;
3149 
3150   PetscFunctionBegin;
3151   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3152 
3153   ierr   = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3154   ierr   = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3155   m      = B->rmap->n;
3156   cstart = B->cmap->rstart;
3157   cend   = B->cmap->rend;
3158   rstart = B->rmap->rstart;
3159 
3160   ierr = PetscMalloc2(m,&d_nnz,m,&o_nnz);CHKERRQ(ierr);
3161 
3162 #if defined(PETSC_USE_DEBUGGING)
3163   for (i=0; i<m; i++) {
3164     nnz = Ii[i+1]- Ii[i];
3165     JJ  = J + Ii[i];
3166     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3167     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3168     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);
3169   }
3170 #endif
3171 
3172   for (i=0; i<m; i++) {
3173     nnz     = Ii[i+1]- Ii[i];
3174     JJ      = J + Ii[i];
3175     nnz_max = PetscMax(nnz_max,nnz);
3176     d       = 0;
3177     for (j=0; j<nnz; j++) {
3178       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3179     }
3180     d_nnz[i] = d;
3181     o_nnz[i] = nnz - d;
3182   }
3183   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3184   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3185 
3186   if (v) values = (PetscScalar*)v;
3187   else {
3188     ierr = PetscCalloc1(nnz_max+1,&values);CHKERRQ(ierr);
3189   }
3190 
3191   for (i=0; i<m; i++) {
3192     ii   = i + rstart;
3193     nnz  = Ii[i+1]- Ii[i];
3194     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3195   }
3196   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3197   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3198 
3199   if (!v) {
3200     ierr = PetscFree(values);CHKERRQ(ierr);
3201   }
3202   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3203   PetscFunctionReturn(0);
3204 }
3205 
3206 #undef __FUNCT__
3207 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR"
3208 /*@
3209    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3210    (the default parallel PETSc format).
3211 
3212    Collective on MPI_Comm
3213 
3214    Input Parameters:
3215 +  B - the matrix
3216 .  i - the indices into j for the start of each local row (starts with zero)
3217 .  j - the column indices for each local row (starts with zero)
3218 -  v - optional values in the matrix
3219 
3220    Level: developer
3221 
3222    Notes:
3223        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3224      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3225      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3226 
3227        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3228 
3229        The format which is used for the sparse matrix input, is equivalent to a
3230     row-major ordering.. i.e for the following matrix, the input data expected is
3231     as shown
3232 
3233 $        1 0 0
3234 $        2 0 3     P0
3235 $       -------
3236 $        4 5 6     P1
3237 $
3238 $     Process0 [P0]: rows_owned=[0,1]
3239 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3240 $        j =  {0,0,2}  [size = 3]
3241 $        v =  {1,2,3}  [size = 3]
3242 $
3243 $     Process1 [P1]: rows_owned=[2]
3244 $        i =  {0,3}    [size = nrow+1  = 1+1]
3245 $        j =  {0,1,2}  [size = 3]
3246 $        v =  {4,5,6}  [size = 3]
3247 
3248 .keywords: matrix, aij, compressed row, sparse, parallel
3249 
3250 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MPIAIJ,
3251           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3252 @*/
3253 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3254 {
3255   PetscErrorCode ierr;
3256 
3257   PetscFunctionBegin;
3258   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3259   PetscFunctionReturn(0);
3260 }
3261 
3262 #undef __FUNCT__
3263 #define __FUNCT__ "MatMPIAIJSetPreallocation"
3264 /*@C
3265    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3266    (the default parallel PETSc format).  For good matrix assembly performance
3267    the user should preallocate the matrix storage by setting the parameters
3268    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3269    performance can be increased by more than a factor of 50.
3270 
3271    Collective on MPI_Comm
3272 
3273    Input Parameters:
3274 +  B - the matrix
3275 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3276            (same value is used for all local rows)
3277 .  d_nnz - array containing the number of nonzeros in the various rows of the
3278            DIAGONAL portion of the local submatrix (possibly different for each row)
3279            or NULL (PETSC_NULL_INTEGER in Fortran), if d_nz is used to specify the nonzero structure.
3280            The size of this array is equal to the number of local rows, i.e 'm'.
3281            For matrices that will be factored, you must leave room for (and set)
3282            the diagonal entry even if it is zero.
3283 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3284            submatrix (same value is used for all local rows).
3285 -  o_nnz - array containing the number of nonzeros in the various rows of the
3286            OFF-DIAGONAL portion of the local submatrix (possibly different for
3287            each row) or NULL (PETSC_NULL_INTEGER in Fortran), if o_nz is used to specify the nonzero
3288            structure. The size of this array is equal to the number
3289            of local rows, i.e 'm'.
3290 
3291    If the *_nnz parameter is given then the *_nz parameter is ignored
3292 
3293    The AIJ format (also called the Yale sparse matrix format or
3294    compressed row storage (CSR)), is fully compatible with standard Fortran 77
3295    storage.  The stored row and column indices begin with zero.
3296    See Users-Manual: ch_mat for details.
3297 
3298    The parallel matrix is partitioned such that the first m0 rows belong to
3299    process 0, the next m1 rows belong to process 1, the next m2 rows belong
3300    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
3301 
3302    The DIAGONAL portion of the local submatrix of a processor can be defined
3303    as the submatrix which is obtained by extraction the part corresponding to
3304    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
3305    first row that belongs to the processor, r2 is the last row belonging to
3306    the this processor, and c1-c2 is range of indices of the local part of a
3307    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
3308    common case of a square matrix, the row and column ranges are the same and
3309    the DIAGONAL part is also square. The remaining portion of the local
3310    submatrix (mxN) constitute the OFF-DIAGONAL portion.
3311 
3312    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3313 
3314    You can call MatGetInfo() to get information on how effective the preallocation was;
3315    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3316    You can also run with the option -info and look for messages with the string
3317    malloc in them to see if additional memory allocation was needed.
3318 
3319    Example usage:
3320 
3321    Consider the following 8x8 matrix with 34 non-zero values, that is
3322    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3323    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3324    as follows:
3325 
3326 .vb
3327             1  2  0  |  0  3  0  |  0  4
3328     Proc0   0  5  6  |  7  0  0  |  8  0
3329             9  0 10  | 11  0  0  | 12  0
3330     -------------------------------------
3331            13  0 14  | 15 16 17  |  0  0
3332     Proc1   0 18  0  | 19 20 21  |  0  0
3333             0  0  0  | 22 23  0  | 24  0
3334     -------------------------------------
3335     Proc2  25 26 27  |  0  0 28  | 29  0
3336            30  0  0  | 31 32 33  |  0 34
3337 .ve
3338 
3339    This can be represented as a collection of submatrices as:
3340 
3341 .vb
3342       A B C
3343       D E F
3344       G H I
3345 .ve
3346 
3347    Where the submatrices A,B,C are owned by proc0, D,E,F are
3348    owned by proc1, G,H,I are owned by proc2.
3349 
3350    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3351    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3352    The 'M','N' parameters are 8,8, and have the same values on all procs.
3353 
3354    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3355    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3356    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3357    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3358    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3359    matrix, ans [DF] as another SeqAIJ matrix.
3360 
3361    When d_nz, o_nz parameters are specified, d_nz storage elements are
3362    allocated for every row of the local diagonal submatrix, and o_nz
3363    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3364    One way to choose d_nz and o_nz is to use the max nonzerors per local
3365    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3366    In this case, the values of d_nz,o_nz are:
3367 .vb
3368      proc0 : dnz = 2, o_nz = 2
3369      proc1 : dnz = 3, o_nz = 2
3370      proc2 : dnz = 1, o_nz = 4
3371 .ve
3372    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3373    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3374    for proc3. i.e we are using 12+15+10=37 storage locations to store
3375    34 values.
3376 
3377    When d_nnz, o_nnz parameters are specified, the storage is specified
3378    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3379    In the above case the values for d_nnz,o_nnz are:
3380 .vb
3381      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3382      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3383      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3384 .ve
3385    Here the space allocated is sum of all the above values i.e 34, and
3386    hence pre-allocation is perfect.
3387 
3388    Level: intermediate
3389 
3390 .keywords: matrix, aij, compressed row, sparse, parallel
3391 
3392 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
3393           MPIAIJ, MatGetInfo(), PetscSplitOwnership()
3394 @*/
3395 PetscErrorCode  MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3396 {
3397   PetscErrorCode ierr;
3398 
3399   PetscFunctionBegin;
3400   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3401   PetscValidType(B,1);
3402   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
3403   PetscFunctionReturn(0);
3404 }
3405 
3406 #undef __FUNCT__
3407 #define __FUNCT__ "MatCreateMPIAIJWithArrays"
3408 /*@
3409      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
3410          CSR format the local rows.
3411 
3412    Collective on MPI_Comm
3413 
3414    Input Parameters:
3415 +  comm - MPI communicator
3416 .  m - number of local rows (Cannot be PETSC_DECIDE)
3417 .  n - This value should be the same as the local size used in creating the
3418        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3419        calculated if N is given) For square matrices n is almost always m.
3420 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3421 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3422 .   i - row indices
3423 .   j - column indices
3424 -   a - matrix values
3425 
3426    Output Parameter:
3427 .   mat - the matrix
3428 
3429    Level: intermediate
3430 
3431    Notes:
3432        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3433      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3434      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3435 
3436        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3437 
3438        The format which is used for the sparse matrix input, is equivalent to a
3439     row-major ordering.. i.e for the following matrix, the input data expected is
3440     as shown
3441 
3442 $        1 0 0
3443 $        2 0 3     P0
3444 $       -------
3445 $        4 5 6     P1
3446 $
3447 $     Process0 [P0]: rows_owned=[0,1]
3448 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3449 $        j =  {0,0,2}  [size = 3]
3450 $        v =  {1,2,3}  [size = 3]
3451 $
3452 $     Process1 [P1]: rows_owned=[2]
3453 $        i =  {0,3}    [size = nrow+1  = 1+1]
3454 $        j =  {0,1,2}  [size = 3]
3455 $        v =  {4,5,6}  [size = 3]
3456 
3457 .keywords: matrix, aij, compressed row, sparse, parallel
3458 
3459 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3460           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
3461 @*/
3462 PetscErrorCode  MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
3463 {
3464   PetscErrorCode ierr;
3465 
3466   PetscFunctionBegin;
3467   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
3468   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
3469   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
3470   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
3471   /* ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr); */
3472   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
3473   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
3474   PetscFunctionReturn(0);
3475 }
3476 
3477 #undef __FUNCT__
3478 #define __FUNCT__ "MatCreateAIJ"
3479 /*@C
3480    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
3481    (the default parallel PETSc format).  For good matrix assembly performance
3482    the user should preallocate the matrix storage by setting the parameters
3483    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3484    performance can be increased by more than a factor of 50.
3485 
3486    Collective on MPI_Comm
3487 
3488    Input Parameters:
3489 +  comm - MPI communicator
3490 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
3491            This value should be the same as the local size used in creating the
3492            y vector for the matrix-vector product y = Ax.
3493 .  n - This value should be the same as the local size used in creating the
3494        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3495        calculated if N is given) For square matrices n is almost always m.
3496 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3497 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3498 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3499            (same value is used for all local rows)
3500 .  d_nnz - array containing the number of nonzeros in the various rows of the
3501            DIAGONAL portion of the local submatrix (possibly different for each row)
3502            or NULL, if d_nz is used to specify the nonzero structure.
3503            The size of this array is equal to the number of local rows, i.e 'm'.
3504 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3505            submatrix (same value is used for all local rows).
3506 -  o_nnz - array containing the number of nonzeros in the various rows of the
3507            OFF-DIAGONAL portion of the local submatrix (possibly different for
3508            each row) or NULL, if o_nz is used to specify the nonzero
3509            structure. The size of this array is equal to the number
3510            of local rows, i.e 'm'.
3511 
3512    Output Parameter:
3513 .  A - the matrix
3514 
3515    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3516    MatXXXXSetPreallocation() paradgm instead of this routine directly.
3517    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3518 
3519    Notes:
3520    If the *_nnz parameter is given then the *_nz parameter is ignored
3521 
3522    m,n,M,N parameters specify the size of the matrix, and its partitioning across
3523    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
3524    storage requirements for this matrix.
3525 
3526    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
3527    processor than it must be used on all processors that share the object for
3528    that argument.
3529 
3530    The user MUST specify either the local or global matrix dimensions
3531    (possibly both).
3532 
3533    The parallel matrix is partitioned across processors such that the
3534    first m0 rows belong to process 0, the next m1 rows belong to
3535    process 1, the next m2 rows belong to process 2 etc.. where
3536    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
3537    values corresponding to [m x N] submatrix.
3538 
3539    The columns are logically partitioned with the n0 columns belonging
3540    to 0th partition, the next n1 columns belonging to the next
3541    partition etc.. where n0,n1,n2... are the input parameter 'n'.
3542 
3543    The DIAGONAL portion of the local submatrix on any given processor
3544    is the submatrix corresponding to the rows and columns m,n
3545    corresponding to the given processor. i.e diagonal matrix on
3546    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
3547    etc. The remaining portion of the local submatrix [m x (N-n)]
3548    constitute the OFF-DIAGONAL portion. The example below better
3549    illustrates this concept.
3550 
3551    For a square global matrix we define each processor's diagonal portion
3552    to be its local rows and the corresponding columns (a square submatrix);
3553    each processor's off-diagonal portion encompasses the remainder of the
3554    local matrix (a rectangular submatrix).
3555 
3556    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3557 
3558    When calling this routine with a single process communicator, a matrix of
3559    type SEQAIJ is returned.  If a matrix of type MPIAIJ is desired for this
3560    type of communicator, use the construction mechanism:
3561      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
3562 
3563    By default, this format uses inodes (identical nodes) when possible.
3564    We search for consecutive rows with the same nonzero structure, thereby
3565    reusing matrix information to achieve increased efficiency.
3566 
3567    Options Database Keys:
3568 +  -mat_no_inode  - Do not use inodes
3569 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3570 -  -mat_aij_oneindex - Internally use indexing starting at 1
3571         rather than 0.  Note that when calling MatSetValues(),
3572         the user still MUST index entries starting at 0!
3573 
3574 
3575    Example usage:
3576 
3577    Consider the following 8x8 matrix with 34 non-zero values, that is
3578    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3579    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3580    as follows:
3581 
3582 .vb
3583             1  2  0  |  0  3  0  |  0  4
3584     Proc0   0  5  6  |  7  0  0  |  8  0
3585             9  0 10  | 11  0  0  | 12  0
3586     -------------------------------------
3587            13  0 14  | 15 16 17  |  0  0
3588     Proc1   0 18  0  | 19 20 21  |  0  0
3589             0  0  0  | 22 23  0  | 24  0
3590     -------------------------------------
3591     Proc2  25 26 27  |  0  0 28  | 29  0
3592            30  0  0  | 31 32 33  |  0 34
3593 .ve
3594 
3595    This can be represented as a collection of submatrices as:
3596 
3597 .vb
3598       A B C
3599       D E F
3600       G H I
3601 .ve
3602 
3603    Where the submatrices A,B,C are owned by proc0, D,E,F are
3604    owned by proc1, G,H,I are owned by proc2.
3605 
3606    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3607    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3608    The 'M','N' parameters are 8,8, and have the same values on all procs.
3609 
3610    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3611    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3612    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3613    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3614    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3615    matrix, ans [DF] as another SeqAIJ matrix.
3616 
3617    When d_nz, o_nz parameters are specified, d_nz storage elements are
3618    allocated for every row of the local diagonal submatrix, and o_nz
3619    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3620    One way to choose d_nz and o_nz is to use the max nonzerors per local
3621    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3622    In this case, the values of d_nz,o_nz are:
3623 .vb
3624      proc0 : dnz = 2, o_nz = 2
3625      proc1 : dnz = 3, o_nz = 2
3626      proc2 : dnz = 1, o_nz = 4
3627 .ve
3628    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3629    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3630    for proc3. i.e we are using 12+15+10=37 storage locations to store
3631    34 values.
3632 
3633    When d_nnz, o_nnz parameters are specified, the storage is specified
3634    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3635    In the above case the values for d_nnz,o_nnz are:
3636 .vb
3637      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3638      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3639      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3640 .ve
3641    Here the space allocated is sum of all the above values i.e 34, and
3642    hence pre-allocation is perfect.
3643 
3644    Level: intermediate
3645 
3646 .keywords: matrix, aij, compressed row, sparse, parallel
3647 
3648 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3649           MPIAIJ, MatCreateMPIAIJWithArrays()
3650 @*/
3651 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)
3652 {
3653   PetscErrorCode ierr;
3654   PetscMPIInt    size;
3655 
3656   PetscFunctionBegin;
3657   ierr = MatCreate(comm,A);CHKERRQ(ierr);
3658   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
3659   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3660   if (size > 1) {
3661     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
3662     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
3663   } else {
3664     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
3665     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
3666   }
3667   PetscFunctionReturn(0);
3668 }
3669 
3670 #undef __FUNCT__
3671 #define __FUNCT__ "MatMPIAIJGetSeqAIJ"
3672 PetscErrorCode  MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
3673 {
3674   Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
3675 
3676   PetscFunctionBegin;
3677   if (Ad)     *Ad     = a->A;
3678   if (Ao)     *Ao     = a->B;
3679   if (colmap) *colmap = a->garray;
3680   PetscFunctionReturn(0);
3681 }
3682 
3683 #undef __FUNCT__
3684 #define __FUNCT__ "MatSetColoring_MPIAIJ"
3685 PetscErrorCode MatSetColoring_MPIAIJ(Mat A,ISColoring coloring)
3686 {
3687   PetscErrorCode ierr;
3688   PetscInt       i;
3689   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3690 
3691   PetscFunctionBegin;
3692   if (coloring->ctype == IS_COLORING_GLOBAL) {
3693     ISColoringValue *allcolors,*colors;
3694     ISColoring      ocoloring;
3695 
3696     /* set coloring for diagonal portion */
3697     ierr = MatSetColoring_SeqAIJ(a->A,coloring);CHKERRQ(ierr);
3698 
3699     /* set coloring for off-diagonal portion */
3700     ierr = ISAllGatherColors(PetscObjectComm((PetscObject)A),coloring->n,coloring->colors,NULL,&allcolors);CHKERRQ(ierr);
3701     ierr = PetscMalloc1(a->B->cmap->n+1,&colors);CHKERRQ(ierr);
3702     for (i=0; i<a->B->cmap->n; i++) {
3703       colors[i] = allcolors[a->garray[i]];
3704     }
3705     ierr = PetscFree(allcolors);CHKERRQ(ierr);
3706     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3707     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
3708     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3709   } else if (coloring->ctype == IS_COLORING_GHOSTED) {
3710     ISColoringValue *colors;
3711     PetscInt        *larray;
3712     ISColoring      ocoloring;
3713 
3714     /* set coloring for diagonal portion */
3715     ierr = PetscMalloc1(a->A->cmap->n+1,&larray);CHKERRQ(ierr);
3716     for (i=0; i<a->A->cmap->n; i++) {
3717       larray[i] = i + A->cmap->rstart;
3718     }
3719     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->A->cmap->n,larray,NULL,larray);CHKERRQ(ierr);
3720     ierr = PetscMalloc1(a->A->cmap->n+1,&colors);CHKERRQ(ierr);
3721     for (i=0; i<a->A->cmap->n; i++) {
3722       colors[i] = coloring->colors[larray[i]];
3723     }
3724     ierr = PetscFree(larray);CHKERRQ(ierr);
3725     ierr = ISColoringCreate(PETSC_COMM_SELF,coloring->n,a->A->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3726     ierr = MatSetColoring_SeqAIJ(a->A,ocoloring);CHKERRQ(ierr);
3727     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3728 
3729     /* set coloring for off-diagonal portion */
3730     ierr = PetscMalloc1(a->B->cmap->n+1,&larray);CHKERRQ(ierr);
3731     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->B->cmap->n,a->garray,NULL,larray);CHKERRQ(ierr);
3732     ierr = PetscMalloc1(a->B->cmap->n+1,&colors);CHKERRQ(ierr);
3733     for (i=0; i<a->B->cmap->n; i++) {
3734       colors[i] = coloring->colors[larray[i]];
3735     }
3736     ierr = PetscFree(larray);CHKERRQ(ierr);
3737     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3738     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
3739     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3740   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support ISColoringType %d",(int)coloring->ctype);
3741   PetscFunctionReturn(0);
3742 }
3743 
3744 #undef __FUNCT__
3745 #define __FUNCT__ "MatSetValuesAdifor_MPIAIJ"
3746 PetscErrorCode MatSetValuesAdifor_MPIAIJ(Mat A,PetscInt nl,void *advalues)
3747 {
3748   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3749   PetscErrorCode ierr;
3750 
3751   PetscFunctionBegin;
3752   ierr = MatSetValuesAdifor_SeqAIJ(a->A,nl,advalues);CHKERRQ(ierr);
3753   ierr = MatSetValuesAdifor_SeqAIJ(a->B,nl,advalues);CHKERRQ(ierr);
3754   PetscFunctionReturn(0);
3755 }
3756 
3757 #undef __FUNCT__
3758 #define __FUNCT__ "MatCreateMPIMatConcatenateSeqMat_MPIAIJ"
3759 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
3760 {
3761   PetscErrorCode ierr;
3762   PetscInt       m,N,i,rstart,nnz,Ii;
3763   PetscInt       *indx;
3764   PetscScalar    *values;
3765 
3766   PetscFunctionBegin;
3767   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
3768   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
3769     PetscInt       *dnz,*onz,sum,bs,cbs;
3770 
3771     if (n == PETSC_DECIDE) {
3772       ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
3773     }
3774     /* Check sum(n) = N */
3775     ierr = MPI_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3776     if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
3777 
3778     ierr    = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3779     rstart -= m;
3780 
3781     ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
3782     for (i=0; i<m; i++) {
3783       ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3784       ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
3785       ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3786     }
3787 
3788     ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
3789     ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
3790     ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
3791     ierr = MatSetBlockSizes(*outmat,bs,cbs);CHKERRQ(ierr);
3792     ierr = MatSetType(*outmat,MATMPIAIJ);CHKERRQ(ierr);
3793     ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
3794     ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
3795   }
3796 
3797   /* numeric phase */
3798   ierr = MatGetOwnershipRange(*outmat,&rstart,NULL);CHKERRQ(ierr);
3799   for (i=0; i<m; i++) {
3800     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3801     Ii   = i + rstart;
3802     ierr = MatSetValues(*outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3803     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3804   }
3805   ierr = MatAssemblyBegin(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3806   ierr = MatAssemblyEnd(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3807   PetscFunctionReturn(0);
3808 }
3809 
3810 #undef __FUNCT__
3811 #define __FUNCT__ "MatFileSplit"
3812 PetscErrorCode MatFileSplit(Mat A,char *outfile)
3813 {
3814   PetscErrorCode    ierr;
3815   PetscMPIInt       rank;
3816   PetscInt          m,N,i,rstart,nnz;
3817   size_t            len;
3818   const PetscInt    *indx;
3819   PetscViewer       out;
3820   char              *name;
3821   Mat               B;
3822   const PetscScalar *values;
3823 
3824   PetscFunctionBegin;
3825   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
3826   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
3827   /* Should this be the type of the diagonal block of A? */
3828   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
3829   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
3830   ierr = MatSetBlockSizesFromMats(B,A,A);CHKERRQ(ierr);
3831   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
3832   ierr = MatSeqAIJSetPreallocation(B,0,NULL);CHKERRQ(ierr);
3833   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
3834   for (i=0; i<m; i++) {
3835     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3836     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3837     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3838   }
3839   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3840   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3841 
3842   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
3843   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
3844   ierr = PetscMalloc1(len+5,&name);CHKERRQ(ierr);
3845   sprintf(name,"%s.%d",outfile,rank);
3846   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
3847   ierr = PetscFree(name);CHKERRQ(ierr);
3848   ierr = MatView(B,out);CHKERRQ(ierr);
3849   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
3850   ierr = MatDestroy(&B);CHKERRQ(ierr);
3851   PetscFunctionReturn(0);
3852 }
3853 
3854 extern PetscErrorCode MatDestroy_MPIAIJ(Mat);
3855 #undef __FUNCT__
3856 #define __FUNCT__ "MatDestroy_MPIAIJ_SeqsToMPI"
3857 PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
3858 {
3859   PetscErrorCode      ierr;
3860   Mat_Merge_SeqsToMPI *merge;
3861   PetscContainer      container;
3862 
3863   PetscFunctionBegin;
3864   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
3865   if (container) {
3866     ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
3867     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
3868     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
3869     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
3870     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
3871     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
3872     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
3873     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
3874     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
3875     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
3876     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
3877     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
3878     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
3879     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
3880     ierr = PetscFree(merge);CHKERRQ(ierr);
3881     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
3882   }
3883   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
3884   PetscFunctionReturn(0);
3885 }
3886 
3887 #include <../src/mat/utils/freespace.h>
3888 #include <petscbt.h>
3889 
3890 #undef __FUNCT__
3891 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJNumeric"
3892 PetscErrorCode  MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
3893 {
3894   PetscErrorCode      ierr;
3895   MPI_Comm            comm;
3896   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
3897   PetscMPIInt         size,rank,taga,*len_s;
3898   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
3899   PetscInt            proc,m;
3900   PetscInt            **buf_ri,**buf_rj;
3901   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
3902   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
3903   MPI_Request         *s_waits,*r_waits;
3904   MPI_Status          *status;
3905   MatScalar           *aa=a->a;
3906   MatScalar           **abuf_r,*ba_i;
3907   Mat_Merge_SeqsToMPI *merge;
3908   PetscContainer      container;
3909 
3910   PetscFunctionBegin;
3911   ierr = PetscObjectGetComm((PetscObject)mpimat,&comm);CHKERRQ(ierr);
3912   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
3913 
3914   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3915   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3916 
3917   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
3918   ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
3919 
3920   bi     = merge->bi;
3921   bj     = merge->bj;
3922   buf_ri = merge->buf_ri;
3923   buf_rj = merge->buf_rj;
3924 
3925   ierr   = PetscMalloc1(size,&status);CHKERRQ(ierr);
3926   owners = merge->rowmap->range;
3927   len_s  = merge->len_s;
3928 
3929   /* send and recv matrix values */
3930   /*-----------------------------*/
3931   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
3932   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
3933 
3934   ierr = PetscMalloc1(merge->nsend+1,&s_waits);CHKERRQ(ierr);
3935   for (proc=0,k=0; proc<size; proc++) {
3936     if (!len_s[proc]) continue;
3937     i    = owners[proc];
3938     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
3939     k++;
3940   }
3941 
3942   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
3943   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
3944   ierr = PetscFree(status);CHKERRQ(ierr);
3945 
3946   ierr = PetscFree(s_waits);CHKERRQ(ierr);
3947   ierr = PetscFree(r_waits);CHKERRQ(ierr);
3948 
3949   /* insert mat values of mpimat */
3950   /*----------------------------*/
3951   ierr = PetscMalloc1(N,&ba_i);CHKERRQ(ierr);
3952   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
3953 
3954   for (k=0; k<merge->nrecv; k++) {
3955     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
3956     nrows       = *(buf_ri_k[k]);
3957     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
3958     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
3959   }
3960 
3961   /* set values of ba */
3962   m = merge->rowmap->n;
3963   for (i=0; i<m; i++) {
3964     arow = owners[rank] + i;
3965     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
3966     bnzi = bi[i+1] - bi[i];
3967     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
3968 
3969     /* add local non-zero vals of this proc's seqmat into ba */
3970     anzi   = ai[arow+1] - ai[arow];
3971     aj     = a->j + ai[arow];
3972     aa     = a->a + ai[arow];
3973     nextaj = 0;
3974     for (j=0; nextaj<anzi; j++) {
3975       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
3976         ba_i[j] += aa[nextaj++];
3977       }
3978     }
3979 
3980     /* add received vals into ba */
3981     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
3982       /* i-th row */
3983       if (i == *nextrow[k]) {
3984         anzi   = *(nextai[k]+1) - *nextai[k];
3985         aj     = buf_rj[k] + *(nextai[k]);
3986         aa     = abuf_r[k] + *(nextai[k]);
3987         nextaj = 0;
3988         for (j=0; nextaj<anzi; j++) {
3989           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
3990             ba_i[j] += aa[nextaj++];
3991           }
3992         }
3993         nextrow[k]++; nextai[k]++;
3994       }
3995     }
3996     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
3997   }
3998   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3999   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4000 
4001   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
4002   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
4003   ierr = PetscFree(ba_i);CHKERRQ(ierr);
4004   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4005   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4006   PetscFunctionReturn(0);
4007 }
4008 
4009 extern PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat);
4010 
4011 #undef __FUNCT__
4012 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJSymbolic"
4013 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4014 {
4015   PetscErrorCode      ierr;
4016   Mat                 B_mpi;
4017   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
4018   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4019   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
4020   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4021   PetscInt            len,proc,*dnz,*onz,bs,cbs;
4022   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4023   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4024   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
4025   MPI_Status          *status;
4026   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
4027   PetscBT             lnkbt;
4028   Mat_Merge_SeqsToMPI *merge;
4029   PetscContainer      container;
4030 
4031   PetscFunctionBegin;
4032   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4033 
4034   /* make sure it is a PETSc comm */
4035   ierr = PetscCommDuplicate(comm,&comm,NULL);CHKERRQ(ierr);
4036   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4037   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4038 
4039   ierr = PetscNew(&merge);CHKERRQ(ierr);
4040   ierr = PetscMalloc1(size,&status);CHKERRQ(ierr);
4041 
4042   /* determine row ownership */
4043   /*---------------------------------------------------------*/
4044   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
4045   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
4046   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
4047   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
4048   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
4049   ierr = PetscMalloc1(size,&len_si);CHKERRQ(ierr);
4050   ierr = PetscMalloc1(size,&merge->len_s);CHKERRQ(ierr);
4051 
4052   m      = merge->rowmap->n;
4053   owners = merge->rowmap->range;
4054 
4055   /* determine the number of messages to send, their lengths */
4056   /*---------------------------------------------------------*/
4057   len_s = merge->len_s;
4058 
4059   len          = 0; /* length of buf_si[] */
4060   merge->nsend = 0;
4061   for (proc=0; proc<size; proc++) {
4062     len_si[proc] = 0;
4063     if (proc == rank) {
4064       len_s[proc] = 0;
4065     } else {
4066       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4067       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4068     }
4069     if (len_s[proc]) {
4070       merge->nsend++;
4071       nrows = 0;
4072       for (i=owners[proc]; i<owners[proc+1]; i++) {
4073         if (ai[i+1] > ai[i]) nrows++;
4074       }
4075       len_si[proc] = 2*(nrows+1);
4076       len         += len_si[proc];
4077     }
4078   }
4079 
4080   /* determine the number and length of messages to receive for ij-structure */
4081   /*-------------------------------------------------------------------------*/
4082   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
4083   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
4084 
4085   /* post the Irecv of j-structure */
4086   /*-------------------------------*/
4087   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
4088   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
4089 
4090   /* post the Isend of j-structure */
4091   /*--------------------------------*/
4092   ierr = PetscMalloc2(merge->nsend,&si_waits,merge->nsend,&sj_waits);CHKERRQ(ierr);
4093 
4094   for (proc=0, k=0; proc<size; proc++) {
4095     if (!len_s[proc]) continue;
4096     i    = owners[proc];
4097     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
4098     k++;
4099   }
4100 
4101   /* receives and sends of j-structure are complete */
4102   /*------------------------------------------------*/
4103   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
4104   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
4105 
4106   /* send and recv i-structure */
4107   /*---------------------------*/
4108   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
4109   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
4110 
4111   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
4112   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4113   for (proc=0,k=0; proc<size; proc++) {
4114     if (!len_s[proc]) continue;
4115     /* form outgoing message for i-structure:
4116          buf_si[0]:                 nrows to be sent
4117                [1:nrows]:           row index (global)
4118                [nrows+1:2*nrows+1]: i-structure index
4119     */
4120     /*-------------------------------------------*/
4121     nrows       = len_si[proc]/2 - 1;
4122     buf_si_i    = buf_si + nrows+1;
4123     buf_si[0]   = nrows;
4124     buf_si_i[0] = 0;
4125     nrows       = 0;
4126     for (i=owners[proc]; i<owners[proc+1]; i++) {
4127       anzi = ai[i+1] - ai[i];
4128       if (anzi) {
4129         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4130         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4131         nrows++;
4132       }
4133     }
4134     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4135     k++;
4136     buf_si += len_si[proc];
4137   }
4138 
4139   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4140   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4141 
4142   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4143   for (i=0; i<merge->nrecv; i++) {
4144     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);
4145   }
4146 
4147   ierr = PetscFree(len_si);CHKERRQ(ierr);
4148   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4149   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4150   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4151   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4152   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4153   ierr = PetscFree(status);CHKERRQ(ierr);
4154 
4155   /* compute a local seq matrix in each processor */
4156   /*----------------------------------------------*/
4157   /* allocate bi array and free space for accumulating nonzero column info */
4158   ierr  = PetscMalloc1(m+1,&bi);CHKERRQ(ierr);
4159   bi[0] = 0;
4160 
4161   /* create and initialize a linked list */
4162   nlnk = N+1;
4163   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4164 
4165   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4166   len  = ai[owners[rank+1]] - ai[owners[rank]];
4167   ierr = PetscFreeSpaceGet((PetscInt)(2*len+1),&free_space);CHKERRQ(ierr);
4168 
4169   current_space = free_space;
4170 
4171   /* determine symbolic info for each local row */
4172   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4173 
4174   for (k=0; k<merge->nrecv; k++) {
4175     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4176     nrows       = *buf_ri_k[k];
4177     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4178     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4179   }
4180 
4181   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4182   len  = 0;
4183   for (i=0; i<m; i++) {
4184     bnzi = 0;
4185     /* add local non-zero cols of this proc's seqmat into lnk */
4186     arow  = owners[rank] + i;
4187     anzi  = ai[arow+1] - ai[arow];
4188     aj    = a->j + ai[arow];
4189     ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4190     bnzi += nlnk;
4191     /* add received col data into lnk */
4192     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4193       if (i == *nextrow[k]) { /* i-th row */
4194         anzi  = *(nextai[k]+1) - *nextai[k];
4195         aj    = buf_rj[k] + *nextai[k];
4196         ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4197         bnzi += nlnk;
4198         nextrow[k]++; nextai[k]++;
4199       }
4200     }
4201     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4202 
4203     /* if free space is not available, make more free space */
4204     if (current_space->local_remaining<bnzi) {
4205       ierr = PetscFreeSpaceGet(bnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
4206       nspacedouble++;
4207     }
4208     /* copy data into free space, then initialize lnk */
4209     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4210     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
4211 
4212     current_space->array           += bnzi;
4213     current_space->local_used      += bnzi;
4214     current_space->local_remaining -= bnzi;
4215 
4216     bi[i+1] = bi[i] + bnzi;
4217   }
4218 
4219   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4220 
4221   ierr = PetscMalloc1(bi[m]+1,&bj);CHKERRQ(ierr);
4222   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
4223   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4224 
4225   /* create symbolic parallel matrix B_mpi */
4226   /*---------------------------------------*/
4227   ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
4228   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
4229   if (n==PETSC_DECIDE) {
4230     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
4231   } else {
4232     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4233   }
4234   ierr = MatSetBlockSizes(B_mpi,bs,cbs);CHKERRQ(ierr);
4235   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
4236   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
4237   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4238   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
4239 
4240   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4241   B_mpi->assembled    = PETSC_FALSE;
4242   B_mpi->ops->destroy = MatDestroy_MPIAIJ_SeqsToMPI;
4243   merge->bi           = bi;
4244   merge->bj           = bj;
4245   merge->buf_ri       = buf_ri;
4246   merge->buf_rj       = buf_rj;
4247   merge->coi          = NULL;
4248   merge->coj          = NULL;
4249   merge->owners_co    = NULL;
4250 
4251   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
4252 
4253   /* attach the supporting struct to B_mpi for reuse */
4254   ierr    = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
4255   ierr    = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
4256   ierr    = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
4257   ierr    = PetscContainerDestroy(&container);CHKERRQ(ierr);
4258   *mpimat = B_mpi;
4259 
4260   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4261   PetscFunctionReturn(0);
4262 }
4263 
4264 #undef __FUNCT__
4265 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJ"
4266 /*@C
4267       MatCreateMPIAIJSumSeqAIJ - Creates a MPIAIJ matrix by adding sequential
4268                  matrices from each processor
4269 
4270     Collective on MPI_Comm
4271 
4272    Input Parameters:
4273 +    comm - the communicators the parallel matrix will live on
4274 .    seqmat - the input sequential matrices
4275 .    m - number of local rows (or PETSC_DECIDE)
4276 .    n - number of local columns (or PETSC_DECIDE)
4277 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4278 
4279    Output Parameter:
4280 .    mpimat - the parallel matrix generated
4281 
4282     Level: advanced
4283 
4284    Notes:
4285      The dimensions of the sequential matrix in each processor MUST be the same.
4286      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
4287      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
4288 @*/
4289 PetscErrorCode  MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
4290 {
4291   PetscErrorCode ierr;
4292   PetscMPIInt    size;
4293 
4294   PetscFunctionBegin;
4295   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4296   if (size == 1) {
4297     ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4298     if (scall == MAT_INITIAL_MATRIX) {
4299       ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
4300     } else {
4301       ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4302     }
4303     ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4304     PetscFunctionReturn(0);
4305   }
4306   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4307   if (scall == MAT_INITIAL_MATRIX) {
4308     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
4309   }
4310   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
4311   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4312   PetscFunctionReturn(0);
4313 }
4314 
4315 #undef __FUNCT__
4316 #define __FUNCT__ "MatMPIAIJGetLocalMat"
4317 /*@
4318      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
4319           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
4320           with MatGetSize()
4321 
4322     Not Collective
4323 
4324    Input Parameters:
4325 +    A - the matrix
4326 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4327 
4328    Output Parameter:
4329 .    A_loc - the local sequential matrix generated
4330 
4331     Level: developer
4332 
4333 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
4334 
4335 @*/
4336 PetscErrorCode  MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
4337 {
4338   PetscErrorCode ierr;
4339   Mat_MPIAIJ     *mpimat=(Mat_MPIAIJ*)A->data;
4340   Mat_SeqAIJ     *mat,*a,*b;
4341   PetscInt       *ai,*aj,*bi,*bj,*cmap=mpimat->garray;
4342   MatScalar      *aa,*ba,*cam;
4343   PetscScalar    *ca;
4344   PetscInt       am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
4345   PetscInt       *ci,*cj,col,ncols_d,ncols_o,jo;
4346   PetscBool      match;
4347   MPI_Comm       comm;
4348   PetscMPIInt    size;
4349 
4350   PetscFunctionBegin;
4351   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4352   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
4353   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4354   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4355   if (size == 1 && scall == MAT_REUSE_MATRIX) PetscFunctionReturn(0);
4356 
4357   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4358   a = (Mat_SeqAIJ*)(mpimat->A)->data;
4359   b = (Mat_SeqAIJ*)(mpimat->B)->data;
4360   ai = a->i; aj = a->j; bi = b->i; bj = b->j;
4361   aa = a->a; ba = b->a;
4362   if (scall == MAT_INITIAL_MATRIX) {
4363     if (size == 1) {
4364       ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ai,aj,aa,A_loc);CHKERRQ(ierr);
4365       PetscFunctionReturn(0);
4366     }
4367 
4368     ierr  = PetscMalloc1(1+am,&ci);CHKERRQ(ierr);
4369     ci[0] = 0;
4370     for (i=0; i<am; i++) {
4371       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
4372     }
4373     ierr = PetscMalloc1(1+ci[am],&cj);CHKERRQ(ierr);
4374     ierr = PetscMalloc1(1+ci[am],&ca);CHKERRQ(ierr);
4375     k    = 0;
4376     for (i=0; i<am; i++) {
4377       ncols_o = bi[i+1] - bi[i];
4378       ncols_d = ai[i+1] - ai[i];
4379       /* off-diagonal portion of A */
4380       for (jo=0; jo<ncols_o; jo++) {
4381         col = cmap[*bj];
4382         if (col >= cstart) break;
4383         cj[k]   = col; bj++;
4384         ca[k++] = *ba++;
4385       }
4386       /* diagonal portion of A */
4387       for (j=0; j<ncols_d; j++) {
4388         cj[k]   = cstart + *aj++;
4389         ca[k++] = *aa++;
4390       }
4391       /* off-diagonal portion of A */
4392       for (j=jo; j<ncols_o; j++) {
4393         cj[k]   = cmap[*bj++];
4394         ca[k++] = *ba++;
4395       }
4396     }
4397     /* put together the new matrix */
4398     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
4399     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4400     /* Since these are PETSc arrays, change flags to free them as necessary. */
4401     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
4402     mat->free_a  = PETSC_TRUE;
4403     mat->free_ij = PETSC_TRUE;
4404     mat->nonew   = 0;
4405   } else if (scall == MAT_REUSE_MATRIX) {
4406     mat=(Mat_SeqAIJ*)(*A_loc)->data;
4407     ci = mat->i; cj = mat->j; cam = mat->a;
4408     for (i=0; i<am; i++) {
4409       /* off-diagonal portion of A */
4410       ncols_o = bi[i+1] - bi[i];
4411       for (jo=0; jo<ncols_o; jo++) {
4412         col = cmap[*bj];
4413         if (col >= cstart) break;
4414         *cam++ = *ba++; bj++;
4415       }
4416       /* diagonal portion of A */
4417       ncols_d = ai[i+1] - ai[i];
4418       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
4419       /* off-diagonal portion of A */
4420       for (j=jo; j<ncols_o; j++) {
4421         *cam++ = *ba++; bj++;
4422       }
4423     }
4424   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
4425   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4426   PetscFunctionReturn(0);
4427 }
4428 
4429 #undef __FUNCT__
4430 #define __FUNCT__ "MatMPIAIJGetLocalMatCondensed"
4431 /*@C
4432      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MPIAIJ matrix by taking all its local rows and NON-ZERO columns
4433 
4434     Not Collective
4435 
4436    Input Parameters:
4437 +    A - the matrix
4438 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4439 -    row, col - index sets of rows and columns to extract (or NULL)
4440 
4441    Output Parameter:
4442 .    A_loc - the local sequential matrix generated
4443 
4444     Level: developer
4445 
4446 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
4447 
4448 @*/
4449 PetscErrorCode  MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
4450 {
4451   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4452   PetscErrorCode ierr;
4453   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
4454   IS             isrowa,iscola;
4455   Mat            *aloc;
4456   PetscBool      match;
4457 
4458   PetscFunctionBegin;
4459   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4460   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
4461   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4462   if (!row) {
4463     start = A->rmap->rstart; end = A->rmap->rend;
4464     ierr  = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
4465   } else {
4466     isrowa = *row;
4467   }
4468   if (!col) {
4469     start = A->cmap->rstart;
4470     cmap  = a->garray;
4471     nzA   = a->A->cmap->n;
4472     nzB   = a->B->cmap->n;
4473     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4474     ncols = 0;
4475     for (i=0; i<nzB; i++) {
4476       if (cmap[i] < start) idx[ncols++] = cmap[i];
4477       else break;
4478     }
4479     imark = i;
4480     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
4481     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
4482     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
4483   } else {
4484     iscola = *col;
4485   }
4486   if (scall != MAT_INITIAL_MATRIX) {
4487     ierr    = PetscMalloc1(1,&aloc);CHKERRQ(ierr);
4488     aloc[0] = *A_loc;
4489   }
4490   ierr   = MatGetSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
4491   *A_loc = aloc[0];
4492   ierr   = PetscFree(aloc);CHKERRQ(ierr);
4493   if (!row) {
4494     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
4495   }
4496   if (!col) {
4497     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
4498   }
4499   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4500   PetscFunctionReturn(0);
4501 }
4502 
4503 #undef __FUNCT__
4504 #define __FUNCT__ "MatGetBrowsOfAcols"
4505 /*@C
4506     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
4507 
4508     Collective on Mat
4509 
4510    Input Parameters:
4511 +    A,B - the matrices in mpiaij format
4512 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4513 -    rowb, colb - index sets of rows and columns of B to extract (or NULL)
4514 
4515    Output Parameter:
4516 +    rowb, colb - index sets of rows and columns of B to extract
4517 -    B_seq - the sequential matrix generated
4518 
4519     Level: developer
4520 
4521 @*/
4522 PetscErrorCode  MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
4523 {
4524   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4525   PetscErrorCode ierr;
4526   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
4527   IS             isrowb,iscolb;
4528   Mat            *bseq=NULL;
4529 
4530   PetscFunctionBegin;
4531   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4532     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);
4533   }
4534   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4535 
4536   if (scall == MAT_INITIAL_MATRIX) {
4537     start = A->cmap->rstart;
4538     cmap  = a->garray;
4539     nzA   = a->A->cmap->n;
4540     nzB   = a->B->cmap->n;
4541     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4542     ncols = 0;
4543     for (i=0; i<nzB; i++) {  /* row < local row index */
4544       if (cmap[i] < start) idx[ncols++] = cmap[i];
4545       else break;
4546     }
4547     imark = i;
4548     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
4549     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
4550     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
4551     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
4552   } else {
4553     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
4554     isrowb  = *rowb; iscolb = *colb;
4555     ierr    = PetscMalloc1(1,&bseq);CHKERRQ(ierr);
4556     bseq[0] = *B_seq;
4557   }
4558   ierr   = MatGetSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
4559   *B_seq = bseq[0];
4560   ierr   = PetscFree(bseq);CHKERRQ(ierr);
4561   if (!rowb) {
4562     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
4563   } else {
4564     *rowb = isrowb;
4565   }
4566   if (!colb) {
4567     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
4568   } else {
4569     *colb = iscolb;
4570   }
4571   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4572   PetscFunctionReturn(0);
4573 }
4574 
4575 #undef __FUNCT__
4576 #define __FUNCT__ "MatGetBrowsOfAoCols_MPIAIJ"
4577 /*
4578     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
4579     of the OFF-DIAGONAL portion of local A
4580 
4581     Collective on Mat
4582 
4583    Input Parameters:
4584 +    A,B - the matrices in mpiaij format
4585 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4586 
4587    Output Parameter:
4588 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
4589 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
4590 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
4591 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
4592 
4593     Level: developer
4594 
4595 */
4596 PetscErrorCode  MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
4597 {
4598   VecScatter_MPI_General *gen_to,*gen_from;
4599   PetscErrorCode         ierr;
4600   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
4601   Mat_SeqAIJ             *b_oth;
4602   VecScatter             ctx =a->Mvctx;
4603   MPI_Comm               comm;
4604   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
4605   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
4606   PetscScalar            *rvalues,*svalues;
4607   MatScalar              *b_otha,*bufa,*bufA;
4608   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
4609   MPI_Request            *rwaits = NULL,*swaits = NULL;
4610   MPI_Status             *sstatus,rstatus;
4611   PetscMPIInt            jj,size;
4612   PetscInt               *cols,sbs,rbs;
4613   PetscScalar            *vals;
4614 
4615   PetscFunctionBegin;
4616   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4617   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4618 
4619   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4620     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);
4621   }
4622   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4623   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4624 
4625   gen_to   = (VecScatter_MPI_General*)ctx->todata;
4626   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
4627   rvalues  = gen_from->values; /* holds the length of receiving row */
4628   svalues  = gen_to->values;   /* holds the length of sending row */
4629   nrecvs   = gen_from->n;
4630   nsends   = gen_to->n;
4631 
4632   ierr    = PetscMalloc2(nrecvs,&rwaits,nsends,&swaits);CHKERRQ(ierr);
4633   srow    = gen_to->indices;    /* local row index to be sent */
4634   sstarts = gen_to->starts;
4635   sprocs  = gen_to->procs;
4636   sstatus = gen_to->sstatus;
4637   sbs     = gen_to->bs;
4638   rstarts = gen_from->starts;
4639   rprocs  = gen_from->procs;
4640   rbs     = gen_from->bs;
4641 
4642   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
4643   if (scall == MAT_INITIAL_MATRIX) {
4644     /* i-array */
4645     /*---------*/
4646     /*  post receives */
4647     for (i=0; i<nrecvs; i++) {
4648       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
4649       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
4650       ierr   = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4651     }
4652 
4653     /* pack the outgoing message */
4654     ierr = PetscMalloc2(nsends+1,&sstartsj,nrecvs+1,&rstartsj);CHKERRQ(ierr);
4655 
4656     sstartsj[0] = 0;
4657     rstartsj[0] = 0;
4658     len         = 0; /* total length of j or a array to be sent */
4659     k           = 0;
4660     for (i=0; i<nsends; i++) {
4661       rowlen = (PetscInt*)svalues + sstarts[i]*sbs;
4662       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
4663       for (j=0; j<nrows; j++) {
4664         row = srow[k] + B->rmap->range[rank]; /* global row idx */
4665         for (l=0; l<sbs; l++) {
4666           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr); /* rowlength */
4667 
4668           rowlen[j*sbs+l] = ncols;
4669 
4670           len += ncols;
4671           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr);
4672         }
4673         k++;
4674       }
4675       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4676 
4677       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
4678     }
4679     /* recvs and sends of i-array are completed */
4680     i = nrecvs;
4681     while (i--) {
4682       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4683     }
4684     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4685 
4686     /* allocate buffers for sending j and a arrays */
4687     ierr = PetscMalloc1(len+1,&bufj);CHKERRQ(ierr);
4688     ierr = PetscMalloc1(len+1,&bufa);CHKERRQ(ierr);
4689 
4690     /* create i-array of B_oth */
4691     ierr = PetscMalloc1(aBn+2,&b_othi);CHKERRQ(ierr);
4692 
4693     b_othi[0] = 0;
4694     len       = 0; /* total length of j or a array to be received */
4695     k         = 0;
4696     for (i=0; i<nrecvs; i++) {
4697       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
4698       nrows  = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be recieved */
4699       for (j=0; j<nrows; j++) {
4700         b_othi[k+1] = b_othi[k] + rowlen[j];
4701         len        += rowlen[j]; k++;
4702       }
4703       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
4704     }
4705 
4706     /* allocate space for j and a arrrays of B_oth */
4707     ierr = PetscMalloc1(b_othi[aBn]+1,&b_othj);CHKERRQ(ierr);
4708     ierr = PetscMalloc1(b_othi[aBn]+1,&b_otha);CHKERRQ(ierr);
4709 
4710     /* j-array */
4711     /*---------*/
4712     /*  post receives of j-array */
4713     for (i=0; i<nrecvs; i++) {
4714       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4715       ierr  = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4716     }
4717 
4718     /* pack the outgoing message j-array */
4719     k = 0;
4720     for (i=0; i<nsends; i++) {
4721       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4722       bufJ  = bufj+sstartsj[i];
4723       for (j=0; j<nrows; j++) {
4724         row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4725         for (ll=0; ll<sbs; ll++) {
4726           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4727           for (l=0; l<ncols; l++) {
4728             *bufJ++ = cols[l];
4729           }
4730           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4731         }
4732       }
4733       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4734     }
4735 
4736     /* recvs and sends of j-array are completed */
4737     i = nrecvs;
4738     while (i--) {
4739       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4740     }
4741     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4742   } else if (scall == MAT_REUSE_MATRIX) {
4743     sstartsj = *startsj_s;
4744     rstartsj = *startsj_r;
4745     bufa     = *bufa_ptr;
4746     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
4747     b_otha   = b_oth->a;
4748   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
4749 
4750   /* a-array */
4751   /*---------*/
4752   /*  post receives of a-array */
4753   for (i=0; i<nrecvs; i++) {
4754     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4755     ierr  = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4756   }
4757 
4758   /* pack the outgoing message a-array */
4759   k = 0;
4760   for (i=0; i<nsends; i++) {
4761     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4762     bufA  = bufa+sstartsj[i];
4763     for (j=0; j<nrows; j++) {
4764       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4765       for (ll=0; ll<sbs; ll++) {
4766         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4767         for (l=0; l<ncols; l++) {
4768           *bufA++ = vals[l];
4769         }
4770         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4771       }
4772     }
4773     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4774   }
4775   /* recvs and sends of a-array are completed */
4776   i = nrecvs;
4777   while (i--) {
4778     ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4779   }
4780   if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4781   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
4782 
4783   if (scall == MAT_INITIAL_MATRIX) {
4784     /* put together the new matrix */
4785     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
4786 
4787     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4788     /* Since these are PETSc arrays, change flags to free them as necessary. */
4789     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
4790     b_oth->free_a  = PETSC_TRUE;
4791     b_oth->free_ij = PETSC_TRUE;
4792     b_oth->nonew   = 0;
4793 
4794     ierr = PetscFree(bufj);CHKERRQ(ierr);
4795     if (!startsj_s || !bufa_ptr) {
4796       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
4797       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
4798     } else {
4799       *startsj_s = sstartsj;
4800       *startsj_r = rstartsj;
4801       *bufa_ptr  = bufa;
4802     }
4803   }
4804   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4805   PetscFunctionReturn(0);
4806 }
4807 
4808 #undef __FUNCT__
4809 #define __FUNCT__ "MatGetCommunicationStructs"
4810 /*@C
4811   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
4812 
4813   Not Collective
4814 
4815   Input Parameters:
4816 . A - The matrix in mpiaij format
4817 
4818   Output Parameter:
4819 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
4820 . colmap - A map from global column index to local index into lvec
4821 - multScatter - A scatter from the argument of a matrix-vector product to lvec
4822 
4823   Level: developer
4824 
4825 @*/
4826 #if defined(PETSC_USE_CTABLE)
4827 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
4828 #else
4829 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
4830 #endif
4831 {
4832   Mat_MPIAIJ *a;
4833 
4834   PetscFunctionBegin;
4835   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4836   PetscValidPointer(lvec, 2);
4837   PetscValidPointer(colmap, 3);
4838   PetscValidPointer(multScatter, 4);
4839   a = (Mat_MPIAIJ*) A->data;
4840   if (lvec) *lvec = a->lvec;
4841   if (colmap) *colmap = a->colmap;
4842   if (multScatter) *multScatter = a->Mvctx;
4843   PetscFunctionReturn(0);
4844 }
4845 
4846 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
4847 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
4848 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
4849 #if defined(PETSC_HAVE_ELEMENTAL)
4850 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
4851 #endif
4852 
4853 #undef __FUNCT__
4854 #define __FUNCT__ "MatMatMultNumeric_MPIDense_MPIAIJ"
4855 /*
4856     Computes (B'*A')' since computing B*A directly is untenable
4857 
4858                n                       p                          p
4859         (              )       (              )         (                  )
4860       m (      A       )  *  n (       B      )   =   m (         C        )
4861         (              )       (              )         (                  )
4862 
4863 */
4864 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
4865 {
4866   PetscErrorCode ierr;
4867   Mat            At,Bt,Ct;
4868 
4869   PetscFunctionBegin;
4870   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
4871   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
4872   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
4873   ierr = MatDestroy(&At);CHKERRQ(ierr);
4874   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
4875   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
4876   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
4877   PetscFunctionReturn(0);
4878 }
4879 
4880 #undef __FUNCT__
4881 #define __FUNCT__ "MatMatMultSymbolic_MPIDense_MPIAIJ"
4882 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
4883 {
4884   PetscErrorCode ierr;
4885   PetscInt       m=A->rmap->n,n=B->cmap->n;
4886   Mat            Cmat;
4887 
4888   PetscFunctionBegin;
4889   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);
4890   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
4891   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4892   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
4893   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
4894   ierr = MatMPIDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
4895   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4896   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4897 
4898   Cmat->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
4899 
4900   *C = Cmat;
4901   PetscFunctionReturn(0);
4902 }
4903 
4904 /* ----------------------------------------------------------------*/
4905 #undef __FUNCT__
4906 #define __FUNCT__ "MatMatMult_MPIDense_MPIAIJ"
4907 PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
4908 {
4909   PetscErrorCode ierr;
4910 
4911   PetscFunctionBegin;
4912   if (scall == MAT_INITIAL_MATRIX) {
4913     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
4914     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
4915     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
4916   }
4917   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
4918   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
4919   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
4920   PetscFunctionReturn(0);
4921 }
4922 
4923 /*MC
4924    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
4925 
4926    Options Database Keys:
4927 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
4928 
4929   Level: beginner
4930 
4931 .seealso: MatCreateAIJ()
4932 M*/
4933 
4934 #undef __FUNCT__
4935 #define __FUNCT__ "MatCreate_MPIAIJ"
4936 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
4937 {
4938   Mat_MPIAIJ     *b;
4939   PetscErrorCode ierr;
4940   PetscMPIInt    size;
4941 
4942   PetscFunctionBegin;
4943   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
4944 
4945   ierr          = PetscNewLog(B,&b);CHKERRQ(ierr);
4946   B->data       = (void*)b;
4947   ierr          = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
4948   B->assembled  = PETSC_FALSE;
4949   B->insertmode = NOT_SET_VALUES;
4950   b->size       = size;
4951 
4952   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank);CHKERRQ(ierr);
4953 
4954   /* build cache for off array entries formed */
4955   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash);CHKERRQ(ierr);
4956 
4957   b->donotstash  = PETSC_FALSE;
4958   b->colmap      = 0;
4959   b->garray      = 0;
4960   b->roworiented = PETSC_TRUE;
4961 
4962   /* stuff used for matrix vector multiply */
4963   b->lvec  = NULL;
4964   b->Mvctx = NULL;
4965 
4966   /* stuff for MatGetRow() */
4967   b->rowindices   = 0;
4968   b->rowvalues    = 0;
4969   b->getrowactive = PETSC_FALSE;
4970 
4971   /* flexible pointer used in CUSP/CUSPARSE classes */
4972   b->spptr = NULL;
4973 
4974   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ);CHKERRQ(ierr);
4975   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
4976   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetDiagonalBlock_C",MatGetDiagonalBlock_MPIAIJ);CHKERRQ(ierr);
4977   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
4978   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
4979   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
4980   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
4981   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
4982   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
4983   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
4984 #if defined(PETSC_HAVE_ELEMENTAL)
4985   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_elemental_C",MatConvert_MPIAIJ_Elemental);CHKERRQ(ierr);
4986 #endif
4987   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
4988   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
4989   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
4990   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
4991   PetscFunctionReturn(0);
4992 }
4993 
4994 #undef __FUNCT__
4995 #define __FUNCT__ "MatCreateMPIAIJWithSplitArrays"
4996 /*@C
4997      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
4998          and "off-diagonal" part of the matrix in CSR format.
4999 
5000    Collective on MPI_Comm
5001 
5002    Input Parameters:
5003 +  comm - MPI communicator
5004 .  m - number of local rows (Cannot be PETSC_DECIDE)
5005 .  n - This value should be the same as the local size used in creating the
5006        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
5007        calculated if N is given) For square matrices n is almost always m.
5008 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
5009 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
5010 .   i - row indices for "diagonal" portion of matrix
5011 .   j - column indices
5012 .   a - matrix values
5013 .   oi - row indices for "off-diagonal" portion of matrix
5014 .   oj - column indices
5015 -   oa - matrix values
5016 
5017    Output Parameter:
5018 .   mat - the matrix
5019 
5020    Level: advanced
5021 
5022    Notes:
5023        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
5024        must free the arrays once the matrix has been destroyed and not before.
5025 
5026        The i and j indices are 0 based
5027 
5028        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
5029 
5030        This sets local rows and cannot be used to set off-processor values.
5031 
5032        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
5033        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
5034        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
5035        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
5036        keep track of the underlying array. Use MatSetOption(A,MAT_IGNORE_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
5037        communication if it is known that only local entries will be set.
5038 
5039 .keywords: matrix, aij, compressed row, sparse, parallel
5040 
5041 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
5042           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
5043 @*/
5044 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)
5045 {
5046   PetscErrorCode ierr;
5047   Mat_MPIAIJ     *maij;
5048 
5049   PetscFunctionBegin;
5050   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
5051   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
5052   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
5053   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
5054   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
5055   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
5056   maij = (Mat_MPIAIJ*) (*mat)->data;
5057 
5058   (*mat)->preallocated = PETSC_TRUE;
5059 
5060   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
5061   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
5062 
5063   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
5064   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
5065 
5066   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5067   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5068   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5069   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5070 
5071   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5072   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5073   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
5074   PetscFunctionReturn(0);
5075 }
5076 
5077 /*
5078     Special version for direct calls from Fortran
5079 */
5080 #include <petsc/private/fortranimpl.h>
5081 
5082 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5083 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
5084 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5085 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
5086 #endif
5087 
5088 /* Change these macros so can be used in void function */
5089 #undef CHKERRQ
5090 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
5091 #undef SETERRQ2
5092 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5093 #undef SETERRQ3
5094 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5095 #undef SETERRQ
5096 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
5097 
5098 #undef __FUNCT__
5099 #define __FUNCT__ "matsetvaluesmpiaij_"
5100 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)
5101 {
5102   Mat            mat  = *mmat;
5103   PetscInt       m    = *mm, n = *mn;
5104   InsertMode     addv = *maddv;
5105   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
5106   PetscScalar    value;
5107   PetscErrorCode ierr;
5108 
5109   MatCheckPreallocated(mat,1);
5110   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
5111 
5112 #if defined(PETSC_USE_DEBUG)
5113   else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
5114 #endif
5115   {
5116     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
5117     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
5118     PetscBool roworiented = aij->roworiented;
5119 
5120     /* Some Variables required in the macro */
5121     Mat        A                 = aij->A;
5122     Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
5123     PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
5124     MatScalar  *aa               = a->a;
5125     PetscBool  ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
5126     Mat        B                 = aij->B;
5127     Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
5128     PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5129     MatScalar  *ba               = b->a;
5130 
5131     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5132     PetscInt  nonew = a->nonew;
5133     MatScalar *ap1,*ap2;
5134 
5135     PetscFunctionBegin;
5136     for (i=0; i<m; i++) {
5137       if (im[i] < 0) continue;
5138 #if defined(PETSC_USE_DEBUG)
5139       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);
5140 #endif
5141       if (im[i] >= rstart && im[i] < rend) {
5142         row      = im[i] - rstart;
5143         lastcol1 = -1;
5144         rp1      = aj + ai[row];
5145         ap1      = aa + ai[row];
5146         rmax1    = aimax[row];
5147         nrow1    = ailen[row];
5148         low1     = 0;
5149         high1    = nrow1;
5150         lastcol2 = -1;
5151         rp2      = bj + bi[row];
5152         ap2      = ba + bi[row];
5153         rmax2    = bimax[row];
5154         nrow2    = bilen[row];
5155         low2     = 0;
5156         high2    = nrow2;
5157 
5158         for (j=0; j<n; j++) {
5159           if (roworiented) value = v[i*n+j];
5160           else value = v[i+j*m];
5161           if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES)) continue;
5162           if (in[j] >= cstart && in[j] < cend) {
5163             col = in[j] - cstart;
5164             MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
5165           } else if (in[j] < 0) continue;
5166 #if defined(PETSC_USE_DEBUG)
5167           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);
5168 #endif
5169           else {
5170             if (mat->was_assembled) {
5171               if (!aij->colmap) {
5172                 ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5173               }
5174 #if defined(PETSC_USE_CTABLE)
5175               ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5176               col--;
5177 #else
5178               col = aij->colmap[in[j]] - 1;
5179 #endif
5180               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5181                 ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5182                 col  =  in[j];
5183                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5184                 B     = aij->B;
5185                 b     = (Mat_SeqAIJ*)B->data;
5186                 bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5187                 rp2   = bj + bi[row];
5188                 ap2   = ba + bi[row];
5189                 rmax2 = bimax[row];
5190                 nrow2 = bilen[row];
5191                 low2  = 0;
5192                 high2 = nrow2;
5193                 bm    = aij->B->rmap->n;
5194                 ba    = b->a;
5195               }
5196             } else col = in[j];
5197             MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
5198           }
5199         }
5200       } else if (!aij->donotstash) {
5201         if (roworiented) {
5202           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5203         } else {
5204           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5205         }
5206       }
5207     }
5208   }
5209   PetscFunctionReturnVoid();
5210 }
5211 
5212