xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision eab890ac70e3f8cf2d8ed246aa467cd84d643ced)
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__ "MatGetInfo_MPIAIJ"
1683 PetscErrorCode MatGetInfo_MPIAIJ(Mat matin,MatInfoType flag,MatInfo *info)
1684 {
1685   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1686   Mat            A    = mat->A,B = mat->B;
1687   PetscErrorCode ierr;
1688   PetscReal      isend[5],irecv[5];
1689 
1690   PetscFunctionBegin;
1691   info->block_size = 1.0;
1692   ierr             = MatGetInfo(A,MAT_LOCAL,info);CHKERRQ(ierr);
1693 
1694   isend[0] = info->nz_used; isend[1] = info->nz_allocated; isend[2] = info->nz_unneeded;
1695   isend[3] = info->memory;  isend[4] = info->mallocs;
1696 
1697   ierr = MatGetInfo(B,MAT_LOCAL,info);CHKERRQ(ierr);
1698 
1699   isend[0] += info->nz_used; isend[1] += info->nz_allocated; isend[2] += info->nz_unneeded;
1700   isend[3] += info->memory;  isend[4] += info->mallocs;
1701   if (flag == MAT_LOCAL) {
1702     info->nz_used      = isend[0];
1703     info->nz_allocated = isend[1];
1704     info->nz_unneeded  = isend[2];
1705     info->memory       = isend[3];
1706     info->mallocs      = isend[4];
1707   } else if (flag == MAT_GLOBAL_MAX) {
1708     ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1709 
1710     info->nz_used      = irecv[0];
1711     info->nz_allocated = irecv[1];
1712     info->nz_unneeded  = irecv[2];
1713     info->memory       = irecv[3];
1714     info->mallocs      = irecv[4];
1715   } else if (flag == MAT_GLOBAL_SUM) {
1716     ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1717 
1718     info->nz_used      = irecv[0];
1719     info->nz_allocated = irecv[1];
1720     info->nz_unneeded  = irecv[2];
1721     info->memory       = irecv[3];
1722     info->mallocs      = irecv[4];
1723   }
1724   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
1725   info->fill_ratio_needed = 0;
1726   info->factor_mallocs    = 0;
1727   PetscFunctionReturn(0);
1728 }
1729 
1730 #undef __FUNCT__
1731 #define __FUNCT__ "MatSetOption_MPIAIJ"
1732 PetscErrorCode MatSetOption_MPIAIJ(Mat A,MatOption op,PetscBool flg)
1733 {
1734   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1735   PetscErrorCode ierr;
1736 
1737   PetscFunctionBegin;
1738   switch (op) {
1739   case MAT_NEW_NONZERO_LOCATIONS:
1740   case MAT_NEW_NONZERO_ALLOCATION_ERR:
1741   case MAT_UNUSED_NONZERO_LOCATION_ERR:
1742   case MAT_KEEP_NONZERO_PATTERN:
1743   case MAT_NEW_NONZERO_LOCATION_ERR:
1744   case MAT_USE_INODES:
1745   case MAT_IGNORE_ZERO_ENTRIES:
1746     MatCheckPreallocated(A,1);
1747     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1748     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1749     break;
1750   case MAT_ROW_ORIENTED:
1751     a->roworiented = flg;
1752 
1753     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1754     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1755     break;
1756   case MAT_NEW_DIAGONALS:
1757     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
1758     break;
1759   case MAT_IGNORE_OFF_PROC_ENTRIES:
1760     a->donotstash = flg;
1761     break;
1762   case MAT_SPD:
1763     A->spd_set = PETSC_TRUE;
1764     A->spd     = flg;
1765     if (flg) {
1766       A->symmetric                  = PETSC_TRUE;
1767       A->structurally_symmetric     = PETSC_TRUE;
1768       A->symmetric_set              = PETSC_TRUE;
1769       A->structurally_symmetric_set = PETSC_TRUE;
1770     }
1771     break;
1772   case MAT_SYMMETRIC:
1773     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1774     break;
1775   case MAT_STRUCTURALLY_SYMMETRIC:
1776     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1777     break;
1778   case MAT_HERMITIAN:
1779     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1780     break;
1781   case MAT_SYMMETRY_ETERNAL:
1782     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1783     break;
1784   default:
1785     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %d",op);
1786   }
1787   PetscFunctionReturn(0);
1788 }
1789 
1790 #undef __FUNCT__
1791 #define __FUNCT__ "MatGetRow_MPIAIJ"
1792 PetscErrorCode MatGetRow_MPIAIJ(Mat matin,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1793 {
1794   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1795   PetscScalar    *vworkA,*vworkB,**pvA,**pvB,*v_p;
1796   PetscErrorCode ierr;
1797   PetscInt       i,*cworkA,*cworkB,**pcA,**pcB,cstart = matin->cmap->rstart;
1798   PetscInt       nztot,nzA,nzB,lrow,rstart = matin->rmap->rstart,rend = matin->rmap->rend;
1799   PetscInt       *cmap,*idx_p;
1800 
1801   PetscFunctionBegin;
1802   if (mat->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Already active");
1803   mat->getrowactive = PETSC_TRUE;
1804 
1805   if (!mat->rowvalues && (idx || v)) {
1806     /*
1807         allocate enough space to hold information from the longest row.
1808     */
1809     Mat_SeqAIJ *Aa = (Mat_SeqAIJ*)mat->A->data,*Ba = (Mat_SeqAIJ*)mat->B->data;
1810     PetscInt   max = 1,tmp;
1811     for (i=0; i<matin->rmap->n; i++) {
1812       tmp = Aa->i[i+1] - Aa->i[i] + Ba->i[i+1] - Ba->i[i];
1813       if (max < tmp) max = tmp;
1814     }
1815     ierr = PetscMalloc2(max,&mat->rowvalues,max,&mat->rowindices);CHKERRQ(ierr);
1816   }
1817 
1818   if (row < rstart || row >= rend) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Only local rows");
1819   lrow = row - rstart;
1820 
1821   pvA = &vworkA; pcA = &cworkA; pvB = &vworkB; pcB = &cworkB;
1822   if (!v)   {pvA = 0; pvB = 0;}
1823   if (!idx) {pcA = 0; if (!v) pcB = 0;}
1824   ierr  = (*mat->A->ops->getrow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1825   ierr  = (*mat->B->ops->getrow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1826   nztot = nzA + nzB;
1827 
1828   cmap = mat->garray;
1829   if (v  || idx) {
1830     if (nztot) {
1831       /* Sort by increasing column numbers, assuming A and B already sorted */
1832       PetscInt imark = -1;
1833       if (v) {
1834         *v = v_p = mat->rowvalues;
1835         for (i=0; i<nzB; i++) {
1836           if (cmap[cworkB[i]] < cstart) v_p[i] = vworkB[i];
1837           else break;
1838         }
1839         imark = i;
1840         for (i=0; i<nzA; i++)     v_p[imark+i] = vworkA[i];
1841         for (i=imark; i<nzB; i++) v_p[nzA+i]   = vworkB[i];
1842       }
1843       if (idx) {
1844         *idx = idx_p = mat->rowindices;
1845         if (imark > -1) {
1846           for (i=0; i<imark; i++) {
1847             idx_p[i] = cmap[cworkB[i]];
1848           }
1849         } else {
1850           for (i=0; i<nzB; i++) {
1851             if (cmap[cworkB[i]] < cstart) idx_p[i] = cmap[cworkB[i]];
1852             else break;
1853           }
1854           imark = i;
1855         }
1856         for (i=0; i<nzA; i++)     idx_p[imark+i] = cstart + cworkA[i];
1857         for (i=imark; i<nzB; i++) idx_p[nzA+i]   = cmap[cworkB[i]];
1858       }
1859     } else {
1860       if (idx) *idx = 0;
1861       if (v)   *v   = 0;
1862     }
1863   }
1864   *nz  = nztot;
1865   ierr = (*mat->A->ops->restorerow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1866   ierr = (*mat->B->ops->restorerow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1867   PetscFunctionReturn(0);
1868 }
1869 
1870 #undef __FUNCT__
1871 #define __FUNCT__ "MatRestoreRow_MPIAIJ"
1872 PetscErrorCode MatRestoreRow_MPIAIJ(Mat mat,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1873 {
1874   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1875 
1876   PetscFunctionBegin;
1877   if (!aij->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"MatGetRow() must be called first");
1878   aij->getrowactive = PETSC_FALSE;
1879   PetscFunctionReturn(0);
1880 }
1881 
1882 #undef __FUNCT__
1883 #define __FUNCT__ "MatNorm_MPIAIJ"
1884 PetscErrorCode MatNorm_MPIAIJ(Mat mat,NormType type,PetscReal *norm)
1885 {
1886   Mat_MPIAIJ     *aij  = (Mat_MPIAIJ*)mat->data;
1887   Mat_SeqAIJ     *amat = (Mat_SeqAIJ*)aij->A->data,*bmat = (Mat_SeqAIJ*)aij->B->data;
1888   PetscErrorCode ierr;
1889   PetscInt       i,j,cstart = mat->cmap->rstart;
1890   PetscReal      sum = 0.0;
1891   MatScalar      *v;
1892 
1893   PetscFunctionBegin;
1894   if (aij->size == 1) {
1895     ierr =  MatNorm(aij->A,type,norm);CHKERRQ(ierr);
1896   } else {
1897     if (type == NORM_FROBENIUS) {
1898       v = amat->a;
1899       for (i=0; i<amat->nz; i++) {
1900         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1901       }
1902       v = bmat->a;
1903       for (i=0; i<bmat->nz; i++) {
1904         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1905       }
1906       ierr  = MPI_Allreduce(&sum,norm,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1907       *norm = PetscSqrtReal(*norm);
1908     } else if (type == NORM_1) { /* max column norm */
1909       PetscReal *tmp,*tmp2;
1910       PetscInt  *jj,*garray = aij->garray;
1911       ierr  = PetscCalloc1(mat->cmap->N+1,&tmp);CHKERRQ(ierr);
1912       ierr  = PetscMalloc1(mat->cmap->N+1,&tmp2);CHKERRQ(ierr);
1913       *norm = 0.0;
1914       v     = amat->a; jj = amat->j;
1915       for (j=0; j<amat->nz; j++) {
1916         tmp[cstart + *jj++] += PetscAbsScalar(*v);  v++;
1917       }
1918       v = bmat->a; jj = bmat->j;
1919       for (j=0; j<bmat->nz; j++) {
1920         tmp[garray[*jj++]] += PetscAbsScalar(*v); v++;
1921       }
1922       ierr = MPI_Allreduce(tmp,tmp2,mat->cmap->N,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1923       for (j=0; j<mat->cmap->N; j++) {
1924         if (tmp2[j] > *norm) *norm = tmp2[j];
1925       }
1926       ierr = PetscFree(tmp);CHKERRQ(ierr);
1927       ierr = PetscFree(tmp2);CHKERRQ(ierr);
1928     } else if (type == NORM_INFINITY) { /* max row norm */
1929       PetscReal ntemp = 0.0;
1930       for (j=0; j<aij->A->rmap->n; j++) {
1931         v   = amat->a + amat->i[j];
1932         sum = 0.0;
1933         for (i=0; i<amat->i[j+1]-amat->i[j]; i++) {
1934           sum += PetscAbsScalar(*v); v++;
1935         }
1936         v = bmat->a + bmat->i[j];
1937         for (i=0; i<bmat->i[j+1]-bmat->i[j]; i++) {
1938           sum += PetscAbsScalar(*v); v++;
1939         }
1940         if (sum > ntemp) ntemp = sum;
1941       }
1942       ierr = MPI_Allreduce(&ntemp,norm,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1943     } else SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"No support for two norm");
1944   }
1945   PetscFunctionReturn(0);
1946 }
1947 
1948 #undef __FUNCT__
1949 #define __FUNCT__ "MatTranspose_MPIAIJ"
1950 PetscErrorCode MatTranspose_MPIAIJ(Mat A,MatReuse reuse,Mat *matout)
1951 {
1952   Mat_MPIAIJ     *a   = (Mat_MPIAIJ*)A->data;
1953   Mat_SeqAIJ     *Aloc=(Mat_SeqAIJ*)a->A->data,*Bloc=(Mat_SeqAIJ*)a->B->data;
1954   PetscErrorCode ierr;
1955   PetscInt       M      = A->rmap->N,N = A->cmap->N,ma,na,mb,nb,*ai,*aj,*bi,*bj,row,*cols,*cols_tmp,i;
1956   PetscInt       cstart = A->cmap->rstart,ncol;
1957   Mat            B;
1958   MatScalar      *array;
1959 
1960   PetscFunctionBegin;
1961   if (reuse == MAT_REUSE_MATRIX && A == *matout && M != N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Square matrix only for in-place");
1962 
1963   ma = A->rmap->n; na = A->cmap->n; mb = a->B->rmap->n; nb = a->B->cmap->n;
1964   ai = Aloc->i; aj = Aloc->j;
1965   bi = Bloc->i; bj = Bloc->j;
1966   if (reuse == MAT_INITIAL_MATRIX || *matout == A) {
1967     PetscInt             *d_nnz,*g_nnz,*o_nnz;
1968     PetscSFNode          *oloc;
1969     PETSC_UNUSED PetscSF sf;
1970 
1971     ierr = PetscMalloc4(na,&d_nnz,na,&o_nnz,nb,&g_nnz,nb,&oloc);CHKERRQ(ierr);
1972     /* compute d_nnz for preallocation */
1973     ierr = PetscMemzero(d_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1974     for (i=0; i<ai[ma]; i++) {
1975       d_nnz[aj[i]]++;
1976       aj[i] += cstart; /* global col index to be used by MatSetValues() */
1977     }
1978     /* compute local off-diagonal contributions */
1979     ierr = PetscMemzero(g_nnz,nb*sizeof(PetscInt));CHKERRQ(ierr);
1980     for (i=0; i<bi[ma]; i++) g_nnz[bj[i]]++;
1981     /* map those to global */
1982     ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1983     ierr = PetscSFSetGraphLayout(sf,A->cmap,nb,NULL,PETSC_USE_POINTER,a->garray);CHKERRQ(ierr);
1984     ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1985     ierr = PetscMemzero(o_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1986     ierr = PetscSFReduceBegin(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
1987     ierr = PetscSFReduceEnd(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
1988     ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1989 
1990     ierr = MatCreate(PetscObjectComm((PetscObject)A),&B);CHKERRQ(ierr);
1991     ierr = MatSetSizes(B,A->cmap->n,A->rmap->n,N,M);CHKERRQ(ierr);
1992     ierr = MatSetBlockSizes(B,PetscAbs(A->cmap->bs),PetscAbs(A->rmap->bs));CHKERRQ(ierr);
1993     ierr = MatSetType(B,((PetscObject)A)->type_name);CHKERRQ(ierr);
1994     ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
1995     ierr = PetscFree4(d_nnz,o_nnz,g_nnz,oloc);CHKERRQ(ierr);
1996   } else {
1997     B    = *matout;
1998     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
1999     for (i=0; i<ai[ma]; i++) aj[i] += cstart; /* global col index to be used by MatSetValues() */
2000   }
2001 
2002   /* copy over the A part */
2003   array = Aloc->a;
2004   row   = A->rmap->rstart;
2005   for (i=0; i<ma; i++) {
2006     ncol = ai[i+1]-ai[i];
2007     ierr = MatSetValues(B,ncol,aj,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
2008     row++;
2009     array += ncol; aj += ncol;
2010   }
2011   aj = Aloc->j;
2012   for (i=0; i<ai[ma]; i++) aj[i] -= cstart; /* resume local col index */
2013 
2014   /* copy over the B part */
2015   ierr  = PetscCalloc1(bi[mb],&cols);CHKERRQ(ierr);
2016   array = Bloc->a;
2017   row   = A->rmap->rstart;
2018   for (i=0; i<bi[mb]; i++) cols[i] = a->garray[bj[i]];
2019   cols_tmp = cols;
2020   for (i=0; i<mb; i++) {
2021     ncol = bi[i+1]-bi[i];
2022     ierr = MatSetValues(B,ncol,cols_tmp,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
2023     row++;
2024     array += ncol; cols_tmp += ncol;
2025   }
2026   ierr = PetscFree(cols);CHKERRQ(ierr);
2027 
2028   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2029   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2030   if (reuse == MAT_INITIAL_MATRIX || *matout != A) {
2031     *matout = B;
2032   } else {
2033     ierr = MatHeaderMerge(A,B);CHKERRQ(ierr);
2034   }
2035   PetscFunctionReturn(0);
2036 }
2037 
2038 #undef __FUNCT__
2039 #define __FUNCT__ "MatDiagonalScale_MPIAIJ"
2040 PetscErrorCode MatDiagonalScale_MPIAIJ(Mat mat,Vec ll,Vec rr)
2041 {
2042   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2043   Mat            a    = aij->A,b = aij->B;
2044   PetscErrorCode ierr;
2045   PetscInt       s1,s2,s3;
2046 
2047   PetscFunctionBegin;
2048   ierr = MatGetLocalSize(mat,&s2,&s3);CHKERRQ(ierr);
2049   if (rr) {
2050     ierr = VecGetLocalSize(rr,&s1);CHKERRQ(ierr);
2051     if (s1!=s3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"right vector non-conforming local size");
2052     /* Overlap communication with computation. */
2053     ierr = VecScatterBegin(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2054   }
2055   if (ll) {
2056     ierr = VecGetLocalSize(ll,&s1);CHKERRQ(ierr);
2057     if (s1!=s2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"left vector non-conforming local size");
2058     ierr = (*b->ops->diagonalscale)(b,ll,0);CHKERRQ(ierr);
2059   }
2060   /* scale  the diagonal block */
2061   ierr = (*a->ops->diagonalscale)(a,ll,rr);CHKERRQ(ierr);
2062 
2063   if (rr) {
2064     /* Do a scatter end and then right scale the off-diagonal block */
2065     ierr = VecScatterEnd(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2066     ierr = (*b->ops->diagonalscale)(b,0,aij->lvec);CHKERRQ(ierr);
2067   }
2068   PetscFunctionReturn(0);
2069 }
2070 
2071 #undef __FUNCT__
2072 #define __FUNCT__ "MatSetUnfactored_MPIAIJ"
2073 PetscErrorCode MatSetUnfactored_MPIAIJ(Mat A)
2074 {
2075   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2076   PetscErrorCode ierr;
2077 
2078   PetscFunctionBegin;
2079   ierr = MatSetUnfactored(a->A);CHKERRQ(ierr);
2080   PetscFunctionReturn(0);
2081 }
2082 
2083 #undef __FUNCT__
2084 #define __FUNCT__ "MatEqual_MPIAIJ"
2085 PetscErrorCode MatEqual_MPIAIJ(Mat A,Mat B,PetscBool  *flag)
2086 {
2087   Mat_MPIAIJ     *matB = (Mat_MPIAIJ*)B->data,*matA = (Mat_MPIAIJ*)A->data;
2088   Mat            a,b,c,d;
2089   PetscBool      flg;
2090   PetscErrorCode ierr;
2091 
2092   PetscFunctionBegin;
2093   a = matA->A; b = matA->B;
2094   c = matB->A; d = matB->B;
2095 
2096   ierr = MatEqual(a,c,&flg);CHKERRQ(ierr);
2097   if (flg) {
2098     ierr = MatEqual(b,d,&flg);CHKERRQ(ierr);
2099   }
2100   ierr = MPI_Allreduce(&flg,flag,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
2101   PetscFunctionReturn(0);
2102 }
2103 
2104 #undef __FUNCT__
2105 #define __FUNCT__ "MatCopy_MPIAIJ"
2106 PetscErrorCode MatCopy_MPIAIJ(Mat A,Mat B,MatStructure str)
2107 {
2108   PetscErrorCode ierr;
2109   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2110   Mat_MPIAIJ     *b = (Mat_MPIAIJ*)B->data;
2111 
2112   PetscFunctionBegin;
2113   /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
2114   if ((str != SAME_NONZERO_PATTERN) || (A->ops->copy != B->ops->copy)) {
2115     /* because of the column compression in the off-processor part of the matrix a->B,
2116        the number of columns in a->B and b->B may be different, hence we cannot call
2117        the MatCopy() directly on the two parts. If need be, we can provide a more
2118        efficient copy than the MatCopy_Basic() by first uncompressing the a->B matrices
2119        then copying the submatrices */
2120     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
2121   } else {
2122     ierr = MatCopy(a->A,b->A,str);CHKERRQ(ierr);
2123     ierr = MatCopy(a->B,b->B,str);CHKERRQ(ierr);
2124   }
2125   PetscFunctionReturn(0);
2126 }
2127 
2128 #undef __FUNCT__
2129 #define __FUNCT__ "MatSetUp_MPIAIJ"
2130 PetscErrorCode MatSetUp_MPIAIJ(Mat A)
2131 {
2132   PetscErrorCode ierr;
2133 
2134   PetscFunctionBegin;
2135   ierr =  MatMPIAIJSetPreallocation(A,PETSC_DEFAULT,0,PETSC_DEFAULT,0);CHKERRQ(ierr);
2136   PetscFunctionReturn(0);
2137 }
2138 
2139 /*
2140    Computes the number of nonzeros per row needed for preallocation when X and Y
2141    have different nonzero structure.
2142 */
2143 #undef __FUNCT__
2144 #define __FUNCT__ "MatAXPYGetPreallocation_MPIX_private"
2145 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)
2146 {
2147   PetscInt       i,j,k,nzx,nzy;
2148 
2149   PetscFunctionBegin;
2150   /* Set the number of nonzeros in the new matrix */
2151   for (i=0; i<m; i++) {
2152     const PetscInt *xjj = xj+xi[i],*yjj = yj+yi[i];
2153     nzx = xi[i+1] - xi[i];
2154     nzy = yi[i+1] - yi[i];
2155     nnz[i] = 0;
2156     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2157       for (; k<nzy && yltog[yjj[k]]<xltog[xjj[j]]; k++) nnz[i]++; /* Catch up to X */
2158       if (k<nzy && yltog[yjj[k]]==xltog[xjj[j]]) k++;             /* Skip duplicate */
2159       nnz[i]++;
2160     }
2161     for (; k<nzy; k++) nnz[i]++;
2162   }
2163   PetscFunctionReturn(0);
2164 }
2165 
2166 /* This is the same as MatAXPYGetPreallocation_SeqAIJ, except that the local-to-global map is provided */
2167 #undef __FUNCT__
2168 #define __FUNCT__ "MatAXPYGetPreallocation_MPIAIJ"
2169 static PetscErrorCode MatAXPYGetPreallocation_MPIAIJ(Mat Y,const PetscInt *yltog,Mat X,const PetscInt *xltog,PetscInt *nnz)
2170 {
2171   PetscErrorCode ierr;
2172   PetscInt       m = Y->rmap->N;
2173   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data;
2174   Mat_SeqAIJ     *y = (Mat_SeqAIJ*)Y->data;
2175 
2176   PetscFunctionBegin;
2177   ierr = MatAXPYGetPreallocation_MPIX_private(m,x->i,x->j,xltog,y->i,y->j,yltog,nnz);CHKERRQ(ierr);
2178   PetscFunctionReturn(0);
2179 }
2180 
2181 #undef __FUNCT__
2182 #define __FUNCT__ "MatAXPY_MPIAIJ"
2183 PetscErrorCode MatAXPY_MPIAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
2184 {
2185   PetscErrorCode ierr;
2186   Mat_MPIAIJ     *xx = (Mat_MPIAIJ*)X->data,*yy = (Mat_MPIAIJ*)Y->data;
2187   PetscBLASInt   bnz,one=1;
2188   Mat_SeqAIJ     *x,*y;
2189 
2190   PetscFunctionBegin;
2191   if (str == SAME_NONZERO_PATTERN) {
2192     PetscScalar alpha = a;
2193     x    = (Mat_SeqAIJ*)xx->A->data;
2194     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2195     y    = (Mat_SeqAIJ*)yy->A->data;
2196     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2197     x    = (Mat_SeqAIJ*)xx->B->data;
2198     y    = (Mat_SeqAIJ*)yy->B->data;
2199     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2200     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2201     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
2202   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
2203     ierr = MatAXPY_Basic(Y,a,X,str);CHKERRQ(ierr);
2204   } else {
2205     Mat      B;
2206     PetscInt *nnz_d,*nnz_o;
2207     ierr = PetscMalloc1(yy->A->rmap->N,&nnz_d);CHKERRQ(ierr);
2208     ierr = PetscMalloc1(yy->B->rmap->N,&nnz_o);CHKERRQ(ierr);
2209     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
2210     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
2211     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
2212     ierr = MatSetBlockSizesFromMats(B,Y,Y);CHKERRQ(ierr);
2213     ierr = MatSetType(B,MATMPIAIJ);CHKERRQ(ierr);
2214     ierr = MatAXPYGetPreallocation_SeqAIJ(yy->A,xx->A,nnz_d);CHKERRQ(ierr);
2215     ierr = MatAXPYGetPreallocation_MPIAIJ(yy->B,yy->garray,xx->B,xx->garray,nnz_o);CHKERRQ(ierr);
2216     ierr = MatMPIAIJSetPreallocation(B,0,nnz_d,0,nnz_o);CHKERRQ(ierr);
2217     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
2218     ierr = MatHeaderReplace(Y,B);CHKERRQ(ierr);
2219     ierr = PetscFree(nnz_d);CHKERRQ(ierr);
2220     ierr = PetscFree(nnz_o);CHKERRQ(ierr);
2221   }
2222   PetscFunctionReturn(0);
2223 }
2224 
2225 extern PetscErrorCode  MatConjugate_SeqAIJ(Mat);
2226 
2227 #undef __FUNCT__
2228 #define __FUNCT__ "MatConjugate_MPIAIJ"
2229 PetscErrorCode  MatConjugate_MPIAIJ(Mat mat)
2230 {
2231 #if defined(PETSC_USE_COMPLEX)
2232   PetscErrorCode ierr;
2233   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2234 
2235   PetscFunctionBegin;
2236   ierr = MatConjugate_SeqAIJ(aij->A);CHKERRQ(ierr);
2237   ierr = MatConjugate_SeqAIJ(aij->B);CHKERRQ(ierr);
2238 #else
2239   PetscFunctionBegin;
2240 #endif
2241   PetscFunctionReturn(0);
2242 }
2243 
2244 #undef __FUNCT__
2245 #define __FUNCT__ "MatRealPart_MPIAIJ"
2246 PetscErrorCode MatRealPart_MPIAIJ(Mat A)
2247 {
2248   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2249   PetscErrorCode ierr;
2250 
2251   PetscFunctionBegin;
2252   ierr = MatRealPart(a->A);CHKERRQ(ierr);
2253   ierr = MatRealPart(a->B);CHKERRQ(ierr);
2254   PetscFunctionReturn(0);
2255 }
2256 
2257 #undef __FUNCT__
2258 #define __FUNCT__ "MatImaginaryPart_MPIAIJ"
2259 PetscErrorCode MatImaginaryPart_MPIAIJ(Mat A)
2260 {
2261   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2262   PetscErrorCode ierr;
2263 
2264   PetscFunctionBegin;
2265   ierr = MatImaginaryPart(a->A);CHKERRQ(ierr);
2266   ierr = MatImaginaryPart(a->B);CHKERRQ(ierr);
2267   PetscFunctionReturn(0);
2268 }
2269 
2270 #if defined(PETSC_HAVE_PBGL)
2271 
2272 #include <boost/parallel/mpi/bsp_process_group.hpp>
2273 #include <boost/graph/distributed/ilu_default_graph.hpp>
2274 #include <boost/graph/distributed/ilu_0_block.hpp>
2275 #include <boost/graph/distributed/ilu_preconditioner.hpp>
2276 #include <boost/graph/distributed/petsc/interface.hpp>
2277 #include <boost/multi_array.hpp>
2278 #include <boost/parallel/distributed_property_map->hpp>
2279 
2280 #undef __FUNCT__
2281 #define __FUNCT__ "MatILUFactorSymbolic_MPIAIJ"
2282 /*
2283   This uses the parallel ILU factorization of Peter Gottschling <pgottsch@osl.iu.edu>
2284 */
2285 PetscErrorCode MatILUFactorSymbolic_MPIAIJ(Mat fact,Mat A, IS isrow, IS iscol, const MatFactorInfo *info)
2286 {
2287   namespace petsc = boost::distributed::petsc;
2288 
2289   namespace graph_dist = boost::graph::distributed;
2290   using boost::graph::distributed::ilu_default::process_group_type;
2291   using boost::graph::ilu_permuted;
2292 
2293   PetscBool      row_identity, col_identity;
2294   PetscContainer c;
2295   PetscInt       m, n, M, N;
2296   PetscErrorCode ierr;
2297 
2298   PetscFunctionBegin;
2299   if (info->levels != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only levels = 0 supported for parallel ilu");
2300   ierr = ISIdentity(isrow, &row_identity);CHKERRQ(ierr);
2301   ierr = ISIdentity(iscol, &col_identity);CHKERRQ(ierr);
2302   if (!row_identity || !col_identity) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Row and column permutations must be identity for parallel ILU");
2303 
2304   process_group_type pg;
2305   typedef graph_dist::ilu_default::ilu_level_graph_type lgraph_type;
2306   lgraph_type  *lgraph_p   = new lgraph_type(petsc::num_global_vertices(A), pg, petsc::matrix_distribution(A, pg));
2307   lgraph_type& level_graph = *lgraph_p;
2308   graph_dist::ilu_default::graph_type&            graph(level_graph.graph);
2309 
2310   petsc::read_matrix(A, graph, get(boost::edge_weight, graph));
2311   ilu_permuted(level_graph);
2312 
2313   /* put together the new matrix */
2314   ierr = MatCreate(PetscObjectComm((PetscObject)A), fact);CHKERRQ(ierr);
2315   ierr = MatGetLocalSize(A, &m, &n);CHKERRQ(ierr);
2316   ierr = MatGetSize(A, &M, &N);CHKERRQ(ierr);
2317   ierr = MatSetSizes(fact, m, n, M, N);CHKERRQ(ierr);
2318   ierr = MatSetBlockSizesFromMats(fact,A,A);CHKERRQ(ierr);
2319   ierr = MatSetType(fact, ((PetscObject)A)->type_name);CHKERRQ(ierr);
2320   ierr = MatAssemblyBegin(fact, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2321   ierr = MatAssemblyEnd(fact, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2322 
2323   ierr = PetscContainerCreate(PetscObjectComm((PetscObject)A), &c);
2324   ierr = PetscContainerSetPointer(c, lgraph_p);
2325   ierr = PetscObjectCompose((PetscObject) (fact), "graph", (PetscObject) c);
2326   ierr = PetscContainerDestroy(&c);
2327   PetscFunctionReturn(0);
2328 }
2329 
2330 #undef __FUNCT__
2331 #define __FUNCT__ "MatLUFactorNumeric_MPIAIJ"
2332 PetscErrorCode MatLUFactorNumeric_MPIAIJ(Mat B,Mat A, const MatFactorInfo *info)
2333 {
2334   PetscFunctionBegin;
2335   PetscFunctionReturn(0);
2336 }
2337 
2338 #undef __FUNCT__
2339 #define __FUNCT__ "MatSolve_MPIAIJ"
2340 /*
2341   This uses the parallel ILU factorization of Peter Gottschling <pgottsch@osl.iu.edu>
2342 */
2343 PetscErrorCode MatSolve_MPIAIJ(Mat A, Vec b, Vec x)
2344 {
2345   namespace graph_dist = boost::graph::distributed;
2346 
2347   typedef graph_dist::ilu_default::ilu_level_graph_type lgraph_type;
2348   lgraph_type    *lgraph_p;
2349   PetscContainer c;
2350   PetscErrorCode ierr;
2351 
2352   PetscFunctionBegin;
2353   ierr = PetscObjectQuery((PetscObject) A, "graph", (PetscObject*) &c);CHKERRQ(ierr);
2354   ierr = PetscContainerGetPointer(c, (void**) &lgraph_p);CHKERRQ(ierr);
2355   ierr = VecCopy(b, x);CHKERRQ(ierr);
2356 
2357   PetscScalar *array_x;
2358   ierr = VecGetArray(x, &array_x);CHKERRQ(ierr);
2359   PetscInt sx;
2360   ierr = VecGetSize(x, &sx);CHKERRQ(ierr);
2361 
2362   PetscScalar *array_b;
2363   ierr = VecGetArray(b, &array_b);CHKERRQ(ierr);
2364   PetscInt sb;
2365   ierr = VecGetSize(b, &sb);CHKERRQ(ierr);
2366 
2367   lgraph_type& level_graph = *lgraph_p;
2368   graph_dist::ilu_default::graph_type&            graph(level_graph.graph);
2369 
2370   typedef boost::multi_array_ref<PetscScalar, 1> array_ref_type;
2371   array_ref_type                                 ref_b(array_b, boost::extents[num_vertices(graph)]);
2372   array_ref_type                                 ref_x(array_x, boost::extents[num_vertices(graph)]);
2373 
2374   typedef boost::iterator_property_map<array_ref_type::iterator,
2375                                        boost::property_map<graph_dist::ilu_default::graph_type, boost::vertex_index_t>::type>  gvector_type;
2376   gvector_type                                   vector_b(ref_b.begin(), get(boost::vertex_index, graph));
2377   gvector_type                                   vector_x(ref_x.begin(), get(boost::vertex_index, graph));
2378 
2379   ilu_set_solve(*lgraph_p, vector_b, vector_x);
2380   PetscFunctionReturn(0);
2381 }
2382 #endif
2383 
2384 #undef __FUNCT__
2385 #define __FUNCT__ "MatGetRowMaxAbs_MPIAIJ"
2386 PetscErrorCode MatGetRowMaxAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2387 {
2388   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2389   PetscErrorCode ierr;
2390   PetscInt       i,*idxb = 0;
2391   PetscScalar    *va,*vb;
2392   Vec            vtmp;
2393 
2394   PetscFunctionBegin;
2395   ierr = MatGetRowMaxAbs(a->A,v,idx);CHKERRQ(ierr);
2396   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2397   if (idx) {
2398     for (i=0; i<A->rmap->n; i++) {
2399       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2400     }
2401   }
2402 
2403   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2404   if (idx) {
2405     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2406   }
2407   ierr = MatGetRowMaxAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2408   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2409 
2410   for (i=0; i<A->rmap->n; i++) {
2411     if (PetscAbsScalar(va[i]) < PetscAbsScalar(vb[i])) {
2412       va[i] = vb[i];
2413       if (idx) idx[i] = a->garray[idxb[i]];
2414     }
2415   }
2416 
2417   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2418   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2419   ierr = PetscFree(idxb);CHKERRQ(ierr);
2420   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2421   PetscFunctionReturn(0);
2422 }
2423 
2424 #undef __FUNCT__
2425 #define __FUNCT__ "MatGetRowMinAbs_MPIAIJ"
2426 PetscErrorCode MatGetRowMinAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2427 {
2428   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2429   PetscErrorCode ierr;
2430   PetscInt       i,*idxb = 0;
2431   PetscScalar    *va,*vb;
2432   Vec            vtmp;
2433 
2434   PetscFunctionBegin;
2435   ierr = MatGetRowMinAbs(a->A,v,idx);CHKERRQ(ierr);
2436   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2437   if (idx) {
2438     for (i=0; i<A->cmap->n; i++) {
2439       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2440     }
2441   }
2442 
2443   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2444   if (idx) {
2445     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2446   }
2447   ierr = MatGetRowMinAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2448   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2449 
2450   for (i=0; i<A->rmap->n; i++) {
2451     if (PetscAbsScalar(va[i]) > PetscAbsScalar(vb[i])) {
2452       va[i] = vb[i];
2453       if (idx) idx[i] = a->garray[idxb[i]];
2454     }
2455   }
2456 
2457   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2458   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2459   ierr = PetscFree(idxb);CHKERRQ(ierr);
2460   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2461   PetscFunctionReturn(0);
2462 }
2463 
2464 #undef __FUNCT__
2465 #define __FUNCT__ "MatGetRowMin_MPIAIJ"
2466 PetscErrorCode MatGetRowMin_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2467 {
2468   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2469   PetscInt       n      = A->rmap->n;
2470   PetscInt       cstart = A->cmap->rstart;
2471   PetscInt       *cmap  = mat->garray;
2472   PetscInt       *diagIdx, *offdiagIdx;
2473   Vec            diagV, offdiagV;
2474   PetscScalar    *a, *diagA, *offdiagA;
2475   PetscInt       r;
2476   PetscErrorCode ierr;
2477 
2478   PetscFunctionBegin;
2479   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2480   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &diagV);CHKERRQ(ierr);
2481   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &offdiagV);CHKERRQ(ierr);
2482   ierr = MatGetRowMin(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2483   ierr = MatGetRowMin(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2484   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2485   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2486   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2487   for (r = 0; r < n; ++r) {
2488     if (PetscAbsScalar(diagA[r]) <= PetscAbsScalar(offdiagA[r])) {
2489       a[r]   = diagA[r];
2490       idx[r] = cstart + diagIdx[r];
2491     } else {
2492       a[r]   = offdiagA[r];
2493       idx[r] = cmap[offdiagIdx[r]];
2494     }
2495   }
2496   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2497   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2498   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2499   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2500   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2501   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2502   PetscFunctionReturn(0);
2503 }
2504 
2505 #undef __FUNCT__
2506 #define __FUNCT__ "MatGetRowMax_MPIAIJ"
2507 PetscErrorCode MatGetRowMax_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2508 {
2509   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2510   PetscInt       n      = A->rmap->n;
2511   PetscInt       cstart = A->cmap->rstart;
2512   PetscInt       *cmap  = mat->garray;
2513   PetscInt       *diagIdx, *offdiagIdx;
2514   Vec            diagV, offdiagV;
2515   PetscScalar    *a, *diagA, *offdiagA;
2516   PetscInt       r;
2517   PetscErrorCode ierr;
2518 
2519   PetscFunctionBegin;
2520   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2521   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &diagV);CHKERRQ(ierr);
2522   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &offdiagV);CHKERRQ(ierr);
2523   ierr = MatGetRowMax(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2524   ierr = MatGetRowMax(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2525   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2526   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2527   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2528   for (r = 0; r < n; ++r) {
2529     if (PetscAbsScalar(diagA[r]) >= PetscAbsScalar(offdiagA[r])) {
2530       a[r]   = diagA[r];
2531       idx[r] = cstart + diagIdx[r];
2532     } else {
2533       a[r]   = offdiagA[r];
2534       idx[r] = cmap[offdiagIdx[r]];
2535     }
2536   }
2537   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2538   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2539   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2540   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2541   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2542   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2543   PetscFunctionReturn(0);
2544 }
2545 
2546 #undef __FUNCT__
2547 #define __FUNCT__ "MatGetSeqNonzeroStructure_MPIAIJ"
2548 PetscErrorCode MatGetSeqNonzeroStructure_MPIAIJ(Mat mat,Mat *newmat)
2549 {
2550   PetscErrorCode ierr;
2551   Mat            *dummy;
2552 
2553   PetscFunctionBegin;
2554   ierr    = MatGetSubMatrix_MPIAIJ_All(mat,MAT_DO_NOT_GET_VALUES,MAT_INITIAL_MATRIX,&dummy);CHKERRQ(ierr);
2555   *newmat = *dummy;
2556   ierr    = PetscFree(dummy);CHKERRQ(ierr);
2557   PetscFunctionReturn(0);
2558 }
2559 
2560 #undef __FUNCT__
2561 #define __FUNCT__ "MatInvertBlockDiagonal_MPIAIJ"
2562 PetscErrorCode  MatInvertBlockDiagonal_MPIAIJ(Mat A,const PetscScalar **values)
2563 {
2564   Mat_MPIAIJ     *a = (Mat_MPIAIJ*) A->data;
2565   PetscErrorCode ierr;
2566 
2567   PetscFunctionBegin;
2568   ierr = MatInvertBlockDiagonal(a->A,values);CHKERRQ(ierr);
2569   PetscFunctionReturn(0);
2570 }
2571 
2572 #undef __FUNCT__
2573 #define __FUNCT__ "MatSetRandom_MPIAIJ"
2574 static PetscErrorCode  MatSetRandom_MPIAIJ(Mat x,PetscRandom rctx)
2575 {
2576   PetscErrorCode ierr;
2577   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)x->data;
2578 
2579   PetscFunctionBegin;
2580   ierr = MatSetRandom(aij->A,rctx);CHKERRQ(ierr);
2581   ierr = MatSetRandom(aij->B,rctx);CHKERRQ(ierr);
2582   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2583   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2584   PetscFunctionReturn(0);
2585 }
2586 
2587 #undef __FUNCT__
2588 #define __FUNCT__ "MatShift_MPIAIJ"
2589 PetscErrorCode MatShift_MPIAIJ(Mat Y,PetscScalar a)
2590 {
2591   PetscErrorCode ierr;
2592   Mat_MPIAIJ     *maij = (Mat_MPIAIJ*)Y->data;
2593   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)maij->A->data,*bij = (Mat_SeqAIJ*)maij->B->data;
2594 
2595   PetscFunctionBegin;
2596   if (!aij->nz && !bij->nz) {
2597     ierr = MatMPIAIJSetPreallocation(Y,1,NULL,0,NULL);CHKERRQ(ierr);
2598   }
2599   ierr = MatShift_Basic(Y,a);CHKERRQ(ierr);
2600   PetscFunctionReturn(0);
2601 }
2602 
2603 /* -------------------------------------------------------------------*/
2604 static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
2605                                        MatGetRow_MPIAIJ,
2606                                        MatRestoreRow_MPIAIJ,
2607                                        MatMult_MPIAIJ,
2608                                 /* 4*/ MatMultAdd_MPIAIJ,
2609                                        MatMultTranspose_MPIAIJ,
2610                                        MatMultTransposeAdd_MPIAIJ,
2611 #if defined(PETSC_HAVE_PBGL)
2612                                        MatSolve_MPIAIJ,
2613 #else
2614                                        0,
2615 #endif
2616                                        0,
2617                                        0,
2618                                 /*10*/ 0,
2619                                        0,
2620                                        0,
2621                                        MatSOR_MPIAIJ,
2622                                        MatTranspose_MPIAIJ,
2623                                 /*15*/ MatGetInfo_MPIAIJ,
2624                                        MatEqual_MPIAIJ,
2625                                        MatGetDiagonal_MPIAIJ,
2626                                        MatDiagonalScale_MPIAIJ,
2627                                        MatNorm_MPIAIJ,
2628                                 /*20*/ MatAssemblyBegin_MPIAIJ,
2629                                        MatAssemblyEnd_MPIAIJ,
2630                                        MatSetOption_MPIAIJ,
2631                                        MatZeroEntries_MPIAIJ,
2632                                 /*24*/ MatZeroRows_MPIAIJ,
2633                                        0,
2634 #if defined(PETSC_HAVE_PBGL)
2635                                        0,
2636 #else
2637                                        0,
2638 #endif
2639                                        0,
2640                                        0,
2641                                 /*29*/ MatSetUp_MPIAIJ,
2642 #if defined(PETSC_HAVE_PBGL)
2643                                        0,
2644 #else
2645                                        0,
2646 #endif
2647                                        0,
2648                                        0,
2649                                        0,
2650                                 /*34*/ MatDuplicate_MPIAIJ,
2651                                        0,
2652                                        0,
2653                                        0,
2654                                        0,
2655                                 /*39*/ MatAXPY_MPIAIJ,
2656                                        MatGetSubMatrices_MPIAIJ,
2657                                        MatIncreaseOverlap_MPIAIJ,
2658                                        MatGetValues_MPIAIJ,
2659                                        MatCopy_MPIAIJ,
2660                                 /*44*/ MatGetRowMax_MPIAIJ,
2661                                        MatScale_MPIAIJ,
2662                                        MatShift_MPIAIJ,
2663                                        MatDiagonalSet_MPIAIJ,
2664                                        MatZeroRowsColumns_MPIAIJ,
2665                                 /*49*/ MatSetRandom_MPIAIJ,
2666                                        0,
2667                                        0,
2668                                        0,
2669                                        0,
2670                                 /*54*/ MatFDColoringCreate_MPIXAIJ,
2671                                        0,
2672                                        MatSetUnfactored_MPIAIJ,
2673                                        MatPermute_MPIAIJ,
2674                                        0,
2675                                 /*59*/ MatGetSubMatrix_MPIAIJ,
2676                                        MatDestroy_MPIAIJ,
2677                                        MatView_MPIAIJ,
2678                                        0,
2679                                        MatMatMatMult_MPIAIJ_MPIAIJ_MPIAIJ,
2680                                 /*64*/ MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ,
2681                                        MatMatMatMultNumeric_MPIAIJ_MPIAIJ_MPIAIJ,
2682                                        0,
2683                                        0,
2684                                        0,
2685                                 /*69*/ MatGetRowMaxAbs_MPIAIJ,
2686                                        MatGetRowMinAbs_MPIAIJ,
2687                                        0,
2688                                        MatSetColoring_MPIAIJ,
2689                                        0,
2690                                        MatSetValuesAdifor_MPIAIJ,
2691                                 /*75*/ MatFDColoringApply_AIJ,
2692                                        0,
2693                                        0,
2694                                        0,
2695                                        MatFindZeroDiagonals_MPIAIJ,
2696                                 /*80*/ 0,
2697                                        0,
2698                                        0,
2699                                 /*83*/ MatLoad_MPIAIJ,
2700                                        0,
2701                                        0,
2702                                        0,
2703                                        0,
2704                                        0,
2705                                 /*89*/ MatMatMult_MPIAIJ_MPIAIJ,
2706                                        MatMatMultSymbolic_MPIAIJ_MPIAIJ,
2707                                        MatMatMultNumeric_MPIAIJ_MPIAIJ,
2708                                        MatPtAP_MPIAIJ_MPIAIJ,
2709                                        MatPtAPSymbolic_MPIAIJ_MPIAIJ,
2710                                 /*94*/ MatPtAPNumeric_MPIAIJ_MPIAIJ,
2711                                        0,
2712                                        0,
2713                                        0,
2714                                        0,
2715                                 /*99*/ 0,
2716                                        0,
2717                                        0,
2718                                        MatConjugate_MPIAIJ,
2719                                        0,
2720                                 /*104*/MatSetValuesRow_MPIAIJ,
2721                                        MatRealPart_MPIAIJ,
2722                                        MatImaginaryPart_MPIAIJ,
2723                                        0,
2724                                        0,
2725                                 /*109*/0,
2726                                        0,
2727                                        MatGetRowMin_MPIAIJ,
2728                                        0,
2729                                        0,
2730                                 /*114*/MatGetSeqNonzeroStructure_MPIAIJ,
2731                                        0,
2732                                        0,
2733                                        0,
2734                                        0,
2735                                 /*119*/0,
2736                                        0,
2737                                        0,
2738                                        0,
2739                                        MatGetMultiProcBlock_MPIAIJ,
2740                                 /*124*/MatFindNonzeroRows_MPIAIJ,
2741                                        MatGetColumnNorms_MPIAIJ,
2742                                        MatInvertBlockDiagonal_MPIAIJ,
2743                                        0,
2744                                        MatGetSubMatricesMPI_MPIAIJ,
2745                                 /*129*/0,
2746                                        MatTransposeMatMult_MPIAIJ_MPIAIJ,
2747                                        MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ,
2748                                        MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ,
2749                                        0,
2750                                 /*134*/0,
2751                                        0,
2752                                        0,
2753                                        0,
2754                                        0,
2755                                 /*139*/0,
2756                                        0,
2757                                        0,
2758                                        MatFDColoringSetUp_MPIXAIJ,
2759                                        MatFindOffBlockDiagonalEntries_MPIAIJ,
2760                                 /*144*/MatCreateMPIMatConcatenateSeqMat_MPIAIJ
2761 };
2762 
2763 /* ----------------------------------------------------------------------------------------*/
2764 
2765 #undef __FUNCT__
2766 #define __FUNCT__ "MatStoreValues_MPIAIJ"
2767 PetscErrorCode  MatStoreValues_MPIAIJ(Mat mat)
2768 {
2769   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2770   PetscErrorCode ierr;
2771 
2772   PetscFunctionBegin;
2773   ierr = MatStoreValues(aij->A);CHKERRQ(ierr);
2774   ierr = MatStoreValues(aij->B);CHKERRQ(ierr);
2775   PetscFunctionReturn(0);
2776 }
2777 
2778 #undef __FUNCT__
2779 #define __FUNCT__ "MatRetrieveValues_MPIAIJ"
2780 PetscErrorCode  MatRetrieveValues_MPIAIJ(Mat mat)
2781 {
2782   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2783   PetscErrorCode ierr;
2784 
2785   PetscFunctionBegin;
2786   ierr = MatRetrieveValues(aij->A);CHKERRQ(ierr);
2787   ierr = MatRetrieveValues(aij->B);CHKERRQ(ierr);
2788   PetscFunctionReturn(0);
2789 }
2790 
2791 #undef __FUNCT__
2792 #define __FUNCT__ "MatMPIAIJSetPreallocation_MPIAIJ"
2793 PetscErrorCode  MatMPIAIJSetPreallocation_MPIAIJ(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
2794 {
2795   Mat_MPIAIJ     *b;
2796   PetscErrorCode ierr;
2797 
2798   PetscFunctionBegin;
2799   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
2800   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
2801   b = (Mat_MPIAIJ*)B->data;
2802 
2803   if (!B->preallocated) {
2804     /* Explicitly create 2 MATSEQAIJ matrices. */
2805     ierr = MatCreate(PETSC_COMM_SELF,&b->A);CHKERRQ(ierr);
2806     ierr = MatSetSizes(b->A,B->rmap->n,B->cmap->n,B->rmap->n,B->cmap->n);CHKERRQ(ierr);
2807     ierr = MatSetBlockSizesFromMats(b->A,B,B);CHKERRQ(ierr);
2808     ierr = MatSetType(b->A,MATSEQAIJ);CHKERRQ(ierr);
2809     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->A);CHKERRQ(ierr);
2810     ierr = MatCreate(PETSC_COMM_SELF,&b->B);CHKERRQ(ierr);
2811     ierr = MatSetSizes(b->B,B->rmap->n,B->cmap->N,B->rmap->n,B->cmap->N);CHKERRQ(ierr);
2812     ierr = MatSetBlockSizesFromMats(b->B,B,B);CHKERRQ(ierr);
2813     ierr = MatSetType(b->B,MATSEQAIJ);CHKERRQ(ierr);
2814     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->B);CHKERRQ(ierr);
2815   }
2816 
2817   ierr = MatSeqAIJSetPreallocation(b->A,d_nz,d_nnz);CHKERRQ(ierr);
2818   ierr = MatSeqAIJSetPreallocation(b->B,o_nz,o_nnz);CHKERRQ(ierr);
2819   B->preallocated = PETSC_TRUE;
2820   PetscFunctionReturn(0);
2821 }
2822 
2823 #undef __FUNCT__
2824 #define __FUNCT__ "MatDuplicate_MPIAIJ"
2825 PetscErrorCode MatDuplicate_MPIAIJ(Mat matin,MatDuplicateOption cpvalues,Mat *newmat)
2826 {
2827   Mat            mat;
2828   Mat_MPIAIJ     *a,*oldmat = (Mat_MPIAIJ*)matin->data;
2829   PetscErrorCode ierr;
2830 
2831   PetscFunctionBegin;
2832   *newmat = 0;
2833   ierr    = MatCreate(PetscObjectComm((PetscObject)matin),&mat);CHKERRQ(ierr);
2834   ierr    = MatSetSizes(mat,matin->rmap->n,matin->cmap->n,matin->rmap->N,matin->cmap->N);CHKERRQ(ierr);
2835   ierr    = MatSetBlockSizesFromMats(mat,matin,matin);CHKERRQ(ierr);
2836   ierr    = MatSetType(mat,((PetscObject)matin)->type_name);CHKERRQ(ierr);
2837   ierr    = PetscMemcpy(mat->ops,matin->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
2838   a       = (Mat_MPIAIJ*)mat->data;
2839 
2840   mat->factortype   = matin->factortype;
2841   mat->assembled    = PETSC_TRUE;
2842   mat->insertmode   = NOT_SET_VALUES;
2843   mat->preallocated = PETSC_TRUE;
2844 
2845   a->size         = oldmat->size;
2846   a->rank         = oldmat->rank;
2847   a->donotstash   = oldmat->donotstash;
2848   a->roworiented  = oldmat->roworiented;
2849   a->rowindices   = 0;
2850   a->rowvalues    = 0;
2851   a->getrowactive = PETSC_FALSE;
2852 
2853   ierr = PetscLayoutReference(matin->rmap,&mat->rmap);CHKERRQ(ierr);
2854   ierr = PetscLayoutReference(matin->cmap,&mat->cmap);CHKERRQ(ierr);
2855 
2856   if (oldmat->colmap) {
2857 #if defined(PETSC_USE_CTABLE)
2858     ierr = PetscTableCreateCopy(oldmat->colmap,&a->colmap);CHKERRQ(ierr);
2859 #else
2860     ierr = PetscMalloc1(mat->cmap->N,&a->colmap);CHKERRQ(ierr);
2861     ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2862     ierr = PetscMemcpy(a->colmap,oldmat->colmap,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2863 #endif
2864   } else a->colmap = 0;
2865   if (oldmat->garray) {
2866     PetscInt len;
2867     len  = oldmat->B->cmap->n;
2868     ierr = PetscMalloc1(len+1,&a->garray);CHKERRQ(ierr);
2869     ierr = PetscLogObjectMemory((PetscObject)mat,len*sizeof(PetscInt));CHKERRQ(ierr);
2870     if (len) { ierr = PetscMemcpy(a->garray,oldmat->garray,len*sizeof(PetscInt));CHKERRQ(ierr); }
2871   } else a->garray = 0;
2872 
2873   ierr    = VecDuplicate(oldmat->lvec,&a->lvec);CHKERRQ(ierr);
2874   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->lvec);CHKERRQ(ierr);
2875   ierr    = VecScatterCopy(oldmat->Mvctx,&a->Mvctx);CHKERRQ(ierr);
2876   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->Mvctx);CHKERRQ(ierr);
2877   ierr    = MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
2878   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->A);CHKERRQ(ierr);
2879   ierr    = MatDuplicate(oldmat->B,cpvalues,&a->B);CHKERRQ(ierr);
2880   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->B);CHKERRQ(ierr);
2881   ierr    = PetscFunctionListDuplicate(((PetscObject)matin)->qlist,&((PetscObject)mat)->qlist);CHKERRQ(ierr);
2882   *newmat = mat;
2883   PetscFunctionReturn(0);
2884 }
2885 
2886 
2887 
2888 #undef __FUNCT__
2889 #define __FUNCT__ "MatLoad_MPIAIJ"
2890 PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
2891 {
2892   PetscScalar    *vals,*svals;
2893   MPI_Comm       comm;
2894   PetscErrorCode ierr;
2895   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
2896   PetscInt       i,nz,j,rstart,rend,mmax,maxnz = 0;
2897   PetscInt       header[4],*rowlengths = 0,M,N,m,*cols;
2898   PetscInt       *ourlens = NULL,*procsnz = NULL,*offlens = NULL,jj,*mycols,*smycols;
2899   PetscInt       cend,cstart,n,*rowners;
2900   int            fd;
2901   PetscInt       bs = newMat->rmap->bs;
2902 
2903   PetscFunctionBegin;
2904   /* force binary viewer to load .info file if it has not yet done so */
2905   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
2906   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
2907   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2908   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2909   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
2910   if (!rank) {
2911     ierr = PetscBinaryRead(fd,(char*)header,4,PETSC_INT);CHKERRQ(ierr);
2912     if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
2913   }
2914 
2915   ierr = PetscOptionsBegin(comm,NULL,"Options for loading MPIAIJ matrix","Mat");CHKERRQ(ierr);
2916   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
2917   ierr = PetscOptionsEnd();CHKERRQ(ierr);
2918   if (bs < 0) bs = 1;
2919 
2920   ierr = MPI_Bcast(header+1,3,MPIU_INT,0,comm);CHKERRQ(ierr);
2921   M    = header[1]; N = header[2];
2922 
2923   /* If global sizes are set, check if they are consistent with that given in the file */
2924   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);
2925   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);
2926 
2927   /* determine ownership of all (block) rows */
2928   if (M%bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Inconsistent # of rows (%d) and block size (%d)",M,bs);
2929   if (newMat->rmap->n < 0) m = bs*((M/bs)/size + (((M/bs) % size) > rank));    /* PETSC_DECIDE */
2930   else m = newMat->rmap->n; /* Set by user */
2931 
2932   ierr = PetscMalloc1(size+1,&rowners);CHKERRQ(ierr);
2933   ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
2934 
2935   /* First process needs enough room for process with most rows */
2936   if (!rank) {
2937     mmax = rowners[1];
2938     for (i=2; i<=size; i++) {
2939       mmax = PetscMax(mmax, rowners[i]);
2940     }
2941   } else mmax = -1;             /* unused, but compilers complain */
2942 
2943   rowners[0] = 0;
2944   for (i=2; i<=size; i++) {
2945     rowners[i] += rowners[i-1];
2946   }
2947   rstart = rowners[rank];
2948   rend   = rowners[rank+1];
2949 
2950   /* distribute row lengths to all processors */
2951   ierr = PetscMalloc2(m,&ourlens,m,&offlens);CHKERRQ(ierr);
2952   if (!rank) {
2953     ierr = PetscBinaryRead(fd,ourlens,m,PETSC_INT);CHKERRQ(ierr);
2954     ierr = PetscMalloc1(mmax,&rowlengths);CHKERRQ(ierr);
2955     ierr = PetscCalloc1(size,&procsnz);CHKERRQ(ierr);
2956     for (j=0; j<m; j++) {
2957       procsnz[0] += ourlens[j];
2958     }
2959     for (i=1; i<size; i++) {
2960       ierr = PetscBinaryRead(fd,rowlengths,rowners[i+1]-rowners[i],PETSC_INT);CHKERRQ(ierr);
2961       /* calculate the number of nonzeros on each processor */
2962       for (j=0; j<rowners[i+1]-rowners[i]; j++) {
2963         procsnz[i] += rowlengths[j];
2964       }
2965       ierr = MPIULong_Send(rowlengths,rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2966     }
2967     ierr = PetscFree(rowlengths);CHKERRQ(ierr);
2968   } else {
2969     ierr = MPIULong_Recv(ourlens,m,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2970   }
2971 
2972   if (!rank) {
2973     /* determine max buffer needed and allocate it */
2974     maxnz = 0;
2975     for (i=0; i<size; i++) {
2976       maxnz = PetscMax(maxnz,procsnz[i]);
2977     }
2978     ierr = PetscMalloc1(maxnz,&cols);CHKERRQ(ierr);
2979 
2980     /* read in my part of the matrix column indices  */
2981     nz   = procsnz[0];
2982     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2983     ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);
2984 
2985     /* read in every one elses and ship off */
2986     for (i=1; i<size; i++) {
2987       nz   = procsnz[i];
2988       ierr = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
2989       ierr = MPIULong_Send(cols,nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2990     }
2991     ierr = PetscFree(cols);CHKERRQ(ierr);
2992   } else {
2993     /* determine buffer space needed for message */
2994     nz = 0;
2995     for (i=0; i<m; i++) {
2996       nz += ourlens[i];
2997     }
2998     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2999 
3000     /* receive message of column indices*/
3001     ierr = MPIULong_Recv(mycols,nz,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
3002   }
3003 
3004   /* determine column ownership if matrix is not square */
3005   if (N != M) {
3006     if (newMat->cmap->n < 0) n = N/size + ((N % size) > rank);
3007     else n = newMat->cmap->n;
3008     ierr   = MPI_Scan(&n,&cend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3009     cstart = cend - n;
3010   } else {
3011     cstart = rstart;
3012     cend   = rend;
3013     n      = cend - cstart;
3014   }
3015 
3016   /* loop over local rows, determining number of off diagonal entries */
3017   ierr = PetscMemzero(offlens,m*sizeof(PetscInt));CHKERRQ(ierr);
3018   jj   = 0;
3019   for (i=0; i<m; i++) {
3020     for (j=0; j<ourlens[i]; j++) {
3021       if (mycols[jj] < cstart || mycols[jj] >= cend) offlens[i]++;
3022       jj++;
3023     }
3024   }
3025 
3026   for (i=0; i<m; i++) {
3027     ourlens[i] -= offlens[i];
3028   }
3029   ierr = MatSetSizes(newMat,m,n,M,N);CHKERRQ(ierr);
3030 
3031   if (bs > 1) {ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);}
3032 
3033   ierr = MatMPIAIJSetPreallocation(newMat,0,ourlens,0,offlens);CHKERRQ(ierr);
3034 
3035   for (i=0; i<m; i++) {
3036     ourlens[i] += offlens[i];
3037   }
3038 
3039   if (!rank) {
3040     ierr = PetscMalloc1(maxnz+1,&vals);CHKERRQ(ierr);
3041 
3042     /* read in my part of the matrix numerical values  */
3043     nz   = procsnz[0];
3044     ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
3045 
3046     /* insert into matrix */
3047     jj      = rstart;
3048     smycols = mycols;
3049     svals   = vals;
3050     for (i=0; i<m; i++) {
3051       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
3052       smycols += ourlens[i];
3053       svals   += ourlens[i];
3054       jj++;
3055     }
3056 
3057     /* read in other processors and ship out */
3058     for (i=1; i<size; i++) {
3059       nz   = procsnz[i];
3060       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
3061       ierr = MPIULong_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
3062     }
3063     ierr = PetscFree(procsnz);CHKERRQ(ierr);
3064   } else {
3065     /* receive numeric values */
3066     ierr = PetscMalloc1(nz+1,&vals);CHKERRQ(ierr);
3067 
3068     /* receive message of values*/
3069     ierr = MPIULong_Recv(vals,nz,MPIU_SCALAR,0,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
3070 
3071     /* insert into matrix */
3072     jj      = rstart;
3073     smycols = mycols;
3074     svals   = vals;
3075     for (i=0; i<m; i++) {
3076       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
3077       smycols += ourlens[i];
3078       svals   += ourlens[i];
3079       jj++;
3080     }
3081   }
3082   ierr = PetscFree2(ourlens,offlens);CHKERRQ(ierr);
3083   ierr = PetscFree(vals);CHKERRQ(ierr);
3084   ierr = PetscFree(mycols);CHKERRQ(ierr);
3085   ierr = PetscFree(rowners);CHKERRQ(ierr);
3086   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3087   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3088   PetscFunctionReturn(0);
3089 }
3090 
3091 #undef __FUNCT__
3092 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ"
3093 /* TODO: Not scalable because of ISAllGather(). */
3094 PetscErrorCode MatGetSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3095 {
3096   PetscErrorCode ierr;
3097   IS             iscol_local;
3098   PetscInt       csize;
3099 
3100   PetscFunctionBegin;
3101   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3102   if (call == MAT_REUSE_MATRIX) {
3103     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3104     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3105   } else {
3106     PetscInt cbs;
3107     ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
3108     ierr = ISAllGather(iscol,&iscol_local);CHKERRQ(ierr);
3109     ierr = ISSetBlockSize(iscol_local,cbs);CHKERRQ(ierr);
3110   }
3111   ierr = MatGetSubMatrix_MPIAIJ_Private(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
3112   if (call == MAT_INITIAL_MATRIX) {
3113     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3114     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3115   }
3116   PetscFunctionReturn(0);
3117 }
3118 
3119 extern PetscErrorCode MatGetSubMatrices_MPIAIJ_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool*,Mat*);
3120 #undef __FUNCT__
3121 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ_Private"
3122 /*
3123     Not great since it makes two copies of the submatrix, first an SeqAIJ
3124   in local and then by concatenating the local matrices the end result.
3125   Writing it directly would be much like MatGetSubMatrices_MPIAIJ()
3126 
3127   Note: This requires a sequential iscol with all indices.
3128 */
3129 PetscErrorCode MatGetSubMatrix_MPIAIJ_Private(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3130 {
3131   PetscErrorCode ierr;
3132   PetscMPIInt    rank,size;
3133   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3134   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal,ncol;
3135   PetscBool      allcolumns, colflag;
3136   Mat            M,Mreuse;
3137   MatScalar      *vwork,*aa;
3138   MPI_Comm       comm;
3139   Mat_SeqAIJ     *aij;
3140 
3141   PetscFunctionBegin;
3142   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3143   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3144   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3145 
3146   ierr = ISIdentity(iscol,&colflag);CHKERRQ(ierr);
3147   ierr = ISGetLocalSize(iscol,&ncol);CHKERRQ(ierr);
3148   if (colflag && ncol == mat->cmap->N) {
3149     allcolumns = PETSC_TRUE;
3150   } else {
3151     allcolumns = PETSC_FALSE;
3152   }
3153   if (call ==  MAT_REUSE_MATRIX) {
3154     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3155     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3156     ierr = MatGetSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,&allcolumns,&Mreuse);CHKERRQ(ierr);
3157   } else {
3158     ierr = MatGetSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&allcolumns,&Mreuse);CHKERRQ(ierr);
3159   }
3160 
3161   /*
3162       m - number of local rows
3163       n - number of columns (same on all processors)
3164       rstart - first row in new global matrix generated
3165   */
3166   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3167   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3168   if (call == MAT_INITIAL_MATRIX) {
3169     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3170     ii  = aij->i;
3171     jj  = aij->j;
3172 
3173     /*
3174         Determine the number of non-zeros in the diagonal and off-diagonal
3175         portions of the matrix in order to do correct preallocation
3176     */
3177 
3178     /* first get start and end of "diagonal" columns */
3179     if (csize == PETSC_DECIDE) {
3180       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3181       if (mglobal == n) { /* square matrix */
3182         nlocal = m;
3183       } else {
3184         nlocal = n/size + ((n % size) > rank);
3185       }
3186     } else {
3187       nlocal = csize;
3188     }
3189     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3190     rstart = rend - nlocal;
3191     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);
3192 
3193     /* next, compute all the lengths */
3194     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3195     olens = dlens + m;
3196     for (i=0; i<m; i++) {
3197       jend = ii[i+1] - ii[i];
3198       olen = 0;
3199       dlen = 0;
3200       for (j=0; j<jend; j++) {
3201         if (*jj < rstart || *jj >= rend) olen++;
3202         else dlen++;
3203         jj++;
3204       }
3205       olens[i] = olen;
3206       dlens[i] = dlen;
3207     }
3208     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3209     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3210     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3211     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3212     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3213     ierr = PetscFree(dlens);CHKERRQ(ierr);
3214   } else {
3215     PetscInt ml,nl;
3216 
3217     M    = *newmat;
3218     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3219     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3220     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3221     /*
3222          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3223        rather than the slower MatSetValues().
3224     */
3225     M->was_assembled = PETSC_TRUE;
3226     M->assembled     = PETSC_FALSE;
3227   }
3228   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3229   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3230   ii   = aij->i;
3231   jj   = aij->j;
3232   aa   = aij->a;
3233   for (i=0; i<m; i++) {
3234     row   = rstart + i;
3235     nz    = ii[i+1] - ii[i];
3236     cwork = jj;     jj += nz;
3237     vwork = aa;     aa += nz;
3238     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3239   }
3240 
3241   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3242   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3243   *newmat = M;
3244 
3245   /* save submatrix used in processor for next request */
3246   if (call ==  MAT_INITIAL_MATRIX) {
3247     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3248     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3249   }
3250   PetscFunctionReturn(0);
3251 }
3252 
3253 #undef __FUNCT__
3254 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR_MPIAIJ"
3255 PetscErrorCode  MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3256 {
3257   PetscInt       m,cstart, cend,j,nnz,i,d;
3258   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3259   const PetscInt *JJ;
3260   PetscScalar    *values;
3261   PetscErrorCode ierr;
3262 
3263   PetscFunctionBegin;
3264   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3265 
3266   ierr   = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3267   ierr   = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3268   m      = B->rmap->n;
3269   cstart = B->cmap->rstart;
3270   cend   = B->cmap->rend;
3271   rstart = B->rmap->rstart;
3272 
3273   ierr = PetscMalloc2(m,&d_nnz,m,&o_nnz);CHKERRQ(ierr);
3274 
3275 #if defined(PETSC_USE_DEBUGGING)
3276   for (i=0; i<m; i++) {
3277     nnz = Ii[i+1]- Ii[i];
3278     JJ  = J + Ii[i];
3279     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3280     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3281     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);
3282   }
3283 #endif
3284 
3285   for (i=0; i<m; i++) {
3286     nnz     = Ii[i+1]- Ii[i];
3287     JJ      = J + Ii[i];
3288     nnz_max = PetscMax(nnz_max,nnz);
3289     d       = 0;
3290     for (j=0; j<nnz; j++) {
3291       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3292     }
3293     d_nnz[i] = d;
3294     o_nnz[i] = nnz - d;
3295   }
3296   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3297   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3298 
3299   if (v) values = (PetscScalar*)v;
3300   else {
3301     ierr = PetscCalloc1(nnz_max+1,&values);CHKERRQ(ierr);
3302   }
3303 
3304   for (i=0; i<m; i++) {
3305     ii   = i + rstart;
3306     nnz  = Ii[i+1]- Ii[i];
3307     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3308   }
3309   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3310   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3311 
3312   if (!v) {
3313     ierr = PetscFree(values);CHKERRQ(ierr);
3314   }
3315   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3316   PetscFunctionReturn(0);
3317 }
3318 
3319 #undef __FUNCT__
3320 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR"
3321 /*@
3322    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3323    (the default parallel PETSc format).
3324 
3325    Collective on MPI_Comm
3326 
3327    Input Parameters:
3328 +  B - the matrix
3329 .  i - the indices into j for the start of each local row (starts with zero)
3330 .  j - the column indices for each local row (starts with zero)
3331 -  v - optional values in the matrix
3332 
3333    Level: developer
3334 
3335    Notes:
3336        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3337      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3338      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3339 
3340        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3341 
3342        The format which is used for the sparse matrix input, is equivalent to a
3343     row-major ordering.. i.e for the following matrix, the input data expected is
3344     as shown:
3345 
3346         1 0 0
3347         2 0 3     P0
3348        -------
3349         4 5 6     P1
3350 
3351      Process0 [P0]: rows_owned=[0,1]
3352         i =  {0,1,3}  [size = nrow+1  = 2+1]
3353         j =  {0,0,2}  [size = nz = 6]
3354         v =  {1,2,3}  [size = nz = 6]
3355 
3356      Process1 [P1]: rows_owned=[2]
3357         i =  {0,3}    [size = nrow+1  = 1+1]
3358         j =  {0,1,2}  [size = nz = 6]
3359         v =  {4,5,6}  [size = nz = 6]
3360 
3361 .keywords: matrix, aij, compressed row, sparse, parallel
3362 
3363 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MPIAIJ,
3364           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3365 @*/
3366 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3367 {
3368   PetscErrorCode ierr;
3369 
3370   PetscFunctionBegin;
3371   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3372   PetscFunctionReturn(0);
3373 }
3374 
3375 #undef __FUNCT__
3376 #define __FUNCT__ "MatMPIAIJSetPreallocation"
3377 /*@C
3378    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3379    (the default parallel PETSc format).  For good matrix assembly performance
3380    the user should preallocate the matrix storage by setting the parameters
3381    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3382    performance can be increased by more than a factor of 50.
3383 
3384    Collective on MPI_Comm
3385 
3386    Input Parameters:
3387 +  B - the matrix
3388 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3389            (same value is used for all local rows)
3390 .  d_nnz - array containing the number of nonzeros in the various rows of the
3391            DIAGONAL portion of the local submatrix (possibly different for each row)
3392            or NULL (PETSC_NULL_INTEGER in Fortran), if d_nz is used to specify the nonzero structure.
3393            The size of this array is equal to the number of local rows, i.e 'm'.
3394            For matrices that will be factored, you must leave room for (and set)
3395            the diagonal entry even if it is zero.
3396 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3397            submatrix (same value is used for all local rows).
3398 -  o_nnz - array containing the number of nonzeros in the various rows of the
3399            OFF-DIAGONAL portion of the local submatrix (possibly different for
3400            each row) or NULL (PETSC_NULL_INTEGER in Fortran), if o_nz is used to specify the nonzero
3401            structure. The size of this array is equal to the number
3402            of local rows, i.e 'm'.
3403 
3404    If the *_nnz parameter is given then the *_nz parameter is ignored
3405 
3406    The AIJ format (also called the Yale sparse matrix format or
3407    compressed row storage (CSR)), is fully compatible with standard Fortran 77
3408    storage.  The stored row and column indices begin with zero.
3409    See Users-Manual: ch_mat for details.
3410 
3411    The parallel matrix is partitioned such that the first m0 rows belong to
3412    process 0, the next m1 rows belong to process 1, the next m2 rows belong
3413    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
3414 
3415    The DIAGONAL portion of the local submatrix of a processor can be defined
3416    as the submatrix which is obtained by extraction the part corresponding to
3417    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
3418    first row that belongs to the processor, r2 is the last row belonging to
3419    the this processor, and c1-c2 is range of indices of the local part of a
3420    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
3421    common case of a square matrix, the row and column ranges are the same and
3422    the DIAGONAL part is also square. The remaining portion of the local
3423    submatrix (mxN) constitute the OFF-DIAGONAL portion.
3424 
3425    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3426 
3427    You can call MatGetInfo() to get information on how effective the preallocation was;
3428    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3429    You can also run with the option -info and look for messages with the string
3430    malloc in them to see if additional memory allocation was needed.
3431 
3432    Example usage:
3433 
3434    Consider the following 8x8 matrix with 34 non-zero values, that is
3435    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3436    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3437    as follows:
3438 
3439 .vb
3440             1  2  0  |  0  3  0  |  0  4
3441     Proc0   0  5  6  |  7  0  0  |  8  0
3442             9  0 10  | 11  0  0  | 12  0
3443     -------------------------------------
3444            13  0 14  | 15 16 17  |  0  0
3445     Proc1   0 18  0  | 19 20 21  |  0  0
3446             0  0  0  | 22 23  0  | 24  0
3447     -------------------------------------
3448     Proc2  25 26 27  |  0  0 28  | 29  0
3449            30  0  0  | 31 32 33  |  0 34
3450 .ve
3451 
3452    This can be represented as a collection of submatrices as:
3453 
3454 .vb
3455       A B C
3456       D E F
3457       G H I
3458 .ve
3459 
3460    Where the submatrices A,B,C are owned by proc0, D,E,F are
3461    owned by proc1, G,H,I are owned by proc2.
3462 
3463    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3464    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3465    The 'M','N' parameters are 8,8, and have the same values on all procs.
3466 
3467    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3468    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3469    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3470    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3471    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3472    matrix, ans [DF] as another SeqAIJ matrix.
3473 
3474    When d_nz, o_nz parameters are specified, d_nz storage elements are
3475    allocated for every row of the local diagonal submatrix, and o_nz
3476    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3477    One way to choose d_nz and o_nz is to use the max nonzerors per local
3478    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3479    In this case, the values of d_nz,o_nz are:
3480 .vb
3481      proc0 : dnz = 2, o_nz = 2
3482      proc1 : dnz = 3, o_nz = 2
3483      proc2 : dnz = 1, o_nz = 4
3484 .ve
3485    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3486    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3487    for proc3. i.e we are using 12+15+10=37 storage locations to store
3488    34 values.
3489 
3490    When d_nnz, o_nnz parameters are specified, the storage is specified
3491    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3492    In the above case the values for d_nnz,o_nnz are:
3493 .vb
3494      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3495      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3496      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3497 .ve
3498    Here the space allocated is sum of all the above values i.e 34, and
3499    hence pre-allocation is perfect.
3500 
3501    Level: intermediate
3502 
3503 .keywords: matrix, aij, compressed row, sparse, parallel
3504 
3505 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
3506           MPIAIJ, MatGetInfo(), PetscSplitOwnership()
3507 @*/
3508 PetscErrorCode  MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3509 {
3510   PetscErrorCode ierr;
3511 
3512   PetscFunctionBegin;
3513   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3514   PetscValidType(B,1);
3515   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
3516   PetscFunctionReturn(0);
3517 }
3518 
3519 #undef __FUNCT__
3520 #define __FUNCT__ "MatCreateMPIAIJWithArrays"
3521 /*@
3522      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
3523          CSR format the local rows.
3524 
3525    Collective on MPI_Comm
3526 
3527    Input Parameters:
3528 +  comm - MPI communicator
3529 .  m - number of local rows (Cannot be PETSC_DECIDE)
3530 .  n - This value should be the same as the local size used in creating the
3531        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3532        calculated if N is given) For square matrices n is almost always m.
3533 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3534 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3535 .   i - row indices
3536 .   j - column indices
3537 -   a - matrix values
3538 
3539    Output Parameter:
3540 .   mat - the matrix
3541 
3542    Level: intermediate
3543 
3544    Notes:
3545        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3546      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3547      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3548 
3549        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3550 
3551        The format which is used for the sparse matrix input, is equivalent to a
3552     row-major ordering.. i.e for the following matrix, the input data expected is
3553     as shown:
3554 
3555         1 0 0
3556         2 0 3     P0
3557        -------
3558         4 5 6     P1
3559 
3560      Process0 [P0]: rows_owned=[0,1]
3561         i =  {0,1,3}  [size = nrow+1  = 2+1]
3562         j =  {0,0,2}  [size = nz = 6]
3563         v =  {1,2,3}  [size = nz = 6]
3564 
3565      Process1 [P1]: rows_owned=[2]
3566         i =  {0,3}    [size = nrow+1  = 1+1]
3567         j =  {0,1,2}  [size = nz = 6]
3568         v =  {4,5,6}  [size = nz = 6]
3569 
3570 .keywords: matrix, aij, compressed row, sparse, parallel
3571 
3572 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3573           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
3574 @*/
3575 PetscErrorCode  MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
3576 {
3577   PetscErrorCode ierr;
3578 
3579   PetscFunctionBegin;
3580   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
3581   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
3582   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
3583   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
3584   /* ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr); */
3585   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
3586   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
3587   PetscFunctionReturn(0);
3588 }
3589 
3590 #undef __FUNCT__
3591 #define __FUNCT__ "MatCreateAIJ"
3592 /*@C
3593    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
3594    (the default parallel PETSc format).  For good matrix assembly performance
3595    the user should preallocate the matrix storage by setting the parameters
3596    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3597    performance can be increased by more than a factor of 50.
3598 
3599    Collective on MPI_Comm
3600 
3601    Input Parameters:
3602 +  comm - MPI communicator
3603 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
3604            This value should be the same as the local size used in creating the
3605            y vector for the matrix-vector product y = Ax.
3606 .  n - This value should be the same as the local size used in creating the
3607        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3608        calculated if N is given) For square matrices n is almost always m.
3609 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3610 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3611 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3612            (same value is used for all local rows)
3613 .  d_nnz - array containing the number of nonzeros in the various rows of the
3614            DIAGONAL portion of the local submatrix (possibly different for each row)
3615            or NULL, if d_nz is used to specify the nonzero structure.
3616            The size of this array is equal to the number of local rows, i.e 'm'.
3617 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3618            submatrix (same value is used for all local rows).
3619 -  o_nnz - array containing the number of nonzeros in the various rows of the
3620            OFF-DIAGONAL portion of the local submatrix (possibly different for
3621            each row) or NULL, if o_nz is used to specify the nonzero
3622            structure. The size of this array is equal to the number
3623            of local rows, i.e 'm'.
3624 
3625    Output Parameter:
3626 .  A - the matrix
3627 
3628    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3629    MatXXXXSetPreallocation() paradgm instead of this routine directly.
3630    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3631 
3632    Notes:
3633    If the *_nnz parameter is given then the *_nz parameter is ignored
3634 
3635    m,n,M,N parameters specify the size of the matrix, and its partitioning across
3636    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
3637    storage requirements for this matrix.
3638 
3639    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
3640    processor than it must be used on all processors that share the object for
3641    that argument.
3642 
3643    The user MUST specify either the local or global matrix dimensions
3644    (possibly both).
3645 
3646    The parallel matrix is partitioned across processors such that the
3647    first m0 rows belong to process 0, the next m1 rows belong to
3648    process 1, the next m2 rows belong to process 2 etc.. where
3649    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
3650    values corresponding to [m x N] submatrix.
3651 
3652    The columns are logically partitioned with the n0 columns belonging
3653    to 0th partition, the next n1 columns belonging to the next
3654    partition etc.. where n0,n1,n2... are the input parameter 'n'.
3655 
3656    The DIAGONAL portion of the local submatrix on any given processor
3657    is the submatrix corresponding to the rows and columns m,n
3658    corresponding to the given processor. i.e diagonal matrix on
3659    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
3660    etc. The remaining portion of the local submatrix [m x (N-n)]
3661    constitute the OFF-DIAGONAL portion. The example below better
3662    illustrates this concept.
3663 
3664    For a square global matrix we define each processor's diagonal portion
3665    to be its local rows and the corresponding columns (a square submatrix);
3666    each processor's off-diagonal portion encompasses the remainder of the
3667    local matrix (a rectangular submatrix).
3668 
3669    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3670 
3671    When calling this routine with a single process communicator, a matrix of
3672    type SEQAIJ is returned.  If a matrix of type MPIAIJ is desired for this
3673    type of communicator, use the construction mechanism:
3674      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
3675 
3676    By default, this format uses inodes (identical nodes) when possible.
3677    We search for consecutive rows with the same nonzero structure, thereby
3678    reusing matrix information to achieve increased efficiency.
3679 
3680    Options Database Keys:
3681 +  -mat_no_inode  - Do not use inodes
3682 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3683 -  -mat_aij_oneindex - Internally use indexing starting at 1
3684         rather than 0.  Note that when calling MatSetValues(),
3685         the user still MUST index entries starting at 0!
3686 
3687 
3688    Example usage:
3689 
3690    Consider the following 8x8 matrix with 34 non-zero values, that is
3691    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3692    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3693    as follows:
3694 
3695 .vb
3696             1  2  0  |  0  3  0  |  0  4
3697     Proc0   0  5  6  |  7  0  0  |  8  0
3698             9  0 10  | 11  0  0  | 12  0
3699     -------------------------------------
3700            13  0 14  | 15 16 17  |  0  0
3701     Proc1   0 18  0  | 19 20 21  |  0  0
3702             0  0  0  | 22 23  0  | 24  0
3703     -------------------------------------
3704     Proc2  25 26 27  |  0  0 28  | 29  0
3705            30  0  0  | 31 32 33  |  0 34
3706 .ve
3707 
3708    This can be represented as a collection of submatrices as:
3709 
3710 .vb
3711       A B C
3712       D E F
3713       G H I
3714 .ve
3715 
3716    Where the submatrices A,B,C are owned by proc0, D,E,F are
3717    owned by proc1, G,H,I are owned by proc2.
3718 
3719    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3720    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3721    The 'M','N' parameters are 8,8, and have the same values on all procs.
3722 
3723    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3724    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3725    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3726    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3727    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3728    matrix, ans [DF] as another SeqAIJ matrix.
3729 
3730    When d_nz, o_nz parameters are specified, d_nz storage elements are
3731    allocated for every row of the local diagonal submatrix, and o_nz
3732    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3733    One way to choose d_nz and o_nz is to use the max nonzerors per local
3734    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3735    In this case, the values of d_nz,o_nz are:
3736 .vb
3737      proc0 : dnz = 2, o_nz = 2
3738      proc1 : dnz = 3, o_nz = 2
3739      proc2 : dnz = 1, o_nz = 4
3740 .ve
3741    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3742    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3743    for proc3. i.e we are using 12+15+10=37 storage locations to store
3744    34 values.
3745 
3746    When d_nnz, o_nnz parameters are specified, the storage is specified
3747    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3748    In the above case the values for d_nnz,o_nnz are:
3749 .vb
3750      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3751      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3752      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3753 .ve
3754    Here the space allocated is sum of all the above values i.e 34, and
3755    hence pre-allocation is perfect.
3756 
3757    Level: intermediate
3758 
3759 .keywords: matrix, aij, compressed row, sparse, parallel
3760 
3761 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3762           MPIAIJ, MatCreateMPIAIJWithArrays()
3763 @*/
3764 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)
3765 {
3766   PetscErrorCode ierr;
3767   PetscMPIInt    size;
3768 
3769   PetscFunctionBegin;
3770   ierr = MatCreate(comm,A);CHKERRQ(ierr);
3771   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
3772   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3773   if (size > 1) {
3774     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
3775     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
3776   } else {
3777     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
3778     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
3779   }
3780   PetscFunctionReturn(0);
3781 }
3782 
3783 #undef __FUNCT__
3784 #define __FUNCT__ "MatMPIAIJGetSeqAIJ"
3785 PetscErrorCode  MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
3786 {
3787   Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
3788 
3789   PetscFunctionBegin;
3790   if (Ad)     *Ad     = a->A;
3791   if (Ao)     *Ao     = a->B;
3792   if (colmap) *colmap = a->garray;
3793   PetscFunctionReturn(0);
3794 }
3795 
3796 #undef __FUNCT__
3797 #define __FUNCT__ "MatSetColoring_MPIAIJ"
3798 PetscErrorCode MatSetColoring_MPIAIJ(Mat A,ISColoring coloring)
3799 {
3800   PetscErrorCode ierr;
3801   PetscInt       i;
3802   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3803 
3804   PetscFunctionBegin;
3805   if (coloring->ctype == IS_COLORING_GLOBAL) {
3806     ISColoringValue *allcolors,*colors;
3807     ISColoring      ocoloring;
3808 
3809     /* set coloring for diagonal portion */
3810     ierr = MatSetColoring_SeqAIJ(a->A,coloring);CHKERRQ(ierr);
3811 
3812     /* set coloring for off-diagonal portion */
3813     ierr = ISAllGatherColors(PetscObjectComm((PetscObject)A),coloring->n,coloring->colors,NULL,&allcolors);CHKERRQ(ierr);
3814     ierr = PetscMalloc1(a->B->cmap->n+1,&colors);CHKERRQ(ierr);
3815     for (i=0; i<a->B->cmap->n; i++) {
3816       colors[i] = allcolors[a->garray[i]];
3817     }
3818     ierr = PetscFree(allcolors);CHKERRQ(ierr);
3819     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3820     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
3821     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3822   } else if (coloring->ctype == IS_COLORING_GHOSTED) {
3823     ISColoringValue *colors;
3824     PetscInt        *larray;
3825     ISColoring      ocoloring;
3826 
3827     /* set coloring for diagonal portion */
3828     ierr = PetscMalloc1(a->A->cmap->n+1,&larray);CHKERRQ(ierr);
3829     for (i=0; i<a->A->cmap->n; i++) {
3830       larray[i] = i + A->cmap->rstart;
3831     }
3832     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->A->cmap->n,larray,NULL,larray);CHKERRQ(ierr);
3833     ierr = PetscMalloc1(a->A->cmap->n+1,&colors);CHKERRQ(ierr);
3834     for (i=0; i<a->A->cmap->n; i++) {
3835       colors[i] = coloring->colors[larray[i]];
3836     }
3837     ierr = PetscFree(larray);CHKERRQ(ierr);
3838     ierr = ISColoringCreate(PETSC_COMM_SELF,coloring->n,a->A->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3839     ierr = MatSetColoring_SeqAIJ(a->A,ocoloring);CHKERRQ(ierr);
3840     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3841 
3842     /* set coloring for off-diagonal portion */
3843     ierr = PetscMalloc1(a->B->cmap->n+1,&larray);CHKERRQ(ierr);
3844     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->B->cmap->n,a->garray,NULL,larray);CHKERRQ(ierr);
3845     ierr = PetscMalloc1(a->B->cmap->n+1,&colors);CHKERRQ(ierr);
3846     for (i=0; i<a->B->cmap->n; i++) {
3847       colors[i] = coloring->colors[larray[i]];
3848     }
3849     ierr = PetscFree(larray);CHKERRQ(ierr);
3850     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3851     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
3852     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3853   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support ISColoringType %d",(int)coloring->ctype);
3854   PetscFunctionReturn(0);
3855 }
3856 
3857 #undef __FUNCT__
3858 #define __FUNCT__ "MatSetValuesAdifor_MPIAIJ"
3859 PetscErrorCode MatSetValuesAdifor_MPIAIJ(Mat A,PetscInt nl,void *advalues)
3860 {
3861   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3862   PetscErrorCode ierr;
3863 
3864   PetscFunctionBegin;
3865   ierr = MatSetValuesAdifor_SeqAIJ(a->A,nl,advalues);CHKERRQ(ierr);
3866   ierr = MatSetValuesAdifor_SeqAIJ(a->B,nl,advalues);CHKERRQ(ierr);
3867   PetscFunctionReturn(0);
3868 }
3869 
3870 #undef __FUNCT__
3871 #define __FUNCT__ "MatCreateMPIMatConcatenateSeqMat_MPIAIJ"
3872 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
3873 {
3874   PetscErrorCode ierr;
3875   PetscInt       m,N,i,rstart,nnz,Ii;
3876   PetscInt       *indx;
3877   PetscScalar    *values;
3878 
3879   PetscFunctionBegin;
3880   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
3881   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
3882     PetscInt       *dnz,*onz,sum,bs,cbs;
3883 
3884     if (n == PETSC_DECIDE) {
3885       ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
3886     }
3887     /* Check sum(n) = N */
3888     ierr = MPI_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3889     if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
3890 
3891     ierr    = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3892     rstart -= m;
3893 
3894     ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
3895     for (i=0; i<m; i++) {
3896       ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3897       ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
3898       ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3899     }
3900 
3901     ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
3902     ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
3903     ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
3904     ierr = MatSetBlockSizes(*outmat,bs,cbs);CHKERRQ(ierr);
3905     ierr = MatSetType(*outmat,MATMPIAIJ);CHKERRQ(ierr);
3906     ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
3907     ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
3908   }
3909 
3910   /* numeric phase */
3911   ierr = MatGetOwnershipRange(*outmat,&rstart,NULL);CHKERRQ(ierr);
3912   for (i=0; i<m; i++) {
3913     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3914     Ii   = i + rstart;
3915     ierr = MatSetValues(*outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3916     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3917   }
3918   ierr = MatAssemblyBegin(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3919   ierr = MatAssemblyEnd(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3920   PetscFunctionReturn(0);
3921 }
3922 
3923 #undef __FUNCT__
3924 #define __FUNCT__ "MatFileSplit"
3925 PetscErrorCode MatFileSplit(Mat A,char *outfile)
3926 {
3927   PetscErrorCode    ierr;
3928   PetscMPIInt       rank;
3929   PetscInt          m,N,i,rstart,nnz;
3930   size_t            len;
3931   const PetscInt    *indx;
3932   PetscViewer       out;
3933   char              *name;
3934   Mat               B;
3935   const PetscScalar *values;
3936 
3937   PetscFunctionBegin;
3938   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
3939   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
3940   /* Should this be the type of the diagonal block of A? */
3941   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
3942   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
3943   ierr = MatSetBlockSizesFromMats(B,A,A);CHKERRQ(ierr);
3944   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
3945   ierr = MatSeqAIJSetPreallocation(B,0,NULL);CHKERRQ(ierr);
3946   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
3947   for (i=0; i<m; i++) {
3948     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3949     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3950     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3951   }
3952   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3953   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3954 
3955   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
3956   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
3957   ierr = PetscMalloc1(len+5,&name);CHKERRQ(ierr);
3958   sprintf(name,"%s.%d",outfile,rank);
3959   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
3960   ierr = PetscFree(name);CHKERRQ(ierr);
3961   ierr = MatView(B,out);CHKERRQ(ierr);
3962   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
3963   ierr = MatDestroy(&B);CHKERRQ(ierr);
3964   PetscFunctionReturn(0);
3965 }
3966 
3967 extern PetscErrorCode MatDestroy_MPIAIJ(Mat);
3968 #undef __FUNCT__
3969 #define __FUNCT__ "MatDestroy_MPIAIJ_SeqsToMPI"
3970 PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
3971 {
3972   PetscErrorCode      ierr;
3973   Mat_Merge_SeqsToMPI *merge;
3974   PetscContainer      container;
3975 
3976   PetscFunctionBegin;
3977   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
3978   if (container) {
3979     ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
3980     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
3981     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
3982     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
3983     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
3984     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
3985     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
3986     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
3987     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
3988     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
3989     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
3990     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
3991     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
3992     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
3993     ierr = PetscFree(merge);CHKERRQ(ierr);
3994     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
3995   }
3996   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
3997   PetscFunctionReturn(0);
3998 }
3999 
4000 #include <../src/mat/utils/freespace.h>
4001 #include <petscbt.h>
4002 
4003 #undef __FUNCT__
4004 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJNumeric"
4005 PetscErrorCode  MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
4006 {
4007   PetscErrorCode      ierr;
4008   MPI_Comm            comm;
4009   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
4010   PetscMPIInt         size,rank,taga,*len_s;
4011   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
4012   PetscInt            proc,m;
4013   PetscInt            **buf_ri,**buf_rj;
4014   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
4015   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
4016   MPI_Request         *s_waits,*r_waits;
4017   MPI_Status          *status;
4018   MatScalar           *aa=a->a;
4019   MatScalar           **abuf_r,*ba_i;
4020   Mat_Merge_SeqsToMPI *merge;
4021   PetscContainer      container;
4022 
4023   PetscFunctionBegin;
4024   ierr = PetscObjectGetComm((PetscObject)mpimat,&comm);CHKERRQ(ierr);
4025   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4026 
4027   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4028   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4029 
4030   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4031   ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4032 
4033   bi     = merge->bi;
4034   bj     = merge->bj;
4035   buf_ri = merge->buf_ri;
4036   buf_rj = merge->buf_rj;
4037 
4038   ierr   = PetscMalloc1(size,&status);CHKERRQ(ierr);
4039   owners = merge->rowmap->range;
4040   len_s  = merge->len_s;
4041 
4042   /* send and recv matrix values */
4043   /*-----------------------------*/
4044   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
4045   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
4046 
4047   ierr = PetscMalloc1(merge->nsend+1,&s_waits);CHKERRQ(ierr);
4048   for (proc=0,k=0; proc<size; proc++) {
4049     if (!len_s[proc]) continue;
4050     i    = owners[proc];
4051     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
4052     k++;
4053   }
4054 
4055   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
4056   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
4057   ierr = PetscFree(status);CHKERRQ(ierr);
4058 
4059   ierr = PetscFree(s_waits);CHKERRQ(ierr);
4060   ierr = PetscFree(r_waits);CHKERRQ(ierr);
4061 
4062   /* insert mat values of mpimat */
4063   /*----------------------------*/
4064   ierr = PetscMalloc1(N,&ba_i);CHKERRQ(ierr);
4065   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4066 
4067   for (k=0; k<merge->nrecv; k++) {
4068     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4069     nrows       = *(buf_ri_k[k]);
4070     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
4071     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4072   }
4073 
4074   /* set values of ba */
4075   m = merge->rowmap->n;
4076   for (i=0; i<m; i++) {
4077     arow = owners[rank] + i;
4078     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
4079     bnzi = bi[i+1] - bi[i];
4080     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
4081 
4082     /* add local non-zero vals of this proc's seqmat into ba */
4083     anzi   = ai[arow+1] - ai[arow];
4084     aj     = a->j + ai[arow];
4085     aa     = a->a + ai[arow];
4086     nextaj = 0;
4087     for (j=0; nextaj<anzi; j++) {
4088       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4089         ba_i[j] += aa[nextaj++];
4090       }
4091     }
4092 
4093     /* add received vals into ba */
4094     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4095       /* i-th row */
4096       if (i == *nextrow[k]) {
4097         anzi   = *(nextai[k]+1) - *nextai[k];
4098         aj     = buf_rj[k] + *(nextai[k]);
4099         aa     = abuf_r[k] + *(nextai[k]);
4100         nextaj = 0;
4101         for (j=0; nextaj<anzi; j++) {
4102           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4103             ba_i[j] += aa[nextaj++];
4104           }
4105         }
4106         nextrow[k]++; nextai[k]++;
4107       }
4108     }
4109     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
4110   }
4111   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4112   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4113 
4114   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
4115   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
4116   ierr = PetscFree(ba_i);CHKERRQ(ierr);
4117   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4118   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4119   PetscFunctionReturn(0);
4120 }
4121 
4122 extern PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat);
4123 
4124 #undef __FUNCT__
4125 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJSymbolic"
4126 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4127 {
4128   PetscErrorCode      ierr;
4129   Mat                 B_mpi;
4130   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
4131   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4132   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
4133   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4134   PetscInt            len,proc,*dnz,*onz,bs,cbs;
4135   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4136   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4137   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
4138   MPI_Status          *status;
4139   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
4140   PetscBT             lnkbt;
4141   Mat_Merge_SeqsToMPI *merge;
4142   PetscContainer      container;
4143 
4144   PetscFunctionBegin;
4145   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4146 
4147   /* make sure it is a PETSc comm */
4148   ierr = PetscCommDuplicate(comm,&comm,NULL);CHKERRQ(ierr);
4149   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4150   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4151 
4152   ierr = PetscNew(&merge);CHKERRQ(ierr);
4153   ierr = PetscMalloc1(size,&status);CHKERRQ(ierr);
4154 
4155   /* determine row ownership */
4156   /*---------------------------------------------------------*/
4157   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
4158   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
4159   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
4160   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
4161   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
4162   ierr = PetscMalloc1(size,&len_si);CHKERRQ(ierr);
4163   ierr = PetscMalloc1(size,&merge->len_s);CHKERRQ(ierr);
4164 
4165   m      = merge->rowmap->n;
4166   owners = merge->rowmap->range;
4167 
4168   /* determine the number of messages to send, their lengths */
4169   /*---------------------------------------------------------*/
4170   len_s = merge->len_s;
4171 
4172   len          = 0; /* length of buf_si[] */
4173   merge->nsend = 0;
4174   for (proc=0; proc<size; proc++) {
4175     len_si[proc] = 0;
4176     if (proc == rank) {
4177       len_s[proc] = 0;
4178     } else {
4179       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4180       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4181     }
4182     if (len_s[proc]) {
4183       merge->nsend++;
4184       nrows = 0;
4185       for (i=owners[proc]; i<owners[proc+1]; i++) {
4186         if (ai[i+1] > ai[i]) nrows++;
4187       }
4188       len_si[proc] = 2*(nrows+1);
4189       len         += len_si[proc];
4190     }
4191   }
4192 
4193   /* determine the number and length of messages to receive for ij-structure */
4194   /*-------------------------------------------------------------------------*/
4195   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
4196   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
4197 
4198   /* post the Irecv of j-structure */
4199   /*-------------------------------*/
4200   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
4201   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
4202 
4203   /* post the Isend of j-structure */
4204   /*--------------------------------*/
4205   ierr = PetscMalloc2(merge->nsend,&si_waits,merge->nsend,&sj_waits);CHKERRQ(ierr);
4206 
4207   for (proc=0, k=0; proc<size; proc++) {
4208     if (!len_s[proc]) continue;
4209     i    = owners[proc];
4210     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
4211     k++;
4212   }
4213 
4214   /* receives and sends of j-structure are complete */
4215   /*------------------------------------------------*/
4216   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
4217   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
4218 
4219   /* send and recv i-structure */
4220   /*---------------------------*/
4221   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
4222   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
4223 
4224   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
4225   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4226   for (proc=0,k=0; proc<size; proc++) {
4227     if (!len_s[proc]) continue;
4228     /* form outgoing message for i-structure:
4229          buf_si[0]:                 nrows to be sent
4230                [1:nrows]:           row index (global)
4231                [nrows+1:2*nrows+1]: i-structure index
4232     */
4233     /*-------------------------------------------*/
4234     nrows       = len_si[proc]/2 - 1;
4235     buf_si_i    = buf_si + nrows+1;
4236     buf_si[0]   = nrows;
4237     buf_si_i[0] = 0;
4238     nrows       = 0;
4239     for (i=owners[proc]; i<owners[proc+1]; i++) {
4240       anzi = ai[i+1] - ai[i];
4241       if (anzi) {
4242         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4243         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4244         nrows++;
4245       }
4246     }
4247     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4248     k++;
4249     buf_si += len_si[proc];
4250   }
4251 
4252   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4253   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4254 
4255   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4256   for (i=0; i<merge->nrecv; i++) {
4257     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);
4258   }
4259 
4260   ierr = PetscFree(len_si);CHKERRQ(ierr);
4261   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4262   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4263   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4264   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4265   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4266   ierr = PetscFree(status);CHKERRQ(ierr);
4267 
4268   /* compute a local seq matrix in each processor */
4269   /*----------------------------------------------*/
4270   /* allocate bi array and free space for accumulating nonzero column info */
4271   ierr  = PetscMalloc1(m+1,&bi);CHKERRQ(ierr);
4272   bi[0] = 0;
4273 
4274   /* create and initialize a linked list */
4275   nlnk = N+1;
4276   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4277 
4278   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4279   len  = ai[owners[rank+1]] - ai[owners[rank]];
4280   ierr = PetscFreeSpaceGet((PetscInt)(2*len+1),&free_space);CHKERRQ(ierr);
4281 
4282   current_space = free_space;
4283 
4284   /* determine symbolic info for each local row */
4285   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4286 
4287   for (k=0; k<merge->nrecv; k++) {
4288     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4289     nrows       = *buf_ri_k[k];
4290     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4291     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4292   }
4293 
4294   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4295   len  = 0;
4296   for (i=0; i<m; i++) {
4297     bnzi = 0;
4298     /* add local non-zero cols of this proc's seqmat into lnk */
4299     arow  = owners[rank] + i;
4300     anzi  = ai[arow+1] - ai[arow];
4301     aj    = a->j + ai[arow];
4302     ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4303     bnzi += nlnk;
4304     /* add received col data into lnk */
4305     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4306       if (i == *nextrow[k]) { /* i-th row */
4307         anzi  = *(nextai[k]+1) - *nextai[k];
4308         aj    = buf_rj[k] + *nextai[k];
4309         ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4310         bnzi += nlnk;
4311         nextrow[k]++; nextai[k]++;
4312       }
4313     }
4314     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4315 
4316     /* if free space is not available, make more free space */
4317     if (current_space->local_remaining<bnzi) {
4318       ierr = PetscFreeSpaceGet(bnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
4319       nspacedouble++;
4320     }
4321     /* copy data into free space, then initialize lnk */
4322     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4323     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
4324 
4325     current_space->array           += bnzi;
4326     current_space->local_used      += bnzi;
4327     current_space->local_remaining -= bnzi;
4328 
4329     bi[i+1] = bi[i] + bnzi;
4330   }
4331 
4332   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4333 
4334   ierr = PetscMalloc1(bi[m]+1,&bj);CHKERRQ(ierr);
4335   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
4336   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4337 
4338   /* create symbolic parallel matrix B_mpi */
4339   /*---------------------------------------*/
4340   ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
4341   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
4342   if (n==PETSC_DECIDE) {
4343     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
4344   } else {
4345     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4346   }
4347   ierr = MatSetBlockSizes(B_mpi,bs,cbs);CHKERRQ(ierr);
4348   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
4349   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
4350   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4351   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
4352 
4353   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4354   B_mpi->assembled    = PETSC_FALSE;
4355   B_mpi->ops->destroy = MatDestroy_MPIAIJ_SeqsToMPI;
4356   merge->bi           = bi;
4357   merge->bj           = bj;
4358   merge->buf_ri       = buf_ri;
4359   merge->buf_rj       = buf_rj;
4360   merge->coi          = NULL;
4361   merge->coj          = NULL;
4362   merge->owners_co    = NULL;
4363 
4364   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
4365 
4366   /* attach the supporting struct to B_mpi for reuse */
4367   ierr    = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
4368   ierr    = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
4369   ierr    = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
4370   ierr    = PetscContainerDestroy(&container);CHKERRQ(ierr);
4371   *mpimat = B_mpi;
4372 
4373   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4374   PetscFunctionReturn(0);
4375 }
4376 
4377 #undef __FUNCT__
4378 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJ"
4379 /*@C
4380       MatCreateMPIAIJSumSeqAIJ - Creates a MPIAIJ matrix by adding sequential
4381                  matrices from each processor
4382 
4383     Collective on MPI_Comm
4384 
4385    Input Parameters:
4386 +    comm - the communicators the parallel matrix will live on
4387 .    seqmat - the input sequential matrices
4388 .    m - number of local rows (or PETSC_DECIDE)
4389 .    n - number of local columns (or PETSC_DECIDE)
4390 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4391 
4392    Output Parameter:
4393 .    mpimat - the parallel matrix generated
4394 
4395     Level: advanced
4396 
4397    Notes:
4398      The dimensions of the sequential matrix in each processor MUST be the same.
4399      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
4400      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
4401 @*/
4402 PetscErrorCode  MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
4403 {
4404   PetscErrorCode ierr;
4405   PetscMPIInt    size;
4406 
4407   PetscFunctionBegin;
4408   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4409   if (size == 1) {
4410     ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4411     if (scall == MAT_INITIAL_MATRIX) {
4412       ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
4413     } else {
4414       ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4415     }
4416     ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4417     PetscFunctionReturn(0);
4418   }
4419   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4420   if (scall == MAT_INITIAL_MATRIX) {
4421     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
4422   }
4423   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
4424   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4425   PetscFunctionReturn(0);
4426 }
4427 
4428 #undef __FUNCT__
4429 #define __FUNCT__ "MatMPIAIJGetLocalMat"
4430 /*@
4431      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
4432           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
4433           with MatGetSize()
4434 
4435     Not Collective
4436 
4437    Input Parameters:
4438 +    A - the matrix
4439 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4440 
4441    Output Parameter:
4442 .    A_loc - the local sequential matrix generated
4443 
4444     Level: developer
4445 
4446 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
4447 
4448 @*/
4449 PetscErrorCode  MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
4450 {
4451   PetscErrorCode ierr;
4452   Mat_MPIAIJ     *mpimat=(Mat_MPIAIJ*)A->data;
4453   Mat_SeqAIJ     *mat,*a,*b;
4454   PetscInt       *ai,*aj,*bi,*bj,*cmap=mpimat->garray;
4455   MatScalar      *aa,*ba,*cam;
4456   PetscScalar    *ca;
4457   PetscInt       am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
4458   PetscInt       *ci,*cj,col,ncols_d,ncols_o,jo;
4459   PetscBool      match;
4460   MPI_Comm       comm;
4461   PetscMPIInt    size;
4462 
4463   PetscFunctionBegin;
4464   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4465   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
4466   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4467   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4468   if (size == 1 && scall == MAT_REUSE_MATRIX) PetscFunctionReturn(0);
4469 
4470   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4471   a = (Mat_SeqAIJ*)(mpimat->A)->data;
4472   b = (Mat_SeqAIJ*)(mpimat->B)->data;
4473   ai = a->i; aj = a->j; bi = b->i; bj = b->j;
4474   aa = a->a; ba = b->a;
4475   if (scall == MAT_INITIAL_MATRIX) {
4476     if (size == 1) {
4477       ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ai,aj,aa,A_loc);CHKERRQ(ierr);
4478       PetscFunctionReturn(0);
4479     }
4480 
4481     ierr  = PetscMalloc1(1+am,&ci);CHKERRQ(ierr);
4482     ci[0] = 0;
4483     for (i=0; i<am; i++) {
4484       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
4485     }
4486     ierr = PetscMalloc1(1+ci[am],&cj);CHKERRQ(ierr);
4487     ierr = PetscMalloc1(1+ci[am],&ca);CHKERRQ(ierr);
4488     k    = 0;
4489     for (i=0; i<am; i++) {
4490       ncols_o = bi[i+1] - bi[i];
4491       ncols_d = ai[i+1] - ai[i];
4492       /* off-diagonal portion of A */
4493       for (jo=0; jo<ncols_o; jo++) {
4494         col = cmap[*bj];
4495         if (col >= cstart) break;
4496         cj[k]   = col; bj++;
4497         ca[k++] = *ba++;
4498       }
4499       /* diagonal portion of A */
4500       for (j=0; j<ncols_d; j++) {
4501         cj[k]   = cstart + *aj++;
4502         ca[k++] = *aa++;
4503       }
4504       /* off-diagonal portion of A */
4505       for (j=jo; j<ncols_o; j++) {
4506         cj[k]   = cmap[*bj++];
4507         ca[k++] = *ba++;
4508       }
4509     }
4510     /* put together the new matrix */
4511     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
4512     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4513     /* Since these are PETSc arrays, change flags to free them as necessary. */
4514     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
4515     mat->free_a  = PETSC_TRUE;
4516     mat->free_ij = PETSC_TRUE;
4517     mat->nonew   = 0;
4518   } else if (scall == MAT_REUSE_MATRIX) {
4519     mat=(Mat_SeqAIJ*)(*A_loc)->data;
4520     ci = mat->i; cj = mat->j; cam = mat->a;
4521     for (i=0; i<am; i++) {
4522       /* off-diagonal portion of A */
4523       ncols_o = bi[i+1] - bi[i];
4524       for (jo=0; jo<ncols_o; jo++) {
4525         col = cmap[*bj];
4526         if (col >= cstart) break;
4527         *cam++ = *ba++; bj++;
4528       }
4529       /* diagonal portion of A */
4530       ncols_d = ai[i+1] - ai[i];
4531       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
4532       /* off-diagonal portion of A */
4533       for (j=jo; j<ncols_o; j++) {
4534         *cam++ = *ba++; bj++;
4535       }
4536     }
4537   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
4538   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4539   PetscFunctionReturn(0);
4540 }
4541 
4542 #undef __FUNCT__
4543 #define __FUNCT__ "MatMPIAIJGetLocalMatCondensed"
4544 /*@C
4545      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MPIAIJ matrix by taking all its local rows and NON-ZERO columns
4546 
4547     Not Collective
4548 
4549    Input Parameters:
4550 +    A - the matrix
4551 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4552 -    row, col - index sets of rows and columns to extract (or NULL)
4553 
4554    Output Parameter:
4555 .    A_loc - the local sequential matrix generated
4556 
4557     Level: developer
4558 
4559 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
4560 
4561 @*/
4562 PetscErrorCode  MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
4563 {
4564   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4565   PetscErrorCode ierr;
4566   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
4567   IS             isrowa,iscola;
4568   Mat            *aloc;
4569   PetscBool      match;
4570 
4571   PetscFunctionBegin;
4572   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4573   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
4574   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4575   if (!row) {
4576     start = A->rmap->rstart; end = A->rmap->rend;
4577     ierr  = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
4578   } else {
4579     isrowa = *row;
4580   }
4581   if (!col) {
4582     start = A->cmap->rstart;
4583     cmap  = a->garray;
4584     nzA   = a->A->cmap->n;
4585     nzB   = a->B->cmap->n;
4586     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4587     ncols = 0;
4588     for (i=0; i<nzB; i++) {
4589       if (cmap[i] < start) idx[ncols++] = cmap[i];
4590       else break;
4591     }
4592     imark = i;
4593     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
4594     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
4595     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
4596   } else {
4597     iscola = *col;
4598   }
4599   if (scall != MAT_INITIAL_MATRIX) {
4600     ierr    = PetscMalloc1(1,&aloc);CHKERRQ(ierr);
4601     aloc[0] = *A_loc;
4602   }
4603   ierr   = MatGetSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
4604   *A_loc = aloc[0];
4605   ierr   = PetscFree(aloc);CHKERRQ(ierr);
4606   if (!row) {
4607     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
4608   }
4609   if (!col) {
4610     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
4611   }
4612   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4613   PetscFunctionReturn(0);
4614 }
4615 
4616 #undef __FUNCT__
4617 #define __FUNCT__ "MatGetBrowsOfAcols"
4618 /*@C
4619     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
4620 
4621     Collective on Mat
4622 
4623    Input Parameters:
4624 +    A,B - the matrices in mpiaij format
4625 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4626 -    rowb, colb - index sets of rows and columns of B to extract (or NULL)
4627 
4628    Output Parameter:
4629 +    rowb, colb - index sets of rows and columns of B to extract
4630 -    B_seq - the sequential matrix generated
4631 
4632     Level: developer
4633 
4634 @*/
4635 PetscErrorCode  MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
4636 {
4637   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4638   PetscErrorCode ierr;
4639   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
4640   IS             isrowb,iscolb;
4641   Mat            *bseq=NULL;
4642 
4643   PetscFunctionBegin;
4644   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4645     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);
4646   }
4647   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4648 
4649   if (scall == MAT_INITIAL_MATRIX) {
4650     start = A->cmap->rstart;
4651     cmap  = a->garray;
4652     nzA   = a->A->cmap->n;
4653     nzB   = a->B->cmap->n;
4654     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4655     ncols = 0;
4656     for (i=0; i<nzB; i++) {  /* row < local row index */
4657       if (cmap[i] < start) idx[ncols++] = cmap[i];
4658       else break;
4659     }
4660     imark = i;
4661     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
4662     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
4663     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
4664     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
4665   } else {
4666     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
4667     isrowb  = *rowb; iscolb = *colb;
4668     ierr    = PetscMalloc1(1,&bseq);CHKERRQ(ierr);
4669     bseq[0] = *B_seq;
4670   }
4671   ierr   = MatGetSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
4672   *B_seq = bseq[0];
4673   ierr   = PetscFree(bseq);CHKERRQ(ierr);
4674   if (!rowb) {
4675     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
4676   } else {
4677     *rowb = isrowb;
4678   }
4679   if (!colb) {
4680     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
4681   } else {
4682     *colb = iscolb;
4683   }
4684   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4685   PetscFunctionReturn(0);
4686 }
4687 
4688 #undef __FUNCT__
4689 #define __FUNCT__ "MatGetBrowsOfAoCols_MPIAIJ"
4690 /*
4691     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
4692     of the OFF-DIAGONAL portion of local A
4693 
4694     Collective on Mat
4695 
4696    Input Parameters:
4697 +    A,B - the matrices in mpiaij format
4698 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4699 
4700    Output Parameter:
4701 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
4702 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
4703 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
4704 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
4705 
4706     Level: developer
4707 
4708 */
4709 PetscErrorCode  MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
4710 {
4711   VecScatter_MPI_General *gen_to,*gen_from;
4712   PetscErrorCode         ierr;
4713   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
4714   Mat_SeqAIJ             *b_oth;
4715   VecScatter             ctx =a->Mvctx;
4716   MPI_Comm               comm;
4717   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
4718   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
4719   PetscScalar            *rvalues,*svalues;
4720   MatScalar              *b_otha,*bufa,*bufA;
4721   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
4722   MPI_Request            *rwaits = NULL,*swaits = NULL;
4723   MPI_Status             *sstatus,rstatus;
4724   PetscMPIInt            jj,size;
4725   PetscInt               *cols,sbs,rbs;
4726   PetscScalar            *vals;
4727 
4728   PetscFunctionBegin;
4729   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4730   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4731 
4732   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4733     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);
4734   }
4735   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4736   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4737 
4738   gen_to   = (VecScatter_MPI_General*)ctx->todata;
4739   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
4740   rvalues  = gen_from->values; /* holds the length of receiving row */
4741   svalues  = gen_to->values;   /* holds the length of sending row */
4742   nrecvs   = gen_from->n;
4743   nsends   = gen_to->n;
4744 
4745   ierr    = PetscMalloc2(nrecvs,&rwaits,nsends,&swaits);CHKERRQ(ierr);
4746   srow    = gen_to->indices;    /* local row index to be sent */
4747   sstarts = gen_to->starts;
4748   sprocs  = gen_to->procs;
4749   sstatus = gen_to->sstatus;
4750   sbs     = gen_to->bs;
4751   rstarts = gen_from->starts;
4752   rprocs  = gen_from->procs;
4753   rbs     = gen_from->bs;
4754 
4755   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
4756   if (scall == MAT_INITIAL_MATRIX) {
4757     /* i-array */
4758     /*---------*/
4759     /*  post receives */
4760     for (i=0; i<nrecvs; i++) {
4761       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
4762       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
4763       ierr   = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4764     }
4765 
4766     /* pack the outgoing message */
4767     ierr = PetscMalloc2(nsends+1,&sstartsj,nrecvs+1,&rstartsj);CHKERRQ(ierr);
4768 
4769     sstartsj[0] = 0;
4770     rstartsj[0] = 0;
4771     len         = 0; /* total length of j or a array to be sent */
4772     k           = 0;
4773     for (i=0; i<nsends; i++) {
4774       rowlen = (PetscInt*)svalues + sstarts[i]*sbs;
4775       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
4776       for (j=0; j<nrows; j++) {
4777         row = srow[k] + B->rmap->range[rank]; /* global row idx */
4778         for (l=0; l<sbs; l++) {
4779           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr); /* rowlength */
4780 
4781           rowlen[j*sbs+l] = ncols;
4782 
4783           len += ncols;
4784           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr);
4785         }
4786         k++;
4787       }
4788       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4789 
4790       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
4791     }
4792     /* recvs and sends of i-array are completed */
4793     i = nrecvs;
4794     while (i--) {
4795       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4796     }
4797     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4798 
4799     /* allocate buffers for sending j and a arrays */
4800     ierr = PetscMalloc1(len+1,&bufj);CHKERRQ(ierr);
4801     ierr = PetscMalloc1(len+1,&bufa);CHKERRQ(ierr);
4802 
4803     /* create i-array of B_oth */
4804     ierr = PetscMalloc1(aBn+2,&b_othi);CHKERRQ(ierr);
4805 
4806     b_othi[0] = 0;
4807     len       = 0; /* total length of j or a array to be received */
4808     k         = 0;
4809     for (i=0; i<nrecvs; i++) {
4810       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
4811       nrows  = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be recieved */
4812       for (j=0; j<nrows; j++) {
4813         b_othi[k+1] = b_othi[k] + rowlen[j];
4814         len        += rowlen[j]; k++;
4815       }
4816       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
4817     }
4818 
4819     /* allocate space for j and a arrrays of B_oth */
4820     ierr = PetscMalloc1(b_othi[aBn]+1,&b_othj);CHKERRQ(ierr);
4821     ierr = PetscMalloc1(b_othi[aBn]+1,&b_otha);CHKERRQ(ierr);
4822 
4823     /* j-array */
4824     /*---------*/
4825     /*  post receives of j-array */
4826     for (i=0; i<nrecvs; i++) {
4827       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4828       ierr  = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4829     }
4830 
4831     /* pack the outgoing message j-array */
4832     k = 0;
4833     for (i=0; i<nsends; i++) {
4834       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4835       bufJ  = bufj+sstartsj[i];
4836       for (j=0; j<nrows; j++) {
4837         row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4838         for (ll=0; ll<sbs; ll++) {
4839           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4840           for (l=0; l<ncols; l++) {
4841             *bufJ++ = cols[l];
4842           }
4843           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4844         }
4845       }
4846       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4847     }
4848 
4849     /* recvs and sends of j-array are completed */
4850     i = nrecvs;
4851     while (i--) {
4852       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4853     }
4854     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4855   } else if (scall == MAT_REUSE_MATRIX) {
4856     sstartsj = *startsj_s;
4857     rstartsj = *startsj_r;
4858     bufa     = *bufa_ptr;
4859     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
4860     b_otha   = b_oth->a;
4861   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
4862 
4863   /* a-array */
4864   /*---------*/
4865   /*  post receives of a-array */
4866   for (i=0; i<nrecvs; i++) {
4867     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4868     ierr  = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4869   }
4870 
4871   /* pack the outgoing message a-array */
4872   k = 0;
4873   for (i=0; i<nsends; i++) {
4874     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4875     bufA  = bufa+sstartsj[i];
4876     for (j=0; j<nrows; j++) {
4877       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4878       for (ll=0; ll<sbs; ll++) {
4879         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4880         for (l=0; l<ncols; l++) {
4881           *bufA++ = vals[l];
4882         }
4883         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4884       }
4885     }
4886     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4887   }
4888   /* recvs and sends of a-array are completed */
4889   i = nrecvs;
4890   while (i--) {
4891     ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4892   }
4893   if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4894   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
4895 
4896   if (scall == MAT_INITIAL_MATRIX) {
4897     /* put together the new matrix */
4898     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
4899 
4900     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4901     /* Since these are PETSc arrays, change flags to free them as necessary. */
4902     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
4903     b_oth->free_a  = PETSC_TRUE;
4904     b_oth->free_ij = PETSC_TRUE;
4905     b_oth->nonew   = 0;
4906 
4907     ierr = PetscFree(bufj);CHKERRQ(ierr);
4908     if (!startsj_s || !bufa_ptr) {
4909       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
4910       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
4911     } else {
4912       *startsj_s = sstartsj;
4913       *startsj_r = rstartsj;
4914       *bufa_ptr  = bufa;
4915     }
4916   }
4917   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4918   PetscFunctionReturn(0);
4919 }
4920 
4921 #undef __FUNCT__
4922 #define __FUNCT__ "MatGetCommunicationStructs"
4923 /*@C
4924   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
4925 
4926   Not Collective
4927 
4928   Input Parameters:
4929 . A - The matrix in mpiaij format
4930 
4931   Output Parameter:
4932 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
4933 . colmap - A map from global column index to local index into lvec
4934 - multScatter - A scatter from the argument of a matrix-vector product to lvec
4935 
4936   Level: developer
4937 
4938 @*/
4939 #if defined(PETSC_USE_CTABLE)
4940 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
4941 #else
4942 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
4943 #endif
4944 {
4945   Mat_MPIAIJ *a;
4946 
4947   PetscFunctionBegin;
4948   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4949   PetscValidPointer(lvec, 2);
4950   PetscValidPointer(colmap, 3);
4951   PetscValidPointer(multScatter, 4);
4952   a = (Mat_MPIAIJ*) A->data;
4953   if (lvec) *lvec = a->lvec;
4954   if (colmap) *colmap = a->colmap;
4955   if (multScatter) *multScatter = a->Mvctx;
4956   PetscFunctionReturn(0);
4957 }
4958 
4959 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
4960 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
4961 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
4962 #if defined(PETSC_HAVE_ELEMENTAL)
4963 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
4964 #endif
4965 
4966 #undef __FUNCT__
4967 #define __FUNCT__ "MatMatMultNumeric_MPIDense_MPIAIJ"
4968 /*
4969     Computes (B'*A')' since computing B*A directly is untenable
4970 
4971                n                       p                          p
4972         (              )       (              )         (                  )
4973       m (      A       )  *  n (       B      )   =   m (         C        )
4974         (              )       (              )         (                  )
4975 
4976 */
4977 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
4978 {
4979   PetscErrorCode ierr;
4980   Mat            At,Bt,Ct;
4981 
4982   PetscFunctionBegin;
4983   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
4984   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
4985   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
4986   ierr = MatDestroy(&At);CHKERRQ(ierr);
4987   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
4988   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
4989   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
4990   PetscFunctionReturn(0);
4991 }
4992 
4993 #undef __FUNCT__
4994 #define __FUNCT__ "MatMatMultSymbolic_MPIDense_MPIAIJ"
4995 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
4996 {
4997   PetscErrorCode ierr;
4998   PetscInt       m=A->rmap->n,n=B->cmap->n;
4999   Mat            Cmat;
5000 
5001   PetscFunctionBegin;
5002   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);
5003   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
5004   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
5005   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
5006   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
5007   ierr = MatMPIDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
5008   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5009   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5010 
5011   Cmat->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
5012 
5013   *C = Cmat;
5014   PetscFunctionReturn(0);
5015 }
5016 
5017 /* ----------------------------------------------------------------*/
5018 #undef __FUNCT__
5019 #define __FUNCT__ "MatMatMult_MPIDense_MPIAIJ"
5020 PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
5021 {
5022   PetscErrorCode ierr;
5023 
5024   PetscFunctionBegin;
5025   if (scall == MAT_INITIAL_MATRIX) {
5026     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5027     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
5028     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5029   }
5030   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5031   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
5032   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5033   PetscFunctionReturn(0);
5034 }
5035 
5036 /*MC
5037    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
5038 
5039    Options Database Keys:
5040 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
5041 
5042   Level: beginner
5043 
5044 .seealso: MatCreateAIJ()
5045 M*/
5046 
5047 #undef __FUNCT__
5048 #define __FUNCT__ "MatCreate_MPIAIJ"
5049 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
5050 {
5051   Mat_MPIAIJ     *b;
5052   PetscErrorCode ierr;
5053   PetscMPIInt    size;
5054 
5055   PetscFunctionBegin;
5056   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
5057 
5058   ierr          = PetscNewLog(B,&b);CHKERRQ(ierr);
5059   B->data       = (void*)b;
5060   ierr          = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
5061   B->assembled  = PETSC_FALSE;
5062   B->insertmode = NOT_SET_VALUES;
5063   b->size       = size;
5064 
5065   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank);CHKERRQ(ierr);
5066 
5067   /* build cache for off array entries formed */
5068   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash);CHKERRQ(ierr);
5069 
5070   b->donotstash  = PETSC_FALSE;
5071   b->colmap      = 0;
5072   b->garray      = 0;
5073   b->roworiented = PETSC_TRUE;
5074 
5075   /* stuff used for matrix vector multiply */
5076   b->lvec  = NULL;
5077   b->Mvctx = NULL;
5078 
5079   /* stuff for MatGetRow() */
5080   b->rowindices   = 0;
5081   b->rowvalues    = 0;
5082   b->getrowactive = PETSC_FALSE;
5083 
5084   /* flexible pointer used in CUSP/CUSPARSE classes */
5085   b->spptr = NULL;
5086 
5087   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ);CHKERRQ(ierr);
5088   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
5089   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetDiagonalBlock_C",MatGetDiagonalBlock_MPIAIJ);CHKERRQ(ierr);
5090   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
5091   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
5092   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
5093   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
5094   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
5095   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
5096   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
5097 #if defined(PETSC_HAVE_ELEMENTAL)
5098   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_elemental_C",MatConvert_MPIAIJ_Elemental);CHKERRQ(ierr);
5099 #endif
5100   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
5101   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
5102   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
5103   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
5104   PetscFunctionReturn(0);
5105 }
5106 
5107 #undef __FUNCT__
5108 #define __FUNCT__ "MatCreateMPIAIJWithSplitArrays"
5109 /*@C
5110      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
5111          and "off-diagonal" part of the matrix in CSR format.
5112 
5113    Collective on MPI_Comm
5114 
5115    Input Parameters:
5116 +  comm - MPI communicator
5117 .  m - number of local rows (Cannot be PETSC_DECIDE)
5118 .  n - This value should be the same as the local size used in creating the
5119        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
5120        calculated if N is given) For square matrices n is almost always m.
5121 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
5122 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
5123 .   i - row indices for "diagonal" portion of matrix
5124 .   j - column indices
5125 .   a - matrix values
5126 .   oi - row indices for "off-diagonal" portion of matrix
5127 .   oj - column indices
5128 -   oa - matrix values
5129 
5130    Output Parameter:
5131 .   mat - the matrix
5132 
5133    Level: advanced
5134 
5135    Notes:
5136        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
5137        must free the arrays once the matrix has been destroyed and not before.
5138 
5139        The i and j indices are 0 based
5140 
5141        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
5142 
5143        This sets local rows and cannot be used to set off-processor values.
5144 
5145        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
5146        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
5147        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
5148        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
5149        keep track of the underlying array. Use MatSetOption(A,MAT_IGNORE_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
5150        communication if it is known that only local entries will be set.
5151 
5152 .keywords: matrix, aij, compressed row, sparse, parallel
5153 
5154 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
5155           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
5156 @*/
5157 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)
5158 {
5159   PetscErrorCode ierr;
5160   Mat_MPIAIJ     *maij;
5161 
5162   PetscFunctionBegin;
5163   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
5164   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
5165   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
5166   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
5167   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
5168   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
5169   maij = (Mat_MPIAIJ*) (*mat)->data;
5170 
5171   (*mat)->preallocated = PETSC_TRUE;
5172 
5173   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
5174   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
5175 
5176   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
5177   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
5178 
5179   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5180   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5181   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5182   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5183 
5184   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5185   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5186   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
5187   PetscFunctionReturn(0);
5188 }
5189 
5190 /*
5191     Special version for direct calls from Fortran
5192 */
5193 #include <petsc/private/fortranimpl.h>
5194 
5195 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5196 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
5197 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5198 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
5199 #endif
5200 
5201 /* Change these macros so can be used in void function */
5202 #undef CHKERRQ
5203 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
5204 #undef SETERRQ2
5205 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5206 #undef SETERRQ3
5207 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5208 #undef SETERRQ
5209 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
5210 
5211 #undef __FUNCT__
5212 #define __FUNCT__ "matsetvaluesmpiaij_"
5213 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)
5214 {
5215   Mat            mat  = *mmat;
5216   PetscInt       m    = *mm, n = *mn;
5217   InsertMode     addv = *maddv;
5218   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
5219   PetscScalar    value;
5220   PetscErrorCode ierr;
5221 
5222   MatCheckPreallocated(mat,1);
5223   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
5224 
5225 #if defined(PETSC_USE_DEBUG)
5226   else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
5227 #endif
5228   {
5229     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
5230     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
5231     PetscBool roworiented = aij->roworiented;
5232 
5233     /* Some Variables required in the macro */
5234     Mat        A                 = aij->A;
5235     Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
5236     PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
5237     MatScalar  *aa               = a->a;
5238     PetscBool  ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
5239     Mat        B                 = aij->B;
5240     Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
5241     PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5242     MatScalar  *ba               = b->a;
5243 
5244     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5245     PetscInt  nonew = a->nonew;
5246     MatScalar *ap1,*ap2;
5247 
5248     PetscFunctionBegin;
5249     for (i=0; i<m; i++) {
5250       if (im[i] < 0) continue;
5251 #if defined(PETSC_USE_DEBUG)
5252       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);
5253 #endif
5254       if (im[i] >= rstart && im[i] < rend) {
5255         row      = im[i] - rstart;
5256         lastcol1 = -1;
5257         rp1      = aj + ai[row];
5258         ap1      = aa + ai[row];
5259         rmax1    = aimax[row];
5260         nrow1    = ailen[row];
5261         low1     = 0;
5262         high1    = nrow1;
5263         lastcol2 = -1;
5264         rp2      = bj + bi[row];
5265         ap2      = ba + bi[row];
5266         rmax2    = bimax[row];
5267         nrow2    = bilen[row];
5268         low2     = 0;
5269         high2    = nrow2;
5270 
5271         for (j=0; j<n; j++) {
5272           if (roworiented) value = v[i*n+j];
5273           else value = v[i+j*m];
5274           if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES)) continue;
5275           if (in[j] >= cstart && in[j] < cend) {
5276             col = in[j] - cstart;
5277             MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
5278           } else if (in[j] < 0) continue;
5279 #if defined(PETSC_USE_DEBUG)
5280           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);
5281 #endif
5282           else {
5283             if (mat->was_assembled) {
5284               if (!aij->colmap) {
5285                 ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5286               }
5287 #if defined(PETSC_USE_CTABLE)
5288               ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5289               col--;
5290 #else
5291               col = aij->colmap[in[j]] - 1;
5292 #endif
5293               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5294                 ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5295                 col  =  in[j];
5296                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5297                 B     = aij->B;
5298                 b     = (Mat_SeqAIJ*)B->data;
5299                 bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5300                 rp2   = bj + bi[row];
5301                 ap2   = ba + bi[row];
5302                 rmax2 = bimax[row];
5303                 nrow2 = bilen[row];
5304                 low2  = 0;
5305                 high2 = nrow2;
5306                 bm    = aij->B->rmap->n;
5307                 ba    = b->a;
5308               }
5309             } else col = in[j];
5310             MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
5311           }
5312         }
5313       } else if (!aij->donotstash) {
5314         if (roworiented) {
5315           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5316         } else {
5317           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5318         }
5319       }
5320     }
5321   }
5322   PetscFunctionReturnVoid();
5323 }
5324 
5325