xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision 8d3c1932cd76dc2d1ac854cce48898cc6ac885a3)
1 
2 #include <../src/mat/impls/aij/mpi/mpiaij.h>   /*I "petscmat.h" I*/
3 #include <petsc/private/vecimpl.h>
4 #include <petsc/private/isimpl.h>
5 #include <petscblaslapack.h>
6 #include <petscsf.h>
7 
8 /*MC
9    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.
10 
11    This matrix type is identical to MATSEQAIJ when constructed with a single process communicator,
12    and MATMPIAIJ otherwise.  As a result, for single process communicators,
13   MatSeqAIJSetPreallocation is supported, and similarly MatMPIAIJSetPreallocation is supported
14   for communicators controlling multiple processes.  It is recommended that you call both of
15   the above preallocation routines for simplicity.
16 
17    Options Database Keys:
18 . -mat_type aij - sets the matrix type to "aij" during a call to MatSetFromOptions()
19 
20   Developer Notes: Subclasses include MATAIJCUSP, MATAIJCUSPARSE, MATAIJPERM, MATAIJCRL, and also automatically switches over to use inodes when
21    enough exist.
22 
23   Level: beginner
24 
25 .seealso: MatCreateAIJ(), MatCreateSeqAIJ(), MATSEQAIJ,MATMPIAIJ
26 M*/
27 
28 /*MC
29    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.
30 
31    This matrix type is identical to MATSEQAIJCRL when constructed with a single process communicator,
32    and MATMPIAIJCRL otherwise.  As a result, for single process communicators,
33    MatSeqAIJSetPreallocation() is supported, and similarly MatMPIAIJSetPreallocation() is supported
34   for communicators controlling multiple processes.  It is recommended that you call both of
35   the above preallocation routines for simplicity.
36 
37    Options Database Keys:
38 . -mat_type aijcrl - sets the matrix type to "aijcrl" during a call to MatSetFromOptions()
39 
40   Level: beginner
41 
42 .seealso: MatCreateMPIAIJCRL,MATSEQAIJCRL,MATMPIAIJCRL, MATSEQAIJCRL, MATMPIAIJCRL
43 M*/
44 
45 #undef __FUNCT__
46 #define __FUNCT__ "MatFindNonzeroRows_MPIAIJ"
47 PetscErrorCode MatFindNonzeroRows_MPIAIJ(Mat M,IS *keptrows)
48 {
49   PetscErrorCode  ierr;
50   Mat_MPIAIJ      *mat = (Mat_MPIAIJ*)M->data;
51   Mat_SeqAIJ      *a   = (Mat_SeqAIJ*)mat->A->data;
52   Mat_SeqAIJ      *b   = (Mat_SeqAIJ*)mat->B->data;
53   const PetscInt  *ia,*ib;
54   const MatScalar *aa,*bb;
55   PetscInt        na,nb,i,j,*rows,cnt=0,n0rows;
56   PetscInt        m = M->rmap->n,rstart = M->rmap->rstart;
57 
58   PetscFunctionBegin;
59   *keptrows = 0;
60   ia        = a->i;
61   ib        = b->i;
62   for (i=0; i<m; i++) {
63     na = ia[i+1] - ia[i];
64     nb = ib[i+1] - ib[i];
65     if (!na && !nb) {
66       cnt++;
67       goto ok1;
68     }
69     aa = a->a + ia[i];
70     for (j=0; j<na; j++) {
71       if (aa[j] != 0.0) goto ok1;
72     }
73     bb = b->a + ib[i];
74     for (j=0; j <nb; j++) {
75       if (bb[j] != 0.0) goto ok1;
76     }
77     cnt++;
78 ok1:;
79   }
80   ierr = MPI_Allreduce(&cnt,&n0rows,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)M));CHKERRQ(ierr);
81   if (!n0rows) PetscFunctionReturn(0);
82   ierr = PetscMalloc1(M->rmap->n-cnt,&rows);CHKERRQ(ierr);
83   cnt  = 0;
84   for (i=0; i<m; i++) {
85     na = ia[i+1] - ia[i];
86     nb = ib[i+1] - ib[i];
87     if (!na && !nb) continue;
88     aa = a->a + ia[i];
89     for (j=0; j<na;j++) {
90       if (aa[j] != 0.0) {
91         rows[cnt++] = rstart + i;
92         goto ok2;
93       }
94     }
95     bb = b->a + ib[i];
96     for (j=0; j<nb; j++) {
97       if (bb[j] != 0.0) {
98         rows[cnt++] = rstart + i;
99         goto ok2;
100       }
101     }
102 ok2:;
103   }
104   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)M),cnt,rows,PETSC_OWN_POINTER,keptrows);CHKERRQ(ierr);
105   PetscFunctionReturn(0);
106 }
107 
108 #undef __FUNCT__
109 #define __FUNCT__ "MatDiagonalSet_MPIAIJ"
110 PetscErrorCode  MatDiagonalSet_MPIAIJ(Mat Y,Vec D,InsertMode is)
111 {
112   PetscErrorCode    ierr;
113   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*) Y->data;
114 
115   PetscFunctionBegin;
116   if (Y->assembled && Y->rmap->rstart == Y->cmap->rstart && Y->rmap->rend == Y->cmap->rend) {
117     ierr = MatDiagonalSet(aij->A,D,is);CHKERRQ(ierr);
118   } else {
119     ierr = MatDiagonalSet_Default(Y,D,is);CHKERRQ(ierr);
120   }
121   PetscFunctionReturn(0);
122 }
123 
124 
125 #undef __FUNCT__
126 #define __FUNCT__ "MatFindZeroDiagonals_MPIAIJ"
127 PetscErrorCode MatFindZeroDiagonals_MPIAIJ(Mat M,IS *zrows)
128 {
129   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)M->data;
130   PetscErrorCode ierr;
131   PetscInt       i,rstart,nrows,*rows;
132 
133   PetscFunctionBegin;
134   *zrows = NULL;
135   ierr   = MatFindZeroDiagonals_SeqAIJ_Private(aij->A,&nrows,&rows);CHKERRQ(ierr);
136   ierr   = MatGetOwnershipRange(M,&rstart,NULL);CHKERRQ(ierr);
137   for (i=0; i<nrows; i++) rows[i] += rstart;
138   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)M),nrows,rows,PETSC_OWN_POINTER,zrows);CHKERRQ(ierr);
139   PetscFunctionReturn(0);
140 }
141 
142 #undef __FUNCT__
143 #define __FUNCT__ "MatGetColumnNorms_MPIAIJ"
144 PetscErrorCode MatGetColumnNorms_MPIAIJ(Mat A,NormType type,PetscReal *norms)
145 {
146   PetscErrorCode ierr;
147   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)A->data;
148   PetscInt       i,n,*garray = aij->garray;
149   Mat_SeqAIJ     *a_aij = (Mat_SeqAIJ*) aij->A->data;
150   Mat_SeqAIJ     *b_aij = (Mat_SeqAIJ*) aij->B->data;
151   PetscReal      *work;
152 
153   PetscFunctionBegin;
154   ierr = MatGetSize(A,NULL,&n);CHKERRQ(ierr);
155   ierr = PetscCalloc1(n,&work);CHKERRQ(ierr);
156   if (type == NORM_2) {
157     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
158       work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i]*a_aij->a[i]);
159     }
160     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
161       work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]*b_aij->a[i]);
162     }
163   } else if (type == NORM_1) {
164     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
165       work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i]);
166     }
167     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
168       work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]);
169     }
170   } else if (type == NORM_INFINITY) {
171     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
172       work[A->cmap->rstart + a_aij->j[i]] = PetscMax(PetscAbsScalar(a_aij->a[i]), work[A->cmap->rstart + a_aij->j[i]]);
173     }
174     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
175       work[garray[b_aij->j[i]]] = PetscMax(PetscAbsScalar(b_aij->a[i]),work[garray[b_aij->j[i]]]);
176     }
177 
178   } else SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Unknown NormType");
179   if (type == NORM_INFINITY) {
180     ierr = MPI_Allreduce(work,norms,n,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
181   } else {
182     ierr = MPI_Allreduce(work,norms,n,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
183   }
184   ierr = PetscFree(work);CHKERRQ(ierr);
185   if (type == NORM_2) {
186     for (i=0; i<n; i++) norms[i] = PetscSqrtReal(norms[i]);
187   }
188   PetscFunctionReturn(0);
189 }
190 
191 #undef __FUNCT__
192 #define __FUNCT__ "MatFindOffBlockDiagonalEntries_MPIAIJ"
193 PetscErrorCode MatFindOffBlockDiagonalEntries_MPIAIJ(Mat A,IS *is)
194 {
195   Mat_MPIAIJ      *a  = (Mat_MPIAIJ*)A->data;
196   IS              sis,gis;
197   PetscErrorCode  ierr;
198   const PetscInt  *isis,*igis;
199   PetscInt        n,*iis,nsis,ngis,rstart,i;
200 
201   PetscFunctionBegin;
202   ierr = MatFindOffBlockDiagonalEntries(a->A,&sis);CHKERRQ(ierr);
203   ierr = MatFindNonzeroRows(a->B,&gis);CHKERRQ(ierr);
204   ierr = ISGetSize(gis,&ngis);CHKERRQ(ierr);
205   ierr = ISGetSize(sis,&nsis);CHKERRQ(ierr);
206   ierr = ISGetIndices(sis,&isis);CHKERRQ(ierr);
207   ierr = ISGetIndices(gis,&igis);CHKERRQ(ierr);
208 
209   ierr = PetscMalloc1(ngis+nsis,&iis);CHKERRQ(ierr);
210   ierr = PetscMemcpy(iis,igis,ngis*sizeof(PetscInt));CHKERRQ(ierr);
211   ierr = PetscMemcpy(iis+ngis,isis,nsis*sizeof(PetscInt));CHKERRQ(ierr);
212   n    = ngis + nsis;
213   ierr = PetscSortRemoveDupsInt(&n,iis);CHKERRQ(ierr);
214   ierr = MatGetOwnershipRange(A,&rstart,NULL);CHKERRQ(ierr);
215   for (i=0; i<n; i++) iis[i] += rstart;
216   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)A),n,iis,PETSC_OWN_POINTER,is);CHKERRQ(ierr);
217 
218   ierr = ISRestoreIndices(sis,&isis);CHKERRQ(ierr);
219   ierr = ISRestoreIndices(gis,&igis);CHKERRQ(ierr);
220   ierr = ISDestroy(&sis);CHKERRQ(ierr);
221   ierr = ISDestroy(&gis);CHKERRQ(ierr);
222   PetscFunctionReturn(0);
223 }
224 
225 #undef __FUNCT__
226 #define __FUNCT__ "MatDistribute_MPIAIJ"
227 /*
228     Distributes a SeqAIJ matrix across a set of processes. Code stolen from
229     MatLoad_MPIAIJ(). Horrible lack of reuse. Should be a routine for each matrix type.
230 
231     Only for square matrices
232 
233     Used by a preconditioner, hence PETSC_EXTERN
234 */
235 PETSC_EXTERN PetscErrorCode MatDistribute_MPIAIJ(MPI_Comm comm,Mat gmat,PetscInt m,MatReuse reuse,Mat *inmat)
236 {
237   PetscMPIInt    rank,size;
238   PetscInt       *rowners,*dlens,*olens,i,rstart,rend,j,jj,nz = 0,*gmataj,cnt,row,*ld,bses[2];
239   PetscErrorCode ierr;
240   Mat            mat;
241   Mat_SeqAIJ     *gmata;
242   PetscMPIInt    tag;
243   MPI_Status     status;
244   PetscBool      aij;
245   MatScalar      *gmataa,*ao,*ad,*gmataarestore=0;
246 
247   PetscFunctionBegin;
248   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
249   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
250   if (!rank) {
251     ierr = PetscObjectTypeCompare((PetscObject)gmat,MATSEQAIJ,&aij);CHKERRQ(ierr);
252     if (!aij) SETERRQ1(PetscObjectComm((PetscObject)gmat),PETSC_ERR_SUP,"Currently no support for input matrix of type %s\n",((PetscObject)gmat)->type_name);
253   }
254   if (reuse == MAT_INITIAL_MATRIX) {
255     ierr = MatCreate(comm,&mat);CHKERRQ(ierr);
256     ierr = MatSetSizes(mat,m,m,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
257     ierr = MatGetBlockSizes(gmat,&bses[0],&bses[1]);CHKERRQ(ierr);
258     ierr = MPI_Bcast(bses,2,MPIU_INT,0,comm);CHKERRQ(ierr);
259     ierr = MatSetBlockSizes(mat,bses[0],bses[1]);CHKERRQ(ierr);
260     ierr = MatSetType(mat,MATAIJ);CHKERRQ(ierr);
261     ierr = PetscMalloc1(size+1,&rowners);CHKERRQ(ierr);
262     ierr = PetscMalloc2(m,&dlens,m,&olens);CHKERRQ(ierr);
263     ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
264 
265     rowners[0] = 0;
266     for (i=2; i<=size; i++) rowners[i] += rowners[i-1];
267     rstart = rowners[rank];
268     rend   = rowners[rank+1];
269     ierr   = PetscObjectGetNewTag((PetscObject)mat,&tag);CHKERRQ(ierr);
270     if (!rank) {
271       gmata = (Mat_SeqAIJ*) gmat->data;
272       /* send row lengths to all processors */
273       for (i=0; i<m; i++) dlens[i] = gmata->ilen[i];
274       for (i=1; i<size; i++) {
275         ierr = MPI_Send(gmata->ilen + rowners[i],rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
276       }
277       /* determine number diagonal and off-diagonal counts */
278       ierr = PetscMemzero(olens,m*sizeof(PetscInt));CHKERRQ(ierr);
279       ierr = PetscCalloc1(m,&ld);CHKERRQ(ierr);
280       jj   = 0;
281       for (i=0; i<m; i++) {
282         for (j=0; j<dlens[i]; j++) {
283           if (gmata->j[jj] < rstart) ld[i]++;
284           if (gmata->j[jj] < rstart || gmata->j[jj] >= rend) olens[i]++;
285           jj++;
286         }
287       }
288       /* send column indices to other processes */
289       for (i=1; i<size; i++) {
290         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
291         ierr = MPI_Send(&nz,1,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
292         ierr = MPI_Send(gmata->j + gmata->i[rowners[i]],nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
293       }
294 
295       /* send numerical values to other processes */
296       for (i=1; i<size; i++) {
297         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
298         ierr = MPI_Send(gmata->a + gmata->i[rowners[i]],nz,MPIU_SCALAR,i,tag,comm);CHKERRQ(ierr);
299       }
300       gmataa = gmata->a;
301       gmataj = gmata->j;
302 
303     } else {
304       /* receive row lengths */
305       ierr = MPI_Recv(dlens,m,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
306       /* receive column indices */
307       ierr = MPI_Recv(&nz,1,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
308       ierr = PetscMalloc2(nz,&gmataa,nz,&gmataj);CHKERRQ(ierr);
309       ierr = MPI_Recv(gmataj,nz,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
310       /* determine number diagonal and off-diagonal counts */
311       ierr = PetscMemzero(olens,m*sizeof(PetscInt));CHKERRQ(ierr);
312       ierr = PetscCalloc1(m,&ld);CHKERRQ(ierr);
313       jj   = 0;
314       for (i=0; i<m; i++) {
315         for (j=0; j<dlens[i]; j++) {
316           if (gmataj[jj] < rstart) ld[i]++;
317           if (gmataj[jj] < rstart || gmataj[jj] >= rend) olens[i]++;
318           jj++;
319         }
320       }
321       /* receive numerical values */
322       ierr = PetscMemzero(gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr);
323       ierr = MPI_Recv(gmataa,nz,MPIU_SCALAR,0,tag,comm,&status);CHKERRQ(ierr);
324     }
325     /* set preallocation */
326     for (i=0; i<m; i++) {
327       dlens[i] -= olens[i];
328     }
329     ierr = MatSeqAIJSetPreallocation(mat,0,dlens);CHKERRQ(ierr);
330     ierr = MatMPIAIJSetPreallocation(mat,0,dlens,0,olens);CHKERRQ(ierr);
331 
332     for (i=0; i<m; i++) {
333       dlens[i] += olens[i];
334     }
335     cnt = 0;
336     for (i=0; i<m; i++) {
337       row  = rstart + i;
338       ierr = MatSetValues(mat,1,&row,dlens[i],gmataj+cnt,gmataa+cnt,INSERT_VALUES);CHKERRQ(ierr);
339       cnt += dlens[i];
340     }
341     if (rank) {
342       ierr = PetscFree2(gmataa,gmataj);CHKERRQ(ierr);
343     }
344     ierr = PetscFree2(dlens,olens);CHKERRQ(ierr);
345     ierr = PetscFree(rowners);CHKERRQ(ierr);
346 
347     ((Mat_MPIAIJ*)(mat->data))->ld = ld;
348 
349     *inmat = mat;
350   } else {   /* column indices are already set; only need to move over numerical values from process 0 */
351     Mat_SeqAIJ *Ad = (Mat_SeqAIJ*)((Mat_MPIAIJ*)((*inmat)->data))->A->data;
352     Mat_SeqAIJ *Ao = (Mat_SeqAIJ*)((Mat_MPIAIJ*)((*inmat)->data))->B->data;
353     mat  = *inmat;
354     ierr = PetscObjectGetNewTag((PetscObject)mat,&tag);CHKERRQ(ierr);
355     if (!rank) {
356       /* send numerical values to other processes */
357       gmata  = (Mat_SeqAIJ*) gmat->data;
358       ierr   = MatGetOwnershipRanges(mat,(const PetscInt**)&rowners);CHKERRQ(ierr);
359       gmataa = gmata->a;
360       for (i=1; i<size; i++) {
361         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
362         ierr = MPI_Send(gmataa + gmata->i[rowners[i]],nz,MPIU_SCALAR,i,tag,comm);CHKERRQ(ierr);
363       }
364       nz = gmata->i[rowners[1]]-gmata->i[rowners[0]];
365     } else {
366       /* receive numerical values from process 0*/
367       nz   = Ad->nz + Ao->nz;
368       ierr = PetscMalloc1(nz,&gmataa);CHKERRQ(ierr); gmataarestore = gmataa;
369       ierr = MPI_Recv(gmataa,nz,MPIU_SCALAR,0,tag,comm,&status);CHKERRQ(ierr);
370     }
371     /* transfer numerical values into the diagonal A and off diagonal B parts of mat */
372     ld = ((Mat_MPIAIJ*)(mat->data))->ld;
373     ad = Ad->a;
374     ao = Ao->a;
375     if (mat->rmap->n) {
376       i  = 0;
377       nz = ld[i];                                   ierr = PetscMemcpy(ao,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ao += nz; gmataa += nz;
378       nz = Ad->i[i+1] - Ad->i[i];                   ierr = PetscMemcpy(ad,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ad += nz; gmataa += nz;
379     }
380     for (i=1; i<mat->rmap->n; i++) {
381       nz = Ao->i[i] - Ao->i[i-1] - ld[i-1] + ld[i]; ierr = PetscMemcpy(ao,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ao += nz; gmataa += nz;
382       nz = Ad->i[i+1] - Ad->i[i];                   ierr = PetscMemcpy(ad,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ad += nz; gmataa += nz;
383     }
384     i--;
385     if (mat->rmap->n) {
386       nz = Ao->i[i+1] - Ao->i[i] - ld[i];           ierr = PetscMemcpy(ao,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr);
387     }
388     if (rank) {
389       ierr = PetscFree(gmataarestore);CHKERRQ(ierr);
390     }
391   }
392   ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
393   ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
394   PetscFunctionReturn(0);
395 }
396 
397 /*
398   Local utility routine that creates a mapping from the global column
399 number to the local number in the off-diagonal part of the local
400 storage of the matrix.  When PETSC_USE_CTABLE is used this is scalable at
401 a slightly higher hash table cost; without it it is not scalable (each processor
402 has an order N integer array but is fast to acess.
403 */
404 #undef __FUNCT__
405 #define __FUNCT__ "MatCreateColmap_MPIAIJ_Private"
406 PetscErrorCode MatCreateColmap_MPIAIJ_Private(Mat mat)
407 {
408   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
409   PetscErrorCode ierr;
410   PetscInt       n = aij->B->cmap->n,i;
411 
412   PetscFunctionBegin;
413   if (!aij->garray) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"MPIAIJ Matrix was assembled but is missing garray");
414 #if defined(PETSC_USE_CTABLE)
415   ierr = PetscTableCreate(n,mat->cmap->N+1,&aij->colmap);CHKERRQ(ierr);
416   for (i=0; i<n; i++) {
417     ierr = PetscTableAdd(aij->colmap,aij->garray[i]+1,i+1,INSERT_VALUES);CHKERRQ(ierr);
418   }
419 #else
420   ierr = PetscCalloc1(mat->cmap->N+1,&aij->colmap);CHKERRQ(ierr);
421   ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N+1)*sizeof(PetscInt));CHKERRQ(ierr);
422   for (i=0; i<n; i++) aij->colmap[aij->garray[i]] = i+1;
423 #endif
424   PetscFunctionReturn(0);
425 }
426 
427 #define MatSetValues_SeqAIJ_A_Private(row,col,value,addv,orow,ocol)     \
428 { \
429     if (col <= lastcol1)  low1 = 0;     \
430     else                 high1 = nrow1; \
431     lastcol1 = col;\
432     while (high1-low1 > 5) { \
433       t = (low1+high1)/2; \
434       if (rp1[t] > col) high1 = t; \
435       else              low1  = t; \
436     } \
437       for (_i=low1; _i<high1; _i++) { \
438         if (rp1[_i] > col) break; \
439         if (rp1[_i] == col) { \
440           if (addv == ADD_VALUES) ap1[_i] += value;   \
441           else                    ap1[_i] = value; \
442           goto a_noinsert; \
443         } \
444       }  \
445       if (value == 0.0 && ignorezeroentries) {low1 = 0; high1 = nrow1;goto a_noinsert;} \
446       if (nonew == 1) {low1 = 0; high1 = nrow1; goto a_noinsert;}                \
447       if (nonew == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at global row/column (%D, %D) into matrix", orow, ocol); \
448       MatSeqXAIJReallocateAIJ(A,am,1,nrow1,row,col,rmax1,aa,ai,aj,rp1,ap1,aimax,nonew,MatScalar); \
449       N = nrow1++ - 1; a->nz++; high1++; \
450       /* shift up all the later entries in this row */ \
451       for (ii=N; ii>=_i; ii--) { \
452         rp1[ii+1] = rp1[ii]; \
453         ap1[ii+1] = ap1[ii]; \
454       } \
455       rp1[_i] = col;  \
456       ap1[_i] = value;  \
457       A->nonzerostate++;\
458       a_noinsert: ; \
459       ailen[row] = nrow1; \
460 }
461 
462 
463 #define MatSetValues_SeqAIJ_B_Private(row,col,value,addv,orow,ocol) \
464   { \
465     if (col <= lastcol2) low2 = 0;                        \
466     else high2 = nrow2;                                   \
467     lastcol2 = col;                                       \
468     while (high2-low2 > 5) {                              \
469       t = (low2+high2)/2;                                 \
470       if (rp2[t] > col) high2 = t;                        \
471       else             low2  = t;                         \
472     }                                                     \
473     for (_i=low2; _i<high2; _i++) {                       \
474       if (rp2[_i] > col) break;                           \
475       if (rp2[_i] == col) {                               \
476         if (addv == ADD_VALUES) ap2[_i] += value;         \
477         else                    ap2[_i] = value;          \
478         goto b_noinsert;                                  \
479       }                                                   \
480     }                                                     \
481     if (value == 0.0 && ignorezeroentries) {low2 = 0; high2 = nrow2; goto b_noinsert;} \
482     if (nonew == 1) {low2 = 0; high2 = nrow2; goto b_noinsert;}                        \
483     if (nonew == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at global row/column (%D, %D) into matrix", orow, ocol); \
484     MatSeqXAIJReallocateAIJ(B,bm,1,nrow2,row,col,rmax2,ba,bi,bj,rp2,ap2,bimax,nonew,MatScalar); \
485     N = nrow2++ - 1; b->nz++; high2++;                    \
486     /* shift up all the later entries in this row */      \
487     for (ii=N; ii>=_i; ii--) {                            \
488       rp2[ii+1] = rp2[ii];                                \
489       ap2[ii+1] = ap2[ii];                                \
490     }                                                     \
491     rp2[_i] = col;                                        \
492     ap2[_i] = value;                                      \
493     B->nonzerostate++;                                    \
494     b_noinsert: ;                                         \
495     bilen[row] = nrow2;                                   \
496   }
497 
498 #undef __FUNCT__
499 #define __FUNCT__ "MatSetValuesRow_MPIAIJ"
500 PetscErrorCode MatSetValuesRow_MPIAIJ(Mat A,PetscInt row,const PetscScalar v[])
501 {
502   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)A->data;
503   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)mat->A->data,*b = (Mat_SeqAIJ*)mat->B->data;
504   PetscErrorCode ierr;
505   PetscInt       l,*garray = mat->garray,diag;
506 
507   PetscFunctionBegin;
508   /* code only works for square matrices A */
509 
510   /* find size of row to the left of the diagonal part */
511   ierr = MatGetOwnershipRange(A,&diag,0);CHKERRQ(ierr);
512   row  = row - diag;
513   for (l=0; l<b->i[row+1]-b->i[row]; l++) {
514     if (garray[b->j[b->i[row]+l]] > diag) break;
515   }
516   ierr = PetscMemcpy(b->a+b->i[row],v,l*sizeof(PetscScalar));CHKERRQ(ierr);
517 
518   /* diagonal part */
519   ierr = PetscMemcpy(a->a+a->i[row],v+l,(a->i[row+1]-a->i[row])*sizeof(PetscScalar));CHKERRQ(ierr);
520 
521   /* right of diagonal part */
522   ierr = PetscMemcpy(b->a+b->i[row]+l,v+l+a->i[row+1]-a->i[row],(b->i[row+1]-b->i[row]-l)*sizeof(PetscScalar));CHKERRQ(ierr);
523   PetscFunctionReturn(0);
524 }
525 
526 #undef __FUNCT__
527 #define __FUNCT__ "MatSetValues_MPIAIJ"
528 PetscErrorCode MatSetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode addv)
529 {
530   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
531   PetscScalar    value;
532   PetscErrorCode ierr;
533   PetscInt       i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
534   PetscInt       cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
535   PetscBool      roworiented = aij->roworiented;
536 
537   /* Some Variables required in the macro */
538   Mat        A                 = aij->A;
539   Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
540   PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
541   MatScalar  *aa               = a->a;
542   PetscBool  ignorezeroentries = a->ignorezeroentries;
543   Mat        B                 = aij->B;
544   Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
545   PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
546   MatScalar  *ba               = b->a;
547 
548   PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
549   PetscInt  nonew;
550   MatScalar *ap1,*ap2;
551 
552   PetscFunctionBegin;
553   for (i=0; i<m; i++) {
554     if (im[i] < 0) continue;
555 #if defined(PETSC_USE_DEBUG)
556     if (im[i] >= mat->rmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %D max %D",im[i],mat->rmap->N-1);
557 #endif
558     if (im[i] >= rstart && im[i] < rend) {
559       row      = im[i] - rstart;
560       lastcol1 = -1;
561       rp1      = aj + ai[row];
562       ap1      = aa + ai[row];
563       rmax1    = aimax[row];
564       nrow1    = ailen[row];
565       low1     = 0;
566       high1    = nrow1;
567       lastcol2 = -1;
568       rp2      = bj + bi[row];
569       ap2      = ba + bi[row];
570       rmax2    = bimax[row];
571       nrow2    = bilen[row];
572       low2     = 0;
573       high2    = nrow2;
574 
575       for (j=0; j<n; j++) {
576         if (roworiented) value = v[i*n+j];
577         else             value = v[i+j*m];
578         if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES)) continue;
579         if (in[j] >= cstart && in[j] < cend) {
580           col   = in[j] - cstart;
581           nonew = a->nonew;
582           MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
583         } else if (in[j] < 0) continue;
584 #if defined(PETSC_USE_DEBUG)
585         else if (in[j] >= mat->cmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %D max %D",in[j],mat->cmap->N-1);
586 #endif
587         else {
588           if (mat->was_assembled) {
589             if (!aij->colmap) {
590               ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
591             }
592 #if defined(PETSC_USE_CTABLE)
593             ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
594             col--;
595 #else
596             col = aij->colmap[in[j]] - 1;
597 #endif
598             if (col < 0 && !((Mat_SeqAIJ*)(aij->B->data))->nonew) {
599               ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
600               col  =  in[j];
601               /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
602               B     = aij->B;
603               b     = (Mat_SeqAIJ*)B->data;
604               bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j; ba = b->a;
605               rp2   = bj + bi[row];
606               ap2   = ba + bi[row];
607               rmax2 = bimax[row];
608               nrow2 = bilen[row];
609               low2  = 0;
610               high2 = nrow2;
611               bm    = aij->B->rmap->n;
612               ba    = b->a;
613             } else if (col < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at global row/column (%D, %D) into matrix", im[i], in[j]);
614           } else col = in[j];
615           nonew = b->nonew;
616           MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
617         }
618       }
619     } else {
620       if (mat->nooffprocentries) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Setting off process row %D even though MatSetOption(,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) was set",im[i]);
621       if (!aij->donotstash) {
622         mat->assembled = PETSC_FALSE;
623         if (roworiented) {
624           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
625         } else {
626           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
627         }
628       }
629     }
630   }
631   PetscFunctionReturn(0);
632 }
633 
634 #undef __FUNCT__
635 #define __FUNCT__ "MatGetValues_MPIAIJ"
636 PetscErrorCode MatGetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],PetscScalar v[])
637 {
638   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
639   PetscErrorCode ierr;
640   PetscInt       i,j,rstart = mat->rmap->rstart,rend = mat->rmap->rend;
641   PetscInt       cstart = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
642 
643   PetscFunctionBegin;
644   for (i=0; i<m; i++) {
645     if (idxm[i] < 0) continue; /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative row: %D",idxm[i]);*/
646     if (idxm[i] >= mat->rmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %D max %D",idxm[i],mat->rmap->N-1);
647     if (idxm[i] >= rstart && idxm[i] < rend) {
648       row = idxm[i] - rstart;
649       for (j=0; j<n; j++) {
650         if (idxn[j] < 0) continue; /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column: %D",idxn[j]); */
651         if (idxn[j] >= mat->cmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %D max %D",idxn[j],mat->cmap->N-1);
652         if (idxn[j] >= cstart && idxn[j] < cend) {
653           col  = idxn[j] - cstart;
654           ierr = MatGetValues(aij->A,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
655         } else {
656           if (!aij->colmap) {
657             ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
658           }
659 #if defined(PETSC_USE_CTABLE)
660           ierr = PetscTableFind(aij->colmap,idxn[j]+1,&col);CHKERRQ(ierr);
661           col--;
662 #else
663           col = aij->colmap[idxn[j]] - 1;
664 #endif
665           if ((col < 0) || (aij->garray[col] != idxn[j])) *(v+i*n+j) = 0.0;
666           else {
667             ierr = MatGetValues(aij->B,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
668           }
669         }
670       }
671     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only local values currently supported");
672   }
673   PetscFunctionReturn(0);
674 }
675 
676 extern PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat,Vec,Vec);
677 
678 #undef __FUNCT__
679 #define __FUNCT__ "MatAssemblyBegin_MPIAIJ"
680 PetscErrorCode MatAssemblyBegin_MPIAIJ(Mat mat,MatAssemblyType mode)
681 {
682   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
683   PetscErrorCode ierr;
684   PetscInt       nstash,reallocs;
685   InsertMode     addv;
686 
687   PetscFunctionBegin;
688   if (aij->donotstash || mat->nooffprocentries) PetscFunctionReturn(0);
689 
690   /* make sure all processors are either in INSERTMODE or ADDMODE */
691   ierr = MPI_Allreduce((PetscEnum*)&mat->insertmode,(PetscEnum*)&addv,1,MPIU_ENUM,MPI_BOR,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
692   if (addv == (ADD_VALUES|INSERT_VALUES)) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Some processors inserted others added");
693   mat->insertmode = addv; /* in case this processor had no cache */
694 
695   ierr = MatStashScatterBegin_Private(mat,&mat->stash,mat->rmap->range);CHKERRQ(ierr);
696   ierr = MatStashGetInfo_Private(&mat->stash,&nstash,&reallocs);CHKERRQ(ierr);
697   ierr = PetscInfo2(aij->A,"Stash has %D entries, uses %D mallocs.\n",nstash,reallocs);CHKERRQ(ierr);
698   PetscFunctionReturn(0);
699 }
700 
701 #undef __FUNCT__
702 #define __FUNCT__ "MatAssemblyEnd_MPIAIJ"
703 PetscErrorCode MatAssemblyEnd_MPIAIJ(Mat mat,MatAssemblyType mode)
704 {
705   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
706   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)aij->A->data;
707   PetscErrorCode ierr;
708   PetscMPIInt    n;
709   PetscInt       i,j,rstart,ncols,flg;
710   PetscInt       *row,*col;
711   PetscBool      other_disassembled;
712   PetscScalar    *val;
713   InsertMode     addv = mat->insertmode;
714 
715   /* do not use 'b = (Mat_SeqAIJ*)aij->B->data' as B can be reset in disassembly */
716 
717   PetscFunctionBegin;
718   if (!aij->donotstash && !mat->nooffprocentries) {
719     while (1) {
720       ierr = MatStashScatterGetMesg_Private(&mat->stash,&n,&row,&col,&val,&flg);CHKERRQ(ierr);
721       if (!flg) break;
722 
723       for (i=0; i<n; ) {
724         /* Now identify the consecutive vals belonging to the same row */
725         for (j=i,rstart=row[j]; j<n; j++) {
726           if (row[j] != rstart) break;
727         }
728         if (j < n) ncols = j-i;
729         else       ncols = n-i;
730         /* Now assemble all these values with a single function call */
731         ierr = MatSetValues_MPIAIJ(mat,1,row+i,ncols,col+i,val+i,addv);CHKERRQ(ierr);
732 
733         i = j;
734       }
735     }
736     ierr = MatStashScatterEnd_Private(&mat->stash);CHKERRQ(ierr);
737   }
738   ierr = MatAssemblyBegin(aij->A,mode);CHKERRQ(ierr);
739   ierr = MatAssemblyEnd(aij->A,mode);CHKERRQ(ierr);
740 
741   /* determine if any processor has disassembled, if so we must
742      also disassemble ourselfs, in order that we may reassemble. */
743   /*
744      if nonzero structure of submatrix B cannot change then we know that
745      no processor disassembled thus we can skip this stuff
746   */
747   if (!((Mat_SeqAIJ*)aij->B->data)->nonew) {
748     ierr = MPI_Allreduce(&mat->was_assembled,&other_disassembled,1,MPIU_BOOL,MPI_PROD,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
749     if (mat->was_assembled && !other_disassembled) {
750       ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
751     }
752   }
753   if (!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) {
754     ierr = MatSetUpMultiply_MPIAIJ(mat);CHKERRQ(ierr);
755   }
756   ierr = MatSetOption(aij->B,MAT_USE_INODES,PETSC_FALSE);CHKERRQ(ierr);
757   ierr = MatAssemblyBegin(aij->B,mode);CHKERRQ(ierr);
758   ierr = MatAssemblyEnd(aij->B,mode);CHKERRQ(ierr);
759 
760   ierr = PetscFree2(aij->rowvalues,aij->rowindices);CHKERRQ(ierr);
761 
762   aij->rowvalues = 0;
763 
764   ierr = VecDestroy(&aij->diag);CHKERRQ(ierr);
765   if (a->inode.size) mat->ops->multdiagonalblock = MatMultDiagonalBlock_MPIAIJ;
766 
767   /* if no new nonzero locations are allowed in matrix then only set the matrix state the first time through */
768   if ((!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) || !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
769     PetscObjectState state = aij->A->nonzerostate + aij->B->nonzerostate;
770     ierr = MPI_Allreduce(&state,&mat->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
771   }
772   PetscFunctionReturn(0);
773 }
774 
775 #undef __FUNCT__
776 #define __FUNCT__ "MatZeroEntries_MPIAIJ"
777 PetscErrorCode MatZeroEntries_MPIAIJ(Mat A)
778 {
779   Mat_MPIAIJ     *l = (Mat_MPIAIJ*)A->data;
780   PetscErrorCode ierr;
781 
782   PetscFunctionBegin;
783   ierr = MatZeroEntries(l->A);CHKERRQ(ierr);
784   ierr = MatZeroEntries(l->B);CHKERRQ(ierr);
785   PetscFunctionReturn(0);
786 }
787 
788 #undef __FUNCT__
789 #define __FUNCT__ "MatZeroRows_MPIAIJ"
790 PetscErrorCode MatZeroRows_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
791 {
792   Mat_MPIAIJ    *mat    = (Mat_MPIAIJ *) A->data;
793   PetscInt      *owners = A->rmap->range;
794   PetscInt       n      = A->rmap->n;
795   PetscSF        sf;
796   PetscInt      *lrows;
797   PetscSFNode   *rrows;
798   PetscInt       r, p = 0, len = 0;
799   PetscErrorCode ierr;
800 
801   PetscFunctionBegin;
802   /* Create SF where leaves are input rows and roots are owned rows */
803   ierr = PetscMalloc1(n, &lrows);CHKERRQ(ierr);
804   for (r = 0; r < n; ++r) lrows[r] = -1;
805   if (!A->nooffproczerorows) {ierr = PetscMalloc1(N, &rrows);CHKERRQ(ierr);}
806   for (r = 0; r < N; ++r) {
807     const PetscInt idx   = rows[r];
808     if (idx < 0 || A->rmap->N <= idx) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row %D out of range [0,%D)",idx,A->rmap->N);
809     if (idx < owners[p] || owners[p+1] <= idx) { /* short-circuit the search if the last p owns this row too */
810       ierr = PetscLayoutFindOwner(A->rmap,idx,&p);CHKERRQ(ierr);
811     }
812     if (A->nooffproczerorows) {
813       if (p != mat->rank) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"MAT_NO_OFF_PROC_ZERO_ROWS set, but row %D is not owned by rank %d",idx,mat->rank);
814       lrows[len++] = idx - owners[p];
815     } else {
816       rrows[r].rank = p;
817       rrows[r].index = rows[r] - owners[p];
818     }
819   }
820   if (!A->nooffproczerorows) {
821     ierr = PetscSFCreate(PetscObjectComm((PetscObject) A), &sf);CHKERRQ(ierr);
822     ierr = PetscSFSetGraph(sf, n, N, NULL, PETSC_OWN_POINTER, rrows, PETSC_OWN_POINTER);CHKERRQ(ierr);
823     /* Collect flags for rows to be zeroed */
824     ierr = PetscSFReduceBegin(sf, MPIU_INT, (PetscInt*)rows, lrows, MPI_LOR);CHKERRQ(ierr);
825     ierr = PetscSFReduceEnd(sf, MPIU_INT, (PetscInt*)rows, lrows, MPI_LOR);CHKERRQ(ierr);
826     ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
827     /* Compress and put in row numbers */
828     for (r = 0; r < n; ++r) if (lrows[r] >= 0) lrows[len++] = r;
829   }
830   /* fix right hand side if needed */
831   if (x && b) {
832     const PetscScalar *xx;
833     PetscScalar       *bb;
834 
835     ierr = VecGetArrayRead(x, &xx);CHKERRQ(ierr);
836     ierr = VecGetArray(b, &bb);CHKERRQ(ierr);
837     for (r = 0; r < len; ++r) bb[lrows[r]] = diag*xx[lrows[r]];
838     ierr = VecRestoreArrayRead(x, &xx);CHKERRQ(ierr);
839     ierr = VecRestoreArray(b, &bb);CHKERRQ(ierr);
840   }
841   /* Must zero l->B before l->A because the (diag) case below may put values into l->B*/
842   ierr = MatZeroRows(mat->B, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
843   if ((diag != 0.0) && (mat->A->rmap->N == mat->A->cmap->N)) {
844     ierr = MatZeroRows(mat->A, len, lrows, diag, NULL, NULL);CHKERRQ(ierr);
845   } else if (diag != 0.0) {
846     ierr = MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
847     if (((Mat_SeqAIJ *) mat->A->data)->nonew) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatZeroRows() on rectangular matrices cannot be used with the Mat options\nMAT_NEW_NONZERO_LOCATIONS,MAT_NEW_NONZERO_LOCATION_ERR,MAT_NEW_NONZERO_ALLOCATION_ERR");
848     for (r = 0; r < len; ++r) {
849       const PetscInt row = lrows[r] + A->rmap->rstart;
850       ierr = MatSetValues(A, 1, &row, 1, &row, &diag, INSERT_VALUES);CHKERRQ(ierr);
851     }
852     ierr = MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
853     ierr = MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
854   } else {
855     ierr = MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
856   }
857   ierr = PetscFree(lrows);CHKERRQ(ierr);
858 
859   /* only change matrix nonzero state if pattern was allowed to be changed */
860   if (!((Mat_SeqAIJ*)(mat->A->data))->keepnonzeropattern) {
861     PetscObjectState state = mat->A->nonzerostate + mat->B->nonzerostate;
862     ierr = MPI_Allreduce(&state,&A->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
863   }
864   PetscFunctionReturn(0);
865 }
866 
867 #undef __FUNCT__
868 #define __FUNCT__ "MatZeroRowsColumns_MPIAIJ"
869 PetscErrorCode MatZeroRowsColumns_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
870 {
871   Mat_MPIAIJ        *l = (Mat_MPIAIJ*)A->data;
872   PetscErrorCode    ierr;
873   PetscMPIInt       n = A->rmap->n;
874   PetscInt          i,j,r,m,p = 0,len = 0;
875   PetscInt          *lrows,*owners = A->rmap->range;
876   PetscSFNode       *rrows;
877   PetscSF           sf;
878   const PetscScalar *xx;
879   PetscScalar       *bb,*mask;
880   Vec               xmask,lmask;
881   Mat_SeqAIJ        *aij = (Mat_SeqAIJ*)l->B->data;
882   const PetscInt    *aj, *ii,*ridx;
883   PetscScalar       *aa;
884 
885   PetscFunctionBegin;
886   /* Create SF where leaves are input rows and roots are owned rows */
887   ierr = PetscMalloc1(n, &lrows);CHKERRQ(ierr);
888   for (r = 0; r < n; ++r) lrows[r] = -1;
889   ierr = PetscMalloc1(N, &rrows);CHKERRQ(ierr);
890   for (r = 0; r < N; ++r) {
891     const PetscInt idx   = rows[r];
892     if (idx < 0 || A->rmap->N <= idx) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row %D out of range [0,%D)",idx,A->rmap->N);
893     if (idx < owners[p] || owners[p+1] <= idx) { /* short-circuit the search if the last p owns this row too */
894       ierr = PetscLayoutFindOwner(A->rmap,idx,&p);CHKERRQ(ierr);
895     }
896     rrows[r].rank  = p;
897     rrows[r].index = rows[r] - owners[p];
898   }
899   ierr = PetscSFCreate(PetscObjectComm((PetscObject) A), &sf);CHKERRQ(ierr);
900   ierr = PetscSFSetGraph(sf, n, N, NULL, PETSC_OWN_POINTER, rrows, PETSC_OWN_POINTER);CHKERRQ(ierr);
901   /* Collect flags for rows to be zeroed */
902   ierr = PetscSFReduceBegin(sf, MPIU_INT, (PetscInt *) rows, lrows, MPI_LOR);CHKERRQ(ierr);
903   ierr = PetscSFReduceEnd(sf, MPIU_INT, (PetscInt *) rows, lrows, MPI_LOR);CHKERRQ(ierr);
904   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
905   /* Compress and put in row numbers */
906   for (r = 0; r < n; ++r) if (lrows[r] >= 0) lrows[len++] = r;
907   /* zero diagonal part of matrix */
908   ierr = MatZeroRowsColumns(l->A,len,lrows,diag,x,b);CHKERRQ(ierr);
909   /* handle off diagonal part of matrix */
910   ierr = MatCreateVecs(A,&xmask,NULL);CHKERRQ(ierr);
911   ierr = VecDuplicate(l->lvec,&lmask);CHKERRQ(ierr);
912   ierr = VecGetArray(xmask,&bb);CHKERRQ(ierr);
913   for (i=0; i<len; i++) bb[lrows[i]] = 1;
914   ierr = VecRestoreArray(xmask,&bb);CHKERRQ(ierr);
915   ierr = VecScatterBegin(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
916   ierr = VecScatterEnd(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
917   ierr = VecDestroy(&xmask);CHKERRQ(ierr);
918   if (x) {
919     ierr = VecScatterBegin(l->Mvctx,x,l->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
920     ierr = VecScatterEnd(l->Mvctx,x,l->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
921     ierr = VecGetArrayRead(l->lvec,&xx);CHKERRQ(ierr);
922     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
923   }
924   ierr = VecGetArray(lmask,&mask);CHKERRQ(ierr);
925   /* remove zeroed rows of off diagonal matrix */
926   ii = aij->i;
927   for (i=0; i<len; i++) {
928     ierr = PetscMemzero(aij->a + ii[lrows[i]],(ii[lrows[i]+1] - ii[lrows[i]])*sizeof(PetscScalar));CHKERRQ(ierr);
929   }
930   /* loop over all elements of off process part of matrix zeroing removed columns*/
931   if (aij->compressedrow.use) {
932     m    = aij->compressedrow.nrows;
933     ii   = aij->compressedrow.i;
934     ridx = aij->compressedrow.rindex;
935     for (i=0; i<m; i++) {
936       n  = ii[i+1] - ii[i];
937       aj = aij->j + ii[i];
938       aa = aij->a + ii[i];
939 
940       for (j=0; j<n; j++) {
941         if (PetscAbsScalar(mask[*aj])) {
942           if (b) bb[*ridx] -= *aa*xx[*aj];
943           *aa = 0.0;
944         }
945         aa++;
946         aj++;
947       }
948       ridx++;
949     }
950   } else { /* do not use compressed row format */
951     m = l->B->rmap->n;
952     for (i=0; i<m; i++) {
953       n  = ii[i+1] - ii[i];
954       aj = aij->j + ii[i];
955       aa = aij->a + ii[i];
956       for (j=0; j<n; j++) {
957         if (PetscAbsScalar(mask[*aj])) {
958           if (b) bb[i] -= *aa*xx[*aj];
959           *aa = 0.0;
960         }
961         aa++;
962         aj++;
963       }
964     }
965   }
966   if (x) {
967     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
968     ierr = VecRestoreArrayRead(l->lvec,&xx);CHKERRQ(ierr);
969   }
970   ierr = VecRestoreArray(lmask,&mask);CHKERRQ(ierr);
971   ierr = VecDestroy(&lmask);CHKERRQ(ierr);
972   ierr = PetscFree(lrows);CHKERRQ(ierr);
973 
974   /* only change matrix nonzero state if pattern was allowed to be changed */
975   if (!((Mat_SeqAIJ*)(l->A->data))->keepnonzeropattern) {
976     PetscObjectState state = l->A->nonzerostate + l->B->nonzerostate;
977     ierr = MPI_Allreduce(&state,&A->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
978   }
979   PetscFunctionReturn(0);
980 }
981 
982 #undef __FUNCT__
983 #define __FUNCT__ "MatMult_MPIAIJ"
984 PetscErrorCode MatMult_MPIAIJ(Mat A,Vec xx,Vec yy)
985 {
986   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
987   PetscErrorCode ierr;
988   PetscInt       nt;
989 
990   PetscFunctionBegin;
991   ierr = VecGetLocalSize(xx,&nt);CHKERRQ(ierr);
992   if (nt != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Incompatible partition of A (%D) and xx (%D)",A->cmap->n,nt);
993   ierr = VecScatterBegin(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
994   ierr = (*a->A->ops->mult)(a->A,xx,yy);CHKERRQ(ierr);
995   ierr = VecScatterEnd(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
996   ierr = (*a->B->ops->multadd)(a->B,a->lvec,yy,yy);CHKERRQ(ierr);
997   PetscFunctionReturn(0);
998 }
999 
1000 #undef __FUNCT__
1001 #define __FUNCT__ "MatMultDiagonalBlock_MPIAIJ"
1002 PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat A,Vec bb,Vec xx)
1003 {
1004   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1005   PetscErrorCode ierr;
1006 
1007   PetscFunctionBegin;
1008   ierr = MatMultDiagonalBlock(a->A,bb,xx);CHKERRQ(ierr);
1009   PetscFunctionReturn(0);
1010 }
1011 
1012 #undef __FUNCT__
1013 #define __FUNCT__ "MatMultAdd_MPIAIJ"
1014 PetscErrorCode MatMultAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1015 {
1016   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1017   PetscErrorCode ierr;
1018 
1019   PetscFunctionBegin;
1020   ierr = VecScatterBegin(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1021   ierr = (*a->A->ops->multadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
1022   ierr = VecScatterEnd(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1023   ierr = (*a->B->ops->multadd)(a->B,a->lvec,zz,zz);CHKERRQ(ierr);
1024   PetscFunctionReturn(0);
1025 }
1026 
1027 #undef __FUNCT__
1028 #define __FUNCT__ "MatMultTranspose_MPIAIJ"
1029 PetscErrorCode MatMultTranspose_MPIAIJ(Mat A,Vec xx,Vec yy)
1030 {
1031   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1032   PetscErrorCode ierr;
1033   PetscBool      merged;
1034 
1035   PetscFunctionBegin;
1036   ierr = VecScatterGetMerged(a->Mvctx,&merged);CHKERRQ(ierr);
1037   /* do nondiagonal part */
1038   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
1039   if (!merged) {
1040     /* send it on its way */
1041     ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1042     /* do local part */
1043     ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
1044     /* receive remote parts: note this assumes the values are not actually */
1045     /* added in yy until the next line, */
1046     ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1047   } else {
1048     /* do local part */
1049     ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
1050     /* send it on its way */
1051     ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1052     /* values actually were received in the Begin() but we need to call this nop */
1053     ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1054   }
1055   PetscFunctionReturn(0);
1056 }
1057 
1058 #undef __FUNCT__
1059 #define __FUNCT__ "MatIsTranspose_MPIAIJ"
1060 PetscErrorCode  MatIsTranspose_MPIAIJ(Mat Amat,Mat Bmat,PetscReal tol,PetscBool  *f)
1061 {
1062   MPI_Comm       comm;
1063   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ*) Amat->data, *Bij;
1064   Mat            Adia = Aij->A, Bdia, Aoff,Boff,*Aoffs,*Boffs;
1065   IS             Me,Notme;
1066   PetscErrorCode ierr;
1067   PetscInt       M,N,first,last,*notme,i;
1068   PetscMPIInt    size;
1069 
1070   PetscFunctionBegin;
1071   /* Easy test: symmetric diagonal block */
1072   Bij  = (Mat_MPIAIJ*) Bmat->data; Bdia = Bij->A;
1073   ierr = MatIsTranspose(Adia,Bdia,tol,f);CHKERRQ(ierr);
1074   if (!*f) PetscFunctionReturn(0);
1075   ierr = PetscObjectGetComm((PetscObject)Amat,&comm);CHKERRQ(ierr);
1076   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1077   if (size == 1) PetscFunctionReturn(0);
1078 
1079   /* Hard test: off-diagonal block. This takes a MatGetSubMatrix. */
1080   ierr = MatGetSize(Amat,&M,&N);CHKERRQ(ierr);
1081   ierr = MatGetOwnershipRange(Amat,&first,&last);CHKERRQ(ierr);
1082   ierr = PetscMalloc1(N-last+first,&notme);CHKERRQ(ierr);
1083   for (i=0; i<first; i++) notme[i] = i;
1084   for (i=last; i<M; i++) notme[i-last+first] = i;
1085   ierr = ISCreateGeneral(MPI_COMM_SELF,N-last+first,notme,PETSC_COPY_VALUES,&Notme);CHKERRQ(ierr);
1086   ierr = ISCreateStride(MPI_COMM_SELF,last-first,first,1,&Me);CHKERRQ(ierr);
1087   ierr = MatGetSubMatrices(Amat,1,&Me,&Notme,MAT_INITIAL_MATRIX,&Aoffs);CHKERRQ(ierr);
1088   Aoff = Aoffs[0];
1089   ierr = MatGetSubMatrices(Bmat,1,&Notme,&Me,MAT_INITIAL_MATRIX,&Boffs);CHKERRQ(ierr);
1090   Boff = Boffs[0];
1091   ierr = MatIsTranspose(Aoff,Boff,tol,f);CHKERRQ(ierr);
1092   ierr = MatDestroyMatrices(1,&Aoffs);CHKERRQ(ierr);
1093   ierr = MatDestroyMatrices(1,&Boffs);CHKERRQ(ierr);
1094   ierr = ISDestroy(&Me);CHKERRQ(ierr);
1095   ierr = ISDestroy(&Notme);CHKERRQ(ierr);
1096   ierr = PetscFree(notme);CHKERRQ(ierr);
1097   PetscFunctionReturn(0);
1098 }
1099 
1100 #undef __FUNCT__
1101 #define __FUNCT__ "MatMultTransposeAdd_MPIAIJ"
1102 PetscErrorCode MatMultTransposeAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1103 {
1104   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1105   PetscErrorCode ierr;
1106 
1107   PetscFunctionBegin;
1108   /* do nondiagonal part */
1109   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
1110   /* send it on its way */
1111   ierr = VecScatterBegin(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1112   /* do local part */
1113   ierr = (*a->A->ops->multtransposeadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
1114   /* receive remote parts */
1115   ierr = VecScatterEnd(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1116   PetscFunctionReturn(0);
1117 }
1118 
1119 /*
1120   This only works correctly for square matrices where the subblock A->A is the
1121    diagonal block
1122 */
1123 #undef __FUNCT__
1124 #define __FUNCT__ "MatGetDiagonal_MPIAIJ"
1125 PetscErrorCode MatGetDiagonal_MPIAIJ(Mat A,Vec v)
1126 {
1127   PetscErrorCode ierr;
1128   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1129 
1130   PetscFunctionBegin;
1131   if (A->rmap->N != A->cmap->N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Supports only square matrix where A->A is diag block");
1132   if (A->rmap->rstart != A->cmap->rstart || A->rmap->rend != A->cmap->rend) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"row partition must equal col partition");
1133   ierr = MatGetDiagonal(a->A,v);CHKERRQ(ierr);
1134   PetscFunctionReturn(0);
1135 }
1136 
1137 #undef __FUNCT__
1138 #define __FUNCT__ "MatScale_MPIAIJ"
1139 PetscErrorCode MatScale_MPIAIJ(Mat A,PetscScalar aa)
1140 {
1141   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1142   PetscErrorCode ierr;
1143 
1144   PetscFunctionBegin;
1145   ierr = MatScale(a->A,aa);CHKERRQ(ierr);
1146   ierr = MatScale(a->B,aa);CHKERRQ(ierr);
1147   PetscFunctionReturn(0);
1148 }
1149 
1150 #undef __FUNCT__
1151 #define __FUNCT__ "MatDestroy_MPIAIJ"
1152 PetscErrorCode MatDestroy_MPIAIJ(Mat mat)
1153 {
1154   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1155   PetscErrorCode ierr;
1156 
1157   PetscFunctionBegin;
1158 #if defined(PETSC_USE_LOG)
1159   PetscLogObjectState((PetscObject)mat,"Rows=%D, Cols=%D",mat->rmap->N,mat->cmap->N);
1160 #endif
1161   ierr = MatStashDestroy_Private(&mat->stash);CHKERRQ(ierr);
1162   ierr = VecDestroy(&aij->diag);CHKERRQ(ierr);
1163   ierr = MatDestroy(&aij->A);CHKERRQ(ierr);
1164   ierr = MatDestroy(&aij->B);CHKERRQ(ierr);
1165 #if defined(PETSC_USE_CTABLE)
1166   ierr = PetscTableDestroy(&aij->colmap);CHKERRQ(ierr);
1167 #else
1168   ierr = PetscFree(aij->colmap);CHKERRQ(ierr);
1169 #endif
1170   ierr = PetscFree(aij->garray);CHKERRQ(ierr);
1171   ierr = VecDestroy(&aij->lvec);CHKERRQ(ierr);
1172   ierr = VecScatterDestroy(&aij->Mvctx);CHKERRQ(ierr);
1173   ierr = PetscFree2(aij->rowvalues,aij->rowindices);CHKERRQ(ierr);
1174   ierr = PetscFree(aij->ld);CHKERRQ(ierr);
1175   ierr = PetscFree(mat->data);CHKERRQ(ierr);
1176 
1177   ierr = PetscObjectChangeTypeName((PetscObject)mat,0);CHKERRQ(ierr);
1178   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatStoreValues_C",NULL);CHKERRQ(ierr);
1179   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatRetrieveValues_C",NULL);CHKERRQ(ierr);
1180   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatGetDiagonalBlock_C",NULL);CHKERRQ(ierr);
1181   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatIsTranspose_C",NULL);CHKERRQ(ierr);
1182   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocation_C",NULL);CHKERRQ(ierr);
1183   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocationCSR_C",NULL);CHKERRQ(ierr);
1184   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDiagonalScaleLocal_C",NULL);CHKERRQ(ierr);
1185   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_mpisbaij_C",NULL);CHKERRQ(ierr);
1186 #if defined(PETSC_HAVE_ELEMENTAL)
1187   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_elemental_C",NULL);CHKERRQ(ierr);
1188 #endif
1189   PetscFunctionReturn(0);
1190 }
1191 
1192 #undef __FUNCT__
1193 #define __FUNCT__ "MatView_MPIAIJ_Binary"
1194 PetscErrorCode MatView_MPIAIJ_Binary(Mat mat,PetscViewer viewer)
1195 {
1196   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1197   Mat_SeqAIJ     *A   = (Mat_SeqAIJ*)aij->A->data;
1198   Mat_SeqAIJ     *B   = (Mat_SeqAIJ*)aij->B->data;
1199   PetscErrorCode ierr;
1200   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
1201   int            fd;
1202   PetscInt       nz,header[4],*row_lengths,*range=0,rlen,i;
1203   PetscInt       nzmax,*column_indices,j,k,col,*garray = aij->garray,cnt,cstart = mat->cmap->rstart,rnz = 0;
1204   PetscScalar    *column_values;
1205   PetscInt       message_count,flowcontrolcount;
1206   FILE           *file;
1207 
1208   PetscFunctionBegin;
1209   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
1210   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);CHKERRQ(ierr);
1211   nz   = A->nz + B->nz;
1212   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
1213   if (!rank) {
1214     header[0] = MAT_FILE_CLASSID;
1215     header[1] = mat->rmap->N;
1216     header[2] = mat->cmap->N;
1217 
1218     ierr = MPI_Reduce(&nz,&header[3],1,MPIU_INT,MPI_SUM,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1219     ierr = PetscBinaryWrite(fd,header,4,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1220     /* get largest number of rows any processor has */
1221     rlen  = mat->rmap->n;
1222     range = mat->rmap->range;
1223     for (i=1; i<size; i++) rlen = PetscMax(rlen,range[i+1] - range[i]);
1224   } else {
1225     ierr = MPI_Reduce(&nz,0,1,MPIU_INT,MPI_SUM,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1226     rlen = mat->rmap->n;
1227   }
1228 
1229   /* load up the local row counts */
1230   ierr = PetscMalloc1(rlen+1,&row_lengths);CHKERRQ(ierr);
1231   for (i=0; i<mat->rmap->n; i++) row_lengths[i] = A->i[i+1] - A->i[i] + B->i[i+1] - B->i[i];
1232 
1233   /* store the row lengths to the file */
1234   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1235   if (!rank) {
1236     ierr = PetscBinaryWrite(fd,row_lengths,mat->rmap->n,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1237     for (i=1; i<size; i++) {
1238       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1239       rlen = range[i+1] - range[i];
1240       ierr = MPIULong_Recv(row_lengths,rlen,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1241       ierr = PetscBinaryWrite(fd,row_lengths,rlen,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1242     }
1243     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1244   } else {
1245     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1246     ierr = MPIULong_Send(row_lengths,mat->rmap->n,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1247     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1248   }
1249   ierr = PetscFree(row_lengths);CHKERRQ(ierr);
1250 
1251   /* load up the local column indices */
1252   nzmax = nz; /* th processor needs space a largest processor needs */
1253   ierr  = MPI_Reduce(&nz,&nzmax,1,MPIU_INT,MPI_MAX,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1254   ierr  = PetscMalloc1(nzmax+1,&column_indices);CHKERRQ(ierr);
1255   cnt   = 0;
1256   for (i=0; i<mat->rmap->n; i++) {
1257     for (j=B->i[i]; j<B->i[i+1]; j++) {
1258       if ((col = garray[B->j[j]]) > cstart) break;
1259       column_indices[cnt++] = col;
1260     }
1261     for (k=A->i[i]; k<A->i[i+1]; k++) column_indices[cnt++] = A->j[k] + cstart;
1262     for (; j<B->i[i+1]; j++) column_indices[cnt++] = garray[B->j[j]];
1263   }
1264   if (cnt != A->nz + B->nz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: cnt = %D nz = %D",cnt,A->nz+B->nz);
1265 
1266   /* store the column indices to the file */
1267   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1268   if (!rank) {
1269     MPI_Status status;
1270     ierr = PetscBinaryWrite(fd,column_indices,nz,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1271     for (i=1; i<size; i++) {
1272       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1273       ierr = MPI_Recv(&rnz,1,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat),&status);CHKERRQ(ierr);
1274       if (rnz > nzmax) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: nz = %D nzmax = %D",nz,nzmax);
1275       ierr = MPIULong_Recv(column_indices,rnz,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1276       ierr = PetscBinaryWrite(fd,column_indices,rnz,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1277     }
1278     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1279   } else {
1280     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1281     ierr = MPI_Send(&nz,1,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1282     ierr = MPIULong_Send(column_indices,nz,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1283     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1284   }
1285   ierr = PetscFree(column_indices);CHKERRQ(ierr);
1286 
1287   /* load up the local column values */
1288   ierr = PetscMalloc1(nzmax+1,&column_values);CHKERRQ(ierr);
1289   cnt  = 0;
1290   for (i=0; i<mat->rmap->n; i++) {
1291     for (j=B->i[i]; j<B->i[i+1]; j++) {
1292       if (garray[B->j[j]] > cstart) break;
1293       column_values[cnt++] = B->a[j];
1294     }
1295     for (k=A->i[i]; k<A->i[i+1]; k++) column_values[cnt++] = A->a[k];
1296     for (; j<B->i[i+1]; j++) column_values[cnt++] = B->a[j];
1297   }
1298   if (cnt != A->nz + B->nz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Internal PETSc error: cnt = %D nz = %D",cnt,A->nz+B->nz);
1299 
1300   /* store the column values to the file */
1301   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1302   if (!rank) {
1303     MPI_Status status;
1304     ierr = PetscBinaryWrite(fd,column_values,nz,PETSC_SCALAR,PETSC_TRUE);CHKERRQ(ierr);
1305     for (i=1; i<size; i++) {
1306       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1307       ierr = MPI_Recv(&rnz,1,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat),&status);CHKERRQ(ierr);
1308       if (rnz > nzmax) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: nz = %D nzmax = %D",nz,nzmax);
1309       ierr = MPIULong_Recv(column_values,rnz,MPIU_SCALAR,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1310       ierr = PetscBinaryWrite(fd,column_values,rnz,PETSC_SCALAR,PETSC_TRUE);CHKERRQ(ierr);
1311     }
1312     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1313   } else {
1314     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1315     ierr = MPI_Send(&nz,1,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1316     ierr = MPIULong_Send(column_values,nz,MPIU_SCALAR,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1317     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1318   }
1319   ierr = PetscFree(column_values);CHKERRQ(ierr);
1320 
1321   ierr = PetscViewerBinaryGetInfoPointer(viewer,&file);CHKERRQ(ierr);
1322   if (file) fprintf(file,"-matload_block_size %d\n",(int)PetscAbs(mat->rmap->bs));
1323   PetscFunctionReturn(0);
1324 }
1325 
1326 #include <petscdraw.h>
1327 #undef __FUNCT__
1328 #define __FUNCT__ "MatView_MPIAIJ_ASCIIorDraworSocket"
1329 PetscErrorCode MatView_MPIAIJ_ASCIIorDraworSocket(Mat mat,PetscViewer viewer)
1330 {
1331   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)mat->data;
1332   PetscErrorCode    ierr;
1333   PetscMPIInt       rank = aij->rank,size = aij->size;
1334   PetscBool         isdraw,iascii,isbinary;
1335   PetscViewer       sviewer;
1336   PetscViewerFormat format;
1337 
1338   PetscFunctionBegin;
1339   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1340   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1341   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1342   if (iascii) {
1343     ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
1344     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
1345       MatInfo   info;
1346       PetscBool inodes;
1347 
1348       ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
1349       ierr = MatGetInfo(mat,MAT_LOCAL,&info);CHKERRQ(ierr);
1350       ierr = MatInodeGetInodeSizes(aij->A,NULL,(PetscInt**)&inodes,NULL);CHKERRQ(ierr);
1351       ierr = PetscViewerASCIISynchronizedAllow(viewer,PETSC_TRUE);CHKERRQ(ierr);
1352       if (!inodes) {
1353         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %D nz %D nz alloced %D mem %D, not using I-node routines\n",
1354                                                   rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
1355       } else {
1356         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %D nz %D nz alloced %D mem %D, using I-node routines\n",
1357                                                   rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
1358       }
1359       ierr = MatGetInfo(aij->A,MAT_LOCAL,&info);CHKERRQ(ierr);
1360       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] on-diagonal part: nz %D \n",rank,(PetscInt)info.nz_used);CHKERRQ(ierr);
1361       ierr = MatGetInfo(aij->B,MAT_LOCAL,&info);CHKERRQ(ierr);
1362       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] off-diagonal part: nz %D \n",rank,(PetscInt)info.nz_used);CHKERRQ(ierr);
1363       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1364       ierr = PetscViewerASCIISynchronizedAllow(viewer,PETSC_FALSE);CHKERRQ(ierr);
1365       ierr = PetscViewerASCIIPrintf(viewer,"Information on VecScatter used in matrix-vector product: \n");CHKERRQ(ierr);
1366       ierr = VecScatterView(aij->Mvctx,viewer);CHKERRQ(ierr);
1367       PetscFunctionReturn(0);
1368     } else if (format == PETSC_VIEWER_ASCII_INFO) {
1369       PetscInt inodecount,inodelimit,*inodes;
1370       ierr = MatInodeGetInodeSizes(aij->A,&inodecount,&inodes,&inodelimit);CHKERRQ(ierr);
1371       if (inodes) {
1372         ierr = PetscViewerASCIIPrintf(viewer,"using I-node (on process 0) routines: found %D nodes, limit used is %D\n",inodecount,inodelimit);CHKERRQ(ierr);
1373       } else {
1374         ierr = PetscViewerASCIIPrintf(viewer,"not using I-node (on process 0) routines\n");CHKERRQ(ierr);
1375       }
1376       PetscFunctionReturn(0);
1377     } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO) {
1378       PetscFunctionReturn(0);
1379     }
1380   } else if (isbinary) {
1381     if (size == 1) {
1382       ierr = PetscObjectSetName((PetscObject)aij->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1383       ierr = MatView(aij->A,viewer);CHKERRQ(ierr);
1384     } else {
1385       ierr = MatView_MPIAIJ_Binary(mat,viewer);CHKERRQ(ierr);
1386     }
1387     PetscFunctionReturn(0);
1388   } else if (isdraw) {
1389     PetscDraw draw;
1390     PetscBool isnull;
1391     ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
1392     ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr); if (isnull) PetscFunctionReturn(0);
1393   }
1394 
1395   {
1396     /* assemble the entire matrix onto first processor. */
1397     Mat        A;
1398     Mat_SeqAIJ *Aloc;
1399     PetscInt   M = mat->rmap->N,N = mat->cmap->N,m,*ai,*aj,row,*cols,i,*ct;
1400     MatScalar  *a;
1401 
1402     ierr = MatCreate(PetscObjectComm((PetscObject)mat),&A);CHKERRQ(ierr);
1403     if (!rank) {
1404       ierr = MatSetSizes(A,M,N,M,N);CHKERRQ(ierr);
1405     } else {
1406       ierr = MatSetSizes(A,0,0,M,N);CHKERRQ(ierr);
1407     }
1408     /* This is just a temporary matrix, so explicitly using MATMPIAIJ is probably best */
1409     ierr = MatSetType(A,MATMPIAIJ);CHKERRQ(ierr);
1410     ierr = MatMPIAIJSetPreallocation(A,0,NULL,0,NULL);CHKERRQ(ierr);
1411     ierr = MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
1412     ierr = PetscLogObjectParent((PetscObject)mat,(PetscObject)A);CHKERRQ(ierr);
1413 
1414     /* copy over the A part */
1415     Aloc = (Mat_SeqAIJ*)aij->A->data;
1416     m    = aij->A->rmap->n; ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
1417     row  = mat->rmap->rstart;
1418     for (i=0; i<ai[m]; i++) aj[i] += mat->cmap->rstart;
1419     for (i=0; i<m; i++) {
1420       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],aj,a,INSERT_VALUES);CHKERRQ(ierr);
1421       row++;
1422       a += ai[i+1]-ai[i]; aj += ai[i+1]-ai[i];
1423     }
1424     aj = Aloc->j;
1425     for (i=0; i<ai[m]; i++) aj[i] -= mat->cmap->rstart;
1426 
1427     /* copy over the B part */
1428     Aloc = (Mat_SeqAIJ*)aij->B->data;
1429     m    = aij->B->rmap->n;  ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
1430     row  = mat->rmap->rstart;
1431     ierr = PetscMalloc1(ai[m]+1,&cols);CHKERRQ(ierr);
1432     ct   = cols;
1433     for (i=0; i<ai[m]; i++) cols[i] = aij->garray[aj[i]];
1434     for (i=0; i<m; i++) {
1435       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],cols,a,INSERT_VALUES);CHKERRQ(ierr);
1436       row++;
1437       a += ai[i+1]-ai[i]; cols += ai[i+1]-ai[i];
1438     }
1439     ierr = PetscFree(ct);CHKERRQ(ierr);
1440     ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1441     ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1442     /*
1443        Everyone has to call to draw the matrix since the graphics waits are
1444        synchronized across all processors that share the PetscDraw object
1445     */
1446     ierr = PetscViewerGetSingleton(viewer,&sviewer);CHKERRQ(ierr);
1447     if (!rank) {
1448       ierr = PetscObjectSetName((PetscObject)((Mat_MPIAIJ*)(A->data))->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1449       ierr = MatView_SeqAIJ(((Mat_MPIAIJ*)(A->data))->A,sviewer);CHKERRQ(ierr);
1450     }
1451     ierr = PetscViewerRestoreSingleton(viewer,&sviewer);CHKERRQ(ierr);
1452     ierr = MatDestroy(&A);CHKERRQ(ierr);
1453   }
1454   PetscFunctionReturn(0);
1455 }
1456 
1457 #undef __FUNCT__
1458 #define __FUNCT__ "MatView_MPIAIJ"
1459 PetscErrorCode MatView_MPIAIJ(Mat mat,PetscViewer viewer)
1460 {
1461   PetscErrorCode ierr;
1462   PetscBool      iascii,isdraw,issocket,isbinary;
1463 
1464   PetscFunctionBegin;
1465   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1466   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1467   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1468   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSOCKET,&issocket);CHKERRQ(ierr);
1469   if (iascii || isdraw || isbinary || issocket) {
1470     ierr = MatView_MPIAIJ_ASCIIorDraworSocket(mat,viewer);CHKERRQ(ierr);
1471   }
1472   PetscFunctionReturn(0);
1473 }
1474 
1475 #undef __FUNCT__
1476 #define __FUNCT__ "MatSOR_MPIAIJ"
1477 PetscErrorCode MatSOR_MPIAIJ(Mat matin,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
1478 {
1479   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1480   PetscErrorCode ierr;
1481   Vec            bb1 = 0;
1482   PetscBool      hasop;
1483 
1484   PetscFunctionBegin;
1485   if (flag == SOR_APPLY_UPPER) {
1486     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1487     PetscFunctionReturn(0);
1488   }
1489 
1490   if (its > 1 || ~flag & SOR_ZERO_INITIAL_GUESS || flag & SOR_EISENSTAT) {
1491     ierr = VecDuplicate(bb,&bb1);CHKERRQ(ierr);
1492   }
1493 
1494   if ((flag & SOR_LOCAL_SYMMETRIC_SWEEP) == SOR_LOCAL_SYMMETRIC_SWEEP) {
1495     if (flag & SOR_ZERO_INITIAL_GUESS) {
1496       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1497       its--;
1498     }
1499 
1500     while (its--) {
1501       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1502       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1503 
1504       /* update rhs: bb1 = bb - B*x */
1505       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1506       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1507 
1508       /* local sweep */
1509       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_SYMMETRIC_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1510     }
1511   } else if (flag & SOR_LOCAL_FORWARD_SWEEP) {
1512     if (flag & SOR_ZERO_INITIAL_GUESS) {
1513       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1514       its--;
1515     }
1516     while (its--) {
1517       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1518       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1519 
1520       /* update rhs: bb1 = bb - B*x */
1521       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1522       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1523 
1524       /* local sweep */
1525       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_FORWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1526     }
1527   } else if (flag & SOR_LOCAL_BACKWARD_SWEEP) {
1528     if (flag & SOR_ZERO_INITIAL_GUESS) {
1529       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1530       its--;
1531     }
1532     while (its--) {
1533       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1534       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1535 
1536       /* update rhs: bb1 = bb - B*x */
1537       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1538       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1539 
1540       /* local sweep */
1541       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_BACKWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1542     }
1543   } else if (flag & SOR_EISENSTAT) {
1544     Vec xx1;
1545 
1546     ierr = VecDuplicate(bb,&xx1);CHKERRQ(ierr);
1547     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_BACKWARD_SWEEP),fshift,lits,1,xx);CHKERRQ(ierr);
1548 
1549     ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1550     ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1551     if (!mat->diag) {
1552       ierr = MatCreateVecs(matin,&mat->diag,NULL);CHKERRQ(ierr);
1553       ierr = MatGetDiagonal(matin,mat->diag);CHKERRQ(ierr);
1554     }
1555     ierr = MatHasOperation(matin,MATOP_MULT_DIAGONAL_BLOCK,&hasop);CHKERRQ(ierr);
1556     if (hasop) {
1557       ierr = MatMultDiagonalBlock(matin,xx,bb1);CHKERRQ(ierr);
1558     } else {
1559       ierr = VecPointwiseMult(bb1,mat->diag,xx);CHKERRQ(ierr);
1560     }
1561     ierr = VecAYPX(bb1,(omega-2.0)/omega,bb);CHKERRQ(ierr);
1562 
1563     ierr = MatMultAdd(mat->B,mat->lvec,bb1,bb1);CHKERRQ(ierr);
1564 
1565     /* local sweep */
1566     ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_FORWARD_SWEEP),fshift,lits,1,xx1);CHKERRQ(ierr);
1567     ierr = VecAXPY(xx,1.0,xx1);CHKERRQ(ierr);
1568     ierr = VecDestroy(&xx1);CHKERRQ(ierr);
1569   } else SETERRQ(PetscObjectComm((PetscObject)matin),PETSC_ERR_SUP,"Parallel SOR not supported");
1570 
1571   ierr = VecDestroy(&bb1);CHKERRQ(ierr);
1572   PetscFunctionReturn(0);
1573 }
1574 
1575 #undef __FUNCT__
1576 #define __FUNCT__ "MatPermute_MPIAIJ"
1577 PetscErrorCode MatPermute_MPIAIJ(Mat A,IS rowp,IS colp,Mat *B)
1578 {
1579   Mat            aA,aB,Aperm;
1580   const PetscInt *rwant,*cwant,*gcols,*ai,*bi,*aj,*bj;
1581   PetscScalar    *aa,*ba;
1582   PetscInt       i,j,m,n,ng,anz,bnz,*dnnz,*onnz,*tdnnz,*tonnz,*rdest,*cdest,*work,*gcdest;
1583   PetscSF        rowsf,sf;
1584   IS             parcolp = NULL;
1585   PetscBool      done;
1586   PetscErrorCode ierr;
1587 
1588   PetscFunctionBegin;
1589   ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
1590   ierr = ISGetIndices(rowp,&rwant);CHKERRQ(ierr);
1591   ierr = ISGetIndices(colp,&cwant);CHKERRQ(ierr);
1592   ierr = PetscMalloc3(PetscMax(m,n),&work,m,&rdest,n,&cdest);CHKERRQ(ierr);
1593 
1594   /* Invert row permutation to find out where my rows should go */
1595   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&rowsf);CHKERRQ(ierr);
1596   ierr = PetscSFSetGraphLayout(rowsf,A->rmap,A->rmap->n,NULL,PETSC_OWN_POINTER,rwant);CHKERRQ(ierr);
1597   ierr = PetscSFSetFromOptions(rowsf);CHKERRQ(ierr);
1598   for (i=0; i<m; i++) work[i] = A->rmap->rstart + i;
1599   ierr = PetscSFReduceBegin(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1600   ierr = PetscSFReduceEnd(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1601 
1602   /* Invert column permutation to find out where my columns should go */
1603   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1604   ierr = PetscSFSetGraphLayout(sf,A->cmap,A->cmap->n,NULL,PETSC_OWN_POINTER,cwant);CHKERRQ(ierr);
1605   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1606   for (i=0; i<n; i++) work[i] = A->cmap->rstart + i;
1607   ierr = PetscSFReduceBegin(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1608   ierr = PetscSFReduceEnd(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1609   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1610 
1611   ierr = ISRestoreIndices(rowp,&rwant);CHKERRQ(ierr);
1612   ierr = ISRestoreIndices(colp,&cwant);CHKERRQ(ierr);
1613   ierr = MatMPIAIJGetSeqAIJ(A,&aA,&aB,&gcols);CHKERRQ(ierr);
1614 
1615   /* Find out where my gcols should go */
1616   ierr = MatGetSize(aB,NULL,&ng);CHKERRQ(ierr);
1617   ierr = PetscMalloc1(ng,&gcdest);CHKERRQ(ierr);
1618   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1619   ierr = PetscSFSetGraphLayout(sf,A->cmap,ng,NULL,PETSC_OWN_POINTER,gcols);CHKERRQ(ierr);
1620   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1621   ierr = PetscSFBcastBegin(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1622   ierr = PetscSFBcastEnd(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1623   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1624 
1625   ierr = PetscCalloc4(m,&dnnz,m,&onnz,m,&tdnnz,m,&tonnz);CHKERRQ(ierr);
1626   ierr = MatGetRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1627   ierr = MatGetRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1628   for (i=0; i<m; i++) {
1629     PetscInt row = rdest[i],rowner;
1630     ierr = PetscLayoutFindOwner(A->rmap,row,&rowner);CHKERRQ(ierr);
1631     for (j=ai[i]; j<ai[i+1]; j++) {
1632       PetscInt cowner,col = cdest[aj[j]];
1633       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr); /* Could build an index for the columns to eliminate this search */
1634       if (rowner == cowner) dnnz[i]++;
1635       else onnz[i]++;
1636     }
1637     for (j=bi[i]; j<bi[i+1]; j++) {
1638       PetscInt cowner,col = gcdest[bj[j]];
1639       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr);
1640       if (rowner == cowner) dnnz[i]++;
1641       else onnz[i]++;
1642     }
1643   }
1644   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1645   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1646   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1647   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1648   ierr = PetscSFDestroy(&rowsf);CHKERRQ(ierr);
1649 
1650   ierr = MatCreateAIJ(PetscObjectComm((PetscObject)A),A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N,0,tdnnz,0,tonnz,&Aperm);CHKERRQ(ierr);
1651   ierr = MatSeqAIJGetArray(aA,&aa);CHKERRQ(ierr);
1652   ierr = MatSeqAIJGetArray(aB,&ba);CHKERRQ(ierr);
1653   for (i=0; i<m; i++) {
1654     PetscInt *acols = dnnz,*bcols = onnz; /* Repurpose now-unneeded arrays */
1655     PetscInt j0,rowlen;
1656     rowlen = ai[i+1] - ai[i];
1657     for (j0=j=0; j<rowlen; j0=j) { /* rowlen could be larger than number of rows m, so sum in batches */
1658       for ( ; j<PetscMin(rowlen,j0+m); j++) acols[j-j0] = cdest[aj[ai[i]+j]];
1659       ierr = MatSetValues(Aperm,1,&rdest[i],j-j0,acols,aa+ai[i]+j0,INSERT_VALUES);CHKERRQ(ierr);
1660     }
1661     rowlen = bi[i+1] - bi[i];
1662     for (j0=j=0; j<rowlen; j0=j) {
1663       for ( ; j<PetscMin(rowlen,j0+m); j++) bcols[j-j0] = gcdest[bj[bi[i]+j]];
1664       ierr = MatSetValues(Aperm,1,&rdest[i],j-j0,bcols,ba+bi[i]+j0,INSERT_VALUES);CHKERRQ(ierr);
1665     }
1666   }
1667   ierr = MatAssemblyBegin(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1668   ierr = MatAssemblyEnd(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1669   ierr = MatRestoreRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1670   ierr = MatRestoreRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1671   ierr = MatSeqAIJRestoreArray(aA,&aa);CHKERRQ(ierr);
1672   ierr = MatSeqAIJRestoreArray(aB,&ba);CHKERRQ(ierr);
1673   ierr = PetscFree4(dnnz,onnz,tdnnz,tonnz);CHKERRQ(ierr);
1674   ierr = PetscFree3(work,rdest,cdest);CHKERRQ(ierr);
1675   ierr = PetscFree(gcdest);CHKERRQ(ierr);
1676   if (parcolp) {ierr = ISDestroy(&colp);CHKERRQ(ierr);}
1677   *B = Aperm;
1678   PetscFunctionReturn(0);
1679 }
1680 
1681 #undef __FUNCT__
1682 #define __FUNCT__ "MatGetGhosts_MPIAIJ"
1683 PetscErrorCode  MatGetGhosts_MPIAIJ(Mat mat,PetscInt *nghosts,const PetscInt *ghosts[])
1684 {
1685   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1686   PetscErrorCode ierr;
1687 
1688   PetscFunctionBegin;
1689   ierr = MatGetSize(aij->B,NULL,nghosts);CHKERRQ(ierr);
1690   if (ghosts) *ghosts = aij->garray;
1691   PetscFunctionReturn(0);
1692 }
1693 
1694 #undef __FUNCT__
1695 #define __FUNCT__ "MatGetInfo_MPIAIJ"
1696 PetscErrorCode MatGetInfo_MPIAIJ(Mat matin,MatInfoType flag,MatInfo *info)
1697 {
1698   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1699   Mat            A    = mat->A,B = mat->B;
1700   PetscErrorCode ierr;
1701   PetscReal      isend[5],irecv[5];
1702 
1703   PetscFunctionBegin;
1704   info->block_size = 1.0;
1705   ierr             = MatGetInfo(A,MAT_LOCAL,info);CHKERRQ(ierr);
1706 
1707   isend[0] = info->nz_used; isend[1] = info->nz_allocated; isend[2] = info->nz_unneeded;
1708   isend[3] = info->memory;  isend[4] = info->mallocs;
1709 
1710   ierr = MatGetInfo(B,MAT_LOCAL,info);CHKERRQ(ierr);
1711 
1712   isend[0] += info->nz_used; isend[1] += info->nz_allocated; isend[2] += info->nz_unneeded;
1713   isend[3] += info->memory;  isend[4] += info->mallocs;
1714   if (flag == MAT_LOCAL) {
1715     info->nz_used      = isend[0];
1716     info->nz_allocated = isend[1];
1717     info->nz_unneeded  = isend[2];
1718     info->memory       = isend[3];
1719     info->mallocs      = isend[4];
1720   } else if (flag == MAT_GLOBAL_MAX) {
1721     ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1722 
1723     info->nz_used      = irecv[0];
1724     info->nz_allocated = irecv[1];
1725     info->nz_unneeded  = irecv[2];
1726     info->memory       = irecv[3];
1727     info->mallocs      = irecv[4];
1728   } else if (flag == MAT_GLOBAL_SUM) {
1729     ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1730 
1731     info->nz_used      = irecv[0];
1732     info->nz_allocated = irecv[1];
1733     info->nz_unneeded  = irecv[2];
1734     info->memory       = irecv[3];
1735     info->mallocs      = irecv[4];
1736   }
1737   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
1738   info->fill_ratio_needed = 0;
1739   info->factor_mallocs    = 0;
1740   PetscFunctionReturn(0);
1741 }
1742 
1743 #undef __FUNCT__
1744 #define __FUNCT__ "MatSetOption_MPIAIJ"
1745 PetscErrorCode MatSetOption_MPIAIJ(Mat A,MatOption op,PetscBool flg)
1746 {
1747   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1748   PetscErrorCode ierr;
1749 
1750   PetscFunctionBegin;
1751   switch (op) {
1752   case MAT_NEW_NONZERO_LOCATIONS:
1753   case MAT_NEW_NONZERO_ALLOCATION_ERR:
1754   case MAT_UNUSED_NONZERO_LOCATION_ERR:
1755   case MAT_KEEP_NONZERO_PATTERN:
1756   case MAT_NEW_NONZERO_LOCATION_ERR:
1757   case MAT_USE_INODES:
1758   case MAT_IGNORE_ZERO_ENTRIES:
1759     MatCheckPreallocated(A,1);
1760     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1761     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1762     break;
1763   case MAT_ROW_ORIENTED:
1764     a->roworiented = flg;
1765 
1766     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1767     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1768     break;
1769   case MAT_NEW_DIAGONALS:
1770     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
1771     break;
1772   case MAT_IGNORE_OFF_PROC_ENTRIES:
1773     a->donotstash = flg;
1774     break;
1775   case MAT_SPD:
1776     A->spd_set = PETSC_TRUE;
1777     A->spd     = flg;
1778     if (flg) {
1779       A->symmetric                  = PETSC_TRUE;
1780       A->structurally_symmetric     = PETSC_TRUE;
1781       A->symmetric_set              = PETSC_TRUE;
1782       A->structurally_symmetric_set = PETSC_TRUE;
1783     }
1784     break;
1785   case MAT_SYMMETRIC:
1786     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1787     break;
1788   case MAT_STRUCTURALLY_SYMMETRIC:
1789     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1790     break;
1791   case MAT_HERMITIAN:
1792     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1793     break;
1794   case MAT_SYMMETRY_ETERNAL:
1795     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1796     break;
1797   default:
1798     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %d",op);
1799   }
1800   PetscFunctionReturn(0);
1801 }
1802 
1803 #undef __FUNCT__
1804 #define __FUNCT__ "MatGetRow_MPIAIJ"
1805 PetscErrorCode MatGetRow_MPIAIJ(Mat matin,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1806 {
1807   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1808   PetscScalar    *vworkA,*vworkB,**pvA,**pvB,*v_p;
1809   PetscErrorCode ierr;
1810   PetscInt       i,*cworkA,*cworkB,**pcA,**pcB,cstart = matin->cmap->rstart;
1811   PetscInt       nztot,nzA,nzB,lrow,rstart = matin->rmap->rstart,rend = matin->rmap->rend;
1812   PetscInt       *cmap,*idx_p;
1813 
1814   PetscFunctionBegin;
1815   if (mat->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Already active");
1816   mat->getrowactive = PETSC_TRUE;
1817 
1818   if (!mat->rowvalues && (idx || v)) {
1819     /*
1820         allocate enough space to hold information from the longest row.
1821     */
1822     Mat_SeqAIJ *Aa = (Mat_SeqAIJ*)mat->A->data,*Ba = (Mat_SeqAIJ*)mat->B->data;
1823     PetscInt   max = 1,tmp;
1824     for (i=0; i<matin->rmap->n; i++) {
1825       tmp = Aa->i[i+1] - Aa->i[i] + Ba->i[i+1] - Ba->i[i];
1826       if (max < tmp) max = tmp;
1827     }
1828     ierr = PetscMalloc2(max,&mat->rowvalues,max,&mat->rowindices);CHKERRQ(ierr);
1829   }
1830 
1831   if (row < rstart || row >= rend) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Only local rows");
1832   lrow = row - rstart;
1833 
1834   pvA = &vworkA; pcA = &cworkA; pvB = &vworkB; pcB = &cworkB;
1835   if (!v)   {pvA = 0; pvB = 0;}
1836   if (!idx) {pcA = 0; if (!v) pcB = 0;}
1837   ierr  = (*mat->A->ops->getrow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1838   ierr  = (*mat->B->ops->getrow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1839   nztot = nzA + nzB;
1840 
1841   cmap = mat->garray;
1842   if (v  || idx) {
1843     if (nztot) {
1844       /* Sort by increasing column numbers, assuming A and B already sorted */
1845       PetscInt imark = -1;
1846       if (v) {
1847         *v = v_p = mat->rowvalues;
1848         for (i=0; i<nzB; i++) {
1849           if (cmap[cworkB[i]] < cstart) v_p[i] = vworkB[i];
1850           else break;
1851         }
1852         imark = i;
1853         for (i=0; i<nzA; i++)     v_p[imark+i] = vworkA[i];
1854         for (i=imark; i<nzB; i++) v_p[nzA+i]   = vworkB[i];
1855       }
1856       if (idx) {
1857         *idx = idx_p = mat->rowindices;
1858         if (imark > -1) {
1859           for (i=0; i<imark; i++) {
1860             idx_p[i] = cmap[cworkB[i]];
1861           }
1862         } else {
1863           for (i=0; i<nzB; i++) {
1864             if (cmap[cworkB[i]] < cstart) idx_p[i] = cmap[cworkB[i]];
1865             else break;
1866           }
1867           imark = i;
1868         }
1869         for (i=0; i<nzA; i++)     idx_p[imark+i] = cstart + cworkA[i];
1870         for (i=imark; i<nzB; i++) idx_p[nzA+i]   = cmap[cworkB[i]];
1871       }
1872     } else {
1873       if (idx) *idx = 0;
1874       if (v)   *v   = 0;
1875     }
1876   }
1877   *nz  = nztot;
1878   ierr = (*mat->A->ops->restorerow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1879   ierr = (*mat->B->ops->restorerow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1880   PetscFunctionReturn(0);
1881 }
1882 
1883 #undef __FUNCT__
1884 #define __FUNCT__ "MatRestoreRow_MPIAIJ"
1885 PetscErrorCode MatRestoreRow_MPIAIJ(Mat mat,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1886 {
1887   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1888 
1889   PetscFunctionBegin;
1890   if (!aij->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"MatGetRow() must be called first");
1891   aij->getrowactive = PETSC_FALSE;
1892   PetscFunctionReturn(0);
1893 }
1894 
1895 #undef __FUNCT__
1896 #define __FUNCT__ "MatNorm_MPIAIJ"
1897 PetscErrorCode MatNorm_MPIAIJ(Mat mat,NormType type,PetscReal *norm)
1898 {
1899   Mat_MPIAIJ     *aij  = (Mat_MPIAIJ*)mat->data;
1900   Mat_SeqAIJ     *amat = (Mat_SeqAIJ*)aij->A->data,*bmat = (Mat_SeqAIJ*)aij->B->data;
1901   PetscErrorCode ierr;
1902   PetscInt       i,j,cstart = mat->cmap->rstart;
1903   PetscReal      sum = 0.0;
1904   MatScalar      *v;
1905 
1906   PetscFunctionBegin;
1907   if (aij->size == 1) {
1908     ierr =  MatNorm(aij->A,type,norm);CHKERRQ(ierr);
1909   } else {
1910     if (type == NORM_FROBENIUS) {
1911       v = amat->a;
1912       for (i=0; i<amat->nz; i++) {
1913         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1914       }
1915       v = bmat->a;
1916       for (i=0; i<bmat->nz; i++) {
1917         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1918       }
1919       ierr  = MPI_Allreduce(&sum,norm,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1920       *norm = PetscSqrtReal(*norm);
1921     } else if (type == NORM_1) { /* max column norm */
1922       PetscReal *tmp,*tmp2;
1923       PetscInt  *jj,*garray = aij->garray;
1924       ierr  = PetscCalloc1(mat->cmap->N+1,&tmp);CHKERRQ(ierr);
1925       ierr  = PetscMalloc1(mat->cmap->N+1,&tmp2);CHKERRQ(ierr);
1926       *norm = 0.0;
1927       v     = amat->a; jj = amat->j;
1928       for (j=0; j<amat->nz; j++) {
1929         tmp[cstart + *jj++] += PetscAbsScalar(*v);  v++;
1930       }
1931       v = bmat->a; jj = bmat->j;
1932       for (j=0; j<bmat->nz; j++) {
1933         tmp[garray[*jj++]] += PetscAbsScalar(*v); v++;
1934       }
1935       ierr = MPI_Allreduce(tmp,tmp2,mat->cmap->N,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1936       for (j=0; j<mat->cmap->N; j++) {
1937         if (tmp2[j] > *norm) *norm = tmp2[j];
1938       }
1939       ierr = PetscFree(tmp);CHKERRQ(ierr);
1940       ierr = PetscFree(tmp2);CHKERRQ(ierr);
1941     } else if (type == NORM_INFINITY) { /* max row norm */
1942       PetscReal ntemp = 0.0;
1943       for (j=0; j<aij->A->rmap->n; j++) {
1944         v   = amat->a + amat->i[j];
1945         sum = 0.0;
1946         for (i=0; i<amat->i[j+1]-amat->i[j]; i++) {
1947           sum += PetscAbsScalar(*v); v++;
1948         }
1949         v = bmat->a + bmat->i[j];
1950         for (i=0; i<bmat->i[j+1]-bmat->i[j]; i++) {
1951           sum += PetscAbsScalar(*v); v++;
1952         }
1953         if (sum > ntemp) ntemp = sum;
1954       }
1955       ierr = MPI_Allreduce(&ntemp,norm,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1956     } else SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"No support for two norm");
1957   }
1958   PetscFunctionReturn(0);
1959 }
1960 
1961 #undef __FUNCT__
1962 #define __FUNCT__ "MatTranspose_MPIAIJ"
1963 PetscErrorCode MatTranspose_MPIAIJ(Mat A,MatReuse reuse,Mat *matout)
1964 {
1965   Mat_MPIAIJ     *a   = (Mat_MPIAIJ*)A->data;
1966   Mat_SeqAIJ     *Aloc=(Mat_SeqAIJ*)a->A->data,*Bloc=(Mat_SeqAIJ*)a->B->data;
1967   PetscErrorCode ierr;
1968   PetscInt       M      = A->rmap->N,N = A->cmap->N,ma,na,mb,nb,*ai,*aj,*bi,*bj,row,*cols,*cols_tmp,i;
1969   PetscInt       cstart = A->cmap->rstart,ncol;
1970   Mat            B;
1971   MatScalar      *array;
1972 
1973   PetscFunctionBegin;
1974   if (reuse == MAT_REUSE_MATRIX && A == *matout && M != N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Square matrix only for in-place");
1975 
1976   ma = A->rmap->n; na = A->cmap->n; mb = a->B->rmap->n; nb = a->B->cmap->n;
1977   ai = Aloc->i; aj = Aloc->j;
1978   bi = Bloc->i; bj = Bloc->j;
1979   if (reuse == MAT_INITIAL_MATRIX || *matout == A) {
1980     PetscInt             *d_nnz,*g_nnz,*o_nnz;
1981     PetscSFNode          *oloc;
1982     PETSC_UNUSED PetscSF sf;
1983 
1984     ierr = PetscMalloc4(na,&d_nnz,na,&o_nnz,nb,&g_nnz,nb,&oloc);CHKERRQ(ierr);
1985     /* compute d_nnz for preallocation */
1986     ierr = PetscMemzero(d_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1987     for (i=0; i<ai[ma]; i++) {
1988       d_nnz[aj[i]]++;
1989       aj[i] += cstart; /* global col index to be used by MatSetValues() */
1990     }
1991     /* compute local off-diagonal contributions */
1992     ierr = PetscMemzero(g_nnz,nb*sizeof(PetscInt));CHKERRQ(ierr);
1993     for (i=0; i<bi[ma]; i++) g_nnz[bj[i]]++;
1994     /* map those to global */
1995     ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1996     ierr = PetscSFSetGraphLayout(sf,A->cmap,nb,NULL,PETSC_USE_POINTER,a->garray);CHKERRQ(ierr);
1997     ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1998     ierr = PetscMemzero(o_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1999     ierr = PetscSFReduceBegin(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
2000     ierr = PetscSFReduceEnd(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
2001     ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
2002 
2003     ierr = MatCreate(PetscObjectComm((PetscObject)A),&B);CHKERRQ(ierr);
2004     ierr = MatSetSizes(B,A->cmap->n,A->rmap->n,N,M);CHKERRQ(ierr);
2005     ierr = MatSetBlockSizes(B,PetscAbs(A->cmap->bs),PetscAbs(A->rmap->bs));CHKERRQ(ierr);
2006     ierr = MatSetType(B,((PetscObject)A)->type_name);CHKERRQ(ierr);
2007     ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
2008     ierr = PetscFree4(d_nnz,o_nnz,g_nnz,oloc);CHKERRQ(ierr);
2009   } else {
2010     B    = *matout;
2011     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
2012     for (i=0; i<ai[ma]; i++) aj[i] += cstart; /* global col index to be used by MatSetValues() */
2013   }
2014 
2015   /* copy over the A part */
2016   array = Aloc->a;
2017   row   = A->rmap->rstart;
2018   for (i=0; i<ma; i++) {
2019     ncol = ai[i+1]-ai[i];
2020     ierr = MatSetValues(B,ncol,aj,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
2021     row++;
2022     array += ncol; aj += ncol;
2023   }
2024   aj = Aloc->j;
2025   for (i=0; i<ai[ma]; i++) aj[i] -= cstart; /* resume local col index */
2026 
2027   /* copy over the B part */
2028   ierr  = PetscCalloc1(bi[mb],&cols);CHKERRQ(ierr);
2029   array = Bloc->a;
2030   row   = A->rmap->rstart;
2031   for (i=0; i<bi[mb]; i++) cols[i] = a->garray[bj[i]];
2032   cols_tmp = cols;
2033   for (i=0; i<mb; i++) {
2034     ncol = bi[i+1]-bi[i];
2035     ierr = MatSetValues(B,ncol,cols_tmp,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
2036     row++;
2037     array += ncol; cols_tmp += ncol;
2038   }
2039   ierr = PetscFree(cols);CHKERRQ(ierr);
2040 
2041   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2042   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2043   if (reuse == MAT_INITIAL_MATRIX || *matout != A) {
2044     *matout = B;
2045   } else {
2046     ierr = MatHeaderMerge(A,B);CHKERRQ(ierr);
2047   }
2048   PetscFunctionReturn(0);
2049 }
2050 
2051 #undef __FUNCT__
2052 #define __FUNCT__ "MatDiagonalScale_MPIAIJ"
2053 PetscErrorCode MatDiagonalScale_MPIAIJ(Mat mat,Vec ll,Vec rr)
2054 {
2055   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2056   Mat            a    = aij->A,b = aij->B;
2057   PetscErrorCode ierr;
2058   PetscInt       s1,s2,s3;
2059 
2060   PetscFunctionBegin;
2061   ierr = MatGetLocalSize(mat,&s2,&s3);CHKERRQ(ierr);
2062   if (rr) {
2063     ierr = VecGetLocalSize(rr,&s1);CHKERRQ(ierr);
2064     if (s1!=s3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"right vector non-conforming local size");
2065     /* Overlap communication with computation. */
2066     ierr = VecScatterBegin(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2067   }
2068   if (ll) {
2069     ierr = VecGetLocalSize(ll,&s1);CHKERRQ(ierr);
2070     if (s1!=s2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"left vector non-conforming local size");
2071     ierr = (*b->ops->diagonalscale)(b,ll,0);CHKERRQ(ierr);
2072   }
2073   /* scale  the diagonal block */
2074   ierr = (*a->ops->diagonalscale)(a,ll,rr);CHKERRQ(ierr);
2075 
2076   if (rr) {
2077     /* Do a scatter end and then right scale the off-diagonal block */
2078     ierr = VecScatterEnd(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2079     ierr = (*b->ops->diagonalscale)(b,0,aij->lvec);CHKERRQ(ierr);
2080   }
2081   PetscFunctionReturn(0);
2082 }
2083 
2084 #undef __FUNCT__
2085 #define __FUNCT__ "MatSetUnfactored_MPIAIJ"
2086 PetscErrorCode MatSetUnfactored_MPIAIJ(Mat A)
2087 {
2088   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2089   PetscErrorCode ierr;
2090 
2091   PetscFunctionBegin;
2092   ierr = MatSetUnfactored(a->A);CHKERRQ(ierr);
2093   PetscFunctionReturn(0);
2094 }
2095 
2096 #undef __FUNCT__
2097 #define __FUNCT__ "MatEqual_MPIAIJ"
2098 PetscErrorCode MatEqual_MPIAIJ(Mat A,Mat B,PetscBool  *flag)
2099 {
2100   Mat_MPIAIJ     *matB = (Mat_MPIAIJ*)B->data,*matA = (Mat_MPIAIJ*)A->data;
2101   Mat            a,b,c,d;
2102   PetscBool      flg;
2103   PetscErrorCode ierr;
2104 
2105   PetscFunctionBegin;
2106   a = matA->A; b = matA->B;
2107   c = matB->A; d = matB->B;
2108 
2109   ierr = MatEqual(a,c,&flg);CHKERRQ(ierr);
2110   if (flg) {
2111     ierr = MatEqual(b,d,&flg);CHKERRQ(ierr);
2112   }
2113   ierr = MPI_Allreduce(&flg,flag,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
2114   PetscFunctionReturn(0);
2115 }
2116 
2117 #undef __FUNCT__
2118 #define __FUNCT__ "MatCopy_MPIAIJ"
2119 PetscErrorCode MatCopy_MPIAIJ(Mat A,Mat B,MatStructure str)
2120 {
2121   PetscErrorCode ierr;
2122   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2123   Mat_MPIAIJ     *b = (Mat_MPIAIJ*)B->data;
2124 
2125   PetscFunctionBegin;
2126   /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
2127   if ((str != SAME_NONZERO_PATTERN) || (A->ops->copy != B->ops->copy)) {
2128     /* because of the column compression in the off-processor part of the matrix a->B,
2129        the number of columns in a->B and b->B may be different, hence we cannot call
2130        the MatCopy() directly on the two parts. If need be, we can provide a more
2131        efficient copy than the MatCopy_Basic() by first uncompressing the a->B matrices
2132        then copying the submatrices */
2133     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
2134   } else {
2135     ierr = MatCopy(a->A,b->A,str);CHKERRQ(ierr);
2136     ierr = MatCopy(a->B,b->B,str);CHKERRQ(ierr);
2137   }
2138   PetscFunctionReturn(0);
2139 }
2140 
2141 #undef __FUNCT__
2142 #define __FUNCT__ "MatSetUp_MPIAIJ"
2143 PetscErrorCode MatSetUp_MPIAIJ(Mat A)
2144 {
2145   PetscErrorCode ierr;
2146 
2147   PetscFunctionBegin;
2148   ierr =  MatMPIAIJSetPreallocation(A,PETSC_DEFAULT,0,PETSC_DEFAULT,0);CHKERRQ(ierr);
2149   PetscFunctionReturn(0);
2150 }
2151 
2152 /*
2153    Computes the number of nonzeros per row needed for preallocation when X and Y
2154    have different nonzero structure.
2155 */
2156 #undef __FUNCT__
2157 #define __FUNCT__ "MatAXPYGetPreallocation_MPIX_private"
2158 PetscErrorCode MatAXPYGetPreallocation_MPIX_private(PetscInt m,const PetscInt *xi,const PetscInt *xj,const PetscInt *xltog,const PetscInt *yi,const PetscInt *yj,const PetscInt *yltog,PetscInt *nnz)
2159 {
2160   PetscInt       i,j,k,nzx,nzy;
2161 
2162   PetscFunctionBegin;
2163   /* Set the number of nonzeros in the new matrix */
2164   for (i=0; i<m; i++) {
2165     const PetscInt *xjj = xj+xi[i],*yjj = yj+yi[i];
2166     nzx = xi[i+1] - xi[i];
2167     nzy = yi[i+1] - yi[i];
2168     nnz[i] = 0;
2169     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2170       for (; k<nzy && yltog[yjj[k]]<xltog[xjj[j]]; k++) nnz[i]++; /* Catch up to X */
2171       if (k<nzy && yltog[yjj[k]]==xltog[xjj[j]]) k++;             /* Skip duplicate */
2172       nnz[i]++;
2173     }
2174     for (; k<nzy; k++) nnz[i]++;
2175   }
2176   PetscFunctionReturn(0);
2177 }
2178 
2179 /* This is the same as MatAXPYGetPreallocation_SeqAIJ, except that the local-to-global map is provided */
2180 #undef __FUNCT__
2181 #define __FUNCT__ "MatAXPYGetPreallocation_MPIAIJ"
2182 static PetscErrorCode MatAXPYGetPreallocation_MPIAIJ(Mat Y,const PetscInt *yltog,Mat X,const PetscInt *xltog,PetscInt *nnz)
2183 {
2184   PetscErrorCode ierr;
2185   PetscInt       m = Y->rmap->N;
2186   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data;
2187   Mat_SeqAIJ     *y = (Mat_SeqAIJ*)Y->data;
2188 
2189   PetscFunctionBegin;
2190   ierr = MatAXPYGetPreallocation_MPIX_private(m,x->i,x->j,xltog,y->i,y->j,yltog,nnz);CHKERRQ(ierr);
2191   PetscFunctionReturn(0);
2192 }
2193 
2194 #undef __FUNCT__
2195 #define __FUNCT__ "MatAXPY_MPIAIJ"
2196 PetscErrorCode MatAXPY_MPIAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
2197 {
2198   PetscErrorCode ierr;
2199   Mat_MPIAIJ     *xx = (Mat_MPIAIJ*)X->data,*yy = (Mat_MPIAIJ*)Y->data;
2200   PetscBLASInt   bnz,one=1;
2201   Mat_SeqAIJ     *x,*y;
2202 
2203   PetscFunctionBegin;
2204   if (str == SAME_NONZERO_PATTERN) {
2205     PetscScalar alpha = a;
2206     x    = (Mat_SeqAIJ*)xx->A->data;
2207     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2208     y    = (Mat_SeqAIJ*)yy->A->data;
2209     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2210     x    = (Mat_SeqAIJ*)xx->B->data;
2211     y    = (Mat_SeqAIJ*)yy->B->data;
2212     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2213     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2214     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
2215   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
2216     ierr = MatAXPY_Basic(Y,a,X,str);CHKERRQ(ierr);
2217   } else {
2218     Mat      B;
2219     PetscInt *nnz_d,*nnz_o;
2220     ierr = PetscMalloc1(yy->A->rmap->N,&nnz_d);CHKERRQ(ierr);
2221     ierr = PetscMalloc1(yy->B->rmap->N,&nnz_o);CHKERRQ(ierr);
2222     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
2223     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
2224     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
2225     ierr = MatSetBlockSizesFromMats(B,Y,Y);CHKERRQ(ierr);
2226     ierr = MatSetType(B,MATMPIAIJ);CHKERRQ(ierr);
2227     ierr = MatAXPYGetPreallocation_SeqAIJ(yy->A,xx->A,nnz_d);CHKERRQ(ierr);
2228     ierr = MatAXPYGetPreallocation_MPIAIJ(yy->B,yy->garray,xx->B,xx->garray,nnz_o);CHKERRQ(ierr);
2229     ierr = MatMPIAIJSetPreallocation(B,0,nnz_d,0,nnz_o);CHKERRQ(ierr);
2230     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
2231     ierr = MatHeaderReplace(Y,B);CHKERRQ(ierr);
2232     ierr = PetscFree(nnz_d);CHKERRQ(ierr);
2233     ierr = PetscFree(nnz_o);CHKERRQ(ierr);
2234   }
2235   PetscFunctionReturn(0);
2236 }
2237 
2238 extern PetscErrorCode  MatConjugate_SeqAIJ(Mat);
2239 
2240 #undef __FUNCT__
2241 #define __FUNCT__ "MatConjugate_MPIAIJ"
2242 PetscErrorCode  MatConjugate_MPIAIJ(Mat mat)
2243 {
2244 #if defined(PETSC_USE_COMPLEX)
2245   PetscErrorCode ierr;
2246   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2247 
2248   PetscFunctionBegin;
2249   ierr = MatConjugate_SeqAIJ(aij->A);CHKERRQ(ierr);
2250   ierr = MatConjugate_SeqAIJ(aij->B);CHKERRQ(ierr);
2251 #else
2252   PetscFunctionBegin;
2253 #endif
2254   PetscFunctionReturn(0);
2255 }
2256 
2257 #undef __FUNCT__
2258 #define __FUNCT__ "MatRealPart_MPIAIJ"
2259 PetscErrorCode MatRealPart_MPIAIJ(Mat A)
2260 {
2261   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2262   PetscErrorCode ierr;
2263 
2264   PetscFunctionBegin;
2265   ierr = MatRealPart(a->A);CHKERRQ(ierr);
2266   ierr = MatRealPart(a->B);CHKERRQ(ierr);
2267   PetscFunctionReturn(0);
2268 }
2269 
2270 #undef __FUNCT__
2271 #define __FUNCT__ "MatImaginaryPart_MPIAIJ"
2272 PetscErrorCode MatImaginaryPart_MPIAIJ(Mat A)
2273 {
2274   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2275   PetscErrorCode ierr;
2276 
2277   PetscFunctionBegin;
2278   ierr = MatImaginaryPart(a->A);CHKERRQ(ierr);
2279   ierr = MatImaginaryPart(a->B);CHKERRQ(ierr);
2280   PetscFunctionReturn(0);
2281 }
2282 
2283 #if defined(PETSC_HAVE_PBGL)
2284 
2285 #include <boost/parallel/mpi/bsp_process_group.hpp>
2286 #include <boost/graph/distributed/ilu_default_graph.hpp>
2287 #include <boost/graph/distributed/ilu_0_block.hpp>
2288 #include <boost/graph/distributed/ilu_preconditioner.hpp>
2289 #include <boost/graph/distributed/petsc/interface.hpp>
2290 #include <boost/multi_array.hpp>
2291 #include <boost/parallel/distributed_property_map->hpp>
2292 
2293 #undef __FUNCT__
2294 #define __FUNCT__ "MatILUFactorSymbolic_MPIAIJ"
2295 /*
2296   This uses the parallel ILU factorization of Peter Gottschling <pgottsch@osl.iu.edu>
2297 */
2298 PetscErrorCode MatILUFactorSymbolic_MPIAIJ(Mat fact,Mat A, IS isrow, IS iscol, const MatFactorInfo *info)
2299 {
2300   namespace petsc = boost::distributed::petsc;
2301 
2302   namespace graph_dist = boost::graph::distributed;
2303   using boost::graph::distributed::ilu_default::process_group_type;
2304   using boost::graph::ilu_permuted;
2305 
2306   PetscBool      row_identity, col_identity;
2307   PetscContainer c;
2308   PetscInt       m, n, M, N;
2309   PetscErrorCode ierr;
2310 
2311   PetscFunctionBegin;
2312   if (info->levels != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only levels = 0 supported for parallel ilu");
2313   ierr = ISIdentity(isrow, &row_identity);CHKERRQ(ierr);
2314   ierr = ISIdentity(iscol, &col_identity);CHKERRQ(ierr);
2315   if (!row_identity || !col_identity) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Row and column permutations must be identity for parallel ILU");
2316 
2317   process_group_type pg;
2318   typedef graph_dist::ilu_default::ilu_level_graph_type lgraph_type;
2319   lgraph_type  *lgraph_p   = new lgraph_type(petsc::num_global_vertices(A), pg, petsc::matrix_distribution(A, pg));
2320   lgraph_type& level_graph = *lgraph_p;
2321   graph_dist::ilu_default::graph_type&            graph(level_graph.graph);
2322 
2323   petsc::read_matrix(A, graph, get(boost::edge_weight, graph));
2324   ilu_permuted(level_graph);
2325 
2326   /* put together the new matrix */
2327   ierr = MatCreate(PetscObjectComm((PetscObject)A), fact);CHKERRQ(ierr);
2328   ierr = MatGetLocalSize(A, &m, &n);CHKERRQ(ierr);
2329   ierr = MatGetSize(A, &M, &N);CHKERRQ(ierr);
2330   ierr = MatSetSizes(fact, m, n, M, N);CHKERRQ(ierr);
2331   ierr = MatSetBlockSizesFromMats(fact,A,A);CHKERRQ(ierr);
2332   ierr = MatSetType(fact, ((PetscObject)A)->type_name);CHKERRQ(ierr);
2333   ierr = MatAssemblyBegin(fact, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2334   ierr = MatAssemblyEnd(fact, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2335 
2336   ierr = PetscContainerCreate(PetscObjectComm((PetscObject)A), &c);
2337   ierr = PetscContainerSetPointer(c, lgraph_p);
2338   ierr = PetscObjectCompose((PetscObject) (fact), "graph", (PetscObject) c);
2339   ierr = PetscContainerDestroy(&c);
2340   PetscFunctionReturn(0);
2341 }
2342 
2343 #undef __FUNCT__
2344 #define __FUNCT__ "MatLUFactorNumeric_MPIAIJ"
2345 PetscErrorCode MatLUFactorNumeric_MPIAIJ(Mat B,Mat A, const MatFactorInfo *info)
2346 {
2347   PetscFunctionBegin;
2348   PetscFunctionReturn(0);
2349 }
2350 
2351 #undef __FUNCT__
2352 #define __FUNCT__ "MatSolve_MPIAIJ"
2353 /*
2354   This uses the parallel ILU factorization of Peter Gottschling <pgottsch@osl.iu.edu>
2355 */
2356 PetscErrorCode MatSolve_MPIAIJ(Mat A, Vec b, Vec x)
2357 {
2358   namespace graph_dist = boost::graph::distributed;
2359 
2360   typedef graph_dist::ilu_default::ilu_level_graph_type lgraph_type;
2361   lgraph_type    *lgraph_p;
2362   PetscContainer c;
2363   PetscErrorCode ierr;
2364 
2365   PetscFunctionBegin;
2366   ierr = PetscObjectQuery((PetscObject) A, "graph", (PetscObject*) &c);CHKERRQ(ierr);
2367   ierr = PetscContainerGetPointer(c, (void**) &lgraph_p);CHKERRQ(ierr);
2368   ierr = VecCopy(b, x);CHKERRQ(ierr);
2369 
2370   PetscScalar *array_x;
2371   ierr = VecGetArray(x, &array_x);CHKERRQ(ierr);
2372   PetscInt sx;
2373   ierr = VecGetSize(x, &sx);CHKERRQ(ierr);
2374 
2375   PetscScalar *array_b;
2376   ierr = VecGetArray(b, &array_b);CHKERRQ(ierr);
2377   PetscInt sb;
2378   ierr = VecGetSize(b, &sb);CHKERRQ(ierr);
2379 
2380   lgraph_type& level_graph = *lgraph_p;
2381   graph_dist::ilu_default::graph_type&            graph(level_graph.graph);
2382 
2383   typedef boost::multi_array_ref<PetscScalar, 1> array_ref_type;
2384   array_ref_type                                 ref_b(array_b, boost::extents[num_vertices(graph)]);
2385   array_ref_type                                 ref_x(array_x, boost::extents[num_vertices(graph)]);
2386 
2387   typedef boost::iterator_property_map<array_ref_type::iterator,
2388                                        boost::property_map<graph_dist::ilu_default::graph_type, boost::vertex_index_t>::type>  gvector_type;
2389   gvector_type                                   vector_b(ref_b.begin(), get(boost::vertex_index, graph));
2390   gvector_type                                   vector_x(ref_x.begin(), get(boost::vertex_index, graph));
2391 
2392   ilu_set_solve(*lgraph_p, vector_b, vector_x);
2393   PetscFunctionReturn(0);
2394 }
2395 #endif
2396 
2397 #undef __FUNCT__
2398 #define __FUNCT__ "MatGetRowMaxAbs_MPIAIJ"
2399 PetscErrorCode MatGetRowMaxAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2400 {
2401   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2402   PetscErrorCode ierr;
2403   PetscInt       i,*idxb = 0;
2404   PetscScalar    *va,*vb;
2405   Vec            vtmp;
2406 
2407   PetscFunctionBegin;
2408   ierr = MatGetRowMaxAbs(a->A,v,idx);CHKERRQ(ierr);
2409   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2410   if (idx) {
2411     for (i=0; i<A->rmap->n; i++) {
2412       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2413     }
2414   }
2415 
2416   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2417   if (idx) {
2418     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2419   }
2420   ierr = MatGetRowMaxAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2421   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2422 
2423   for (i=0; i<A->rmap->n; i++) {
2424     if (PetscAbsScalar(va[i]) < PetscAbsScalar(vb[i])) {
2425       va[i] = vb[i];
2426       if (idx) idx[i] = a->garray[idxb[i]];
2427     }
2428   }
2429 
2430   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2431   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2432   ierr = PetscFree(idxb);CHKERRQ(ierr);
2433   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2434   PetscFunctionReturn(0);
2435 }
2436 
2437 #undef __FUNCT__
2438 #define __FUNCT__ "MatGetRowMinAbs_MPIAIJ"
2439 PetscErrorCode MatGetRowMinAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2440 {
2441   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2442   PetscErrorCode ierr;
2443   PetscInt       i,*idxb = 0;
2444   PetscScalar    *va,*vb;
2445   Vec            vtmp;
2446 
2447   PetscFunctionBegin;
2448   ierr = MatGetRowMinAbs(a->A,v,idx);CHKERRQ(ierr);
2449   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2450   if (idx) {
2451     for (i=0; i<A->cmap->n; i++) {
2452       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2453     }
2454   }
2455 
2456   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2457   if (idx) {
2458     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2459   }
2460   ierr = MatGetRowMinAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2461   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2462 
2463   for (i=0; i<A->rmap->n; i++) {
2464     if (PetscAbsScalar(va[i]) > PetscAbsScalar(vb[i])) {
2465       va[i] = vb[i];
2466       if (idx) idx[i] = a->garray[idxb[i]];
2467     }
2468   }
2469 
2470   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2471   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2472   ierr = PetscFree(idxb);CHKERRQ(ierr);
2473   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2474   PetscFunctionReturn(0);
2475 }
2476 
2477 #undef __FUNCT__
2478 #define __FUNCT__ "MatGetRowMin_MPIAIJ"
2479 PetscErrorCode MatGetRowMin_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2480 {
2481   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2482   PetscInt       n      = A->rmap->n;
2483   PetscInt       cstart = A->cmap->rstart;
2484   PetscInt       *cmap  = mat->garray;
2485   PetscInt       *diagIdx, *offdiagIdx;
2486   Vec            diagV, offdiagV;
2487   PetscScalar    *a, *diagA, *offdiagA;
2488   PetscInt       r;
2489   PetscErrorCode ierr;
2490 
2491   PetscFunctionBegin;
2492   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2493   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &diagV);CHKERRQ(ierr);
2494   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &offdiagV);CHKERRQ(ierr);
2495   ierr = MatGetRowMin(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2496   ierr = MatGetRowMin(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2497   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2498   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2499   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2500   for (r = 0; r < n; ++r) {
2501     if (PetscAbsScalar(diagA[r]) <= PetscAbsScalar(offdiagA[r])) {
2502       a[r]   = diagA[r];
2503       idx[r] = cstart + diagIdx[r];
2504     } else {
2505       a[r]   = offdiagA[r];
2506       idx[r] = cmap[offdiagIdx[r]];
2507     }
2508   }
2509   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2510   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2511   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2512   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2513   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2514   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2515   PetscFunctionReturn(0);
2516 }
2517 
2518 #undef __FUNCT__
2519 #define __FUNCT__ "MatGetRowMax_MPIAIJ"
2520 PetscErrorCode MatGetRowMax_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2521 {
2522   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2523   PetscInt       n      = A->rmap->n;
2524   PetscInt       cstart = A->cmap->rstart;
2525   PetscInt       *cmap  = mat->garray;
2526   PetscInt       *diagIdx, *offdiagIdx;
2527   Vec            diagV, offdiagV;
2528   PetscScalar    *a, *diagA, *offdiagA;
2529   PetscInt       r;
2530   PetscErrorCode ierr;
2531 
2532   PetscFunctionBegin;
2533   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2534   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &diagV);CHKERRQ(ierr);
2535   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &offdiagV);CHKERRQ(ierr);
2536   ierr = MatGetRowMax(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2537   ierr = MatGetRowMax(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2538   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2539   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2540   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2541   for (r = 0; r < n; ++r) {
2542     if (PetscAbsScalar(diagA[r]) >= PetscAbsScalar(offdiagA[r])) {
2543       a[r]   = diagA[r];
2544       idx[r] = cstart + diagIdx[r];
2545     } else {
2546       a[r]   = offdiagA[r];
2547       idx[r] = cmap[offdiagIdx[r]];
2548     }
2549   }
2550   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2551   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2552   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2553   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2554   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2555   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2556   PetscFunctionReturn(0);
2557 }
2558 
2559 #undef __FUNCT__
2560 #define __FUNCT__ "MatGetSeqNonzeroStructure_MPIAIJ"
2561 PetscErrorCode MatGetSeqNonzeroStructure_MPIAIJ(Mat mat,Mat *newmat)
2562 {
2563   PetscErrorCode ierr;
2564   Mat            *dummy;
2565 
2566   PetscFunctionBegin;
2567   ierr    = MatGetSubMatrix_MPIAIJ_All(mat,MAT_DO_NOT_GET_VALUES,MAT_INITIAL_MATRIX,&dummy);CHKERRQ(ierr);
2568   *newmat = *dummy;
2569   ierr    = PetscFree(dummy);CHKERRQ(ierr);
2570   PetscFunctionReturn(0);
2571 }
2572 
2573 #undef __FUNCT__
2574 #define __FUNCT__ "MatInvertBlockDiagonal_MPIAIJ"
2575 PetscErrorCode  MatInvertBlockDiagonal_MPIAIJ(Mat A,const PetscScalar **values)
2576 {
2577   Mat_MPIAIJ     *a = (Mat_MPIAIJ*) A->data;
2578   PetscErrorCode ierr;
2579 
2580   PetscFunctionBegin;
2581   ierr = MatInvertBlockDiagonal(a->A,values);CHKERRQ(ierr);
2582   PetscFunctionReturn(0);
2583 }
2584 
2585 #undef __FUNCT__
2586 #define __FUNCT__ "MatSetRandom_MPIAIJ"
2587 static PetscErrorCode  MatSetRandom_MPIAIJ(Mat x,PetscRandom rctx)
2588 {
2589   PetscErrorCode ierr;
2590   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)x->data;
2591 
2592   PetscFunctionBegin;
2593   ierr = MatSetRandom(aij->A,rctx);CHKERRQ(ierr);
2594   ierr = MatSetRandom(aij->B,rctx);CHKERRQ(ierr);
2595   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2596   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2597   PetscFunctionReturn(0);
2598 }
2599 
2600 #undef __FUNCT__
2601 #define __FUNCT__ "MatShift_MPIAIJ"
2602 PetscErrorCode MatShift_MPIAIJ(Mat Y,PetscScalar a)
2603 {
2604   PetscErrorCode ierr;
2605   Mat_MPIAIJ     *maij = (Mat_MPIAIJ*)Y->data;
2606   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)maij->A->data,*bij = (Mat_SeqAIJ*)maij->B->data;
2607 
2608   PetscFunctionBegin;
2609   if (!aij->nz && !bij->nz) {
2610     ierr = MatMPIAIJSetPreallocation(Y,1,NULL,0,NULL);CHKERRQ(ierr);
2611   }
2612   ierr = MatShift_Basic(Y,a);CHKERRQ(ierr);
2613   PetscFunctionReturn(0);
2614 }
2615 
2616 /* -------------------------------------------------------------------*/
2617 static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
2618                                        MatGetRow_MPIAIJ,
2619                                        MatRestoreRow_MPIAIJ,
2620                                        MatMult_MPIAIJ,
2621                                 /* 4*/ MatMultAdd_MPIAIJ,
2622                                        MatMultTranspose_MPIAIJ,
2623                                        MatMultTransposeAdd_MPIAIJ,
2624 #if defined(PETSC_HAVE_PBGL)
2625                                        MatSolve_MPIAIJ,
2626 #else
2627                                        0,
2628 #endif
2629                                        0,
2630                                        0,
2631                                 /*10*/ 0,
2632                                        0,
2633                                        0,
2634                                        MatSOR_MPIAIJ,
2635                                        MatTranspose_MPIAIJ,
2636                                 /*15*/ MatGetInfo_MPIAIJ,
2637                                        MatEqual_MPIAIJ,
2638                                        MatGetDiagonal_MPIAIJ,
2639                                        MatDiagonalScale_MPIAIJ,
2640                                        MatNorm_MPIAIJ,
2641                                 /*20*/ MatAssemblyBegin_MPIAIJ,
2642                                        MatAssemblyEnd_MPIAIJ,
2643                                        MatSetOption_MPIAIJ,
2644                                        MatZeroEntries_MPIAIJ,
2645                                 /*24*/ MatZeroRows_MPIAIJ,
2646                                        0,
2647 #if defined(PETSC_HAVE_PBGL)
2648                                        0,
2649 #else
2650                                        0,
2651 #endif
2652                                        0,
2653                                        0,
2654                                 /*29*/ MatSetUp_MPIAIJ,
2655 #if defined(PETSC_HAVE_PBGL)
2656                                        0,
2657 #else
2658                                        0,
2659 #endif
2660                                        0,
2661                                        0,
2662                                        0,
2663                                 /*34*/ MatDuplicate_MPIAIJ,
2664                                        0,
2665                                        0,
2666                                        0,
2667                                        0,
2668                                 /*39*/ MatAXPY_MPIAIJ,
2669                                        MatGetSubMatrices_MPIAIJ,
2670                                        MatIncreaseOverlap_MPIAIJ,
2671                                        MatGetValues_MPIAIJ,
2672                                        MatCopy_MPIAIJ,
2673                                 /*44*/ MatGetRowMax_MPIAIJ,
2674                                        MatScale_MPIAIJ,
2675                                        MatShift_MPIAIJ,
2676                                        MatDiagonalSet_MPIAIJ,
2677                                        MatZeroRowsColumns_MPIAIJ,
2678                                 /*49*/ MatSetRandom_MPIAIJ,
2679                                        0,
2680                                        0,
2681                                        0,
2682                                        0,
2683                                 /*54*/ MatFDColoringCreate_MPIXAIJ,
2684                                        0,
2685                                        MatSetUnfactored_MPIAIJ,
2686                                        MatPermute_MPIAIJ,
2687                                        0,
2688                                 /*59*/ MatGetSubMatrix_MPIAIJ,
2689                                        MatDestroy_MPIAIJ,
2690                                        MatView_MPIAIJ,
2691                                        0,
2692                                        MatMatMatMult_MPIAIJ_MPIAIJ_MPIAIJ,
2693                                 /*64*/ MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ,
2694                                        MatMatMatMultNumeric_MPIAIJ_MPIAIJ_MPIAIJ,
2695                                        0,
2696                                        0,
2697                                        0,
2698                                 /*69*/ MatGetRowMaxAbs_MPIAIJ,
2699                                        MatGetRowMinAbs_MPIAIJ,
2700                                        0,
2701                                        MatSetColoring_MPIAIJ,
2702                                        0,
2703                                        MatSetValuesAdifor_MPIAIJ,
2704                                 /*75*/ MatFDColoringApply_AIJ,
2705                                        0,
2706                                        0,
2707                                        0,
2708                                        MatFindZeroDiagonals_MPIAIJ,
2709                                 /*80*/ 0,
2710                                        0,
2711                                        0,
2712                                 /*83*/ MatLoad_MPIAIJ,
2713                                        0,
2714                                        0,
2715                                        0,
2716                                        0,
2717                                        0,
2718                                 /*89*/ MatMatMult_MPIAIJ_MPIAIJ,
2719                                        MatMatMultSymbolic_MPIAIJ_MPIAIJ,
2720                                        MatMatMultNumeric_MPIAIJ_MPIAIJ,
2721                                        MatPtAP_MPIAIJ_MPIAIJ,
2722                                        MatPtAPSymbolic_MPIAIJ_MPIAIJ,
2723                                 /*94*/ MatPtAPNumeric_MPIAIJ_MPIAIJ,
2724                                        0,
2725                                        0,
2726                                        0,
2727                                        0,
2728                                 /*99*/ 0,
2729                                        0,
2730                                        0,
2731                                        MatConjugate_MPIAIJ,
2732                                        0,
2733                                 /*104*/MatSetValuesRow_MPIAIJ,
2734                                        MatRealPart_MPIAIJ,
2735                                        MatImaginaryPart_MPIAIJ,
2736                                        0,
2737                                        0,
2738                                 /*109*/0,
2739                                        0,
2740                                        MatGetRowMin_MPIAIJ,
2741                                        0,
2742                                        0,
2743                                 /*114*/MatGetSeqNonzeroStructure_MPIAIJ,
2744                                        0,
2745                                        MatGetGhosts_MPIAIJ,
2746                                        0,
2747                                        0,
2748                                 /*119*/0,
2749                                        0,
2750                                        0,
2751                                        0,
2752                                        MatGetMultiProcBlock_MPIAIJ,
2753                                 /*124*/MatFindNonzeroRows_MPIAIJ,
2754                                        MatGetColumnNorms_MPIAIJ,
2755                                        MatInvertBlockDiagonal_MPIAIJ,
2756                                        0,
2757                                        MatGetSubMatricesMPI_MPIAIJ,
2758                                 /*129*/0,
2759                                        MatTransposeMatMult_MPIAIJ_MPIAIJ,
2760                                        MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ,
2761                                        MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ,
2762                                        0,
2763                                 /*134*/0,
2764                                        0,
2765                                        0,
2766                                        0,
2767                                        0,
2768                                 /*139*/0,
2769                                        0,
2770                                        0,
2771                                        MatFDColoringSetUp_MPIXAIJ,
2772                                        MatFindOffBlockDiagonalEntries_MPIAIJ,
2773                                 /*144*/MatCreateMPIMatConcatenateSeqMat_MPIAIJ
2774 };
2775 
2776 /* ----------------------------------------------------------------------------------------*/
2777 
2778 #undef __FUNCT__
2779 #define __FUNCT__ "MatStoreValues_MPIAIJ"
2780 PetscErrorCode  MatStoreValues_MPIAIJ(Mat mat)
2781 {
2782   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2783   PetscErrorCode ierr;
2784 
2785   PetscFunctionBegin;
2786   ierr = MatStoreValues(aij->A);CHKERRQ(ierr);
2787   ierr = MatStoreValues(aij->B);CHKERRQ(ierr);
2788   PetscFunctionReturn(0);
2789 }
2790 
2791 #undef __FUNCT__
2792 #define __FUNCT__ "MatRetrieveValues_MPIAIJ"
2793 PetscErrorCode  MatRetrieveValues_MPIAIJ(Mat mat)
2794 {
2795   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2796   PetscErrorCode ierr;
2797 
2798   PetscFunctionBegin;
2799   ierr = MatRetrieveValues(aij->A);CHKERRQ(ierr);
2800   ierr = MatRetrieveValues(aij->B);CHKERRQ(ierr);
2801   PetscFunctionReturn(0);
2802 }
2803 
2804 #undef __FUNCT__
2805 #define __FUNCT__ "MatMPIAIJSetPreallocation_MPIAIJ"
2806 PetscErrorCode  MatMPIAIJSetPreallocation_MPIAIJ(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
2807 {
2808   Mat_MPIAIJ     *b;
2809   PetscErrorCode ierr;
2810 
2811   PetscFunctionBegin;
2812   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
2813   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
2814   b = (Mat_MPIAIJ*)B->data;
2815 
2816   if (!B->preallocated) {
2817     /* Explicitly create 2 MATSEQAIJ matrices. */
2818     ierr = MatCreate(PETSC_COMM_SELF,&b->A);CHKERRQ(ierr);
2819     ierr = MatSetSizes(b->A,B->rmap->n,B->cmap->n,B->rmap->n,B->cmap->n);CHKERRQ(ierr);
2820     ierr = MatSetBlockSizesFromMats(b->A,B,B);CHKERRQ(ierr);
2821     ierr = MatSetType(b->A,MATSEQAIJ);CHKERRQ(ierr);
2822     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->A);CHKERRQ(ierr);
2823     ierr = MatCreate(PETSC_COMM_SELF,&b->B);CHKERRQ(ierr);
2824     ierr = MatSetSizes(b->B,B->rmap->n,B->cmap->N,B->rmap->n,B->cmap->N);CHKERRQ(ierr);
2825     ierr = MatSetBlockSizesFromMats(b->B,B,B);CHKERRQ(ierr);
2826     ierr = MatSetType(b->B,MATSEQAIJ);CHKERRQ(ierr);
2827     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->B);CHKERRQ(ierr);
2828   }
2829 
2830   ierr = MatSeqAIJSetPreallocation(b->A,d_nz,d_nnz);CHKERRQ(ierr);
2831   ierr = MatSeqAIJSetPreallocation(b->B,o_nz,o_nnz);CHKERRQ(ierr);
2832   B->preallocated = PETSC_TRUE;
2833   PetscFunctionReturn(0);
2834 }
2835 
2836 #undef __FUNCT__
2837 #define __FUNCT__ "MatDuplicate_MPIAIJ"
2838 PetscErrorCode MatDuplicate_MPIAIJ(Mat matin,MatDuplicateOption cpvalues,Mat *newmat)
2839 {
2840   Mat            mat;
2841   Mat_MPIAIJ     *a,*oldmat = (Mat_MPIAIJ*)matin->data;
2842   PetscErrorCode ierr;
2843 
2844   PetscFunctionBegin;
2845   *newmat = 0;
2846   ierr    = MatCreate(PetscObjectComm((PetscObject)matin),&mat);CHKERRQ(ierr);
2847   ierr    = MatSetSizes(mat,matin->rmap->n,matin->cmap->n,matin->rmap->N,matin->cmap->N);CHKERRQ(ierr);
2848   ierr    = MatSetBlockSizesFromMats(mat,matin,matin);CHKERRQ(ierr);
2849   ierr    = MatSetType(mat,((PetscObject)matin)->type_name);CHKERRQ(ierr);
2850   ierr    = PetscMemcpy(mat->ops,matin->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
2851   a       = (Mat_MPIAIJ*)mat->data;
2852 
2853   mat->factortype   = matin->factortype;
2854   mat->assembled    = PETSC_TRUE;
2855   mat->insertmode   = NOT_SET_VALUES;
2856   mat->preallocated = PETSC_TRUE;
2857 
2858   a->size         = oldmat->size;
2859   a->rank         = oldmat->rank;
2860   a->donotstash   = oldmat->donotstash;
2861   a->roworiented  = oldmat->roworiented;
2862   a->rowindices   = 0;
2863   a->rowvalues    = 0;
2864   a->getrowactive = PETSC_FALSE;
2865 
2866   ierr = PetscLayoutReference(matin->rmap,&mat->rmap);CHKERRQ(ierr);
2867   ierr = PetscLayoutReference(matin->cmap,&mat->cmap);CHKERRQ(ierr);
2868 
2869   if (oldmat->colmap) {
2870 #if defined(PETSC_USE_CTABLE)
2871     ierr = PetscTableCreateCopy(oldmat->colmap,&a->colmap);CHKERRQ(ierr);
2872 #else
2873     ierr = PetscMalloc1(mat->cmap->N,&a->colmap);CHKERRQ(ierr);
2874     ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2875     ierr = PetscMemcpy(a->colmap,oldmat->colmap,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2876 #endif
2877   } else a->colmap = 0;
2878   if (oldmat->garray) {
2879     PetscInt len;
2880     len  = oldmat->B->cmap->n;
2881     ierr = PetscMalloc1(len+1,&a->garray);CHKERRQ(ierr);
2882     ierr = PetscLogObjectMemory((PetscObject)mat,len*sizeof(PetscInt));CHKERRQ(ierr);
2883     if (len) { ierr = PetscMemcpy(a->garray,oldmat->garray,len*sizeof(PetscInt));CHKERRQ(ierr); }
2884   } else a->garray = 0;
2885 
2886   ierr    = VecDuplicate(oldmat->lvec,&a->lvec);CHKERRQ(ierr);
2887   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->lvec);CHKERRQ(ierr);
2888   ierr    = VecScatterCopy(oldmat->Mvctx,&a->Mvctx);CHKERRQ(ierr);
2889   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->Mvctx);CHKERRQ(ierr);
2890   ierr    = MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
2891   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->A);CHKERRQ(ierr);
2892   ierr    = MatDuplicate(oldmat->B,cpvalues,&a->B);CHKERRQ(ierr);
2893   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->B);CHKERRQ(ierr);
2894   ierr    = PetscFunctionListDuplicate(((PetscObject)matin)->qlist,&((PetscObject)mat)->qlist);CHKERRQ(ierr);
2895   *newmat = mat;
2896   PetscFunctionReturn(0);
2897 }
2898 
2899 
2900 
2901 #undef __FUNCT__
2902 #define __FUNCT__ "MatLoad_MPIAIJ"
2903 PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
2904 {
2905   PetscScalar    *vals,*svals;
2906   MPI_Comm       comm;
2907   PetscErrorCode ierr;
2908   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
2909   PetscInt       i,nz,j,rstart,rend,mmax,maxnz = 0;
2910   PetscInt       header[4],*rowlengths = 0,M,N,m,*cols;
2911   PetscInt       *ourlens = NULL,*procsnz = NULL,*offlens = NULL,jj,*mycols,*smycols;
2912   PetscInt       cend,cstart,n,*rowners;
2913   int            fd;
2914   PetscInt       bs = newMat->rmap->bs;
2915 
2916   PetscFunctionBegin;
2917   /* force binary viewer to load .info file if it has not yet done so */
2918   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
2919   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
2920   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2921   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2922   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
2923   if (!rank) {
2924     ierr = PetscBinaryRead(fd,(char*)header,4,PETSC_INT);CHKERRQ(ierr);
2925     if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
2926   }
2927 
2928   ierr = PetscOptionsBegin(comm,NULL,"Options for loading MPIAIJ matrix","Mat");CHKERRQ(ierr);
2929   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
2930   ierr = PetscOptionsEnd();CHKERRQ(ierr);
2931   if (bs < 0) bs = 1;
2932 
2933   ierr = MPI_Bcast(header+1,3,MPIU_INT,0,comm);CHKERRQ(ierr);
2934   M    = header[1]; N = header[2];
2935 
2936   /* If global sizes are set, check if they are consistent with that given in the file */
2937   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);
2938   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);
2939 
2940   /* determine ownership of all (block) rows */
2941   if (M%bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Inconsistent # of rows (%d) and block size (%d)",M,bs);
2942   if (newMat->rmap->n < 0) m = bs*((M/bs)/size + (((M/bs) % size) > rank));    /* PETSC_DECIDE */
2943   else m = newMat->rmap->n; /* Set by user */
2944 
2945   ierr = PetscMalloc1(size+1,&rowners);CHKERRQ(ierr);
2946   ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
2947 
2948   /* First process needs enough room for process with most rows */
2949   if (!rank) {
2950     mmax = rowners[1];
2951     for (i=2; i<=size; i++) {
2952       mmax = PetscMax(mmax, rowners[i]);
2953     }
2954   } else mmax = -1;             /* unused, but compilers complain */
2955 
2956   rowners[0] = 0;
2957   for (i=2; i<=size; i++) {
2958     rowners[i] += rowners[i-1];
2959   }
2960   rstart = rowners[rank];
2961   rend   = rowners[rank+1];
2962 
2963   /* distribute row lengths to all processors */
2964   ierr = PetscMalloc2(m,&ourlens,m,&offlens);CHKERRQ(ierr);
2965   if (!rank) {
2966     ierr = PetscBinaryRead(fd,ourlens,m,PETSC_INT);CHKERRQ(ierr);
2967     ierr = PetscMalloc1(mmax,&rowlengths);CHKERRQ(ierr);
2968     ierr = PetscCalloc1(size,&procsnz);CHKERRQ(ierr);
2969     for (j=0; j<m; j++) {
2970       procsnz[0] += ourlens[j];
2971     }
2972     for (i=1; i<size; i++) {
2973       ierr = PetscBinaryRead(fd,rowlengths,rowners[i+1]-rowners[i],PETSC_INT);CHKERRQ(ierr);
2974       /* calculate the number of nonzeros on each processor */
2975       for (j=0; j<rowners[i+1]-rowners[i]; j++) {
2976         procsnz[i] += rowlengths[j];
2977       }
2978       ierr = MPIULong_Send(rowlengths,rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2979     }
2980     ierr = PetscFree(rowlengths);CHKERRQ(ierr);
2981   } else {
2982     ierr = MPIULong_Recv(ourlens,m,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2983   }
2984 
2985   if (!rank) {
2986     /* determine max buffer needed and allocate it */
2987     maxnz = 0;
2988     for (i=0; i<size; i++) {
2989       maxnz = PetscMax(maxnz,procsnz[i]);
2990     }
2991     ierr = PetscMalloc1(maxnz,&cols);CHKERRQ(ierr);
2992 
2993     /* read in my part of the matrix column indices  */
2994     nz   = procsnz[0];
2995     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2996     ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);
2997 
2998     /* read in every one elses and ship off */
2999     for (i=1; i<size; i++) {
3000       nz   = procsnz[i];
3001       ierr = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
3002       ierr = MPIULong_Send(cols,nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
3003     }
3004     ierr = PetscFree(cols);CHKERRQ(ierr);
3005   } else {
3006     /* determine buffer space needed for message */
3007     nz = 0;
3008     for (i=0; i<m; i++) {
3009       nz += ourlens[i];
3010     }
3011     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
3012 
3013     /* receive message of column indices*/
3014     ierr = MPIULong_Recv(mycols,nz,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
3015   }
3016 
3017   /* determine column ownership if matrix is not square */
3018   if (N != M) {
3019     if (newMat->cmap->n < 0) n = N/size + ((N % size) > rank);
3020     else n = newMat->cmap->n;
3021     ierr   = MPI_Scan(&n,&cend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3022     cstart = cend - n;
3023   } else {
3024     cstart = rstart;
3025     cend   = rend;
3026     n      = cend - cstart;
3027   }
3028 
3029   /* loop over local rows, determining number of off diagonal entries */
3030   ierr = PetscMemzero(offlens,m*sizeof(PetscInt));CHKERRQ(ierr);
3031   jj   = 0;
3032   for (i=0; i<m; i++) {
3033     for (j=0; j<ourlens[i]; j++) {
3034       if (mycols[jj] < cstart || mycols[jj] >= cend) offlens[i]++;
3035       jj++;
3036     }
3037   }
3038 
3039   for (i=0; i<m; i++) {
3040     ourlens[i] -= offlens[i];
3041   }
3042   ierr = MatSetSizes(newMat,m,n,M,N);CHKERRQ(ierr);
3043 
3044   if (bs > 1) {ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);}
3045 
3046   ierr = MatMPIAIJSetPreallocation(newMat,0,ourlens,0,offlens);CHKERRQ(ierr);
3047 
3048   for (i=0; i<m; i++) {
3049     ourlens[i] += offlens[i];
3050   }
3051 
3052   if (!rank) {
3053     ierr = PetscMalloc1(maxnz+1,&vals);CHKERRQ(ierr);
3054 
3055     /* read in my part of the matrix numerical values  */
3056     nz   = procsnz[0];
3057     ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
3058 
3059     /* insert into matrix */
3060     jj      = rstart;
3061     smycols = mycols;
3062     svals   = vals;
3063     for (i=0; i<m; i++) {
3064       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
3065       smycols += ourlens[i];
3066       svals   += ourlens[i];
3067       jj++;
3068     }
3069 
3070     /* read in other processors and ship out */
3071     for (i=1; i<size; i++) {
3072       nz   = procsnz[i];
3073       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
3074       ierr = MPIULong_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
3075     }
3076     ierr = PetscFree(procsnz);CHKERRQ(ierr);
3077   } else {
3078     /* receive numeric values */
3079     ierr = PetscMalloc1(nz+1,&vals);CHKERRQ(ierr);
3080 
3081     /* receive message of values*/
3082     ierr = MPIULong_Recv(vals,nz,MPIU_SCALAR,0,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
3083 
3084     /* insert into matrix */
3085     jj      = rstart;
3086     smycols = mycols;
3087     svals   = vals;
3088     for (i=0; i<m; i++) {
3089       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
3090       smycols += ourlens[i];
3091       svals   += ourlens[i];
3092       jj++;
3093     }
3094   }
3095   ierr = PetscFree2(ourlens,offlens);CHKERRQ(ierr);
3096   ierr = PetscFree(vals);CHKERRQ(ierr);
3097   ierr = PetscFree(mycols);CHKERRQ(ierr);
3098   ierr = PetscFree(rowners);CHKERRQ(ierr);
3099   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3100   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3101   PetscFunctionReturn(0);
3102 }
3103 
3104 #undef __FUNCT__
3105 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ"
3106 /* TODO: Not scalable because of ISAllGather(). */
3107 PetscErrorCode MatGetSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3108 {
3109   PetscErrorCode ierr;
3110   IS             iscol_local;
3111   PetscInt       csize;
3112 
3113   PetscFunctionBegin;
3114   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3115   if (call == MAT_REUSE_MATRIX) {
3116     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3117     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3118   } else {
3119     PetscInt cbs;
3120     ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
3121     ierr = ISAllGather(iscol,&iscol_local);CHKERRQ(ierr);
3122     ierr = ISSetBlockSize(iscol_local,cbs);CHKERRQ(ierr);
3123   }
3124   ierr = MatGetSubMatrix_MPIAIJ_Private(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
3125   if (call == MAT_INITIAL_MATRIX) {
3126     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3127     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3128   }
3129   PetscFunctionReturn(0);
3130 }
3131 
3132 extern PetscErrorCode MatGetSubMatrices_MPIAIJ_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool*,Mat*);
3133 #undef __FUNCT__
3134 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ_Private"
3135 /*
3136     Not great since it makes two copies of the submatrix, first an SeqAIJ
3137   in local and then by concatenating the local matrices the end result.
3138   Writing it directly would be much like MatGetSubMatrices_MPIAIJ()
3139 
3140   Note: This requires a sequential iscol with all indices.
3141 */
3142 PetscErrorCode MatGetSubMatrix_MPIAIJ_Private(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3143 {
3144   PetscErrorCode ierr;
3145   PetscMPIInt    rank,size;
3146   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3147   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal,ncol;
3148   PetscBool      allcolumns, colflag;
3149   Mat            M,Mreuse;
3150   MatScalar      *vwork,*aa;
3151   MPI_Comm       comm;
3152   Mat_SeqAIJ     *aij;
3153 
3154   PetscFunctionBegin;
3155   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3156   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3157   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3158 
3159   ierr = ISIdentity(iscol,&colflag);CHKERRQ(ierr);
3160   ierr = ISGetLocalSize(iscol,&ncol);CHKERRQ(ierr);
3161   if (colflag && ncol == mat->cmap->N) {
3162     allcolumns = PETSC_TRUE;
3163   } else {
3164     allcolumns = PETSC_FALSE;
3165   }
3166   if (call ==  MAT_REUSE_MATRIX) {
3167     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3168     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3169     ierr = MatGetSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,&allcolumns,&Mreuse);CHKERRQ(ierr);
3170   } else {
3171     ierr = MatGetSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&allcolumns,&Mreuse);CHKERRQ(ierr);
3172   }
3173 
3174   /*
3175       m - number of local rows
3176       n - number of columns (same on all processors)
3177       rstart - first row in new global matrix generated
3178   */
3179   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3180   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3181   if (call == MAT_INITIAL_MATRIX) {
3182     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3183     ii  = aij->i;
3184     jj  = aij->j;
3185 
3186     /*
3187         Determine the number of non-zeros in the diagonal and off-diagonal
3188         portions of the matrix in order to do correct preallocation
3189     */
3190 
3191     /* first get start and end of "diagonal" columns */
3192     if (csize == PETSC_DECIDE) {
3193       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3194       if (mglobal == n) { /* square matrix */
3195         nlocal = m;
3196       } else {
3197         nlocal = n/size + ((n % size) > rank);
3198       }
3199     } else {
3200       nlocal = csize;
3201     }
3202     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3203     rstart = rend - nlocal;
3204     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);
3205 
3206     /* next, compute all the lengths */
3207     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3208     olens = dlens + m;
3209     for (i=0; i<m; i++) {
3210       jend = ii[i+1] - ii[i];
3211       olen = 0;
3212       dlen = 0;
3213       for (j=0; j<jend; j++) {
3214         if (*jj < rstart || *jj >= rend) olen++;
3215         else dlen++;
3216         jj++;
3217       }
3218       olens[i] = olen;
3219       dlens[i] = dlen;
3220     }
3221     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3222     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3223     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3224     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3225     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3226     ierr = PetscFree(dlens);CHKERRQ(ierr);
3227   } else {
3228     PetscInt ml,nl;
3229 
3230     M    = *newmat;
3231     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3232     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3233     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3234     /*
3235          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3236        rather than the slower MatSetValues().
3237     */
3238     M->was_assembled = PETSC_TRUE;
3239     M->assembled     = PETSC_FALSE;
3240   }
3241   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3242   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3243   ii   = aij->i;
3244   jj   = aij->j;
3245   aa   = aij->a;
3246   for (i=0; i<m; i++) {
3247     row   = rstart + i;
3248     nz    = ii[i+1] - ii[i];
3249     cwork = jj;     jj += nz;
3250     vwork = aa;     aa += nz;
3251     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3252   }
3253 
3254   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3255   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3256   *newmat = M;
3257 
3258   /* save submatrix used in processor for next request */
3259   if (call ==  MAT_INITIAL_MATRIX) {
3260     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3261     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3262   }
3263   PetscFunctionReturn(0);
3264 }
3265 
3266 #undef __FUNCT__
3267 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR_MPIAIJ"
3268 PetscErrorCode  MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3269 {
3270   PetscInt       m,cstart, cend,j,nnz,i,d;
3271   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3272   const PetscInt *JJ;
3273   PetscScalar    *values;
3274   PetscErrorCode ierr;
3275 
3276   PetscFunctionBegin;
3277   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3278 
3279   ierr   = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3280   ierr   = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3281   m      = B->rmap->n;
3282   cstart = B->cmap->rstart;
3283   cend   = B->cmap->rend;
3284   rstart = B->rmap->rstart;
3285 
3286   ierr = PetscMalloc2(m,&d_nnz,m,&o_nnz);CHKERRQ(ierr);
3287 
3288 #if defined(PETSC_USE_DEBUGGING)
3289   for (i=0; i<m; i++) {
3290     nnz = Ii[i+1]- Ii[i];
3291     JJ  = J + Ii[i];
3292     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3293     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3294     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);
3295   }
3296 #endif
3297 
3298   for (i=0; i<m; i++) {
3299     nnz     = Ii[i+1]- Ii[i];
3300     JJ      = J + Ii[i];
3301     nnz_max = PetscMax(nnz_max,nnz);
3302     d       = 0;
3303     for (j=0; j<nnz; j++) {
3304       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3305     }
3306     d_nnz[i] = d;
3307     o_nnz[i] = nnz - d;
3308   }
3309   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3310   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3311 
3312   if (v) values = (PetscScalar*)v;
3313   else {
3314     ierr = PetscCalloc1(nnz_max+1,&values);CHKERRQ(ierr);
3315   }
3316 
3317   for (i=0; i<m; i++) {
3318     ii   = i + rstart;
3319     nnz  = Ii[i+1]- Ii[i];
3320     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3321   }
3322   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3323   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3324 
3325   if (!v) {
3326     ierr = PetscFree(values);CHKERRQ(ierr);
3327   }
3328   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3329   PetscFunctionReturn(0);
3330 }
3331 
3332 #undef __FUNCT__
3333 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR"
3334 /*@
3335    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3336    (the default parallel PETSc format).
3337 
3338    Collective on MPI_Comm
3339 
3340    Input Parameters:
3341 +  B - the matrix
3342 .  i - the indices into j for the start of each local row (starts with zero)
3343 .  j - the column indices for each local row (starts with zero)
3344 -  v - optional values in the matrix
3345 
3346    Level: developer
3347 
3348    Notes:
3349        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3350      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3351      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3352 
3353        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3354 
3355        The format which is used for the sparse matrix input, is equivalent to a
3356     row-major ordering.. i.e for the following matrix, the input data expected is
3357     as shown
3358 
3359 $        1 0 0
3360 $        2 0 3     P0
3361 $       -------
3362 $        4 5 6     P1
3363 $
3364 $     Process0 [P0]: rows_owned=[0,1]
3365 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3366 $        j =  {0,0,2}  [size = 3]
3367 $        v =  {1,2,3}  [size = 3]
3368 $
3369 $     Process1 [P1]: rows_owned=[2]
3370 $        i =  {0,3}    [size = nrow+1  = 1+1]
3371 $        j =  {0,1,2}  [size = 3]
3372 $        v =  {4,5,6}  [size = 3]
3373 
3374 .keywords: matrix, aij, compressed row, sparse, parallel
3375 
3376 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MPIAIJ,
3377           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3378 @*/
3379 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3380 {
3381   PetscErrorCode ierr;
3382 
3383   PetscFunctionBegin;
3384   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3385   PetscFunctionReturn(0);
3386 }
3387 
3388 #undef __FUNCT__
3389 #define __FUNCT__ "MatMPIAIJSetPreallocation"
3390 /*@C
3391    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3392    (the default parallel PETSc format).  For good matrix assembly performance
3393    the user should preallocate the matrix storage by setting the parameters
3394    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3395    performance can be increased by more than a factor of 50.
3396 
3397    Collective on MPI_Comm
3398 
3399    Input Parameters:
3400 +  B - the matrix
3401 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3402            (same value is used for all local rows)
3403 .  d_nnz - array containing the number of nonzeros in the various rows of the
3404            DIAGONAL portion of the local submatrix (possibly different for each row)
3405            or NULL (PETSC_NULL_INTEGER in Fortran), if d_nz is used to specify the nonzero structure.
3406            The size of this array is equal to the number of local rows, i.e 'm'.
3407            For matrices that will be factored, you must leave room for (and set)
3408            the diagonal entry even if it is zero.
3409 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3410            submatrix (same value is used for all local rows).
3411 -  o_nnz - array containing the number of nonzeros in the various rows of the
3412            OFF-DIAGONAL portion of the local submatrix (possibly different for
3413            each row) or NULL (PETSC_NULL_INTEGER in Fortran), if o_nz is used to specify the nonzero
3414            structure. The size of this array is equal to the number
3415            of local rows, i.e 'm'.
3416 
3417    If the *_nnz parameter is given then the *_nz parameter is ignored
3418 
3419    The AIJ format (also called the Yale sparse matrix format or
3420    compressed row storage (CSR)), is fully compatible with standard Fortran 77
3421    storage.  The stored row and column indices begin with zero.
3422    See Users-Manual: ch_mat for details.
3423 
3424    The parallel matrix is partitioned such that the first m0 rows belong to
3425    process 0, the next m1 rows belong to process 1, the next m2 rows belong
3426    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
3427 
3428    The DIAGONAL portion of the local submatrix of a processor can be defined
3429    as the submatrix which is obtained by extraction the part corresponding to
3430    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
3431    first row that belongs to the processor, r2 is the last row belonging to
3432    the this processor, and c1-c2 is range of indices of the local part of a
3433    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
3434    common case of a square matrix, the row and column ranges are the same and
3435    the DIAGONAL part is also square. The remaining portion of the local
3436    submatrix (mxN) constitute the OFF-DIAGONAL portion.
3437 
3438    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3439 
3440    You can call MatGetInfo() to get information on how effective the preallocation was;
3441    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3442    You can also run with the option -info and look for messages with the string
3443    malloc in them to see if additional memory allocation was needed.
3444 
3445    Example usage:
3446 
3447    Consider the following 8x8 matrix with 34 non-zero values, that is
3448    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3449    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3450    as follows:
3451 
3452 .vb
3453             1  2  0  |  0  3  0  |  0  4
3454     Proc0   0  5  6  |  7  0  0  |  8  0
3455             9  0 10  | 11  0  0  | 12  0
3456     -------------------------------------
3457            13  0 14  | 15 16 17  |  0  0
3458     Proc1   0 18  0  | 19 20 21  |  0  0
3459             0  0  0  | 22 23  0  | 24  0
3460     -------------------------------------
3461     Proc2  25 26 27  |  0  0 28  | 29  0
3462            30  0  0  | 31 32 33  |  0 34
3463 .ve
3464 
3465    This can be represented as a collection of submatrices as:
3466 
3467 .vb
3468       A B C
3469       D E F
3470       G H I
3471 .ve
3472 
3473    Where the submatrices A,B,C are owned by proc0, D,E,F are
3474    owned by proc1, G,H,I are owned by proc2.
3475 
3476    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3477    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3478    The 'M','N' parameters are 8,8, and have the same values on all procs.
3479 
3480    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3481    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3482    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3483    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3484    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3485    matrix, ans [DF] as another SeqAIJ matrix.
3486 
3487    When d_nz, o_nz parameters are specified, d_nz storage elements are
3488    allocated for every row of the local diagonal submatrix, and o_nz
3489    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3490    One way to choose d_nz and o_nz is to use the max nonzerors per local
3491    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3492    In this case, the values of d_nz,o_nz are:
3493 .vb
3494      proc0 : dnz = 2, o_nz = 2
3495      proc1 : dnz = 3, o_nz = 2
3496      proc2 : dnz = 1, o_nz = 4
3497 .ve
3498    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3499    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3500    for proc3. i.e we are using 12+15+10=37 storage locations to store
3501    34 values.
3502 
3503    When d_nnz, o_nnz parameters are specified, the storage is specified
3504    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3505    In the above case the values for d_nnz,o_nnz are:
3506 .vb
3507      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3508      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3509      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3510 .ve
3511    Here the space allocated is sum of all the above values i.e 34, and
3512    hence pre-allocation is perfect.
3513 
3514    Level: intermediate
3515 
3516 .keywords: matrix, aij, compressed row, sparse, parallel
3517 
3518 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
3519           MPIAIJ, MatGetInfo(), PetscSplitOwnership()
3520 @*/
3521 PetscErrorCode  MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3522 {
3523   PetscErrorCode ierr;
3524 
3525   PetscFunctionBegin;
3526   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3527   PetscValidType(B,1);
3528   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
3529   PetscFunctionReturn(0);
3530 }
3531 
3532 #undef __FUNCT__
3533 #define __FUNCT__ "MatCreateMPIAIJWithArrays"
3534 /*@
3535      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
3536          CSR format the local rows.
3537 
3538    Collective on MPI_Comm
3539 
3540    Input Parameters:
3541 +  comm - MPI communicator
3542 .  m - number of local rows (Cannot be PETSC_DECIDE)
3543 .  n - This value should be the same as the local size used in creating the
3544        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3545        calculated if N is given) For square matrices n is almost always m.
3546 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3547 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3548 .   i - row indices
3549 .   j - column indices
3550 -   a - matrix values
3551 
3552    Output Parameter:
3553 .   mat - the matrix
3554 
3555    Level: intermediate
3556 
3557    Notes:
3558        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3559      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3560      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3561 
3562        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3563 
3564        The format which is used for the sparse matrix input, is equivalent to a
3565     row-major ordering.. i.e for the following matrix, the input data expected is
3566     as shown
3567 
3568 $        1 0 0
3569 $        2 0 3     P0
3570 $       -------
3571 $        4 5 6     P1
3572 $
3573 $     Process0 [P0]: rows_owned=[0,1]
3574 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3575 $        j =  {0,0,2}  [size = 3]
3576 $        v =  {1,2,3}  [size = 3]
3577 $
3578 $     Process1 [P1]: rows_owned=[2]
3579 $        i =  {0,3}    [size = nrow+1  = 1+1]
3580 $        j =  {0,1,2}  [size = 3]
3581 $        v =  {4,5,6}  [size = 3]
3582 
3583 .keywords: matrix, aij, compressed row, sparse, parallel
3584 
3585 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3586           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
3587 @*/
3588 PetscErrorCode  MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
3589 {
3590   PetscErrorCode ierr;
3591 
3592   PetscFunctionBegin;
3593   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
3594   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
3595   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
3596   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
3597   /* ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr); */
3598   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
3599   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
3600   PetscFunctionReturn(0);
3601 }
3602 
3603 #undef __FUNCT__
3604 #define __FUNCT__ "MatCreateAIJ"
3605 /*@C
3606    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
3607    (the default parallel PETSc format).  For good matrix assembly performance
3608    the user should preallocate the matrix storage by setting the parameters
3609    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3610    performance can be increased by more than a factor of 50.
3611 
3612    Collective on MPI_Comm
3613 
3614    Input Parameters:
3615 +  comm - MPI communicator
3616 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
3617            This value should be the same as the local size used in creating the
3618            y vector for the matrix-vector product y = Ax.
3619 .  n - This value should be the same as the local size used in creating the
3620        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3621        calculated if N is given) For square matrices n is almost always m.
3622 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3623 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3624 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3625            (same value is used for all local rows)
3626 .  d_nnz - array containing the number of nonzeros in the various rows of the
3627            DIAGONAL portion of the local submatrix (possibly different for each row)
3628            or NULL, if d_nz is used to specify the nonzero structure.
3629            The size of this array is equal to the number of local rows, i.e 'm'.
3630 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3631            submatrix (same value is used for all local rows).
3632 -  o_nnz - array containing the number of nonzeros in the various rows of the
3633            OFF-DIAGONAL portion of the local submatrix (possibly different for
3634            each row) or NULL, if o_nz is used to specify the nonzero
3635            structure. The size of this array is equal to the number
3636            of local rows, i.e 'm'.
3637 
3638    Output Parameter:
3639 .  A - the matrix
3640 
3641    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3642    MatXXXXSetPreallocation() paradgm instead of this routine directly.
3643    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3644 
3645    Notes:
3646    If the *_nnz parameter is given then the *_nz parameter is ignored
3647 
3648    m,n,M,N parameters specify the size of the matrix, and its partitioning across
3649    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
3650    storage requirements for this matrix.
3651 
3652    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
3653    processor than it must be used on all processors that share the object for
3654    that argument.
3655 
3656    The user MUST specify either the local or global matrix dimensions
3657    (possibly both).
3658 
3659    The parallel matrix is partitioned across processors such that the
3660    first m0 rows belong to process 0, the next m1 rows belong to
3661    process 1, the next m2 rows belong to process 2 etc.. where
3662    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
3663    values corresponding to [m x N] submatrix.
3664 
3665    The columns are logically partitioned with the n0 columns belonging
3666    to 0th partition, the next n1 columns belonging to the next
3667    partition etc.. where n0,n1,n2... are the input parameter 'n'.
3668 
3669    The DIAGONAL portion of the local submatrix on any given processor
3670    is the submatrix corresponding to the rows and columns m,n
3671    corresponding to the given processor. i.e diagonal matrix on
3672    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
3673    etc. The remaining portion of the local submatrix [m x (N-n)]
3674    constitute the OFF-DIAGONAL portion. The example below better
3675    illustrates this concept.
3676 
3677    For a square global matrix we define each processor's diagonal portion
3678    to be its local rows and the corresponding columns (a square submatrix);
3679    each processor's off-diagonal portion encompasses the remainder of the
3680    local matrix (a rectangular submatrix).
3681 
3682    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3683 
3684    When calling this routine with a single process communicator, a matrix of
3685    type SEQAIJ is returned.  If a matrix of type MPIAIJ is desired for this
3686    type of communicator, use the construction mechanism:
3687      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
3688 
3689    By default, this format uses inodes (identical nodes) when possible.
3690    We search for consecutive rows with the same nonzero structure, thereby
3691    reusing matrix information to achieve increased efficiency.
3692 
3693    Options Database Keys:
3694 +  -mat_no_inode  - Do not use inodes
3695 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3696 -  -mat_aij_oneindex - Internally use indexing starting at 1
3697         rather than 0.  Note that when calling MatSetValues(),
3698         the user still MUST index entries starting at 0!
3699 
3700 
3701    Example usage:
3702 
3703    Consider the following 8x8 matrix with 34 non-zero values, that is
3704    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3705    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3706    as follows:
3707 
3708 .vb
3709             1  2  0  |  0  3  0  |  0  4
3710     Proc0   0  5  6  |  7  0  0  |  8  0
3711             9  0 10  | 11  0  0  | 12  0
3712     -------------------------------------
3713            13  0 14  | 15 16 17  |  0  0
3714     Proc1   0 18  0  | 19 20 21  |  0  0
3715             0  0  0  | 22 23  0  | 24  0
3716     -------------------------------------
3717     Proc2  25 26 27  |  0  0 28  | 29  0
3718            30  0  0  | 31 32 33  |  0 34
3719 .ve
3720 
3721    This can be represented as a collection of submatrices as:
3722 
3723 .vb
3724       A B C
3725       D E F
3726       G H I
3727 .ve
3728 
3729    Where the submatrices A,B,C are owned by proc0, D,E,F are
3730    owned by proc1, G,H,I are owned by proc2.
3731 
3732    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3733    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3734    The 'M','N' parameters are 8,8, and have the same values on all procs.
3735 
3736    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3737    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3738    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3739    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3740    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3741    matrix, ans [DF] as another SeqAIJ matrix.
3742 
3743    When d_nz, o_nz parameters are specified, d_nz storage elements are
3744    allocated for every row of the local diagonal submatrix, and o_nz
3745    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3746    One way to choose d_nz and o_nz is to use the max nonzerors per local
3747    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3748    In this case, the values of d_nz,o_nz are:
3749 .vb
3750      proc0 : dnz = 2, o_nz = 2
3751      proc1 : dnz = 3, o_nz = 2
3752      proc2 : dnz = 1, o_nz = 4
3753 .ve
3754    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3755    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3756    for proc3. i.e we are using 12+15+10=37 storage locations to store
3757    34 values.
3758 
3759    When d_nnz, o_nnz parameters are specified, the storage is specified
3760    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3761    In the above case the values for d_nnz,o_nnz are:
3762 .vb
3763      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3764      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3765      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3766 .ve
3767    Here the space allocated is sum of all the above values i.e 34, and
3768    hence pre-allocation is perfect.
3769 
3770    Level: intermediate
3771 
3772 .keywords: matrix, aij, compressed row, sparse, parallel
3773 
3774 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3775           MPIAIJ, MatCreateMPIAIJWithArrays()
3776 @*/
3777 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)
3778 {
3779   PetscErrorCode ierr;
3780   PetscMPIInt    size;
3781 
3782   PetscFunctionBegin;
3783   ierr = MatCreate(comm,A);CHKERRQ(ierr);
3784   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
3785   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3786   if (size > 1) {
3787     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
3788     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
3789   } else {
3790     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
3791     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
3792   }
3793   PetscFunctionReturn(0);
3794 }
3795 
3796 #undef __FUNCT__
3797 #define __FUNCT__ "MatMPIAIJGetSeqAIJ"
3798 PetscErrorCode  MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
3799 {
3800   Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
3801 
3802   PetscFunctionBegin;
3803   if (Ad)     *Ad     = a->A;
3804   if (Ao)     *Ao     = a->B;
3805   if (colmap) *colmap = a->garray;
3806   PetscFunctionReturn(0);
3807 }
3808 
3809 #undef __FUNCT__
3810 #define __FUNCT__ "MatSetColoring_MPIAIJ"
3811 PetscErrorCode MatSetColoring_MPIAIJ(Mat A,ISColoring coloring)
3812 {
3813   PetscErrorCode ierr;
3814   PetscInt       i;
3815   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3816 
3817   PetscFunctionBegin;
3818   if (coloring->ctype == IS_COLORING_GLOBAL) {
3819     ISColoringValue *allcolors,*colors;
3820     ISColoring      ocoloring;
3821 
3822     /* set coloring for diagonal portion */
3823     ierr = MatSetColoring_SeqAIJ(a->A,coloring);CHKERRQ(ierr);
3824 
3825     /* set coloring for off-diagonal portion */
3826     ierr = ISAllGatherColors(PetscObjectComm((PetscObject)A),coloring->n,coloring->colors,NULL,&allcolors);CHKERRQ(ierr);
3827     ierr = PetscMalloc1(a->B->cmap->n+1,&colors);CHKERRQ(ierr);
3828     for (i=0; i<a->B->cmap->n; i++) {
3829       colors[i] = allcolors[a->garray[i]];
3830     }
3831     ierr = PetscFree(allcolors);CHKERRQ(ierr);
3832     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3833     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
3834     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3835   } else if (coloring->ctype == IS_COLORING_GHOSTED) {
3836     ISColoringValue *colors;
3837     PetscInt        *larray;
3838     ISColoring      ocoloring;
3839 
3840     /* set coloring for diagonal portion */
3841     ierr = PetscMalloc1(a->A->cmap->n+1,&larray);CHKERRQ(ierr);
3842     for (i=0; i<a->A->cmap->n; i++) {
3843       larray[i] = i + A->cmap->rstart;
3844     }
3845     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->A->cmap->n,larray,NULL,larray);CHKERRQ(ierr);
3846     ierr = PetscMalloc1(a->A->cmap->n+1,&colors);CHKERRQ(ierr);
3847     for (i=0; i<a->A->cmap->n; i++) {
3848       colors[i] = coloring->colors[larray[i]];
3849     }
3850     ierr = PetscFree(larray);CHKERRQ(ierr);
3851     ierr = ISColoringCreate(PETSC_COMM_SELF,coloring->n,a->A->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3852     ierr = MatSetColoring_SeqAIJ(a->A,ocoloring);CHKERRQ(ierr);
3853     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3854 
3855     /* set coloring for off-diagonal portion */
3856     ierr = PetscMalloc1(a->B->cmap->n+1,&larray);CHKERRQ(ierr);
3857     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->B->cmap->n,a->garray,NULL,larray);CHKERRQ(ierr);
3858     ierr = PetscMalloc1(a->B->cmap->n+1,&colors);CHKERRQ(ierr);
3859     for (i=0; i<a->B->cmap->n; i++) {
3860       colors[i] = coloring->colors[larray[i]];
3861     }
3862     ierr = PetscFree(larray);CHKERRQ(ierr);
3863     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3864     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
3865     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3866   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support ISColoringType %d",(int)coloring->ctype);
3867   PetscFunctionReturn(0);
3868 }
3869 
3870 #undef __FUNCT__
3871 #define __FUNCT__ "MatSetValuesAdifor_MPIAIJ"
3872 PetscErrorCode MatSetValuesAdifor_MPIAIJ(Mat A,PetscInt nl,void *advalues)
3873 {
3874   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3875   PetscErrorCode ierr;
3876 
3877   PetscFunctionBegin;
3878   ierr = MatSetValuesAdifor_SeqAIJ(a->A,nl,advalues);CHKERRQ(ierr);
3879   ierr = MatSetValuesAdifor_SeqAIJ(a->B,nl,advalues);CHKERRQ(ierr);
3880   PetscFunctionReturn(0);
3881 }
3882 
3883 #undef __FUNCT__
3884 #define __FUNCT__ "MatCreateMPIMatConcatenateSeqMat_MPIAIJ"
3885 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
3886 {
3887   PetscErrorCode ierr;
3888   PetscInt       m,N,i,rstart,nnz,Ii;
3889   PetscInt       *indx;
3890   PetscScalar    *values;
3891 
3892   PetscFunctionBegin;
3893   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
3894   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
3895     PetscInt       *dnz,*onz,sum,bs,cbs;
3896 
3897     if (n == PETSC_DECIDE) {
3898       ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
3899     }
3900     /* Check sum(n) = N */
3901     ierr = MPI_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3902     if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
3903 
3904     ierr    = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3905     rstart -= m;
3906 
3907     ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
3908     for (i=0; i<m; i++) {
3909       ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3910       ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
3911       ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3912     }
3913 
3914     ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
3915     ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
3916     ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
3917     ierr = MatSetBlockSizes(*outmat,bs,cbs);CHKERRQ(ierr);
3918     ierr = MatSetType(*outmat,MATMPIAIJ);CHKERRQ(ierr);
3919     ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
3920     ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
3921   }
3922 
3923   /* numeric phase */
3924   ierr = MatGetOwnershipRange(*outmat,&rstart,NULL);CHKERRQ(ierr);
3925   for (i=0; i<m; i++) {
3926     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3927     Ii   = i + rstart;
3928     ierr = MatSetValues(*outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3929     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3930   }
3931   ierr = MatAssemblyBegin(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3932   ierr = MatAssemblyEnd(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3933   PetscFunctionReturn(0);
3934 }
3935 
3936 #undef __FUNCT__
3937 #define __FUNCT__ "MatFileSplit"
3938 PetscErrorCode MatFileSplit(Mat A,char *outfile)
3939 {
3940   PetscErrorCode    ierr;
3941   PetscMPIInt       rank;
3942   PetscInt          m,N,i,rstart,nnz;
3943   size_t            len;
3944   const PetscInt    *indx;
3945   PetscViewer       out;
3946   char              *name;
3947   Mat               B;
3948   const PetscScalar *values;
3949 
3950   PetscFunctionBegin;
3951   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
3952   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
3953   /* Should this be the type of the diagonal block of A? */
3954   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
3955   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
3956   ierr = MatSetBlockSizesFromMats(B,A,A);CHKERRQ(ierr);
3957   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
3958   ierr = MatSeqAIJSetPreallocation(B,0,NULL);CHKERRQ(ierr);
3959   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
3960   for (i=0; i<m; i++) {
3961     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3962     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3963     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3964   }
3965   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3966   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3967 
3968   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
3969   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
3970   ierr = PetscMalloc1(len+5,&name);CHKERRQ(ierr);
3971   sprintf(name,"%s.%d",outfile,rank);
3972   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
3973   ierr = PetscFree(name);CHKERRQ(ierr);
3974   ierr = MatView(B,out);CHKERRQ(ierr);
3975   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
3976   ierr = MatDestroy(&B);CHKERRQ(ierr);
3977   PetscFunctionReturn(0);
3978 }
3979 
3980 extern PetscErrorCode MatDestroy_MPIAIJ(Mat);
3981 #undef __FUNCT__
3982 #define __FUNCT__ "MatDestroy_MPIAIJ_SeqsToMPI"
3983 PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
3984 {
3985   PetscErrorCode      ierr;
3986   Mat_Merge_SeqsToMPI *merge;
3987   PetscContainer      container;
3988 
3989   PetscFunctionBegin;
3990   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
3991   if (container) {
3992     ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
3993     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
3994     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
3995     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
3996     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
3997     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
3998     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
3999     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
4000     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
4001     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
4002     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
4003     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
4004     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
4005     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
4006     ierr = PetscFree(merge);CHKERRQ(ierr);
4007     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
4008   }
4009   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
4010   PetscFunctionReturn(0);
4011 }
4012 
4013 #include <../src/mat/utils/freespace.h>
4014 #include <petscbt.h>
4015 
4016 #undef __FUNCT__
4017 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJNumeric"
4018 PetscErrorCode  MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
4019 {
4020   PetscErrorCode      ierr;
4021   MPI_Comm            comm;
4022   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
4023   PetscMPIInt         size,rank,taga,*len_s;
4024   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
4025   PetscInt            proc,m;
4026   PetscInt            **buf_ri,**buf_rj;
4027   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
4028   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
4029   MPI_Request         *s_waits,*r_waits;
4030   MPI_Status          *status;
4031   MatScalar           *aa=a->a;
4032   MatScalar           **abuf_r,*ba_i;
4033   Mat_Merge_SeqsToMPI *merge;
4034   PetscContainer      container;
4035 
4036   PetscFunctionBegin;
4037   ierr = PetscObjectGetComm((PetscObject)mpimat,&comm);CHKERRQ(ierr);
4038   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4039 
4040   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4041   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4042 
4043   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4044   ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4045 
4046   bi     = merge->bi;
4047   bj     = merge->bj;
4048   buf_ri = merge->buf_ri;
4049   buf_rj = merge->buf_rj;
4050 
4051   ierr   = PetscMalloc1(size,&status);CHKERRQ(ierr);
4052   owners = merge->rowmap->range;
4053   len_s  = merge->len_s;
4054 
4055   /* send and recv matrix values */
4056   /*-----------------------------*/
4057   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
4058   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
4059 
4060   ierr = PetscMalloc1(merge->nsend+1,&s_waits);CHKERRQ(ierr);
4061   for (proc=0,k=0; proc<size; proc++) {
4062     if (!len_s[proc]) continue;
4063     i    = owners[proc];
4064     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
4065     k++;
4066   }
4067 
4068   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
4069   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
4070   ierr = PetscFree(status);CHKERRQ(ierr);
4071 
4072   ierr = PetscFree(s_waits);CHKERRQ(ierr);
4073   ierr = PetscFree(r_waits);CHKERRQ(ierr);
4074 
4075   /* insert mat values of mpimat */
4076   /*----------------------------*/
4077   ierr = PetscMalloc1(N,&ba_i);CHKERRQ(ierr);
4078   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4079 
4080   for (k=0; k<merge->nrecv; k++) {
4081     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4082     nrows       = *(buf_ri_k[k]);
4083     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
4084     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4085   }
4086 
4087   /* set values of ba */
4088   m = merge->rowmap->n;
4089   for (i=0; i<m; i++) {
4090     arow = owners[rank] + i;
4091     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
4092     bnzi = bi[i+1] - bi[i];
4093     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
4094 
4095     /* add local non-zero vals of this proc's seqmat into ba */
4096     anzi   = ai[arow+1] - ai[arow];
4097     aj     = a->j + ai[arow];
4098     aa     = a->a + ai[arow];
4099     nextaj = 0;
4100     for (j=0; nextaj<anzi; j++) {
4101       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4102         ba_i[j] += aa[nextaj++];
4103       }
4104     }
4105 
4106     /* add received vals into ba */
4107     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4108       /* i-th row */
4109       if (i == *nextrow[k]) {
4110         anzi   = *(nextai[k]+1) - *nextai[k];
4111         aj     = buf_rj[k] + *(nextai[k]);
4112         aa     = abuf_r[k] + *(nextai[k]);
4113         nextaj = 0;
4114         for (j=0; nextaj<anzi; j++) {
4115           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4116             ba_i[j] += aa[nextaj++];
4117           }
4118         }
4119         nextrow[k]++; nextai[k]++;
4120       }
4121     }
4122     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
4123   }
4124   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4125   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4126 
4127   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
4128   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
4129   ierr = PetscFree(ba_i);CHKERRQ(ierr);
4130   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4131   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4132   PetscFunctionReturn(0);
4133 }
4134 
4135 extern PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat);
4136 
4137 #undef __FUNCT__
4138 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJSymbolic"
4139 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4140 {
4141   PetscErrorCode      ierr;
4142   Mat                 B_mpi;
4143   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
4144   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4145   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
4146   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4147   PetscInt            len,proc,*dnz,*onz,bs,cbs;
4148   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4149   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4150   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
4151   MPI_Status          *status;
4152   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
4153   PetscBT             lnkbt;
4154   Mat_Merge_SeqsToMPI *merge;
4155   PetscContainer      container;
4156 
4157   PetscFunctionBegin;
4158   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4159 
4160   /* make sure it is a PETSc comm */
4161   ierr = PetscCommDuplicate(comm,&comm,NULL);CHKERRQ(ierr);
4162   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4163   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4164 
4165   ierr = PetscNew(&merge);CHKERRQ(ierr);
4166   ierr = PetscMalloc1(size,&status);CHKERRQ(ierr);
4167 
4168   /* determine row ownership */
4169   /*---------------------------------------------------------*/
4170   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
4171   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
4172   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
4173   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
4174   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
4175   ierr = PetscMalloc1(size,&len_si);CHKERRQ(ierr);
4176   ierr = PetscMalloc1(size,&merge->len_s);CHKERRQ(ierr);
4177 
4178   m      = merge->rowmap->n;
4179   owners = merge->rowmap->range;
4180 
4181   /* determine the number of messages to send, their lengths */
4182   /*---------------------------------------------------------*/
4183   len_s = merge->len_s;
4184 
4185   len          = 0; /* length of buf_si[] */
4186   merge->nsend = 0;
4187   for (proc=0; proc<size; proc++) {
4188     len_si[proc] = 0;
4189     if (proc == rank) {
4190       len_s[proc] = 0;
4191     } else {
4192       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4193       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4194     }
4195     if (len_s[proc]) {
4196       merge->nsend++;
4197       nrows = 0;
4198       for (i=owners[proc]; i<owners[proc+1]; i++) {
4199         if (ai[i+1] > ai[i]) nrows++;
4200       }
4201       len_si[proc] = 2*(nrows+1);
4202       len         += len_si[proc];
4203     }
4204   }
4205 
4206   /* determine the number and length of messages to receive for ij-structure */
4207   /*-------------------------------------------------------------------------*/
4208   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
4209   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
4210 
4211   /* post the Irecv of j-structure */
4212   /*-------------------------------*/
4213   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
4214   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
4215 
4216   /* post the Isend of j-structure */
4217   /*--------------------------------*/
4218   ierr = PetscMalloc2(merge->nsend,&si_waits,merge->nsend,&sj_waits);CHKERRQ(ierr);
4219 
4220   for (proc=0, k=0; proc<size; proc++) {
4221     if (!len_s[proc]) continue;
4222     i    = owners[proc];
4223     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
4224     k++;
4225   }
4226 
4227   /* receives and sends of j-structure are complete */
4228   /*------------------------------------------------*/
4229   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
4230   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
4231 
4232   /* send and recv i-structure */
4233   /*---------------------------*/
4234   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
4235   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
4236 
4237   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
4238   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4239   for (proc=0,k=0; proc<size; proc++) {
4240     if (!len_s[proc]) continue;
4241     /* form outgoing message for i-structure:
4242          buf_si[0]:                 nrows to be sent
4243                [1:nrows]:           row index (global)
4244                [nrows+1:2*nrows+1]: i-structure index
4245     */
4246     /*-------------------------------------------*/
4247     nrows       = len_si[proc]/2 - 1;
4248     buf_si_i    = buf_si + nrows+1;
4249     buf_si[0]   = nrows;
4250     buf_si_i[0] = 0;
4251     nrows       = 0;
4252     for (i=owners[proc]; i<owners[proc+1]; i++) {
4253       anzi = ai[i+1] - ai[i];
4254       if (anzi) {
4255         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4256         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4257         nrows++;
4258       }
4259     }
4260     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4261     k++;
4262     buf_si += len_si[proc];
4263   }
4264 
4265   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4266   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4267 
4268   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4269   for (i=0; i<merge->nrecv; i++) {
4270     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);
4271   }
4272 
4273   ierr = PetscFree(len_si);CHKERRQ(ierr);
4274   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4275   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4276   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4277   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4278   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4279   ierr = PetscFree(status);CHKERRQ(ierr);
4280 
4281   /* compute a local seq matrix in each processor */
4282   /*----------------------------------------------*/
4283   /* allocate bi array and free space for accumulating nonzero column info */
4284   ierr  = PetscMalloc1(m+1,&bi);CHKERRQ(ierr);
4285   bi[0] = 0;
4286 
4287   /* create and initialize a linked list */
4288   nlnk = N+1;
4289   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4290 
4291   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4292   len  = ai[owners[rank+1]] - ai[owners[rank]];
4293   ierr = PetscFreeSpaceGet((PetscInt)(2*len+1),&free_space);CHKERRQ(ierr);
4294 
4295   current_space = free_space;
4296 
4297   /* determine symbolic info for each local row */
4298   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4299 
4300   for (k=0; k<merge->nrecv; k++) {
4301     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4302     nrows       = *buf_ri_k[k];
4303     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4304     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4305   }
4306 
4307   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4308   len  = 0;
4309   for (i=0; i<m; i++) {
4310     bnzi = 0;
4311     /* add local non-zero cols of this proc's seqmat into lnk */
4312     arow  = owners[rank] + i;
4313     anzi  = ai[arow+1] - ai[arow];
4314     aj    = a->j + ai[arow];
4315     ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4316     bnzi += nlnk;
4317     /* add received col data into lnk */
4318     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4319       if (i == *nextrow[k]) { /* i-th row */
4320         anzi  = *(nextai[k]+1) - *nextai[k];
4321         aj    = buf_rj[k] + *nextai[k];
4322         ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4323         bnzi += nlnk;
4324         nextrow[k]++; nextai[k]++;
4325       }
4326     }
4327     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4328 
4329     /* if free space is not available, make more free space */
4330     if (current_space->local_remaining<bnzi) {
4331       ierr = PetscFreeSpaceGet(bnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
4332       nspacedouble++;
4333     }
4334     /* copy data into free space, then initialize lnk */
4335     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4336     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
4337 
4338     current_space->array           += bnzi;
4339     current_space->local_used      += bnzi;
4340     current_space->local_remaining -= bnzi;
4341 
4342     bi[i+1] = bi[i] + bnzi;
4343   }
4344 
4345   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4346 
4347   ierr = PetscMalloc1(bi[m]+1,&bj);CHKERRQ(ierr);
4348   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
4349   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4350 
4351   /* create symbolic parallel matrix B_mpi */
4352   /*---------------------------------------*/
4353   ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
4354   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
4355   if (n==PETSC_DECIDE) {
4356     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
4357   } else {
4358     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4359   }
4360   ierr = MatSetBlockSizes(B_mpi,bs,cbs);CHKERRQ(ierr);
4361   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
4362   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
4363   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4364   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
4365 
4366   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4367   B_mpi->assembled    = PETSC_FALSE;
4368   B_mpi->ops->destroy = MatDestroy_MPIAIJ_SeqsToMPI;
4369   merge->bi           = bi;
4370   merge->bj           = bj;
4371   merge->buf_ri       = buf_ri;
4372   merge->buf_rj       = buf_rj;
4373   merge->coi          = NULL;
4374   merge->coj          = NULL;
4375   merge->owners_co    = NULL;
4376 
4377   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
4378 
4379   /* attach the supporting struct to B_mpi for reuse */
4380   ierr    = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
4381   ierr    = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
4382   ierr    = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
4383   ierr    = PetscContainerDestroy(&container);CHKERRQ(ierr);
4384   *mpimat = B_mpi;
4385 
4386   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4387   PetscFunctionReturn(0);
4388 }
4389 
4390 #undef __FUNCT__
4391 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJ"
4392 /*@C
4393       MatCreateMPIAIJSumSeqAIJ - Creates a MPIAIJ matrix by adding sequential
4394                  matrices from each processor
4395 
4396     Collective on MPI_Comm
4397 
4398    Input Parameters:
4399 +    comm - the communicators the parallel matrix will live on
4400 .    seqmat - the input sequential matrices
4401 .    m - number of local rows (or PETSC_DECIDE)
4402 .    n - number of local columns (or PETSC_DECIDE)
4403 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4404 
4405    Output Parameter:
4406 .    mpimat - the parallel matrix generated
4407 
4408     Level: advanced
4409 
4410    Notes:
4411      The dimensions of the sequential matrix in each processor MUST be the same.
4412      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
4413      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
4414 @*/
4415 PetscErrorCode  MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
4416 {
4417   PetscErrorCode ierr;
4418   PetscMPIInt    size;
4419 
4420   PetscFunctionBegin;
4421   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4422   if (size == 1) {
4423     ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4424     if (scall == MAT_INITIAL_MATRIX) {
4425       ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
4426     } else {
4427       ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4428     }
4429     ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4430     PetscFunctionReturn(0);
4431   }
4432   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4433   if (scall == MAT_INITIAL_MATRIX) {
4434     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
4435   }
4436   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
4437   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4438   PetscFunctionReturn(0);
4439 }
4440 
4441 #undef __FUNCT__
4442 #define __FUNCT__ "MatMPIAIJGetLocalMat"
4443 /*@
4444      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
4445           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
4446           with MatGetSize()
4447 
4448     Not Collective
4449 
4450    Input Parameters:
4451 +    A - the matrix
4452 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4453 
4454    Output Parameter:
4455 .    A_loc - the local sequential matrix generated
4456 
4457     Level: developer
4458 
4459 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
4460 
4461 @*/
4462 PetscErrorCode  MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
4463 {
4464   PetscErrorCode ierr;
4465   Mat_MPIAIJ     *mpimat=(Mat_MPIAIJ*)A->data;
4466   Mat_SeqAIJ     *mat,*a,*b;
4467   PetscInt       *ai,*aj,*bi,*bj,*cmap=mpimat->garray;
4468   MatScalar      *aa,*ba,*cam;
4469   PetscScalar    *ca;
4470   PetscInt       am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
4471   PetscInt       *ci,*cj,col,ncols_d,ncols_o,jo;
4472   PetscBool      match;
4473   MPI_Comm       comm;
4474   PetscMPIInt    size;
4475 
4476   PetscFunctionBegin;
4477   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4478   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
4479   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4480   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4481   if (size == 1 && scall == MAT_REUSE_MATRIX) PetscFunctionReturn(0);
4482 
4483   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4484   a = (Mat_SeqAIJ*)(mpimat->A)->data;
4485   b = (Mat_SeqAIJ*)(mpimat->B)->data;
4486   ai = a->i; aj = a->j; bi = b->i; bj = b->j;
4487   aa = a->a; ba = b->a;
4488   if (scall == MAT_INITIAL_MATRIX) {
4489     if (size == 1) {
4490       ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ai,aj,aa,A_loc);CHKERRQ(ierr);
4491       PetscFunctionReturn(0);
4492     }
4493 
4494     ierr  = PetscMalloc1(1+am,&ci);CHKERRQ(ierr);
4495     ci[0] = 0;
4496     for (i=0; i<am; i++) {
4497       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
4498     }
4499     ierr = PetscMalloc1(1+ci[am],&cj);CHKERRQ(ierr);
4500     ierr = PetscMalloc1(1+ci[am],&ca);CHKERRQ(ierr);
4501     k    = 0;
4502     for (i=0; i<am; i++) {
4503       ncols_o = bi[i+1] - bi[i];
4504       ncols_d = ai[i+1] - ai[i];
4505       /* off-diagonal portion of A */
4506       for (jo=0; jo<ncols_o; jo++) {
4507         col = cmap[*bj];
4508         if (col >= cstart) break;
4509         cj[k]   = col; bj++;
4510         ca[k++] = *ba++;
4511       }
4512       /* diagonal portion of A */
4513       for (j=0; j<ncols_d; j++) {
4514         cj[k]   = cstart + *aj++;
4515         ca[k++] = *aa++;
4516       }
4517       /* off-diagonal portion of A */
4518       for (j=jo; j<ncols_o; j++) {
4519         cj[k]   = cmap[*bj++];
4520         ca[k++] = *ba++;
4521       }
4522     }
4523     /* put together the new matrix */
4524     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
4525     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4526     /* Since these are PETSc arrays, change flags to free them as necessary. */
4527     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
4528     mat->free_a  = PETSC_TRUE;
4529     mat->free_ij = PETSC_TRUE;
4530     mat->nonew   = 0;
4531   } else if (scall == MAT_REUSE_MATRIX) {
4532     mat=(Mat_SeqAIJ*)(*A_loc)->data;
4533     ci = mat->i; cj = mat->j; cam = mat->a;
4534     for (i=0; i<am; i++) {
4535       /* off-diagonal portion of A */
4536       ncols_o = bi[i+1] - bi[i];
4537       for (jo=0; jo<ncols_o; jo++) {
4538         col = cmap[*bj];
4539         if (col >= cstart) break;
4540         *cam++ = *ba++; bj++;
4541       }
4542       /* diagonal portion of A */
4543       ncols_d = ai[i+1] - ai[i];
4544       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
4545       /* off-diagonal portion of A */
4546       for (j=jo; j<ncols_o; j++) {
4547         *cam++ = *ba++; bj++;
4548       }
4549     }
4550   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
4551   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4552   PetscFunctionReturn(0);
4553 }
4554 
4555 #undef __FUNCT__
4556 #define __FUNCT__ "MatMPIAIJGetLocalMatCondensed"
4557 /*@C
4558      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MPIAIJ matrix by taking all its local rows and NON-ZERO columns
4559 
4560     Not Collective
4561 
4562    Input Parameters:
4563 +    A - the matrix
4564 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4565 -    row, col - index sets of rows and columns to extract (or NULL)
4566 
4567    Output Parameter:
4568 .    A_loc - the local sequential matrix generated
4569 
4570     Level: developer
4571 
4572 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
4573 
4574 @*/
4575 PetscErrorCode  MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
4576 {
4577   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4578   PetscErrorCode ierr;
4579   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
4580   IS             isrowa,iscola;
4581   Mat            *aloc;
4582   PetscBool      match;
4583 
4584   PetscFunctionBegin;
4585   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4586   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
4587   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4588   if (!row) {
4589     start = A->rmap->rstart; end = A->rmap->rend;
4590     ierr  = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
4591   } else {
4592     isrowa = *row;
4593   }
4594   if (!col) {
4595     start = A->cmap->rstart;
4596     cmap  = a->garray;
4597     nzA   = a->A->cmap->n;
4598     nzB   = a->B->cmap->n;
4599     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4600     ncols = 0;
4601     for (i=0; i<nzB; i++) {
4602       if (cmap[i] < start) idx[ncols++] = cmap[i];
4603       else break;
4604     }
4605     imark = i;
4606     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
4607     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
4608     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
4609   } else {
4610     iscola = *col;
4611   }
4612   if (scall != MAT_INITIAL_MATRIX) {
4613     ierr    = PetscMalloc1(1,&aloc);CHKERRQ(ierr);
4614     aloc[0] = *A_loc;
4615   }
4616   ierr   = MatGetSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
4617   *A_loc = aloc[0];
4618   ierr   = PetscFree(aloc);CHKERRQ(ierr);
4619   if (!row) {
4620     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
4621   }
4622   if (!col) {
4623     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
4624   }
4625   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4626   PetscFunctionReturn(0);
4627 }
4628 
4629 #undef __FUNCT__
4630 #define __FUNCT__ "MatGetBrowsOfAcols"
4631 /*@C
4632     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
4633 
4634     Collective on Mat
4635 
4636    Input Parameters:
4637 +    A,B - the matrices in mpiaij format
4638 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4639 -    rowb, colb - index sets of rows and columns of B to extract (or NULL)
4640 
4641    Output Parameter:
4642 +    rowb, colb - index sets of rows and columns of B to extract
4643 -    B_seq - the sequential matrix generated
4644 
4645     Level: developer
4646 
4647 @*/
4648 PetscErrorCode  MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
4649 {
4650   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4651   PetscErrorCode ierr;
4652   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
4653   IS             isrowb,iscolb;
4654   Mat            *bseq=NULL;
4655 
4656   PetscFunctionBegin;
4657   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4658     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);
4659   }
4660   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4661 
4662   if (scall == MAT_INITIAL_MATRIX) {
4663     start = A->cmap->rstart;
4664     cmap  = a->garray;
4665     nzA   = a->A->cmap->n;
4666     nzB   = a->B->cmap->n;
4667     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4668     ncols = 0;
4669     for (i=0; i<nzB; i++) {  /* row < local row index */
4670       if (cmap[i] < start) idx[ncols++] = cmap[i];
4671       else break;
4672     }
4673     imark = i;
4674     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
4675     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
4676     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
4677     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
4678   } else {
4679     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
4680     isrowb  = *rowb; iscolb = *colb;
4681     ierr    = PetscMalloc1(1,&bseq);CHKERRQ(ierr);
4682     bseq[0] = *B_seq;
4683   }
4684   ierr   = MatGetSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
4685   *B_seq = bseq[0];
4686   ierr   = PetscFree(bseq);CHKERRQ(ierr);
4687   if (!rowb) {
4688     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
4689   } else {
4690     *rowb = isrowb;
4691   }
4692   if (!colb) {
4693     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
4694   } else {
4695     *colb = iscolb;
4696   }
4697   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4698   PetscFunctionReturn(0);
4699 }
4700 
4701 #undef __FUNCT__
4702 #define __FUNCT__ "MatGetBrowsOfAoCols_MPIAIJ"
4703 /*
4704     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
4705     of the OFF-DIAGONAL portion of local A
4706 
4707     Collective on Mat
4708 
4709    Input Parameters:
4710 +    A,B - the matrices in mpiaij format
4711 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4712 
4713    Output Parameter:
4714 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
4715 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
4716 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
4717 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
4718 
4719     Level: developer
4720 
4721 */
4722 PetscErrorCode  MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
4723 {
4724   VecScatter_MPI_General *gen_to,*gen_from;
4725   PetscErrorCode         ierr;
4726   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
4727   Mat_SeqAIJ             *b_oth;
4728   VecScatter             ctx =a->Mvctx;
4729   MPI_Comm               comm;
4730   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
4731   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
4732   PetscScalar            *rvalues,*svalues;
4733   MatScalar              *b_otha,*bufa,*bufA;
4734   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
4735   MPI_Request            *rwaits = NULL,*swaits = NULL;
4736   MPI_Status             *sstatus,rstatus;
4737   PetscMPIInt            jj,size;
4738   PetscInt               *cols,sbs,rbs;
4739   PetscScalar            *vals;
4740 
4741   PetscFunctionBegin;
4742   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4743   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4744 
4745   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4746     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);
4747   }
4748   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4749   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4750 
4751   gen_to   = (VecScatter_MPI_General*)ctx->todata;
4752   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
4753   rvalues  = gen_from->values; /* holds the length of receiving row */
4754   svalues  = gen_to->values;   /* holds the length of sending row */
4755   nrecvs   = gen_from->n;
4756   nsends   = gen_to->n;
4757 
4758   ierr    = PetscMalloc2(nrecvs,&rwaits,nsends,&swaits);CHKERRQ(ierr);
4759   srow    = gen_to->indices;    /* local row index to be sent */
4760   sstarts = gen_to->starts;
4761   sprocs  = gen_to->procs;
4762   sstatus = gen_to->sstatus;
4763   sbs     = gen_to->bs;
4764   rstarts = gen_from->starts;
4765   rprocs  = gen_from->procs;
4766   rbs     = gen_from->bs;
4767 
4768   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
4769   if (scall == MAT_INITIAL_MATRIX) {
4770     /* i-array */
4771     /*---------*/
4772     /*  post receives */
4773     for (i=0; i<nrecvs; i++) {
4774       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
4775       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
4776       ierr   = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4777     }
4778 
4779     /* pack the outgoing message */
4780     ierr = PetscMalloc2(nsends+1,&sstartsj,nrecvs+1,&rstartsj);CHKERRQ(ierr);
4781 
4782     sstartsj[0] = 0;
4783     rstartsj[0] = 0;
4784     len         = 0; /* total length of j or a array to be sent */
4785     k           = 0;
4786     for (i=0; i<nsends; i++) {
4787       rowlen = (PetscInt*)svalues + sstarts[i]*sbs;
4788       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
4789       for (j=0; j<nrows; j++) {
4790         row = srow[k] + B->rmap->range[rank]; /* global row idx */
4791         for (l=0; l<sbs; l++) {
4792           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr); /* rowlength */
4793 
4794           rowlen[j*sbs+l] = ncols;
4795 
4796           len += ncols;
4797           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr);
4798         }
4799         k++;
4800       }
4801       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4802 
4803       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
4804     }
4805     /* recvs and sends of i-array are completed */
4806     i = nrecvs;
4807     while (i--) {
4808       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4809     }
4810     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4811 
4812     /* allocate buffers for sending j and a arrays */
4813     ierr = PetscMalloc1(len+1,&bufj);CHKERRQ(ierr);
4814     ierr = PetscMalloc1(len+1,&bufa);CHKERRQ(ierr);
4815 
4816     /* create i-array of B_oth */
4817     ierr = PetscMalloc1(aBn+2,&b_othi);CHKERRQ(ierr);
4818 
4819     b_othi[0] = 0;
4820     len       = 0; /* total length of j or a array to be received */
4821     k         = 0;
4822     for (i=0; i<nrecvs; i++) {
4823       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
4824       nrows  = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be recieved */
4825       for (j=0; j<nrows; j++) {
4826         b_othi[k+1] = b_othi[k] + rowlen[j];
4827         len        += rowlen[j]; k++;
4828       }
4829       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
4830     }
4831 
4832     /* allocate space for j and a arrrays of B_oth */
4833     ierr = PetscMalloc1(b_othi[aBn]+1,&b_othj);CHKERRQ(ierr);
4834     ierr = PetscMalloc1(b_othi[aBn]+1,&b_otha);CHKERRQ(ierr);
4835 
4836     /* j-array */
4837     /*---------*/
4838     /*  post receives of j-array */
4839     for (i=0; i<nrecvs; i++) {
4840       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4841       ierr  = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4842     }
4843 
4844     /* pack the outgoing message j-array */
4845     k = 0;
4846     for (i=0; i<nsends; i++) {
4847       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4848       bufJ  = bufj+sstartsj[i];
4849       for (j=0; j<nrows; j++) {
4850         row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4851         for (ll=0; ll<sbs; ll++) {
4852           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4853           for (l=0; l<ncols; l++) {
4854             *bufJ++ = cols[l];
4855           }
4856           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4857         }
4858       }
4859       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4860     }
4861 
4862     /* recvs and sends of j-array are completed */
4863     i = nrecvs;
4864     while (i--) {
4865       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4866     }
4867     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4868   } else if (scall == MAT_REUSE_MATRIX) {
4869     sstartsj = *startsj_s;
4870     rstartsj = *startsj_r;
4871     bufa     = *bufa_ptr;
4872     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
4873     b_otha   = b_oth->a;
4874   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
4875 
4876   /* a-array */
4877   /*---------*/
4878   /*  post receives of a-array */
4879   for (i=0; i<nrecvs; i++) {
4880     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4881     ierr  = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4882   }
4883 
4884   /* pack the outgoing message a-array */
4885   k = 0;
4886   for (i=0; i<nsends; i++) {
4887     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4888     bufA  = bufa+sstartsj[i];
4889     for (j=0; j<nrows; j++) {
4890       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4891       for (ll=0; ll<sbs; ll++) {
4892         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4893         for (l=0; l<ncols; l++) {
4894           *bufA++ = vals[l];
4895         }
4896         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4897       }
4898     }
4899     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4900   }
4901   /* recvs and sends of a-array are completed */
4902   i = nrecvs;
4903   while (i--) {
4904     ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4905   }
4906   if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4907   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
4908 
4909   if (scall == MAT_INITIAL_MATRIX) {
4910     /* put together the new matrix */
4911     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
4912 
4913     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4914     /* Since these are PETSc arrays, change flags to free them as necessary. */
4915     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
4916     b_oth->free_a  = PETSC_TRUE;
4917     b_oth->free_ij = PETSC_TRUE;
4918     b_oth->nonew   = 0;
4919 
4920     ierr = PetscFree(bufj);CHKERRQ(ierr);
4921     if (!startsj_s || !bufa_ptr) {
4922       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
4923       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
4924     } else {
4925       *startsj_s = sstartsj;
4926       *startsj_r = rstartsj;
4927       *bufa_ptr  = bufa;
4928     }
4929   }
4930   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4931   PetscFunctionReturn(0);
4932 }
4933 
4934 #undef __FUNCT__
4935 #define __FUNCT__ "MatGetCommunicationStructs"
4936 /*@C
4937   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
4938 
4939   Not Collective
4940 
4941   Input Parameters:
4942 . A - The matrix in mpiaij format
4943 
4944   Output Parameter:
4945 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
4946 . colmap - A map from global column index to local index into lvec
4947 - multScatter - A scatter from the argument of a matrix-vector product to lvec
4948 
4949   Level: developer
4950 
4951 @*/
4952 #if defined(PETSC_USE_CTABLE)
4953 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
4954 #else
4955 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
4956 #endif
4957 {
4958   Mat_MPIAIJ *a;
4959 
4960   PetscFunctionBegin;
4961   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4962   PetscValidPointer(lvec, 2);
4963   PetscValidPointer(colmap, 3);
4964   PetscValidPointer(multScatter, 4);
4965   a = (Mat_MPIAIJ*) A->data;
4966   if (lvec) *lvec = a->lvec;
4967   if (colmap) *colmap = a->colmap;
4968   if (multScatter) *multScatter = a->Mvctx;
4969   PetscFunctionReturn(0);
4970 }
4971 
4972 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
4973 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
4974 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
4975 #if defined(PETSC_HAVE_ELEMENTAL)
4976 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
4977 #endif
4978 
4979 #undef __FUNCT__
4980 #define __FUNCT__ "MatMatMultNumeric_MPIDense_MPIAIJ"
4981 /*
4982     Computes (B'*A')' since computing B*A directly is untenable
4983 
4984                n                       p                          p
4985         (              )       (              )         (                  )
4986       m (      A       )  *  n (       B      )   =   m (         C        )
4987         (              )       (              )         (                  )
4988 
4989 */
4990 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
4991 {
4992   PetscErrorCode ierr;
4993   Mat            At,Bt,Ct;
4994 
4995   PetscFunctionBegin;
4996   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
4997   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
4998   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
4999   ierr = MatDestroy(&At);CHKERRQ(ierr);
5000   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
5001   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
5002   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
5003   PetscFunctionReturn(0);
5004 }
5005 
5006 #undef __FUNCT__
5007 #define __FUNCT__ "MatMatMultSymbolic_MPIDense_MPIAIJ"
5008 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
5009 {
5010   PetscErrorCode ierr;
5011   PetscInt       m=A->rmap->n,n=B->cmap->n;
5012   Mat            Cmat;
5013 
5014   PetscFunctionBegin;
5015   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);
5016   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
5017   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
5018   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
5019   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
5020   ierr = MatMPIDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
5021   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5022   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5023 
5024   Cmat->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
5025 
5026   *C = Cmat;
5027   PetscFunctionReturn(0);
5028 }
5029 
5030 /* ----------------------------------------------------------------*/
5031 #undef __FUNCT__
5032 #define __FUNCT__ "MatMatMult_MPIDense_MPIAIJ"
5033 PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
5034 {
5035   PetscErrorCode ierr;
5036 
5037   PetscFunctionBegin;
5038   if (scall == MAT_INITIAL_MATRIX) {
5039     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5040     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
5041     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5042   }
5043   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5044   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
5045   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5046   PetscFunctionReturn(0);
5047 }
5048 
5049 /*MC
5050    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
5051 
5052    Options Database Keys:
5053 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
5054 
5055   Level: beginner
5056 
5057 .seealso: MatCreateAIJ()
5058 M*/
5059 
5060 #undef __FUNCT__
5061 #define __FUNCT__ "MatCreate_MPIAIJ"
5062 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
5063 {
5064   Mat_MPIAIJ     *b;
5065   PetscErrorCode ierr;
5066   PetscMPIInt    size;
5067 
5068   PetscFunctionBegin;
5069   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
5070 
5071   ierr          = PetscNewLog(B,&b);CHKERRQ(ierr);
5072   B->data       = (void*)b;
5073   ierr          = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
5074   B->assembled  = PETSC_FALSE;
5075   B->insertmode = NOT_SET_VALUES;
5076   b->size       = size;
5077 
5078   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank);CHKERRQ(ierr);
5079 
5080   /* build cache for off array entries formed */
5081   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash);CHKERRQ(ierr);
5082 
5083   b->donotstash  = PETSC_FALSE;
5084   b->colmap      = 0;
5085   b->garray      = 0;
5086   b->roworiented = PETSC_TRUE;
5087 
5088   /* stuff used for matrix vector multiply */
5089   b->lvec  = NULL;
5090   b->Mvctx = NULL;
5091 
5092   /* stuff for MatGetRow() */
5093   b->rowindices   = 0;
5094   b->rowvalues    = 0;
5095   b->getrowactive = PETSC_FALSE;
5096 
5097   /* flexible pointer used in CUSP/CUSPARSE classes */
5098   b->spptr = NULL;
5099 
5100   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ);CHKERRQ(ierr);
5101   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
5102   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetDiagonalBlock_C",MatGetDiagonalBlock_MPIAIJ);CHKERRQ(ierr);
5103   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
5104   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
5105   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
5106   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
5107   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
5108   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
5109   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
5110 #if defined(PETSC_HAVE_ELEMENTAL)
5111   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_elemental_C",MatConvert_MPIAIJ_Elemental);CHKERRQ(ierr);
5112 #endif
5113   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
5114   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
5115   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
5116   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
5117   PetscFunctionReturn(0);
5118 }
5119 
5120 #undef __FUNCT__
5121 #define __FUNCT__ "MatCreateMPIAIJWithSplitArrays"
5122 /*@C
5123      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
5124          and "off-diagonal" part of the matrix in CSR format.
5125 
5126    Collective on MPI_Comm
5127 
5128    Input Parameters:
5129 +  comm - MPI communicator
5130 .  m - number of local rows (Cannot be PETSC_DECIDE)
5131 .  n - This value should be the same as the local size used in creating the
5132        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
5133        calculated if N is given) For square matrices n is almost always m.
5134 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
5135 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
5136 .   i - row indices for "diagonal" portion of matrix
5137 .   j - column indices
5138 .   a - matrix values
5139 .   oi - row indices for "off-diagonal" portion of matrix
5140 .   oj - column indices
5141 -   oa - matrix values
5142 
5143    Output Parameter:
5144 .   mat - the matrix
5145 
5146    Level: advanced
5147 
5148    Notes:
5149        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
5150        must free the arrays once the matrix has been destroyed and not before.
5151 
5152        The i and j indices are 0 based
5153 
5154        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
5155 
5156        This sets local rows and cannot be used to set off-processor values.
5157 
5158        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
5159        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
5160        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
5161        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
5162        keep track of the underlying array. Use MatSetOption(A,MAT_IGNORE_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
5163        communication if it is known that only local entries will be set.
5164 
5165 .keywords: matrix, aij, compressed row, sparse, parallel
5166 
5167 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
5168           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
5169 @*/
5170 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)
5171 {
5172   PetscErrorCode ierr;
5173   Mat_MPIAIJ     *maij;
5174 
5175   PetscFunctionBegin;
5176   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
5177   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
5178   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
5179   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
5180   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
5181   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
5182   maij = (Mat_MPIAIJ*) (*mat)->data;
5183 
5184   (*mat)->preallocated = PETSC_TRUE;
5185 
5186   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
5187   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
5188 
5189   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
5190   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
5191 
5192   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5193   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5194   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5195   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5196 
5197   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5198   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5199   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
5200   PetscFunctionReturn(0);
5201 }
5202 
5203 /*
5204     Special version for direct calls from Fortran
5205 */
5206 #include <petsc/private/fortranimpl.h>
5207 
5208 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5209 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
5210 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5211 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
5212 #endif
5213 
5214 /* Change these macros so can be used in void function */
5215 #undef CHKERRQ
5216 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
5217 #undef SETERRQ2
5218 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5219 #undef SETERRQ3
5220 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5221 #undef SETERRQ
5222 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
5223 
5224 #undef __FUNCT__
5225 #define __FUNCT__ "matsetvaluesmpiaij_"
5226 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)
5227 {
5228   Mat            mat  = *mmat;
5229   PetscInt       m    = *mm, n = *mn;
5230   InsertMode     addv = *maddv;
5231   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
5232   PetscScalar    value;
5233   PetscErrorCode ierr;
5234 
5235   MatCheckPreallocated(mat,1);
5236   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
5237 
5238 #if defined(PETSC_USE_DEBUG)
5239   else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
5240 #endif
5241   {
5242     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
5243     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
5244     PetscBool roworiented = aij->roworiented;
5245 
5246     /* Some Variables required in the macro */
5247     Mat        A                 = aij->A;
5248     Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
5249     PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
5250     MatScalar  *aa               = a->a;
5251     PetscBool  ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
5252     Mat        B                 = aij->B;
5253     Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
5254     PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5255     MatScalar  *ba               = b->a;
5256 
5257     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5258     PetscInt  nonew = a->nonew;
5259     MatScalar *ap1,*ap2;
5260 
5261     PetscFunctionBegin;
5262     for (i=0; i<m; i++) {
5263       if (im[i] < 0) continue;
5264 #if defined(PETSC_USE_DEBUG)
5265       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);
5266 #endif
5267       if (im[i] >= rstart && im[i] < rend) {
5268         row      = im[i] - rstart;
5269         lastcol1 = -1;
5270         rp1      = aj + ai[row];
5271         ap1      = aa + ai[row];
5272         rmax1    = aimax[row];
5273         nrow1    = ailen[row];
5274         low1     = 0;
5275         high1    = nrow1;
5276         lastcol2 = -1;
5277         rp2      = bj + bi[row];
5278         ap2      = ba + bi[row];
5279         rmax2    = bimax[row];
5280         nrow2    = bilen[row];
5281         low2     = 0;
5282         high2    = nrow2;
5283 
5284         for (j=0; j<n; j++) {
5285           if (roworiented) value = v[i*n+j];
5286           else value = v[i+j*m];
5287           if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES)) continue;
5288           if (in[j] >= cstart && in[j] < cend) {
5289             col = in[j] - cstart;
5290             MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
5291           } else if (in[j] < 0) continue;
5292 #if defined(PETSC_USE_DEBUG)
5293           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);
5294 #endif
5295           else {
5296             if (mat->was_assembled) {
5297               if (!aij->colmap) {
5298                 ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5299               }
5300 #if defined(PETSC_USE_CTABLE)
5301               ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5302               col--;
5303 #else
5304               col = aij->colmap[in[j]] - 1;
5305 #endif
5306               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5307                 ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5308                 col  =  in[j];
5309                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5310                 B     = aij->B;
5311                 b     = (Mat_SeqAIJ*)B->data;
5312                 bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5313                 rp2   = bj + bi[row];
5314                 ap2   = ba + bi[row];
5315                 rmax2 = bimax[row];
5316                 nrow2 = bilen[row];
5317                 low2  = 0;
5318                 high2 = nrow2;
5319                 bm    = aij->B->rmap->n;
5320                 ba    = b->a;
5321               }
5322             } else col = in[j];
5323             MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
5324           }
5325         }
5326       } else if (!aij->donotstash) {
5327         if (roworiented) {
5328           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5329         } else {
5330           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5331         }
5332       }
5333     }
5334   }
5335   PetscFunctionReturnVoid();
5336 }
5337 
5338