xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision fb53af6bf358dc0fb9ec89f143f818fb1a97b062)
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;
2607 
2608   PetscFunctionBegin;
2609   if (!Y->preallocated) {
2610     ierr = MatMPIAIJSetPreallocation(Y,1,NULL,0,NULL);CHKERRQ(ierr);
2611   } else if (!aij->nz) {
2612     ierr = MatSeqAIJSetPreallocation(maij->A,1,NULL);CHKERRQ(ierr);
2613   }
2614   ierr = MatShift_Basic(Y,a);CHKERRQ(ierr);
2615   PetscFunctionReturn(0);
2616 }
2617 
2618 /* -------------------------------------------------------------------*/
2619 static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
2620                                        MatGetRow_MPIAIJ,
2621                                        MatRestoreRow_MPIAIJ,
2622                                        MatMult_MPIAIJ,
2623                                 /* 4*/ MatMultAdd_MPIAIJ,
2624                                        MatMultTranspose_MPIAIJ,
2625                                        MatMultTransposeAdd_MPIAIJ,
2626 #if defined(PETSC_HAVE_PBGL)
2627                                        MatSolve_MPIAIJ,
2628 #else
2629                                        0,
2630 #endif
2631                                        0,
2632                                        0,
2633                                 /*10*/ 0,
2634                                        0,
2635                                        0,
2636                                        MatSOR_MPIAIJ,
2637                                        MatTranspose_MPIAIJ,
2638                                 /*15*/ MatGetInfo_MPIAIJ,
2639                                        MatEqual_MPIAIJ,
2640                                        MatGetDiagonal_MPIAIJ,
2641                                        MatDiagonalScale_MPIAIJ,
2642                                        MatNorm_MPIAIJ,
2643                                 /*20*/ MatAssemblyBegin_MPIAIJ,
2644                                        MatAssemblyEnd_MPIAIJ,
2645                                        MatSetOption_MPIAIJ,
2646                                        MatZeroEntries_MPIAIJ,
2647                                 /*24*/ MatZeroRows_MPIAIJ,
2648                                        0,
2649 #if defined(PETSC_HAVE_PBGL)
2650                                        0,
2651 #else
2652                                        0,
2653 #endif
2654                                        0,
2655                                        0,
2656                                 /*29*/ MatSetUp_MPIAIJ,
2657 #if defined(PETSC_HAVE_PBGL)
2658                                        0,
2659 #else
2660                                        0,
2661 #endif
2662                                        0,
2663                                        0,
2664                                        0,
2665                                 /*34*/ MatDuplicate_MPIAIJ,
2666                                        0,
2667                                        0,
2668                                        0,
2669                                        0,
2670                                 /*39*/ MatAXPY_MPIAIJ,
2671                                        MatGetSubMatrices_MPIAIJ,
2672                                        MatIncreaseOverlap_MPIAIJ,
2673                                        MatGetValues_MPIAIJ,
2674                                        MatCopy_MPIAIJ,
2675                                 /*44*/ MatGetRowMax_MPIAIJ,
2676                                        MatScale_MPIAIJ,
2677                                        MatShift_MPIAIJ,
2678                                        MatDiagonalSet_MPIAIJ,
2679                                        MatZeroRowsColumns_MPIAIJ,
2680                                 /*49*/ MatSetRandom_MPIAIJ,
2681                                        0,
2682                                        0,
2683                                        0,
2684                                        0,
2685                                 /*54*/ MatFDColoringCreate_MPIXAIJ,
2686                                        0,
2687                                        MatSetUnfactored_MPIAIJ,
2688                                        MatPermute_MPIAIJ,
2689                                        0,
2690                                 /*59*/ MatGetSubMatrix_MPIAIJ,
2691                                        MatDestroy_MPIAIJ,
2692                                        MatView_MPIAIJ,
2693                                        0,
2694                                        MatMatMatMult_MPIAIJ_MPIAIJ_MPIAIJ,
2695                                 /*64*/ MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ,
2696                                        MatMatMatMultNumeric_MPIAIJ_MPIAIJ_MPIAIJ,
2697                                        0,
2698                                        0,
2699                                        0,
2700                                 /*69*/ MatGetRowMaxAbs_MPIAIJ,
2701                                        MatGetRowMinAbs_MPIAIJ,
2702                                        0,
2703                                        MatSetColoring_MPIAIJ,
2704                                        0,
2705                                        MatSetValuesAdifor_MPIAIJ,
2706                                 /*75*/ MatFDColoringApply_AIJ,
2707                                        0,
2708                                        0,
2709                                        0,
2710                                        MatFindZeroDiagonals_MPIAIJ,
2711                                 /*80*/ 0,
2712                                        0,
2713                                        0,
2714                                 /*83*/ MatLoad_MPIAIJ,
2715                                        0,
2716                                        0,
2717                                        0,
2718                                        0,
2719                                        0,
2720                                 /*89*/ MatMatMult_MPIAIJ_MPIAIJ,
2721                                        MatMatMultSymbolic_MPIAIJ_MPIAIJ,
2722                                        MatMatMultNumeric_MPIAIJ_MPIAIJ,
2723                                        MatPtAP_MPIAIJ_MPIAIJ,
2724                                        MatPtAPSymbolic_MPIAIJ_MPIAIJ,
2725                                 /*94*/ MatPtAPNumeric_MPIAIJ_MPIAIJ,
2726                                        0,
2727                                        0,
2728                                        0,
2729                                        0,
2730                                 /*99*/ 0,
2731                                        0,
2732                                        0,
2733                                        MatConjugate_MPIAIJ,
2734                                        0,
2735                                 /*104*/MatSetValuesRow_MPIAIJ,
2736                                        MatRealPart_MPIAIJ,
2737                                        MatImaginaryPart_MPIAIJ,
2738                                        0,
2739                                        0,
2740                                 /*109*/0,
2741                                        0,
2742                                        MatGetRowMin_MPIAIJ,
2743                                        0,
2744                                        0,
2745                                 /*114*/MatGetSeqNonzeroStructure_MPIAIJ,
2746                                        0,
2747                                        MatGetGhosts_MPIAIJ,
2748                                        0,
2749                                        0,
2750                                 /*119*/0,
2751                                        0,
2752                                        0,
2753                                        0,
2754                                        MatGetMultiProcBlock_MPIAIJ,
2755                                 /*124*/MatFindNonzeroRows_MPIAIJ,
2756                                        MatGetColumnNorms_MPIAIJ,
2757                                        MatInvertBlockDiagonal_MPIAIJ,
2758                                        0,
2759                                        MatGetSubMatricesMPI_MPIAIJ,
2760                                 /*129*/0,
2761                                        MatTransposeMatMult_MPIAIJ_MPIAIJ,
2762                                        MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ,
2763                                        MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ,
2764                                        0,
2765                                 /*134*/0,
2766                                        0,
2767                                        0,
2768                                        0,
2769                                        0,
2770                                 /*139*/0,
2771                                        0,
2772                                        0,
2773                                        MatFDColoringSetUp_MPIXAIJ,
2774                                        MatFindOffBlockDiagonalEntries_MPIAIJ,
2775                                 /*144*/MatCreateMPIMatConcatenateSeqMat_MPIAIJ
2776 };
2777 
2778 /* ----------------------------------------------------------------------------------------*/
2779 
2780 #undef __FUNCT__
2781 #define __FUNCT__ "MatStoreValues_MPIAIJ"
2782 PetscErrorCode  MatStoreValues_MPIAIJ(Mat mat)
2783 {
2784   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2785   PetscErrorCode ierr;
2786 
2787   PetscFunctionBegin;
2788   ierr = MatStoreValues(aij->A);CHKERRQ(ierr);
2789   ierr = MatStoreValues(aij->B);CHKERRQ(ierr);
2790   PetscFunctionReturn(0);
2791 }
2792 
2793 #undef __FUNCT__
2794 #define __FUNCT__ "MatRetrieveValues_MPIAIJ"
2795 PetscErrorCode  MatRetrieveValues_MPIAIJ(Mat mat)
2796 {
2797   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2798   PetscErrorCode ierr;
2799 
2800   PetscFunctionBegin;
2801   ierr = MatRetrieveValues(aij->A);CHKERRQ(ierr);
2802   ierr = MatRetrieveValues(aij->B);CHKERRQ(ierr);
2803   PetscFunctionReturn(0);
2804 }
2805 
2806 #undef __FUNCT__
2807 #define __FUNCT__ "MatMPIAIJSetPreallocation_MPIAIJ"
2808 PetscErrorCode  MatMPIAIJSetPreallocation_MPIAIJ(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
2809 {
2810   Mat_MPIAIJ     *b;
2811   PetscErrorCode ierr;
2812 
2813   PetscFunctionBegin;
2814   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
2815   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
2816   b = (Mat_MPIAIJ*)B->data;
2817 
2818   if (!B->preallocated) {
2819     /* Explicitly create 2 MATSEQAIJ matrices. */
2820     ierr = MatCreate(PETSC_COMM_SELF,&b->A);CHKERRQ(ierr);
2821     ierr = MatSetSizes(b->A,B->rmap->n,B->cmap->n,B->rmap->n,B->cmap->n);CHKERRQ(ierr);
2822     ierr = MatSetBlockSizesFromMats(b->A,B,B);CHKERRQ(ierr);
2823     ierr = MatSetType(b->A,MATSEQAIJ);CHKERRQ(ierr);
2824     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->A);CHKERRQ(ierr);
2825     ierr = MatCreate(PETSC_COMM_SELF,&b->B);CHKERRQ(ierr);
2826     ierr = MatSetSizes(b->B,B->rmap->n,B->cmap->N,B->rmap->n,B->cmap->N);CHKERRQ(ierr);
2827     ierr = MatSetBlockSizesFromMats(b->B,B,B);CHKERRQ(ierr);
2828     ierr = MatSetType(b->B,MATSEQAIJ);CHKERRQ(ierr);
2829     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->B);CHKERRQ(ierr);
2830   }
2831 
2832   ierr = MatSeqAIJSetPreallocation(b->A,d_nz,d_nnz);CHKERRQ(ierr);
2833   ierr = MatSeqAIJSetPreallocation(b->B,o_nz,o_nnz);CHKERRQ(ierr);
2834   B->preallocated = PETSC_TRUE;
2835   PetscFunctionReturn(0);
2836 }
2837 
2838 #undef __FUNCT__
2839 #define __FUNCT__ "MatDuplicate_MPIAIJ"
2840 PetscErrorCode MatDuplicate_MPIAIJ(Mat matin,MatDuplicateOption cpvalues,Mat *newmat)
2841 {
2842   Mat            mat;
2843   Mat_MPIAIJ     *a,*oldmat = (Mat_MPIAIJ*)matin->data;
2844   PetscErrorCode ierr;
2845 
2846   PetscFunctionBegin;
2847   *newmat = 0;
2848   ierr    = MatCreate(PetscObjectComm((PetscObject)matin),&mat);CHKERRQ(ierr);
2849   ierr    = MatSetSizes(mat,matin->rmap->n,matin->cmap->n,matin->rmap->N,matin->cmap->N);CHKERRQ(ierr);
2850   ierr    = MatSetBlockSizesFromMats(mat,matin,matin);CHKERRQ(ierr);
2851   ierr    = MatSetType(mat,((PetscObject)matin)->type_name);CHKERRQ(ierr);
2852   ierr    = PetscMemcpy(mat->ops,matin->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
2853   a       = (Mat_MPIAIJ*)mat->data;
2854 
2855   mat->factortype   = matin->factortype;
2856   mat->assembled    = PETSC_TRUE;
2857   mat->insertmode   = NOT_SET_VALUES;
2858   mat->preallocated = PETSC_TRUE;
2859 
2860   a->size         = oldmat->size;
2861   a->rank         = oldmat->rank;
2862   a->donotstash   = oldmat->donotstash;
2863   a->roworiented  = oldmat->roworiented;
2864   a->rowindices   = 0;
2865   a->rowvalues    = 0;
2866   a->getrowactive = PETSC_FALSE;
2867 
2868   ierr = PetscLayoutReference(matin->rmap,&mat->rmap);CHKERRQ(ierr);
2869   ierr = PetscLayoutReference(matin->cmap,&mat->cmap);CHKERRQ(ierr);
2870 
2871   if (oldmat->colmap) {
2872 #if defined(PETSC_USE_CTABLE)
2873     ierr = PetscTableCreateCopy(oldmat->colmap,&a->colmap);CHKERRQ(ierr);
2874 #else
2875     ierr = PetscMalloc1(mat->cmap->N,&a->colmap);CHKERRQ(ierr);
2876     ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2877     ierr = PetscMemcpy(a->colmap,oldmat->colmap,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2878 #endif
2879   } else a->colmap = 0;
2880   if (oldmat->garray) {
2881     PetscInt len;
2882     len  = oldmat->B->cmap->n;
2883     ierr = PetscMalloc1(len+1,&a->garray);CHKERRQ(ierr);
2884     ierr = PetscLogObjectMemory((PetscObject)mat,len*sizeof(PetscInt));CHKERRQ(ierr);
2885     if (len) { ierr = PetscMemcpy(a->garray,oldmat->garray,len*sizeof(PetscInt));CHKERRQ(ierr); }
2886   } else a->garray = 0;
2887 
2888   ierr    = VecDuplicate(oldmat->lvec,&a->lvec);CHKERRQ(ierr);
2889   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->lvec);CHKERRQ(ierr);
2890   ierr    = VecScatterCopy(oldmat->Mvctx,&a->Mvctx);CHKERRQ(ierr);
2891   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->Mvctx);CHKERRQ(ierr);
2892   ierr    = MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
2893   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->A);CHKERRQ(ierr);
2894   ierr    = MatDuplicate(oldmat->B,cpvalues,&a->B);CHKERRQ(ierr);
2895   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->B);CHKERRQ(ierr);
2896   ierr    = PetscFunctionListDuplicate(((PetscObject)matin)->qlist,&((PetscObject)mat)->qlist);CHKERRQ(ierr);
2897   *newmat = mat;
2898   PetscFunctionReturn(0);
2899 }
2900 
2901 
2902 
2903 #undef __FUNCT__
2904 #define __FUNCT__ "MatLoad_MPIAIJ"
2905 PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
2906 {
2907   PetscScalar    *vals,*svals;
2908   MPI_Comm       comm;
2909   PetscErrorCode ierr;
2910   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
2911   PetscInt       i,nz,j,rstart,rend,mmax,maxnz = 0;
2912   PetscInt       header[4],*rowlengths = 0,M,N,m,*cols;
2913   PetscInt       *ourlens = NULL,*procsnz = NULL,*offlens = NULL,jj,*mycols,*smycols;
2914   PetscInt       cend,cstart,n,*rowners;
2915   int            fd;
2916   PetscInt       bs = newMat->rmap->bs;
2917 
2918   PetscFunctionBegin;
2919   /* force binary viewer to load .info file if it has not yet done so */
2920   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
2921   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
2922   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2923   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2924   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
2925   if (!rank) {
2926     ierr = PetscBinaryRead(fd,(char*)header,4,PETSC_INT);CHKERRQ(ierr);
2927     if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
2928   }
2929 
2930   ierr = PetscOptionsBegin(comm,NULL,"Options for loading MPIAIJ matrix","Mat");CHKERRQ(ierr);
2931   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
2932   ierr = PetscOptionsEnd();CHKERRQ(ierr);
2933   if (bs < 0) bs = 1;
2934 
2935   ierr = MPI_Bcast(header+1,3,MPIU_INT,0,comm);CHKERRQ(ierr);
2936   M    = header[1]; N = header[2];
2937 
2938   /* If global sizes are set, check if they are consistent with that given in the file */
2939   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);
2940   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);
2941 
2942   /* determine ownership of all (block) rows */
2943   if (M%bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Inconsistent # of rows (%d) and block size (%d)",M,bs);
2944   if (newMat->rmap->n < 0) m = bs*((M/bs)/size + (((M/bs) % size) > rank));    /* PETSC_DECIDE */
2945   else m = newMat->rmap->n; /* Set by user */
2946 
2947   ierr = PetscMalloc1(size+1,&rowners);CHKERRQ(ierr);
2948   ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
2949 
2950   /* First process needs enough room for process with most rows */
2951   if (!rank) {
2952     mmax = rowners[1];
2953     for (i=2; i<=size; i++) {
2954       mmax = PetscMax(mmax, rowners[i]);
2955     }
2956   } else mmax = -1;             /* unused, but compilers complain */
2957 
2958   rowners[0] = 0;
2959   for (i=2; i<=size; i++) {
2960     rowners[i] += rowners[i-1];
2961   }
2962   rstart = rowners[rank];
2963   rend   = rowners[rank+1];
2964 
2965   /* distribute row lengths to all processors */
2966   ierr = PetscMalloc2(m,&ourlens,m,&offlens);CHKERRQ(ierr);
2967   if (!rank) {
2968     ierr = PetscBinaryRead(fd,ourlens,m,PETSC_INT);CHKERRQ(ierr);
2969     ierr = PetscMalloc1(mmax,&rowlengths);CHKERRQ(ierr);
2970     ierr = PetscCalloc1(size,&procsnz);CHKERRQ(ierr);
2971     for (j=0; j<m; j++) {
2972       procsnz[0] += ourlens[j];
2973     }
2974     for (i=1; i<size; i++) {
2975       ierr = PetscBinaryRead(fd,rowlengths,rowners[i+1]-rowners[i],PETSC_INT);CHKERRQ(ierr);
2976       /* calculate the number of nonzeros on each processor */
2977       for (j=0; j<rowners[i+1]-rowners[i]; j++) {
2978         procsnz[i] += rowlengths[j];
2979       }
2980       ierr = MPIULong_Send(rowlengths,rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2981     }
2982     ierr = PetscFree(rowlengths);CHKERRQ(ierr);
2983   } else {
2984     ierr = MPIULong_Recv(ourlens,m,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2985   }
2986 
2987   if (!rank) {
2988     /* determine max buffer needed and allocate it */
2989     maxnz = 0;
2990     for (i=0; i<size; i++) {
2991       maxnz = PetscMax(maxnz,procsnz[i]);
2992     }
2993     ierr = PetscMalloc1(maxnz,&cols);CHKERRQ(ierr);
2994 
2995     /* read in my part of the matrix column indices  */
2996     nz   = procsnz[0];
2997     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2998     ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);
2999 
3000     /* read in every one elses and ship off */
3001     for (i=1; i<size; i++) {
3002       nz   = procsnz[i];
3003       ierr = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
3004       ierr = MPIULong_Send(cols,nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
3005     }
3006     ierr = PetscFree(cols);CHKERRQ(ierr);
3007   } else {
3008     /* determine buffer space needed for message */
3009     nz = 0;
3010     for (i=0; i<m; i++) {
3011       nz += ourlens[i];
3012     }
3013     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
3014 
3015     /* receive message of column indices*/
3016     ierr = MPIULong_Recv(mycols,nz,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
3017   }
3018 
3019   /* determine column ownership if matrix is not square */
3020   if (N != M) {
3021     if (newMat->cmap->n < 0) n = N/size + ((N % size) > rank);
3022     else n = newMat->cmap->n;
3023     ierr   = MPI_Scan(&n,&cend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3024     cstart = cend - n;
3025   } else {
3026     cstart = rstart;
3027     cend   = rend;
3028     n      = cend - cstart;
3029   }
3030 
3031   /* loop over local rows, determining number of off diagonal entries */
3032   ierr = PetscMemzero(offlens,m*sizeof(PetscInt));CHKERRQ(ierr);
3033   jj   = 0;
3034   for (i=0; i<m; i++) {
3035     for (j=0; j<ourlens[i]; j++) {
3036       if (mycols[jj] < cstart || mycols[jj] >= cend) offlens[i]++;
3037       jj++;
3038     }
3039   }
3040 
3041   for (i=0; i<m; i++) {
3042     ourlens[i] -= offlens[i];
3043   }
3044   ierr = MatSetSizes(newMat,m,n,M,N);CHKERRQ(ierr);
3045 
3046   if (bs > 1) {ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);}
3047 
3048   ierr = MatMPIAIJSetPreallocation(newMat,0,ourlens,0,offlens);CHKERRQ(ierr);
3049 
3050   for (i=0; i<m; i++) {
3051     ourlens[i] += offlens[i];
3052   }
3053 
3054   if (!rank) {
3055     ierr = PetscMalloc1(maxnz+1,&vals);CHKERRQ(ierr);
3056 
3057     /* read in my part of the matrix numerical values  */
3058     nz   = procsnz[0];
3059     ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
3060 
3061     /* insert into matrix */
3062     jj      = rstart;
3063     smycols = mycols;
3064     svals   = vals;
3065     for (i=0; i<m; i++) {
3066       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
3067       smycols += ourlens[i];
3068       svals   += ourlens[i];
3069       jj++;
3070     }
3071 
3072     /* read in other processors and ship out */
3073     for (i=1; i<size; i++) {
3074       nz   = procsnz[i];
3075       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
3076       ierr = MPIULong_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
3077     }
3078     ierr = PetscFree(procsnz);CHKERRQ(ierr);
3079   } else {
3080     /* receive numeric values */
3081     ierr = PetscMalloc1(nz+1,&vals);CHKERRQ(ierr);
3082 
3083     /* receive message of values*/
3084     ierr = MPIULong_Recv(vals,nz,MPIU_SCALAR,0,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
3085 
3086     /* insert into matrix */
3087     jj      = rstart;
3088     smycols = mycols;
3089     svals   = vals;
3090     for (i=0; i<m; i++) {
3091       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
3092       smycols += ourlens[i];
3093       svals   += ourlens[i];
3094       jj++;
3095     }
3096   }
3097   ierr = PetscFree2(ourlens,offlens);CHKERRQ(ierr);
3098   ierr = PetscFree(vals);CHKERRQ(ierr);
3099   ierr = PetscFree(mycols);CHKERRQ(ierr);
3100   ierr = PetscFree(rowners);CHKERRQ(ierr);
3101   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3102   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3103   PetscFunctionReturn(0);
3104 }
3105 
3106 #undef __FUNCT__
3107 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ"
3108 /* TODO: Not scalable because of ISAllGather(). */
3109 PetscErrorCode MatGetSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3110 {
3111   PetscErrorCode ierr;
3112   IS             iscol_local;
3113   PetscInt       csize;
3114 
3115   PetscFunctionBegin;
3116   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3117   if (call == MAT_REUSE_MATRIX) {
3118     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3119     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3120   } else {
3121     PetscInt cbs;
3122     ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
3123     ierr = ISAllGather(iscol,&iscol_local);CHKERRQ(ierr);
3124     ierr = ISSetBlockSize(iscol_local,cbs);CHKERRQ(ierr);
3125   }
3126   ierr = MatGetSubMatrix_MPIAIJ_Private(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
3127   if (call == MAT_INITIAL_MATRIX) {
3128     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3129     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3130   }
3131   PetscFunctionReturn(0);
3132 }
3133 
3134 extern PetscErrorCode MatGetSubMatrices_MPIAIJ_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool*,Mat*);
3135 #undef __FUNCT__
3136 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ_Private"
3137 /*
3138     Not great since it makes two copies of the submatrix, first an SeqAIJ
3139   in local and then by concatenating the local matrices the end result.
3140   Writing it directly would be much like MatGetSubMatrices_MPIAIJ()
3141 
3142   Note: This requires a sequential iscol with all indices.
3143 */
3144 PetscErrorCode MatGetSubMatrix_MPIAIJ_Private(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3145 {
3146   PetscErrorCode ierr;
3147   PetscMPIInt    rank,size;
3148   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3149   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal,ncol;
3150   PetscBool      allcolumns, colflag;
3151   Mat            M,Mreuse;
3152   MatScalar      *vwork,*aa;
3153   MPI_Comm       comm;
3154   Mat_SeqAIJ     *aij;
3155 
3156   PetscFunctionBegin;
3157   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3158   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3159   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3160 
3161   ierr = ISIdentity(iscol,&colflag);CHKERRQ(ierr);
3162   ierr = ISGetLocalSize(iscol,&ncol);CHKERRQ(ierr);
3163   if (colflag && ncol == mat->cmap->N) {
3164     allcolumns = PETSC_TRUE;
3165   } else {
3166     allcolumns = PETSC_FALSE;
3167   }
3168   if (call ==  MAT_REUSE_MATRIX) {
3169     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3170     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3171     ierr = MatGetSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,&allcolumns,&Mreuse);CHKERRQ(ierr);
3172   } else {
3173     ierr = MatGetSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&allcolumns,&Mreuse);CHKERRQ(ierr);
3174   }
3175 
3176   /*
3177       m - number of local rows
3178       n - number of columns (same on all processors)
3179       rstart - first row in new global matrix generated
3180   */
3181   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3182   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3183   if (call == MAT_INITIAL_MATRIX) {
3184     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3185     ii  = aij->i;
3186     jj  = aij->j;
3187 
3188     /*
3189         Determine the number of non-zeros in the diagonal and off-diagonal
3190         portions of the matrix in order to do correct preallocation
3191     */
3192 
3193     /* first get start and end of "diagonal" columns */
3194     if (csize == PETSC_DECIDE) {
3195       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3196       if (mglobal == n) { /* square matrix */
3197         nlocal = m;
3198       } else {
3199         nlocal = n/size + ((n % size) > rank);
3200       }
3201     } else {
3202       nlocal = csize;
3203     }
3204     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3205     rstart = rend - nlocal;
3206     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);
3207 
3208     /* next, compute all the lengths */
3209     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3210     olens = dlens + m;
3211     for (i=0; i<m; i++) {
3212       jend = ii[i+1] - ii[i];
3213       olen = 0;
3214       dlen = 0;
3215       for (j=0; j<jend; j++) {
3216         if (*jj < rstart || *jj >= rend) olen++;
3217         else dlen++;
3218         jj++;
3219       }
3220       olens[i] = olen;
3221       dlens[i] = dlen;
3222     }
3223     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3224     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3225     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3226     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3227     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3228     ierr = PetscFree(dlens);CHKERRQ(ierr);
3229   } else {
3230     PetscInt ml,nl;
3231 
3232     M    = *newmat;
3233     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3234     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3235     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3236     /*
3237          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3238        rather than the slower MatSetValues().
3239     */
3240     M->was_assembled = PETSC_TRUE;
3241     M->assembled     = PETSC_FALSE;
3242   }
3243   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3244   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3245   ii   = aij->i;
3246   jj   = aij->j;
3247   aa   = aij->a;
3248   for (i=0; i<m; i++) {
3249     row   = rstart + i;
3250     nz    = ii[i+1] - ii[i];
3251     cwork = jj;     jj += nz;
3252     vwork = aa;     aa += nz;
3253     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3254   }
3255 
3256   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3257   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3258   *newmat = M;
3259 
3260   /* save submatrix used in processor for next request */
3261   if (call ==  MAT_INITIAL_MATRIX) {
3262     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3263     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3264   }
3265   PetscFunctionReturn(0);
3266 }
3267 
3268 #undef __FUNCT__
3269 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR_MPIAIJ"
3270 PetscErrorCode  MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3271 {
3272   PetscInt       m,cstart, cend,j,nnz,i,d;
3273   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3274   const PetscInt *JJ;
3275   PetscScalar    *values;
3276   PetscErrorCode ierr;
3277 
3278   PetscFunctionBegin;
3279   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3280 
3281   ierr   = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3282   ierr   = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3283   m      = B->rmap->n;
3284   cstart = B->cmap->rstart;
3285   cend   = B->cmap->rend;
3286   rstart = B->rmap->rstart;
3287 
3288   ierr = PetscMalloc2(m,&d_nnz,m,&o_nnz);CHKERRQ(ierr);
3289 
3290 #if defined(PETSC_USE_DEBUGGING)
3291   for (i=0; i<m; i++) {
3292     nnz = Ii[i+1]- Ii[i];
3293     JJ  = J + Ii[i];
3294     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3295     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3296     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);
3297   }
3298 #endif
3299 
3300   for (i=0; i<m; i++) {
3301     nnz     = Ii[i+1]- Ii[i];
3302     JJ      = J + Ii[i];
3303     nnz_max = PetscMax(nnz_max,nnz);
3304     d       = 0;
3305     for (j=0; j<nnz; j++) {
3306       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3307     }
3308     d_nnz[i] = d;
3309     o_nnz[i] = nnz - d;
3310   }
3311   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3312   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3313 
3314   if (v) values = (PetscScalar*)v;
3315   else {
3316     ierr = PetscCalloc1(nnz_max+1,&values);CHKERRQ(ierr);
3317   }
3318 
3319   for (i=0; i<m; i++) {
3320     ii   = i + rstart;
3321     nnz  = Ii[i+1]- Ii[i];
3322     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3323   }
3324   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3325   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3326 
3327   if (!v) {
3328     ierr = PetscFree(values);CHKERRQ(ierr);
3329   }
3330   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3331   PetscFunctionReturn(0);
3332 }
3333 
3334 #undef __FUNCT__
3335 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR"
3336 /*@
3337    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3338    (the default parallel PETSc format).
3339 
3340    Collective on MPI_Comm
3341 
3342    Input Parameters:
3343 +  B - the matrix
3344 .  i - the indices into j for the start of each local row (starts with zero)
3345 .  j - the column indices for each local row (starts with zero)
3346 -  v - optional values in the matrix
3347 
3348    Level: developer
3349 
3350    Notes:
3351        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3352      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3353      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3354 
3355        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3356 
3357        The format which is used for the sparse matrix input, is equivalent to a
3358     row-major ordering.. i.e for the following matrix, the input data expected is
3359     as shown:
3360 
3361         1 0 0
3362         2 0 3     P0
3363        -------
3364         4 5 6     P1
3365 
3366      Process0 [P0]: rows_owned=[0,1]
3367         i =  {0,1,3}  [size = nrow+1  = 2+1]
3368         j =  {0,0,2}  [size = nz = 6]
3369         v =  {1,2,3}  [size = nz = 6]
3370 
3371      Process1 [P1]: rows_owned=[2]
3372         i =  {0,3}    [size = nrow+1  = 1+1]
3373         j =  {0,1,2}  [size = nz = 6]
3374         v =  {4,5,6}  [size = nz = 6]
3375 
3376 .keywords: matrix, aij, compressed row, sparse, parallel
3377 
3378 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MPIAIJ,
3379           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3380 @*/
3381 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3382 {
3383   PetscErrorCode ierr;
3384 
3385   PetscFunctionBegin;
3386   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3387   PetscFunctionReturn(0);
3388 }
3389 
3390 #undef __FUNCT__
3391 #define __FUNCT__ "MatMPIAIJSetPreallocation"
3392 /*@C
3393    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3394    (the default parallel PETSc format).  For good matrix assembly performance
3395    the user should preallocate the matrix storage by setting the parameters
3396    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3397    performance can be increased by more than a factor of 50.
3398 
3399    Collective on MPI_Comm
3400 
3401    Input Parameters:
3402 +  B - the matrix
3403 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3404            (same value is used for all local rows)
3405 .  d_nnz - array containing the number of nonzeros in the various rows of the
3406            DIAGONAL portion of the local submatrix (possibly different for each row)
3407            or NULL (PETSC_NULL_INTEGER in Fortran), if d_nz is used to specify the nonzero structure.
3408            The size of this array is equal to the number of local rows, i.e 'm'.
3409            For matrices that will be factored, you must leave room for (and set)
3410            the diagonal entry even if it is zero.
3411 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3412            submatrix (same value is used for all local rows).
3413 -  o_nnz - array containing the number of nonzeros in the various rows of the
3414            OFF-DIAGONAL portion of the local submatrix (possibly different for
3415            each row) or NULL (PETSC_NULL_INTEGER in Fortran), if o_nz is used to specify the nonzero
3416            structure. The size of this array is equal to the number
3417            of local rows, i.e 'm'.
3418 
3419    If the *_nnz parameter is given then the *_nz parameter is ignored
3420 
3421    The AIJ format (also called the Yale sparse matrix format or
3422    compressed row storage (CSR)), is fully compatible with standard Fortran 77
3423    storage.  The stored row and column indices begin with zero.
3424    See Users-Manual: ch_mat for details.
3425 
3426    The parallel matrix is partitioned such that the first m0 rows belong to
3427    process 0, the next m1 rows belong to process 1, the next m2 rows belong
3428    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
3429 
3430    The DIAGONAL portion of the local submatrix of a processor can be defined
3431    as the submatrix which is obtained by extraction the part corresponding to
3432    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
3433    first row that belongs to the processor, r2 is the last row belonging to
3434    the this processor, and c1-c2 is range of indices of the local part of a
3435    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
3436    common case of a square matrix, the row and column ranges are the same and
3437    the DIAGONAL part is also square. The remaining portion of the local
3438    submatrix (mxN) constitute the OFF-DIAGONAL portion.
3439 
3440    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3441 
3442    You can call MatGetInfo() to get information on how effective the preallocation was;
3443    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3444    You can also run with the option -info and look for messages with the string
3445    malloc in them to see if additional memory allocation was needed.
3446 
3447    Example usage:
3448 
3449    Consider the following 8x8 matrix with 34 non-zero values, that is
3450    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3451    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3452    as follows:
3453 
3454 .vb
3455             1  2  0  |  0  3  0  |  0  4
3456     Proc0   0  5  6  |  7  0  0  |  8  0
3457             9  0 10  | 11  0  0  | 12  0
3458     -------------------------------------
3459            13  0 14  | 15 16 17  |  0  0
3460     Proc1   0 18  0  | 19 20 21  |  0  0
3461             0  0  0  | 22 23  0  | 24  0
3462     -------------------------------------
3463     Proc2  25 26 27  |  0  0 28  | 29  0
3464            30  0  0  | 31 32 33  |  0 34
3465 .ve
3466 
3467    This can be represented as a collection of submatrices as:
3468 
3469 .vb
3470       A B C
3471       D E F
3472       G H I
3473 .ve
3474 
3475    Where the submatrices A,B,C are owned by proc0, D,E,F are
3476    owned by proc1, G,H,I are owned by proc2.
3477 
3478    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3479    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3480    The 'M','N' parameters are 8,8, and have the same values on all procs.
3481 
3482    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3483    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3484    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3485    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3486    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3487    matrix, ans [DF] as another SeqAIJ matrix.
3488 
3489    When d_nz, o_nz parameters are specified, d_nz storage elements are
3490    allocated for every row of the local diagonal submatrix, and o_nz
3491    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3492    One way to choose d_nz and o_nz is to use the max nonzerors per local
3493    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3494    In this case, the values of d_nz,o_nz are:
3495 .vb
3496      proc0 : dnz = 2, o_nz = 2
3497      proc1 : dnz = 3, o_nz = 2
3498      proc2 : dnz = 1, o_nz = 4
3499 .ve
3500    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3501    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3502    for proc3. i.e we are using 12+15+10=37 storage locations to store
3503    34 values.
3504 
3505    When d_nnz, o_nnz parameters are specified, the storage is specified
3506    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3507    In the above case the values for d_nnz,o_nnz are:
3508 .vb
3509      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3510      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3511      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3512 .ve
3513    Here the space allocated is sum of all the above values i.e 34, and
3514    hence pre-allocation is perfect.
3515 
3516    Level: intermediate
3517 
3518 .keywords: matrix, aij, compressed row, sparse, parallel
3519 
3520 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
3521           MPIAIJ, MatGetInfo(), PetscSplitOwnership()
3522 @*/
3523 PetscErrorCode  MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3524 {
3525   PetscErrorCode ierr;
3526 
3527   PetscFunctionBegin;
3528   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3529   PetscValidType(B,1);
3530   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
3531   PetscFunctionReturn(0);
3532 }
3533 
3534 #undef __FUNCT__
3535 #define __FUNCT__ "MatCreateMPIAIJWithArrays"
3536 /*@
3537      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
3538          CSR format the local rows.
3539 
3540    Collective on MPI_Comm
3541 
3542    Input Parameters:
3543 +  comm - MPI communicator
3544 .  m - number of local rows (Cannot be PETSC_DECIDE)
3545 .  n - This value should be the same as the local size used in creating the
3546        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3547        calculated if N is given) For square matrices n is almost always m.
3548 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3549 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3550 .   i - row indices
3551 .   j - column indices
3552 -   a - matrix values
3553 
3554    Output Parameter:
3555 .   mat - the matrix
3556 
3557    Level: intermediate
3558 
3559    Notes:
3560        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3561      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3562      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3563 
3564        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3565 
3566        The format which is used for the sparse matrix input, is equivalent to a
3567     row-major ordering.. i.e for the following matrix, the input data expected is
3568     as shown:
3569 
3570         1 0 0
3571         2 0 3     P0
3572        -------
3573         4 5 6     P1
3574 
3575      Process0 [P0]: rows_owned=[0,1]
3576         i =  {0,1,3}  [size = nrow+1  = 2+1]
3577         j =  {0,0,2}  [size = nz = 6]
3578         v =  {1,2,3}  [size = nz = 6]
3579 
3580      Process1 [P1]: rows_owned=[2]
3581         i =  {0,3}    [size = nrow+1  = 1+1]
3582         j =  {0,1,2}  [size = nz = 6]
3583         v =  {4,5,6}  [size = nz = 6]
3584 
3585 .keywords: matrix, aij, compressed row, sparse, parallel
3586 
3587 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3588           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
3589 @*/
3590 PetscErrorCode  MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
3591 {
3592   PetscErrorCode ierr;
3593 
3594   PetscFunctionBegin;
3595   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
3596   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
3597   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
3598   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
3599   /* ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr); */
3600   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
3601   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
3602   PetscFunctionReturn(0);
3603 }
3604 
3605 #undef __FUNCT__
3606 #define __FUNCT__ "MatCreateAIJ"
3607 /*@C
3608    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
3609    (the default parallel PETSc format).  For good matrix assembly performance
3610    the user should preallocate the matrix storage by setting the parameters
3611    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3612    performance can be increased by more than a factor of 50.
3613 
3614    Collective on MPI_Comm
3615 
3616    Input Parameters:
3617 +  comm - MPI communicator
3618 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
3619            This value should be the same as the local size used in creating the
3620            y vector for the matrix-vector product y = Ax.
3621 .  n - This value should be the same as the local size used in creating the
3622        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3623        calculated if N is given) For square matrices n is almost always m.
3624 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3625 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3626 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3627            (same value is used for all local rows)
3628 .  d_nnz - array containing the number of nonzeros in the various rows of the
3629            DIAGONAL portion of the local submatrix (possibly different for each row)
3630            or NULL, if d_nz is used to specify the nonzero structure.
3631            The size of this array is equal to the number of local rows, i.e 'm'.
3632 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3633            submatrix (same value is used for all local rows).
3634 -  o_nnz - array containing the number of nonzeros in the various rows of the
3635            OFF-DIAGONAL portion of the local submatrix (possibly different for
3636            each row) or NULL, if o_nz is used to specify the nonzero
3637            structure. The size of this array is equal to the number
3638            of local rows, i.e 'm'.
3639 
3640    Output Parameter:
3641 .  A - the matrix
3642 
3643    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3644    MatXXXXSetPreallocation() paradgm instead of this routine directly.
3645    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3646 
3647    Notes:
3648    If the *_nnz parameter is given then the *_nz parameter is ignored
3649 
3650    m,n,M,N parameters specify the size of the matrix, and its partitioning across
3651    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
3652    storage requirements for this matrix.
3653 
3654    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
3655    processor than it must be used on all processors that share the object for
3656    that argument.
3657 
3658    The user MUST specify either the local or global matrix dimensions
3659    (possibly both).
3660 
3661    The parallel matrix is partitioned across processors such that the
3662    first m0 rows belong to process 0, the next m1 rows belong to
3663    process 1, the next m2 rows belong to process 2 etc.. where
3664    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
3665    values corresponding to [m x N] submatrix.
3666 
3667    The columns are logically partitioned with the n0 columns belonging
3668    to 0th partition, the next n1 columns belonging to the next
3669    partition etc.. where n0,n1,n2... are the input parameter 'n'.
3670 
3671    The DIAGONAL portion of the local submatrix on any given processor
3672    is the submatrix corresponding to the rows and columns m,n
3673    corresponding to the given processor. i.e diagonal matrix on
3674    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
3675    etc. The remaining portion of the local submatrix [m x (N-n)]
3676    constitute the OFF-DIAGONAL portion. The example below better
3677    illustrates this concept.
3678 
3679    For a square global matrix we define each processor's diagonal portion
3680    to be its local rows and the corresponding columns (a square submatrix);
3681    each processor's off-diagonal portion encompasses the remainder of the
3682    local matrix (a rectangular submatrix).
3683 
3684    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3685 
3686    When calling this routine with a single process communicator, a matrix of
3687    type SEQAIJ is returned.  If a matrix of type MPIAIJ is desired for this
3688    type of communicator, use the construction mechanism:
3689      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
3690 
3691    By default, this format uses inodes (identical nodes) when possible.
3692    We search for consecutive rows with the same nonzero structure, thereby
3693    reusing matrix information to achieve increased efficiency.
3694 
3695    Options Database Keys:
3696 +  -mat_no_inode  - Do not use inodes
3697 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3698 -  -mat_aij_oneindex - Internally use indexing starting at 1
3699         rather than 0.  Note that when calling MatSetValues(),
3700         the user still MUST index entries starting at 0!
3701 
3702 
3703    Example usage:
3704 
3705    Consider the following 8x8 matrix with 34 non-zero values, that is
3706    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3707    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3708    as follows:
3709 
3710 .vb
3711             1  2  0  |  0  3  0  |  0  4
3712     Proc0   0  5  6  |  7  0  0  |  8  0
3713             9  0 10  | 11  0  0  | 12  0
3714     -------------------------------------
3715            13  0 14  | 15 16 17  |  0  0
3716     Proc1   0 18  0  | 19 20 21  |  0  0
3717             0  0  0  | 22 23  0  | 24  0
3718     -------------------------------------
3719     Proc2  25 26 27  |  0  0 28  | 29  0
3720            30  0  0  | 31 32 33  |  0 34
3721 .ve
3722 
3723    This can be represented as a collection of submatrices as:
3724 
3725 .vb
3726       A B C
3727       D E F
3728       G H I
3729 .ve
3730 
3731    Where the submatrices A,B,C are owned by proc0, D,E,F are
3732    owned by proc1, G,H,I are owned by proc2.
3733 
3734    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3735    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3736    The 'M','N' parameters are 8,8, and have the same values on all procs.
3737 
3738    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3739    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3740    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3741    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3742    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3743    matrix, ans [DF] as another SeqAIJ matrix.
3744 
3745    When d_nz, o_nz parameters are specified, d_nz storage elements are
3746    allocated for every row of the local diagonal submatrix, and o_nz
3747    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3748    One way to choose d_nz and o_nz is to use the max nonzerors per local
3749    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3750    In this case, the values of d_nz,o_nz are:
3751 .vb
3752      proc0 : dnz = 2, o_nz = 2
3753      proc1 : dnz = 3, o_nz = 2
3754      proc2 : dnz = 1, o_nz = 4
3755 .ve
3756    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3757    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3758    for proc3. i.e we are using 12+15+10=37 storage locations to store
3759    34 values.
3760 
3761    When d_nnz, o_nnz parameters are specified, the storage is specified
3762    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3763    In the above case the values for d_nnz,o_nnz are:
3764 .vb
3765      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3766      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3767      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3768 .ve
3769    Here the space allocated is sum of all the above values i.e 34, and
3770    hence pre-allocation is perfect.
3771 
3772    Level: intermediate
3773 
3774 .keywords: matrix, aij, compressed row, sparse, parallel
3775 
3776 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3777           MPIAIJ, MatCreateMPIAIJWithArrays()
3778 @*/
3779 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)
3780 {
3781   PetscErrorCode ierr;
3782   PetscMPIInt    size;
3783 
3784   PetscFunctionBegin;
3785   ierr = MatCreate(comm,A);CHKERRQ(ierr);
3786   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
3787   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3788   if (size > 1) {
3789     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
3790     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
3791   } else {
3792     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
3793     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
3794   }
3795   PetscFunctionReturn(0);
3796 }
3797 
3798 #undef __FUNCT__
3799 #define __FUNCT__ "MatMPIAIJGetSeqAIJ"
3800 PetscErrorCode  MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
3801 {
3802   Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
3803 
3804   PetscFunctionBegin;
3805   if (Ad)     *Ad     = a->A;
3806   if (Ao)     *Ao     = a->B;
3807   if (colmap) *colmap = a->garray;
3808   PetscFunctionReturn(0);
3809 }
3810 
3811 #undef __FUNCT__
3812 #define __FUNCT__ "MatSetColoring_MPIAIJ"
3813 PetscErrorCode MatSetColoring_MPIAIJ(Mat A,ISColoring coloring)
3814 {
3815   PetscErrorCode ierr;
3816   PetscInt       i;
3817   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3818 
3819   PetscFunctionBegin;
3820   if (coloring->ctype == IS_COLORING_GLOBAL) {
3821     ISColoringValue *allcolors,*colors;
3822     ISColoring      ocoloring;
3823 
3824     /* set coloring for diagonal portion */
3825     ierr = MatSetColoring_SeqAIJ(a->A,coloring);CHKERRQ(ierr);
3826 
3827     /* set coloring for off-diagonal portion */
3828     ierr = ISAllGatherColors(PetscObjectComm((PetscObject)A),coloring->n,coloring->colors,NULL,&allcolors);CHKERRQ(ierr);
3829     ierr = PetscMalloc1(a->B->cmap->n+1,&colors);CHKERRQ(ierr);
3830     for (i=0; i<a->B->cmap->n; i++) {
3831       colors[i] = allcolors[a->garray[i]];
3832     }
3833     ierr = PetscFree(allcolors);CHKERRQ(ierr);
3834     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3835     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
3836     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3837   } else if (coloring->ctype == IS_COLORING_GHOSTED) {
3838     ISColoringValue *colors;
3839     PetscInt        *larray;
3840     ISColoring      ocoloring;
3841 
3842     /* set coloring for diagonal portion */
3843     ierr = PetscMalloc1(a->A->cmap->n+1,&larray);CHKERRQ(ierr);
3844     for (i=0; i<a->A->cmap->n; i++) {
3845       larray[i] = i + A->cmap->rstart;
3846     }
3847     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->A->cmap->n,larray,NULL,larray);CHKERRQ(ierr);
3848     ierr = PetscMalloc1(a->A->cmap->n+1,&colors);CHKERRQ(ierr);
3849     for (i=0; i<a->A->cmap->n; i++) {
3850       colors[i] = coloring->colors[larray[i]];
3851     }
3852     ierr = PetscFree(larray);CHKERRQ(ierr);
3853     ierr = ISColoringCreate(PETSC_COMM_SELF,coloring->n,a->A->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3854     ierr = MatSetColoring_SeqAIJ(a->A,ocoloring);CHKERRQ(ierr);
3855     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3856 
3857     /* set coloring for off-diagonal portion */
3858     ierr = PetscMalloc1(a->B->cmap->n+1,&larray);CHKERRQ(ierr);
3859     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->B->cmap->n,a->garray,NULL,larray);CHKERRQ(ierr);
3860     ierr = PetscMalloc1(a->B->cmap->n+1,&colors);CHKERRQ(ierr);
3861     for (i=0; i<a->B->cmap->n; i++) {
3862       colors[i] = coloring->colors[larray[i]];
3863     }
3864     ierr = PetscFree(larray);CHKERRQ(ierr);
3865     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3866     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
3867     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3868   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support ISColoringType %d",(int)coloring->ctype);
3869   PetscFunctionReturn(0);
3870 }
3871 
3872 #undef __FUNCT__
3873 #define __FUNCT__ "MatSetValuesAdifor_MPIAIJ"
3874 PetscErrorCode MatSetValuesAdifor_MPIAIJ(Mat A,PetscInt nl,void *advalues)
3875 {
3876   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3877   PetscErrorCode ierr;
3878 
3879   PetscFunctionBegin;
3880   ierr = MatSetValuesAdifor_SeqAIJ(a->A,nl,advalues);CHKERRQ(ierr);
3881   ierr = MatSetValuesAdifor_SeqAIJ(a->B,nl,advalues);CHKERRQ(ierr);
3882   PetscFunctionReturn(0);
3883 }
3884 
3885 #undef __FUNCT__
3886 #define __FUNCT__ "MatCreateMPIMatConcatenateSeqMat_MPIAIJ"
3887 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
3888 {
3889   PetscErrorCode ierr;
3890   PetscInt       m,N,i,rstart,nnz,Ii;
3891   PetscInt       *indx;
3892   PetscScalar    *values;
3893 
3894   PetscFunctionBegin;
3895   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
3896   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
3897     PetscInt       *dnz,*onz,sum,bs,cbs;
3898 
3899     if (n == PETSC_DECIDE) {
3900       ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
3901     }
3902     /* Check sum(n) = N */
3903     ierr = MPI_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3904     if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
3905 
3906     ierr    = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3907     rstart -= m;
3908 
3909     ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
3910     for (i=0; i<m; i++) {
3911       ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3912       ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
3913       ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3914     }
3915 
3916     ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
3917     ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
3918     ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
3919     ierr = MatSetBlockSizes(*outmat,bs,cbs);CHKERRQ(ierr);
3920     ierr = MatSetType(*outmat,MATMPIAIJ);CHKERRQ(ierr);
3921     ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
3922     ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
3923   }
3924 
3925   /* numeric phase */
3926   ierr = MatGetOwnershipRange(*outmat,&rstart,NULL);CHKERRQ(ierr);
3927   for (i=0; i<m; i++) {
3928     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3929     Ii   = i + rstart;
3930     ierr = MatSetValues(*outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3931     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3932   }
3933   ierr = MatAssemblyBegin(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3934   ierr = MatAssemblyEnd(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3935   PetscFunctionReturn(0);
3936 }
3937 
3938 #undef __FUNCT__
3939 #define __FUNCT__ "MatFileSplit"
3940 PetscErrorCode MatFileSplit(Mat A,char *outfile)
3941 {
3942   PetscErrorCode    ierr;
3943   PetscMPIInt       rank;
3944   PetscInt          m,N,i,rstart,nnz;
3945   size_t            len;
3946   const PetscInt    *indx;
3947   PetscViewer       out;
3948   char              *name;
3949   Mat               B;
3950   const PetscScalar *values;
3951 
3952   PetscFunctionBegin;
3953   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
3954   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
3955   /* Should this be the type of the diagonal block of A? */
3956   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
3957   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
3958   ierr = MatSetBlockSizesFromMats(B,A,A);CHKERRQ(ierr);
3959   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
3960   ierr = MatSeqAIJSetPreallocation(B,0,NULL);CHKERRQ(ierr);
3961   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
3962   for (i=0; i<m; i++) {
3963     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3964     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3965     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3966   }
3967   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3968   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3969 
3970   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
3971   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
3972   ierr = PetscMalloc1(len+5,&name);CHKERRQ(ierr);
3973   sprintf(name,"%s.%d",outfile,rank);
3974   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
3975   ierr = PetscFree(name);CHKERRQ(ierr);
3976   ierr = MatView(B,out);CHKERRQ(ierr);
3977   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
3978   ierr = MatDestroy(&B);CHKERRQ(ierr);
3979   PetscFunctionReturn(0);
3980 }
3981 
3982 extern PetscErrorCode MatDestroy_MPIAIJ(Mat);
3983 #undef __FUNCT__
3984 #define __FUNCT__ "MatDestroy_MPIAIJ_SeqsToMPI"
3985 PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
3986 {
3987   PetscErrorCode      ierr;
3988   Mat_Merge_SeqsToMPI *merge;
3989   PetscContainer      container;
3990 
3991   PetscFunctionBegin;
3992   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
3993   if (container) {
3994     ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
3995     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
3996     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
3997     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
3998     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
3999     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
4000     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
4001     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
4002     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
4003     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
4004     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
4005     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
4006     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
4007     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
4008     ierr = PetscFree(merge);CHKERRQ(ierr);
4009     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
4010   }
4011   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
4012   PetscFunctionReturn(0);
4013 }
4014 
4015 #include <../src/mat/utils/freespace.h>
4016 #include <petscbt.h>
4017 
4018 #undef __FUNCT__
4019 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJNumeric"
4020 PetscErrorCode  MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
4021 {
4022   PetscErrorCode      ierr;
4023   MPI_Comm            comm;
4024   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
4025   PetscMPIInt         size,rank,taga,*len_s;
4026   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
4027   PetscInt            proc,m;
4028   PetscInt            **buf_ri,**buf_rj;
4029   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
4030   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
4031   MPI_Request         *s_waits,*r_waits;
4032   MPI_Status          *status;
4033   MatScalar           *aa=a->a;
4034   MatScalar           **abuf_r,*ba_i;
4035   Mat_Merge_SeqsToMPI *merge;
4036   PetscContainer      container;
4037 
4038   PetscFunctionBegin;
4039   ierr = PetscObjectGetComm((PetscObject)mpimat,&comm);CHKERRQ(ierr);
4040   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4041 
4042   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4043   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4044 
4045   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4046   ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4047 
4048   bi     = merge->bi;
4049   bj     = merge->bj;
4050   buf_ri = merge->buf_ri;
4051   buf_rj = merge->buf_rj;
4052 
4053   ierr   = PetscMalloc1(size,&status);CHKERRQ(ierr);
4054   owners = merge->rowmap->range;
4055   len_s  = merge->len_s;
4056 
4057   /* send and recv matrix values */
4058   /*-----------------------------*/
4059   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
4060   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
4061 
4062   ierr = PetscMalloc1(merge->nsend+1,&s_waits);CHKERRQ(ierr);
4063   for (proc=0,k=0; proc<size; proc++) {
4064     if (!len_s[proc]) continue;
4065     i    = owners[proc];
4066     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
4067     k++;
4068   }
4069 
4070   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
4071   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
4072   ierr = PetscFree(status);CHKERRQ(ierr);
4073 
4074   ierr = PetscFree(s_waits);CHKERRQ(ierr);
4075   ierr = PetscFree(r_waits);CHKERRQ(ierr);
4076 
4077   /* insert mat values of mpimat */
4078   /*----------------------------*/
4079   ierr = PetscMalloc1(N,&ba_i);CHKERRQ(ierr);
4080   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4081 
4082   for (k=0; k<merge->nrecv; k++) {
4083     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4084     nrows       = *(buf_ri_k[k]);
4085     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
4086     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4087   }
4088 
4089   /* set values of ba */
4090   m = merge->rowmap->n;
4091   for (i=0; i<m; i++) {
4092     arow = owners[rank] + i;
4093     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
4094     bnzi = bi[i+1] - bi[i];
4095     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
4096 
4097     /* add local non-zero vals of this proc's seqmat into ba */
4098     anzi   = ai[arow+1] - ai[arow];
4099     aj     = a->j + ai[arow];
4100     aa     = a->a + ai[arow];
4101     nextaj = 0;
4102     for (j=0; nextaj<anzi; j++) {
4103       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4104         ba_i[j] += aa[nextaj++];
4105       }
4106     }
4107 
4108     /* add received vals into ba */
4109     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4110       /* i-th row */
4111       if (i == *nextrow[k]) {
4112         anzi   = *(nextai[k]+1) - *nextai[k];
4113         aj     = buf_rj[k] + *(nextai[k]);
4114         aa     = abuf_r[k] + *(nextai[k]);
4115         nextaj = 0;
4116         for (j=0; nextaj<anzi; j++) {
4117           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4118             ba_i[j] += aa[nextaj++];
4119           }
4120         }
4121         nextrow[k]++; nextai[k]++;
4122       }
4123     }
4124     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
4125   }
4126   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4127   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4128 
4129   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
4130   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
4131   ierr = PetscFree(ba_i);CHKERRQ(ierr);
4132   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4133   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4134   PetscFunctionReturn(0);
4135 }
4136 
4137 extern PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat);
4138 
4139 #undef __FUNCT__
4140 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJSymbolic"
4141 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4142 {
4143   PetscErrorCode      ierr;
4144   Mat                 B_mpi;
4145   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
4146   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4147   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
4148   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4149   PetscInt            len,proc,*dnz,*onz,bs,cbs;
4150   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4151   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4152   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
4153   MPI_Status          *status;
4154   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
4155   PetscBT             lnkbt;
4156   Mat_Merge_SeqsToMPI *merge;
4157   PetscContainer      container;
4158 
4159   PetscFunctionBegin;
4160   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4161 
4162   /* make sure it is a PETSc comm */
4163   ierr = PetscCommDuplicate(comm,&comm,NULL);CHKERRQ(ierr);
4164   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4165   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4166 
4167   ierr = PetscNew(&merge);CHKERRQ(ierr);
4168   ierr = PetscMalloc1(size,&status);CHKERRQ(ierr);
4169 
4170   /* determine row ownership */
4171   /*---------------------------------------------------------*/
4172   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
4173   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
4174   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
4175   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
4176   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
4177   ierr = PetscMalloc1(size,&len_si);CHKERRQ(ierr);
4178   ierr = PetscMalloc1(size,&merge->len_s);CHKERRQ(ierr);
4179 
4180   m      = merge->rowmap->n;
4181   owners = merge->rowmap->range;
4182 
4183   /* determine the number of messages to send, their lengths */
4184   /*---------------------------------------------------------*/
4185   len_s = merge->len_s;
4186 
4187   len          = 0; /* length of buf_si[] */
4188   merge->nsend = 0;
4189   for (proc=0; proc<size; proc++) {
4190     len_si[proc] = 0;
4191     if (proc == rank) {
4192       len_s[proc] = 0;
4193     } else {
4194       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4195       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4196     }
4197     if (len_s[proc]) {
4198       merge->nsend++;
4199       nrows = 0;
4200       for (i=owners[proc]; i<owners[proc+1]; i++) {
4201         if (ai[i+1] > ai[i]) nrows++;
4202       }
4203       len_si[proc] = 2*(nrows+1);
4204       len         += len_si[proc];
4205     }
4206   }
4207 
4208   /* determine the number and length of messages to receive for ij-structure */
4209   /*-------------------------------------------------------------------------*/
4210   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
4211   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
4212 
4213   /* post the Irecv of j-structure */
4214   /*-------------------------------*/
4215   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
4216   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
4217 
4218   /* post the Isend of j-structure */
4219   /*--------------------------------*/
4220   ierr = PetscMalloc2(merge->nsend,&si_waits,merge->nsend,&sj_waits);CHKERRQ(ierr);
4221 
4222   for (proc=0, k=0; proc<size; proc++) {
4223     if (!len_s[proc]) continue;
4224     i    = owners[proc];
4225     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
4226     k++;
4227   }
4228 
4229   /* receives and sends of j-structure are complete */
4230   /*------------------------------------------------*/
4231   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
4232   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
4233 
4234   /* send and recv i-structure */
4235   /*---------------------------*/
4236   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
4237   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
4238 
4239   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
4240   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4241   for (proc=0,k=0; proc<size; proc++) {
4242     if (!len_s[proc]) continue;
4243     /* form outgoing message for i-structure:
4244          buf_si[0]:                 nrows to be sent
4245                [1:nrows]:           row index (global)
4246                [nrows+1:2*nrows+1]: i-structure index
4247     */
4248     /*-------------------------------------------*/
4249     nrows       = len_si[proc]/2 - 1;
4250     buf_si_i    = buf_si + nrows+1;
4251     buf_si[0]   = nrows;
4252     buf_si_i[0] = 0;
4253     nrows       = 0;
4254     for (i=owners[proc]; i<owners[proc+1]; i++) {
4255       anzi = ai[i+1] - ai[i];
4256       if (anzi) {
4257         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4258         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4259         nrows++;
4260       }
4261     }
4262     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4263     k++;
4264     buf_si += len_si[proc];
4265   }
4266 
4267   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4268   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4269 
4270   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4271   for (i=0; i<merge->nrecv; i++) {
4272     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);
4273   }
4274 
4275   ierr = PetscFree(len_si);CHKERRQ(ierr);
4276   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4277   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4278   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4279   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4280   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4281   ierr = PetscFree(status);CHKERRQ(ierr);
4282 
4283   /* compute a local seq matrix in each processor */
4284   /*----------------------------------------------*/
4285   /* allocate bi array and free space for accumulating nonzero column info */
4286   ierr  = PetscMalloc1(m+1,&bi);CHKERRQ(ierr);
4287   bi[0] = 0;
4288 
4289   /* create and initialize a linked list */
4290   nlnk = N+1;
4291   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4292 
4293   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4294   len  = ai[owners[rank+1]] - ai[owners[rank]];
4295   ierr = PetscFreeSpaceGet((PetscInt)(2*len+1),&free_space);CHKERRQ(ierr);
4296 
4297   current_space = free_space;
4298 
4299   /* determine symbolic info for each local row */
4300   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4301 
4302   for (k=0; k<merge->nrecv; k++) {
4303     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4304     nrows       = *buf_ri_k[k];
4305     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4306     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4307   }
4308 
4309   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4310   len  = 0;
4311   for (i=0; i<m; i++) {
4312     bnzi = 0;
4313     /* add local non-zero cols of this proc's seqmat into lnk */
4314     arow  = owners[rank] + i;
4315     anzi  = ai[arow+1] - ai[arow];
4316     aj    = a->j + ai[arow];
4317     ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4318     bnzi += nlnk;
4319     /* add received col data into lnk */
4320     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4321       if (i == *nextrow[k]) { /* i-th row */
4322         anzi  = *(nextai[k]+1) - *nextai[k];
4323         aj    = buf_rj[k] + *nextai[k];
4324         ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4325         bnzi += nlnk;
4326         nextrow[k]++; nextai[k]++;
4327       }
4328     }
4329     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4330 
4331     /* if free space is not available, make more free space */
4332     if (current_space->local_remaining<bnzi) {
4333       ierr = PetscFreeSpaceGet(bnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
4334       nspacedouble++;
4335     }
4336     /* copy data into free space, then initialize lnk */
4337     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4338     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
4339 
4340     current_space->array           += bnzi;
4341     current_space->local_used      += bnzi;
4342     current_space->local_remaining -= bnzi;
4343 
4344     bi[i+1] = bi[i] + bnzi;
4345   }
4346 
4347   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4348 
4349   ierr = PetscMalloc1(bi[m]+1,&bj);CHKERRQ(ierr);
4350   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
4351   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4352 
4353   /* create symbolic parallel matrix B_mpi */
4354   /*---------------------------------------*/
4355   ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
4356   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
4357   if (n==PETSC_DECIDE) {
4358     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
4359   } else {
4360     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4361   }
4362   ierr = MatSetBlockSizes(B_mpi,bs,cbs);CHKERRQ(ierr);
4363   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
4364   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
4365   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4366   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
4367 
4368   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4369   B_mpi->assembled    = PETSC_FALSE;
4370   B_mpi->ops->destroy = MatDestroy_MPIAIJ_SeqsToMPI;
4371   merge->bi           = bi;
4372   merge->bj           = bj;
4373   merge->buf_ri       = buf_ri;
4374   merge->buf_rj       = buf_rj;
4375   merge->coi          = NULL;
4376   merge->coj          = NULL;
4377   merge->owners_co    = NULL;
4378 
4379   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
4380 
4381   /* attach the supporting struct to B_mpi for reuse */
4382   ierr    = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
4383   ierr    = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
4384   ierr    = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
4385   ierr    = PetscContainerDestroy(&container);CHKERRQ(ierr);
4386   *mpimat = B_mpi;
4387 
4388   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4389   PetscFunctionReturn(0);
4390 }
4391 
4392 #undef __FUNCT__
4393 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJ"
4394 /*@C
4395       MatCreateMPIAIJSumSeqAIJ - Creates a MPIAIJ matrix by adding sequential
4396                  matrices from each processor
4397 
4398     Collective on MPI_Comm
4399 
4400    Input Parameters:
4401 +    comm - the communicators the parallel matrix will live on
4402 .    seqmat - the input sequential matrices
4403 .    m - number of local rows (or PETSC_DECIDE)
4404 .    n - number of local columns (or PETSC_DECIDE)
4405 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4406 
4407    Output Parameter:
4408 .    mpimat - the parallel matrix generated
4409 
4410     Level: advanced
4411 
4412    Notes:
4413      The dimensions of the sequential matrix in each processor MUST be the same.
4414      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
4415      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
4416 @*/
4417 PetscErrorCode  MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
4418 {
4419   PetscErrorCode ierr;
4420   PetscMPIInt    size;
4421 
4422   PetscFunctionBegin;
4423   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4424   if (size == 1) {
4425     ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4426     if (scall == MAT_INITIAL_MATRIX) {
4427       ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
4428     } else {
4429       ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4430     }
4431     ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4432     PetscFunctionReturn(0);
4433   }
4434   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4435   if (scall == MAT_INITIAL_MATRIX) {
4436     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
4437   }
4438   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
4439   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4440   PetscFunctionReturn(0);
4441 }
4442 
4443 #undef __FUNCT__
4444 #define __FUNCT__ "MatMPIAIJGetLocalMat"
4445 /*@
4446      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
4447           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
4448           with MatGetSize()
4449 
4450     Not Collective
4451 
4452    Input Parameters:
4453 +    A - the matrix
4454 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4455 
4456    Output Parameter:
4457 .    A_loc - the local sequential matrix generated
4458 
4459     Level: developer
4460 
4461 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
4462 
4463 @*/
4464 PetscErrorCode  MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
4465 {
4466   PetscErrorCode ierr;
4467   Mat_MPIAIJ     *mpimat=(Mat_MPIAIJ*)A->data;
4468   Mat_SeqAIJ     *mat,*a,*b;
4469   PetscInt       *ai,*aj,*bi,*bj,*cmap=mpimat->garray;
4470   MatScalar      *aa,*ba,*cam;
4471   PetscScalar    *ca;
4472   PetscInt       am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
4473   PetscInt       *ci,*cj,col,ncols_d,ncols_o,jo;
4474   PetscBool      match;
4475   MPI_Comm       comm;
4476   PetscMPIInt    size;
4477 
4478   PetscFunctionBegin;
4479   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4480   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
4481   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4482   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4483   if (size == 1 && scall == MAT_REUSE_MATRIX) PetscFunctionReturn(0);
4484 
4485   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4486   a = (Mat_SeqAIJ*)(mpimat->A)->data;
4487   b = (Mat_SeqAIJ*)(mpimat->B)->data;
4488   ai = a->i; aj = a->j; bi = b->i; bj = b->j;
4489   aa = a->a; ba = b->a;
4490   if (scall == MAT_INITIAL_MATRIX) {
4491     if (size == 1) {
4492       ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ai,aj,aa,A_loc);CHKERRQ(ierr);
4493       PetscFunctionReturn(0);
4494     }
4495 
4496     ierr  = PetscMalloc1(1+am,&ci);CHKERRQ(ierr);
4497     ci[0] = 0;
4498     for (i=0; i<am; i++) {
4499       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
4500     }
4501     ierr = PetscMalloc1(1+ci[am],&cj);CHKERRQ(ierr);
4502     ierr = PetscMalloc1(1+ci[am],&ca);CHKERRQ(ierr);
4503     k    = 0;
4504     for (i=0; i<am; i++) {
4505       ncols_o = bi[i+1] - bi[i];
4506       ncols_d = ai[i+1] - ai[i];
4507       /* off-diagonal portion of A */
4508       for (jo=0; jo<ncols_o; jo++) {
4509         col = cmap[*bj];
4510         if (col >= cstart) break;
4511         cj[k]   = col; bj++;
4512         ca[k++] = *ba++;
4513       }
4514       /* diagonal portion of A */
4515       for (j=0; j<ncols_d; j++) {
4516         cj[k]   = cstart + *aj++;
4517         ca[k++] = *aa++;
4518       }
4519       /* off-diagonal portion of A */
4520       for (j=jo; j<ncols_o; j++) {
4521         cj[k]   = cmap[*bj++];
4522         ca[k++] = *ba++;
4523       }
4524     }
4525     /* put together the new matrix */
4526     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
4527     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4528     /* Since these are PETSc arrays, change flags to free them as necessary. */
4529     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
4530     mat->free_a  = PETSC_TRUE;
4531     mat->free_ij = PETSC_TRUE;
4532     mat->nonew   = 0;
4533   } else if (scall == MAT_REUSE_MATRIX) {
4534     mat=(Mat_SeqAIJ*)(*A_loc)->data;
4535     ci = mat->i; cj = mat->j; cam = mat->a;
4536     for (i=0; i<am; i++) {
4537       /* off-diagonal portion of A */
4538       ncols_o = bi[i+1] - bi[i];
4539       for (jo=0; jo<ncols_o; jo++) {
4540         col = cmap[*bj];
4541         if (col >= cstart) break;
4542         *cam++ = *ba++; bj++;
4543       }
4544       /* diagonal portion of A */
4545       ncols_d = ai[i+1] - ai[i];
4546       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
4547       /* off-diagonal portion of A */
4548       for (j=jo; j<ncols_o; j++) {
4549         *cam++ = *ba++; bj++;
4550       }
4551     }
4552   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
4553   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4554   PetscFunctionReturn(0);
4555 }
4556 
4557 #undef __FUNCT__
4558 #define __FUNCT__ "MatMPIAIJGetLocalMatCondensed"
4559 /*@C
4560      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MPIAIJ matrix by taking all its local rows and NON-ZERO columns
4561 
4562     Not Collective
4563 
4564    Input Parameters:
4565 +    A - the matrix
4566 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4567 -    row, col - index sets of rows and columns to extract (or NULL)
4568 
4569    Output Parameter:
4570 .    A_loc - the local sequential matrix generated
4571 
4572     Level: developer
4573 
4574 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
4575 
4576 @*/
4577 PetscErrorCode  MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
4578 {
4579   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4580   PetscErrorCode ierr;
4581   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
4582   IS             isrowa,iscola;
4583   Mat            *aloc;
4584   PetscBool      match;
4585 
4586   PetscFunctionBegin;
4587   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4588   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
4589   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4590   if (!row) {
4591     start = A->rmap->rstart; end = A->rmap->rend;
4592     ierr  = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
4593   } else {
4594     isrowa = *row;
4595   }
4596   if (!col) {
4597     start = A->cmap->rstart;
4598     cmap  = a->garray;
4599     nzA   = a->A->cmap->n;
4600     nzB   = a->B->cmap->n;
4601     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4602     ncols = 0;
4603     for (i=0; i<nzB; i++) {
4604       if (cmap[i] < start) idx[ncols++] = cmap[i];
4605       else break;
4606     }
4607     imark = i;
4608     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
4609     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
4610     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
4611   } else {
4612     iscola = *col;
4613   }
4614   if (scall != MAT_INITIAL_MATRIX) {
4615     ierr    = PetscMalloc1(1,&aloc);CHKERRQ(ierr);
4616     aloc[0] = *A_loc;
4617   }
4618   ierr   = MatGetSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
4619   *A_loc = aloc[0];
4620   ierr   = PetscFree(aloc);CHKERRQ(ierr);
4621   if (!row) {
4622     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
4623   }
4624   if (!col) {
4625     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
4626   }
4627   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4628   PetscFunctionReturn(0);
4629 }
4630 
4631 #undef __FUNCT__
4632 #define __FUNCT__ "MatGetBrowsOfAcols"
4633 /*@C
4634     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
4635 
4636     Collective on Mat
4637 
4638    Input Parameters:
4639 +    A,B - the matrices in mpiaij format
4640 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4641 -    rowb, colb - index sets of rows and columns of B to extract (or NULL)
4642 
4643    Output Parameter:
4644 +    rowb, colb - index sets of rows and columns of B to extract
4645 -    B_seq - the sequential matrix generated
4646 
4647     Level: developer
4648 
4649 @*/
4650 PetscErrorCode  MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
4651 {
4652   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4653   PetscErrorCode ierr;
4654   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
4655   IS             isrowb,iscolb;
4656   Mat            *bseq=NULL;
4657 
4658   PetscFunctionBegin;
4659   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4660     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);
4661   }
4662   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4663 
4664   if (scall == MAT_INITIAL_MATRIX) {
4665     start = A->cmap->rstart;
4666     cmap  = a->garray;
4667     nzA   = a->A->cmap->n;
4668     nzB   = a->B->cmap->n;
4669     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4670     ncols = 0;
4671     for (i=0; i<nzB; i++) {  /* row < local row index */
4672       if (cmap[i] < start) idx[ncols++] = cmap[i];
4673       else break;
4674     }
4675     imark = i;
4676     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
4677     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
4678     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
4679     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
4680   } else {
4681     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
4682     isrowb  = *rowb; iscolb = *colb;
4683     ierr    = PetscMalloc1(1,&bseq);CHKERRQ(ierr);
4684     bseq[0] = *B_seq;
4685   }
4686   ierr   = MatGetSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
4687   *B_seq = bseq[0];
4688   ierr   = PetscFree(bseq);CHKERRQ(ierr);
4689   if (!rowb) {
4690     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
4691   } else {
4692     *rowb = isrowb;
4693   }
4694   if (!colb) {
4695     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
4696   } else {
4697     *colb = iscolb;
4698   }
4699   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4700   PetscFunctionReturn(0);
4701 }
4702 
4703 #undef __FUNCT__
4704 #define __FUNCT__ "MatGetBrowsOfAoCols_MPIAIJ"
4705 /*
4706     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
4707     of the OFF-DIAGONAL portion of local A
4708 
4709     Collective on Mat
4710 
4711    Input Parameters:
4712 +    A,B - the matrices in mpiaij format
4713 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4714 
4715    Output Parameter:
4716 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
4717 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
4718 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
4719 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
4720 
4721     Level: developer
4722 
4723 */
4724 PetscErrorCode  MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
4725 {
4726   VecScatter_MPI_General *gen_to,*gen_from;
4727   PetscErrorCode         ierr;
4728   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
4729   Mat_SeqAIJ             *b_oth;
4730   VecScatter             ctx =a->Mvctx;
4731   MPI_Comm               comm;
4732   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
4733   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
4734   PetscScalar            *rvalues,*svalues;
4735   MatScalar              *b_otha,*bufa,*bufA;
4736   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
4737   MPI_Request            *rwaits = NULL,*swaits = NULL;
4738   MPI_Status             *sstatus,rstatus;
4739   PetscMPIInt            jj,size;
4740   PetscInt               *cols,sbs,rbs;
4741   PetscScalar            *vals;
4742 
4743   PetscFunctionBegin;
4744   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4745   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4746 
4747   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4748     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);
4749   }
4750   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4751   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4752 
4753   gen_to   = (VecScatter_MPI_General*)ctx->todata;
4754   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
4755   rvalues  = gen_from->values; /* holds the length of receiving row */
4756   svalues  = gen_to->values;   /* holds the length of sending row */
4757   nrecvs   = gen_from->n;
4758   nsends   = gen_to->n;
4759 
4760   ierr    = PetscMalloc2(nrecvs,&rwaits,nsends,&swaits);CHKERRQ(ierr);
4761   srow    = gen_to->indices;    /* local row index to be sent */
4762   sstarts = gen_to->starts;
4763   sprocs  = gen_to->procs;
4764   sstatus = gen_to->sstatus;
4765   sbs     = gen_to->bs;
4766   rstarts = gen_from->starts;
4767   rprocs  = gen_from->procs;
4768   rbs     = gen_from->bs;
4769 
4770   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
4771   if (scall == MAT_INITIAL_MATRIX) {
4772     /* i-array */
4773     /*---------*/
4774     /*  post receives */
4775     for (i=0; i<nrecvs; i++) {
4776       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
4777       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
4778       ierr   = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4779     }
4780 
4781     /* pack the outgoing message */
4782     ierr = PetscMalloc2(nsends+1,&sstartsj,nrecvs+1,&rstartsj);CHKERRQ(ierr);
4783 
4784     sstartsj[0] = 0;
4785     rstartsj[0] = 0;
4786     len         = 0; /* total length of j or a array to be sent */
4787     k           = 0;
4788     for (i=0; i<nsends; i++) {
4789       rowlen = (PetscInt*)svalues + sstarts[i]*sbs;
4790       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
4791       for (j=0; j<nrows; j++) {
4792         row = srow[k] + B->rmap->range[rank]; /* global row idx */
4793         for (l=0; l<sbs; l++) {
4794           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr); /* rowlength */
4795 
4796           rowlen[j*sbs+l] = ncols;
4797 
4798           len += ncols;
4799           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr);
4800         }
4801         k++;
4802       }
4803       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4804 
4805       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
4806     }
4807     /* recvs and sends of i-array are completed */
4808     i = nrecvs;
4809     while (i--) {
4810       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4811     }
4812     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4813 
4814     /* allocate buffers for sending j and a arrays */
4815     ierr = PetscMalloc1(len+1,&bufj);CHKERRQ(ierr);
4816     ierr = PetscMalloc1(len+1,&bufa);CHKERRQ(ierr);
4817 
4818     /* create i-array of B_oth */
4819     ierr = PetscMalloc1(aBn+2,&b_othi);CHKERRQ(ierr);
4820 
4821     b_othi[0] = 0;
4822     len       = 0; /* total length of j or a array to be received */
4823     k         = 0;
4824     for (i=0; i<nrecvs; i++) {
4825       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
4826       nrows  = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be recieved */
4827       for (j=0; j<nrows; j++) {
4828         b_othi[k+1] = b_othi[k] + rowlen[j];
4829         len        += rowlen[j]; k++;
4830       }
4831       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
4832     }
4833 
4834     /* allocate space for j and a arrrays of B_oth */
4835     ierr = PetscMalloc1(b_othi[aBn]+1,&b_othj);CHKERRQ(ierr);
4836     ierr = PetscMalloc1(b_othi[aBn]+1,&b_otha);CHKERRQ(ierr);
4837 
4838     /* j-array */
4839     /*---------*/
4840     /*  post receives of j-array */
4841     for (i=0; i<nrecvs; i++) {
4842       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4843       ierr  = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4844     }
4845 
4846     /* pack the outgoing message j-array */
4847     k = 0;
4848     for (i=0; i<nsends; i++) {
4849       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4850       bufJ  = bufj+sstartsj[i];
4851       for (j=0; j<nrows; j++) {
4852         row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4853         for (ll=0; ll<sbs; ll++) {
4854           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4855           for (l=0; l<ncols; l++) {
4856             *bufJ++ = cols[l];
4857           }
4858           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4859         }
4860       }
4861       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4862     }
4863 
4864     /* recvs and sends of j-array are completed */
4865     i = nrecvs;
4866     while (i--) {
4867       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4868     }
4869     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4870   } else if (scall == MAT_REUSE_MATRIX) {
4871     sstartsj = *startsj_s;
4872     rstartsj = *startsj_r;
4873     bufa     = *bufa_ptr;
4874     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
4875     b_otha   = b_oth->a;
4876   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
4877 
4878   /* a-array */
4879   /*---------*/
4880   /*  post receives of a-array */
4881   for (i=0; i<nrecvs; i++) {
4882     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4883     ierr  = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4884   }
4885 
4886   /* pack the outgoing message a-array */
4887   k = 0;
4888   for (i=0; i<nsends; i++) {
4889     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4890     bufA  = bufa+sstartsj[i];
4891     for (j=0; j<nrows; j++) {
4892       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4893       for (ll=0; ll<sbs; ll++) {
4894         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4895         for (l=0; l<ncols; l++) {
4896           *bufA++ = vals[l];
4897         }
4898         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4899       }
4900     }
4901     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4902   }
4903   /* recvs and sends of a-array are completed */
4904   i = nrecvs;
4905   while (i--) {
4906     ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4907   }
4908   if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4909   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
4910 
4911   if (scall == MAT_INITIAL_MATRIX) {
4912     /* put together the new matrix */
4913     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
4914 
4915     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4916     /* Since these are PETSc arrays, change flags to free them as necessary. */
4917     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
4918     b_oth->free_a  = PETSC_TRUE;
4919     b_oth->free_ij = PETSC_TRUE;
4920     b_oth->nonew   = 0;
4921 
4922     ierr = PetscFree(bufj);CHKERRQ(ierr);
4923     if (!startsj_s || !bufa_ptr) {
4924       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
4925       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
4926     } else {
4927       *startsj_s = sstartsj;
4928       *startsj_r = rstartsj;
4929       *bufa_ptr  = bufa;
4930     }
4931   }
4932   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4933   PetscFunctionReturn(0);
4934 }
4935 
4936 #undef __FUNCT__
4937 #define __FUNCT__ "MatGetCommunicationStructs"
4938 /*@C
4939   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
4940 
4941   Not Collective
4942 
4943   Input Parameters:
4944 . A - The matrix in mpiaij format
4945 
4946   Output Parameter:
4947 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
4948 . colmap - A map from global column index to local index into lvec
4949 - multScatter - A scatter from the argument of a matrix-vector product to lvec
4950 
4951   Level: developer
4952 
4953 @*/
4954 #if defined(PETSC_USE_CTABLE)
4955 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
4956 #else
4957 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
4958 #endif
4959 {
4960   Mat_MPIAIJ *a;
4961 
4962   PetscFunctionBegin;
4963   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4964   PetscValidPointer(lvec, 2);
4965   PetscValidPointer(colmap, 3);
4966   PetscValidPointer(multScatter, 4);
4967   a = (Mat_MPIAIJ*) A->data;
4968   if (lvec) *lvec = a->lvec;
4969   if (colmap) *colmap = a->colmap;
4970   if (multScatter) *multScatter = a->Mvctx;
4971   PetscFunctionReturn(0);
4972 }
4973 
4974 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
4975 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
4976 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
4977 #if defined(PETSC_HAVE_ELEMENTAL)
4978 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
4979 #endif
4980 
4981 #undef __FUNCT__
4982 #define __FUNCT__ "MatMatMultNumeric_MPIDense_MPIAIJ"
4983 /*
4984     Computes (B'*A')' since computing B*A directly is untenable
4985 
4986                n                       p                          p
4987         (              )       (              )         (                  )
4988       m (      A       )  *  n (       B      )   =   m (         C        )
4989         (              )       (              )         (                  )
4990 
4991 */
4992 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
4993 {
4994   PetscErrorCode ierr;
4995   Mat            At,Bt,Ct;
4996 
4997   PetscFunctionBegin;
4998   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
4999   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
5000   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
5001   ierr = MatDestroy(&At);CHKERRQ(ierr);
5002   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
5003   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
5004   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
5005   PetscFunctionReturn(0);
5006 }
5007 
5008 #undef __FUNCT__
5009 #define __FUNCT__ "MatMatMultSymbolic_MPIDense_MPIAIJ"
5010 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
5011 {
5012   PetscErrorCode ierr;
5013   PetscInt       m=A->rmap->n,n=B->cmap->n;
5014   Mat            Cmat;
5015 
5016   PetscFunctionBegin;
5017   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);
5018   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
5019   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
5020   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
5021   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
5022   ierr = MatMPIDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
5023   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5024   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5025 
5026   Cmat->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
5027 
5028   *C = Cmat;
5029   PetscFunctionReturn(0);
5030 }
5031 
5032 /* ----------------------------------------------------------------*/
5033 #undef __FUNCT__
5034 #define __FUNCT__ "MatMatMult_MPIDense_MPIAIJ"
5035 PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
5036 {
5037   PetscErrorCode ierr;
5038 
5039   PetscFunctionBegin;
5040   if (scall == MAT_INITIAL_MATRIX) {
5041     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5042     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
5043     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5044   }
5045   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5046   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
5047   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5048   PetscFunctionReturn(0);
5049 }
5050 
5051 /*MC
5052    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
5053 
5054    Options Database Keys:
5055 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
5056 
5057   Level: beginner
5058 
5059 .seealso: MatCreateAIJ()
5060 M*/
5061 
5062 #undef __FUNCT__
5063 #define __FUNCT__ "MatCreate_MPIAIJ"
5064 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
5065 {
5066   Mat_MPIAIJ     *b;
5067   PetscErrorCode ierr;
5068   PetscMPIInt    size;
5069 
5070   PetscFunctionBegin;
5071   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
5072 
5073   ierr          = PetscNewLog(B,&b);CHKERRQ(ierr);
5074   B->data       = (void*)b;
5075   ierr          = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
5076   B->assembled  = PETSC_FALSE;
5077   B->insertmode = NOT_SET_VALUES;
5078   b->size       = size;
5079 
5080   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank);CHKERRQ(ierr);
5081 
5082   /* build cache for off array entries formed */
5083   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash);CHKERRQ(ierr);
5084 
5085   b->donotstash  = PETSC_FALSE;
5086   b->colmap      = 0;
5087   b->garray      = 0;
5088   b->roworiented = PETSC_TRUE;
5089 
5090   /* stuff used for matrix vector multiply */
5091   b->lvec  = NULL;
5092   b->Mvctx = NULL;
5093 
5094   /* stuff for MatGetRow() */
5095   b->rowindices   = 0;
5096   b->rowvalues    = 0;
5097   b->getrowactive = PETSC_FALSE;
5098 
5099   /* flexible pointer used in CUSP/CUSPARSE classes */
5100   b->spptr = NULL;
5101 
5102   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ);CHKERRQ(ierr);
5103   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
5104   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetDiagonalBlock_C",MatGetDiagonalBlock_MPIAIJ);CHKERRQ(ierr);
5105   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
5106   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
5107   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
5108   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
5109   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
5110   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
5111   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
5112 #if defined(PETSC_HAVE_ELEMENTAL)
5113   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_elemental_C",MatConvert_MPIAIJ_Elemental);CHKERRQ(ierr);
5114 #endif
5115   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
5116   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
5117   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
5118   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
5119   PetscFunctionReturn(0);
5120 }
5121 
5122 #undef __FUNCT__
5123 #define __FUNCT__ "MatCreateMPIAIJWithSplitArrays"
5124 /*@C
5125      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
5126          and "off-diagonal" part of the matrix in CSR format.
5127 
5128    Collective on MPI_Comm
5129 
5130    Input Parameters:
5131 +  comm - MPI communicator
5132 .  m - number of local rows (Cannot be PETSC_DECIDE)
5133 .  n - This value should be the same as the local size used in creating the
5134        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
5135        calculated if N is given) For square matrices n is almost always m.
5136 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
5137 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
5138 .   i - row indices for "diagonal" portion of matrix
5139 .   j - column indices
5140 .   a - matrix values
5141 .   oi - row indices for "off-diagonal" portion of matrix
5142 .   oj - column indices
5143 -   oa - matrix values
5144 
5145    Output Parameter:
5146 .   mat - the matrix
5147 
5148    Level: advanced
5149 
5150    Notes:
5151        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
5152        must free the arrays once the matrix has been destroyed and not before.
5153 
5154        The i and j indices are 0 based
5155 
5156        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
5157 
5158        This sets local rows and cannot be used to set off-processor values.
5159 
5160        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
5161        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
5162        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
5163        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
5164        keep track of the underlying array. Use MatSetOption(A,MAT_IGNORE_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
5165        communication if it is known that only local entries will be set.
5166 
5167 .keywords: matrix, aij, compressed row, sparse, parallel
5168 
5169 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
5170           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
5171 @*/
5172 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)
5173 {
5174   PetscErrorCode ierr;
5175   Mat_MPIAIJ     *maij;
5176 
5177   PetscFunctionBegin;
5178   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
5179   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
5180   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
5181   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
5182   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
5183   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
5184   maij = (Mat_MPIAIJ*) (*mat)->data;
5185 
5186   (*mat)->preallocated = PETSC_TRUE;
5187 
5188   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
5189   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
5190 
5191   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
5192   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
5193 
5194   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5195   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5196   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5197   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5198 
5199   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5200   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5201   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
5202   PetscFunctionReturn(0);
5203 }
5204 
5205 /*
5206     Special version for direct calls from Fortran
5207 */
5208 #include <petsc/private/fortranimpl.h>
5209 
5210 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5211 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
5212 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5213 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
5214 #endif
5215 
5216 /* Change these macros so can be used in void function */
5217 #undef CHKERRQ
5218 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
5219 #undef SETERRQ2
5220 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5221 #undef SETERRQ3
5222 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5223 #undef SETERRQ
5224 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
5225 
5226 #undef __FUNCT__
5227 #define __FUNCT__ "matsetvaluesmpiaij_"
5228 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)
5229 {
5230   Mat            mat  = *mmat;
5231   PetscInt       m    = *mm, n = *mn;
5232   InsertMode     addv = *maddv;
5233   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
5234   PetscScalar    value;
5235   PetscErrorCode ierr;
5236 
5237   MatCheckPreallocated(mat,1);
5238   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
5239 
5240 #if defined(PETSC_USE_DEBUG)
5241   else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
5242 #endif
5243   {
5244     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
5245     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
5246     PetscBool roworiented = aij->roworiented;
5247 
5248     /* Some Variables required in the macro */
5249     Mat        A                 = aij->A;
5250     Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
5251     PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
5252     MatScalar  *aa               = a->a;
5253     PetscBool  ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
5254     Mat        B                 = aij->B;
5255     Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
5256     PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5257     MatScalar  *ba               = b->a;
5258 
5259     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5260     PetscInt  nonew = a->nonew;
5261     MatScalar *ap1,*ap2;
5262 
5263     PetscFunctionBegin;
5264     for (i=0; i<m; i++) {
5265       if (im[i] < 0) continue;
5266 #if defined(PETSC_USE_DEBUG)
5267       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);
5268 #endif
5269       if (im[i] >= rstart && im[i] < rend) {
5270         row      = im[i] - rstart;
5271         lastcol1 = -1;
5272         rp1      = aj + ai[row];
5273         ap1      = aa + ai[row];
5274         rmax1    = aimax[row];
5275         nrow1    = ailen[row];
5276         low1     = 0;
5277         high1    = nrow1;
5278         lastcol2 = -1;
5279         rp2      = bj + bi[row];
5280         ap2      = ba + bi[row];
5281         rmax2    = bimax[row];
5282         nrow2    = bilen[row];
5283         low2     = 0;
5284         high2    = nrow2;
5285 
5286         for (j=0; j<n; j++) {
5287           if (roworiented) value = v[i*n+j];
5288           else value = v[i+j*m];
5289           if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES)) continue;
5290           if (in[j] >= cstart && in[j] < cend) {
5291             col = in[j] - cstart;
5292             MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
5293           } else if (in[j] < 0) continue;
5294 #if defined(PETSC_USE_DEBUG)
5295           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);
5296 #endif
5297           else {
5298             if (mat->was_assembled) {
5299               if (!aij->colmap) {
5300                 ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5301               }
5302 #if defined(PETSC_USE_CTABLE)
5303               ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5304               col--;
5305 #else
5306               col = aij->colmap[in[j]] - 1;
5307 #endif
5308               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5309                 ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5310                 col  =  in[j];
5311                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5312                 B     = aij->B;
5313                 b     = (Mat_SeqAIJ*)B->data;
5314                 bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5315                 rp2   = bj + bi[row];
5316                 ap2   = ba + bi[row];
5317                 rmax2 = bimax[row];
5318                 nrow2 = bilen[row];
5319                 low2  = 0;
5320                 high2 = nrow2;
5321                 bm    = aij->B->rmap->n;
5322                 ba    = b->a;
5323               }
5324             } else col = in[j];
5325             MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
5326           }
5327         }
5328       } else if (!aij->donotstash) {
5329         if (roworiented) {
5330           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5331         } else {
5332           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5333         }
5334       }
5335     }
5336   }
5337   PetscFunctionReturnVoid();
5338 }
5339 
5340