xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision bebe2cf65d55febe21a5af8db2bd2e168caaa2e7)
1 
2 #include <../src/mat/impls/aij/mpi/mpiaij.h>   /*I "petscmat.h" I*/
3 #include <petsc/private/vecimpl.h>
4 #include <petsc/private/isimpl.h>
5 #include <petscblaslapack.h>
6 #include <petscsf.h>
7 
8 /*MC
9    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.
10 
11    This matrix type is identical to MATSEQAIJ when constructed with a single process communicator,
12    and MATMPIAIJ otherwise.  As a result, for single process communicators,
13   MatSeqAIJSetPreallocation is supported, and similarly MatMPIAIJSetPreallocation is supported
14   for communicators controlling multiple processes.  It is recommended that you call both of
15   the above preallocation routines for simplicity.
16 
17    Options Database Keys:
18 . -mat_type aij - sets the matrix type to "aij" during a call to MatSetFromOptions()
19 
20   Developer Notes: Subclasses include MATAIJCUSP, MATAIJCUSPARSE, MATAIJPERM, MATAIJCRL, and also automatically switches over to use inodes when
21    enough exist.
22 
23   Level: beginner
24 
25 .seealso: MatCreateAIJ(), MatCreateSeqAIJ(), MATSEQAIJ,MATMPIAIJ
26 M*/
27 
28 /*MC
29    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.
30 
31    This matrix type is identical to MATSEQAIJCRL when constructed with a single process communicator,
32    and MATMPIAIJCRL otherwise.  As a result, for single process communicators,
33    MatSeqAIJSetPreallocation() is supported, and similarly MatMPIAIJSetPreallocation() is supported
34   for communicators controlling multiple processes.  It is recommended that you call both of
35   the above preallocation routines for simplicity.
36 
37    Options Database Keys:
38 . -mat_type aijcrl - sets the matrix type to "aijcrl" during a call to MatSetFromOptions()
39 
40   Level: beginner
41 
42 .seealso: MatCreateMPIAIJCRL,MATSEQAIJCRL,MATMPIAIJCRL, MATSEQAIJCRL, MATMPIAIJCRL
43 M*/
44 
45 #undef __FUNCT__
46 #define __FUNCT__ "MatFindNonzeroRows_MPIAIJ"
47 PetscErrorCode MatFindNonzeroRows_MPIAIJ(Mat M,IS *keptrows)
48 {
49   PetscErrorCode  ierr;
50   Mat_MPIAIJ      *mat = (Mat_MPIAIJ*)M->data;
51   Mat_SeqAIJ      *a   = (Mat_SeqAIJ*)mat->A->data;
52   Mat_SeqAIJ      *b   = (Mat_SeqAIJ*)mat->B->data;
53   const PetscInt  *ia,*ib;
54   const MatScalar *aa,*bb;
55   PetscInt        na,nb,i,j,*rows,cnt=0,n0rows;
56   PetscInt        m = M->rmap->n,rstart = M->rmap->rstart;
57 
58   PetscFunctionBegin;
59   *keptrows = 0;
60   ia        = a->i;
61   ib        = b->i;
62   for (i=0; i<m; i++) {
63     na = ia[i+1] - ia[i];
64     nb = ib[i+1] - ib[i];
65     if (!na && !nb) {
66       cnt++;
67       goto ok1;
68     }
69     aa = a->a + ia[i];
70     for (j=0; j<na; j++) {
71       if (aa[j] != 0.0) goto ok1;
72     }
73     bb = b->a + ib[i];
74     for (j=0; j <nb; j++) {
75       if (bb[j] != 0.0) goto ok1;
76     }
77     cnt++;
78 ok1:;
79   }
80   ierr = MPI_Allreduce(&cnt,&n0rows,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)M));CHKERRQ(ierr);
81   if (!n0rows) PetscFunctionReturn(0);
82   ierr = PetscMalloc1(M->rmap->n-cnt,&rows);CHKERRQ(ierr);
83   cnt  = 0;
84   for (i=0; i<m; i++) {
85     na = ia[i+1] - ia[i];
86     nb = ib[i+1] - ib[i];
87     if (!na && !nb) continue;
88     aa = a->a + ia[i];
89     for (j=0; j<na;j++) {
90       if (aa[j] != 0.0) {
91         rows[cnt++] = rstart + i;
92         goto ok2;
93       }
94     }
95     bb = b->a + ib[i];
96     for (j=0; j<nb; j++) {
97       if (bb[j] != 0.0) {
98         rows[cnt++] = rstart + i;
99         goto ok2;
100       }
101     }
102 ok2:;
103   }
104   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)M),cnt,rows,PETSC_OWN_POINTER,keptrows);CHKERRQ(ierr);
105   PetscFunctionReturn(0);
106 }
107 
108 #undef __FUNCT__
109 #define __FUNCT__ "MatDiagonalSet_MPIAIJ"
110 PetscErrorCode  MatDiagonalSet_MPIAIJ(Mat Y,Vec D,InsertMode is)
111 {
112   PetscErrorCode    ierr;
113   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*) Y->data;
114 
115   PetscFunctionBegin;
116   if (Y->assembled && Y->rmap->rstart == Y->cmap->rstart && Y->rmap->rend == Y->cmap->rend) {
117     ierr = MatDiagonalSet(aij->A,D,is);CHKERRQ(ierr);
118   } else {
119     ierr = MatDiagonalSet_Default(Y,D,is);CHKERRQ(ierr);
120   }
121   PetscFunctionReturn(0);
122 }
123 
124 
125 #undef __FUNCT__
126 #define __FUNCT__ "MatFindZeroDiagonals_MPIAIJ"
127 PetscErrorCode MatFindZeroDiagonals_MPIAIJ(Mat M,IS *zrows)
128 {
129   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)M->data;
130   PetscErrorCode ierr;
131   PetscInt       i,rstart,nrows,*rows;
132 
133   PetscFunctionBegin;
134   *zrows = NULL;
135   ierr   = MatFindZeroDiagonals_SeqAIJ_Private(aij->A,&nrows,&rows);CHKERRQ(ierr);
136   ierr   = MatGetOwnershipRange(M,&rstart,NULL);CHKERRQ(ierr);
137   for (i=0; i<nrows; i++) rows[i] += rstart;
138   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)M),nrows,rows,PETSC_OWN_POINTER,zrows);CHKERRQ(ierr);
139   PetscFunctionReturn(0);
140 }
141 
142 #undef __FUNCT__
143 #define __FUNCT__ "MatGetColumnNorms_MPIAIJ"
144 PetscErrorCode MatGetColumnNorms_MPIAIJ(Mat A,NormType type,PetscReal *norms)
145 {
146   PetscErrorCode ierr;
147   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)A->data;
148   PetscInt       i,n,*garray = aij->garray;
149   Mat_SeqAIJ     *a_aij = (Mat_SeqAIJ*) aij->A->data;
150   Mat_SeqAIJ     *b_aij = (Mat_SeqAIJ*) aij->B->data;
151   PetscReal      *work;
152 
153   PetscFunctionBegin;
154   ierr = MatGetSize(A,NULL,&n);CHKERRQ(ierr);
155   ierr = PetscCalloc1(n,&work);CHKERRQ(ierr);
156   if (type == NORM_2) {
157     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
158       work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i]*a_aij->a[i]);
159     }
160     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
161       work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]*b_aij->a[i]);
162     }
163   } else if (type == NORM_1) {
164     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
165       work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i]);
166     }
167     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
168       work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]);
169     }
170   } else if (type == NORM_INFINITY) {
171     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
172       work[A->cmap->rstart + a_aij->j[i]] = PetscMax(PetscAbsScalar(a_aij->a[i]), work[A->cmap->rstart + a_aij->j[i]]);
173     }
174     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
175       work[garray[b_aij->j[i]]] = PetscMax(PetscAbsScalar(b_aij->a[i]),work[garray[b_aij->j[i]]]);
176     }
177 
178   } else SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Unknown NormType");
179   if (type == NORM_INFINITY) {
180     ierr = MPI_Allreduce(work,norms,n,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
181   } else {
182     ierr = MPI_Allreduce(work,norms,n,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
183   }
184   ierr = PetscFree(work);CHKERRQ(ierr);
185   if (type == NORM_2) {
186     for (i=0; i<n; i++) norms[i] = PetscSqrtReal(norms[i]);
187   }
188   PetscFunctionReturn(0);
189 }
190 
191 #undef __FUNCT__
192 #define __FUNCT__ "MatFindOffBlockDiagonalEntries_MPIAIJ"
193 PetscErrorCode MatFindOffBlockDiagonalEntries_MPIAIJ(Mat A,IS *is)
194 {
195   Mat_MPIAIJ      *a  = (Mat_MPIAIJ*)A->data;
196   IS              sis,gis;
197   PetscErrorCode  ierr;
198   const PetscInt  *isis,*igis;
199   PetscInt        n,*iis,nsis,ngis,rstart,i;
200 
201   PetscFunctionBegin;
202   ierr = MatFindOffBlockDiagonalEntries(a->A,&sis);CHKERRQ(ierr);
203   ierr = MatFindNonzeroRows(a->B,&gis);CHKERRQ(ierr);
204   ierr = ISGetSize(gis,&ngis);CHKERRQ(ierr);
205   ierr = ISGetSize(sis,&nsis);CHKERRQ(ierr);
206   ierr = ISGetIndices(sis,&isis);CHKERRQ(ierr);
207   ierr = ISGetIndices(gis,&igis);CHKERRQ(ierr);
208 
209   ierr = PetscMalloc1(ngis+nsis,&iis);CHKERRQ(ierr);
210   ierr = PetscMemcpy(iis,igis,ngis*sizeof(PetscInt));CHKERRQ(ierr);
211   ierr = PetscMemcpy(iis+ngis,isis,nsis*sizeof(PetscInt));CHKERRQ(ierr);
212   n    = ngis + nsis;
213   ierr = PetscSortRemoveDupsInt(&n,iis);CHKERRQ(ierr);
214   ierr = MatGetOwnershipRange(A,&rstart,NULL);CHKERRQ(ierr);
215   for (i=0; i<n; i++) iis[i] += rstart;
216   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)A),n,iis,PETSC_OWN_POINTER,is);CHKERRQ(ierr);
217 
218   ierr = ISRestoreIndices(sis,&isis);CHKERRQ(ierr);
219   ierr = ISRestoreIndices(gis,&igis);CHKERRQ(ierr);
220   ierr = ISDestroy(&sis);CHKERRQ(ierr);
221   ierr = ISDestroy(&gis);CHKERRQ(ierr);
222   PetscFunctionReturn(0);
223 }
224 
225 #undef __FUNCT__
226 #define __FUNCT__ "MatDistribute_MPIAIJ"
227 /*
228     Distributes a SeqAIJ matrix across a set of processes. Code stolen from
229     MatLoad_MPIAIJ(). Horrible lack of reuse. Should be a routine for each matrix type.
230 
231     Only for square matrices
232 
233     Used by a preconditioner, hence PETSC_EXTERN
234 */
235 PETSC_EXTERN PetscErrorCode MatDistribute_MPIAIJ(MPI_Comm comm,Mat gmat,PetscInt m,MatReuse reuse,Mat *inmat)
236 {
237   PetscMPIInt    rank,size;
238   PetscInt       *rowners,*dlens,*olens,i,rstart,rend,j,jj,nz = 0,*gmataj,cnt,row,*ld,bses[2];
239   PetscErrorCode ierr;
240   Mat            mat;
241   Mat_SeqAIJ     *gmata;
242   PetscMPIInt    tag;
243   MPI_Status     status;
244   PetscBool      aij;
245   MatScalar      *gmataa,*ao,*ad,*gmataarestore=0;
246 
247   PetscFunctionBegin;
248   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
249   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
250   if (!rank) {
251     ierr = PetscObjectTypeCompare((PetscObject)gmat,MATSEQAIJ,&aij);CHKERRQ(ierr);
252     if (!aij) SETERRQ1(PetscObjectComm((PetscObject)gmat),PETSC_ERR_SUP,"Currently no support for input matrix of type %s\n",((PetscObject)gmat)->type_name);
253   }
254   if (reuse == MAT_INITIAL_MATRIX) {
255     ierr = MatCreate(comm,&mat);CHKERRQ(ierr);
256     ierr = MatSetSizes(mat,m,m,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
257     ierr = MatGetBlockSizes(gmat,&bses[0],&bses[1]);CHKERRQ(ierr);
258     ierr = MPI_Bcast(bses,2,MPIU_INT,0,comm);CHKERRQ(ierr);
259     ierr = MatSetBlockSizes(mat,bses[0],bses[1]);CHKERRQ(ierr);
260     ierr = MatSetType(mat,MATAIJ);CHKERRQ(ierr);
261     ierr = PetscMalloc1(size+1,&rowners);CHKERRQ(ierr);
262     ierr = PetscMalloc2(m,&dlens,m,&olens);CHKERRQ(ierr);
263     ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
264 
265     rowners[0] = 0;
266     for (i=2; i<=size; i++) rowners[i] += rowners[i-1];
267     rstart = rowners[rank];
268     rend   = rowners[rank+1];
269     ierr   = PetscObjectGetNewTag((PetscObject)mat,&tag);CHKERRQ(ierr);
270     if (!rank) {
271       gmata = (Mat_SeqAIJ*) gmat->data;
272       /* send row lengths to all processors */
273       for (i=0; i<m; i++) dlens[i] = gmata->ilen[i];
274       for (i=1; i<size; i++) {
275         ierr = MPI_Send(gmata->ilen + rowners[i],rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
276       }
277       /* determine number diagonal and off-diagonal counts */
278       ierr = PetscMemzero(olens,m*sizeof(PetscInt));CHKERRQ(ierr);
279       ierr = PetscCalloc1(m,&ld);CHKERRQ(ierr);
280       jj   = 0;
281       for (i=0; i<m; i++) {
282         for (j=0; j<dlens[i]; j++) {
283           if (gmata->j[jj] < rstart) ld[i]++;
284           if (gmata->j[jj] < rstart || gmata->j[jj] >= rend) olens[i]++;
285           jj++;
286         }
287       }
288       /* send column indices to other processes */
289       for (i=1; i<size; i++) {
290         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
291         ierr = MPI_Send(&nz,1,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
292         ierr = MPI_Send(gmata->j + gmata->i[rowners[i]],nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
293       }
294 
295       /* send numerical values to other processes */
296       for (i=1; i<size; i++) {
297         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
298         ierr = MPI_Send(gmata->a + gmata->i[rowners[i]],nz,MPIU_SCALAR,i,tag,comm);CHKERRQ(ierr);
299       }
300       gmataa = gmata->a;
301       gmataj = gmata->j;
302 
303     } else {
304       /* receive row lengths */
305       ierr = MPI_Recv(dlens,m,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
306       /* receive column indices */
307       ierr = MPI_Recv(&nz,1,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
308       ierr = PetscMalloc2(nz,&gmataa,nz,&gmataj);CHKERRQ(ierr);
309       ierr = MPI_Recv(gmataj,nz,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
310       /* determine number diagonal and off-diagonal counts */
311       ierr = PetscMemzero(olens,m*sizeof(PetscInt));CHKERRQ(ierr);
312       ierr = PetscCalloc1(m,&ld);CHKERRQ(ierr);
313       jj   = 0;
314       for (i=0; i<m; i++) {
315         for (j=0; j<dlens[i]; j++) {
316           if (gmataj[jj] < rstart) ld[i]++;
317           if (gmataj[jj] < rstart || gmataj[jj] >= rend) olens[i]++;
318           jj++;
319         }
320       }
321       /* receive numerical values */
322       ierr = PetscMemzero(gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr);
323       ierr = MPI_Recv(gmataa,nz,MPIU_SCALAR,0,tag,comm,&status);CHKERRQ(ierr);
324     }
325     /* set preallocation */
326     for (i=0; i<m; i++) {
327       dlens[i] -= olens[i];
328     }
329     ierr = MatSeqAIJSetPreallocation(mat,0,dlens);CHKERRQ(ierr);
330     ierr = MatMPIAIJSetPreallocation(mat,0,dlens,0,olens);CHKERRQ(ierr);
331 
332     for (i=0; i<m; i++) {
333       dlens[i] += olens[i];
334     }
335     cnt = 0;
336     for (i=0; i<m; i++) {
337       row  = rstart + i;
338       ierr = MatSetValues(mat,1,&row,dlens[i],gmataj+cnt,gmataa+cnt,INSERT_VALUES);CHKERRQ(ierr);
339       cnt += dlens[i];
340     }
341     if (rank) {
342       ierr = PetscFree2(gmataa,gmataj);CHKERRQ(ierr);
343     }
344     ierr = PetscFree2(dlens,olens);CHKERRQ(ierr);
345     ierr = PetscFree(rowners);CHKERRQ(ierr);
346 
347     ((Mat_MPIAIJ*)(mat->data))->ld = ld;
348 
349     *inmat = mat;
350   } else {   /* column indices are already set; only need to move over numerical values from process 0 */
351     Mat_SeqAIJ *Ad = (Mat_SeqAIJ*)((Mat_MPIAIJ*)((*inmat)->data))->A->data;
352     Mat_SeqAIJ *Ao = (Mat_SeqAIJ*)((Mat_MPIAIJ*)((*inmat)->data))->B->data;
353     mat  = *inmat;
354     ierr = PetscObjectGetNewTag((PetscObject)mat,&tag);CHKERRQ(ierr);
355     if (!rank) {
356       /* send numerical values to other processes */
357       gmata  = (Mat_SeqAIJ*) gmat->data;
358       ierr   = MatGetOwnershipRanges(mat,(const PetscInt**)&rowners);CHKERRQ(ierr);
359       gmataa = gmata->a;
360       for (i=1; i<size; i++) {
361         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
362         ierr = MPI_Send(gmataa + gmata->i[rowners[i]],nz,MPIU_SCALAR,i,tag,comm);CHKERRQ(ierr);
363       }
364       nz = gmata->i[rowners[1]]-gmata->i[rowners[0]];
365     } else {
366       /* receive numerical values from process 0*/
367       nz   = Ad->nz + Ao->nz;
368       ierr = PetscMalloc1(nz,&gmataa);CHKERRQ(ierr); gmataarestore = gmataa;
369       ierr = MPI_Recv(gmataa,nz,MPIU_SCALAR,0,tag,comm,&status);CHKERRQ(ierr);
370     }
371     /* transfer numerical values into the diagonal A and off diagonal B parts of mat */
372     ld = ((Mat_MPIAIJ*)(mat->data))->ld;
373     ad = Ad->a;
374     ao = Ao->a;
375     if (mat->rmap->n) {
376       i  = 0;
377       nz = ld[i];                                   ierr = PetscMemcpy(ao,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ao += nz; gmataa += nz;
378       nz = Ad->i[i+1] - Ad->i[i];                   ierr = PetscMemcpy(ad,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ad += nz; gmataa += nz;
379     }
380     for (i=1; i<mat->rmap->n; i++) {
381       nz = Ao->i[i] - Ao->i[i-1] - ld[i-1] + ld[i]; ierr = PetscMemcpy(ao,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ao += nz; gmataa += nz;
382       nz = Ad->i[i+1] - Ad->i[i];                   ierr = PetscMemcpy(ad,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ad += nz; gmataa += nz;
383     }
384     i--;
385     if (mat->rmap->n) {
386       nz = Ao->i[i+1] - Ao->i[i] - ld[i];           ierr = PetscMemcpy(ao,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr);
387     }
388     if (rank) {
389       ierr = PetscFree(gmataarestore);CHKERRQ(ierr);
390     }
391   }
392   ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
393   ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
394   PetscFunctionReturn(0);
395 }
396 
397 /*
398   Local utility routine that creates a mapping from the global column
399 number to the local number in the off-diagonal part of the local
400 storage of the matrix.  When PETSC_USE_CTABLE is used this is scalable at
401 a slightly higher hash table cost; without it it is not scalable (each processor
402 has an order N integer array but is fast to acess.
403 */
404 #undef __FUNCT__
405 #define __FUNCT__ "MatCreateColmap_MPIAIJ_Private"
406 PetscErrorCode MatCreateColmap_MPIAIJ_Private(Mat mat)
407 {
408   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
409   PetscErrorCode ierr;
410   PetscInt       n = aij->B->cmap->n,i;
411 
412   PetscFunctionBegin;
413   if (!aij->garray) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"MPIAIJ Matrix was assembled but is missing garray");
414 #if defined(PETSC_USE_CTABLE)
415   ierr = PetscTableCreate(n,mat->cmap->N+1,&aij->colmap);CHKERRQ(ierr);
416   for (i=0; i<n; i++) {
417     ierr = PetscTableAdd(aij->colmap,aij->garray[i]+1,i+1,INSERT_VALUES);CHKERRQ(ierr);
418   }
419 #else
420   ierr = PetscCalloc1(mat->cmap->N+1,&aij->colmap);CHKERRQ(ierr);
421   ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N+1)*sizeof(PetscInt));CHKERRQ(ierr);
422   for (i=0; i<n; i++) aij->colmap[aij->garray[i]] = i+1;
423 #endif
424   PetscFunctionReturn(0);
425 }
426 
427 #define MatSetValues_SeqAIJ_A_Private(row,col,value,addv,orow,ocol)     \
428 { \
429     if (col <= lastcol1)  low1 = 0;     \
430     else                 high1 = nrow1; \
431     lastcol1 = col;\
432     while (high1-low1 > 5) { \
433       t = (low1+high1)/2; \
434       if (rp1[t] > col) high1 = t; \
435       else              low1  = t; \
436     } \
437       for (_i=low1; _i<high1; _i++) { \
438         if (rp1[_i] > col) break; \
439         if (rp1[_i] == col) { \
440           if (addv == ADD_VALUES) ap1[_i] += value;   \
441           else                    ap1[_i] = value; \
442           goto a_noinsert; \
443         } \
444       }  \
445       if (value == 0.0 && ignorezeroentries) {low1 = 0; high1 = nrow1;goto a_noinsert;} \
446       if (nonew == 1) {low1 = 0; high1 = nrow1; goto a_noinsert;}                \
447       if (nonew == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at global row/column (%D, %D) into matrix", orow, ocol); \
448       MatSeqXAIJReallocateAIJ(A,am,1,nrow1,row,col,rmax1,aa,ai,aj,rp1,ap1,aimax,nonew,MatScalar); \
449       N = nrow1++ - 1; a->nz++; high1++; \
450       /* shift up all the later entries in this row */ \
451       for (ii=N; ii>=_i; ii--) { \
452         rp1[ii+1] = rp1[ii]; \
453         ap1[ii+1] = ap1[ii]; \
454       } \
455       rp1[_i] = col;  \
456       ap1[_i] = value;  \
457       A->nonzerostate++;\
458       a_noinsert: ; \
459       ailen[row] = nrow1; \
460 }
461 
462 
463 #define MatSetValues_SeqAIJ_B_Private(row,col,value,addv,orow,ocol) \
464   { \
465     if (col <= lastcol2) low2 = 0;                        \
466     else high2 = nrow2;                                   \
467     lastcol2 = col;                                       \
468     while (high2-low2 > 5) {                              \
469       t = (low2+high2)/2;                                 \
470       if (rp2[t] > col) high2 = t;                        \
471       else             low2  = t;                         \
472     }                                                     \
473     for (_i=low2; _i<high2; _i++) {                       \
474       if (rp2[_i] > col) break;                           \
475       if (rp2[_i] == col) {                               \
476         if (addv == ADD_VALUES) ap2[_i] += value;         \
477         else                    ap2[_i] = value;          \
478         goto b_noinsert;                                  \
479       }                                                   \
480     }                                                     \
481     if (value == 0.0 && ignorezeroentries) {low2 = 0; high2 = nrow2; goto b_noinsert;} \
482     if (nonew == 1) {low2 = 0; high2 = nrow2; goto b_noinsert;}                        \
483     if (nonew == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at global row/column (%D, %D) into matrix", orow, ocol); \
484     MatSeqXAIJReallocateAIJ(B,bm,1,nrow2,row,col,rmax2,ba,bi,bj,rp2,ap2,bimax,nonew,MatScalar); \
485     N = nrow2++ - 1; b->nz++; high2++;                    \
486     /* shift up all the later entries in this row */      \
487     for (ii=N; ii>=_i; ii--) {                            \
488       rp2[ii+1] = rp2[ii];                                \
489       ap2[ii+1] = ap2[ii];                                \
490     }                                                     \
491     rp2[_i] = col;                                        \
492     ap2[_i] = value;                                      \
493     B->nonzerostate++;                                    \
494     b_noinsert: ;                                         \
495     bilen[row] = nrow2;                                   \
496   }
497 
498 #undef __FUNCT__
499 #define __FUNCT__ "MatSetValuesRow_MPIAIJ"
500 PetscErrorCode MatSetValuesRow_MPIAIJ(Mat A,PetscInt row,const PetscScalar v[])
501 {
502   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)A->data;
503   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)mat->A->data,*b = (Mat_SeqAIJ*)mat->B->data;
504   PetscErrorCode ierr;
505   PetscInt       l,*garray = mat->garray,diag;
506 
507   PetscFunctionBegin;
508   /* code only works for square matrices A */
509 
510   /* find size of row to the left of the diagonal part */
511   ierr = MatGetOwnershipRange(A,&diag,0);CHKERRQ(ierr);
512   row  = row - diag;
513   for (l=0; l<b->i[row+1]-b->i[row]; l++) {
514     if (garray[b->j[b->i[row]+l]] > diag) break;
515   }
516   ierr = PetscMemcpy(b->a+b->i[row],v,l*sizeof(PetscScalar));CHKERRQ(ierr);
517 
518   /* diagonal part */
519   ierr = PetscMemcpy(a->a+a->i[row],v+l,(a->i[row+1]-a->i[row])*sizeof(PetscScalar));CHKERRQ(ierr);
520 
521   /* right of diagonal part */
522   ierr = PetscMemcpy(b->a+b->i[row]+l,v+l+a->i[row+1]-a->i[row],(b->i[row+1]-b->i[row]-l)*sizeof(PetscScalar));CHKERRQ(ierr);
523   PetscFunctionReturn(0);
524 }
525 
526 #undef __FUNCT__
527 #define __FUNCT__ "MatSetValues_MPIAIJ"
528 PetscErrorCode MatSetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode addv)
529 {
530   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
531   PetscScalar    value;
532   PetscErrorCode ierr;
533   PetscInt       i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
534   PetscInt       cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
535   PetscBool      roworiented = aij->roworiented;
536 
537   /* Some Variables required in the macro */
538   Mat        A                 = aij->A;
539   Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
540   PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
541   MatScalar  *aa               = a->a;
542   PetscBool  ignorezeroentries = a->ignorezeroentries;
543   Mat        B                 = aij->B;
544   Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
545   PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
546   MatScalar  *ba               = b->a;
547 
548   PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
549   PetscInt  nonew;
550   MatScalar *ap1,*ap2;
551 
552   PetscFunctionBegin;
553   for (i=0; i<m; i++) {
554     if (im[i] < 0) continue;
555 #if defined(PETSC_USE_DEBUG)
556     if (im[i] >= mat->rmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %D max %D",im[i],mat->rmap->N-1);
557 #endif
558     if (im[i] >= rstart && im[i] < rend) {
559       row      = im[i] - rstart;
560       lastcol1 = -1;
561       rp1      = aj + ai[row];
562       ap1      = aa + ai[row];
563       rmax1    = aimax[row];
564       nrow1    = ailen[row];
565       low1     = 0;
566       high1    = nrow1;
567       lastcol2 = -1;
568       rp2      = bj + bi[row];
569       ap2      = ba + bi[row];
570       rmax2    = bimax[row];
571       nrow2    = bilen[row];
572       low2     = 0;
573       high2    = nrow2;
574 
575       for (j=0; j<n; j++) {
576         if (roworiented) value = v[i*n+j];
577         else             value = v[i+j*m];
578         if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES)) continue;
579         if (in[j] >= cstart && in[j] < cend) {
580           col   = in[j] - cstart;
581           nonew = a->nonew;
582           MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
583         } else if (in[j] < 0) continue;
584 #if defined(PETSC_USE_DEBUG)
585         else if (in[j] >= mat->cmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %D max %D",in[j],mat->cmap->N-1);
586 #endif
587         else {
588           if (mat->was_assembled) {
589             if (!aij->colmap) {
590               ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
591             }
592 #if defined(PETSC_USE_CTABLE)
593             ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
594             col--;
595 #else
596             col = aij->colmap[in[j]] - 1;
597 #endif
598             if (col < 0 && !((Mat_SeqAIJ*)(aij->B->data))->nonew) {
599               ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
600               col  =  in[j];
601               /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
602               B     = aij->B;
603               b     = (Mat_SeqAIJ*)B->data;
604               bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j; ba = b->a;
605               rp2   = bj + bi[row];
606               ap2   = ba + bi[row];
607               rmax2 = bimax[row];
608               nrow2 = bilen[row];
609               low2  = 0;
610               high2 = nrow2;
611               bm    = aij->B->rmap->n;
612               ba    = b->a;
613             } else if (col < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at global row/column (%D, %D) into matrix", im[i], in[j]);
614           } else col = in[j];
615           nonew = b->nonew;
616           MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
617         }
618       }
619     } else {
620       if (mat->nooffprocentries) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Setting off process row %D even though MatSetOption(,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) was set",im[i]);
621       if (!aij->donotstash) {
622         mat->assembled = PETSC_FALSE;
623         if (roworiented) {
624           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
625         } else {
626           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
627         }
628       }
629     }
630   }
631   PetscFunctionReturn(0);
632 }
633 
634 #undef __FUNCT__
635 #define __FUNCT__ "MatGetValues_MPIAIJ"
636 PetscErrorCode MatGetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],PetscScalar v[])
637 {
638   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
639   PetscErrorCode ierr;
640   PetscInt       i,j,rstart = mat->rmap->rstart,rend = mat->rmap->rend;
641   PetscInt       cstart = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
642 
643   PetscFunctionBegin;
644   for (i=0; i<m; i++) {
645     if (idxm[i] < 0) continue; /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative row: %D",idxm[i]);*/
646     if (idxm[i] >= mat->rmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %D max %D",idxm[i],mat->rmap->N-1);
647     if (idxm[i] >= rstart && idxm[i] < rend) {
648       row = idxm[i] - rstart;
649       for (j=0; j<n; j++) {
650         if (idxn[j] < 0) continue; /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column: %D",idxn[j]); */
651         if (idxn[j] >= mat->cmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %D max %D",idxn[j],mat->cmap->N-1);
652         if (idxn[j] >= cstart && idxn[j] < cend) {
653           col  = idxn[j] - cstart;
654           ierr = MatGetValues(aij->A,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
655         } else {
656           if (!aij->colmap) {
657             ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
658           }
659 #if defined(PETSC_USE_CTABLE)
660           ierr = PetscTableFind(aij->colmap,idxn[j]+1,&col);CHKERRQ(ierr);
661           col--;
662 #else
663           col = aij->colmap[idxn[j]] - 1;
664 #endif
665           if ((col < 0) || (aij->garray[col] != idxn[j])) *(v+i*n+j) = 0.0;
666           else {
667             ierr = MatGetValues(aij->B,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
668           }
669         }
670       }
671     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only local values currently supported");
672   }
673   PetscFunctionReturn(0);
674 }
675 
676 extern PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat,Vec,Vec);
677 
678 #undef __FUNCT__
679 #define __FUNCT__ "MatAssemblyBegin_MPIAIJ"
680 PetscErrorCode MatAssemblyBegin_MPIAIJ(Mat mat,MatAssemblyType mode)
681 {
682   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
683   PetscErrorCode ierr;
684   PetscInt       nstash,reallocs;
685   InsertMode     addv;
686 
687   PetscFunctionBegin;
688   if (aij->donotstash || mat->nooffprocentries) PetscFunctionReturn(0);
689 
690   /* make sure all processors are either in INSERTMODE or ADDMODE */
691   ierr = MPI_Allreduce((PetscEnum*)&mat->insertmode,(PetscEnum*)&addv,1,MPIU_ENUM,MPI_BOR,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
692   if (addv == (ADD_VALUES|INSERT_VALUES)) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Some processors inserted others added");
693   mat->insertmode = addv; /* in case this processor had no cache */
694 
695   ierr = MatStashScatterBegin_Private(mat,&mat->stash,mat->rmap->range);CHKERRQ(ierr);
696   ierr = MatStashGetInfo_Private(&mat->stash,&nstash,&reallocs);CHKERRQ(ierr);
697   ierr = PetscInfo2(aij->A,"Stash has %D entries, uses %D mallocs.\n",nstash,reallocs);CHKERRQ(ierr);
698   PetscFunctionReturn(0);
699 }
700 
701 #undef __FUNCT__
702 #define __FUNCT__ "MatAssemblyEnd_MPIAIJ"
703 PetscErrorCode MatAssemblyEnd_MPIAIJ(Mat mat,MatAssemblyType mode)
704 {
705   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
706   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)aij->A->data;
707   PetscErrorCode ierr;
708   PetscMPIInt    n;
709   PetscInt       i,j,rstart,ncols,flg;
710   PetscInt       *row,*col;
711   PetscBool      other_disassembled;
712   PetscScalar    *val;
713   InsertMode     addv = mat->insertmode;
714 
715   /* do not use 'b = (Mat_SeqAIJ*)aij->B->data' as B can be reset in disassembly */
716 
717   PetscFunctionBegin;
718   if (!aij->donotstash && !mat->nooffprocentries) {
719     while (1) {
720       ierr = MatStashScatterGetMesg_Private(&mat->stash,&n,&row,&col,&val,&flg);CHKERRQ(ierr);
721       if (!flg) break;
722 
723       for (i=0; i<n; ) {
724         /* Now identify the consecutive vals belonging to the same row */
725         for (j=i,rstart=row[j]; j<n; j++) {
726           if (row[j] != rstart) break;
727         }
728         if (j < n) ncols = j-i;
729         else       ncols = n-i;
730         /* Now assemble all these values with a single function call */
731         ierr = MatSetValues_MPIAIJ(mat,1,row+i,ncols,col+i,val+i,addv);CHKERRQ(ierr);
732 
733         i = j;
734       }
735     }
736     ierr = MatStashScatterEnd_Private(&mat->stash);CHKERRQ(ierr);
737   }
738   ierr = MatAssemblyBegin(aij->A,mode);CHKERRQ(ierr);
739   ierr = MatAssemblyEnd(aij->A,mode);CHKERRQ(ierr);
740 
741   /* determine if any processor has disassembled, if so we must
742      also disassemble ourselfs, in order that we may reassemble. */
743   /*
744      if nonzero structure of submatrix B cannot change then we know that
745      no processor disassembled thus we can skip this stuff
746   */
747   if (!((Mat_SeqAIJ*)aij->B->data)->nonew) {
748     ierr = MPI_Allreduce(&mat->was_assembled,&other_disassembled,1,MPIU_BOOL,MPI_PROD,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
749     if (mat->was_assembled && !other_disassembled) {
750       ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
751     }
752   }
753   if (!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) {
754     ierr = MatSetUpMultiply_MPIAIJ(mat);CHKERRQ(ierr);
755   }
756   ierr = MatSetOption(aij->B,MAT_USE_INODES,PETSC_FALSE);CHKERRQ(ierr);
757   ierr = MatAssemblyBegin(aij->B,mode);CHKERRQ(ierr);
758   ierr = MatAssemblyEnd(aij->B,mode);CHKERRQ(ierr);
759 
760   ierr = PetscFree2(aij->rowvalues,aij->rowindices);CHKERRQ(ierr);
761 
762   aij->rowvalues = 0;
763 
764   ierr = VecDestroy(&aij->diag);CHKERRQ(ierr);
765   if (a->inode.size) mat->ops->multdiagonalblock = MatMultDiagonalBlock_MPIAIJ;
766 
767   /* if no new nonzero locations are allowed in matrix then only set the matrix state the first time through */
768   if ((!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) || !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
769     PetscObjectState state = aij->A->nonzerostate + aij->B->nonzerostate;
770     ierr = MPI_Allreduce(&state,&mat->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
771   }
772   PetscFunctionReturn(0);
773 }
774 
775 #undef __FUNCT__
776 #define __FUNCT__ "MatZeroEntries_MPIAIJ"
777 PetscErrorCode MatZeroEntries_MPIAIJ(Mat A)
778 {
779   Mat_MPIAIJ     *l = (Mat_MPIAIJ*)A->data;
780   PetscErrorCode ierr;
781 
782   PetscFunctionBegin;
783   ierr = MatZeroEntries(l->A);CHKERRQ(ierr);
784   ierr = MatZeroEntries(l->B);CHKERRQ(ierr);
785   PetscFunctionReturn(0);
786 }
787 
788 #undef __FUNCT__
789 #define __FUNCT__ "MatZeroRows_MPIAIJ"
790 PetscErrorCode MatZeroRows_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
791 {
792   Mat_MPIAIJ    *mat    = (Mat_MPIAIJ *) A->data;
793   PetscInt      *owners = A->rmap->range;
794   PetscInt       n      = A->rmap->n;
795   PetscSF        sf;
796   PetscInt      *lrows;
797   PetscSFNode   *rrows;
798   PetscInt       r, p = 0, len = 0;
799   PetscErrorCode ierr;
800 
801   PetscFunctionBegin;
802   /* Create SF where leaves are input rows and roots are owned rows */
803   ierr = PetscMalloc1(n, &lrows);CHKERRQ(ierr);
804   for (r = 0; r < n; ++r) lrows[r] = -1;
805   if (!A->nooffproczerorows) {ierr = PetscMalloc1(N, &rrows);CHKERRQ(ierr);}
806   for (r = 0; r < N; ++r) {
807     const PetscInt idx   = rows[r];
808     if (idx < 0 || A->rmap->N <= idx) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row %D out of range [0,%D)",idx,A->rmap->N);
809     if (idx < owners[p] || owners[p+1] <= idx) { /* short-circuit the search if the last p owns this row too */
810       ierr = PetscLayoutFindOwner(A->rmap,idx,&p);CHKERRQ(ierr);
811     }
812     if (A->nooffproczerorows) {
813       if (p != mat->rank) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"MAT_NO_OFF_PROC_ZERO_ROWS set, but row %D is not owned by rank %d",idx,mat->rank);
814       lrows[len++] = idx - owners[p];
815     } else {
816       rrows[r].rank = p;
817       rrows[r].index = rows[r] - owners[p];
818     }
819   }
820   if (!A->nooffproczerorows) {
821     ierr = PetscSFCreate(PetscObjectComm((PetscObject) A), &sf);CHKERRQ(ierr);
822     ierr = PetscSFSetGraph(sf, n, N, NULL, PETSC_OWN_POINTER, rrows, PETSC_OWN_POINTER);CHKERRQ(ierr);
823     /* Collect flags for rows to be zeroed */
824     ierr = PetscSFReduceBegin(sf, MPIU_INT, (PetscInt*)rows, lrows, MPI_LOR);CHKERRQ(ierr);
825     ierr = PetscSFReduceEnd(sf, MPIU_INT, (PetscInt*)rows, lrows, MPI_LOR);CHKERRQ(ierr);
826     ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
827     /* Compress and put in row numbers */
828     for (r = 0; r < n; ++r) if (lrows[r] >= 0) lrows[len++] = r;
829   }
830   /* fix right hand side if needed */
831   if (x && b) {
832     const PetscScalar *xx;
833     PetscScalar       *bb;
834 
835     ierr = VecGetArrayRead(x, &xx);CHKERRQ(ierr);
836     ierr = VecGetArray(b, &bb);CHKERRQ(ierr);
837     for (r = 0; r < len; ++r) bb[lrows[r]] = diag*xx[lrows[r]];
838     ierr = VecRestoreArrayRead(x, &xx);CHKERRQ(ierr);
839     ierr = VecRestoreArray(b, &bb);CHKERRQ(ierr);
840   }
841   /* Must zero l->B before l->A because the (diag) case below may put values into l->B*/
842   ierr = MatZeroRows(mat->B, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
843   if ((diag != 0.0) && (mat->A->rmap->N == mat->A->cmap->N)) {
844     ierr = MatZeroRows(mat->A, len, lrows, diag, NULL, NULL);CHKERRQ(ierr);
845   } else if (diag != 0.0) {
846     ierr = MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
847     if (((Mat_SeqAIJ *) mat->A->data)->nonew) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatZeroRows() on rectangular matrices cannot be used with the Mat options\nMAT_NEW_NONZERO_LOCATIONS,MAT_NEW_NONZERO_LOCATION_ERR,MAT_NEW_NONZERO_ALLOCATION_ERR");
848     for (r = 0; r < len; ++r) {
849       const PetscInt row = lrows[r] + A->rmap->rstart;
850       ierr = MatSetValues(A, 1, &row, 1, &row, &diag, INSERT_VALUES);CHKERRQ(ierr);
851     }
852     ierr = MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
853     ierr = MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
854   } else {
855     ierr = MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
856   }
857   ierr = PetscFree(lrows);CHKERRQ(ierr);
858 
859   /* only change matrix nonzero state if pattern was allowed to be changed */
860   if (!((Mat_SeqAIJ*)(mat->A->data))->keepnonzeropattern) {
861     PetscObjectState state = mat->A->nonzerostate + mat->B->nonzerostate;
862     ierr = MPI_Allreduce(&state,&A->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
863   }
864   PetscFunctionReturn(0);
865 }
866 
867 #undef __FUNCT__
868 #define __FUNCT__ "MatZeroRowsColumns_MPIAIJ"
869 PetscErrorCode MatZeroRowsColumns_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
870 {
871   Mat_MPIAIJ        *l = (Mat_MPIAIJ*)A->data;
872   PetscErrorCode    ierr;
873   PetscMPIInt       n = A->rmap->n;
874   PetscInt          i,j,r,m,p = 0,len = 0;
875   PetscInt          *lrows,*owners = A->rmap->range;
876   PetscSFNode       *rrows;
877   PetscSF           sf;
878   const PetscScalar *xx;
879   PetscScalar       *bb,*mask;
880   Vec               xmask,lmask;
881   Mat_SeqAIJ        *aij = (Mat_SeqAIJ*)l->B->data;
882   const PetscInt    *aj, *ii,*ridx;
883   PetscScalar       *aa;
884 
885   PetscFunctionBegin;
886   /* Create SF where leaves are input rows and roots are owned rows */
887   ierr = PetscMalloc1(n, &lrows);CHKERRQ(ierr);
888   for (r = 0; r < n; ++r) lrows[r] = -1;
889   ierr = PetscMalloc1(N, &rrows);CHKERRQ(ierr);
890   for (r = 0; r < N; ++r) {
891     const PetscInt idx   = rows[r];
892     if (idx < 0 || A->rmap->N <= idx) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row %D out of range [0,%D)",idx,A->rmap->N);
893     if (idx < owners[p] || owners[p+1] <= idx) { /* short-circuit the search if the last p owns this row too */
894       ierr = PetscLayoutFindOwner(A->rmap,idx,&p);CHKERRQ(ierr);
895     }
896     rrows[r].rank  = p;
897     rrows[r].index = rows[r] - owners[p];
898   }
899   ierr = PetscSFCreate(PetscObjectComm((PetscObject) A), &sf);CHKERRQ(ierr);
900   ierr = PetscSFSetGraph(sf, n, N, NULL, PETSC_OWN_POINTER, rrows, PETSC_OWN_POINTER);CHKERRQ(ierr);
901   /* Collect flags for rows to be zeroed */
902   ierr = PetscSFReduceBegin(sf, MPIU_INT, (PetscInt *) rows, lrows, MPI_LOR);CHKERRQ(ierr);
903   ierr = PetscSFReduceEnd(sf, MPIU_INT, (PetscInt *) rows, lrows, MPI_LOR);CHKERRQ(ierr);
904   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
905   /* Compress and put in row numbers */
906   for (r = 0; r < n; ++r) if (lrows[r] >= 0) lrows[len++] = r;
907   /* zero diagonal part of matrix */
908   ierr = MatZeroRowsColumns(l->A,len,lrows,diag,x,b);CHKERRQ(ierr);
909   /* handle off diagonal part of matrix */
910   ierr = MatCreateVecs(A,&xmask,NULL);CHKERRQ(ierr);
911   ierr = VecDuplicate(l->lvec,&lmask);CHKERRQ(ierr);
912   ierr = VecGetArray(xmask,&bb);CHKERRQ(ierr);
913   for (i=0; i<len; i++) bb[lrows[i]] = 1;
914   ierr = VecRestoreArray(xmask,&bb);CHKERRQ(ierr);
915   ierr = VecScatterBegin(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
916   ierr = VecScatterEnd(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
917   ierr = VecDestroy(&xmask);CHKERRQ(ierr);
918   if (x) {
919     ierr = VecScatterBegin(l->Mvctx,x,l->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
920     ierr = VecScatterEnd(l->Mvctx,x,l->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
921     ierr = VecGetArrayRead(l->lvec,&xx);CHKERRQ(ierr);
922     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
923   }
924   ierr = VecGetArray(lmask,&mask);CHKERRQ(ierr);
925   /* remove zeroed rows of off diagonal matrix */
926   ii = aij->i;
927   for (i=0; i<len; i++) {
928     ierr = PetscMemzero(aij->a + ii[lrows[i]],(ii[lrows[i]+1] - ii[lrows[i]])*sizeof(PetscScalar));CHKERRQ(ierr);
929   }
930   /* loop over all elements of off process part of matrix zeroing removed columns*/
931   if (aij->compressedrow.use) {
932     m    = aij->compressedrow.nrows;
933     ii   = aij->compressedrow.i;
934     ridx = aij->compressedrow.rindex;
935     for (i=0; i<m; i++) {
936       n  = ii[i+1] - ii[i];
937       aj = aij->j + ii[i];
938       aa = aij->a + ii[i];
939 
940       for (j=0; j<n; j++) {
941         if (PetscAbsScalar(mask[*aj])) {
942           if (b) bb[*ridx] -= *aa*xx[*aj];
943           *aa = 0.0;
944         }
945         aa++;
946         aj++;
947       }
948       ridx++;
949     }
950   } else { /* do not use compressed row format */
951     m = l->B->rmap->n;
952     for (i=0; i<m; i++) {
953       n  = ii[i+1] - ii[i];
954       aj = aij->j + ii[i];
955       aa = aij->a + ii[i];
956       for (j=0; j<n; j++) {
957         if (PetscAbsScalar(mask[*aj])) {
958           if (b) bb[i] -= *aa*xx[*aj];
959           *aa = 0.0;
960         }
961         aa++;
962         aj++;
963       }
964     }
965   }
966   if (x) {
967     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
968     ierr = VecRestoreArrayRead(l->lvec,&xx);CHKERRQ(ierr);
969   }
970   ierr = VecRestoreArray(lmask,&mask);CHKERRQ(ierr);
971   ierr = VecDestroy(&lmask);CHKERRQ(ierr);
972   ierr = PetscFree(lrows);CHKERRQ(ierr);
973 
974   /* only change matrix nonzero state if pattern was allowed to be changed */
975   if (!((Mat_SeqAIJ*)(l->A->data))->keepnonzeropattern) {
976     PetscObjectState state = l->A->nonzerostate + l->B->nonzerostate;
977     ierr = MPI_Allreduce(&state,&A->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
978   }
979   PetscFunctionReturn(0);
980 }
981 
982 #undef __FUNCT__
983 #define __FUNCT__ "MatMult_MPIAIJ"
984 PetscErrorCode MatMult_MPIAIJ(Mat A,Vec xx,Vec yy)
985 {
986   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
987   PetscErrorCode ierr;
988   PetscInt       nt;
989 
990   PetscFunctionBegin;
991   ierr = VecGetLocalSize(xx,&nt);CHKERRQ(ierr);
992   if (nt != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Incompatible partition of A (%D) and xx (%D)",A->cmap->n,nt);
993   ierr = VecScatterBegin(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
994   ierr = (*a->A->ops->mult)(a->A,xx,yy);CHKERRQ(ierr);
995   ierr = VecScatterEnd(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
996   ierr = (*a->B->ops->multadd)(a->B,a->lvec,yy,yy);CHKERRQ(ierr);
997   PetscFunctionReturn(0);
998 }
999 
1000 #undef __FUNCT__
1001 #define __FUNCT__ "MatMultDiagonalBlock_MPIAIJ"
1002 PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat A,Vec bb,Vec xx)
1003 {
1004   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1005   PetscErrorCode ierr;
1006 
1007   PetscFunctionBegin;
1008   ierr = MatMultDiagonalBlock(a->A,bb,xx);CHKERRQ(ierr);
1009   PetscFunctionReturn(0);
1010 }
1011 
1012 #undef __FUNCT__
1013 #define __FUNCT__ "MatMultAdd_MPIAIJ"
1014 PetscErrorCode MatMultAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1015 {
1016   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1017   PetscErrorCode ierr;
1018 
1019   PetscFunctionBegin;
1020   ierr = VecScatterBegin(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1021   ierr = (*a->A->ops->multadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
1022   ierr = VecScatterEnd(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1023   ierr = (*a->B->ops->multadd)(a->B,a->lvec,zz,zz);CHKERRQ(ierr);
1024   PetscFunctionReturn(0);
1025 }
1026 
1027 #undef __FUNCT__
1028 #define __FUNCT__ "MatMultTranspose_MPIAIJ"
1029 PetscErrorCode MatMultTranspose_MPIAIJ(Mat A,Vec xx,Vec yy)
1030 {
1031   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1032   PetscErrorCode ierr;
1033   PetscBool      merged;
1034 
1035   PetscFunctionBegin;
1036   ierr = VecScatterGetMerged(a->Mvctx,&merged);CHKERRQ(ierr);
1037   /* do nondiagonal part */
1038   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
1039   if (!merged) {
1040     /* send it on its way */
1041     ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1042     /* do local part */
1043     ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
1044     /* receive remote parts: note this assumes the values are not actually */
1045     /* added in yy until the next line, */
1046     ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1047   } else {
1048     /* do local part */
1049     ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
1050     /* send it on its way */
1051     ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1052     /* values actually were received in the Begin() but we need to call this nop */
1053     ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1054   }
1055   PetscFunctionReturn(0);
1056 }
1057 
1058 #undef __FUNCT__
1059 #define __FUNCT__ "MatIsTranspose_MPIAIJ"
1060 PetscErrorCode  MatIsTranspose_MPIAIJ(Mat Amat,Mat Bmat,PetscReal tol,PetscBool  *f)
1061 {
1062   MPI_Comm       comm;
1063   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ*) Amat->data, *Bij;
1064   Mat            Adia = Aij->A, Bdia, Aoff,Boff,*Aoffs,*Boffs;
1065   IS             Me,Notme;
1066   PetscErrorCode ierr;
1067   PetscInt       M,N,first,last,*notme,i;
1068   PetscMPIInt    size;
1069 
1070   PetscFunctionBegin;
1071   /* Easy test: symmetric diagonal block */
1072   Bij  = (Mat_MPIAIJ*) Bmat->data; Bdia = Bij->A;
1073   ierr = MatIsTranspose(Adia,Bdia,tol,f);CHKERRQ(ierr);
1074   if (!*f) PetscFunctionReturn(0);
1075   ierr = PetscObjectGetComm((PetscObject)Amat,&comm);CHKERRQ(ierr);
1076   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1077   if (size == 1) PetscFunctionReturn(0);
1078 
1079   /* Hard test: off-diagonal block. This takes a MatGetSubMatrix. */
1080   ierr = MatGetSize(Amat,&M,&N);CHKERRQ(ierr);
1081   ierr = MatGetOwnershipRange(Amat,&first,&last);CHKERRQ(ierr);
1082   ierr = PetscMalloc1(N-last+first,&notme);CHKERRQ(ierr);
1083   for (i=0; i<first; i++) notme[i] = i;
1084   for (i=last; i<M; i++) notme[i-last+first] = i;
1085   ierr = ISCreateGeneral(MPI_COMM_SELF,N-last+first,notme,PETSC_COPY_VALUES,&Notme);CHKERRQ(ierr);
1086   ierr = ISCreateStride(MPI_COMM_SELF,last-first,first,1,&Me);CHKERRQ(ierr);
1087   ierr = MatGetSubMatrices(Amat,1,&Me,&Notme,MAT_INITIAL_MATRIX,&Aoffs);CHKERRQ(ierr);
1088   Aoff = Aoffs[0];
1089   ierr = MatGetSubMatrices(Bmat,1,&Notme,&Me,MAT_INITIAL_MATRIX,&Boffs);CHKERRQ(ierr);
1090   Boff = Boffs[0];
1091   ierr = MatIsTranspose(Aoff,Boff,tol,f);CHKERRQ(ierr);
1092   ierr = MatDestroyMatrices(1,&Aoffs);CHKERRQ(ierr);
1093   ierr = MatDestroyMatrices(1,&Boffs);CHKERRQ(ierr);
1094   ierr = ISDestroy(&Me);CHKERRQ(ierr);
1095   ierr = ISDestroy(&Notme);CHKERRQ(ierr);
1096   ierr = PetscFree(notme);CHKERRQ(ierr);
1097   PetscFunctionReturn(0);
1098 }
1099 
1100 #undef __FUNCT__
1101 #define __FUNCT__ "MatMultTransposeAdd_MPIAIJ"
1102 PetscErrorCode MatMultTransposeAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1103 {
1104   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1105   PetscErrorCode ierr;
1106 
1107   PetscFunctionBegin;
1108   /* do nondiagonal part */
1109   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
1110   /* send it on its way */
1111   ierr = VecScatterBegin(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1112   /* do local part */
1113   ierr = (*a->A->ops->multtransposeadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
1114   /* receive remote parts */
1115   ierr = VecScatterEnd(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1116   PetscFunctionReturn(0);
1117 }
1118 
1119 /*
1120   This only works correctly for square matrices where the subblock A->A is the
1121    diagonal block
1122 */
1123 #undef __FUNCT__
1124 #define __FUNCT__ "MatGetDiagonal_MPIAIJ"
1125 PetscErrorCode MatGetDiagonal_MPIAIJ(Mat A,Vec v)
1126 {
1127   PetscErrorCode ierr;
1128   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1129 
1130   PetscFunctionBegin;
1131   if (A->rmap->N != A->cmap->N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Supports only square matrix where A->A is diag block");
1132   if (A->rmap->rstart != A->cmap->rstart || A->rmap->rend != A->cmap->rend) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"row partition must equal col partition");
1133   ierr = MatGetDiagonal(a->A,v);CHKERRQ(ierr);
1134   PetscFunctionReturn(0);
1135 }
1136 
1137 #undef __FUNCT__
1138 #define __FUNCT__ "MatScale_MPIAIJ"
1139 PetscErrorCode MatScale_MPIAIJ(Mat A,PetscScalar aa)
1140 {
1141   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1142   PetscErrorCode ierr;
1143 
1144   PetscFunctionBegin;
1145   ierr = MatScale(a->A,aa);CHKERRQ(ierr);
1146   ierr = MatScale(a->B,aa);CHKERRQ(ierr);
1147   PetscFunctionReturn(0);
1148 }
1149 
1150 #undef __FUNCT__
1151 #define __FUNCT__ "MatDestroy_MPIAIJ"
1152 PetscErrorCode MatDestroy_MPIAIJ(Mat mat)
1153 {
1154   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1155   PetscErrorCode ierr;
1156 
1157   PetscFunctionBegin;
1158 #if defined(PETSC_USE_LOG)
1159   PetscLogObjectState((PetscObject)mat,"Rows=%D, Cols=%D",mat->rmap->N,mat->cmap->N);
1160 #endif
1161   ierr = MatStashDestroy_Private(&mat->stash);CHKERRQ(ierr);
1162   ierr = VecDestroy(&aij->diag);CHKERRQ(ierr);
1163   ierr = MatDestroy(&aij->A);CHKERRQ(ierr);
1164   ierr = MatDestroy(&aij->B);CHKERRQ(ierr);
1165 #if defined(PETSC_USE_CTABLE)
1166   ierr = PetscTableDestroy(&aij->colmap);CHKERRQ(ierr);
1167 #else
1168   ierr = PetscFree(aij->colmap);CHKERRQ(ierr);
1169 #endif
1170   ierr = PetscFree(aij->garray);CHKERRQ(ierr);
1171   ierr = VecDestroy(&aij->lvec);CHKERRQ(ierr);
1172   ierr = VecScatterDestroy(&aij->Mvctx);CHKERRQ(ierr);
1173   ierr = PetscFree2(aij->rowvalues,aij->rowindices);CHKERRQ(ierr);
1174   ierr = PetscFree(aij->ld);CHKERRQ(ierr);
1175   ierr = PetscFree(mat->data);CHKERRQ(ierr);
1176 
1177   ierr = PetscObjectChangeTypeName((PetscObject)mat,0);CHKERRQ(ierr);
1178   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatStoreValues_C",NULL);CHKERRQ(ierr);
1179   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatRetrieveValues_C",NULL);CHKERRQ(ierr);
1180   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatGetDiagonalBlock_C",NULL);CHKERRQ(ierr);
1181   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatIsTranspose_C",NULL);CHKERRQ(ierr);
1182   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocation_C",NULL);CHKERRQ(ierr);
1183   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocationCSR_C",NULL);CHKERRQ(ierr);
1184   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDiagonalScaleLocal_C",NULL);CHKERRQ(ierr);
1185   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_mpisbaij_C",NULL);CHKERRQ(ierr);
1186 #if defined(PETSC_HAVE_ELEMENTAL)
1187   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_elemental_C",NULL);CHKERRQ(ierr);
1188 #endif
1189   PetscFunctionReturn(0);
1190 }
1191 
1192 #undef __FUNCT__
1193 #define __FUNCT__ "MatView_MPIAIJ_Binary"
1194 PetscErrorCode MatView_MPIAIJ_Binary(Mat mat,PetscViewer viewer)
1195 {
1196   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1197   Mat_SeqAIJ     *A   = (Mat_SeqAIJ*)aij->A->data;
1198   Mat_SeqAIJ     *B   = (Mat_SeqAIJ*)aij->B->data;
1199   PetscErrorCode ierr;
1200   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
1201   int            fd;
1202   PetscInt       nz,header[4],*row_lengths,*range=0,rlen,i;
1203   PetscInt       nzmax,*column_indices,j,k,col,*garray = aij->garray,cnt,cstart = mat->cmap->rstart,rnz = 0;
1204   PetscScalar    *column_values;
1205   PetscInt       message_count,flowcontrolcount;
1206   FILE           *file;
1207 
1208   PetscFunctionBegin;
1209   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
1210   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);CHKERRQ(ierr);
1211   nz   = A->nz + B->nz;
1212   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
1213   if (!rank) {
1214     header[0] = MAT_FILE_CLASSID;
1215     header[1] = mat->rmap->N;
1216     header[2] = mat->cmap->N;
1217 
1218     ierr = MPI_Reduce(&nz,&header[3],1,MPIU_INT,MPI_SUM,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1219     ierr = PetscBinaryWrite(fd,header,4,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1220     /* get largest number of rows any processor has */
1221     rlen  = mat->rmap->n;
1222     range = mat->rmap->range;
1223     for (i=1; i<size; i++) rlen = PetscMax(rlen,range[i+1] - range[i]);
1224   } else {
1225     ierr = MPI_Reduce(&nz,0,1,MPIU_INT,MPI_SUM,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1226     rlen = mat->rmap->n;
1227   }
1228 
1229   /* load up the local row counts */
1230   ierr = PetscMalloc1(rlen+1,&row_lengths);CHKERRQ(ierr);
1231   for (i=0; i<mat->rmap->n; i++) row_lengths[i] = A->i[i+1] - A->i[i] + B->i[i+1] - B->i[i];
1232 
1233   /* store the row lengths to the file */
1234   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1235   if (!rank) {
1236     ierr = PetscBinaryWrite(fd,row_lengths,mat->rmap->n,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1237     for (i=1; i<size; i++) {
1238       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1239       rlen = range[i+1] - range[i];
1240       ierr = MPIULong_Recv(row_lengths,rlen,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1241       ierr = PetscBinaryWrite(fd,row_lengths,rlen,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1242     }
1243     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1244   } else {
1245     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1246     ierr = MPIULong_Send(row_lengths,mat->rmap->n,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1247     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1248   }
1249   ierr = PetscFree(row_lengths);CHKERRQ(ierr);
1250 
1251   /* load up the local column indices */
1252   nzmax = nz; /* th processor needs space a largest processor needs */
1253   ierr  = MPI_Reduce(&nz,&nzmax,1,MPIU_INT,MPI_MAX,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1254   ierr  = PetscMalloc1(nzmax+1,&column_indices);CHKERRQ(ierr);
1255   cnt   = 0;
1256   for (i=0; i<mat->rmap->n; i++) {
1257     for (j=B->i[i]; j<B->i[i+1]; j++) {
1258       if ((col = garray[B->j[j]]) > cstart) break;
1259       column_indices[cnt++] = col;
1260     }
1261     for (k=A->i[i]; k<A->i[i+1]; k++) column_indices[cnt++] = A->j[k] + cstart;
1262     for (; j<B->i[i+1]; j++) column_indices[cnt++] = garray[B->j[j]];
1263   }
1264   if (cnt != A->nz + B->nz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: cnt = %D nz = %D",cnt,A->nz+B->nz);
1265 
1266   /* store the column indices to the file */
1267   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1268   if (!rank) {
1269     MPI_Status status;
1270     ierr = PetscBinaryWrite(fd,column_indices,nz,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1271     for (i=1; i<size; i++) {
1272       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1273       ierr = MPI_Recv(&rnz,1,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat),&status);CHKERRQ(ierr);
1274       if (rnz > nzmax) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: nz = %D nzmax = %D",nz,nzmax);
1275       ierr = MPIULong_Recv(column_indices,rnz,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1276       ierr = PetscBinaryWrite(fd,column_indices,rnz,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1277     }
1278     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1279   } else {
1280     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1281     ierr = MPI_Send(&nz,1,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1282     ierr = MPIULong_Send(column_indices,nz,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1283     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1284   }
1285   ierr = PetscFree(column_indices);CHKERRQ(ierr);
1286 
1287   /* load up the local column values */
1288   ierr = PetscMalloc1(nzmax+1,&column_values);CHKERRQ(ierr);
1289   cnt  = 0;
1290   for (i=0; i<mat->rmap->n; i++) {
1291     for (j=B->i[i]; j<B->i[i+1]; j++) {
1292       if (garray[B->j[j]] > cstart) break;
1293       column_values[cnt++] = B->a[j];
1294     }
1295     for (k=A->i[i]; k<A->i[i+1]; k++) column_values[cnt++] = A->a[k];
1296     for (; j<B->i[i+1]; j++) column_values[cnt++] = B->a[j];
1297   }
1298   if (cnt != A->nz + B->nz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Internal PETSc error: cnt = %D nz = %D",cnt,A->nz+B->nz);
1299 
1300   /* store the column values to the file */
1301   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1302   if (!rank) {
1303     MPI_Status status;
1304     ierr = PetscBinaryWrite(fd,column_values,nz,PETSC_SCALAR,PETSC_TRUE);CHKERRQ(ierr);
1305     for (i=1; i<size; i++) {
1306       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1307       ierr = MPI_Recv(&rnz,1,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat),&status);CHKERRQ(ierr);
1308       if (rnz > nzmax) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: nz = %D nzmax = %D",nz,nzmax);
1309       ierr = MPIULong_Recv(column_values,rnz,MPIU_SCALAR,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1310       ierr = PetscBinaryWrite(fd,column_values,rnz,PETSC_SCALAR,PETSC_TRUE);CHKERRQ(ierr);
1311     }
1312     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1313   } else {
1314     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1315     ierr = MPI_Send(&nz,1,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1316     ierr = MPIULong_Send(column_values,nz,MPIU_SCALAR,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1317     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1318   }
1319   ierr = PetscFree(column_values);CHKERRQ(ierr);
1320 
1321   ierr = PetscViewerBinaryGetInfoPointer(viewer,&file);CHKERRQ(ierr);
1322   if (file) fprintf(file,"-matload_block_size %d\n",(int)PetscAbs(mat->rmap->bs));
1323   PetscFunctionReturn(0);
1324 }
1325 
1326 #include <petscdraw.h>
1327 #undef __FUNCT__
1328 #define __FUNCT__ "MatView_MPIAIJ_ASCIIorDraworSocket"
1329 PetscErrorCode MatView_MPIAIJ_ASCIIorDraworSocket(Mat mat,PetscViewer viewer)
1330 {
1331   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)mat->data;
1332   PetscErrorCode    ierr;
1333   PetscMPIInt       rank = aij->rank,size = aij->size;
1334   PetscBool         isdraw,iascii,isbinary;
1335   PetscViewer       sviewer;
1336   PetscViewerFormat format;
1337 
1338   PetscFunctionBegin;
1339   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1340   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1341   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1342   if (iascii) {
1343     ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
1344     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
1345       MatInfo   info;
1346       PetscBool inodes;
1347 
1348       ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
1349       ierr = MatGetInfo(mat,MAT_LOCAL,&info);CHKERRQ(ierr);
1350       ierr = MatInodeGetInodeSizes(aij->A,NULL,(PetscInt**)&inodes,NULL);CHKERRQ(ierr);
1351       ierr = PetscViewerASCIISynchronizedAllow(viewer,PETSC_TRUE);CHKERRQ(ierr);
1352       if (!inodes) {
1353         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %D nz %D nz alloced %D mem %D, not using I-node routines\n",
1354                                                   rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
1355       } else {
1356         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %D nz %D nz alloced %D mem %D, using I-node routines\n",
1357                                                   rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
1358       }
1359       ierr = MatGetInfo(aij->A,MAT_LOCAL,&info);CHKERRQ(ierr);
1360       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] on-diagonal part: nz %D \n",rank,(PetscInt)info.nz_used);CHKERRQ(ierr);
1361       ierr = MatGetInfo(aij->B,MAT_LOCAL,&info);CHKERRQ(ierr);
1362       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] off-diagonal part: nz %D \n",rank,(PetscInt)info.nz_used);CHKERRQ(ierr);
1363       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1364       ierr = PetscViewerASCIISynchronizedAllow(viewer,PETSC_FALSE);CHKERRQ(ierr);
1365       ierr = PetscViewerASCIIPrintf(viewer,"Information on VecScatter used in matrix-vector product: \n");CHKERRQ(ierr);
1366       ierr = VecScatterView(aij->Mvctx,viewer);CHKERRQ(ierr);
1367       PetscFunctionReturn(0);
1368     } else if (format == PETSC_VIEWER_ASCII_INFO) {
1369       PetscInt inodecount,inodelimit,*inodes;
1370       ierr = MatInodeGetInodeSizes(aij->A,&inodecount,&inodes,&inodelimit);CHKERRQ(ierr);
1371       if (inodes) {
1372         ierr = PetscViewerASCIIPrintf(viewer,"using I-node (on process 0) routines: found %D nodes, limit used is %D\n",inodecount,inodelimit);CHKERRQ(ierr);
1373       } else {
1374         ierr = PetscViewerASCIIPrintf(viewer,"not using I-node (on process 0) routines\n");CHKERRQ(ierr);
1375       }
1376       PetscFunctionReturn(0);
1377     } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO) {
1378       PetscFunctionReturn(0);
1379     }
1380   } else if (isbinary) {
1381     if (size == 1) {
1382       ierr = PetscObjectSetName((PetscObject)aij->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1383       ierr = MatView(aij->A,viewer);CHKERRQ(ierr);
1384     } else {
1385       ierr = MatView_MPIAIJ_Binary(mat,viewer);CHKERRQ(ierr);
1386     }
1387     PetscFunctionReturn(0);
1388   } else if (isdraw) {
1389     PetscDraw draw;
1390     PetscBool isnull;
1391     ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
1392     ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr); if (isnull) PetscFunctionReturn(0);
1393   }
1394 
1395   {
1396     /* assemble the entire matrix onto first processor. */
1397     Mat        A;
1398     Mat_SeqAIJ *Aloc;
1399     PetscInt   M = mat->rmap->N,N = mat->cmap->N,m,*ai,*aj,row,*cols,i,*ct;
1400     MatScalar  *a;
1401 
1402     ierr = MatCreate(PetscObjectComm((PetscObject)mat),&A);CHKERRQ(ierr);
1403     if (!rank) {
1404       ierr = MatSetSizes(A,M,N,M,N);CHKERRQ(ierr);
1405     } else {
1406       ierr = MatSetSizes(A,0,0,M,N);CHKERRQ(ierr);
1407     }
1408     /* This is just a temporary matrix, so explicitly using MATMPIAIJ is probably best */
1409     ierr = MatSetType(A,MATMPIAIJ);CHKERRQ(ierr);
1410     ierr = MatMPIAIJSetPreallocation(A,0,NULL,0,NULL);CHKERRQ(ierr);
1411     ierr = MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
1412     ierr = PetscLogObjectParent((PetscObject)mat,(PetscObject)A);CHKERRQ(ierr);
1413 
1414     /* copy over the A part */
1415     Aloc = (Mat_SeqAIJ*)aij->A->data;
1416     m    = aij->A->rmap->n; ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
1417     row  = mat->rmap->rstart;
1418     for (i=0; i<ai[m]; i++) aj[i] += mat->cmap->rstart;
1419     for (i=0; i<m; i++) {
1420       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],aj,a,INSERT_VALUES);CHKERRQ(ierr);
1421       row++;
1422       a += ai[i+1]-ai[i]; aj += ai[i+1]-ai[i];
1423     }
1424     aj = Aloc->j;
1425     for (i=0; i<ai[m]; i++) aj[i] -= mat->cmap->rstart;
1426 
1427     /* copy over the B part */
1428     Aloc = (Mat_SeqAIJ*)aij->B->data;
1429     m    = aij->B->rmap->n;  ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
1430     row  = mat->rmap->rstart;
1431     ierr = PetscMalloc1(ai[m]+1,&cols);CHKERRQ(ierr);
1432     ct   = cols;
1433     for (i=0; i<ai[m]; i++) cols[i] = aij->garray[aj[i]];
1434     for (i=0; i<m; i++) {
1435       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],cols,a,INSERT_VALUES);CHKERRQ(ierr);
1436       row++;
1437       a += ai[i+1]-ai[i]; cols += ai[i+1]-ai[i];
1438     }
1439     ierr = PetscFree(ct);CHKERRQ(ierr);
1440     ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1441     ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1442     /*
1443        Everyone has to call to draw the matrix since the graphics waits are
1444        synchronized across all processors that share the PetscDraw object
1445     */
1446     ierr = PetscViewerGetSingleton(viewer,&sviewer);CHKERRQ(ierr);
1447     if (!rank) {
1448       ierr = PetscObjectSetName((PetscObject)((Mat_MPIAIJ*)(A->data))->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1449       ierr = MatView_SeqAIJ(((Mat_MPIAIJ*)(A->data))->A,sviewer);CHKERRQ(ierr);
1450     }
1451     ierr = PetscViewerRestoreSingleton(viewer,&sviewer);CHKERRQ(ierr);
1452     ierr = MatDestroy(&A);CHKERRQ(ierr);
1453   }
1454   PetscFunctionReturn(0);
1455 }
1456 
1457 #undef __FUNCT__
1458 #define __FUNCT__ "MatView_MPIAIJ"
1459 PetscErrorCode MatView_MPIAIJ(Mat mat,PetscViewer viewer)
1460 {
1461   PetscErrorCode ierr;
1462   PetscBool      iascii,isdraw,issocket,isbinary;
1463 
1464   PetscFunctionBegin;
1465   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1466   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1467   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1468   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSOCKET,&issocket);CHKERRQ(ierr);
1469   if (iascii || isdraw || isbinary || issocket) {
1470     ierr = MatView_MPIAIJ_ASCIIorDraworSocket(mat,viewer);CHKERRQ(ierr);
1471   }
1472   PetscFunctionReturn(0);
1473 }
1474 
1475 #undef __FUNCT__
1476 #define __FUNCT__ "MatSOR_MPIAIJ"
1477 PetscErrorCode MatSOR_MPIAIJ(Mat matin,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
1478 {
1479   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1480   PetscErrorCode ierr;
1481   Vec            bb1 = 0;
1482   PetscBool      hasop;
1483 
1484   PetscFunctionBegin;
1485   if (flag == SOR_APPLY_UPPER) {
1486     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1487     PetscFunctionReturn(0);
1488   }
1489 
1490   if (its > 1 || ~flag & SOR_ZERO_INITIAL_GUESS || flag & SOR_EISENSTAT) {
1491     ierr = VecDuplicate(bb,&bb1);CHKERRQ(ierr);
1492   }
1493 
1494   if ((flag & SOR_LOCAL_SYMMETRIC_SWEEP) == SOR_LOCAL_SYMMETRIC_SWEEP) {
1495     if (flag & SOR_ZERO_INITIAL_GUESS) {
1496       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1497       its--;
1498     }
1499 
1500     while (its--) {
1501       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1502       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1503 
1504       /* update rhs: bb1 = bb - B*x */
1505       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1506       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1507 
1508       /* local sweep */
1509       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_SYMMETRIC_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1510     }
1511   } else if (flag & SOR_LOCAL_FORWARD_SWEEP) {
1512     if (flag & SOR_ZERO_INITIAL_GUESS) {
1513       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1514       its--;
1515     }
1516     while (its--) {
1517       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1518       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1519 
1520       /* update rhs: bb1 = bb - B*x */
1521       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1522       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1523 
1524       /* local sweep */
1525       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_FORWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1526     }
1527   } else if (flag & SOR_LOCAL_BACKWARD_SWEEP) {
1528     if (flag & SOR_ZERO_INITIAL_GUESS) {
1529       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1530       its--;
1531     }
1532     while (its--) {
1533       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1534       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1535 
1536       /* update rhs: bb1 = bb - B*x */
1537       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1538       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1539 
1540       /* local sweep */
1541       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_BACKWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1542     }
1543   } else if (flag & SOR_EISENSTAT) {
1544     Vec xx1;
1545 
1546     ierr = VecDuplicate(bb,&xx1);CHKERRQ(ierr);
1547     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_BACKWARD_SWEEP),fshift,lits,1,xx);CHKERRQ(ierr);
1548 
1549     ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1550     ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1551     if (!mat->diag) {
1552       ierr = MatCreateVecs(matin,&mat->diag,NULL);CHKERRQ(ierr);
1553       ierr = MatGetDiagonal(matin,mat->diag);CHKERRQ(ierr);
1554     }
1555     ierr = MatHasOperation(matin,MATOP_MULT_DIAGONAL_BLOCK,&hasop);CHKERRQ(ierr);
1556     if (hasop) {
1557       ierr = MatMultDiagonalBlock(matin,xx,bb1);CHKERRQ(ierr);
1558     } else {
1559       ierr = VecPointwiseMult(bb1,mat->diag,xx);CHKERRQ(ierr);
1560     }
1561     ierr = VecAYPX(bb1,(omega-2.0)/omega,bb);CHKERRQ(ierr);
1562 
1563     ierr = MatMultAdd(mat->B,mat->lvec,bb1,bb1);CHKERRQ(ierr);
1564 
1565     /* local sweep */
1566     ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_FORWARD_SWEEP),fshift,lits,1,xx1);CHKERRQ(ierr);
1567     ierr = VecAXPY(xx,1.0,xx1);CHKERRQ(ierr);
1568     ierr = VecDestroy(&xx1);CHKERRQ(ierr);
1569   } else SETERRQ(PetscObjectComm((PetscObject)matin),PETSC_ERR_SUP,"Parallel SOR not supported");
1570 
1571   ierr = VecDestroy(&bb1);CHKERRQ(ierr);
1572   PetscFunctionReturn(0);
1573 }
1574 
1575 #undef __FUNCT__
1576 #define __FUNCT__ "MatPermute_MPIAIJ"
1577 PetscErrorCode MatPermute_MPIAIJ(Mat A,IS rowp,IS colp,Mat *B)
1578 {
1579   Mat            aA,aB,Aperm;
1580   const PetscInt *rwant,*cwant,*gcols,*ai,*bi,*aj,*bj;
1581   PetscScalar    *aa,*ba;
1582   PetscInt       i,j,m,n,ng,anz,bnz,*dnnz,*onnz,*tdnnz,*tonnz,*rdest,*cdest,*work,*gcdest;
1583   PetscSF        rowsf,sf;
1584   IS             parcolp = NULL;
1585   PetscBool      done;
1586   PetscErrorCode ierr;
1587 
1588   PetscFunctionBegin;
1589   ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
1590   ierr = ISGetIndices(rowp,&rwant);CHKERRQ(ierr);
1591   ierr = ISGetIndices(colp,&cwant);CHKERRQ(ierr);
1592   ierr = PetscMalloc3(PetscMax(m,n),&work,m,&rdest,n,&cdest);CHKERRQ(ierr);
1593 
1594   /* Invert row permutation to find out where my rows should go */
1595   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&rowsf);CHKERRQ(ierr);
1596   ierr = PetscSFSetGraphLayout(rowsf,A->rmap,A->rmap->n,NULL,PETSC_OWN_POINTER,rwant);CHKERRQ(ierr);
1597   ierr = PetscSFSetFromOptions(rowsf);CHKERRQ(ierr);
1598   for (i=0; i<m; i++) work[i] = A->rmap->rstart + i;
1599   ierr = PetscSFReduceBegin(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1600   ierr = PetscSFReduceEnd(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1601 
1602   /* Invert column permutation to find out where my columns should go */
1603   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1604   ierr = PetscSFSetGraphLayout(sf,A->cmap,A->cmap->n,NULL,PETSC_OWN_POINTER,cwant);CHKERRQ(ierr);
1605   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1606   for (i=0; i<n; i++) work[i] = A->cmap->rstart + i;
1607   ierr = PetscSFReduceBegin(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1608   ierr = PetscSFReduceEnd(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1609   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1610 
1611   ierr = ISRestoreIndices(rowp,&rwant);CHKERRQ(ierr);
1612   ierr = ISRestoreIndices(colp,&cwant);CHKERRQ(ierr);
1613   ierr = MatMPIAIJGetSeqAIJ(A,&aA,&aB,&gcols);CHKERRQ(ierr);
1614 
1615   /* Find out where my gcols should go */
1616   ierr = MatGetSize(aB,NULL,&ng);CHKERRQ(ierr);
1617   ierr = PetscMalloc1(ng,&gcdest);CHKERRQ(ierr);
1618   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1619   ierr = PetscSFSetGraphLayout(sf,A->cmap,ng,NULL,PETSC_OWN_POINTER,gcols);CHKERRQ(ierr);
1620   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1621   ierr = PetscSFBcastBegin(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1622   ierr = PetscSFBcastEnd(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1623   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1624 
1625   ierr = PetscCalloc4(m,&dnnz,m,&onnz,m,&tdnnz,m,&tonnz);CHKERRQ(ierr);
1626   ierr = MatGetRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1627   ierr = MatGetRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1628   for (i=0; i<m; i++) {
1629     PetscInt row = rdest[i],rowner;
1630     ierr = PetscLayoutFindOwner(A->rmap,row,&rowner);CHKERRQ(ierr);
1631     for (j=ai[i]; j<ai[i+1]; j++) {
1632       PetscInt cowner,col = cdest[aj[j]];
1633       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr); /* Could build an index for the columns to eliminate this search */
1634       if (rowner == cowner) dnnz[i]++;
1635       else onnz[i]++;
1636     }
1637     for (j=bi[i]; j<bi[i+1]; j++) {
1638       PetscInt cowner,col = gcdest[bj[j]];
1639       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr);
1640       if (rowner == cowner) dnnz[i]++;
1641       else onnz[i]++;
1642     }
1643   }
1644   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1645   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1646   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1647   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1648   ierr = PetscSFDestroy(&rowsf);CHKERRQ(ierr);
1649 
1650   ierr = MatCreateAIJ(PetscObjectComm((PetscObject)A),A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N,0,tdnnz,0,tonnz,&Aperm);CHKERRQ(ierr);
1651   ierr = MatSeqAIJGetArray(aA,&aa);CHKERRQ(ierr);
1652   ierr = MatSeqAIJGetArray(aB,&ba);CHKERRQ(ierr);
1653   for (i=0; i<m; i++) {
1654     PetscInt *acols = dnnz,*bcols = onnz; /* Repurpose now-unneeded arrays */
1655     PetscInt j0,rowlen;
1656     rowlen = ai[i+1] - ai[i];
1657     for (j0=j=0; j<rowlen; j0=j) { /* rowlen could be larger than number of rows m, so sum in batches */
1658       for ( ; j<PetscMin(rowlen,j0+m); j++) acols[j-j0] = cdest[aj[ai[i]+j]];
1659       ierr = MatSetValues(Aperm,1,&rdest[i],j-j0,acols,aa+ai[i]+j0,INSERT_VALUES);CHKERRQ(ierr);
1660     }
1661     rowlen = bi[i+1] - bi[i];
1662     for (j0=j=0; j<rowlen; j0=j) {
1663       for ( ; j<PetscMin(rowlen,j0+m); j++) bcols[j-j0] = gcdest[bj[bi[i]+j]];
1664       ierr = MatSetValues(Aperm,1,&rdest[i],j-j0,bcols,ba+bi[i]+j0,INSERT_VALUES);CHKERRQ(ierr);
1665     }
1666   }
1667   ierr = MatAssemblyBegin(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1668   ierr = MatAssemblyEnd(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1669   ierr = MatRestoreRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1670   ierr = MatRestoreRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1671   ierr = MatSeqAIJRestoreArray(aA,&aa);CHKERRQ(ierr);
1672   ierr = MatSeqAIJRestoreArray(aB,&ba);CHKERRQ(ierr);
1673   ierr = PetscFree4(dnnz,onnz,tdnnz,tonnz);CHKERRQ(ierr);
1674   ierr = PetscFree3(work,rdest,cdest);CHKERRQ(ierr);
1675   ierr = PetscFree(gcdest);CHKERRQ(ierr);
1676   if (parcolp) {ierr = ISDestroy(&colp);CHKERRQ(ierr);}
1677   *B = Aperm;
1678   PetscFunctionReturn(0);
1679 }
1680 
1681 #undef __FUNCT__
1682 #define __FUNCT__ "MatGetInfo_MPIAIJ"
1683 PetscErrorCode MatGetInfo_MPIAIJ(Mat matin,MatInfoType flag,MatInfo *info)
1684 {
1685   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1686   Mat            A    = mat->A,B = mat->B;
1687   PetscErrorCode ierr;
1688   PetscReal      isend[5],irecv[5];
1689 
1690   PetscFunctionBegin;
1691   info->block_size = 1.0;
1692   ierr             = MatGetInfo(A,MAT_LOCAL,info);CHKERRQ(ierr);
1693 
1694   isend[0] = info->nz_used; isend[1] = info->nz_allocated; isend[2] = info->nz_unneeded;
1695   isend[3] = info->memory;  isend[4] = info->mallocs;
1696 
1697   ierr = MatGetInfo(B,MAT_LOCAL,info);CHKERRQ(ierr);
1698 
1699   isend[0] += info->nz_used; isend[1] += info->nz_allocated; isend[2] += info->nz_unneeded;
1700   isend[3] += info->memory;  isend[4] += info->mallocs;
1701   if (flag == MAT_LOCAL) {
1702     info->nz_used      = isend[0];
1703     info->nz_allocated = isend[1];
1704     info->nz_unneeded  = isend[2];
1705     info->memory       = isend[3];
1706     info->mallocs      = isend[4];
1707   } else if (flag == MAT_GLOBAL_MAX) {
1708     ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1709 
1710     info->nz_used      = irecv[0];
1711     info->nz_allocated = irecv[1];
1712     info->nz_unneeded  = irecv[2];
1713     info->memory       = irecv[3];
1714     info->mallocs      = irecv[4];
1715   } else if (flag == MAT_GLOBAL_SUM) {
1716     ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1717 
1718     info->nz_used      = irecv[0];
1719     info->nz_allocated = irecv[1];
1720     info->nz_unneeded  = irecv[2];
1721     info->memory       = irecv[3];
1722     info->mallocs      = irecv[4];
1723   }
1724   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
1725   info->fill_ratio_needed = 0;
1726   info->factor_mallocs    = 0;
1727   PetscFunctionReturn(0);
1728 }
1729 
1730 #undef __FUNCT__
1731 #define __FUNCT__ "MatSetOption_MPIAIJ"
1732 PetscErrorCode MatSetOption_MPIAIJ(Mat A,MatOption op,PetscBool flg)
1733 {
1734   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1735   PetscErrorCode ierr;
1736 
1737   PetscFunctionBegin;
1738   switch (op) {
1739   case MAT_NEW_NONZERO_LOCATIONS:
1740   case MAT_NEW_NONZERO_ALLOCATION_ERR:
1741   case MAT_UNUSED_NONZERO_LOCATION_ERR:
1742   case MAT_KEEP_NONZERO_PATTERN:
1743   case MAT_NEW_NONZERO_LOCATION_ERR:
1744   case MAT_USE_INODES:
1745   case MAT_IGNORE_ZERO_ENTRIES:
1746     MatCheckPreallocated(A,1);
1747     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1748     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1749     break;
1750   case MAT_ROW_ORIENTED:
1751     a->roworiented = flg;
1752 
1753     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1754     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1755     break;
1756   case MAT_NEW_DIAGONALS:
1757     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
1758     break;
1759   case MAT_IGNORE_OFF_PROC_ENTRIES:
1760     a->donotstash = flg;
1761     break;
1762   case MAT_SPD:
1763     A->spd_set = PETSC_TRUE;
1764     A->spd     = flg;
1765     if (flg) {
1766       A->symmetric                  = PETSC_TRUE;
1767       A->structurally_symmetric     = PETSC_TRUE;
1768       A->symmetric_set              = PETSC_TRUE;
1769       A->structurally_symmetric_set = PETSC_TRUE;
1770     }
1771     break;
1772   case MAT_SYMMETRIC:
1773     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1774     break;
1775   case MAT_STRUCTURALLY_SYMMETRIC:
1776     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1777     break;
1778   case MAT_HERMITIAN:
1779     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1780     break;
1781   case MAT_SYMMETRY_ETERNAL:
1782     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1783     break;
1784   default:
1785     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %d",op);
1786   }
1787   PetscFunctionReturn(0);
1788 }
1789 
1790 #undef __FUNCT__
1791 #define __FUNCT__ "MatGetRow_MPIAIJ"
1792 PetscErrorCode MatGetRow_MPIAIJ(Mat matin,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1793 {
1794   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1795   PetscScalar    *vworkA,*vworkB,**pvA,**pvB,*v_p;
1796   PetscErrorCode ierr;
1797   PetscInt       i,*cworkA,*cworkB,**pcA,**pcB,cstart = matin->cmap->rstart;
1798   PetscInt       nztot,nzA,nzB,lrow,rstart = matin->rmap->rstart,rend = matin->rmap->rend;
1799   PetscInt       *cmap,*idx_p;
1800 
1801   PetscFunctionBegin;
1802   if (mat->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Already active");
1803   mat->getrowactive = PETSC_TRUE;
1804 
1805   if (!mat->rowvalues && (idx || v)) {
1806     /*
1807         allocate enough space to hold information from the longest row.
1808     */
1809     Mat_SeqAIJ *Aa = (Mat_SeqAIJ*)mat->A->data,*Ba = (Mat_SeqAIJ*)mat->B->data;
1810     PetscInt   max = 1,tmp;
1811     for (i=0; i<matin->rmap->n; i++) {
1812       tmp = Aa->i[i+1] - Aa->i[i] + Ba->i[i+1] - Ba->i[i];
1813       if (max < tmp) max = tmp;
1814     }
1815     ierr = PetscMalloc2(max,&mat->rowvalues,max,&mat->rowindices);CHKERRQ(ierr);
1816   }
1817 
1818   if (row < rstart || row >= rend) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Only local rows");
1819   lrow = row - rstart;
1820 
1821   pvA = &vworkA; pcA = &cworkA; pvB = &vworkB; pcB = &cworkB;
1822   if (!v)   {pvA = 0; pvB = 0;}
1823   if (!idx) {pcA = 0; if (!v) pcB = 0;}
1824   ierr  = (*mat->A->ops->getrow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1825   ierr  = (*mat->B->ops->getrow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1826   nztot = nzA + nzB;
1827 
1828   cmap = mat->garray;
1829   if (v  || idx) {
1830     if (nztot) {
1831       /* Sort by increasing column numbers, assuming A and B already sorted */
1832       PetscInt imark = -1;
1833       if (v) {
1834         *v = v_p = mat->rowvalues;
1835         for (i=0; i<nzB; i++) {
1836           if (cmap[cworkB[i]] < cstart) v_p[i] = vworkB[i];
1837           else break;
1838         }
1839         imark = i;
1840         for (i=0; i<nzA; i++)     v_p[imark+i] = vworkA[i];
1841         for (i=imark; i<nzB; i++) v_p[nzA+i]   = vworkB[i];
1842       }
1843       if (idx) {
1844         *idx = idx_p = mat->rowindices;
1845         if (imark > -1) {
1846           for (i=0; i<imark; i++) {
1847             idx_p[i] = cmap[cworkB[i]];
1848           }
1849         } else {
1850           for (i=0; i<nzB; i++) {
1851             if (cmap[cworkB[i]] < cstart) idx_p[i] = cmap[cworkB[i]];
1852             else break;
1853           }
1854           imark = i;
1855         }
1856         for (i=0; i<nzA; i++)     idx_p[imark+i] = cstart + cworkA[i];
1857         for (i=imark; i<nzB; i++) idx_p[nzA+i]   = cmap[cworkB[i]];
1858       }
1859     } else {
1860       if (idx) *idx = 0;
1861       if (v)   *v   = 0;
1862     }
1863   }
1864   *nz  = nztot;
1865   ierr = (*mat->A->ops->restorerow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1866   ierr = (*mat->B->ops->restorerow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1867   PetscFunctionReturn(0);
1868 }
1869 
1870 #undef __FUNCT__
1871 #define __FUNCT__ "MatRestoreRow_MPIAIJ"
1872 PetscErrorCode MatRestoreRow_MPIAIJ(Mat mat,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1873 {
1874   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1875 
1876   PetscFunctionBegin;
1877   if (!aij->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"MatGetRow() must be called first");
1878   aij->getrowactive = PETSC_FALSE;
1879   PetscFunctionReturn(0);
1880 }
1881 
1882 #undef __FUNCT__
1883 #define __FUNCT__ "MatNorm_MPIAIJ"
1884 PetscErrorCode MatNorm_MPIAIJ(Mat mat,NormType type,PetscReal *norm)
1885 {
1886   Mat_MPIAIJ     *aij  = (Mat_MPIAIJ*)mat->data;
1887   Mat_SeqAIJ     *amat = (Mat_SeqAIJ*)aij->A->data,*bmat = (Mat_SeqAIJ*)aij->B->data;
1888   PetscErrorCode ierr;
1889   PetscInt       i,j,cstart = mat->cmap->rstart;
1890   PetscReal      sum = 0.0;
1891   MatScalar      *v;
1892 
1893   PetscFunctionBegin;
1894   if (aij->size == 1) {
1895     ierr =  MatNorm(aij->A,type,norm);CHKERRQ(ierr);
1896   } else {
1897     if (type == NORM_FROBENIUS) {
1898       v = amat->a;
1899       for (i=0; i<amat->nz; i++) {
1900         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1901       }
1902       v = bmat->a;
1903       for (i=0; i<bmat->nz; i++) {
1904         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1905       }
1906       ierr  = MPI_Allreduce(&sum,norm,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1907       *norm = PetscSqrtReal(*norm);
1908     } else if (type == NORM_1) { /* max column norm */
1909       PetscReal *tmp,*tmp2;
1910       PetscInt  *jj,*garray = aij->garray;
1911       ierr  = PetscCalloc1(mat->cmap->N+1,&tmp);CHKERRQ(ierr);
1912       ierr  = PetscMalloc1(mat->cmap->N+1,&tmp2);CHKERRQ(ierr);
1913       *norm = 0.0;
1914       v     = amat->a; jj = amat->j;
1915       for (j=0; j<amat->nz; j++) {
1916         tmp[cstart + *jj++] += PetscAbsScalar(*v);  v++;
1917       }
1918       v = bmat->a; jj = bmat->j;
1919       for (j=0; j<bmat->nz; j++) {
1920         tmp[garray[*jj++]] += PetscAbsScalar(*v); v++;
1921       }
1922       ierr = MPI_Allreduce(tmp,tmp2,mat->cmap->N,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1923       for (j=0; j<mat->cmap->N; j++) {
1924         if (tmp2[j] > *norm) *norm = tmp2[j];
1925       }
1926       ierr = PetscFree(tmp);CHKERRQ(ierr);
1927       ierr = PetscFree(tmp2);CHKERRQ(ierr);
1928     } else if (type == NORM_INFINITY) { /* max row norm */
1929       PetscReal ntemp = 0.0;
1930       for (j=0; j<aij->A->rmap->n; j++) {
1931         v   = amat->a + amat->i[j];
1932         sum = 0.0;
1933         for (i=0; i<amat->i[j+1]-amat->i[j]; i++) {
1934           sum += PetscAbsScalar(*v); v++;
1935         }
1936         v = bmat->a + bmat->i[j];
1937         for (i=0; i<bmat->i[j+1]-bmat->i[j]; i++) {
1938           sum += PetscAbsScalar(*v); v++;
1939         }
1940         if (sum > ntemp) ntemp = sum;
1941       }
1942       ierr = MPI_Allreduce(&ntemp,norm,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1943     } else SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"No support for two norm");
1944   }
1945   PetscFunctionReturn(0);
1946 }
1947 
1948 #undef __FUNCT__
1949 #define __FUNCT__ "MatTranspose_MPIAIJ"
1950 PetscErrorCode MatTranspose_MPIAIJ(Mat A,MatReuse reuse,Mat *matout)
1951 {
1952   Mat_MPIAIJ     *a   = (Mat_MPIAIJ*)A->data;
1953   Mat_SeqAIJ     *Aloc=(Mat_SeqAIJ*)a->A->data,*Bloc=(Mat_SeqAIJ*)a->B->data;
1954   PetscErrorCode ierr;
1955   PetscInt       M      = A->rmap->N,N = A->cmap->N,ma,na,mb,nb,*ai,*aj,*bi,*bj,row,*cols,*cols_tmp,i;
1956   PetscInt       cstart = A->cmap->rstart,ncol;
1957   Mat            B;
1958   MatScalar      *array;
1959 
1960   PetscFunctionBegin;
1961   if (reuse == MAT_REUSE_MATRIX && A == *matout && M != N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Square matrix only for in-place");
1962 
1963   ma = A->rmap->n; na = A->cmap->n; mb = a->B->rmap->n; nb = a->B->cmap->n;
1964   ai = Aloc->i; aj = Aloc->j;
1965   bi = Bloc->i; bj = Bloc->j;
1966   if (reuse == MAT_INITIAL_MATRIX || *matout == A) {
1967     PetscInt             *d_nnz,*g_nnz,*o_nnz;
1968     PetscSFNode          *oloc;
1969     PETSC_UNUSED PetscSF sf;
1970 
1971     ierr = PetscMalloc4(na,&d_nnz,na,&o_nnz,nb,&g_nnz,nb,&oloc);CHKERRQ(ierr);
1972     /* compute d_nnz for preallocation */
1973     ierr = PetscMemzero(d_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1974     for (i=0; i<ai[ma]; i++) {
1975       d_nnz[aj[i]]++;
1976       aj[i] += cstart; /* global col index to be used by MatSetValues() */
1977     }
1978     /* compute local off-diagonal contributions */
1979     ierr = PetscMemzero(g_nnz,nb*sizeof(PetscInt));CHKERRQ(ierr);
1980     for (i=0; i<bi[ma]; i++) g_nnz[bj[i]]++;
1981     /* map those to global */
1982     ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1983     ierr = PetscSFSetGraphLayout(sf,A->cmap,nb,NULL,PETSC_USE_POINTER,a->garray);CHKERRQ(ierr);
1984     ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1985     ierr = PetscMemzero(o_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1986     ierr = PetscSFReduceBegin(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
1987     ierr = PetscSFReduceEnd(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
1988     ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1989 
1990     ierr = MatCreate(PetscObjectComm((PetscObject)A),&B);CHKERRQ(ierr);
1991     ierr = MatSetSizes(B,A->cmap->n,A->rmap->n,N,M);CHKERRQ(ierr);
1992     ierr = MatSetBlockSizes(B,PetscAbs(A->cmap->bs),PetscAbs(A->rmap->bs));CHKERRQ(ierr);
1993     ierr = MatSetType(B,((PetscObject)A)->type_name);CHKERRQ(ierr);
1994     ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
1995     ierr = PetscFree4(d_nnz,o_nnz,g_nnz,oloc);CHKERRQ(ierr);
1996   } else {
1997     B    = *matout;
1998     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
1999     for (i=0; i<ai[ma]; i++) aj[i] += cstart; /* global col index to be used by MatSetValues() */
2000   }
2001 
2002   /* copy over the A part */
2003   array = Aloc->a;
2004   row   = A->rmap->rstart;
2005   for (i=0; i<ma; i++) {
2006     ncol = ai[i+1]-ai[i];
2007     ierr = MatSetValues(B,ncol,aj,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
2008     row++;
2009     array += ncol; aj += ncol;
2010   }
2011   aj = Aloc->j;
2012   for (i=0; i<ai[ma]; i++) aj[i] -= cstart; /* resume local col index */
2013 
2014   /* copy over the B part */
2015   ierr  = PetscCalloc1(bi[mb],&cols);CHKERRQ(ierr);
2016   array = Bloc->a;
2017   row   = A->rmap->rstart;
2018   for (i=0; i<bi[mb]; i++) cols[i] = a->garray[bj[i]];
2019   cols_tmp = cols;
2020   for (i=0; i<mb; i++) {
2021     ncol = bi[i+1]-bi[i];
2022     ierr = MatSetValues(B,ncol,cols_tmp,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
2023     row++;
2024     array += ncol; cols_tmp += ncol;
2025   }
2026   ierr = PetscFree(cols);CHKERRQ(ierr);
2027 
2028   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2029   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2030   if (reuse == MAT_INITIAL_MATRIX || *matout != A) {
2031     *matout = B;
2032   } else {
2033     ierr = MatHeaderMerge(A,B);CHKERRQ(ierr);
2034   }
2035   PetscFunctionReturn(0);
2036 }
2037 
2038 #undef __FUNCT__
2039 #define __FUNCT__ "MatDiagonalScale_MPIAIJ"
2040 PetscErrorCode MatDiagonalScale_MPIAIJ(Mat mat,Vec ll,Vec rr)
2041 {
2042   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2043   Mat            a    = aij->A,b = aij->B;
2044   PetscErrorCode ierr;
2045   PetscInt       s1,s2,s3;
2046 
2047   PetscFunctionBegin;
2048   ierr = MatGetLocalSize(mat,&s2,&s3);CHKERRQ(ierr);
2049   if (rr) {
2050     ierr = VecGetLocalSize(rr,&s1);CHKERRQ(ierr);
2051     if (s1!=s3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"right vector non-conforming local size");
2052     /* Overlap communication with computation. */
2053     ierr = VecScatterBegin(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2054   }
2055   if (ll) {
2056     ierr = VecGetLocalSize(ll,&s1);CHKERRQ(ierr);
2057     if (s1!=s2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"left vector non-conforming local size");
2058     ierr = (*b->ops->diagonalscale)(b,ll,0);CHKERRQ(ierr);
2059   }
2060   /* scale  the diagonal block */
2061   ierr = (*a->ops->diagonalscale)(a,ll,rr);CHKERRQ(ierr);
2062 
2063   if (rr) {
2064     /* Do a scatter end and then right scale the off-diagonal block */
2065     ierr = VecScatterEnd(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2066     ierr = (*b->ops->diagonalscale)(b,0,aij->lvec);CHKERRQ(ierr);
2067   }
2068   PetscFunctionReturn(0);
2069 }
2070 
2071 #undef __FUNCT__
2072 #define __FUNCT__ "MatSetUnfactored_MPIAIJ"
2073 PetscErrorCode MatSetUnfactored_MPIAIJ(Mat A)
2074 {
2075   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2076   PetscErrorCode ierr;
2077 
2078   PetscFunctionBegin;
2079   ierr = MatSetUnfactored(a->A);CHKERRQ(ierr);
2080   PetscFunctionReturn(0);
2081 }
2082 
2083 #undef __FUNCT__
2084 #define __FUNCT__ "MatEqual_MPIAIJ"
2085 PetscErrorCode MatEqual_MPIAIJ(Mat A,Mat B,PetscBool  *flag)
2086 {
2087   Mat_MPIAIJ     *matB = (Mat_MPIAIJ*)B->data,*matA = (Mat_MPIAIJ*)A->data;
2088   Mat            a,b,c,d;
2089   PetscBool      flg;
2090   PetscErrorCode ierr;
2091 
2092   PetscFunctionBegin;
2093   a = matA->A; b = matA->B;
2094   c = matB->A; d = matB->B;
2095 
2096   ierr = MatEqual(a,c,&flg);CHKERRQ(ierr);
2097   if (flg) {
2098     ierr = MatEqual(b,d,&flg);CHKERRQ(ierr);
2099   }
2100   ierr = MPI_Allreduce(&flg,flag,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
2101   PetscFunctionReturn(0);
2102 }
2103 
2104 #undef __FUNCT__
2105 #define __FUNCT__ "MatCopy_MPIAIJ"
2106 PetscErrorCode MatCopy_MPIAIJ(Mat A,Mat B,MatStructure str)
2107 {
2108   PetscErrorCode ierr;
2109   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2110   Mat_MPIAIJ     *b = (Mat_MPIAIJ*)B->data;
2111 
2112   PetscFunctionBegin;
2113   /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
2114   if ((str != SAME_NONZERO_PATTERN) || (A->ops->copy != B->ops->copy)) {
2115     /* because of the column compression in the off-processor part of the matrix a->B,
2116        the number of columns in a->B and b->B may be different, hence we cannot call
2117        the MatCopy() directly on the two parts. If need be, we can provide a more
2118        efficient copy than the MatCopy_Basic() by first uncompressing the a->B matrices
2119        then copying the submatrices */
2120     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
2121   } else {
2122     ierr = MatCopy(a->A,b->A,str);CHKERRQ(ierr);
2123     ierr = MatCopy(a->B,b->B,str);CHKERRQ(ierr);
2124   }
2125   PetscFunctionReturn(0);
2126 }
2127 
2128 #undef __FUNCT__
2129 #define __FUNCT__ "MatSetUp_MPIAIJ"
2130 PetscErrorCode MatSetUp_MPIAIJ(Mat A)
2131 {
2132   PetscErrorCode ierr;
2133 
2134   PetscFunctionBegin;
2135   ierr =  MatMPIAIJSetPreallocation(A,PETSC_DEFAULT,0,PETSC_DEFAULT,0);CHKERRQ(ierr);
2136   PetscFunctionReturn(0);
2137 }
2138 
2139 /*
2140    Computes the number of nonzeros per row needed for preallocation when X and Y
2141    have different nonzero structure.
2142 */
2143 #undef __FUNCT__
2144 #define __FUNCT__ "MatAXPYGetPreallocation_MPIX_private"
2145 PetscErrorCode MatAXPYGetPreallocation_MPIX_private(PetscInt m,const PetscInt *xi,const PetscInt *xj,const PetscInt *xltog,const PetscInt *yi,const PetscInt *yj,const PetscInt *yltog,PetscInt *nnz)
2146 {
2147   PetscInt       i,j,k,nzx,nzy;
2148 
2149   PetscFunctionBegin;
2150   /* Set the number of nonzeros in the new matrix */
2151   for (i=0; i<m; i++) {
2152     const PetscInt *xjj = xj+xi[i],*yjj = yj+yi[i];
2153     nzx = xi[i+1] - xi[i];
2154     nzy = yi[i+1] - yi[i];
2155     nnz[i] = 0;
2156     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2157       for (; k<nzy && yltog[yjj[k]]<xltog[xjj[j]]; k++) nnz[i]++; /* Catch up to X */
2158       if (k<nzy && yltog[yjj[k]]==xltog[xjj[j]]) k++;             /* Skip duplicate */
2159       nnz[i]++;
2160     }
2161     for (; k<nzy; k++) nnz[i]++;
2162   }
2163   PetscFunctionReturn(0);
2164 }
2165 
2166 /* This is the same as MatAXPYGetPreallocation_SeqAIJ, except that the local-to-global map is provided */
2167 #undef __FUNCT__
2168 #define __FUNCT__ "MatAXPYGetPreallocation_MPIAIJ"
2169 static PetscErrorCode MatAXPYGetPreallocation_MPIAIJ(Mat Y,const PetscInt *yltog,Mat X,const PetscInt *xltog,PetscInt *nnz)
2170 {
2171   PetscErrorCode ierr;
2172   PetscInt       m = Y->rmap->N;
2173   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data;
2174   Mat_SeqAIJ     *y = (Mat_SeqAIJ*)Y->data;
2175 
2176   PetscFunctionBegin;
2177   ierr = MatAXPYGetPreallocation_MPIX_private(m,x->i,x->j,xltog,y->i,y->j,yltog,nnz);CHKERRQ(ierr);
2178   PetscFunctionReturn(0);
2179 }
2180 
2181 #undef __FUNCT__
2182 #define __FUNCT__ "MatAXPY_MPIAIJ"
2183 PetscErrorCode MatAXPY_MPIAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
2184 {
2185   PetscErrorCode ierr;
2186   Mat_MPIAIJ     *xx = (Mat_MPIAIJ*)X->data,*yy = (Mat_MPIAIJ*)Y->data;
2187   PetscBLASInt   bnz,one=1;
2188   Mat_SeqAIJ     *x,*y;
2189 
2190   PetscFunctionBegin;
2191   if (str == SAME_NONZERO_PATTERN) {
2192     PetscScalar alpha = a;
2193     x    = (Mat_SeqAIJ*)xx->A->data;
2194     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2195     y    = (Mat_SeqAIJ*)yy->A->data;
2196     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2197     x    = (Mat_SeqAIJ*)xx->B->data;
2198     y    = (Mat_SeqAIJ*)yy->B->data;
2199     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2200     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2201     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
2202   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
2203     ierr = MatAXPY_Basic(Y,a,X,str);CHKERRQ(ierr);
2204   } else {
2205     Mat      B;
2206     PetscInt *nnz_d,*nnz_o;
2207     ierr = PetscMalloc1(yy->A->rmap->N,&nnz_d);CHKERRQ(ierr);
2208     ierr = PetscMalloc1(yy->B->rmap->N,&nnz_o);CHKERRQ(ierr);
2209     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
2210     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
2211     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
2212     ierr = MatSetBlockSizesFromMats(B,Y,Y);CHKERRQ(ierr);
2213     ierr = MatSetType(B,MATMPIAIJ);CHKERRQ(ierr);
2214     ierr = MatAXPYGetPreallocation_SeqAIJ(yy->A,xx->A,nnz_d);CHKERRQ(ierr);
2215     ierr = MatAXPYGetPreallocation_MPIAIJ(yy->B,yy->garray,xx->B,xx->garray,nnz_o);CHKERRQ(ierr);
2216     ierr = MatMPIAIJSetPreallocation(B,0,nnz_d,0,nnz_o);CHKERRQ(ierr);
2217     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
2218     ierr = MatHeaderReplace(Y,B);CHKERRQ(ierr);
2219     ierr = PetscFree(nnz_d);CHKERRQ(ierr);
2220     ierr = PetscFree(nnz_o);CHKERRQ(ierr);
2221   }
2222   PetscFunctionReturn(0);
2223 }
2224 
2225 extern PetscErrorCode  MatConjugate_SeqAIJ(Mat);
2226 
2227 #undef __FUNCT__
2228 #define __FUNCT__ "MatConjugate_MPIAIJ"
2229 PetscErrorCode  MatConjugate_MPIAIJ(Mat mat)
2230 {
2231 #if defined(PETSC_USE_COMPLEX)
2232   PetscErrorCode ierr;
2233   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2234 
2235   PetscFunctionBegin;
2236   ierr = MatConjugate_SeqAIJ(aij->A);CHKERRQ(ierr);
2237   ierr = MatConjugate_SeqAIJ(aij->B);CHKERRQ(ierr);
2238 #else
2239   PetscFunctionBegin;
2240 #endif
2241   PetscFunctionReturn(0);
2242 }
2243 
2244 #undef __FUNCT__
2245 #define __FUNCT__ "MatRealPart_MPIAIJ"
2246 PetscErrorCode MatRealPart_MPIAIJ(Mat A)
2247 {
2248   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2249   PetscErrorCode ierr;
2250 
2251   PetscFunctionBegin;
2252   ierr = MatRealPart(a->A);CHKERRQ(ierr);
2253   ierr = MatRealPart(a->B);CHKERRQ(ierr);
2254   PetscFunctionReturn(0);
2255 }
2256 
2257 #undef __FUNCT__
2258 #define __FUNCT__ "MatImaginaryPart_MPIAIJ"
2259 PetscErrorCode MatImaginaryPart_MPIAIJ(Mat A)
2260 {
2261   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2262   PetscErrorCode ierr;
2263 
2264   PetscFunctionBegin;
2265   ierr = MatImaginaryPart(a->A);CHKERRQ(ierr);
2266   ierr = MatImaginaryPart(a->B);CHKERRQ(ierr);
2267   PetscFunctionReturn(0);
2268 }
2269 
2270 #if defined(PETSC_HAVE_PBGL)
2271 
2272 #include <boost/parallel/mpi/bsp_process_group.hpp>
2273 #include <boost/graph/distributed/ilu_default_graph.hpp>
2274 #include <boost/graph/distributed/ilu_0_block.hpp>
2275 #include <boost/graph/distributed/ilu_preconditioner.hpp>
2276 #include <boost/graph/distributed/petsc/interface.hpp>
2277 #include <boost/multi_array.hpp>
2278 #include <boost/parallel/distributed_property_map->hpp>
2279 
2280 #undef __FUNCT__
2281 #define __FUNCT__ "MatILUFactorSymbolic_MPIAIJ"
2282 /*
2283   This uses the parallel ILU factorization of Peter Gottschling <pgottsch@osl.iu.edu>
2284 */
2285 PetscErrorCode MatILUFactorSymbolic_MPIAIJ(Mat fact,Mat A, IS isrow, IS iscol, const MatFactorInfo *info)
2286 {
2287   namespace petsc = boost::distributed::petsc;
2288 
2289   namespace graph_dist = boost::graph::distributed;
2290   using boost::graph::distributed::ilu_default::process_group_type;
2291   using boost::graph::ilu_permuted;
2292 
2293   PetscBool      row_identity, col_identity;
2294   PetscContainer c;
2295   PetscInt       m, n, M, N;
2296   PetscErrorCode ierr;
2297 
2298   PetscFunctionBegin;
2299   if (info->levels != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only levels = 0 supported for parallel ilu");
2300   ierr = ISIdentity(isrow, &row_identity);CHKERRQ(ierr);
2301   ierr = ISIdentity(iscol, &col_identity);CHKERRQ(ierr);
2302   if (!row_identity || !col_identity) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Row and column permutations must be identity for parallel ILU");
2303 
2304   process_group_type pg;
2305   typedef graph_dist::ilu_default::ilu_level_graph_type lgraph_type;
2306   lgraph_type  *lgraph_p   = new lgraph_type(petsc::num_global_vertices(A), pg, petsc::matrix_distribution(A, pg));
2307   lgraph_type& level_graph = *lgraph_p;
2308   graph_dist::ilu_default::graph_type&            graph(level_graph.graph);
2309 
2310   petsc::read_matrix(A, graph, get(boost::edge_weight, graph));
2311   ilu_permuted(level_graph);
2312 
2313   /* put together the new matrix */
2314   ierr = MatCreate(PetscObjectComm((PetscObject)A), fact);CHKERRQ(ierr);
2315   ierr = MatGetLocalSize(A, &m, &n);CHKERRQ(ierr);
2316   ierr = MatGetSize(A, &M, &N);CHKERRQ(ierr);
2317   ierr = MatSetSizes(fact, m, n, M, N);CHKERRQ(ierr);
2318   ierr = MatSetBlockSizesFromMats(fact,A,A);CHKERRQ(ierr);
2319   ierr = MatSetType(fact, ((PetscObject)A)->type_name);CHKERRQ(ierr);
2320   ierr = MatAssemblyBegin(fact, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2321   ierr = MatAssemblyEnd(fact, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2322 
2323   ierr = PetscContainerCreate(PetscObjectComm((PetscObject)A), &c);
2324   ierr = PetscContainerSetPointer(c, lgraph_p);
2325   ierr = PetscObjectCompose((PetscObject) (fact), "graph", (PetscObject) c);
2326   ierr = PetscContainerDestroy(&c);
2327   PetscFunctionReturn(0);
2328 }
2329 
2330 #undef __FUNCT__
2331 #define __FUNCT__ "MatLUFactorNumeric_MPIAIJ"
2332 PetscErrorCode MatLUFactorNumeric_MPIAIJ(Mat B,Mat A, const MatFactorInfo *info)
2333 {
2334   PetscFunctionBegin;
2335   PetscFunctionReturn(0);
2336 }
2337 
2338 #undef __FUNCT__
2339 #define __FUNCT__ "MatSolve_MPIAIJ"
2340 /*
2341   This uses the parallel ILU factorization of Peter Gottschling <pgottsch@osl.iu.edu>
2342 */
2343 PetscErrorCode MatSolve_MPIAIJ(Mat A, Vec b, Vec x)
2344 {
2345   namespace graph_dist = boost::graph::distributed;
2346 
2347   typedef graph_dist::ilu_default::ilu_level_graph_type lgraph_type;
2348   lgraph_type    *lgraph_p;
2349   PetscContainer c;
2350   PetscErrorCode ierr;
2351 
2352   PetscFunctionBegin;
2353   ierr = PetscObjectQuery((PetscObject) A, "graph", (PetscObject*) &c);CHKERRQ(ierr);
2354   ierr = PetscContainerGetPointer(c, (void**) &lgraph_p);CHKERRQ(ierr);
2355   ierr = VecCopy(b, x);CHKERRQ(ierr);
2356 
2357   PetscScalar *array_x;
2358   ierr = VecGetArray(x, &array_x);CHKERRQ(ierr);
2359   PetscInt sx;
2360   ierr = VecGetSize(x, &sx);CHKERRQ(ierr);
2361 
2362   PetscScalar *array_b;
2363   ierr = VecGetArray(b, &array_b);CHKERRQ(ierr);
2364   PetscInt sb;
2365   ierr = VecGetSize(b, &sb);CHKERRQ(ierr);
2366 
2367   lgraph_type& level_graph = *lgraph_p;
2368   graph_dist::ilu_default::graph_type&            graph(level_graph.graph);
2369 
2370   typedef boost::multi_array_ref<PetscScalar, 1> array_ref_type;
2371   array_ref_type                                 ref_b(array_b, boost::extents[num_vertices(graph)]);
2372   array_ref_type                                 ref_x(array_x, boost::extents[num_vertices(graph)]);
2373 
2374   typedef boost::iterator_property_map<array_ref_type::iterator,
2375                                        boost::property_map<graph_dist::ilu_default::graph_type, boost::vertex_index_t>::type>  gvector_type;
2376   gvector_type                                   vector_b(ref_b.begin(), get(boost::vertex_index, graph));
2377   gvector_type                                   vector_x(ref_x.begin(), get(boost::vertex_index, graph));
2378 
2379   ilu_set_solve(*lgraph_p, vector_b, vector_x);
2380   PetscFunctionReturn(0);
2381 }
2382 #endif
2383 
2384 #undef __FUNCT__
2385 #define __FUNCT__ "MatGetRowMaxAbs_MPIAIJ"
2386 PetscErrorCode MatGetRowMaxAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2387 {
2388   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2389   PetscErrorCode ierr;
2390   PetscInt       i,*idxb = 0;
2391   PetscScalar    *va,*vb;
2392   Vec            vtmp;
2393 
2394   PetscFunctionBegin;
2395   ierr = MatGetRowMaxAbs(a->A,v,idx);CHKERRQ(ierr);
2396   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2397   if (idx) {
2398     for (i=0; i<A->rmap->n; i++) {
2399       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2400     }
2401   }
2402 
2403   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2404   if (idx) {
2405     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2406   }
2407   ierr = MatGetRowMaxAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2408   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2409 
2410   for (i=0; i<A->rmap->n; i++) {
2411     if (PetscAbsScalar(va[i]) < PetscAbsScalar(vb[i])) {
2412       va[i] = vb[i];
2413       if (idx) idx[i] = a->garray[idxb[i]];
2414     }
2415   }
2416 
2417   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2418   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2419   ierr = PetscFree(idxb);CHKERRQ(ierr);
2420   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2421   PetscFunctionReturn(0);
2422 }
2423 
2424 #undef __FUNCT__
2425 #define __FUNCT__ "MatGetRowMinAbs_MPIAIJ"
2426 PetscErrorCode MatGetRowMinAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2427 {
2428   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2429   PetscErrorCode ierr;
2430   PetscInt       i,*idxb = 0;
2431   PetscScalar    *va,*vb;
2432   Vec            vtmp;
2433 
2434   PetscFunctionBegin;
2435   ierr = MatGetRowMinAbs(a->A,v,idx);CHKERRQ(ierr);
2436   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2437   if (idx) {
2438     for (i=0; i<A->cmap->n; i++) {
2439       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2440     }
2441   }
2442 
2443   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2444   if (idx) {
2445     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2446   }
2447   ierr = MatGetRowMinAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2448   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2449 
2450   for (i=0; i<A->rmap->n; i++) {
2451     if (PetscAbsScalar(va[i]) > PetscAbsScalar(vb[i])) {
2452       va[i] = vb[i];
2453       if (idx) idx[i] = a->garray[idxb[i]];
2454     }
2455   }
2456 
2457   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2458   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2459   ierr = PetscFree(idxb);CHKERRQ(ierr);
2460   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2461   PetscFunctionReturn(0);
2462 }
2463 
2464 #undef __FUNCT__
2465 #define __FUNCT__ "MatGetRowMin_MPIAIJ"
2466 PetscErrorCode MatGetRowMin_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2467 {
2468   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2469   PetscInt       n      = A->rmap->n;
2470   PetscInt       cstart = A->cmap->rstart;
2471   PetscInt       *cmap  = mat->garray;
2472   PetscInt       *diagIdx, *offdiagIdx;
2473   Vec            diagV, offdiagV;
2474   PetscScalar    *a, *diagA, *offdiagA;
2475   PetscInt       r;
2476   PetscErrorCode ierr;
2477 
2478   PetscFunctionBegin;
2479   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2480   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &diagV);CHKERRQ(ierr);
2481   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &offdiagV);CHKERRQ(ierr);
2482   ierr = MatGetRowMin(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2483   ierr = MatGetRowMin(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2484   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2485   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2486   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2487   for (r = 0; r < n; ++r) {
2488     if (PetscAbsScalar(diagA[r]) <= PetscAbsScalar(offdiagA[r])) {
2489       a[r]   = diagA[r];
2490       idx[r] = cstart + diagIdx[r];
2491     } else {
2492       a[r]   = offdiagA[r];
2493       idx[r] = cmap[offdiagIdx[r]];
2494     }
2495   }
2496   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2497   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2498   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2499   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2500   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2501   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2502   PetscFunctionReturn(0);
2503 }
2504 
2505 #undef __FUNCT__
2506 #define __FUNCT__ "MatGetRowMax_MPIAIJ"
2507 PetscErrorCode MatGetRowMax_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2508 {
2509   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2510   PetscInt       n      = A->rmap->n;
2511   PetscInt       cstart = A->cmap->rstart;
2512   PetscInt       *cmap  = mat->garray;
2513   PetscInt       *diagIdx, *offdiagIdx;
2514   Vec            diagV, offdiagV;
2515   PetscScalar    *a, *diagA, *offdiagA;
2516   PetscInt       r;
2517   PetscErrorCode ierr;
2518 
2519   PetscFunctionBegin;
2520   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2521   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &diagV);CHKERRQ(ierr);
2522   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &offdiagV);CHKERRQ(ierr);
2523   ierr = MatGetRowMax(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2524   ierr = MatGetRowMax(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2525   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2526   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2527   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2528   for (r = 0; r < n; ++r) {
2529     if (PetscAbsScalar(diagA[r]) >= PetscAbsScalar(offdiagA[r])) {
2530       a[r]   = diagA[r];
2531       idx[r] = cstart + diagIdx[r];
2532     } else {
2533       a[r]   = offdiagA[r];
2534       idx[r] = cmap[offdiagIdx[r]];
2535     }
2536   }
2537   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2538   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2539   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2540   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2541   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2542   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2543   PetscFunctionReturn(0);
2544 }
2545 
2546 #undef __FUNCT__
2547 #define __FUNCT__ "MatGetSeqNonzeroStructure_MPIAIJ"
2548 PetscErrorCode MatGetSeqNonzeroStructure_MPIAIJ(Mat mat,Mat *newmat)
2549 {
2550   PetscErrorCode ierr;
2551   Mat            *dummy;
2552 
2553   PetscFunctionBegin;
2554   ierr    = MatGetSubMatrix_MPIAIJ_All(mat,MAT_DO_NOT_GET_VALUES,MAT_INITIAL_MATRIX,&dummy);CHKERRQ(ierr);
2555   *newmat = *dummy;
2556   ierr    = PetscFree(dummy);CHKERRQ(ierr);
2557   PetscFunctionReturn(0);
2558 }
2559 
2560 #undef __FUNCT__
2561 #define __FUNCT__ "MatInvertBlockDiagonal_MPIAIJ"
2562 PetscErrorCode  MatInvertBlockDiagonal_MPIAIJ(Mat A,const PetscScalar **values)
2563 {
2564   Mat_MPIAIJ     *a = (Mat_MPIAIJ*) A->data;
2565   PetscErrorCode ierr;
2566 
2567   PetscFunctionBegin;
2568   ierr = MatInvertBlockDiagonal(a->A,values);CHKERRQ(ierr);
2569   PetscFunctionReturn(0);
2570 }
2571 
2572 #undef __FUNCT__
2573 #define __FUNCT__ "MatSetRandom_MPIAIJ"
2574 static PetscErrorCode  MatSetRandom_MPIAIJ(Mat x,PetscRandom rctx)
2575 {
2576   PetscErrorCode ierr;
2577   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)x->data;
2578 
2579   PetscFunctionBegin;
2580   ierr = MatSetRandom(aij->A,rctx);CHKERRQ(ierr);
2581   ierr = MatSetRandom(aij->B,rctx);CHKERRQ(ierr);
2582   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2583   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2584   PetscFunctionReturn(0);
2585 }
2586 
2587 #undef __FUNCT__
2588 #define __FUNCT__ "MatShift_MPIAIJ"
2589 PetscErrorCode MatShift_MPIAIJ(Mat Y,PetscScalar a)
2590 {
2591   PetscErrorCode ierr;
2592   Mat_MPIAIJ     *maij = (Mat_MPIAIJ*)Y->data;
2593   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)maij->A->data,*bij = (Mat_SeqAIJ*)maij->B->data;
2594 
2595   PetscFunctionBegin;
2596   if (!aij->nz && !bij->nz) {
2597     ierr = MatMPIAIJSetPreallocation(Y,1,NULL,0,NULL);CHKERRQ(ierr);
2598   }
2599   ierr = MatShift_Basic(Y,a);CHKERRQ(ierr);
2600   PetscFunctionReturn(0);
2601 }
2602 
2603 /* -------------------------------------------------------------------*/
2604 static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
2605                                        MatGetRow_MPIAIJ,
2606                                        MatRestoreRow_MPIAIJ,
2607                                        MatMult_MPIAIJ,
2608                                 /* 4*/ MatMultAdd_MPIAIJ,
2609                                        MatMultTranspose_MPIAIJ,
2610                                        MatMultTransposeAdd_MPIAIJ,
2611 #if defined(PETSC_HAVE_PBGL)
2612                                        MatSolve_MPIAIJ,
2613 #else
2614                                        0,
2615 #endif
2616                                        0,
2617                                        0,
2618                                 /*10*/ 0,
2619                                        0,
2620                                        0,
2621                                        MatSOR_MPIAIJ,
2622                                        MatTranspose_MPIAIJ,
2623                                 /*15*/ MatGetInfo_MPIAIJ,
2624                                        MatEqual_MPIAIJ,
2625                                        MatGetDiagonal_MPIAIJ,
2626                                        MatDiagonalScale_MPIAIJ,
2627                                        MatNorm_MPIAIJ,
2628                                 /*20*/ MatAssemblyBegin_MPIAIJ,
2629                                        MatAssemblyEnd_MPIAIJ,
2630                                        MatSetOption_MPIAIJ,
2631                                        MatZeroEntries_MPIAIJ,
2632                                 /*24*/ MatZeroRows_MPIAIJ,
2633                                        0,
2634 #if defined(PETSC_HAVE_PBGL)
2635                                        0,
2636 #else
2637                                        0,
2638 #endif
2639                                        0,
2640                                        0,
2641                                 /*29*/ MatSetUp_MPIAIJ,
2642 #if defined(PETSC_HAVE_PBGL)
2643                                        0,
2644 #else
2645                                        0,
2646 #endif
2647                                        0,
2648                                        0,
2649                                        0,
2650                                 /*34*/ MatDuplicate_MPIAIJ,
2651                                        0,
2652                                        0,
2653                                        0,
2654                                        0,
2655                                 /*39*/ MatAXPY_MPIAIJ,
2656                                        MatGetSubMatrices_MPIAIJ,
2657                                        MatIncreaseOverlap_MPIAIJ,
2658                                        MatGetValues_MPIAIJ,
2659                                        MatCopy_MPIAIJ,
2660                                 /*44*/ MatGetRowMax_MPIAIJ,
2661                                        MatScale_MPIAIJ,
2662                                        MatShift_MPIAIJ,
2663                                        MatDiagonalSet_MPIAIJ,
2664                                        MatZeroRowsColumns_MPIAIJ,
2665                                 /*49*/ MatSetRandom_MPIAIJ,
2666                                        0,
2667                                        0,
2668                                        0,
2669                                        0,
2670                                 /*54*/ MatFDColoringCreate_MPIXAIJ,
2671                                        0,
2672                                        MatSetUnfactored_MPIAIJ,
2673                                        MatPermute_MPIAIJ,
2674                                        0,
2675                                 /*59*/ MatGetSubMatrix_MPIAIJ,
2676                                        MatDestroy_MPIAIJ,
2677                                        MatView_MPIAIJ,
2678                                        0,
2679                                        MatMatMatMult_MPIAIJ_MPIAIJ_MPIAIJ,
2680                                 /*64*/ MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ,
2681                                        MatMatMatMultNumeric_MPIAIJ_MPIAIJ_MPIAIJ,
2682                                        0,
2683                                        0,
2684                                        0,
2685                                 /*69*/ MatGetRowMaxAbs_MPIAIJ,
2686                                        MatGetRowMinAbs_MPIAIJ,
2687                                        0,
2688                                        MatSetColoring_MPIAIJ,
2689                                        0,
2690                                        MatSetValuesAdifor_MPIAIJ,
2691                                 /*75*/ MatFDColoringApply_AIJ,
2692                                        0,
2693                                        0,
2694                                        0,
2695                                        MatFindZeroDiagonals_MPIAIJ,
2696                                 /*80*/ 0,
2697                                        0,
2698                                        0,
2699                                 /*83*/ MatLoad_MPIAIJ,
2700                                        0,
2701                                        0,
2702                                        0,
2703                                        0,
2704                                        0,
2705                                 /*89*/ MatMatMult_MPIAIJ_MPIAIJ,
2706                                        MatMatMultSymbolic_MPIAIJ_MPIAIJ,
2707                                        MatMatMultNumeric_MPIAIJ_MPIAIJ,
2708                                        MatPtAP_MPIAIJ_MPIAIJ,
2709                                        MatPtAPSymbolic_MPIAIJ_MPIAIJ,
2710                                 /*94*/ MatPtAPNumeric_MPIAIJ_MPIAIJ,
2711                                        0,
2712                                        0,
2713                                        0,
2714                                        0,
2715                                 /*99*/ 0,
2716                                        0,
2717                                        0,
2718                                        MatConjugate_MPIAIJ,
2719                                        0,
2720                                 /*104*/MatSetValuesRow_MPIAIJ,
2721                                        MatRealPart_MPIAIJ,
2722                                        MatImaginaryPart_MPIAIJ,
2723                                        0,
2724                                        0,
2725                                 /*109*/0,
2726                                        0,
2727                                        MatGetRowMin_MPIAIJ,
2728                                        0,
2729                                        0,
2730                                 /*114*/MatGetSeqNonzeroStructure_MPIAIJ,
2731                                        0,
2732                                        0,
2733                                        0,
2734                                        0,
2735                                 /*119*/0,
2736                                        0,
2737                                        0,
2738                                        0,
2739                                        MatGetMultiProcBlock_MPIAIJ,
2740                                 /*124*/MatFindNonzeroRows_MPIAIJ,
2741                                        MatGetColumnNorms_MPIAIJ,
2742                                        MatInvertBlockDiagonal_MPIAIJ,
2743                                        0,
2744                                        MatGetSubMatricesParallel_MPIAIJ,
2745                                 /*129*/0,
2746                                        MatTransposeMatMult_MPIAIJ_MPIAIJ,
2747                                        MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ,
2748                                        MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ,
2749                                        0,
2750                                 /*134*/0,
2751                                        0,
2752                                        0,
2753                                        0,
2754                                        0,
2755                                 /*139*/0,
2756                                        0,
2757                                        0,
2758                                        MatFDColoringSetUp_MPIXAIJ,
2759                                        MatFindOffBlockDiagonalEntries_MPIAIJ,
2760                                 /*144*/MatCreateMPIMatConcatenateSeqMat_MPIAIJ
2761 };
2762 
2763 /* ----------------------------------------------------------------------------------------*/
2764 
2765 #undef __FUNCT__
2766 #define __FUNCT__ "MatStoreValues_MPIAIJ"
2767 PetscErrorCode  MatStoreValues_MPIAIJ(Mat mat)
2768 {
2769   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2770   PetscErrorCode ierr;
2771 
2772   PetscFunctionBegin;
2773   ierr = MatStoreValues(aij->A);CHKERRQ(ierr);
2774   ierr = MatStoreValues(aij->B);CHKERRQ(ierr);
2775   PetscFunctionReturn(0);
2776 }
2777 
2778 #undef __FUNCT__
2779 #define __FUNCT__ "MatRetrieveValues_MPIAIJ"
2780 PetscErrorCode  MatRetrieveValues_MPIAIJ(Mat mat)
2781 {
2782   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2783   PetscErrorCode ierr;
2784 
2785   PetscFunctionBegin;
2786   ierr = MatRetrieveValues(aij->A);CHKERRQ(ierr);
2787   ierr = MatRetrieveValues(aij->B);CHKERRQ(ierr);
2788   PetscFunctionReturn(0);
2789 }
2790 
2791 #undef __FUNCT__
2792 #define __FUNCT__ "MatMPIAIJSetPreallocation_MPIAIJ"
2793 PetscErrorCode  MatMPIAIJSetPreallocation_MPIAIJ(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
2794 {
2795   Mat_MPIAIJ     *b;
2796   PetscErrorCode ierr;
2797 
2798   PetscFunctionBegin;
2799   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
2800   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
2801   b = (Mat_MPIAIJ*)B->data;
2802 
2803   if (!B->preallocated) {
2804     /* Explicitly create 2 MATSEQAIJ matrices. */
2805     ierr = MatCreate(PETSC_COMM_SELF,&b->A);CHKERRQ(ierr);
2806     ierr = MatSetSizes(b->A,B->rmap->n,B->cmap->n,B->rmap->n,B->cmap->n);CHKERRQ(ierr);
2807     ierr = MatSetBlockSizesFromMats(b->A,B,B);CHKERRQ(ierr);
2808     ierr = MatSetType(b->A,MATSEQAIJ);CHKERRQ(ierr);
2809     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->A);CHKERRQ(ierr);
2810     ierr = MatCreate(PETSC_COMM_SELF,&b->B);CHKERRQ(ierr);
2811     ierr = MatSetSizes(b->B,B->rmap->n,B->cmap->N,B->rmap->n,B->cmap->N);CHKERRQ(ierr);
2812     ierr = MatSetBlockSizesFromMats(b->B,B,B);CHKERRQ(ierr);
2813     ierr = MatSetType(b->B,MATSEQAIJ);CHKERRQ(ierr);
2814     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->B);CHKERRQ(ierr);
2815   }
2816 
2817   ierr = MatSeqAIJSetPreallocation(b->A,d_nz,d_nnz);CHKERRQ(ierr);
2818   ierr = MatSeqAIJSetPreallocation(b->B,o_nz,o_nnz);CHKERRQ(ierr);
2819   B->preallocated = PETSC_TRUE;
2820   PetscFunctionReturn(0);
2821 }
2822 
2823 #undef __FUNCT__
2824 #define __FUNCT__ "MatDuplicate_MPIAIJ"
2825 PetscErrorCode MatDuplicate_MPIAIJ(Mat matin,MatDuplicateOption cpvalues,Mat *newmat)
2826 {
2827   Mat            mat;
2828   Mat_MPIAIJ     *a,*oldmat = (Mat_MPIAIJ*)matin->data;
2829   PetscErrorCode ierr;
2830 
2831   PetscFunctionBegin;
2832   *newmat = 0;
2833   ierr    = MatCreate(PetscObjectComm((PetscObject)matin),&mat);CHKERRQ(ierr);
2834   ierr    = MatSetSizes(mat,matin->rmap->n,matin->cmap->n,matin->rmap->N,matin->cmap->N);CHKERRQ(ierr);
2835   ierr    = MatSetBlockSizesFromMats(mat,matin,matin);CHKERRQ(ierr);
2836   ierr    = MatSetType(mat,((PetscObject)matin)->type_name);CHKERRQ(ierr);
2837   ierr    = PetscMemcpy(mat->ops,matin->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
2838   a       = (Mat_MPIAIJ*)mat->data;
2839 
2840   mat->factortype   = matin->factortype;
2841   mat->assembled    = PETSC_TRUE;
2842   mat->insertmode   = NOT_SET_VALUES;
2843   mat->preallocated = PETSC_TRUE;
2844 
2845   a->size         = oldmat->size;
2846   a->rank         = oldmat->rank;
2847   a->donotstash   = oldmat->donotstash;
2848   a->roworiented  = oldmat->roworiented;
2849   a->rowindices   = 0;
2850   a->rowvalues    = 0;
2851   a->getrowactive = PETSC_FALSE;
2852 
2853   ierr = PetscLayoutReference(matin->rmap,&mat->rmap);CHKERRQ(ierr);
2854   ierr = PetscLayoutReference(matin->cmap,&mat->cmap);CHKERRQ(ierr);
2855 
2856   if (oldmat->colmap) {
2857 #if defined(PETSC_USE_CTABLE)
2858     ierr = PetscTableCreateCopy(oldmat->colmap,&a->colmap);CHKERRQ(ierr);
2859 #else
2860     ierr = PetscMalloc1(mat->cmap->N,&a->colmap);CHKERRQ(ierr);
2861     ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2862     ierr = PetscMemcpy(a->colmap,oldmat->colmap,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2863 #endif
2864   } else a->colmap = 0;
2865   if (oldmat->garray) {
2866     PetscInt len;
2867     len  = oldmat->B->cmap->n;
2868     ierr = PetscMalloc1(len+1,&a->garray);CHKERRQ(ierr);
2869     ierr = PetscLogObjectMemory((PetscObject)mat,len*sizeof(PetscInt));CHKERRQ(ierr);
2870     if (len) { ierr = PetscMemcpy(a->garray,oldmat->garray,len*sizeof(PetscInt));CHKERRQ(ierr); }
2871   } else a->garray = 0;
2872 
2873   ierr    = VecDuplicate(oldmat->lvec,&a->lvec);CHKERRQ(ierr);
2874   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->lvec);CHKERRQ(ierr);
2875   ierr    = VecScatterCopy(oldmat->Mvctx,&a->Mvctx);CHKERRQ(ierr);
2876   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->Mvctx);CHKERRQ(ierr);
2877   ierr    = MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
2878   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->A);CHKERRQ(ierr);
2879   ierr    = MatDuplicate(oldmat->B,cpvalues,&a->B);CHKERRQ(ierr);
2880   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->B);CHKERRQ(ierr);
2881   ierr    = PetscFunctionListDuplicate(((PetscObject)matin)->qlist,&((PetscObject)mat)->qlist);CHKERRQ(ierr);
2882   *newmat = mat;
2883   PetscFunctionReturn(0);
2884 }
2885 
2886 
2887 
2888 #undef __FUNCT__
2889 #define __FUNCT__ "MatLoad_MPIAIJ"
2890 PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
2891 {
2892   PetscScalar    *vals,*svals;
2893   MPI_Comm       comm;
2894   PetscErrorCode ierr;
2895   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
2896   PetscInt       i,nz,j,rstart,rend,mmax,maxnz = 0;
2897   PetscInt       header[4],*rowlengths = 0,M,N,m,*cols;
2898   PetscInt       *ourlens = NULL,*procsnz = NULL,*offlens = NULL,jj,*mycols,*smycols;
2899   PetscInt       cend,cstart,n,*rowners;
2900   int            fd;
2901   PetscInt       bs = newMat->rmap->bs;
2902 
2903   PetscFunctionBegin;
2904   /* force binary viewer to load .info file if it has not yet done so */
2905   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
2906   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
2907   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2908   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2909   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
2910   if (!rank) {
2911     ierr = PetscBinaryRead(fd,(char*)header,4,PETSC_INT);CHKERRQ(ierr);
2912     if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
2913   }
2914 
2915   ierr = PetscOptionsBegin(comm,NULL,"Options for loading MPIAIJ matrix","Mat");CHKERRQ(ierr);
2916   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
2917   ierr = PetscOptionsEnd();CHKERRQ(ierr);
2918   if (bs < 0) bs = 1;
2919 
2920   ierr = MPI_Bcast(header+1,3,MPIU_INT,0,comm);CHKERRQ(ierr);
2921   M    = header[1]; N = header[2];
2922 
2923   /* If global sizes are set, check if they are consistent with that given in the file */
2924   if (newMat->rmap->N >= 0 && newMat->rmap->N != M) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Inconsistent # of rows:Matrix in file has (%D) and input matrix has (%D)",newMat->rmap->N,M);
2925   if (newMat->cmap->N >=0 && newMat->cmap->N != N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Inconsistent # of cols:Matrix in file has (%D) and input matrix has (%D)",newMat->cmap->N,N);
2926 
2927   /* determine ownership of all (block) rows */
2928   if (M%bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Inconsistent # of rows (%d) and block size (%d)",M,bs);
2929   if (newMat->rmap->n < 0) m = bs*((M/bs)/size + (((M/bs) % size) > rank));    /* PETSC_DECIDE */
2930   else m = newMat->rmap->n; /* Set by user */
2931 
2932   ierr = PetscMalloc1(size+1,&rowners);CHKERRQ(ierr);
2933   ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
2934 
2935   /* First process needs enough room for process with most rows */
2936   if (!rank) {
2937     mmax = rowners[1];
2938     for (i=2; i<=size; i++) {
2939       mmax = PetscMax(mmax, rowners[i]);
2940     }
2941   } else mmax = -1;             /* unused, but compilers complain */
2942 
2943   rowners[0] = 0;
2944   for (i=2; i<=size; i++) {
2945     rowners[i] += rowners[i-1];
2946   }
2947   rstart = rowners[rank];
2948   rend   = rowners[rank+1];
2949 
2950   /* distribute row lengths to all processors */
2951   ierr = PetscMalloc2(m,&ourlens,m,&offlens);CHKERRQ(ierr);
2952   if (!rank) {
2953     ierr = PetscBinaryRead(fd,ourlens,m,PETSC_INT);CHKERRQ(ierr);
2954     ierr = PetscMalloc1(mmax,&rowlengths);CHKERRQ(ierr);
2955     ierr = PetscCalloc1(size,&procsnz);CHKERRQ(ierr);
2956     for (j=0; j<m; j++) {
2957       procsnz[0] += ourlens[j];
2958     }
2959     for (i=1; i<size; i++) {
2960       ierr = PetscBinaryRead(fd,rowlengths,rowners[i+1]-rowners[i],PETSC_INT);CHKERRQ(ierr);
2961       /* calculate the number of nonzeros on each processor */
2962       for (j=0; j<rowners[i+1]-rowners[i]; j++) {
2963         procsnz[i] += rowlengths[j];
2964       }
2965       ierr = MPIULong_Send(rowlengths,rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2966     }
2967     ierr = PetscFree(rowlengths);CHKERRQ(ierr);
2968   } else {
2969     ierr = MPIULong_Recv(ourlens,m,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2970   }
2971 
2972   if (!rank) {
2973     /* determine max buffer needed and allocate it */
2974     maxnz = 0;
2975     for (i=0; i<size; i++) {
2976       maxnz = PetscMax(maxnz,procsnz[i]);
2977     }
2978     ierr = PetscMalloc1(maxnz,&cols);CHKERRQ(ierr);
2979 
2980     /* read in my part of the matrix column indices  */
2981     nz   = procsnz[0];
2982     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2983     ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);
2984 
2985     /* read in every one elses and ship off */
2986     for (i=1; i<size; i++) {
2987       nz   = procsnz[i];
2988       ierr = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
2989       ierr = MPIULong_Send(cols,nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2990     }
2991     ierr = PetscFree(cols);CHKERRQ(ierr);
2992   } else {
2993     /* determine buffer space needed for message */
2994     nz = 0;
2995     for (i=0; i<m; i++) {
2996       nz += ourlens[i];
2997     }
2998     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2999 
3000     /* receive message of column indices*/
3001     ierr = MPIULong_Recv(mycols,nz,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
3002   }
3003 
3004   /* determine column ownership if matrix is not square */
3005   if (N != M) {
3006     if (newMat->cmap->n < 0) n = N/size + ((N % size) > rank);
3007     else n = newMat->cmap->n;
3008     ierr   = MPI_Scan(&n,&cend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3009     cstart = cend - n;
3010   } else {
3011     cstart = rstart;
3012     cend   = rend;
3013     n      = cend - cstart;
3014   }
3015 
3016   /* loop over local rows, determining number of off diagonal entries */
3017   ierr = PetscMemzero(offlens,m*sizeof(PetscInt));CHKERRQ(ierr);
3018   jj   = 0;
3019   for (i=0; i<m; i++) {
3020     for (j=0; j<ourlens[i]; j++) {
3021       if (mycols[jj] < cstart || mycols[jj] >= cend) offlens[i]++;
3022       jj++;
3023     }
3024   }
3025 
3026   for (i=0; i<m; i++) {
3027     ourlens[i] -= offlens[i];
3028   }
3029   ierr = MatSetSizes(newMat,m,n,M,N);CHKERRQ(ierr);
3030 
3031   if (bs > 1) {ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);}
3032 
3033   ierr = MatMPIAIJSetPreallocation(newMat,0,ourlens,0,offlens);CHKERRQ(ierr);
3034 
3035   for (i=0; i<m; i++) {
3036     ourlens[i] += offlens[i];
3037   }
3038 
3039   if (!rank) {
3040     ierr = PetscMalloc1(maxnz+1,&vals);CHKERRQ(ierr);
3041 
3042     /* read in my part of the matrix numerical values  */
3043     nz   = procsnz[0];
3044     ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
3045 
3046     /* insert into matrix */
3047     jj      = rstart;
3048     smycols = mycols;
3049     svals   = vals;
3050     for (i=0; i<m; i++) {
3051       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
3052       smycols += ourlens[i];
3053       svals   += ourlens[i];
3054       jj++;
3055     }
3056 
3057     /* read in other processors and ship out */
3058     for (i=1; i<size; i++) {
3059       nz   = procsnz[i];
3060       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
3061       ierr = MPIULong_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
3062     }
3063     ierr = PetscFree(procsnz);CHKERRQ(ierr);
3064   } else {
3065     /* receive numeric values */
3066     ierr = PetscMalloc1(nz+1,&vals);CHKERRQ(ierr);
3067 
3068     /* receive message of values*/
3069     ierr = MPIULong_Recv(vals,nz,MPIU_SCALAR,0,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
3070 
3071     /* insert into matrix */
3072     jj      = rstart;
3073     smycols = mycols;
3074     svals   = vals;
3075     for (i=0; i<m; i++) {
3076       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
3077       smycols += ourlens[i];
3078       svals   += ourlens[i];
3079       jj++;
3080     }
3081   }
3082   ierr = PetscFree2(ourlens,offlens);CHKERRQ(ierr);
3083   ierr = PetscFree(vals);CHKERRQ(ierr);
3084   ierr = PetscFree(mycols);CHKERRQ(ierr);
3085   ierr = PetscFree(rowners);CHKERRQ(ierr);
3086   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3087   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3088   PetscFunctionReturn(0);
3089 }
3090 
3091 #undef __FUNCT__
3092 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ"
3093 PetscErrorCode MatGetSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3094 {
3095   PetscErrorCode ierr;
3096   IS             iscol_local;
3097   PetscInt       csize;
3098 
3099   PetscFunctionBegin;
3100   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3101   if (call == MAT_REUSE_MATRIX) {
3102     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3103     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3104   } else {
3105     PetscInt cbs;
3106     ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
3107     ierr = ISAllGather(iscol,&iscol_local);CHKERRQ(ierr);
3108     ierr = ISSetBlockSize(iscol_local,cbs);CHKERRQ(ierr);
3109   }
3110   ierr = MatGetSubMatrix_MPIAIJ_Private(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
3111   if (call == MAT_INITIAL_MATRIX) {
3112     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3113     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3114   }
3115   PetscFunctionReturn(0);
3116 }
3117 
3118 extern PetscErrorCode MatGetSubMatrices_MPIAIJ_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool*,Mat*);
3119 #undef __FUNCT__
3120 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ_Private"
3121 /*
3122     Not great since it makes two copies of the submatrix, first an SeqAIJ
3123   in local and then by concatenating the local matrices the end result.
3124   Writing it directly would be much like MatGetSubMatrices_MPIAIJ()
3125 
3126   Note: This requires a sequential iscol with all indices.
3127 */
3128 PetscErrorCode MatGetSubMatrix_MPIAIJ_Private(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3129 {
3130   PetscErrorCode ierr;
3131   PetscMPIInt    rank,size;
3132   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3133   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal,ncol;
3134   PetscBool      allcolumns, colflag;
3135   Mat            M,Mreuse;
3136   MatScalar      *vwork,*aa;
3137   MPI_Comm       comm;
3138   Mat_SeqAIJ     *aij;
3139 
3140   PetscFunctionBegin;
3141   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3142   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3143   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3144 
3145   ierr = ISIdentity(iscol,&colflag);CHKERRQ(ierr);
3146   ierr = ISGetLocalSize(iscol,&ncol);CHKERRQ(ierr);
3147   if (colflag && ncol == mat->cmap->N) {
3148     allcolumns = PETSC_TRUE;
3149   } else {
3150     allcolumns = PETSC_FALSE;
3151   }
3152   if (call ==  MAT_REUSE_MATRIX) {
3153     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3154     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3155     ierr = MatGetSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,&allcolumns,&Mreuse);CHKERRQ(ierr);
3156   } else {
3157     ierr = MatGetSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&allcolumns,&Mreuse);CHKERRQ(ierr);
3158   }
3159 
3160   /*
3161       m - number of local rows
3162       n - number of columns (same on all processors)
3163       rstart - first row in new global matrix generated
3164   */
3165   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3166   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3167   if (call == MAT_INITIAL_MATRIX) {
3168     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3169     ii  = aij->i;
3170     jj  = aij->j;
3171 
3172     /*
3173         Determine the number of non-zeros in the diagonal and off-diagonal
3174         portions of the matrix in order to do correct preallocation
3175     */
3176 
3177     /* first get start and end of "diagonal" columns */
3178     if (csize == PETSC_DECIDE) {
3179       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3180       if (mglobal == n) { /* square matrix */
3181         nlocal = m;
3182       } else {
3183         nlocal = n/size + ((n % size) > rank);
3184       }
3185     } else {
3186       nlocal = csize;
3187     }
3188     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3189     rstart = rend - nlocal;
3190     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);
3191 
3192     /* next, compute all the lengths */
3193     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3194     olens = dlens + m;
3195     for (i=0; i<m; i++) {
3196       jend = ii[i+1] - ii[i];
3197       olen = 0;
3198       dlen = 0;
3199       for (j=0; j<jend; j++) {
3200         if (*jj < rstart || *jj >= rend) olen++;
3201         else dlen++;
3202         jj++;
3203       }
3204       olens[i] = olen;
3205       dlens[i] = dlen;
3206     }
3207     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3208     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3209     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3210     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3211     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3212     ierr = PetscFree(dlens);CHKERRQ(ierr);
3213   } else {
3214     PetscInt ml,nl;
3215 
3216     M    = *newmat;
3217     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3218     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3219     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3220     /*
3221          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3222        rather than the slower MatSetValues().
3223     */
3224     M->was_assembled = PETSC_TRUE;
3225     M->assembled     = PETSC_FALSE;
3226   }
3227   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3228   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3229   ii   = aij->i;
3230   jj   = aij->j;
3231   aa   = aij->a;
3232   for (i=0; i<m; i++) {
3233     row   = rstart + i;
3234     nz    = ii[i+1] - ii[i];
3235     cwork = jj;     jj += nz;
3236     vwork = aa;     aa += nz;
3237     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3238   }
3239 
3240   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3241   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3242   *newmat = M;
3243 
3244   /* save submatrix used in processor for next request */
3245   if (call ==  MAT_INITIAL_MATRIX) {
3246     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3247     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3248   }
3249   PetscFunctionReturn(0);
3250 }
3251 
3252 #undef __FUNCT__
3253 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR_MPIAIJ"
3254 PetscErrorCode  MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3255 {
3256   PetscInt       m,cstart, cend,j,nnz,i,d;
3257   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3258   const PetscInt *JJ;
3259   PetscScalar    *values;
3260   PetscErrorCode ierr;
3261 
3262   PetscFunctionBegin;
3263   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3264 
3265   ierr   = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3266   ierr   = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3267   m      = B->rmap->n;
3268   cstart = B->cmap->rstart;
3269   cend   = B->cmap->rend;
3270   rstart = B->rmap->rstart;
3271 
3272   ierr = PetscMalloc2(m,&d_nnz,m,&o_nnz);CHKERRQ(ierr);
3273 
3274 #if defined(PETSC_USE_DEBUGGING)
3275   for (i=0; i<m; i++) {
3276     nnz = Ii[i+1]- Ii[i];
3277     JJ  = J + Ii[i];
3278     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3279     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3280     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);
3281   }
3282 #endif
3283 
3284   for (i=0; i<m; i++) {
3285     nnz     = Ii[i+1]- Ii[i];
3286     JJ      = J + Ii[i];
3287     nnz_max = PetscMax(nnz_max,nnz);
3288     d       = 0;
3289     for (j=0; j<nnz; j++) {
3290       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3291     }
3292     d_nnz[i] = d;
3293     o_nnz[i] = nnz - d;
3294   }
3295   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3296   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3297 
3298   if (v) values = (PetscScalar*)v;
3299   else {
3300     ierr = PetscCalloc1(nnz_max+1,&values);CHKERRQ(ierr);
3301   }
3302 
3303   for (i=0; i<m; i++) {
3304     ii   = i + rstart;
3305     nnz  = Ii[i+1]- Ii[i];
3306     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3307   }
3308   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3309   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3310 
3311   if (!v) {
3312     ierr = PetscFree(values);CHKERRQ(ierr);
3313   }
3314   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3315   PetscFunctionReturn(0);
3316 }
3317 
3318 #undef __FUNCT__
3319 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR"
3320 /*@
3321    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3322    (the default parallel PETSc format).
3323 
3324    Collective on MPI_Comm
3325 
3326    Input Parameters:
3327 +  B - the matrix
3328 .  i - the indices into j for the start of each local row (starts with zero)
3329 .  j - the column indices for each local row (starts with zero)
3330 -  v - optional values in the matrix
3331 
3332    Level: developer
3333 
3334    Notes:
3335        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3336      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3337      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3338 
3339        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3340 
3341        The format which is used for the sparse matrix input, is equivalent to a
3342     row-major ordering.. i.e for the following matrix, the input data expected is
3343     as shown:
3344 
3345         1 0 0
3346         2 0 3     P0
3347        -------
3348         4 5 6     P1
3349 
3350      Process0 [P0]: rows_owned=[0,1]
3351         i =  {0,1,3}  [size = nrow+1  = 2+1]
3352         j =  {0,0,2}  [size = nz = 6]
3353         v =  {1,2,3}  [size = nz = 6]
3354 
3355      Process1 [P1]: rows_owned=[2]
3356         i =  {0,3}    [size = nrow+1  = 1+1]
3357         j =  {0,1,2}  [size = nz = 6]
3358         v =  {4,5,6}  [size = nz = 6]
3359 
3360 .keywords: matrix, aij, compressed row, sparse, parallel
3361 
3362 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MPIAIJ,
3363           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3364 @*/
3365 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3366 {
3367   PetscErrorCode ierr;
3368 
3369   PetscFunctionBegin;
3370   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3371   PetscFunctionReturn(0);
3372 }
3373 
3374 #undef __FUNCT__
3375 #define __FUNCT__ "MatMPIAIJSetPreallocation"
3376 /*@C
3377    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3378    (the default parallel PETSc format).  For good matrix assembly performance
3379    the user should preallocate the matrix storage by setting the parameters
3380    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3381    performance can be increased by more than a factor of 50.
3382 
3383    Collective on MPI_Comm
3384 
3385    Input Parameters:
3386 +  B - the matrix
3387 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3388            (same value is used for all local rows)
3389 .  d_nnz - array containing the number of nonzeros in the various rows of the
3390            DIAGONAL portion of the local submatrix (possibly different for each row)
3391            or NULL (PETSC_NULL_INTEGER in Fortran), if d_nz is used to specify the nonzero structure.
3392            The size of this array is equal to the number of local rows, i.e 'm'.
3393            For matrices that will be factored, you must leave room for (and set)
3394            the diagonal entry even if it is zero.
3395 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3396            submatrix (same value is used for all local rows).
3397 -  o_nnz - array containing the number of nonzeros in the various rows of the
3398            OFF-DIAGONAL portion of the local submatrix (possibly different for
3399            each row) or NULL (PETSC_NULL_INTEGER in Fortran), if o_nz is used to specify the nonzero
3400            structure. The size of this array is equal to the number
3401            of local rows, i.e 'm'.
3402 
3403    If the *_nnz parameter is given then the *_nz parameter is ignored
3404 
3405    The AIJ format (also called the Yale sparse matrix format or
3406    compressed row storage (CSR)), is fully compatible with standard Fortran 77
3407    storage.  The stored row and column indices begin with zero.
3408    See Users-Manual: ch_mat for details.
3409 
3410    The parallel matrix is partitioned such that the first m0 rows belong to
3411    process 0, the next m1 rows belong to process 1, the next m2 rows belong
3412    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
3413 
3414    The DIAGONAL portion of the local submatrix of a processor can be defined
3415    as the submatrix which is obtained by extraction the part corresponding to
3416    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
3417    first row that belongs to the processor, r2 is the last row belonging to
3418    the this processor, and c1-c2 is range of indices of the local part of a
3419    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
3420    common case of a square matrix, the row and column ranges are the same and
3421    the DIAGONAL part is also square. The remaining portion of the local
3422    submatrix (mxN) constitute the OFF-DIAGONAL portion.
3423 
3424    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3425 
3426    You can call MatGetInfo() to get information on how effective the preallocation was;
3427    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3428    You can also run with the option -info and look for messages with the string
3429    malloc in them to see if additional memory allocation was needed.
3430 
3431    Example usage:
3432 
3433    Consider the following 8x8 matrix with 34 non-zero values, that is
3434    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3435    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3436    as follows:
3437 
3438 .vb
3439             1  2  0  |  0  3  0  |  0  4
3440     Proc0   0  5  6  |  7  0  0  |  8  0
3441             9  0 10  | 11  0  0  | 12  0
3442     -------------------------------------
3443            13  0 14  | 15 16 17  |  0  0
3444     Proc1   0 18  0  | 19 20 21  |  0  0
3445             0  0  0  | 22 23  0  | 24  0
3446     -------------------------------------
3447     Proc2  25 26 27  |  0  0 28  | 29  0
3448            30  0  0  | 31 32 33  |  0 34
3449 .ve
3450 
3451    This can be represented as a collection of submatrices as:
3452 
3453 .vb
3454       A B C
3455       D E F
3456       G H I
3457 .ve
3458 
3459    Where the submatrices A,B,C are owned by proc0, D,E,F are
3460    owned by proc1, G,H,I are owned by proc2.
3461 
3462    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3463    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3464    The 'M','N' parameters are 8,8, and have the same values on all procs.
3465 
3466    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3467    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3468    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3469    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3470    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3471    matrix, ans [DF] as another SeqAIJ matrix.
3472 
3473    When d_nz, o_nz parameters are specified, d_nz storage elements are
3474    allocated for every row of the local diagonal submatrix, and o_nz
3475    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3476    One way to choose d_nz and o_nz is to use the max nonzerors per local
3477    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3478    In this case, the values of d_nz,o_nz are:
3479 .vb
3480      proc0 : dnz = 2, o_nz = 2
3481      proc1 : dnz = 3, o_nz = 2
3482      proc2 : dnz = 1, o_nz = 4
3483 .ve
3484    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3485    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3486    for proc3. i.e we are using 12+15+10=37 storage locations to store
3487    34 values.
3488 
3489    When d_nnz, o_nnz parameters are specified, the storage is specified
3490    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3491    In the above case the values for d_nnz,o_nnz are:
3492 .vb
3493      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3494      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3495      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3496 .ve
3497    Here the space allocated is sum of all the above values i.e 34, and
3498    hence pre-allocation is perfect.
3499 
3500    Level: intermediate
3501 
3502 .keywords: matrix, aij, compressed row, sparse, parallel
3503 
3504 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
3505           MPIAIJ, MatGetInfo(), PetscSplitOwnership()
3506 @*/
3507 PetscErrorCode  MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3508 {
3509   PetscErrorCode ierr;
3510 
3511   PetscFunctionBegin;
3512   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3513   PetscValidType(B,1);
3514   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
3515   PetscFunctionReturn(0);
3516 }
3517 
3518 #undef __FUNCT__
3519 #define __FUNCT__ "MatCreateMPIAIJWithArrays"
3520 /*@
3521      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
3522          CSR format the local rows.
3523 
3524    Collective on MPI_Comm
3525 
3526    Input Parameters:
3527 +  comm - MPI communicator
3528 .  m - number of local rows (Cannot be PETSC_DECIDE)
3529 .  n - This value should be the same as the local size used in creating the
3530        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3531        calculated if N is given) For square matrices n is almost always m.
3532 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3533 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3534 .   i - row indices
3535 .   j - column indices
3536 -   a - matrix values
3537 
3538    Output Parameter:
3539 .   mat - the matrix
3540 
3541    Level: intermediate
3542 
3543    Notes:
3544        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3545      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3546      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3547 
3548        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3549 
3550        The format which is used for the sparse matrix input, is equivalent to a
3551     row-major ordering.. i.e for the following matrix, the input data expected is
3552     as shown:
3553 
3554         1 0 0
3555         2 0 3     P0
3556        -------
3557         4 5 6     P1
3558 
3559      Process0 [P0]: rows_owned=[0,1]
3560         i =  {0,1,3}  [size = nrow+1  = 2+1]
3561         j =  {0,0,2}  [size = nz = 6]
3562         v =  {1,2,3}  [size = nz = 6]
3563 
3564      Process1 [P1]: rows_owned=[2]
3565         i =  {0,3}    [size = nrow+1  = 1+1]
3566         j =  {0,1,2}  [size = nz = 6]
3567         v =  {4,5,6}  [size = nz = 6]
3568 
3569 .keywords: matrix, aij, compressed row, sparse, parallel
3570 
3571 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3572           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
3573 @*/
3574 PetscErrorCode  MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
3575 {
3576   PetscErrorCode ierr;
3577 
3578   PetscFunctionBegin;
3579   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
3580   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
3581   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
3582   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
3583   /* ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr); */
3584   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
3585   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
3586   PetscFunctionReturn(0);
3587 }
3588 
3589 #undef __FUNCT__
3590 #define __FUNCT__ "MatCreateAIJ"
3591 /*@C
3592    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
3593    (the default parallel PETSc format).  For good matrix assembly performance
3594    the user should preallocate the matrix storage by setting the parameters
3595    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3596    performance can be increased by more than a factor of 50.
3597 
3598    Collective on MPI_Comm
3599 
3600    Input Parameters:
3601 +  comm - MPI communicator
3602 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
3603            This value should be the same as the local size used in creating the
3604            y vector for the matrix-vector product y = Ax.
3605 .  n - This value should be the same as the local size used in creating the
3606        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3607        calculated if N is given) For square matrices n is almost always m.
3608 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3609 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3610 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3611            (same value is used for all local rows)
3612 .  d_nnz - array containing the number of nonzeros in the various rows of the
3613            DIAGONAL portion of the local submatrix (possibly different for each row)
3614            or NULL, if d_nz is used to specify the nonzero structure.
3615            The size of this array is equal to the number of local rows, i.e 'm'.
3616 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3617            submatrix (same value is used for all local rows).
3618 -  o_nnz - array containing the number of nonzeros in the various rows of the
3619            OFF-DIAGONAL portion of the local submatrix (possibly different for
3620            each row) or NULL, if o_nz is used to specify the nonzero
3621            structure. The size of this array is equal to the number
3622            of local rows, i.e 'm'.
3623 
3624    Output Parameter:
3625 .  A - the matrix
3626 
3627    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3628    MatXXXXSetPreallocation() paradgm instead of this routine directly.
3629    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3630 
3631    Notes:
3632    If the *_nnz parameter is given then the *_nz parameter is ignored
3633 
3634    m,n,M,N parameters specify the size of the matrix, and its partitioning across
3635    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
3636    storage requirements for this matrix.
3637 
3638    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
3639    processor than it must be used on all processors that share the object for
3640    that argument.
3641 
3642    The user MUST specify either the local or global matrix dimensions
3643    (possibly both).
3644 
3645    The parallel matrix is partitioned across processors such that the
3646    first m0 rows belong to process 0, the next m1 rows belong to
3647    process 1, the next m2 rows belong to process 2 etc.. where
3648    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
3649    values corresponding to [m x N] submatrix.
3650 
3651    The columns are logically partitioned with the n0 columns belonging
3652    to 0th partition, the next n1 columns belonging to the next
3653    partition etc.. where n0,n1,n2... are the input parameter 'n'.
3654 
3655    The DIAGONAL portion of the local submatrix on any given processor
3656    is the submatrix corresponding to the rows and columns m,n
3657    corresponding to the given processor. i.e diagonal matrix on
3658    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
3659    etc. The remaining portion of the local submatrix [m x (N-n)]
3660    constitute the OFF-DIAGONAL portion. The example below better
3661    illustrates this concept.
3662 
3663    For a square global matrix we define each processor's diagonal portion
3664    to be its local rows and the corresponding columns (a square submatrix);
3665    each processor's off-diagonal portion encompasses the remainder of the
3666    local matrix (a rectangular submatrix).
3667 
3668    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3669 
3670    When calling this routine with a single process communicator, a matrix of
3671    type SEQAIJ is returned.  If a matrix of type MPIAIJ is desired for this
3672    type of communicator, use the construction mechanism:
3673      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
3674 
3675    By default, this format uses inodes (identical nodes) when possible.
3676    We search for consecutive rows with the same nonzero structure, thereby
3677    reusing matrix information to achieve increased efficiency.
3678 
3679    Options Database Keys:
3680 +  -mat_no_inode  - Do not use inodes
3681 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3682 -  -mat_aij_oneindex - Internally use indexing starting at 1
3683         rather than 0.  Note that when calling MatSetValues(),
3684         the user still MUST index entries starting at 0!
3685 
3686 
3687    Example usage:
3688 
3689    Consider the following 8x8 matrix with 34 non-zero values, that is
3690    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3691    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3692    as follows:
3693 
3694 .vb
3695             1  2  0  |  0  3  0  |  0  4
3696     Proc0   0  5  6  |  7  0  0  |  8  0
3697             9  0 10  | 11  0  0  | 12  0
3698     -------------------------------------
3699            13  0 14  | 15 16 17  |  0  0
3700     Proc1   0 18  0  | 19 20 21  |  0  0
3701             0  0  0  | 22 23  0  | 24  0
3702     -------------------------------------
3703     Proc2  25 26 27  |  0  0 28  | 29  0
3704            30  0  0  | 31 32 33  |  0 34
3705 .ve
3706 
3707    This can be represented as a collection of submatrices as:
3708 
3709 .vb
3710       A B C
3711       D E F
3712       G H I
3713 .ve
3714 
3715    Where the submatrices A,B,C are owned by proc0, D,E,F are
3716    owned by proc1, G,H,I are owned by proc2.
3717 
3718    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3719    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3720    The 'M','N' parameters are 8,8, and have the same values on all procs.
3721 
3722    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3723    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3724    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3725    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3726    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3727    matrix, ans [DF] as another SeqAIJ matrix.
3728 
3729    When d_nz, o_nz parameters are specified, d_nz storage elements are
3730    allocated for every row of the local diagonal submatrix, and o_nz
3731    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3732    One way to choose d_nz and o_nz is to use the max nonzerors per local
3733    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3734    In this case, the values of d_nz,o_nz are:
3735 .vb
3736      proc0 : dnz = 2, o_nz = 2
3737      proc1 : dnz = 3, o_nz = 2
3738      proc2 : dnz = 1, o_nz = 4
3739 .ve
3740    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3741    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3742    for proc3. i.e we are using 12+15+10=37 storage locations to store
3743    34 values.
3744 
3745    When d_nnz, o_nnz parameters are specified, the storage is specified
3746    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3747    In the above case the values for d_nnz,o_nnz are:
3748 .vb
3749      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3750      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3751      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3752 .ve
3753    Here the space allocated is sum of all the above values i.e 34, and
3754    hence pre-allocation is perfect.
3755 
3756    Level: intermediate
3757 
3758 .keywords: matrix, aij, compressed row, sparse, parallel
3759 
3760 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3761           MPIAIJ, MatCreateMPIAIJWithArrays()
3762 @*/
3763 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)
3764 {
3765   PetscErrorCode ierr;
3766   PetscMPIInt    size;
3767 
3768   PetscFunctionBegin;
3769   ierr = MatCreate(comm,A);CHKERRQ(ierr);
3770   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
3771   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3772   if (size > 1) {
3773     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
3774     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
3775   } else {
3776     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
3777     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
3778   }
3779   PetscFunctionReturn(0);
3780 }
3781 
3782 #undef __FUNCT__
3783 #define __FUNCT__ "MatMPIAIJGetSeqAIJ"
3784 PetscErrorCode  MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
3785 {
3786   Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
3787 
3788   PetscFunctionBegin;
3789   if (Ad)     *Ad     = a->A;
3790   if (Ao)     *Ao     = a->B;
3791   if (colmap) *colmap = a->garray;
3792   PetscFunctionReturn(0);
3793 }
3794 
3795 #undef __FUNCT__
3796 #define __FUNCT__ "MatSetColoring_MPIAIJ"
3797 PetscErrorCode MatSetColoring_MPIAIJ(Mat A,ISColoring coloring)
3798 {
3799   PetscErrorCode ierr;
3800   PetscInt       i;
3801   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3802 
3803   PetscFunctionBegin;
3804   if (coloring->ctype == IS_COLORING_GLOBAL) {
3805     ISColoringValue *allcolors,*colors;
3806     ISColoring      ocoloring;
3807 
3808     /* set coloring for diagonal portion */
3809     ierr = MatSetColoring_SeqAIJ(a->A,coloring);CHKERRQ(ierr);
3810 
3811     /* set coloring for off-diagonal portion */
3812     ierr = ISAllGatherColors(PetscObjectComm((PetscObject)A),coloring->n,coloring->colors,NULL,&allcolors);CHKERRQ(ierr);
3813     ierr = PetscMalloc1(a->B->cmap->n+1,&colors);CHKERRQ(ierr);
3814     for (i=0; i<a->B->cmap->n; i++) {
3815       colors[i] = allcolors[a->garray[i]];
3816     }
3817     ierr = PetscFree(allcolors);CHKERRQ(ierr);
3818     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3819     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
3820     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3821   } else if (coloring->ctype == IS_COLORING_GHOSTED) {
3822     ISColoringValue *colors;
3823     PetscInt        *larray;
3824     ISColoring      ocoloring;
3825 
3826     /* set coloring for diagonal portion */
3827     ierr = PetscMalloc1(a->A->cmap->n+1,&larray);CHKERRQ(ierr);
3828     for (i=0; i<a->A->cmap->n; i++) {
3829       larray[i] = i + A->cmap->rstart;
3830     }
3831     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->A->cmap->n,larray,NULL,larray);CHKERRQ(ierr);
3832     ierr = PetscMalloc1(a->A->cmap->n+1,&colors);CHKERRQ(ierr);
3833     for (i=0; i<a->A->cmap->n; i++) {
3834       colors[i] = coloring->colors[larray[i]];
3835     }
3836     ierr = PetscFree(larray);CHKERRQ(ierr);
3837     ierr = ISColoringCreate(PETSC_COMM_SELF,coloring->n,a->A->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3838     ierr = MatSetColoring_SeqAIJ(a->A,ocoloring);CHKERRQ(ierr);
3839     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3840 
3841     /* set coloring for off-diagonal portion */
3842     ierr = PetscMalloc1(a->B->cmap->n+1,&larray);CHKERRQ(ierr);
3843     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->B->cmap->n,a->garray,NULL,larray);CHKERRQ(ierr);
3844     ierr = PetscMalloc1(a->B->cmap->n+1,&colors);CHKERRQ(ierr);
3845     for (i=0; i<a->B->cmap->n; i++) {
3846       colors[i] = coloring->colors[larray[i]];
3847     }
3848     ierr = PetscFree(larray);CHKERRQ(ierr);
3849     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3850     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
3851     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3852   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support ISColoringType %d",(int)coloring->ctype);
3853   PetscFunctionReturn(0);
3854 }
3855 
3856 #undef __FUNCT__
3857 #define __FUNCT__ "MatSetValuesAdifor_MPIAIJ"
3858 PetscErrorCode MatSetValuesAdifor_MPIAIJ(Mat A,PetscInt nl,void *advalues)
3859 {
3860   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3861   PetscErrorCode ierr;
3862 
3863   PetscFunctionBegin;
3864   ierr = MatSetValuesAdifor_SeqAIJ(a->A,nl,advalues);CHKERRQ(ierr);
3865   ierr = MatSetValuesAdifor_SeqAIJ(a->B,nl,advalues);CHKERRQ(ierr);
3866   PetscFunctionReturn(0);
3867 }
3868 
3869 #undef __FUNCT__
3870 #define __FUNCT__ "MatCreateMPIMatConcatenateSeqMat_MPIAIJ"
3871 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
3872 {
3873   PetscErrorCode ierr;
3874   PetscInt       m,N,i,rstart,nnz,Ii;
3875   PetscInt       *indx;
3876   PetscScalar    *values;
3877 
3878   PetscFunctionBegin;
3879   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
3880   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
3881     PetscInt       *dnz,*onz,sum,bs,cbs;
3882 
3883     if (n == PETSC_DECIDE) {
3884       ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
3885     }
3886     /* Check sum(n) = N */
3887     ierr = MPI_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3888     if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
3889 
3890     ierr    = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3891     rstart -= m;
3892 
3893     ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
3894     for (i=0; i<m; i++) {
3895       ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3896       ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
3897       ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3898     }
3899 
3900     ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
3901     ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
3902     ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
3903     ierr = MatSetBlockSizes(*outmat,bs,cbs);CHKERRQ(ierr);
3904     ierr = MatSetType(*outmat,MATMPIAIJ);CHKERRQ(ierr);
3905     ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
3906     ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
3907   }
3908 
3909   /* numeric phase */
3910   ierr = MatGetOwnershipRange(*outmat,&rstart,NULL);CHKERRQ(ierr);
3911   for (i=0; i<m; i++) {
3912     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3913     Ii   = i + rstart;
3914     ierr = MatSetValues(*outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3915     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3916   }
3917   ierr = MatAssemblyBegin(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3918   ierr = MatAssemblyEnd(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3919   PetscFunctionReturn(0);
3920 }
3921 
3922 #undef __FUNCT__
3923 #define __FUNCT__ "MatFileSplit"
3924 PetscErrorCode MatFileSplit(Mat A,char *outfile)
3925 {
3926   PetscErrorCode    ierr;
3927   PetscMPIInt       rank;
3928   PetscInt          m,N,i,rstart,nnz;
3929   size_t            len;
3930   const PetscInt    *indx;
3931   PetscViewer       out;
3932   char              *name;
3933   Mat               B;
3934   const PetscScalar *values;
3935 
3936   PetscFunctionBegin;
3937   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
3938   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
3939   /* Should this be the type of the diagonal block of A? */
3940   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
3941   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
3942   ierr = MatSetBlockSizesFromMats(B,A,A);CHKERRQ(ierr);
3943   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
3944   ierr = MatSeqAIJSetPreallocation(B,0,NULL);CHKERRQ(ierr);
3945   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
3946   for (i=0; i<m; i++) {
3947     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3948     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3949     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3950   }
3951   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3952   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3953 
3954   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
3955   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
3956   ierr = PetscMalloc1(len+5,&name);CHKERRQ(ierr);
3957   sprintf(name,"%s.%d",outfile,rank);
3958   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
3959   ierr = PetscFree(name);CHKERRQ(ierr);
3960   ierr = MatView(B,out);CHKERRQ(ierr);
3961   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
3962   ierr = MatDestroy(&B);CHKERRQ(ierr);
3963   PetscFunctionReturn(0);
3964 }
3965 
3966 extern PetscErrorCode MatDestroy_MPIAIJ(Mat);
3967 #undef __FUNCT__
3968 #define __FUNCT__ "MatDestroy_MPIAIJ_SeqsToMPI"
3969 PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
3970 {
3971   PetscErrorCode      ierr;
3972   Mat_Merge_SeqsToMPI *merge;
3973   PetscContainer      container;
3974 
3975   PetscFunctionBegin;
3976   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
3977   if (container) {
3978     ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
3979     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
3980     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
3981     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
3982     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
3983     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
3984     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
3985     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
3986     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
3987     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
3988     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
3989     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
3990     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
3991     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
3992     ierr = PetscFree(merge);CHKERRQ(ierr);
3993     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
3994   }
3995   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
3996   PetscFunctionReturn(0);
3997 }
3998 
3999 #include <../src/mat/utils/freespace.h>
4000 #include <petscbt.h>
4001 
4002 #undef __FUNCT__
4003 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJNumeric"
4004 PetscErrorCode  MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
4005 {
4006   PetscErrorCode      ierr;
4007   MPI_Comm            comm;
4008   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
4009   PetscMPIInt         size,rank,taga,*len_s;
4010   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
4011   PetscInt            proc,m;
4012   PetscInt            **buf_ri,**buf_rj;
4013   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
4014   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
4015   MPI_Request         *s_waits,*r_waits;
4016   MPI_Status          *status;
4017   MatScalar           *aa=a->a;
4018   MatScalar           **abuf_r,*ba_i;
4019   Mat_Merge_SeqsToMPI *merge;
4020   PetscContainer      container;
4021 
4022   PetscFunctionBegin;
4023   ierr = PetscObjectGetComm((PetscObject)mpimat,&comm);CHKERRQ(ierr);
4024   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4025 
4026   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4027   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4028 
4029   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4030   ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4031 
4032   bi     = merge->bi;
4033   bj     = merge->bj;
4034   buf_ri = merge->buf_ri;
4035   buf_rj = merge->buf_rj;
4036 
4037   ierr   = PetscMalloc1(size,&status);CHKERRQ(ierr);
4038   owners = merge->rowmap->range;
4039   len_s  = merge->len_s;
4040 
4041   /* send and recv matrix values */
4042   /*-----------------------------*/
4043   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
4044   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
4045 
4046   ierr = PetscMalloc1(merge->nsend+1,&s_waits);CHKERRQ(ierr);
4047   for (proc=0,k=0; proc<size; proc++) {
4048     if (!len_s[proc]) continue;
4049     i    = owners[proc];
4050     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
4051     k++;
4052   }
4053 
4054   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
4055   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
4056   ierr = PetscFree(status);CHKERRQ(ierr);
4057 
4058   ierr = PetscFree(s_waits);CHKERRQ(ierr);
4059   ierr = PetscFree(r_waits);CHKERRQ(ierr);
4060 
4061   /* insert mat values of mpimat */
4062   /*----------------------------*/
4063   ierr = PetscMalloc1(N,&ba_i);CHKERRQ(ierr);
4064   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4065 
4066   for (k=0; k<merge->nrecv; k++) {
4067     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4068     nrows       = *(buf_ri_k[k]);
4069     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
4070     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4071   }
4072 
4073   /* set values of ba */
4074   m = merge->rowmap->n;
4075   for (i=0; i<m; i++) {
4076     arow = owners[rank] + i;
4077     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
4078     bnzi = bi[i+1] - bi[i];
4079     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
4080 
4081     /* add local non-zero vals of this proc's seqmat into ba */
4082     anzi   = ai[arow+1] - ai[arow];
4083     aj     = a->j + ai[arow];
4084     aa     = a->a + ai[arow];
4085     nextaj = 0;
4086     for (j=0; nextaj<anzi; j++) {
4087       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4088         ba_i[j] += aa[nextaj++];
4089       }
4090     }
4091 
4092     /* add received vals into ba */
4093     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4094       /* i-th row */
4095       if (i == *nextrow[k]) {
4096         anzi   = *(nextai[k]+1) - *nextai[k];
4097         aj     = buf_rj[k] + *(nextai[k]);
4098         aa     = abuf_r[k] + *(nextai[k]);
4099         nextaj = 0;
4100         for (j=0; nextaj<anzi; j++) {
4101           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4102             ba_i[j] += aa[nextaj++];
4103           }
4104         }
4105         nextrow[k]++; nextai[k]++;
4106       }
4107     }
4108     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
4109   }
4110   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4111   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4112 
4113   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
4114   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
4115   ierr = PetscFree(ba_i);CHKERRQ(ierr);
4116   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4117   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4118   PetscFunctionReturn(0);
4119 }
4120 
4121 extern PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat);
4122 
4123 #undef __FUNCT__
4124 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJSymbolic"
4125 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4126 {
4127   PetscErrorCode      ierr;
4128   Mat                 B_mpi;
4129   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
4130   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4131   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
4132   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4133   PetscInt            len,proc,*dnz,*onz,bs,cbs;
4134   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4135   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4136   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
4137   MPI_Status          *status;
4138   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
4139   PetscBT             lnkbt;
4140   Mat_Merge_SeqsToMPI *merge;
4141   PetscContainer      container;
4142 
4143   PetscFunctionBegin;
4144   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4145 
4146   /* make sure it is a PETSc comm */
4147   ierr = PetscCommDuplicate(comm,&comm,NULL);CHKERRQ(ierr);
4148   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4149   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4150 
4151   ierr = PetscNew(&merge);CHKERRQ(ierr);
4152   ierr = PetscMalloc1(size,&status);CHKERRQ(ierr);
4153 
4154   /* determine row ownership */
4155   /*---------------------------------------------------------*/
4156   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
4157   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
4158   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
4159   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
4160   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
4161   ierr = PetscMalloc1(size,&len_si);CHKERRQ(ierr);
4162   ierr = PetscMalloc1(size,&merge->len_s);CHKERRQ(ierr);
4163 
4164   m      = merge->rowmap->n;
4165   owners = merge->rowmap->range;
4166 
4167   /* determine the number of messages to send, their lengths */
4168   /*---------------------------------------------------------*/
4169   len_s = merge->len_s;
4170 
4171   len          = 0; /* length of buf_si[] */
4172   merge->nsend = 0;
4173   for (proc=0; proc<size; proc++) {
4174     len_si[proc] = 0;
4175     if (proc == rank) {
4176       len_s[proc] = 0;
4177     } else {
4178       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4179       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4180     }
4181     if (len_s[proc]) {
4182       merge->nsend++;
4183       nrows = 0;
4184       for (i=owners[proc]; i<owners[proc+1]; i++) {
4185         if (ai[i+1] > ai[i]) nrows++;
4186       }
4187       len_si[proc] = 2*(nrows+1);
4188       len         += len_si[proc];
4189     }
4190   }
4191 
4192   /* determine the number and length of messages to receive for ij-structure */
4193   /*-------------------------------------------------------------------------*/
4194   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
4195   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
4196 
4197   /* post the Irecv of j-structure */
4198   /*-------------------------------*/
4199   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
4200   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
4201 
4202   /* post the Isend of j-structure */
4203   /*--------------------------------*/
4204   ierr = PetscMalloc2(merge->nsend,&si_waits,merge->nsend,&sj_waits);CHKERRQ(ierr);
4205 
4206   for (proc=0, k=0; proc<size; proc++) {
4207     if (!len_s[proc]) continue;
4208     i    = owners[proc];
4209     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
4210     k++;
4211   }
4212 
4213   /* receives and sends of j-structure are complete */
4214   /*------------------------------------------------*/
4215   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
4216   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
4217 
4218   /* send and recv i-structure */
4219   /*---------------------------*/
4220   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
4221   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
4222 
4223   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
4224   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4225   for (proc=0,k=0; proc<size; proc++) {
4226     if (!len_s[proc]) continue;
4227     /* form outgoing message for i-structure:
4228          buf_si[0]:                 nrows to be sent
4229                [1:nrows]:           row index (global)
4230                [nrows+1:2*nrows+1]: i-structure index
4231     */
4232     /*-------------------------------------------*/
4233     nrows       = len_si[proc]/2 - 1;
4234     buf_si_i    = buf_si + nrows+1;
4235     buf_si[0]   = nrows;
4236     buf_si_i[0] = 0;
4237     nrows       = 0;
4238     for (i=owners[proc]; i<owners[proc+1]; i++) {
4239       anzi = ai[i+1] - ai[i];
4240       if (anzi) {
4241         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4242         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4243         nrows++;
4244       }
4245     }
4246     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4247     k++;
4248     buf_si += len_si[proc];
4249   }
4250 
4251   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4252   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4253 
4254   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4255   for (i=0; i<merge->nrecv; i++) {
4256     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);
4257   }
4258 
4259   ierr = PetscFree(len_si);CHKERRQ(ierr);
4260   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4261   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4262   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4263   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4264   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4265   ierr = PetscFree(status);CHKERRQ(ierr);
4266 
4267   /* compute a local seq matrix in each processor */
4268   /*----------------------------------------------*/
4269   /* allocate bi array and free space for accumulating nonzero column info */
4270   ierr  = PetscMalloc1(m+1,&bi);CHKERRQ(ierr);
4271   bi[0] = 0;
4272 
4273   /* create and initialize a linked list */
4274   nlnk = N+1;
4275   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4276 
4277   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4278   len  = ai[owners[rank+1]] - ai[owners[rank]];
4279   ierr = PetscFreeSpaceGet((PetscInt)(2*len+1),&free_space);CHKERRQ(ierr);
4280 
4281   current_space = free_space;
4282 
4283   /* determine symbolic info for each local row */
4284   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4285 
4286   for (k=0; k<merge->nrecv; k++) {
4287     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4288     nrows       = *buf_ri_k[k];
4289     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4290     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4291   }
4292 
4293   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4294   len  = 0;
4295   for (i=0; i<m; i++) {
4296     bnzi = 0;
4297     /* add local non-zero cols of this proc's seqmat into lnk */
4298     arow  = owners[rank] + i;
4299     anzi  = ai[arow+1] - ai[arow];
4300     aj    = a->j + ai[arow];
4301     ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4302     bnzi += nlnk;
4303     /* add received col data into lnk */
4304     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4305       if (i == *nextrow[k]) { /* i-th row */
4306         anzi  = *(nextai[k]+1) - *nextai[k];
4307         aj    = buf_rj[k] + *nextai[k];
4308         ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4309         bnzi += nlnk;
4310         nextrow[k]++; nextai[k]++;
4311       }
4312     }
4313     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4314 
4315     /* if free space is not available, make more free space */
4316     if (current_space->local_remaining<bnzi) {
4317       ierr = PetscFreeSpaceGet(bnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
4318       nspacedouble++;
4319     }
4320     /* copy data into free space, then initialize lnk */
4321     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4322     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
4323 
4324     current_space->array           += bnzi;
4325     current_space->local_used      += bnzi;
4326     current_space->local_remaining -= bnzi;
4327 
4328     bi[i+1] = bi[i] + bnzi;
4329   }
4330 
4331   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4332 
4333   ierr = PetscMalloc1(bi[m]+1,&bj);CHKERRQ(ierr);
4334   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
4335   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4336 
4337   /* create symbolic parallel matrix B_mpi */
4338   /*---------------------------------------*/
4339   ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
4340   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
4341   if (n==PETSC_DECIDE) {
4342     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
4343   } else {
4344     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4345   }
4346   ierr = MatSetBlockSizes(B_mpi,bs,cbs);CHKERRQ(ierr);
4347   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
4348   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
4349   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4350   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
4351 
4352   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4353   B_mpi->assembled    = PETSC_FALSE;
4354   B_mpi->ops->destroy = MatDestroy_MPIAIJ_SeqsToMPI;
4355   merge->bi           = bi;
4356   merge->bj           = bj;
4357   merge->buf_ri       = buf_ri;
4358   merge->buf_rj       = buf_rj;
4359   merge->coi          = NULL;
4360   merge->coj          = NULL;
4361   merge->owners_co    = NULL;
4362 
4363   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
4364 
4365   /* attach the supporting struct to B_mpi for reuse */
4366   ierr    = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
4367   ierr    = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
4368   ierr    = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
4369   ierr    = PetscContainerDestroy(&container);CHKERRQ(ierr);
4370   *mpimat = B_mpi;
4371 
4372   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4373   PetscFunctionReturn(0);
4374 }
4375 
4376 #undef __FUNCT__
4377 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJ"
4378 /*@C
4379       MatCreateMPIAIJSumSeqAIJ - Creates a MPIAIJ matrix by adding sequential
4380                  matrices from each processor
4381 
4382     Collective on MPI_Comm
4383 
4384    Input Parameters:
4385 +    comm - the communicators the parallel matrix will live on
4386 .    seqmat - the input sequential matrices
4387 .    m - number of local rows (or PETSC_DECIDE)
4388 .    n - number of local columns (or PETSC_DECIDE)
4389 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4390 
4391    Output Parameter:
4392 .    mpimat - the parallel matrix generated
4393 
4394     Level: advanced
4395 
4396    Notes:
4397      The dimensions of the sequential matrix in each processor MUST be the same.
4398      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
4399      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
4400 @*/
4401 PetscErrorCode  MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
4402 {
4403   PetscErrorCode ierr;
4404   PetscMPIInt    size;
4405 
4406   PetscFunctionBegin;
4407   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4408   if (size == 1) {
4409     ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4410     if (scall == MAT_INITIAL_MATRIX) {
4411       ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
4412     } else {
4413       ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4414     }
4415     ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4416     PetscFunctionReturn(0);
4417   }
4418   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4419   if (scall == MAT_INITIAL_MATRIX) {
4420     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
4421   }
4422   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
4423   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4424   PetscFunctionReturn(0);
4425 }
4426 
4427 #undef __FUNCT__
4428 #define __FUNCT__ "MatMPIAIJGetLocalMat"
4429 /*@
4430      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
4431           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
4432           with MatGetSize()
4433 
4434     Not Collective
4435 
4436    Input Parameters:
4437 +    A - the matrix
4438 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4439 
4440    Output Parameter:
4441 .    A_loc - the local sequential matrix generated
4442 
4443     Level: developer
4444 
4445 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
4446 
4447 @*/
4448 PetscErrorCode  MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
4449 {
4450   PetscErrorCode ierr;
4451   Mat_MPIAIJ     *mpimat=(Mat_MPIAIJ*)A->data;
4452   Mat_SeqAIJ     *mat,*a,*b;
4453   PetscInt       *ai,*aj,*bi,*bj,*cmap=mpimat->garray;
4454   MatScalar      *aa,*ba,*cam;
4455   PetscScalar    *ca;
4456   PetscInt       am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
4457   PetscInt       *ci,*cj,col,ncols_d,ncols_o,jo;
4458   PetscBool      match;
4459   MPI_Comm       comm;
4460   PetscMPIInt    size;
4461 
4462   PetscFunctionBegin;
4463   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4464   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
4465   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4466   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4467   if (size == 1 && scall == MAT_REUSE_MATRIX) PetscFunctionReturn(0);
4468 
4469   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4470   a = (Mat_SeqAIJ*)(mpimat->A)->data;
4471   b = (Mat_SeqAIJ*)(mpimat->B)->data;
4472   ai = a->i; aj = a->j; bi = b->i; bj = b->j;
4473   aa = a->a; ba = b->a;
4474   if (scall == MAT_INITIAL_MATRIX) {
4475     if (size == 1) {
4476       ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ai,aj,aa,A_loc);CHKERRQ(ierr);
4477       PetscFunctionReturn(0);
4478     }
4479 
4480     ierr  = PetscMalloc1(1+am,&ci);CHKERRQ(ierr);
4481     ci[0] = 0;
4482     for (i=0; i<am; i++) {
4483       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
4484     }
4485     ierr = PetscMalloc1(1+ci[am],&cj);CHKERRQ(ierr);
4486     ierr = PetscMalloc1(1+ci[am],&ca);CHKERRQ(ierr);
4487     k    = 0;
4488     for (i=0; i<am; i++) {
4489       ncols_o = bi[i+1] - bi[i];
4490       ncols_d = ai[i+1] - ai[i];
4491       /* off-diagonal portion of A */
4492       for (jo=0; jo<ncols_o; jo++) {
4493         col = cmap[*bj];
4494         if (col >= cstart) break;
4495         cj[k]   = col; bj++;
4496         ca[k++] = *ba++;
4497       }
4498       /* diagonal portion of A */
4499       for (j=0; j<ncols_d; j++) {
4500         cj[k]   = cstart + *aj++;
4501         ca[k++] = *aa++;
4502       }
4503       /* off-diagonal portion of A */
4504       for (j=jo; j<ncols_o; j++) {
4505         cj[k]   = cmap[*bj++];
4506         ca[k++] = *ba++;
4507       }
4508     }
4509     /* put together the new matrix */
4510     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
4511     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4512     /* Since these are PETSc arrays, change flags to free them as necessary. */
4513     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
4514     mat->free_a  = PETSC_TRUE;
4515     mat->free_ij = PETSC_TRUE;
4516     mat->nonew   = 0;
4517   } else if (scall == MAT_REUSE_MATRIX) {
4518     mat=(Mat_SeqAIJ*)(*A_loc)->data;
4519     ci = mat->i; cj = mat->j; cam = mat->a;
4520     for (i=0; i<am; i++) {
4521       /* off-diagonal portion of A */
4522       ncols_o = bi[i+1] - bi[i];
4523       for (jo=0; jo<ncols_o; jo++) {
4524         col = cmap[*bj];
4525         if (col >= cstart) break;
4526         *cam++ = *ba++; bj++;
4527       }
4528       /* diagonal portion of A */
4529       ncols_d = ai[i+1] - ai[i];
4530       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
4531       /* off-diagonal portion of A */
4532       for (j=jo; j<ncols_o; j++) {
4533         *cam++ = *ba++; bj++;
4534       }
4535     }
4536   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
4537   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4538   PetscFunctionReturn(0);
4539 }
4540 
4541 #undef __FUNCT__
4542 #define __FUNCT__ "MatMPIAIJGetLocalMatCondensed"
4543 /*@C
4544      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MPIAIJ matrix by taking all its local rows and NON-ZERO columns
4545 
4546     Not Collective
4547 
4548    Input Parameters:
4549 +    A - the matrix
4550 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4551 -    row, col - index sets of rows and columns to extract (or NULL)
4552 
4553    Output Parameter:
4554 .    A_loc - the local sequential matrix generated
4555 
4556     Level: developer
4557 
4558 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
4559 
4560 @*/
4561 PetscErrorCode  MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
4562 {
4563   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4564   PetscErrorCode ierr;
4565   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
4566   IS             isrowa,iscola;
4567   Mat            *aloc;
4568   PetscBool      match;
4569 
4570   PetscFunctionBegin;
4571   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4572   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
4573   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4574   if (!row) {
4575     start = A->rmap->rstart; end = A->rmap->rend;
4576     ierr  = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
4577   } else {
4578     isrowa = *row;
4579   }
4580   if (!col) {
4581     start = A->cmap->rstart;
4582     cmap  = a->garray;
4583     nzA   = a->A->cmap->n;
4584     nzB   = a->B->cmap->n;
4585     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4586     ncols = 0;
4587     for (i=0; i<nzB; i++) {
4588       if (cmap[i] < start) idx[ncols++] = cmap[i];
4589       else break;
4590     }
4591     imark = i;
4592     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
4593     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
4594     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
4595   } else {
4596     iscola = *col;
4597   }
4598   if (scall != MAT_INITIAL_MATRIX) {
4599     ierr    = PetscMalloc1(1,&aloc);CHKERRQ(ierr);
4600     aloc[0] = *A_loc;
4601   }
4602   ierr   = MatGetSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
4603   *A_loc = aloc[0];
4604   ierr   = PetscFree(aloc);CHKERRQ(ierr);
4605   if (!row) {
4606     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
4607   }
4608   if (!col) {
4609     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
4610   }
4611   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4612   PetscFunctionReturn(0);
4613 }
4614 
4615 #undef __FUNCT__
4616 #define __FUNCT__ "MatGetBrowsOfAcols"
4617 /*@C
4618     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
4619 
4620     Collective on Mat
4621 
4622    Input Parameters:
4623 +    A,B - the matrices in mpiaij format
4624 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4625 -    rowb, colb - index sets of rows and columns of B to extract (or NULL)
4626 
4627    Output Parameter:
4628 +    rowb, colb - index sets of rows and columns of B to extract
4629 -    B_seq - the sequential matrix generated
4630 
4631     Level: developer
4632 
4633 @*/
4634 PetscErrorCode  MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
4635 {
4636   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4637   PetscErrorCode ierr;
4638   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
4639   IS             isrowb,iscolb;
4640   Mat            *bseq=NULL;
4641 
4642   PetscFunctionBegin;
4643   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4644     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);
4645   }
4646   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4647 
4648   if (scall == MAT_INITIAL_MATRIX) {
4649     start = A->cmap->rstart;
4650     cmap  = a->garray;
4651     nzA   = a->A->cmap->n;
4652     nzB   = a->B->cmap->n;
4653     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4654     ncols = 0;
4655     for (i=0; i<nzB; i++) {  /* row < local row index */
4656       if (cmap[i] < start) idx[ncols++] = cmap[i];
4657       else break;
4658     }
4659     imark = i;
4660     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
4661     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
4662     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
4663     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
4664   } else {
4665     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
4666     isrowb  = *rowb; iscolb = *colb;
4667     ierr    = PetscMalloc1(1,&bseq);CHKERRQ(ierr);
4668     bseq[0] = *B_seq;
4669   }
4670   ierr   = MatGetSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
4671   *B_seq = bseq[0];
4672   ierr   = PetscFree(bseq);CHKERRQ(ierr);
4673   if (!rowb) {
4674     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
4675   } else {
4676     *rowb = isrowb;
4677   }
4678   if (!colb) {
4679     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
4680   } else {
4681     *colb = iscolb;
4682   }
4683   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4684   PetscFunctionReturn(0);
4685 }
4686 
4687 #undef __FUNCT__
4688 #define __FUNCT__ "MatGetBrowsOfAoCols_MPIAIJ"
4689 /*
4690     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
4691     of the OFF-DIAGONAL portion of local A
4692 
4693     Collective on Mat
4694 
4695    Input Parameters:
4696 +    A,B - the matrices in mpiaij format
4697 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4698 
4699    Output Parameter:
4700 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
4701 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
4702 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
4703 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
4704 
4705     Level: developer
4706 
4707 */
4708 PetscErrorCode  MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
4709 {
4710   VecScatter_MPI_General *gen_to,*gen_from;
4711   PetscErrorCode         ierr;
4712   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
4713   Mat_SeqAIJ             *b_oth;
4714   VecScatter             ctx =a->Mvctx;
4715   MPI_Comm               comm;
4716   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
4717   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
4718   PetscScalar            *rvalues,*svalues;
4719   MatScalar              *b_otha,*bufa,*bufA;
4720   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
4721   MPI_Request            *rwaits = NULL,*swaits = NULL;
4722   MPI_Status             *sstatus,rstatus;
4723   PetscMPIInt            jj,size;
4724   PetscInt               *cols,sbs,rbs;
4725   PetscScalar            *vals;
4726 
4727   PetscFunctionBegin;
4728   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4729   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4730 
4731   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4732     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);
4733   }
4734   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4735   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4736 
4737   gen_to   = (VecScatter_MPI_General*)ctx->todata;
4738   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
4739   rvalues  = gen_from->values; /* holds the length of receiving row */
4740   svalues  = gen_to->values;   /* holds the length of sending row */
4741   nrecvs   = gen_from->n;
4742   nsends   = gen_to->n;
4743 
4744   ierr    = PetscMalloc2(nrecvs,&rwaits,nsends,&swaits);CHKERRQ(ierr);
4745   srow    = gen_to->indices;    /* local row index to be sent */
4746   sstarts = gen_to->starts;
4747   sprocs  = gen_to->procs;
4748   sstatus = gen_to->sstatus;
4749   sbs     = gen_to->bs;
4750   rstarts = gen_from->starts;
4751   rprocs  = gen_from->procs;
4752   rbs     = gen_from->bs;
4753 
4754   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
4755   if (scall == MAT_INITIAL_MATRIX) {
4756     /* i-array */
4757     /*---------*/
4758     /*  post receives */
4759     for (i=0; i<nrecvs; i++) {
4760       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
4761       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
4762       ierr   = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4763     }
4764 
4765     /* pack the outgoing message */
4766     ierr = PetscMalloc2(nsends+1,&sstartsj,nrecvs+1,&rstartsj);CHKERRQ(ierr);
4767 
4768     sstartsj[0] = 0;
4769     rstartsj[0] = 0;
4770     len         = 0; /* total length of j or a array to be sent */
4771     k           = 0;
4772     for (i=0; i<nsends; i++) {
4773       rowlen = (PetscInt*)svalues + sstarts[i]*sbs;
4774       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
4775       for (j=0; j<nrows; j++) {
4776         row = srow[k] + B->rmap->range[rank]; /* global row idx */
4777         for (l=0; l<sbs; l++) {
4778           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr); /* rowlength */
4779 
4780           rowlen[j*sbs+l] = ncols;
4781 
4782           len += ncols;
4783           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr);
4784         }
4785         k++;
4786       }
4787       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4788 
4789       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
4790     }
4791     /* recvs and sends of i-array are completed */
4792     i = nrecvs;
4793     while (i--) {
4794       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4795     }
4796     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4797 
4798     /* allocate buffers for sending j and a arrays */
4799     ierr = PetscMalloc1(len+1,&bufj);CHKERRQ(ierr);
4800     ierr = PetscMalloc1(len+1,&bufa);CHKERRQ(ierr);
4801 
4802     /* create i-array of B_oth */
4803     ierr = PetscMalloc1(aBn+2,&b_othi);CHKERRQ(ierr);
4804 
4805     b_othi[0] = 0;
4806     len       = 0; /* total length of j or a array to be received */
4807     k         = 0;
4808     for (i=0; i<nrecvs; i++) {
4809       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
4810       nrows  = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be recieved */
4811       for (j=0; j<nrows; j++) {
4812         b_othi[k+1] = b_othi[k] + rowlen[j];
4813         len        += rowlen[j]; k++;
4814       }
4815       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
4816     }
4817 
4818     /* allocate space for j and a arrrays of B_oth */
4819     ierr = PetscMalloc1(b_othi[aBn]+1,&b_othj);CHKERRQ(ierr);
4820     ierr = PetscMalloc1(b_othi[aBn]+1,&b_otha);CHKERRQ(ierr);
4821 
4822     /* j-array */
4823     /*---------*/
4824     /*  post receives of j-array */
4825     for (i=0; i<nrecvs; i++) {
4826       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4827       ierr  = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4828     }
4829 
4830     /* pack the outgoing message j-array */
4831     k = 0;
4832     for (i=0; i<nsends; i++) {
4833       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4834       bufJ  = bufj+sstartsj[i];
4835       for (j=0; j<nrows; j++) {
4836         row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4837         for (ll=0; ll<sbs; ll++) {
4838           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4839           for (l=0; l<ncols; l++) {
4840             *bufJ++ = cols[l];
4841           }
4842           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4843         }
4844       }
4845       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4846     }
4847 
4848     /* recvs and sends of j-array are completed */
4849     i = nrecvs;
4850     while (i--) {
4851       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4852     }
4853     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4854   } else if (scall == MAT_REUSE_MATRIX) {
4855     sstartsj = *startsj_s;
4856     rstartsj = *startsj_r;
4857     bufa     = *bufa_ptr;
4858     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
4859     b_otha   = b_oth->a;
4860   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
4861 
4862   /* a-array */
4863   /*---------*/
4864   /*  post receives of a-array */
4865   for (i=0; i<nrecvs; i++) {
4866     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4867     ierr  = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4868   }
4869 
4870   /* pack the outgoing message a-array */
4871   k = 0;
4872   for (i=0; i<nsends; i++) {
4873     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4874     bufA  = bufa+sstartsj[i];
4875     for (j=0; j<nrows; j++) {
4876       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4877       for (ll=0; ll<sbs; ll++) {
4878         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4879         for (l=0; l<ncols; l++) {
4880           *bufA++ = vals[l];
4881         }
4882         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4883       }
4884     }
4885     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4886   }
4887   /* recvs and sends of a-array are completed */
4888   i = nrecvs;
4889   while (i--) {
4890     ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4891   }
4892   if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4893   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
4894 
4895   if (scall == MAT_INITIAL_MATRIX) {
4896     /* put together the new matrix */
4897     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
4898 
4899     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4900     /* Since these are PETSc arrays, change flags to free them as necessary. */
4901     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
4902     b_oth->free_a  = PETSC_TRUE;
4903     b_oth->free_ij = PETSC_TRUE;
4904     b_oth->nonew   = 0;
4905 
4906     ierr = PetscFree(bufj);CHKERRQ(ierr);
4907     if (!startsj_s || !bufa_ptr) {
4908       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
4909       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
4910     } else {
4911       *startsj_s = sstartsj;
4912       *startsj_r = rstartsj;
4913       *bufa_ptr  = bufa;
4914     }
4915   }
4916   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4917   PetscFunctionReturn(0);
4918 }
4919 
4920 #undef __FUNCT__
4921 #define __FUNCT__ "MatGetCommunicationStructs"
4922 /*@C
4923   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
4924 
4925   Not Collective
4926 
4927   Input Parameters:
4928 . A - The matrix in mpiaij format
4929 
4930   Output Parameter:
4931 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
4932 . colmap - A map from global column index to local index into lvec
4933 - multScatter - A scatter from the argument of a matrix-vector product to lvec
4934 
4935   Level: developer
4936 
4937 @*/
4938 #if defined(PETSC_USE_CTABLE)
4939 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
4940 #else
4941 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
4942 #endif
4943 {
4944   Mat_MPIAIJ *a;
4945 
4946   PetscFunctionBegin;
4947   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4948   PetscValidPointer(lvec, 2);
4949   PetscValidPointer(colmap, 3);
4950   PetscValidPointer(multScatter, 4);
4951   a = (Mat_MPIAIJ*) A->data;
4952   if (lvec) *lvec = a->lvec;
4953   if (colmap) *colmap = a->colmap;
4954   if (multScatter) *multScatter = a->Mvctx;
4955   PetscFunctionReturn(0);
4956 }
4957 
4958 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
4959 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
4960 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
4961 #if defined(PETSC_HAVE_ELEMENTAL)
4962 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
4963 #endif
4964 
4965 #undef __FUNCT__
4966 #define __FUNCT__ "MatMatMultNumeric_MPIDense_MPIAIJ"
4967 /*
4968     Computes (B'*A')' since computing B*A directly is untenable
4969 
4970                n                       p                          p
4971         (              )       (              )         (                  )
4972       m (      A       )  *  n (       B      )   =   m (         C        )
4973         (              )       (              )         (                  )
4974 
4975 */
4976 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
4977 {
4978   PetscErrorCode ierr;
4979   Mat            At,Bt,Ct;
4980 
4981   PetscFunctionBegin;
4982   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
4983   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
4984   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
4985   ierr = MatDestroy(&At);CHKERRQ(ierr);
4986   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
4987   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
4988   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
4989   PetscFunctionReturn(0);
4990 }
4991 
4992 #undef __FUNCT__
4993 #define __FUNCT__ "MatMatMultSymbolic_MPIDense_MPIAIJ"
4994 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
4995 {
4996   PetscErrorCode ierr;
4997   PetscInt       m=A->rmap->n,n=B->cmap->n;
4998   Mat            Cmat;
4999 
5000   PetscFunctionBegin;
5001   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);
5002   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
5003   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
5004   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
5005   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
5006   ierr = MatMPIDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
5007   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5008   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5009 
5010   Cmat->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
5011 
5012   *C = Cmat;
5013   PetscFunctionReturn(0);
5014 }
5015 
5016 /* ----------------------------------------------------------------*/
5017 #undef __FUNCT__
5018 #define __FUNCT__ "MatMatMult_MPIDense_MPIAIJ"
5019 PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
5020 {
5021   PetscErrorCode ierr;
5022 
5023   PetscFunctionBegin;
5024   if (scall == MAT_INITIAL_MATRIX) {
5025     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5026     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
5027     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5028   }
5029   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5030   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
5031   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5032   PetscFunctionReturn(0);
5033 }
5034 
5035 /*MC
5036    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
5037 
5038    Options Database Keys:
5039 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
5040 
5041   Level: beginner
5042 
5043 .seealso: MatCreateAIJ()
5044 M*/
5045 
5046 #undef __FUNCT__
5047 #define __FUNCT__ "MatCreate_MPIAIJ"
5048 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
5049 {
5050   Mat_MPIAIJ     *b;
5051   PetscErrorCode ierr;
5052   PetscMPIInt    size;
5053 
5054   PetscFunctionBegin;
5055   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
5056 
5057   ierr          = PetscNewLog(B,&b);CHKERRQ(ierr);
5058   B->data       = (void*)b;
5059   ierr          = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
5060   B->assembled  = PETSC_FALSE;
5061   B->insertmode = NOT_SET_VALUES;
5062   b->size       = size;
5063 
5064   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank);CHKERRQ(ierr);
5065 
5066   /* build cache for off array entries formed */
5067   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash);CHKERRQ(ierr);
5068 
5069   b->donotstash  = PETSC_FALSE;
5070   b->colmap      = 0;
5071   b->garray      = 0;
5072   b->roworiented = PETSC_TRUE;
5073 
5074   /* stuff used for matrix vector multiply */
5075   b->lvec  = NULL;
5076   b->Mvctx = NULL;
5077 
5078   /* stuff for MatGetRow() */
5079   b->rowindices   = 0;
5080   b->rowvalues    = 0;
5081   b->getrowactive = PETSC_FALSE;
5082 
5083   /* flexible pointer used in CUSP/CUSPARSE classes */
5084   b->spptr = NULL;
5085 
5086   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ);CHKERRQ(ierr);
5087   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
5088   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetDiagonalBlock_C",MatGetDiagonalBlock_MPIAIJ);CHKERRQ(ierr);
5089   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
5090   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
5091   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
5092   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
5093   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
5094   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
5095   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
5096 #if defined(PETSC_HAVE_ELEMENTAL)
5097   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_elemental_C",MatConvert_MPIAIJ_Elemental);CHKERRQ(ierr);
5098 #endif
5099   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
5100   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
5101   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
5102   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
5103   PetscFunctionReturn(0);
5104 }
5105 
5106 #undef __FUNCT__
5107 #define __FUNCT__ "MatCreateMPIAIJWithSplitArrays"
5108 /*@C
5109      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
5110          and "off-diagonal" part of the matrix in CSR format.
5111 
5112    Collective on MPI_Comm
5113 
5114    Input Parameters:
5115 +  comm - MPI communicator
5116 .  m - number of local rows (Cannot be PETSC_DECIDE)
5117 .  n - This value should be the same as the local size used in creating the
5118        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
5119        calculated if N is given) For square matrices n is almost always m.
5120 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
5121 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
5122 .   i - row indices for "diagonal" portion of matrix
5123 .   j - column indices
5124 .   a - matrix values
5125 .   oi - row indices for "off-diagonal" portion of matrix
5126 .   oj - column indices
5127 -   oa - matrix values
5128 
5129    Output Parameter:
5130 .   mat - the matrix
5131 
5132    Level: advanced
5133 
5134    Notes:
5135        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
5136        must free the arrays once the matrix has been destroyed and not before.
5137 
5138        The i and j indices are 0 based
5139 
5140        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
5141 
5142        This sets local rows and cannot be used to set off-processor values.
5143 
5144        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
5145        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
5146        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
5147        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
5148        keep track of the underlying array. Use MatSetOption(A,MAT_IGNORE_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
5149        communication if it is known that only local entries will be set.
5150 
5151 .keywords: matrix, aij, compressed row, sparse, parallel
5152 
5153 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
5154           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
5155 @*/
5156 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)
5157 {
5158   PetscErrorCode ierr;
5159   Mat_MPIAIJ     *maij;
5160 
5161   PetscFunctionBegin;
5162   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
5163   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
5164   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
5165   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
5166   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
5167   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
5168   maij = (Mat_MPIAIJ*) (*mat)->data;
5169 
5170   (*mat)->preallocated = PETSC_TRUE;
5171 
5172   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
5173   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
5174 
5175   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
5176   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
5177 
5178   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5179   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5180   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5181   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5182 
5183   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5184   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5185   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
5186   PetscFunctionReturn(0);
5187 }
5188 
5189 /*
5190     Special version for direct calls from Fortran
5191 */
5192 #include <petsc/private/fortranimpl.h>
5193 
5194 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5195 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
5196 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5197 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
5198 #endif
5199 
5200 /* Change these macros so can be used in void function */
5201 #undef CHKERRQ
5202 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
5203 #undef SETERRQ2
5204 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5205 #undef SETERRQ3
5206 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5207 #undef SETERRQ
5208 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
5209 
5210 #undef __FUNCT__
5211 #define __FUNCT__ "matsetvaluesmpiaij_"
5212 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)
5213 {
5214   Mat            mat  = *mmat;
5215   PetscInt       m    = *mm, n = *mn;
5216   InsertMode     addv = *maddv;
5217   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
5218   PetscScalar    value;
5219   PetscErrorCode ierr;
5220 
5221   MatCheckPreallocated(mat,1);
5222   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
5223 
5224 #if defined(PETSC_USE_DEBUG)
5225   else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
5226 #endif
5227   {
5228     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
5229     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
5230     PetscBool roworiented = aij->roworiented;
5231 
5232     /* Some Variables required in the macro */
5233     Mat        A                 = aij->A;
5234     Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
5235     PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
5236     MatScalar  *aa               = a->a;
5237     PetscBool  ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
5238     Mat        B                 = aij->B;
5239     Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
5240     PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5241     MatScalar  *ba               = b->a;
5242 
5243     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5244     PetscInt  nonew = a->nonew;
5245     MatScalar *ap1,*ap2;
5246 
5247     PetscFunctionBegin;
5248     for (i=0; i<m; i++) {
5249       if (im[i] < 0) continue;
5250 #if defined(PETSC_USE_DEBUG)
5251       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);
5252 #endif
5253       if (im[i] >= rstart && im[i] < rend) {
5254         row      = im[i] - rstart;
5255         lastcol1 = -1;
5256         rp1      = aj + ai[row];
5257         ap1      = aa + ai[row];
5258         rmax1    = aimax[row];
5259         nrow1    = ailen[row];
5260         low1     = 0;
5261         high1    = nrow1;
5262         lastcol2 = -1;
5263         rp2      = bj + bi[row];
5264         ap2      = ba + bi[row];
5265         rmax2    = bimax[row];
5266         nrow2    = bilen[row];
5267         low2     = 0;
5268         high2    = nrow2;
5269 
5270         for (j=0; j<n; j++) {
5271           if (roworiented) value = v[i*n+j];
5272           else value = v[i+j*m];
5273           if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES)) continue;
5274           if (in[j] >= cstart && in[j] < cend) {
5275             col = in[j] - cstart;
5276             MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
5277           } else if (in[j] < 0) continue;
5278 #if defined(PETSC_USE_DEBUG)
5279           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);
5280 #endif
5281           else {
5282             if (mat->was_assembled) {
5283               if (!aij->colmap) {
5284                 ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5285               }
5286 #if defined(PETSC_USE_CTABLE)
5287               ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5288               col--;
5289 #else
5290               col = aij->colmap[in[j]] - 1;
5291 #endif
5292               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5293                 ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5294                 col  =  in[j];
5295                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5296                 B     = aij->B;
5297                 b     = (Mat_SeqAIJ*)B->data;
5298                 bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5299                 rp2   = bj + bi[row];
5300                 ap2   = ba + bi[row];
5301                 rmax2 = bimax[row];
5302                 nrow2 = bilen[row];
5303                 low2  = 0;
5304                 high2 = nrow2;
5305                 bm    = aij->B->rmap->n;
5306                 ba    = b->a;
5307               }
5308             } else col = in[j];
5309             MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
5310           }
5311         }
5312       } else if (!aij->donotstash) {
5313         if (roworiented) {
5314           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5315         } else {
5316           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5317         }
5318       }
5319     }
5320   }
5321   PetscFunctionReturnVoid();
5322 }
5323 
5324