xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision cf2e76e06d18222cc34ecb2bedce2dfa098c54c2)
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 = MPIU_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 = MPIU_Allreduce(work,norms,n,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
181   } else {
182     ierr = MPIU_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 
686   PetscFunctionBegin;
687   if (aij->donotstash || mat->nooffprocentries) PetscFunctionReturn(0);
688 
689   ierr = MatStashScatterBegin_Private(mat,&mat->stash,mat->rmap->range);CHKERRQ(ierr);
690   ierr = MatStashGetInfo_Private(&mat->stash,&nstash,&reallocs);CHKERRQ(ierr);
691   ierr = PetscInfo2(aij->A,"Stash has %D entries, uses %D mallocs.\n",nstash,reallocs);CHKERRQ(ierr);
692   PetscFunctionReturn(0);
693 }
694 
695 #undef __FUNCT__
696 #define __FUNCT__ "MatAssemblyEnd_MPIAIJ"
697 PetscErrorCode MatAssemblyEnd_MPIAIJ(Mat mat,MatAssemblyType mode)
698 {
699   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
700   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)aij->A->data;
701   PetscErrorCode ierr;
702   PetscMPIInt    n;
703   PetscInt       i,j,rstart,ncols,flg;
704   PetscInt       *row,*col;
705   PetscBool      other_disassembled;
706   PetscScalar    *val;
707 
708   /* do not use 'b = (Mat_SeqAIJ*)aij->B->data' as B can be reset in disassembly */
709 
710   PetscFunctionBegin;
711   if (!aij->donotstash && !mat->nooffprocentries) {
712     while (1) {
713       ierr = MatStashScatterGetMesg_Private(&mat->stash,&n,&row,&col,&val,&flg);CHKERRQ(ierr);
714       if (!flg) break;
715 
716       for (i=0; i<n; ) {
717         /* Now identify the consecutive vals belonging to the same row */
718         for (j=i,rstart=row[j]; j<n; j++) {
719           if (row[j] != rstart) break;
720         }
721         if (j < n) ncols = j-i;
722         else       ncols = n-i;
723         /* Now assemble all these values with a single function call */
724         ierr = MatSetValues_MPIAIJ(mat,1,row+i,ncols,col+i,val+i,mat->insertmode);CHKERRQ(ierr);
725 
726         i = j;
727       }
728     }
729     ierr = MatStashScatterEnd_Private(&mat->stash);CHKERRQ(ierr);
730   }
731   ierr = MatAssemblyBegin(aij->A,mode);CHKERRQ(ierr);
732   ierr = MatAssemblyEnd(aij->A,mode);CHKERRQ(ierr);
733 
734   /* determine if any processor has disassembled, if so we must
735      also disassemble ourselfs, in order that we may reassemble. */
736   /*
737      if nonzero structure of submatrix B cannot change then we know that
738      no processor disassembled thus we can skip this stuff
739   */
740   if (!((Mat_SeqAIJ*)aij->B->data)->nonew) {
741     ierr = MPIU_Allreduce(&mat->was_assembled,&other_disassembled,1,MPIU_BOOL,MPI_PROD,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
742     if (mat->was_assembled && !other_disassembled) {
743       ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
744     }
745   }
746   if (!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) {
747     ierr = MatSetUpMultiply_MPIAIJ(mat);CHKERRQ(ierr);
748   }
749   ierr = MatSetOption(aij->B,MAT_USE_INODES,PETSC_FALSE);CHKERRQ(ierr);
750   ierr = MatAssemblyBegin(aij->B,mode);CHKERRQ(ierr);
751   ierr = MatAssemblyEnd(aij->B,mode);CHKERRQ(ierr);
752 
753   ierr = PetscFree2(aij->rowvalues,aij->rowindices);CHKERRQ(ierr);
754 
755   aij->rowvalues = 0;
756 
757   ierr = VecDestroy(&aij->diag);CHKERRQ(ierr);
758   if (a->inode.size) mat->ops->multdiagonalblock = MatMultDiagonalBlock_MPIAIJ;
759 
760   /* if no new nonzero locations are allowed in matrix then only set the matrix state the first time through */
761   if ((!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) || !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
762     PetscObjectState state = aij->A->nonzerostate + aij->B->nonzerostate;
763     ierr = MPIU_Allreduce(&state,&mat->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
764   }
765   PetscFunctionReturn(0);
766 }
767 
768 #undef __FUNCT__
769 #define __FUNCT__ "MatZeroEntries_MPIAIJ"
770 PetscErrorCode MatZeroEntries_MPIAIJ(Mat A)
771 {
772   Mat_MPIAIJ     *l = (Mat_MPIAIJ*)A->data;
773   PetscErrorCode ierr;
774 
775   PetscFunctionBegin;
776   ierr = MatZeroEntries(l->A);CHKERRQ(ierr);
777   ierr = MatZeroEntries(l->B);CHKERRQ(ierr);
778   PetscFunctionReturn(0);
779 }
780 
781 #undef __FUNCT__
782 #define __FUNCT__ "MatZeroRows_MPIAIJ"
783 PetscErrorCode MatZeroRows_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
784 {
785   Mat_MPIAIJ    *mat    = (Mat_MPIAIJ *) A->data;
786   PetscInt      *owners = A->rmap->range;
787   PetscInt       n      = A->rmap->n;
788   PetscSF        sf;
789   PetscInt      *lrows;
790   PetscSFNode   *rrows;
791   PetscInt       r, p = 0, len = 0;
792   PetscErrorCode ierr;
793 
794   PetscFunctionBegin;
795   /* Create SF where leaves are input rows and roots are owned rows */
796   ierr = PetscMalloc1(n, &lrows);CHKERRQ(ierr);
797   for (r = 0; r < n; ++r) lrows[r] = -1;
798   if (!A->nooffproczerorows) {ierr = PetscMalloc1(N, &rrows);CHKERRQ(ierr);}
799   for (r = 0; r < N; ++r) {
800     const PetscInt idx   = rows[r];
801     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);
802     if (idx < owners[p] || owners[p+1] <= idx) { /* short-circuit the search if the last p owns this row too */
803       ierr = PetscLayoutFindOwner(A->rmap,idx,&p);CHKERRQ(ierr);
804     }
805     if (A->nooffproczerorows) {
806       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);
807       lrows[len++] = idx - owners[p];
808     } else {
809       rrows[r].rank = p;
810       rrows[r].index = rows[r] - owners[p];
811     }
812   }
813   if (!A->nooffproczerorows) {
814     ierr = PetscSFCreate(PetscObjectComm((PetscObject) A), &sf);CHKERRQ(ierr);
815     ierr = PetscSFSetGraph(sf, n, N, NULL, PETSC_OWN_POINTER, rrows, PETSC_OWN_POINTER);CHKERRQ(ierr);
816     /* Collect flags for rows to be zeroed */
817     ierr = PetscSFReduceBegin(sf, MPIU_INT, (PetscInt*)rows, lrows, MPI_LOR);CHKERRQ(ierr);
818     ierr = PetscSFReduceEnd(sf, MPIU_INT, (PetscInt*)rows, lrows, MPI_LOR);CHKERRQ(ierr);
819     ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
820     /* Compress and put in row numbers */
821     for (r = 0; r < n; ++r) if (lrows[r] >= 0) lrows[len++] = r;
822   }
823   /* fix right hand side if needed */
824   if (x && b) {
825     const PetscScalar *xx;
826     PetscScalar       *bb;
827 
828     ierr = VecGetArrayRead(x, &xx);CHKERRQ(ierr);
829     ierr = VecGetArray(b, &bb);CHKERRQ(ierr);
830     for (r = 0; r < len; ++r) bb[lrows[r]] = diag*xx[lrows[r]];
831     ierr = VecRestoreArrayRead(x, &xx);CHKERRQ(ierr);
832     ierr = VecRestoreArray(b, &bb);CHKERRQ(ierr);
833   }
834   /* Must zero l->B before l->A because the (diag) case below may put values into l->B*/
835   ierr = MatZeroRows(mat->B, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
836   if ((diag != 0.0) && (mat->A->rmap->N == mat->A->cmap->N)) {
837     ierr = MatZeroRows(mat->A, len, lrows, diag, NULL, NULL);CHKERRQ(ierr);
838   } else if (diag != 0.0) {
839     ierr = MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
840     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");
841     for (r = 0; r < len; ++r) {
842       const PetscInt row = lrows[r] + A->rmap->rstart;
843       ierr = MatSetValues(A, 1, &row, 1, &row, &diag, INSERT_VALUES);CHKERRQ(ierr);
844     }
845     ierr = MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
846     ierr = MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
847   } else {
848     ierr = MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
849   }
850   ierr = PetscFree(lrows);CHKERRQ(ierr);
851 
852   /* only change matrix nonzero state if pattern was allowed to be changed */
853   if (!((Mat_SeqAIJ*)(mat->A->data))->keepnonzeropattern) {
854     PetscObjectState state = mat->A->nonzerostate + mat->B->nonzerostate;
855     ierr = MPIU_Allreduce(&state,&A->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
856   }
857   PetscFunctionReturn(0);
858 }
859 
860 #undef __FUNCT__
861 #define __FUNCT__ "MatZeroRowsColumns_MPIAIJ"
862 PetscErrorCode MatZeroRowsColumns_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
863 {
864   Mat_MPIAIJ        *l = (Mat_MPIAIJ*)A->data;
865   PetscErrorCode    ierr;
866   PetscMPIInt       n = A->rmap->n;
867   PetscInt          i,j,r,m,p = 0,len = 0;
868   PetscInt          *lrows,*owners = A->rmap->range;
869   PetscSFNode       *rrows;
870   PetscSF           sf;
871   const PetscScalar *xx;
872   PetscScalar       *bb,*mask;
873   Vec               xmask,lmask;
874   Mat_SeqAIJ        *aij = (Mat_SeqAIJ*)l->B->data;
875   const PetscInt    *aj, *ii,*ridx;
876   PetscScalar       *aa;
877 
878   PetscFunctionBegin;
879   /* Create SF where leaves are input rows and roots are owned rows */
880   ierr = PetscMalloc1(n, &lrows);CHKERRQ(ierr);
881   for (r = 0; r < n; ++r) lrows[r] = -1;
882   ierr = PetscMalloc1(N, &rrows);CHKERRQ(ierr);
883   for (r = 0; r < N; ++r) {
884     const PetscInt idx   = rows[r];
885     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);
886     if (idx < owners[p] || owners[p+1] <= idx) { /* short-circuit the search if the last p owns this row too */
887       ierr = PetscLayoutFindOwner(A->rmap,idx,&p);CHKERRQ(ierr);
888     }
889     rrows[r].rank  = p;
890     rrows[r].index = rows[r] - owners[p];
891   }
892   ierr = PetscSFCreate(PetscObjectComm((PetscObject) A), &sf);CHKERRQ(ierr);
893   ierr = PetscSFSetGraph(sf, n, N, NULL, PETSC_OWN_POINTER, rrows, PETSC_OWN_POINTER);CHKERRQ(ierr);
894   /* Collect flags for rows to be zeroed */
895   ierr = PetscSFReduceBegin(sf, MPIU_INT, (PetscInt *) rows, lrows, MPI_LOR);CHKERRQ(ierr);
896   ierr = PetscSFReduceEnd(sf, MPIU_INT, (PetscInt *) rows, lrows, MPI_LOR);CHKERRQ(ierr);
897   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
898   /* Compress and put in row numbers */
899   for (r = 0; r < n; ++r) if (lrows[r] >= 0) lrows[len++] = r;
900   /* zero diagonal part of matrix */
901   ierr = MatZeroRowsColumns(l->A,len,lrows,diag,x,b);CHKERRQ(ierr);
902   /* handle off diagonal part of matrix */
903   ierr = MatCreateVecs(A,&xmask,NULL);CHKERRQ(ierr);
904   ierr = VecDuplicate(l->lvec,&lmask);CHKERRQ(ierr);
905   ierr = VecGetArray(xmask,&bb);CHKERRQ(ierr);
906   for (i=0; i<len; i++) bb[lrows[i]] = 1;
907   ierr = VecRestoreArray(xmask,&bb);CHKERRQ(ierr);
908   ierr = VecScatterBegin(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
909   ierr = VecScatterEnd(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
910   ierr = VecDestroy(&xmask);CHKERRQ(ierr);
911   if (x) {
912     ierr = VecScatterBegin(l->Mvctx,x,l->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
913     ierr = VecScatterEnd(l->Mvctx,x,l->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
914     ierr = VecGetArrayRead(l->lvec,&xx);CHKERRQ(ierr);
915     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
916   }
917   ierr = VecGetArray(lmask,&mask);CHKERRQ(ierr);
918   /* remove zeroed rows of off diagonal matrix */
919   ii = aij->i;
920   for (i=0; i<len; i++) {
921     ierr = PetscMemzero(aij->a + ii[lrows[i]],(ii[lrows[i]+1] - ii[lrows[i]])*sizeof(PetscScalar));CHKERRQ(ierr);
922   }
923   /* loop over all elements of off process part of matrix zeroing removed columns*/
924   if (aij->compressedrow.use) {
925     m    = aij->compressedrow.nrows;
926     ii   = aij->compressedrow.i;
927     ridx = aij->compressedrow.rindex;
928     for (i=0; i<m; i++) {
929       n  = ii[i+1] - ii[i];
930       aj = aij->j + ii[i];
931       aa = aij->a + ii[i];
932 
933       for (j=0; j<n; j++) {
934         if (PetscAbsScalar(mask[*aj])) {
935           if (b) bb[*ridx] -= *aa*xx[*aj];
936           *aa = 0.0;
937         }
938         aa++;
939         aj++;
940       }
941       ridx++;
942     }
943   } else { /* do not use compressed row format */
944     m = l->B->rmap->n;
945     for (i=0; i<m; i++) {
946       n  = ii[i+1] - ii[i];
947       aj = aij->j + ii[i];
948       aa = aij->a + ii[i];
949       for (j=0; j<n; j++) {
950         if (PetscAbsScalar(mask[*aj])) {
951           if (b) bb[i] -= *aa*xx[*aj];
952           *aa = 0.0;
953         }
954         aa++;
955         aj++;
956       }
957     }
958   }
959   if (x) {
960     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
961     ierr = VecRestoreArrayRead(l->lvec,&xx);CHKERRQ(ierr);
962   }
963   ierr = VecRestoreArray(lmask,&mask);CHKERRQ(ierr);
964   ierr = VecDestroy(&lmask);CHKERRQ(ierr);
965   ierr = PetscFree(lrows);CHKERRQ(ierr);
966 
967   /* only change matrix nonzero state if pattern was allowed to be changed */
968   if (!((Mat_SeqAIJ*)(l->A->data))->keepnonzeropattern) {
969     PetscObjectState state = l->A->nonzerostate + l->B->nonzerostate;
970     ierr = MPIU_Allreduce(&state,&A->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
971   }
972   PetscFunctionReturn(0);
973 }
974 
975 #undef __FUNCT__
976 #define __FUNCT__ "MatMult_MPIAIJ"
977 PetscErrorCode MatMult_MPIAIJ(Mat A,Vec xx,Vec yy)
978 {
979   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
980   PetscErrorCode ierr;
981   PetscInt       nt;
982 
983   PetscFunctionBegin;
984   ierr = VecGetLocalSize(xx,&nt);CHKERRQ(ierr);
985   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);
986   ierr = VecScatterBegin(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
987   ierr = (*a->A->ops->mult)(a->A,xx,yy);CHKERRQ(ierr);
988   ierr = VecScatterEnd(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
989   ierr = (*a->B->ops->multadd)(a->B,a->lvec,yy,yy);CHKERRQ(ierr);
990   PetscFunctionReturn(0);
991 }
992 
993 #undef __FUNCT__
994 #define __FUNCT__ "MatMultDiagonalBlock_MPIAIJ"
995 PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat A,Vec bb,Vec xx)
996 {
997   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
998   PetscErrorCode ierr;
999 
1000   PetscFunctionBegin;
1001   ierr = MatMultDiagonalBlock(a->A,bb,xx);CHKERRQ(ierr);
1002   PetscFunctionReturn(0);
1003 }
1004 
1005 #undef __FUNCT__
1006 #define __FUNCT__ "MatMultAdd_MPIAIJ"
1007 PetscErrorCode MatMultAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1008 {
1009   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1010   PetscErrorCode ierr;
1011 
1012   PetscFunctionBegin;
1013   ierr = VecScatterBegin(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1014   ierr = (*a->A->ops->multadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
1015   ierr = VecScatterEnd(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1016   ierr = (*a->B->ops->multadd)(a->B,a->lvec,zz,zz);CHKERRQ(ierr);
1017   PetscFunctionReturn(0);
1018 }
1019 
1020 #undef __FUNCT__
1021 #define __FUNCT__ "MatMultTranspose_MPIAIJ"
1022 PetscErrorCode MatMultTranspose_MPIAIJ(Mat A,Vec xx,Vec yy)
1023 {
1024   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1025   PetscErrorCode ierr;
1026   PetscBool      merged;
1027 
1028   PetscFunctionBegin;
1029   ierr = VecScatterGetMerged(a->Mvctx,&merged);CHKERRQ(ierr);
1030   /* do nondiagonal part */
1031   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
1032   if (!merged) {
1033     /* send it on its way */
1034     ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1035     /* do local part */
1036     ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
1037     /* receive remote parts: note this assumes the values are not actually */
1038     /* added in yy until the next line, */
1039     ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1040   } else {
1041     /* do local part */
1042     ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
1043     /* send it on its way */
1044     ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1045     /* values actually were received in the Begin() but we need to call this nop */
1046     ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1047   }
1048   PetscFunctionReturn(0);
1049 }
1050 
1051 #undef __FUNCT__
1052 #define __FUNCT__ "MatIsTranspose_MPIAIJ"
1053 PetscErrorCode  MatIsTranspose_MPIAIJ(Mat Amat,Mat Bmat,PetscReal tol,PetscBool  *f)
1054 {
1055   MPI_Comm       comm;
1056   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ*) Amat->data, *Bij;
1057   Mat            Adia = Aij->A, Bdia, Aoff,Boff,*Aoffs,*Boffs;
1058   IS             Me,Notme;
1059   PetscErrorCode ierr;
1060   PetscInt       M,N,first,last,*notme,i;
1061   PetscMPIInt    size;
1062 
1063   PetscFunctionBegin;
1064   /* Easy test: symmetric diagonal block */
1065   Bij  = (Mat_MPIAIJ*) Bmat->data; Bdia = Bij->A;
1066   ierr = MatIsTranspose(Adia,Bdia,tol,f);CHKERRQ(ierr);
1067   if (!*f) PetscFunctionReturn(0);
1068   ierr = PetscObjectGetComm((PetscObject)Amat,&comm);CHKERRQ(ierr);
1069   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1070   if (size == 1) PetscFunctionReturn(0);
1071 
1072   /* Hard test: off-diagonal block. This takes a MatGetSubMatrix. */
1073   ierr = MatGetSize(Amat,&M,&N);CHKERRQ(ierr);
1074   ierr = MatGetOwnershipRange(Amat,&first,&last);CHKERRQ(ierr);
1075   ierr = PetscMalloc1(N-last+first,&notme);CHKERRQ(ierr);
1076   for (i=0; i<first; i++) notme[i] = i;
1077   for (i=last; i<M; i++) notme[i-last+first] = i;
1078   ierr = ISCreateGeneral(MPI_COMM_SELF,N-last+first,notme,PETSC_COPY_VALUES,&Notme);CHKERRQ(ierr);
1079   ierr = ISCreateStride(MPI_COMM_SELF,last-first,first,1,&Me);CHKERRQ(ierr);
1080   ierr = MatGetSubMatrices(Amat,1,&Me,&Notme,MAT_INITIAL_MATRIX,&Aoffs);CHKERRQ(ierr);
1081   Aoff = Aoffs[0];
1082   ierr = MatGetSubMatrices(Bmat,1,&Notme,&Me,MAT_INITIAL_MATRIX,&Boffs);CHKERRQ(ierr);
1083   Boff = Boffs[0];
1084   ierr = MatIsTranspose(Aoff,Boff,tol,f);CHKERRQ(ierr);
1085   ierr = MatDestroyMatrices(1,&Aoffs);CHKERRQ(ierr);
1086   ierr = MatDestroyMatrices(1,&Boffs);CHKERRQ(ierr);
1087   ierr = ISDestroy(&Me);CHKERRQ(ierr);
1088   ierr = ISDestroy(&Notme);CHKERRQ(ierr);
1089   ierr = PetscFree(notme);CHKERRQ(ierr);
1090   PetscFunctionReturn(0);
1091 }
1092 
1093 #undef __FUNCT__
1094 #define __FUNCT__ "MatMultTransposeAdd_MPIAIJ"
1095 PetscErrorCode MatMultTransposeAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1096 {
1097   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1098   PetscErrorCode ierr;
1099 
1100   PetscFunctionBegin;
1101   /* do nondiagonal part */
1102   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
1103   /* send it on its way */
1104   ierr = VecScatterBegin(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1105   /* do local part */
1106   ierr = (*a->A->ops->multtransposeadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
1107   /* receive remote parts */
1108   ierr = VecScatterEnd(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1109   PetscFunctionReturn(0);
1110 }
1111 
1112 /*
1113   This only works correctly for square matrices where the subblock A->A is the
1114    diagonal block
1115 */
1116 #undef __FUNCT__
1117 #define __FUNCT__ "MatGetDiagonal_MPIAIJ"
1118 PetscErrorCode MatGetDiagonal_MPIAIJ(Mat A,Vec v)
1119 {
1120   PetscErrorCode ierr;
1121   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1122 
1123   PetscFunctionBegin;
1124   if (A->rmap->N != A->cmap->N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Supports only square matrix where A->A is diag block");
1125   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");
1126   ierr = MatGetDiagonal(a->A,v);CHKERRQ(ierr);
1127   PetscFunctionReturn(0);
1128 }
1129 
1130 #undef __FUNCT__
1131 #define __FUNCT__ "MatScale_MPIAIJ"
1132 PetscErrorCode MatScale_MPIAIJ(Mat A,PetscScalar aa)
1133 {
1134   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1135   PetscErrorCode ierr;
1136 
1137   PetscFunctionBegin;
1138   ierr = MatScale(a->A,aa);CHKERRQ(ierr);
1139   ierr = MatScale(a->B,aa);CHKERRQ(ierr);
1140   PetscFunctionReturn(0);
1141 }
1142 
1143 #undef __FUNCT__
1144 #define __FUNCT__ "MatDestroy_MPIAIJ"
1145 PetscErrorCode MatDestroy_MPIAIJ(Mat mat)
1146 {
1147   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1148   PetscErrorCode ierr;
1149 
1150   PetscFunctionBegin;
1151 #if defined(PETSC_USE_LOG)
1152   PetscLogObjectState((PetscObject)mat,"Rows=%D, Cols=%D",mat->rmap->N,mat->cmap->N);
1153 #endif
1154   ierr = MatStashDestroy_Private(&mat->stash);CHKERRQ(ierr);
1155   ierr = VecDestroy(&aij->diag);CHKERRQ(ierr);
1156   ierr = MatDestroy(&aij->A);CHKERRQ(ierr);
1157   ierr = MatDestroy(&aij->B);CHKERRQ(ierr);
1158 #if defined(PETSC_USE_CTABLE)
1159   ierr = PetscTableDestroy(&aij->colmap);CHKERRQ(ierr);
1160 #else
1161   ierr = PetscFree(aij->colmap);CHKERRQ(ierr);
1162 #endif
1163   ierr = PetscFree(aij->garray);CHKERRQ(ierr);
1164   ierr = VecDestroy(&aij->lvec);CHKERRQ(ierr);
1165   ierr = VecScatterDestroy(&aij->Mvctx);CHKERRQ(ierr);
1166   ierr = PetscFree2(aij->rowvalues,aij->rowindices);CHKERRQ(ierr);
1167   ierr = PetscFree(aij->ld);CHKERRQ(ierr);
1168   ierr = PetscFree(mat->data);CHKERRQ(ierr);
1169 
1170   ierr = PetscObjectChangeTypeName((PetscObject)mat,0);CHKERRQ(ierr);
1171   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatStoreValues_C",NULL);CHKERRQ(ierr);
1172   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatRetrieveValues_C",NULL);CHKERRQ(ierr);
1173   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatGetDiagonalBlock_C",NULL);CHKERRQ(ierr);
1174   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatIsTranspose_C",NULL);CHKERRQ(ierr);
1175   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocation_C",NULL);CHKERRQ(ierr);
1176   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocationCSR_C",NULL);CHKERRQ(ierr);
1177   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDiagonalScaleLocal_C",NULL);CHKERRQ(ierr);
1178   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_mpisbaij_C",NULL);CHKERRQ(ierr);
1179 #if defined(PETSC_HAVE_ELEMENTAL)
1180   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_elemental_C",NULL);CHKERRQ(ierr);
1181 #endif
1182   PetscFunctionReturn(0);
1183 }
1184 
1185 #undef __FUNCT__
1186 #define __FUNCT__ "MatView_MPIAIJ_Binary"
1187 PetscErrorCode MatView_MPIAIJ_Binary(Mat mat,PetscViewer viewer)
1188 {
1189   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1190   Mat_SeqAIJ     *A   = (Mat_SeqAIJ*)aij->A->data;
1191   Mat_SeqAIJ     *B   = (Mat_SeqAIJ*)aij->B->data;
1192   PetscErrorCode ierr;
1193   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
1194   int            fd;
1195   PetscInt       nz,header[4],*row_lengths,*range=0,rlen,i;
1196   PetscInt       nzmax,*column_indices,j,k,col,*garray = aij->garray,cnt,cstart = mat->cmap->rstart,rnz = 0;
1197   PetscScalar    *column_values;
1198   PetscInt       message_count,flowcontrolcount;
1199   FILE           *file;
1200 
1201   PetscFunctionBegin;
1202   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
1203   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);CHKERRQ(ierr);
1204   nz   = A->nz + B->nz;
1205   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
1206   if (!rank) {
1207     header[0] = MAT_FILE_CLASSID;
1208     header[1] = mat->rmap->N;
1209     header[2] = mat->cmap->N;
1210 
1211     ierr = MPI_Reduce(&nz,&header[3],1,MPIU_INT,MPI_SUM,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1212     ierr = PetscBinaryWrite(fd,header,4,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1213     /* get largest number of rows any processor has */
1214     rlen  = mat->rmap->n;
1215     range = mat->rmap->range;
1216     for (i=1; i<size; i++) rlen = PetscMax(rlen,range[i+1] - range[i]);
1217   } else {
1218     ierr = MPI_Reduce(&nz,0,1,MPIU_INT,MPI_SUM,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1219     rlen = mat->rmap->n;
1220   }
1221 
1222   /* load up the local row counts */
1223   ierr = PetscMalloc1(rlen+1,&row_lengths);CHKERRQ(ierr);
1224   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];
1225 
1226   /* store the row lengths to the file */
1227   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1228   if (!rank) {
1229     ierr = PetscBinaryWrite(fd,row_lengths,mat->rmap->n,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1230     for (i=1; i<size; i++) {
1231       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1232       rlen = range[i+1] - range[i];
1233       ierr = MPIULong_Recv(row_lengths,rlen,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1234       ierr = PetscBinaryWrite(fd,row_lengths,rlen,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1235     }
1236     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1237   } else {
1238     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1239     ierr = MPIULong_Send(row_lengths,mat->rmap->n,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1240     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1241   }
1242   ierr = PetscFree(row_lengths);CHKERRQ(ierr);
1243 
1244   /* load up the local column indices */
1245   nzmax = nz; /* th processor needs space a largest processor needs */
1246   ierr  = MPI_Reduce(&nz,&nzmax,1,MPIU_INT,MPI_MAX,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1247   ierr  = PetscMalloc1(nzmax+1,&column_indices);CHKERRQ(ierr);
1248   cnt   = 0;
1249   for (i=0; i<mat->rmap->n; i++) {
1250     for (j=B->i[i]; j<B->i[i+1]; j++) {
1251       if ((col = garray[B->j[j]]) > cstart) break;
1252       column_indices[cnt++] = col;
1253     }
1254     for (k=A->i[i]; k<A->i[i+1]; k++) column_indices[cnt++] = A->j[k] + cstart;
1255     for (; j<B->i[i+1]; j++) column_indices[cnt++] = garray[B->j[j]];
1256   }
1257   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);
1258 
1259   /* store the column indices to the file */
1260   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1261   if (!rank) {
1262     MPI_Status status;
1263     ierr = PetscBinaryWrite(fd,column_indices,nz,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1264     for (i=1; i<size; i++) {
1265       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1266       ierr = MPI_Recv(&rnz,1,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat),&status);CHKERRQ(ierr);
1267       if (rnz > nzmax) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: nz = %D nzmax = %D",nz,nzmax);
1268       ierr = MPIULong_Recv(column_indices,rnz,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1269       ierr = PetscBinaryWrite(fd,column_indices,rnz,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1270     }
1271     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1272   } else {
1273     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1274     ierr = MPI_Send(&nz,1,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1275     ierr = MPIULong_Send(column_indices,nz,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1276     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1277   }
1278   ierr = PetscFree(column_indices);CHKERRQ(ierr);
1279 
1280   /* load up the local column values */
1281   ierr = PetscMalloc1(nzmax+1,&column_values);CHKERRQ(ierr);
1282   cnt  = 0;
1283   for (i=0; i<mat->rmap->n; i++) {
1284     for (j=B->i[i]; j<B->i[i+1]; j++) {
1285       if (garray[B->j[j]] > cstart) break;
1286       column_values[cnt++] = B->a[j];
1287     }
1288     for (k=A->i[i]; k<A->i[i+1]; k++) column_values[cnt++] = A->a[k];
1289     for (; j<B->i[i+1]; j++) column_values[cnt++] = B->a[j];
1290   }
1291   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);
1292 
1293   /* store the column values to the file */
1294   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1295   if (!rank) {
1296     MPI_Status status;
1297     ierr = PetscBinaryWrite(fd,column_values,nz,PETSC_SCALAR,PETSC_TRUE);CHKERRQ(ierr);
1298     for (i=1; i<size; i++) {
1299       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1300       ierr = MPI_Recv(&rnz,1,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat),&status);CHKERRQ(ierr);
1301       if (rnz > nzmax) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: nz = %D nzmax = %D",nz,nzmax);
1302       ierr = MPIULong_Recv(column_values,rnz,MPIU_SCALAR,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1303       ierr = PetscBinaryWrite(fd,column_values,rnz,PETSC_SCALAR,PETSC_TRUE);CHKERRQ(ierr);
1304     }
1305     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1306   } else {
1307     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1308     ierr = MPI_Send(&nz,1,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1309     ierr = MPIULong_Send(column_values,nz,MPIU_SCALAR,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1310     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1311   }
1312   ierr = PetscFree(column_values);CHKERRQ(ierr);
1313 
1314   ierr = PetscViewerBinaryGetInfoPointer(viewer,&file);CHKERRQ(ierr);
1315   if (file) fprintf(file,"-matload_block_size %d\n",(int)PetscAbs(mat->rmap->bs));
1316   PetscFunctionReturn(0);
1317 }
1318 
1319 #include <petscdraw.h>
1320 #undef __FUNCT__
1321 #define __FUNCT__ "MatView_MPIAIJ_ASCIIorDraworSocket"
1322 PetscErrorCode MatView_MPIAIJ_ASCIIorDraworSocket(Mat mat,PetscViewer viewer)
1323 {
1324   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)mat->data;
1325   PetscErrorCode    ierr;
1326   PetscMPIInt       rank = aij->rank,size = aij->size;
1327   PetscBool         isdraw,iascii,isbinary;
1328   PetscViewer       sviewer;
1329   PetscViewerFormat format;
1330 
1331   PetscFunctionBegin;
1332   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1333   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1334   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1335   if (iascii) {
1336     ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
1337     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
1338       MatInfo   info;
1339       PetscBool inodes;
1340 
1341       ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
1342       ierr = MatGetInfo(mat,MAT_LOCAL,&info);CHKERRQ(ierr);
1343       ierr = MatInodeGetInodeSizes(aij->A,NULL,(PetscInt**)&inodes,NULL);CHKERRQ(ierr);
1344       ierr = PetscViewerASCIIPushSynchronized(viewer);CHKERRQ(ierr);
1345       if (!inodes) {
1346         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %D nz %D nz alloced %D mem %D, not using I-node routines\n",
1347                                                   rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
1348       } else {
1349         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %D nz %D nz alloced %D mem %D, using I-node routines\n",
1350                                                   rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
1351       }
1352       ierr = MatGetInfo(aij->A,MAT_LOCAL,&info);CHKERRQ(ierr);
1353       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] on-diagonal part: nz %D \n",rank,(PetscInt)info.nz_used);CHKERRQ(ierr);
1354       ierr = MatGetInfo(aij->B,MAT_LOCAL,&info);CHKERRQ(ierr);
1355       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] off-diagonal part: nz %D \n",rank,(PetscInt)info.nz_used);CHKERRQ(ierr);
1356       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1357       ierr = PetscViewerASCIIPopSynchronized(viewer);CHKERRQ(ierr);
1358       ierr = PetscViewerASCIIPrintf(viewer,"Information on VecScatter used in matrix-vector product: \n");CHKERRQ(ierr);
1359       ierr = VecScatterView(aij->Mvctx,viewer);CHKERRQ(ierr);
1360       PetscFunctionReturn(0);
1361     } else if (format == PETSC_VIEWER_ASCII_INFO) {
1362       PetscInt inodecount,inodelimit,*inodes;
1363       ierr = MatInodeGetInodeSizes(aij->A,&inodecount,&inodes,&inodelimit);CHKERRQ(ierr);
1364       if (inodes) {
1365         ierr = PetscViewerASCIIPrintf(viewer,"using I-node (on process 0) routines: found %D nodes, limit used is %D\n",inodecount,inodelimit);CHKERRQ(ierr);
1366       } else {
1367         ierr = PetscViewerASCIIPrintf(viewer,"not using I-node (on process 0) routines\n");CHKERRQ(ierr);
1368       }
1369       PetscFunctionReturn(0);
1370     } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO) {
1371       PetscFunctionReturn(0);
1372     }
1373   } else if (isbinary) {
1374     if (size == 1) {
1375       ierr = PetscObjectSetName((PetscObject)aij->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1376       ierr = MatView(aij->A,viewer);CHKERRQ(ierr);
1377     } else {
1378       ierr = MatView_MPIAIJ_Binary(mat,viewer);CHKERRQ(ierr);
1379     }
1380     PetscFunctionReturn(0);
1381   } else if (isdraw) {
1382     PetscDraw draw;
1383     PetscBool isnull;
1384     ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
1385     ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr); if (isnull) PetscFunctionReturn(0);
1386   }
1387 
1388   {
1389     /* assemble the entire matrix onto first processor. */
1390     Mat        A;
1391     Mat_SeqAIJ *Aloc;
1392     PetscInt   M = mat->rmap->N,N = mat->cmap->N,m,*ai,*aj,row,*cols,i,*ct;
1393     MatScalar  *a;
1394 
1395     ierr = MatCreate(PetscObjectComm((PetscObject)mat),&A);CHKERRQ(ierr);
1396     if (!rank) {
1397       ierr = MatSetSizes(A,M,N,M,N);CHKERRQ(ierr);
1398     } else {
1399       ierr = MatSetSizes(A,0,0,M,N);CHKERRQ(ierr);
1400     }
1401     /* This is just a temporary matrix, so explicitly using MATMPIAIJ is probably best */
1402     ierr = MatSetType(A,MATMPIAIJ);CHKERRQ(ierr);
1403     ierr = MatMPIAIJSetPreallocation(A,0,NULL,0,NULL);CHKERRQ(ierr);
1404     ierr = MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
1405     ierr = PetscLogObjectParent((PetscObject)mat,(PetscObject)A);CHKERRQ(ierr);
1406 
1407     /* copy over the A part */
1408     Aloc = (Mat_SeqAIJ*)aij->A->data;
1409     m    = aij->A->rmap->n; ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
1410     row  = mat->rmap->rstart;
1411     for (i=0; i<ai[m]; i++) aj[i] += mat->cmap->rstart;
1412     for (i=0; i<m; i++) {
1413       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],aj,a,INSERT_VALUES);CHKERRQ(ierr);
1414       row++;
1415       a += ai[i+1]-ai[i]; aj += ai[i+1]-ai[i];
1416     }
1417     aj = Aloc->j;
1418     for (i=0; i<ai[m]; i++) aj[i] -= mat->cmap->rstart;
1419 
1420     /* copy over the B part */
1421     Aloc = (Mat_SeqAIJ*)aij->B->data;
1422     m    = aij->B->rmap->n;  ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
1423     row  = mat->rmap->rstart;
1424     ierr = PetscMalloc1(ai[m]+1,&cols);CHKERRQ(ierr);
1425     ct   = cols;
1426     for (i=0; i<ai[m]; i++) cols[i] = aij->garray[aj[i]];
1427     for (i=0; i<m; i++) {
1428       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],cols,a,INSERT_VALUES);CHKERRQ(ierr);
1429       row++;
1430       a += ai[i+1]-ai[i]; cols += ai[i+1]-ai[i];
1431     }
1432     ierr = PetscFree(ct);CHKERRQ(ierr);
1433     ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1434     ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1435     /*
1436        Everyone has to call to draw the matrix since the graphics waits are
1437        synchronized across all processors that share the PetscDraw object
1438     */
1439     ierr = PetscViewerGetSubViewer(viewer,PETSC_COMM_SELF,&sviewer);CHKERRQ(ierr);
1440     if (!rank) {
1441       ierr = PetscObjectSetName((PetscObject)((Mat_MPIAIJ*)(A->data))->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1442       ierr = MatView_SeqAIJ(((Mat_MPIAIJ*)(A->data))->A,sviewer);CHKERRQ(ierr);
1443     }
1444     ierr = PetscViewerRestoreSubViewer(viewer,PETSC_COMM_SELF,&sviewer);CHKERRQ(ierr);
1445     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1446     ierr = MatDestroy(&A);CHKERRQ(ierr);
1447   }
1448   PetscFunctionReturn(0);
1449 }
1450 
1451 #undef __FUNCT__
1452 #define __FUNCT__ "MatView_MPIAIJ"
1453 PetscErrorCode MatView_MPIAIJ(Mat mat,PetscViewer viewer)
1454 {
1455   PetscErrorCode ierr;
1456   PetscBool      iascii,isdraw,issocket,isbinary;
1457 
1458   PetscFunctionBegin;
1459   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1460   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1461   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1462   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSOCKET,&issocket);CHKERRQ(ierr);
1463   if (iascii || isdraw || isbinary || issocket) {
1464     ierr = MatView_MPIAIJ_ASCIIorDraworSocket(mat,viewer);CHKERRQ(ierr);
1465   }
1466   PetscFunctionReturn(0);
1467 }
1468 
1469 #undef __FUNCT__
1470 #define __FUNCT__ "MatSOR_MPIAIJ"
1471 PetscErrorCode MatSOR_MPIAIJ(Mat matin,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
1472 {
1473   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1474   PetscErrorCode ierr;
1475   Vec            bb1 = 0;
1476   PetscBool      hasop;
1477 
1478   PetscFunctionBegin;
1479   if (flag == SOR_APPLY_UPPER) {
1480     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1481     PetscFunctionReturn(0);
1482   }
1483 
1484   if (its > 1 || ~flag & SOR_ZERO_INITIAL_GUESS || flag & SOR_EISENSTAT) {
1485     ierr = VecDuplicate(bb,&bb1);CHKERRQ(ierr);
1486   }
1487 
1488   if ((flag & SOR_LOCAL_SYMMETRIC_SWEEP) == SOR_LOCAL_SYMMETRIC_SWEEP) {
1489     if (flag & SOR_ZERO_INITIAL_GUESS) {
1490       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1491       its--;
1492     }
1493 
1494     while (its--) {
1495       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1496       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1497 
1498       /* update rhs: bb1 = bb - B*x */
1499       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1500       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1501 
1502       /* local sweep */
1503       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_SYMMETRIC_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1504     }
1505   } else if (flag & SOR_LOCAL_FORWARD_SWEEP) {
1506     if (flag & SOR_ZERO_INITIAL_GUESS) {
1507       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1508       its--;
1509     }
1510     while (its--) {
1511       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1512       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1513 
1514       /* update rhs: bb1 = bb - B*x */
1515       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1516       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1517 
1518       /* local sweep */
1519       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_FORWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1520     }
1521   } else if (flag & SOR_LOCAL_BACKWARD_SWEEP) {
1522     if (flag & SOR_ZERO_INITIAL_GUESS) {
1523       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1524       its--;
1525     }
1526     while (its--) {
1527       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1528       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1529 
1530       /* update rhs: bb1 = bb - B*x */
1531       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1532       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1533 
1534       /* local sweep */
1535       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_BACKWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1536     }
1537   } else if (flag & SOR_EISENSTAT) {
1538     Vec xx1;
1539 
1540     ierr = VecDuplicate(bb,&xx1);CHKERRQ(ierr);
1541     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_BACKWARD_SWEEP),fshift,lits,1,xx);CHKERRQ(ierr);
1542 
1543     ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1544     ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1545     if (!mat->diag) {
1546       ierr = MatCreateVecs(matin,&mat->diag,NULL);CHKERRQ(ierr);
1547       ierr = MatGetDiagonal(matin,mat->diag);CHKERRQ(ierr);
1548     }
1549     ierr = MatHasOperation(matin,MATOP_MULT_DIAGONAL_BLOCK,&hasop);CHKERRQ(ierr);
1550     if (hasop) {
1551       ierr = MatMultDiagonalBlock(matin,xx,bb1);CHKERRQ(ierr);
1552     } else {
1553       ierr = VecPointwiseMult(bb1,mat->diag,xx);CHKERRQ(ierr);
1554     }
1555     ierr = VecAYPX(bb1,(omega-2.0)/omega,bb);CHKERRQ(ierr);
1556 
1557     ierr = MatMultAdd(mat->B,mat->lvec,bb1,bb1);CHKERRQ(ierr);
1558 
1559     /* local sweep */
1560     ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_FORWARD_SWEEP),fshift,lits,1,xx1);CHKERRQ(ierr);
1561     ierr = VecAXPY(xx,1.0,xx1);CHKERRQ(ierr);
1562     ierr = VecDestroy(&xx1);CHKERRQ(ierr);
1563   } else SETERRQ(PetscObjectComm((PetscObject)matin),PETSC_ERR_SUP,"Parallel SOR not supported");
1564 
1565   ierr = VecDestroy(&bb1);CHKERRQ(ierr);
1566 
1567   matin->errortype = mat->A->errortype;
1568   PetscFunctionReturn(0);
1569 }
1570 
1571 #undef __FUNCT__
1572 #define __FUNCT__ "MatPermute_MPIAIJ"
1573 PetscErrorCode MatPermute_MPIAIJ(Mat A,IS rowp,IS colp,Mat *B)
1574 {
1575   Mat            aA,aB,Aperm;
1576   const PetscInt *rwant,*cwant,*gcols,*ai,*bi,*aj,*bj;
1577   PetscScalar    *aa,*ba;
1578   PetscInt       i,j,m,n,ng,anz,bnz,*dnnz,*onnz,*tdnnz,*tonnz,*rdest,*cdest,*work,*gcdest;
1579   PetscSF        rowsf,sf;
1580   IS             parcolp = NULL;
1581   PetscBool      done;
1582   PetscErrorCode ierr;
1583 
1584   PetscFunctionBegin;
1585   ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
1586   ierr = ISGetIndices(rowp,&rwant);CHKERRQ(ierr);
1587   ierr = ISGetIndices(colp,&cwant);CHKERRQ(ierr);
1588   ierr = PetscMalloc3(PetscMax(m,n),&work,m,&rdest,n,&cdest);CHKERRQ(ierr);
1589 
1590   /* Invert row permutation to find out where my rows should go */
1591   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&rowsf);CHKERRQ(ierr);
1592   ierr = PetscSFSetGraphLayout(rowsf,A->rmap,A->rmap->n,NULL,PETSC_OWN_POINTER,rwant);CHKERRQ(ierr);
1593   ierr = PetscSFSetFromOptions(rowsf);CHKERRQ(ierr);
1594   for (i=0; i<m; i++) work[i] = A->rmap->rstart + i;
1595   ierr = PetscSFReduceBegin(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1596   ierr = PetscSFReduceEnd(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1597 
1598   /* Invert column permutation to find out where my columns should go */
1599   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1600   ierr = PetscSFSetGraphLayout(sf,A->cmap,A->cmap->n,NULL,PETSC_OWN_POINTER,cwant);CHKERRQ(ierr);
1601   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1602   for (i=0; i<n; i++) work[i] = A->cmap->rstart + i;
1603   ierr = PetscSFReduceBegin(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1604   ierr = PetscSFReduceEnd(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1605   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1606 
1607   ierr = ISRestoreIndices(rowp,&rwant);CHKERRQ(ierr);
1608   ierr = ISRestoreIndices(colp,&cwant);CHKERRQ(ierr);
1609   ierr = MatMPIAIJGetSeqAIJ(A,&aA,&aB,&gcols);CHKERRQ(ierr);
1610 
1611   /* Find out where my gcols should go */
1612   ierr = MatGetSize(aB,NULL,&ng);CHKERRQ(ierr);
1613   ierr = PetscMalloc1(ng,&gcdest);CHKERRQ(ierr);
1614   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1615   ierr = PetscSFSetGraphLayout(sf,A->cmap,ng,NULL,PETSC_OWN_POINTER,gcols);CHKERRQ(ierr);
1616   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1617   ierr = PetscSFBcastBegin(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1618   ierr = PetscSFBcastEnd(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1619   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1620 
1621   ierr = PetscCalloc4(m,&dnnz,m,&onnz,m,&tdnnz,m,&tonnz);CHKERRQ(ierr);
1622   ierr = MatGetRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1623   ierr = MatGetRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1624   for (i=0; i<m; i++) {
1625     PetscInt row = rdest[i],rowner;
1626     ierr = PetscLayoutFindOwner(A->rmap,row,&rowner);CHKERRQ(ierr);
1627     for (j=ai[i]; j<ai[i+1]; j++) {
1628       PetscInt cowner,col = cdest[aj[j]];
1629       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr); /* Could build an index for the columns to eliminate this search */
1630       if (rowner == cowner) dnnz[i]++;
1631       else onnz[i]++;
1632     }
1633     for (j=bi[i]; j<bi[i+1]; j++) {
1634       PetscInt cowner,col = gcdest[bj[j]];
1635       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr);
1636       if (rowner == cowner) dnnz[i]++;
1637       else onnz[i]++;
1638     }
1639   }
1640   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1641   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1642   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1643   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1644   ierr = PetscSFDestroy(&rowsf);CHKERRQ(ierr);
1645 
1646   ierr = MatCreateAIJ(PetscObjectComm((PetscObject)A),A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N,0,tdnnz,0,tonnz,&Aperm);CHKERRQ(ierr);
1647   ierr = MatSeqAIJGetArray(aA,&aa);CHKERRQ(ierr);
1648   ierr = MatSeqAIJGetArray(aB,&ba);CHKERRQ(ierr);
1649   for (i=0; i<m; i++) {
1650     PetscInt *acols = dnnz,*bcols = onnz; /* Repurpose now-unneeded arrays */
1651     PetscInt j0,rowlen;
1652     rowlen = ai[i+1] - ai[i];
1653     for (j0=j=0; j<rowlen; j0=j) { /* rowlen could be larger than number of rows m, so sum in batches */
1654       for ( ; j<PetscMin(rowlen,j0+m); j++) acols[j-j0] = cdest[aj[ai[i]+j]];
1655       ierr = MatSetValues(Aperm,1,&rdest[i],j-j0,acols,aa+ai[i]+j0,INSERT_VALUES);CHKERRQ(ierr);
1656     }
1657     rowlen = bi[i+1] - bi[i];
1658     for (j0=j=0; j<rowlen; j0=j) {
1659       for ( ; j<PetscMin(rowlen,j0+m); j++) bcols[j-j0] = gcdest[bj[bi[i]+j]];
1660       ierr = MatSetValues(Aperm,1,&rdest[i],j-j0,bcols,ba+bi[i]+j0,INSERT_VALUES);CHKERRQ(ierr);
1661     }
1662   }
1663   ierr = MatAssemblyBegin(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1664   ierr = MatAssemblyEnd(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1665   ierr = MatRestoreRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1666   ierr = MatRestoreRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1667   ierr = MatSeqAIJRestoreArray(aA,&aa);CHKERRQ(ierr);
1668   ierr = MatSeqAIJRestoreArray(aB,&ba);CHKERRQ(ierr);
1669   ierr = PetscFree4(dnnz,onnz,tdnnz,tonnz);CHKERRQ(ierr);
1670   ierr = PetscFree3(work,rdest,cdest);CHKERRQ(ierr);
1671   ierr = PetscFree(gcdest);CHKERRQ(ierr);
1672   if (parcolp) {ierr = ISDestroy(&colp);CHKERRQ(ierr);}
1673   *B = Aperm;
1674   PetscFunctionReturn(0);
1675 }
1676 
1677 #undef __FUNCT__
1678 #define __FUNCT__ "MatGetGhosts_MPIAIJ"
1679 PetscErrorCode  MatGetGhosts_MPIAIJ(Mat mat,PetscInt *nghosts,const PetscInt *ghosts[])
1680 {
1681   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1682   PetscErrorCode ierr;
1683 
1684   PetscFunctionBegin;
1685   ierr = MatGetSize(aij->B,NULL,nghosts);CHKERRQ(ierr);
1686   if (ghosts) *ghosts = aij->garray;
1687   PetscFunctionReturn(0);
1688 }
1689 
1690 #undef __FUNCT__
1691 #define __FUNCT__ "MatGetInfo_MPIAIJ"
1692 PetscErrorCode MatGetInfo_MPIAIJ(Mat matin,MatInfoType flag,MatInfo *info)
1693 {
1694   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1695   Mat            A    = mat->A,B = mat->B;
1696   PetscErrorCode ierr;
1697   PetscReal      isend[5],irecv[5];
1698 
1699   PetscFunctionBegin;
1700   info->block_size = 1.0;
1701   ierr             = MatGetInfo(A,MAT_LOCAL,info);CHKERRQ(ierr);
1702 
1703   isend[0] = info->nz_used; isend[1] = info->nz_allocated; isend[2] = info->nz_unneeded;
1704   isend[3] = info->memory;  isend[4] = info->mallocs;
1705 
1706   ierr = MatGetInfo(B,MAT_LOCAL,info);CHKERRQ(ierr);
1707 
1708   isend[0] += info->nz_used; isend[1] += info->nz_allocated; isend[2] += info->nz_unneeded;
1709   isend[3] += info->memory;  isend[4] += info->mallocs;
1710   if (flag == MAT_LOCAL) {
1711     info->nz_used      = isend[0];
1712     info->nz_allocated = isend[1];
1713     info->nz_unneeded  = isend[2];
1714     info->memory       = isend[3];
1715     info->mallocs      = isend[4];
1716   } else if (flag == MAT_GLOBAL_MAX) {
1717     ierr = MPIU_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1718 
1719     info->nz_used      = irecv[0];
1720     info->nz_allocated = irecv[1];
1721     info->nz_unneeded  = irecv[2];
1722     info->memory       = irecv[3];
1723     info->mallocs      = irecv[4];
1724   } else if (flag == MAT_GLOBAL_SUM) {
1725     ierr = MPIU_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1726 
1727     info->nz_used      = irecv[0];
1728     info->nz_allocated = irecv[1];
1729     info->nz_unneeded  = irecv[2];
1730     info->memory       = irecv[3];
1731     info->mallocs      = irecv[4];
1732   }
1733   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
1734   info->fill_ratio_needed = 0;
1735   info->factor_mallocs    = 0;
1736   PetscFunctionReturn(0);
1737 }
1738 
1739 #undef __FUNCT__
1740 #define __FUNCT__ "MatSetOption_MPIAIJ"
1741 PetscErrorCode MatSetOption_MPIAIJ(Mat A,MatOption op,PetscBool flg)
1742 {
1743   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1744   PetscErrorCode ierr;
1745 
1746   PetscFunctionBegin;
1747   switch (op) {
1748   case MAT_NEW_NONZERO_LOCATIONS:
1749   case MAT_NEW_NONZERO_ALLOCATION_ERR:
1750   case MAT_UNUSED_NONZERO_LOCATION_ERR:
1751   case MAT_KEEP_NONZERO_PATTERN:
1752   case MAT_NEW_NONZERO_LOCATION_ERR:
1753   case MAT_USE_INODES:
1754   case MAT_IGNORE_ZERO_ENTRIES:
1755     MatCheckPreallocated(A,1);
1756     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1757     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1758     break;
1759   case MAT_ROW_ORIENTED:
1760     a->roworiented = flg;
1761 
1762     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1763     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1764     break;
1765   case MAT_NEW_DIAGONALS:
1766     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
1767     break;
1768   case MAT_IGNORE_OFF_PROC_ENTRIES:
1769     a->donotstash = flg;
1770     break;
1771   case MAT_SPD:
1772     A->spd_set = PETSC_TRUE;
1773     A->spd     = flg;
1774     if (flg) {
1775       A->symmetric                  = PETSC_TRUE;
1776       A->structurally_symmetric     = PETSC_TRUE;
1777       A->symmetric_set              = PETSC_TRUE;
1778       A->structurally_symmetric_set = PETSC_TRUE;
1779     }
1780     break;
1781   case MAT_SYMMETRIC:
1782     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1783     break;
1784   case MAT_STRUCTURALLY_SYMMETRIC:
1785     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1786     break;
1787   case MAT_HERMITIAN:
1788     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1789     break;
1790   case MAT_SYMMETRY_ETERNAL:
1791     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1792     break;
1793   default:
1794     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %d",op);
1795   }
1796   PetscFunctionReturn(0);
1797 }
1798 
1799 #undef __FUNCT__
1800 #define __FUNCT__ "MatGetRow_MPIAIJ"
1801 PetscErrorCode MatGetRow_MPIAIJ(Mat matin,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1802 {
1803   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1804   PetscScalar    *vworkA,*vworkB,**pvA,**pvB,*v_p;
1805   PetscErrorCode ierr;
1806   PetscInt       i,*cworkA,*cworkB,**pcA,**pcB,cstart = matin->cmap->rstart;
1807   PetscInt       nztot,nzA,nzB,lrow,rstart = matin->rmap->rstart,rend = matin->rmap->rend;
1808   PetscInt       *cmap,*idx_p;
1809 
1810   PetscFunctionBegin;
1811   if (mat->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Already active");
1812   mat->getrowactive = PETSC_TRUE;
1813 
1814   if (!mat->rowvalues && (idx || v)) {
1815     /*
1816         allocate enough space to hold information from the longest row.
1817     */
1818     Mat_SeqAIJ *Aa = (Mat_SeqAIJ*)mat->A->data,*Ba = (Mat_SeqAIJ*)mat->B->data;
1819     PetscInt   max = 1,tmp;
1820     for (i=0; i<matin->rmap->n; i++) {
1821       tmp = Aa->i[i+1] - Aa->i[i] + Ba->i[i+1] - Ba->i[i];
1822       if (max < tmp) max = tmp;
1823     }
1824     ierr = PetscMalloc2(max,&mat->rowvalues,max,&mat->rowindices);CHKERRQ(ierr);
1825   }
1826 
1827   if (row < rstart || row >= rend) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Only local rows");
1828   lrow = row - rstart;
1829 
1830   pvA = &vworkA; pcA = &cworkA; pvB = &vworkB; pcB = &cworkB;
1831   if (!v)   {pvA = 0; pvB = 0;}
1832   if (!idx) {pcA = 0; if (!v) pcB = 0;}
1833   ierr  = (*mat->A->ops->getrow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1834   ierr  = (*mat->B->ops->getrow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1835   nztot = nzA + nzB;
1836 
1837   cmap = mat->garray;
1838   if (v  || idx) {
1839     if (nztot) {
1840       /* Sort by increasing column numbers, assuming A and B already sorted */
1841       PetscInt imark = -1;
1842       if (v) {
1843         *v = v_p = mat->rowvalues;
1844         for (i=0; i<nzB; i++) {
1845           if (cmap[cworkB[i]] < cstart) v_p[i] = vworkB[i];
1846           else break;
1847         }
1848         imark = i;
1849         for (i=0; i<nzA; i++)     v_p[imark+i] = vworkA[i];
1850         for (i=imark; i<nzB; i++) v_p[nzA+i]   = vworkB[i];
1851       }
1852       if (idx) {
1853         *idx = idx_p = mat->rowindices;
1854         if (imark > -1) {
1855           for (i=0; i<imark; i++) {
1856             idx_p[i] = cmap[cworkB[i]];
1857           }
1858         } else {
1859           for (i=0; i<nzB; i++) {
1860             if (cmap[cworkB[i]] < cstart) idx_p[i] = cmap[cworkB[i]];
1861             else break;
1862           }
1863           imark = i;
1864         }
1865         for (i=0; i<nzA; i++)     idx_p[imark+i] = cstart + cworkA[i];
1866         for (i=imark; i<nzB; i++) idx_p[nzA+i]   = cmap[cworkB[i]];
1867       }
1868     } else {
1869       if (idx) *idx = 0;
1870       if (v)   *v   = 0;
1871     }
1872   }
1873   *nz  = nztot;
1874   ierr = (*mat->A->ops->restorerow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1875   ierr = (*mat->B->ops->restorerow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1876   PetscFunctionReturn(0);
1877 }
1878 
1879 #undef __FUNCT__
1880 #define __FUNCT__ "MatRestoreRow_MPIAIJ"
1881 PetscErrorCode MatRestoreRow_MPIAIJ(Mat mat,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1882 {
1883   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1884 
1885   PetscFunctionBegin;
1886   if (!aij->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"MatGetRow() must be called first");
1887   aij->getrowactive = PETSC_FALSE;
1888   PetscFunctionReturn(0);
1889 }
1890 
1891 #undef __FUNCT__
1892 #define __FUNCT__ "MatNorm_MPIAIJ"
1893 PetscErrorCode MatNorm_MPIAIJ(Mat mat,NormType type,PetscReal *norm)
1894 {
1895   Mat_MPIAIJ     *aij  = (Mat_MPIAIJ*)mat->data;
1896   Mat_SeqAIJ     *amat = (Mat_SeqAIJ*)aij->A->data,*bmat = (Mat_SeqAIJ*)aij->B->data;
1897   PetscErrorCode ierr;
1898   PetscInt       i,j,cstart = mat->cmap->rstart;
1899   PetscReal      sum = 0.0;
1900   MatScalar      *v;
1901 
1902   PetscFunctionBegin;
1903   if (aij->size == 1) {
1904     ierr =  MatNorm(aij->A,type,norm);CHKERRQ(ierr);
1905   } else {
1906     if (type == NORM_FROBENIUS) {
1907       v = amat->a;
1908       for (i=0; i<amat->nz; i++) {
1909         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1910       }
1911       v = bmat->a;
1912       for (i=0; i<bmat->nz; i++) {
1913         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1914       }
1915       ierr  = MPIU_Allreduce(&sum,norm,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1916       *norm = PetscSqrtReal(*norm);
1917     } else if (type == NORM_1) { /* max column norm */
1918       PetscReal *tmp,*tmp2;
1919       PetscInt  *jj,*garray = aij->garray;
1920       ierr  = PetscCalloc1(mat->cmap->N+1,&tmp);CHKERRQ(ierr);
1921       ierr  = PetscMalloc1(mat->cmap->N+1,&tmp2);CHKERRQ(ierr);
1922       *norm = 0.0;
1923       v     = amat->a; jj = amat->j;
1924       for (j=0; j<amat->nz; j++) {
1925         tmp[cstart + *jj++] += PetscAbsScalar(*v);  v++;
1926       }
1927       v = bmat->a; jj = bmat->j;
1928       for (j=0; j<bmat->nz; j++) {
1929         tmp[garray[*jj++]] += PetscAbsScalar(*v); v++;
1930       }
1931       ierr = MPIU_Allreduce(tmp,tmp2,mat->cmap->N,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1932       for (j=0; j<mat->cmap->N; j++) {
1933         if (tmp2[j] > *norm) *norm = tmp2[j];
1934       }
1935       ierr = PetscFree(tmp);CHKERRQ(ierr);
1936       ierr = PetscFree(tmp2);CHKERRQ(ierr);
1937     } else if (type == NORM_INFINITY) { /* max row norm */
1938       PetscReal ntemp = 0.0;
1939       for (j=0; j<aij->A->rmap->n; j++) {
1940         v   = amat->a + amat->i[j];
1941         sum = 0.0;
1942         for (i=0; i<amat->i[j+1]-amat->i[j]; i++) {
1943           sum += PetscAbsScalar(*v); v++;
1944         }
1945         v = bmat->a + bmat->i[j];
1946         for (i=0; i<bmat->i[j+1]-bmat->i[j]; i++) {
1947           sum += PetscAbsScalar(*v); v++;
1948         }
1949         if (sum > ntemp) ntemp = sum;
1950       }
1951       ierr = MPIU_Allreduce(&ntemp,norm,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1952     } else SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"No support for two norm");
1953   }
1954   PetscFunctionReturn(0);
1955 }
1956 
1957 #undef __FUNCT__
1958 #define __FUNCT__ "MatTranspose_MPIAIJ"
1959 PetscErrorCode MatTranspose_MPIAIJ(Mat A,MatReuse reuse,Mat *matout)
1960 {
1961   Mat_MPIAIJ     *a   = (Mat_MPIAIJ*)A->data;
1962   Mat_SeqAIJ     *Aloc=(Mat_SeqAIJ*)a->A->data,*Bloc=(Mat_SeqAIJ*)a->B->data;
1963   PetscErrorCode ierr;
1964   PetscInt       M      = A->rmap->N,N = A->cmap->N,ma,na,mb,nb,*ai,*aj,*bi,*bj,row,*cols,*cols_tmp,i;
1965   PetscInt       cstart = A->cmap->rstart,ncol;
1966   Mat            B;
1967   MatScalar      *array;
1968 
1969   PetscFunctionBegin;
1970   if (reuse == MAT_REUSE_MATRIX && A == *matout && M != N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Square matrix only for in-place");
1971 
1972   ma = A->rmap->n; na = A->cmap->n; mb = a->B->rmap->n; nb = a->B->cmap->n;
1973   ai = Aloc->i; aj = Aloc->j;
1974   bi = Bloc->i; bj = Bloc->j;
1975   if (reuse == MAT_INITIAL_MATRIX || *matout == A) {
1976     PetscInt             *d_nnz,*g_nnz,*o_nnz;
1977     PetscSFNode          *oloc;
1978     PETSC_UNUSED PetscSF sf;
1979 
1980     ierr = PetscMalloc4(na,&d_nnz,na,&o_nnz,nb,&g_nnz,nb,&oloc);CHKERRQ(ierr);
1981     /* compute d_nnz for preallocation */
1982     ierr = PetscMemzero(d_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1983     for (i=0; i<ai[ma]; i++) {
1984       d_nnz[aj[i]]++;
1985       aj[i] += cstart; /* global col index to be used by MatSetValues() */
1986     }
1987     /* compute local off-diagonal contributions */
1988     ierr = PetscMemzero(g_nnz,nb*sizeof(PetscInt));CHKERRQ(ierr);
1989     for (i=0; i<bi[ma]; i++) g_nnz[bj[i]]++;
1990     /* map those to global */
1991     ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1992     ierr = PetscSFSetGraphLayout(sf,A->cmap,nb,NULL,PETSC_USE_POINTER,a->garray);CHKERRQ(ierr);
1993     ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1994     ierr = PetscMemzero(o_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1995     ierr = PetscSFReduceBegin(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
1996     ierr = PetscSFReduceEnd(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
1997     ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1998 
1999     ierr = MatCreate(PetscObjectComm((PetscObject)A),&B);CHKERRQ(ierr);
2000     ierr = MatSetSizes(B,A->cmap->n,A->rmap->n,N,M);CHKERRQ(ierr);
2001     ierr = MatSetBlockSizes(B,PetscAbs(A->cmap->bs),PetscAbs(A->rmap->bs));CHKERRQ(ierr);
2002     ierr = MatSetType(B,((PetscObject)A)->type_name);CHKERRQ(ierr);
2003     ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
2004     ierr = PetscFree4(d_nnz,o_nnz,g_nnz,oloc);CHKERRQ(ierr);
2005   } else {
2006     B    = *matout;
2007     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
2008     for (i=0; i<ai[ma]; i++) aj[i] += cstart; /* global col index to be used by MatSetValues() */
2009   }
2010 
2011   /* copy over the A part */
2012   array = Aloc->a;
2013   row   = A->rmap->rstart;
2014   for (i=0; i<ma; i++) {
2015     ncol = ai[i+1]-ai[i];
2016     ierr = MatSetValues(B,ncol,aj,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
2017     row++;
2018     array += ncol; aj += ncol;
2019   }
2020   aj = Aloc->j;
2021   for (i=0; i<ai[ma]; i++) aj[i] -= cstart; /* resume local col index */
2022 
2023   /* copy over the B part */
2024   ierr  = PetscCalloc1(bi[mb],&cols);CHKERRQ(ierr);
2025   array = Bloc->a;
2026   row   = A->rmap->rstart;
2027   for (i=0; i<bi[mb]; i++) cols[i] = a->garray[bj[i]];
2028   cols_tmp = cols;
2029   for (i=0; i<mb; i++) {
2030     ncol = bi[i+1]-bi[i];
2031     ierr = MatSetValues(B,ncol,cols_tmp,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
2032     row++;
2033     array += ncol; cols_tmp += ncol;
2034   }
2035   ierr = PetscFree(cols);CHKERRQ(ierr);
2036 
2037   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2038   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2039   if (reuse == MAT_INITIAL_MATRIX || *matout != A) {
2040     *matout = B;
2041   } else {
2042     ierr = MatHeaderMerge(A,&B);CHKERRQ(ierr);
2043   }
2044   PetscFunctionReturn(0);
2045 }
2046 
2047 #undef __FUNCT__
2048 #define __FUNCT__ "MatDiagonalScale_MPIAIJ"
2049 PetscErrorCode MatDiagonalScale_MPIAIJ(Mat mat,Vec ll,Vec rr)
2050 {
2051   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2052   Mat            a    = aij->A,b = aij->B;
2053   PetscErrorCode ierr;
2054   PetscInt       s1,s2,s3;
2055 
2056   PetscFunctionBegin;
2057   ierr = MatGetLocalSize(mat,&s2,&s3);CHKERRQ(ierr);
2058   if (rr) {
2059     ierr = VecGetLocalSize(rr,&s1);CHKERRQ(ierr);
2060     if (s1!=s3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"right vector non-conforming local size");
2061     /* Overlap communication with computation. */
2062     ierr = VecScatterBegin(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2063   }
2064   if (ll) {
2065     ierr = VecGetLocalSize(ll,&s1);CHKERRQ(ierr);
2066     if (s1!=s2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"left vector non-conforming local size");
2067     ierr = (*b->ops->diagonalscale)(b,ll,0);CHKERRQ(ierr);
2068   }
2069   /* scale  the diagonal block */
2070   ierr = (*a->ops->diagonalscale)(a,ll,rr);CHKERRQ(ierr);
2071 
2072   if (rr) {
2073     /* Do a scatter end and then right scale the off-diagonal block */
2074     ierr = VecScatterEnd(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2075     ierr = (*b->ops->diagonalscale)(b,0,aij->lvec);CHKERRQ(ierr);
2076   }
2077   PetscFunctionReturn(0);
2078 }
2079 
2080 #undef __FUNCT__
2081 #define __FUNCT__ "MatSetUnfactored_MPIAIJ"
2082 PetscErrorCode MatSetUnfactored_MPIAIJ(Mat A)
2083 {
2084   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2085   PetscErrorCode ierr;
2086 
2087   PetscFunctionBegin;
2088   ierr = MatSetUnfactored(a->A);CHKERRQ(ierr);
2089   PetscFunctionReturn(0);
2090 }
2091 
2092 #undef __FUNCT__
2093 #define __FUNCT__ "MatEqual_MPIAIJ"
2094 PetscErrorCode MatEqual_MPIAIJ(Mat A,Mat B,PetscBool  *flag)
2095 {
2096   Mat_MPIAIJ     *matB = (Mat_MPIAIJ*)B->data,*matA = (Mat_MPIAIJ*)A->data;
2097   Mat            a,b,c,d;
2098   PetscBool      flg;
2099   PetscErrorCode ierr;
2100 
2101   PetscFunctionBegin;
2102   a = matA->A; b = matA->B;
2103   c = matB->A; d = matB->B;
2104 
2105   ierr = MatEqual(a,c,&flg);CHKERRQ(ierr);
2106   if (flg) {
2107     ierr = MatEqual(b,d,&flg);CHKERRQ(ierr);
2108   }
2109   ierr = MPIU_Allreduce(&flg,flag,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
2110   PetscFunctionReturn(0);
2111 }
2112 
2113 #undef __FUNCT__
2114 #define __FUNCT__ "MatCopy_MPIAIJ"
2115 PetscErrorCode MatCopy_MPIAIJ(Mat A,Mat B,MatStructure str)
2116 {
2117   PetscErrorCode ierr;
2118   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2119   Mat_MPIAIJ     *b = (Mat_MPIAIJ*)B->data;
2120 
2121   PetscFunctionBegin;
2122   /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
2123   if ((str != SAME_NONZERO_PATTERN) || (A->ops->copy != B->ops->copy)) {
2124     /* because of the column compression in the off-processor part of the matrix a->B,
2125        the number of columns in a->B and b->B may be different, hence we cannot call
2126        the MatCopy() directly on the two parts. If need be, we can provide a more
2127        efficient copy than the MatCopy_Basic() by first uncompressing the a->B matrices
2128        then copying the submatrices */
2129     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
2130   } else {
2131     ierr = MatCopy(a->A,b->A,str);CHKERRQ(ierr);
2132     ierr = MatCopy(a->B,b->B,str);CHKERRQ(ierr);
2133   }
2134   PetscFunctionReturn(0);
2135 }
2136 
2137 #undef __FUNCT__
2138 #define __FUNCT__ "MatSetUp_MPIAIJ"
2139 PetscErrorCode MatSetUp_MPIAIJ(Mat A)
2140 {
2141   PetscErrorCode ierr;
2142 
2143   PetscFunctionBegin;
2144   ierr =  MatMPIAIJSetPreallocation(A,PETSC_DEFAULT,0,PETSC_DEFAULT,0);CHKERRQ(ierr);
2145   PetscFunctionReturn(0);
2146 }
2147 
2148 /*
2149    Computes the number of nonzeros per row needed for preallocation when X and Y
2150    have different nonzero structure.
2151 */
2152 #undef __FUNCT__
2153 #define __FUNCT__ "MatAXPYGetPreallocation_MPIX_private"
2154 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)
2155 {
2156   PetscInt       i,j,k,nzx,nzy;
2157 
2158   PetscFunctionBegin;
2159   /* Set the number of nonzeros in the new matrix */
2160   for (i=0; i<m; i++) {
2161     const PetscInt *xjj = xj+xi[i],*yjj = yj+yi[i];
2162     nzx = xi[i+1] - xi[i];
2163     nzy = yi[i+1] - yi[i];
2164     nnz[i] = 0;
2165     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2166       for (; k<nzy && yltog[yjj[k]]<xltog[xjj[j]]; k++) nnz[i]++; /* Catch up to X */
2167       if (k<nzy && yltog[yjj[k]]==xltog[xjj[j]]) k++;             /* Skip duplicate */
2168       nnz[i]++;
2169     }
2170     for (; k<nzy; k++) nnz[i]++;
2171   }
2172   PetscFunctionReturn(0);
2173 }
2174 
2175 /* This is the same as MatAXPYGetPreallocation_SeqAIJ, except that the local-to-global map is provided */
2176 #undef __FUNCT__
2177 #define __FUNCT__ "MatAXPYGetPreallocation_MPIAIJ"
2178 static PetscErrorCode MatAXPYGetPreallocation_MPIAIJ(Mat Y,const PetscInt *yltog,Mat X,const PetscInt *xltog,PetscInt *nnz)
2179 {
2180   PetscErrorCode ierr;
2181   PetscInt       m = Y->rmap->N;
2182   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data;
2183   Mat_SeqAIJ     *y = (Mat_SeqAIJ*)Y->data;
2184 
2185   PetscFunctionBegin;
2186   ierr = MatAXPYGetPreallocation_MPIX_private(m,x->i,x->j,xltog,y->i,y->j,yltog,nnz);CHKERRQ(ierr);
2187   PetscFunctionReturn(0);
2188 }
2189 
2190 #undef __FUNCT__
2191 #define __FUNCT__ "MatAXPY_MPIAIJ"
2192 PetscErrorCode MatAXPY_MPIAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
2193 {
2194   PetscErrorCode ierr;
2195   Mat_MPIAIJ     *xx = (Mat_MPIAIJ*)X->data,*yy = (Mat_MPIAIJ*)Y->data;
2196   PetscBLASInt   bnz,one=1;
2197   Mat_SeqAIJ     *x,*y;
2198 
2199   PetscFunctionBegin;
2200   if (str == SAME_NONZERO_PATTERN) {
2201     PetscScalar alpha = a;
2202     x    = (Mat_SeqAIJ*)xx->A->data;
2203     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2204     y    = (Mat_SeqAIJ*)yy->A->data;
2205     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2206     x    = (Mat_SeqAIJ*)xx->B->data;
2207     y    = (Mat_SeqAIJ*)yy->B->data;
2208     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2209     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2210     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
2211   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
2212     ierr = MatAXPY_Basic(Y,a,X,str);CHKERRQ(ierr);
2213   } else {
2214     Mat      B;
2215     PetscInt *nnz_d,*nnz_o;
2216     ierr = PetscMalloc1(yy->A->rmap->N,&nnz_d);CHKERRQ(ierr);
2217     ierr = PetscMalloc1(yy->B->rmap->N,&nnz_o);CHKERRQ(ierr);
2218     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
2219     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
2220     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
2221     ierr = MatSetBlockSizesFromMats(B,Y,Y);CHKERRQ(ierr);
2222     ierr = MatSetType(B,MATMPIAIJ);CHKERRQ(ierr);
2223     ierr = MatAXPYGetPreallocation_SeqAIJ(yy->A,xx->A,nnz_d);CHKERRQ(ierr);
2224     ierr = MatAXPYGetPreallocation_MPIAIJ(yy->B,yy->garray,xx->B,xx->garray,nnz_o);CHKERRQ(ierr);
2225     ierr = MatMPIAIJSetPreallocation(B,0,nnz_d,0,nnz_o);CHKERRQ(ierr);
2226     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
2227     ierr = MatHeaderReplace(Y,&B);CHKERRQ(ierr);
2228     ierr = PetscFree(nnz_d);CHKERRQ(ierr);
2229     ierr = PetscFree(nnz_o);CHKERRQ(ierr);
2230   }
2231   PetscFunctionReturn(0);
2232 }
2233 
2234 extern PetscErrorCode  MatConjugate_SeqAIJ(Mat);
2235 
2236 #undef __FUNCT__
2237 #define __FUNCT__ "MatConjugate_MPIAIJ"
2238 PetscErrorCode  MatConjugate_MPIAIJ(Mat mat)
2239 {
2240 #if defined(PETSC_USE_COMPLEX)
2241   PetscErrorCode ierr;
2242   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2243 
2244   PetscFunctionBegin;
2245   ierr = MatConjugate_SeqAIJ(aij->A);CHKERRQ(ierr);
2246   ierr = MatConjugate_SeqAIJ(aij->B);CHKERRQ(ierr);
2247 #else
2248   PetscFunctionBegin;
2249 #endif
2250   PetscFunctionReturn(0);
2251 }
2252 
2253 #undef __FUNCT__
2254 #define __FUNCT__ "MatRealPart_MPIAIJ"
2255 PetscErrorCode MatRealPart_MPIAIJ(Mat A)
2256 {
2257   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2258   PetscErrorCode ierr;
2259 
2260   PetscFunctionBegin;
2261   ierr = MatRealPart(a->A);CHKERRQ(ierr);
2262   ierr = MatRealPart(a->B);CHKERRQ(ierr);
2263   PetscFunctionReturn(0);
2264 }
2265 
2266 #undef __FUNCT__
2267 #define __FUNCT__ "MatImaginaryPart_MPIAIJ"
2268 PetscErrorCode MatImaginaryPart_MPIAIJ(Mat A)
2269 {
2270   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2271   PetscErrorCode ierr;
2272 
2273   PetscFunctionBegin;
2274   ierr = MatImaginaryPart(a->A);CHKERRQ(ierr);
2275   ierr = MatImaginaryPart(a->B);CHKERRQ(ierr);
2276   PetscFunctionReturn(0);
2277 }
2278 
2279 #undef __FUNCT__
2280 #define __FUNCT__ "MatGetRowMaxAbs_MPIAIJ"
2281 PetscErrorCode MatGetRowMaxAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2282 {
2283   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2284   PetscErrorCode ierr;
2285   PetscInt       i,*idxb = 0;
2286   PetscScalar    *va,*vb;
2287   Vec            vtmp;
2288 
2289   PetscFunctionBegin;
2290   ierr = MatGetRowMaxAbs(a->A,v,idx);CHKERRQ(ierr);
2291   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2292   if (idx) {
2293     for (i=0; i<A->rmap->n; i++) {
2294       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2295     }
2296   }
2297 
2298   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2299   if (idx) {
2300     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2301   }
2302   ierr = MatGetRowMaxAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2303   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2304 
2305   for (i=0; i<A->rmap->n; i++) {
2306     if (PetscAbsScalar(va[i]) < PetscAbsScalar(vb[i])) {
2307       va[i] = vb[i];
2308       if (idx) idx[i] = a->garray[idxb[i]];
2309     }
2310   }
2311 
2312   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2313   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2314   ierr = PetscFree(idxb);CHKERRQ(ierr);
2315   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2316   PetscFunctionReturn(0);
2317 }
2318 
2319 #undef __FUNCT__
2320 #define __FUNCT__ "MatGetRowMinAbs_MPIAIJ"
2321 PetscErrorCode MatGetRowMinAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2322 {
2323   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2324   PetscErrorCode ierr;
2325   PetscInt       i,*idxb = 0;
2326   PetscScalar    *va,*vb;
2327   Vec            vtmp;
2328 
2329   PetscFunctionBegin;
2330   ierr = MatGetRowMinAbs(a->A,v,idx);CHKERRQ(ierr);
2331   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2332   if (idx) {
2333     for (i=0; i<A->cmap->n; i++) {
2334       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2335     }
2336   }
2337 
2338   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2339   if (idx) {
2340     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2341   }
2342   ierr = MatGetRowMinAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2343   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2344 
2345   for (i=0; i<A->rmap->n; i++) {
2346     if (PetscAbsScalar(va[i]) > PetscAbsScalar(vb[i])) {
2347       va[i] = vb[i];
2348       if (idx) idx[i] = a->garray[idxb[i]];
2349     }
2350   }
2351 
2352   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2353   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2354   ierr = PetscFree(idxb);CHKERRQ(ierr);
2355   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2356   PetscFunctionReturn(0);
2357 }
2358 
2359 #undef __FUNCT__
2360 #define __FUNCT__ "MatGetRowMin_MPIAIJ"
2361 PetscErrorCode MatGetRowMin_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2362 {
2363   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2364   PetscInt       n      = A->rmap->n;
2365   PetscInt       cstart = A->cmap->rstart;
2366   PetscInt       *cmap  = mat->garray;
2367   PetscInt       *diagIdx, *offdiagIdx;
2368   Vec            diagV, offdiagV;
2369   PetscScalar    *a, *diagA, *offdiagA;
2370   PetscInt       r;
2371   PetscErrorCode ierr;
2372 
2373   PetscFunctionBegin;
2374   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2375   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &diagV);CHKERRQ(ierr);
2376   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &offdiagV);CHKERRQ(ierr);
2377   ierr = MatGetRowMin(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2378   ierr = MatGetRowMin(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2379   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2380   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2381   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2382   for (r = 0; r < n; ++r) {
2383     if (PetscAbsScalar(diagA[r]) <= PetscAbsScalar(offdiagA[r])) {
2384       a[r]   = diagA[r];
2385       idx[r] = cstart + diagIdx[r];
2386     } else {
2387       a[r]   = offdiagA[r];
2388       idx[r] = cmap[offdiagIdx[r]];
2389     }
2390   }
2391   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2392   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2393   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2394   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2395   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2396   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2397   PetscFunctionReturn(0);
2398 }
2399 
2400 #undef __FUNCT__
2401 #define __FUNCT__ "MatGetRowMax_MPIAIJ"
2402 PetscErrorCode MatGetRowMax_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2403 {
2404   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2405   PetscInt       n      = A->rmap->n;
2406   PetscInt       cstart = A->cmap->rstart;
2407   PetscInt       *cmap  = mat->garray;
2408   PetscInt       *diagIdx, *offdiagIdx;
2409   Vec            diagV, offdiagV;
2410   PetscScalar    *a, *diagA, *offdiagA;
2411   PetscInt       r;
2412   PetscErrorCode ierr;
2413 
2414   PetscFunctionBegin;
2415   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2416   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &diagV);CHKERRQ(ierr);
2417   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &offdiagV);CHKERRQ(ierr);
2418   ierr = MatGetRowMax(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2419   ierr = MatGetRowMax(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2420   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2421   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2422   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2423   for (r = 0; r < n; ++r) {
2424     if (PetscAbsScalar(diagA[r]) >= PetscAbsScalar(offdiagA[r])) {
2425       a[r]   = diagA[r];
2426       idx[r] = cstart + diagIdx[r];
2427     } else {
2428       a[r]   = offdiagA[r];
2429       idx[r] = cmap[offdiagIdx[r]];
2430     }
2431   }
2432   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2433   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2434   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2435   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2436   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2437   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2438   PetscFunctionReturn(0);
2439 }
2440 
2441 #undef __FUNCT__
2442 #define __FUNCT__ "MatGetSeqNonzeroStructure_MPIAIJ"
2443 PetscErrorCode MatGetSeqNonzeroStructure_MPIAIJ(Mat mat,Mat *newmat)
2444 {
2445   PetscErrorCode ierr;
2446   Mat            *dummy;
2447 
2448   PetscFunctionBegin;
2449   ierr    = MatGetSubMatrix_MPIAIJ_All(mat,MAT_DO_NOT_GET_VALUES,MAT_INITIAL_MATRIX,&dummy);CHKERRQ(ierr);
2450   *newmat = *dummy;
2451   ierr    = PetscFree(dummy);CHKERRQ(ierr);
2452   PetscFunctionReturn(0);
2453 }
2454 
2455 #undef __FUNCT__
2456 #define __FUNCT__ "MatInvertBlockDiagonal_MPIAIJ"
2457 PetscErrorCode  MatInvertBlockDiagonal_MPIAIJ(Mat A,const PetscScalar **values)
2458 {
2459   Mat_MPIAIJ     *a = (Mat_MPIAIJ*) A->data;
2460   PetscErrorCode ierr;
2461 
2462   PetscFunctionBegin;
2463   ierr = MatInvertBlockDiagonal(a->A,values);CHKERRQ(ierr);
2464   PetscFunctionReturn(0);
2465 }
2466 
2467 #undef __FUNCT__
2468 #define __FUNCT__ "MatSetRandom_MPIAIJ"
2469 static PetscErrorCode  MatSetRandom_MPIAIJ(Mat x,PetscRandom rctx)
2470 {
2471   PetscErrorCode ierr;
2472   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)x->data;
2473 
2474   PetscFunctionBegin;
2475   ierr = MatSetRandom(aij->A,rctx);CHKERRQ(ierr);
2476   ierr = MatSetRandom(aij->B,rctx);CHKERRQ(ierr);
2477   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2478   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2479   PetscFunctionReturn(0);
2480 }
2481 
2482 #undef __FUNCT__
2483 #define __FUNCT__ "MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ"
2484 PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ(Mat A,PetscBool sc)
2485 {
2486   PetscFunctionBegin;
2487   if (sc) A->ops->increaseoverlap = MatIncreaseOverlap_MPIAIJ_Scalable;
2488   else A->ops->increaseoverlap    = MatIncreaseOverlap_MPIAIJ;
2489   PetscFunctionReturn(0);
2490 }
2491 
2492 #undef __FUNCT__
2493 #define __FUNCT__ "MatMPIAIJSetUseScalableIncreaseOverlap"
2494 /*@
2495    MatMPIAIJSetUseScalableIncreaseOverlap - Determine if the matrix uses a scalable algorithm to compute the overlap
2496 
2497    Collective on Mat
2498 
2499    Input Parameters:
2500 +    A - the matrix
2501 -    sc - PETSC_TRUE indicates use the scalable algorithm (default is not to use the scalable algorithm)
2502 
2503  Level: advanced
2504 
2505 @*/
2506 PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap(Mat A,PetscBool sc)
2507 {
2508   PetscErrorCode       ierr;
2509 
2510   PetscFunctionBegin;
2511   ierr = PetscTryMethod(A,"MatMPIAIJSetUseScalableIncreaseOverlap_C",(Mat,PetscBool),(A,sc));CHKERRQ(ierr);
2512   PetscFunctionReturn(0);
2513 }
2514 
2515 #undef __FUNCT__
2516 #define __FUNCT__ "MatSetFromOptions_MPIAIJ"
2517 PetscErrorCode MatSetFromOptions_MPIAIJ(PetscOptionItems *PetscOptionsObject,Mat A)
2518 {
2519   PetscErrorCode       ierr;
2520   PetscBool            sc = PETSC_FALSE,flg;
2521 
2522   PetscFunctionBegin;
2523   ierr = PetscOptionsHead(PetscOptionsObject,"MPIAIJ options");CHKERRQ(ierr);
2524   ierr = PetscObjectOptionsBegin((PetscObject)A);
2525     if (A->ops->increaseoverlap == MatIncreaseOverlap_MPIAIJ_Scalable) sc = PETSC_TRUE;
2526     ierr = PetscOptionsBool("-mat_increase_overlap_scalable","Use a scalable algorithm to compute the overlap","MatIncreaseOverlap",sc,&sc,&flg);CHKERRQ(ierr);
2527     if (flg) {
2528       ierr = MatMPIAIJSetUseScalableIncreaseOverlap(A,sc);CHKERRQ(ierr);
2529     }
2530   ierr = PetscOptionsEnd();CHKERRQ(ierr);
2531   PetscFunctionReturn(0);
2532 }
2533 
2534 #undef __FUNCT__
2535 #define __FUNCT__ "MatShift_MPIAIJ"
2536 PetscErrorCode MatShift_MPIAIJ(Mat Y,PetscScalar a)
2537 {
2538   PetscErrorCode ierr;
2539   Mat_MPIAIJ     *maij = (Mat_MPIAIJ*)Y->data;
2540   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)maij->A->data;
2541 
2542   PetscFunctionBegin;
2543   if (!Y->preallocated) {
2544     ierr = MatMPIAIJSetPreallocation(Y,1,NULL,0,NULL);CHKERRQ(ierr);
2545   } else if (!aij->nz) {
2546     PetscInt nonew = aij->nonew;
2547     ierr = MatSeqAIJSetPreallocation(maij->A,1,NULL);CHKERRQ(ierr);
2548     aij->nonew = nonew;
2549   }
2550   ierr = MatShift_Basic(Y,a);CHKERRQ(ierr);
2551   PetscFunctionReturn(0);
2552 }
2553 
2554 #undef __FUNCT__
2555 #define __FUNCT__ "MatMissingDiagonal_MPIAIJ"
2556 PetscErrorCode MatMissingDiagonal_MPIAIJ(Mat A,PetscBool  *missing,PetscInt *d)
2557 {
2558   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2559   PetscErrorCode ierr;
2560 
2561   PetscFunctionBegin;
2562   if (A->rmap->n != A->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only works for square matrices");
2563   ierr = MatMissingDiagonal(a->A,missing,d);CHKERRQ(ierr);
2564   if (d) {
2565     PetscInt rstart;
2566     ierr = MatGetOwnershipRange(A,&rstart,NULL);CHKERRQ(ierr);
2567     *d += rstart;
2568 
2569   }
2570   PetscFunctionReturn(0);
2571 }
2572 
2573 
2574 /* -------------------------------------------------------------------*/
2575 static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
2576                                        MatGetRow_MPIAIJ,
2577                                        MatRestoreRow_MPIAIJ,
2578                                        MatMult_MPIAIJ,
2579                                 /* 4*/ MatMultAdd_MPIAIJ,
2580                                        MatMultTranspose_MPIAIJ,
2581                                        MatMultTransposeAdd_MPIAIJ,
2582                                        0,
2583                                        0,
2584                                        0,
2585                                 /*10*/ 0,
2586                                        0,
2587                                        0,
2588                                        MatSOR_MPIAIJ,
2589                                        MatTranspose_MPIAIJ,
2590                                 /*15*/ MatGetInfo_MPIAIJ,
2591                                        MatEqual_MPIAIJ,
2592                                        MatGetDiagonal_MPIAIJ,
2593                                        MatDiagonalScale_MPIAIJ,
2594                                        MatNorm_MPIAIJ,
2595                                 /*20*/ MatAssemblyBegin_MPIAIJ,
2596                                        MatAssemblyEnd_MPIAIJ,
2597                                        MatSetOption_MPIAIJ,
2598                                        MatZeroEntries_MPIAIJ,
2599                                 /*24*/ MatZeroRows_MPIAIJ,
2600                                        0,
2601                                        0,
2602                                        0,
2603                                        0,
2604                                 /*29*/ MatSetUp_MPIAIJ,
2605                                        0,
2606                                        0,
2607                                        0,
2608                                        0,
2609                                 /*34*/ MatDuplicate_MPIAIJ,
2610                                        0,
2611                                        0,
2612                                        0,
2613                                        0,
2614                                 /*39*/ MatAXPY_MPIAIJ,
2615                                        MatGetSubMatrices_MPIAIJ,
2616                                        MatIncreaseOverlap_MPIAIJ,
2617                                        MatGetValues_MPIAIJ,
2618                                        MatCopy_MPIAIJ,
2619                                 /*44*/ MatGetRowMax_MPIAIJ,
2620                                        MatScale_MPIAIJ,
2621                                        MatShift_MPIAIJ,
2622                                        MatDiagonalSet_MPIAIJ,
2623                                        MatZeroRowsColumns_MPIAIJ,
2624                                 /*49*/ MatSetRandom_MPIAIJ,
2625                                        0,
2626                                        0,
2627                                        0,
2628                                        0,
2629                                 /*54*/ MatFDColoringCreate_MPIXAIJ,
2630                                        0,
2631                                        MatSetUnfactored_MPIAIJ,
2632                                        MatPermute_MPIAIJ,
2633                                        0,
2634                                 /*59*/ MatGetSubMatrix_MPIAIJ,
2635                                        MatDestroy_MPIAIJ,
2636                                        MatView_MPIAIJ,
2637                                        0,
2638                                        MatMatMatMult_MPIAIJ_MPIAIJ_MPIAIJ,
2639                                 /*64*/ MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ,
2640                                        MatMatMatMultNumeric_MPIAIJ_MPIAIJ_MPIAIJ,
2641                                        0,
2642                                        0,
2643                                        0,
2644                                 /*69*/ MatGetRowMaxAbs_MPIAIJ,
2645                                        MatGetRowMinAbs_MPIAIJ,
2646                                        0,
2647                                        MatSetColoring_MPIAIJ,
2648                                        0,
2649                                        MatSetValuesAdifor_MPIAIJ,
2650                                 /*75*/ MatFDColoringApply_AIJ,
2651                                        MatSetFromOptions_MPIAIJ,
2652                                        0,
2653                                        0,
2654                                        MatFindZeroDiagonals_MPIAIJ,
2655                                 /*80*/ 0,
2656                                        0,
2657                                        0,
2658                                 /*83*/ MatLoad_MPIAIJ,
2659                                        0,
2660                                        0,
2661                                        0,
2662                                        0,
2663                                        0,
2664                                 /*89*/ MatMatMult_MPIAIJ_MPIAIJ,
2665                                        MatMatMultSymbolic_MPIAIJ_MPIAIJ,
2666                                        MatMatMultNumeric_MPIAIJ_MPIAIJ,
2667                                        MatPtAP_MPIAIJ_MPIAIJ,
2668                                        MatPtAPSymbolic_MPIAIJ_MPIAIJ,
2669                                 /*94*/ MatPtAPNumeric_MPIAIJ_MPIAIJ,
2670                                        0,
2671                                        0,
2672                                        0,
2673                                        0,
2674                                 /*99*/ 0,
2675                                        0,
2676                                        0,
2677                                        MatConjugate_MPIAIJ,
2678                                        0,
2679                                 /*104*/MatSetValuesRow_MPIAIJ,
2680                                        MatRealPart_MPIAIJ,
2681                                        MatImaginaryPart_MPIAIJ,
2682                                        0,
2683                                        0,
2684                                 /*109*/0,
2685                                        0,
2686                                        MatGetRowMin_MPIAIJ,
2687                                        0,
2688                                        MatMissingDiagonal_MPIAIJ,
2689                                 /*114*/MatGetSeqNonzeroStructure_MPIAIJ,
2690                                        0,
2691                                        MatGetGhosts_MPIAIJ,
2692                                        0,
2693                                        0,
2694                                 /*119*/0,
2695                                        0,
2696                                        0,
2697                                        0,
2698                                        MatGetMultiProcBlock_MPIAIJ,
2699                                 /*124*/MatFindNonzeroRows_MPIAIJ,
2700                                        MatGetColumnNorms_MPIAIJ,
2701                                        MatInvertBlockDiagonal_MPIAIJ,
2702                                        0,
2703                                        MatGetSubMatricesMPI_MPIAIJ,
2704                                 /*129*/0,
2705                                        MatTransposeMatMult_MPIAIJ_MPIAIJ,
2706                                        MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ,
2707                                        MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ,
2708                                        0,
2709                                 /*134*/0,
2710                                        0,
2711                                        0,
2712                                        0,
2713                                        0,
2714                                 /*139*/0,
2715                                        0,
2716                                        0,
2717                                        MatFDColoringSetUp_MPIXAIJ,
2718                                        MatFindOffBlockDiagonalEntries_MPIAIJ,
2719                                 /*144*/MatCreateMPIMatConcatenateSeqMat_MPIAIJ
2720 };
2721 
2722 /* ----------------------------------------------------------------------------------------*/
2723 
2724 #undef __FUNCT__
2725 #define __FUNCT__ "MatStoreValues_MPIAIJ"
2726 PetscErrorCode  MatStoreValues_MPIAIJ(Mat mat)
2727 {
2728   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2729   PetscErrorCode ierr;
2730 
2731   PetscFunctionBegin;
2732   ierr = MatStoreValues(aij->A);CHKERRQ(ierr);
2733   ierr = MatStoreValues(aij->B);CHKERRQ(ierr);
2734   PetscFunctionReturn(0);
2735 }
2736 
2737 #undef __FUNCT__
2738 #define __FUNCT__ "MatRetrieveValues_MPIAIJ"
2739 PetscErrorCode  MatRetrieveValues_MPIAIJ(Mat mat)
2740 {
2741   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2742   PetscErrorCode ierr;
2743 
2744   PetscFunctionBegin;
2745   ierr = MatRetrieveValues(aij->A);CHKERRQ(ierr);
2746   ierr = MatRetrieveValues(aij->B);CHKERRQ(ierr);
2747   PetscFunctionReturn(0);
2748 }
2749 
2750 #undef __FUNCT__
2751 #define __FUNCT__ "MatMPIAIJSetPreallocation_MPIAIJ"
2752 PetscErrorCode  MatMPIAIJSetPreallocation_MPIAIJ(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
2753 {
2754   Mat_MPIAIJ     *b;
2755   PetscErrorCode ierr;
2756 
2757   PetscFunctionBegin;
2758   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
2759   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
2760   b = (Mat_MPIAIJ*)B->data;
2761 
2762   if (!B->preallocated) {
2763     /* Explicitly create 2 MATSEQAIJ matrices. */
2764     ierr = MatCreate(PETSC_COMM_SELF,&b->A);CHKERRQ(ierr);
2765     ierr = MatSetSizes(b->A,B->rmap->n,B->cmap->n,B->rmap->n,B->cmap->n);CHKERRQ(ierr);
2766     ierr = MatSetBlockSizesFromMats(b->A,B,B);CHKERRQ(ierr);
2767     ierr = MatSetType(b->A,MATSEQAIJ);CHKERRQ(ierr);
2768     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->A);CHKERRQ(ierr);
2769     ierr = MatCreate(PETSC_COMM_SELF,&b->B);CHKERRQ(ierr);
2770     ierr = MatSetSizes(b->B,B->rmap->n,B->cmap->N,B->rmap->n,B->cmap->N);CHKERRQ(ierr);
2771     ierr = MatSetBlockSizesFromMats(b->B,B,B);CHKERRQ(ierr);
2772     ierr = MatSetType(b->B,MATSEQAIJ);CHKERRQ(ierr);
2773     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->B);CHKERRQ(ierr);
2774   }
2775 
2776   ierr = MatSeqAIJSetPreallocation(b->A,d_nz,d_nnz);CHKERRQ(ierr);
2777   ierr = MatSeqAIJSetPreallocation(b->B,o_nz,o_nnz);CHKERRQ(ierr);
2778   B->preallocated = PETSC_TRUE;
2779   PetscFunctionReturn(0);
2780 }
2781 
2782 #undef __FUNCT__
2783 #define __FUNCT__ "MatDuplicate_MPIAIJ"
2784 PetscErrorCode MatDuplicate_MPIAIJ(Mat matin,MatDuplicateOption cpvalues,Mat *newmat)
2785 {
2786   Mat            mat;
2787   Mat_MPIAIJ     *a,*oldmat = (Mat_MPIAIJ*)matin->data;
2788   PetscErrorCode ierr;
2789 
2790   PetscFunctionBegin;
2791   *newmat = 0;
2792   ierr    = MatCreate(PetscObjectComm((PetscObject)matin),&mat);CHKERRQ(ierr);
2793   ierr    = MatSetSizes(mat,matin->rmap->n,matin->cmap->n,matin->rmap->N,matin->cmap->N);CHKERRQ(ierr);
2794   ierr    = MatSetBlockSizesFromMats(mat,matin,matin);CHKERRQ(ierr);
2795   ierr    = MatSetType(mat,((PetscObject)matin)->type_name);CHKERRQ(ierr);
2796   ierr    = PetscMemcpy(mat->ops,matin->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
2797   a       = (Mat_MPIAIJ*)mat->data;
2798 
2799   mat->factortype   = matin->factortype;
2800   mat->assembled    = PETSC_TRUE;
2801   mat->insertmode   = NOT_SET_VALUES;
2802   mat->preallocated = PETSC_TRUE;
2803 
2804   a->size         = oldmat->size;
2805   a->rank         = oldmat->rank;
2806   a->donotstash   = oldmat->donotstash;
2807   a->roworiented  = oldmat->roworiented;
2808   a->rowindices   = 0;
2809   a->rowvalues    = 0;
2810   a->getrowactive = PETSC_FALSE;
2811 
2812   ierr = PetscLayoutReference(matin->rmap,&mat->rmap);CHKERRQ(ierr);
2813   ierr = PetscLayoutReference(matin->cmap,&mat->cmap);CHKERRQ(ierr);
2814 
2815   if (oldmat->colmap) {
2816 #if defined(PETSC_USE_CTABLE)
2817     ierr = PetscTableCreateCopy(oldmat->colmap,&a->colmap);CHKERRQ(ierr);
2818 #else
2819     ierr = PetscMalloc1(mat->cmap->N,&a->colmap);CHKERRQ(ierr);
2820     ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2821     ierr = PetscMemcpy(a->colmap,oldmat->colmap,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2822 #endif
2823   } else a->colmap = 0;
2824   if (oldmat->garray) {
2825     PetscInt len;
2826     len  = oldmat->B->cmap->n;
2827     ierr = PetscMalloc1(len+1,&a->garray);CHKERRQ(ierr);
2828     ierr = PetscLogObjectMemory((PetscObject)mat,len*sizeof(PetscInt));CHKERRQ(ierr);
2829     if (len) { ierr = PetscMemcpy(a->garray,oldmat->garray,len*sizeof(PetscInt));CHKERRQ(ierr); }
2830   } else a->garray = 0;
2831 
2832   ierr    = VecDuplicate(oldmat->lvec,&a->lvec);CHKERRQ(ierr);
2833   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->lvec);CHKERRQ(ierr);
2834   ierr    = VecScatterCopy(oldmat->Mvctx,&a->Mvctx);CHKERRQ(ierr);
2835   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->Mvctx);CHKERRQ(ierr);
2836   ierr    = MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
2837   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->A);CHKERRQ(ierr);
2838   ierr    = MatDuplicate(oldmat->B,cpvalues,&a->B);CHKERRQ(ierr);
2839   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->B);CHKERRQ(ierr);
2840   ierr    = PetscFunctionListDuplicate(((PetscObject)matin)->qlist,&((PetscObject)mat)->qlist);CHKERRQ(ierr);
2841   *newmat = mat;
2842   PetscFunctionReturn(0);
2843 }
2844 
2845 
2846 
2847 #undef __FUNCT__
2848 #define __FUNCT__ "MatLoad_MPIAIJ"
2849 PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
2850 {
2851   PetscScalar    *vals,*svals;
2852   MPI_Comm       comm;
2853   PetscErrorCode ierr;
2854   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
2855   PetscInt       i,nz,j,rstart,rend,mmax,maxnz = 0;
2856   PetscInt       header[4],*rowlengths = 0,M,N,m,*cols;
2857   PetscInt       *ourlens = NULL,*procsnz = NULL,*offlens = NULL,jj,*mycols,*smycols;
2858   PetscInt       cend,cstart,n,*rowners;
2859   int            fd;
2860   PetscInt       bs = newMat->rmap->bs;
2861 
2862   PetscFunctionBegin;
2863   /* force binary viewer to load .info file if it has not yet done so */
2864   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
2865   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
2866   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2867   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2868   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
2869   if (!rank) {
2870     ierr = PetscBinaryRead(fd,(char*)header,4,PETSC_INT);CHKERRQ(ierr);
2871     if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
2872   }
2873 
2874   ierr = PetscOptionsBegin(comm,NULL,"Options for loading MPIAIJ matrix","Mat");CHKERRQ(ierr);
2875   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
2876   ierr = PetscOptionsEnd();CHKERRQ(ierr);
2877   if (bs < 0) bs = 1;
2878 
2879   ierr = MPI_Bcast(header+1,3,MPIU_INT,0,comm);CHKERRQ(ierr);
2880   M    = header[1]; N = header[2];
2881 
2882   /* If global sizes are set, check if they are consistent with that given in the file */
2883   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);
2884   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);
2885 
2886   /* determine ownership of all (block) rows */
2887   if (M%bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Inconsistent # of rows (%d) and block size (%d)",M,bs);
2888   if (newMat->rmap->n < 0) m = bs*((M/bs)/size + (((M/bs) % size) > rank));    /* PETSC_DECIDE */
2889   else m = newMat->rmap->n; /* Set by user */
2890 
2891   ierr = PetscMalloc1(size+1,&rowners);CHKERRQ(ierr);
2892   ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
2893 
2894   /* First process needs enough room for process with most rows */
2895   if (!rank) {
2896     mmax = rowners[1];
2897     for (i=2; i<=size; i++) {
2898       mmax = PetscMax(mmax, rowners[i]);
2899     }
2900   } else mmax = -1;             /* unused, but compilers complain */
2901 
2902   rowners[0] = 0;
2903   for (i=2; i<=size; i++) {
2904     rowners[i] += rowners[i-1];
2905   }
2906   rstart = rowners[rank];
2907   rend   = rowners[rank+1];
2908 
2909   /* distribute row lengths to all processors */
2910   ierr = PetscMalloc2(m,&ourlens,m,&offlens);CHKERRQ(ierr);
2911   if (!rank) {
2912     ierr = PetscBinaryRead(fd,ourlens,m,PETSC_INT);CHKERRQ(ierr);
2913     ierr = PetscMalloc1(mmax,&rowlengths);CHKERRQ(ierr);
2914     ierr = PetscCalloc1(size,&procsnz);CHKERRQ(ierr);
2915     for (j=0; j<m; j++) {
2916       procsnz[0] += ourlens[j];
2917     }
2918     for (i=1; i<size; i++) {
2919       ierr = PetscBinaryRead(fd,rowlengths,rowners[i+1]-rowners[i],PETSC_INT);CHKERRQ(ierr);
2920       /* calculate the number of nonzeros on each processor */
2921       for (j=0; j<rowners[i+1]-rowners[i]; j++) {
2922         procsnz[i] += rowlengths[j];
2923       }
2924       ierr = MPIULong_Send(rowlengths,rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2925     }
2926     ierr = PetscFree(rowlengths);CHKERRQ(ierr);
2927   } else {
2928     ierr = MPIULong_Recv(ourlens,m,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2929   }
2930 
2931   if (!rank) {
2932     /* determine max buffer needed and allocate it */
2933     maxnz = 0;
2934     for (i=0; i<size; i++) {
2935       maxnz = PetscMax(maxnz,procsnz[i]);
2936     }
2937     ierr = PetscMalloc1(maxnz,&cols);CHKERRQ(ierr);
2938 
2939     /* read in my part of the matrix column indices  */
2940     nz   = procsnz[0];
2941     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2942     ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);
2943 
2944     /* read in every one elses and ship off */
2945     for (i=1; i<size; i++) {
2946       nz   = procsnz[i];
2947       ierr = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
2948       ierr = MPIULong_Send(cols,nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2949     }
2950     ierr = PetscFree(cols);CHKERRQ(ierr);
2951   } else {
2952     /* determine buffer space needed for message */
2953     nz = 0;
2954     for (i=0; i<m; i++) {
2955       nz += ourlens[i];
2956     }
2957     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2958 
2959     /* receive message of column indices*/
2960     ierr = MPIULong_Recv(mycols,nz,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2961   }
2962 
2963   /* determine column ownership if matrix is not square */
2964   if (N != M) {
2965     if (newMat->cmap->n < 0) n = N/size + ((N % size) > rank);
2966     else n = newMat->cmap->n;
2967     ierr   = MPI_Scan(&n,&cend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
2968     cstart = cend - n;
2969   } else {
2970     cstart = rstart;
2971     cend   = rend;
2972     n      = cend - cstart;
2973   }
2974 
2975   /* loop over local rows, determining number of off diagonal entries */
2976   ierr = PetscMemzero(offlens,m*sizeof(PetscInt));CHKERRQ(ierr);
2977   jj   = 0;
2978   for (i=0; i<m; i++) {
2979     for (j=0; j<ourlens[i]; j++) {
2980       if (mycols[jj] < cstart || mycols[jj] >= cend) offlens[i]++;
2981       jj++;
2982     }
2983   }
2984 
2985   for (i=0; i<m; i++) {
2986     ourlens[i] -= offlens[i];
2987   }
2988   ierr = MatSetSizes(newMat,m,n,M,N);CHKERRQ(ierr);
2989 
2990   if (bs > 1) {ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);}
2991 
2992   ierr = MatMPIAIJSetPreallocation(newMat,0,ourlens,0,offlens);CHKERRQ(ierr);
2993 
2994   for (i=0; i<m; i++) {
2995     ourlens[i] += offlens[i];
2996   }
2997 
2998   if (!rank) {
2999     ierr = PetscMalloc1(maxnz+1,&vals);CHKERRQ(ierr);
3000 
3001     /* read in my part of the matrix numerical values  */
3002     nz   = procsnz[0];
3003     ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
3004 
3005     /* insert into matrix */
3006     jj      = rstart;
3007     smycols = mycols;
3008     svals   = vals;
3009     for (i=0; i<m; i++) {
3010       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
3011       smycols += ourlens[i];
3012       svals   += ourlens[i];
3013       jj++;
3014     }
3015 
3016     /* read in other processors and ship out */
3017     for (i=1; i<size; i++) {
3018       nz   = procsnz[i];
3019       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
3020       ierr = MPIULong_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
3021     }
3022     ierr = PetscFree(procsnz);CHKERRQ(ierr);
3023   } else {
3024     /* receive numeric values */
3025     ierr = PetscMalloc1(nz+1,&vals);CHKERRQ(ierr);
3026 
3027     /* receive message of values*/
3028     ierr = MPIULong_Recv(vals,nz,MPIU_SCALAR,0,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
3029 
3030     /* insert into matrix */
3031     jj      = rstart;
3032     smycols = mycols;
3033     svals   = vals;
3034     for (i=0; i<m; i++) {
3035       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
3036       smycols += ourlens[i];
3037       svals   += ourlens[i];
3038       jj++;
3039     }
3040   }
3041   ierr = PetscFree2(ourlens,offlens);CHKERRQ(ierr);
3042   ierr = PetscFree(vals);CHKERRQ(ierr);
3043   ierr = PetscFree(mycols);CHKERRQ(ierr);
3044   ierr = PetscFree(rowners);CHKERRQ(ierr);
3045   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3046   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3047   PetscFunctionReturn(0);
3048 }
3049 
3050 #undef __FUNCT__
3051 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ"
3052 /* TODO: Not scalable because of ISAllGather() unless getting all columns. */
3053 PetscErrorCode MatGetSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3054 {
3055   PetscErrorCode ierr;
3056   IS             iscol_local;
3057   PetscInt       csize;
3058 
3059   PetscFunctionBegin;
3060   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3061   if (call == MAT_REUSE_MATRIX) {
3062     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3063     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3064   } else {
3065     /* check if we are grabbing all columns*/
3066     PetscBool    isstride;
3067     PetscMPIInt  lisstride = 0,gisstride;
3068     ierr = PetscObjectTypeCompare((PetscObject)iscol,ISSTRIDE,&isstride);CHKERRQ(ierr);
3069     if (isstride) {
3070       PetscInt  start,len,mstart,mlen;
3071       ierr = ISStrideGetInfo(iscol,&start,NULL);CHKERRQ(ierr);
3072       ierr = ISGetLocalSize(iscol,&len);CHKERRQ(ierr);
3073       ierr = MatGetOwnershipRangeColumn(mat,&mstart,&mlen);CHKERRQ(ierr);
3074       if (mstart == start && mlen-mstart == len) lisstride = 1;
3075     }
3076     ierr = MPIU_Allreduce(&lisstride,&gisstride,1,MPI_INT,MPI_MIN,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
3077     if (gisstride) {
3078       PetscInt N;
3079       ierr = MatGetSize(mat,NULL,&N);CHKERRQ(ierr);
3080       ierr = ISCreateStride(PetscObjectComm((PetscObject)mat),N,0,1,&iscol_local);CHKERRQ(ierr);
3081       ierr = ISSetIdentity(iscol_local);CHKERRQ(ierr);
3082       ierr = PetscInfo(mat,"Optimizing for obtaining all columns of the matrix; skipping ISAllGather()\n");CHKERRQ(ierr);
3083     } else {
3084       PetscInt cbs;
3085       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
3086       ierr = ISAllGather(iscol,&iscol_local);CHKERRQ(ierr);
3087       ierr = ISSetBlockSize(iscol_local,cbs);CHKERRQ(ierr);
3088     }
3089   }
3090   ierr = MatGetSubMatrix_MPIAIJ_Private(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
3091   if (call == MAT_INITIAL_MATRIX) {
3092     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3093     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3094   }
3095   PetscFunctionReturn(0);
3096 }
3097 
3098 extern PetscErrorCode MatGetSubMatrices_MPIAIJ_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool*,Mat*);
3099 #undef __FUNCT__
3100 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ_Private"
3101 /*
3102     Not great since it makes two copies of the submatrix, first an SeqAIJ
3103   in local and then by concatenating the local matrices the end result.
3104   Writing it directly would be much like MatGetSubMatrices_MPIAIJ()
3105 
3106   Note: This requires a sequential iscol with all indices.
3107 */
3108 PetscErrorCode MatGetSubMatrix_MPIAIJ_Private(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3109 {
3110   PetscErrorCode ierr;
3111   PetscMPIInt    rank,size;
3112   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3113   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal,ncol;
3114   PetscBool      allcolumns, colflag;
3115   Mat            M,Mreuse;
3116   MatScalar      *vwork,*aa;
3117   MPI_Comm       comm;
3118   Mat_SeqAIJ     *aij;
3119 
3120   PetscFunctionBegin;
3121   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3122   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3123   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3124 
3125   ierr = ISIdentity(iscol,&colflag);CHKERRQ(ierr);
3126   ierr = ISGetLocalSize(iscol,&ncol);CHKERRQ(ierr);
3127   if (colflag && ncol == mat->cmap->N) {
3128     allcolumns = PETSC_TRUE;
3129     ierr = PetscInfo(mat,"Optimizing for obtaining all columns of the matrix\n");CHKERRQ(ierr);
3130   } else {
3131     allcolumns = PETSC_FALSE;
3132   }
3133   if (call ==  MAT_REUSE_MATRIX) {
3134     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3135     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3136     ierr = MatGetSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,&allcolumns,&Mreuse);CHKERRQ(ierr);
3137   } else {
3138     ierr = MatGetSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&allcolumns,&Mreuse);CHKERRQ(ierr);
3139   }
3140 
3141   /*
3142       m - number of local rows
3143       n - number of columns (same on all processors)
3144       rstart - first row in new global matrix generated
3145   */
3146   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3147   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3148   if (call == MAT_INITIAL_MATRIX) {
3149     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3150     ii  = aij->i;
3151     jj  = aij->j;
3152 
3153     /*
3154         Determine the number of non-zeros in the diagonal and off-diagonal
3155         portions of the matrix in order to do correct preallocation
3156     */
3157 
3158     /* first get start and end of "diagonal" columns */
3159     if (csize == PETSC_DECIDE) {
3160       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3161       if (mglobal == n) { /* square matrix */
3162         nlocal = m;
3163       } else {
3164         nlocal = n/size + ((n % size) > rank);
3165       }
3166     } else {
3167       nlocal = csize;
3168     }
3169     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3170     rstart = rend - nlocal;
3171     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);
3172 
3173     /* next, compute all the lengths */
3174     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3175     olens = dlens + m;
3176     for (i=0; i<m; i++) {
3177       jend = ii[i+1] - ii[i];
3178       olen = 0;
3179       dlen = 0;
3180       for (j=0; j<jend; j++) {
3181         if (*jj < rstart || *jj >= rend) olen++;
3182         else dlen++;
3183         jj++;
3184       }
3185       olens[i] = olen;
3186       dlens[i] = dlen;
3187     }
3188     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3189     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3190     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3191     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3192     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3193     ierr = PetscFree(dlens);CHKERRQ(ierr);
3194   } else {
3195     PetscInt ml,nl;
3196 
3197     M    = *newmat;
3198     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3199     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3200     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3201     /*
3202          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3203        rather than the slower MatSetValues().
3204     */
3205     M->was_assembled = PETSC_TRUE;
3206     M->assembled     = PETSC_FALSE;
3207   }
3208   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3209   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3210   ii   = aij->i;
3211   jj   = aij->j;
3212   aa   = aij->a;
3213   for (i=0; i<m; i++) {
3214     row   = rstart + i;
3215     nz    = ii[i+1] - ii[i];
3216     cwork = jj;     jj += nz;
3217     vwork = aa;     aa += nz;
3218     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3219   }
3220 
3221   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3222   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3223   *newmat = M;
3224 
3225   /* save submatrix used in processor for next request */
3226   if (call ==  MAT_INITIAL_MATRIX) {
3227     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3228     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3229   }
3230   PetscFunctionReturn(0);
3231 }
3232 
3233 #undef __FUNCT__
3234 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR_MPIAIJ"
3235 PetscErrorCode  MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3236 {
3237   PetscInt       m,cstart, cend,j,nnz,i,d;
3238   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3239   const PetscInt *JJ;
3240   PetscScalar    *values;
3241   PetscErrorCode ierr;
3242 
3243   PetscFunctionBegin;
3244   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3245 
3246   ierr   = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3247   ierr   = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3248   m      = B->rmap->n;
3249   cstart = B->cmap->rstart;
3250   cend   = B->cmap->rend;
3251   rstart = B->rmap->rstart;
3252 
3253   ierr = PetscMalloc2(m,&d_nnz,m,&o_nnz);CHKERRQ(ierr);
3254 
3255 #if defined(PETSC_USE_DEBUGGING)
3256   for (i=0; i<m; i++) {
3257     nnz = Ii[i+1]- Ii[i];
3258     JJ  = J + Ii[i];
3259     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3260     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3261     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);
3262   }
3263 #endif
3264 
3265   for (i=0; i<m; i++) {
3266     nnz     = Ii[i+1]- Ii[i];
3267     JJ      = J + Ii[i];
3268     nnz_max = PetscMax(nnz_max,nnz);
3269     d       = 0;
3270     for (j=0; j<nnz; j++) {
3271       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3272     }
3273     d_nnz[i] = d;
3274     o_nnz[i] = nnz - d;
3275   }
3276   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3277   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3278 
3279   if (v) values = (PetscScalar*)v;
3280   else {
3281     ierr = PetscCalloc1(nnz_max+1,&values);CHKERRQ(ierr);
3282   }
3283 
3284   for (i=0; i<m; i++) {
3285     ii   = i + rstart;
3286     nnz  = Ii[i+1]- Ii[i];
3287     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3288   }
3289   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3290   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3291 
3292   if (!v) {
3293     ierr = PetscFree(values);CHKERRQ(ierr);
3294   }
3295   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3296   PetscFunctionReturn(0);
3297 }
3298 
3299 #undef __FUNCT__
3300 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR"
3301 /*@
3302    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3303    (the default parallel PETSc format).
3304 
3305    Collective on MPI_Comm
3306 
3307    Input Parameters:
3308 +  B - the matrix
3309 .  i - the indices into j for the start of each local row (starts with zero)
3310 .  j - the column indices for each local row (starts with zero)
3311 -  v - optional values in the matrix
3312 
3313    Level: developer
3314 
3315    Notes:
3316        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3317      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3318      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3319 
3320        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3321 
3322        The format which is used for the sparse matrix input, is equivalent to a
3323     row-major ordering.. i.e for the following matrix, the input data expected is
3324     as shown
3325 
3326 $        1 0 0
3327 $        2 0 3     P0
3328 $       -------
3329 $        4 5 6     P1
3330 $
3331 $     Process0 [P0]: rows_owned=[0,1]
3332 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3333 $        j =  {0,0,2}  [size = 3]
3334 $        v =  {1,2,3}  [size = 3]
3335 $
3336 $     Process1 [P1]: rows_owned=[2]
3337 $        i =  {0,3}    [size = nrow+1  = 1+1]
3338 $        j =  {0,1,2}  [size = 3]
3339 $        v =  {4,5,6}  [size = 3]
3340 
3341 .keywords: matrix, aij, compressed row, sparse, parallel
3342 
3343 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MPIAIJ,
3344           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3345 @*/
3346 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3347 {
3348   PetscErrorCode ierr;
3349 
3350   PetscFunctionBegin;
3351   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3352   PetscFunctionReturn(0);
3353 }
3354 
3355 #undef __FUNCT__
3356 #define __FUNCT__ "MatMPIAIJSetPreallocation"
3357 /*@C
3358    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3359    (the default parallel PETSc format).  For good matrix assembly performance
3360    the user should preallocate the matrix storage by setting the parameters
3361    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3362    performance can be increased by more than a factor of 50.
3363 
3364    Collective on MPI_Comm
3365 
3366    Input Parameters:
3367 +  B - the matrix
3368 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3369            (same value is used for all local rows)
3370 .  d_nnz - array containing the number of nonzeros in the various rows of the
3371            DIAGONAL portion of the local submatrix (possibly different for each row)
3372            or NULL (PETSC_NULL_INTEGER in Fortran), if d_nz is used to specify the nonzero structure.
3373            The size of this array is equal to the number of local rows, i.e 'm'.
3374            For matrices that will be factored, you must leave room for (and set)
3375            the diagonal entry even if it is zero.
3376 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3377            submatrix (same value is used for all local rows).
3378 -  o_nnz - array containing the number of nonzeros in the various rows of the
3379            OFF-DIAGONAL portion of the local submatrix (possibly different for
3380            each row) or NULL (PETSC_NULL_INTEGER in Fortran), if o_nz is used to specify the nonzero
3381            structure. The size of this array is equal to the number
3382            of local rows, i.e 'm'.
3383 
3384    If the *_nnz parameter is given then the *_nz parameter is ignored
3385 
3386    The AIJ format (also called the Yale sparse matrix format or
3387    compressed row storage (CSR)), is fully compatible with standard Fortran 77
3388    storage.  The stored row and column indices begin with zero.
3389    See Users-Manual: ch_mat for details.
3390 
3391    The parallel matrix is partitioned such that the first m0 rows belong to
3392    process 0, the next m1 rows belong to process 1, the next m2 rows belong
3393    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
3394 
3395    The DIAGONAL portion of the local submatrix of a processor can be defined
3396    as the submatrix which is obtained by extraction the part corresponding to
3397    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
3398    first row that belongs to the processor, r2 is the last row belonging to
3399    the this processor, and c1-c2 is range of indices of the local part of a
3400    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
3401    common case of a square matrix, the row and column ranges are the same and
3402    the DIAGONAL part is also square. The remaining portion of the local
3403    submatrix (mxN) constitute the OFF-DIAGONAL portion.
3404 
3405    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3406 
3407    You can call MatGetInfo() to get information on how effective the preallocation was;
3408    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3409    You can also run with the option -info and look for messages with the string
3410    malloc in them to see if additional memory allocation was needed.
3411 
3412    Example usage:
3413 
3414    Consider the following 8x8 matrix with 34 non-zero values, that is
3415    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3416    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3417    as follows:
3418 
3419 .vb
3420             1  2  0  |  0  3  0  |  0  4
3421     Proc0   0  5  6  |  7  0  0  |  8  0
3422             9  0 10  | 11  0  0  | 12  0
3423     -------------------------------------
3424            13  0 14  | 15 16 17  |  0  0
3425     Proc1   0 18  0  | 19 20 21  |  0  0
3426             0  0  0  | 22 23  0  | 24  0
3427     -------------------------------------
3428     Proc2  25 26 27  |  0  0 28  | 29  0
3429            30  0  0  | 31 32 33  |  0 34
3430 .ve
3431 
3432    This can be represented as a collection of submatrices as:
3433 
3434 .vb
3435       A B C
3436       D E F
3437       G H I
3438 .ve
3439 
3440    Where the submatrices A,B,C are owned by proc0, D,E,F are
3441    owned by proc1, G,H,I are owned by proc2.
3442 
3443    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3444    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3445    The 'M','N' parameters are 8,8, and have the same values on all procs.
3446 
3447    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3448    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3449    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3450    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3451    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3452    matrix, ans [DF] as another SeqAIJ matrix.
3453 
3454    When d_nz, o_nz parameters are specified, d_nz storage elements are
3455    allocated for every row of the local diagonal submatrix, and o_nz
3456    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3457    One way to choose d_nz and o_nz is to use the max nonzerors per local
3458    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3459    In this case, the values of d_nz,o_nz are:
3460 .vb
3461      proc0 : dnz = 2, o_nz = 2
3462      proc1 : dnz = 3, o_nz = 2
3463      proc2 : dnz = 1, o_nz = 4
3464 .ve
3465    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3466    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3467    for proc3. i.e we are using 12+15+10=37 storage locations to store
3468    34 values.
3469 
3470    When d_nnz, o_nnz parameters are specified, the storage is specified
3471    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3472    In the above case the values for d_nnz,o_nnz are:
3473 .vb
3474      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3475      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3476      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3477 .ve
3478    Here the space allocated is sum of all the above values i.e 34, and
3479    hence pre-allocation is perfect.
3480 
3481    Level: intermediate
3482 
3483 .keywords: matrix, aij, compressed row, sparse, parallel
3484 
3485 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
3486           MPIAIJ, MatGetInfo(), PetscSplitOwnership()
3487 @*/
3488 PetscErrorCode  MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3489 {
3490   PetscErrorCode ierr;
3491 
3492   PetscFunctionBegin;
3493   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3494   PetscValidType(B,1);
3495   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
3496   PetscFunctionReturn(0);
3497 }
3498 
3499 #undef __FUNCT__
3500 #define __FUNCT__ "MatCreateMPIAIJWithArrays"
3501 /*@
3502      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
3503          CSR format the local rows.
3504 
3505    Collective on MPI_Comm
3506 
3507    Input Parameters:
3508 +  comm - MPI communicator
3509 .  m - number of local rows (Cannot be PETSC_DECIDE)
3510 .  n - This value should be the same as the local size used in creating the
3511        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3512        calculated if N is given) For square matrices n is almost always m.
3513 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3514 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3515 .   i - row indices
3516 .   j - column indices
3517 -   a - matrix values
3518 
3519    Output Parameter:
3520 .   mat - the matrix
3521 
3522    Level: intermediate
3523 
3524    Notes:
3525        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3526      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3527      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3528 
3529        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3530 
3531        The format which is used for the sparse matrix input, is equivalent to a
3532     row-major ordering.. i.e for the following matrix, the input data expected is
3533     as shown
3534 
3535 $        1 0 0
3536 $        2 0 3     P0
3537 $       -------
3538 $        4 5 6     P1
3539 $
3540 $     Process0 [P0]: rows_owned=[0,1]
3541 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3542 $        j =  {0,0,2}  [size = 3]
3543 $        v =  {1,2,3}  [size = 3]
3544 $
3545 $     Process1 [P1]: rows_owned=[2]
3546 $        i =  {0,3}    [size = nrow+1  = 1+1]
3547 $        j =  {0,1,2}  [size = 3]
3548 $        v =  {4,5,6}  [size = 3]
3549 
3550 .keywords: matrix, aij, compressed row, sparse, parallel
3551 
3552 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3553           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
3554 @*/
3555 PetscErrorCode  MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
3556 {
3557   PetscErrorCode ierr;
3558 
3559   PetscFunctionBegin;
3560   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
3561   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
3562   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
3563   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
3564   /* ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr); */
3565   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
3566   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
3567   PetscFunctionReturn(0);
3568 }
3569 
3570 #undef __FUNCT__
3571 #define __FUNCT__ "MatCreateAIJ"
3572 /*@C
3573    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
3574    (the default parallel PETSc format).  For good matrix assembly performance
3575    the user should preallocate the matrix storage by setting the parameters
3576    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3577    performance can be increased by more than a factor of 50.
3578 
3579    Collective on MPI_Comm
3580 
3581    Input Parameters:
3582 +  comm - MPI communicator
3583 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
3584            This value should be the same as the local size used in creating the
3585            y vector for the matrix-vector product y = Ax.
3586 .  n - This value should be the same as the local size used in creating the
3587        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3588        calculated if N is given) For square matrices n is almost always m.
3589 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3590 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3591 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3592            (same value is used for all local rows)
3593 .  d_nnz - array containing the number of nonzeros in the various rows of the
3594            DIAGONAL portion of the local submatrix (possibly different for each row)
3595            or NULL, if d_nz is used to specify the nonzero structure.
3596            The size of this array is equal to the number of local rows, i.e 'm'.
3597 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3598            submatrix (same value is used for all local rows).
3599 -  o_nnz - array containing the number of nonzeros in the various rows of the
3600            OFF-DIAGONAL portion of the local submatrix (possibly different for
3601            each row) or NULL, if o_nz is used to specify the nonzero
3602            structure. The size of this array is equal to the number
3603            of local rows, i.e 'm'.
3604 
3605    Output Parameter:
3606 .  A - the matrix
3607 
3608    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3609    MatXXXXSetPreallocation() paradgm instead of this routine directly.
3610    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3611 
3612    Notes:
3613    If the *_nnz parameter is given then the *_nz parameter is ignored
3614 
3615    m,n,M,N parameters specify the size of the matrix, and its partitioning across
3616    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
3617    storage requirements for this matrix.
3618 
3619    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
3620    processor than it must be used on all processors that share the object for
3621    that argument.
3622 
3623    The user MUST specify either the local or global matrix dimensions
3624    (possibly both).
3625 
3626    The parallel matrix is partitioned across processors such that the
3627    first m0 rows belong to process 0, the next m1 rows belong to
3628    process 1, the next m2 rows belong to process 2 etc.. where
3629    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
3630    values corresponding to [m x N] submatrix.
3631 
3632    The columns are logically partitioned with the n0 columns belonging
3633    to 0th partition, the next n1 columns belonging to the next
3634    partition etc.. where n0,n1,n2... are the input parameter 'n'.
3635 
3636    The DIAGONAL portion of the local submatrix on any given processor
3637    is the submatrix corresponding to the rows and columns m,n
3638    corresponding to the given processor. i.e diagonal matrix on
3639    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
3640    etc. The remaining portion of the local submatrix [m x (N-n)]
3641    constitute the OFF-DIAGONAL portion. The example below better
3642    illustrates this concept.
3643 
3644    For a square global matrix we define each processor's diagonal portion
3645    to be its local rows and the corresponding columns (a square submatrix);
3646    each processor's off-diagonal portion encompasses the remainder of the
3647    local matrix (a rectangular submatrix).
3648 
3649    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3650 
3651    When calling this routine with a single process communicator, a matrix of
3652    type SEQAIJ is returned.  If a matrix of type MPIAIJ is desired for this
3653    type of communicator, use the construction mechanism:
3654      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
3655 
3656    By default, this format uses inodes (identical nodes) when possible.
3657    We search for consecutive rows with the same nonzero structure, thereby
3658    reusing matrix information to achieve increased efficiency.
3659 
3660    Options Database Keys:
3661 +  -mat_no_inode  - Do not use inodes
3662 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3663 -  -mat_aij_oneindex - Internally use indexing starting at 1
3664         rather than 0.  Note that when calling MatSetValues(),
3665         the user still MUST index entries starting at 0!
3666 
3667 
3668    Example usage:
3669 
3670    Consider the following 8x8 matrix with 34 non-zero values, that is
3671    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3672    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3673    as follows:
3674 
3675 .vb
3676             1  2  0  |  0  3  0  |  0  4
3677     Proc0   0  5  6  |  7  0  0  |  8  0
3678             9  0 10  | 11  0  0  | 12  0
3679     -------------------------------------
3680            13  0 14  | 15 16 17  |  0  0
3681     Proc1   0 18  0  | 19 20 21  |  0  0
3682             0  0  0  | 22 23  0  | 24  0
3683     -------------------------------------
3684     Proc2  25 26 27  |  0  0 28  | 29  0
3685            30  0  0  | 31 32 33  |  0 34
3686 .ve
3687 
3688    This can be represented as a collection of submatrices as:
3689 
3690 .vb
3691       A B C
3692       D E F
3693       G H I
3694 .ve
3695 
3696    Where the submatrices A,B,C are owned by proc0, D,E,F are
3697    owned by proc1, G,H,I are owned by proc2.
3698 
3699    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3700    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3701    The 'M','N' parameters are 8,8, and have the same values on all procs.
3702 
3703    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3704    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3705    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3706    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3707    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3708    matrix, ans [DF] as another SeqAIJ matrix.
3709 
3710    When d_nz, o_nz parameters are specified, d_nz storage elements are
3711    allocated for every row of the local diagonal submatrix, and o_nz
3712    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3713    One way to choose d_nz and o_nz is to use the max nonzerors per local
3714    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3715    In this case, the values of d_nz,o_nz are:
3716 .vb
3717      proc0 : dnz = 2, o_nz = 2
3718      proc1 : dnz = 3, o_nz = 2
3719      proc2 : dnz = 1, o_nz = 4
3720 .ve
3721    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3722    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3723    for proc3. i.e we are using 12+15+10=37 storage locations to store
3724    34 values.
3725 
3726    When d_nnz, o_nnz parameters are specified, the storage is specified
3727    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3728    In the above case the values for d_nnz,o_nnz are:
3729 .vb
3730      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3731      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3732      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3733 .ve
3734    Here the space allocated is sum of all the above values i.e 34, and
3735    hence pre-allocation is perfect.
3736 
3737    Level: intermediate
3738 
3739 .keywords: matrix, aij, compressed row, sparse, parallel
3740 
3741 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3742           MPIAIJ, MatCreateMPIAIJWithArrays()
3743 @*/
3744 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)
3745 {
3746   PetscErrorCode ierr;
3747   PetscMPIInt    size;
3748 
3749   PetscFunctionBegin;
3750   ierr = MatCreate(comm,A);CHKERRQ(ierr);
3751   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
3752   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3753   if (size > 1) {
3754     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
3755     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
3756   } else {
3757     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
3758     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
3759   }
3760   PetscFunctionReturn(0);
3761 }
3762 
3763 #undef __FUNCT__
3764 #define __FUNCT__ "MatMPIAIJGetSeqAIJ"
3765 PetscErrorCode  MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
3766 {
3767   Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
3768 
3769   PetscFunctionBegin;
3770   if (Ad)     *Ad     = a->A;
3771   if (Ao)     *Ao     = a->B;
3772   if (colmap) *colmap = a->garray;
3773   PetscFunctionReturn(0);
3774 }
3775 
3776 #undef __FUNCT__
3777 #define __FUNCT__ "MatSetColoring_MPIAIJ"
3778 PetscErrorCode MatSetColoring_MPIAIJ(Mat A,ISColoring coloring)
3779 {
3780   PetscErrorCode ierr;
3781   PetscInt       i;
3782   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3783 
3784   PetscFunctionBegin;
3785   if (coloring->ctype == IS_COLORING_GLOBAL) {
3786     ISColoringValue *allcolors,*colors;
3787     ISColoring      ocoloring;
3788 
3789     /* set coloring for diagonal portion */
3790     ierr = MatSetColoring_SeqAIJ(a->A,coloring);CHKERRQ(ierr);
3791 
3792     /* set coloring for off-diagonal portion */
3793     ierr = ISAllGatherColors(PetscObjectComm((PetscObject)A),coloring->n,coloring->colors,NULL,&allcolors);CHKERRQ(ierr);
3794     ierr = PetscMalloc1(a->B->cmap->n+1,&colors);CHKERRQ(ierr);
3795     for (i=0; i<a->B->cmap->n; i++) {
3796       colors[i] = allcolors[a->garray[i]];
3797     }
3798     ierr = PetscFree(allcolors);CHKERRQ(ierr);
3799     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3800     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
3801     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3802   } else if (coloring->ctype == IS_COLORING_GHOSTED) {
3803     ISColoringValue *colors;
3804     PetscInt        *larray;
3805     ISColoring      ocoloring;
3806 
3807     /* set coloring for diagonal portion */
3808     ierr = PetscMalloc1(a->A->cmap->n+1,&larray);CHKERRQ(ierr);
3809     for (i=0; i<a->A->cmap->n; i++) {
3810       larray[i] = i + A->cmap->rstart;
3811     }
3812     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->A->cmap->n,larray,NULL,larray);CHKERRQ(ierr);
3813     ierr = PetscMalloc1(a->A->cmap->n+1,&colors);CHKERRQ(ierr);
3814     for (i=0; i<a->A->cmap->n; i++) {
3815       colors[i] = coloring->colors[larray[i]];
3816     }
3817     ierr = PetscFree(larray);CHKERRQ(ierr);
3818     ierr = ISColoringCreate(PETSC_COMM_SELF,coloring->n,a->A->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3819     ierr = MatSetColoring_SeqAIJ(a->A,ocoloring);CHKERRQ(ierr);
3820     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3821 
3822     /* set coloring for off-diagonal portion */
3823     ierr = PetscMalloc1(a->B->cmap->n+1,&larray);CHKERRQ(ierr);
3824     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->B->cmap->n,a->garray,NULL,larray);CHKERRQ(ierr);
3825     ierr = PetscMalloc1(a->B->cmap->n+1,&colors);CHKERRQ(ierr);
3826     for (i=0; i<a->B->cmap->n; i++) {
3827       colors[i] = coloring->colors[larray[i]];
3828     }
3829     ierr = PetscFree(larray);CHKERRQ(ierr);
3830     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3831     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
3832     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3833   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support ISColoringType %d",(int)coloring->ctype);
3834   PetscFunctionReturn(0);
3835 }
3836 
3837 #undef __FUNCT__
3838 #define __FUNCT__ "MatSetValuesAdifor_MPIAIJ"
3839 PetscErrorCode MatSetValuesAdifor_MPIAIJ(Mat A,PetscInt nl,void *advalues)
3840 {
3841   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3842   PetscErrorCode ierr;
3843 
3844   PetscFunctionBegin;
3845   ierr = MatSetValuesAdifor_SeqAIJ(a->A,nl,advalues);CHKERRQ(ierr);
3846   ierr = MatSetValuesAdifor_SeqAIJ(a->B,nl,advalues);CHKERRQ(ierr);
3847   PetscFunctionReturn(0);
3848 }
3849 
3850 #undef __FUNCT__
3851 #define __FUNCT__ "MatCreateMPIMatConcatenateSeqMat_MPIAIJ"
3852 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
3853 {
3854   PetscErrorCode ierr;
3855   PetscInt       m,N,i,rstart,nnz,Ii;
3856   PetscInt       *indx;
3857   PetscScalar    *values;
3858 
3859   PetscFunctionBegin;
3860   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
3861   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
3862     PetscInt       *dnz,*onz,sum,bs,cbs;
3863 
3864     if (n == PETSC_DECIDE) {
3865       ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
3866     }
3867     /* Check sum(n) = N */
3868     ierr = MPIU_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3869     if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
3870 
3871     ierr    = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3872     rstart -= m;
3873 
3874     ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
3875     for (i=0; i<m; i++) {
3876       ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3877       ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
3878       ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3879     }
3880 
3881     ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
3882     ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
3883     ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
3884     ierr = MatSetBlockSizes(*outmat,bs,cbs);CHKERRQ(ierr);
3885     ierr = MatSetType(*outmat,MATMPIAIJ);CHKERRQ(ierr);
3886     ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
3887     ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
3888   }
3889 
3890   /* numeric phase */
3891   ierr = MatGetOwnershipRange(*outmat,&rstart,NULL);CHKERRQ(ierr);
3892   for (i=0; i<m; i++) {
3893     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3894     Ii   = i + rstart;
3895     ierr = MatSetValues(*outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3896     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3897   }
3898   ierr = MatAssemblyBegin(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3899   ierr = MatAssemblyEnd(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3900   PetscFunctionReturn(0);
3901 }
3902 
3903 #undef __FUNCT__
3904 #define __FUNCT__ "MatFileSplit"
3905 PetscErrorCode MatFileSplit(Mat A,char *outfile)
3906 {
3907   PetscErrorCode    ierr;
3908   PetscMPIInt       rank;
3909   PetscInt          m,N,i,rstart,nnz;
3910   size_t            len;
3911   const PetscInt    *indx;
3912   PetscViewer       out;
3913   char              *name;
3914   Mat               B;
3915   const PetscScalar *values;
3916 
3917   PetscFunctionBegin;
3918   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
3919   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
3920   /* Should this be the type of the diagonal block of A? */
3921   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
3922   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
3923   ierr = MatSetBlockSizesFromMats(B,A,A);CHKERRQ(ierr);
3924   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
3925   ierr = MatSeqAIJSetPreallocation(B,0,NULL);CHKERRQ(ierr);
3926   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
3927   for (i=0; i<m; i++) {
3928     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3929     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3930     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3931   }
3932   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3933   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3934 
3935   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
3936   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
3937   ierr = PetscMalloc1(len+5,&name);CHKERRQ(ierr);
3938   sprintf(name,"%s.%d",outfile,rank);
3939   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
3940   ierr = PetscFree(name);CHKERRQ(ierr);
3941   ierr = MatView(B,out);CHKERRQ(ierr);
3942   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
3943   ierr = MatDestroy(&B);CHKERRQ(ierr);
3944   PetscFunctionReturn(0);
3945 }
3946 
3947 extern PetscErrorCode MatDestroy_MPIAIJ(Mat);
3948 #undef __FUNCT__
3949 #define __FUNCT__ "MatDestroy_MPIAIJ_SeqsToMPI"
3950 PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
3951 {
3952   PetscErrorCode      ierr;
3953   Mat_Merge_SeqsToMPI *merge;
3954   PetscContainer      container;
3955 
3956   PetscFunctionBegin;
3957   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
3958   if (container) {
3959     ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
3960     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
3961     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
3962     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
3963     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
3964     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
3965     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
3966     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
3967     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
3968     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
3969     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
3970     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
3971     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
3972     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
3973     ierr = PetscFree(merge);CHKERRQ(ierr);
3974     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
3975   }
3976   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
3977   PetscFunctionReturn(0);
3978 }
3979 
3980 #include <../src/mat/utils/freespace.h>
3981 #include <petscbt.h>
3982 
3983 #undef __FUNCT__
3984 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJNumeric"
3985 PetscErrorCode  MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
3986 {
3987   PetscErrorCode      ierr;
3988   MPI_Comm            comm;
3989   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
3990   PetscMPIInt         size,rank,taga,*len_s;
3991   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
3992   PetscInt            proc,m;
3993   PetscInt            **buf_ri,**buf_rj;
3994   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
3995   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
3996   MPI_Request         *s_waits,*r_waits;
3997   MPI_Status          *status;
3998   MatScalar           *aa=a->a;
3999   MatScalar           **abuf_r,*ba_i;
4000   Mat_Merge_SeqsToMPI *merge;
4001   PetscContainer      container;
4002 
4003   PetscFunctionBegin;
4004   ierr = PetscObjectGetComm((PetscObject)mpimat,&comm);CHKERRQ(ierr);
4005   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4006 
4007   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4008   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4009 
4010   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4011   ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4012 
4013   bi     = merge->bi;
4014   bj     = merge->bj;
4015   buf_ri = merge->buf_ri;
4016   buf_rj = merge->buf_rj;
4017 
4018   ierr   = PetscMalloc1(size,&status);CHKERRQ(ierr);
4019   owners = merge->rowmap->range;
4020   len_s  = merge->len_s;
4021 
4022   /* send and recv matrix values */
4023   /*-----------------------------*/
4024   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
4025   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
4026 
4027   ierr = PetscMalloc1(merge->nsend+1,&s_waits);CHKERRQ(ierr);
4028   for (proc=0,k=0; proc<size; proc++) {
4029     if (!len_s[proc]) continue;
4030     i    = owners[proc];
4031     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
4032     k++;
4033   }
4034 
4035   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
4036   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
4037   ierr = PetscFree(status);CHKERRQ(ierr);
4038 
4039   ierr = PetscFree(s_waits);CHKERRQ(ierr);
4040   ierr = PetscFree(r_waits);CHKERRQ(ierr);
4041 
4042   /* insert mat values of mpimat */
4043   /*----------------------------*/
4044   ierr = PetscMalloc1(N,&ba_i);CHKERRQ(ierr);
4045   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4046 
4047   for (k=0; k<merge->nrecv; k++) {
4048     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4049     nrows       = *(buf_ri_k[k]);
4050     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
4051     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4052   }
4053 
4054   /* set values of ba */
4055   m = merge->rowmap->n;
4056   for (i=0; i<m; i++) {
4057     arow = owners[rank] + i;
4058     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
4059     bnzi = bi[i+1] - bi[i];
4060     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
4061 
4062     /* add local non-zero vals of this proc's seqmat into ba */
4063     anzi   = ai[arow+1] - ai[arow];
4064     aj     = a->j + ai[arow];
4065     aa     = a->a + ai[arow];
4066     nextaj = 0;
4067     for (j=0; nextaj<anzi; j++) {
4068       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4069         ba_i[j] += aa[nextaj++];
4070       }
4071     }
4072 
4073     /* add received vals into ba */
4074     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4075       /* i-th row */
4076       if (i == *nextrow[k]) {
4077         anzi   = *(nextai[k]+1) - *nextai[k];
4078         aj     = buf_rj[k] + *(nextai[k]);
4079         aa     = abuf_r[k] + *(nextai[k]);
4080         nextaj = 0;
4081         for (j=0; nextaj<anzi; j++) {
4082           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4083             ba_i[j] += aa[nextaj++];
4084           }
4085         }
4086         nextrow[k]++; nextai[k]++;
4087       }
4088     }
4089     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
4090   }
4091   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4092   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4093 
4094   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
4095   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
4096   ierr = PetscFree(ba_i);CHKERRQ(ierr);
4097   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4098   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4099   PetscFunctionReturn(0);
4100 }
4101 
4102 extern PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat);
4103 
4104 #undef __FUNCT__
4105 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJSymbolic"
4106 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4107 {
4108   PetscErrorCode      ierr;
4109   Mat                 B_mpi;
4110   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
4111   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4112   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
4113   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4114   PetscInt            len,proc,*dnz,*onz,bs,cbs;
4115   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4116   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4117   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
4118   MPI_Status          *status;
4119   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
4120   PetscBT             lnkbt;
4121   Mat_Merge_SeqsToMPI *merge;
4122   PetscContainer      container;
4123 
4124   PetscFunctionBegin;
4125   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4126 
4127   /* make sure it is a PETSc comm */
4128   ierr = PetscCommDuplicate(comm,&comm,NULL);CHKERRQ(ierr);
4129   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4130   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4131 
4132   ierr = PetscNew(&merge);CHKERRQ(ierr);
4133   ierr = PetscMalloc1(size,&status);CHKERRQ(ierr);
4134 
4135   /* determine row ownership */
4136   /*---------------------------------------------------------*/
4137   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
4138   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
4139   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
4140   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
4141   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
4142   ierr = PetscMalloc1(size,&len_si);CHKERRQ(ierr);
4143   ierr = PetscMalloc1(size,&merge->len_s);CHKERRQ(ierr);
4144 
4145   m      = merge->rowmap->n;
4146   owners = merge->rowmap->range;
4147 
4148   /* determine the number of messages to send, their lengths */
4149   /*---------------------------------------------------------*/
4150   len_s = merge->len_s;
4151 
4152   len          = 0; /* length of buf_si[] */
4153   merge->nsend = 0;
4154   for (proc=0; proc<size; proc++) {
4155     len_si[proc] = 0;
4156     if (proc == rank) {
4157       len_s[proc] = 0;
4158     } else {
4159       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4160       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4161     }
4162     if (len_s[proc]) {
4163       merge->nsend++;
4164       nrows = 0;
4165       for (i=owners[proc]; i<owners[proc+1]; i++) {
4166         if (ai[i+1] > ai[i]) nrows++;
4167       }
4168       len_si[proc] = 2*(nrows+1);
4169       len         += len_si[proc];
4170     }
4171   }
4172 
4173   /* determine the number and length of messages to receive for ij-structure */
4174   /*-------------------------------------------------------------------------*/
4175   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
4176   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
4177 
4178   /* post the Irecv of j-structure */
4179   /*-------------------------------*/
4180   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
4181   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
4182 
4183   /* post the Isend of j-structure */
4184   /*--------------------------------*/
4185   ierr = PetscMalloc2(merge->nsend,&si_waits,merge->nsend,&sj_waits);CHKERRQ(ierr);
4186 
4187   for (proc=0, k=0; proc<size; proc++) {
4188     if (!len_s[proc]) continue;
4189     i    = owners[proc];
4190     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
4191     k++;
4192   }
4193 
4194   /* receives and sends of j-structure are complete */
4195   /*------------------------------------------------*/
4196   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
4197   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
4198 
4199   /* send and recv i-structure */
4200   /*---------------------------*/
4201   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
4202   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
4203 
4204   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
4205   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4206   for (proc=0,k=0; proc<size; proc++) {
4207     if (!len_s[proc]) continue;
4208     /* form outgoing message for i-structure:
4209          buf_si[0]:                 nrows to be sent
4210                [1:nrows]:           row index (global)
4211                [nrows+1:2*nrows+1]: i-structure index
4212     */
4213     /*-------------------------------------------*/
4214     nrows       = len_si[proc]/2 - 1;
4215     buf_si_i    = buf_si + nrows+1;
4216     buf_si[0]   = nrows;
4217     buf_si_i[0] = 0;
4218     nrows       = 0;
4219     for (i=owners[proc]; i<owners[proc+1]; i++) {
4220       anzi = ai[i+1] - ai[i];
4221       if (anzi) {
4222         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4223         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4224         nrows++;
4225       }
4226     }
4227     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4228     k++;
4229     buf_si += len_si[proc];
4230   }
4231 
4232   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4233   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4234 
4235   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4236   for (i=0; i<merge->nrecv; i++) {
4237     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);
4238   }
4239 
4240   ierr = PetscFree(len_si);CHKERRQ(ierr);
4241   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4242   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4243   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4244   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4245   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4246   ierr = PetscFree(status);CHKERRQ(ierr);
4247 
4248   /* compute a local seq matrix in each processor */
4249   /*----------------------------------------------*/
4250   /* allocate bi array and free space for accumulating nonzero column info */
4251   ierr  = PetscMalloc1(m+1,&bi);CHKERRQ(ierr);
4252   bi[0] = 0;
4253 
4254   /* create and initialize a linked list */
4255   nlnk = N+1;
4256   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4257 
4258   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4259   len  = ai[owners[rank+1]] - ai[owners[rank]];
4260   ierr = PetscFreeSpaceGet(PetscIntMultTruncate(2,len)+1,&free_space);CHKERRQ(ierr);
4261 
4262   current_space = free_space;
4263 
4264   /* determine symbolic info for each local row */
4265   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4266 
4267   for (k=0; k<merge->nrecv; k++) {
4268     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4269     nrows       = *buf_ri_k[k];
4270     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4271     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4272   }
4273 
4274   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4275   len  = 0;
4276   for (i=0; i<m; i++) {
4277     bnzi = 0;
4278     /* add local non-zero cols of this proc's seqmat into lnk */
4279     arow  = owners[rank] + i;
4280     anzi  = ai[arow+1] - ai[arow];
4281     aj    = a->j + ai[arow];
4282     ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4283     bnzi += nlnk;
4284     /* add received col data into lnk */
4285     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4286       if (i == *nextrow[k]) { /* i-th row */
4287         anzi  = *(nextai[k]+1) - *nextai[k];
4288         aj    = buf_rj[k] + *nextai[k];
4289         ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4290         bnzi += nlnk;
4291         nextrow[k]++; nextai[k]++;
4292       }
4293     }
4294     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4295 
4296     /* if free space is not available, make more free space */
4297     if (current_space->local_remaining<bnzi) {
4298       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(bnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
4299       nspacedouble++;
4300     }
4301     /* copy data into free space, then initialize lnk */
4302     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4303     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
4304 
4305     current_space->array           += bnzi;
4306     current_space->local_used      += bnzi;
4307     current_space->local_remaining -= bnzi;
4308 
4309     bi[i+1] = bi[i] + bnzi;
4310   }
4311 
4312   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4313 
4314   ierr = PetscMalloc1(bi[m]+1,&bj);CHKERRQ(ierr);
4315   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
4316   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4317 
4318   /* create symbolic parallel matrix B_mpi */
4319   /*---------------------------------------*/
4320   ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
4321   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
4322   if (n==PETSC_DECIDE) {
4323     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
4324   } else {
4325     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4326   }
4327   ierr = MatSetBlockSizes(B_mpi,bs,cbs);CHKERRQ(ierr);
4328   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
4329   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
4330   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4331   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
4332 
4333   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4334   B_mpi->assembled    = PETSC_FALSE;
4335   B_mpi->ops->destroy = MatDestroy_MPIAIJ_SeqsToMPI;
4336   merge->bi           = bi;
4337   merge->bj           = bj;
4338   merge->buf_ri       = buf_ri;
4339   merge->buf_rj       = buf_rj;
4340   merge->coi          = NULL;
4341   merge->coj          = NULL;
4342   merge->owners_co    = NULL;
4343 
4344   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
4345 
4346   /* attach the supporting struct to B_mpi for reuse */
4347   ierr    = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
4348   ierr    = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
4349   ierr    = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
4350   ierr    = PetscContainerDestroy(&container);CHKERRQ(ierr);
4351   *mpimat = B_mpi;
4352 
4353   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4354   PetscFunctionReturn(0);
4355 }
4356 
4357 #undef __FUNCT__
4358 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJ"
4359 /*@C
4360       MatCreateMPIAIJSumSeqAIJ - Creates a MPIAIJ matrix by adding sequential
4361                  matrices from each processor
4362 
4363     Collective on MPI_Comm
4364 
4365    Input Parameters:
4366 +    comm - the communicators the parallel matrix will live on
4367 .    seqmat - the input sequential matrices
4368 .    m - number of local rows (or PETSC_DECIDE)
4369 .    n - number of local columns (or PETSC_DECIDE)
4370 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4371 
4372    Output Parameter:
4373 .    mpimat - the parallel matrix generated
4374 
4375     Level: advanced
4376 
4377    Notes:
4378      The dimensions of the sequential matrix in each processor MUST be the same.
4379      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
4380      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
4381 @*/
4382 PetscErrorCode  MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
4383 {
4384   PetscErrorCode ierr;
4385   PetscMPIInt    size;
4386 
4387   PetscFunctionBegin;
4388   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4389   if (size == 1) {
4390     ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4391     if (scall == MAT_INITIAL_MATRIX) {
4392       ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
4393     } else {
4394       ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4395     }
4396     ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4397     PetscFunctionReturn(0);
4398   }
4399   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4400   if (scall == MAT_INITIAL_MATRIX) {
4401     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
4402   }
4403   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
4404   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4405   PetscFunctionReturn(0);
4406 }
4407 
4408 #undef __FUNCT__
4409 #define __FUNCT__ "MatMPIAIJGetLocalMat"
4410 /*@
4411      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
4412           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
4413           with MatGetSize()
4414 
4415     Not Collective
4416 
4417    Input Parameters:
4418 +    A - the matrix
4419 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4420 
4421    Output Parameter:
4422 .    A_loc - the local sequential matrix generated
4423 
4424     Level: developer
4425 
4426 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
4427 
4428 @*/
4429 PetscErrorCode  MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
4430 {
4431   PetscErrorCode ierr;
4432   Mat_MPIAIJ     *mpimat=(Mat_MPIAIJ*)A->data;
4433   Mat_SeqAIJ     *mat,*a,*b;
4434   PetscInt       *ai,*aj,*bi,*bj,*cmap=mpimat->garray;
4435   MatScalar      *aa,*ba,*cam;
4436   PetscScalar    *ca;
4437   PetscInt       am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
4438   PetscInt       *ci,*cj,col,ncols_d,ncols_o,jo;
4439   PetscBool      match;
4440   MPI_Comm       comm;
4441   PetscMPIInt    size;
4442 
4443   PetscFunctionBegin;
4444   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4445   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
4446   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4447   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4448   if (size == 1 && scall == MAT_REUSE_MATRIX) PetscFunctionReturn(0);
4449 
4450   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4451   a = (Mat_SeqAIJ*)(mpimat->A)->data;
4452   b = (Mat_SeqAIJ*)(mpimat->B)->data;
4453   ai = a->i; aj = a->j; bi = b->i; bj = b->j;
4454   aa = a->a; ba = b->a;
4455   if (scall == MAT_INITIAL_MATRIX) {
4456     if (size == 1) {
4457       ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ai,aj,aa,A_loc);CHKERRQ(ierr);
4458       PetscFunctionReturn(0);
4459     }
4460 
4461     ierr  = PetscMalloc1(1+am,&ci);CHKERRQ(ierr);
4462     ci[0] = 0;
4463     for (i=0; i<am; i++) {
4464       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
4465     }
4466     ierr = PetscMalloc1(1+ci[am],&cj);CHKERRQ(ierr);
4467     ierr = PetscMalloc1(1+ci[am],&ca);CHKERRQ(ierr);
4468     k    = 0;
4469     for (i=0; i<am; i++) {
4470       ncols_o = bi[i+1] - bi[i];
4471       ncols_d = ai[i+1] - ai[i];
4472       /* off-diagonal portion of A */
4473       for (jo=0; jo<ncols_o; jo++) {
4474         col = cmap[*bj];
4475         if (col >= cstart) break;
4476         cj[k]   = col; bj++;
4477         ca[k++] = *ba++;
4478       }
4479       /* diagonal portion of A */
4480       for (j=0; j<ncols_d; j++) {
4481         cj[k]   = cstart + *aj++;
4482         ca[k++] = *aa++;
4483       }
4484       /* off-diagonal portion of A */
4485       for (j=jo; j<ncols_o; j++) {
4486         cj[k]   = cmap[*bj++];
4487         ca[k++] = *ba++;
4488       }
4489     }
4490     /* put together the new matrix */
4491     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
4492     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4493     /* Since these are PETSc arrays, change flags to free them as necessary. */
4494     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
4495     mat->free_a  = PETSC_TRUE;
4496     mat->free_ij = PETSC_TRUE;
4497     mat->nonew   = 0;
4498   } else if (scall == MAT_REUSE_MATRIX) {
4499     mat=(Mat_SeqAIJ*)(*A_loc)->data;
4500     ci = mat->i; cj = mat->j; cam = mat->a;
4501     for (i=0; i<am; i++) {
4502       /* off-diagonal portion of A */
4503       ncols_o = bi[i+1] - bi[i];
4504       for (jo=0; jo<ncols_o; jo++) {
4505         col = cmap[*bj];
4506         if (col >= cstart) break;
4507         *cam++ = *ba++; bj++;
4508       }
4509       /* diagonal portion of A */
4510       ncols_d = ai[i+1] - ai[i];
4511       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
4512       /* off-diagonal portion of A */
4513       for (j=jo; j<ncols_o; j++) {
4514         *cam++ = *ba++; bj++;
4515       }
4516     }
4517   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
4518   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4519   PetscFunctionReturn(0);
4520 }
4521 
4522 #undef __FUNCT__
4523 #define __FUNCT__ "MatMPIAIJGetLocalMatCondensed"
4524 /*@C
4525      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MPIAIJ matrix by taking all its local rows and NON-ZERO columns
4526 
4527     Not Collective
4528 
4529    Input Parameters:
4530 +    A - the matrix
4531 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4532 -    row, col - index sets of rows and columns to extract (or NULL)
4533 
4534    Output Parameter:
4535 .    A_loc - the local sequential matrix generated
4536 
4537     Level: developer
4538 
4539 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
4540 
4541 @*/
4542 PetscErrorCode  MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
4543 {
4544   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4545   PetscErrorCode ierr;
4546   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
4547   IS             isrowa,iscola;
4548   Mat            *aloc;
4549   PetscBool      match;
4550 
4551   PetscFunctionBegin;
4552   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4553   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
4554   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4555   if (!row) {
4556     start = A->rmap->rstart; end = A->rmap->rend;
4557     ierr  = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
4558   } else {
4559     isrowa = *row;
4560   }
4561   if (!col) {
4562     start = A->cmap->rstart;
4563     cmap  = a->garray;
4564     nzA   = a->A->cmap->n;
4565     nzB   = a->B->cmap->n;
4566     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4567     ncols = 0;
4568     for (i=0; i<nzB; i++) {
4569       if (cmap[i] < start) idx[ncols++] = cmap[i];
4570       else break;
4571     }
4572     imark = i;
4573     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
4574     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
4575     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
4576   } else {
4577     iscola = *col;
4578   }
4579   if (scall != MAT_INITIAL_MATRIX) {
4580     ierr    = PetscMalloc1(1,&aloc);CHKERRQ(ierr);
4581     aloc[0] = *A_loc;
4582   }
4583   ierr   = MatGetSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
4584   *A_loc = aloc[0];
4585   ierr   = PetscFree(aloc);CHKERRQ(ierr);
4586   if (!row) {
4587     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
4588   }
4589   if (!col) {
4590     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
4591   }
4592   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4593   PetscFunctionReturn(0);
4594 }
4595 
4596 #undef __FUNCT__
4597 #define __FUNCT__ "MatGetBrowsOfAcols"
4598 /*@C
4599     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
4600 
4601     Collective on Mat
4602 
4603    Input Parameters:
4604 +    A,B - the matrices in mpiaij format
4605 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4606 -    rowb, colb - index sets of rows and columns of B to extract (or NULL)
4607 
4608    Output Parameter:
4609 +    rowb, colb - index sets of rows and columns of B to extract
4610 -    B_seq - the sequential matrix generated
4611 
4612     Level: developer
4613 
4614 @*/
4615 PetscErrorCode  MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
4616 {
4617   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4618   PetscErrorCode ierr;
4619   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
4620   IS             isrowb,iscolb;
4621   Mat            *bseq=NULL;
4622 
4623   PetscFunctionBegin;
4624   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4625     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);
4626   }
4627   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4628 
4629   if (scall == MAT_INITIAL_MATRIX) {
4630     start = A->cmap->rstart;
4631     cmap  = a->garray;
4632     nzA   = a->A->cmap->n;
4633     nzB   = a->B->cmap->n;
4634     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4635     ncols = 0;
4636     for (i=0; i<nzB; i++) {  /* row < local row index */
4637       if (cmap[i] < start) idx[ncols++] = cmap[i];
4638       else break;
4639     }
4640     imark = i;
4641     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
4642     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
4643     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
4644     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
4645   } else {
4646     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
4647     isrowb  = *rowb; iscolb = *colb;
4648     ierr    = PetscMalloc1(1,&bseq);CHKERRQ(ierr);
4649     bseq[0] = *B_seq;
4650   }
4651   ierr   = MatGetSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
4652   *B_seq = bseq[0];
4653   ierr   = PetscFree(bseq);CHKERRQ(ierr);
4654   if (!rowb) {
4655     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
4656   } else {
4657     *rowb = isrowb;
4658   }
4659   if (!colb) {
4660     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
4661   } else {
4662     *colb = iscolb;
4663   }
4664   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4665   PetscFunctionReturn(0);
4666 }
4667 
4668 #undef __FUNCT__
4669 #define __FUNCT__ "MatGetBrowsOfAoCols_MPIAIJ"
4670 /*
4671     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
4672     of the OFF-DIAGONAL portion of local A
4673 
4674     Collective on Mat
4675 
4676    Input Parameters:
4677 +    A,B - the matrices in mpiaij format
4678 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4679 
4680    Output Parameter:
4681 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
4682 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
4683 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
4684 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
4685 
4686     Level: developer
4687 
4688 */
4689 PetscErrorCode  MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
4690 {
4691   VecScatter_MPI_General *gen_to,*gen_from;
4692   PetscErrorCode         ierr;
4693   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
4694   Mat_SeqAIJ             *b_oth;
4695   VecScatter             ctx =a->Mvctx;
4696   MPI_Comm               comm;
4697   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
4698   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
4699   PetscScalar            *rvalues,*svalues;
4700   MatScalar              *b_otha,*bufa,*bufA;
4701   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
4702   MPI_Request            *rwaits = NULL,*swaits = NULL;
4703   MPI_Status             *sstatus,rstatus;
4704   PetscMPIInt            jj,size;
4705   PetscInt               *cols,sbs,rbs;
4706   PetscScalar            *vals;
4707 
4708   PetscFunctionBegin;
4709   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4710   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4711 
4712   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4713     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);
4714   }
4715   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4716   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4717 
4718   gen_to   = (VecScatter_MPI_General*)ctx->todata;
4719   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
4720   rvalues  = gen_from->values; /* holds the length of receiving row */
4721   svalues  = gen_to->values;   /* holds the length of sending row */
4722   nrecvs   = gen_from->n;
4723   nsends   = gen_to->n;
4724 
4725   ierr    = PetscMalloc2(nrecvs,&rwaits,nsends,&swaits);CHKERRQ(ierr);
4726   srow    = gen_to->indices;    /* local row index to be sent */
4727   sstarts = gen_to->starts;
4728   sprocs  = gen_to->procs;
4729   sstatus = gen_to->sstatus;
4730   sbs     = gen_to->bs;
4731   rstarts = gen_from->starts;
4732   rprocs  = gen_from->procs;
4733   rbs     = gen_from->bs;
4734 
4735   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
4736   if (scall == MAT_INITIAL_MATRIX) {
4737     /* i-array */
4738     /*---------*/
4739     /*  post receives */
4740     for (i=0; i<nrecvs; i++) {
4741       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
4742       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
4743       ierr   = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4744     }
4745 
4746     /* pack the outgoing message */
4747     ierr = PetscMalloc2(nsends+1,&sstartsj,nrecvs+1,&rstartsj);CHKERRQ(ierr);
4748 
4749     sstartsj[0] = 0;
4750     rstartsj[0] = 0;
4751     len         = 0; /* total length of j or a array to be sent */
4752     k           = 0;
4753     for (i=0; i<nsends; i++) {
4754       rowlen = (PetscInt*)svalues + sstarts[i]*sbs;
4755       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
4756       for (j=0; j<nrows; j++) {
4757         row = srow[k] + B->rmap->range[rank]; /* global row idx */
4758         for (l=0; l<sbs; l++) {
4759           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr); /* rowlength */
4760 
4761           rowlen[j*sbs+l] = ncols;
4762 
4763           len += ncols;
4764           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr);
4765         }
4766         k++;
4767       }
4768       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4769 
4770       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
4771     }
4772     /* recvs and sends of i-array are completed */
4773     i = nrecvs;
4774     while (i--) {
4775       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4776     }
4777     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4778 
4779     /* allocate buffers for sending j and a arrays */
4780     ierr = PetscMalloc1(len+1,&bufj);CHKERRQ(ierr);
4781     ierr = PetscMalloc1(len+1,&bufa);CHKERRQ(ierr);
4782 
4783     /* create i-array of B_oth */
4784     ierr = PetscMalloc1(aBn+2,&b_othi);CHKERRQ(ierr);
4785 
4786     b_othi[0] = 0;
4787     len       = 0; /* total length of j or a array to be received */
4788     k         = 0;
4789     for (i=0; i<nrecvs; i++) {
4790       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
4791       nrows  = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be received */
4792       for (j=0; j<nrows; j++) {
4793         b_othi[k+1] = b_othi[k] + rowlen[j];
4794         ierr = PetscIntSumError(rowlen[j],len,&len);
4795         k++;
4796       }
4797       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
4798     }
4799 
4800     /* allocate space for j and a arrrays of B_oth */
4801     ierr = PetscMalloc1(b_othi[aBn]+1,&b_othj);CHKERRQ(ierr);
4802     ierr = PetscMalloc1(b_othi[aBn]+1,&b_otha);CHKERRQ(ierr);
4803 
4804     /* j-array */
4805     /*---------*/
4806     /*  post receives of j-array */
4807     for (i=0; i<nrecvs; i++) {
4808       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4809       ierr  = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4810     }
4811 
4812     /* pack the outgoing message j-array */
4813     k = 0;
4814     for (i=0; i<nsends; i++) {
4815       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4816       bufJ  = bufj+sstartsj[i];
4817       for (j=0; j<nrows; j++) {
4818         row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4819         for (ll=0; ll<sbs; ll++) {
4820           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4821           for (l=0; l<ncols; l++) {
4822             *bufJ++ = cols[l];
4823           }
4824           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4825         }
4826       }
4827       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4828     }
4829 
4830     /* recvs and sends of j-array are completed */
4831     i = nrecvs;
4832     while (i--) {
4833       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4834     }
4835     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4836   } else if (scall == MAT_REUSE_MATRIX) {
4837     sstartsj = *startsj_s;
4838     rstartsj = *startsj_r;
4839     bufa     = *bufa_ptr;
4840     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
4841     b_otha   = b_oth->a;
4842   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
4843 
4844   /* a-array */
4845   /*---------*/
4846   /*  post receives of a-array */
4847   for (i=0; i<nrecvs; i++) {
4848     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4849     ierr  = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4850   }
4851 
4852   /* pack the outgoing message a-array */
4853   k = 0;
4854   for (i=0; i<nsends; i++) {
4855     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4856     bufA  = bufa+sstartsj[i];
4857     for (j=0; j<nrows; j++) {
4858       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4859       for (ll=0; ll<sbs; ll++) {
4860         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4861         for (l=0; l<ncols; l++) {
4862           *bufA++ = vals[l];
4863         }
4864         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4865       }
4866     }
4867     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4868   }
4869   /* recvs and sends of a-array are completed */
4870   i = nrecvs;
4871   while (i--) {
4872     ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4873   }
4874   if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4875   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
4876 
4877   if (scall == MAT_INITIAL_MATRIX) {
4878     /* put together the new matrix */
4879     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
4880 
4881     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4882     /* Since these are PETSc arrays, change flags to free them as necessary. */
4883     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
4884     b_oth->free_a  = PETSC_TRUE;
4885     b_oth->free_ij = PETSC_TRUE;
4886     b_oth->nonew   = 0;
4887 
4888     ierr = PetscFree(bufj);CHKERRQ(ierr);
4889     if (!startsj_s || !bufa_ptr) {
4890       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
4891       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
4892     } else {
4893       *startsj_s = sstartsj;
4894       *startsj_r = rstartsj;
4895       *bufa_ptr  = bufa;
4896     }
4897   }
4898   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4899   PetscFunctionReturn(0);
4900 }
4901 
4902 #undef __FUNCT__
4903 #define __FUNCT__ "MatGetCommunicationStructs"
4904 /*@C
4905   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
4906 
4907   Not Collective
4908 
4909   Input Parameters:
4910 . A - The matrix in mpiaij format
4911 
4912   Output Parameter:
4913 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
4914 . colmap - A map from global column index to local index into lvec
4915 - multScatter - A scatter from the argument of a matrix-vector product to lvec
4916 
4917   Level: developer
4918 
4919 @*/
4920 #if defined(PETSC_USE_CTABLE)
4921 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
4922 #else
4923 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
4924 #endif
4925 {
4926   Mat_MPIAIJ *a;
4927 
4928   PetscFunctionBegin;
4929   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4930   PetscValidPointer(lvec, 2);
4931   PetscValidPointer(colmap, 3);
4932   PetscValidPointer(multScatter, 4);
4933   a = (Mat_MPIAIJ*) A->data;
4934   if (lvec) *lvec = a->lvec;
4935   if (colmap) *colmap = a->colmap;
4936   if (multScatter) *multScatter = a->Mvctx;
4937   PetscFunctionReturn(0);
4938 }
4939 
4940 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
4941 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
4942 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
4943 #if defined(PETSC_HAVE_ELEMENTAL)
4944 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
4945 #endif
4946 
4947 #undef __FUNCT__
4948 #define __FUNCT__ "MatMatMultNumeric_MPIDense_MPIAIJ"
4949 /*
4950     Computes (B'*A')' since computing B*A directly is untenable
4951 
4952                n                       p                          p
4953         (              )       (              )         (                  )
4954       m (      A       )  *  n (       B      )   =   m (         C        )
4955         (              )       (              )         (                  )
4956 
4957 */
4958 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
4959 {
4960   PetscErrorCode ierr;
4961   Mat            At,Bt,Ct;
4962 
4963   PetscFunctionBegin;
4964   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
4965   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
4966   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
4967   ierr = MatDestroy(&At);CHKERRQ(ierr);
4968   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
4969   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
4970   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
4971   PetscFunctionReturn(0);
4972 }
4973 
4974 #undef __FUNCT__
4975 #define __FUNCT__ "MatMatMultSymbolic_MPIDense_MPIAIJ"
4976 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
4977 {
4978   PetscErrorCode ierr;
4979   PetscInt       m=A->rmap->n,n=B->cmap->n;
4980   Mat            Cmat;
4981 
4982   PetscFunctionBegin;
4983   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);
4984   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
4985   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4986   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
4987   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
4988   ierr = MatMPIDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
4989   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4990   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4991 
4992   Cmat->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
4993 
4994   *C = Cmat;
4995   PetscFunctionReturn(0);
4996 }
4997 
4998 /* ----------------------------------------------------------------*/
4999 #undef __FUNCT__
5000 #define __FUNCT__ "MatMatMult_MPIDense_MPIAIJ"
5001 PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
5002 {
5003   PetscErrorCode ierr;
5004 
5005   PetscFunctionBegin;
5006   if (scall == MAT_INITIAL_MATRIX) {
5007     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5008     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
5009     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5010   }
5011   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5012   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
5013   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5014   PetscFunctionReturn(0);
5015 }
5016 
5017 /*MC
5018    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
5019 
5020    Options Database Keys:
5021 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
5022 
5023   Level: beginner
5024 
5025 .seealso: MatCreateAIJ()
5026 M*/
5027 
5028 #undef __FUNCT__
5029 #define __FUNCT__ "MatCreate_MPIAIJ"
5030 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
5031 {
5032   Mat_MPIAIJ     *b;
5033   PetscErrorCode ierr;
5034   PetscMPIInt    size;
5035 
5036   PetscFunctionBegin;
5037   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
5038 
5039   ierr          = PetscNewLog(B,&b);CHKERRQ(ierr);
5040   B->data       = (void*)b;
5041   ierr          = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
5042   B->assembled  = PETSC_FALSE;
5043   B->insertmode = NOT_SET_VALUES;
5044   b->size       = size;
5045 
5046   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank);CHKERRQ(ierr);
5047 
5048   /* build cache for off array entries formed */
5049   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash);CHKERRQ(ierr);
5050 
5051   b->donotstash  = PETSC_FALSE;
5052   b->colmap      = 0;
5053   b->garray      = 0;
5054   b->roworiented = PETSC_TRUE;
5055 
5056   /* stuff used for matrix vector multiply */
5057   b->lvec  = NULL;
5058   b->Mvctx = NULL;
5059 
5060   /* stuff for MatGetRow() */
5061   b->rowindices   = 0;
5062   b->rowvalues    = 0;
5063   b->getrowactive = PETSC_FALSE;
5064 
5065   /* flexible pointer used in CUSP/CUSPARSE classes */
5066   b->spptr = NULL;
5067 
5068   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetUseScalableIncreaseOverlap_C",MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ);CHKERRQ(ierr);
5069   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ);CHKERRQ(ierr);
5070   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
5071   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetDiagonalBlock_C",MatGetDiagonalBlock_MPIAIJ);CHKERRQ(ierr);
5072   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
5073   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
5074   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
5075   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
5076   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
5077   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
5078   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
5079 #if defined(PETSC_HAVE_ELEMENTAL)
5080   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_elemental_C",MatConvert_MPIAIJ_Elemental);CHKERRQ(ierr);
5081 #endif
5082   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
5083   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
5084   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
5085   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
5086   PetscFunctionReturn(0);
5087 }
5088 
5089 #undef __FUNCT__
5090 #define __FUNCT__ "MatCreateMPIAIJWithSplitArrays"
5091 /*@C
5092      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
5093          and "off-diagonal" part of the matrix in CSR format.
5094 
5095    Collective on MPI_Comm
5096 
5097    Input Parameters:
5098 +  comm - MPI communicator
5099 .  m - number of local rows (Cannot be PETSC_DECIDE)
5100 .  n - This value should be the same as the local size used in creating the
5101        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
5102        calculated if N is given) For square matrices n is almost always m.
5103 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
5104 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
5105 .   i - row indices for "diagonal" portion of matrix
5106 .   j - column indices
5107 .   a - matrix values
5108 .   oi - row indices for "off-diagonal" portion of matrix
5109 .   oj - column indices
5110 -   oa - matrix values
5111 
5112    Output Parameter:
5113 .   mat - the matrix
5114 
5115    Level: advanced
5116 
5117    Notes:
5118        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
5119        must free the arrays once the matrix has been destroyed and not before.
5120 
5121        The i and j indices are 0 based
5122 
5123        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
5124 
5125        This sets local rows and cannot be used to set off-processor values.
5126 
5127        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
5128        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
5129        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
5130        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
5131        keep track of the underlying array. Use MatSetOption(A,MAT_IGNORE_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
5132        communication if it is known that only local entries will be set.
5133 
5134 .keywords: matrix, aij, compressed row, sparse, parallel
5135 
5136 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
5137           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
5138 @*/
5139 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)
5140 {
5141   PetscErrorCode ierr;
5142   Mat_MPIAIJ     *maij;
5143 
5144   PetscFunctionBegin;
5145   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
5146   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
5147   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
5148   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
5149   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
5150   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
5151   maij = (Mat_MPIAIJ*) (*mat)->data;
5152 
5153   (*mat)->preallocated = PETSC_TRUE;
5154 
5155   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
5156   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
5157 
5158   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
5159   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
5160 
5161   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5162   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5163   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5164   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5165 
5166   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5167   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5168   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
5169   PetscFunctionReturn(0);
5170 }
5171 
5172 /*
5173     Special version for direct calls from Fortran
5174 */
5175 #include <petsc/private/fortranimpl.h>
5176 
5177 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5178 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
5179 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5180 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
5181 #endif
5182 
5183 /* Change these macros so can be used in void function */
5184 #undef CHKERRQ
5185 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
5186 #undef SETERRQ2
5187 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5188 #undef SETERRQ3
5189 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5190 #undef SETERRQ
5191 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
5192 
5193 #undef __FUNCT__
5194 #define __FUNCT__ "matsetvaluesmpiaij_"
5195 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)
5196 {
5197   Mat            mat  = *mmat;
5198   PetscInt       m    = *mm, n = *mn;
5199   InsertMode     addv = *maddv;
5200   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
5201   PetscScalar    value;
5202   PetscErrorCode ierr;
5203 
5204   MatCheckPreallocated(mat,1);
5205   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
5206 
5207 #if defined(PETSC_USE_DEBUG)
5208   else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
5209 #endif
5210   {
5211     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
5212     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
5213     PetscBool roworiented = aij->roworiented;
5214 
5215     /* Some Variables required in the macro */
5216     Mat        A                 = aij->A;
5217     Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
5218     PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
5219     MatScalar  *aa               = a->a;
5220     PetscBool  ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
5221     Mat        B                 = aij->B;
5222     Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
5223     PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5224     MatScalar  *ba               = b->a;
5225 
5226     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5227     PetscInt  nonew = a->nonew;
5228     MatScalar *ap1,*ap2;
5229 
5230     PetscFunctionBegin;
5231     for (i=0; i<m; i++) {
5232       if (im[i] < 0) continue;
5233 #if defined(PETSC_USE_DEBUG)
5234       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);
5235 #endif
5236       if (im[i] >= rstart && im[i] < rend) {
5237         row      = im[i] - rstart;
5238         lastcol1 = -1;
5239         rp1      = aj + ai[row];
5240         ap1      = aa + ai[row];
5241         rmax1    = aimax[row];
5242         nrow1    = ailen[row];
5243         low1     = 0;
5244         high1    = nrow1;
5245         lastcol2 = -1;
5246         rp2      = bj + bi[row];
5247         ap2      = ba + bi[row];
5248         rmax2    = bimax[row];
5249         nrow2    = bilen[row];
5250         low2     = 0;
5251         high2    = nrow2;
5252 
5253         for (j=0; j<n; j++) {
5254           if (roworiented) value = v[i*n+j];
5255           else value = v[i+j*m];
5256           if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES)) continue;
5257           if (in[j] >= cstart && in[j] < cend) {
5258             col = in[j] - cstart;
5259             MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
5260           } else if (in[j] < 0) continue;
5261 #if defined(PETSC_USE_DEBUG)
5262           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);
5263 #endif
5264           else {
5265             if (mat->was_assembled) {
5266               if (!aij->colmap) {
5267                 ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5268               }
5269 #if defined(PETSC_USE_CTABLE)
5270               ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5271               col--;
5272 #else
5273               col = aij->colmap[in[j]] - 1;
5274 #endif
5275               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5276                 ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5277                 col  =  in[j];
5278                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5279                 B     = aij->B;
5280                 b     = (Mat_SeqAIJ*)B->data;
5281                 bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5282                 rp2   = bj + bi[row];
5283                 ap2   = ba + bi[row];
5284                 rmax2 = bimax[row];
5285                 nrow2 = bilen[row];
5286                 low2  = 0;
5287                 high2 = nrow2;
5288                 bm    = aij->B->rmap->n;
5289                 ba    = b->a;
5290               }
5291             } else col = in[j];
5292             MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
5293           }
5294         }
5295       } else if (!aij->donotstash) {
5296         if (roworiented) {
5297           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5298         } else {
5299           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5300         }
5301       }
5302     }
5303   }
5304   PetscFunctionReturnVoid();
5305 }
5306 
5307