xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision a44bcdf57b2bdc3efd71d40abec79a20d8d3f002)
1 
2 #include <../src/mat/impls/aij/mpi/mpiaij.h>   /*I "petscmat.h" I*/
3 #include <petsc/private/vecimpl.h>
4 #include <petsc/private/isimpl.h>
5 #include <petscblaslapack.h>
6 #include <petscsf.h>
7 
8 /*MC
9    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.
10 
11    This matrix type is identical to MATSEQAIJ when constructed with a single process communicator,
12    and MATMPIAIJ otherwise.  As a result, for single process communicators,
13   MatSeqAIJSetPreallocation is supported, and similarly MatMPIAIJSetPreallocation is supported
14   for communicators controlling multiple processes.  It is recommended that you call both of
15   the above preallocation routines for simplicity.
16 
17    Options Database Keys:
18 . -mat_type aij - sets the matrix type to "aij" during a call to MatSetFromOptions()
19 
20   Developer Notes: Subclasses include MATAIJCUSP, MATAIJCUSPARSE, MATAIJPERM, MATAIJCRL, and also automatically switches over to use inodes when
21    enough exist.
22 
23   Level: beginner
24 
25 .seealso: MatCreateAIJ(), MatCreateSeqAIJ(), MATSEQAIJ,MATMPIAIJ
26 M*/
27 
28 /*MC
29    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.
30 
31    This matrix type is identical to MATSEQAIJCRL when constructed with a single process communicator,
32    and MATMPIAIJCRL otherwise.  As a result, for single process communicators,
33    MatSeqAIJSetPreallocation() is supported, and similarly MatMPIAIJSetPreallocation() is supported
34   for communicators controlling multiple processes.  It is recommended that you call both of
35   the above preallocation routines for simplicity.
36 
37    Options Database Keys:
38 . -mat_type aijcrl - sets the matrix type to "aijcrl" during a call to MatSetFromOptions()
39 
40   Level: beginner
41 
42 .seealso: MatCreateMPIAIJCRL,MATSEQAIJCRL,MATMPIAIJCRL, MATSEQAIJCRL, MATMPIAIJCRL
43 M*/
44 
45 #undef __FUNCT__
46 #define __FUNCT__ "MatFindNonzeroRows_MPIAIJ"
47 PetscErrorCode MatFindNonzeroRows_MPIAIJ(Mat M,IS *keptrows)
48 {
49   PetscErrorCode  ierr;
50   Mat_MPIAIJ      *mat = (Mat_MPIAIJ*)M->data;
51   Mat_SeqAIJ      *a   = (Mat_SeqAIJ*)mat->A->data;
52   Mat_SeqAIJ      *b   = (Mat_SeqAIJ*)mat->B->data;
53   const PetscInt  *ia,*ib;
54   const MatScalar *aa,*bb;
55   PetscInt        na,nb,i,j,*rows,cnt=0,n0rows;
56   PetscInt        m = M->rmap->n,rstart = M->rmap->rstart;
57 
58   PetscFunctionBegin;
59   *keptrows = 0;
60   ia        = a->i;
61   ib        = b->i;
62   for (i=0; i<m; i++) {
63     na = ia[i+1] - ia[i];
64     nb = ib[i+1] - ib[i];
65     if (!na && !nb) {
66       cnt++;
67       goto ok1;
68     }
69     aa = a->a + ia[i];
70     for (j=0; j<na; j++) {
71       if (aa[j] != 0.0) goto ok1;
72     }
73     bb = b->a + ib[i];
74     for (j=0; j <nb; j++) {
75       if (bb[j] != 0.0) goto ok1;
76     }
77     cnt++;
78 ok1:;
79   }
80   ierr = MPI_Allreduce(&cnt,&n0rows,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)M));CHKERRQ(ierr);
81   if (!n0rows) PetscFunctionReturn(0);
82   ierr = PetscMalloc1(M->rmap->n-cnt,&rows);CHKERRQ(ierr);
83   cnt  = 0;
84   for (i=0; i<m; i++) {
85     na = ia[i+1] - ia[i];
86     nb = ib[i+1] - ib[i];
87     if (!na && !nb) continue;
88     aa = a->a + ia[i];
89     for (j=0; j<na;j++) {
90       if (aa[j] != 0.0) {
91         rows[cnt++] = rstart + i;
92         goto ok2;
93       }
94     }
95     bb = b->a + ib[i];
96     for (j=0; j<nb; j++) {
97       if (bb[j] != 0.0) {
98         rows[cnt++] = rstart + i;
99         goto ok2;
100       }
101     }
102 ok2:;
103   }
104   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)M),cnt,rows,PETSC_OWN_POINTER,keptrows);CHKERRQ(ierr);
105   PetscFunctionReturn(0);
106 }
107 
108 #undef __FUNCT__
109 #define __FUNCT__ "MatDiagonalSet_MPIAIJ"
110 PetscErrorCode  MatDiagonalSet_MPIAIJ(Mat Y,Vec D,InsertMode is)
111 {
112   PetscErrorCode    ierr;
113   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*) Y->data;
114 
115   PetscFunctionBegin;
116   if (Y->assembled && Y->rmap->rstart == Y->cmap->rstart && Y->rmap->rend == Y->cmap->rend) {
117     ierr = MatDiagonalSet(aij->A,D,is);CHKERRQ(ierr);
118   } else {
119     ierr = MatDiagonalSet_Default(Y,D,is);CHKERRQ(ierr);
120   }
121   PetscFunctionReturn(0);
122 }
123 
124 
125 #undef __FUNCT__
126 #define __FUNCT__ "MatFindZeroDiagonals_MPIAIJ"
127 PetscErrorCode MatFindZeroDiagonals_MPIAIJ(Mat M,IS *zrows)
128 {
129   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)M->data;
130   PetscErrorCode ierr;
131   PetscInt       i,rstart,nrows,*rows;
132 
133   PetscFunctionBegin;
134   *zrows = NULL;
135   ierr   = MatFindZeroDiagonals_SeqAIJ_Private(aij->A,&nrows,&rows);CHKERRQ(ierr);
136   ierr   = MatGetOwnershipRange(M,&rstart,NULL);CHKERRQ(ierr);
137   for (i=0; i<nrows; i++) rows[i] += rstart;
138   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)M),nrows,rows,PETSC_OWN_POINTER,zrows);CHKERRQ(ierr);
139   PetscFunctionReturn(0);
140 }
141 
142 #undef __FUNCT__
143 #define __FUNCT__ "MatGetColumnNorms_MPIAIJ"
144 PetscErrorCode MatGetColumnNorms_MPIAIJ(Mat A,NormType type,PetscReal *norms)
145 {
146   PetscErrorCode ierr;
147   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)A->data;
148   PetscInt       i,n,*garray = aij->garray;
149   Mat_SeqAIJ     *a_aij = (Mat_SeqAIJ*) aij->A->data;
150   Mat_SeqAIJ     *b_aij = (Mat_SeqAIJ*) aij->B->data;
151   PetscReal      *work;
152 
153   PetscFunctionBegin;
154   ierr = MatGetSize(A,NULL,&n);CHKERRQ(ierr);
155   ierr = PetscCalloc1(n,&work);CHKERRQ(ierr);
156   if (type == NORM_2) {
157     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
158       work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i]*a_aij->a[i]);
159     }
160     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
161       work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]*b_aij->a[i]);
162     }
163   } else if (type == NORM_1) {
164     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
165       work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i]);
166     }
167     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
168       work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]);
169     }
170   } else if (type == NORM_INFINITY) {
171     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
172       work[A->cmap->rstart + a_aij->j[i]] = PetscMax(PetscAbsScalar(a_aij->a[i]), work[A->cmap->rstart + a_aij->j[i]]);
173     }
174     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
175       work[garray[b_aij->j[i]]] = PetscMax(PetscAbsScalar(b_aij->a[i]),work[garray[b_aij->j[i]]]);
176     }
177 
178   } else SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Unknown NormType");
179   if (type == NORM_INFINITY) {
180     ierr = MPI_Allreduce(work,norms,n,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
181   } else {
182     ierr = MPI_Allreduce(work,norms,n,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
183   }
184   ierr = PetscFree(work);CHKERRQ(ierr);
185   if (type == NORM_2) {
186     for (i=0; i<n; i++) norms[i] = PetscSqrtReal(norms[i]);
187   }
188   PetscFunctionReturn(0);
189 }
190 
191 #undef __FUNCT__
192 #define __FUNCT__ "MatFindOffBlockDiagonalEntries_MPIAIJ"
193 PetscErrorCode MatFindOffBlockDiagonalEntries_MPIAIJ(Mat A,IS *is)
194 {
195   Mat_MPIAIJ      *a  = (Mat_MPIAIJ*)A->data;
196   IS              sis,gis;
197   PetscErrorCode  ierr;
198   const PetscInt  *isis,*igis;
199   PetscInt        n,*iis,nsis,ngis,rstart,i;
200 
201   PetscFunctionBegin;
202   ierr = MatFindOffBlockDiagonalEntries(a->A,&sis);CHKERRQ(ierr);
203   ierr = MatFindNonzeroRows(a->B,&gis);CHKERRQ(ierr);
204   ierr = ISGetSize(gis,&ngis);CHKERRQ(ierr);
205   ierr = ISGetSize(sis,&nsis);CHKERRQ(ierr);
206   ierr = ISGetIndices(sis,&isis);CHKERRQ(ierr);
207   ierr = ISGetIndices(gis,&igis);CHKERRQ(ierr);
208 
209   ierr = PetscMalloc1(ngis+nsis,&iis);CHKERRQ(ierr);
210   ierr = PetscMemcpy(iis,igis,ngis*sizeof(PetscInt));CHKERRQ(ierr);
211   ierr = PetscMemcpy(iis+ngis,isis,nsis*sizeof(PetscInt));CHKERRQ(ierr);
212   n    = ngis + nsis;
213   ierr = PetscSortRemoveDupsInt(&n,iis);CHKERRQ(ierr);
214   ierr = MatGetOwnershipRange(A,&rstart,NULL);CHKERRQ(ierr);
215   for (i=0; i<n; i++) iis[i] += rstart;
216   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)A),n,iis,PETSC_OWN_POINTER,is);CHKERRQ(ierr);
217 
218   ierr = ISRestoreIndices(sis,&isis);CHKERRQ(ierr);
219   ierr = ISRestoreIndices(gis,&igis);CHKERRQ(ierr);
220   ierr = ISDestroy(&sis);CHKERRQ(ierr);
221   ierr = ISDestroy(&gis);CHKERRQ(ierr);
222   PetscFunctionReturn(0);
223 }
224 
225 #undef __FUNCT__
226 #define __FUNCT__ "MatDistribute_MPIAIJ"
227 /*
228     Distributes a SeqAIJ matrix across a set of processes. Code stolen from
229     MatLoad_MPIAIJ(). Horrible lack of reuse. Should be a routine for each matrix type.
230 
231     Only for square matrices
232 
233     Used by a preconditioner, hence PETSC_EXTERN
234 */
235 PETSC_EXTERN PetscErrorCode MatDistribute_MPIAIJ(MPI_Comm comm,Mat gmat,PetscInt m,MatReuse reuse,Mat *inmat)
236 {
237   PetscMPIInt    rank,size;
238   PetscInt       *rowners,*dlens,*olens,i,rstart,rend,j,jj,nz = 0,*gmataj,cnt,row,*ld,bses[2];
239   PetscErrorCode ierr;
240   Mat            mat;
241   Mat_SeqAIJ     *gmata;
242   PetscMPIInt    tag;
243   MPI_Status     status;
244   PetscBool      aij;
245   MatScalar      *gmataa,*ao,*ad,*gmataarestore=0;
246 
247   PetscFunctionBegin;
248   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
249   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
250   if (!rank) {
251     ierr = PetscObjectTypeCompare((PetscObject)gmat,MATSEQAIJ,&aij);CHKERRQ(ierr);
252     if (!aij) SETERRQ1(PetscObjectComm((PetscObject)gmat),PETSC_ERR_SUP,"Currently no support for input matrix of type %s\n",((PetscObject)gmat)->type_name);
253   }
254   if (reuse == MAT_INITIAL_MATRIX) {
255     ierr = MatCreate(comm,&mat);CHKERRQ(ierr);
256     ierr = MatSetSizes(mat,m,m,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
257     ierr = MatGetBlockSizes(gmat,&bses[0],&bses[1]);CHKERRQ(ierr);
258     ierr = MPI_Bcast(bses,2,MPIU_INT,0,comm);CHKERRQ(ierr);
259     ierr = MatSetBlockSizes(mat,bses[0],bses[1]);CHKERRQ(ierr);
260     ierr = MatSetType(mat,MATAIJ);CHKERRQ(ierr);
261     ierr = PetscMalloc1(size+1,&rowners);CHKERRQ(ierr);
262     ierr = PetscMalloc2(m,&dlens,m,&olens);CHKERRQ(ierr);
263     ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
264 
265     rowners[0] = 0;
266     for (i=2; i<=size; i++) rowners[i] += rowners[i-1];
267     rstart = rowners[rank];
268     rend   = rowners[rank+1];
269     ierr   = PetscObjectGetNewTag((PetscObject)mat,&tag);CHKERRQ(ierr);
270     if (!rank) {
271       gmata = (Mat_SeqAIJ*) gmat->data;
272       /* send row lengths to all processors */
273       for (i=0; i<m; i++) dlens[i] = gmata->ilen[i];
274       for (i=1; i<size; i++) {
275         ierr = MPI_Send(gmata->ilen + rowners[i],rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
276       }
277       /* determine number diagonal and off-diagonal counts */
278       ierr = PetscMemzero(olens,m*sizeof(PetscInt));CHKERRQ(ierr);
279       ierr = PetscCalloc1(m,&ld);CHKERRQ(ierr);
280       jj   = 0;
281       for (i=0; i<m; i++) {
282         for (j=0; j<dlens[i]; j++) {
283           if (gmata->j[jj] < rstart) ld[i]++;
284           if (gmata->j[jj] < rstart || gmata->j[jj] >= rend) olens[i]++;
285           jj++;
286         }
287       }
288       /* send column indices to other processes */
289       for (i=1; i<size; i++) {
290         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
291         ierr = MPI_Send(&nz,1,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
292         ierr = MPI_Send(gmata->j + gmata->i[rowners[i]],nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
293       }
294 
295       /* send numerical values to other processes */
296       for (i=1; i<size; i++) {
297         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
298         ierr = MPI_Send(gmata->a + gmata->i[rowners[i]],nz,MPIU_SCALAR,i,tag,comm);CHKERRQ(ierr);
299       }
300       gmataa = gmata->a;
301       gmataj = gmata->j;
302 
303     } else {
304       /* receive row lengths */
305       ierr = MPI_Recv(dlens,m,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
306       /* receive column indices */
307       ierr = MPI_Recv(&nz,1,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
308       ierr = PetscMalloc2(nz,&gmataa,nz,&gmataj);CHKERRQ(ierr);
309       ierr = MPI_Recv(gmataj,nz,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
310       /* determine number diagonal and off-diagonal counts */
311       ierr = PetscMemzero(olens,m*sizeof(PetscInt));CHKERRQ(ierr);
312       ierr = PetscCalloc1(m,&ld);CHKERRQ(ierr);
313       jj   = 0;
314       for (i=0; i<m; i++) {
315         for (j=0; j<dlens[i]; j++) {
316           if (gmataj[jj] < rstart) ld[i]++;
317           if (gmataj[jj] < rstart || gmataj[jj] >= rend) olens[i]++;
318           jj++;
319         }
320       }
321       /* receive numerical values */
322       ierr = PetscMemzero(gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr);
323       ierr = MPI_Recv(gmataa,nz,MPIU_SCALAR,0,tag,comm,&status);CHKERRQ(ierr);
324     }
325     /* set preallocation */
326     for (i=0; i<m; i++) {
327       dlens[i] -= olens[i];
328     }
329     ierr = MatSeqAIJSetPreallocation(mat,0,dlens);CHKERRQ(ierr);
330     ierr = MatMPIAIJSetPreallocation(mat,0,dlens,0,olens);CHKERRQ(ierr);
331 
332     for (i=0; i<m; i++) {
333       dlens[i] += olens[i];
334     }
335     cnt = 0;
336     for (i=0; i<m; i++) {
337       row  = rstart + i;
338       ierr = MatSetValues(mat,1,&row,dlens[i],gmataj+cnt,gmataa+cnt,INSERT_VALUES);CHKERRQ(ierr);
339       cnt += dlens[i];
340     }
341     if (rank) {
342       ierr = PetscFree2(gmataa,gmataj);CHKERRQ(ierr);
343     }
344     ierr = PetscFree2(dlens,olens);CHKERRQ(ierr);
345     ierr = PetscFree(rowners);CHKERRQ(ierr);
346 
347     ((Mat_MPIAIJ*)(mat->data))->ld = ld;
348 
349     *inmat = mat;
350   } else {   /* column indices are already set; only need to move over numerical values from process 0 */
351     Mat_SeqAIJ *Ad = (Mat_SeqAIJ*)((Mat_MPIAIJ*)((*inmat)->data))->A->data;
352     Mat_SeqAIJ *Ao = (Mat_SeqAIJ*)((Mat_MPIAIJ*)((*inmat)->data))->B->data;
353     mat  = *inmat;
354     ierr = PetscObjectGetNewTag((PetscObject)mat,&tag);CHKERRQ(ierr);
355     if (!rank) {
356       /* send numerical values to other processes */
357       gmata  = (Mat_SeqAIJ*) gmat->data;
358       ierr   = MatGetOwnershipRanges(mat,(const PetscInt**)&rowners);CHKERRQ(ierr);
359       gmataa = gmata->a;
360       for (i=1; i<size; i++) {
361         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
362         ierr = MPI_Send(gmataa + gmata->i[rowners[i]],nz,MPIU_SCALAR,i,tag,comm);CHKERRQ(ierr);
363       }
364       nz = gmata->i[rowners[1]]-gmata->i[rowners[0]];
365     } else {
366       /* receive numerical values from process 0*/
367       nz   = Ad->nz + Ao->nz;
368       ierr = PetscMalloc1(nz,&gmataa);CHKERRQ(ierr); gmataarestore = gmataa;
369       ierr = MPI_Recv(gmataa,nz,MPIU_SCALAR,0,tag,comm,&status);CHKERRQ(ierr);
370     }
371     /* transfer numerical values into the diagonal A and off diagonal B parts of mat */
372     ld = ((Mat_MPIAIJ*)(mat->data))->ld;
373     ad = Ad->a;
374     ao = Ao->a;
375     if (mat->rmap->n) {
376       i  = 0;
377       nz = ld[i];                                   ierr = PetscMemcpy(ao,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ao += nz; gmataa += nz;
378       nz = Ad->i[i+1] - Ad->i[i];                   ierr = PetscMemcpy(ad,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ad += nz; gmataa += nz;
379     }
380     for (i=1; i<mat->rmap->n; i++) {
381       nz = Ao->i[i] - Ao->i[i-1] - ld[i-1] + ld[i]; ierr = PetscMemcpy(ao,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ao += nz; gmataa += nz;
382       nz = Ad->i[i+1] - Ad->i[i];                   ierr = PetscMemcpy(ad,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ad += nz; gmataa += nz;
383     }
384     i--;
385     if (mat->rmap->n) {
386       nz = Ao->i[i+1] - Ao->i[i] - ld[i];           ierr = PetscMemcpy(ao,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr);
387     }
388     if (rank) {
389       ierr = PetscFree(gmataarestore);CHKERRQ(ierr);
390     }
391   }
392   ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
393   ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
394   PetscFunctionReturn(0);
395 }
396 
397 /*
398   Local utility routine that creates a mapping from the global column
399 number to the local number in the off-diagonal part of the local
400 storage of the matrix.  When PETSC_USE_CTABLE is used this is scalable at
401 a slightly higher hash table cost; without it it is not scalable (each processor
402 has an order N integer array but is fast to acess.
403 */
404 #undef __FUNCT__
405 #define __FUNCT__ "MatCreateColmap_MPIAIJ_Private"
406 PetscErrorCode MatCreateColmap_MPIAIJ_Private(Mat mat)
407 {
408   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
409   PetscErrorCode ierr;
410   PetscInt       n = aij->B->cmap->n,i;
411 
412   PetscFunctionBegin;
413   if (!aij->garray) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"MPIAIJ Matrix was assembled but is missing garray");
414 #if defined(PETSC_USE_CTABLE)
415   ierr = PetscTableCreate(n,mat->cmap->N+1,&aij->colmap);CHKERRQ(ierr);
416   for (i=0; i<n; i++) {
417     ierr = PetscTableAdd(aij->colmap,aij->garray[i]+1,i+1,INSERT_VALUES);CHKERRQ(ierr);
418   }
419 #else
420   ierr = PetscCalloc1(mat->cmap->N+1,&aij->colmap);CHKERRQ(ierr);
421   ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N+1)*sizeof(PetscInt));CHKERRQ(ierr);
422   for (i=0; i<n; i++) aij->colmap[aij->garray[i]] = i+1;
423 #endif
424   PetscFunctionReturn(0);
425 }
426 
427 #define MatSetValues_SeqAIJ_A_Private(row,col,value,addv,orow,ocol)     \
428 { \
429     if (col <= lastcol1)  low1 = 0;     \
430     else                 high1 = nrow1; \
431     lastcol1 = col;\
432     while (high1-low1 > 5) { \
433       t = (low1+high1)/2; \
434       if (rp1[t] > col) high1 = t; \
435       else              low1  = t; \
436     } \
437       for (_i=low1; _i<high1; _i++) { \
438         if (rp1[_i] > col) break; \
439         if (rp1[_i] == col) { \
440           if (addv == ADD_VALUES) ap1[_i] += value;   \
441           else                    ap1[_i] = value; \
442           goto a_noinsert; \
443         } \
444       }  \
445       if (value == 0.0 && ignorezeroentries) {low1 = 0; high1 = nrow1;goto a_noinsert;} \
446       if (nonew == 1) {low1 = 0; high1 = nrow1; goto a_noinsert;}                \
447       if (nonew == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at global row/column (%D, %D) into matrix", orow, ocol); \
448       MatSeqXAIJReallocateAIJ(A,am,1,nrow1,row,col,rmax1,aa,ai,aj,rp1,ap1,aimax,nonew,MatScalar); \
449       N = nrow1++ - 1; a->nz++; high1++; \
450       /* shift up all the later entries in this row */ \
451       for (ii=N; ii>=_i; ii--) { \
452         rp1[ii+1] = rp1[ii]; \
453         ap1[ii+1] = ap1[ii]; \
454       } \
455       rp1[_i] = col;  \
456       ap1[_i] = value;  \
457       A->nonzerostate++;\
458       a_noinsert: ; \
459       ailen[row] = nrow1; \
460 }
461 
462 
463 #define MatSetValues_SeqAIJ_B_Private(row,col,value,addv,orow,ocol) \
464   { \
465     if (col <= lastcol2) low2 = 0;                        \
466     else high2 = nrow2;                                   \
467     lastcol2 = col;                                       \
468     while (high2-low2 > 5) {                              \
469       t = (low2+high2)/2;                                 \
470       if (rp2[t] > col) high2 = t;                        \
471       else             low2  = t;                         \
472     }                                                     \
473     for (_i=low2; _i<high2; _i++) {                       \
474       if (rp2[_i] > col) break;                           \
475       if (rp2[_i] == col) {                               \
476         if (addv == ADD_VALUES) ap2[_i] += value;         \
477         else                    ap2[_i] = value;          \
478         goto b_noinsert;                                  \
479       }                                                   \
480     }                                                     \
481     if (value == 0.0 && ignorezeroentries) {low2 = 0; high2 = nrow2; goto b_noinsert;} \
482     if (nonew == 1) {low2 = 0; high2 = nrow2; goto b_noinsert;}                        \
483     if (nonew == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at global row/column (%D, %D) into matrix", orow, ocol); \
484     MatSeqXAIJReallocateAIJ(B,bm,1,nrow2,row,col,rmax2,ba,bi,bj,rp2,ap2,bimax,nonew,MatScalar); \
485     N = nrow2++ - 1; b->nz++; high2++;                    \
486     /* shift up all the later entries in this row */      \
487     for (ii=N; ii>=_i; ii--) {                            \
488       rp2[ii+1] = rp2[ii];                                \
489       ap2[ii+1] = ap2[ii];                                \
490     }                                                     \
491     rp2[_i] = col;                                        \
492     ap2[_i] = value;                                      \
493     B->nonzerostate++;                                    \
494     b_noinsert: ;                                         \
495     bilen[row] = nrow2;                                   \
496   }
497 
498 #undef __FUNCT__
499 #define __FUNCT__ "MatSetValuesRow_MPIAIJ"
500 PetscErrorCode MatSetValuesRow_MPIAIJ(Mat A,PetscInt row,const PetscScalar v[])
501 {
502   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)A->data;
503   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)mat->A->data,*b = (Mat_SeqAIJ*)mat->B->data;
504   PetscErrorCode ierr;
505   PetscInt       l,*garray = mat->garray,diag;
506 
507   PetscFunctionBegin;
508   /* code only works for square matrices A */
509 
510   /* find size of row to the left of the diagonal part */
511   ierr = MatGetOwnershipRange(A,&diag,0);CHKERRQ(ierr);
512   row  = row - diag;
513   for (l=0; l<b->i[row+1]-b->i[row]; l++) {
514     if (garray[b->j[b->i[row]+l]] > diag) break;
515   }
516   ierr = PetscMemcpy(b->a+b->i[row],v,l*sizeof(PetscScalar));CHKERRQ(ierr);
517 
518   /* diagonal part */
519   ierr = PetscMemcpy(a->a+a->i[row],v+l,(a->i[row+1]-a->i[row])*sizeof(PetscScalar));CHKERRQ(ierr);
520 
521   /* right of diagonal part */
522   ierr = PetscMemcpy(b->a+b->i[row]+l,v+l+a->i[row+1]-a->i[row],(b->i[row+1]-b->i[row]-l)*sizeof(PetscScalar));CHKERRQ(ierr);
523   PetscFunctionReturn(0);
524 }
525 
526 #undef __FUNCT__
527 #define __FUNCT__ "MatSetValues_MPIAIJ"
528 PetscErrorCode MatSetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode addv)
529 {
530   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
531   PetscScalar    value;
532   PetscErrorCode ierr;
533   PetscInt       i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
534   PetscInt       cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
535   PetscBool      roworiented = aij->roworiented;
536 
537   /* Some Variables required in the macro */
538   Mat        A                 = aij->A;
539   Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
540   PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
541   MatScalar  *aa               = a->a;
542   PetscBool  ignorezeroentries = a->ignorezeroentries;
543   Mat        B                 = aij->B;
544   Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
545   PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
546   MatScalar  *ba               = b->a;
547 
548   PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
549   PetscInt  nonew;
550   MatScalar *ap1,*ap2;
551 
552   PetscFunctionBegin;
553   for (i=0; i<m; i++) {
554     if (im[i] < 0) continue;
555 #if defined(PETSC_USE_DEBUG)
556     if (im[i] >= mat->rmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %D max %D",im[i],mat->rmap->N-1);
557 #endif
558     if (im[i] >= rstart && im[i] < rend) {
559       row      = im[i] - rstart;
560       lastcol1 = -1;
561       rp1      = aj + ai[row];
562       ap1      = aa + ai[row];
563       rmax1    = aimax[row];
564       nrow1    = ailen[row];
565       low1     = 0;
566       high1    = nrow1;
567       lastcol2 = -1;
568       rp2      = bj + bi[row];
569       ap2      = ba + bi[row];
570       rmax2    = bimax[row];
571       nrow2    = bilen[row];
572       low2     = 0;
573       high2    = nrow2;
574 
575       for (j=0; j<n; j++) {
576         if (roworiented) value = v[i*n+j];
577         else             value = v[i+j*m];
578         if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES)) continue;
579         if (in[j] >= cstart && in[j] < cend) {
580           col   = in[j] - cstart;
581           nonew = a->nonew;
582           MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
583         } else if (in[j] < 0) continue;
584 #if defined(PETSC_USE_DEBUG)
585         else if (in[j] >= mat->cmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %D max %D",in[j],mat->cmap->N-1);
586 #endif
587         else {
588           if (mat->was_assembled) {
589             if (!aij->colmap) {
590               ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
591             }
592 #if defined(PETSC_USE_CTABLE)
593             ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
594             col--;
595 #else
596             col = aij->colmap[in[j]] - 1;
597 #endif
598             if (col < 0 && !((Mat_SeqAIJ*)(aij->B->data))->nonew) {
599               ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
600               col  =  in[j];
601               /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
602               B     = aij->B;
603               b     = (Mat_SeqAIJ*)B->data;
604               bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j; ba = b->a;
605               rp2   = bj + bi[row];
606               ap2   = ba + bi[row];
607               rmax2 = bimax[row];
608               nrow2 = bilen[row];
609               low2  = 0;
610               high2 = nrow2;
611               bm    = aij->B->rmap->n;
612               ba    = b->a;
613             } else if (col < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at global row/column (%D, %D) into matrix", im[i], in[j]);
614           } else col = in[j];
615           nonew = b->nonew;
616           MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
617         }
618       }
619     } else {
620       if (mat->nooffprocentries) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Setting off process row %D even though MatSetOption(,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) was set",im[i]);
621       if (!aij->donotstash) {
622         mat->assembled = PETSC_FALSE;
623         if (roworiented) {
624           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
625         } else {
626           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
627         }
628       }
629     }
630   }
631   PetscFunctionReturn(0);
632 }
633 
634 #undef __FUNCT__
635 #define __FUNCT__ "MatGetValues_MPIAIJ"
636 PetscErrorCode MatGetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],PetscScalar v[])
637 {
638   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
639   PetscErrorCode ierr;
640   PetscInt       i,j,rstart = mat->rmap->rstart,rend = mat->rmap->rend;
641   PetscInt       cstart = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
642 
643   PetscFunctionBegin;
644   for (i=0; i<m; i++) {
645     if (idxm[i] < 0) continue; /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative row: %D",idxm[i]);*/
646     if (idxm[i] >= mat->rmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %D max %D",idxm[i],mat->rmap->N-1);
647     if (idxm[i] >= rstart && idxm[i] < rend) {
648       row = idxm[i] - rstart;
649       for (j=0; j<n; j++) {
650         if (idxn[j] < 0) continue; /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column: %D",idxn[j]); */
651         if (idxn[j] >= mat->cmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %D max %D",idxn[j],mat->cmap->N-1);
652         if (idxn[j] >= cstart && idxn[j] < cend) {
653           col  = idxn[j] - cstart;
654           ierr = MatGetValues(aij->A,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
655         } else {
656           if (!aij->colmap) {
657             ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
658           }
659 #if defined(PETSC_USE_CTABLE)
660           ierr = PetscTableFind(aij->colmap,idxn[j]+1,&col);CHKERRQ(ierr);
661           col--;
662 #else
663           col = aij->colmap[idxn[j]] - 1;
664 #endif
665           if ((col < 0) || (aij->garray[col] != idxn[j])) *(v+i*n+j) = 0.0;
666           else {
667             ierr = MatGetValues(aij->B,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
668           }
669         }
670       }
671     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only local values currently supported");
672   }
673   PetscFunctionReturn(0);
674 }
675 
676 extern PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat,Vec,Vec);
677 
678 #undef __FUNCT__
679 #define __FUNCT__ "MatAssemblyBegin_MPIAIJ"
680 PetscErrorCode MatAssemblyBegin_MPIAIJ(Mat mat,MatAssemblyType mode)
681 {
682   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
683   PetscErrorCode ierr;
684   PetscInt       nstash,reallocs;
685 
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 = MPI_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 = MPI_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 = MPI_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 = MPI_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   PetscFunctionReturn(0);
1567 }
1568 
1569 #undef __FUNCT__
1570 #define __FUNCT__ "MatPermute_MPIAIJ"
1571 PetscErrorCode MatPermute_MPIAIJ(Mat A,IS rowp,IS colp,Mat *B)
1572 {
1573   Mat            aA,aB,Aperm;
1574   const PetscInt *rwant,*cwant,*gcols,*ai,*bi,*aj,*bj;
1575   PetscScalar    *aa,*ba;
1576   PetscInt       i,j,m,n,ng,anz,bnz,*dnnz,*onnz,*tdnnz,*tonnz,*rdest,*cdest,*work,*gcdest;
1577   PetscSF        rowsf,sf;
1578   IS             parcolp = NULL;
1579   PetscBool      done;
1580   PetscErrorCode ierr;
1581 
1582   PetscFunctionBegin;
1583   ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
1584   ierr = ISGetIndices(rowp,&rwant);CHKERRQ(ierr);
1585   ierr = ISGetIndices(colp,&cwant);CHKERRQ(ierr);
1586   ierr = PetscMalloc3(PetscMax(m,n),&work,m,&rdest,n,&cdest);CHKERRQ(ierr);
1587 
1588   /* Invert row permutation to find out where my rows should go */
1589   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&rowsf);CHKERRQ(ierr);
1590   ierr = PetscSFSetGraphLayout(rowsf,A->rmap,A->rmap->n,NULL,PETSC_OWN_POINTER,rwant);CHKERRQ(ierr);
1591   ierr = PetscSFSetFromOptions(rowsf);CHKERRQ(ierr);
1592   for (i=0; i<m; i++) work[i] = A->rmap->rstart + i;
1593   ierr = PetscSFReduceBegin(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1594   ierr = PetscSFReduceEnd(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1595 
1596   /* Invert column permutation to find out where my columns should go */
1597   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1598   ierr = PetscSFSetGraphLayout(sf,A->cmap,A->cmap->n,NULL,PETSC_OWN_POINTER,cwant);CHKERRQ(ierr);
1599   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1600   for (i=0; i<n; i++) work[i] = A->cmap->rstart + i;
1601   ierr = PetscSFReduceBegin(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1602   ierr = PetscSFReduceEnd(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1603   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1604 
1605   ierr = ISRestoreIndices(rowp,&rwant);CHKERRQ(ierr);
1606   ierr = ISRestoreIndices(colp,&cwant);CHKERRQ(ierr);
1607   ierr = MatMPIAIJGetSeqAIJ(A,&aA,&aB,&gcols);CHKERRQ(ierr);
1608 
1609   /* Find out where my gcols should go */
1610   ierr = MatGetSize(aB,NULL,&ng);CHKERRQ(ierr);
1611   ierr = PetscMalloc1(ng,&gcdest);CHKERRQ(ierr);
1612   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1613   ierr = PetscSFSetGraphLayout(sf,A->cmap,ng,NULL,PETSC_OWN_POINTER,gcols);CHKERRQ(ierr);
1614   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1615   ierr = PetscSFBcastBegin(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1616   ierr = PetscSFBcastEnd(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1617   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1618 
1619   ierr = PetscCalloc4(m,&dnnz,m,&onnz,m,&tdnnz,m,&tonnz);CHKERRQ(ierr);
1620   ierr = MatGetRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1621   ierr = MatGetRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1622   for (i=0; i<m; i++) {
1623     PetscInt row = rdest[i],rowner;
1624     ierr = PetscLayoutFindOwner(A->rmap,row,&rowner);CHKERRQ(ierr);
1625     for (j=ai[i]; j<ai[i+1]; j++) {
1626       PetscInt cowner,col = cdest[aj[j]];
1627       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr); /* Could build an index for the columns to eliminate this search */
1628       if (rowner == cowner) dnnz[i]++;
1629       else onnz[i]++;
1630     }
1631     for (j=bi[i]; j<bi[i+1]; j++) {
1632       PetscInt cowner,col = gcdest[bj[j]];
1633       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr);
1634       if (rowner == cowner) dnnz[i]++;
1635       else onnz[i]++;
1636     }
1637   }
1638   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1639   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1640   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1641   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1642   ierr = PetscSFDestroy(&rowsf);CHKERRQ(ierr);
1643 
1644   ierr = MatCreateAIJ(PetscObjectComm((PetscObject)A),A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N,0,tdnnz,0,tonnz,&Aperm);CHKERRQ(ierr);
1645   ierr = MatSeqAIJGetArray(aA,&aa);CHKERRQ(ierr);
1646   ierr = MatSeqAIJGetArray(aB,&ba);CHKERRQ(ierr);
1647   for (i=0; i<m; i++) {
1648     PetscInt *acols = dnnz,*bcols = onnz; /* Repurpose now-unneeded arrays */
1649     PetscInt j0,rowlen;
1650     rowlen = ai[i+1] - ai[i];
1651     for (j0=j=0; j<rowlen; j0=j) { /* rowlen could be larger than number of rows m, so sum in batches */
1652       for ( ; j<PetscMin(rowlen,j0+m); j++) acols[j-j0] = cdest[aj[ai[i]+j]];
1653       ierr = MatSetValues(Aperm,1,&rdest[i],j-j0,acols,aa+ai[i]+j0,INSERT_VALUES);CHKERRQ(ierr);
1654     }
1655     rowlen = bi[i+1] - bi[i];
1656     for (j0=j=0; j<rowlen; j0=j) {
1657       for ( ; j<PetscMin(rowlen,j0+m); j++) bcols[j-j0] = gcdest[bj[bi[i]+j]];
1658       ierr = MatSetValues(Aperm,1,&rdest[i],j-j0,bcols,ba+bi[i]+j0,INSERT_VALUES);CHKERRQ(ierr);
1659     }
1660   }
1661   ierr = MatAssemblyBegin(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1662   ierr = MatAssemblyEnd(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1663   ierr = MatRestoreRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1664   ierr = MatRestoreRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1665   ierr = MatSeqAIJRestoreArray(aA,&aa);CHKERRQ(ierr);
1666   ierr = MatSeqAIJRestoreArray(aB,&ba);CHKERRQ(ierr);
1667   ierr = PetscFree4(dnnz,onnz,tdnnz,tonnz);CHKERRQ(ierr);
1668   ierr = PetscFree3(work,rdest,cdest);CHKERRQ(ierr);
1669   ierr = PetscFree(gcdest);CHKERRQ(ierr);
1670   if (parcolp) {ierr = ISDestroy(&colp);CHKERRQ(ierr);}
1671   *B = Aperm;
1672   PetscFunctionReturn(0);
1673 }
1674 
1675 #undef __FUNCT__
1676 #define __FUNCT__ "MatGetGhosts_MPIAIJ"
1677 PetscErrorCode  MatGetGhosts_MPIAIJ(Mat mat,PetscInt *nghosts,const PetscInt *ghosts[])
1678 {
1679   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1680   PetscErrorCode ierr;
1681 
1682   PetscFunctionBegin;
1683   ierr = MatGetSize(aij->B,NULL,nghosts);CHKERRQ(ierr);
1684   if (ghosts) *ghosts = aij->garray;
1685   PetscFunctionReturn(0);
1686 }
1687 
1688 #undef __FUNCT__
1689 #define __FUNCT__ "MatGetInfo_MPIAIJ"
1690 PetscErrorCode MatGetInfo_MPIAIJ(Mat matin,MatInfoType flag,MatInfo *info)
1691 {
1692   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1693   Mat            A    = mat->A,B = mat->B;
1694   PetscErrorCode ierr;
1695   PetscReal      isend[5],irecv[5];
1696 
1697   PetscFunctionBegin;
1698   info->block_size = 1.0;
1699   ierr             = MatGetInfo(A,MAT_LOCAL,info);CHKERRQ(ierr);
1700 
1701   isend[0] = info->nz_used; isend[1] = info->nz_allocated; isend[2] = info->nz_unneeded;
1702   isend[3] = info->memory;  isend[4] = info->mallocs;
1703 
1704   ierr = MatGetInfo(B,MAT_LOCAL,info);CHKERRQ(ierr);
1705 
1706   isend[0] += info->nz_used; isend[1] += info->nz_allocated; isend[2] += info->nz_unneeded;
1707   isend[3] += info->memory;  isend[4] += info->mallocs;
1708   if (flag == MAT_LOCAL) {
1709     info->nz_used      = isend[0];
1710     info->nz_allocated = isend[1];
1711     info->nz_unneeded  = isend[2];
1712     info->memory       = isend[3];
1713     info->mallocs      = isend[4];
1714   } else if (flag == MAT_GLOBAL_MAX) {
1715     ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1716 
1717     info->nz_used      = irecv[0];
1718     info->nz_allocated = irecv[1];
1719     info->nz_unneeded  = irecv[2];
1720     info->memory       = irecv[3];
1721     info->mallocs      = irecv[4];
1722   } else if (flag == MAT_GLOBAL_SUM) {
1723     ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1724 
1725     info->nz_used      = irecv[0];
1726     info->nz_allocated = irecv[1];
1727     info->nz_unneeded  = irecv[2];
1728     info->memory       = irecv[3];
1729     info->mallocs      = irecv[4];
1730   }
1731   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
1732   info->fill_ratio_needed = 0;
1733   info->factor_mallocs    = 0;
1734   PetscFunctionReturn(0);
1735 }
1736 
1737 #undef __FUNCT__
1738 #define __FUNCT__ "MatSetOption_MPIAIJ"
1739 PetscErrorCode MatSetOption_MPIAIJ(Mat A,MatOption op,PetscBool flg)
1740 {
1741   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1742   PetscErrorCode ierr;
1743 
1744   PetscFunctionBegin;
1745   switch (op) {
1746   case MAT_NEW_NONZERO_LOCATIONS:
1747   case MAT_NEW_NONZERO_ALLOCATION_ERR:
1748   case MAT_UNUSED_NONZERO_LOCATION_ERR:
1749   case MAT_KEEP_NONZERO_PATTERN:
1750   case MAT_NEW_NONZERO_LOCATION_ERR:
1751   case MAT_USE_INODES:
1752   case MAT_IGNORE_ZERO_ENTRIES:
1753     MatCheckPreallocated(A,1);
1754     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1755     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1756     break;
1757   case MAT_ROW_ORIENTED:
1758     a->roworiented = flg;
1759 
1760     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1761     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1762     break;
1763   case MAT_NEW_DIAGONALS:
1764     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
1765     break;
1766   case MAT_IGNORE_OFF_PROC_ENTRIES:
1767     a->donotstash = flg;
1768     break;
1769   case MAT_SPD:
1770     A->spd_set = PETSC_TRUE;
1771     A->spd     = flg;
1772     if (flg) {
1773       A->symmetric                  = PETSC_TRUE;
1774       A->structurally_symmetric     = PETSC_TRUE;
1775       A->symmetric_set              = PETSC_TRUE;
1776       A->structurally_symmetric_set = PETSC_TRUE;
1777     }
1778     break;
1779   case MAT_SYMMETRIC:
1780     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1781     break;
1782   case MAT_STRUCTURALLY_SYMMETRIC:
1783     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1784     break;
1785   case MAT_HERMITIAN:
1786     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1787     break;
1788   case MAT_SYMMETRY_ETERNAL:
1789     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1790     break;
1791   default:
1792     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %d",op);
1793   }
1794   PetscFunctionReturn(0);
1795 }
1796 
1797 #undef __FUNCT__
1798 #define __FUNCT__ "MatGetRow_MPIAIJ"
1799 PetscErrorCode MatGetRow_MPIAIJ(Mat matin,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1800 {
1801   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1802   PetscScalar    *vworkA,*vworkB,**pvA,**pvB,*v_p;
1803   PetscErrorCode ierr;
1804   PetscInt       i,*cworkA,*cworkB,**pcA,**pcB,cstart = matin->cmap->rstart;
1805   PetscInt       nztot,nzA,nzB,lrow,rstart = matin->rmap->rstart,rend = matin->rmap->rend;
1806   PetscInt       *cmap,*idx_p;
1807 
1808   PetscFunctionBegin;
1809   if (mat->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Already active");
1810   mat->getrowactive = PETSC_TRUE;
1811 
1812   if (!mat->rowvalues && (idx || v)) {
1813     /*
1814         allocate enough space to hold information from the longest row.
1815     */
1816     Mat_SeqAIJ *Aa = (Mat_SeqAIJ*)mat->A->data,*Ba = (Mat_SeqAIJ*)mat->B->data;
1817     PetscInt   max = 1,tmp;
1818     for (i=0; i<matin->rmap->n; i++) {
1819       tmp = Aa->i[i+1] - Aa->i[i] + Ba->i[i+1] - Ba->i[i];
1820       if (max < tmp) max = tmp;
1821     }
1822     ierr = PetscMalloc2(max,&mat->rowvalues,max,&mat->rowindices);CHKERRQ(ierr);
1823   }
1824 
1825   if (row < rstart || row >= rend) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Only local rows");
1826   lrow = row - rstart;
1827 
1828   pvA = &vworkA; pcA = &cworkA; pvB = &vworkB; pcB = &cworkB;
1829   if (!v)   {pvA = 0; pvB = 0;}
1830   if (!idx) {pcA = 0; if (!v) pcB = 0;}
1831   ierr  = (*mat->A->ops->getrow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1832   ierr  = (*mat->B->ops->getrow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1833   nztot = nzA + nzB;
1834 
1835   cmap = mat->garray;
1836   if (v  || idx) {
1837     if (nztot) {
1838       /* Sort by increasing column numbers, assuming A and B already sorted */
1839       PetscInt imark = -1;
1840       if (v) {
1841         *v = v_p = mat->rowvalues;
1842         for (i=0; i<nzB; i++) {
1843           if (cmap[cworkB[i]] < cstart) v_p[i] = vworkB[i];
1844           else break;
1845         }
1846         imark = i;
1847         for (i=0; i<nzA; i++)     v_p[imark+i] = vworkA[i];
1848         for (i=imark; i<nzB; i++) v_p[nzA+i]   = vworkB[i];
1849       }
1850       if (idx) {
1851         *idx = idx_p = mat->rowindices;
1852         if (imark > -1) {
1853           for (i=0; i<imark; i++) {
1854             idx_p[i] = cmap[cworkB[i]];
1855           }
1856         } else {
1857           for (i=0; i<nzB; i++) {
1858             if (cmap[cworkB[i]] < cstart) idx_p[i] = cmap[cworkB[i]];
1859             else break;
1860           }
1861           imark = i;
1862         }
1863         for (i=0; i<nzA; i++)     idx_p[imark+i] = cstart + cworkA[i];
1864         for (i=imark; i<nzB; i++) idx_p[nzA+i]   = cmap[cworkB[i]];
1865       }
1866     } else {
1867       if (idx) *idx = 0;
1868       if (v)   *v   = 0;
1869     }
1870   }
1871   *nz  = nztot;
1872   ierr = (*mat->A->ops->restorerow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1873   ierr = (*mat->B->ops->restorerow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1874   PetscFunctionReturn(0);
1875 }
1876 
1877 #undef __FUNCT__
1878 #define __FUNCT__ "MatRestoreRow_MPIAIJ"
1879 PetscErrorCode MatRestoreRow_MPIAIJ(Mat mat,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1880 {
1881   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1882 
1883   PetscFunctionBegin;
1884   if (!aij->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"MatGetRow() must be called first");
1885   aij->getrowactive = PETSC_FALSE;
1886   PetscFunctionReturn(0);
1887 }
1888 
1889 #undef __FUNCT__
1890 #define __FUNCT__ "MatNorm_MPIAIJ"
1891 PetscErrorCode MatNorm_MPIAIJ(Mat mat,NormType type,PetscReal *norm)
1892 {
1893   Mat_MPIAIJ     *aij  = (Mat_MPIAIJ*)mat->data;
1894   Mat_SeqAIJ     *amat = (Mat_SeqAIJ*)aij->A->data,*bmat = (Mat_SeqAIJ*)aij->B->data;
1895   PetscErrorCode ierr;
1896   PetscInt       i,j,cstart = mat->cmap->rstart;
1897   PetscReal      sum = 0.0;
1898   MatScalar      *v;
1899 
1900   PetscFunctionBegin;
1901   if (aij->size == 1) {
1902     ierr =  MatNorm(aij->A,type,norm);CHKERRQ(ierr);
1903   } else {
1904     if (type == NORM_FROBENIUS) {
1905       v = amat->a;
1906       for (i=0; i<amat->nz; i++) {
1907         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1908       }
1909       v = bmat->a;
1910       for (i=0; i<bmat->nz; i++) {
1911         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1912       }
1913       ierr  = MPI_Allreduce(&sum,norm,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1914       *norm = PetscSqrtReal(*norm);
1915     } else if (type == NORM_1) { /* max column norm */
1916       PetscReal *tmp,*tmp2;
1917       PetscInt  *jj,*garray = aij->garray;
1918       ierr  = PetscCalloc1(mat->cmap->N+1,&tmp);CHKERRQ(ierr);
1919       ierr  = PetscMalloc1(mat->cmap->N+1,&tmp2);CHKERRQ(ierr);
1920       *norm = 0.0;
1921       v     = amat->a; jj = amat->j;
1922       for (j=0; j<amat->nz; j++) {
1923         tmp[cstart + *jj++] += PetscAbsScalar(*v);  v++;
1924       }
1925       v = bmat->a; jj = bmat->j;
1926       for (j=0; j<bmat->nz; j++) {
1927         tmp[garray[*jj++]] += PetscAbsScalar(*v); v++;
1928       }
1929       ierr = MPI_Allreduce(tmp,tmp2,mat->cmap->N,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1930       for (j=0; j<mat->cmap->N; j++) {
1931         if (tmp2[j] > *norm) *norm = tmp2[j];
1932       }
1933       ierr = PetscFree(tmp);CHKERRQ(ierr);
1934       ierr = PetscFree(tmp2);CHKERRQ(ierr);
1935     } else if (type == NORM_INFINITY) { /* max row norm */
1936       PetscReal ntemp = 0.0;
1937       for (j=0; j<aij->A->rmap->n; j++) {
1938         v   = amat->a + amat->i[j];
1939         sum = 0.0;
1940         for (i=0; i<amat->i[j+1]-amat->i[j]; i++) {
1941           sum += PetscAbsScalar(*v); v++;
1942         }
1943         v = bmat->a + bmat->i[j];
1944         for (i=0; i<bmat->i[j+1]-bmat->i[j]; i++) {
1945           sum += PetscAbsScalar(*v); v++;
1946         }
1947         if (sum > ntemp) ntemp = sum;
1948       }
1949       ierr = MPI_Allreduce(&ntemp,norm,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1950     } else SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"No support for two norm");
1951   }
1952   PetscFunctionReturn(0);
1953 }
1954 
1955 #undef __FUNCT__
1956 #define __FUNCT__ "MatTranspose_MPIAIJ"
1957 PetscErrorCode MatTranspose_MPIAIJ(Mat A,MatReuse reuse,Mat *matout)
1958 {
1959   Mat_MPIAIJ     *a   = (Mat_MPIAIJ*)A->data;
1960   Mat_SeqAIJ     *Aloc=(Mat_SeqAIJ*)a->A->data,*Bloc=(Mat_SeqAIJ*)a->B->data;
1961   PetscErrorCode ierr;
1962   PetscInt       M      = A->rmap->N,N = A->cmap->N,ma,na,mb,nb,*ai,*aj,*bi,*bj,row,*cols,*cols_tmp,i;
1963   PetscInt       cstart = A->cmap->rstart,ncol;
1964   Mat            B;
1965   MatScalar      *array;
1966 
1967   PetscFunctionBegin;
1968   if (reuse == MAT_REUSE_MATRIX && A == *matout && M != N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Square matrix only for in-place");
1969 
1970   ma = A->rmap->n; na = A->cmap->n; mb = a->B->rmap->n; nb = a->B->cmap->n;
1971   ai = Aloc->i; aj = Aloc->j;
1972   bi = Bloc->i; bj = Bloc->j;
1973   if (reuse == MAT_INITIAL_MATRIX || *matout == A) {
1974     PetscInt             *d_nnz,*g_nnz,*o_nnz;
1975     PetscSFNode          *oloc;
1976     PETSC_UNUSED PetscSF sf;
1977 
1978     ierr = PetscMalloc4(na,&d_nnz,na,&o_nnz,nb,&g_nnz,nb,&oloc);CHKERRQ(ierr);
1979     /* compute d_nnz for preallocation */
1980     ierr = PetscMemzero(d_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1981     for (i=0; i<ai[ma]; i++) {
1982       d_nnz[aj[i]]++;
1983       aj[i] += cstart; /* global col index to be used by MatSetValues() */
1984     }
1985     /* compute local off-diagonal contributions */
1986     ierr = PetscMemzero(g_nnz,nb*sizeof(PetscInt));CHKERRQ(ierr);
1987     for (i=0; i<bi[ma]; i++) g_nnz[bj[i]]++;
1988     /* map those to global */
1989     ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1990     ierr = PetscSFSetGraphLayout(sf,A->cmap,nb,NULL,PETSC_USE_POINTER,a->garray);CHKERRQ(ierr);
1991     ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1992     ierr = PetscMemzero(o_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1993     ierr = PetscSFReduceBegin(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
1994     ierr = PetscSFReduceEnd(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
1995     ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1996 
1997     ierr = MatCreate(PetscObjectComm((PetscObject)A),&B);CHKERRQ(ierr);
1998     ierr = MatSetSizes(B,A->cmap->n,A->rmap->n,N,M);CHKERRQ(ierr);
1999     ierr = MatSetBlockSizes(B,PetscAbs(A->cmap->bs),PetscAbs(A->rmap->bs));CHKERRQ(ierr);
2000     ierr = MatSetType(B,((PetscObject)A)->type_name);CHKERRQ(ierr);
2001     ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
2002     ierr = PetscFree4(d_nnz,o_nnz,g_nnz,oloc);CHKERRQ(ierr);
2003   } else {
2004     B    = *matout;
2005     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
2006     for (i=0; i<ai[ma]; i++) aj[i] += cstart; /* global col index to be used by MatSetValues() */
2007   }
2008 
2009   /* copy over the A part */
2010   array = Aloc->a;
2011   row   = A->rmap->rstart;
2012   for (i=0; i<ma; i++) {
2013     ncol = ai[i+1]-ai[i];
2014     ierr = MatSetValues(B,ncol,aj,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
2015     row++;
2016     array += ncol; aj += ncol;
2017   }
2018   aj = Aloc->j;
2019   for (i=0; i<ai[ma]; i++) aj[i] -= cstart; /* resume local col index */
2020 
2021   /* copy over the B part */
2022   ierr  = PetscCalloc1(bi[mb],&cols);CHKERRQ(ierr);
2023   array = Bloc->a;
2024   row   = A->rmap->rstart;
2025   for (i=0; i<bi[mb]; i++) cols[i] = a->garray[bj[i]];
2026   cols_tmp = cols;
2027   for (i=0; i<mb; i++) {
2028     ncol = bi[i+1]-bi[i];
2029     ierr = MatSetValues(B,ncol,cols_tmp,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
2030     row++;
2031     array += ncol; cols_tmp += ncol;
2032   }
2033   ierr = PetscFree(cols);CHKERRQ(ierr);
2034 
2035   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2036   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2037   if (reuse == MAT_INITIAL_MATRIX || *matout != A) {
2038     *matout = B;
2039   } else {
2040     ierr = MatHeaderMerge(A,B);CHKERRQ(ierr);
2041   }
2042   PetscFunctionReturn(0);
2043 }
2044 
2045 #undef __FUNCT__
2046 #define __FUNCT__ "MatDiagonalScale_MPIAIJ"
2047 PetscErrorCode MatDiagonalScale_MPIAIJ(Mat mat,Vec ll,Vec rr)
2048 {
2049   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2050   Mat            a    = aij->A,b = aij->B;
2051   PetscErrorCode ierr;
2052   PetscInt       s1,s2,s3;
2053 
2054   PetscFunctionBegin;
2055   ierr = MatGetLocalSize(mat,&s2,&s3);CHKERRQ(ierr);
2056   if (rr) {
2057     ierr = VecGetLocalSize(rr,&s1);CHKERRQ(ierr);
2058     if (s1!=s3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"right vector non-conforming local size");
2059     /* Overlap communication with computation. */
2060     ierr = VecScatterBegin(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2061   }
2062   if (ll) {
2063     ierr = VecGetLocalSize(ll,&s1);CHKERRQ(ierr);
2064     if (s1!=s2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"left vector non-conforming local size");
2065     ierr = (*b->ops->diagonalscale)(b,ll,0);CHKERRQ(ierr);
2066   }
2067   /* scale  the diagonal block */
2068   ierr = (*a->ops->diagonalscale)(a,ll,rr);CHKERRQ(ierr);
2069 
2070   if (rr) {
2071     /* Do a scatter end and then right scale the off-diagonal block */
2072     ierr = VecScatterEnd(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2073     ierr = (*b->ops->diagonalscale)(b,0,aij->lvec);CHKERRQ(ierr);
2074   }
2075   PetscFunctionReturn(0);
2076 }
2077 
2078 #undef __FUNCT__
2079 #define __FUNCT__ "MatSetUnfactored_MPIAIJ"
2080 PetscErrorCode MatSetUnfactored_MPIAIJ(Mat A)
2081 {
2082   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2083   PetscErrorCode ierr;
2084 
2085   PetscFunctionBegin;
2086   ierr = MatSetUnfactored(a->A);CHKERRQ(ierr);
2087   PetscFunctionReturn(0);
2088 }
2089 
2090 #undef __FUNCT__
2091 #define __FUNCT__ "MatEqual_MPIAIJ"
2092 PetscErrorCode MatEqual_MPIAIJ(Mat A,Mat B,PetscBool  *flag)
2093 {
2094   Mat_MPIAIJ     *matB = (Mat_MPIAIJ*)B->data,*matA = (Mat_MPIAIJ*)A->data;
2095   Mat            a,b,c,d;
2096   PetscBool      flg;
2097   PetscErrorCode ierr;
2098 
2099   PetscFunctionBegin;
2100   a = matA->A; b = matA->B;
2101   c = matB->A; d = matB->B;
2102 
2103   ierr = MatEqual(a,c,&flg);CHKERRQ(ierr);
2104   if (flg) {
2105     ierr = MatEqual(b,d,&flg);CHKERRQ(ierr);
2106   }
2107   ierr = MPI_Allreduce(&flg,flag,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
2108   PetscFunctionReturn(0);
2109 }
2110 
2111 #undef __FUNCT__
2112 #define __FUNCT__ "MatCopy_MPIAIJ"
2113 PetscErrorCode MatCopy_MPIAIJ(Mat A,Mat B,MatStructure str)
2114 {
2115   PetscErrorCode ierr;
2116   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2117   Mat_MPIAIJ     *b = (Mat_MPIAIJ*)B->data;
2118 
2119   PetscFunctionBegin;
2120   /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
2121   if ((str != SAME_NONZERO_PATTERN) || (A->ops->copy != B->ops->copy)) {
2122     /* because of the column compression in the off-processor part of the matrix a->B,
2123        the number of columns in a->B and b->B may be different, hence we cannot call
2124        the MatCopy() directly on the two parts. If need be, we can provide a more
2125        efficient copy than the MatCopy_Basic() by first uncompressing the a->B matrices
2126        then copying the submatrices */
2127     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
2128   } else {
2129     ierr = MatCopy(a->A,b->A,str);CHKERRQ(ierr);
2130     ierr = MatCopy(a->B,b->B,str);CHKERRQ(ierr);
2131   }
2132   PetscFunctionReturn(0);
2133 }
2134 
2135 #undef __FUNCT__
2136 #define __FUNCT__ "MatSetUp_MPIAIJ"
2137 PetscErrorCode MatSetUp_MPIAIJ(Mat A)
2138 {
2139   PetscErrorCode ierr;
2140 
2141   PetscFunctionBegin;
2142   ierr =  MatMPIAIJSetPreallocation(A,PETSC_DEFAULT,0,PETSC_DEFAULT,0);CHKERRQ(ierr);
2143   PetscFunctionReturn(0);
2144 }
2145 
2146 /*
2147    Computes the number of nonzeros per row needed for preallocation when X and Y
2148    have different nonzero structure.
2149 */
2150 #undef __FUNCT__
2151 #define __FUNCT__ "MatAXPYGetPreallocation_MPIX_private"
2152 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)
2153 {
2154   PetscInt       i,j,k,nzx,nzy;
2155 
2156   PetscFunctionBegin;
2157   /* Set the number of nonzeros in the new matrix */
2158   for (i=0; i<m; i++) {
2159     const PetscInt *xjj = xj+xi[i],*yjj = yj+yi[i];
2160     nzx = xi[i+1] - xi[i];
2161     nzy = yi[i+1] - yi[i];
2162     nnz[i] = 0;
2163     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2164       for (; k<nzy && yltog[yjj[k]]<xltog[xjj[j]]; k++) nnz[i]++; /* Catch up to X */
2165       if (k<nzy && yltog[yjj[k]]==xltog[xjj[j]]) k++;             /* Skip duplicate */
2166       nnz[i]++;
2167     }
2168     for (; k<nzy; k++) nnz[i]++;
2169   }
2170   PetscFunctionReturn(0);
2171 }
2172 
2173 /* This is the same as MatAXPYGetPreallocation_SeqAIJ, except that the local-to-global map is provided */
2174 #undef __FUNCT__
2175 #define __FUNCT__ "MatAXPYGetPreallocation_MPIAIJ"
2176 static PetscErrorCode MatAXPYGetPreallocation_MPIAIJ(Mat Y,const PetscInt *yltog,Mat X,const PetscInt *xltog,PetscInt *nnz)
2177 {
2178   PetscErrorCode ierr;
2179   PetscInt       m = Y->rmap->N;
2180   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data;
2181   Mat_SeqAIJ     *y = (Mat_SeqAIJ*)Y->data;
2182 
2183   PetscFunctionBegin;
2184   ierr = MatAXPYGetPreallocation_MPIX_private(m,x->i,x->j,xltog,y->i,y->j,yltog,nnz);CHKERRQ(ierr);
2185   PetscFunctionReturn(0);
2186 }
2187 
2188 #undef __FUNCT__
2189 #define __FUNCT__ "MatAXPY_MPIAIJ"
2190 PetscErrorCode MatAXPY_MPIAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
2191 {
2192   PetscErrorCode ierr;
2193   Mat_MPIAIJ     *xx = (Mat_MPIAIJ*)X->data,*yy = (Mat_MPIAIJ*)Y->data;
2194   PetscBLASInt   bnz,one=1;
2195   Mat_SeqAIJ     *x,*y;
2196 
2197   PetscFunctionBegin;
2198   if (str == SAME_NONZERO_PATTERN) {
2199     PetscScalar alpha = a;
2200     x    = (Mat_SeqAIJ*)xx->A->data;
2201     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2202     y    = (Mat_SeqAIJ*)yy->A->data;
2203     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2204     x    = (Mat_SeqAIJ*)xx->B->data;
2205     y    = (Mat_SeqAIJ*)yy->B->data;
2206     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2207     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2208     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
2209   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
2210     ierr = MatAXPY_Basic(Y,a,X,str);CHKERRQ(ierr);
2211   } else {
2212     Mat      B;
2213     PetscInt *nnz_d,*nnz_o;
2214     ierr = PetscMalloc1(yy->A->rmap->N,&nnz_d);CHKERRQ(ierr);
2215     ierr = PetscMalloc1(yy->B->rmap->N,&nnz_o);CHKERRQ(ierr);
2216     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
2217     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
2218     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
2219     ierr = MatSetBlockSizesFromMats(B,Y,Y);CHKERRQ(ierr);
2220     ierr = MatSetType(B,MATMPIAIJ);CHKERRQ(ierr);
2221     ierr = MatAXPYGetPreallocation_SeqAIJ(yy->A,xx->A,nnz_d);CHKERRQ(ierr);
2222     ierr = MatAXPYGetPreallocation_MPIAIJ(yy->B,yy->garray,xx->B,xx->garray,nnz_o);CHKERRQ(ierr);
2223     ierr = MatMPIAIJSetPreallocation(B,0,nnz_d,0,nnz_o);CHKERRQ(ierr);
2224     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
2225     ierr = MatHeaderReplace(Y,B);CHKERRQ(ierr);
2226     ierr = PetscFree(nnz_d);CHKERRQ(ierr);
2227     ierr = PetscFree(nnz_o);CHKERRQ(ierr);
2228   }
2229   PetscFunctionReturn(0);
2230 }
2231 
2232 extern PetscErrorCode  MatConjugate_SeqAIJ(Mat);
2233 
2234 #undef __FUNCT__
2235 #define __FUNCT__ "MatConjugate_MPIAIJ"
2236 PetscErrorCode  MatConjugate_MPIAIJ(Mat mat)
2237 {
2238 #if defined(PETSC_USE_COMPLEX)
2239   PetscErrorCode ierr;
2240   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2241 
2242   PetscFunctionBegin;
2243   ierr = MatConjugate_SeqAIJ(aij->A);CHKERRQ(ierr);
2244   ierr = MatConjugate_SeqAIJ(aij->B);CHKERRQ(ierr);
2245 #else
2246   PetscFunctionBegin;
2247 #endif
2248   PetscFunctionReturn(0);
2249 }
2250 
2251 #undef __FUNCT__
2252 #define __FUNCT__ "MatRealPart_MPIAIJ"
2253 PetscErrorCode MatRealPart_MPIAIJ(Mat A)
2254 {
2255   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2256   PetscErrorCode ierr;
2257 
2258   PetscFunctionBegin;
2259   ierr = MatRealPart(a->A);CHKERRQ(ierr);
2260   ierr = MatRealPart(a->B);CHKERRQ(ierr);
2261   PetscFunctionReturn(0);
2262 }
2263 
2264 #undef __FUNCT__
2265 #define __FUNCT__ "MatImaginaryPart_MPIAIJ"
2266 PetscErrorCode MatImaginaryPart_MPIAIJ(Mat A)
2267 {
2268   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2269   PetscErrorCode ierr;
2270 
2271   PetscFunctionBegin;
2272   ierr = MatImaginaryPart(a->A);CHKERRQ(ierr);
2273   ierr = MatImaginaryPart(a->B);CHKERRQ(ierr);
2274   PetscFunctionReturn(0);
2275 }
2276 
2277 #undef __FUNCT__
2278 #define __FUNCT__ "MatGetRowMaxAbs_MPIAIJ"
2279 PetscErrorCode MatGetRowMaxAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2280 {
2281   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2282   PetscErrorCode ierr;
2283   PetscInt       i,*idxb = 0;
2284   PetscScalar    *va,*vb;
2285   Vec            vtmp;
2286 
2287   PetscFunctionBegin;
2288   ierr = MatGetRowMaxAbs(a->A,v,idx);CHKERRQ(ierr);
2289   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2290   if (idx) {
2291     for (i=0; i<A->rmap->n; i++) {
2292       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2293     }
2294   }
2295 
2296   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2297   if (idx) {
2298     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2299   }
2300   ierr = MatGetRowMaxAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2301   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2302 
2303   for (i=0; i<A->rmap->n; i++) {
2304     if (PetscAbsScalar(va[i]) < PetscAbsScalar(vb[i])) {
2305       va[i] = vb[i];
2306       if (idx) idx[i] = a->garray[idxb[i]];
2307     }
2308   }
2309 
2310   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2311   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2312   ierr = PetscFree(idxb);CHKERRQ(ierr);
2313   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2314   PetscFunctionReturn(0);
2315 }
2316 
2317 #undef __FUNCT__
2318 #define __FUNCT__ "MatGetRowMinAbs_MPIAIJ"
2319 PetscErrorCode MatGetRowMinAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2320 {
2321   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2322   PetscErrorCode ierr;
2323   PetscInt       i,*idxb = 0;
2324   PetscScalar    *va,*vb;
2325   Vec            vtmp;
2326 
2327   PetscFunctionBegin;
2328   ierr = MatGetRowMinAbs(a->A,v,idx);CHKERRQ(ierr);
2329   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2330   if (idx) {
2331     for (i=0; i<A->cmap->n; i++) {
2332       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2333     }
2334   }
2335 
2336   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2337   if (idx) {
2338     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2339   }
2340   ierr = MatGetRowMinAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2341   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2342 
2343   for (i=0; i<A->rmap->n; i++) {
2344     if (PetscAbsScalar(va[i]) > PetscAbsScalar(vb[i])) {
2345       va[i] = vb[i];
2346       if (idx) idx[i] = a->garray[idxb[i]];
2347     }
2348   }
2349 
2350   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2351   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2352   ierr = PetscFree(idxb);CHKERRQ(ierr);
2353   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2354   PetscFunctionReturn(0);
2355 }
2356 
2357 #undef __FUNCT__
2358 #define __FUNCT__ "MatGetRowMin_MPIAIJ"
2359 PetscErrorCode MatGetRowMin_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2360 {
2361   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2362   PetscInt       n      = A->rmap->n;
2363   PetscInt       cstart = A->cmap->rstart;
2364   PetscInt       *cmap  = mat->garray;
2365   PetscInt       *diagIdx, *offdiagIdx;
2366   Vec            diagV, offdiagV;
2367   PetscScalar    *a, *diagA, *offdiagA;
2368   PetscInt       r;
2369   PetscErrorCode ierr;
2370 
2371   PetscFunctionBegin;
2372   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2373   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &diagV);CHKERRQ(ierr);
2374   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &offdiagV);CHKERRQ(ierr);
2375   ierr = MatGetRowMin(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2376   ierr = MatGetRowMin(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2377   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2378   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2379   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2380   for (r = 0; r < n; ++r) {
2381     if (PetscAbsScalar(diagA[r]) <= PetscAbsScalar(offdiagA[r])) {
2382       a[r]   = diagA[r];
2383       idx[r] = cstart + diagIdx[r];
2384     } else {
2385       a[r]   = offdiagA[r];
2386       idx[r] = cmap[offdiagIdx[r]];
2387     }
2388   }
2389   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2390   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2391   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2392   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2393   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2394   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2395   PetscFunctionReturn(0);
2396 }
2397 
2398 #undef __FUNCT__
2399 #define __FUNCT__ "MatGetRowMax_MPIAIJ"
2400 PetscErrorCode MatGetRowMax_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2401 {
2402   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2403   PetscInt       n      = A->rmap->n;
2404   PetscInt       cstart = A->cmap->rstart;
2405   PetscInt       *cmap  = mat->garray;
2406   PetscInt       *diagIdx, *offdiagIdx;
2407   Vec            diagV, offdiagV;
2408   PetscScalar    *a, *diagA, *offdiagA;
2409   PetscInt       r;
2410   PetscErrorCode ierr;
2411 
2412   PetscFunctionBegin;
2413   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2414   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &diagV);CHKERRQ(ierr);
2415   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &offdiagV);CHKERRQ(ierr);
2416   ierr = MatGetRowMax(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2417   ierr = MatGetRowMax(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2418   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2419   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2420   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2421   for (r = 0; r < n; ++r) {
2422     if (PetscAbsScalar(diagA[r]) >= PetscAbsScalar(offdiagA[r])) {
2423       a[r]   = diagA[r];
2424       idx[r] = cstart + diagIdx[r];
2425     } else {
2426       a[r]   = offdiagA[r];
2427       idx[r] = cmap[offdiagIdx[r]];
2428     }
2429   }
2430   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2431   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2432   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2433   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2434   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2435   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2436   PetscFunctionReturn(0);
2437 }
2438 
2439 #undef __FUNCT__
2440 #define __FUNCT__ "MatGetSeqNonzeroStructure_MPIAIJ"
2441 PetscErrorCode MatGetSeqNonzeroStructure_MPIAIJ(Mat mat,Mat *newmat)
2442 {
2443   PetscErrorCode ierr;
2444   Mat            *dummy;
2445 
2446   PetscFunctionBegin;
2447   ierr    = MatGetSubMatrix_MPIAIJ_All(mat,MAT_DO_NOT_GET_VALUES,MAT_INITIAL_MATRIX,&dummy);CHKERRQ(ierr);
2448   *newmat = *dummy;
2449   ierr    = PetscFree(dummy);CHKERRQ(ierr);
2450   PetscFunctionReturn(0);
2451 }
2452 
2453 #undef __FUNCT__
2454 #define __FUNCT__ "MatInvertBlockDiagonal_MPIAIJ"
2455 PetscErrorCode  MatInvertBlockDiagonal_MPIAIJ(Mat A,const PetscScalar **values)
2456 {
2457   Mat_MPIAIJ     *a = (Mat_MPIAIJ*) A->data;
2458   PetscErrorCode ierr;
2459 
2460   PetscFunctionBegin;
2461   ierr = MatInvertBlockDiagonal(a->A,values);CHKERRQ(ierr);
2462   PetscFunctionReturn(0);
2463 }
2464 
2465 #undef __FUNCT__
2466 #define __FUNCT__ "MatSetRandom_MPIAIJ"
2467 static PetscErrorCode  MatSetRandom_MPIAIJ(Mat x,PetscRandom rctx)
2468 {
2469   PetscErrorCode ierr;
2470   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)x->data;
2471 
2472   PetscFunctionBegin;
2473   ierr = MatSetRandom(aij->A,rctx);CHKERRQ(ierr);
2474   ierr = MatSetRandom(aij->B,rctx);CHKERRQ(ierr);
2475   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2476   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2477   PetscFunctionReturn(0);
2478 }
2479 
2480 #undef __FUNCT__
2481 #define __FUNCT__ "MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ"
2482 PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ(Mat A,PetscBool sc)
2483 {
2484   PetscFunctionBegin;
2485   if (sc) A->ops->increaseoverlap = MatIncreaseOverlap_MPIAIJ_Scalable;
2486   else A->ops->increaseoverlap    = MatIncreaseOverlap_MPIAIJ;
2487   PetscFunctionReturn(0);
2488 }
2489 
2490 #undef __FUNCT__
2491 #define __FUNCT__ "MatMPIAIJSetUseScalableIncreaseOverlap"
2492 /*@
2493    MatMPIAIJSetUseScalableIncreaseOverlap - Determine if the matrix uses a scalable algorithm to compute the overlap
2494 
2495    Collective on Mat
2496 
2497    Input Parameters:
2498 +    A - the matrix
2499 -    sc - PETSC_TRUE indicates use the scalable algorithm (default is not to use the scalable algorithm)
2500 
2501 @*/
2502 PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap(Mat A,PetscBool sc)
2503 {
2504   PetscErrorCode       ierr;
2505 
2506   PetscFunctionBegin;
2507   ierr = PetscTryMethod(A,"MatMPIAIJSetUseScalableIncreaseOverlap_C",(Mat,PetscBool),(A,sc));CHKERRQ(ierr);
2508   PetscFunctionReturn(0);
2509 }
2510 
2511 #undef __FUNCT__
2512 #define __FUNCT__ "MatSetFromOptions_MPIAIJ"
2513 PetscErrorCode MatSetFromOptions_MPIAIJ(PetscOptions *PetscOptionsObject,Mat A)
2514 {
2515   PetscErrorCode       ierr;
2516   PetscBool            sc = PETSC_FALSE,flg;
2517 
2518   PetscFunctionBegin;
2519   ierr = PetscOptionsHead(PetscOptionsObject,"MPIAIJ options");CHKERRQ(ierr);
2520   ierr = PetscObjectOptionsBegin((PetscObject)A);
2521     if (A->ops->increaseoverlap == MatIncreaseOverlap_MPIAIJ_Scalable) sc = PETSC_TRUE;
2522     ierr = PetscOptionsBool("-mat_increase_overlap_scalable","Use a scalable algorithm to compute the overlap","MatIncreaseOverlap",sc,&sc,&flg);CHKERRQ(ierr);
2523     if (flg) {
2524       ierr = MatMPIAIJSetUseScalableIncreaseOverlap(A,sc);CHKERRQ(ierr);
2525     }
2526   ierr = PetscOptionsEnd();CHKERRQ(ierr);
2527   PetscFunctionReturn(0);
2528 }
2529 
2530 #undef __FUNCT__
2531 #define __FUNCT__ "MatShift_MPIAIJ"
2532 PetscErrorCode MatShift_MPIAIJ(Mat Y,PetscScalar a)
2533 {
2534   PetscErrorCode ierr;
2535   Mat_MPIAIJ     *maij = (Mat_MPIAIJ*)Y->data;
2536   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)maij->A->data;
2537 
2538   PetscFunctionBegin;
2539   if (!Y->preallocated) {
2540     ierr = MatMPIAIJSetPreallocation(Y,1,NULL,0,NULL);CHKERRQ(ierr);
2541   } else if (!aij->nz) {
2542     ierr = MatSeqAIJSetPreallocation(maij->A,1,NULL);CHKERRQ(ierr);
2543   }
2544   ierr = MatShift_Basic(Y,a);CHKERRQ(ierr);
2545   PetscFunctionReturn(0);
2546 }
2547 
2548 /* -------------------------------------------------------------------*/
2549 static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
2550                                        MatGetRow_MPIAIJ,
2551                                        MatRestoreRow_MPIAIJ,
2552                                        MatMult_MPIAIJ,
2553                                 /* 4*/ MatMultAdd_MPIAIJ,
2554                                        MatMultTranspose_MPIAIJ,
2555                                        MatMultTransposeAdd_MPIAIJ,
2556                                        0,
2557                                        0,
2558                                        0,
2559                                 /*10*/ 0,
2560                                        0,
2561                                        0,
2562                                        MatSOR_MPIAIJ,
2563                                        MatTranspose_MPIAIJ,
2564                                 /*15*/ MatGetInfo_MPIAIJ,
2565                                        MatEqual_MPIAIJ,
2566                                        MatGetDiagonal_MPIAIJ,
2567                                        MatDiagonalScale_MPIAIJ,
2568                                        MatNorm_MPIAIJ,
2569                                 /*20*/ MatAssemblyBegin_MPIAIJ,
2570                                        MatAssemblyEnd_MPIAIJ,
2571                                        MatSetOption_MPIAIJ,
2572                                        MatZeroEntries_MPIAIJ,
2573                                 /*24*/ MatZeroRows_MPIAIJ,
2574                                        0,
2575                                        0,
2576                                        0,
2577                                        0,
2578                                 /*29*/ MatSetUp_MPIAIJ,
2579                                        0,
2580                                        0,
2581                                        0,
2582                                        0,
2583                                 /*34*/ MatDuplicate_MPIAIJ,
2584                                        0,
2585                                        0,
2586                                        0,
2587                                        0,
2588                                 /*39*/ MatAXPY_MPIAIJ,
2589                                        MatGetSubMatrices_MPIAIJ,
2590                                        MatIncreaseOverlap_MPIAIJ,
2591                                        MatGetValues_MPIAIJ,
2592                                        MatCopy_MPIAIJ,
2593                                 /*44*/ MatGetRowMax_MPIAIJ,
2594                                        MatScale_MPIAIJ,
2595                                        MatShift_MPIAIJ,
2596                                        MatDiagonalSet_MPIAIJ,
2597                                        MatZeroRowsColumns_MPIAIJ,
2598                                 /*49*/ MatSetRandom_MPIAIJ,
2599                                        0,
2600                                        0,
2601                                        0,
2602                                        0,
2603                                 /*54*/ MatFDColoringCreate_MPIXAIJ,
2604                                        0,
2605                                        MatSetUnfactored_MPIAIJ,
2606                                        MatPermute_MPIAIJ,
2607                                        0,
2608                                 /*59*/ MatGetSubMatrix_MPIAIJ,
2609                                        MatDestroy_MPIAIJ,
2610                                        MatView_MPIAIJ,
2611                                        0,
2612                                        MatMatMatMult_MPIAIJ_MPIAIJ_MPIAIJ,
2613                                 /*64*/ MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ,
2614                                        MatMatMatMultNumeric_MPIAIJ_MPIAIJ_MPIAIJ,
2615                                        0,
2616                                        0,
2617                                        0,
2618                                 /*69*/ MatGetRowMaxAbs_MPIAIJ,
2619                                        MatGetRowMinAbs_MPIAIJ,
2620                                        0,
2621                                        MatSetColoring_MPIAIJ,
2622                                        0,
2623                                        MatSetValuesAdifor_MPIAIJ,
2624                                 /*75*/ MatFDColoringApply_AIJ,
2625                                        MatSetFromOptions_MPIAIJ,
2626                                        0,
2627                                        0,
2628                                        MatFindZeroDiagonals_MPIAIJ,
2629                                 /*80*/ 0,
2630                                        0,
2631                                        0,
2632                                 /*83*/ MatLoad_MPIAIJ,
2633                                        0,
2634                                        0,
2635                                        0,
2636                                        0,
2637                                        0,
2638                                 /*89*/ MatMatMult_MPIAIJ_MPIAIJ,
2639                                        MatMatMultSymbolic_MPIAIJ_MPIAIJ,
2640                                        MatMatMultNumeric_MPIAIJ_MPIAIJ,
2641                                        MatPtAP_MPIAIJ_MPIAIJ,
2642                                        MatPtAPSymbolic_MPIAIJ_MPIAIJ,
2643                                 /*94*/ MatPtAPNumeric_MPIAIJ_MPIAIJ,
2644                                        0,
2645                                        0,
2646                                        0,
2647                                        0,
2648                                 /*99*/ 0,
2649                                        0,
2650                                        0,
2651                                        MatConjugate_MPIAIJ,
2652                                        0,
2653                                 /*104*/MatSetValuesRow_MPIAIJ,
2654                                        MatRealPart_MPIAIJ,
2655                                        MatImaginaryPart_MPIAIJ,
2656                                        0,
2657                                        0,
2658                                 /*109*/0,
2659                                        0,
2660                                        MatGetRowMin_MPIAIJ,
2661                                        0,
2662                                        0,
2663                                 /*114*/MatGetSeqNonzeroStructure_MPIAIJ,
2664                                        0,
2665                                        MatGetGhosts_MPIAIJ,
2666                                        0,
2667                                        0,
2668                                 /*119*/0,
2669                                        0,
2670                                        0,
2671                                        0,
2672                                        MatGetMultiProcBlock_MPIAIJ,
2673                                 /*124*/MatFindNonzeroRows_MPIAIJ,
2674                                        MatGetColumnNorms_MPIAIJ,
2675                                        MatInvertBlockDiagonal_MPIAIJ,
2676                                        0,
2677                                        MatGetSubMatricesMPI_MPIAIJ,
2678                                 /*129*/0,
2679                                        MatTransposeMatMult_MPIAIJ_MPIAIJ,
2680                                        MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ,
2681                                        MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ,
2682                                        0,
2683                                 /*134*/0,
2684                                        0,
2685                                        0,
2686                                        0,
2687                                        0,
2688                                 /*139*/0,
2689                                        0,
2690                                        0,
2691                                        MatFDColoringSetUp_MPIXAIJ,
2692                                        MatFindOffBlockDiagonalEntries_MPIAIJ,
2693                                 /*144*/MatCreateMPIMatConcatenateSeqMat_MPIAIJ
2694 };
2695 
2696 /* ----------------------------------------------------------------------------------------*/
2697 
2698 #undef __FUNCT__
2699 #define __FUNCT__ "MatStoreValues_MPIAIJ"
2700 PetscErrorCode  MatStoreValues_MPIAIJ(Mat mat)
2701 {
2702   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2703   PetscErrorCode ierr;
2704 
2705   PetscFunctionBegin;
2706   ierr = MatStoreValues(aij->A);CHKERRQ(ierr);
2707   ierr = MatStoreValues(aij->B);CHKERRQ(ierr);
2708   PetscFunctionReturn(0);
2709 }
2710 
2711 #undef __FUNCT__
2712 #define __FUNCT__ "MatRetrieveValues_MPIAIJ"
2713 PetscErrorCode  MatRetrieveValues_MPIAIJ(Mat mat)
2714 {
2715   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2716   PetscErrorCode ierr;
2717 
2718   PetscFunctionBegin;
2719   ierr = MatRetrieveValues(aij->A);CHKERRQ(ierr);
2720   ierr = MatRetrieveValues(aij->B);CHKERRQ(ierr);
2721   PetscFunctionReturn(0);
2722 }
2723 
2724 #undef __FUNCT__
2725 #define __FUNCT__ "MatMPIAIJSetPreallocation_MPIAIJ"
2726 PetscErrorCode  MatMPIAIJSetPreallocation_MPIAIJ(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
2727 {
2728   Mat_MPIAIJ     *b;
2729   PetscErrorCode ierr;
2730 
2731   PetscFunctionBegin;
2732   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
2733   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
2734   b = (Mat_MPIAIJ*)B->data;
2735 
2736   if (!B->preallocated) {
2737     /* Explicitly create 2 MATSEQAIJ matrices. */
2738     ierr = MatCreate(PETSC_COMM_SELF,&b->A);CHKERRQ(ierr);
2739     ierr = MatSetSizes(b->A,B->rmap->n,B->cmap->n,B->rmap->n,B->cmap->n);CHKERRQ(ierr);
2740     ierr = MatSetBlockSizesFromMats(b->A,B,B);CHKERRQ(ierr);
2741     ierr = MatSetType(b->A,MATSEQAIJ);CHKERRQ(ierr);
2742     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->A);CHKERRQ(ierr);
2743     ierr = MatCreate(PETSC_COMM_SELF,&b->B);CHKERRQ(ierr);
2744     ierr = MatSetSizes(b->B,B->rmap->n,B->cmap->N,B->rmap->n,B->cmap->N);CHKERRQ(ierr);
2745     ierr = MatSetBlockSizesFromMats(b->B,B,B);CHKERRQ(ierr);
2746     ierr = MatSetType(b->B,MATSEQAIJ);CHKERRQ(ierr);
2747     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->B);CHKERRQ(ierr);
2748   }
2749 
2750   ierr = MatSeqAIJSetPreallocation(b->A,d_nz,d_nnz);CHKERRQ(ierr);
2751   ierr = MatSeqAIJSetPreallocation(b->B,o_nz,o_nnz);CHKERRQ(ierr);
2752   B->preallocated = PETSC_TRUE;
2753   PetscFunctionReturn(0);
2754 }
2755 
2756 #undef __FUNCT__
2757 #define __FUNCT__ "MatDuplicate_MPIAIJ"
2758 PetscErrorCode MatDuplicate_MPIAIJ(Mat matin,MatDuplicateOption cpvalues,Mat *newmat)
2759 {
2760   Mat            mat;
2761   Mat_MPIAIJ     *a,*oldmat = (Mat_MPIAIJ*)matin->data;
2762   PetscErrorCode ierr;
2763 
2764   PetscFunctionBegin;
2765   *newmat = 0;
2766   ierr    = MatCreate(PetscObjectComm((PetscObject)matin),&mat);CHKERRQ(ierr);
2767   ierr    = MatSetSizes(mat,matin->rmap->n,matin->cmap->n,matin->rmap->N,matin->cmap->N);CHKERRQ(ierr);
2768   ierr    = MatSetBlockSizesFromMats(mat,matin,matin);CHKERRQ(ierr);
2769   ierr    = MatSetType(mat,((PetscObject)matin)->type_name);CHKERRQ(ierr);
2770   ierr    = PetscMemcpy(mat->ops,matin->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
2771   a       = (Mat_MPIAIJ*)mat->data;
2772 
2773   mat->factortype   = matin->factortype;
2774   mat->assembled    = PETSC_TRUE;
2775   mat->insertmode   = NOT_SET_VALUES;
2776   mat->preallocated = PETSC_TRUE;
2777 
2778   a->size         = oldmat->size;
2779   a->rank         = oldmat->rank;
2780   a->donotstash   = oldmat->donotstash;
2781   a->roworiented  = oldmat->roworiented;
2782   a->rowindices   = 0;
2783   a->rowvalues    = 0;
2784   a->getrowactive = PETSC_FALSE;
2785 
2786   ierr = PetscLayoutReference(matin->rmap,&mat->rmap);CHKERRQ(ierr);
2787   ierr = PetscLayoutReference(matin->cmap,&mat->cmap);CHKERRQ(ierr);
2788 
2789   if (oldmat->colmap) {
2790 #if defined(PETSC_USE_CTABLE)
2791     ierr = PetscTableCreateCopy(oldmat->colmap,&a->colmap);CHKERRQ(ierr);
2792 #else
2793     ierr = PetscMalloc1(mat->cmap->N,&a->colmap);CHKERRQ(ierr);
2794     ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2795     ierr = PetscMemcpy(a->colmap,oldmat->colmap,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2796 #endif
2797   } else a->colmap = 0;
2798   if (oldmat->garray) {
2799     PetscInt len;
2800     len  = oldmat->B->cmap->n;
2801     ierr = PetscMalloc1(len+1,&a->garray);CHKERRQ(ierr);
2802     ierr = PetscLogObjectMemory((PetscObject)mat,len*sizeof(PetscInt));CHKERRQ(ierr);
2803     if (len) { ierr = PetscMemcpy(a->garray,oldmat->garray,len*sizeof(PetscInt));CHKERRQ(ierr); }
2804   } else a->garray = 0;
2805 
2806   ierr    = VecDuplicate(oldmat->lvec,&a->lvec);CHKERRQ(ierr);
2807   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->lvec);CHKERRQ(ierr);
2808   ierr    = VecScatterCopy(oldmat->Mvctx,&a->Mvctx);CHKERRQ(ierr);
2809   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->Mvctx);CHKERRQ(ierr);
2810   ierr    = MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
2811   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->A);CHKERRQ(ierr);
2812   ierr    = MatDuplicate(oldmat->B,cpvalues,&a->B);CHKERRQ(ierr);
2813   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->B);CHKERRQ(ierr);
2814   ierr    = PetscFunctionListDuplicate(((PetscObject)matin)->qlist,&((PetscObject)mat)->qlist);CHKERRQ(ierr);
2815   *newmat = mat;
2816   PetscFunctionReturn(0);
2817 }
2818 
2819 
2820 
2821 #undef __FUNCT__
2822 #define __FUNCT__ "MatLoad_MPIAIJ"
2823 PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
2824 {
2825   PetscScalar    *vals,*svals;
2826   MPI_Comm       comm;
2827   PetscErrorCode ierr;
2828   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
2829   PetscInt       i,nz,j,rstart,rend,mmax,maxnz = 0;
2830   PetscInt       header[4],*rowlengths = 0,M,N,m,*cols;
2831   PetscInt       *ourlens = NULL,*procsnz = NULL,*offlens = NULL,jj,*mycols,*smycols;
2832   PetscInt       cend,cstart,n,*rowners;
2833   int            fd;
2834   PetscInt       bs = newMat->rmap->bs;
2835 
2836   PetscFunctionBegin;
2837   /* force binary viewer to load .info file if it has not yet done so */
2838   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
2839   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
2840   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2841   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2842   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
2843   if (!rank) {
2844     ierr = PetscBinaryRead(fd,(char*)header,4,PETSC_INT);CHKERRQ(ierr);
2845     if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
2846   }
2847 
2848   ierr = PetscOptionsBegin(comm,NULL,"Options for loading MPIAIJ matrix","Mat");CHKERRQ(ierr);
2849   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
2850   ierr = PetscOptionsEnd();CHKERRQ(ierr);
2851   if (bs < 0) bs = 1;
2852 
2853   ierr = MPI_Bcast(header+1,3,MPIU_INT,0,comm);CHKERRQ(ierr);
2854   M    = header[1]; N = header[2];
2855 
2856   /* If global sizes are set, check if they are consistent with that given in the file */
2857   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);
2858   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);
2859 
2860   /* determine ownership of all (block) rows */
2861   if (M%bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Inconsistent # of rows (%d) and block size (%d)",M,bs);
2862   if (newMat->rmap->n < 0) m = bs*((M/bs)/size + (((M/bs) % size) > rank));    /* PETSC_DECIDE */
2863   else m = newMat->rmap->n; /* Set by user */
2864 
2865   ierr = PetscMalloc1(size+1,&rowners);CHKERRQ(ierr);
2866   ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
2867 
2868   /* First process needs enough room for process with most rows */
2869   if (!rank) {
2870     mmax = rowners[1];
2871     for (i=2; i<=size; i++) {
2872       mmax = PetscMax(mmax, rowners[i]);
2873     }
2874   } else mmax = -1;             /* unused, but compilers complain */
2875 
2876   rowners[0] = 0;
2877   for (i=2; i<=size; i++) {
2878     rowners[i] += rowners[i-1];
2879   }
2880   rstart = rowners[rank];
2881   rend   = rowners[rank+1];
2882 
2883   /* distribute row lengths to all processors */
2884   ierr = PetscMalloc2(m,&ourlens,m,&offlens);CHKERRQ(ierr);
2885   if (!rank) {
2886     ierr = PetscBinaryRead(fd,ourlens,m,PETSC_INT);CHKERRQ(ierr);
2887     ierr = PetscMalloc1(mmax,&rowlengths);CHKERRQ(ierr);
2888     ierr = PetscCalloc1(size,&procsnz);CHKERRQ(ierr);
2889     for (j=0; j<m; j++) {
2890       procsnz[0] += ourlens[j];
2891     }
2892     for (i=1; i<size; i++) {
2893       ierr = PetscBinaryRead(fd,rowlengths,rowners[i+1]-rowners[i],PETSC_INT);CHKERRQ(ierr);
2894       /* calculate the number of nonzeros on each processor */
2895       for (j=0; j<rowners[i+1]-rowners[i]; j++) {
2896         procsnz[i] += rowlengths[j];
2897       }
2898       ierr = MPIULong_Send(rowlengths,rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2899     }
2900     ierr = PetscFree(rowlengths);CHKERRQ(ierr);
2901   } else {
2902     ierr = MPIULong_Recv(ourlens,m,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2903   }
2904 
2905   if (!rank) {
2906     /* determine max buffer needed and allocate it */
2907     maxnz = 0;
2908     for (i=0; i<size; i++) {
2909       maxnz = PetscMax(maxnz,procsnz[i]);
2910     }
2911     ierr = PetscMalloc1(maxnz,&cols);CHKERRQ(ierr);
2912 
2913     /* read in my part of the matrix column indices  */
2914     nz   = procsnz[0];
2915     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2916     ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);
2917 
2918     /* read in every one elses and ship off */
2919     for (i=1; i<size; i++) {
2920       nz   = procsnz[i];
2921       ierr = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
2922       ierr = MPIULong_Send(cols,nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2923     }
2924     ierr = PetscFree(cols);CHKERRQ(ierr);
2925   } else {
2926     /* determine buffer space needed for message */
2927     nz = 0;
2928     for (i=0; i<m; i++) {
2929       nz += ourlens[i];
2930     }
2931     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2932 
2933     /* receive message of column indices*/
2934     ierr = MPIULong_Recv(mycols,nz,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2935   }
2936 
2937   /* determine column ownership if matrix is not square */
2938   if (N != M) {
2939     if (newMat->cmap->n < 0) n = N/size + ((N % size) > rank);
2940     else n = newMat->cmap->n;
2941     ierr   = MPI_Scan(&n,&cend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
2942     cstart = cend - n;
2943   } else {
2944     cstart = rstart;
2945     cend   = rend;
2946     n      = cend - cstart;
2947   }
2948 
2949   /* loop over local rows, determining number of off diagonal entries */
2950   ierr = PetscMemzero(offlens,m*sizeof(PetscInt));CHKERRQ(ierr);
2951   jj   = 0;
2952   for (i=0; i<m; i++) {
2953     for (j=0; j<ourlens[i]; j++) {
2954       if (mycols[jj] < cstart || mycols[jj] >= cend) offlens[i]++;
2955       jj++;
2956     }
2957   }
2958 
2959   for (i=0; i<m; i++) {
2960     ourlens[i] -= offlens[i];
2961   }
2962   ierr = MatSetSizes(newMat,m,n,M,N);CHKERRQ(ierr);
2963 
2964   if (bs > 1) {ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);}
2965 
2966   ierr = MatMPIAIJSetPreallocation(newMat,0,ourlens,0,offlens);CHKERRQ(ierr);
2967 
2968   for (i=0; i<m; i++) {
2969     ourlens[i] += offlens[i];
2970   }
2971 
2972   if (!rank) {
2973     ierr = PetscMalloc1(maxnz+1,&vals);CHKERRQ(ierr);
2974 
2975     /* read in my part of the matrix numerical values  */
2976     nz   = procsnz[0];
2977     ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
2978 
2979     /* insert into matrix */
2980     jj      = rstart;
2981     smycols = mycols;
2982     svals   = vals;
2983     for (i=0; i<m; i++) {
2984       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
2985       smycols += ourlens[i];
2986       svals   += ourlens[i];
2987       jj++;
2988     }
2989 
2990     /* read in other processors and ship out */
2991     for (i=1; i<size; i++) {
2992       nz   = procsnz[i];
2993       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
2994       ierr = MPIULong_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
2995     }
2996     ierr = PetscFree(procsnz);CHKERRQ(ierr);
2997   } else {
2998     /* receive numeric values */
2999     ierr = PetscMalloc1(nz+1,&vals);CHKERRQ(ierr);
3000 
3001     /* receive message of values*/
3002     ierr = MPIULong_Recv(vals,nz,MPIU_SCALAR,0,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
3003 
3004     /* insert into matrix */
3005     jj      = rstart;
3006     smycols = mycols;
3007     svals   = vals;
3008     for (i=0; i<m; i++) {
3009       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
3010       smycols += ourlens[i];
3011       svals   += ourlens[i];
3012       jj++;
3013     }
3014   }
3015   ierr = PetscFree2(ourlens,offlens);CHKERRQ(ierr);
3016   ierr = PetscFree(vals);CHKERRQ(ierr);
3017   ierr = PetscFree(mycols);CHKERRQ(ierr);
3018   ierr = PetscFree(rowners);CHKERRQ(ierr);
3019   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3020   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3021   PetscFunctionReturn(0);
3022 }
3023 
3024 #undef __FUNCT__
3025 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ"
3026 /* TODO: Not scalable because of ISAllGather() unless getting all columns. */
3027 PetscErrorCode MatGetSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3028 {
3029   PetscErrorCode ierr;
3030   IS             iscol_local;
3031   PetscInt       csize;
3032 
3033   PetscFunctionBegin;
3034   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3035   if (call == MAT_REUSE_MATRIX) {
3036     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3037     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3038   } else {
3039     /* check if we are grabbing all columns*/
3040     PetscBool    isstride;
3041     PetscMPIInt  lisstride = 0,gisstride;
3042     ierr = PetscObjectTypeCompare((PetscObject)iscol,ISSTRIDE,&isstride);CHKERRQ(ierr);
3043     if (isstride) {
3044       PetscInt  start,len,mstart,mlen;
3045       ierr = ISStrideGetInfo(iscol,&start,NULL);CHKERRQ(ierr);
3046       ierr = ISGetLocalSize(iscol,&len);CHKERRQ(ierr);
3047       ierr = MatGetOwnershipRangeColumn(mat,&mstart,&mlen);CHKERRQ(ierr);
3048       if (mstart == start && mlen-mstart == len) lisstride = 1;
3049     }
3050     ierr = MPI_Allreduce(&lisstride,&gisstride,1,MPI_INT,MPI_MIN,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
3051     if (gisstride) {
3052       PetscInt N;
3053       ierr = MatGetSize(mat,NULL,&N);CHKERRQ(ierr);
3054       ierr = ISCreateStride(PetscObjectComm((PetscObject)mat),N,0,1,&iscol_local);CHKERRQ(ierr);
3055       ierr = ISSetIdentity(iscol_local);CHKERRQ(ierr);
3056       ierr = PetscInfo(mat,"Optimizing for obtaining all columns of the matrix; skipping ISAllGather()\n");CHKERRQ(ierr);
3057     } else {
3058       PetscInt cbs;
3059       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
3060       ierr = ISAllGather(iscol,&iscol_local);CHKERRQ(ierr);
3061       ierr = ISSetBlockSize(iscol_local,cbs);CHKERRQ(ierr);
3062     }
3063   }
3064   ierr = MatGetSubMatrix_MPIAIJ_Private(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
3065   if (call == MAT_INITIAL_MATRIX) {
3066     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3067     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3068   }
3069   PetscFunctionReturn(0);
3070 }
3071 
3072 extern PetscErrorCode MatGetSubMatrices_MPIAIJ_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool*,Mat*);
3073 #undef __FUNCT__
3074 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ_Private"
3075 /*
3076     Not great since it makes two copies of the submatrix, first an SeqAIJ
3077   in local and then by concatenating the local matrices the end result.
3078   Writing it directly would be much like MatGetSubMatrices_MPIAIJ()
3079 
3080   Note: This requires a sequential iscol with all indices.
3081 */
3082 PetscErrorCode MatGetSubMatrix_MPIAIJ_Private(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3083 {
3084   PetscErrorCode ierr;
3085   PetscMPIInt    rank,size;
3086   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3087   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal,ncol;
3088   PetscBool      allcolumns, colflag;
3089   Mat            M,Mreuse;
3090   MatScalar      *vwork,*aa;
3091   MPI_Comm       comm;
3092   Mat_SeqAIJ     *aij;
3093 
3094   PetscFunctionBegin;
3095   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3096   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3097   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3098 
3099   ierr = ISIdentity(iscol,&colflag);CHKERRQ(ierr);
3100   ierr = ISGetLocalSize(iscol,&ncol);CHKERRQ(ierr);
3101   if (colflag && ncol == mat->cmap->N) {
3102     allcolumns = PETSC_TRUE;
3103     ierr = PetscInfo(mat,"Optimizing for obtaining all columns of the matrix\n");CHKERRQ(ierr);
3104   } else {
3105     allcolumns = PETSC_FALSE;
3106   }
3107   if (call ==  MAT_REUSE_MATRIX) {
3108     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3109     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3110     ierr = MatGetSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,&allcolumns,&Mreuse);CHKERRQ(ierr);
3111   } else {
3112     ierr = MatGetSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&allcolumns,&Mreuse);CHKERRQ(ierr);
3113   }
3114 
3115   /*
3116       m - number of local rows
3117       n - number of columns (same on all processors)
3118       rstart - first row in new global matrix generated
3119   */
3120   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3121   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3122   if (call == MAT_INITIAL_MATRIX) {
3123     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3124     ii  = aij->i;
3125     jj  = aij->j;
3126 
3127     /*
3128         Determine the number of non-zeros in the diagonal and off-diagonal
3129         portions of the matrix in order to do correct preallocation
3130     */
3131 
3132     /* first get start and end of "diagonal" columns */
3133     if (csize == PETSC_DECIDE) {
3134       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3135       if (mglobal == n) { /* square matrix */
3136         nlocal = m;
3137       } else {
3138         nlocal = n/size + ((n % size) > rank);
3139       }
3140     } else {
3141       nlocal = csize;
3142     }
3143     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3144     rstart = rend - nlocal;
3145     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);
3146 
3147     /* next, compute all the lengths */
3148     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3149     olens = dlens + m;
3150     for (i=0; i<m; i++) {
3151       jend = ii[i+1] - ii[i];
3152       olen = 0;
3153       dlen = 0;
3154       for (j=0; j<jend; j++) {
3155         if (*jj < rstart || *jj >= rend) olen++;
3156         else dlen++;
3157         jj++;
3158       }
3159       olens[i] = olen;
3160       dlens[i] = dlen;
3161     }
3162     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3163     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3164     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3165     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3166     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3167     ierr = PetscFree(dlens);CHKERRQ(ierr);
3168   } else {
3169     PetscInt ml,nl;
3170 
3171     M    = *newmat;
3172     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3173     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3174     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3175     /*
3176          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3177        rather than the slower MatSetValues().
3178     */
3179     M->was_assembled = PETSC_TRUE;
3180     M->assembled     = PETSC_FALSE;
3181   }
3182   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3183   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3184   ii   = aij->i;
3185   jj   = aij->j;
3186   aa   = aij->a;
3187   for (i=0; i<m; i++) {
3188     row   = rstart + i;
3189     nz    = ii[i+1] - ii[i];
3190     cwork = jj;     jj += nz;
3191     vwork = aa;     aa += nz;
3192     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3193   }
3194 
3195   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3196   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3197   *newmat = M;
3198 
3199   /* save submatrix used in processor for next request */
3200   if (call ==  MAT_INITIAL_MATRIX) {
3201     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3202     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3203   }
3204   PetscFunctionReturn(0);
3205 }
3206 
3207 #undef __FUNCT__
3208 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR_MPIAIJ"
3209 PetscErrorCode  MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3210 {
3211   PetscInt       m,cstart, cend,j,nnz,i,d;
3212   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3213   const PetscInt *JJ;
3214   PetscScalar    *values;
3215   PetscErrorCode ierr;
3216 
3217   PetscFunctionBegin;
3218   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3219 
3220   ierr   = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3221   ierr   = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3222   m      = B->rmap->n;
3223   cstart = B->cmap->rstart;
3224   cend   = B->cmap->rend;
3225   rstart = B->rmap->rstart;
3226 
3227   ierr = PetscMalloc2(m,&d_nnz,m,&o_nnz);CHKERRQ(ierr);
3228 
3229 #if defined(PETSC_USE_DEBUGGING)
3230   for (i=0; i<m; i++) {
3231     nnz = Ii[i+1]- Ii[i];
3232     JJ  = J + Ii[i];
3233     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3234     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3235     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);
3236   }
3237 #endif
3238 
3239   for (i=0; i<m; i++) {
3240     nnz     = Ii[i+1]- Ii[i];
3241     JJ      = J + Ii[i];
3242     nnz_max = PetscMax(nnz_max,nnz);
3243     d       = 0;
3244     for (j=0; j<nnz; j++) {
3245       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3246     }
3247     d_nnz[i] = d;
3248     o_nnz[i] = nnz - d;
3249   }
3250   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3251   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3252 
3253   if (v) values = (PetscScalar*)v;
3254   else {
3255     ierr = PetscCalloc1(nnz_max+1,&values);CHKERRQ(ierr);
3256   }
3257 
3258   for (i=0; i<m; i++) {
3259     ii   = i + rstart;
3260     nnz  = Ii[i+1]- Ii[i];
3261     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3262   }
3263   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3264   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3265 
3266   if (!v) {
3267     ierr = PetscFree(values);CHKERRQ(ierr);
3268   }
3269   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3270   PetscFunctionReturn(0);
3271 }
3272 
3273 #undef __FUNCT__
3274 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR"
3275 /*@
3276    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3277    (the default parallel PETSc format).
3278 
3279    Collective on MPI_Comm
3280 
3281    Input Parameters:
3282 +  B - the matrix
3283 .  i - the indices into j for the start of each local row (starts with zero)
3284 .  j - the column indices for each local row (starts with zero)
3285 -  v - optional values in the matrix
3286 
3287    Level: developer
3288 
3289    Notes:
3290        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3291      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3292      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3293 
3294        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3295 
3296        The format which is used for the sparse matrix input, is equivalent to a
3297     row-major ordering.. i.e for the following matrix, the input data expected is
3298     as shown
3299 
3300 $        1 0 0
3301 $        2 0 3     P0
3302 $       -------
3303 $        4 5 6     P1
3304 $
3305 $     Process0 [P0]: rows_owned=[0,1]
3306 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3307 $        j =  {0,0,2}  [size = 3]
3308 $        v =  {1,2,3}  [size = 3]
3309 $
3310 $     Process1 [P1]: rows_owned=[2]
3311 $        i =  {0,3}    [size = nrow+1  = 1+1]
3312 $        j =  {0,1,2}  [size = 3]
3313 $        v =  {4,5,6}  [size = 3]
3314 
3315 .keywords: matrix, aij, compressed row, sparse, parallel
3316 
3317 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MPIAIJ,
3318           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3319 @*/
3320 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3321 {
3322   PetscErrorCode ierr;
3323 
3324   PetscFunctionBegin;
3325   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3326   PetscFunctionReturn(0);
3327 }
3328 
3329 #undef __FUNCT__
3330 #define __FUNCT__ "MatMPIAIJSetPreallocation"
3331 /*@C
3332    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3333    (the default parallel PETSc format).  For good matrix assembly performance
3334    the user should preallocate the matrix storage by setting the parameters
3335    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3336    performance can be increased by more than a factor of 50.
3337 
3338    Collective on MPI_Comm
3339 
3340    Input Parameters:
3341 +  B - the matrix
3342 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3343            (same value is used for all local rows)
3344 .  d_nnz - array containing the number of nonzeros in the various rows of the
3345            DIAGONAL portion of the local submatrix (possibly different for each row)
3346            or NULL (PETSC_NULL_INTEGER in Fortran), if d_nz is used to specify the nonzero structure.
3347            The size of this array is equal to the number of local rows, i.e 'm'.
3348            For matrices that will be factored, you must leave room for (and set)
3349            the diagonal entry even if it is zero.
3350 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3351            submatrix (same value is used for all local rows).
3352 -  o_nnz - array containing the number of nonzeros in the various rows of the
3353            OFF-DIAGONAL portion of the local submatrix (possibly different for
3354            each row) or NULL (PETSC_NULL_INTEGER in Fortran), if o_nz is used to specify the nonzero
3355            structure. The size of this array is equal to the number
3356            of local rows, i.e 'm'.
3357 
3358    If the *_nnz parameter is given then the *_nz parameter is ignored
3359 
3360    The AIJ format (also called the Yale sparse matrix format or
3361    compressed row storage (CSR)), is fully compatible with standard Fortran 77
3362    storage.  The stored row and column indices begin with zero.
3363    See Users-Manual: ch_mat for details.
3364 
3365    The parallel matrix is partitioned such that the first m0 rows belong to
3366    process 0, the next m1 rows belong to process 1, the next m2 rows belong
3367    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
3368 
3369    The DIAGONAL portion of the local submatrix of a processor can be defined
3370    as the submatrix which is obtained by extraction the part corresponding to
3371    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
3372    first row that belongs to the processor, r2 is the last row belonging to
3373    the this processor, and c1-c2 is range of indices of the local part of a
3374    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
3375    common case of a square matrix, the row and column ranges are the same and
3376    the DIAGONAL part is also square. The remaining portion of the local
3377    submatrix (mxN) constitute the OFF-DIAGONAL portion.
3378 
3379    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3380 
3381    You can call MatGetInfo() to get information on how effective the preallocation was;
3382    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3383    You can also run with the option -info and look for messages with the string
3384    malloc in them to see if additional memory allocation was needed.
3385 
3386    Example usage:
3387 
3388    Consider the following 8x8 matrix with 34 non-zero values, that is
3389    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3390    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3391    as follows:
3392 
3393 .vb
3394             1  2  0  |  0  3  0  |  0  4
3395     Proc0   0  5  6  |  7  0  0  |  8  0
3396             9  0 10  | 11  0  0  | 12  0
3397     -------------------------------------
3398            13  0 14  | 15 16 17  |  0  0
3399     Proc1   0 18  0  | 19 20 21  |  0  0
3400             0  0  0  | 22 23  0  | 24  0
3401     -------------------------------------
3402     Proc2  25 26 27  |  0  0 28  | 29  0
3403            30  0  0  | 31 32 33  |  0 34
3404 .ve
3405 
3406    This can be represented as a collection of submatrices as:
3407 
3408 .vb
3409       A B C
3410       D E F
3411       G H I
3412 .ve
3413 
3414    Where the submatrices A,B,C are owned by proc0, D,E,F are
3415    owned by proc1, G,H,I are owned by proc2.
3416 
3417    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3418    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3419    The 'M','N' parameters are 8,8, and have the same values on all procs.
3420 
3421    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3422    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3423    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3424    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3425    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3426    matrix, ans [DF] as another SeqAIJ matrix.
3427 
3428    When d_nz, o_nz parameters are specified, d_nz storage elements are
3429    allocated for every row of the local diagonal submatrix, and o_nz
3430    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3431    One way to choose d_nz and o_nz is to use the max nonzerors per local
3432    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3433    In this case, the values of d_nz,o_nz are:
3434 .vb
3435      proc0 : dnz = 2, o_nz = 2
3436      proc1 : dnz = 3, o_nz = 2
3437      proc2 : dnz = 1, o_nz = 4
3438 .ve
3439    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3440    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3441    for proc3. i.e we are using 12+15+10=37 storage locations to store
3442    34 values.
3443 
3444    When d_nnz, o_nnz parameters are specified, the storage is specified
3445    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3446    In the above case the values for d_nnz,o_nnz are:
3447 .vb
3448      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3449      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3450      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3451 .ve
3452    Here the space allocated is sum of all the above values i.e 34, and
3453    hence pre-allocation is perfect.
3454 
3455    Level: intermediate
3456 
3457 .keywords: matrix, aij, compressed row, sparse, parallel
3458 
3459 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
3460           MPIAIJ, MatGetInfo(), PetscSplitOwnership()
3461 @*/
3462 PetscErrorCode  MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3463 {
3464   PetscErrorCode ierr;
3465 
3466   PetscFunctionBegin;
3467   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3468   PetscValidType(B,1);
3469   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
3470   PetscFunctionReturn(0);
3471 }
3472 
3473 #undef __FUNCT__
3474 #define __FUNCT__ "MatCreateMPIAIJWithArrays"
3475 /*@
3476      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
3477          CSR format the local rows.
3478 
3479    Collective on MPI_Comm
3480 
3481    Input Parameters:
3482 +  comm - MPI communicator
3483 .  m - number of local rows (Cannot be PETSC_DECIDE)
3484 .  n - This value should be the same as the local size used in creating the
3485        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3486        calculated if N is given) For square matrices n is almost always m.
3487 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3488 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3489 .   i - row indices
3490 .   j - column indices
3491 -   a - matrix values
3492 
3493    Output Parameter:
3494 .   mat - the matrix
3495 
3496    Level: intermediate
3497 
3498    Notes:
3499        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3500      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3501      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3502 
3503        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3504 
3505        The format which is used for the sparse matrix input, is equivalent to a
3506     row-major ordering.. i.e for the following matrix, the input data expected is
3507     as shown
3508 
3509 $        1 0 0
3510 $        2 0 3     P0
3511 $       -------
3512 $        4 5 6     P1
3513 $
3514 $     Process0 [P0]: rows_owned=[0,1]
3515 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3516 $        j =  {0,0,2}  [size = 3]
3517 $        v =  {1,2,3}  [size = 3]
3518 $
3519 $     Process1 [P1]: rows_owned=[2]
3520 $        i =  {0,3}    [size = nrow+1  = 1+1]
3521 $        j =  {0,1,2}  [size = 3]
3522 $        v =  {4,5,6}  [size = 3]
3523 
3524 .keywords: matrix, aij, compressed row, sparse, parallel
3525 
3526 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3527           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
3528 @*/
3529 PetscErrorCode  MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
3530 {
3531   PetscErrorCode ierr;
3532 
3533   PetscFunctionBegin;
3534   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
3535   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
3536   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
3537   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
3538   /* ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr); */
3539   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
3540   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
3541   PetscFunctionReturn(0);
3542 }
3543 
3544 #undef __FUNCT__
3545 #define __FUNCT__ "MatCreateAIJ"
3546 /*@C
3547    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
3548    (the default parallel PETSc format).  For good matrix assembly performance
3549    the user should preallocate the matrix storage by setting the parameters
3550    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3551    performance can be increased by more than a factor of 50.
3552 
3553    Collective on MPI_Comm
3554 
3555    Input Parameters:
3556 +  comm - MPI communicator
3557 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
3558            This value should be the same as the local size used in creating the
3559            y vector for the matrix-vector product y = Ax.
3560 .  n - This value should be the same as the local size used in creating the
3561        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3562        calculated if N is given) For square matrices n is almost always m.
3563 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3564 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3565 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3566            (same value is used for all local rows)
3567 .  d_nnz - array containing the number of nonzeros in the various rows of the
3568            DIAGONAL portion of the local submatrix (possibly different for each row)
3569            or NULL, if d_nz is used to specify the nonzero structure.
3570            The size of this array is equal to the number of local rows, i.e 'm'.
3571 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3572            submatrix (same value is used for all local rows).
3573 -  o_nnz - array containing the number of nonzeros in the various rows of the
3574            OFF-DIAGONAL portion of the local submatrix (possibly different for
3575            each row) or NULL, if o_nz is used to specify the nonzero
3576            structure. The size of this array is equal to the number
3577            of local rows, i.e 'm'.
3578 
3579    Output Parameter:
3580 .  A - the matrix
3581 
3582    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3583    MatXXXXSetPreallocation() paradgm instead of this routine directly.
3584    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3585 
3586    Notes:
3587    If the *_nnz parameter is given then the *_nz parameter is ignored
3588 
3589    m,n,M,N parameters specify the size of the matrix, and its partitioning across
3590    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
3591    storage requirements for this matrix.
3592 
3593    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
3594    processor than it must be used on all processors that share the object for
3595    that argument.
3596 
3597    The user MUST specify either the local or global matrix dimensions
3598    (possibly both).
3599 
3600    The parallel matrix is partitioned across processors such that the
3601    first m0 rows belong to process 0, the next m1 rows belong to
3602    process 1, the next m2 rows belong to process 2 etc.. where
3603    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
3604    values corresponding to [m x N] submatrix.
3605 
3606    The columns are logically partitioned with the n0 columns belonging
3607    to 0th partition, the next n1 columns belonging to the next
3608    partition etc.. where n0,n1,n2... are the input parameter 'n'.
3609 
3610    The DIAGONAL portion of the local submatrix on any given processor
3611    is the submatrix corresponding to the rows and columns m,n
3612    corresponding to the given processor. i.e diagonal matrix on
3613    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
3614    etc. The remaining portion of the local submatrix [m x (N-n)]
3615    constitute the OFF-DIAGONAL portion. The example below better
3616    illustrates this concept.
3617 
3618    For a square global matrix we define each processor's diagonal portion
3619    to be its local rows and the corresponding columns (a square submatrix);
3620    each processor's off-diagonal portion encompasses the remainder of the
3621    local matrix (a rectangular submatrix).
3622 
3623    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3624 
3625    When calling this routine with a single process communicator, a matrix of
3626    type SEQAIJ is returned.  If a matrix of type MPIAIJ is desired for this
3627    type of communicator, use the construction mechanism:
3628      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
3629 
3630    By default, this format uses inodes (identical nodes) when possible.
3631    We search for consecutive rows with the same nonzero structure, thereby
3632    reusing matrix information to achieve increased efficiency.
3633 
3634    Options Database Keys:
3635 +  -mat_no_inode  - Do not use inodes
3636 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3637 -  -mat_aij_oneindex - Internally use indexing starting at 1
3638         rather than 0.  Note that when calling MatSetValues(),
3639         the user still MUST index entries starting at 0!
3640 
3641 
3642    Example usage:
3643 
3644    Consider the following 8x8 matrix with 34 non-zero values, that is
3645    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3646    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3647    as follows:
3648 
3649 .vb
3650             1  2  0  |  0  3  0  |  0  4
3651     Proc0   0  5  6  |  7  0  0  |  8  0
3652             9  0 10  | 11  0  0  | 12  0
3653     -------------------------------------
3654            13  0 14  | 15 16 17  |  0  0
3655     Proc1   0 18  0  | 19 20 21  |  0  0
3656             0  0  0  | 22 23  0  | 24  0
3657     -------------------------------------
3658     Proc2  25 26 27  |  0  0 28  | 29  0
3659            30  0  0  | 31 32 33  |  0 34
3660 .ve
3661 
3662    This can be represented as a collection of submatrices as:
3663 
3664 .vb
3665       A B C
3666       D E F
3667       G H I
3668 .ve
3669 
3670    Where the submatrices A,B,C are owned by proc0, D,E,F are
3671    owned by proc1, G,H,I are owned by proc2.
3672 
3673    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3674    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3675    The 'M','N' parameters are 8,8, and have the same values on all procs.
3676 
3677    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3678    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3679    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3680    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3681    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3682    matrix, ans [DF] as another SeqAIJ matrix.
3683 
3684    When d_nz, o_nz parameters are specified, d_nz storage elements are
3685    allocated for every row of the local diagonal submatrix, and o_nz
3686    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3687    One way to choose d_nz and o_nz is to use the max nonzerors per local
3688    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3689    In this case, the values of d_nz,o_nz are:
3690 .vb
3691      proc0 : dnz = 2, o_nz = 2
3692      proc1 : dnz = 3, o_nz = 2
3693      proc2 : dnz = 1, o_nz = 4
3694 .ve
3695    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3696    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3697    for proc3. i.e we are using 12+15+10=37 storage locations to store
3698    34 values.
3699 
3700    When d_nnz, o_nnz parameters are specified, the storage is specified
3701    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3702    In the above case the values for d_nnz,o_nnz are:
3703 .vb
3704      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3705      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3706      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3707 .ve
3708    Here the space allocated is sum of all the above values i.e 34, and
3709    hence pre-allocation is perfect.
3710 
3711    Level: intermediate
3712 
3713 .keywords: matrix, aij, compressed row, sparse, parallel
3714 
3715 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3716           MPIAIJ, MatCreateMPIAIJWithArrays()
3717 @*/
3718 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)
3719 {
3720   PetscErrorCode ierr;
3721   PetscMPIInt    size;
3722 
3723   PetscFunctionBegin;
3724   ierr = MatCreate(comm,A);CHKERRQ(ierr);
3725   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
3726   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3727   if (size > 1) {
3728     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
3729     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
3730   } else {
3731     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
3732     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
3733   }
3734   PetscFunctionReturn(0);
3735 }
3736 
3737 #undef __FUNCT__
3738 #define __FUNCT__ "MatMPIAIJGetSeqAIJ"
3739 PetscErrorCode  MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
3740 {
3741   Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
3742 
3743   PetscFunctionBegin;
3744   if (Ad)     *Ad     = a->A;
3745   if (Ao)     *Ao     = a->B;
3746   if (colmap) *colmap = a->garray;
3747   PetscFunctionReturn(0);
3748 }
3749 
3750 #undef __FUNCT__
3751 #define __FUNCT__ "MatSetColoring_MPIAIJ"
3752 PetscErrorCode MatSetColoring_MPIAIJ(Mat A,ISColoring coloring)
3753 {
3754   PetscErrorCode ierr;
3755   PetscInt       i;
3756   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3757 
3758   PetscFunctionBegin;
3759   if (coloring->ctype == IS_COLORING_GLOBAL) {
3760     ISColoringValue *allcolors,*colors;
3761     ISColoring      ocoloring;
3762 
3763     /* set coloring for diagonal portion */
3764     ierr = MatSetColoring_SeqAIJ(a->A,coloring);CHKERRQ(ierr);
3765 
3766     /* set coloring for off-diagonal portion */
3767     ierr = ISAllGatherColors(PetscObjectComm((PetscObject)A),coloring->n,coloring->colors,NULL,&allcolors);CHKERRQ(ierr);
3768     ierr = PetscMalloc1(a->B->cmap->n+1,&colors);CHKERRQ(ierr);
3769     for (i=0; i<a->B->cmap->n; i++) {
3770       colors[i] = allcolors[a->garray[i]];
3771     }
3772     ierr = PetscFree(allcolors);CHKERRQ(ierr);
3773     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3774     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
3775     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3776   } else if (coloring->ctype == IS_COLORING_GHOSTED) {
3777     ISColoringValue *colors;
3778     PetscInt        *larray;
3779     ISColoring      ocoloring;
3780 
3781     /* set coloring for diagonal portion */
3782     ierr = PetscMalloc1(a->A->cmap->n+1,&larray);CHKERRQ(ierr);
3783     for (i=0; i<a->A->cmap->n; i++) {
3784       larray[i] = i + A->cmap->rstart;
3785     }
3786     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->A->cmap->n,larray,NULL,larray);CHKERRQ(ierr);
3787     ierr = PetscMalloc1(a->A->cmap->n+1,&colors);CHKERRQ(ierr);
3788     for (i=0; i<a->A->cmap->n; i++) {
3789       colors[i] = coloring->colors[larray[i]];
3790     }
3791     ierr = PetscFree(larray);CHKERRQ(ierr);
3792     ierr = ISColoringCreate(PETSC_COMM_SELF,coloring->n,a->A->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3793     ierr = MatSetColoring_SeqAIJ(a->A,ocoloring);CHKERRQ(ierr);
3794     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3795 
3796     /* set coloring for off-diagonal portion */
3797     ierr = PetscMalloc1(a->B->cmap->n+1,&larray);CHKERRQ(ierr);
3798     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->B->cmap->n,a->garray,NULL,larray);CHKERRQ(ierr);
3799     ierr = PetscMalloc1(a->B->cmap->n+1,&colors);CHKERRQ(ierr);
3800     for (i=0; i<a->B->cmap->n; i++) {
3801       colors[i] = coloring->colors[larray[i]];
3802     }
3803     ierr = PetscFree(larray);CHKERRQ(ierr);
3804     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3805     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
3806     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3807   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support ISColoringType %d",(int)coloring->ctype);
3808   PetscFunctionReturn(0);
3809 }
3810 
3811 #undef __FUNCT__
3812 #define __FUNCT__ "MatSetValuesAdifor_MPIAIJ"
3813 PetscErrorCode MatSetValuesAdifor_MPIAIJ(Mat A,PetscInt nl,void *advalues)
3814 {
3815   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3816   PetscErrorCode ierr;
3817 
3818   PetscFunctionBegin;
3819   ierr = MatSetValuesAdifor_SeqAIJ(a->A,nl,advalues);CHKERRQ(ierr);
3820   ierr = MatSetValuesAdifor_SeqAIJ(a->B,nl,advalues);CHKERRQ(ierr);
3821   PetscFunctionReturn(0);
3822 }
3823 
3824 #undef __FUNCT__
3825 #define __FUNCT__ "MatCreateMPIMatConcatenateSeqMat_MPIAIJ"
3826 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
3827 {
3828   PetscErrorCode ierr;
3829   PetscInt       m,N,i,rstart,nnz,Ii;
3830   PetscInt       *indx;
3831   PetscScalar    *values;
3832 
3833   PetscFunctionBegin;
3834   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
3835   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
3836     PetscInt       *dnz,*onz,sum,bs,cbs;
3837 
3838     if (n == PETSC_DECIDE) {
3839       ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
3840     }
3841     /* Check sum(n) = N */
3842     ierr = MPI_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3843     if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
3844 
3845     ierr    = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3846     rstart -= m;
3847 
3848     ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
3849     for (i=0; i<m; i++) {
3850       ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3851       ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
3852       ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3853     }
3854 
3855     ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
3856     ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
3857     ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
3858     ierr = MatSetBlockSizes(*outmat,bs,cbs);CHKERRQ(ierr);
3859     ierr = MatSetType(*outmat,MATMPIAIJ);CHKERRQ(ierr);
3860     ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
3861     ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
3862   }
3863 
3864   /* numeric phase */
3865   ierr = MatGetOwnershipRange(*outmat,&rstart,NULL);CHKERRQ(ierr);
3866   for (i=0; i<m; i++) {
3867     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3868     Ii   = i + rstart;
3869     ierr = MatSetValues(*outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3870     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3871   }
3872   ierr = MatAssemblyBegin(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3873   ierr = MatAssemblyEnd(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3874   PetscFunctionReturn(0);
3875 }
3876 
3877 #undef __FUNCT__
3878 #define __FUNCT__ "MatFileSplit"
3879 PetscErrorCode MatFileSplit(Mat A,char *outfile)
3880 {
3881   PetscErrorCode    ierr;
3882   PetscMPIInt       rank;
3883   PetscInt          m,N,i,rstart,nnz;
3884   size_t            len;
3885   const PetscInt    *indx;
3886   PetscViewer       out;
3887   char              *name;
3888   Mat               B;
3889   const PetscScalar *values;
3890 
3891   PetscFunctionBegin;
3892   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
3893   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
3894   /* Should this be the type of the diagonal block of A? */
3895   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
3896   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
3897   ierr = MatSetBlockSizesFromMats(B,A,A);CHKERRQ(ierr);
3898   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
3899   ierr = MatSeqAIJSetPreallocation(B,0,NULL);CHKERRQ(ierr);
3900   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
3901   for (i=0; i<m; i++) {
3902     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3903     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3904     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3905   }
3906   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3907   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3908 
3909   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
3910   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
3911   ierr = PetscMalloc1(len+5,&name);CHKERRQ(ierr);
3912   sprintf(name,"%s.%d",outfile,rank);
3913   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
3914   ierr = PetscFree(name);CHKERRQ(ierr);
3915   ierr = MatView(B,out);CHKERRQ(ierr);
3916   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
3917   ierr = MatDestroy(&B);CHKERRQ(ierr);
3918   PetscFunctionReturn(0);
3919 }
3920 
3921 extern PetscErrorCode MatDestroy_MPIAIJ(Mat);
3922 #undef __FUNCT__
3923 #define __FUNCT__ "MatDestroy_MPIAIJ_SeqsToMPI"
3924 PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
3925 {
3926   PetscErrorCode      ierr;
3927   Mat_Merge_SeqsToMPI *merge;
3928   PetscContainer      container;
3929 
3930   PetscFunctionBegin;
3931   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
3932   if (container) {
3933     ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
3934     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
3935     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
3936     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
3937     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
3938     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
3939     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
3940     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
3941     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
3942     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
3943     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
3944     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
3945     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
3946     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
3947     ierr = PetscFree(merge);CHKERRQ(ierr);
3948     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
3949   }
3950   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
3951   PetscFunctionReturn(0);
3952 }
3953 
3954 #include <../src/mat/utils/freespace.h>
3955 #include <petscbt.h>
3956 
3957 #undef __FUNCT__
3958 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJNumeric"
3959 PetscErrorCode  MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
3960 {
3961   PetscErrorCode      ierr;
3962   MPI_Comm            comm;
3963   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
3964   PetscMPIInt         size,rank,taga,*len_s;
3965   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
3966   PetscInt            proc,m;
3967   PetscInt            **buf_ri,**buf_rj;
3968   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
3969   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
3970   MPI_Request         *s_waits,*r_waits;
3971   MPI_Status          *status;
3972   MatScalar           *aa=a->a;
3973   MatScalar           **abuf_r,*ba_i;
3974   Mat_Merge_SeqsToMPI *merge;
3975   PetscContainer      container;
3976 
3977   PetscFunctionBegin;
3978   ierr = PetscObjectGetComm((PetscObject)mpimat,&comm);CHKERRQ(ierr);
3979   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
3980 
3981   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3982   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3983 
3984   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
3985   ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
3986 
3987   bi     = merge->bi;
3988   bj     = merge->bj;
3989   buf_ri = merge->buf_ri;
3990   buf_rj = merge->buf_rj;
3991 
3992   ierr   = PetscMalloc1(size,&status);CHKERRQ(ierr);
3993   owners = merge->rowmap->range;
3994   len_s  = merge->len_s;
3995 
3996   /* send and recv matrix values */
3997   /*-----------------------------*/
3998   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
3999   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
4000 
4001   ierr = PetscMalloc1(merge->nsend+1,&s_waits);CHKERRQ(ierr);
4002   for (proc=0,k=0; proc<size; proc++) {
4003     if (!len_s[proc]) continue;
4004     i    = owners[proc];
4005     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
4006     k++;
4007   }
4008 
4009   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
4010   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
4011   ierr = PetscFree(status);CHKERRQ(ierr);
4012 
4013   ierr = PetscFree(s_waits);CHKERRQ(ierr);
4014   ierr = PetscFree(r_waits);CHKERRQ(ierr);
4015 
4016   /* insert mat values of mpimat */
4017   /*----------------------------*/
4018   ierr = PetscMalloc1(N,&ba_i);CHKERRQ(ierr);
4019   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4020 
4021   for (k=0; k<merge->nrecv; k++) {
4022     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4023     nrows       = *(buf_ri_k[k]);
4024     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
4025     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4026   }
4027 
4028   /* set values of ba */
4029   m = merge->rowmap->n;
4030   for (i=0; i<m; i++) {
4031     arow = owners[rank] + i;
4032     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
4033     bnzi = bi[i+1] - bi[i];
4034     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
4035 
4036     /* add local non-zero vals of this proc's seqmat into ba */
4037     anzi   = ai[arow+1] - ai[arow];
4038     aj     = a->j + ai[arow];
4039     aa     = a->a + ai[arow];
4040     nextaj = 0;
4041     for (j=0; nextaj<anzi; j++) {
4042       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4043         ba_i[j] += aa[nextaj++];
4044       }
4045     }
4046 
4047     /* add received vals into ba */
4048     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4049       /* i-th row */
4050       if (i == *nextrow[k]) {
4051         anzi   = *(nextai[k]+1) - *nextai[k];
4052         aj     = buf_rj[k] + *(nextai[k]);
4053         aa     = abuf_r[k] + *(nextai[k]);
4054         nextaj = 0;
4055         for (j=0; nextaj<anzi; j++) {
4056           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4057             ba_i[j] += aa[nextaj++];
4058           }
4059         }
4060         nextrow[k]++; nextai[k]++;
4061       }
4062     }
4063     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
4064   }
4065   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4066   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4067 
4068   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
4069   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
4070   ierr = PetscFree(ba_i);CHKERRQ(ierr);
4071   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4072   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4073   PetscFunctionReturn(0);
4074 }
4075 
4076 extern PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat);
4077 
4078 #undef __FUNCT__
4079 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJSymbolic"
4080 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4081 {
4082   PetscErrorCode      ierr;
4083   Mat                 B_mpi;
4084   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
4085   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4086   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
4087   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4088   PetscInt            len,proc,*dnz,*onz,bs,cbs;
4089   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4090   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4091   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
4092   MPI_Status          *status;
4093   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
4094   PetscBT             lnkbt;
4095   Mat_Merge_SeqsToMPI *merge;
4096   PetscContainer      container;
4097 
4098   PetscFunctionBegin;
4099   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4100 
4101   /* make sure it is a PETSc comm */
4102   ierr = PetscCommDuplicate(comm,&comm,NULL);CHKERRQ(ierr);
4103   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4104   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4105 
4106   ierr = PetscNew(&merge);CHKERRQ(ierr);
4107   ierr = PetscMalloc1(size,&status);CHKERRQ(ierr);
4108 
4109   /* determine row ownership */
4110   /*---------------------------------------------------------*/
4111   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
4112   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
4113   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
4114   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
4115   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
4116   ierr = PetscMalloc1(size,&len_si);CHKERRQ(ierr);
4117   ierr = PetscMalloc1(size,&merge->len_s);CHKERRQ(ierr);
4118 
4119   m      = merge->rowmap->n;
4120   owners = merge->rowmap->range;
4121 
4122   /* determine the number of messages to send, their lengths */
4123   /*---------------------------------------------------------*/
4124   len_s = merge->len_s;
4125 
4126   len          = 0; /* length of buf_si[] */
4127   merge->nsend = 0;
4128   for (proc=0; proc<size; proc++) {
4129     len_si[proc] = 0;
4130     if (proc == rank) {
4131       len_s[proc] = 0;
4132     } else {
4133       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4134       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4135     }
4136     if (len_s[proc]) {
4137       merge->nsend++;
4138       nrows = 0;
4139       for (i=owners[proc]; i<owners[proc+1]; i++) {
4140         if (ai[i+1] > ai[i]) nrows++;
4141       }
4142       len_si[proc] = 2*(nrows+1);
4143       len         += len_si[proc];
4144     }
4145   }
4146 
4147   /* determine the number and length of messages to receive for ij-structure */
4148   /*-------------------------------------------------------------------------*/
4149   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
4150   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
4151 
4152   /* post the Irecv of j-structure */
4153   /*-------------------------------*/
4154   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
4155   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
4156 
4157   /* post the Isend of j-structure */
4158   /*--------------------------------*/
4159   ierr = PetscMalloc2(merge->nsend,&si_waits,merge->nsend,&sj_waits);CHKERRQ(ierr);
4160 
4161   for (proc=0, k=0; proc<size; proc++) {
4162     if (!len_s[proc]) continue;
4163     i    = owners[proc];
4164     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
4165     k++;
4166   }
4167 
4168   /* receives and sends of j-structure are complete */
4169   /*------------------------------------------------*/
4170   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
4171   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
4172 
4173   /* send and recv i-structure */
4174   /*---------------------------*/
4175   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
4176   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
4177 
4178   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
4179   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4180   for (proc=0,k=0; proc<size; proc++) {
4181     if (!len_s[proc]) continue;
4182     /* form outgoing message for i-structure:
4183          buf_si[0]:                 nrows to be sent
4184                [1:nrows]:           row index (global)
4185                [nrows+1:2*nrows+1]: i-structure index
4186     */
4187     /*-------------------------------------------*/
4188     nrows       = len_si[proc]/2 - 1;
4189     buf_si_i    = buf_si + nrows+1;
4190     buf_si[0]   = nrows;
4191     buf_si_i[0] = 0;
4192     nrows       = 0;
4193     for (i=owners[proc]; i<owners[proc+1]; i++) {
4194       anzi = ai[i+1] - ai[i];
4195       if (anzi) {
4196         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4197         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4198         nrows++;
4199       }
4200     }
4201     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4202     k++;
4203     buf_si += len_si[proc];
4204   }
4205 
4206   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4207   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4208 
4209   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4210   for (i=0; i<merge->nrecv; i++) {
4211     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);
4212   }
4213 
4214   ierr = PetscFree(len_si);CHKERRQ(ierr);
4215   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4216   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4217   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4218   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4219   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4220   ierr = PetscFree(status);CHKERRQ(ierr);
4221 
4222   /* compute a local seq matrix in each processor */
4223   /*----------------------------------------------*/
4224   /* allocate bi array and free space for accumulating nonzero column info */
4225   ierr  = PetscMalloc1(m+1,&bi);CHKERRQ(ierr);
4226   bi[0] = 0;
4227 
4228   /* create and initialize a linked list */
4229   nlnk = N+1;
4230   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4231 
4232   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4233   len  = ai[owners[rank+1]] - ai[owners[rank]];
4234   ierr = PetscFreeSpaceGet((PetscInt)(2*len+1),&free_space);CHKERRQ(ierr);
4235 
4236   current_space = free_space;
4237 
4238   /* determine symbolic info for each local row */
4239   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4240 
4241   for (k=0; k<merge->nrecv; k++) {
4242     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4243     nrows       = *buf_ri_k[k];
4244     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4245     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4246   }
4247 
4248   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4249   len  = 0;
4250   for (i=0; i<m; i++) {
4251     bnzi = 0;
4252     /* add local non-zero cols of this proc's seqmat into lnk */
4253     arow  = owners[rank] + i;
4254     anzi  = ai[arow+1] - ai[arow];
4255     aj    = a->j + ai[arow];
4256     ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4257     bnzi += nlnk;
4258     /* add received col data into lnk */
4259     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4260       if (i == *nextrow[k]) { /* i-th row */
4261         anzi  = *(nextai[k]+1) - *nextai[k];
4262         aj    = buf_rj[k] + *nextai[k];
4263         ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4264         bnzi += nlnk;
4265         nextrow[k]++; nextai[k]++;
4266       }
4267     }
4268     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4269 
4270     /* if free space is not available, make more free space */
4271     if (current_space->local_remaining<bnzi) {
4272       ierr = PetscFreeSpaceGet(bnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
4273       nspacedouble++;
4274     }
4275     /* copy data into free space, then initialize lnk */
4276     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4277     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
4278 
4279     current_space->array           += bnzi;
4280     current_space->local_used      += bnzi;
4281     current_space->local_remaining -= bnzi;
4282 
4283     bi[i+1] = bi[i] + bnzi;
4284   }
4285 
4286   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4287 
4288   ierr = PetscMalloc1(bi[m]+1,&bj);CHKERRQ(ierr);
4289   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
4290   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4291 
4292   /* create symbolic parallel matrix B_mpi */
4293   /*---------------------------------------*/
4294   ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
4295   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
4296   if (n==PETSC_DECIDE) {
4297     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
4298   } else {
4299     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4300   }
4301   ierr = MatSetBlockSizes(B_mpi,bs,cbs);CHKERRQ(ierr);
4302   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
4303   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
4304   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4305   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
4306 
4307   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4308   B_mpi->assembled    = PETSC_FALSE;
4309   B_mpi->ops->destroy = MatDestroy_MPIAIJ_SeqsToMPI;
4310   merge->bi           = bi;
4311   merge->bj           = bj;
4312   merge->buf_ri       = buf_ri;
4313   merge->buf_rj       = buf_rj;
4314   merge->coi          = NULL;
4315   merge->coj          = NULL;
4316   merge->owners_co    = NULL;
4317 
4318   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
4319 
4320   /* attach the supporting struct to B_mpi for reuse */
4321   ierr    = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
4322   ierr    = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
4323   ierr    = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
4324   ierr    = PetscContainerDestroy(&container);CHKERRQ(ierr);
4325   *mpimat = B_mpi;
4326 
4327   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4328   PetscFunctionReturn(0);
4329 }
4330 
4331 #undef __FUNCT__
4332 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJ"
4333 /*@C
4334       MatCreateMPIAIJSumSeqAIJ - Creates a MPIAIJ matrix by adding sequential
4335                  matrices from each processor
4336 
4337     Collective on MPI_Comm
4338 
4339    Input Parameters:
4340 +    comm - the communicators the parallel matrix will live on
4341 .    seqmat - the input sequential matrices
4342 .    m - number of local rows (or PETSC_DECIDE)
4343 .    n - number of local columns (or PETSC_DECIDE)
4344 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4345 
4346    Output Parameter:
4347 .    mpimat - the parallel matrix generated
4348 
4349     Level: advanced
4350 
4351    Notes:
4352      The dimensions of the sequential matrix in each processor MUST be the same.
4353      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
4354      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
4355 @*/
4356 PetscErrorCode  MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
4357 {
4358   PetscErrorCode ierr;
4359   PetscMPIInt    size;
4360 
4361   PetscFunctionBegin;
4362   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4363   if (size == 1) {
4364     ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4365     if (scall == MAT_INITIAL_MATRIX) {
4366       ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
4367     } else {
4368       ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4369     }
4370     ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4371     PetscFunctionReturn(0);
4372   }
4373   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4374   if (scall == MAT_INITIAL_MATRIX) {
4375     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
4376   }
4377   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
4378   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4379   PetscFunctionReturn(0);
4380 }
4381 
4382 #undef __FUNCT__
4383 #define __FUNCT__ "MatMPIAIJGetLocalMat"
4384 /*@
4385      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
4386           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
4387           with MatGetSize()
4388 
4389     Not Collective
4390 
4391    Input Parameters:
4392 +    A - the matrix
4393 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4394 
4395    Output Parameter:
4396 .    A_loc - the local sequential matrix generated
4397 
4398     Level: developer
4399 
4400 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
4401 
4402 @*/
4403 PetscErrorCode  MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
4404 {
4405   PetscErrorCode ierr;
4406   Mat_MPIAIJ     *mpimat=(Mat_MPIAIJ*)A->data;
4407   Mat_SeqAIJ     *mat,*a,*b;
4408   PetscInt       *ai,*aj,*bi,*bj,*cmap=mpimat->garray;
4409   MatScalar      *aa,*ba,*cam;
4410   PetscScalar    *ca;
4411   PetscInt       am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
4412   PetscInt       *ci,*cj,col,ncols_d,ncols_o,jo;
4413   PetscBool      match;
4414   MPI_Comm       comm;
4415   PetscMPIInt    size;
4416 
4417   PetscFunctionBegin;
4418   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4419   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
4420   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4421   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4422   if (size == 1 && scall == MAT_REUSE_MATRIX) PetscFunctionReturn(0);
4423 
4424   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4425   a = (Mat_SeqAIJ*)(mpimat->A)->data;
4426   b = (Mat_SeqAIJ*)(mpimat->B)->data;
4427   ai = a->i; aj = a->j; bi = b->i; bj = b->j;
4428   aa = a->a; ba = b->a;
4429   if (scall == MAT_INITIAL_MATRIX) {
4430     if (size == 1) {
4431       ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ai,aj,aa,A_loc);CHKERRQ(ierr);
4432       PetscFunctionReturn(0);
4433     }
4434 
4435     ierr  = PetscMalloc1(1+am,&ci);CHKERRQ(ierr);
4436     ci[0] = 0;
4437     for (i=0; i<am; i++) {
4438       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
4439     }
4440     ierr = PetscMalloc1(1+ci[am],&cj);CHKERRQ(ierr);
4441     ierr = PetscMalloc1(1+ci[am],&ca);CHKERRQ(ierr);
4442     k    = 0;
4443     for (i=0; i<am; i++) {
4444       ncols_o = bi[i+1] - bi[i];
4445       ncols_d = ai[i+1] - ai[i];
4446       /* off-diagonal portion of A */
4447       for (jo=0; jo<ncols_o; jo++) {
4448         col = cmap[*bj];
4449         if (col >= cstart) break;
4450         cj[k]   = col; bj++;
4451         ca[k++] = *ba++;
4452       }
4453       /* diagonal portion of A */
4454       for (j=0; j<ncols_d; j++) {
4455         cj[k]   = cstart + *aj++;
4456         ca[k++] = *aa++;
4457       }
4458       /* off-diagonal portion of A */
4459       for (j=jo; j<ncols_o; j++) {
4460         cj[k]   = cmap[*bj++];
4461         ca[k++] = *ba++;
4462       }
4463     }
4464     /* put together the new matrix */
4465     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
4466     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4467     /* Since these are PETSc arrays, change flags to free them as necessary. */
4468     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
4469     mat->free_a  = PETSC_TRUE;
4470     mat->free_ij = PETSC_TRUE;
4471     mat->nonew   = 0;
4472   } else if (scall == MAT_REUSE_MATRIX) {
4473     mat=(Mat_SeqAIJ*)(*A_loc)->data;
4474     ci = mat->i; cj = mat->j; cam = mat->a;
4475     for (i=0; i<am; i++) {
4476       /* off-diagonal portion of A */
4477       ncols_o = bi[i+1] - bi[i];
4478       for (jo=0; jo<ncols_o; jo++) {
4479         col = cmap[*bj];
4480         if (col >= cstart) break;
4481         *cam++ = *ba++; bj++;
4482       }
4483       /* diagonal portion of A */
4484       ncols_d = ai[i+1] - ai[i];
4485       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
4486       /* off-diagonal portion of A */
4487       for (j=jo; j<ncols_o; j++) {
4488         *cam++ = *ba++; bj++;
4489       }
4490     }
4491   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
4492   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4493   PetscFunctionReturn(0);
4494 }
4495 
4496 #undef __FUNCT__
4497 #define __FUNCT__ "MatMPIAIJGetLocalMatCondensed"
4498 /*@C
4499      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MPIAIJ matrix by taking all its local rows and NON-ZERO columns
4500 
4501     Not Collective
4502 
4503    Input Parameters:
4504 +    A - the matrix
4505 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4506 -    row, col - index sets of rows and columns to extract (or NULL)
4507 
4508    Output Parameter:
4509 .    A_loc - the local sequential matrix generated
4510 
4511     Level: developer
4512 
4513 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
4514 
4515 @*/
4516 PetscErrorCode  MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
4517 {
4518   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4519   PetscErrorCode ierr;
4520   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
4521   IS             isrowa,iscola;
4522   Mat            *aloc;
4523   PetscBool      match;
4524 
4525   PetscFunctionBegin;
4526   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4527   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
4528   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4529   if (!row) {
4530     start = A->rmap->rstart; end = A->rmap->rend;
4531     ierr  = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
4532   } else {
4533     isrowa = *row;
4534   }
4535   if (!col) {
4536     start = A->cmap->rstart;
4537     cmap  = a->garray;
4538     nzA   = a->A->cmap->n;
4539     nzB   = a->B->cmap->n;
4540     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4541     ncols = 0;
4542     for (i=0; i<nzB; i++) {
4543       if (cmap[i] < start) idx[ncols++] = cmap[i];
4544       else break;
4545     }
4546     imark = i;
4547     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
4548     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
4549     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
4550   } else {
4551     iscola = *col;
4552   }
4553   if (scall != MAT_INITIAL_MATRIX) {
4554     ierr    = PetscMalloc1(1,&aloc);CHKERRQ(ierr);
4555     aloc[0] = *A_loc;
4556   }
4557   ierr   = MatGetSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
4558   *A_loc = aloc[0];
4559   ierr   = PetscFree(aloc);CHKERRQ(ierr);
4560   if (!row) {
4561     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
4562   }
4563   if (!col) {
4564     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
4565   }
4566   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4567   PetscFunctionReturn(0);
4568 }
4569 
4570 #undef __FUNCT__
4571 #define __FUNCT__ "MatGetBrowsOfAcols"
4572 /*@C
4573     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
4574 
4575     Collective on Mat
4576 
4577    Input Parameters:
4578 +    A,B - the matrices in mpiaij format
4579 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4580 -    rowb, colb - index sets of rows and columns of B to extract (or NULL)
4581 
4582    Output Parameter:
4583 +    rowb, colb - index sets of rows and columns of B to extract
4584 -    B_seq - the sequential matrix generated
4585 
4586     Level: developer
4587 
4588 @*/
4589 PetscErrorCode  MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
4590 {
4591   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4592   PetscErrorCode ierr;
4593   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
4594   IS             isrowb,iscolb;
4595   Mat            *bseq=NULL;
4596 
4597   PetscFunctionBegin;
4598   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4599     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);
4600   }
4601   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4602 
4603   if (scall == MAT_INITIAL_MATRIX) {
4604     start = A->cmap->rstart;
4605     cmap  = a->garray;
4606     nzA   = a->A->cmap->n;
4607     nzB   = a->B->cmap->n;
4608     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4609     ncols = 0;
4610     for (i=0; i<nzB; i++) {  /* row < local row index */
4611       if (cmap[i] < start) idx[ncols++] = cmap[i];
4612       else break;
4613     }
4614     imark = i;
4615     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
4616     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
4617     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
4618     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
4619   } else {
4620     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
4621     isrowb  = *rowb; iscolb = *colb;
4622     ierr    = PetscMalloc1(1,&bseq);CHKERRQ(ierr);
4623     bseq[0] = *B_seq;
4624   }
4625   ierr   = MatGetSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
4626   *B_seq = bseq[0];
4627   ierr   = PetscFree(bseq);CHKERRQ(ierr);
4628   if (!rowb) {
4629     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
4630   } else {
4631     *rowb = isrowb;
4632   }
4633   if (!colb) {
4634     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
4635   } else {
4636     *colb = iscolb;
4637   }
4638   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4639   PetscFunctionReturn(0);
4640 }
4641 
4642 #undef __FUNCT__
4643 #define __FUNCT__ "MatGetBrowsOfAoCols_MPIAIJ"
4644 /*
4645     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
4646     of the OFF-DIAGONAL portion of local A
4647 
4648     Collective on Mat
4649 
4650    Input Parameters:
4651 +    A,B - the matrices in mpiaij format
4652 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4653 
4654    Output Parameter:
4655 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
4656 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
4657 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
4658 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
4659 
4660     Level: developer
4661 
4662 */
4663 PetscErrorCode  MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
4664 {
4665   VecScatter_MPI_General *gen_to,*gen_from;
4666   PetscErrorCode         ierr;
4667   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
4668   Mat_SeqAIJ             *b_oth;
4669   VecScatter             ctx =a->Mvctx;
4670   MPI_Comm               comm;
4671   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
4672   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
4673   PetscScalar            *rvalues,*svalues;
4674   MatScalar              *b_otha,*bufa,*bufA;
4675   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
4676   MPI_Request            *rwaits = NULL,*swaits = NULL;
4677   MPI_Status             *sstatus,rstatus;
4678   PetscMPIInt            jj,size;
4679   PetscInt               *cols,sbs,rbs;
4680   PetscScalar            *vals;
4681 
4682   PetscFunctionBegin;
4683   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4684   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4685 
4686   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4687     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);
4688   }
4689   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4690   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4691 
4692   gen_to   = (VecScatter_MPI_General*)ctx->todata;
4693   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
4694   rvalues  = gen_from->values; /* holds the length of receiving row */
4695   svalues  = gen_to->values;   /* holds the length of sending row */
4696   nrecvs   = gen_from->n;
4697   nsends   = gen_to->n;
4698 
4699   ierr    = PetscMalloc2(nrecvs,&rwaits,nsends,&swaits);CHKERRQ(ierr);
4700   srow    = gen_to->indices;    /* local row index to be sent */
4701   sstarts = gen_to->starts;
4702   sprocs  = gen_to->procs;
4703   sstatus = gen_to->sstatus;
4704   sbs     = gen_to->bs;
4705   rstarts = gen_from->starts;
4706   rprocs  = gen_from->procs;
4707   rbs     = gen_from->bs;
4708 
4709   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
4710   if (scall == MAT_INITIAL_MATRIX) {
4711     /* i-array */
4712     /*---------*/
4713     /*  post receives */
4714     for (i=0; i<nrecvs; i++) {
4715       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
4716       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
4717       ierr   = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4718     }
4719 
4720     /* pack the outgoing message */
4721     ierr = PetscMalloc2(nsends+1,&sstartsj,nrecvs+1,&rstartsj);CHKERRQ(ierr);
4722 
4723     sstartsj[0] = 0;
4724     rstartsj[0] = 0;
4725     len         = 0; /* total length of j or a array to be sent */
4726     k           = 0;
4727     for (i=0; i<nsends; i++) {
4728       rowlen = (PetscInt*)svalues + sstarts[i]*sbs;
4729       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
4730       for (j=0; j<nrows; j++) {
4731         row = srow[k] + B->rmap->range[rank]; /* global row idx */
4732         for (l=0; l<sbs; l++) {
4733           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr); /* rowlength */
4734 
4735           rowlen[j*sbs+l] = ncols;
4736 
4737           len += ncols;
4738           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr);
4739         }
4740         k++;
4741       }
4742       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4743 
4744       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
4745     }
4746     /* recvs and sends of i-array are completed */
4747     i = nrecvs;
4748     while (i--) {
4749       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4750     }
4751     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4752 
4753     /* allocate buffers for sending j and a arrays */
4754     ierr = PetscMalloc1(len+1,&bufj);CHKERRQ(ierr);
4755     ierr = PetscMalloc1(len+1,&bufa);CHKERRQ(ierr);
4756 
4757     /* create i-array of B_oth */
4758     ierr = PetscMalloc1(aBn+2,&b_othi);CHKERRQ(ierr);
4759 
4760     b_othi[0] = 0;
4761     len       = 0; /* total length of j or a array to be received */
4762     k         = 0;
4763     for (i=0; i<nrecvs; i++) {
4764       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
4765       nrows  = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be recieved */
4766       for (j=0; j<nrows; j++) {
4767         b_othi[k+1] = b_othi[k] + rowlen[j];
4768         len        += rowlen[j]; k++;
4769       }
4770       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
4771     }
4772 
4773     /* allocate space for j and a arrrays of B_oth */
4774     ierr = PetscMalloc1(b_othi[aBn]+1,&b_othj);CHKERRQ(ierr);
4775     ierr = PetscMalloc1(b_othi[aBn]+1,&b_otha);CHKERRQ(ierr);
4776 
4777     /* j-array */
4778     /*---------*/
4779     /*  post receives of j-array */
4780     for (i=0; i<nrecvs; i++) {
4781       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4782       ierr  = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4783     }
4784 
4785     /* pack the outgoing message j-array */
4786     k = 0;
4787     for (i=0; i<nsends; i++) {
4788       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4789       bufJ  = bufj+sstartsj[i];
4790       for (j=0; j<nrows; j++) {
4791         row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4792         for (ll=0; ll<sbs; ll++) {
4793           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4794           for (l=0; l<ncols; l++) {
4795             *bufJ++ = cols[l];
4796           }
4797           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4798         }
4799       }
4800       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4801     }
4802 
4803     /* recvs and sends of j-array are completed */
4804     i = nrecvs;
4805     while (i--) {
4806       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4807     }
4808     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4809   } else if (scall == MAT_REUSE_MATRIX) {
4810     sstartsj = *startsj_s;
4811     rstartsj = *startsj_r;
4812     bufa     = *bufa_ptr;
4813     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
4814     b_otha   = b_oth->a;
4815   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
4816 
4817   /* a-array */
4818   /*---------*/
4819   /*  post receives of a-array */
4820   for (i=0; i<nrecvs; i++) {
4821     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4822     ierr  = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4823   }
4824 
4825   /* pack the outgoing message a-array */
4826   k = 0;
4827   for (i=0; i<nsends; i++) {
4828     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4829     bufA  = bufa+sstartsj[i];
4830     for (j=0; j<nrows; j++) {
4831       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4832       for (ll=0; ll<sbs; ll++) {
4833         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4834         for (l=0; l<ncols; l++) {
4835           *bufA++ = vals[l];
4836         }
4837         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4838       }
4839     }
4840     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4841   }
4842   /* recvs and sends of a-array are completed */
4843   i = nrecvs;
4844   while (i--) {
4845     ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4846   }
4847   if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4848   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
4849 
4850   if (scall == MAT_INITIAL_MATRIX) {
4851     /* put together the new matrix */
4852     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
4853 
4854     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4855     /* Since these are PETSc arrays, change flags to free them as necessary. */
4856     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
4857     b_oth->free_a  = PETSC_TRUE;
4858     b_oth->free_ij = PETSC_TRUE;
4859     b_oth->nonew   = 0;
4860 
4861     ierr = PetscFree(bufj);CHKERRQ(ierr);
4862     if (!startsj_s || !bufa_ptr) {
4863       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
4864       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
4865     } else {
4866       *startsj_s = sstartsj;
4867       *startsj_r = rstartsj;
4868       *bufa_ptr  = bufa;
4869     }
4870   }
4871   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4872   PetscFunctionReturn(0);
4873 }
4874 
4875 #undef __FUNCT__
4876 #define __FUNCT__ "MatGetCommunicationStructs"
4877 /*@C
4878   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
4879 
4880   Not Collective
4881 
4882   Input Parameters:
4883 . A - The matrix in mpiaij format
4884 
4885   Output Parameter:
4886 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
4887 . colmap - A map from global column index to local index into lvec
4888 - multScatter - A scatter from the argument of a matrix-vector product to lvec
4889 
4890   Level: developer
4891 
4892 @*/
4893 #if defined(PETSC_USE_CTABLE)
4894 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
4895 #else
4896 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
4897 #endif
4898 {
4899   Mat_MPIAIJ *a;
4900 
4901   PetscFunctionBegin;
4902   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4903   PetscValidPointer(lvec, 2);
4904   PetscValidPointer(colmap, 3);
4905   PetscValidPointer(multScatter, 4);
4906   a = (Mat_MPIAIJ*) A->data;
4907   if (lvec) *lvec = a->lvec;
4908   if (colmap) *colmap = a->colmap;
4909   if (multScatter) *multScatter = a->Mvctx;
4910   PetscFunctionReturn(0);
4911 }
4912 
4913 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
4914 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
4915 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
4916 #if defined(PETSC_HAVE_ELEMENTAL)
4917 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
4918 #endif
4919 
4920 #undef __FUNCT__
4921 #define __FUNCT__ "MatMatMultNumeric_MPIDense_MPIAIJ"
4922 /*
4923     Computes (B'*A')' since computing B*A directly is untenable
4924 
4925                n                       p                          p
4926         (              )       (              )         (                  )
4927       m (      A       )  *  n (       B      )   =   m (         C        )
4928         (              )       (              )         (                  )
4929 
4930 */
4931 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
4932 {
4933   PetscErrorCode ierr;
4934   Mat            At,Bt,Ct;
4935 
4936   PetscFunctionBegin;
4937   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
4938   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
4939   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
4940   ierr = MatDestroy(&At);CHKERRQ(ierr);
4941   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
4942   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
4943   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
4944   PetscFunctionReturn(0);
4945 }
4946 
4947 #undef __FUNCT__
4948 #define __FUNCT__ "MatMatMultSymbolic_MPIDense_MPIAIJ"
4949 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
4950 {
4951   PetscErrorCode ierr;
4952   PetscInt       m=A->rmap->n,n=B->cmap->n;
4953   Mat            Cmat;
4954 
4955   PetscFunctionBegin;
4956   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);
4957   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
4958   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4959   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
4960   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
4961   ierr = MatMPIDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
4962   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4963   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4964 
4965   Cmat->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
4966 
4967   *C = Cmat;
4968   PetscFunctionReturn(0);
4969 }
4970 
4971 /* ----------------------------------------------------------------*/
4972 #undef __FUNCT__
4973 #define __FUNCT__ "MatMatMult_MPIDense_MPIAIJ"
4974 PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
4975 {
4976   PetscErrorCode ierr;
4977 
4978   PetscFunctionBegin;
4979   if (scall == MAT_INITIAL_MATRIX) {
4980     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
4981     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
4982     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
4983   }
4984   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
4985   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
4986   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
4987   PetscFunctionReturn(0);
4988 }
4989 
4990 /*MC
4991    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
4992 
4993    Options Database Keys:
4994 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
4995 
4996   Level: beginner
4997 
4998 .seealso: MatCreateAIJ()
4999 M*/
5000 
5001 #undef __FUNCT__
5002 #define __FUNCT__ "MatCreate_MPIAIJ"
5003 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
5004 {
5005   Mat_MPIAIJ     *b;
5006   PetscErrorCode ierr;
5007   PetscMPIInt    size;
5008 
5009   PetscFunctionBegin;
5010   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
5011 
5012   ierr          = PetscNewLog(B,&b);CHKERRQ(ierr);
5013   B->data       = (void*)b;
5014   ierr          = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
5015   B->assembled  = PETSC_FALSE;
5016   B->insertmode = NOT_SET_VALUES;
5017   b->size       = size;
5018 
5019   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank);CHKERRQ(ierr);
5020 
5021   /* build cache for off array entries formed */
5022   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash);CHKERRQ(ierr);
5023 
5024   b->donotstash  = PETSC_FALSE;
5025   b->colmap      = 0;
5026   b->garray      = 0;
5027   b->roworiented = PETSC_TRUE;
5028 
5029   /* stuff used for matrix vector multiply */
5030   b->lvec  = NULL;
5031   b->Mvctx = NULL;
5032 
5033   /* stuff for MatGetRow() */
5034   b->rowindices   = 0;
5035   b->rowvalues    = 0;
5036   b->getrowactive = PETSC_FALSE;
5037 
5038   /* flexible pointer used in CUSP/CUSPARSE classes */
5039   b->spptr = NULL;
5040 
5041   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetUseScalableIncreaseOverlap_C",MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ);CHKERRQ(ierr);
5042   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ);CHKERRQ(ierr);
5043   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
5044   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetDiagonalBlock_C",MatGetDiagonalBlock_MPIAIJ);CHKERRQ(ierr);
5045   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
5046   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
5047   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
5048   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
5049   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
5050   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
5051   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
5052 #if defined(PETSC_HAVE_ELEMENTAL)
5053   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_elemental_C",MatConvert_MPIAIJ_Elemental);CHKERRQ(ierr);
5054 #endif
5055   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
5056   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
5057   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
5058   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
5059   PetscFunctionReturn(0);
5060 }
5061 
5062 #undef __FUNCT__
5063 #define __FUNCT__ "MatCreateMPIAIJWithSplitArrays"
5064 /*@C
5065      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
5066          and "off-diagonal" part of the matrix in CSR format.
5067 
5068    Collective on MPI_Comm
5069 
5070    Input Parameters:
5071 +  comm - MPI communicator
5072 .  m - number of local rows (Cannot be PETSC_DECIDE)
5073 .  n - This value should be the same as the local size used in creating the
5074        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
5075        calculated if N is given) For square matrices n is almost always m.
5076 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
5077 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
5078 .   i - row indices for "diagonal" portion of matrix
5079 .   j - column indices
5080 .   a - matrix values
5081 .   oi - row indices for "off-diagonal" portion of matrix
5082 .   oj - column indices
5083 -   oa - matrix values
5084 
5085    Output Parameter:
5086 .   mat - the matrix
5087 
5088    Level: advanced
5089 
5090    Notes:
5091        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
5092        must free the arrays once the matrix has been destroyed and not before.
5093 
5094        The i and j indices are 0 based
5095 
5096        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
5097 
5098        This sets local rows and cannot be used to set off-processor values.
5099 
5100        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
5101        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
5102        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
5103        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
5104        keep track of the underlying array. Use MatSetOption(A,MAT_IGNORE_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
5105        communication if it is known that only local entries will be set.
5106 
5107 .keywords: matrix, aij, compressed row, sparse, parallel
5108 
5109 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
5110           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
5111 @*/
5112 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)
5113 {
5114   PetscErrorCode ierr;
5115   Mat_MPIAIJ     *maij;
5116 
5117   PetscFunctionBegin;
5118   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
5119   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
5120   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
5121   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
5122   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
5123   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
5124   maij = (Mat_MPIAIJ*) (*mat)->data;
5125 
5126   (*mat)->preallocated = PETSC_TRUE;
5127 
5128   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
5129   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
5130 
5131   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
5132   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
5133 
5134   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5135   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5136   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5137   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5138 
5139   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5140   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5141   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
5142   PetscFunctionReturn(0);
5143 }
5144 
5145 /*
5146     Special version for direct calls from Fortran
5147 */
5148 #include <petsc/private/fortranimpl.h>
5149 
5150 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5151 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
5152 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5153 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
5154 #endif
5155 
5156 /* Change these macros so can be used in void function */
5157 #undef CHKERRQ
5158 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
5159 #undef SETERRQ2
5160 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5161 #undef SETERRQ3
5162 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5163 #undef SETERRQ
5164 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
5165 
5166 #undef __FUNCT__
5167 #define __FUNCT__ "matsetvaluesmpiaij_"
5168 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)
5169 {
5170   Mat            mat  = *mmat;
5171   PetscInt       m    = *mm, n = *mn;
5172   InsertMode     addv = *maddv;
5173   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
5174   PetscScalar    value;
5175   PetscErrorCode ierr;
5176 
5177   MatCheckPreallocated(mat,1);
5178   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
5179 
5180 #if defined(PETSC_USE_DEBUG)
5181   else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
5182 #endif
5183   {
5184     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
5185     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
5186     PetscBool roworiented = aij->roworiented;
5187 
5188     /* Some Variables required in the macro */
5189     Mat        A                 = aij->A;
5190     Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
5191     PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
5192     MatScalar  *aa               = a->a;
5193     PetscBool  ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
5194     Mat        B                 = aij->B;
5195     Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
5196     PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5197     MatScalar  *ba               = b->a;
5198 
5199     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5200     PetscInt  nonew = a->nonew;
5201     MatScalar *ap1,*ap2;
5202 
5203     PetscFunctionBegin;
5204     for (i=0; i<m; i++) {
5205       if (im[i] < 0) continue;
5206 #if defined(PETSC_USE_DEBUG)
5207       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);
5208 #endif
5209       if (im[i] >= rstart && im[i] < rend) {
5210         row      = im[i] - rstart;
5211         lastcol1 = -1;
5212         rp1      = aj + ai[row];
5213         ap1      = aa + ai[row];
5214         rmax1    = aimax[row];
5215         nrow1    = ailen[row];
5216         low1     = 0;
5217         high1    = nrow1;
5218         lastcol2 = -1;
5219         rp2      = bj + bi[row];
5220         ap2      = ba + bi[row];
5221         rmax2    = bimax[row];
5222         nrow2    = bilen[row];
5223         low2     = 0;
5224         high2    = nrow2;
5225 
5226         for (j=0; j<n; j++) {
5227           if (roworiented) value = v[i*n+j];
5228           else value = v[i+j*m];
5229           if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES)) continue;
5230           if (in[j] >= cstart && in[j] < cend) {
5231             col = in[j] - cstart;
5232             MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
5233           } else if (in[j] < 0) continue;
5234 #if defined(PETSC_USE_DEBUG)
5235           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);
5236 #endif
5237           else {
5238             if (mat->was_assembled) {
5239               if (!aij->colmap) {
5240                 ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5241               }
5242 #if defined(PETSC_USE_CTABLE)
5243               ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5244               col--;
5245 #else
5246               col = aij->colmap[in[j]] - 1;
5247 #endif
5248               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5249                 ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5250                 col  =  in[j];
5251                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5252                 B     = aij->B;
5253                 b     = (Mat_SeqAIJ*)B->data;
5254                 bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5255                 rp2   = bj + bi[row];
5256                 ap2   = ba + bi[row];
5257                 rmax2 = bimax[row];
5258                 nrow2 = bilen[row];
5259                 low2  = 0;
5260                 high2 = nrow2;
5261                 bm    = aij->B->rmap->n;
5262                 ba    = b->a;
5263               }
5264             } else col = in[j];
5265             MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
5266           }
5267         }
5268       } else if (!aij->donotstash) {
5269         if (roworiented) {
5270           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5271         } else {
5272           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5273         }
5274       }
5275     }
5276   }
5277   PetscFunctionReturnVoid();
5278 }
5279 
5280