xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision 262ecc7176e93fbdedf2c042ec9dcb340e9750eb)
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,MPIU_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) \
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 (%D, %D) into matrix", row, col); \
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) \
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 (%D, %D) into matrix", row, col); \
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);
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 (%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);
617         }
618       }
619     } else {
620       if (mat->nooffprocentries) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Setting off process row %D even though MatSetOption(,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) was set",im[i]);
621       if (!aij->donotstash) {
622         mat->assembled = PETSC_FALSE;
623         if (roworiented) {
624           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
625         } else {
626           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
627         }
628       }
629     }
630   }
631   PetscFunctionReturn(0);
632 }
633 
634 #undef __FUNCT__
635 #define __FUNCT__ "MatGetValues_MPIAIJ"
636 PetscErrorCode MatGetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],PetscScalar v[])
637 {
638   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
639   PetscErrorCode ierr;
640   PetscInt       i,j,rstart = mat->rmap->rstart,rend = mat->rmap->rend;
641   PetscInt       cstart = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
642 
643   PetscFunctionBegin;
644   for (i=0; i<m; i++) {
645     if (idxm[i] < 0) continue; /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative row: %D",idxm[i]);*/
646     if (idxm[i] >= mat->rmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %D max %D",idxm[i],mat->rmap->N-1);
647     if (idxm[i] >= rstart && idxm[i] < rend) {
648       row = idxm[i] - rstart;
649       for (j=0; j<n; j++) {
650         if (idxn[j] < 0) continue; /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column: %D",idxn[j]); */
651         if (idxn[j] >= mat->cmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %D max %D",idxn[j],mat->cmap->N-1);
652         if (idxn[j] >= cstart && idxn[j] < cend) {
653           col  = idxn[j] - cstart;
654           ierr = MatGetValues(aij->A,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
655         } else {
656           if (!aij->colmap) {
657             ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
658           }
659 #if defined(PETSC_USE_CTABLE)
660           ierr = PetscTableFind(aij->colmap,idxn[j]+1,&col);CHKERRQ(ierr);
661           col--;
662 #else
663           col = aij->colmap[idxn[j]] - 1;
664 #endif
665           if ((col < 0) || (aij->garray[col] != idxn[j])) *(v+i*n+j) = 0.0;
666           else {
667             ierr = MatGetValues(aij->B,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
668           }
669         }
670       }
671     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only local values currently supported");
672   }
673   PetscFunctionReturn(0);
674 }
675 
676 extern PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat,Vec,Vec);
677 
678 #undef __FUNCT__
679 #define __FUNCT__ "MatAssemblyBegin_MPIAIJ"
680 PetscErrorCode MatAssemblyBegin_MPIAIJ(Mat mat,MatAssemblyType mode)
681 {
682   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
683   PetscErrorCode ierr;
684   PetscInt       nstash,reallocs;
685   InsertMode     addv;
686 
687   PetscFunctionBegin;
688   if (aij->donotstash || mat->nooffprocentries) PetscFunctionReturn(0);
689 
690   /* make sure all processors are either in INSERTMODE or ADDMODE */
691   ierr = MPI_Allreduce((PetscEnum*)&mat->insertmode,(PetscEnum*)&addv,1,MPIU_ENUM,MPI_BOR,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
692   if (addv == (ADD_VALUES|INSERT_VALUES)) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Some processors inserted others added");
693   mat->insertmode = addv; /* in case this processor had no cache */
694 
695   ierr = MatStashScatterBegin_Private(mat,&mat->stash,mat->rmap->range);CHKERRQ(ierr);
696   ierr = MatStashGetInfo_Private(&mat->stash,&nstash,&reallocs);CHKERRQ(ierr);
697   ierr = PetscInfo2(aij->A,"Stash has %D entries, uses %D mallocs.\n",nstash,reallocs);CHKERRQ(ierr);
698   PetscFunctionReturn(0);
699 }
700 
701 #undef __FUNCT__
702 #define __FUNCT__ "MatAssemblyEnd_MPIAIJ"
703 PetscErrorCode MatAssemblyEnd_MPIAIJ(Mat mat,MatAssemblyType mode)
704 {
705   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
706   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)aij->A->data;
707   PetscErrorCode ierr;
708   PetscMPIInt    n;
709   PetscInt       i,j,rstart,ncols,flg;
710   PetscInt       *row,*col;
711   PetscBool      other_disassembled;
712   PetscScalar    *val;
713   InsertMode     addv = mat->insertmode;
714 
715   /* do not use 'b = (Mat_SeqAIJ*)aij->B->data' as B can be reset in disassembly */
716 
717   PetscFunctionBegin;
718   if (!aij->donotstash && !mat->nooffprocentries) {
719     while (1) {
720       ierr = MatStashScatterGetMesg_Private(&mat->stash,&n,&row,&col,&val,&flg);CHKERRQ(ierr);
721       if (!flg) break;
722 
723       for (i=0; i<n; ) {
724         /* Now identify the consecutive vals belonging to the same row */
725         for (j=i,rstart=row[j]; j<n; j++) {
726           if (row[j] != rstart) break;
727         }
728         if (j < n) ncols = j-i;
729         else       ncols = n-i;
730         /* Now assemble all these values with a single function call */
731         ierr = MatSetValues_MPIAIJ(mat,1,row+i,ncols,col+i,val+i,addv);CHKERRQ(ierr);
732 
733         i = j;
734       }
735     }
736     ierr = MatStashScatterEnd_Private(&mat->stash);CHKERRQ(ierr);
737   }
738   ierr = MatAssemblyBegin(aij->A,mode);CHKERRQ(ierr);
739   ierr = MatAssemblyEnd(aij->A,mode);CHKERRQ(ierr);
740 
741   /* determine if any processor has disassembled, if so we must
742      also disassemble ourselfs, in order that we may reassemble. */
743   /*
744      if nonzero structure of submatrix B cannot change then we know that
745      no processor disassembled thus we can skip this stuff
746   */
747   if (!((Mat_SeqAIJ*)aij->B->data)->nonew) {
748     ierr = MPI_Allreduce(&mat->was_assembled,&other_disassembled,1,MPIU_BOOL,MPI_PROD,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
749     if (mat->was_assembled && !other_disassembled) {
750       ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
751     }
752   }
753   if (!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) {
754     ierr = MatSetUpMultiply_MPIAIJ(mat);CHKERRQ(ierr);
755   }
756   ierr = MatSetOption(aij->B,MAT_USE_INODES,PETSC_FALSE);CHKERRQ(ierr);
757   ierr = MatAssemblyBegin(aij->B,mode);CHKERRQ(ierr);
758   ierr = MatAssemblyEnd(aij->B,mode);CHKERRQ(ierr);
759 
760   ierr = PetscFree2(aij->rowvalues,aij->rowindices);CHKERRQ(ierr);
761 
762   aij->rowvalues = 0;
763 
764   ierr = VecDestroy(&aij->diag);CHKERRQ(ierr);
765   if (a->inode.size) mat->ops->multdiagonalblock = MatMultDiagonalBlock_MPIAIJ;
766 
767   /* if no new nonzero locations are allowed in matrix then only set the matrix state the first time through */
768   if ((!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) || !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
769     PetscObjectState state = aij->A->nonzerostate + aij->B->nonzerostate;
770     ierr = MPI_Allreduce(&state,&mat->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
771   }
772   PetscFunctionReturn(0);
773 }
774 
775 #undef __FUNCT__
776 #define __FUNCT__ "MatZeroEntries_MPIAIJ"
777 PetscErrorCode MatZeroEntries_MPIAIJ(Mat A)
778 {
779   Mat_MPIAIJ     *l = (Mat_MPIAIJ*)A->data;
780   PetscErrorCode ierr;
781 
782   PetscFunctionBegin;
783   ierr = MatZeroEntries(l->A);CHKERRQ(ierr);
784   ierr = MatZeroEntries(l->B);CHKERRQ(ierr);
785   PetscFunctionReturn(0);
786 }
787 
788 #undef __FUNCT__
789 #define __FUNCT__ "MatZeroRows_MPIAIJ"
790 PetscErrorCode MatZeroRows_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
791 {
792   Mat_MPIAIJ    *mat    = (Mat_MPIAIJ *) A->data;
793   PetscInt      *owners = A->rmap->range;
794   PetscInt       n      = A->rmap->n;
795   PetscSF        sf;
796   PetscInt      *lrows;
797   PetscSFNode   *rrows;
798   PetscInt       r, p = 0, len = 0;
799   PetscErrorCode ierr;
800 
801   PetscFunctionBegin;
802   /* Create SF where leaves are input rows and roots are owned rows */
803   ierr = PetscMalloc1(n, &lrows);CHKERRQ(ierr);
804   for (r = 0; r < n; ++r) lrows[r] = -1;
805   if (!A->nooffproczerorows) {ierr = PetscMalloc1(N, &rrows);CHKERRQ(ierr);}
806   for (r = 0; r < N; ++r) {
807     const PetscInt idx   = rows[r];
808     if (idx < 0 || A->rmap->N <= idx) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row %D out of range [0,%D)",idx,A->rmap->N);
809     if (idx < owners[p] || owners[p+1] <= idx) { /* short-circuit the search if the last p owns this row too */
810       ierr = PetscLayoutFindOwner(A->rmap,idx,&p);CHKERRQ(ierr);
811     }
812     if (A->nooffproczerorows) {
813       if (p != mat->rank) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"MAT_NO_OFF_PROC_ZERO_ROWS set, but row %D is not owned by rank %d",idx,mat->rank);
814       lrows[len++] = idx - owners[p];
815     } else {
816       rrows[r].rank = p;
817       rrows[r].index = rows[r] - owners[p];
818     }
819   }
820   if (!A->nooffproczerorows) {
821     ierr = PetscSFCreate(PetscObjectComm((PetscObject) A), &sf);CHKERRQ(ierr);
822     ierr = PetscSFSetGraph(sf, n, N, NULL, PETSC_OWN_POINTER, rrows, PETSC_OWN_POINTER);CHKERRQ(ierr);
823     /* Collect flags for rows to be zeroed */
824     ierr = PetscSFReduceBegin(sf, MPIU_INT, (PetscInt*)rows, lrows, MPI_LOR);CHKERRQ(ierr);
825     ierr = PetscSFReduceEnd(sf, MPIU_INT, (PetscInt*)rows, lrows, MPI_LOR);CHKERRQ(ierr);
826     ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
827     /* Compress and put in row numbers */
828     for (r = 0; r < n; ++r) if (lrows[r] >= 0) lrows[len++] = r;
829   }
830   /* fix right hand side if needed */
831   if (x && b) {
832     const PetscScalar *xx;
833     PetscScalar       *bb;
834 
835     ierr = VecGetArrayRead(x, &xx);CHKERRQ(ierr);
836     ierr = VecGetArray(b, &bb);CHKERRQ(ierr);
837     for (r = 0; r < len; ++r) bb[lrows[r]] = diag*xx[lrows[r]];
838     ierr = VecRestoreArrayRead(x, &xx);CHKERRQ(ierr);
839     ierr = VecRestoreArray(b, &bb);CHKERRQ(ierr);
840   }
841   /* Must zero l->B before l->A because the (diag) case below may put values into l->B*/
842   ierr = MatZeroRows(mat->B, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
843   if ((diag != 0.0) && (mat->A->rmap->N == mat->A->cmap->N)) {
844     ierr = MatZeroRows(mat->A, len, lrows, diag, NULL, NULL);CHKERRQ(ierr);
845   } else if (diag != 0.0) {
846     ierr = MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
847     if (((Mat_SeqAIJ *) mat->A->data)->nonew) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatZeroRows() on rectangular matrices cannot be used with the Mat options\nMAT_NEW_NONZERO_LOCATIONS,MAT_NEW_NONZERO_LOCATION_ERR,MAT_NEW_NONZERO_ALLOCATION_ERR");
848     for (r = 0; r < len; ++r) {
849       const PetscInt row = lrows[r] + A->rmap->rstart;
850       ierr = MatSetValues(A, 1, &row, 1, &row, &diag, INSERT_VALUES);CHKERRQ(ierr);
851     }
852     ierr = MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
853     ierr = MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
854   } else {
855     ierr = MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
856   }
857   ierr = PetscFree(lrows);CHKERRQ(ierr);
858 
859   /* only change matrix nonzero state if pattern was allowed to be changed */
860   if (!((Mat_SeqAIJ*)(mat->A->data))->keepnonzeropattern) {
861     PetscObjectState state = mat->A->nonzerostate + mat->B->nonzerostate;
862     ierr = MPI_Allreduce(&state,&A->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
863   }
864   PetscFunctionReturn(0);
865 }
866 
867 #undef __FUNCT__
868 #define __FUNCT__ "MatZeroRowsColumns_MPIAIJ"
869 PetscErrorCode MatZeroRowsColumns_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
870 {
871   Mat_MPIAIJ        *l = (Mat_MPIAIJ*)A->data;
872   PetscErrorCode    ierr;
873   PetscMPIInt       n = A->rmap->n;
874   PetscInt          i,j,r,m,p = 0,len = 0;
875   PetscInt          *lrows,*owners = A->rmap->range;
876   PetscSFNode       *rrows;
877   PetscSF           sf;
878   const PetscScalar *xx;
879   PetscScalar       *bb,*mask;
880   Vec               xmask,lmask;
881   Mat_SeqAIJ        *aij = (Mat_SeqAIJ*)l->B->data;
882   const PetscInt    *aj, *ii,*ridx;
883   PetscScalar       *aa;
884 
885   PetscFunctionBegin;
886   /* Create SF where leaves are input rows and roots are owned rows */
887   ierr = PetscMalloc1(n, &lrows);CHKERRQ(ierr);
888   for (r = 0; r < n; ++r) lrows[r] = -1;
889   ierr = PetscMalloc1(N, &rrows);CHKERRQ(ierr);
890   for (r = 0; r < N; ++r) {
891     const PetscInt idx   = rows[r];
892     if (idx < 0 || A->rmap->N <= idx) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row %D out of range [0,%D)",idx,A->rmap->N);
893     if (idx < owners[p] || owners[p+1] <= idx) { /* short-circuit the search if the last p owns this row too */
894       ierr = PetscLayoutFindOwner(A->rmap,idx,&p);CHKERRQ(ierr);
895     }
896     rrows[r].rank  = p;
897     rrows[r].index = rows[r] - owners[p];
898   }
899   ierr = PetscSFCreate(PetscObjectComm((PetscObject) A), &sf);CHKERRQ(ierr);
900   ierr = PetscSFSetGraph(sf, n, N, NULL, PETSC_OWN_POINTER, rrows, PETSC_OWN_POINTER);CHKERRQ(ierr);
901   /* Collect flags for rows to be zeroed */
902   ierr = PetscSFReduceBegin(sf, MPIU_INT, (PetscInt *) rows, lrows, MPI_LOR);CHKERRQ(ierr);
903   ierr = PetscSFReduceEnd(sf, MPIU_INT, (PetscInt *) rows, lrows, MPI_LOR);CHKERRQ(ierr);
904   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
905   /* Compress and put in row numbers */
906   for (r = 0; r < n; ++r) if (lrows[r] >= 0) lrows[len++] = r;
907   /* zero diagonal part of matrix */
908   ierr = MatZeroRowsColumns(l->A,len,lrows,diag,x,b);CHKERRQ(ierr);
909   /* handle off diagonal part of matrix */
910   ierr = MatCreateVecs(A,&xmask,NULL);CHKERRQ(ierr);
911   ierr = VecDuplicate(l->lvec,&lmask);CHKERRQ(ierr);
912   ierr = VecGetArray(xmask,&bb);CHKERRQ(ierr);
913   for (i=0; i<len; i++) bb[lrows[i]] = 1;
914   ierr = VecRestoreArray(xmask,&bb);CHKERRQ(ierr);
915   ierr = VecScatterBegin(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
916   ierr = VecScatterEnd(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
917   ierr = VecDestroy(&xmask);CHKERRQ(ierr);
918   if (x) {
919     ierr = VecScatterBegin(l->Mvctx,x,l->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
920     ierr = VecScatterEnd(l->Mvctx,x,l->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
921     ierr = VecGetArrayRead(l->lvec,&xx);CHKERRQ(ierr);
922     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
923   }
924   ierr = VecGetArray(lmask,&mask);CHKERRQ(ierr);
925   /* remove zeroed rows of off diagonal matrix */
926   ii = aij->i;
927   for (i=0; i<len; i++) {
928     ierr = PetscMemzero(aij->a + ii[lrows[i]],(ii[lrows[i]+1] - ii[lrows[i]])*sizeof(PetscScalar));CHKERRQ(ierr);
929   }
930   /* loop over all elements of off process part of matrix zeroing removed columns*/
931   if (aij->compressedrow.use) {
932     m    = aij->compressedrow.nrows;
933     ii   = aij->compressedrow.i;
934     ridx = aij->compressedrow.rindex;
935     for (i=0; i<m; i++) {
936       n  = ii[i+1] - ii[i];
937       aj = aij->j + ii[i];
938       aa = aij->a + ii[i];
939 
940       for (j=0; j<n; j++) {
941         if (PetscAbsScalar(mask[*aj])) {
942           if (b) bb[*ridx] -= *aa*xx[*aj];
943           *aa = 0.0;
944         }
945         aa++;
946         aj++;
947       }
948       ridx++;
949     }
950   } else { /* do not use compressed row format */
951     m = l->B->rmap->n;
952     for (i=0; i<m; i++) {
953       n  = ii[i+1] - ii[i];
954       aj = aij->j + ii[i];
955       aa = aij->a + ii[i];
956       for (j=0; j<n; j++) {
957         if (PetscAbsScalar(mask[*aj])) {
958           if (b) bb[i] -= *aa*xx[*aj];
959           *aa = 0.0;
960         }
961         aa++;
962         aj++;
963       }
964     }
965   }
966   if (x) {
967     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
968     ierr = VecRestoreArrayRead(l->lvec,&xx);CHKERRQ(ierr);
969   }
970   ierr = VecRestoreArray(lmask,&mask);CHKERRQ(ierr);
971   ierr = VecDestroy(&lmask);CHKERRQ(ierr);
972   ierr = PetscFree(lrows);CHKERRQ(ierr);
973 
974   /* only change matrix nonzero state if pattern was allowed to be changed */
975   if (!((Mat_SeqAIJ*)(l->A->data))->keepnonzeropattern) {
976     PetscObjectState state = l->A->nonzerostate + l->B->nonzerostate;
977     ierr = MPI_Allreduce(&state,&A->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
978   }
979   PetscFunctionReturn(0);
980 }
981 
982 #undef __FUNCT__
983 #define __FUNCT__ "MatMult_MPIAIJ"
984 PetscErrorCode MatMult_MPIAIJ(Mat A,Vec xx,Vec yy)
985 {
986   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
987   PetscErrorCode ierr;
988   PetscInt       nt;
989 
990   PetscFunctionBegin;
991   ierr = VecGetLocalSize(xx,&nt);CHKERRQ(ierr);
992   if (nt != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Incompatible partition of A (%D) and xx (%D)",A->cmap->n,nt);
993   ierr = VecScatterBegin(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
994   ierr = (*a->A->ops->mult)(a->A,xx,yy);CHKERRQ(ierr);
995   ierr = VecScatterEnd(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
996   ierr = (*a->B->ops->multadd)(a->B,a->lvec,yy,yy);CHKERRQ(ierr);
997   PetscFunctionReturn(0);
998 }
999 
1000 #undef __FUNCT__
1001 #define __FUNCT__ "MatMultDiagonalBlock_MPIAIJ"
1002 PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat A,Vec bb,Vec xx)
1003 {
1004   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1005   PetscErrorCode ierr;
1006 
1007   PetscFunctionBegin;
1008   ierr = MatMultDiagonalBlock(a->A,bb,xx);CHKERRQ(ierr);
1009   PetscFunctionReturn(0);
1010 }
1011 
1012 #undef __FUNCT__
1013 #define __FUNCT__ "MatMultAdd_MPIAIJ"
1014 PetscErrorCode MatMultAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1015 {
1016   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1017   PetscErrorCode ierr;
1018 
1019   PetscFunctionBegin;
1020   ierr = VecScatterBegin(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1021   ierr = (*a->A->ops->multadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
1022   ierr = VecScatterEnd(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1023   ierr = (*a->B->ops->multadd)(a->B,a->lvec,zz,zz);CHKERRQ(ierr);
1024   PetscFunctionReturn(0);
1025 }
1026 
1027 #undef __FUNCT__
1028 #define __FUNCT__ "MatMultTranspose_MPIAIJ"
1029 PetscErrorCode MatMultTranspose_MPIAIJ(Mat A,Vec xx,Vec yy)
1030 {
1031   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1032   PetscErrorCode ierr;
1033   PetscBool      merged;
1034 
1035   PetscFunctionBegin;
1036   ierr = VecScatterGetMerged(a->Mvctx,&merged);CHKERRQ(ierr);
1037   /* do nondiagonal part */
1038   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
1039   if (!merged) {
1040     /* send it on its way */
1041     ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1042     /* do local part */
1043     ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
1044     /* receive remote parts: note this assumes the values are not actually */
1045     /* added in yy until the next line, */
1046     ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1047   } else {
1048     /* do local part */
1049     ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
1050     /* send it on its way */
1051     ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1052     /* values actually were received in the Begin() but we need to call this nop */
1053     ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1054   }
1055   PetscFunctionReturn(0);
1056 }
1057 
1058 #undef __FUNCT__
1059 #define __FUNCT__ "MatIsTranspose_MPIAIJ"
1060 PetscErrorCode  MatIsTranspose_MPIAIJ(Mat Amat,Mat Bmat,PetscReal tol,PetscBool  *f)
1061 {
1062   MPI_Comm       comm;
1063   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ*) Amat->data, *Bij;
1064   Mat            Adia = Aij->A, Bdia, Aoff,Boff,*Aoffs,*Boffs;
1065   IS             Me,Notme;
1066   PetscErrorCode ierr;
1067   PetscInt       M,N,first,last,*notme,i;
1068   PetscMPIInt    size;
1069 
1070   PetscFunctionBegin;
1071   /* Easy test: symmetric diagonal block */
1072   Bij  = (Mat_MPIAIJ*) Bmat->data; Bdia = Bij->A;
1073   ierr = MatIsTranspose(Adia,Bdia,tol,f);CHKERRQ(ierr);
1074   if (!*f) PetscFunctionReturn(0);
1075   ierr = PetscObjectGetComm((PetscObject)Amat,&comm);CHKERRQ(ierr);
1076   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1077   if (size == 1) PetscFunctionReturn(0);
1078 
1079   /* Hard test: off-diagonal block. This takes a MatGetSubMatrix. */
1080   ierr = MatGetSize(Amat,&M,&N);CHKERRQ(ierr);
1081   ierr = MatGetOwnershipRange(Amat,&first,&last);CHKERRQ(ierr);
1082   ierr = PetscMalloc1(N-last+first,&notme);CHKERRQ(ierr);
1083   for (i=0; i<first; i++) notme[i] = i;
1084   for (i=last; i<M; i++) notme[i-last+first] = i;
1085   ierr = ISCreateGeneral(MPI_COMM_SELF,N-last+first,notme,PETSC_COPY_VALUES,&Notme);CHKERRQ(ierr);
1086   ierr = ISCreateStride(MPI_COMM_SELF,last-first,first,1,&Me);CHKERRQ(ierr);
1087   ierr = MatGetSubMatrices(Amat,1,&Me,&Notme,MAT_INITIAL_MATRIX,&Aoffs);CHKERRQ(ierr);
1088   Aoff = Aoffs[0];
1089   ierr = MatGetSubMatrices(Bmat,1,&Notme,&Me,MAT_INITIAL_MATRIX,&Boffs);CHKERRQ(ierr);
1090   Boff = Boffs[0];
1091   ierr = MatIsTranspose(Aoff,Boff,tol,f);CHKERRQ(ierr);
1092   ierr = MatDestroyMatrices(1,&Aoffs);CHKERRQ(ierr);
1093   ierr = MatDestroyMatrices(1,&Boffs);CHKERRQ(ierr);
1094   ierr = ISDestroy(&Me);CHKERRQ(ierr);
1095   ierr = ISDestroy(&Notme);CHKERRQ(ierr);
1096   ierr = PetscFree(notme);CHKERRQ(ierr);
1097   PetscFunctionReturn(0);
1098 }
1099 
1100 #undef __FUNCT__
1101 #define __FUNCT__ "MatMultTransposeAdd_MPIAIJ"
1102 PetscErrorCode MatMultTransposeAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1103 {
1104   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1105   PetscErrorCode ierr;
1106 
1107   PetscFunctionBegin;
1108   /* do nondiagonal part */
1109   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
1110   /* send it on its way */
1111   ierr = VecScatterBegin(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1112   /* do local part */
1113   ierr = (*a->A->ops->multtransposeadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
1114   /* receive remote parts */
1115   ierr = VecScatterEnd(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1116   PetscFunctionReturn(0);
1117 }
1118 
1119 /*
1120   This only works correctly for square matrices where the subblock A->A is the
1121    diagonal block
1122 */
1123 #undef __FUNCT__
1124 #define __FUNCT__ "MatGetDiagonal_MPIAIJ"
1125 PetscErrorCode MatGetDiagonal_MPIAIJ(Mat A,Vec v)
1126 {
1127   PetscErrorCode ierr;
1128   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1129 
1130   PetscFunctionBegin;
1131   if (A->rmap->N != A->cmap->N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Supports only square matrix where A->A is diag block");
1132   if (A->rmap->rstart != A->cmap->rstart || A->rmap->rend != A->cmap->rend) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"row partition must equal col partition");
1133   ierr = MatGetDiagonal(a->A,v);CHKERRQ(ierr);
1134   PetscFunctionReturn(0);
1135 }
1136 
1137 #undef __FUNCT__
1138 #define __FUNCT__ "MatScale_MPIAIJ"
1139 PetscErrorCode MatScale_MPIAIJ(Mat A,PetscScalar aa)
1140 {
1141   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1142   PetscErrorCode ierr;
1143 
1144   PetscFunctionBegin;
1145   ierr = MatScale(a->A,aa);CHKERRQ(ierr);
1146   ierr = MatScale(a->B,aa);CHKERRQ(ierr);
1147   PetscFunctionReturn(0);
1148 }
1149 
1150 #undef __FUNCT__
1151 #define __FUNCT__ "MatDestroy_MPIAIJ"
1152 PetscErrorCode MatDestroy_MPIAIJ(Mat mat)
1153 {
1154   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1155   PetscErrorCode ierr;
1156 
1157   PetscFunctionBegin;
1158 #if defined(PETSC_USE_LOG)
1159   PetscLogObjectState((PetscObject)mat,"Rows=%D, Cols=%D",mat->rmap->N,mat->cmap->N);
1160 #endif
1161   ierr = MatStashDestroy_Private(&mat->stash);CHKERRQ(ierr);
1162   ierr = VecDestroy(&aij->diag);CHKERRQ(ierr);
1163   ierr = MatDestroy(&aij->A);CHKERRQ(ierr);
1164   ierr = MatDestroy(&aij->B);CHKERRQ(ierr);
1165 #if defined(PETSC_USE_CTABLE)
1166   ierr = PetscTableDestroy(&aij->colmap);CHKERRQ(ierr);
1167 #else
1168   ierr = PetscFree(aij->colmap);CHKERRQ(ierr);
1169 #endif
1170   ierr = PetscFree(aij->garray);CHKERRQ(ierr);
1171   ierr = VecDestroy(&aij->lvec);CHKERRQ(ierr);
1172   ierr = VecScatterDestroy(&aij->Mvctx);CHKERRQ(ierr);
1173   ierr = PetscFree2(aij->rowvalues,aij->rowindices);CHKERRQ(ierr);
1174   ierr = PetscFree(aij->ld);CHKERRQ(ierr);
1175   ierr = PetscFree(mat->data);CHKERRQ(ierr);
1176 
1177   ierr = PetscObjectChangeTypeName((PetscObject)mat,0);CHKERRQ(ierr);
1178   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatStoreValues_C",NULL);CHKERRQ(ierr);
1179   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatRetrieveValues_C",NULL);CHKERRQ(ierr);
1180   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatGetDiagonalBlock_C",NULL);CHKERRQ(ierr);
1181   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatIsTranspose_C",NULL);CHKERRQ(ierr);
1182   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocation_C",NULL);CHKERRQ(ierr);
1183   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocationCSR_C",NULL);CHKERRQ(ierr);
1184   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDiagonalScaleLocal_C",NULL);CHKERRQ(ierr);
1185   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_mpisbaij_C",NULL);CHKERRQ(ierr);
1186 #if defined(PETSC_HAVE_ELEMENTAL)
1187   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_elemental_C",NULL);CHKERRQ(ierr);
1188 #endif
1189   PetscFunctionReturn(0);
1190 }
1191 
1192 #undef __FUNCT__
1193 #define __FUNCT__ "MatView_MPIAIJ_Binary"
1194 PetscErrorCode MatView_MPIAIJ_Binary(Mat mat,PetscViewer viewer)
1195 {
1196   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1197   Mat_SeqAIJ     *A   = (Mat_SeqAIJ*)aij->A->data;
1198   Mat_SeqAIJ     *B   = (Mat_SeqAIJ*)aij->B->data;
1199   PetscErrorCode ierr;
1200   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
1201   int            fd;
1202   PetscInt       nz,header[4],*row_lengths,*range=0,rlen,i;
1203   PetscInt       nzmax,*column_indices,j,k,col,*garray = aij->garray,cnt,cstart = mat->cmap->rstart,rnz = 0;
1204   PetscScalar    *column_values;
1205   PetscInt       message_count,flowcontrolcount;
1206   FILE           *file;
1207 
1208   PetscFunctionBegin;
1209   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
1210   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);CHKERRQ(ierr);
1211   nz   = A->nz + B->nz;
1212   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
1213   if (!rank) {
1214     header[0] = MAT_FILE_CLASSID;
1215     header[1] = mat->rmap->N;
1216     header[2] = mat->cmap->N;
1217 
1218     ierr = MPI_Reduce(&nz,&header[3],1,MPIU_INT,MPI_SUM,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1219     ierr = PetscBinaryWrite(fd,header,4,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1220     /* get largest number of rows any processor has */
1221     rlen  = mat->rmap->n;
1222     range = mat->rmap->range;
1223     for (i=1; i<size; i++) rlen = PetscMax(rlen,range[i+1] - range[i]);
1224   } else {
1225     ierr = MPI_Reduce(&nz,0,1,MPIU_INT,MPI_SUM,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1226     rlen = mat->rmap->n;
1227   }
1228 
1229   /* load up the local row counts */
1230   ierr = PetscMalloc1(rlen+1,&row_lengths);CHKERRQ(ierr);
1231   for (i=0; i<mat->rmap->n; i++) row_lengths[i] = A->i[i+1] - A->i[i] + B->i[i+1] - B->i[i];
1232 
1233   /* store the row lengths to the file */
1234   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1235   if (!rank) {
1236     ierr = PetscBinaryWrite(fd,row_lengths,mat->rmap->n,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1237     for (i=1; i<size; i++) {
1238       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1239       rlen = range[i+1] - range[i];
1240       ierr = MPIULong_Recv(row_lengths,rlen,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1241       ierr = PetscBinaryWrite(fd,row_lengths,rlen,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1242     }
1243     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1244   } else {
1245     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1246     ierr = MPIULong_Send(row_lengths,mat->rmap->n,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1247     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1248   }
1249   ierr = PetscFree(row_lengths);CHKERRQ(ierr);
1250 
1251   /* load up the local column indices */
1252   nzmax = nz; /* th processor needs space a largest processor needs */
1253   ierr  = MPI_Reduce(&nz,&nzmax,1,MPIU_INT,MPI_MAX,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1254   ierr  = PetscMalloc1(nzmax+1,&column_indices);CHKERRQ(ierr);
1255   cnt   = 0;
1256   for (i=0; i<mat->rmap->n; i++) {
1257     for (j=B->i[i]; j<B->i[i+1]; j++) {
1258       if ((col = garray[B->j[j]]) > cstart) break;
1259       column_indices[cnt++] = col;
1260     }
1261     for (k=A->i[i]; k<A->i[i+1]; k++) column_indices[cnt++] = A->j[k] + cstart;
1262     for (; j<B->i[i+1]; j++) column_indices[cnt++] = garray[B->j[j]];
1263   }
1264   if (cnt != A->nz + B->nz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: cnt = %D nz = %D",cnt,A->nz+B->nz);
1265 
1266   /* store the column indices to the file */
1267   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1268   if (!rank) {
1269     MPI_Status status;
1270     ierr = PetscBinaryWrite(fd,column_indices,nz,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1271     for (i=1; i<size; i++) {
1272       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1273       ierr = MPI_Recv(&rnz,1,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat),&status);CHKERRQ(ierr);
1274       if (rnz > nzmax) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: nz = %D nzmax = %D",nz,nzmax);
1275       ierr = MPIULong_Recv(column_indices,rnz,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1276       ierr = PetscBinaryWrite(fd,column_indices,rnz,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1277     }
1278     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1279   } else {
1280     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1281     ierr = MPI_Send(&nz,1,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1282     ierr = MPIULong_Send(column_indices,nz,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1283     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1284   }
1285   ierr = PetscFree(column_indices);CHKERRQ(ierr);
1286 
1287   /* load up the local column values */
1288   ierr = PetscMalloc1(nzmax+1,&column_values);CHKERRQ(ierr);
1289   cnt  = 0;
1290   for (i=0; i<mat->rmap->n; i++) {
1291     for (j=B->i[i]; j<B->i[i+1]; j++) {
1292       if (garray[B->j[j]] > cstart) break;
1293       column_values[cnt++] = B->a[j];
1294     }
1295     for (k=A->i[i]; k<A->i[i+1]; k++) column_values[cnt++] = A->a[k];
1296     for (; j<B->i[i+1]; j++) column_values[cnt++] = B->a[j];
1297   }
1298   if (cnt != A->nz + B->nz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Internal PETSc error: cnt = %D nz = %D",cnt,A->nz+B->nz);
1299 
1300   /* store the column values to the file */
1301   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1302   if (!rank) {
1303     MPI_Status status;
1304     ierr = PetscBinaryWrite(fd,column_values,nz,PETSC_SCALAR,PETSC_TRUE);CHKERRQ(ierr);
1305     for (i=1; i<size; i++) {
1306       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1307       ierr = MPI_Recv(&rnz,1,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat),&status);CHKERRQ(ierr);
1308       if (rnz > nzmax) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: nz = %D nzmax = %D",nz,nzmax);
1309       ierr = MPIULong_Recv(column_values,rnz,MPIU_SCALAR,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1310       ierr = PetscBinaryWrite(fd,column_values,rnz,PETSC_SCALAR,PETSC_TRUE);CHKERRQ(ierr);
1311     }
1312     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1313   } else {
1314     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1315     ierr = MPI_Send(&nz,1,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1316     ierr = MPIULong_Send(column_values,nz,MPIU_SCALAR,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1317     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1318   }
1319   ierr = PetscFree(column_values);CHKERRQ(ierr);
1320 
1321   ierr = PetscViewerBinaryGetInfoPointer(viewer,&file);CHKERRQ(ierr);
1322   if (file) fprintf(file,"-matload_block_size %d\n",(int)PetscAbs(mat->rmap->bs));
1323   PetscFunctionReturn(0);
1324 }
1325 
1326 #include <petscdraw.h>
1327 #undef __FUNCT__
1328 #define __FUNCT__ "MatView_MPIAIJ_ASCIIorDraworSocket"
1329 PetscErrorCode MatView_MPIAIJ_ASCIIorDraworSocket(Mat mat,PetscViewer viewer)
1330 {
1331   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)mat->data;
1332   PetscErrorCode    ierr;
1333   PetscMPIInt       rank = aij->rank,size = aij->size;
1334   PetscBool         isdraw,iascii,isbinary;
1335   PetscViewer       sviewer;
1336   PetscViewerFormat format;
1337 
1338   PetscFunctionBegin;
1339   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1340   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1341   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1342   if (iascii) {
1343     ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
1344     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
1345       MatInfo   info;
1346       PetscBool inodes;
1347 
1348       ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
1349       ierr = MatGetInfo(mat,MAT_LOCAL,&info);CHKERRQ(ierr);
1350       ierr = MatInodeGetInodeSizes(aij->A,NULL,(PetscInt**)&inodes,NULL);CHKERRQ(ierr);
1351       ierr = PetscViewerASCIISynchronizedAllow(viewer,PETSC_TRUE);CHKERRQ(ierr);
1352       if (!inodes) {
1353         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %D nz %D nz alloced %D mem %D, not using I-node routines\n",
1354                                                   rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
1355       } else {
1356         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %D nz %D nz alloced %D mem %D, using I-node routines\n",
1357                                                   rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
1358       }
1359       ierr = MatGetInfo(aij->A,MAT_LOCAL,&info);CHKERRQ(ierr);
1360       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] on-diagonal part: nz %D \n",rank,(PetscInt)info.nz_used);CHKERRQ(ierr);
1361       ierr = MatGetInfo(aij->B,MAT_LOCAL,&info);CHKERRQ(ierr);
1362       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] off-diagonal part: nz %D \n",rank,(PetscInt)info.nz_used);CHKERRQ(ierr);
1363       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1364       ierr = PetscViewerASCIISynchronizedAllow(viewer,PETSC_FALSE);CHKERRQ(ierr);
1365       ierr = PetscViewerASCIIPrintf(viewer,"Information on VecScatter used in matrix-vector product: \n");CHKERRQ(ierr);
1366       ierr = VecScatterView(aij->Mvctx,viewer);CHKERRQ(ierr);
1367       PetscFunctionReturn(0);
1368     } else if (format == PETSC_VIEWER_ASCII_INFO) {
1369       PetscInt inodecount,inodelimit,*inodes;
1370       ierr = MatInodeGetInodeSizes(aij->A,&inodecount,&inodes,&inodelimit);CHKERRQ(ierr);
1371       if (inodes) {
1372         ierr = PetscViewerASCIIPrintf(viewer,"using I-node (on process 0) routines: found %D nodes, limit used is %D\n",inodecount,inodelimit);CHKERRQ(ierr);
1373       } else {
1374         ierr = PetscViewerASCIIPrintf(viewer,"not using I-node (on process 0) routines\n");CHKERRQ(ierr);
1375       }
1376       PetscFunctionReturn(0);
1377     } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO) {
1378       PetscFunctionReturn(0);
1379     }
1380   } else if (isbinary) {
1381     if (size == 1) {
1382       ierr = PetscObjectSetName((PetscObject)aij->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1383       ierr = MatView(aij->A,viewer);CHKERRQ(ierr);
1384     } else {
1385       ierr = MatView_MPIAIJ_Binary(mat,viewer);CHKERRQ(ierr);
1386     }
1387     PetscFunctionReturn(0);
1388   } else if (isdraw) {
1389     PetscDraw draw;
1390     PetscBool isnull;
1391     ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
1392     ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr); if (isnull) PetscFunctionReturn(0);
1393   }
1394 
1395   {
1396     /* assemble the entire matrix onto first processor. */
1397     Mat        A;
1398     Mat_SeqAIJ *Aloc;
1399     PetscInt   M = mat->rmap->N,N = mat->cmap->N,m,*ai,*aj,row,*cols,i,*ct;
1400     MatScalar  *a;
1401     const char *matname;
1402 
1403     ierr = MatCreate(PetscObjectComm((PetscObject)mat),&A);CHKERRQ(ierr);
1404     if (!rank) {
1405       ierr = MatSetSizes(A,M,N,M,N);CHKERRQ(ierr);
1406     } else {
1407       ierr = MatSetSizes(A,0,0,M,N);CHKERRQ(ierr);
1408     }
1409     /* This is just a temporary matrix, so explicitly using MATMPIAIJ is probably best */
1410     ierr = MatSetType(A,MATMPIAIJ);CHKERRQ(ierr);
1411     ierr = MatMPIAIJSetPreallocation(A,0,NULL,0,NULL);CHKERRQ(ierr);
1412     ierr = MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
1413     ierr = PetscLogObjectParent((PetscObject)mat,(PetscObject)A);CHKERRQ(ierr);
1414 
1415     /* copy over the A part */
1416     Aloc = (Mat_SeqAIJ*)aij->A->data;
1417     m    = aij->A->rmap->n; ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
1418     row  = mat->rmap->rstart;
1419     for (i=0; i<ai[m]; i++) aj[i] += mat->cmap->rstart;
1420     for (i=0; i<m; i++) {
1421       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],aj,a,INSERT_VALUES);CHKERRQ(ierr);
1422       row++;
1423       a += ai[i+1]-ai[i]; aj += ai[i+1]-ai[i];
1424     }
1425     aj = Aloc->j;
1426     for (i=0; i<ai[m]; i++) aj[i] -= mat->cmap->rstart;
1427 
1428     /* copy over the B part */
1429     Aloc = (Mat_SeqAIJ*)aij->B->data;
1430     m    = aij->B->rmap->n;  ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
1431     row  = mat->rmap->rstart;
1432     ierr = PetscMalloc1(ai[m]+1,&cols);CHKERRQ(ierr);
1433     ct   = cols;
1434     for (i=0; i<ai[m]; i++) cols[i] = aij->garray[aj[i]];
1435     for (i=0; i<m; i++) {
1436       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],cols,a,INSERT_VALUES);CHKERRQ(ierr);
1437       row++;
1438       a += ai[i+1]-ai[i]; cols += ai[i+1]-ai[i];
1439     }
1440     ierr = PetscFree(ct);CHKERRQ(ierr);
1441     ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1442     ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1443     /*
1444        Everyone has to call to draw the matrix since the graphics waits are
1445        synchronized across all processors that share the PetscDraw object
1446     */
1447     ierr = PetscViewerGetSingleton(viewer,&sviewer);CHKERRQ(ierr);
1448     ierr = PetscObjectGetName((PetscObject)mat,&matname);CHKERRQ(ierr);
1449     if (!rank) {
1450       ierr = PetscObjectSetName((PetscObject)((Mat_MPIAIJ*)(A->data))->A,matname);CHKERRQ(ierr);
1451       ierr = MatView_SeqAIJ(((Mat_MPIAIJ*)(A->data))->A,sviewer);CHKERRQ(ierr);
1452     }
1453     ierr = PetscViewerRestoreSingleton(viewer,&sviewer);CHKERRQ(ierr);
1454     ierr = MatDestroy(&A);CHKERRQ(ierr);
1455   }
1456   PetscFunctionReturn(0);
1457 }
1458 
1459 #undef __FUNCT__
1460 #define __FUNCT__ "MatView_MPIAIJ"
1461 PetscErrorCode MatView_MPIAIJ(Mat mat,PetscViewer viewer)
1462 {
1463   PetscErrorCode ierr;
1464   PetscBool      iascii,isdraw,issocket,isbinary;
1465 
1466   PetscFunctionBegin;
1467   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1468   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1469   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1470   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSOCKET,&issocket);CHKERRQ(ierr);
1471   if (iascii || isdraw || isbinary || issocket) {
1472     ierr = MatView_MPIAIJ_ASCIIorDraworSocket(mat,viewer);CHKERRQ(ierr);
1473   }
1474   PetscFunctionReturn(0);
1475 }
1476 
1477 #undef __FUNCT__
1478 #define __FUNCT__ "MatSOR_MPIAIJ"
1479 PetscErrorCode MatSOR_MPIAIJ(Mat matin,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
1480 {
1481   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1482   PetscErrorCode ierr;
1483   Vec            bb1 = 0;
1484   PetscBool      hasop;
1485 
1486   PetscFunctionBegin;
1487   if (flag == SOR_APPLY_UPPER) {
1488     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1489     PetscFunctionReturn(0);
1490   }
1491 
1492   if (its > 1 || ~flag & SOR_ZERO_INITIAL_GUESS || flag & SOR_EISENSTAT) {
1493     ierr = VecDuplicate(bb,&bb1);CHKERRQ(ierr);
1494   }
1495 
1496   if ((flag & SOR_LOCAL_SYMMETRIC_SWEEP) == SOR_LOCAL_SYMMETRIC_SWEEP) {
1497     if (flag & SOR_ZERO_INITIAL_GUESS) {
1498       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1499       its--;
1500     }
1501 
1502     while (its--) {
1503       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1504       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1505 
1506       /* update rhs: bb1 = bb - B*x */
1507       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1508       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1509 
1510       /* local sweep */
1511       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_SYMMETRIC_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1512     }
1513   } else if (flag & SOR_LOCAL_FORWARD_SWEEP) {
1514     if (flag & SOR_ZERO_INITIAL_GUESS) {
1515       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1516       its--;
1517     }
1518     while (its--) {
1519       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1520       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1521 
1522       /* update rhs: bb1 = bb - B*x */
1523       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1524       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1525 
1526       /* local sweep */
1527       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_FORWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1528     }
1529   } else if (flag & SOR_LOCAL_BACKWARD_SWEEP) {
1530     if (flag & SOR_ZERO_INITIAL_GUESS) {
1531       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1532       its--;
1533     }
1534     while (its--) {
1535       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1536       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1537 
1538       /* update rhs: bb1 = bb - B*x */
1539       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1540       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1541 
1542       /* local sweep */
1543       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_BACKWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1544     }
1545   } else if (flag & SOR_EISENSTAT) {
1546     Vec xx1;
1547 
1548     ierr = VecDuplicate(bb,&xx1);CHKERRQ(ierr);
1549     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_BACKWARD_SWEEP),fshift,lits,1,xx);CHKERRQ(ierr);
1550 
1551     ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1552     ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1553     if (!mat->diag) {
1554       ierr = MatCreateVecs(matin,&mat->diag,NULL);CHKERRQ(ierr);
1555       ierr = MatGetDiagonal(matin,mat->diag);CHKERRQ(ierr);
1556     }
1557     ierr = MatHasOperation(matin,MATOP_MULT_DIAGONAL_BLOCK,&hasop);CHKERRQ(ierr);
1558     if (hasop) {
1559       ierr = MatMultDiagonalBlock(matin,xx,bb1);CHKERRQ(ierr);
1560     } else {
1561       ierr = VecPointwiseMult(bb1,mat->diag,xx);CHKERRQ(ierr);
1562     }
1563     ierr = VecAYPX(bb1,(omega-2.0)/omega,bb);CHKERRQ(ierr);
1564 
1565     ierr = MatMultAdd(mat->B,mat->lvec,bb1,bb1);CHKERRQ(ierr);
1566 
1567     /* local sweep */
1568     ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_FORWARD_SWEEP),fshift,lits,1,xx1);CHKERRQ(ierr);
1569     ierr = VecAXPY(xx,1.0,xx1);CHKERRQ(ierr);
1570     ierr = VecDestroy(&xx1);CHKERRQ(ierr);
1571   } else SETERRQ(PetscObjectComm((PetscObject)matin),PETSC_ERR_SUP,"Parallel SOR not supported");
1572 
1573   ierr = VecDestroy(&bb1);CHKERRQ(ierr);
1574   PetscFunctionReturn(0);
1575 }
1576 
1577 #undef __FUNCT__
1578 #define __FUNCT__ "MatPermute_MPIAIJ"
1579 PetscErrorCode MatPermute_MPIAIJ(Mat A,IS rowp,IS colp,Mat *B)
1580 {
1581   Mat            aA,aB,Aperm;
1582   const PetscInt *rwant,*cwant,*gcols,*ai,*bi,*aj,*bj;
1583   PetscScalar    *aa,*ba;
1584   PetscInt       i,j,m,n,ng,anz,bnz,*dnnz,*onnz,*tdnnz,*tonnz,*rdest,*cdest,*work,*gcdest;
1585   PetscSF        rowsf,sf;
1586   IS             parcolp = NULL;
1587   PetscBool      done;
1588   PetscErrorCode ierr;
1589 
1590   PetscFunctionBegin;
1591   ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
1592   ierr = ISGetIndices(rowp,&rwant);CHKERRQ(ierr);
1593   ierr = ISGetIndices(colp,&cwant);CHKERRQ(ierr);
1594   ierr = PetscMalloc3(PetscMax(m,n),&work,m,&rdest,n,&cdest);CHKERRQ(ierr);
1595 
1596   /* Invert row permutation to find out where my rows should go */
1597   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&rowsf);CHKERRQ(ierr);
1598   ierr = PetscSFSetGraphLayout(rowsf,A->rmap,A->rmap->n,NULL,PETSC_OWN_POINTER,rwant);CHKERRQ(ierr);
1599   ierr = PetscSFSetFromOptions(rowsf);CHKERRQ(ierr);
1600   for (i=0; i<m; i++) work[i] = A->rmap->rstart + i;
1601   ierr = PetscSFReduceBegin(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1602   ierr = PetscSFReduceEnd(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1603 
1604   /* Invert column permutation to find out where my columns should go */
1605   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1606   ierr = PetscSFSetGraphLayout(sf,A->cmap,A->cmap->n,NULL,PETSC_OWN_POINTER,cwant);CHKERRQ(ierr);
1607   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1608   for (i=0; i<n; i++) work[i] = A->cmap->rstart + i;
1609   ierr = PetscSFReduceBegin(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1610   ierr = PetscSFReduceEnd(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1611   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1612 
1613   ierr = ISRestoreIndices(rowp,&rwant);CHKERRQ(ierr);
1614   ierr = ISRestoreIndices(colp,&cwant);CHKERRQ(ierr);
1615   ierr = MatMPIAIJGetSeqAIJ(A,&aA,&aB,&gcols);CHKERRQ(ierr);
1616 
1617   /* Find out where my gcols should go */
1618   ierr = MatGetSize(aB,NULL,&ng);CHKERRQ(ierr);
1619   ierr = PetscMalloc1(ng,&gcdest);CHKERRQ(ierr);
1620   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1621   ierr = PetscSFSetGraphLayout(sf,A->cmap,ng,NULL,PETSC_OWN_POINTER,gcols);CHKERRQ(ierr);
1622   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1623   ierr = PetscSFBcastBegin(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1624   ierr = PetscSFBcastEnd(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1625   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1626 
1627   ierr = PetscCalloc4(m,&dnnz,m,&onnz,m,&tdnnz,m,&tonnz);CHKERRQ(ierr);
1628   ierr = MatGetRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1629   ierr = MatGetRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1630   for (i=0; i<m; i++) {
1631     PetscInt row = rdest[i],rowner;
1632     ierr = PetscLayoutFindOwner(A->rmap,row,&rowner);CHKERRQ(ierr);
1633     for (j=ai[i]; j<ai[i+1]; j++) {
1634       PetscInt cowner,col = cdest[aj[j]];
1635       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr); /* Could build an index for the columns to eliminate this search */
1636       if (rowner == cowner) dnnz[i]++;
1637       else onnz[i]++;
1638     }
1639     for (j=bi[i]; j<bi[i+1]; j++) {
1640       PetscInt cowner,col = gcdest[bj[j]];
1641       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr);
1642       if (rowner == cowner) dnnz[i]++;
1643       else onnz[i]++;
1644     }
1645   }
1646   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1647   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1648   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1649   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1650   ierr = PetscSFDestroy(&rowsf);CHKERRQ(ierr);
1651 
1652   ierr = MatCreateAIJ(PetscObjectComm((PetscObject)A),A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N,0,tdnnz,0,tonnz,&Aperm);CHKERRQ(ierr);
1653   ierr = MatSeqAIJGetArray(aA,&aa);CHKERRQ(ierr);
1654   ierr = MatSeqAIJGetArray(aB,&ba);CHKERRQ(ierr);
1655   for (i=0; i<m; i++) {
1656     PetscInt *acols = dnnz,*bcols = onnz; /* Repurpose now-unneeded arrays */
1657     PetscInt j0,rowlen;
1658     rowlen = ai[i+1] - ai[i];
1659     for (j0=j=0; j<rowlen; j0=j) { /* rowlen could be larger than number of rows m, so sum in batches */
1660       for ( ; j<PetscMin(rowlen,j0+m); j++) acols[j-j0] = cdest[aj[ai[i]+j]];
1661       ierr = MatSetValues(Aperm,1,&rdest[i],j-j0,acols,aa+ai[i]+j0,INSERT_VALUES);CHKERRQ(ierr);
1662     }
1663     rowlen = bi[i+1] - bi[i];
1664     for (j0=j=0; j<rowlen; j0=j) {
1665       for ( ; j<PetscMin(rowlen,j0+m); j++) bcols[j-j0] = gcdest[bj[bi[i]+j]];
1666       ierr = MatSetValues(Aperm,1,&rdest[i],j-j0,bcols,ba+bi[i]+j0,INSERT_VALUES);CHKERRQ(ierr);
1667     }
1668   }
1669   ierr = MatAssemblyBegin(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1670   ierr = MatAssemblyEnd(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1671   ierr = MatRestoreRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1672   ierr = MatRestoreRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1673   ierr = MatSeqAIJRestoreArray(aA,&aa);CHKERRQ(ierr);
1674   ierr = MatSeqAIJRestoreArray(aB,&ba);CHKERRQ(ierr);
1675   ierr = PetscFree4(dnnz,onnz,tdnnz,tonnz);CHKERRQ(ierr);
1676   ierr = PetscFree3(work,rdest,cdest);CHKERRQ(ierr);
1677   ierr = PetscFree(gcdest);CHKERRQ(ierr);
1678   if (parcolp) {ierr = ISDestroy(&colp);CHKERRQ(ierr);}
1679   *B = Aperm;
1680   PetscFunctionReturn(0);
1681 }
1682 
1683 #undef __FUNCT__
1684 #define __FUNCT__ "MatGetInfo_MPIAIJ"
1685 PetscErrorCode MatGetInfo_MPIAIJ(Mat matin,MatInfoType flag,MatInfo *info)
1686 {
1687   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1688   Mat            A    = mat->A,B = mat->B;
1689   PetscErrorCode ierr;
1690   PetscReal      isend[5],irecv[5];
1691 
1692   PetscFunctionBegin;
1693   info->block_size = 1.0;
1694   ierr             = MatGetInfo(A,MAT_LOCAL,info);CHKERRQ(ierr);
1695 
1696   isend[0] = info->nz_used; isend[1] = info->nz_allocated; isend[2] = info->nz_unneeded;
1697   isend[3] = info->memory;  isend[4] = info->mallocs;
1698 
1699   ierr = MatGetInfo(B,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   if (flag == MAT_LOCAL) {
1704     info->nz_used      = isend[0];
1705     info->nz_allocated = isend[1];
1706     info->nz_unneeded  = isend[2];
1707     info->memory       = isend[3];
1708     info->mallocs      = isend[4];
1709   } else if (flag == MAT_GLOBAL_MAX) {
1710     ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1711 
1712     info->nz_used      = irecv[0];
1713     info->nz_allocated = irecv[1];
1714     info->nz_unneeded  = irecv[2];
1715     info->memory       = irecv[3];
1716     info->mallocs      = irecv[4];
1717   } else if (flag == MAT_GLOBAL_SUM) {
1718     ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1719 
1720     info->nz_used      = irecv[0];
1721     info->nz_allocated = irecv[1];
1722     info->nz_unneeded  = irecv[2];
1723     info->memory       = irecv[3];
1724     info->mallocs      = irecv[4];
1725   }
1726   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
1727   info->fill_ratio_needed = 0;
1728   info->factor_mallocs    = 0;
1729   PetscFunctionReturn(0);
1730 }
1731 
1732 #undef __FUNCT__
1733 #define __FUNCT__ "MatSetOption_MPIAIJ"
1734 PetscErrorCode MatSetOption_MPIAIJ(Mat A,MatOption op,PetscBool flg)
1735 {
1736   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1737   PetscErrorCode ierr;
1738 
1739   PetscFunctionBegin;
1740   switch (op) {
1741   case MAT_NEW_NONZERO_LOCATIONS:
1742   case MAT_NEW_NONZERO_ALLOCATION_ERR:
1743   case MAT_UNUSED_NONZERO_LOCATION_ERR:
1744   case MAT_KEEP_NONZERO_PATTERN:
1745   case MAT_NEW_NONZERO_LOCATION_ERR:
1746   case MAT_USE_INODES:
1747   case MAT_IGNORE_ZERO_ENTRIES:
1748     MatCheckPreallocated(A,1);
1749     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1750     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1751     break;
1752   case MAT_ROW_ORIENTED:
1753     a->roworiented = flg;
1754 
1755     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1756     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1757     break;
1758   case MAT_NEW_DIAGONALS:
1759     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
1760     break;
1761   case MAT_IGNORE_OFF_PROC_ENTRIES:
1762     a->donotstash = flg;
1763     break;
1764   case MAT_SPD:
1765     A->spd_set = PETSC_TRUE;
1766     A->spd     = flg;
1767     if (flg) {
1768       A->symmetric                  = PETSC_TRUE;
1769       A->structurally_symmetric     = PETSC_TRUE;
1770       A->symmetric_set              = PETSC_TRUE;
1771       A->structurally_symmetric_set = PETSC_TRUE;
1772     }
1773     break;
1774   case MAT_SYMMETRIC:
1775     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1776     break;
1777   case MAT_STRUCTURALLY_SYMMETRIC:
1778     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1779     break;
1780   case MAT_HERMITIAN:
1781     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1782     break;
1783   case MAT_SYMMETRY_ETERNAL:
1784     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1785     break;
1786   default:
1787     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %d",op);
1788   }
1789   PetscFunctionReturn(0);
1790 }
1791 
1792 #undef __FUNCT__
1793 #define __FUNCT__ "MatGetRow_MPIAIJ"
1794 PetscErrorCode MatGetRow_MPIAIJ(Mat matin,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1795 {
1796   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1797   PetscScalar    *vworkA,*vworkB,**pvA,**pvB,*v_p;
1798   PetscErrorCode ierr;
1799   PetscInt       i,*cworkA,*cworkB,**pcA,**pcB,cstart = matin->cmap->rstart;
1800   PetscInt       nztot,nzA,nzB,lrow,rstart = matin->rmap->rstart,rend = matin->rmap->rend;
1801   PetscInt       *cmap,*idx_p;
1802 
1803   PetscFunctionBegin;
1804   if (mat->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Already active");
1805   mat->getrowactive = PETSC_TRUE;
1806 
1807   if (!mat->rowvalues && (idx || v)) {
1808     /*
1809         allocate enough space to hold information from the longest row.
1810     */
1811     Mat_SeqAIJ *Aa = (Mat_SeqAIJ*)mat->A->data,*Ba = (Mat_SeqAIJ*)mat->B->data;
1812     PetscInt   max = 1,tmp;
1813     for (i=0; i<matin->rmap->n; i++) {
1814       tmp = Aa->i[i+1] - Aa->i[i] + Ba->i[i+1] - Ba->i[i];
1815       if (max < tmp) max = tmp;
1816     }
1817     ierr = PetscMalloc2(max,&mat->rowvalues,max,&mat->rowindices);CHKERRQ(ierr);
1818   }
1819 
1820   if (row < rstart || row >= rend) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Only local rows");
1821   lrow = row - rstart;
1822 
1823   pvA = &vworkA; pcA = &cworkA; pvB = &vworkB; pcB = &cworkB;
1824   if (!v)   {pvA = 0; pvB = 0;}
1825   if (!idx) {pcA = 0; if (!v) pcB = 0;}
1826   ierr  = (*mat->A->ops->getrow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1827   ierr  = (*mat->B->ops->getrow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1828   nztot = nzA + nzB;
1829 
1830   cmap = mat->garray;
1831   if (v  || idx) {
1832     if (nztot) {
1833       /* Sort by increasing column numbers, assuming A and B already sorted */
1834       PetscInt imark = -1;
1835       if (v) {
1836         *v = v_p = mat->rowvalues;
1837         for (i=0; i<nzB; i++) {
1838           if (cmap[cworkB[i]] < cstart) v_p[i] = vworkB[i];
1839           else break;
1840         }
1841         imark = i;
1842         for (i=0; i<nzA; i++)     v_p[imark+i] = vworkA[i];
1843         for (i=imark; i<nzB; i++) v_p[nzA+i]   = vworkB[i];
1844       }
1845       if (idx) {
1846         *idx = idx_p = mat->rowindices;
1847         if (imark > -1) {
1848           for (i=0; i<imark; i++) {
1849             idx_p[i] = cmap[cworkB[i]];
1850           }
1851         } else {
1852           for (i=0; i<nzB; i++) {
1853             if (cmap[cworkB[i]] < cstart) idx_p[i] = cmap[cworkB[i]];
1854             else break;
1855           }
1856           imark = i;
1857         }
1858         for (i=0; i<nzA; i++)     idx_p[imark+i] = cstart + cworkA[i];
1859         for (i=imark; i<nzB; i++) idx_p[nzA+i]   = cmap[cworkB[i]];
1860       }
1861     } else {
1862       if (idx) *idx = 0;
1863       if (v)   *v   = 0;
1864     }
1865   }
1866   *nz  = nztot;
1867   ierr = (*mat->A->ops->restorerow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1868   ierr = (*mat->B->ops->restorerow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1869   PetscFunctionReturn(0);
1870 }
1871 
1872 #undef __FUNCT__
1873 #define __FUNCT__ "MatRestoreRow_MPIAIJ"
1874 PetscErrorCode MatRestoreRow_MPIAIJ(Mat mat,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1875 {
1876   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1877 
1878   PetscFunctionBegin;
1879   if (!aij->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"MatGetRow() must be called first");
1880   aij->getrowactive = PETSC_FALSE;
1881   PetscFunctionReturn(0);
1882 }
1883 
1884 #undef __FUNCT__
1885 #define __FUNCT__ "MatNorm_MPIAIJ"
1886 PetscErrorCode MatNorm_MPIAIJ(Mat mat,NormType type,PetscReal *norm)
1887 {
1888   Mat_MPIAIJ     *aij  = (Mat_MPIAIJ*)mat->data;
1889   Mat_SeqAIJ     *amat = (Mat_SeqAIJ*)aij->A->data,*bmat = (Mat_SeqAIJ*)aij->B->data;
1890   PetscErrorCode ierr;
1891   PetscInt       i,j,cstart = mat->cmap->rstart;
1892   PetscReal      sum = 0.0;
1893   MatScalar      *v;
1894 
1895   PetscFunctionBegin;
1896   if (aij->size == 1) {
1897     ierr =  MatNorm(aij->A,type,norm);CHKERRQ(ierr);
1898   } else {
1899     if (type == NORM_FROBENIUS) {
1900       v = amat->a;
1901       for (i=0; i<amat->nz; i++) {
1902         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1903       }
1904       v = bmat->a;
1905       for (i=0; i<bmat->nz; i++) {
1906         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1907       }
1908       ierr  = MPI_Allreduce(&sum,norm,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1909       *norm = PetscSqrtReal(*norm);
1910     } else if (type == NORM_1) { /* max column norm */
1911       PetscReal *tmp,*tmp2;
1912       PetscInt  *jj,*garray = aij->garray;
1913       ierr  = PetscCalloc1(mat->cmap->N+1,&tmp);CHKERRQ(ierr);
1914       ierr  = PetscMalloc1(mat->cmap->N+1,&tmp2);CHKERRQ(ierr);
1915       *norm = 0.0;
1916       v     = amat->a; jj = amat->j;
1917       for (j=0; j<amat->nz; j++) {
1918         tmp[cstart + *jj++] += PetscAbsScalar(*v);  v++;
1919       }
1920       v = bmat->a; jj = bmat->j;
1921       for (j=0; j<bmat->nz; j++) {
1922         tmp[garray[*jj++]] += PetscAbsScalar(*v); v++;
1923       }
1924       ierr = MPI_Allreduce(tmp,tmp2,mat->cmap->N,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1925       for (j=0; j<mat->cmap->N; j++) {
1926         if (tmp2[j] > *norm) *norm = tmp2[j];
1927       }
1928       ierr = PetscFree(tmp);CHKERRQ(ierr);
1929       ierr = PetscFree(tmp2);CHKERRQ(ierr);
1930     } else if (type == NORM_INFINITY) { /* max row norm */
1931       PetscReal ntemp = 0.0;
1932       for (j=0; j<aij->A->rmap->n; j++) {
1933         v   = amat->a + amat->i[j];
1934         sum = 0.0;
1935         for (i=0; i<amat->i[j+1]-amat->i[j]; i++) {
1936           sum += PetscAbsScalar(*v); v++;
1937         }
1938         v = bmat->a + bmat->i[j];
1939         for (i=0; i<bmat->i[j+1]-bmat->i[j]; i++) {
1940           sum += PetscAbsScalar(*v); v++;
1941         }
1942         if (sum > ntemp) ntemp = sum;
1943       }
1944       ierr = MPI_Allreduce(&ntemp,norm,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1945     } else SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"No support for two norm");
1946   }
1947   PetscFunctionReturn(0);
1948 }
1949 
1950 #undef __FUNCT__
1951 #define __FUNCT__ "MatTranspose_MPIAIJ"
1952 PetscErrorCode MatTranspose_MPIAIJ(Mat A,MatReuse reuse,Mat *matout)
1953 {
1954   Mat_MPIAIJ     *a   = (Mat_MPIAIJ*)A->data;
1955   Mat_SeqAIJ     *Aloc=(Mat_SeqAIJ*)a->A->data,*Bloc=(Mat_SeqAIJ*)a->B->data;
1956   PetscErrorCode ierr;
1957   PetscInt       M      = A->rmap->N,N = A->cmap->N,ma,na,mb,nb,*ai,*aj,*bi,*bj,row,*cols,*cols_tmp,i;
1958   PetscInt       cstart = A->cmap->rstart,ncol;
1959   Mat            B;
1960   MatScalar      *array;
1961 
1962   PetscFunctionBegin;
1963   if (reuse == MAT_REUSE_MATRIX && A == *matout && M != N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Square matrix only for in-place");
1964 
1965   ma = A->rmap->n; na = A->cmap->n; mb = a->B->rmap->n; nb = a->B->cmap->n;
1966   ai = Aloc->i; aj = Aloc->j;
1967   bi = Bloc->i; bj = Bloc->j;
1968   if (reuse == MAT_INITIAL_MATRIX || *matout == A) {
1969     PetscInt             *d_nnz,*g_nnz,*o_nnz;
1970     PetscSFNode          *oloc;
1971     PETSC_UNUSED PetscSF sf;
1972 
1973     ierr = PetscMalloc4(na,&d_nnz,na,&o_nnz,nb,&g_nnz,nb,&oloc);CHKERRQ(ierr);
1974     /* compute d_nnz for preallocation */
1975     ierr = PetscMemzero(d_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1976     for (i=0; i<ai[ma]; i++) {
1977       d_nnz[aj[i]]++;
1978       aj[i] += cstart; /* global col index to be used by MatSetValues() */
1979     }
1980     /* compute local off-diagonal contributions */
1981     ierr = PetscMemzero(g_nnz,nb*sizeof(PetscInt));CHKERRQ(ierr);
1982     for (i=0; i<bi[ma]; i++) g_nnz[bj[i]]++;
1983     /* map those to global */
1984     ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1985     ierr = PetscSFSetGraphLayout(sf,A->cmap,nb,NULL,PETSC_USE_POINTER,a->garray);CHKERRQ(ierr);
1986     ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1987     ierr = PetscMemzero(o_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1988     ierr = PetscSFReduceBegin(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
1989     ierr = PetscSFReduceEnd(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
1990     ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1991 
1992     ierr = MatCreate(PetscObjectComm((PetscObject)A),&B);CHKERRQ(ierr);
1993     ierr = MatSetSizes(B,A->cmap->n,A->rmap->n,N,M);CHKERRQ(ierr);
1994     ierr = MatSetBlockSizes(B,PetscAbs(A->cmap->bs),PetscAbs(A->rmap->bs));CHKERRQ(ierr);
1995     ierr = MatSetType(B,((PetscObject)A)->type_name);CHKERRQ(ierr);
1996     ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
1997     ierr = PetscFree4(d_nnz,o_nnz,g_nnz,oloc);CHKERRQ(ierr);
1998   } else {
1999     B    = *matout;
2000     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
2001     for (i=0; i<ai[ma]; i++) aj[i] += cstart; /* global col index to be used by MatSetValues() */
2002   }
2003 
2004   /* copy over the A part */
2005   array = Aloc->a;
2006   row   = A->rmap->rstart;
2007   for (i=0; i<ma; i++) {
2008     ncol = ai[i+1]-ai[i];
2009     ierr = MatSetValues(B,ncol,aj,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
2010     row++;
2011     array += ncol; aj += ncol;
2012   }
2013   aj = Aloc->j;
2014   for (i=0; i<ai[ma]; i++) aj[i] -= cstart; /* resume local col index */
2015 
2016   /* copy over the B part */
2017   ierr  = PetscCalloc1(bi[mb],&cols);CHKERRQ(ierr);
2018   array = Bloc->a;
2019   row   = A->rmap->rstart;
2020   for (i=0; i<bi[mb]; i++) cols[i] = a->garray[bj[i]];
2021   cols_tmp = cols;
2022   for (i=0; i<mb; i++) {
2023     ncol = bi[i+1]-bi[i];
2024     ierr = MatSetValues(B,ncol,cols_tmp,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
2025     row++;
2026     array += ncol; cols_tmp += ncol;
2027   }
2028   ierr = PetscFree(cols);CHKERRQ(ierr);
2029 
2030   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2031   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2032   if (reuse == MAT_INITIAL_MATRIX || *matout != A) {
2033     *matout = B;
2034   } else {
2035     ierr = MatHeaderMerge(A,B);CHKERRQ(ierr);
2036   }
2037   PetscFunctionReturn(0);
2038 }
2039 
2040 #undef __FUNCT__
2041 #define __FUNCT__ "MatDiagonalScale_MPIAIJ"
2042 PetscErrorCode MatDiagonalScale_MPIAIJ(Mat mat,Vec ll,Vec rr)
2043 {
2044   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2045   Mat            a    = aij->A,b = aij->B;
2046   PetscErrorCode ierr;
2047   PetscInt       s1,s2,s3;
2048 
2049   PetscFunctionBegin;
2050   ierr = MatGetLocalSize(mat,&s2,&s3);CHKERRQ(ierr);
2051   if (rr) {
2052     ierr = VecGetLocalSize(rr,&s1);CHKERRQ(ierr);
2053     if (s1!=s3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"right vector non-conforming local size");
2054     /* Overlap communication with computation. */
2055     ierr = VecScatterBegin(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2056   }
2057   if (ll) {
2058     ierr = VecGetLocalSize(ll,&s1);CHKERRQ(ierr);
2059     if (s1!=s2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"left vector non-conforming local size");
2060     ierr = (*b->ops->diagonalscale)(b,ll,0);CHKERRQ(ierr);
2061   }
2062   /* scale  the diagonal block */
2063   ierr = (*a->ops->diagonalscale)(a,ll,rr);CHKERRQ(ierr);
2064 
2065   if (rr) {
2066     /* Do a scatter end and then right scale the off-diagonal block */
2067     ierr = VecScatterEnd(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2068     ierr = (*b->ops->diagonalscale)(b,0,aij->lvec);CHKERRQ(ierr);
2069   }
2070   PetscFunctionReturn(0);
2071 }
2072 
2073 #undef __FUNCT__
2074 #define __FUNCT__ "MatSetUnfactored_MPIAIJ"
2075 PetscErrorCode MatSetUnfactored_MPIAIJ(Mat A)
2076 {
2077   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2078   PetscErrorCode ierr;
2079 
2080   PetscFunctionBegin;
2081   ierr = MatSetUnfactored(a->A);CHKERRQ(ierr);
2082   PetscFunctionReturn(0);
2083 }
2084 
2085 #undef __FUNCT__
2086 #define __FUNCT__ "MatEqual_MPIAIJ"
2087 PetscErrorCode MatEqual_MPIAIJ(Mat A,Mat B,PetscBool  *flag)
2088 {
2089   Mat_MPIAIJ     *matB = (Mat_MPIAIJ*)B->data,*matA = (Mat_MPIAIJ*)A->data;
2090   Mat            a,b,c,d;
2091   PetscBool      flg;
2092   PetscErrorCode ierr;
2093 
2094   PetscFunctionBegin;
2095   a = matA->A; b = matA->B;
2096   c = matB->A; d = matB->B;
2097 
2098   ierr = MatEqual(a,c,&flg);CHKERRQ(ierr);
2099   if (flg) {
2100     ierr = MatEqual(b,d,&flg);CHKERRQ(ierr);
2101   }
2102   ierr = MPI_Allreduce(&flg,flag,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
2103   PetscFunctionReturn(0);
2104 }
2105 
2106 #undef __FUNCT__
2107 #define __FUNCT__ "MatCopy_MPIAIJ"
2108 PetscErrorCode MatCopy_MPIAIJ(Mat A,Mat B,MatStructure str)
2109 {
2110   PetscErrorCode ierr;
2111   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2112   Mat_MPIAIJ     *b = (Mat_MPIAIJ*)B->data;
2113 
2114   PetscFunctionBegin;
2115   /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
2116   if ((str != SAME_NONZERO_PATTERN) || (A->ops->copy != B->ops->copy)) {
2117     /* because of the column compression in the off-processor part of the matrix a->B,
2118        the number of columns in a->B and b->B may be different, hence we cannot call
2119        the MatCopy() directly on the two parts. If need be, we can provide a more
2120        efficient copy than the MatCopy_Basic() by first uncompressing the a->B matrices
2121        then copying the submatrices */
2122     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
2123   } else {
2124     ierr = MatCopy(a->A,b->A,str);CHKERRQ(ierr);
2125     ierr = MatCopy(a->B,b->B,str);CHKERRQ(ierr);
2126   }
2127   PetscFunctionReturn(0);
2128 }
2129 
2130 #undef __FUNCT__
2131 #define __FUNCT__ "MatSetUp_MPIAIJ"
2132 PetscErrorCode MatSetUp_MPIAIJ(Mat A)
2133 {
2134   PetscErrorCode ierr;
2135 
2136   PetscFunctionBegin;
2137   ierr =  MatMPIAIJSetPreallocation(A,PETSC_DEFAULT,0,PETSC_DEFAULT,0);CHKERRQ(ierr);
2138   PetscFunctionReturn(0);
2139 }
2140 
2141 /*
2142    Computes the number of nonzeros per row needed for preallocation when X and Y
2143    have different nonzero structure.
2144 */
2145 #undef __FUNCT__
2146 #define __FUNCT__ "MatAXPYGetPreallocation_MPIX_private"
2147 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)
2148 {
2149   PetscInt       i,j,k,nzx,nzy;
2150 
2151   PetscFunctionBegin;
2152   /* Set the number of nonzeros in the new matrix */
2153   for (i=0; i<m; i++) {
2154     const PetscInt *xjj = xj+xi[i],*yjj = yj+yi[i];
2155     nzx = xi[i+1] - xi[i];
2156     nzy = yi[i+1] - yi[i];
2157     nnz[i] = 0;
2158     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2159       for (; k<nzy && yltog[yjj[k]]<xltog[xjj[j]]; k++) nnz[i]++; /* Catch up to X */
2160       if (k<nzy && yltog[yjj[k]]==xltog[xjj[j]]) k++;             /* Skip duplicate */
2161       nnz[i]++;
2162     }
2163     for (; k<nzy; k++) nnz[i]++;
2164   }
2165   PetscFunctionReturn(0);
2166 }
2167 
2168 /* This is the same as MatAXPYGetPreallocation_SeqAIJ, except that the local-to-global map is provided */
2169 #undef __FUNCT__
2170 #define __FUNCT__ "MatAXPYGetPreallocation_MPIAIJ"
2171 static PetscErrorCode MatAXPYGetPreallocation_MPIAIJ(Mat Y,const PetscInt *yltog,Mat X,const PetscInt *xltog,PetscInt *nnz)
2172 {
2173   PetscErrorCode ierr;
2174   PetscInt       m = Y->rmap->N;
2175   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data;
2176   Mat_SeqAIJ     *y = (Mat_SeqAIJ*)Y->data;
2177 
2178   PetscFunctionBegin;
2179   ierr = MatAXPYGetPreallocation_MPIX_private(m,x->i,x->j,xltog,y->i,y->j,yltog,nnz);CHKERRQ(ierr);
2180   PetscFunctionReturn(0);
2181 }
2182 
2183 #undef __FUNCT__
2184 #define __FUNCT__ "MatAXPY_MPIAIJ"
2185 PetscErrorCode MatAXPY_MPIAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
2186 {
2187   PetscErrorCode ierr;
2188   Mat_MPIAIJ     *xx = (Mat_MPIAIJ*)X->data,*yy = (Mat_MPIAIJ*)Y->data;
2189   PetscBLASInt   bnz,one=1;
2190   Mat_SeqAIJ     *x,*y;
2191 
2192   PetscFunctionBegin;
2193   if (str == SAME_NONZERO_PATTERN) {
2194     PetscScalar alpha = a;
2195     x    = (Mat_SeqAIJ*)xx->A->data;
2196     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2197     y    = (Mat_SeqAIJ*)yy->A->data;
2198     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2199     x    = (Mat_SeqAIJ*)xx->B->data;
2200     y    = (Mat_SeqAIJ*)yy->B->data;
2201     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2202     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2203     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
2204   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
2205     ierr = MatAXPY_Basic(Y,a,X,str);CHKERRQ(ierr);
2206   } else {
2207     Mat      B;
2208     PetscInt *nnz_d,*nnz_o;
2209     ierr = PetscMalloc1(yy->A->rmap->N,&nnz_d);CHKERRQ(ierr);
2210     ierr = PetscMalloc1(yy->B->rmap->N,&nnz_o);CHKERRQ(ierr);
2211     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
2212     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
2213     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
2214     ierr = MatSetBlockSizesFromMats(B,Y,Y);CHKERRQ(ierr);
2215     ierr = MatSetType(B,MATMPIAIJ);CHKERRQ(ierr);
2216     ierr = MatAXPYGetPreallocation_SeqAIJ(yy->A,xx->A,nnz_d);CHKERRQ(ierr);
2217     ierr = MatAXPYGetPreallocation_MPIAIJ(yy->B,yy->garray,xx->B,xx->garray,nnz_o);CHKERRQ(ierr);
2218     ierr = MatMPIAIJSetPreallocation(B,0,nnz_d,0,nnz_o);CHKERRQ(ierr);
2219     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
2220     ierr = MatHeaderReplace(Y,B);CHKERRQ(ierr);
2221     ierr = PetscFree(nnz_d);CHKERRQ(ierr);
2222     ierr = PetscFree(nnz_o);CHKERRQ(ierr);
2223   }
2224   PetscFunctionReturn(0);
2225 }
2226 
2227 extern PetscErrorCode  MatConjugate_SeqAIJ(Mat);
2228 
2229 #undef __FUNCT__
2230 #define __FUNCT__ "MatConjugate_MPIAIJ"
2231 PetscErrorCode  MatConjugate_MPIAIJ(Mat mat)
2232 {
2233 #if defined(PETSC_USE_COMPLEX)
2234   PetscErrorCode ierr;
2235   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2236 
2237   PetscFunctionBegin;
2238   ierr = MatConjugate_SeqAIJ(aij->A);CHKERRQ(ierr);
2239   ierr = MatConjugate_SeqAIJ(aij->B);CHKERRQ(ierr);
2240 #else
2241   PetscFunctionBegin;
2242 #endif
2243   PetscFunctionReturn(0);
2244 }
2245 
2246 #undef __FUNCT__
2247 #define __FUNCT__ "MatRealPart_MPIAIJ"
2248 PetscErrorCode MatRealPart_MPIAIJ(Mat A)
2249 {
2250   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2251   PetscErrorCode ierr;
2252 
2253   PetscFunctionBegin;
2254   ierr = MatRealPart(a->A);CHKERRQ(ierr);
2255   ierr = MatRealPart(a->B);CHKERRQ(ierr);
2256   PetscFunctionReturn(0);
2257 }
2258 
2259 #undef __FUNCT__
2260 #define __FUNCT__ "MatImaginaryPart_MPIAIJ"
2261 PetscErrorCode MatImaginaryPart_MPIAIJ(Mat A)
2262 {
2263   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2264   PetscErrorCode ierr;
2265 
2266   PetscFunctionBegin;
2267   ierr = MatImaginaryPart(a->A);CHKERRQ(ierr);
2268   ierr = MatImaginaryPart(a->B);CHKERRQ(ierr);
2269   PetscFunctionReturn(0);
2270 }
2271 
2272 #if defined(PETSC_HAVE_PBGL)
2273 
2274 #include <boost/parallel/mpi/bsp_process_group.hpp>
2275 #include <boost/graph/distributed/ilu_default_graph.hpp>
2276 #include <boost/graph/distributed/ilu_0_block.hpp>
2277 #include <boost/graph/distributed/ilu_preconditioner.hpp>
2278 #include <boost/graph/distributed/petsc/interface.hpp>
2279 #include <boost/multi_array.hpp>
2280 #include <boost/parallel/distributed_property_map->hpp>
2281 
2282 #undef __FUNCT__
2283 #define __FUNCT__ "MatILUFactorSymbolic_MPIAIJ"
2284 /*
2285   This uses the parallel ILU factorization of Peter Gottschling <pgottsch@osl.iu.edu>
2286 */
2287 PetscErrorCode MatILUFactorSymbolic_MPIAIJ(Mat fact,Mat A, IS isrow, IS iscol, const MatFactorInfo *info)
2288 {
2289   namespace petsc = boost::distributed::petsc;
2290 
2291   namespace graph_dist = boost::graph::distributed;
2292   using boost::graph::distributed::ilu_default::process_group_type;
2293   using boost::graph::ilu_permuted;
2294 
2295   PetscBool      row_identity, col_identity;
2296   PetscContainer c;
2297   PetscInt       m, n, M, N;
2298   PetscErrorCode ierr;
2299 
2300   PetscFunctionBegin;
2301   if (info->levels != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only levels = 0 supported for parallel ilu");
2302   ierr = ISIdentity(isrow, &row_identity);CHKERRQ(ierr);
2303   ierr = ISIdentity(iscol, &col_identity);CHKERRQ(ierr);
2304   if (!row_identity || !col_identity) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Row and column permutations must be identity for parallel ILU");
2305 
2306   process_group_type pg;
2307   typedef graph_dist::ilu_default::ilu_level_graph_type lgraph_type;
2308   lgraph_type  *lgraph_p   = new lgraph_type(petsc::num_global_vertices(A), pg, petsc::matrix_distribution(A, pg));
2309   lgraph_type& level_graph = *lgraph_p;
2310   graph_dist::ilu_default::graph_type&            graph(level_graph.graph);
2311 
2312   petsc::read_matrix(A, graph, get(boost::edge_weight, graph));
2313   ilu_permuted(level_graph);
2314 
2315   /* put together the new matrix */
2316   ierr = MatCreate(PetscObjectComm((PetscObject)A), fact);CHKERRQ(ierr);
2317   ierr = MatGetLocalSize(A, &m, &n);CHKERRQ(ierr);
2318   ierr = MatGetSize(A, &M, &N);CHKERRQ(ierr);
2319   ierr = MatSetSizes(fact, m, n, M, N);CHKERRQ(ierr);
2320   ierr = MatSetBlockSizesFromMats(fact,A,A);CHKERRQ(ierr);
2321   ierr = MatSetType(fact, ((PetscObject)A)->type_name);CHKERRQ(ierr);
2322   ierr = MatAssemblyBegin(fact, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2323   ierr = MatAssemblyEnd(fact, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2324 
2325   ierr = PetscContainerCreate(PetscObjectComm((PetscObject)A), &c);
2326   ierr = PetscContainerSetPointer(c, lgraph_p);
2327   ierr = PetscObjectCompose((PetscObject) (fact), "graph", (PetscObject) c);
2328   ierr = PetscContainerDestroy(&c);
2329   PetscFunctionReturn(0);
2330 }
2331 
2332 #undef __FUNCT__
2333 #define __FUNCT__ "MatLUFactorNumeric_MPIAIJ"
2334 PetscErrorCode MatLUFactorNumeric_MPIAIJ(Mat B,Mat A, const MatFactorInfo *info)
2335 {
2336   PetscFunctionBegin;
2337   PetscFunctionReturn(0);
2338 }
2339 
2340 #undef __FUNCT__
2341 #define __FUNCT__ "MatSolve_MPIAIJ"
2342 /*
2343   This uses the parallel ILU factorization of Peter Gottschling <pgottsch@osl.iu.edu>
2344 */
2345 PetscErrorCode MatSolve_MPIAIJ(Mat A, Vec b, Vec x)
2346 {
2347   namespace graph_dist = boost::graph::distributed;
2348 
2349   typedef graph_dist::ilu_default::ilu_level_graph_type lgraph_type;
2350   lgraph_type    *lgraph_p;
2351   PetscContainer c;
2352   PetscErrorCode ierr;
2353 
2354   PetscFunctionBegin;
2355   ierr = PetscObjectQuery((PetscObject) A, "graph", (PetscObject*) &c);CHKERRQ(ierr);
2356   ierr = PetscContainerGetPointer(c, (void**) &lgraph_p);CHKERRQ(ierr);
2357   ierr = VecCopy(b, x);CHKERRQ(ierr);
2358 
2359   PetscScalar *array_x;
2360   ierr = VecGetArray(x, &array_x);CHKERRQ(ierr);
2361   PetscInt sx;
2362   ierr = VecGetSize(x, &sx);CHKERRQ(ierr);
2363 
2364   PetscScalar *array_b;
2365   ierr = VecGetArray(b, &array_b);CHKERRQ(ierr);
2366   PetscInt sb;
2367   ierr = VecGetSize(b, &sb);CHKERRQ(ierr);
2368 
2369   lgraph_type& level_graph = *lgraph_p;
2370   graph_dist::ilu_default::graph_type&            graph(level_graph.graph);
2371 
2372   typedef boost::multi_array_ref<PetscScalar, 1> array_ref_type;
2373   array_ref_type                                 ref_b(array_b, boost::extents[num_vertices(graph)]);
2374   array_ref_type                                 ref_x(array_x, boost::extents[num_vertices(graph)]);
2375 
2376   typedef boost::iterator_property_map<array_ref_type::iterator,
2377                                        boost::property_map<graph_dist::ilu_default::graph_type, boost::vertex_index_t>::type>  gvector_type;
2378   gvector_type                                   vector_b(ref_b.begin(), get(boost::vertex_index, graph));
2379   gvector_type                                   vector_x(ref_x.begin(), get(boost::vertex_index, graph));
2380 
2381   ilu_set_solve(*lgraph_p, vector_b, vector_x);
2382   PetscFunctionReturn(0);
2383 }
2384 #endif
2385 
2386 #undef __FUNCT__
2387 #define __FUNCT__ "MatGetRowMaxAbs_MPIAIJ"
2388 PetscErrorCode MatGetRowMaxAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2389 {
2390   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2391   PetscErrorCode ierr;
2392   PetscInt       i,*idxb = 0;
2393   PetscScalar    *va,*vb;
2394   Vec            vtmp;
2395 
2396   PetscFunctionBegin;
2397   ierr = MatGetRowMaxAbs(a->A,v,idx);CHKERRQ(ierr);
2398   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2399   if (idx) {
2400     for (i=0; i<A->rmap->n; i++) {
2401       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2402     }
2403   }
2404 
2405   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2406   if (idx) {
2407     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2408   }
2409   ierr = MatGetRowMaxAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2410   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2411 
2412   for (i=0; i<A->rmap->n; i++) {
2413     if (PetscAbsScalar(va[i]) < PetscAbsScalar(vb[i])) {
2414       va[i] = vb[i];
2415       if (idx) idx[i] = a->garray[idxb[i]];
2416     }
2417   }
2418 
2419   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2420   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2421   ierr = PetscFree(idxb);CHKERRQ(ierr);
2422   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2423   PetscFunctionReturn(0);
2424 }
2425 
2426 #undef __FUNCT__
2427 #define __FUNCT__ "MatGetRowMinAbs_MPIAIJ"
2428 PetscErrorCode MatGetRowMinAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2429 {
2430   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2431   PetscErrorCode ierr;
2432   PetscInt       i,*idxb = 0;
2433   PetscScalar    *va,*vb;
2434   Vec            vtmp;
2435 
2436   PetscFunctionBegin;
2437   ierr = MatGetRowMinAbs(a->A,v,idx);CHKERRQ(ierr);
2438   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2439   if (idx) {
2440     for (i=0; i<A->cmap->n; i++) {
2441       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2442     }
2443   }
2444 
2445   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2446   if (idx) {
2447     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2448   }
2449   ierr = MatGetRowMinAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2450   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2451 
2452   for (i=0; i<A->rmap->n; i++) {
2453     if (PetscAbsScalar(va[i]) > PetscAbsScalar(vb[i])) {
2454       va[i] = vb[i];
2455       if (idx) idx[i] = a->garray[idxb[i]];
2456     }
2457   }
2458 
2459   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2460   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2461   ierr = PetscFree(idxb);CHKERRQ(ierr);
2462   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2463   PetscFunctionReturn(0);
2464 }
2465 
2466 #undef __FUNCT__
2467 #define __FUNCT__ "MatGetRowMin_MPIAIJ"
2468 PetscErrorCode MatGetRowMin_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2469 {
2470   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2471   PetscInt       n      = A->rmap->n;
2472   PetscInt       cstart = A->cmap->rstart;
2473   PetscInt       *cmap  = mat->garray;
2474   PetscInt       *diagIdx, *offdiagIdx;
2475   Vec            diagV, offdiagV;
2476   PetscScalar    *a, *diagA, *offdiagA;
2477   PetscInt       r;
2478   PetscErrorCode ierr;
2479 
2480   PetscFunctionBegin;
2481   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2482   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &diagV);CHKERRQ(ierr);
2483   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &offdiagV);CHKERRQ(ierr);
2484   ierr = MatGetRowMin(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2485   ierr = MatGetRowMin(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2486   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2487   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2488   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2489   for (r = 0; r < n; ++r) {
2490     if (PetscAbsScalar(diagA[r]) <= PetscAbsScalar(offdiagA[r])) {
2491       a[r]   = diagA[r];
2492       idx[r] = cstart + diagIdx[r];
2493     } else {
2494       a[r]   = offdiagA[r];
2495       idx[r] = cmap[offdiagIdx[r]];
2496     }
2497   }
2498   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2499   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2500   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2501   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2502   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2503   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2504   PetscFunctionReturn(0);
2505 }
2506 
2507 #undef __FUNCT__
2508 #define __FUNCT__ "MatGetRowMax_MPIAIJ"
2509 PetscErrorCode MatGetRowMax_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2510 {
2511   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2512   PetscInt       n      = A->rmap->n;
2513   PetscInt       cstart = A->cmap->rstart;
2514   PetscInt       *cmap  = mat->garray;
2515   PetscInt       *diagIdx, *offdiagIdx;
2516   Vec            diagV, offdiagV;
2517   PetscScalar    *a, *diagA, *offdiagA;
2518   PetscInt       r;
2519   PetscErrorCode ierr;
2520 
2521   PetscFunctionBegin;
2522   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2523   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &diagV);CHKERRQ(ierr);
2524   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &offdiagV);CHKERRQ(ierr);
2525   ierr = MatGetRowMax(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2526   ierr = MatGetRowMax(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2527   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2528   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2529   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2530   for (r = 0; r < n; ++r) {
2531     if (PetscAbsScalar(diagA[r]) >= PetscAbsScalar(offdiagA[r])) {
2532       a[r]   = diagA[r];
2533       idx[r] = cstart + diagIdx[r];
2534     } else {
2535       a[r]   = offdiagA[r];
2536       idx[r] = cmap[offdiagIdx[r]];
2537     }
2538   }
2539   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2540   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2541   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2542   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2543   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2544   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2545   PetscFunctionReturn(0);
2546 }
2547 
2548 #undef __FUNCT__
2549 #define __FUNCT__ "MatGetSeqNonzeroStructure_MPIAIJ"
2550 PetscErrorCode MatGetSeqNonzeroStructure_MPIAIJ(Mat mat,Mat *newmat)
2551 {
2552   PetscErrorCode ierr;
2553   Mat            *dummy;
2554 
2555   PetscFunctionBegin;
2556   ierr    = MatGetSubMatrix_MPIAIJ_All(mat,MAT_DO_NOT_GET_VALUES,MAT_INITIAL_MATRIX,&dummy);CHKERRQ(ierr);
2557   *newmat = *dummy;
2558   ierr    = PetscFree(dummy);CHKERRQ(ierr);
2559   PetscFunctionReturn(0);
2560 }
2561 
2562 #undef __FUNCT__
2563 #define __FUNCT__ "MatInvertBlockDiagonal_MPIAIJ"
2564 PetscErrorCode  MatInvertBlockDiagonal_MPIAIJ(Mat A,const PetscScalar **values)
2565 {
2566   Mat_MPIAIJ     *a = (Mat_MPIAIJ*) A->data;
2567   PetscErrorCode ierr;
2568 
2569   PetscFunctionBegin;
2570   ierr = MatInvertBlockDiagonal(a->A,values);CHKERRQ(ierr);
2571   PetscFunctionReturn(0);
2572 }
2573 
2574 #undef __FUNCT__
2575 #define __FUNCT__ "MatSetRandom_MPIAIJ"
2576 static PetscErrorCode  MatSetRandom_MPIAIJ(Mat x,PetscRandom rctx)
2577 {
2578   PetscErrorCode ierr;
2579   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)x->data;
2580 
2581   PetscFunctionBegin;
2582   ierr = MatSetRandom(aij->A,rctx);CHKERRQ(ierr);
2583   ierr = MatSetRandom(aij->B,rctx);CHKERRQ(ierr);
2584   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2585   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2586   PetscFunctionReturn(0);
2587 }
2588 
2589 /* -------------------------------------------------------------------*/
2590 static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
2591                                        MatGetRow_MPIAIJ,
2592                                        MatRestoreRow_MPIAIJ,
2593                                        MatMult_MPIAIJ,
2594                                 /* 4*/ MatMultAdd_MPIAIJ,
2595                                        MatMultTranspose_MPIAIJ,
2596                                        MatMultTransposeAdd_MPIAIJ,
2597 #if defined(PETSC_HAVE_PBGL)
2598                                        MatSolve_MPIAIJ,
2599 #else
2600                                        0,
2601 #endif
2602                                        0,
2603                                        0,
2604                                 /*10*/ 0,
2605                                        0,
2606                                        0,
2607                                        MatSOR_MPIAIJ,
2608                                        MatTranspose_MPIAIJ,
2609                                 /*15*/ MatGetInfo_MPIAIJ,
2610                                        MatEqual_MPIAIJ,
2611                                        MatGetDiagonal_MPIAIJ,
2612                                        MatDiagonalScale_MPIAIJ,
2613                                        MatNorm_MPIAIJ,
2614                                 /*20*/ MatAssemblyBegin_MPIAIJ,
2615                                        MatAssemblyEnd_MPIAIJ,
2616                                        MatSetOption_MPIAIJ,
2617                                        MatZeroEntries_MPIAIJ,
2618                                 /*24*/ MatZeroRows_MPIAIJ,
2619                                        0,
2620 #if defined(PETSC_HAVE_PBGL)
2621                                        0,
2622 #else
2623                                        0,
2624 #endif
2625                                        0,
2626                                        0,
2627                                 /*29*/ MatSetUp_MPIAIJ,
2628 #if defined(PETSC_HAVE_PBGL)
2629                                        0,
2630 #else
2631                                        0,
2632 #endif
2633                                        0,
2634                                        0,
2635                                        0,
2636                                 /*34*/ MatDuplicate_MPIAIJ,
2637                                        0,
2638                                        0,
2639                                        0,
2640                                        0,
2641                                 /*39*/ MatAXPY_MPIAIJ,
2642                                        MatGetSubMatrices_MPIAIJ,
2643                                        MatIncreaseOverlap_MPIAIJ,
2644                                        MatGetValues_MPIAIJ,
2645                                        MatCopy_MPIAIJ,
2646                                 /*44*/ MatGetRowMax_MPIAIJ,
2647                                        MatScale_MPIAIJ,
2648                                        0,
2649                                        MatDiagonalSet_MPIAIJ,
2650                                        MatZeroRowsColumns_MPIAIJ,
2651                                 /*49*/ MatSetRandom_MPIAIJ,
2652                                        0,
2653                                        0,
2654                                        0,
2655                                        0,
2656                                 /*54*/ MatFDColoringCreate_MPIXAIJ,
2657                                        0,
2658                                        MatSetUnfactored_MPIAIJ,
2659                                        MatPermute_MPIAIJ,
2660                                        0,
2661                                 /*59*/ MatGetSubMatrix_MPIAIJ,
2662                                        MatDestroy_MPIAIJ,
2663                                        MatView_MPIAIJ,
2664                                        0,
2665                                        MatMatMatMult_MPIAIJ_MPIAIJ_MPIAIJ,
2666                                 /*64*/ MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ,
2667                                        MatMatMatMultNumeric_MPIAIJ_MPIAIJ_MPIAIJ,
2668                                        0,
2669                                        0,
2670                                        0,
2671                                 /*69*/ MatGetRowMaxAbs_MPIAIJ,
2672                                        MatGetRowMinAbs_MPIAIJ,
2673                                        0,
2674                                        MatSetColoring_MPIAIJ,
2675                                        0,
2676                                        MatSetValuesAdifor_MPIAIJ,
2677                                 /*75*/ MatFDColoringApply_AIJ,
2678                                        0,
2679                                        0,
2680                                        0,
2681                                        MatFindZeroDiagonals_MPIAIJ,
2682                                 /*80*/ 0,
2683                                        0,
2684                                        0,
2685                                 /*83*/ MatLoad_MPIAIJ,
2686                                        0,
2687                                        0,
2688                                        0,
2689                                        0,
2690                                        0,
2691                                 /*89*/ MatMatMult_MPIAIJ_MPIAIJ,
2692                                        MatMatMultSymbolic_MPIAIJ_MPIAIJ,
2693                                        MatMatMultNumeric_MPIAIJ_MPIAIJ,
2694                                        MatPtAP_MPIAIJ_MPIAIJ,
2695                                        MatPtAPSymbolic_MPIAIJ_MPIAIJ,
2696                                 /*94*/ MatPtAPNumeric_MPIAIJ_MPIAIJ,
2697                                        0,
2698                                        0,
2699                                        0,
2700                                        0,
2701                                 /*99*/ 0,
2702                                        0,
2703                                        0,
2704                                        MatConjugate_MPIAIJ,
2705                                        0,
2706                                 /*104*/MatSetValuesRow_MPIAIJ,
2707                                        MatRealPart_MPIAIJ,
2708                                        MatImaginaryPart_MPIAIJ,
2709                                        0,
2710                                        0,
2711                                 /*109*/0,
2712                                        0,
2713                                        MatGetRowMin_MPIAIJ,
2714                                        0,
2715                                        0,
2716                                 /*114*/MatGetSeqNonzeroStructure_MPIAIJ,
2717                                        0,
2718                                        0,
2719                                        0,
2720                                        0,
2721                                 /*119*/0,
2722                                        0,
2723                                        0,
2724                                        0,
2725                                        MatGetMultiProcBlock_MPIAIJ,
2726                                 /*124*/MatFindNonzeroRows_MPIAIJ,
2727                                        MatGetColumnNorms_MPIAIJ,
2728                                        MatInvertBlockDiagonal_MPIAIJ,
2729                                        0,
2730                                        MatGetSubMatricesParallel_MPIAIJ,
2731                                 /*129*/0,
2732                                        MatTransposeMatMult_MPIAIJ_MPIAIJ,
2733                                        MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ,
2734                                        MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ,
2735                                        0,
2736                                 /*134*/0,
2737                                        0,
2738                                        0,
2739                                        0,
2740                                        0,
2741                                 /*139*/0,
2742                                        0,
2743                                        0,
2744                                        MatFDColoringSetUp_MPIXAIJ,
2745                                        MatFindOffBlockDiagonalEntries_MPIAIJ,
2746                                 /*144*/MatCreateMPIMatConcatenateSeqMat_MPIAIJ
2747 };
2748 
2749 /* ----------------------------------------------------------------------------------------*/
2750 
2751 #undef __FUNCT__
2752 #define __FUNCT__ "MatStoreValues_MPIAIJ"
2753 PetscErrorCode  MatStoreValues_MPIAIJ(Mat mat)
2754 {
2755   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2756   PetscErrorCode ierr;
2757 
2758   PetscFunctionBegin;
2759   ierr = MatStoreValues(aij->A);CHKERRQ(ierr);
2760   ierr = MatStoreValues(aij->B);CHKERRQ(ierr);
2761   PetscFunctionReturn(0);
2762 }
2763 
2764 #undef __FUNCT__
2765 #define __FUNCT__ "MatRetrieveValues_MPIAIJ"
2766 PetscErrorCode  MatRetrieveValues_MPIAIJ(Mat mat)
2767 {
2768   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2769   PetscErrorCode ierr;
2770 
2771   PetscFunctionBegin;
2772   ierr = MatRetrieveValues(aij->A);CHKERRQ(ierr);
2773   ierr = MatRetrieveValues(aij->B);CHKERRQ(ierr);
2774   PetscFunctionReturn(0);
2775 }
2776 
2777 #undef __FUNCT__
2778 #define __FUNCT__ "MatMPIAIJSetPreallocation_MPIAIJ"
2779 PetscErrorCode  MatMPIAIJSetPreallocation_MPIAIJ(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
2780 {
2781   Mat_MPIAIJ     *b;
2782   PetscErrorCode ierr;
2783 
2784   PetscFunctionBegin;
2785   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
2786   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
2787   b = (Mat_MPIAIJ*)B->data;
2788 
2789   if (!B->preallocated) {
2790     /* Explicitly create 2 MATSEQAIJ matrices. */
2791     ierr = MatCreate(PETSC_COMM_SELF,&b->A);CHKERRQ(ierr);
2792     ierr = MatSetSizes(b->A,B->rmap->n,B->cmap->n,B->rmap->n,B->cmap->n);CHKERRQ(ierr);
2793     ierr = MatSetBlockSizesFromMats(b->A,B,B);CHKERRQ(ierr);
2794     ierr = MatSetType(b->A,MATSEQAIJ);CHKERRQ(ierr);
2795     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->A);CHKERRQ(ierr);
2796     ierr = MatCreate(PETSC_COMM_SELF,&b->B);CHKERRQ(ierr);
2797     ierr = MatSetSizes(b->B,B->rmap->n,B->cmap->N,B->rmap->n,B->cmap->N);CHKERRQ(ierr);
2798     ierr = MatSetBlockSizesFromMats(b->B,B,B);CHKERRQ(ierr);
2799     ierr = MatSetType(b->B,MATSEQAIJ);CHKERRQ(ierr);
2800     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->B);CHKERRQ(ierr);
2801   }
2802 
2803   ierr = MatSeqAIJSetPreallocation(b->A,d_nz,d_nnz);CHKERRQ(ierr);
2804   ierr = MatSeqAIJSetPreallocation(b->B,o_nz,o_nnz);CHKERRQ(ierr);
2805   B->preallocated = PETSC_TRUE;
2806   PetscFunctionReturn(0);
2807 }
2808 
2809 #undef __FUNCT__
2810 #define __FUNCT__ "MatDuplicate_MPIAIJ"
2811 PetscErrorCode MatDuplicate_MPIAIJ(Mat matin,MatDuplicateOption cpvalues,Mat *newmat)
2812 {
2813   Mat            mat;
2814   Mat_MPIAIJ     *a,*oldmat = (Mat_MPIAIJ*)matin->data;
2815   PetscErrorCode ierr;
2816 
2817   PetscFunctionBegin;
2818   *newmat = 0;
2819   ierr    = MatCreate(PetscObjectComm((PetscObject)matin),&mat);CHKERRQ(ierr);
2820   ierr    = MatSetSizes(mat,matin->rmap->n,matin->cmap->n,matin->rmap->N,matin->cmap->N);CHKERRQ(ierr);
2821   ierr    = MatSetBlockSizesFromMats(mat,matin,matin);CHKERRQ(ierr);
2822   ierr    = MatSetType(mat,((PetscObject)matin)->type_name);CHKERRQ(ierr);
2823   ierr    = PetscMemcpy(mat->ops,matin->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
2824   a       = (Mat_MPIAIJ*)mat->data;
2825 
2826   mat->factortype   = matin->factortype;
2827   mat->assembled    = PETSC_TRUE;
2828   mat->insertmode   = NOT_SET_VALUES;
2829   mat->preallocated = PETSC_TRUE;
2830 
2831   a->size         = oldmat->size;
2832   a->rank         = oldmat->rank;
2833   a->donotstash   = oldmat->donotstash;
2834   a->roworiented  = oldmat->roworiented;
2835   a->rowindices   = 0;
2836   a->rowvalues    = 0;
2837   a->getrowactive = PETSC_FALSE;
2838 
2839   ierr = PetscLayoutReference(matin->rmap,&mat->rmap);CHKERRQ(ierr);
2840   ierr = PetscLayoutReference(matin->cmap,&mat->cmap);CHKERRQ(ierr);
2841 
2842   if (oldmat->colmap) {
2843 #if defined(PETSC_USE_CTABLE)
2844     ierr = PetscTableCreateCopy(oldmat->colmap,&a->colmap);CHKERRQ(ierr);
2845 #else
2846     ierr = PetscMalloc1(mat->cmap->N,&a->colmap);CHKERRQ(ierr);
2847     ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2848     ierr = PetscMemcpy(a->colmap,oldmat->colmap,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2849 #endif
2850   } else a->colmap = 0;
2851   if (oldmat->garray) {
2852     PetscInt len;
2853     len  = oldmat->B->cmap->n;
2854     ierr = PetscMalloc1(len+1,&a->garray);CHKERRQ(ierr);
2855     ierr = PetscLogObjectMemory((PetscObject)mat,len*sizeof(PetscInt));CHKERRQ(ierr);
2856     if (len) { ierr = PetscMemcpy(a->garray,oldmat->garray,len*sizeof(PetscInt));CHKERRQ(ierr); }
2857   } else a->garray = 0;
2858 
2859   ierr    = VecDuplicate(oldmat->lvec,&a->lvec);CHKERRQ(ierr);
2860   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->lvec);CHKERRQ(ierr);
2861   ierr    = VecScatterCopy(oldmat->Mvctx,&a->Mvctx);CHKERRQ(ierr);
2862   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->Mvctx);CHKERRQ(ierr);
2863   ierr    = MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
2864   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->A);CHKERRQ(ierr);
2865   ierr    = MatDuplicate(oldmat->B,cpvalues,&a->B);CHKERRQ(ierr);
2866   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->B);CHKERRQ(ierr);
2867   ierr    = PetscFunctionListDuplicate(((PetscObject)matin)->qlist,&((PetscObject)mat)->qlist);CHKERRQ(ierr);
2868   *newmat = mat;
2869   PetscFunctionReturn(0);
2870 }
2871 
2872 
2873 
2874 #undef __FUNCT__
2875 #define __FUNCT__ "MatLoad_MPIAIJ"
2876 PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
2877 {
2878   PetscScalar    *vals,*svals;
2879   MPI_Comm       comm;
2880   PetscErrorCode ierr;
2881   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
2882   PetscInt       i,nz,j,rstart,rend,mmax,maxnz = 0,grows,gcols;
2883   PetscInt       header[4],*rowlengths = 0,M,N,m,*cols;
2884   PetscInt       *ourlens = NULL,*procsnz = NULL,*offlens = NULL,jj,*mycols,*smycols;
2885   PetscInt       cend,cstart,n,*rowners,sizesset=1;
2886   int            fd;
2887   PetscInt       bs = newMat->rmap->bs;
2888 
2889   PetscFunctionBegin;
2890   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
2891   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2892   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2893   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
2894   if (!rank) {
2895     ierr = PetscBinaryRead(fd,(char*)header,4,PETSC_INT);CHKERRQ(ierr);
2896     if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
2897   }
2898 
2899   ierr = PetscOptionsBegin(comm,NULL,"Options for loading SEQAIJ matrix","Mat");CHKERRQ(ierr);
2900   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
2901   ierr = PetscOptionsEnd();CHKERRQ(ierr);
2902   if (bs < 0) bs = 1;
2903 
2904   if (newMat->rmap->n < 0 && newMat->rmap->N < 0 && newMat->cmap->n < 0 && newMat->cmap->N < 0) sizesset = 0;
2905 
2906   ierr = MPI_Bcast(header+1,3,MPIU_INT,0,comm);CHKERRQ(ierr);
2907   M    = header[1]; N = header[2];
2908   /* If global rows/cols are set to PETSC_DECIDE, set it to the sizes given in the file */
2909   if (sizesset && newMat->rmap->N < 0) newMat->rmap->N = M;
2910   if (sizesset && newMat->cmap->N < 0) newMat->cmap->N = N;
2911 
2912   /* If global sizes are set, check if they are consistent with that given in the file */
2913   if (sizesset) {
2914     ierr = MatGetSize(newMat,&grows,&gcols);CHKERRQ(ierr);
2915   }
2916   if (sizesset && newMat->rmap->N != grows) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Inconsistent # of rows:Matrix in file has (%d) and input matrix has (%d)",M,grows);
2917   if (sizesset && newMat->cmap->N != gcols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Inconsistent # of cols:Matrix in file has (%d) and input matrix has (%d)",N,gcols);
2918 
2919   /* determine ownership of all (block) rows */
2920   if (M%bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Inconsistent # of rows (%d) and block size (%d)",M,bs);
2921   if (newMat->rmap->n < 0) m = bs*((M/bs)/size + (((M/bs) % size) > rank));    /* PETSC_DECIDE */
2922   else m = newMat->rmap->n; /* Set by user */
2923 
2924   ierr = PetscMalloc1(size+1,&rowners);CHKERRQ(ierr);
2925   ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
2926 
2927   /* First process needs enough room for process with most rows */
2928   if (!rank) {
2929     mmax = rowners[1];
2930     for (i=2; i<=size; i++) {
2931       mmax = PetscMax(mmax, rowners[i]);
2932     }
2933   } else mmax = -1;             /* unused, but compilers complain */
2934 
2935   rowners[0] = 0;
2936   for (i=2; i<=size; i++) {
2937     rowners[i] += rowners[i-1];
2938   }
2939   rstart = rowners[rank];
2940   rend   = rowners[rank+1];
2941 
2942   /* distribute row lengths to all processors */
2943   ierr = PetscMalloc2(m,&ourlens,m,&offlens);CHKERRQ(ierr);
2944   if (!rank) {
2945     ierr = PetscBinaryRead(fd,ourlens,m,PETSC_INT);CHKERRQ(ierr);
2946     ierr = PetscMalloc1(mmax,&rowlengths);CHKERRQ(ierr);
2947     ierr = PetscCalloc1(size,&procsnz);CHKERRQ(ierr);
2948     for (j=0; j<m; j++) {
2949       procsnz[0] += ourlens[j];
2950     }
2951     for (i=1; i<size; i++) {
2952       ierr = PetscBinaryRead(fd,rowlengths,rowners[i+1]-rowners[i],PETSC_INT);CHKERRQ(ierr);
2953       /* calculate the number of nonzeros on each processor */
2954       for (j=0; j<rowners[i+1]-rowners[i]; j++) {
2955         procsnz[i] += rowlengths[j];
2956       }
2957       ierr = MPIULong_Send(rowlengths,rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2958     }
2959     ierr = PetscFree(rowlengths);CHKERRQ(ierr);
2960   } else {
2961     ierr = MPIULong_Recv(ourlens,m,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2962   }
2963 
2964   if (!rank) {
2965     /* determine max buffer needed and allocate it */
2966     maxnz = 0;
2967     for (i=0; i<size; i++) {
2968       maxnz = PetscMax(maxnz,procsnz[i]);
2969     }
2970     ierr = PetscMalloc1(maxnz,&cols);CHKERRQ(ierr);
2971 
2972     /* read in my part of the matrix column indices  */
2973     nz   = procsnz[0];
2974     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2975     ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);
2976 
2977     /* read in every one elses and ship off */
2978     for (i=1; i<size; i++) {
2979       nz   = procsnz[i];
2980       ierr = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
2981       ierr = MPIULong_Send(cols,nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2982     }
2983     ierr = PetscFree(cols);CHKERRQ(ierr);
2984   } else {
2985     /* determine buffer space needed for message */
2986     nz = 0;
2987     for (i=0; i<m; i++) {
2988       nz += ourlens[i];
2989     }
2990     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2991 
2992     /* receive message of column indices*/
2993     ierr = MPIULong_Recv(mycols,nz,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2994   }
2995 
2996   /* determine column ownership if matrix is not square */
2997   if (N != M) {
2998     if (newMat->cmap->n < 0) n = N/size + ((N % size) > rank);
2999     else n = newMat->cmap->n;
3000     ierr   = MPI_Scan(&n,&cend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3001     cstart = cend - n;
3002   } else {
3003     cstart = rstart;
3004     cend   = rend;
3005     n      = cend - cstart;
3006   }
3007 
3008   /* loop over local rows, determining number of off diagonal entries */
3009   ierr = PetscMemzero(offlens,m*sizeof(PetscInt));CHKERRQ(ierr);
3010   jj   = 0;
3011   for (i=0; i<m; i++) {
3012     for (j=0; j<ourlens[i]; j++) {
3013       if (mycols[jj] < cstart || mycols[jj] >= cend) offlens[i]++;
3014       jj++;
3015     }
3016   }
3017 
3018   for (i=0; i<m; i++) {
3019     ourlens[i] -= offlens[i];
3020   }
3021   if (!sizesset) {
3022     ierr = MatSetSizes(newMat,m,n,M,N);CHKERRQ(ierr);
3023   }
3024 
3025   if (bs > 1) {ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);}
3026 
3027   ierr = MatMPIAIJSetPreallocation(newMat,0,ourlens,0,offlens);CHKERRQ(ierr);
3028 
3029   for (i=0; i<m; i++) {
3030     ourlens[i] += offlens[i];
3031   }
3032 
3033   if (!rank) {
3034     ierr = PetscMalloc1(maxnz+1,&vals);CHKERRQ(ierr);
3035 
3036     /* read in my part of the matrix numerical values  */
3037     nz   = procsnz[0];
3038     ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
3039 
3040     /* insert into matrix */
3041     jj      = rstart;
3042     smycols = mycols;
3043     svals   = vals;
3044     for (i=0; i<m; i++) {
3045       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
3046       smycols += ourlens[i];
3047       svals   += ourlens[i];
3048       jj++;
3049     }
3050 
3051     /* read in other processors and ship out */
3052     for (i=1; i<size; i++) {
3053       nz   = procsnz[i];
3054       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
3055       ierr = MPIULong_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
3056     }
3057     ierr = PetscFree(procsnz);CHKERRQ(ierr);
3058   } else {
3059     /* receive numeric values */
3060     ierr = PetscMalloc1(nz+1,&vals);CHKERRQ(ierr);
3061 
3062     /* receive message of values*/
3063     ierr = MPIULong_Recv(vals,nz,MPIU_SCALAR,0,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
3064 
3065     /* insert into matrix */
3066     jj      = rstart;
3067     smycols = mycols;
3068     svals   = vals;
3069     for (i=0; i<m; i++) {
3070       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
3071       smycols += ourlens[i];
3072       svals   += ourlens[i];
3073       jj++;
3074     }
3075   }
3076   ierr = PetscFree2(ourlens,offlens);CHKERRQ(ierr);
3077   ierr = PetscFree(vals);CHKERRQ(ierr);
3078   ierr = PetscFree(mycols);CHKERRQ(ierr);
3079   ierr = PetscFree(rowners);CHKERRQ(ierr);
3080   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3081   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3082   PetscFunctionReturn(0);
3083 }
3084 
3085 #undef __FUNCT__
3086 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ"
3087 PetscErrorCode MatGetSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3088 {
3089   PetscErrorCode ierr;
3090   IS             iscol_local;
3091   PetscInt       csize;
3092 
3093   PetscFunctionBegin;
3094   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3095   if (call == MAT_REUSE_MATRIX) {
3096     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3097     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3098   } else {
3099     PetscInt cbs;
3100     ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
3101     ierr = ISAllGather(iscol,&iscol_local);CHKERRQ(ierr);
3102     ierr = ISSetBlockSize(iscol_local,cbs);CHKERRQ(ierr);
3103   }
3104   ierr = MatGetSubMatrix_MPIAIJ_Private(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
3105   if (call == MAT_INITIAL_MATRIX) {
3106     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3107     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3108   }
3109   PetscFunctionReturn(0);
3110 }
3111 
3112 extern PetscErrorCode MatGetSubMatrices_MPIAIJ_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool*,Mat*);
3113 #undef __FUNCT__
3114 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ_Private"
3115 /*
3116     Not great since it makes two copies of the submatrix, first an SeqAIJ
3117   in local and then by concatenating the local matrices the end result.
3118   Writing it directly would be much like MatGetSubMatrices_MPIAIJ()
3119 
3120   Note: This requires a sequential iscol with all indices.
3121 */
3122 PetscErrorCode MatGetSubMatrix_MPIAIJ_Private(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3123 {
3124   PetscErrorCode ierr;
3125   PetscMPIInt    rank,size;
3126   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3127   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal,ncol;
3128   PetscBool      allcolumns, colflag;
3129   Mat            M,Mreuse;
3130   MatScalar      *vwork,*aa;
3131   MPI_Comm       comm;
3132   Mat_SeqAIJ     *aij;
3133 
3134   PetscFunctionBegin;
3135   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3136   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3137   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3138 
3139   ierr = ISIdentity(iscol,&colflag);CHKERRQ(ierr);
3140   ierr = ISGetLocalSize(iscol,&ncol);CHKERRQ(ierr);
3141   if (colflag && ncol == mat->cmap->N) {
3142     allcolumns = PETSC_TRUE;
3143   } else {
3144     allcolumns = PETSC_FALSE;
3145   }
3146   if (call ==  MAT_REUSE_MATRIX) {
3147     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3148     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3149     ierr = MatGetSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,&allcolumns,&Mreuse);CHKERRQ(ierr);
3150   } else {
3151     ierr = MatGetSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&allcolumns,&Mreuse);CHKERRQ(ierr);
3152   }
3153 
3154   /*
3155       m - number of local rows
3156       n - number of columns (same on all processors)
3157       rstart - first row in new global matrix generated
3158   */
3159   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3160   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3161   if (call == MAT_INITIAL_MATRIX) {
3162     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3163     ii  = aij->i;
3164     jj  = aij->j;
3165 
3166     /*
3167         Determine the number of non-zeros in the diagonal and off-diagonal
3168         portions of the matrix in order to do correct preallocation
3169     */
3170 
3171     /* first get start and end of "diagonal" columns */
3172     if (csize == PETSC_DECIDE) {
3173       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3174       if (mglobal == n) { /* square matrix */
3175         nlocal = m;
3176       } else {
3177         nlocal = n/size + ((n % size) > rank);
3178       }
3179     } else {
3180       nlocal = csize;
3181     }
3182     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3183     rstart = rend - nlocal;
3184     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);
3185 
3186     /* next, compute all the lengths */
3187     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3188     olens = dlens + m;
3189     for (i=0; i<m; i++) {
3190       jend = ii[i+1] - ii[i];
3191       olen = 0;
3192       dlen = 0;
3193       for (j=0; j<jend; j++) {
3194         if (*jj < rstart || *jj >= rend) olen++;
3195         else dlen++;
3196         jj++;
3197       }
3198       olens[i] = olen;
3199       dlens[i] = dlen;
3200     }
3201     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3202     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3203     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3204     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3205     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3206     ierr = PetscFree(dlens);CHKERRQ(ierr);
3207   } else {
3208     PetscInt ml,nl;
3209 
3210     M    = *newmat;
3211     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3212     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3213     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3214     /*
3215          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3216        rather than the slower MatSetValues().
3217     */
3218     M->was_assembled = PETSC_TRUE;
3219     M->assembled     = PETSC_FALSE;
3220   }
3221   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3222   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3223   ii   = aij->i;
3224   jj   = aij->j;
3225   aa   = aij->a;
3226   for (i=0; i<m; i++) {
3227     row   = rstart + i;
3228     nz    = ii[i+1] - ii[i];
3229     cwork = jj;     jj += nz;
3230     vwork = aa;     aa += nz;
3231     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3232   }
3233 
3234   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3235   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3236   *newmat = M;
3237 
3238   /* save submatrix used in processor for next request */
3239   if (call ==  MAT_INITIAL_MATRIX) {
3240     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3241     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3242   }
3243   PetscFunctionReturn(0);
3244 }
3245 
3246 #undef __FUNCT__
3247 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR_MPIAIJ"
3248 PetscErrorCode  MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3249 {
3250   PetscInt       m,cstart, cend,j,nnz,i,d;
3251   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3252   const PetscInt *JJ;
3253   PetscScalar    *values;
3254   PetscErrorCode ierr;
3255 
3256   PetscFunctionBegin;
3257   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3258 
3259   ierr   = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3260   ierr   = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3261   m      = B->rmap->n;
3262   cstart = B->cmap->rstart;
3263   cend   = B->cmap->rend;
3264   rstart = B->rmap->rstart;
3265 
3266   ierr = PetscMalloc2(m,&d_nnz,m,&o_nnz);CHKERRQ(ierr);
3267 
3268 #if defined(PETSC_USE_DEBUGGING)
3269   for (i=0; i<m; i++) {
3270     nnz = Ii[i+1]- Ii[i];
3271     JJ  = J + Ii[i];
3272     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3273     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3274     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);
3275   }
3276 #endif
3277 
3278   for (i=0; i<m; i++) {
3279     nnz     = Ii[i+1]- Ii[i];
3280     JJ      = J + Ii[i];
3281     nnz_max = PetscMax(nnz_max,nnz);
3282     d       = 0;
3283     for (j=0; j<nnz; j++) {
3284       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3285     }
3286     d_nnz[i] = d;
3287     o_nnz[i] = nnz - d;
3288   }
3289   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3290   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3291 
3292   if (v) values = (PetscScalar*)v;
3293   else {
3294     ierr = PetscCalloc1(nnz_max+1,&values);CHKERRQ(ierr);
3295   }
3296 
3297   for (i=0; i<m; i++) {
3298     ii   = i + rstart;
3299     nnz  = Ii[i+1]- Ii[i];
3300     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3301   }
3302   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3303   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3304 
3305   if (!v) {
3306     ierr = PetscFree(values);CHKERRQ(ierr);
3307   }
3308   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3309   PetscFunctionReturn(0);
3310 }
3311 
3312 #undef __FUNCT__
3313 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR"
3314 /*@
3315    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3316    (the default parallel PETSc format).
3317 
3318    Collective on MPI_Comm
3319 
3320    Input Parameters:
3321 +  B - the matrix
3322 .  i - the indices into j for the start of each local row (starts with zero)
3323 .  j - the column indices for each local row (starts with zero)
3324 -  v - optional values in the matrix
3325 
3326    Level: developer
3327 
3328    Notes:
3329        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3330      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3331      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3332 
3333        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3334 
3335        The format which is used for the sparse matrix input, is equivalent to a
3336     row-major ordering.. i.e for the following matrix, the input data expected is
3337     as shown:
3338 
3339         1 0 0
3340         2 0 3     P0
3341        -------
3342         4 5 6     P1
3343 
3344      Process0 [P0]: rows_owned=[0,1]
3345         i =  {0,1,3}  [size = nrow+1  = 2+1]
3346         j =  {0,0,2}  [size = nz = 6]
3347         v =  {1,2,3}  [size = nz = 6]
3348 
3349      Process1 [P1]: rows_owned=[2]
3350         i =  {0,3}    [size = nrow+1  = 1+1]
3351         j =  {0,1,2}  [size = nz = 6]
3352         v =  {4,5,6}  [size = nz = 6]
3353 
3354 .keywords: matrix, aij, compressed row, sparse, parallel
3355 
3356 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MPIAIJ,
3357           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3358 @*/
3359 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3360 {
3361   PetscErrorCode ierr;
3362 
3363   PetscFunctionBegin;
3364   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3365   PetscFunctionReturn(0);
3366 }
3367 
3368 #undef __FUNCT__
3369 #define __FUNCT__ "MatMPIAIJSetPreallocation"
3370 /*@C
3371    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3372    (the default parallel PETSc format).  For good matrix assembly performance
3373    the user should preallocate the matrix storage by setting the parameters
3374    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3375    performance can be increased by more than a factor of 50.
3376 
3377    Collective on MPI_Comm
3378 
3379    Input Parameters:
3380 +  B - the matrix
3381 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3382            (same value is used for all local rows)
3383 .  d_nnz - array containing the number of nonzeros in the various rows of the
3384            DIAGONAL portion of the local submatrix (possibly different for each row)
3385            or NULL, if d_nz is used to specify the nonzero structure.
3386            The size of this array is equal to the number of local rows, i.e 'm'.
3387            For matrices that will be factored, you must leave room for (and set)
3388            the diagonal entry even if it is zero.
3389 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3390            submatrix (same value is used for all local rows).
3391 -  o_nnz - array containing the number of nonzeros in the various rows of the
3392            OFF-DIAGONAL portion of the local submatrix (possibly different for
3393            each row) or NULL, if o_nz is used to specify the nonzero
3394            structure. The size of this array is equal to the number
3395            of local rows, i.e 'm'.
3396 
3397    If the *_nnz parameter is given then the *_nz parameter is ignored
3398 
3399    The AIJ format (also called the Yale sparse matrix format or
3400    compressed row storage (CSR)), is fully compatible with standard Fortran 77
3401    storage.  The stored row and column indices begin with zero.
3402    See Users-Manual: ch_mat for details.
3403 
3404    The parallel matrix is partitioned such that the first m0 rows belong to
3405    process 0, the next m1 rows belong to process 1, the next m2 rows belong
3406    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
3407 
3408    The DIAGONAL portion of the local submatrix of a processor can be defined
3409    as the submatrix which is obtained by extraction the part corresponding to
3410    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
3411    first row that belongs to the processor, r2 is the last row belonging to
3412    the this processor, and c1-c2 is range of indices of the local part of a
3413    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
3414    common case of a square matrix, the row and column ranges are the same and
3415    the DIAGONAL part is also square. The remaining portion of the local
3416    submatrix (mxN) constitute the OFF-DIAGONAL portion.
3417 
3418    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3419 
3420    You can call MatGetInfo() to get information on how effective the preallocation was;
3421    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3422    You can also run with the option -info and look for messages with the string
3423    malloc in them to see if additional memory allocation was needed.
3424 
3425    Example usage:
3426 
3427    Consider the following 8x8 matrix with 34 non-zero values, that is
3428    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3429    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3430    as follows:
3431 
3432 .vb
3433             1  2  0  |  0  3  0  |  0  4
3434     Proc0   0  5  6  |  7  0  0  |  8  0
3435             9  0 10  | 11  0  0  | 12  0
3436     -------------------------------------
3437            13  0 14  | 15 16 17  |  0  0
3438     Proc1   0 18  0  | 19 20 21  |  0  0
3439             0  0  0  | 22 23  0  | 24  0
3440     -------------------------------------
3441     Proc2  25 26 27  |  0  0 28  | 29  0
3442            30  0  0  | 31 32 33  |  0 34
3443 .ve
3444 
3445    This can be represented as a collection of submatrices as:
3446 
3447 .vb
3448       A B C
3449       D E F
3450       G H I
3451 .ve
3452 
3453    Where the submatrices A,B,C are owned by proc0, D,E,F are
3454    owned by proc1, G,H,I are owned by proc2.
3455 
3456    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3457    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3458    The 'M','N' parameters are 8,8, and have the same values on all procs.
3459 
3460    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3461    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3462    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3463    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3464    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3465    matrix, ans [DF] as another SeqAIJ matrix.
3466 
3467    When d_nz, o_nz parameters are specified, d_nz storage elements are
3468    allocated for every row of the local diagonal submatrix, and o_nz
3469    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3470    One way to choose d_nz and o_nz is to use the max nonzerors per local
3471    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3472    In this case, the values of d_nz,o_nz are:
3473 .vb
3474      proc0 : dnz = 2, o_nz = 2
3475      proc1 : dnz = 3, o_nz = 2
3476      proc2 : dnz = 1, o_nz = 4
3477 .ve
3478    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3479    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3480    for proc3. i.e we are using 12+15+10=37 storage locations to store
3481    34 values.
3482 
3483    When d_nnz, o_nnz parameters are specified, the storage is specified
3484    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3485    In the above case the values for d_nnz,o_nnz are:
3486 .vb
3487      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3488      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3489      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3490 .ve
3491    Here the space allocated is sum of all the above values i.e 34, and
3492    hence pre-allocation is perfect.
3493 
3494    Level: intermediate
3495 
3496 .keywords: matrix, aij, compressed row, sparse, parallel
3497 
3498 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
3499           MPIAIJ, MatGetInfo(), PetscSplitOwnership()
3500 @*/
3501 PetscErrorCode  MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3502 {
3503   PetscErrorCode ierr;
3504 
3505   PetscFunctionBegin;
3506   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3507   PetscValidType(B,1);
3508   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
3509   PetscFunctionReturn(0);
3510 }
3511 
3512 #undef __FUNCT__
3513 #define __FUNCT__ "MatCreateMPIAIJWithArrays"
3514 /*@
3515      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
3516          CSR format the local rows.
3517 
3518    Collective on MPI_Comm
3519 
3520    Input Parameters:
3521 +  comm - MPI communicator
3522 .  m - number of local rows (Cannot be PETSC_DECIDE)
3523 .  n - This value should be the same as the local size used in creating the
3524        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3525        calculated if N is given) For square matrices n is almost always m.
3526 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3527 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3528 .   i - row indices
3529 .   j - column indices
3530 -   a - matrix values
3531 
3532    Output Parameter:
3533 .   mat - the matrix
3534 
3535    Level: intermediate
3536 
3537    Notes:
3538        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3539      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3540      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3541 
3542        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3543 
3544        The format which is used for the sparse matrix input, is equivalent to a
3545     row-major ordering.. i.e for the following matrix, the input data expected is
3546     as shown:
3547 
3548         1 0 0
3549         2 0 3     P0
3550        -------
3551         4 5 6     P1
3552 
3553      Process0 [P0]: rows_owned=[0,1]
3554         i =  {0,1,3}  [size = nrow+1  = 2+1]
3555         j =  {0,0,2}  [size = nz = 6]
3556         v =  {1,2,3}  [size = nz = 6]
3557 
3558      Process1 [P1]: rows_owned=[2]
3559         i =  {0,3}    [size = nrow+1  = 1+1]
3560         j =  {0,1,2}  [size = nz = 6]
3561         v =  {4,5,6}  [size = nz = 6]
3562 
3563 .keywords: matrix, aij, compressed row, sparse, parallel
3564 
3565 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3566           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
3567 @*/
3568 PetscErrorCode  MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
3569 {
3570   PetscErrorCode ierr;
3571 
3572   PetscFunctionBegin;
3573   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
3574   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
3575   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
3576   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
3577   /* ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr); */
3578   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
3579   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
3580   PetscFunctionReturn(0);
3581 }
3582 
3583 #undef __FUNCT__
3584 #define __FUNCT__ "MatCreateAIJ"
3585 /*@C
3586    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
3587    (the default parallel PETSc format).  For good matrix assembly performance
3588    the user should preallocate the matrix storage by setting the parameters
3589    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3590    performance can be increased by more than a factor of 50.
3591 
3592    Collective on MPI_Comm
3593 
3594    Input Parameters:
3595 +  comm - MPI communicator
3596 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
3597            This value should be the same as the local size used in creating the
3598            y vector for the matrix-vector product y = Ax.
3599 .  n - This value should be the same as the local size used in creating the
3600        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3601        calculated if N is given) For square matrices n is almost always m.
3602 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3603 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3604 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3605            (same value is used for all local rows)
3606 .  d_nnz - array containing the number of nonzeros in the various rows of the
3607            DIAGONAL portion of the local submatrix (possibly different for each row)
3608            or NULL, if d_nz is used to specify the nonzero structure.
3609            The size of this array is equal to the number of local rows, i.e 'm'.
3610 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3611            submatrix (same value is used for all local rows).
3612 -  o_nnz - array containing the number of nonzeros in the various rows of the
3613            OFF-DIAGONAL portion of the local submatrix (possibly different for
3614            each row) or NULL, if o_nz is used to specify the nonzero
3615            structure. The size of this array is equal to the number
3616            of local rows, i.e 'm'.
3617 
3618    Output Parameter:
3619 .  A - the matrix
3620 
3621    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3622    MatXXXXSetPreallocation() paradgm instead of this routine directly.
3623    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3624 
3625    Notes:
3626    If the *_nnz parameter is given then the *_nz parameter is ignored
3627 
3628    m,n,M,N parameters specify the size of the matrix, and its partitioning across
3629    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
3630    storage requirements for this matrix.
3631 
3632    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
3633    processor than it must be used on all processors that share the object for
3634    that argument.
3635 
3636    The user MUST specify either the local or global matrix dimensions
3637    (possibly both).
3638 
3639    The parallel matrix is partitioned across processors such that the
3640    first m0 rows belong to process 0, the next m1 rows belong to
3641    process 1, the next m2 rows belong to process 2 etc.. where
3642    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
3643    values corresponding to [m x N] submatrix.
3644 
3645    The columns are logically partitioned with the n0 columns belonging
3646    to 0th partition, the next n1 columns belonging to the next
3647    partition etc.. where n0,n1,n2... are the input parameter 'n'.
3648 
3649    The DIAGONAL portion of the local submatrix on any given processor
3650    is the submatrix corresponding to the rows and columns m,n
3651    corresponding to the given processor. i.e diagonal matrix on
3652    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
3653    etc. The remaining portion of the local submatrix [m x (N-n)]
3654    constitute the OFF-DIAGONAL portion. The example below better
3655    illustrates this concept.
3656 
3657    For a square global matrix we define each processor's diagonal portion
3658    to be its local rows and the corresponding columns (a square submatrix);
3659    each processor's off-diagonal portion encompasses the remainder of the
3660    local matrix (a rectangular submatrix).
3661 
3662    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3663 
3664    When calling this routine with a single process communicator, a matrix of
3665    type SEQAIJ is returned.  If a matrix of type MPIAIJ is desired for this
3666    type of communicator, use the construction mechanism:
3667      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
3668 
3669    By default, this format uses inodes (identical nodes) when possible.
3670    We search for consecutive rows with the same nonzero structure, thereby
3671    reusing matrix information to achieve increased efficiency.
3672 
3673    Options Database Keys:
3674 +  -mat_no_inode  - Do not use inodes
3675 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3676 -  -mat_aij_oneindex - Internally use indexing starting at 1
3677         rather than 0.  Note that when calling MatSetValues(),
3678         the user still MUST index entries starting at 0!
3679 
3680 
3681    Example usage:
3682 
3683    Consider the following 8x8 matrix with 34 non-zero values, that is
3684    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3685    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3686    as follows:
3687 
3688 .vb
3689             1  2  0  |  0  3  0  |  0  4
3690     Proc0   0  5  6  |  7  0  0  |  8  0
3691             9  0 10  | 11  0  0  | 12  0
3692     -------------------------------------
3693            13  0 14  | 15 16 17  |  0  0
3694     Proc1   0 18  0  | 19 20 21  |  0  0
3695             0  0  0  | 22 23  0  | 24  0
3696     -------------------------------------
3697     Proc2  25 26 27  |  0  0 28  | 29  0
3698            30  0  0  | 31 32 33  |  0 34
3699 .ve
3700 
3701    This can be represented as a collection of submatrices as:
3702 
3703 .vb
3704       A B C
3705       D E F
3706       G H I
3707 .ve
3708 
3709    Where the submatrices A,B,C are owned by proc0, D,E,F are
3710    owned by proc1, G,H,I are owned by proc2.
3711 
3712    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3713    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3714    The 'M','N' parameters are 8,8, and have the same values on all procs.
3715 
3716    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3717    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3718    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3719    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3720    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3721    matrix, ans [DF] as another SeqAIJ matrix.
3722 
3723    When d_nz, o_nz parameters are specified, d_nz storage elements are
3724    allocated for every row of the local diagonal submatrix, and o_nz
3725    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3726    One way to choose d_nz and o_nz is to use the max nonzerors per local
3727    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3728    In this case, the values of d_nz,o_nz are:
3729 .vb
3730      proc0 : dnz = 2, o_nz = 2
3731      proc1 : dnz = 3, o_nz = 2
3732      proc2 : dnz = 1, o_nz = 4
3733 .ve
3734    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3735    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3736    for proc3. i.e we are using 12+15+10=37 storage locations to store
3737    34 values.
3738 
3739    When d_nnz, o_nnz parameters are specified, the storage is specified
3740    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3741    In the above case the values for d_nnz,o_nnz are:
3742 .vb
3743      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3744      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3745      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3746 .ve
3747    Here the space allocated is sum of all the above values i.e 34, and
3748    hence pre-allocation is perfect.
3749 
3750    Level: intermediate
3751 
3752 .keywords: matrix, aij, compressed row, sparse, parallel
3753 
3754 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3755           MPIAIJ, MatCreateMPIAIJWithArrays()
3756 @*/
3757 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)
3758 {
3759   PetscErrorCode ierr;
3760   PetscMPIInt    size;
3761 
3762   PetscFunctionBegin;
3763   ierr = MatCreate(comm,A);CHKERRQ(ierr);
3764   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
3765   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3766   if (size > 1) {
3767     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
3768     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
3769   } else {
3770     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
3771     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
3772   }
3773   PetscFunctionReturn(0);
3774 }
3775 
3776 #undef __FUNCT__
3777 #define __FUNCT__ "MatMPIAIJGetSeqAIJ"
3778 PetscErrorCode  MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
3779 {
3780   Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
3781 
3782   PetscFunctionBegin;
3783   if (Ad)     *Ad     = a->A;
3784   if (Ao)     *Ao     = a->B;
3785   if (colmap) *colmap = a->garray;
3786   PetscFunctionReturn(0);
3787 }
3788 
3789 #undef __FUNCT__
3790 #define __FUNCT__ "MatSetColoring_MPIAIJ"
3791 PetscErrorCode MatSetColoring_MPIAIJ(Mat A,ISColoring coloring)
3792 {
3793   PetscErrorCode ierr;
3794   PetscInt       i;
3795   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3796 
3797   PetscFunctionBegin;
3798   if (coloring->ctype == IS_COLORING_GLOBAL) {
3799     ISColoringValue *allcolors,*colors;
3800     ISColoring      ocoloring;
3801 
3802     /* set coloring for diagonal portion */
3803     ierr = MatSetColoring_SeqAIJ(a->A,coloring);CHKERRQ(ierr);
3804 
3805     /* set coloring for off-diagonal portion */
3806     ierr = ISAllGatherColors(PetscObjectComm((PetscObject)A),coloring->n,coloring->colors,NULL,&allcolors);CHKERRQ(ierr);
3807     ierr = PetscMalloc1(a->B->cmap->n+1,&colors);CHKERRQ(ierr);
3808     for (i=0; i<a->B->cmap->n; i++) {
3809       colors[i] = allcolors[a->garray[i]];
3810     }
3811     ierr = PetscFree(allcolors);CHKERRQ(ierr);
3812     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3813     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
3814     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3815   } else if (coloring->ctype == IS_COLORING_GHOSTED) {
3816     ISColoringValue *colors;
3817     PetscInt        *larray;
3818     ISColoring      ocoloring;
3819 
3820     /* set coloring for diagonal portion */
3821     ierr = PetscMalloc1(a->A->cmap->n+1,&larray);CHKERRQ(ierr);
3822     for (i=0; i<a->A->cmap->n; i++) {
3823       larray[i] = i + A->cmap->rstart;
3824     }
3825     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->A->cmap->n,larray,NULL,larray);CHKERRQ(ierr);
3826     ierr = PetscMalloc1(a->A->cmap->n+1,&colors);CHKERRQ(ierr);
3827     for (i=0; i<a->A->cmap->n; i++) {
3828       colors[i] = coloring->colors[larray[i]];
3829     }
3830     ierr = PetscFree(larray);CHKERRQ(ierr);
3831     ierr = ISColoringCreate(PETSC_COMM_SELF,coloring->n,a->A->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3832     ierr = MatSetColoring_SeqAIJ(a->A,ocoloring);CHKERRQ(ierr);
3833     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3834 
3835     /* set coloring for off-diagonal portion */
3836     ierr = PetscMalloc1(a->B->cmap->n+1,&larray);CHKERRQ(ierr);
3837     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->B->cmap->n,a->garray,NULL,larray);CHKERRQ(ierr);
3838     ierr = PetscMalloc1(a->B->cmap->n+1,&colors);CHKERRQ(ierr);
3839     for (i=0; i<a->B->cmap->n; i++) {
3840       colors[i] = coloring->colors[larray[i]];
3841     }
3842     ierr = PetscFree(larray);CHKERRQ(ierr);
3843     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,PETSC_OWN_POINTER,&ocoloring);CHKERRQ(ierr);
3844     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
3845     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
3846   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support ISColoringType %d",(int)coloring->ctype);
3847   PetscFunctionReturn(0);
3848 }
3849 
3850 #undef __FUNCT__
3851 #define __FUNCT__ "MatSetValuesAdifor_MPIAIJ"
3852 PetscErrorCode MatSetValuesAdifor_MPIAIJ(Mat A,PetscInt nl,void *advalues)
3853 {
3854   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3855   PetscErrorCode ierr;
3856 
3857   PetscFunctionBegin;
3858   ierr = MatSetValuesAdifor_SeqAIJ(a->A,nl,advalues);CHKERRQ(ierr);
3859   ierr = MatSetValuesAdifor_SeqAIJ(a->B,nl,advalues);CHKERRQ(ierr);
3860   PetscFunctionReturn(0);
3861 }
3862 
3863 #undef __FUNCT__
3864 #define __FUNCT__ "MatCreateMPIMatConcatenateSeqMat_MPIAIJ"
3865 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
3866 {
3867   PetscErrorCode ierr;
3868   PetscInt       m,N,i,rstart,nnz,Ii;
3869   PetscInt       *indx;
3870   PetscScalar    *values;
3871 
3872   PetscFunctionBegin;
3873   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
3874   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
3875     PetscInt       *dnz,*onz,sum,bs,cbs;
3876 
3877     if (n == PETSC_DECIDE) {
3878       ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
3879     }
3880     /* Check sum(n) = N */
3881     ierr = MPI_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3882     if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
3883 
3884     ierr    = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3885     rstart -= m;
3886 
3887     ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
3888     for (i=0; i<m; i++) {
3889       ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3890       ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
3891       ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3892     }
3893 
3894     ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
3895     ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
3896     ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
3897     ierr = MatSetBlockSizes(*outmat,bs,cbs);CHKERRQ(ierr);
3898     ierr = MatSetType(*outmat,MATMPIAIJ);CHKERRQ(ierr);
3899     ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
3900     ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
3901   }
3902 
3903   /* numeric phase */
3904   ierr = MatGetOwnershipRange(*outmat,&rstart,NULL);CHKERRQ(ierr);
3905   for (i=0; i<m; i++) {
3906     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3907     Ii   = i + rstart;
3908     ierr = MatSetValues(*outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3909     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3910   }
3911   ierr = MatAssemblyBegin(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3912   ierr = MatAssemblyEnd(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3913   PetscFunctionReturn(0);
3914 }
3915 
3916 #undef __FUNCT__
3917 #define __FUNCT__ "MatFileSplit"
3918 PetscErrorCode MatFileSplit(Mat A,char *outfile)
3919 {
3920   PetscErrorCode    ierr;
3921   PetscMPIInt       rank;
3922   PetscInt          m,N,i,rstart,nnz;
3923   size_t            len;
3924   const PetscInt    *indx;
3925   PetscViewer       out;
3926   char              *name;
3927   Mat               B;
3928   const PetscScalar *values;
3929 
3930   PetscFunctionBegin;
3931   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
3932   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
3933   /* Should this be the type of the diagonal block of A? */
3934   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
3935   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
3936   ierr = MatSetBlockSizesFromMats(B,A,A);CHKERRQ(ierr);
3937   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
3938   ierr = MatSeqAIJSetPreallocation(B,0,NULL);CHKERRQ(ierr);
3939   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
3940   for (i=0; i<m; i++) {
3941     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3942     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3943     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3944   }
3945   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3946   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3947 
3948   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
3949   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
3950   ierr = PetscMalloc1(len+5,&name);CHKERRQ(ierr);
3951   sprintf(name,"%s.%d",outfile,rank);
3952   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
3953   ierr = PetscFree(name);CHKERRQ(ierr);
3954   ierr = MatView(B,out);CHKERRQ(ierr);
3955   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
3956   ierr = MatDestroy(&B);CHKERRQ(ierr);
3957   PetscFunctionReturn(0);
3958 }
3959 
3960 extern PetscErrorCode MatDestroy_MPIAIJ(Mat);
3961 #undef __FUNCT__
3962 #define __FUNCT__ "MatDestroy_MPIAIJ_SeqsToMPI"
3963 PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
3964 {
3965   PetscErrorCode      ierr;
3966   Mat_Merge_SeqsToMPI *merge;
3967   PetscContainer      container;
3968 
3969   PetscFunctionBegin;
3970   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
3971   if (container) {
3972     ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
3973     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
3974     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
3975     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
3976     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
3977     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
3978     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
3979     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
3980     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
3981     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
3982     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
3983     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
3984     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
3985     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
3986     ierr = PetscFree(merge);CHKERRQ(ierr);
3987     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
3988   }
3989   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
3990   PetscFunctionReturn(0);
3991 }
3992 
3993 #include <../src/mat/utils/freespace.h>
3994 #include <petscbt.h>
3995 
3996 #undef __FUNCT__
3997 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJNumeric"
3998 PetscErrorCode  MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
3999 {
4000   PetscErrorCode      ierr;
4001   MPI_Comm            comm;
4002   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
4003   PetscMPIInt         size,rank,taga,*len_s;
4004   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
4005   PetscInt            proc,m;
4006   PetscInt            **buf_ri,**buf_rj;
4007   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
4008   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
4009   MPI_Request         *s_waits,*r_waits;
4010   MPI_Status          *status;
4011   MatScalar           *aa=a->a;
4012   MatScalar           **abuf_r,*ba_i;
4013   Mat_Merge_SeqsToMPI *merge;
4014   PetscContainer      container;
4015 
4016   PetscFunctionBegin;
4017   ierr = PetscObjectGetComm((PetscObject)mpimat,&comm);CHKERRQ(ierr);
4018   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4019 
4020   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4021   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4022 
4023   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4024   ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4025 
4026   bi     = merge->bi;
4027   bj     = merge->bj;
4028   buf_ri = merge->buf_ri;
4029   buf_rj = merge->buf_rj;
4030 
4031   ierr   = PetscMalloc1(size,&status);CHKERRQ(ierr);
4032   owners = merge->rowmap->range;
4033   len_s  = merge->len_s;
4034 
4035   /* send and recv matrix values */
4036   /*-----------------------------*/
4037   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
4038   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
4039 
4040   ierr = PetscMalloc1(merge->nsend+1,&s_waits);CHKERRQ(ierr);
4041   for (proc=0,k=0; proc<size; proc++) {
4042     if (!len_s[proc]) continue;
4043     i    = owners[proc];
4044     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
4045     k++;
4046   }
4047 
4048   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
4049   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
4050   ierr = PetscFree(status);CHKERRQ(ierr);
4051 
4052   ierr = PetscFree(s_waits);CHKERRQ(ierr);
4053   ierr = PetscFree(r_waits);CHKERRQ(ierr);
4054 
4055   /* insert mat values of mpimat */
4056   /*----------------------------*/
4057   ierr = PetscMalloc1(N,&ba_i);CHKERRQ(ierr);
4058   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4059 
4060   for (k=0; k<merge->nrecv; k++) {
4061     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4062     nrows       = *(buf_ri_k[k]);
4063     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
4064     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4065   }
4066 
4067   /* set values of ba */
4068   m = merge->rowmap->n;
4069   for (i=0; i<m; i++) {
4070     arow = owners[rank] + i;
4071     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
4072     bnzi = bi[i+1] - bi[i];
4073     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
4074 
4075     /* add local non-zero vals of this proc's seqmat into ba */
4076     anzi   = ai[arow+1] - ai[arow];
4077     aj     = a->j + ai[arow];
4078     aa     = a->a + ai[arow];
4079     nextaj = 0;
4080     for (j=0; nextaj<anzi; j++) {
4081       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4082         ba_i[j] += aa[nextaj++];
4083       }
4084     }
4085 
4086     /* add received vals into ba */
4087     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4088       /* i-th row */
4089       if (i == *nextrow[k]) {
4090         anzi   = *(nextai[k]+1) - *nextai[k];
4091         aj     = buf_rj[k] + *(nextai[k]);
4092         aa     = abuf_r[k] + *(nextai[k]);
4093         nextaj = 0;
4094         for (j=0; nextaj<anzi; j++) {
4095           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4096             ba_i[j] += aa[nextaj++];
4097           }
4098         }
4099         nextrow[k]++; nextai[k]++;
4100       }
4101     }
4102     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
4103   }
4104   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4105   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4106 
4107   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
4108   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
4109   ierr = PetscFree(ba_i);CHKERRQ(ierr);
4110   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4111   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4112   PetscFunctionReturn(0);
4113 }
4114 
4115 extern PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat);
4116 
4117 #undef __FUNCT__
4118 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJSymbolic"
4119 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4120 {
4121   PetscErrorCode      ierr;
4122   Mat                 B_mpi;
4123   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
4124   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4125   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
4126   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4127   PetscInt            len,proc,*dnz,*onz,bs,cbs;
4128   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4129   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4130   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
4131   MPI_Status          *status;
4132   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
4133   PetscBT             lnkbt;
4134   Mat_Merge_SeqsToMPI *merge;
4135   PetscContainer      container;
4136 
4137   PetscFunctionBegin;
4138   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4139 
4140   /* make sure it is a PETSc comm */
4141   ierr = PetscCommDuplicate(comm,&comm,NULL);CHKERRQ(ierr);
4142   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4143   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4144 
4145   ierr = PetscNew(&merge);CHKERRQ(ierr);
4146   ierr = PetscMalloc1(size,&status);CHKERRQ(ierr);
4147 
4148   /* determine row ownership */
4149   /*---------------------------------------------------------*/
4150   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
4151   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
4152   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
4153   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
4154   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
4155   ierr = PetscMalloc1(size,&len_si);CHKERRQ(ierr);
4156   ierr = PetscMalloc1(size,&merge->len_s);CHKERRQ(ierr);
4157 
4158   m      = merge->rowmap->n;
4159   owners = merge->rowmap->range;
4160 
4161   /* determine the number of messages to send, their lengths */
4162   /*---------------------------------------------------------*/
4163   len_s = merge->len_s;
4164 
4165   len          = 0; /* length of buf_si[] */
4166   merge->nsend = 0;
4167   for (proc=0; proc<size; proc++) {
4168     len_si[proc] = 0;
4169     if (proc == rank) {
4170       len_s[proc] = 0;
4171     } else {
4172       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4173       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4174     }
4175     if (len_s[proc]) {
4176       merge->nsend++;
4177       nrows = 0;
4178       for (i=owners[proc]; i<owners[proc+1]; i++) {
4179         if (ai[i+1] > ai[i]) nrows++;
4180       }
4181       len_si[proc] = 2*(nrows+1);
4182       len         += len_si[proc];
4183     }
4184   }
4185 
4186   /* determine the number and length of messages to receive for ij-structure */
4187   /*-------------------------------------------------------------------------*/
4188   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
4189   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
4190 
4191   /* post the Irecv of j-structure */
4192   /*-------------------------------*/
4193   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
4194   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
4195 
4196   /* post the Isend of j-structure */
4197   /*--------------------------------*/
4198   ierr = PetscMalloc2(merge->nsend,&si_waits,merge->nsend,&sj_waits);CHKERRQ(ierr);
4199 
4200   for (proc=0, k=0; proc<size; proc++) {
4201     if (!len_s[proc]) continue;
4202     i    = owners[proc];
4203     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
4204     k++;
4205   }
4206 
4207   /* receives and sends of j-structure are complete */
4208   /*------------------------------------------------*/
4209   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
4210   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
4211 
4212   /* send and recv i-structure */
4213   /*---------------------------*/
4214   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
4215   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
4216 
4217   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
4218   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4219   for (proc=0,k=0; proc<size; proc++) {
4220     if (!len_s[proc]) continue;
4221     /* form outgoing message for i-structure:
4222          buf_si[0]:                 nrows to be sent
4223                [1:nrows]:           row index (global)
4224                [nrows+1:2*nrows+1]: i-structure index
4225     */
4226     /*-------------------------------------------*/
4227     nrows       = len_si[proc]/2 - 1;
4228     buf_si_i    = buf_si + nrows+1;
4229     buf_si[0]   = nrows;
4230     buf_si_i[0] = 0;
4231     nrows       = 0;
4232     for (i=owners[proc]; i<owners[proc+1]; i++) {
4233       anzi = ai[i+1] - ai[i];
4234       if (anzi) {
4235         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4236         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4237         nrows++;
4238       }
4239     }
4240     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4241     k++;
4242     buf_si += len_si[proc];
4243   }
4244 
4245   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4246   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4247 
4248   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4249   for (i=0; i<merge->nrecv; i++) {
4250     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);
4251   }
4252 
4253   ierr = PetscFree(len_si);CHKERRQ(ierr);
4254   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4255   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4256   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4257   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4258   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4259   ierr = PetscFree(status);CHKERRQ(ierr);
4260 
4261   /* compute a local seq matrix in each processor */
4262   /*----------------------------------------------*/
4263   /* allocate bi array and free space for accumulating nonzero column info */
4264   ierr  = PetscMalloc1(m+1,&bi);CHKERRQ(ierr);
4265   bi[0] = 0;
4266 
4267   /* create and initialize a linked list */
4268   nlnk = N+1;
4269   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4270 
4271   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4272   len  = ai[owners[rank+1]] - ai[owners[rank]];
4273   ierr = PetscFreeSpaceGet((PetscInt)(2*len+1),&free_space);CHKERRQ(ierr);
4274 
4275   current_space = free_space;
4276 
4277   /* determine symbolic info for each local row */
4278   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4279 
4280   for (k=0; k<merge->nrecv; k++) {
4281     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4282     nrows       = *buf_ri_k[k];
4283     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4284     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4285   }
4286 
4287   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4288   len  = 0;
4289   for (i=0; i<m; i++) {
4290     bnzi = 0;
4291     /* add local non-zero cols of this proc's seqmat into lnk */
4292     arow  = owners[rank] + i;
4293     anzi  = ai[arow+1] - ai[arow];
4294     aj    = a->j + ai[arow];
4295     ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4296     bnzi += nlnk;
4297     /* add received col data into lnk */
4298     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4299       if (i == *nextrow[k]) { /* i-th row */
4300         anzi  = *(nextai[k]+1) - *nextai[k];
4301         aj    = buf_rj[k] + *nextai[k];
4302         ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4303         bnzi += nlnk;
4304         nextrow[k]++; nextai[k]++;
4305       }
4306     }
4307     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4308 
4309     /* if free space is not available, make more free space */
4310     if (current_space->local_remaining<bnzi) {
4311       ierr = PetscFreeSpaceGet(bnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
4312       nspacedouble++;
4313     }
4314     /* copy data into free space, then initialize lnk */
4315     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4316     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
4317 
4318     current_space->array           += bnzi;
4319     current_space->local_used      += bnzi;
4320     current_space->local_remaining -= bnzi;
4321 
4322     bi[i+1] = bi[i] + bnzi;
4323   }
4324 
4325   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4326 
4327   ierr = PetscMalloc1(bi[m]+1,&bj);CHKERRQ(ierr);
4328   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
4329   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4330 
4331   /* create symbolic parallel matrix B_mpi */
4332   /*---------------------------------------*/
4333   ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
4334   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
4335   if (n==PETSC_DECIDE) {
4336     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
4337   } else {
4338     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4339   }
4340   ierr = MatSetBlockSizes(B_mpi,bs,cbs);CHKERRQ(ierr);
4341   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
4342   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
4343   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4344   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
4345 
4346   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4347   B_mpi->assembled    = PETSC_FALSE;
4348   B_mpi->ops->destroy = MatDestroy_MPIAIJ_SeqsToMPI;
4349   merge->bi           = bi;
4350   merge->bj           = bj;
4351   merge->buf_ri       = buf_ri;
4352   merge->buf_rj       = buf_rj;
4353   merge->coi          = NULL;
4354   merge->coj          = NULL;
4355   merge->owners_co    = NULL;
4356 
4357   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
4358 
4359   /* attach the supporting struct to B_mpi for reuse */
4360   ierr    = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
4361   ierr    = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
4362   ierr    = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
4363   ierr    = PetscContainerDestroy(&container);CHKERRQ(ierr);
4364   *mpimat = B_mpi;
4365 
4366   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4367   PetscFunctionReturn(0);
4368 }
4369 
4370 #undef __FUNCT__
4371 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJ"
4372 /*@C
4373       MatCreateMPIAIJSumSeqAIJ - Creates a MPIAIJ matrix by adding sequential
4374                  matrices from each processor
4375 
4376     Collective on MPI_Comm
4377 
4378    Input Parameters:
4379 +    comm - the communicators the parallel matrix will live on
4380 .    seqmat - the input sequential matrices
4381 .    m - number of local rows (or PETSC_DECIDE)
4382 .    n - number of local columns (or PETSC_DECIDE)
4383 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4384 
4385    Output Parameter:
4386 .    mpimat - the parallel matrix generated
4387 
4388     Level: advanced
4389 
4390    Notes:
4391      The dimensions of the sequential matrix in each processor MUST be the same.
4392      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
4393      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
4394 @*/
4395 PetscErrorCode  MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
4396 {
4397   PetscErrorCode ierr;
4398   PetscMPIInt    size;
4399 
4400   PetscFunctionBegin;
4401   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4402   if (size == 1) {
4403     ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4404     if (scall == MAT_INITIAL_MATRIX) {
4405       ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
4406     } else {
4407       ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4408     }
4409     ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4410     PetscFunctionReturn(0);
4411   }
4412   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4413   if (scall == MAT_INITIAL_MATRIX) {
4414     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
4415   }
4416   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
4417   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4418   PetscFunctionReturn(0);
4419 }
4420 
4421 #undef __FUNCT__
4422 #define __FUNCT__ "MatMPIAIJGetLocalMat"
4423 /*@
4424      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
4425           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
4426           with MatGetSize()
4427 
4428     Not Collective
4429 
4430    Input Parameters:
4431 +    A - the matrix
4432 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4433 
4434    Output Parameter:
4435 .    A_loc - the local sequential matrix generated
4436 
4437     Level: developer
4438 
4439 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
4440 
4441 @*/
4442 PetscErrorCode  MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
4443 {
4444   PetscErrorCode ierr;
4445   Mat_MPIAIJ     *mpimat=(Mat_MPIAIJ*)A->data;
4446   Mat_SeqAIJ     *mat,*a,*b;
4447   PetscInt       *ai,*aj,*bi,*bj,*cmap=mpimat->garray;
4448   MatScalar      *aa,*ba,*cam;
4449   PetscScalar    *ca;
4450   PetscInt       am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
4451   PetscInt       *ci,*cj,col,ncols_d,ncols_o,jo;
4452   PetscBool      match;
4453   MPI_Comm       comm;
4454   PetscMPIInt    size;
4455 
4456   PetscFunctionBegin;
4457   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4458   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
4459   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4460   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4461   if (size == 1 && scall == MAT_REUSE_MATRIX) PetscFunctionReturn(0);
4462 
4463   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4464   a = (Mat_SeqAIJ*)(mpimat->A)->data;
4465   b = (Mat_SeqAIJ*)(mpimat->B)->data;
4466   ai = a->i; aj = a->j; bi = b->i; bj = b->j;
4467   aa = a->a; ba = b->a;
4468   if (scall == MAT_INITIAL_MATRIX) {
4469     if (size == 1) {
4470       ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ai,aj,aa,A_loc);CHKERRQ(ierr);
4471       PetscFunctionReturn(0);
4472     }
4473 
4474     ierr  = PetscMalloc1(1+am,&ci);CHKERRQ(ierr);
4475     ci[0] = 0;
4476     for (i=0; i<am; i++) {
4477       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
4478     }
4479     ierr = PetscMalloc1(1+ci[am],&cj);CHKERRQ(ierr);
4480     ierr = PetscMalloc1(1+ci[am],&ca);CHKERRQ(ierr);
4481     k    = 0;
4482     for (i=0; i<am; i++) {
4483       ncols_o = bi[i+1] - bi[i];
4484       ncols_d = ai[i+1] - ai[i];
4485       /* off-diagonal portion of A */
4486       for (jo=0; jo<ncols_o; jo++) {
4487         col = cmap[*bj];
4488         if (col >= cstart) break;
4489         cj[k]   = col; bj++;
4490         ca[k++] = *ba++;
4491       }
4492       /* diagonal portion of A */
4493       for (j=0; j<ncols_d; j++) {
4494         cj[k]   = cstart + *aj++;
4495         ca[k++] = *aa++;
4496       }
4497       /* off-diagonal portion of A */
4498       for (j=jo; j<ncols_o; j++) {
4499         cj[k]   = cmap[*bj++];
4500         ca[k++] = *ba++;
4501       }
4502     }
4503     /* put together the new matrix */
4504     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
4505     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4506     /* Since these are PETSc arrays, change flags to free them as necessary. */
4507     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
4508     mat->free_a  = PETSC_TRUE;
4509     mat->free_ij = PETSC_TRUE;
4510     mat->nonew   = 0;
4511   } else if (scall == MAT_REUSE_MATRIX) {
4512     mat=(Mat_SeqAIJ*)(*A_loc)->data;
4513     ci = mat->i; cj = mat->j; cam = mat->a;
4514     for (i=0; i<am; i++) {
4515       /* off-diagonal portion of A */
4516       ncols_o = bi[i+1] - bi[i];
4517       for (jo=0; jo<ncols_o; jo++) {
4518         col = cmap[*bj];
4519         if (col >= cstart) break;
4520         *cam++ = *ba++; bj++;
4521       }
4522       /* diagonal portion of A */
4523       ncols_d = ai[i+1] - ai[i];
4524       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
4525       /* off-diagonal portion of A */
4526       for (j=jo; j<ncols_o; j++) {
4527         *cam++ = *ba++; bj++;
4528       }
4529     }
4530   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
4531   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4532   PetscFunctionReturn(0);
4533 }
4534 
4535 #undef __FUNCT__
4536 #define __FUNCT__ "MatMPIAIJGetLocalMatCondensed"
4537 /*@C
4538      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MPIAIJ matrix by taking all its local rows and NON-ZERO columns
4539 
4540     Not Collective
4541 
4542    Input Parameters:
4543 +    A - the matrix
4544 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4545 -    row, col - index sets of rows and columns to extract (or NULL)
4546 
4547    Output Parameter:
4548 .    A_loc - the local sequential matrix generated
4549 
4550     Level: developer
4551 
4552 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
4553 
4554 @*/
4555 PetscErrorCode  MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
4556 {
4557   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4558   PetscErrorCode ierr;
4559   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
4560   IS             isrowa,iscola;
4561   Mat            *aloc;
4562   PetscBool      match;
4563 
4564   PetscFunctionBegin;
4565   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4566   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
4567   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4568   if (!row) {
4569     start = A->rmap->rstart; end = A->rmap->rend;
4570     ierr  = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
4571   } else {
4572     isrowa = *row;
4573   }
4574   if (!col) {
4575     start = A->cmap->rstart;
4576     cmap  = a->garray;
4577     nzA   = a->A->cmap->n;
4578     nzB   = a->B->cmap->n;
4579     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4580     ncols = 0;
4581     for (i=0; i<nzB; i++) {
4582       if (cmap[i] < start) idx[ncols++] = cmap[i];
4583       else break;
4584     }
4585     imark = i;
4586     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
4587     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
4588     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
4589   } else {
4590     iscola = *col;
4591   }
4592   if (scall != MAT_INITIAL_MATRIX) {
4593     ierr    = PetscMalloc1(1,&aloc);CHKERRQ(ierr);
4594     aloc[0] = *A_loc;
4595   }
4596   ierr   = MatGetSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
4597   *A_loc = aloc[0];
4598   ierr   = PetscFree(aloc);CHKERRQ(ierr);
4599   if (!row) {
4600     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
4601   }
4602   if (!col) {
4603     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
4604   }
4605   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4606   PetscFunctionReturn(0);
4607 }
4608 
4609 #undef __FUNCT__
4610 #define __FUNCT__ "MatGetBrowsOfAcols"
4611 /*@C
4612     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
4613 
4614     Collective on Mat
4615 
4616    Input Parameters:
4617 +    A,B - the matrices in mpiaij format
4618 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4619 -    rowb, colb - index sets of rows and columns of B to extract (or NULL)
4620 
4621    Output Parameter:
4622 +    rowb, colb - index sets of rows and columns of B to extract
4623 -    B_seq - the sequential matrix generated
4624 
4625     Level: developer
4626 
4627 @*/
4628 PetscErrorCode  MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
4629 {
4630   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4631   PetscErrorCode ierr;
4632   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
4633   IS             isrowb,iscolb;
4634   Mat            *bseq=NULL;
4635 
4636   PetscFunctionBegin;
4637   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4638     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);
4639   }
4640   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4641 
4642   if (scall == MAT_INITIAL_MATRIX) {
4643     start = A->cmap->rstart;
4644     cmap  = a->garray;
4645     nzA   = a->A->cmap->n;
4646     nzB   = a->B->cmap->n;
4647     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4648     ncols = 0;
4649     for (i=0; i<nzB; i++) {  /* row < local row index */
4650       if (cmap[i] < start) idx[ncols++] = cmap[i];
4651       else break;
4652     }
4653     imark = i;
4654     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
4655     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
4656     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
4657     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
4658   } else {
4659     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
4660     isrowb  = *rowb; iscolb = *colb;
4661     ierr    = PetscMalloc1(1,&bseq);CHKERRQ(ierr);
4662     bseq[0] = *B_seq;
4663   }
4664   ierr   = MatGetSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
4665   *B_seq = bseq[0];
4666   ierr   = PetscFree(bseq);CHKERRQ(ierr);
4667   if (!rowb) {
4668     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
4669   } else {
4670     *rowb = isrowb;
4671   }
4672   if (!colb) {
4673     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
4674   } else {
4675     *colb = iscolb;
4676   }
4677   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4678   PetscFunctionReturn(0);
4679 }
4680 
4681 #undef __FUNCT__
4682 #define __FUNCT__ "MatGetBrowsOfAoCols_MPIAIJ"
4683 /*
4684     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
4685     of the OFF-DIAGONAL portion of local A
4686 
4687     Collective on Mat
4688 
4689    Input Parameters:
4690 +    A,B - the matrices in mpiaij format
4691 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4692 
4693    Output Parameter:
4694 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
4695 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
4696 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
4697 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
4698 
4699     Level: developer
4700 
4701 */
4702 PetscErrorCode  MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
4703 {
4704   VecScatter_MPI_General *gen_to,*gen_from;
4705   PetscErrorCode         ierr;
4706   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
4707   Mat_SeqAIJ             *b_oth;
4708   VecScatter             ctx =a->Mvctx;
4709   MPI_Comm               comm;
4710   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
4711   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
4712   PetscScalar            *rvalues,*svalues;
4713   MatScalar              *b_otha,*bufa,*bufA;
4714   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
4715   MPI_Request            *rwaits = NULL,*swaits = NULL;
4716   MPI_Status             *sstatus,rstatus;
4717   PetscMPIInt            jj,size;
4718   PetscInt               *cols,sbs,rbs;
4719   PetscScalar            *vals;
4720 
4721   PetscFunctionBegin;
4722   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4723   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4724   if (size == 1) PetscFunctionReturn(0);
4725 
4726   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4727     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);
4728   }
4729   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4730   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4731 
4732   gen_to   = (VecScatter_MPI_General*)ctx->todata;
4733   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
4734   rvalues  = gen_from->values; /* holds the length of receiving row */
4735   svalues  = gen_to->values;   /* holds the length of sending row */
4736   nrecvs   = gen_from->n;
4737   nsends   = gen_to->n;
4738 
4739   ierr    = PetscMalloc2(nrecvs,&rwaits,nsends,&swaits);CHKERRQ(ierr);
4740   srow    = gen_to->indices;    /* local row index to be sent */
4741   sstarts = gen_to->starts;
4742   sprocs  = gen_to->procs;
4743   sstatus = gen_to->sstatus;
4744   sbs     = gen_to->bs;
4745   rstarts = gen_from->starts;
4746   rprocs  = gen_from->procs;
4747   rbs     = gen_from->bs;
4748 
4749   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
4750   if (scall == MAT_INITIAL_MATRIX) {
4751     /* i-array */
4752     /*---------*/
4753     /*  post receives */
4754     for (i=0; i<nrecvs; i++) {
4755       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
4756       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
4757       ierr   = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4758     }
4759 
4760     /* pack the outgoing message */
4761     ierr = PetscMalloc2(nsends+1,&sstartsj,nrecvs+1,&rstartsj);CHKERRQ(ierr);
4762 
4763     sstartsj[0] = 0;
4764     rstartsj[0] = 0;
4765     len         = 0; /* total length of j or a array to be sent */
4766     k           = 0;
4767     for (i=0; i<nsends; i++) {
4768       rowlen = (PetscInt*)svalues + sstarts[i]*sbs;
4769       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
4770       for (j=0; j<nrows; j++) {
4771         row = srow[k] + B->rmap->range[rank]; /* global row idx */
4772         for (l=0; l<sbs; l++) {
4773           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr); /* rowlength */
4774 
4775           rowlen[j*sbs+l] = ncols;
4776 
4777           len += ncols;
4778           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr);
4779         }
4780         k++;
4781       }
4782       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4783 
4784       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
4785     }
4786     /* recvs and sends of i-array are completed */
4787     i = nrecvs;
4788     while (i--) {
4789       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4790     }
4791     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4792 
4793     /* allocate buffers for sending j and a arrays */
4794     ierr = PetscMalloc1(len+1,&bufj);CHKERRQ(ierr);
4795     ierr = PetscMalloc1(len+1,&bufa);CHKERRQ(ierr);
4796 
4797     /* create i-array of B_oth */
4798     ierr = PetscMalloc1(aBn+2,&b_othi);CHKERRQ(ierr);
4799 
4800     b_othi[0] = 0;
4801     len       = 0; /* total length of j or a array to be received */
4802     k         = 0;
4803     for (i=0; i<nrecvs; i++) {
4804       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
4805       nrows  = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be recieved */
4806       for (j=0; j<nrows; j++) {
4807         b_othi[k+1] = b_othi[k] + rowlen[j];
4808         len        += rowlen[j]; k++;
4809       }
4810       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
4811     }
4812 
4813     /* allocate space for j and a arrrays of B_oth */
4814     ierr = PetscMalloc1(b_othi[aBn]+1,&b_othj);CHKERRQ(ierr);
4815     ierr = PetscMalloc1(b_othi[aBn]+1,&b_otha);CHKERRQ(ierr);
4816 
4817     /* j-array */
4818     /*---------*/
4819     /*  post receives of j-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_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4823     }
4824 
4825     /* pack the outgoing message j-array */
4826     k = 0;
4827     for (i=0; i<nsends; i++) {
4828       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4829       bufJ  = bufj+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,&cols,NULL);CHKERRQ(ierr);
4834           for (l=0; l<ncols; l++) {
4835             *bufJ++ = cols[l];
4836           }
4837           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4838         }
4839       }
4840       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4841     }
4842 
4843     /* recvs and sends of j-array are completed */
4844     i = nrecvs;
4845     while (i--) {
4846       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4847     }
4848     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4849   } else if (scall == MAT_REUSE_MATRIX) {
4850     sstartsj = *startsj_s;
4851     rstartsj = *startsj_r;
4852     bufa     = *bufa_ptr;
4853     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
4854     b_otha   = b_oth->a;
4855   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
4856 
4857   /* a-array */
4858   /*---------*/
4859   /*  post receives of a-array */
4860   for (i=0; i<nrecvs; i++) {
4861     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4862     ierr  = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4863   }
4864 
4865   /* pack the outgoing message a-array */
4866   k = 0;
4867   for (i=0; i<nsends; i++) {
4868     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4869     bufA  = bufa+sstartsj[i];
4870     for (j=0; j<nrows; j++) {
4871       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4872       for (ll=0; ll<sbs; ll++) {
4873         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4874         for (l=0; l<ncols; l++) {
4875           *bufA++ = vals[l];
4876         }
4877         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4878       }
4879     }
4880     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4881   }
4882   /* recvs and sends of a-array are completed */
4883   i = nrecvs;
4884   while (i--) {
4885     ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4886   }
4887   if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4888   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
4889 
4890   if (scall == MAT_INITIAL_MATRIX) {
4891     /* put together the new matrix */
4892     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
4893 
4894     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4895     /* Since these are PETSc arrays, change flags to free them as necessary. */
4896     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
4897     b_oth->free_a  = PETSC_TRUE;
4898     b_oth->free_ij = PETSC_TRUE;
4899     b_oth->nonew   = 0;
4900 
4901     ierr = PetscFree(bufj);CHKERRQ(ierr);
4902     if (!startsj_s || !bufa_ptr) {
4903       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
4904       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
4905     } else {
4906       *startsj_s = sstartsj;
4907       *startsj_r = rstartsj;
4908       *bufa_ptr  = bufa;
4909     }
4910   }
4911   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4912   PetscFunctionReturn(0);
4913 }
4914 
4915 #undef __FUNCT__
4916 #define __FUNCT__ "MatGetCommunicationStructs"
4917 /*@C
4918   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
4919 
4920   Not Collective
4921 
4922   Input Parameters:
4923 . A - The matrix in mpiaij format
4924 
4925   Output Parameter:
4926 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
4927 . colmap - A map from global column index to local index into lvec
4928 - multScatter - A scatter from the argument of a matrix-vector product to lvec
4929 
4930   Level: developer
4931 
4932 @*/
4933 #if defined(PETSC_USE_CTABLE)
4934 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
4935 #else
4936 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
4937 #endif
4938 {
4939   Mat_MPIAIJ *a;
4940 
4941   PetscFunctionBegin;
4942   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4943   PetscValidPointer(lvec, 2);
4944   PetscValidPointer(colmap, 3);
4945   PetscValidPointer(multScatter, 4);
4946   a = (Mat_MPIAIJ*) A->data;
4947   if (lvec) *lvec = a->lvec;
4948   if (colmap) *colmap = a->colmap;
4949   if (multScatter) *multScatter = a->Mvctx;
4950   PetscFunctionReturn(0);
4951 }
4952 
4953 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
4954 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
4955 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
4956 #if defined(PETSC_HAVE_ELEMENTAL)
4957 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
4958 #endif
4959 
4960 #undef __FUNCT__
4961 #define __FUNCT__ "MatMatMultNumeric_MPIDense_MPIAIJ"
4962 /*
4963     Computes (B'*A')' since computing B*A directly is untenable
4964 
4965                n                       p                          p
4966         (              )       (              )         (                  )
4967       m (      A       )  *  n (       B      )   =   m (         C        )
4968         (              )       (              )         (                  )
4969 
4970 */
4971 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
4972 {
4973   PetscErrorCode ierr;
4974   Mat            At,Bt,Ct;
4975 
4976   PetscFunctionBegin;
4977   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
4978   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
4979   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
4980   ierr = MatDestroy(&At);CHKERRQ(ierr);
4981   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
4982   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
4983   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
4984   PetscFunctionReturn(0);
4985 }
4986 
4987 #undef __FUNCT__
4988 #define __FUNCT__ "MatMatMultSymbolic_MPIDense_MPIAIJ"
4989 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
4990 {
4991   PetscErrorCode ierr;
4992   PetscInt       m=A->rmap->n,n=B->cmap->n;
4993   Mat            Cmat;
4994 
4995   PetscFunctionBegin;
4996   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);
4997   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
4998   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4999   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
5000   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
5001   ierr = MatMPIDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
5002   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5003   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5004 
5005   Cmat->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
5006 
5007   *C = Cmat;
5008   PetscFunctionReturn(0);
5009 }
5010 
5011 /* ----------------------------------------------------------------*/
5012 #undef __FUNCT__
5013 #define __FUNCT__ "MatMatMult_MPIDense_MPIAIJ"
5014 PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
5015 {
5016   PetscErrorCode ierr;
5017 
5018   PetscFunctionBegin;
5019   if (scall == MAT_INITIAL_MATRIX) {
5020     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5021     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
5022     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5023   }
5024   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5025   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
5026   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5027   PetscFunctionReturn(0);
5028 }
5029 
5030 /*MC
5031    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
5032 
5033    Options Database Keys:
5034 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
5035 
5036   Level: beginner
5037 
5038 .seealso: MatCreateAIJ()
5039 M*/
5040 
5041 #undef __FUNCT__
5042 #define __FUNCT__ "MatCreate_MPIAIJ"
5043 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
5044 {
5045   Mat_MPIAIJ     *b;
5046   PetscErrorCode ierr;
5047   PetscMPIInt    size;
5048 
5049   PetscFunctionBegin;
5050   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
5051 
5052   ierr          = PetscNewLog(B,&b);CHKERRQ(ierr);
5053   B->data       = (void*)b;
5054   ierr          = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
5055   B->assembled  = PETSC_FALSE;
5056   B->insertmode = NOT_SET_VALUES;
5057   b->size       = size;
5058 
5059   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank);CHKERRQ(ierr);
5060 
5061   /* build cache for off array entries formed */
5062   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash);CHKERRQ(ierr);
5063 
5064   b->donotstash  = PETSC_FALSE;
5065   b->colmap      = 0;
5066   b->garray      = 0;
5067   b->roworiented = PETSC_TRUE;
5068 
5069   /* stuff used for matrix vector multiply */
5070   b->lvec  = NULL;
5071   b->Mvctx = NULL;
5072 
5073   /* stuff for MatGetRow() */
5074   b->rowindices   = 0;
5075   b->rowvalues    = 0;
5076   b->getrowactive = PETSC_FALSE;
5077 
5078   /* flexible pointer used in CUSP/CUSPARSE classes */
5079   b->spptr = NULL;
5080 
5081   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ);CHKERRQ(ierr);
5082   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
5083   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetDiagonalBlock_C",MatGetDiagonalBlock_MPIAIJ);CHKERRQ(ierr);
5084   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
5085   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
5086   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
5087   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
5088   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
5089   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
5090   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
5091 #if defined(PETSC_HAVE_ELEMENTAL)
5092   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_elemental_C",MatConvert_MPIAIJ_Elemental);CHKERRQ(ierr);
5093 #endif
5094   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
5095   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
5096   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
5097   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
5098   PetscFunctionReturn(0);
5099 }
5100 
5101 #undef __FUNCT__
5102 #define __FUNCT__ "MatCreateMPIAIJWithSplitArrays"
5103 /*@C
5104      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
5105          and "off-diagonal" part of the matrix in CSR format.
5106 
5107    Collective on MPI_Comm
5108 
5109    Input Parameters:
5110 +  comm - MPI communicator
5111 .  m - number of local rows (Cannot be PETSC_DECIDE)
5112 .  n - This value should be the same as the local size used in creating the
5113        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
5114        calculated if N is given) For square matrices n is almost always m.
5115 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
5116 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
5117 .   i - row indices for "diagonal" portion of matrix
5118 .   j - column indices
5119 .   a - matrix values
5120 .   oi - row indices for "off-diagonal" portion of matrix
5121 .   oj - column indices
5122 -   oa - matrix values
5123 
5124    Output Parameter:
5125 .   mat - the matrix
5126 
5127    Level: advanced
5128 
5129    Notes:
5130        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
5131        must free the arrays once the matrix has been destroyed and not before.
5132 
5133        The i and j indices are 0 based
5134 
5135        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
5136 
5137        This sets local rows and cannot be used to set off-processor values.
5138 
5139        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
5140        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
5141        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
5142        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
5143        keep track of the underlying array. Use MatSetOption(A,MAT_IGNORE_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
5144        communication if it is known that only local entries will be set.
5145 
5146 .keywords: matrix, aij, compressed row, sparse, parallel
5147 
5148 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
5149           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
5150 @*/
5151 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)
5152 {
5153   PetscErrorCode ierr;
5154   Mat_MPIAIJ     *maij;
5155 
5156   PetscFunctionBegin;
5157   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
5158   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
5159   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
5160   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
5161   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
5162   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
5163   maij = (Mat_MPIAIJ*) (*mat)->data;
5164 
5165   (*mat)->preallocated = PETSC_TRUE;
5166 
5167   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
5168   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
5169 
5170   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
5171   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
5172 
5173   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5174   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5175   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5176   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5177 
5178   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5179   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5180   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
5181   PetscFunctionReturn(0);
5182 }
5183 
5184 /*
5185     Special version for direct calls from Fortran
5186 */
5187 #include <petsc-private/fortranimpl.h>
5188 
5189 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5190 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
5191 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5192 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
5193 #endif
5194 
5195 /* Change these macros so can be used in void function */
5196 #undef CHKERRQ
5197 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
5198 #undef SETERRQ2
5199 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5200 #undef SETERRQ3
5201 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5202 #undef SETERRQ
5203 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
5204 
5205 #undef __FUNCT__
5206 #define __FUNCT__ "matsetvaluesmpiaij_"
5207 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)
5208 {
5209   Mat            mat  = *mmat;
5210   PetscInt       m    = *mm, n = *mn;
5211   InsertMode     addv = *maddv;
5212   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
5213   PetscScalar    value;
5214   PetscErrorCode ierr;
5215 
5216   MatCheckPreallocated(mat,1);
5217   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
5218 
5219 #if defined(PETSC_USE_DEBUG)
5220   else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
5221 #endif
5222   {
5223     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
5224     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
5225     PetscBool roworiented = aij->roworiented;
5226 
5227     /* Some Variables required in the macro */
5228     Mat        A                 = aij->A;
5229     Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
5230     PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
5231     MatScalar  *aa               = a->a;
5232     PetscBool  ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
5233     Mat        B                 = aij->B;
5234     Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
5235     PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5236     MatScalar  *ba               = b->a;
5237 
5238     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5239     PetscInt  nonew = a->nonew;
5240     MatScalar *ap1,*ap2;
5241 
5242     PetscFunctionBegin;
5243     for (i=0; i<m; i++) {
5244       if (im[i] < 0) continue;
5245 #if defined(PETSC_USE_DEBUG)
5246       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);
5247 #endif
5248       if (im[i] >= rstart && im[i] < rend) {
5249         row      = im[i] - rstart;
5250         lastcol1 = -1;
5251         rp1      = aj + ai[row];
5252         ap1      = aa + ai[row];
5253         rmax1    = aimax[row];
5254         nrow1    = ailen[row];
5255         low1     = 0;
5256         high1    = nrow1;
5257         lastcol2 = -1;
5258         rp2      = bj + bi[row];
5259         ap2      = ba + bi[row];
5260         rmax2    = bimax[row];
5261         nrow2    = bilen[row];
5262         low2     = 0;
5263         high2    = nrow2;
5264 
5265         for (j=0; j<n; j++) {
5266           if (roworiented) value = v[i*n+j];
5267           else value = v[i+j*m];
5268           if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES)) continue;
5269           if (in[j] >= cstart && in[j] < cend) {
5270             col = in[j] - cstart;
5271             MatSetValues_SeqAIJ_A_Private(row,col,value,addv);
5272           } else if (in[j] < 0) continue;
5273 #if defined(PETSC_USE_DEBUG)
5274           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);
5275 #endif
5276           else {
5277             if (mat->was_assembled) {
5278               if (!aij->colmap) {
5279                 ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5280               }
5281 #if defined(PETSC_USE_CTABLE)
5282               ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5283               col--;
5284 #else
5285               col = aij->colmap[in[j]] - 1;
5286 #endif
5287               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5288                 ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5289                 col  =  in[j];
5290                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5291                 B     = aij->B;
5292                 b     = (Mat_SeqAIJ*)B->data;
5293                 bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5294                 rp2   = bj + bi[row];
5295                 ap2   = ba + bi[row];
5296                 rmax2 = bimax[row];
5297                 nrow2 = bilen[row];
5298                 low2  = 0;
5299                 high2 = nrow2;
5300                 bm    = aij->B->rmap->n;
5301                 ba    = b->a;
5302               }
5303             } else col = in[j];
5304             MatSetValues_SeqAIJ_B_Private(row,col,value,addv);
5305           }
5306         }
5307       } else if (!aij->donotstash) {
5308         if (roworiented) {
5309           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5310         } else {
5311           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5312         }
5313       }
5314     }
5315   }
5316   PetscFunctionReturnVoid();
5317 }
5318 
5319