xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision a5348796144b39cd37695f2b231684936dd6a0c9)
1 
2 
3 #include <../src/mat/impls/aij/mpi/mpiaij.h>   /*I "petscmat.h" I*/
4 #include <petsc/private/vecimpl.h>
5 #include <petsc/private/isimpl.h>
6 #include <petscblaslapack.h>
7 #include <petscsf.h>
8 
9 /*MC
10    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.
11 
12    This matrix type is identical to MATSEQAIJ when constructed with a single process communicator,
13    and MATMPIAIJ otherwise.  As a result, for single process communicators,
14   MatSeqAIJSetPreallocation is supported, and similarly MatMPIAIJSetPreallocation is supported
15   for communicators controlling multiple processes.  It is recommended that you call both of
16   the above preallocation routines for simplicity.
17 
18    Options Database Keys:
19 . -mat_type aij - sets the matrix type to "aij" during a call to MatSetFromOptions()
20 
21   Developer Notes: Subclasses include MATAIJCUSP, MATAIJCUSPARSE, MATAIJPERM, MATAIJCRL, and also automatically switches over to use inodes when
22    enough exist.
23 
24   Level: beginner
25 
26 .seealso: MatCreateAIJ(), MatCreateSeqAIJ(), MATSEQAIJ, MATMPIAIJ
27 M*/
28 
29 /*MC
30    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.
31 
32    This matrix type is identical to MATSEQAIJCRL when constructed with a single process communicator,
33    and MATMPIAIJCRL otherwise.  As a result, for single process communicators,
34    MatSeqAIJSetPreallocation() is supported, and similarly MatMPIAIJSetPreallocation() is supported
35   for communicators controlling multiple processes.  It is recommended that you call both of
36   the above preallocation routines for simplicity.
37 
38    Options Database Keys:
39 . -mat_type aijcrl - sets the matrix type to "aijcrl" during a call to MatSetFromOptions()
40 
41   Level: beginner
42 
43 .seealso: MatCreateMPIAIJCRL,MATSEQAIJCRL,MATMPIAIJCRL, MATSEQAIJCRL, MATMPIAIJCRL
44 M*/
45 
46 PetscErrorCode MatSetBlockSizes_MPIAIJ(Mat M, PetscInt rbs, PetscInt cbs)
47 {
48   PetscErrorCode ierr;
49   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)M->data;
50 
51   PetscFunctionBegin;
52   if (mat->A) {
53     ierr = MatSetBlockSizes(mat->A,rbs,cbs);CHKERRQ(ierr);
54     ierr = MatSetBlockSizes(mat->B,rbs,1);CHKERRQ(ierr);
55   }
56   PetscFunctionReturn(0);
57 }
58 
59 PetscErrorCode MatFindNonzeroRows_MPIAIJ(Mat M,IS *keptrows)
60 {
61   PetscErrorCode  ierr;
62   Mat_MPIAIJ      *mat = (Mat_MPIAIJ*)M->data;
63   Mat_SeqAIJ      *a   = (Mat_SeqAIJ*)mat->A->data;
64   Mat_SeqAIJ      *b   = (Mat_SeqAIJ*)mat->B->data;
65   const PetscInt  *ia,*ib;
66   const MatScalar *aa,*bb;
67   PetscInt        na,nb,i,j,*rows,cnt=0,n0rows;
68   PetscInt        m = M->rmap->n,rstart = M->rmap->rstart;
69 
70   PetscFunctionBegin;
71   *keptrows = 0;
72   ia        = a->i;
73   ib        = b->i;
74   for (i=0; i<m; i++) {
75     na = ia[i+1] - ia[i];
76     nb = ib[i+1] - ib[i];
77     if (!na && !nb) {
78       cnt++;
79       goto ok1;
80     }
81     aa = a->a + ia[i];
82     for (j=0; j<na; j++) {
83       if (aa[j] != 0.0) goto ok1;
84     }
85     bb = b->a + ib[i];
86     for (j=0; j <nb; j++) {
87       if (bb[j] != 0.0) goto ok1;
88     }
89     cnt++;
90 ok1:;
91   }
92   ierr = MPIU_Allreduce(&cnt,&n0rows,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)M));CHKERRQ(ierr);
93   if (!n0rows) PetscFunctionReturn(0);
94   ierr = PetscMalloc1(M->rmap->n-cnt,&rows);CHKERRQ(ierr);
95   cnt  = 0;
96   for (i=0; i<m; i++) {
97     na = ia[i+1] - ia[i];
98     nb = ib[i+1] - ib[i];
99     if (!na && !nb) continue;
100     aa = a->a + ia[i];
101     for (j=0; j<na;j++) {
102       if (aa[j] != 0.0) {
103         rows[cnt++] = rstart + i;
104         goto ok2;
105       }
106     }
107     bb = b->a + ib[i];
108     for (j=0; j<nb; j++) {
109       if (bb[j] != 0.0) {
110         rows[cnt++] = rstart + i;
111         goto ok2;
112       }
113     }
114 ok2:;
115   }
116   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)M),cnt,rows,PETSC_OWN_POINTER,keptrows);CHKERRQ(ierr);
117   PetscFunctionReturn(0);
118 }
119 
120 PetscErrorCode  MatDiagonalSet_MPIAIJ(Mat Y,Vec D,InsertMode is)
121 {
122   PetscErrorCode    ierr;
123   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*) Y->data;
124 
125   PetscFunctionBegin;
126   if (Y->assembled && Y->rmap->rstart == Y->cmap->rstart && Y->rmap->rend == Y->cmap->rend) {
127     ierr = MatDiagonalSet(aij->A,D,is);CHKERRQ(ierr);
128   } else {
129     ierr = MatDiagonalSet_Default(Y,D,is);CHKERRQ(ierr);
130   }
131   PetscFunctionReturn(0);
132 }
133 
134 PetscErrorCode MatFindZeroDiagonals_MPIAIJ(Mat M,IS *zrows)
135 {
136   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)M->data;
137   PetscErrorCode ierr;
138   PetscInt       i,rstart,nrows,*rows;
139 
140   PetscFunctionBegin;
141   *zrows = NULL;
142   ierr   = MatFindZeroDiagonals_SeqAIJ_Private(aij->A,&nrows,&rows);CHKERRQ(ierr);
143   ierr   = MatGetOwnershipRange(M,&rstart,NULL);CHKERRQ(ierr);
144   for (i=0; i<nrows; i++) rows[i] += rstart;
145   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)M),nrows,rows,PETSC_OWN_POINTER,zrows);CHKERRQ(ierr);
146   PetscFunctionReturn(0);
147 }
148 
149 PetscErrorCode MatGetColumnNorms_MPIAIJ(Mat A,NormType type,PetscReal *norms)
150 {
151   PetscErrorCode ierr;
152   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)A->data;
153   PetscInt       i,n,*garray = aij->garray;
154   Mat_SeqAIJ     *a_aij = (Mat_SeqAIJ*) aij->A->data;
155   Mat_SeqAIJ     *b_aij = (Mat_SeqAIJ*) aij->B->data;
156   PetscReal      *work;
157 
158   PetscFunctionBegin;
159   ierr = MatGetSize(A,NULL,&n);CHKERRQ(ierr);
160   ierr = PetscCalloc1(n,&work);CHKERRQ(ierr);
161   if (type == NORM_2) {
162     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
163       work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i]*a_aij->a[i]);
164     }
165     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
166       work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]*b_aij->a[i]);
167     }
168   } else if (type == NORM_1) {
169     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
170       work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i]);
171     }
172     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
173       work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]);
174     }
175   } else if (type == NORM_INFINITY) {
176     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
177       work[A->cmap->rstart + a_aij->j[i]] = PetscMax(PetscAbsScalar(a_aij->a[i]), work[A->cmap->rstart + a_aij->j[i]]);
178     }
179     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
180       work[garray[b_aij->j[i]]] = PetscMax(PetscAbsScalar(b_aij->a[i]),work[garray[b_aij->j[i]]]);
181     }
182 
183   } else SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Unknown NormType");
184   if (type == NORM_INFINITY) {
185     ierr = MPIU_Allreduce(work,norms,n,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
186   } else {
187     ierr = MPIU_Allreduce(work,norms,n,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
188   }
189   ierr = PetscFree(work);CHKERRQ(ierr);
190   if (type == NORM_2) {
191     for (i=0; i<n; i++) norms[i] = PetscSqrtReal(norms[i]);
192   }
193   PetscFunctionReturn(0);
194 }
195 
196 PetscErrorCode MatFindOffBlockDiagonalEntries_MPIAIJ(Mat A,IS *is)
197 {
198   Mat_MPIAIJ      *a  = (Mat_MPIAIJ*)A->data;
199   IS              sis,gis;
200   PetscErrorCode  ierr;
201   const PetscInt  *isis,*igis;
202   PetscInt        n,*iis,nsis,ngis,rstart,i;
203 
204   PetscFunctionBegin;
205   ierr = MatFindOffBlockDiagonalEntries(a->A,&sis);CHKERRQ(ierr);
206   ierr = MatFindNonzeroRows(a->B,&gis);CHKERRQ(ierr);
207   ierr = ISGetSize(gis,&ngis);CHKERRQ(ierr);
208   ierr = ISGetSize(sis,&nsis);CHKERRQ(ierr);
209   ierr = ISGetIndices(sis,&isis);CHKERRQ(ierr);
210   ierr = ISGetIndices(gis,&igis);CHKERRQ(ierr);
211 
212   ierr = PetscMalloc1(ngis+nsis,&iis);CHKERRQ(ierr);
213   ierr = PetscMemcpy(iis,igis,ngis*sizeof(PetscInt));CHKERRQ(ierr);
214   ierr = PetscMemcpy(iis+ngis,isis,nsis*sizeof(PetscInt));CHKERRQ(ierr);
215   n    = ngis + nsis;
216   ierr = PetscSortRemoveDupsInt(&n,iis);CHKERRQ(ierr);
217   ierr = MatGetOwnershipRange(A,&rstart,NULL);CHKERRQ(ierr);
218   for (i=0; i<n; i++) iis[i] += rstart;
219   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)A),n,iis,PETSC_OWN_POINTER,is);CHKERRQ(ierr);
220 
221   ierr = ISRestoreIndices(sis,&isis);CHKERRQ(ierr);
222   ierr = ISRestoreIndices(gis,&igis);CHKERRQ(ierr);
223   ierr = ISDestroy(&sis);CHKERRQ(ierr);
224   ierr = ISDestroy(&gis);CHKERRQ(ierr);
225   PetscFunctionReturn(0);
226 }
227 
228 /*
229     Distributes a SeqAIJ matrix across a set of processes. Code stolen from
230     MatLoad_MPIAIJ(). Horrible lack of reuse. Should be a routine for each matrix type.
231 
232     Only for square matrices
233 
234     Used by a preconditioner, hence PETSC_EXTERN
235 */
236 PETSC_EXTERN PetscErrorCode MatDistribute_MPIAIJ(MPI_Comm comm,Mat gmat,PetscInt m,MatReuse reuse,Mat *inmat)
237 {
238   PetscMPIInt    rank,size;
239   PetscInt       *rowners,*dlens,*olens,i,rstart,rend,j,jj,nz = 0,*gmataj,cnt,row,*ld,bses[2];
240   PetscErrorCode ierr;
241   Mat            mat;
242   Mat_SeqAIJ     *gmata;
243   PetscMPIInt    tag;
244   MPI_Status     status;
245   PetscBool      aij;
246   MatScalar      *gmataa,*ao,*ad,*gmataarestore=0;
247 
248   PetscFunctionBegin;
249   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
250   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
251   if (!rank) {
252     ierr = PetscObjectTypeCompare((PetscObject)gmat,MATSEQAIJ,&aij);CHKERRQ(ierr);
253     if (!aij) SETERRQ1(PetscObjectComm((PetscObject)gmat),PETSC_ERR_SUP,"Currently no support for input matrix of type %s\n",((PetscObject)gmat)->type_name);
254   }
255   if (reuse == MAT_INITIAL_MATRIX) {
256     ierr = MatCreate(comm,&mat);CHKERRQ(ierr);
257     ierr = MatSetSizes(mat,m,m,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
258     ierr = MatGetBlockSizes(gmat,&bses[0],&bses[1]);CHKERRQ(ierr);
259     ierr = MPI_Bcast(bses,2,MPIU_INT,0,comm);CHKERRQ(ierr);
260     ierr = MatSetBlockSizes(mat,bses[0],bses[1]);CHKERRQ(ierr);
261     ierr = MatSetType(mat,MATAIJ);CHKERRQ(ierr);
262     ierr = PetscMalloc1(size+1,&rowners);CHKERRQ(ierr);
263     ierr = PetscMalloc2(m,&dlens,m,&olens);CHKERRQ(ierr);
264     ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
265 
266     rowners[0] = 0;
267     for (i=2; i<=size; i++) rowners[i] += rowners[i-1];
268     rstart = rowners[rank];
269     rend   = rowners[rank+1];
270     ierr   = PetscObjectGetNewTag((PetscObject)mat,&tag);CHKERRQ(ierr);
271     if (!rank) {
272       gmata = (Mat_SeqAIJ*) gmat->data;
273       /* send row lengths to all processors */
274       for (i=0; i<m; i++) dlens[i] = gmata->ilen[i];
275       for (i=1; i<size; i++) {
276         ierr = MPI_Send(gmata->ilen + rowners[i],rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
277       }
278       /* determine number diagonal and off-diagonal counts */
279       ierr = PetscMemzero(olens,m*sizeof(PetscInt));CHKERRQ(ierr);
280       ierr = PetscCalloc1(m,&ld);CHKERRQ(ierr);
281       jj   = 0;
282       for (i=0; i<m; i++) {
283         for (j=0; j<dlens[i]; j++) {
284           if (gmata->j[jj] < rstart) ld[i]++;
285           if (gmata->j[jj] < rstart || gmata->j[jj] >= rend) olens[i]++;
286           jj++;
287         }
288       }
289       /* send column indices to other processes */
290       for (i=1; i<size; i++) {
291         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
292         ierr = MPI_Send(&nz,1,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
293         ierr = MPI_Send(gmata->j + gmata->i[rowners[i]],nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
294       }
295 
296       /* send numerical values to other processes */
297       for (i=1; i<size; i++) {
298         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
299         ierr = MPI_Send(gmata->a + gmata->i[rowners[i]],nz,MPIU_SCALAR,i,tag,comm);CHKERRQ(ierr);
300       }
301       gmataa = gmata->a;
302       gmataj = gmata->j;
303 
304     } else {
305       /* receive row lengths */
306       ierr = MPI_Recv(dlens,m,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
307       /* receive column indices */
308       ierr = MPI_Recv(&nz,1,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
309       ierr = PetscMalloc2(nz,&gmataa,nz,&gmataj);CHKERRQ(ierr);
310       ierr = MPI_Recv(gmataj,nz,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
311       /* determine number diagonal and off-diagonal counts */
312       ierr = PetscMemzero(olens,m*sizeof(PetscInt));CHKERRQ(ierr);
313       ierr = PetscCalloc1(m,&ld);CHKERRQ(ierr);
314       jj   = 0;
315       for (i=0; i<m; i++) {
316         for (j=0; j<dlens[i]; j++) {
317           if (gmataj[jj] < rstart) ld[i]++;
318           if (gmataj[jj] < rstart || gmataj[jj] >= rend) olens[i]++;
319           jj++;
320         }
321       }
322       /* receive numerical values */
323       ierr = PetscMemzero(gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr);
324       ierr = MPI_Recv(gmataa,nz,MPIU_SCALAR,0,tag,comm,&status);CHKERRQ(ierr);
325     }
326     /* set preallocation */
327     for (i=0; i<m; i++) {
328       dlens[i] -= olens[i];
329     }
330     ierr = MatSeqAIJSetPreallocation(mat,0,dlens);CHKERRQ(ierr);
331     ierr = MatMPIAIJSetPreallocation(mat,0,dlens,0,olens);CHKERRQ(ierr);
332 
333     for (i=0; i<m; i++) {
334       dlens[i] += olens[i];
335     }
336     cnt = 0;
337     for (i=0; i<m; i++) {
338       row  = rstart + i;
339       ierr = MatSetValues(mat,1,&row,dlens[i],gmataj+cnt,gmataa+cnt,INSERT_VALUES);CHKERRQ(ierr);
340       cnt += dlens[i];
341     }
342     if (rank) {
343       ierr = PetscFree2(gmataa,gmataj);CHKERRQ(ierr);
344     }
345     ierr = PetscFree2(dlens,olens);CHKERRQ(ierr);
346     ierr = PetscFree(rowners);CHKERRQ(ierr);
347 
348     ((Mat_MPIAIJ*)(mat->data))->ld = ld;
349 
350     *inmat = mat;
351   } else {   /* column indices are already set; only need to move over numerical values from process 0 */
352     Mat_SeqAIJ *Ad = (Mat_SeqAIJ*)((Mat_MPIAIJ*)((*inmat)->data))->A->data;
353     Mat_SeqAIJ *Ao = (Mat_SeqAIJ*)((Mat_MPIAIJ*)((*inmat)->data))->B->data;
354     mat  = *inmat;
355     ierr = PetscObjectGetNewTag((PetscObject)mat,&tag);CHKERRQ(ierr);
356     if (!rank) {
357       /* send numerical values to other processes */
358       gmata  = (Mat_SeqAIJ*) gmat->data;
359       ierr   = MatGetOwnershipRanges(mat,(const PetscInt**)&rowners);CHKERRQ(ierr);
360       gmataa = gmata->a;
361       for (i=1; i<size; i++) {
362         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
363         ierr = MPI_Send(gmataa + gmata->i[rowners[i]],nz,MPIU_SCALAR,i,tag,comm);CHKERRQ(ierr);
364       }
365       nz = gmata->i[rowners[1]]-gmata->i[rowners[0]];
366     } else {
367       /* receive numerical values from process 0*/
368       nz   = Ad->nz + Ao->nz;
369       ierr = PetscMalloc1(nz,&gmataa);CHKERRQ(ierr); gmataarestore = gmataa;
370       ierr = MPI_Recv(gmataa,nz,MPIU_SCALAR,0,tag,comm,&status);CHKERRQ(ierr);
371     }
372     /* transfer numerical values into the diagonal A and off diagonal B parts of mat */
373     ld = ((Mat_MPIAIJ*)(mat->data))->ld;
374     ad = Ad->a;
375     ao = Ao->a;
376     if (mat->rmap->n) {
377       i  = 0;
378       nz = ld[i];                                   ierr = PetscMemcpy(ao,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ao += nz; gmataa += nz;
379       nz = Ad->i[i+1] - Ad->i[i];                   ierr = PetscMemcpy(ad,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ad += nz; gmataa += nz;
380     }
381     for (i=1; i<mat->rmap->n; i++) {
382       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;
383       nz = Ad->i[i+1] - Ad->i[i];                   ierr = PetscMemcpy(ad,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ad += nz; gmataa += nz;
384     }
385     i--;
386     if (mat->rmap->n) {
387       nz = Ao->i[i+1] - Ao->i[i] - ld[i];           ierr = PetscMemcpy(ao,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr);
388     }
389     if (rank) {
390       ierr = PetscFree(gmataarestore);CHKERRQ(ierr);
391     }
392   }
393   ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
394   ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
395   PetscFunctionReturn(0);
396 }
397 
398 /*
399   Local utility routine that creates a mapping from the global column
400 number to the local number in the off-diagonal part of the local
401 storage of the matrix.  When PETSC_USE_CTABLE is used this is scalable at
402 a slightly higher hash table cost; without it it is not scalable (each processor
403 has an order N integer array but is fast to acess.
404 */
405 PetscErrorCode MatCreateColmap_MPIAIJ_Private(Mat mat)
406 {
407   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
408   PetscErrorCode ierr;
409   PetscInt       n = aij->B->cmap->n,i;
410 
411   PetscFunctionBegin;
412   if (!aij->garray) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"MPIAIJ Matrix was assembled but is missing garray");
413 #if defined(PETSC_USE_CTABLE)
414   ierr = PetscTableCreate(n,mat->cmap->N+1,&aij->colmap);CHKERRQ(ierr);
415   for (i=0; i<n; i++) {
416     ierr = PetscTableAdd(aij->colmap,aij->garray[i]+1,i+1,INSERT_VALUES);CHKERRQ(ierr);
417   }
418 #else
419   ierr = PetscCalloc1(mat->cmap->N+1,&aij->colmap);CHKERRQ(ierr);
420   ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N+1)*sizeof(PetscInt));CHKERRQ(ierr);
421   for (i=0; i<n; i++) aij->colmap[aij->garray[i]] = i+1;
422 #endif
423   PetscFunctionReturn(0);
424 }
425 
426 #define MatSetValues_SeqAIJ_A_Private(row,col,value,addv,orow,ocol)     \
427 { \
428     if (col <= lastcol1)  low1 = 0;     \
429     else                 high1 = nrow1; \
430     lastcol1 = col;\
431     while (high1-low1 > 5) { \
432       t = (low1+high1)/2; \
433       if (rp1[t] > col) high1 = t; \
434       else              low1  = t; \
435     } \
436       for (_i=low1; _i<high1; _i++) { \
437         if (rp1[_i] > col) break; \
438         if (rp1[_i] == col) { \
439           if (addv == ADD_VALUES) ap1[_i] += value;   \
440           else                    ap1[_i] = value; \
441           goto a_noinsert; \
442         } \
443       }  \
444       if (value == 0.0 && ignorezeroentries && row != col) {low1 = 0; high1 = nrow1;goto a_noinsert;} \
445       if (nonew == 1) {low1 = 0; high1 = nrow1; goto a_noinsert;}                \
446       if (nonew == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at global row/column (%D, %D) into matrix", orow, ocol); \
447       MatSeqXAIJReallocateAIJ(A,am,1,nrow1,row,col,rmax1,aa,ai,aj,rp1,ap1,aimax,nonew,MatScalar); \
448       N = nrow1++ - 1; a->nz++; high1++; \
449       /* shift up all the later entries in this row */ \
450       for (ii=N; ii>=_i; ii--) { \
451         rp1[ii+1] = rp1[ii]; \
452         ap1[ii+1] = ap1[ii]; \
453       } \
454       rp1[_i] = col;  \
455       ap1[_i] = value;  \
456       A->nonzerostate++;\
457       a_noinsert: ; \
458       ailen[row] = nrow1; \
459 }
460 
461 #define MatSetValues_SeqAIJ_B_Private(row,col,value,addv,orow,ocol) \
462   { \
463     if (col <= lastcol2) low2 = 0;                        \
464     else high2 = nrow2;                                   \
465     lastcol2 = col;                                       \
466     while (high2-low2 > 5) {                              \
467       t = (low2+high2)/2;                                 \
468       if (rp2[t] > col) high2 = t;                        \
469       else             low2  = t;                         \
470     }                                                     \
471     for (_i=low2; _i<high2; _i++) {                       \
472       if (rp2[_i] > col) break;                           \
473       if (rp2[_i] == col) {                               \
474         if (addv == ADD_VALUES) ap2[_i] += value;         \
475         else                    ap2[_i] = value;          \
476         goto b_noinsert;                                  \
477       }                                                   \
478     }                                                     \
479     if (value == 0.0 && ignorezeroentries) {low2 = 0; high2 = nrow2; goto b_noinsert;} \
480     if (nonew == 1) {low2 = 0; high2 = nrow2; goto b_noinsert;}                        \
481     if (nonew == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at global row/column (%D, %D) into matrix", orow, ocol); \
482     MatSeqXAIJReallocateAIJ(B,bm,1,nrow2,row,col,rmax2,ba,bi,bj,rp2,ap2,bimax,nonew,MatScalar); \
483     N = nrow2++ - 1; b->nz++; high2++;                    \
484     /* shift up all the later entries in this row */      \
485     for (ii=N; ii>=_i; ii--) {                            \
486       rp2[ii+1] = rp2[ii];                                \
487       ap2[ii+1] = ap2[ii];                                \
488     }                                                     \
489     rp2[_i] = col;                                        \
490     ap2[_i] = value;                                      \
491     B->nonzerostate++;                                    \
492     b_noinsert: ;                                         \
493     bilen[row] = nrow2;                                   \
494   }
495 
496 PetscErrorCode MatSetValuesRow_MPIAIJ(Mat A,PetscInt row,const PetscScalar v[])
497 {
498   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)A->data;
499   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)mat->A->data,*b = (Mat_SeqAIJ*)mat->B->data;
500   PetscErrorCode ierr;
501   PetscInt       l,*garray = mat->garray,diag;
502 
503   PetscFunctionBegin;
504   /* code only works for square matrices A */
505 
506   /* find size of row to the left of the diagonal part */
507   ierr = MatGetOwnershipRange(A,&diag,0);CHKERRQ(ierr);
508   row  = row - diag;
509   for (l=0; l<b->i[row+1]-b->i[row]; l++) {
510     if (garray[b->j[b->i[row]+l]] > diag) break;
511   }
512   ierr = PetscMemcpy(b->a+b->i[row],v,l*sizeof(PetscScalar));CHKERRQ(ierr);
513 
514   /* diagonal part */
515   ierr = PetscMemcpy(a->a+a->i[row],v+l,(a->i[row+1]-a->i[row])*sizeof(PetscScalar));CHKERRQ(ierr);
516 
517   /* right of diagonal part */
518   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);
519   PetscFunctionReturn(0);
520 }
521 
522 PetscErrorCode MatSetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode addv)
523 {
524   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
525   PetscScalar    value;
526   PetscErrorCode ierr;
527   PetscInt       i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
528   PetscInt       cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
529   PetscBool      roworiented = aij->roworiented;
530 
531   /* Some Variables required in the macro */
532   Mat        A                 = aij->A;
533   Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
534   PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
535   MatScalar  *aa               = a->a;
536   PetscBool  ignorezeroentries = a->ignorezeroentries;
537   Mat        B                 = aij->B;
538   Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
539   PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
540   MatScalar  *ba               = b->a;
541 
542   PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
543   PetscInt  nonew;
544   MatScalar *ap1,*ap2;
545 
546   PetscFunctionBegin;
547   for (i=0; i<m; i++) {
548     if (im[i] < 0) continue;
549 #if defined(PETSC_USE_DEBUG)
550     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);
551 #endif
552     if (im[i] >= rstart && im[i] < rend) {
553       row      = im[i] - rstart;
554       lastcol1 = -1;
555       rp1      = aj + ai[row];
556       ap1      = aa + ai[row];
557       rmax1    = aimax[row];
558       nrow1    = ailen[row];
559       low1     = 0;
560       high1    = nrow1;
561       lastcol2 = -1;
562       rp2      = bj + bi[row];
563       ap2      = ba + bi[row];
564       rmax2    = bimax[row];
565       nrow2    = bilen[row];
566       low2     = 0;
567       high2    = nrow2;
568 
569       for (j=0; j<n; j++) {
570         if (roworiented) value = v[i*n+j];
571         else             value = v[i+j*m];
572         if (in[j] >= cstart && in[j] < cend) {
573           col   = in[j] - cstart;
574           nonew = a->nonew;
575           if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
576           MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
577         } else if (in[j] < 0) continue;
578 #if defined(PETSC_USE_DEBUG)
579         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);
580 #endif
581         else {
582           if (mat->was_assembled) {
583             if (!aij->colmap) {
584               ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
585             }
586 #if defined(PETSC_USE_CTABLE)
587             ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
588             col--;
589 #else
590             col = aij->colmap[in[j]] - 1;
591 #endif
592             if (col < 0 && !((Mat_SeqAIJ*)(aij->B->data))->nonew) {
593               ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
594               col  =  in[j];
595               /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
596               B     = aij->B;
597               b     = (Mat_SeqAIJ*)B->data;
598               bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j; ba = b->a;
599               rp2   = bj + bi[row];
600               ap2   = ba + bi[row];
601               rmax2 = bimax[row];
602               nrow2 = bilen[row];
603               low2  = 0;
604               high2 = nrow2;
605               bm    = aij->B->rmap->n;
606               ba    = b->a;
607             } else if (col < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at global row/column (%D, %D) into matrix", im[i], in[j]);
608           } else col = in[j];
609           nonew = b->nonew;
610           MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
611         }
612       }
613     } else {
614       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]);
615       if (!aij->donotstash) {
616         mat->assembled = PETSC_FALSE;
617         if (roworiented) {
618           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
619         } else {
620           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
621         }
622       }
623     }
624   }
625   PetscFunctionReturn(0);
626 }
627 
628 PetscErrorCode MatGetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],PetscScalar v[])
629 {
630   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
631   PetscErrorCode ierr;
632   PetscInt       i,j,rstart = mat->rmap->rstart,rend = mat->rmap->rend;
633   PetscInt       cstart = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
634 
635   PetscFunctionBegin;
636   for (i=0; i<m; i++) {
637     if (idxm[i] < 0) continue; /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative row: %D",idxm[i]);*/
638     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);
639     if (idxm[i] >= rstart && idxm[i] < rend) {
640       row = idxm[i] - rstart;
641       for (j=0; j<n; j++) {
642         if (idxn[j] < 0) continue; /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column: %D",idxn[j]); */
643         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);
644         if (idxn[j] >= cstart && idxn[j] < cend) {
645           col  = idxn[j] - cstart;
646           ierr = MatGetValues(aij->A,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
647         } else {
648           if (!aij->colmap) {
649             ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
650           }
651 #if defined(PETSC_USE_CTABLE)
652           ierr = PetscTableFind(aij->colmap,idxn[j]+1,&col);CHKERRQ(ierr);
653           col--;
654 #else
655           col = aij->colmap[idxn[j]] - 1;
656 #endif
657           if ((col < 0) || (aij->garray[col] != idxn[j])) *(v+i*n+j) = 0.0;
658           else {
659             ierr = MatGetValues(aij->B,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
660           }
661         }
662       }
663     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only local values currently supported");
664   }
665   PetscFunctionReturn(0);
666 }
667 
668 extern PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat,Vec,Vec);
669 
670 PetscErrorCode MatAssemblyBegin_MPIAIJ(Mat mat,MatAssemblyType mode)
671 {
672   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
673   PetscErrorCode ierr;
674   PetscInt       nstash,reallocs;
675 
676   PetscFunctionBegin;
677   if (aij->donotstash || mat->nooffprocentries) PetscFunctionReturn(0);
678 
679   ierr = MatStashScatterBegin_Private(mat,&mat->stash,mat->rmap->range);CHKERRQ(ierr);
680   ierr = MatStashGetInfo_Private(&mat->stash,&nstash,&reallocs);CHKERRQ(ierr);
681   ierr = PetscInfo2(aij->A,"Stash has %D entries, uses %D mallocs.\n",nstash,reallocs);CHKERRQ(ierr);
682   PetscFunctionReturn(0);
683 }
684 
685 PetscErrorCode MatAssemblyEnd_MPIAIJ(Mat mat,MatAssemblyType mode)
686 {
687   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
688   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)aij->A->data;
689   PetscErrorCode ierr;
690   PetscMPIInt    n;
691   PetscInt       i,j,rstart,ncols,flg;
692   PetscInt       *row,*col;
693   PetscBool      other_disassembled;
694   PetscScalar    *val;
695 
696   /* do not use 'b = (Mat_SeqAIJ*)aij->B->data' as B can be reset in disassembly */
697 
698   PetscFunctionBegin;
699   if (!aij->donotstash && !mat->nooffprocentries) {
700     while (1) {
701       ierr = MatStashScatterGetMesg_Private(&mat->stash,&n,&row,&col,&val,&flg);CHKERRQ(ierr);
702       if (!flg) break;
703 
704       for (i=0; i<n; ) {
705         /* Now identify the consecutive vals belonging to the same row */
706         for (j=i,rstart=row[j]; j<n; j++) {
707           if (row[j] != rstart) break;
708         }
709         if (j < n) ncols = j-i;
710         else       ncols = n-i;
711         /* Now assemble all these values with a single function call */
712         ierr = MatSetValues_MPIAIJ(mat,1,row+i,ncols,col+i,val+i,mat->insertmode);CHKERRQ(ierr);
713 
714         i = j;
715       }
716     }
717     ierr = MatStashScatterEnd_Private(&mat->stash);CHKERRQ(ierr);
718   }
719   ierr = MatAssemblyBegin(aij->A,mode);CHKERRQ(ierr);
720   ierr = MatAssemblyEnd(aij->A,mode);CHKERRQ(ierr);
721 
722   /* determine if any processor has disassembled, if so we must
723      also disassemble ourselfs, in order that we may reassemble. */
724   /*
725      if nonzero structure of submatrix B cannot change then we know that
726      no processor disassembled thus we can skip this stuff
727   */
728   if (!((Mat_SeqAIJ*)aij->B->data)->nonew) {
729     ierr = MPIU_Allreduce(&mat->was_assembled,&other_disassembled,1,MPIU_BOOL,MPI_PROD,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
730     if (mat->was_assembled && !other_disassembled) {
731       ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
732     }
733   }
734   if (!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) {
735     ierr = MatSetUpMultiply_MPIAIJ(mat);CHKERRQ(ierr);
736   }
737   ierr = MatSetOption(aij->B,MAT_USE_INODES,PETSC_FALSE);CHKERRQ(ierr);
738   ierr = MatAssemblyBegin(aij->B,mode);CHKERRQ(ierr);
739   ierr = MatAssemblyEnd(aij->B,mode);CHKERRQ(ierr);
740 
741   ierr = PetscFree2(aij->rowvalues,aij->rowindices);CHKERRQ(ierr);
742 
743   aij->rowvalues = 0;
744 
745   ierr = VecDestroy(&aij->diag);CHKERRQ(ierr);
746   if (a->inode.size) mat->ops->multdiagonalblock = MatMultDiagonalBlock_MPIAIJ;
747 
748   /* if no new nonzero locations are allowed in matrix then only set the matrix state the first time through */
749   if ((!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) || !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
750     PetscObjectState state = aij->A->nonzerostate + aij->B->nonzerostate;
751     ierr = MPIU_Allreduce(&state,&mat->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
752   }
753   PetscFunctionReturn(0);
754 }
755 
756 PetscErrorCode MatZeroEntries_MPIAIJ(Mat A)
757 {
758   Mat_MPIAIJ     *l = (Mat_MPIAIJ*)A->data;
759   PetscErrorCode ierr;
760 
761   PetscFunctionBegin;
762   ierr = MatZeroEntries(l->A);CHKERRQ(ierr);
763   ierr = MatZeroEntries(l->B);CHKERRQ(ierr);
764   PetscFunctionReturn(0);
765 }
766 
767 PetscErrorCode MatZeroRows_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
768 {
769   Mat_MPIAIJ    *mat    = (Mat_MPIAIJ *) A->data;
770   PetscInt      *lrows;
771   PetscInt       r, len;
772   PetscErrorCode ierr;
773 
774   PetscFunctionBegin;
775   /* get locally owned rows */
776   ierr = MatZeroRowsMapLocal_Private(A,N,rows,&len,&lrows);CHKERRQ(ierr);
777   /* fix right hand side if needed */
778   if (x && b) {
779     const PetscScalar *xx;
780     PetscScalar       *bb;
781 
782     ierr = VecGetArrayRead(x, &xx);CHKERRQ(ierr);
783     ierr = VecGetArray(b, &bb);CHKERRQ(ierr);
784     for (r = 0; r < len; ++r) bb[lrows[r]] = diag*xx[lrows[r]];
785     ierr = VecRestoreArrayRead(x, &xx);CHKERRQ(ierr);
786     ierr = VecRestoreArray(b, &bb);CHKERRQ(ierr);
787   }
788   /* Must zero l->B before l->A because the (diag) case below may put values into l->B*/
789   ierr = MatZeroRows(mat->B, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
790   if (A->congruentlayouts == -1) { /* first time we compare rows and cols layouts */
791     PetscBool cong;
792     ierr = PetscLayoutCompare(A->rmap,A->cmap,&cong);CHKERRQ(ierr);
793     if (cong) A->congruentlayouts = 1;
794     else      A->congruentlayouts = 0;
795   }
796   if ((diag != 0.0) && A->congruentlayouts) {
797     ierr = MatZeroRows(mat->A, len, lrows, diag, NULL, NULL);CHKERRQ(ierr);
798   } else if (diag != 0.0) {
799     ierr = MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
800     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");
801     for (r = 0; r < len; ++r) {
802       const PetscInt row = lrows[r] + A->rmap->rstart;
803       ierr = MatSetValues(A, 1, &row, 1, &row, &diag, INSERT_VALUES);CHKERRQ(ierr);
804     }
805     ierr = MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
806     ierr = MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
807   } else {
808     ierr = MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
809   }
810   ierr = PetscFree(lrows);CHKERRQ(ierr);
811 
812   /* only change matrix nonzero state if pattern was allowed to be changed */
813   if (!((Mat_SeqAIJ*)(mat->A->data))->keepnonzeropattern) {
814     PetscObjectState state = mat->A->nonzerostate + mat->B->nonzerostate;
815     ierr = MPIU_Allreduce(&state,&A->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
816   }
817   PetscFunctionReturn(0);
818 }
819 
820 PetscErrorCode MatZeroRowsColumns_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
821 {
822   Mat_MPIAIJ        *l = (Mat_MPIAIJ*)A->data;
823   PetscErrorCode    ierr;
824   PetscMPIInt       n = A->rmap->n;
825   PetscInt          i,j,r,m,p = 0,len = 0;
826   PetscInt          *lrows,*owners = A->rmap->range;
827   PetscSFNode       *rrows;
828   PetscSF           sf;
829   const PetscScalar *xx;
830   PetscScalar       *bb,*mask;
831   Vec               xmask,lmask;
832   Mat_SeqAIJ        *aij = (Mat_SeqAIJ*)l->B->data;
833   const PetscInt    *aj, *ii,*ridx;
834   PetscScalar       *aa;
835 
836   PetscFunctionBegin;
837   /* Create SF where leaves are input rows and roots are owned rows */
838   ierr = PetscMalloc1(n, &lrows);CHKERRQ(ierr);
839   for (r = 0; r < n; ++r) lrows[r] = -1;
840   ierr = PetscMalloc1(N, &rrows);CHKERRQ(ierr);
841   for (r = 0; r < N; ++r) {
842     const PetscInt idx   = rows[r];
843     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);
844     if (idx < owners[p] || owners[p+1] <= idx) { /* short-circuit the search if the last p owns this row too */
845       ierr = PetscLayoutFindOwner(A->rmap,idx,&p);CHKERRQ(ierr);
846     }
847     rrows[r].rank  = p;
848     rrows[r].index = rows[r] - owners[p];
849   }
850   ierr = PetscSFCreate(PetscObjectComm((PetscObject) A), &sf);CHKERRQ(ierr);
851   ierr = PetscSFSetGraph(sf, n, N, NULL, PETSC_OWN_POINTER, rrows, PETSC_OWN_POINTER);CHKERRQ(ierr);
852   /* Collect flags for rows to be zeroed */
853   ierr = PetscSFReduceBegin(sf, MPIU_INT, (PetscInt *) rows, lrows, MPI_LOR);CHKERRQ(ierr);
854   ierr = PetscSFReduceEnd(sf, MPIU_INT, (PetscInt *) rows, lrows, MPI_LOR);CHKERRQ(ierr);
855   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
856   /* Compress and put in row numbers */
857   for (r = 0; r < n; ++r) if (lrows[r] >= 0) lrows[len++] = r;
858   /* zero diagonal part of matrix */
859   ierr = MatZeroRowsColumns(l->A,len,lrows,diag,x,b);CHKERRQ(ierr);
860   /* handle off diagonal part of matrix */
861   ierr = MatCreateVecs(A,&xmask,NULL);CHKERRQ(ierr);
862   ierr = VecDuplicate(l->lvec,&lmask);CHKERRQ(ierr);
863   ierr = VecGetArray(xmask,&bb);CHKERRQ(ierr);
864   for (i=0; i<len; i++) bb[lrows[i]] = 1;
865   ierr = VecRestoreArray(xmask,&bb);CHKERRQ(ierr);
866   ierr = VecScatterBegin(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
867   ierr = VecScatterEnd(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
868   ierr = VecDestroy(&xmask);CHKERRQ(ierr);
869   if (x) {
870     ierr = VecScatterBegin(l->Mvctx,x,l->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
871     ierr = VecScatterEnd(l->Mvctx,x,l->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
872     ierr = VecGetArrayRead(l->lvec,&xx);CHKERRQ(ierr);
873     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
874   }
875   ierr = VecGetArray(lmask,&mask);CHKERRQ(ierr);
876   /* remove zeroed rows of off diagonal matrix */
877   ii = aij->i;
878   for (i=0; i<len; i++) {
879     ierr = PetscMemzero(aij->a + ii[lrows[i]],(ii[lrows[i]+1] - ii[lrows[i]])*sizeof(PetscScalar));CHKERRQ(ierr);
880   }
881   /* loop over all elements of off process part of matrix zeroing removed columns*/
882   if (aij->compressedrow.use) {
883     m    = aij->compressedrow.nrows;
884     ii   = aij->compressedrow.i;
885     ridx = aij->compressedrow.rindex;
886     for (i=0; i<m; i++) {
887       n  = ii[i+1] - ii[i];
888       aj = aij->j + ii[i];
889       aa = aij->a + ii[i];
890 
891       for (j=0; j<n; j++) {
892         if (PetscAbsScalar(mask[*aj])) {
893           if (b) bb[*ridx] -= *aa*xx[*aj];
894           *aa = 0.0;
895         }
896         aa++;
897         aj++;
898       }
899       ridx++;
900     }
901   } else { /* do not use compressed row format */
902     m = l->B->rmap->n;
903     for (i=0; i<m; i++) {
904       n  = ii[i+1] - ii[i];
905       aj = aij->j + ii[i];
906       aa = aij->a + ii[i];
907       for (j=0; j<n; j++) {
908         if (PetscAbsScalar(mask[*aj])) {
909           if (b) bb[i] -= *aa*xx[*aj];
910           *aa = 0.0;
911         }
912         aa++;
913         aj++;
914       }
915     }
916   }
917   if (x) {
918     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
919     ierr = VecRestoreArrayRead(l->lvec,&xx);CHKERRQ(ierr);
920   }
921   ierr = VecRestoreArray(lmask,&mask);CHKERRQ(ierr);
922   ierr = VecDestroy(&lmask);CHKERRQ(ierr);
923   ierr = PetscFree(lrows);CHKERRQ(ierr);
924 
925   /* only change matrix nonzero state if pattern was allowed to be changed */
926   if (!((Mat_SeqAIJ*)(l->A->data))->keepnonzeropattern) {
927     PetscObjectState state = l->A->nonzerostate + l->B->nonzerostate;
928     ierr = MPIU_Allreduce(&state,&A->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
929   }
930   PetscFunctionReturn(0);
931 }
932 
933 PetscErrorCode MatMult_MPIAIJ(Mat A,Vec xx,Vec yy)
934 {
935   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
936   PetscErrorCode ierr;
937   PetscInt       nt;
938 
939   PetscFunctionBegin;
940   ierr = VecGetLocalSize(xx,&nt);CHKERRQ(ierr);
941   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);
942   ierr = VecScatterBegin(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
943   ierr = (*a->A->ops->mult)(a->A,xx,yy);CHKERRQ(ierr);
944   ierr = VecScatterEnd(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
945   ierr = (*a->B->ops->multadd)(a->B,a->lvec,yy,yy);CHKERRQ(ierr);
946   PetscFunctionReturn(0);
947 }
948 
949 PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat A,Vec bb,Vec xx)
950 {
951   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
952   PetscErrorCode ierr;
953 
954   PetscFunctionBegin;
955   ierr = MatMultDiagonalBlock(a->A,bb,xx);CHKERRQ(ierr);
956   PetscFunctionReturn(0);
957 }
958 
959 PetscErrorCode MatMultAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
960 {
961   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
962   PetscErrorCode ierr;
963 
964   PetscFunctionBegin;
965   ierr = VecScatterBegin(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
966   ierr = (*a->A->ops->multadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
967   ierr = VecScatterEnd(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
968   ierr = (*a->B->ops->multadd)(a->B,a->lvec,zz,zz);CHKERRQ(ierr);
969   PetscFunctionReturn(0);
970 }
971 
972 PetscErrorCode MatMultTranspose_MPIAIJ(Mat A,Vec xx,Vec yy)
973 {
974   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
975   PetscErrorCode ierr;
976   PetscBool      merged;
977 
978   PetscFunctionBegin;
979   ierr = VecScatterGetMerged(a->Mvctx,&merged);CHKERRQ(ierr);
980   /* do nondiagonal part */
981   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
982   if (!merged) {
983     /* send it on its way */
984     ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
985     /* do local part */
986     ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
987     /* receive remote parts: note this assumes the values are not actually */
988     /* added in yy until the next line, */
989     ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
990   } else {
991     /* do local part */
992     ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
993     /* send it on its way */
994     ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
995     /* values actually were received in the Begin() but we need to call this nop */
996     ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
997   }
998   PetscFunctionReturn(0);
999 }
1000 
1001 PetscErrorCode MatIsTranspose_MPIAIJ(Mat Amat,Mat Bmat,PetscReal tol,PetscBool  *f)
1002 {
1003   MPI_Comm       comm;
1004   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ*) Amat->data, *Bij;
1005   Mat            Adia = Aij->A, Bdia, Aoff,Boff,*Aoffs,*Boffs;
1006   IS             Me,Notme;
1007   PetscErrorCode ierr;
1008   PetscInt       M,N,first,last,*notme,i;
1009   PetscMPIInt    size;
1010 
1011   PetscFunctionBegin;
1012   /* Easy test: symmetric diagonal block */
1013   Bij  = (Mat_MPIAIJ*) Bmat->data; Bdia = Bij->A;
1014   ierr = MatIsTranspose(Adia,Bdia,tol,f);CHKERRQ(ierr);
1015   if (!*f) PetscFunctionReturn(0);
1016   ierr = PetscObjectGetComm((PetscObject)Amat,&comm);CHKERRQ(ierr);
1017   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1018   if (size == 1) PetscFunctionReturn(0);
1019 
1020   /* Hard test: off-diagonal block. This takes a MatCreateSubMatrix. */
1021   ierr = MatGetSize(Amat,&M,&N);CHKERRQ(ierr);
1022   ierr = MatGetOwnershipRange(Amat,&first,&last);CHKERRQ(ierr);
1023   ierr = PetscMalloc1(N-last+first,&notme);CHKERRQ(ierr);
1024   for (i=0; i<first; i++) notme[i] = i;
1025   for (i=last; i<M; i++) notme[i-last+first] = i;
1026   ierr = ISCreateGeneral(MPI_COMM_SELF,N-last+first,notme,PETSC_COPY_VALUES,&Notme);CHKERRQ(ierr);
1027   ierr = ISCreateStride(MPI_COMM_SELF,last-first,first,1,&Me);CHKERRQ(ierr);
1028   ierr = MatCreateSubMatrices(Amat,1,&Me,&Notme,MAT_INITIAL_MATRIX,&Aoffs);CHKERRQ(ierr);
1029   Aoff = Aoffs[0];
1030   ierr = MatCreateSubMatrices(Bmat,1,&Notme,&Me,MAT_INITIAL_MATRIX,&Boffs);CHKERRQ(ierr);
1031   Boff = Boffs[0];
1032   ierr = MatIsTranspose(Aoff,Boff,tol,f);CHKERRQ(ierr);
1033   ierr = MatDestroyMatrices(1,&Aoffs);CHKERRQ(ierr);
1034   ierr = MatDestroyMatrices(1,&Boffs);CHKERRQ(ierr);
1035   ierr = ISDestroy(&Me);CHKERRQ(ierr);
1036   ierr = ISDestroy(&Notme);CHKERRQ(ierr);
1037   ierr = PetscFree(notme);CHKERRQ(ierr);
1038   PetscFunctionReturn(0);
1039 }
1040 
1041 PetscErrorCode MatMultTransposeAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1042 {
1043   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1044   PetscErrorCode ierr;
1045 
1046   PetscFunctionBegin;
1047   /* do nondiagonal part */
1048   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
1049   /* send it on its way */
1050   ierr = VecScatterBegin(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1051   /* do local part */
1052   ierr = (*a->A->ops->multtransposeadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
1053   /* receive remote parts */
1054   ierr = VecScatterEnd(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1055   PetscFunctionReturn(0);
1056 }
1057 
1058 /*
1059   This only works correctly for square matrices where the subblock A->A is the
1060    diagonal block
1061 */
1062 PetscErrorCode MatGetDiagonal_MPIAIJ(Mat A,Vec v)
1063 {
1064   PetscErrorCode ierr;
1065   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1066 
1067   PetscFunctionBegin;
1068   if (A->rmap->N != A->cmap->N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Supports only square matrix where A->A is diag block");
1069   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");
1070   ierr = MatGetDiagonal(a->A,v);CHKERRQ(ierr);
1071   PetscFunctionReturn(0);
1072 }
1073 
1074 PetscErrorCode MatScale_MPIAIJ(Mat A,PetscScalar aa)
1075 {
1076   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1077   PetscErrorCode ierr;
1078 
1079   PetscFunctionBegin;
1080   ierr = MatScale(a->A,aa);CHKERRQ(ierr);
1081   ierr = MatScale(a->B,aa);CHKERRQ(ierr);
1082   PetscFunctionReturn(0);
1083 }
1084 
1085 PetscErrorCode MatDestroy_MPIAIJ(Mat mat)
1086 {
1087   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1088   PetscErrorCode ierr;
1089 
1090   PetscFunctionBegin;
1091 #if defined(PETSC_USE_LOG)
1092   PetscLogObjectState((PetscObject)mat,"Rows=%D, Cols=%D",mat->rmap->N,mat->cmap->N);
1093 #endif
1094   ierr = MatStashDestroy_Private(&mat->stash);CHKERRQ(ierr);
1095   ierr = VecDestroy(&aij->diag);CHKERRQ(ierr);
1096   ierr = MatDestroy(&aij->A);CHKERRQ(ierr);
1097   ierr = MatDestroy(&aij->B);CHKERRQ(ierr);
1098 #if defined(PETSC_USE_CTABLE)
1099   ierr = PetscTableDestroy(&aij->colmap);CHKERRQ(ierr);
1100 #else
1101   ierr = PetscFree(aij->colmap);CHKERRQ(ierr);
1102 #endif
1103   ierr = PetscFree(aij->garray);CHKERRQ(ierr);
1104   ierr = VecDestroy(&aij->lvec);CHKERRQ(ierr);
1105   ierr = VecScatterDestroy(&aij->Mvctx);CHKERRQ(ierr);
1106   ierr = PetscFree2(aij->rowvalues,aij->rowindices);CHKERRQ(ierr);
1107   ierr = PetscFree(aij->ld);CHKERRQ(ierr);
1108   ierr = PetscFree(mat->data);CHKERRQ(ierr);
1109 
1110   ierr = PetscObjectChangeTypeName((PetscObject)mat,0);CHKERRQ(ierr);
1111   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatStoreValues_C",NULL);CHKERRQ(ierr);
1112   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatRetrieveValues_C",NULL);CHKERRQ(ierr);
1113   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatIsTranspose_C",NULL);CHKERRQ(ierr);
1114   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocation_C",NULL);CHKERRQ(ierr);
1115   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocationCSR_C",NULL);CHKERRQ(ierr);
1116   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDiagonalScaleLocal_C",NULL);CHKERRQ(ierr);
1117   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_mpisbaij_C",NULL);CHKERRQ(ierr);
1118 #if defined(PETSC_HAVE_ELEMENTAL)
1119   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_elemental_C",NULL);CHKERRQ(ierr);
1120 #endif
1121 #if defined(PETSC_HAVE_HYPRE)
1122   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_hypre_C",NULL);CHKERRQ(ierr);
1123   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMatMatMult_transpose_mpiaij_mpiaij_C",NULL);CHKERRQ(ierr);
1124 #endif
1125   PetscFunctionReturn(0);
1126 }
1127 
1128 PetscErrorCode MatView_MPIAIJ_Binary(Mat mat,PetscViewer viewer)
1129 {
1130   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1131   Mat_SeqAIJ     *A   = (Mat_SeqAIJ*)aij->A->data;
1132   Mat_SeqAIJ     *B   = (Mat_SeqAIJ*)aij->B->data;
1133   PetscErrorCode ierr;
1134   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
1135   int            fd;
1136   PetscInt       nz,header[4],*row_lengths,*range=0,rlen,i;
1137   PetscInt       nzmax,*column_indices,j,k,col,*garray = aij->garray,cnt,cstart = mat->cmap->rstart,rnz = 0;
1138   PetscScalar    *column_values;
1139   PetscInt       message_count,flowcontrolcount;
1140   FILE           *file;
1141 
1142   PetscFunctionBegin;
1143   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
1144   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);CHKERRQ(ierr);
1145   nz   = A->nz + B->nz;
1146   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
1147   if (!rank) {
1148     header[0] = MAT_FILE_CLASSID;
1149     header[1] = mat->rmap->N;
1150     header[2] = mat->cmap->N;
1151 
1152     ierr = MPI_Reduce(&nz,&header[3],1,MPIU_INT,MPI_SUM,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1153     ierr = PetscBinaryWrite(fd,header,4,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1154     /* get largest number of rows any processor has */
1155     rlen  = mat->rmap->n;
1156     range = mat->rmap->range;
1157     for (i=1; i<size; i++) rlen = PetscMax(rlen,range[i+1] - range[i]);
1158   } else {
1159     ierr = MPI_Reduce(&nz,0,1,MPIU_INT,MPI_SUM,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1160     rlen = mat->rmap->n;
1161   }
1162 
1163   /* load up the local row counts */
1164   ierr = PetscMalloc1(rlen+1,&row_lengths);CHKERRQ(ierr);
1165   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];
1166 
1167   /* store the row lengths to the file */
1168   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1169   if (!rank) {
1170     ierr = PetscBinaryWrite(fd,row_lengths,mat->rmap->n,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1171     for (i=1; i<size; i++) {
1172       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1173       rlen = range[i+1] - range[i];
1174       ierr = MPIULong_Recv(row_lengths,rlen,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1175       ierr = PetscBinaryWrite(fd,row_lengths,rlen,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1176     }
1177     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1178   } else {
1179     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1180     ierr = MPIULong_Send(row_lengths,mat->rmap->n,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1181     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1182   }
1183   ierr = PetscFree(row_lengths);CHKERRQ(ierr);
1184 
1185   /* load up the local column indices */
1186   nzmax = nz; /* th processor needs space a largest processor needs */
1187   ierr  = MPI_Reduce(&nz,&nzmax,1,MPIU_INT,MPI_MAX,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1188   ierr  = PetscMalloc1(nzmax+1,&column_indices);CHKERRQ(ierr);
1189   cnt   = 0;
1190   for (i=0; i<mat->rmap->n; i++) {
1191     for (j=B->i[i]; j<B->i[i+1]; j++) {
1192       if ((col = garray[B->j[j]]) > cstart) break;
1193       column_indices[cnt++] = col;
1194     }
1195     for (k=A->i[i]; k<A->i[i+1]; k++) column_indices[cnt++] = A->j[k] + cstart;
1196     for (; j<B->i[i+1]; j++) column_indices[cnt++] = garray[B->j[j]];
1197   }
1198   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);
1199 
1200   /* store the column indices to the file */
1201   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1202   if (!rank) {
1203     MPI_Status status;
1204     ierr = PetscBinaryWrite(fd,column_indices,nz,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1205     for (i=1; i<size; i++) {
1206       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1207       ierr = MPI_Recv(&rnz,1,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat),&status);CHKERRQ(ierr);
1208       if (rnz > nzmax) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: nz = %D nzmax = %D",nz,nzmax);
1209       ierr = MPIULong_Recv(column_indices,rnz,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1210       ierr = PetscBinaryWrite(fd,column_indices,rnz,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1211     }
1212     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1213   } else {
1214     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1215     ierr = MPI_Send(&nz,1,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1216     ierr = MPIULong_Send(column_indices,nz,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1217     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1218   }
1219   ierr = PetscFree(column_indices);CHKERRQ(ierr);
1220 
1221   /* load up the local column values */
1222   ierr = PetscMalloc1(nzmax+1,&column_values);CHKERRQ(ierr);
1223   cnt  = 0;
1224   for (i=0; i<mat->rmap->n; i++) {
1225     for (j=B->i[i]; j<B->i[i+1]; j++) {
1226       if (garray[B->j[j]] > cstart) break;
1227       column_values[cnt++] = B->a[j];
1228     }
1229     for (k=A->i[i]; k<A->i[i+1]; k++) column_values[cnt++] = A->a[k];
1230     for (; j<B->i[i+1]; j++) column_values[cnt++] = B->a[j];
1231   }
1232   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);
1233 
1234   /* store the column values to the file */
1235   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1236   if (!rank) {
1237     MPI_Status status;
1238     ierr = PetscBinaryWrite(fd,column_values,nz,PETSC_SCALAR,PETSC_TRUE);CHKERRQ(ierr);
1239     for (i=1; i<size; i++) {
1240       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1241       ierr = MPI_Recv(&rnz,1,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat),&status);CHKERRQ(ierr);
1242       if (rnz > nzmax) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: nz = %D nzmax = %D",nz,nzmax);
1243       ierr = MPIULong_Recv(column_values,rnz,MPIU_SCALAR,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1244       ierr = PetscBinaryWrite(fd,column_values,rnz,PETSC_SCALAR,PETSC_TRUE);CHKERRQ(ierr);
1245     }
1246     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1247   } else {
1248     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1249     ierr = MPI_Send(&nz,1,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1250     ierr = MPIULong_Send(column_values,nz,MPIU_SCALAR,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1251     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1252   }
1253   ierr = PetscFree(column_values);CHKERRQ(ierr);
1254 
1255   ierr = PetscViewerBinaryGetInfoPointer(viewer,&file);CHKERRQ(ierr);
1256   if (file) fprintf(file,"-matload_block_size %d\n",(int)PetscAbs(mat->rmap->bs));
1257   PetscFunctionReturn(0);
1258 }
1259 
1260 #include <petscdraw.h>
1261 PetscErrorCode MatView_MPIAIJ_ASCIIorDraworSocket(Mat mat,PetscViewer viewer)
1262 {
1263   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)mat->data;
1264   PetscErrorCode    ierr;
1265   PetscMPIInt       rank = aij->rank,size = aij->size;
1266   PetscBool         isdraw,iascii,isbinary;
1267   PetscViewer       sviewer;
1268   PetscViewerFormat format;
1269 
1270   PetscFunctionBegin;
1271   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1272   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1273   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1274   if (iascii) {
1275     ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
1276     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
1277       MatInfo   info;
1278       PetscBool inodes;
1279 
1280       ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
1281       ierr = MatGetInfo(mat,MAT_LOCAL,&info);CHKERRQ(ierr);
1282       ierr = MatInodeGetInodeSizes(aij->A,NULL,(PetscInt**)&inodes,NULL);CHKERRQ(ierr);
1283       ierr = PetscViewerASCIIPushSynchronized(viewer);CHKERRQ(ierr);
1284       if (!inodes) {
1285         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %D nz %D nz alloced %D mem %D, not using I-node routines\n",
1286                                                   rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
1287       } else {
1288         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %D nz %D nz alloced %D mem %D, using I-node routines\n",
1289                                                   rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
1290       }
1291       ierr = MatGetInfo(aij->A,MAT_LOCAL,&info);CHKERRQ(ierr);
1292       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] on-diagonal part: nz %D \n",rank,(PetscInt)info.nz_used);CHKERRQ(ierr);
1293       ierr = MatGetInfo(aij->B,MAT_LOCAL,&info);CHKERRQ(ierr);
1294       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] off-diagonal part: nz %D \n",rank,(PetscInt)info.nz_used);CHKERRQ(ierr);
1295       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1296       ierr = PetscViewerASCIIPopSynchronized(viewer);CHKERRQ(ierr);
1297       ierr = PetscViewerASCIIPrintf(viewer,"Information on VecScatter used in matrix-vector product: \n");CHKERRQ(ierr);
1298       ierr = VecScatterView(aij->Mvctx,viewer);CHKERRQ(ierr);
1299       PetscFunctionReturn(0);
1300     } else if (format == PETSC_VIEWER_ASCII_INFO) {
1301       PetscInt inodecount,inodelimit,*inodes;
1302       ierr = MatInodeGetInodeSizes(aij->A,&inodecount,&inodes,&inodelimit);CHKERRQ(ierr);
1303       if (inodes) {
1304         ierr = PetscViewerASCIIPrintf(viewer,"using I-node (on process 0) routines: found %D nodes, limit used is %D\n",inodecount,inodelimit);CHKERRQ(ierr);
1305       } else {
1306         ierr = PetscViewerASCIIPrintf(viewer,"not using I-node (on process 0) routines\n");CHKERRQ(ierr);
1307       }
1308       PetscFunctionReturn(0);
1309     } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO) {
1310       PetscFunctionReturn(0);
1311     }
1312   } else if (isbinary) {
1313     if (size == 1) {
1314       ierr = PetscObjectSetName((PetscObject)aij->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1315       ierr = MatView(aij->A,viewer);CHKERRQ(ierr);
1316     } else {
1317       ierr = MatView_MPIAIJ_Binary(mat,viewer);CHKERRQ(ierr);
1318     }
1319     PetscFunctionReturn(0);
1320   } else if (isdraw) {
1321     PetscDraw draw;
1322     PetscBool isnull;
1323     ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
1324     ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr);
1325     if (isnull) PetscFunctionReturn(0);
1326   }
1327 
1328   {
1329     /* assemble the entire matrix onto first processor. */
1330     Mat        A;
1331     Mat_SeqAIJ *Aloc;
1332     PetscInt   M = mat->rmap->N,N = mat->cmap->N,m,*ai,*aj,row,*cols,i,*ct;
1333     MatScalar  *a;
1334 
1335     ierr = MatCreate(PetscObjectComm((PetscObject)mat),&A);CHKERRQ(ierr);
1336     if (!rank) {
1337       ierr = MatSetSizes(A,M,N,M,N);CHKERRQ(ierr);
1338     } else {
1339       ierr = MatSetSizes(A,0,0,M,N);CHKERRQ(ierr);
1340     }
1341     /* This is just a temporary matrix, so explicitly using MATMPIAIJ is probably best */
1342     ierr = MatSetType(A,MATMPIAIJ);CHKERRQ(ierr);
1343     ierr = MatMPIAIJSetPreallocation(A,0,NULL,0,NULL);CHKERRQ(ierr);
1344     ierr = MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
1345     ierr = PetscLogObjectParent((PetscObject)mat,(PetscObject)A);CHKERRQ(ierr);
1346 
1347     /* copy over the A part */
1348     Aloc = (Mat_SeqAIJ*)aij->A->data;
1349     m    = aij->A->rmap->n; ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
1350     row  = mat->rmap->rstart;
1351     for (i=0; i<ai[m]; i++) aj[i] += mat->cmap->rstart;
1352     for (i=0; i<m; i++) {
1353       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],aj,a,INSERT_VALUES);CHKERRQ(ierr);
1354       row++;
1355       a += ai[i+1]-ai[i]; aj += ai[i+1]-ai[i];
1356     }
1357     aj = Aloc->j;
1358     for (i=0; i<ai[m]; i++) aj[i] -= mat->cmap->rstart;
1359 
1360     /* copy over the B part */
1361     Aloc = (Mat_SeqAIJ*)aij->B->data;
1362     m    = aij->B->rmap->n;  ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
1363     row  = mat->rmap->rstart;
1364     ierr = PetscMalloc1(ai[m]+1,&cols);CHKERRQ(ierr);
1365     ct   = cols;
1366     for (i=0; i<ai[m]; i++) cols[i] = aij->garray[aj[i]];
1367     for (i=0; i<m; i++) {
1368       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],cols,a,INSERT_VALUES);CHKERRQ(ierr);
1369       row++;
1370       a += ai[i+1]-ai[i]; cols += ai[i+1]-ai[i];
1371     }
1372     ierr = PetscFree(ct);CHKERRQ(ierr);
1373     ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1374     ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1375     /*
1376        Everyone has to call to draw the matrix since the graphics waits are
1377        synchronized across all processors that share the PetscDraw object
1378     */
1379     ierr = PetscViewerGetSubViewer(viewer,PETSC_COMM_SELF,&sviewer);CHKERRQ(ierr);
1380     if (!rank) {
1381       ierr = PetscObjectSetName((PetscObject)((Mat_MPIAIJ*)(A->data))->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1382       ierr = MatView_SeqAIJ(((Mat_MPIAIJ*)(A->data))->A,sviewer);CHKERRQ(ierr);
1383     }
1384     ierr = PetscViewerRestoreSubViewer(viewer,PETSC_COMM_SELF,&sviewer);CHKERRQ(ierr);
1385     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1386     ierr = MatDestroy(&A);CHKERRQ(ierr);
1387   }
1388   PetscFunctionReturn(0);
1389 }
1390 
1391 PetscErrorCode MatView_MPIAIJ(Mat mat,PetscViewer viewer)
1392 {
1393   PetscErrorCode ierr;
1394   PetscBool      iascii,isdraw,issocket,isbinary;
1395 
1396   PetscFunctionBegin;
1397   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1398   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1399   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1400   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSOCKET,&issocket);CHKERRQ(ierr);
1401   if (iascii || isdraw || isbinary || issocket) {
1402     ierr = MatView_MPIAIJ_ASCIIorDraworSocket(mat,viewer);CHKERRQ(ierr);
1403   }
1404   PetscFunctionReturn(0);
1405 }
1406 
1407 PetscErrorCode MatSOR_MPIAIJ(Mat matin,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
1408 {
1409   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1410   PetscErrorCode ierr;
1411   Vec            bb1 = 0;
1412   PetscBool      hasop;
1413 
1414   PetscFunctionBegin;
1415   if (flag == SOR_APPLY_UPPER) {
1416     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1417     PetscFunctionReturn(0);
1418   }
1419 
1420   if (its > 1 || ~flag & SOR_ZERO_INITIAL_GUESS || flag & SOR_EISENSTAT) {
1421     ierr = VecDuplicate(bb,&bb1);CHKERRQ(ierr);
1422   }
1423 
1424   if ((flag & SOR_LOCAL_SYMMETRIC_SWEEP) == SOR_LOCAL_SYMMETRIC_SWEEP) {
1425     if (flag & SOR_ZERO_INITIAL_GUESS) {
1426       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1427       its--;
1428     }
1429 
1430     while (its--) {
1431       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1432       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1433 
1434       /* update rhs: bb1 = bb - B*x */
1435       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1436       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1437 
1438       /* local sweep */
1439       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_SYMMETRIC_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1440     }
1441   } else if (flag & SOR_LOCAL_FORWARD_SWEEP) {
1442     if (flag & SOR_ZERO_INITIAL_GUESS) {
1443       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1444       its--;
1445     }
1446     while (its--) {
1447       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1448       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1449 
1450       /* update rhs: bb1 = bb - B*x */
1451       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1452       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1453 
1454       /* local sweep */
1455       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_FORWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1456     }
1457   } else if (flag & SOR_LOCAL_BACKWARD_SWEEP) {
1458     if (flag & SOR_ZERO_INITIAL_GUESS) {
1459       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1460       its--;
1461     }
1462     while (its--) {
1463       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1464       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1465 
1466       /* update rhs: bb1 = bb - B*x */
1467       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1468       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1469 
1470       /* local sweep */
1471       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_BACKWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1472     }
1473   } else if (flag & SOR_EISENSTAT) {
1474     Vec xx1;
1475 
1476     ierr = VecDuplicate(bb,&xx1);CHKERRQ(ierr);
1477     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_BACKWARD_SWEEP),fshift,lits,1,xx);CHKERRQ(ierr);
1478 
1479     ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1480     ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1481     if (!mat->diag) {
1482       ierr = MatCreateVecs(matin,&mat->diag,NULL);CHKERRQ(ierr);
1483       ierr = MatGetDiagonal(matin,mat->diag);CHKERRQ(ierr);
1484     }
1485     ierr = MatHasOperation(matin,MATOP_MULT_DIAGONAL_BLOCK,&hasop);CHKERRQ(ierr);
1486     if (hasop) {
1487       ierr = MatMultDiagonalBlock(matin,xx,bb1);CHKERRQ(ierr);
1488     } else {
1489       ierr = VecPointwiseMult(bb1,mat->diag,xx);CHKERRQ(ierr);
1490     }
1491     ierr = VecAYPX(bb1,(omega-2.0)/omega,bb);CHKERRQ(ierr);
1492 
1493     ierr = MatMultAdd(mat->B,mat->lvec,bb1,bb1);CHKERRQ(ierr);
1494 
1495     /* local sweep */
1496     ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_FORWARD_SWEEP),fshift,lits,1,xx1);CHKERRQ(ierr);
1497     ierr = VecAXPY(xx,1.0,xx1);CHKERRQ(ierr);
1498     ierr = VecDestroy(&xx1);CHKERRQ(ierr);
1499   } else SETERRQ(PetscObjectComm((PetscObject)matin),PETSC_ERR_SUP,"Parallel SOR not supported");
1500 
1501   ierr = VecDestroy(&bb1);CHKERRQ(ierr);
1502 
1503   matin->factorerrortype = mat->A->factorerrortype;
1504   PetscFunctionReturn(0);
1505 }
1506 
1507 PetscErrorCode MatPermute_MPIAIJ(Mat A,IS rowp,IS colp,Mat *B)
1508 {
1509   Mat            aA,aB,Aperm;
1510   const PetscInt *rwant,*cwant,*gcols,*ai,*bi,*aj,*bj;
1511   PetscScalar    *aa,*ba;
1512   PetscInt       i,j,m,n,ng,anz,bnz,*dnnz,*onnz,*tdnnz,*tonnz,*rdest,*cdest,*work,*gcdest;
1513   PetscSF        rowsf,sf;
1514   IS             parcolp = NULL;
1515   PetscBool      done;
1516   PetscErrorCode ierr;
1517 
1518   PetscFunctionBegin;
1519   ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
1520   ierr = ISGetIndices(rowp,&rwant);CHKERRQ(ierr);
1521   ierr = ISGetIndices(colp,&cwant);CHKERRQ(ierr);
1522   ierr = PetscMalloc3(PetscMax(m,n),&work,m,&rdest,n,&cdest);CHKERRQ(ierr);
1523 
1524   /* Invert row permutation to find out where my rows should go */
1525   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&rowsf);CHKERRQ(ierr);
1526   ierr = PetscSFSetGraphLayout(rowsf,A->rmap,A->rmap->n,NULL,PETSC_OWN_POINTER,rwant);CHKERRQ(ierr);
1527   ierr = PetscSFSetFromOptions(rowsf);CHKERRQ(ierr);
1528   for (i=0; i<m; i++) work[i] = A->rmap->rstart + i;
1529   ierr = PetscSFReduceBegin(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1530   ierr = PetscSFReduceEnd(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1531 
1532   /* Invert column permutation to find out where my columns should go */
1533   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1534   ierr = PetscSFSetGraphLayout(sf,A->cmap,A->cmap->n,NULL,PETSC_OWN_POINTER,cwant);CHKERRQ(ierr);
1535   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1536   for (i=0; i<n; i++) work[i] = A->cmap->rstart + i;
1537   ierr = PetscSFReduceBegin(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1538   ierr = PetscSFReduceEnd(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1539   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1540 
1541   ierr = ISRestoreIndices(rowp,&rwant);CHKERRQ(ierr);
1542   ierr = ISRestoreIndices(colp,&cwant);CHKERRQ(ierr);
1543   ierr = MatMPIAIJGetSeqAIJ(A,&aA,&aB,&gcols);CHKERRQ(ierr);
1544 
1545   /* Find out where my gcols should go */
1546   ierr = MatGetSize(aB,NULL,&ng);CHKERRQ(ierr);
1547   ierr = PetscMalloc1(ng,&gcdest);CHKERRQ(ierr);
1548   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1549   ierr = PetscSFSetGraphLayout(sf,A->cmap,ng,NULL,PETSC_OWN_POINTER,gcols);CHKERRQ(ierr);
1550   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1551   ierr = PetscSFBcastBegin(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1552   ierr = PetscSFBcastEnd(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1553   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1554 
1555   ierr = PetscCalloc4(m,&dnnz,m,&onnz,m,&tdnnz,m,&tonnz);CHKERRQ(ierr);
1556   ierr = MatGetRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1557   ierr = MatGetRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1558   for (i=0; i<m; i++) {
1559     PetscInt row = rdest[i],rowner;
1560     ierr = PetscLayoutFindOwner(A->rmap,row,&rowner);CHKERRQ(ierr);
1561     for (j=ai[i]; j<ai[i+1]; j++) {
1562       PetscInt cowner,col = cdest[aj[j]];
1563       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr); /* Could build an index for the columns to eliminate this search */
1564       if (rowner == cowner) dnnz[i]++;
1565       else onnz[i]++;
1566     }
1567     for (j=bi[i]; j<bi[i+1]; j++) {
1568       PetscInt cowner,col = gcdest[bj[j]];
1569       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr);
1570       if (rowner == cowner) dnnz[i]++;
1571       else onnz[i]++;
1572     }
1573   }
1574   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1575   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1576   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1577   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1578   ierr = PetscSFDestroy(&rowsf);CHKERRQ(ierr);
1579 
1580   ierr = MatCreateAIJ(PetscObjectComm((PetscObject)A),A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N,0,tdnnz,0,tonnz,&Aperm);CHKERRQ(ierr);
1581   ierr = MatSeqAIJGetArray(aA,&aa);CHKERRQ(ierr);
1582   ierr = MatSeqAIJGetArray(aB,&ba);CHKERRQ(ierr);
1583   for (i=0; i<m; i++) {
1584     PetscInt *acols = dnnz,*bcols = onnz; /* Repurpose now-unneeded arrays */
1585     PetscInt j0,rowlen;
1586     rowlen = ai[i+1] - ai[i];
1587     for (j0=j=0; j<rowlen; j0=j) { /* rowlen could be larger than number of rows m, so sum in batches */
1588       for ( ; j<PetscMin(rowlen,j0+m); j++) acols[j-j0] = cdest[aj[ai[i]+j]];
1589       ierr = MatSetValues(Aperm,1,&rdest[i],j-j0,acols,aa+ai[i]+j0,INSERT_VALUES);CHKERRQ(ierr);
1590     }
1591     rowlen = bi[i+1] - bi[i];
1592     for (j0=j=0; j<rowlen; j0=j) {
1593       for ( ; j<PetscMin(rowlen,j0+m); j++) bcols[j-j0] = gcdest[bj[bi[i]+j]];
1594       ierr = MatSetValues(Aperm,1,&rdest[i],j-j0,bcols,ba+bi[i]+j0,INSERT_VALUES);CHKERRQ(ierr);
1595     }
1596   }
1597   ierr = MatAssemblyBegin(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1598   ierr = MatAssemblyEnd(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1599   ierr = MatRestoreRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1600   ierr = MatRestoreRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1601   ierr = MatSeqAIJRestoreArray(aA,&aa);CHKERRQ(ierr);
1602   ierr = MatSeqAIJRestoreArray(aB,&ba);CHKERRQ(ierr);
1603   ierr = PetscFree4(dnnz,onnz,tdnnz,tonnz);CHKERRQ(ierr);
1604   ierr = PetscFree3(work,rdest,cdest);CHKERRQ(ierr);
1605   ierr = PetscFree(gcdest);CHKERRQ(ierr);
1606   if (parcolp) {ierr = ISDestroy(&colp);CHKERRQ(ierr);}
1607   *B = Aperm;
1608   PetscFunctionReturn(0);
1609 }
1610 
1611 PetscErrorCode  MatGetGhosts_MPIAIJ(Mat mat,PetscInt *nghosts,const PetscInt *ghosts[])
1612 {
1613   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1614   PetscErrorCode ierr;
1615 
1616   PetscFunctionBegin;
1617   ierr = MatGetSize(aij->B,NULL,nghosts);CHKERRQ(ierr);
1618   if (ghosts) *ghosts = aij->garray;
1619   PetscFunctionReturn(0);
1620 }
1621 
1622 PetscErrorCode MatGetInfo_MPIAIJ(Mat matin,MatInfoType flag,MatInfo *info)
1623 {
1624   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1625   Mat            A    = mat->A,B = mat->B;
1626   PetscErrorCode ierr;
1627   PetscReal      isend[5],irecv[5];
1628 
1629   PetscFunctionBegin;
1630   info->block_size = 1.0;
1631   ierr             = MatGetInfo(A,MAT_LOCAL,info);CHKERRQ(ierr);
1632 
1633   isend[0] = info->nz_used; isend[1] = info->nz_allocated; isend[2] = info->nz_unneeded;
1634   isend[3] = info->memory;  isend[4] = info->mallocs;
1635 
1636   ierr = MatGetInfo(B,MAT_LOCAL,info);CHKERRQ(ierr);
1637 
1638   isend[0] += info->nz_used; isend[1] += info->nz_allocated; isend[2] += info->nz_unneeded;
1639   isend[3] += info->memory;  isend[4] += info->mallocs;
1640   if (flag == MAT_LOCAL) {
1641     info->nz_used      = isend[0];
1642     info->nz_allocated = isend[1];
1643     info->nz_unneeded  = isend[2];
1644     info->memory       = isend[3];
1645     info->mallocs      = isend[4];
1646   } else if (flag == MAT_GLOBAL_MAX) {
1647     ierr = MPIU_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1648 
1649     info->nz_used      = irecv[0];
1650     info->nz_allocated = irecv[1];
1651     info->nz_unneeded  = irecv[2];
1652     info->memory       = irecv[3];
1653     info->mallocs      = irecv[4];
1654   } else if (flag == MAT_GLOBAL_SUM) {
1655     ierr = MPIU_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1656 
1657     info->nz_used      = irecv[0];
1658     info->nz_allocated = irecv[1];
1659     info->nz_unneeded  = irecv[2];
1660     info->memory       = irecv[3];
1661     info->mallocs      = irecv[4];
1662   }
1663   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
1664   info->fill_ratio_needed = 0;
1665   info->factor_mallocs    = 0;
1666   PetscFunctionReturn(0);
1667 }
1668 
1669 PetscErrorCode MatSetOption_MPIAIJ(Mat A,MatOption op,PetscBool flg)
1670 {
1671   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1672   PetscErrorCode ierr;
1673 
1674   PetscFunctionBegin;
1675   switch (op) {
1676   case MAT_NEW_NONZERO_LOCATIONS:
1677   case MAT_NEW_NONZERO_ALLOCATION_ERR:
1678   case MAT_UNUSED_NONZERO_LOCATION_ERR:
1679   case MAT_KEEP_NONZERO_PATTERN:
1680   case MAT_NEW_NONZERO_LOCATION_ERR:
1681   case MAT_USE_INODES:
1682   case MAT_IGNORE_ZERO_ENTRIES:
1683     MatCheckPreallocated(A,1);
1684     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1685     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1686     break;
1687   case MAT_ROW_ORIENTED:
1688     MatCheckPreallocated(A,1);
1689     a->roworiented = flg;
1690 
1691     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1692     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1693     break;
1694   case MAT_NEW_DIAGONALS:
1695     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
1696     break;
1697   case MAT_IGNORE_OFF_PROC_ENTRIES:
1698     a->donotstash = flg;
1699     break;
1700   case MAT_SPD:
1701     A->spd_set = PETSC_TRUE;
1702     A->spd     = flg;
1703     if (flg) {
1704       A->symmetric                  = PETSC_TRUE;
1705       A->structurally_symmetric     = PETSC_TRUE;
1706       A->symmetric_set              = PETSC_TRUE;
1707       A->structurally_symmetric_set = PETSC_TRUE;
1708     }
1709     break;
1710   case MAT_SYMMETRIC:
1711     MatCheckPreallocated(A,1);
1712     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1713     break;
1714   case MAT_STRUCTURALLY_SYMMETRIC:
1715     MatCheckPreallocated(A,1);
1716     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1717     break;
1718   case MAT_HERMITIAN:
1719     MatCheckPreallocated(A,1);
1720     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1721     break;
1722   case MAT_SYMMETRY_ETERNAL:
1723     MatCheckPreallocated(A,1);
1724     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1725     break;
1726   case MAT_SUBMAT_SINGLEIS:
1727     A->submat_singleis = flg;
1728     break;
1729   default:
1730     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %d",op);
1731   }
1732   PetscFunctionReturn(0);
1733 }
1734 
1735 PetscErrorCode MatGetRow_MPIAIJ(Mat matin,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1736 {
1737   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1738   PetscScalar    *vworkA,*vworkB,**pvA,**pvB,*v_p;
1739   PetscErrorCode ierr;
1740   PetscInt       i,*cworkA,*cworkB,**pcA,**pcB,cstart = matin->cmap->rstart;
1741   PetscInt       nztot,nzA,nzB,lrow,rstart = matin->rmap->rstart,rend = matin->rmap->rend;
1742   PetscInt       *cmap,*idx_p;
1743 
1744   PetscFunctionBegin;
1745   if (mat->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Already active");
1746   mat->getrowactive = PETSC_TRUE;
1747 
1748   if (!mat->rowvalues && (idx || v)) {
1749     /*
1750         allocate enough space to hold information from the longest row.
1751     */
1752     Mat_SeqAIJ *Aa = (Mat_SeqAIJ*)mat->A->data,*Ba = (Mat_SeqAIJ*)mat->B->data;
1753     PetscInt   max = 1,tmp;
1754     for (i=0; i<matin->rmap->n; i++) {
1755       tmp = Aa->i[i+1] - Aa->i[i] + Ba->i[i+1] - Ba->i[i];
1756       if (max < tmp) max = tmp;
1757     }
1758     ierr = PetscMalloc2(max,&mat->rowvalues,max,&mat->rowindices);CHKERRQ(ierr);
1759   }
1760 
1761   if (row < rstart || row >= rend) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Only local rows");
1762   lrow = row - rstart;
1763 
1764   pvA = &vworkA; pcA = &cworkA; pvB = &vworkB; pcB = &cworkB;
1765   if (!v)   {pvA = 0; pvB = 0;}
1766   if (!idx) {pcA = 0; if (!v) pcB = 0;}
1767   ierr  = (*mat->A->ops->getrow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1768   ierr  = (*mat->B->ops->getrow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1769   nztot = nzA + nzB;
1770 
1771   cmap = mat->garray;
1772   if (v  || idx) {
1773     if (nztot) {
1774       /* Sort by increasing column numbers, assuming A and B already sorted */
1775       PetscInt imark = -1;
1776       if (v) {
1777         *v = v_p = mat->rowvalues;
1778         for (i=0; i<nzB; i++) {
1779           if (cmap[cworkB[i]] < cstart) v_p[i] = vworkB[i];
1780           else break;
1781         }
1782         imark = i;
1783         for (i=0; i<nzA; i++)     v_p[imark+i] = vworkA[i];
1784         for (i=imark; i<nzB; i++) v_p[nzA+i]   = vworkB[i];
1785       }
1786       if (idx) {
1787         *idx = idx_p = mat->rowindices;
1788         if (imark > -1) {
1789           for (i=0; i<imark; i++) {
1790             idx_p[i] = cmap[cworkB[i]];
1791           }
1792         } else {
1793           for (i=0; i<nzB; i++) {
1794             if (cmap[cworkB[i]] < cstart) idx_p[i] = cmap[cworkB[i]];
1795             else break;
1796           }
1797           imark = i;
1798         }
1799         for (i=0; i<nzA; i++)     idx_p[imark+i] = cstart + cworkA[i];
1800         for (i=imark; i<nzB; i++) idx_p[nzA+i]   = cmap[cworkB[i]];
1801       }
1802     } else {
1803       if (idx) *idx = 0;
1804       if (v)   *v   = 0;
1805     }
1806   }
1807   *nz  = nztot;
1808   ierr = (*mat->A->ops->restorerow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1809   ierr = (*mat->B->ops->restorerow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1810   PetscFunctionReturn(0);
1811 }
1812 
1813 PetscErrorCode MatRestoreRow_MPIAIJ(Mat mat,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1814 {
1815   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1816 
1817   PetscFunctionBegin;
1818   if (!aij->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"MatGetRow() must be called first");
1819   aij->getrowactive = PETSC_FALSE;
1820   PetscFunctionReturn(0);
1821 }
1822 
1823 PetscErrorCode MatNorm_MPIAIJ(Mat mat,NormType type,PetscReal *norm)
1824 {
1825   Mat_MPIAIJ     *aij  = (Mat_MPIAIJ*)mat->data;
1826   Mat_SeqAIJ     *amat = (Mat_SeqAIJ*)aij->A->data,*bmat = (Mat_SeqAIJ*)aij->B->data;
1827   PetscErrorCode ierr;
1828   PetscInt       i,j,cstart = mat->cmap->rstart;
1829   PetscReal      sum = 0.0;
1830   MatScalar      *v;
1831 
1832   PetscFunctionBegin;
1833   if (aij->size == 1) {
1834     ierr =  MatNorm(aij->A,type,norm);CHKERRQ(ierr);
1835   } else {
1836     if (type == NORM_FROBENIUS) {
1837       v = amat->a;
1838       for (i=0; i<amat->nz; i++) {
1839         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1840       }
1841       v = bmat->a;
1842       for (i=0; i<bmat->nz; i++) {
1843         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1844       }
1845       ierr  = MPIU_Allreduce(&sum,norm,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1846       *norm = PetscSqrtReal(*norm);
1847       ierr = PetscLogFlops(2*amat->nz+2*bmat->nz);CHKERRQ(ierr);
1848     } else if (type == NORM_1) { /* max column norm */
1849       PetscReal *tmp,*tmp2;
1850       PetscInt  *jj,*garray = aij->garray;
1851       ierr  = PetscCalloc1(mat->cmap->N+1,&tmp);CHKERRQ(ierr);
1852       ierr  = PetscMalloc1(mat->cmap->N+1,&tmp2);CHKERRQ(ierr);
1853       *norm = 0.0;
1854       v     = amat->a; jj = amat->j;
1855       for (j=0; j<amat->nz; j++) {
1856         tmp[cstart + *jj++] += PetscAbsScalar(*v);  v++;
1857       }
1858       v = bmat->a; jj = bmat->j;
1859       for (j=0; j<bmat->nz; j++) {
1860         tmp[garray[*jj++]] += PetscAbsScalar(*v); v++;
1861       }
1862       ierr = MPIU_Allreduce(tmp,tmp2,mat->cmap->N,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1863       for (j=0; j<mat->cmap->N; j++) {
1864         if (tmp2[j] > *norm) *norm = tmp2[j];
1865       }
1866       ierr = PetscFree(tmp);CHKERRQ(ierr);
1867       ierr = PetscFree(tmp2);CHKERRQ(ierr);
1868       ierr = PetscLogFlops(PetscMax(amat->nz+bmat->nz-1,0));CHKERRQ(ierr);
1869     } else if (type == NORM_INFINITY) { /* max row norm */
1870       PetscReal ntemp = 0.0;
1871       for (j=0; j<aij->A->rmap->n; j++) {
1872         v   = amat->a + amat->i[j];
1873         sum = 0.0;
1874         for (i=0; i<amat->i[j+1]-amat->i[j]; i++) {
1875           sum += PetscAbsScalar(*v); v++;
1876         }
1877         v = bmat->a + bmat->i[j];
1878         for (i=0; i<bmat->i[j+1]-bmat->i[j]; i++) {
1879           sum += PetscAbsScalar(*v); v++;
1880         }
1881         if (sum > ntemp) ntemp = sum;
1882       }
1883       ierr = MPIU_Allreduce(&ntemp,norm,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1884       ierr = PetscLogFlops(PetscMax(amat->nz+bmat->nz-1,0));CHKERRQ(ierr);
1885     } else SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"No support for two norm");
1886   }
1887   PetscFunctionReturn(0);
1888 }
1889 
1890 PetscErrorCode MatTranspose_MPIAIJ(Mat A,MatReuse reuse,Mat *matout)
1891 {
1892   Mat_MPIAIJ     *a   = (Mat_MPIAIJ*)A->data;
1893   Mat_SeqAIJ     *Aloc=(Mat_SeqAIJ*)a->A->data,*Bloc=(Mat_SeqAIJ*)a->B->data;
1894   PetscErrorCode ierr;
1895   PetscInt       M      = A->rmap->N,N = A->cmap->N,ma,na,mb,nb,*ai,*aj,*bi,*bj,row,*cols,*cols_tmp,i;
1896   PetscInt       cstart = A->cmap->rstart,ncol;
1897   Mat            B;
1898   MatScalar      *array;
1899 
1900   PetscFunctionBegin;
1901   if (reuse == MAT_INPLACE_MATRIX && M != N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Square matrix only for in-place");
1902 
1903   ma = A->rmap->n; na = A->cmap->n; mb = a->B->rmap->n; nb = a->B->cmap->n;
1904   ai = Aloc->i; aj = Aloc->j;
1905   bi = Bloc->i; bj = Bloc->j;
1906   if (reuse == MAT_INITIAL_MATRIX || *matout == A) {
1907     PetscInt             *d_nnz,*g_nnz,*o_nnz;
1908     PetscSFNode          *oloc;
1909     PETSC_UNUSED PetscSF sf;
1910 
1911     ierr = PetscMalloc4(na,&d_nnz,na,&o_nnz,nb,&g_nnz,nb,&oloc);CHKERRQ(ierr);
1912     /* compute d_nnz for preallocation */
1913     ierr = PetscMemzero(d_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1914     for (i=0; i<ai[ma]; i++) {
1915       d_nnz[aj[i]]++;
1916       aj[i] += cstart; /* global col index to be used by MatSetValues() */
1917     }
1918     /* compute local off-diagonal contributions */
1919     ierr = PetscMemzero(g_nnz,nb*sizeof(PetscInt));CHKERRQ(ierr);
1920     for (i=0; i<bi[ma]; i++) g_nnz[bj[i]]++;
1921     /* map those to global */
1922     ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1923     ierr = PetscSFSetGraphLayout(sf,A->cmap,nb,NULL,PETSC_USE_POINTER,a->garray);CHKERRQ(ierr);
1924     ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1925     ierr = PetscMemzero(o_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1926     ierr = PetscSFReduceBegin(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
1927     ierr = PetscSFReduceEnd(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
1928     ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1929 
1930     ierr = MatCreate(PetscObjectComm((PetscObject)A),&B);CHKERRQ(ierr);
1931     ierr = MatSetSizes(B,A->cmap->n,A->rmap->n,N,M);CHKERRQ(ierr);
1932     ierr = MatSetBlockSizes(B,PetscAbs(A->cmap->bs),PetscAbs(A->rmap->bs));CHKERRQ(ierr);
1933     ierr = MatSetType(B,((PetscObject)A)->type_name);CHKERRQ(ierr);
1934     ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
1935     ierr = PetscFree4(d_nnz,o_nnz,g_nnz,oloc);CHKERRQ(ierr);
1936   } else {
1937     B    = *matout;
1938     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
1939     for (i=0; i<ai[ma]; i++) aj[i] += cstart; /* global col index to be used by MatSetValues() */
1940   }
1941 
1942   /* copy over the A part */
1943   array = Aloc->a;
1944   row   = A->rmap->rstart;
1945   for (i=0; i<ma; i++) {
1946     ncol = ai[i+1]-ai[i];
1947     ierr = MatSetValues(B,ncol,aj,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
1948     row++;
1949     array += ncol; aj += ncol;
1950   }
1951   aj = Aloc->j;
1952   for (i=0; i<ai[ma]; i++) aj[i] -= cstart; /* resume local col index */
1953 
1954   /* copy over the B part */
1955   ierr  = PetscCalloc1(bi[mb],&cols);CHKERRQ(ierr);
1956   array = Bloc->a;
1957   row   = A->rmap->rstart;
1958   for (i=0; i<bi[mb]; i++) cols[i] = a->garray[bj[i]];
1959   cols_tmp = cols;
1960   for (i=0; i<mb; i++) {
1961     ncol = bi[i+1]-bi[i];
1962     ierr = MatSetValues(B,ncol,cols_tmp,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
1963     row++;
1964     array += ncol; cols_tmp += ncol;
1965   }
1966   ierr = PetscFree(cols);CHKERRQ(ierr);
1967 
1968   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1969   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1970   if (reuse == MAT_INITIAL_MATRIX || reuse == MAT_REUSE_MATRIX) {
1971     *matout = B;
1972   } else {
1973     ierr = MatHeaderMerge(A,&B);CHKERRQ(ierr);
1974   }
1975   PetscFunctionReturn(0);
1976 }
1977 
1978 PetscErrorCode MatDiagonalScale_MPIAIJ(Mat mat,Vec ll,Vec rr)
1979 {
1980   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1981   Mat            a    = aij->A,b = aij->B;
1982   PetscErrorCode ierr;
1983   PetscInt       s1,s2,s3;
1984 
1985   PetscFunctionBegin;
1986   ierr = MatGetLocalSize(mat,&s2,&s3);CHKERRQ(ierr);
1987   if (rr) {
1988     ierr = VecGetLocalSize(rr,&s1);CHKERRQ(ierr);
1989     if (s1!=s3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"right vector non-conforming local size");
1990     /* Overlap communication with computation. */
1991     ierr = VecScatterBegin(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1992   }
1993   if (ll) {
1994     ierr = VecGetLocalSize(ll,&s1);CHKERRQ(ierr);
1995     if (s1!=s2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"left vector non-conforming local size");
1996     ierr = (*b->ops->diagonalscale)(b,ll,0);CHKERRQ(ierr);
1997   }
1998   /* scale  the diagonal block */
1999   ierr = (*a->ops->diagonalscale)(a,ll,rr);CHKERRQ(ierr);
2000 
2001   if (rr) {
2002     /* Do a scatter end and then right scale the off-diagonal block */
2003     ierr = VecScatterEnd(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2004     ierr = (*b->ops->diagonalscale)(b,0,aij->lvec);CHKERRQ(ierr);
2005   }
2006   PetscFunctionReturn(0);
2007 }
2008 
2009 PetscErrorCode MatSetUnfactored_MPIAIJ(Mat A)
2010 {
2011   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2012   PetscErrorCode ierr;
2013 
2014   PetscFunctionBegin;
2015   ierr = MatSetUnfactored(a->A);CHKERRQ(ierr);
2016   PetscFunctionReturn(0);
2017 }
2018 
2019 PetscErrorCode MatEqual_MPIAIJ(Mat A,Mat B,PetscBool  *flag)
2020 {
2021   Mat_MPIAIJ     *matB = (Mat_MPIAIJ*)B->data,*matA = (Mat_MPIAIJ*)A->data;
2022   Mat            a,b,c,d;
2023   PetscBool      flg;
2024   PetscErrorCode ierr;
2025 
2026   PetscFunctionBegin;
2027   a = matA->A; b = matA->B;
2028   c = matB->A; d = matB->B;
2029 
2030   ierr = MatEqual(a,c,&flg);CHKERRQ(ierr);
2031   if (flg) {
2032     ierr = MatEqual(b,d,&flg);CHKERRQ(ierr);
2033   }
2034   ierr = MPIU_Allreduce(&flg,flag,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
2035   PetscFunctionReturn(0);
2036 }
2037 
2038 PetscErrorCode MatCopy_MPIAIJ(Mat A,Mat B,MatStructure str)
2039 {
2040   PetscErrorCode ierr;
2041   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2042   Mat_MPIAIJ     *b = (Mat_MPIAIJ*)B->data;
2043 
2044   PetscFunctionBegin;
2045   /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
2046   if ((str != SAME_NONZERO_PATTERN) || (A->ops->copy != B->ops->copy)) {
2047     /* because of the column compression in the off-processor part of the matrix a->B,
2048        the number of columns in a->B and b->B may be different, hence we cannot call
2049        the MatCopy() directly on the two parts. If need be, we can provide a more
2050        efficient copy than the MatCopy_Basic() by first uncompressing the a->B matrices
2051        then copying the submatrices */
2052     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
2053   } else {
2054     ierr = MatCopy(a->A,b->A,str);CHKERRQ(ierr);
2055     ierr = MatCopy(a->B,b->B,str);CHKERRQ(ierr);
2056   }
2057   PetscFunctionReturn(0);
2058 }
2059 
2060 PetscErrorCode MatSetUp_MPIAIJ(Mat A)
2061 {
2062   PetscErrorCode ierr;
2063 
2064   PetscFunctionBegin;
2065   ierr =  MatMPIAIJSetPreallocation(A,PETSC_DEFAULT,0,PETSC_DEFAULT,0);CHKERRQ(ierr);
2066   PetscFunctionReturn(0);
2067 }
2068 
2069 /*
2070    Computes the number of nonzeros per row needed for preallocation when X and Y
2071    have different nonzero structure.
2072 */
2073 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)
2074 {
2075   PetscInt       i,j,k,nzx,nzy;
2076 
2077   PetscFunctionBegin;
2078   /* Set the number of nonzeros in the new matrix */
2079   for (i=0; i<m; i++) {
2080     const PetscInt *xjj = xj+xi[i],*yjj = yj+yi[i];
2081     nzx = xi[i+1] - xi[i];
2082     nzy = yi[i+1] - yi[i];
2083     nnz[i] = 0;
2084     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2085       for (; k<nzy && yltog[yjj[k]]<xltog[xjj[j]]; k++) nnz[i]++; /* Catch up to X */
2086       if (k<nzy && yltog[yjj[k]]==xltog[xjj[j]]) k++;             /* Skip duplicate */
2087       nnz[i]++;
2088     }
2089     for (; k<nzy; k++) nnz[i]++;
2090   }
2091   PetscFunctionReturn(0);
2092 }
2093 
2094 /* This is the same as MatAXPYGetPreallocation_SeqAIJ, except that the local-to-global map is provided */
2095 static PetscErrorCode MatAXPYGetPreallocation_MPIAIJ(Mat Y,const PetscInt *yltog,Mat X,const PetscInt *xltog,PetscInt *nnz)
2096 {
2097   PetscErrorCode ierr;
2098   PetscInt       m = Y->rmap->N;
2099   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data;
2100   Mat_SeqAIJ     *y = (Mat_SeqAIJ*)Y->data;
2101 
2102   PetscFunctionBegin;
2103   ierr = MatAXPYGetPreallocation_MPIX_private(m,x->i,x->j,xltog,y->i,y->j,yltog,nnz);CHKERRQ(ierr);
2104   PetscFunctionReturn(0);
2105 }
2106 
2107 PetscErrorCode MatAXPY_MPIAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
2108 {
2109   PetscErrorCode ierr;
2110   Mat_MPIAIJ     *xx = (Mat_MPIAIJ*)X->data,*yy = (Mat_MPIAIJ*)Y->data;
2111   PetscBLASInt   bnz,one=1;
2112   Mat_SeqAIJ     *x,*y;
2113 
2114   PetscFunctionBegin;
2115   if (str == SAME_NONZERO_PATTERN) {
2116     PetscScalar alpha = a;
2117     x    = (Mat_SeqAIJ*)xx->A->data;
2118     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2119     y    = (Mat_SeqAIJ*)yy->A->data;
2120     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2121     x    = (Mat_SeqAIJ*)xx->B->data;
2122     y    = (Mat_SeqAIJ*)yy->B->data;
2123     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2124     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2125     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
2126   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
2127     ierr = MatAXPY_Basic(Y,a,X,str);CHKERRQ(ierr);
2128   } else {
2129     Mat      B;
2130     PetscInt *nnz_d,*nnz_o;
2131     ierr = PetscMalloc1(yy->A->rmap->N,&nnz_d);CHKERRQ(ierr);
2132     ierr = PetscMalloc1(yy->B->rmap->N,&nnz_o);CHKERRQ(ierr);
2133     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
2134     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
2135     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
2136     ierr = MatSetBlockSizesFromMats(B,Y,Y);CHKERRQ(ierr);
2137     ierr = MatSetType(B,MATMPIAIJ);CHKERRQ(ierr);
2138     ierr = MatAXPYGetPreallocation_SeqAIJ(yy->A,xx->A,nnz_d);CHKERRQ(ierr);
2139     ierr = MatAXPYGetPreallocation_MPIAIJ(yy->B,yy->garray,xx->B,xx->garray,nnz_o);CHKERRQ(ierr);
2140     ierr = MatMPIAIJSetPreallocation(B,0,nnz_d,0,nnz_o);CHKERRQ(ierr);
2141     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
2142     ierr = MatHeaderReplace(Y,&B);CHKERRQ(ierr);
2143     ierr = PetscFree(nnz_d);CHKERRQ(ierr);
2144     ierr = PetscFree(nnz_o);CHKERRQ(ierr);
2145   }
2146   PetscFunctionReturn(0);
2147 }
2148 
2149 extern PetscErrorCode  MatConjugate_SeqAIJ(Mat);
2150 
2151 PetscErrorCode  MatConjugate_MPIAIJ(Mat mat)
2152 {
2153 #if defined(PETSC_USE_COMPLEX)
2154   PetscErrorCode ierr;
2155   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2156 
2157   PetscFunctionBegin;
2158   ierr = MatConjugate_SeqAIJ(aij->A);CHKERRQ(ierr);
2159   ierr = MatConjugate_SeqAIJ(aij->B);CHKERRQ(ierr);
2160 #else
2161   PetscFunctionBegin;
2162 #endif
2163   PetscFunctionReturn(0);
2164 }
2165 
2166 PetscErrorCode MatRealPart_MPIAIJ(Mat A)
2167 {
2168   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2169   PetscErrorCode ierr;
2170 
2171   PetscFunctionBegin;
2172   ierr = MatRealPart(a->A);CHKERRQ(ierr);
2173   ierr = MatRealPart(a->B);CHKERRQ(ierr);
2174   PetscFunctionReturn(0);
2175 }
2176 
2177 PetscErrorCode MatImaginaryPart_MPIAIJ(Mat A)
2178 {
2179   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2180   PetscErrorCode ierr;
2181 
2182   PetscFunctionBegin;
2183   ierr = MatImaginaryPart(a->A);CHKERRQ(ierr);
2184   ierr = MatImaginaryPart(a->B);CHKERRQ(ierr);
2185   PetscFunctionReturn(0);
2186 }
2187 
2188 PetscErrorCode MatGetRowMaxAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2189 {
2190   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2191   PetscErrorCode ierr;
2192   PetscInt       i,*idxb = 0;
2193   PetscScalar    *va,*vb;
2194   Vec            vtmp;
2195 
2196   PetscFunctionBegin;
2197   ierr = MatGetRowMaxAbs(a->A,v,idx);CHKERRQ(ierr);
2198   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2199   if (idx) {
2200     for (i=0; i<A->rmap->n; i++) {
2201       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2202     }
2203   }
2204 
2205   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2206   if (idx) {
2207     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2208   }
2209   ierr = MatGetRowMaxAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2210   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2211 
2212   for (i=0; i<A->rmap->n; i++) {
2213     if (PetscAbsScalar(va[i]) < PetscAbsScalar(vb[i])) {
2214       va[i] = vb[i];
2215       if (idx) idx[i] = a->garray[idxb[i]];
2216     }
2217   }
2218 
2219   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2220   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2221   ierr = PetscFree(idxb);CHKERRQ(ierr);
2222   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2223   PetscFunctionReturn(0);
2224 }
2225 
2226 PetscErrorCode MatGetRowMinAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2227 {
2228   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2229   PetscErrorCode ierr;
2230   PetscInt       i,*idxb = 0;
2231   PetscScalar    *va,*vb;
2232   Vec            vtmp;
2233 
2234   PetscFunctionBegin;
2235   ierr = MatGetRowMinAbs(a->A,v,idx);CHKERRQ(ierr);
2236   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2237   if (idx) {
2238     for (i=0; i<A->cmap->n; i++) {
2239       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2240     }
2241   }
2242 
2243   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2244   if (idx) {
2245     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2246   }
2247   ierr = MatGetRowMinAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2248   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2249 
2250   for (i=0; i<A->rmap->n; i++) {
2251     if (PetscAbsScalar(va[i]) > PetscAbsScalar(vb[i])) {
2252       va[i] = vb[i];
2253       if (idx) idx[i] = a->garray[idxb[i]];
2254     }
2255   }
2256 
2257   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2258   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2259   ierr = PetscFree(idxb);CHKERRQ(ierr);
2260   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2261   PetscFunctionReturn(0);
2262 }
2263 
2264 PetscErrorCode MatGetRowMin_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2265 {
2266   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2267   PetscInt       n      = A->rmap->n;
2268   PetscInt       cstart = A->cmap->rstart;
2269   PetscInt       *cmap  = mat->garray;
2270   PetscInt       *diagIdx, *offdiagIdx;
2271   Vec            diagV, offdiagV;
2272   PetscScalar    *a, *diagA, *offdiagA;
2273   PetscInt       r;
2274   PetscErrorCode ierr;
2275 
2276   PetscFunctionBegin;
2277   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2278   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &diagV);CHKERRQ(ierr);
2279   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &offdiagV);CHKERRQ(ierr);
2280   ierr = MatGetRowMin(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2281   ierr = MatGetRowMin(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2282   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2283   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2284   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2285   for (r = 0; r < n; ++r) {
2286     if (PetscAbsScalar(diagA[r]) <= PetscAbsScalar(offdiagA[r])) {
2287       a[r]   = diagA[r];
2288       idx[r] = cstart + diagIdx[r];
2289     } else {
2290       a[r]   = offdiagA[r];
2291       idx[r] = cmap[offdiagIdx[r]];
2292     }
2293   }
2294   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2295   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2296   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2297   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2298   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2299   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2300   PetscFunctionReturn(0);
2301 }
2302 
2303 PetscErrorCode MatGetRowMax_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2304 {
2305   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2306   PetscInt       n      = A->rmap->n;
2307   PetscInt       cstart = A->cmap->rstart;
2308   PetscInt       *cmap  = mat->garray;
2309   PetscInt       *diagIdx, *offdiagIdx;
2310   Vec            diagV, offdiagV;
2311   PetscScalar    *a, *diagA, *offdiagA;
2312   PetscInt       r;
2313   PetscErrorCode ierr;
2314 
2315   PetscFunctionBegin;
2316   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2317   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &diagV);CHKERRQ(ierr);
2318   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &offdiagV);CHKERRQ(ierr);
2319   ierr = MatGetRowMax(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2320   ierr = MatGetRowMax(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2321   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2322   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2323   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2324   for (r = 0; r < n; ++r) {
2325     if (PetscAbsScalar(diagA[r]) >= PetscAbsScalar(offdiagA[r])) {
2326       a[r]   = diagA[r];
2327       idx[r] = cstart + diagIdx[r];
2328     } else {
2329       a[r]   = offdiagA[r];
2330       idx[r] = cmap[offdiagIdx[r]];
2331     }
2332   }
2333   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2334   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2335   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2336   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2337   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2338   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2339   PetscFunctionReturn(0);
2340 }
2341 
2342 PetscErrorCode MatGetSeqNonzeroStructure_MPIAIJ(Mat mat,Mat *newmat)
2343 {
2344   PetscErrorCode ierr;
2345   Mat            *dummy;
2346 
2347   PetscFunctionBegin;
2348   ierr    = MatCreateSubMatrix_MPIAIJ_All(mat,MAT_DO_NOT_GET_VALUES,MAT_INITIAL_MATRIX,&dummy);CHKERRQ(ierr);
2349   *newmat = *dummy;
2350   ierr    = PetscFree(dummy);CHKERRQ(ierr);
2351   PetscFunctionReturn(0);
2352 }
2353 
2354 PetscErrorCode  MatInvertBlockDiagonal_MPIAIJ(Mat A,const PetscScalar **values)
2355 {
2356   Mat_MPIAIJ     *a = (Mat_MPIAIJ*) A->data;
2357   PetscErrorCode ierr;
2358 
2359   PetscFunctionBegin;
2360   ierr = MatInvertBlockDiagonal(a->A,values);CHKERRQ(ierr);
2361   A->factorerrortype = a->A->factorerrortype;
2362   PetscFunctionReturn(0);
2363 }
2364 
2365 static PetscErrorCode  MatSetRandom_MPIAIJ(Mat x,PetscRandom rctx)
2366 {
2367   PetscErrorCode ierr;
2368   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)x->data;
2369 
2370   PetscFunctionBegin;
2371   ierr = MatSetRandom(aij->A,rctx);CHKERRQ(ierr);
2372   ierr = MatSetRandom(aij->B,rctx);CHKERRQ(ierr);
2373   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2374   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2375   PetscFunctionReturn(0);
2376 }
2377 
2378 PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ(Mat A,PetscBool sc)
2379 {
2380   PetscFunctionBegin;
2381   if (sc) A->ops->increaseoverlap = MatIncreaseOverlap_MPIAIJ_Scalable;
2382   else A->ops->increaseoverlap    = MatIncreaseOverlap_MPIAIJ;
2383   PetscFunctionReturn(0);
2384 }
2385 
2386 /*@
2387    MatMPIAIJSetUseScalableIncreaseOverlap - Determine if the matrix uses a scalable algorithm to compute the overlap
2388 
2389    Collective on Mat
2390 
2391    Input Parameters:
2392 +    A - the matrix
2393 -    sc - PETSC_TRUE indicates use the scalable algorithm (default is not to use the scalable algorithm)
2394 
2395  Level: advanced
2396 
2397 @*/
2398 PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap(Mat A,PetscBool sc)
2399 {
2400   PetscErrorCode       ierr;
2401 
2402   PetscFunctionBegin;
2403   ierr = PetscTryMethod(A,"MatMPIAIJSetUseScalableIncreaseOverlap_C",(Mat,PetscBool),(A,sc));CHKERRQ(ierr);
2404   PetscFunctionReturn(0);
2405 }
2406 
2407 PetscErrorCode MatSetFromOptions_MPIAIJ(PetscOptionItems *PetscOptionsObject,Mat A)
2408 {
2409   PetscErrorCode       ierr;
2410   PetscBool            sc = PETSC_FALSE,flg;
2411 
2412   PetscFunctionBegin;
2413   ierr = PetscOptionsHead(PetscOptionsObject,"MPIAIJ options");CHKERRQ(ierr);
2414   ierr = PetscObjectOptionsBegin((PetscObject)A);
2415     if (A->ops->increaseoverlap == MatIncreaseOverlap_MPIAIJ_Scalable) sc = PETSC_TRUE;
2416     ierr = PetscOptionsBool("-mat_increase_overlap_scalable","Use a scalable algorithm to compute the overlap","MatIncreaseOverlap",sc,&sc,&flg);CHKERRQ(ierr);
2417     if (flg) {
2418       ierr = MatMPIAIJSetUseScalableIncreaseOverlap(A,sc);CHKERRQ(ierr);
2419     }
2420   ierr = PetscOptionsEnd();CHKERRQ(ierr);
2421   PetscFunctionReturn(0);
2422 }
2423 
2424 PetscErrorCode MatShift_MPIAIJ(Mat Y,PetscScalar a)
2425 {
2426   PetscErrorCode ierr;
2427   Mat_MPIAIJ     *maij = (Mat_MPIAIJ*)Y->data;
2428   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)maij->A->data;
2429 
2430   PetscFunctionBegin;
2431   if (!Y->preallocated) {
2432     ierr = MatMPIAIJSetPreallocation(Y,1,NULL,0,NULL);CHKERRQ(ierr);
2433   } else if (!aij->nz) {
2434     PetscInt nonew = aij->nonew;
2435     ierr = MatSeqAIJSetPreallocation(maij->A,1,NULL);CHKERRQ(ierr);
2436     aij->nonew = nonew;
2437   }
2438   ierr = MatShift_Basic(Y,a);CHKERRQ(ierr);
2439   PetscFunctionReturn(0);
2440 }
2441 
2442 PetscErrorCode MatMissingDiagonal_MPIAIJ(Mat A,PetscBool  *missing,PetscInt *d)
2443 {
2444   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2445   PetscErrorCode ierr;
2446 
2447   PetscFunctionBegin;
2448   if (A->rmap->n != A->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only works for square matrices");
2449   ierr = MatMissingDiagonal(a->A,missing,d);CHKERRQ(ierr);
2450   if (d) {
2451     PetscInt rstart;
2452     ierr = MatGetOwnershipRange(A,&rstart,NULL);CHKERRQ(ierr);
2453     *d += rstart;
2454 
2455   }
2456   PetscFunctionReturn(0);
2457 }
2458 
2459 
2460 /* -------------------------------------------------------------------*/
2461 static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
2462                                        MatGetRow_MPIAIJ,
2463                                        MatRestoreRow_MPIAIJ,
2464                                        MatMult_MPIAIJ,
2465                                 /* 4*/ MatMultAdd_MPIAIJ,
2466                                        MatMultTranspose_MPIAIJ,
2467                                        MatMultTransposeAdd_MPIAIJ,
2468                                        0,
2469                                        0,
2470                                        0,
2471                                 /*10*/ 0,
2472                                        0,
2473                                        0,
2474                                        MatSOR_MPIAIJ,
2475                                        MatTranspose_MPIAIJ,
2476                                 /*15*/ MatGetInfo_MPIAIJ,
2477                                        MatEqual_MPIAIJ,
2478                                        MatGetDiagonal_MPIAIJ,
2479                                        MatDiagonalScale_MPIAIJ,
2480                                        MatNorm_MPIAIJ,
2481                                 /*20*/ MatAssemblyBegin_MPIAIJ,
2482                                        MatAssemblyEnd_MPIAIJ,
2483                                        MatSetOption_MPIAIJ,
2484                                        MatZeroEntries_MPIAIJ,
2485                                 /*24*/ MatZeroRows_MPIAIJ,
2486                                        0,
2487                                        0,
2488                                        0,
2489                                        0,
2490                                 /*29*/ MatSetUp_MPIAIJ,
2491                                        0,
2492                                        0,
2493                                        MatGetDiagonalBlock_MPIAIJ,
2494                                        0,
2495                                 /*34*/ MatDuplicate_MPIAIJ,
2496                                        0,
2497                                        0,
2498                                        0,
2499                                        0,
2500                                 /*39*/ MatAXPY_MPIAIJ,
2501                                        MatCreateSubMatrices_MPIAIJ,
2502                                        MatIncreaseOverlap_MPIAIJ,
2503                                        MatGetValues_MPIAIJ,
2504                                        MatCopy_MPIAIJ,
2505                                 /*44*/ MatGetRowMax_MPIAIJ,
2506                                        MatScale_MPIAIJ,
2507                                        MatShift_MPIAIJ,
2508                                        MatDiagonalSet_MPIAIJ,
2509                                        MatZeroRowsColumns_MPIAIJ,
2510                                 /*49*/ MatSetRandom_MPIAIJ,
2511                                        0,
2512                                        0,
2513                                        0,
2514                                        0,
2515                                 /*54*/ MatFDColoringCreate_MPIXAIJ,
2516                                        0,
2517                                        MatSetUnfactored_MPIAIJ,
2518                                        MatPermute_MPIAIJ,
2519                                        0,
2520                                 /*59*/ MatCreateSubMatrix_MPIAIJ,
2521                                        MatDestroy_MPIAIJ,
2522                                        MatView_MPIAIJ,
2523                                        0,
2524                                        MatMatMatMult_MPIAIJ_MPIAIJ_MPIAIJ,
2525                                 /*64*/ MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ,
2526                                        MatMatMatMultNumeric_MPIAIJ_MPIAIJ_MPIAIJ,
2527                                        0,
2528                                        0,
2529                                        0,
2530                                 /*69*/ MatGetRowMaxAbs_MPIAIJ,
2531                                        MatGetRowMinAbs_MPIAIJ,
2532                                        0,
2533                                        0,
2534                                        0,
2535                                        0,
2536                                 /*75*/ MatFDColoringApply_AIJ,
2537                                        MatSetFromOptions_MPIAIJ,
2538                                        0,
2539                                        0,
2540                                        MatFindZeroDiagonals_MPIAIJ,
2541                                 /*80*/ 0,
2542                                        0,
2543                                        0,
2544                                 /*83*/ MatLoad_MPIAIJ,
2545                                        0,
2546                                        0,
2547                                        0,
2548                                        0,
2549                                        0,
2550                                 /*89*/ MatMatMult_MPIAIJ_MPIAIJ,
2551                                        MatMatMultSymbolic_MPIAIJ_MPIAIJ,
2552                                        MatMatMultNumeric_MPIAIJ_MPIAIJ,
2553                                        MatPtAP_MPIAIJ_MPIAIJ,
2554                                        MatPtAPSymbolic_MPIAIJ_MPIAIJ,
2555                                 /*94*/ MatPtAPNumeric_MPIAIJ_MPIAIJ,
2556                                        0,
2557                                        0,
2558                                        0,
2559                                        0,
2560                                 /*99*/ 0,
2561                                        0,
2562                                        0,
2563                                        MatConjugate_MPIAIJ,
2564                                        0,
2565                                 /*104*/MatSetValuesRow_MPIAIJ,
2566                                        MatRealPart_MPIAIJ,
2567                                        MatImaginaryPart_MPIAIJ,
2568                                        0,
2569                                        0,
2570                                 /*109*/0,
2571                                        0,
2572                                        MatGetRowMin_MPIAIJ,
2573                                        0,
2574                                        MatMissingDiagonal_MPIAIJ,
2575                                 /*114*/MatGetSeqNonzeroStructure_MPIAIJ,
2576                                        0,
2577                                        MatGetGhosts_MPIAIJ,
2578                                        0,
2579                                        0,
2580                                 /*119*/0,
2581                                        0,
2582                                        0,
2583                                        0,
2584                                        MatGetMultiProcBlock_MPIAIJ,
2585                                 /*124*/MatFindNonzeroRows_MPIAIJ,
2586                                        MatGetColumnNorms_MPIAIJ,
2587                                        MatInvertBlockDiagonal_MPIAIJ,
2588                                        0,
2589                                        MatCreateSubMatricesMPI_MPIAIJ,
2590                                 /*129*/0,
2591                                        MatTransposeMatMult_MPIAIJ_MPIAIJ,
2592                                        MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ,
2593                                        MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ,
2594                                        0,
2595                                 /*134*/0,
2596                                        0,
2597                                        0,
2598                                        0,
2599                                        0,
2600                                 /*139*/MatSetBlockSizes_MPIAIJ,
2601                                        0,
2602                                        0,
2603                                        MatFDColoringSetUp_MPIXAIJ,
2604                                        MatFindOffBlockDiagonalEntries_MPIAIJ,
2605                                 /*144*/MatCreateMPIMatConcatenateSeqMat_MPIAIJ
2606 };
2607 
2608 /* ----------------------------------------------------------------------------------------*/
2609 
2610 PetscErrorCode  MatStoreValues_MPIAIJ(Mat mat)
2611 {
2612   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2613   PetscErrorCode ierr;
2614 
2615   PetscFunctionBegin;
2616   ierr = MatStoreValues(aij->A);CHKERRQ(ierr);
2617   ierr = MatStoreValues(aij->B);CHKERRQ(ierr);
2618   PetscFunctionReturn(0);
2619 }
2620 
2621 PetscErrorCode  MatRetrieveValues_MPIAIJ(Mat mat)
2622 {
2623   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2624   PetscErrorCode ierr;
2625 
2626   PetscFunctionBegin;
2627   ierr = MatRetrieveValues(aij->A);CHKERRQ(ierr);
2628   ierr = MatRetrieveValues(aij->B);CHKERRQ(ierr);
2629   PetscFunctionReturn(0);
2630 }
2631 
2632 PetscErrorCode  MatMPIAIJSetPreallocation_MPIAIJ(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
2633 {
2634   Mat_MPIAIJ     *b;
2635   PetscErrorCode ierr;
2636 
2637   PetscFunctionBegin;
2638   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
2639   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
2640   b = (Mat_MPIAIJ*)B->data;
2641 
2642 #if defined(PETSC_USE_CTABLE)
2643   ierr = PetscTableDestroy(&b->colmap);CHKERRQ(ierr);
2644 #else
2645   ierr = PetscFree(b->colmap);CHKERRQ(ierr);
2646 #endif
2647   ierr = PetscFree(b->garray);CHKERRQ(ierr);
2648   ierr = VecDestroy(&b->lvec);CHKERRQ(ierr);
2649   ierr = VecScatterDestroy(&b->Mvctx);CHKERRQ(ierr);
2650 
2651   /* Because the B will have been resized we simply destroy it and create a new one each time */
2652   ierr = MatDestroy(&b->B);CHKERRQ(ierr);
2653   ierr = MatCreate(PETSC_COMM_SELF,&b->B);CHKERRQ(ierr);
2654   ierr = MatSetSizes(b->B,B->rmap->n,B->cmap->N,B->rmap->n,B->cmap->N);CHKERRQ(ierr);
2655   ierr = MatSetBlockSizesFromMats(b->B,B,B);CHKERRQ(ierr);
2656   ierr = MatSetType(b->B,MATSEQAIJ);CHKERRQ(ierr);
2657   ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->B);CHKERRQ(ierr);
2658 
2659   if (!B->preallocated) {
2660     ierr = MatCreate(PETSC_COMM_SELF,&b->A);CHKERRQ(ierr);
2661     ierr = MatSetSizes(b->A,B->rmap->n,B->cmap->n,B->rmap->n,B->cmap->n);CHKERRQ(ierr);
2662     ierr = MatSetBlockSizesFromMats(b->A,B,B);CHKERRQ(ierr);
2663     ierr = MatSetType(b->A,MATSEQAIJ);CHKERRQ(ierr);
2664     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->A);CHKERRQ(ierr);
2665   }
2666 
2667   ierr = MatSeqAIJSetPreallocation(b->A,d_nz,d_nnz);CHKERRQ(ierr);
2668   ierr = MatSeqAIJSetPreallocation(b->B,o_nz,o_nnz);CHKERRQ(ierr);
2669   B->preallocated  = PETSC_TRUE;
2670   B->was_assembled = PETSC_FALSE;
2671   B->assembled     = PETSC_FALSE;;
2672   PetscFunctionReturn(0);
2673 }
2674 
2675 PetscErrorCode MatDuplicate_MPIAIJ(Mat matin,MatDuplicateOption cpvalues,Mat *newmat)
2676 {
2677   Mat            mat;
2678   Mat_MPIAIJ     *a,*oldmat = (Mat_MPIAIJ*)matin->data;
2679   PetscErrorCode ierr;
2680 
2681   PetscFunctionBegin;
2682   *newmat = 0;
2683   ierr    = MatCreate(PetscObjectComm((PetscObject)matin),&mat);CHKERRQ(ierr);
2684   ierr    = MatSetSizes(mat,matin->rmap->n,matin->cmap->n,matin->rmap->N,matin->cmap->N);CHKERRQ(ierr);
2685   ierr    = MatSetBlockSizesFromMats(mat,matin,matin);CHKERRQ(ierr);
2686   ierr    = MatSetType(mat,((PetscObject)matin)->type_name);CHKERRQ(ierr);
2687   ierr    = PetscMemcpy(mat->ops,matin->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
2688   a       = (Mat_MPIAIJ*)mat->data;
2689 
2690   mat->factortype   = matin->factortype;
2691   mat->assembled    = PETSC_TRUE;
2692   mat->insertmode   = NOT_SET_VALUES;
2693   mat->preallocated = PETSC_TRUE;
2694 
2695   a->size         = oldmat->size;
2696   a->rank         = oldmat->rank;
2697   a->donotstash   = oldmat->donotstash;
2698   a->roworiented  = oldmat->roworiented;
2699   a->rowindices   = 0;
2700   a->rowvalues    = 0;
2701   a->getrowactive = PETSC_FALSE;
2702 
2703   ierr = PetscLayoutReference(matin->rmap,&mat->rmap);CHKERRQ(ierr);
2704   ierr = PetscLayoutReference(matin->cmap,&mat->cmap);CHKERRQ(ierr);
2705 
2706   if (oldmat->colmap) {
2707 #if defined(PETSC_USE_CTABLE)
2708     ierr = PetscTableCreateCopy(oldmat->colmap,&a->colmap);CHKERRQ(ierr);
2709 #else
2710     ierr = PetscMalloc1(mat->cmap->N,&a->colmap);CHKERRQ(ierr);
2711     ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2712     ierr = PetscMemcpy(a->colmap,oldmat->colmap,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2713 #endif
2714   } else a->colmap = 0;
2715   if (oldmat->garray) {
2716     PetscInt len;
2717     len  = oldmat->B->cmap->n;
2718     ierr = PetscMalloc1(len+1,&a->garray);CHKERRQ(ierr);
2719     ierr = PetscLogObjectMemory((PetscObject)mat,len*sizeof(PetscInt));CHKERRQ(ierr);
2720     if (len) { ierr = PetscMemcpy(a->garray,oldmat->garray,len*sizeof(PetscInt));CHKERRQ(ierr); }
2721   } else a->garray = 0;
2722 
2723   ierr    = VecDuplicate(oldmat->lvec,&a->lvec);CHKERRQ(ierr);
2724   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->lvec);CHKERRQ(ierr);
2725   ierr    = VecScatterCopy(oldmat->Mvctx,&a->Mvctx);CHKERRQ(ierr);
2726   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->Mvctx);CHKERRQ(ierr);
2727   ierr    = MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
2728   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->A);CHKERRQ(ierr);
2729   ierr    = MatDuplicate(oldmat->B,cpvalues,&a->B);CHKERRQ(ierr);
2730   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->B);CHKERRQ(ierr);
2731   ierr    = PetscFunctionListDuplicate(((PetscObject)matin)->qlist,&((PetscObject)mat)->qlist);CHKERRQ(ierr);
2732   *newmat = mat;
2733   PetscFunctionReturn(0);
2734 }
2735 
2736 PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
2737 {
2738   PetscScalar    *vals,*svals;
2739   MPI_Comm       comm;
2740   PetscErrorCode ierr;
2741   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
2742   PetscInt       i,nz,j,rstart,rend,mmax,maxnz = 0;
2743   PetscInt       header[4],*rowlengths = 0,M,N,m,*cols;
2744   PetscInt       *ourlens = NULL,*procsnz = NULL,*offlens = NULL,jj,*mycols,*smycols;
2745   PetscInt       cend,cstart,n,*rowners;
2746   int            fd;
2747   PetscInt       bs = newMat->rmap->bs;
2748 
2749   PetscFunctionBegin;
2750   /* force binary viewer to load .info file if it has not yet done so */
2751   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
2752   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
2753   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2754   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2755   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
2756   if (!rank) {
2757     ierr = PetscBinaryRead(fd,(char*)header,4,PETSC_INT);CHKERRQ(ierr);
2758     if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
2759     if (header[3] < 0) SETERRQ(PetscObjectComm((PetscObject)newMat),PETSC_ERR_FILE_UNEXPECTED,"Matrix stored in special format on disk,cannot load as MATMPIAIJ");
2760   }
2761 
2762   ierr = PetscOptionsBegin(comm,NULL,"Options for loading MATMPIAIJ matrix","Mat");CHKERRQ(ierr);
2763   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
2764   ierr = PetscOptionsEnd();CHKERRQ(ierr);
2765   if (bs < 0) bs = 1;
2766 
2767   ierr = MPI_Bcast(header+1,3,MPIU_INT,0,comm);CHKERRQ(ierr);
2768   M    = header[1]; N = header[2];
2769 
2770   /* If global sizes are set, check if they are consistent with that given in the file */
2771   if (newMat->rmap->N >= 0 && newMat->rmap->N != M) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Inconsistent # of rows:Matrix in file has (%D) and input matrix has (%D)",newMat->rmap->N,M);
2772   if (newMat->cmap->N >=0 && newMat->cmap->N != N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Inconsistent # of cols:Matrix in file has (%D) and input matrix has (%D)",newMat->cmap->N,N);
2773 
2774   /* determine ownership of all (block) rows */
2775   if (M%bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Inconsistent # of rows (%d) and block size (%d)",M,bs);
2776   if (newMat->rmap->n < 0) m = bs*((M/bs)/size + (((M/bs) % size) > rank));    /* PETSC_DECIDE */
2777   else m = newMat->rmap->n; /* Set by user */
2778 
2779   ierr = PetscMalloc1(size+1,&rowners);CHKERRQ(ierr);
2780   ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
2781 
2782   /* First process needs enough room for process with most rows */
2783   if (!rank) {
2784     mmax = rowners[1];
2785     for (i=2; i<=size; i++) {
2786       mmax = PetscMax(mmax, rowners[i]);
2787     }
2788   } else mmax = -1;             /* unused, but compilers complain */
2789 
2790   rowners[0] = 0;
2791   for (i=2; i<=size; i++) {
2792     rowners[i] += rowners[i-1];
2793   }
2794   rstart = rowners[rank];
2795   rend   = rowners[rank+1];
2796 
2797   /* distribute row lengths to all processors */
2798   ierr = PetscMalloc2(m,&ourlens,m,&offlens);CHKERRQ(ierr);
2799   if (!rank) {
2800     ierr = PetscBinaryRead(fd,ourlens,m,PETSC_INT);CHKERRQ(ierr);
2801     ierr = PetscMalloc1(mmax,&rowlengths);CHKERRQ(ierr);
2802     ierr = PetscCalloc1(size,&procsnz);CHKERRQ(ierr);
2803     for (j=0; j<m; j++) {
2804       procsnz[0] += ourlens[j];
2805     }
2806     for (i=1; i<size; i++) {
2807       ierr = PetscBinaryRead(fd,rowlengths,rowners[i+1]-rowners[i],PETSC_INT);CHKERRQ(ierr);
2808       /* calculate the number of nonzeros on each processor */
2809       for (j=0; j<rowners[i+1]-rowners[i]; j++) {
2810         procsnz[i] += rowlengths[j];
2811       }
2812       ierr = MPIULong_Send(rowlengths,rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2813     }
2814     ierr = PetscFree(rowlengths);CHKERRQ(ierr);
2815   } else {
2816     ierr = MPIULong_Recv(ourlens,m,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2817   }
2818 
2819   if (!rank) {
2820     /* determine max buffer needed and allocate it */
2821     maxnz = 0;
2822     for (i=0; i<size; i++) {
2823       maxnz = PetscMax(maxnz,procsnz[i]);
2824     }
2825     ierr = PetscMalloc1(maxnz,&cols);CHKERRQ(ierr);
2826 
2827     /* read in my part of the matrix column indices  */
2828     nz   = procsnz[0];
2829     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2830     ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);
2831 
2832     /* read in every one elses and ship off */
2833     for (i=1; i<size; i++) {
2834       nz   = procsnz[i];
2835       ierr = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
2836       ierr = MPIULong_Send(cols,nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2837     }
2838     ierr = PetscFree(cols);CHKERRQ(ierr);
2839   } else {
2840     /* determine buffer space needed for message */
2841     nz = 0;
2842     for (i=0; i<m; i++) {
2843       nz += ourlens[i];
2844     }
2845     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2846 
2847     /* receive message of column indices*/
2848     ierr = MPIULong_Recv(mycols,nz,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2849   }
2850 
2851   /* determine column ownership if matrix is not square */
2852   if (N != M) {
2853     if (newMat->cmap->n < 0) n = N/size + ((N % size) > rank);
2854     else n = newMat->cmap->n;
2855     ierr   = MPI_Scan(&n,&cend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
2856     cstart = cend - n;
2857   } else {
2858     cstart = rstart;
2859     cend   = rend;
2860     n      = cend - cstart;
2861   }
2862 
2863   /* loop over local rows, determining number of off diagonal entries */
2864   ierr = PetscMemzero(offlens,m*sizeof(PetscInt));CHKERRQ(ierr);
2865   jj   = 0;
2866   for (i=0; i<m; i++) {
2867     for (j=0; j<ourlens[i]; j++) {
2868       if (mycols[jj] < cstart || mycols[jj] >= cend) offlens[i]++;
2869       jj++;
2870     }
2871   }
2872 
2873   for (i=0; i<m; i++) {
2874     ourlens[i] -= offlens[i];
2875   }
2876   ierr = MatSetSizes(newMat,m,n,M,N);CHKERRQ(ierr);
2877 
2878   if (bs > 1) {ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);}
2879 
2880   ierr = MatMPIAIJSetPreallocation(newMat,0,ourlens,0,offlens);CHKERRQ(ierr);
2881 
2882   for (i=0; i<m; i++) {
2883     ourlens[i] += offlens[i];
2884   }
2885 
2886   if (!rank) {
2887     ierr = PetscMalloc1(maxnz+1,&vals);CHKERRQ(ierr);
2888 
2889     /* read in my part of the matrix numerical values  */
2890     nz   = procsnz[0];
2891     ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
2892 
2893     /* insert into matrix */
2894     jj      = rstart;
2895     smycols = mycols;
2896     svals   = vals;
2897     for (i=0; i<m; i++) {
2898       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
2899       smycols += ourlens[i];
2900       svals   += ourlens[i];
2901       jj++;
2902     }
2903 
2904     /* read in other processors and ship out */
2905     for (i=1; i<size; i++) {
2906       nz   = procsnz[i];
2907       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
2908       ierr = MPIULong_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
2909     }
2910     ierr = PetscFree(procsnz);CHKERRQ(ierr);
2911   } else {
2912     /* receive numeric values */
2913     ierr = PetscMalloc1(nz+1,&vals);CHKERRQ(ierr);
2914 
2915     /* receive message of values*/
2916     ierr = MPIULong_Recv(vals,nz,MPIU_SCALAR,0,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
2917 
2918     /* insert into matrix */
2919     jj      = rstart;
2920     smycols = mycols;
2921     svals   = vals;
2922     for (i=0; i<m; i++) {
2923       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
2924       smycols += ourlens[i];
2925       svals   += ourlens[i];
2926       jj++;
2927     }
2928   }
2929   ierr = PetscFree2(ourlens,offlens);CHKERRQ(ierr);
2930   ierr = PetscFree(vals);CHKERRQ(ierr);
2931   ierr = PetscFree(mycols);CHKERRQ(ierr);
2932   ierr = PetscFree(rowners);CHKERRQ(ierr);
2933   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2934   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2935   PetscFunctionReturn(0);
2936 }
2937 
2938 /* Not scalable because of ISAllGather() unless getting all columns. */
2939 PetscErrorCode ISGetSeqIS_Private(Mat mat,IS iscol,IS *isseq)
2940 {
2941   PetscErrorCode ierr;
2942   IS             iscol_local;
2943   PetscBool      isstride;
2944   PetscMPIInt    lisstride=0,gisstride;
2945 
2946   PetscFunctionBegin;
2947   /* check if we are grabbing all columns*/
2948   ierr = PetscObjectTypeCompare((PetscObject)iscol,ISSTRIDE,&isstride);CHKERRQ(ierr);
2949 
2950   if (isstride) {
2951     PetscInt  start,len,mstart,mlen;
2952     ierr = ISStrideGetInfo(iscol,&start,NULL);CHKERRQ(ierr);
2953     ierr = ISGetLocalSize(iscol,&len);CHKERRQ(ierr);
2954     ierr = MatGetOwnershipRangeColumn(mat,&mstart,&mlen);CHKERRQ(ierr);
2955     if (mstart == start && mlen-mstart == len) lisstride = 1;
2956   }
2957 
2958   ierr = MPIU_Allreduce(&lisstride,&gisstride,1,MPI_INT,MPI_MIN,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
2959   if (gisstride) {
2960     PetscInt N;
2961     ierr = MatGetSize(mat,NULL,&N);CHKERRQ(ierr);
2962     ierr = ISCreateStride(PetscObjectComm((PetscObject)mat),N,0,1,&iscol_local);CHKERRQ(ierr);
2963     ierr = ISSetIdentity(iscol_local);CHKERRQ(ierr);
2964     ierr = PetscInfo(mat,"Optimizing for obtaining all columns of the matrix; skipping ISAllGather()\n");CHKERRQ(ierr);
2965   } else {
2966     PetscInt cbs;
2967     ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
2968     ierr = ISAllGather(iscol,&iscol_local);CHKERRQ(ierr);
2969     ierr = ISSetBlockSize(iscol_local,cbs);CHKERRQ(ierr);
2970   }
2971 
2972   *isseq = iscol_local;
2973   PetscFunctionReturn(0);
2974 }
2975 
2976 /*
2977  Used for avoiding ISAllGather() and global size of iscol_local (see MatCreateSubMatrix_MPIAIJ_nonscalable)
2978 
2979  Input Parameters:
2980    mat - matrix
2981    iscol - parallel column index set; its local indices are a subset of local columns of mat,
2982            i.e., mat->cstart <= iscol[i] < mat->cend
2983  Output Parameter:
2984    iscol_sub - sequential column index set, a subset of iscol
2985    iscmap - column map; iscmap[i] indicates global location of iscol_sub[i] in iscol
2986  */
2987 PetscErrorCode ISGetSeqIS_SameColDist_Private(Mat mat,IS isrow,IS iscol,IS *iscol_sub,IS *iscmap,IS *isrow_d,IS *iscol_d,IS *iscol_o,IS *isgarray)
2988 {
2989   PetscErrorCode ierr;
2990   Vec            x,cmap;
2991   const PetscInt *is_idx;
2992   PetscScalar    *xarray,*cmaparray;
2993   PetscInt       ncols,isstart,*idx,*camp,count,m,rstart;
2994   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)mat->data;
2995   Mat            B=a->B;
2996   Vec            lvec=a->lvec,lcmap;
2997   PetscInt       i,cstart,cend,Bn=B->cmap->N;
2998   MPI_Comm       comm;
2999 
3000   PetscFunctionBegin;
3001   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3002   PetscMPIInt rank;
3003   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3004   ierr = ISGetLocalSize(iscol,&ncols);CHKERRQ(ierr);
3005 
3006   /* (1) iscol is a sub-column vector of mat, pad it with '-1.' to form a full vector x */
3007   ierr = MatCreateVecs(mat,&x,NULL);CHKERRQ(ierr);
3008   ierr = VecDuplicate(x,&cmap);CHKERRQ(ierr);
3009   ierr = VecSet(x,-1.0);CHKERRQ(ierr);
3010 
3011   /* get start indices */
3012   ierr = MPI_Scan(&ncols,&isstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3013   isstart -= ncols;
3014   ierr = MatGetOwnershipRangeColumn(mat,&cstart,&cend);CHKERRQ(ierr);
3015 
3016   ierr = ISGetIndices(iscol,&is_idx);CHKERRQ(ierr);
3017   ierr = VecGetArray(x,&xarray);CHKERRQ(ierr);
3018   ierr = VecGetArray(cmap,&cmaparray);CHKERRQ(ierr);
3019   ierr = PetscMalloc1(ncols,&idx);CHKERRQ(ierr);
3020   for (i=0; i<ncols; i++) {
3021     xarray[is_idx[i]-cstart]    = (PetscScalar)is_idx[i];
3022     cmaparray[is_idx[i]-cstart] = i + isstart; /* global index of iscol[i] */
3023 
3024     idx[i]                      = is_idx[i]-cstart;
3025   }
3026   ierr = VecRestoreArray(x,&xarray);CHKERRQ(ierr);
3027   ierr = VecRestoreArray(cmap,&cmaparray);CHKERRQ(ierr);
3028   ierr = ISRestoreIndices(iscol,&is_idx);CHKERRQ(ierr);
3029 
3030   ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_COPY_VALUES,iscol_d);CHKERRQ(ierr);
3031   ierr = ISGetBlockSize(iscol,&i);CHKERRQ(ierr);
3032   ierr = ISSetBlockSize(*iscol_d,i);CHKERRQ(ierr);
3033   ierr = PetscFree(idx);CHKERRQ(ierr);
3034 
3035   ierr = ISGetLocalSize(isrow,&m);CHKERRQ(ierr);
3036   rstart = mat->rmap->rstart;
3037   ierr = PetscMalloc1(m,&idx);CHKERRQ(ierr);
3038   ierr = ISGetIndices(isrow,&is_idx);CHKERRQ(ierr);
3039   for (i=0; i<m; i++) {
3040     idx[i] = is_idx[i]-rstart;
3041   }
3042   ierr = ISRestoreIndices(isrow,&is_idx);CHKERRQ(ierr);
3043 
3044   ierr = ISCreateGeneral(PETSC_COMM_SELF,m,idx,PETSC_COPY_VALUES,isrow_d);CHKERRQ(ierr);
3045   ierr = ISGetBlockSize(isrow,&i);CHKERRQ(ierr);
3046   ierr = ISSetBlockSize(*isrow_d,i);CHKERRQ(ierr);
3047   ierr = PetscFree(idx);CHKERRQ(ierr);
3048 
3049   /* (2) scatter x and cmap using aij->Mvctx to get their off-process portions (see MatMult_MPIAIJ) */
3050   ierr = VecScatterBegin(a->Mvctx,x,lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3051 
3052   ierr = VecDuplicate(lvec,&lcmap);CHKERRQ(ierr);
3053 
3054   ierr = VecScatterEnd(a->Mvctx,x,lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3055   ierr = VecScatterBegin(a->Mvctx,cmap,lcmap,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3056 
3057   count = ncols + Bn;
3058   ierr  = PetscMalloc2(count,&idx,count,&camp);CHKERRQ(ierr);
3059 
3060   ierr = VecScatterEnd(a->Mvctx,cmap,lcmap,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3061 
3062   /* (3) create scalable iscol_sub (a subset of iscol) and iscmap */
3063   /* local column indices */
3064   ierr = ISGetIndices(iscol,&is_idx);CHKERRQ(ierr);
3065   for (i=0; i<ncols; i++) {
3066     idx[i]  = is_idx[i];
3067     camp[i] = i + isstart; /* global index of iscol = column index in submat */
3068   }
3069   ierr = ISRestoreIndices(iscol,&is_idx);CHKERRQ(ierr);
3070   count = ncols;
3071 
3072   /* off-process column indices */
3073   PetscInt *idx1,*cmap1,count1=0;
3074   ierr = PetscMalloc2(Bn,&idx1,Bn,&cmap1);CHKERRQ(ierr);
3075 
3076   ierr = VecGetArray(lvec,&xarray);CHKERRQ(ierr);
3077   ierr = VecGetArray(lcmap,&cmaparray);CHKERRQ(ierr);
3078   for (i=0; i<Bn; i++) {
3079     if (PetscRealPart(xarray[i]) > -1.0) {
3080       //if (rank == 1) printf("[%d] xarray[%d] = %g; cstart %d\n",rank,i,xarray[i],cstart);
3081       idx1[count1]    = i; /* local column index in off-diagonal part B */
3082       cmap1[count1++] = (PetscInt)PetscRealPart(cmaparray[i]);  /* column index in submat */
3083 
3084       idx[count]    = (PetscInt)PetscRealPart(xarray[i]);
3085       camp[count++] = (PetscInt)PetscRealPart(cmaparray[i]);  /* column index in submat */
3086     }
3087   }
3088   ierr = VecRestoreArray(lvec,&xarray);CHKERRQ(ierr);
3089   ierr = VecRestoreArray(lcmap,&cmaparray);CHKERRQ(ierr);
3090 
3091   ierr = PetscSortIntWithArray(count,camp,idx);CHKERRQ(ierr);
3092   ierr = ISCreateGeneral(PETSC_COMM_SELF,count,idx,PETSC_COPY_VALUES,iscol_sub);CHKERRQ(ierr);
3093   ierr = ISCreateGeneral(PETSC_COMM_SELF,count,camp,PETSC_COPY_VALUES,iscmap);CHKERRQ(ierr);
3094   ierr = ISGetBlockSize(iscol,&i);CHKERRQ(ierr);
3095   ierr = ISSetBlockSize(*iscol_sub,i);CHKERRQ(ierr);
3096 
3097   ierr = ISCreateGeneral(PETSC_COMM_SELF,count1,idx1,PETSC_COPY_VALUES,iscol_o);CHKERRQ(ierr);
3098   ierr = ISCreateGeneral(PETSC_COMM_SELF,count1,cmap1,PETSC_COPY_VALUES,isgarray);CHKERRQ(ierr);
3099   ierr = ISGetBlockSize(iscol,&i);CHKERRQ(ierr);
3100   ierr = ISSetBlockSize(*iscol_o,i);CHKERRQ(ierr);
3101   ierr = PetscFree2(idx1,cmap1);CHKERRQ(ierr);
3102 
3103   ierr = PetscFree2(idx,camp);CHKERRQ(ierr);
3104   ierr = VecDestroy(&x);CHKERRQ(ierr);
3105   ierr = VecDestroy(&cmap);CHKERRQ(ierr);
3106   ierr = VecDestroy(&lcmap);CHKERRQ(ierr);
3107   PetscFunctionReturn(0);
3108 }
3109 
3110 PetscErrorCode MatCreateSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3111 {
3112   PetscErrorCode ierr;
3113   IS             iscol_local;
3114   PetscInt       csize;
3115   PetscInt       n,i,j,start,end;
3116   PetscBool      sameRowDist=PETSC_FALSE,sameDist[2],tsameDist[2];
3117   MPI_Comm       comm;
3118 
3119   PetscFunctionBegin;
3120   /* If isrow has same processor distribution as mat,
3121      call MatCreateSubMatrix_MPIAIJ_SameRowDist() to avoid using a hash table with global size of iscol */
3122   if (call == MAT_REUSE_MATRIX) {
3123     ierr = PetscObjectQuery((PetscObject)*newmat,"SubIScol",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3124     if (iscol_local) sameRowDist = PETSC_TRUE;
3125   } else {
3126     /* check if isrow has same processor distribution as mat */
3127     sameDist[0] = PETSC_FALSE;
3128     ierr = ISGetLocalSize(isrow,&n);CHKERRQ(ierr);
3129     if (!n) {
3130       sameDist[0] = PETSC_TRUE;
3131     } else {
3132       ierr = ISGetMinMax(isrow,&i,&j);CHKERRQ(ierr);
3133       ierr = MatGetOwnershipRange(mat,&start,&end);CHKERRQ(ierr);
3134       if (i >= start && j < end) {
3135         sameDist[0] = PETSC_TRUE;
3136       }
3137     }
3138 
3139     /* check if iscol has same processor distribution as mat */
3140     sameDist[1] = PETSC_FALSE;
3141     ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr);
3142     if (!n) {
3143       sameDist[1] = PETSC_TRUE;
3144     } else {
3145       ierr = ISGetMinMax(iscol,&i,&j);CHKERRQ(ierr);
3146       ierr = MatGetOwnershipRangeColumn(mat,&start,&end);CHKERRQ(ierr);
3147       if (i >= start && j < end) sameDist[1] = PETSC_TRUE;
3148     }
3149 
3150     ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3151     ierr = MPIU_Allreduce(&sameDist,&tsameDist,2,MPIU_BOOL,MPI_LAND,comm);CHKERRQ(ierr);
3152     sameRowDist = tsameDist[0];
3153   }
3154 
3155   if (sameRowDist) {
3156     ierr = MatCreateSubMatrix_MPIAIJ_SameRowDist(mat,isrow,iscol,call,tsameDist[1],newmat);CHKERRQ(ierr);
3157     PetscFunctionReturn(0);
3158   }
3159 
3160   /* General case: iscol -> iscol_local which has global size of iscol */
3161   if (call == MAT_REUSE_MATRIX) {
3162     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3163     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3164   } else {
3165     ierr = ISGetSeqIS_Private(mat,iscol,&iscol_local);CHKERRQ(ierr);
3166   }
3167 
3168   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3169   ierr = MatCreateSubMatrix_MPIAIJ_nonscalable(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
3170 
3171   if (call == MAT_INITIAL_MATRIX) {
3172     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3173     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3174   }
3175   PetscFunctionReturn(0);
3176 }
3177 
3178 /*@C
3179      MatCreateMPIAIJWithSeqAIJ - creates a MPIAIJ matrix using SeqAIJ matrices that contain the "diagonal"
3180          and "off-diagonal" part of the matrix in CSR format.
3181 
3182    Collective on MPI_Comm
3183 
3184    Input Parameters:
3185 +  comm - MPI communicator
3186 .  A - "diagonal" portion of matrix
3187 .  B - "off-diagonal" portion of matrix
3188 -  garray - global index of B columns
3189 
3190    Output Parameter:
3191 .   mat - the matrix
3192 
3193    Level: advanced
3194 
3195    Notes:
3196        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
3197 
3198 .keywords: matrix, aij, compressed row, sparse, parallel
3199 
3200 .seealso: MatCreateMPIAIJWithSplitArrays()
3201 @*/
3202 PetscErrorCode MatCreateMPIAIJWithSeqAIJ(MPI_Comm comm,Mat A,Mat B,const PetscInt garray[],Mat *mat)
3203 {
3204   PetscErrorCode ierr;
3205   Mat_MPIAIJ     *maij;
3206   Mat_SeqAIJ     *b=(Mat_SeqAIJ*)B->data;
3207   PetscInt       *oi=b->i,*oj=b->j,i,nz,col;
3208   PetscScalar    *oa=b->a;
3209   Mat            Btmp;
3210   PetscInt       m,n,N;
3211 
3212   PetscFunctionBegin;
3213   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
3214   ierr = MatGetSize(A,&m,&n);CHKERRQ(ierr);
3215   if (m != B->rmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Am %d != Bm %d",m,B->rmap->N);
3216 
3217   /* get global columns of mat */
3218   ierr = MPIU_Allreduce(&n,&N,1,MPI_INT,MPI_SUM,comm);CHKERRQ(ierr);
3219 
3220   ierr = MatSetSizes(*mat,m,n,PETSC_DECIDE,N);CHKERRQ(ierr);
3221   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
3222   maij = (Mat_MPIAIJ*)(*mat)->data;
3223 
3224   (*mat)->preallocated = PETSC_TRUE;
3225 
3226   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
3227   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
3228 
3229   maij->A = A;
3230 
3231   nz = oi[m];
3232   for (i=0; i<nz; i++) {
3233     col   = oj[i];
3234     oj[i] = garray[col];
3235   }
3236 
3237   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,N,oi,oj,oa,&Btmp);CHKERRQ(ierr);
3238   maij->B = Btmp; /* cannot destroy B because its arrays are used by Btmp? */
3239   //b->free_ij = PETSC_FALSE;
3240   //b->free_a  = PETSC_FALSE;
3241   //ierr = MatDestroy(&B);CHKERRQ(ierr);
3242   //B = Btmp;
3243 
3244   /* condense columns of maij->B */
3245   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
3246   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3247   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3248   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_FALSE);CHKERRQ(ierr);
3249   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3250   PetscFunctionReturn(0);
3251 }
3252 
3253 extern PetscErrorCode MatCreateSubMatrices_MPIAIJ_SingleIS_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool,Mat*);
3254 
3255 PetscErrorCode MatCreateSubMatrix_MPIAIJ_SameRowDist(Mat mat,IS isrow,IS iscol,MatReuse call,PetscBool sameColDist,Mat *newmat)
3256 {
3257   PetscErrorCode ierr;
3258   PetscInt       i,m,n,rstart,row,rend,nz,j,bs,cbs;
3259   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
3260   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)mat->data;
3261   Mat            M,Msub,B=a->B,Mnew=NULL;
3262   MatScalar      *aa;
3263   Mat_SeqAIJ     *aij;
3264   PetscInt       *garray = a->garray,*colsub,Ncols;
3265   PetscInt       count,Bn=B->cmap->N,cstart=mat->cmap->rstart,cend=mat->cmap->rend;
3266   IS             iscol_sub,iscmap;
3267   const PetscInt *is_idx,*cmap;
3268   PetscBool      allcolumns=PETSC_FALSE;
3269   IS             iscol_local=NULL;
3270   MPI_Comm       comm;
3271   IS             iscol_d,isrow_d,iscol_o,isgarray;
3272   Mat            Asub=NULL,Bsub=NULL;
3273 
3274   PetscFunctionBegin;
3275   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3276   PetscMPIInt rank;
3277   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3278 
3279   if (call == MAT_INITIAL_MATRIX) {
3280     ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr);
3281     ierr = ISGetSize(iscol,&Ncols);CHKERRQ(ierr);
3282 
3283     /* (1) Create scalable iscol_sub and iscmap */
3284     if (sameColDist) {
3285       /* iscol has same processor distribution as mat, use a scalable routine to generate iscol_sub and iscmap */
3286       ierr = ISGetSeqIS_SameColDist_Private(mat,isrow,iscol,&iscol_sub,&iscmap,&isrow_d,&iscol_d,&iscol_o,&isgarray);CHKERRQ(ierr);
3287 
3288       //======================================
3289 
3290       if (rank == -1) {
3291         //printf("[%d] isrow_d\n",rank);
3292         //ierr = ISView(isrow_d,0);CHKERRQ(ierr);
3293 
3294         //printf("[%d] iscol_diag\n",rank);
3295         //ierr = ISView(iscol_d,0);CHKERRQ(ierr);
3296 
3297         printf("[%d] iscol_o\n",rank);
3298         ierr = ISView(iscol_o,0);CHKERRQ(ierr);
3299 
3300         printf("[%d] a->B, %d, %d\n",rank,a->B->rmap->N,a->B->cmap->N);
3301         ierr = MatView(a->B,0);CHKERRQ(ierr);
3302       }
3303 
3304       ierr = MatCreateSubMatrix_SeqAIJ(a->A,isrow_d,iscol_d,PETSC_DECIDE,call,&Asub);CHKERRQ(ierr);
3305       ierr = MatCreateSubMatrix_SeqAIJ(a->B,isrow_d,iscol_o,PETSC_DECIDE,call,&Bsub);CHKERRQ(ierr);
3306       if (rank == -1) {
3307         printf("[%d] Bsub\n",rank);
3308         ierr = MatView(Bsub,0);CHKERRQ(ierr);
3309       }
3310 
3311       const PetscInt *garray1;
3312       ierr = ISGetIndices(isgarray,&garray1);CHKERRQ(ierr);
3313       ierr = MatCreateMPIAIJWithSeqAIJ(comm,Asub,Bsub,garray1,&Mnew);CHKERRQ(ierr);
3314       ierr = ISRestoreIndices(isgarray,&garray1);CHKERRQ(ierr);
3315       //ierr = MatView(Mnew,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
3316 
3317       ierr = ISDestroy(&isrow_d);CHKERRQ(ierr);
3318       ierr = ISDestroy(&iscol_d);CHKERRQ(ierr);
3319       ierr = ISDestroy(&iscol_o);CHKERRQ(ierr);
3320       //======================================
3321 
3322     } else { /* iscol -> nonscalable iscol_local, then get scalable iscol_sub and iscmap */
3323       PetscBool flg;
3324 
3325       /* iscol -> nonscalable iscol_local */
3326       ierr = ISGetSeqIS_Private(mat,iscol,&iscol_local);CHKERRQ(ierr);
3327       ierr = ISGetLocalSize(iscol_local,&n);CHKERRQ(ierr); /* local size of iscol_local = global columns of newmat */
3328       if (n != Ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"n %d != Ncols %d",n,Ncols);
3329 
3330       /* Check for special case: each processor gets entire matrix columns */
3331       ierr = ISIdentity(iscol_local,&flg);CHKERRQ(ierr);
3332       if (flg && n == mat->cmap->N) allcolumns = PETSC_TRUE;
3333       if (allcolumns) {
3334         iscol_sub = iscol_local;
3335         ierr = PetscObjectReference((PetscObject)iscol_local);CHKERRQ(ierr);
3336         ierr = ISCreateStride(PETSC_COMM_SELF,n,0,1,&iscmap);CHKERRQ(ierr);
3337 
3338       } else { /* iscol_local -> iscol_sub and iscmap */
3339         PetscInt *idx,*cmap1,k,cbs;
3340 
3341         /* implementation below requires iscol_local be sorted, it can have duplicate indices */
3342         ierr = ISSorted(iscol_local,&flg);CHKERRQ(ierr);
3343         if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"unsorted iscol_local is not implemented yet");
3344 
3345         ierr = PetscMalloc2(Ncols,&idx,Ncols,&cmap1);CHKERRQ(ierr);
3346         ierr = ISGetIndices(iscol_local,&is_idx);CHKERRQ(ierr);
3347         count = 0;
3348         k     = 0;
3349         for (i=0; i<Ncols; i++) {
3350           j = is_idx[i];
3351           if (j >= cstart && j < cend) {
3352             /* diagonal part of mat */
3353             idx[count]     = j;
3354             cmap1[count++] = i; /* column index in submat */
3355           } else if (Bn) {
3356             /* off-diagonal part of mat */
3357             if (j == garray[k]) {
3358               idx[count]     = j;
3359               cmap1[count++] = i;  /* column index in submat */
3360             } else if (j > garray[k]) {
3361               while (j > garray[k] && k < Bn-1) k++;
3362               if (j == garray[k]) {
3363                 idx[count]     = j;
3364                 cmap1[count++] = i; /* column index in submat */
3365               }
3366             }
3367           }
3368         }
3369         ierr = ISRestoreIndices(iscol_local,&is_idx);CHKERRQ(ierr);
3370 
3371         ierr = ISCreateGeneral(PETSC_COMM_SELF,count,idx,PETSC_COPY_VALUES,&iscol_sub);CHKERRQ(ierr);
3372         ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
3373         ierr = ISSetBlockSize(iscol_sub,cbs);CHKERRQ(ierr);
3374 
3375         ierr = ISCreateGeneral(PetscObjectComm((PetscObject)iscol_local),count,cmap1,PETSC_COPY_VALUES,&iscmap);CHKERRQ(ierr);
3376         ierr = PetscFree2(idx,cmap1);CHKERRQ(ierr);
3377       }
3378     }
3379 
3380     /* (2) Create sequential Msub */
3381     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol_sub,MAT_INITIAL_MATRIX,allcolumns,&Msub);CHKERRQ(ierr);
3382 
3383   } else { /* call ==  MAT_REUSE_MATRIX */
3384     ierr = PetscObjectQuery((PetscObject)*newmat,"SubIScol",(PetscObject*)&iscol_sub);CHKERRQ(ierr);
3385     if (!iscol_sub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"SubIScol passed in was not used before, cannot reuse");
3386     ierr = ISGetLocalSize(iscol_sub,&count);CHKERRQ(ierr);
3387 
3388     ierr = PetscObjectQuery((PetscObject)*newmat,"Subcmap",(PetscObject*)&iscmap);CHKERRQ(ierr);
3389     if (!iscmap) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Subcmap passed in was not used before, cannot reuse");
3390 
3391     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Msub);CHKERRQ(ierr);
3392     if (!Msub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3393 
3394     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol_sub,MAT_REUSE_MATRIX,PETSC_FALSE,&Msub);CHKERRQ(ierr);
3395   }
3396 
3397   ierr = ISGetLocalSize(iscol_sub,&count);CHKERRQ(ierr);
3398   aij  = (Mat_SeqAIJ*)(Msub)->data;
3399   ii   = aij->i;
3400   ierr = ISGetIndices(iscmap,&cmap);CHKERRQ(ierr);
3401 
3402   /*
3403       m - number of local rows
3404       Ncols - number of columns (same on all processors)
3405       rstart - first row in new global matrix generated
3406   */
3407   ierr = MatGetSize(Msub,&m,NULL);CHKERRQ(ierr);
3408 
3409   if (call == MAT_INITIAL_MATRIX) {
3410     /* (3) Create parallel newmat */
3411     PetscMPIInt    rank,size;
3412     PetscInt       csize;
3413 
3414     ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3415     ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3416 
3417     /*
3418         Determine the number of non-zeros in the diagonal and off-diagonal
3419         portions of the matrix in order to do correct preallocation
3420     */
3421 
3422     /* first get start and end of "diagonal" columns */
3423     ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3424     if (csize == PETSC_DECIDE) {
3425       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3426       if (mglobal == Ncols) { /* square matrix */
3427         nlocal = m;
3428       } else {
3429         nlocal = Ncols/size + ((Ncols % size) > rank);
3430       }
3431     } else {
3432       nlocal = csize;
3433     }
3434     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3435     rstart = rend - nlocal;
3436     if (rank == size - 1 && rend != Ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local column sizes %D do not add up to total number of columns %D",rend,Ncols);
3437 
3438     /* next, compute all the lengths */
3439     jj    = aij->j;
3440     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3441     olens = dlens + m;
3442     for (i=0; i<m; i++) {
3443       jend = ii[i+1] - ii[i];
3444       olen = 0;
3445       dlen = 0;
3446       for (j=0; j<jend; j++) {
3447         if (cmap[*jj] < rstart || cmap[*jj] >= rend) olen++;
3448         else dlen++;
3449         jj++;
3450       }
3451       olens[i] = olen;
3452       dlens[i] = dlen;
3453     }
3454     ierr = MatGetBlockSizes(Msub,&bs,&cbs);CHKERRQ(ierr);
3455 
3456     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3457     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,Ncols);CHKERRQ(ierr);
3458     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3459     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3460     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3461     ierr = PetscFree(dlens);CHKERRQ(ierr);
3462   } else {
3463     M    = *newmat;
3464     ierr = MatGetLocalSize(M,&i,NULL);CHKERRQ(ierr);
3465     if (i != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3466     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3467     /*
3468          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3469        rather than the slower MatSetValues().
3470     */
3471     M->was_assembled = PETSC_TRUE;
3472     M->assembled     = PETSC_FALSE;
3473   }
3474 
3475   /* (4) Set values of Msub to *newmat */
3476   ierr = PetscMalloc1(count,&colsub);CHKERRQ(ierr);
3477   ierr = MatGetOwnershipRange(M,&rstart,NULL);CHKERRQ(ierr);
3478 
3479   jj   = aij->j;
3480   aa   = aij->a;
3481   for (i=0; i<m; i++) {
3482     row = rstart + i;
3483     nz  = ii[i+1] - ii[i];
3484     for (j=0; j<nz; j++) colsub[j] = cmap[jj[j]];
3485     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,colsub,aa,INSERT_VALUES);CHKERRQ(ierr);
3486     jj += nz; aa += nz;
3487   }
3488   ierr = ISRestoreIndices(iscmap,&cmap);CHKERRQ(ierr);
3489 
3490   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3491   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3492   *newmat = M;
3493 
3494   ierr = PetscFree(colsub);CHKERRQ(ierr);
3495 
3496   /* save Msub, iscol_sub and iscmap used in processor for next request */
3497   if (call ==  MAT_INITIAL_MATRIX) {
3498     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Msub);CHKERRQ(ierr);
3499     ierr = MatDestroy(&Msub);CHKERRQ(ierr);
3500 
3501     ierr = PetscObjectCompose((PetscObject)M,"SubIScol",(PetscObject)iscol_sub);CHKERRQ(ierr);
3502     ierr = ISDestroy(&iscol_sub);CHKERRQ(ierr);
3503 
3504     ierr = PetscObjectCompose((PetscObject)M,"Subcmap",(PetscObject)iscmap);CHKERRQ(ierr);
3505     ierr = ISDestroy(&iscmap);CHKERRQ(ierr);
3506 
3507     if (iscol_local) {
3508       ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3509       ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3510     }
3511 
3512     if (Mnew) {
3513       PetscBool equal;
3514       ierr = MatEqual(M,Mnew,&equal);CHKERRQ(ierr);
3515       if (!equal) SETERRQ(PETSC_COMM_SELF,0,"M != Mnew");
3516       ierr = MatDestroy(&Mnew);CHKERRQ(ierr);
3517       ierr = MatDestroy(&Bsub);CHKERRQ(ierr);
3518       ierr = ISDestroy(&isgarray);CHKERRQ(ierr);
3519     }
3520   }
3521   PetscFunctionReturn(0);
3522 }
3523 
3524 /*
3525     Not great since it makes two copies of the submatrix, first an SeqAIJ
3526   in local and then by concatenating the local matrices the end result.
3527   Writing it directly would be much like MatCreateSubMatrices_MPIAIJ()
3528 
3529   Note: This requires a sequential iscol with all indices.
3530 */
3531 PetscErrorCode MatCreateSubMatrix_MPIAIJ_nonscalable(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3532 {
3533   PetscErrorCode ierr;
3534   PetscMPIInt    rank,size;
3535   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3536   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
3537   Mat            M,Mreuse;
3538   MatScalar      *aa,*vwork;
3539   MPI_Comm       comm;
3540   Mat_SeqAIJ     *aij;
3541   PetscBool      colflag,allcolumns=PETSC_FALSE;
3542 
3543   PetscFunctionBegin;
3544   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3545   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3546   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3547 
3548   /* Check for special case: each processor gets entire matrix columns */
3549   ierr = ISIdentity(iscol,&colflag);CHKERRQ(ierr);
3550   ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr);
3551   if (colflag && n == mat->cmap->N) allcolumns = PETSC_TRUE;
3552 
3553   if (call ==  MAT_REUSE_MATRIX) {
3554     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3555     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3556     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,allcolumns,&Mreuse);CHKERRQ(ierr);
3557   } else {
3558     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,allcolumns,&Mreuse);CHKERRQ(ierr);
3559   }
3560 
3561   /*
3562       m - number of local rows
3563       n - number of columns (same on all processors)
3564       rstart - first row in new global matrix generated
3565   */
3566   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3567   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3568   if (call == MAT_INITIAL_MATRIX) {
3569     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3570     ii  = aij->i;
3571     jj  = aij->j;
3572 
3573     /*
3574         Determine the number of non-zeros in the diagonal and off-diagonal
3575         portions of the matrix in order to do correct preallocation
3576     */
3577 
3578     /* first get start and end of "diagonal" columns */
3579     if (csize == PETSC_DECIDE) {
3580       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3581       if (mglobal == n) { /* square matrix */
3582         nlocal = m;
3583       } else {
3584         nlocal = n/size + ((n % size) > rank);
3585       }
3586     } else {
3587       nlocal = csize;
3588     }
3589     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3590     rstart = rend - nlocal;
3591     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);
3592 
3593     /* next, compute all the lengths */
3594     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3595     olens = dlens + m;
3596     for (i=0; i<m; i++) {
3597       jend = ii[i+1] - ii[i];
3598       olen = 0;
3599       dlen = 0;
3600       for (j=0; j<jend; j++) {
3601         if (*jj < rstart || *jj >= rend) olen++;
3602         else dlen++;
3603         jj++;
3604       }
3605       olens[i] = olen;
3606       dlens[i] = dlen;
3607     }
3608     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3609     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3610     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3611     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3612     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3613     ierr = PetscFree(dlens);CHKERRQ(ierr);
3614   } else {
3615     PetscInt ml,nl;
3616 
3617     M    = *newmat;
3618     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3619     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3620     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3621     /*
3622          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3623        rather than the slower MatSetValues().
3624     */
3625     M->was_assembled = PETSC_TRUE;
3626     M->assembled     = PETSC_FALSE;
3627   }
3628   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3629   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3630   ii   = aij->i;
3631   jj   = aij->j;
3632   aa   = aij->a;
3633   for (i=0; i<m; i++) {
3634     row   = rstart + i;
3635     nz    = ii[i+1] - ii[i];
3636     cwork = jj;     jj += nz;
3637     vwork = aa;     aa += nz;
3638     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3639   }
3640 
3641   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3642   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3643   *newmat = M;
3644 
3645   /* save submatrix used in processor for next request */
3646   if (call ==  MAT_INITIAL_MATRIX) {
3647     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3648     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3649   }
3650   PetscFunctionReturn(0);
3651 }
3652 
3653 PetscErrorCode MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3654 {
3655   PetscInt       m,cstart, cend,j,nnz,i,d;
3656   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3657   const PetscInt *JJ;
3658   PetscScalar    *values;
3659   PetscErrorCode ierr;
3660   PetscBool      nooffprocentries;
3661 
3662   PetscFunctionBegin;
3663   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3664 
3665   ierr   = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3666   ierr   = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3667   m      = B->rmap->n;
3668   cstart = B->cmap->rstart;
3669   cend   = B->cmap->rend;
3670   rstart = B->rmap->rstart;
3671 
3672   ierr = PetscMalloc2(m,&d_nnz,m,&o_nnz);CHKERRQ(ierr);
3673 
3674 #if defined(PETSC_USE_DEBUGGING)
3675   for (i=0; i<m; i++) {
3676     nnz = Ii[i+1]- Ii[i];
3677     JJ  = J + Ii[i];
3678     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3679     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3680     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);
3681   }
3682 #endif
3683 
3684   for (i=0; i<m; i++) {
3685     nnz     = Ii[i+1]- Ii[i];
3686     JJ      = J + Ii[i];
3687     nnz_max = PetscMax(nnz_max,nnz);
3688     d       = 0;
3689     for (j=0; j<nnz; j++) {
3690       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3691     }
3692     d_nnz[i] = d;
3693     o_nnz[i] = nnz - d;
3694   }
3695   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3696   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3697 
3698   if (v) values = (PetscScalar*)v;
3699   else {
3700     ierr = PetscCalloc1(nnz_max+1,&values);CHKERRQ(ierr);
3701   }
3702 
3703   for (i=0; i<m; i++) {
3704     ii   = i + rstart;
3705     nnz  = Ii[i+1]- Ii[i];
3706     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3707   }
3708   nooffprocentries    = B->nooffprocentries;
3709   B->nooffprocentries = PETSC_TRUE;
3710   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3711   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3712   B->nooffprocentries = nooffprocentries;
3713 
3714   if (!v) {
3715     ierr = PetscFree(values);CHKERRQ(ierr);
3716   }
3717   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3718   PetscFunctionReturn(0);
3719 }
3720 
3721 /*@
3722    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3723    (the default parallel PETSc format).
3724 
3725    Collective on MPI_Comm
3726 
3727    Input Parameters:
3728 +  B - the matrix
3729 .  i - the indices into j for the start of each local row (starts with zero)
3730 .  j - the column indices for each local row (starts with zero)
3731 -  v - optional values in the matrix
3732 
3733    Level: developer
3734 
3735    Notes:
3736        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3737      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3738      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3739 
3740        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3741 
3742        The format which is used for the sparse matrix input, is equivalent to a
3743     row-major ordering.. i.e for the following matrix, the input data expected is
3744     as shown
3745 
3746 $        1 0 0
3747 $        2 0 3     P0
3748 $       -------
3749 $        4 5 6     P1
3750 $
3751 $     Process0 [P0]: rows_owned=[0,1]
3752 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3753 $        j =  {0,0,2}  [size = 3]
3754 $        v =  {1,2,3}  [size = 3]
3755 $
3756 $     Process1 [P1]: rows_owned=[2]
3757 $        i =  {0,3}    [size = nrow+1  = 1+1]
3758 $        j =  {0,1,2}  [size = 3]
3759 $        v =  {4,5,6}  [size = 3]
3760 
3761 .keywords: matrix, aij, compressed row, sparse, parallel
3762 
3763 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MATMPIAIJ,
3764           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3765 @*/
3766 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3767 {
3768   PetscErrorCode ierr;
3769 
3770   PetscFunctionBegin;
3771   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3772   PetscFunctionReturn(0);
3773 }
3774 
3775 /*@C
3776    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3777    (the default parallel PETSc format).  For good matrix assembly performance
3778    the user should preallocate the matrix storage by setting the parameters
3779    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3780    performance can be increased by more than a factor of 50.
3781 
3782    Collective on MPI_Comm
3783 
3784    Input Parameters:
3785 +  B - the matrix
3786 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3787            (same value is used for all local rows)
3788 .  d_nnz - array containing the number of nonzeros in the various rows of the
3789            DIAGONAL portion of the local submatrix (possibly different for each row)
3790            or NULL (PETSC_NULL_INTEGER in Fortran), if d_nz is used to specify the nonzero structure.
3791            The size of this array is equal to the number of local rows, i.e 'm'.
3792            For matrices that will be factored, you must leave room for (and set)
3793            the diagonal entry even if it is zero.
3794 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3795            submatrix (same value is used for all local rows).
3796 -  o_nnz - array containing the number of nonzeros in the various rows of the
3797            OFF-DIAGONAL portion of the local submatrix (possibly different for
3798            each row) or NULL (PETSC_NULL_INTEGER in Fortran), if o_nz is used to specify the nonzero
3799            structure. The size of this array is equal to the number
3800            of local rows, i.e 'm'.
3801 
3802    If the *_nnz parameter is given then the *_nz parameter is ignored
3803 
3804    The AIJ format (also called the Yale sparse matrix format or
3805    compressed row storage (CSR)), is fully compatible with standard Fortran 77
3806    storage.  The stored row and column indices begin with zero.
3807    See Users-Manual: ch_mat for details.
3808 
3809    The parallel matrix is partitioned such that the first m0 rows belong to
3810    process 0, the next m1 rows belong to process 1, the next m2 rows belong
3811    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
3812 
3813    The DIAGONAL portion of the local submatrix of a processor can be defined
3814    as the submatrix which is obtained by extraction the part corresponding to
3815    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
3816    first row that belongs to the processor, r2 is the last row belonging to
3817    the this processor, and c1-c2 is range of indices of the local part of a
3818    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
3819    common case of a square matrix, the row and column ranges are the same and
3820    the DIAGONAL part is also square. The remaining portion of the local
3821    submatrix (mxN) constitute the OFF-DIAGONAL portion.
3822 
3823    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3824 
3825    You can call MatGetInfo() to get information on how effective the preallocation was;
3826    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3827    You can also run with the option -info and look for messages with the string
3828    malloc in them to see if additional memory allocation was needed.
3829 
3830    Example usage:
3831 
3832    Consider the following 8x8 matrix with 34 non-zero values, that is
3833    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3834    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3835    as follows:
3836 
3837 .vb
3838             1  2  0  |  0  3  0  |  0  4
3839     Proc0   0  5  6  |  7  0  0  |  8  0
3840             9  0 10  | 11  0  0  | 12  0
3841     -------------------------------------
3842            13  0 14  | 15 16 17  |  0  0
3843     Proc1   0 18  0  | 19 20 21  |  0  0
3844             0  0  0  | 22 23  0  | 24  0
3845     -------------------------------------
3846     Proc2  25 26 27  |  0  0 28  | 29  0
3847            30  0  0  | 31 32 33  |  0 34
3848 .ve
3849 
3850    This can be represented as a collection of submatrices as:
3851 
3852 .vb
3853       A B C
3854       D E F
3855       G H I
3856 .ve
3857 
3858    Where the submatrices A,B,C are owned by proc0, D,E,F are
3859    owned by proc1, G,H,I are owned by proc2.
3860 
3861    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3862    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3863    The 'M','N' parameters are 8,8, and have the same values on all procs.
3864 
3865    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3866    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3867    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3868    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3869    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3870    matrix, ans [DF] as another SeqAIJ matrix.
3871 
3872    When d_nz, o_nz parameters are specified, d_nz storage elements are
3873    allocated for every row of the local diagonal submatrix, and o_nz
3874    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3875    One way to choose d_nz and o_nz is to use the max nonzerors per local
3876    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3877    In this case, the values of d_nz,o_nz are:
3878 .vb
3879      proc0 : dnz = 2, o_nz = 2
3880      proc1 : dnz = 3, o_nz = 2
3881      proc2 : dnz = 1, o_nz = 4
3882 .ve
3883    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3884    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3885    for proc3. i.e we are using 12+15+10=37 storage locations to store
3886    34 values.
3887 
3888    When d_nnz, o_nnz parameters are specified, the storage is specified
3889    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3890    In the above case the values for d_nnz,o_nnz are:
3891 .vb
3892      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3893      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3894      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3895 .ve
3896    Here the space allocated is sum of all the above values i.e 34, and
3897    hence pre-allocation is perfect.
3898 
3899    Level: intermediate
3900 
3901 .keywords: matrix, aij, compressed row, sparse, parallel
3902 
3903 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
3904           MATMPIAIJ, MatGetInfo(), PetscSplitOwnership()
3905 @*/
3906 PetscErrorCode MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3907 {
3908   PetscErrorCode ierr;
3909 
3910   PetscFunctionBegin;
3911   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3912   PetscValidType(B,1);
3913   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
3914   PetscFunctionReturn(0);
3915 }
3916 
3917 /*@
3918      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
3919          CSR format the local rows.
3920 
3921    Collective on MPI_Comm
3922 
3923    Input Parameters:
3924 +  comm - MPI communicator
3925 .  m - number of local rows (Cannot be PETSC_DECIDE)
3926 .  n - This value should be the same as the local size used in creating the
3927        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3928        calculated if N is given) For square matrices n is almost always m.
3929 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3930 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3931 .   i - row indices
3932 .   j - column indices
3933 -   a - matrix values
3934 
3935    Output Parameter:
3936 .   mat - the matrix
3937 
3938    Level: intermediate
3939 
3940    Notes:
3941        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3942      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3943      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3944 
3945        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3946 
3947        The format which is used for the sparse matrix input, is equivalent to a
3948     row-major ordering.. i.e for the following matrix, the input data expected is
3949     as shown
3950 
3951 $        1 0 0
3952 $        2 0 3     P0
3953 $       -------
3954 $        4 5 6     P1
3955 $
3956 $     Process0 [P0]: rows_owned=[0,1]
3957 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3958 $        j =  {0,0,2}  [size = 3]
3959 $        v =  {1,2,3}  [size = 3]
3960 $
3961 $     Process1 [P1]: rows_owned=[2]
3962 $        i =  {0,3}    [size = nrow+1  = 1+1]
3963 $        j =  {0,1,2}  [size = 3]
3964 $        v =  {4,5,6}  [size = 3]
3965 
3966 .keywords: matrix, aij, compressed row, sparse, parallel
3967 
3968 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3969           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
3970 @*/
3971 PetscErrorCode MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
3972 {
3973   PetscErrorCode ierr;
3974 
3975   PetscFunctionBegin;
3976   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
3977   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
3978   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
3979   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
3980   /* ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr); */
3981   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
3982   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
3983   PetscFunctionReturn(0);
3984 }
3985 
3986 /*@C
3987    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
3988    (the default parallel PETSc format).  For good matrix assembly performance
3989    the user should preallocate the matrix storage by setting the parameters
3990    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3991    performance can be increased by more than a factor of 50.
3992 
3993    Collective on MPI_Comm
3994 
3995    Input Parameters:
3996 +  comm - MPI communicator
3997 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
3998            This value should be the same as the local size used in creating the
3999            y vector for the matrix-vector product y = Ax.
4000 .  n - This value should be the same as the local size used in creating the
4001        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
4002        calculated if N is given) For square matrices n is almost always m.
4003 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
4004 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
4005 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
4006            (same value is used for all local rows)
4007 .  d_nnz - array containing the number of nonzeros in the various rows of the
4008            DIAGONAL portion of the local submatrix (possibly different for each row)
4009            or NULL, if d_nz is used to specify the nonzero structure.
4010            The size of this array is equal to the number of local rows, i.e 'm'.
4011 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
4012            submatrix (same value is used for all local rows).
4013 -  o_nnz - array containing the number of nonzeros in the various rows of the
4014            OFF-DIAGONAL portion of the local submatrix (possibly different for
4015            each row) or NULL, if o_nz is used to specify the nonzero
4016            structure. The size of this array is equal to the number
4017            of local rows, i.e 'm'.
4018 
4019    Output Parameter:
4020 .  A - the matrix
4021 
4022    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
4023    MatXXXXSetPreallocation() paradgm instead of this routine directly.
4024    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
4025 
4026    Notes:
4027    If the *_nnz parameter is given then the *_nz parameter is ignored
4028 
4029    m,n,M,N parameters specify the size of the matrix, and its partitioning across
4030    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
4031    storage requirements for this matrix.
4032 
4033    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
4034    processor than it must be used on all processors that share the object for
4035    that argument.
4036 
4037    The user MUST specify either the local or global matrix dimensions
4038    (possibly both).
4039 
4040    The parallel matrix is partitioned across processors such that the
4041    first m0 rows belong to process 0, the next m1 rows belong to
4042    process 1, the next m2 rows belong to process 2 etc.. where
4043    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
4044    values corresponding to [m x N] submatrix.
4045 
4046    The columns are logically partitioned with the n0 columns belonging
4047    to 0th partition, the next n1 columns belonging to the next
4048    partition etc.. where n0,n1,n2... are the input parameter 'n'.
4049 
4050    The DIAGONAL portion of the local submatrix on any given processor
4051    is the submatrix corresponding to the rows and columns m,n
4052    corresponding to the given processor. i.e diagonal matrix on
4053    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
4054    etc. The remaining portion of the local submatrix [m x (N-n)]
4055    constitute the OFF-DIAGONAL portion. The example below better
4056    illustrates this concept.
4057 
4058    For a square global matrix we define each processor's diagonal portion
4059    to be its local rows and the corresponding columns (a square submatrix);
4060    each processor's off-diagonal portion encompasses the remainder of the
4061    local matrix (a rectangular submatrix).
4062 
4063    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
4064 
4065    When calling this routine with a single process communicator, a matrix of
4066    type SEQAIJ is returned.  If a matrix of type MATMPIAIJ is desired for this
4067    type of communicator, use the construction mechanism:
4068      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
4069 
4070    By default, this format uses inodes (identical nodes) when possible.
4071    We search for consecutive rows with the same nonzero structure, thereby
4072    reusing matrix information to achieve increased efficiency.
4073 
4074    Options Database Keys:
4075 +  -mat_no_inode  - Do not use inodes
4076 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
4077 -  -mat_aij_oneindex - Internally use indexing starting at 1
4078         rather than 0.  Note that when calling MatSetValues(),
4079         the user still MUST index entries starting at 0!
4080 
4081 
4082    Example usage:
4083 
4084    Consider the following 8x8 matrix with 34 non-zero values, that is
4085    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
4086    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
4087    as follows:
4088 
4089 .vb
4090             1  2  0  |  0  3  0  |  0  4
4091     Proc0   0  5  6  |  7  0  0  |  8  0
4092             9  0 10  | 11  0  0  | 12  0
4093     -------------------------------------
4094            13  0 14  | 15 16 17  |  0  0
4095     Proc1   0 18  0  | 19 20 21  |  0  0
4096             0  0  0  | 22 23  0  | 24  0
4097     -------------------------------------
4098     Proc2  25 26 27  |  0  0 28  | 29  0
4099            30  0  0  | 31 32 33  |  0 34
4100 .ve
4101 
4102    This can be represented as a collection of submatrices as:
4103 
4104 .vb
4105       A B C
4106       D E F
4107       G H I
4108 .ve
4109 
4110    Where the submatrices A,B,C are owned by proc0, D,E,F are
4111    owned by proc1, G,H,I are owned by proc2.
4112 
4113    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4114    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4115    The 'M','N' parameters are 8,8, and have the same values on all procs.
4116 
4117    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
4118    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
4119    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
4120    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
4121    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
4122    matrix, ans [DF] as another SeqAIJ matrix.
4123 
4124    When d_nz, o_nz parameters are specified, d_nz storage elements are
4125    allocated for every row of the local diagonal submatrix, and o_nz
4126    storage locations are allocated for every row of the OFF-DIAGONAL submat.
4127    One way to choose d_nz and o_nz is to use the max nonzerors per local
4128    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
4129    In this case, the values of d_nz,o_nz are:
4130 .vb
4131      proc0 : dnz = 2, o_nz = 2
4132      proc1 : dnz = 3, o_nz = 2
4133      proc2 : dnz = 1, o_nz = 4
4134 .ve
4135    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
4136    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
4137    for proc3. i.e we are using 12+15+10=37 storage locations to store
4138    34 values.
4139 
4140    When d_nnz, o_nnz parameters are specified, the storage is specified
4141    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
4142    In the above case the values for d_nnz,o_nnz are:
4143 .vb
4144      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
4145      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
4146      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
4147 .ve
4148    Here the space allocated is sum of all the above values i.e 34, and
4149    hence pre-allocation is perfect.
4150 
4151    Level: intermediate
4152 
4153 .keywords: matrix, aij, compressed row, sparse, parallel
4154 
4155 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
4156           MATMPIAIJ, MatCreateMPIAIJWithArrays()
4157 @*/
4158 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)
4159 {
4160   PetscErrorCode ierr;
4161   PetscMPIInt    size;
4162 
4163   PetscFunctionBegin;
4164   ierr = MatCreate(comm,A);CHKERRQ(ierr);
4165   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
4166   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4167   if (size > 1) {
4168     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
4169     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
4170   } else {
4171     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
4172     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
4173   }
4174   PetscFunctionReturn(0);
4175 }
4176 
4177 PetscErrorCode MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
4178 {
4179   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
4180   PetscBool      flg;
4181   PetscErrorCode ierr;
4182 
4183   PetscFunctionBegin;
4184   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&flg);CHKERRQ(ierr);
4185   if (!flg) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"This function requires a MATMPIAIJ matrix as input");
4186   if (Ad)     *Ad     = a->A;
4187   if (Ao)     *Ao     = a->B;
4188   if (colmap) *colmap = a->garray;
4189   PetscFunctionReturn(0);
4190 }
4191 
4192 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
4193 {
4194   PetscErrorCode ierr;
4195   PetscInt       m,N,i,rstart,nnz,Ii;
4196   PetscInt       *indx;
4197   PetscScalar    *values;
4198 
4199   PetscFunctionBegin;
4200   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
4201   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
4202     PetscInt       *dnz,*onz,sum,bs,cbs;
4203 
4204     if (n == PETSC_DECIDE) {
4205       ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
4206     }
4207     /* Check sum(n) = N */
4208     ierr = MPIU_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4209     if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
4210 
4211     ierr    = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4212     rstart -= m;
4213 
4214     ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4215     for (i=0; i<m; i++) {
4216       ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
4217       ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
4218       ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
4219     }
4220 
4221     ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
4222     ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4223     ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
4224     ierr = MatSetBlockSizes(*outmat,bs,cbs);CHKERRQ(ierr);
4225     ierr = MatSetType(*outmat,MATAIJ);CHKERRQ(ierr);
4226     ierr = MatSeqAIJSetPreallocation(*outmat,0,dnz);CHKERRQ(ierr);
4227     ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
4228     ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4229   }
4230 
4231   /* numeric phase */
4232   ierr = MatGetOwnershipRange(*outmat,&rstart,NULL);CHKERRQ(ierr);
4233   for (i=0; i<m; i++) {
4234     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4235     Ii   = i + rstart;
4236     ierr = MatSetValues(*outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4237     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4238   }
4239   ierr = MatAssemblyBegin(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4240   ierr = MatAssemblyEnd(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4241   PetscFunctionReturn(0);
4242 }
4243 
4244 PetscErrorCode MatFileSplit(Mat A,char *outfile)
4245 {
4246   PetscErrorCode    ierr;
4247   PetscMPIInt       rank;
4248   PetscInt          m,N,i,rstart,nnz;
4249   size_t            len;
4250   const PetscInt    *indx;
4251   PetscViewer       out;
4252   char              *name;
4253   Mat               B;
4254   const PetscScalar *values;
4255 
4256   PetscFunctionBegin;
4257   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
4258   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
4259   /* Should this be the type of the diagonal block of A? */
4260   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
4261   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
4262   ierr = MatSetBlockSizesFromMats(B,A,A);CHKERRQ(ierr);
4263   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
4264   ierr = MatSeqAIJSetPreallocation(B,0,NULL);CHKERRQ(ierr);
4265   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
4266   for (i=0; i<m; i++) {
4267     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4268     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4269     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4270   }
4271   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4272   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4273 
4274   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
4275   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
4276   ierr = PetscMalloc1(len+5,&name);CHKERRQ(ierr);
4277   sprintf(name,"%s.%d",outfile,rank);
4278   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
4279   ierr = PetscFree(name);CHKERRQ(ierr);
4280   ierr = MatView(B,out);CHKERRQ(ierr);
4281   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
4282   ierr = MatDestroy(&B);CHKERRQ(ierr);
4283   PetscFunctionReturn(0);
4284 }
4285 
4286 PetscErrorCode MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
4287 {
4288   PetscErrorCode      ierr;
4289   Mat_Merge_SeqsToMPI *merge;
4290   PetscContainer      container;
4291 
4292   PetscFunctionBegin;
4293   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4294   if (container) {
4295     ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4296     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
4297     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
4298     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
4299     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
4300     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
4301     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
4302     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
4303     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
4304     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
4305     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
4306     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
4307     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
4308     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
4309     ierr = PetscFree(merge);CHKERRQ(ierr);
4310     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
4311   }
4312   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
4313   PetscFunctionReturn(0);
4314 }
4315 
4316 #include <../src/mat/utils/freespace.h>
4317 #include <petscbt.h>
4318 
4319 PetscErrorCode MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
4320 {
4321   PetscErrorCode      ierr;
4322   MPI_Comm            comm;
4323   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
4324   PetscMPIInt         size,rank,taga,*len_s;
4325   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
4326   PetscInt            proc,m;
4327   PetscInt            **buf_ri,**buf_rj;
4328   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
4329   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
4330   MPI_Request         *s_waits,*r_waits;
4331   MPI_Status          *status;
4332   MatScalar           *aa=a->a;
4333   MatScalar           **abuf_r,*ba_i;
4334   Mat_Merge_SeqsToMPI *merge;
4335   PetscContainer      container;
4336 
4337   PetscFunctionBegin;
4338   ierr = PetscObjectGetComm((PetscObject)mpimat,&comm);CHKERRQ(ierr);
4339   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4340 
4341   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4342   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4343 
4344   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4345   ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4346 
4347   bi     = merge->bi;
4348   bj     = merge->bj;
4349   buf_ri = merge->buf_ri;
4350   buf_rj = merge->buf_rj;
4351 
4352   ierr   = PetscMalloc1(size,&status);CHKERRQ(ierr);
4353   owners = merge->rowmap->range;
4354   len_s  = merge->len_s;
4355 
4356   /* send and recv matrix values */
4357   /*-----------------------------*/
4358   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
4359   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
4360 
4361   ierr = PetscMalloc1(merge->nsend+1,&s_waits);CHKERRQ(ierr);
4362   for (proc=0,k=0; proc<size; proc++) {
4363     if (!len_s[proc]) continue;
4364     i    = owners[proc];
4365     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
4366     k++;
4367   }
4368 
4369   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
4370   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
4371   ierr = PetscFree(status);CHKERRQ(ierr);
4372 
4373   ierr = PetscFree(s_waits);CHKERRQ(ierr);
4374   ierr = PetscFree(r_waits);CHKERRQ(ierr);
4375 
4376   /* insert mat values of mpimat */
4377   /*----------------------------*/
4378   ierr = PetscMalloc1(N,&ba_i);CHKERRQ(ierr);
4379   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4380 
4381   for (k=0; k<merge->nrecv; k++) {
4382     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4383     nrows       = *(buf_ri_k[k]);
4384     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
4385     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4386   }
4387 
4388   /* set values of ba */
4389   m = merge->rowmap->n;
4390   for (i=0; i<m; i++) {
4391     arow = owners[rank] + i;
4392     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
4393     bnzi = bi[i+1] - bi[i];
4394     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
4395 
4396     /* add local non-zero vals of this proc's seqmat into ba */
4397     anzi   = ai[arow+1] - ai[arow];
4398     aj     = a->j + ai[arow];
4399     aa     = a->a + ai[arow];
4400     nextaj = 0;
4401     for (j=0; nextaj<anzi; j++) {
4402       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4403         ba_i[j] += aa[nextaj++];
4404       }
4405     }
4406 
4407     /* add received vals into ba */
4408     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4409       /* i-th row */
4410       if (i == *nextrow[k]) {
4411         anzi   = *(nextai[k]+1) - *nextai[k];
4412         aj     = buf_rj[k] + *(nextai[k]);
4413         aa     = abuf_r[k] + *(nextai[k]);
4414         nextaj = 0;
4415         for (j=0; nextaj<anzi; j++) {
4416           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4417             ba_i[j] += aa[nextaj++];
4418           }
4419         }
4420         nextrow[k]++; nextai[k]++;
4421       }
4422     }
4423     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
4424   }
4425   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4426   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4427 
4428   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
4429   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
4430   ierr = PetscFree(ba_i);CHKERRQ(ierr);
4431   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4432   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4433   PetscFunctionReturn(0);
4434 }
4435 
4436 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4437 {
4438   PetscErrorCode      ierr;
4439   Mat                 B_mpi;
4440   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
4441   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4442   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
4443   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4444   PetscInt            len,proc,*dnz,*onz,bs,cbs;
4445   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4446   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4447   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
4448   MPI_Status          *status;
4449   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
4450   PetscBT             lnkbt;
4451   Mat_Merge_SeqsToMPI *merge;
4452   PetscContainer      container;
4453 
4454   PetscFunctionBegin;
4455   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4456 
4457   /* make sure it is a PETSc comm */
4458   ierr = PetscCommDuplicate(comm,&comm,NULL);CHKERRQ(ierr);
4459   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4460   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4461 
4462   ierr = PetscNew(&merge);CHKERRQ(ierr);
4463   ierr = PetscMalloc1(size,&status);CHKERRQ(ierr);
4464 
4465   /* determine row ownership */
4466   /*---------------------------------------------------------*/
4467   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
4468   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
4469   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
4470   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
4471   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
4472   ierr = PetscMalloc1(size,&len_si);CHKERRQ(ierr);
4473   ierr = PetscMalloc1(size,&merge->len_s);CHKERRQ(ierr);
4474 
4475   m      = merge->rowmap->n;
4476   owners = merge->rowmap->range;
4477 
4478   /* determine the number of messages to send, their lengths */
4479   /*---------------------------------------------------------*/
4480   len_s = merge->len_s;
4481 
4482   len          = 0; /* length of buf_si[] */
4483   merge->nsend = 0;
4484   for (proc=0; proc<size; proc++) {
4485     len_si[proc] = 0;
4486     if (proc == rank) {
4487       len_s[proc] = 0;
4488     } else {
4489       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4490       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4491     }
4492     if (len_s[proc]) {
4493       merge->nsend++;
4494       nrows = 0;
4495       for (i=owners[proc]; i<owners[proc+1]; i++) {
4496         if (ai[i+1] > ai[i]) nrows++;
4497       }
4498       len_si[proc] = 2*(nrows+1);
4499       len         += len_si[proc];
4500     }
4501   }
4502 
4503   /* determine the number and length of messages to receive for ij-structure */
4504   /*-------------------------------------------------------------------------*/
4505   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
4506   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
4507 
4508   /* post the Irecv of j-structure */
4509   /*-------------------------------*/
4510   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
4511   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
4512 
4513   /* post the Isend of j-structure */
4514   /*--------------------------------*/
4515   ierr = PetscMalloc2(merge->nsend,&si_waits,merge->nsend,&sj_waits);CHKERRQ(ierr);
4516 
4517   for (proc=0, k=0; proc<size; proc++) {
4518     if (!len_s[proc]) continue;
4519     i    = owners[proc];
4520     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
4521     k++;
4522   }
4523 
4524   /* receives and sends of j-structure are complete */
4525   /*------------------------------------------------*/
4526   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
4527   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
4528 
4529   /* send and recv i-structure */
4530   /*---------------------------*/
4531   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
4532   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
4533 
4534   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
4535   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4536   for (proc=0,k=0; proc<size; proc++) {
4537     if (!len_s[proc]) continue;
4538     /* form outgoing message for i-structure:
4539          buf_si[0]:                 nrows to be sent
4540                [1:nrows]:           row index (global)
4541                [nrows+1:2*nrows+1]: i-structure index
4542     */
4543     /*-------------------------------------------*/
4544     nrows       = len_si[proc]/2 - 1;
4545     buf_si_i    = buf_si + nrows+1;
4546     buf_si[0]   = nrows;
4547     buf_si_i[0] = 0;
4548     nrows       = 0;
4549     for (i=owners[proc]; i<owners[proc+1]; i++) {
4550       anzi = ai[i+1] - ai[i];
4551       if (anzi) {
4552         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4553         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4554         nrows++;
4555       }
4556     }
4557     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4558     k++;
4559     buf_si += len_si[proc];
4560   }
4561 
4562   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4563   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4564 
4565   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4566   for (i=0; i<merge->nrecv; i++) {
4567     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);
4568   }
4569 
4570   ierr = PetscFree(len_si);CHKERRQ(ierr);
4571   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4572   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4573   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4574   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4575   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4576   ierr = PetscFree(status);CHKERRQ(ierr);
4577 
4578   /* compute a local seq matrix in each processor */
4579   /*----------------------------------------------*/
4580   /* allocate bi array and free space for accumulating nonzero column info */
4581   ierr  = PetscMalloc1(m+1,&bi);CHKERRQ(ierr);
4582   bi[0] = 0;
4583 
4584   /* create and initialize a linked list */
4585   nlnk = N+1;
4586   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4587 
4588   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4589   len  = ai[owners[rank+1]] - ai[owners[rank]];
4590   ierr = PetscFreeSpaceGet(PetscIntMultTruncate(2,len)+1,&free_space);CHKERRQ(ierr);
4591 
4592   current_space = free_space;
4593 
4594   /* determine symbolic info for each local row */
4595   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4596 
4597   for (k=0; k<merge->nrecv; k++) {
4598     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4599     nrows       = *buf_ri_k[k];
4600     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4601     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4602   }
4603 
4604   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4605   len  = 0;
4606   for (i=0; i<m; i++) {
4607     bnzi = 0;
4608     /* add local non-zero cols of this proc's seqmat into lnk */
4609     arow  = owners[rank] + i;
4610     anzi  = ai[arow+1] - ai[arow];
4611     aj    = a->j + ai[arow];
4612     ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4613     bnzi += nlnk;
4614     /* add received col data into lnk */
4615     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4616       if (i == *nextrow[k]) { /* i-th row */
4617         anzi  = *(nextai[k]+1) - *nextai[k];
4618         aj    = buf_rj[k] + *nextai[k];
4619         ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4620         bnzi += nlnk;
4621         nextrow[k]++; nextai[k]++;
4622       }
4623     }
4624     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4625 
4626     /* if free space is not available, make more free space */
4627     if (current_space->local_remaining<bnzi) {
4628       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(bnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
4629       nspacedouble++;
4630     }
4631     /* copy data into free space, then initialize lnk */
4632     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4633     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
4634 
4635     current_space->array           += bnzi;
4636     current_space->local_used      += bnzi;
4637     current_space->local_remaining -= bnzi;
4638 
4639     bi[i+1] = bi[i] + bnzi;
4640   }
4641 
4642   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4643 
4644   ierr = PetscMalloc1(bi[m]+1,&bj);CHKERRQ(ierr);
4645   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
4646   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4647 
4648   /* create symbolic parallel matrix B_mpi */
4649   /*---------------------------------------*/
4650   ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
4651   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
4652   if (n==PETSC_DECIDE) {
4653     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
4654   } else {
4655     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4656   }
4657   ierr = MatSetBlockSizes(B_mpi,bs,cbs);CHKERRQ(ierr);
4658   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
4659   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
4660   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4661   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
4662 
4663   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4664   B_mpi->assembled    = PETSC_FALSE;
4665   B_mpi->ops->destroy = MatDestroy_MPIAIJ_SeqsToMPI;
4666   merge->bi           = bi;
4667   merge->bj           = bj;
4668   merge->buf_ri       = buf_ri;
4669   merge->buf_rj       = buf_rj;
4670   merge->coi          = NULL;
4671   merge->coj          = NULL;
4672   merge->owners_co    = NULL;
4673 
4674   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
4675 
4676   /* attach the supporting struct to B_mpi for reuse */
4677   ierr    = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
4678   ierr    = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
4679   ierr    = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
4680   ierr    = PetscContainerDestroy(&container);CHKERRQ(ierr);
4681   *mpimat = B_mpi;
4682 
4683   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4684   PetscFunctionReturn(0);
4685 }
4686 
4687 /*@C
4688       MatCreateMPIAIJSumSeqAIJ - Creates a MATMPIAIJ matrix by adding sequential
4689                  matrices from each processor
4690 
4691     Collective on MPI_Comm
4692 
4693    Input Parameters:
4694 +    comm - the communicators the parallel matrix will live on
4695 .    seqmat - the input sequential matrices
4696 .    m - number of local rows (or PETSC_DECIDE)
4697 .    n - number of local columns (or PETSC_DECIDE)
4698 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4699 
4700    Output Parameter:
4701 .    mpimat - the parallel matrix generated
4702 
4703     Level: advanced
4704 
4705    Notes:
4706      The dimensions of the sequential matrix in each processor MUST be the same.
4707      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
4708      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
4709 @*/
4710 PetscErrorCode MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
4711 {
4712   PetscErrorCode ierr;
4713   PetscMPIInt    size;
4714 
4715   PetscFunctionBegin;
4716   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4717   if (size == 1) {
4718     ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4719     if (scall == MAT_INITIAL_MATRIX) {
4720       ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
4721     } else {
4722       ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4723     }
4724     ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4725     PetscFunctionReturn(0);
4726   }
4727   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4728   if (scall == MAT_INITIAL_MATRIX) {
4729     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
4730   }
4731   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
4732   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4733   PetscFunctionReturn(0);
4734 }
4735 
4736 /*@
4737      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MATMPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
4738           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
4739           with MatGetSize()
4740 
4741     Not Collective
4742 
4743    Input Parameters:
4744 +    A - the matrix
4745 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4746 
4747    Output Parameter:
4748 .    A_loc - the local sequential matrix generated
4749 
4750     Level: developer
4751 
4752 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
4753 
4754 @*/
4755 PetscErrorCode MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
4756 {
4757   PetscErrorCode ierr;
4758   Mat_MPIAIJ     *mpimat=(Mat_MPIAIJ*)A->data;
4759   Mat_SeqAIJ     *mat,*a,*b;
4760   PetscInt       *ai,*aj,*bi,*bj,*cmap=mpimat->garray;
4761   MatScalar      *aa,*ba,*cam;
4762   PetscScalar    *ca;
4763   PetscInt       am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
4764   PetscInt       *ci,*cj,col,ncols_d,ncols_o,jo;
4765   PetscBool      match;
4766   MPI_Comm       comm;
4767   PetscMPIInt    size;
4768 
4769   PetscFunctionBegin;
4770   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4771   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
4772   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4773   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4774   if (size == 1 && scall == MAT_REUSE_MATRIX) PetscFunctionReturn(0);
4775 
4776   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4777   a = (Mat_SeqAIJ*)(mpimat->A)->data;
4778   b = (Mat_SeqAIJ*)(mpimat->B)->data;
4779   ai = a->i; aj = a->j; bi = b->i; bj = b->j;
4780   aa = a->a; ba = b->a;
4781   if (scall == MAT_INITIAL_MATRIX) {
4782     if (size == 1) {
4783       ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ai,aj,aa,A_loc);CHKERRQ(ierr);
4784       PetscFunctionReturn(0);
4785     }
4786 
4787     ierr  = PetscMalloc1(1+am,&ci);CHKERRQ(ierr);
4788     ci[0] = 0;
4789     for (i=0; i<am; i++) {
4790       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
4791     }
4792     ierr = PetscMalloc1(1+ci[am],&cj);CHKERRQ(ierr);
4793     ierr = PetscMalloc1(1+ci[am],&ca);CHKERRQ(ierr);
4794     k    = 0;
4795     for (i=0; i<am; i++) {
4796       ncols_o = bi[i+1] - bi[i];
4797       ncols_d = ai[i+1] - ai[i];
4798       /* off-diagonal portion of A */
4799       for (jo=0; jo<ncols_o; jo++) {
4800         col = cmap[*bj];
4801         if (col >= cstart) break;
4802         cj[k]   = col; bj++;
4803         ca[k++] = *ba++;
4804       }
4805       /* diagonal portion of A */
4806       for (j=0; j<ncols_d; j++) {
4807         cj[k]   = cstart + *aj++;
4808         ca[k++] = *aa++;
4809       }
4810       /* off-diagonal portion of A */
4811       for (j=jo; j<ncols_o; j++) {
4812         cj[k]   = cmap[*bj++];
4813         ca[k++] = *ba++;
4814       }
4815     }
4816     /* put together the new matrix */
4817     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
4818     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4819     /* Since these are PETSc arrays, change flags to free them as necessary. */
4820     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
4821     mat->free_a  = PETSC_TRUE;
4822     mat->free_ij = PETSC_TRUE;
4823     mat->nonew   = 0;
4824   } else if (scall == MAT_REUSE_MATRIX) {
4825     mat=(Mat_SeqAIJ*)(*A_loc)->data;
4826     ci = mat->i; cj = mat->j; cam = mat->a;
4827     for (i=0; i<am; i++) {
4828       /* off-diagonal portion of A */
4829       ncols_o = bi[i+1] - bi[i];
4830       for (jo=0; jo<ncols_o; jo++) {
4831         col = cmap[*bj];
4832         if (col >= cstart) break;
4833         *cam++ = *ba++; bj++;
4834       }
4835       /* diagonal portion of A */
4836       ncols_d = ai[i+1] - ai[i];
4837       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
4838       /* off-diagonal portion of A */
4839       for (j=jo; j<ncols_o; j++) {
4840         *cam++ = *ba++; bj++;
4841       }
4842     }
4843   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
4844   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4845   PetscFunctionReturn(0);
4846 }
4847 
4848 /*@C
4849      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MATMPIAIJ matrix by taking all its local rows and NON-ZERO columns
4850 
4851     Not Collective
4852 
4853    Input Parameters:
4854 +    A - the matrix
4855 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4856 -    row, col - index sets of rows and columns to extract (or NULL)
4857 
4858    Output Parameter:
4859 .    A_loc - the local sequential matrix generated
4860 
4861     Level: developer
4862 
4863 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
4864 
4865 @*/
4866 PetscErrorCode MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
4867 {
4868   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4869   PetscErrorCode ierr;
4870   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
4871   IS             isrowa,iscola;
4872   Mat            *aloc;
4873   PetscBool      match;
4874 
4875   PetscFunctionBegin;
4876   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4877   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
4878   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4879   if (!row) {
4880     start = A->rmap->rstart; end = A->rmap->rend;
4881     ierr  = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
4882   } else {
4883     isrowa = *row;
4884   }
4885   if (!col) {
4886     start = A->cmap->rstart;
4887     cmap  = a->garray;
4888     nzA   = a->A->cmap->n;
4889     nzB   = a->B->cmap->n;
4890     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4891     ncols = 0;
4892     for (i=0; i<nzB; i++) {
4893       if (cmap[i] < start) idx[ncols++] = cmap[i];
4894       else break;
4895     }
4896     imark = i;
4897     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
4898     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
4899     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
4900   } else {
4901     iscola = *col;
4902   }
4903   if (scall != MAT_INITIAL_MATRIX) {
4904     ierr    = PetscMalloc1(1,&aloc);CHKERRQ(ierr);
4905     aloc[0] = *A_loc;
4906   }
4907   ierr   = MatCreateSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
4908   *A_loc = aloc[0];
4909   ierr   = PetscFree(aloc);CHKERRQ(ierr);
4910   if (!row) {
4911     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
4912   }
4913   if (!col) {
4914     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
4915   }
4916   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4917   PetscFunctionReturn(0);
4918 }
4919 
4920 /*@C
4921     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
4922 
4923     Collective on Mat
4924 
4925    Input Parameters:
4926 +    A,B - the matrices in mpiaij format
4927 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4928 -    rowb, colb - index sets of rows and columns of B to extract (or NULL)
4929 
4930    Output Parameter:
4931 +    rowb, colb - index sets of rows and columns of B to extract
4932 -    B_seq - the sequential matrix generated
4933 
4934     Level: developer
4935 
4936 @*/
4937 PetscErrorCode MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
4938 {
4939   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4940   PetscErrorCode ierr;
4941   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
4942   IS             isrowb,iscolb;
4943   Mat            *bseq=NULL;
4944 
4945   PetscFunctionBegin;
4946   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4947     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);
4948   }
4949   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4950 
4951   if (scall == MAT_INITIAL_MATRIX) {
4952     start = A->cmap->rstart;
4953     cmap  = a->garray;
4954     nzA   = a->A->cmap->n;
4955     nzB   = a->B->cmap->n;
4956     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4957     ncols = 0;
4958     for (i=0; i<nzB; i++) {  /* row < local row index */
4959       if (cmap[i] < start) idx[ncols++] = cmap[i];
4960       else break;
4961     }
4962     imark = i;
4963     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
4964     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
4965     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
4966     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
4967   } else {
4968     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
4969     isrowb  = *rowb; iscolb = *colb;
4970     ierr    = PetscMalloc1(1,&bseq);CHKERRQ(ierr);
4971     bseq[0] = *B_seq;
4972   }
4973   ierr   = MatCreateSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
4974   *B_seq = bseq[0];
4975   ierr   = PetscFree(bseq);CHKERRQ(ierr);
4976   if (!rowb) {
4977     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
4978   } else {
4979     *rowb = isrowb;
4980   }
4981   if (!colb) {
4982     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
4983   } else {
4984     *colb = iscolb;
4985   }
4986   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4987   PetscFunctionReturn(0);
4988 }
4989 
4990 /*
4991     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
4992     of the OFF-DIAGONAL portion of local A
4993 
4994     Collective on Mat
4995 
4996    Input Parameters:
4997 +    A,B - the matrices in mpiaij format
4998 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4999 
5000    Output Parameter:
5001 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
5002 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
5003 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
5004 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
5005 
5006     Level: developer
5007 
5008 */
5009 PetscErrorCode MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
5010 {
5011   VecScatter_MPI_General *gen_to,*gen_from;
5012   PetscErrorCode         ierr;
5013   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
5014   Mat_SeqAIJ             *b_oth;
5015   VecScatter             ctx =a->Mvctx;
5016   MPI_Comm               comm;
5017   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
5018   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
5019   PetscInt               *rvalues,*svalues;
5020   MatScalar              *b_otha,*bufa,*bufA;
5021   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
5022   MPI_Request            *rwaits = NULL,*swaits = NULL;
5023   MPI_Status             *sstatus,rstatus;
5024   PetscMPIInt            jj,size;
5025   PetscInt               *cols,sbs,rbs;
5026   PetscScalar            *vals;
5027 
5028   PetscFunctionBegin;
5029   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
5030   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
5031 
5032   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
5033     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);
5034   }
5035   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5036   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
5037 
5038   if (size == 1) {
5039     startsj_s = NULL;
5040     bufa_ptr  = NULL;
5041     *B_oth    = NULL;
5042     PetscFunctionReturn(0);
5043   }
5044 
5045   gen_to   = (VecScatter_MPI_General*)ctx->todata;
5046   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
5047   nrecvs   = gen_from->n;
5048   nsends   = gen_to->n;
5049 
5050   ierr    = PetscMalloc2(nrecvs,&rwaits,nsends,&swaits);CHKERRQ(ierr);
5051   srow    = gen_to->indices;    /* local row index to be sent */
5052   sstarts = gen_to->starts;
5053   sprocs  = gen_to->procs;
5054   sstatus = gen_to->sstatus;
5055   sbs     = gen_to->bs;
5056   rstarts = gen_from->starts;
5057   rprocs  = gen_from->procs;
5058   rbs     = gen_from->bs;
5059 
5060   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
5061   if (scall == MAT_INITIAL_MATRIX) {
5062     /* i-array */
5063     /*---------*/
5064     /*  post receives */
5065     ierr = PetscMalloc1(rbs*(rstarts[nrecvs] - rstarts[0]),&rvalues);CHKERRQ(ierr);
5066     for (i=0; i<nrecvs; i++) {
5067       rowlen = rvalues + rstarts[i]*rbs;
5068       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
5069       ierr   = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5070     }
5071 
5072     /* pack the outgoing message */
5073     ierr = PetscMalloc2(nsends+1,&sstartsj,nrecvs+1,&rstartsj);CHKERRQ(ierr);
5074 
5075     sstartsj[0] = 0;
5076     rstartsj[0] = 0;
5077     len         = 0; /* total length of j or a array to be sent */
5078     k           = 0;
5079     ierr = PetscMalloc1(sbs*(sstarts[nsends] - sstarts[0]),&svalues);CHKERRQ(ierr);
5080     for (i=0; i<nsends; i++) {
5081       rowlen = svalues + sstarts[i]*sbs;
5082       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
5083       for (j=0; j<nrows; j++) {
5084         row = srow[k] + B->rmap->range[rank]; /* global row idx */
5085         for (l=0; l<sbs; l++) {
5086           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr); /* rowlength */
5087 
5088           rowlen[j*sbs+l] = ncols;
5089 
5090           len += ncols;
5091           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr);
5092         }
5093         k++;
5094       }
5095       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5096 
5097       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
5098     }
5099     /* recvs and sends of i-array are completed */
5100     i = nrecvs;
5101     while (i--) {
5102       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5103     }
5104     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5105     ierr = PetscFree(svalues);CHKERRQ(ierr);
5106 
5107     /* allocate buffers for sending j and a arrays */
5108     ierr = PetscMalloc1(len+1,&bufj);CHKERRQ(ierr);
5109     ierr = PetscMalloc1(len+1,&bufa);CHKERRQ(ierr);
5110 
5111     /* create i-array of B_oth */
5112     ierr = PetscMalloc1(aBn+2,&b_othi);CHKERRQ(ierr);
5113 
5114     b_othi[0] = 0;
5115     len       = 0; /* total length of j or a array to be received */
5116     k         = 0;
5117     for (i=0; i<nrecvs; i++) {
5118       rowlen = rvalues + rstarts[i]*rbs;
5119       nrows  = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be received */
5120       for (j=0; j<nrows; j++) {
5121         b_othi[k+1] = b_othi[k] + rowlen[j];
5122         ierr = PetscIntSumError(rowlen[j],len,&len);CHKERRQ(ierr);
5123         k++;
5124       }
5125       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
5126     }
5127     ierr = PetscFree(rvalues);CHKERRQ(ierr);
5128 
5129     /* allocate space for j and a arrrays of B_oth */
5130     ierr = PetscMalloc1(b_othi[aBn]+1,&b_othj);CHKERRQ(ierr);
5131     ierr = PetscMalloc1(b_othi[aBn]+1,&b_otha);CHKERRQ(ierr);
5132 
5133     /* j-array */
5134     /*---------*/
5135     /*  post receives of j-array */
5136     for (i=0; i<nrecvs; i++) {
5137       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5138       ierr  = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5139     }
5140 
5141     /* pack the outgoing message j-array */
5142     k = 0;
5143     for (i=0; i<nsends; i++) {
5144       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5145       bufJ  = bufj+sstartsj[i];
5146       for (j=0; j<nrows; j++) {
5147         row = srow[k++] + B->rmap->range[rank];  /* global row idx */
5148         for (ll=0; ll<sbs; ll++) {
5149           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
5150           for (l=0; l<ncols; l++) {
5151             *bufJ++ = cols[l];
5152           }
5153           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
5154         }
5155       }
5156       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5157     }
5158 
5159     /* recvs and sends of j-array are completed */
5160     i = nrecvs;
5161     while (i--) {
5162       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5163     }
5164     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5165   } else if (scall == MAT_REUSE_MATRIX) {
5166     sstartsj = *startsj_s;
5167     rstartsj = *startsj_r;
5168     bufa     = *bufa_ptr;
5169     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
5170     b_otha   = b_oth->a;
5171   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
5172 
5173   /* a-array */
5174   /*---------*/
5175   /*  post receives of a-array */
5176   for (i=0; i<nrecvs; i++) {
5177     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5178     ierr  = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5179   }
5180 
5181   /* pack the outgoing message a-array */
5182   k = 0;
5183   for (i=0; i<nsends; i++) {
5184     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5185     bufA  = bufa+sstartsj[i];
5186     for (j=0; j<nrows; j++) {
5187       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
5188       for (ll=0; ll<sbs; ll++) {
5189         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
5190         for (l=0; l<ncols; l++) {
5191           *bufA++ = vals[l];
5192         }
5193         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
5194       }
5195     }
5196     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5197   }
5198   /* recvs and sends of a-array are completed */
5199   i = nrecvs;
5200   while (i--) {
5201     ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5202   }
5203   if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5204   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
5205 
5206   if (scall == MAT_INITIAL_MATRIX) {
5207     /* put together the new matrix */
5208     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
5209 
5210     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
5211     /* Since these are PETSc arrays, change flags to free them as necessary. */
5212     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
5213     b_oth->free_a  = PETSC_TRUE;
5214     b_oth->free_ij = PETSC_TRUE;
5215     b_oth->nonew   = 0;
5216 
5217     ierr = PetscFree(bufj);CHKERRQ(ierr);
5218     if (!startsj_s || !bufa_ptr) {
5219       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
5220       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
5221     } else {
5222       *startsj_s = sstartsj;
5223       *startsj_r = rstartsj;
5224       *bufa_ptr  = bufa;
5225     }
5226   }
5227   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5228   PetscFunctionReturn(0);
5229 }
5230 
5231 /*@C
5232   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
5233 
5234   Not Collective
5235 
5236   Input Parameters:
5237 . A - The matrix in mpiaij format
5238 
5239   Output Parameter:
5240 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
5241 . colmap - A map from global column index to local index into lvec
5242 - multScatter - A scatter from the argument of a matrix-vector product to lvec
5243 
5244   Level: developer
5245 
5246 @*/
5247 #if defined(PETSC_USE_CTABLE)
5248 PetscErrorCode MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
5249 #else
5250 PetscErrorCode MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
5251 #endif
5252 {
5253   Mat_MPIAIJ *a;
5254 
5255   PetscFunctionBegin;
5256   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
5257   PetscValidPointer(lvec, 2);
5258   PetscValidPointer(colmap, 3);
5259   PetscValidPointer(multScatter, 4);
5260   a = (Mat_MPIAIJ*) A->data;
5261   if (lvec) *lvec = a->lvec;
5262   if (colmap) *colmap = a->colmap;
5263   if (multScatter) *multScatter = a->Mvctx;
5264   PetscFunctionReturn(0);
5265 }
5266 
5267 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
5268 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
5269 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
5270 #if defined(PETSC_HAVE_ELEMENTAL)
5271 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
5272 #endif
5273 #if defined(PETSC_HAVE_HYPRE)
5274 PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat,MatType,MatReuse,Mat*);
5275 PETSC_INTERN PetscErrorCode MatMatMatMult_Transpose_AIJ_AIJ(Mat,Mat,Mat,MatReuse,PetscReal,Mat*);
5276 #endif
5277 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_IS(Mat,MatType,MatReuse,Mat*);
5278 
5279 /*
5280     Computes (B'*A')' since computing B*A directly is untenable
5281 
5282                n                       p                          p
5283         (              )       (              )         (                  )
5284       m (      A       )  *  n (       B      )   =   m (         C        )
5285         (              )       (              )         (                  )
5286 
5287 */
5288 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
5289 {
5290   PetscErrorCode ierr;
5291   Mat            At,Bt,Ct;
5292 
5293   PetscFunctionBegin;
5294   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
5295   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
5296   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
5297   ierr = MatDestroy(&At);CHKERRQ(ierr);
5298   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
5299   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
5300   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
5301   PetscFunctionReturn(0);
5302 }
5303 
5304 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
5305 {
5306   PetscErrorCode ierr;
5307   PetscInt       m=A->rmap->n,n=B->cmap->n;
5308   Mat            Cmat;
5309 
5310   PetscFunctionBegin;
5311   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);
5312   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
5313   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
5314   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
5315   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
5316   ierr = MatMPIDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
5317   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5318   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5319 
5320   Cmat->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
5321 
5322   *C = Cmat;
5323   PetscFunctionReturn(0);
5324 }
5325 
5326 /* ----------------------------------------------------------------*/
5327 PETSC_INTERN PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
5328 {
5329   PetscErrorCode ierr;
5330 
5331   PetscFunctionBegin;
5332   if (scall == MAT_INITIAL_MATRIX) {
5333     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5334     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
5335     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5336   }
5337   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5338   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
5339   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5340   PetscFunctionReturn(0);
5341 }
5342 
5343 /*MC
5344    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
5345 
5346    Options Database Keys:
5347 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
5348 
5349   Level: beginner
5350 
5351 .seealso: MatCreateAIJ()
5352 M*/
5353 
5354 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
5355 {
5356   Mat_MPIAIJ     *b;
5357   PetscErrorCode ierr;
5358   PetscMPIInt    size;
5359 
5360   PetscFunctionBegin;
5361   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
5362 
5363   ierr          = PetscNewLog(B,&b);CHKERRQ(ierr);
5364   B->data       = (void*)b;
5365   ierr          = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
5366   B->assembled  = PETSC_FALSE;
5367   B->insertmode = NOT_SET_VALUES;
5368   b->size       = size;
5369 
5370   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank);CHKERRQ(ierr);
5371 
5372   /* build cache for off array entries formed */
5373   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash);CHKERRQ(ierr);
5374 
5375   b->donotstash  = PETSC_FALSE;
5376   b->colmap      = 0;
5377   b->garray      = 0;
5378   b->roworiented = PETSC_TRUE;
5379 
5380   /* stuff used for matrix vector multiply */
5381   b->lvec  = NULL;
5382   b->Mvctx = NULL;
5383 
5384   /* stuff for MatGetRow() */
5385   b->rowindices   = 0;
5386   b->rowvalues    = 0;
5387   b->getrowactive = PETSC_FALSE;
5388 
5389   /* flexible pointer used in CUSP/CUSPARSE classes */
5390   b->spptr = NULL;
5391 
5392   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetUseScalableIncreaseOverlap_C",MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ);CHKERRQ(ierr);
5393   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ);CHKERRQ(ierr);
5394   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
5395   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
5396   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
5397   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
5398   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
5399   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
5400   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
5401   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
5402 #if defined(PETSC_HAVE_ELEMENTAL)
5403   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_elemental_C",MatConvert_MPIAIJ_Elemental);CHKERRQ(ierr);
5404 #endif
5405 #if defined(PETSC_HAVE_HYPRE)
5406   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_hypre_C",MatConvert_AIJ_HYPRE);CHKERRQ(ierr);
5407 #endif
5408   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_is_C",MatConvert_MPIAIJ_IS);CHKERRQ(ierr);
5409   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
5410   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
5411   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
5412 #if defined(PETSC_HAVE_HYPRE)
5413   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMatMult_transpose_mpiaij_mpiaij_C",MatMatMatMult_Transpose_AIJ_AIJ);CHKERRQ(ierr);
5414 #endif
5415   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
5416   PetscFunctionReturn(0);
5417 }
5418 
5419 /*@C
5420      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
5421          and "off-diagonal" part of the matrix in CSR format.
5422 
5423    Collective on MPI_Comm
5424 
5425    Input Parameters:
5426 +  comm - MPI communicator
5427 .  m - number of local rows (Cannot be PETSC_DECIDE)
5428 .  n - This value should be the same as the local size used in creating the
5429        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
5430        calculated if N is given) For square matrices n is almost always m.
5431 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
5432 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
5433 .   i - row indices for "diagonal" portion of matrix
5434 .   j - column indices
5435 .   a - matrix values
5436 .   oi - row indices for "off-diagonal" portion of matrix
5437 .   oj - column indices
5438 -   oa - matrix values
5439 
5440    Output Parameter:
5441 .   mat - the matrix
5442 
5443    Level: advanced
5444 
5445    Notes:
5446        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
5447        must free the arrays once the matrix has been destroyed and not before.
5448 
5449        The i and j indices are 0 based
5450 
5451        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
5452 
5453        This sets local rows and cannot be used to set off-processor values.
5454 
5455        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
5456        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
5457        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
5458        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
5459        keep track of the underlying array. Use MatSetOption(A,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
5460        communication if it is known that only local entries will be set.
5461 
5462 .keywords: matrix, aij, compressed row, sparse, parallel
5463 
5464 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
5465           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
5466 @*/
5467 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)
5468 {
5469   PetscErrorCode ierr;
5470   Mat_MPIAIJ     *maij;
5471 
5472   PetscFunctionBegin;
5473   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
5474   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
5475   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
5476   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
5477   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
5478   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
5479   maij = (Mat_MPIAIJ*) (*mat)->data;
5480 
5481   (*mat)->preallocated = PETSC_TRUE;
5482 
5483   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
5484   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
5485 
5486   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
5487   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
5488 
5489   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5490   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5491   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5492   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5493 
5494   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
5495   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5496   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5497   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_FALSE);CHKERRQ(ierr);
5498   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
5499   PetscFunctionReturn(0);
5500 }
5501 
5502 /*
5503     Special version for direct calls from Fortran
5504 */
5505 #include <petsc/private/fortranimpl.h>
5506 
5507 /* Change these macros so can be used in void function */
5508 #undef CHKERRQ
5509 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
5510 #undef SETERRQ2
5511 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5512 #undef SETERRQ3
5513 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5514 #undef SETERRQ
5515 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
5516 
5517 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5518 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
5519 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5520 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
5521 #else
5522 #endif
5523 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)
5524 {
5525   Mat            mat  = *mmat;
5526   PetscInt       m    = *mm, n = *mn;
5527   InsertMode     addv = *maddv;
5528   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
5529   PetscScalar    value;
5530   PetscErrorCode ierr;
5531 
5532   MatCheckPreallocated(mat,1);
5533   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
5534 
5535 #if defined(PETSC_USE_DEBUG)
5536   else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
5537 #endif
5538   {
5539     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
5540     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
5541     PetscBool roworiented = aij->roworiented;
5542 
5543     /* Some Variables required in the macro */
5544     Mat        A                 = aij->A;
5545     Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
5546     PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
5547     MatScalar  *aa               = a->a;
5548     PetscBool  ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
5549     Mat        B                 = aij->B;
5550     Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
5551     PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5552     MatScalar  *ba               = b->a;
5553 
5554     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5555     PetscInt  nonew = a->nonew;
5556     MatScalar *ap1,*ap2;
5557 
5558     PetscFunctionBegin;
5559     for (i=0; i<m; i++) {
5560       if (im[i] < 0) continue;
5561 #if defined(PETSC_USE_DEBUG)
5562       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);
5563 #endif
5564       if (im[i] >= rstart && im[i] < rend) {
5565         row      = im[i] - rstart;
5566         lastcol1 = -1;
5567         rp1      = aj + ai[row];
5568         ap1      = aa + ai[row];
5569         rmax1    = aimax[row];
5570         nrow1    = ailen[row];
5571         low1     = 0;
5572         high1    = nrow1;
5573         lastcol2 = -1;
5574         rp2      = bj + bi[row];
5575         ap2      = ba + bi[row];
5576         rmax2    = bimax[row];
5577         nrow2    = bilen[row];
5578         low2     = 0;
5579         high2    = nrow2;
5580 
5581         for (j=0; j<n; j++) {
5582           if (roworiented) value = v[i*n+j];
5583           else value = v[i+j*m];
5584           if (in[j] >= cstart && in[j] < cend) {
5585             col = in[j] - cstart;
5586             if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
5587             MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
5588           } else if (in[j] < 0) continue;
5589 #if defined(PETSC_USE_DEBUG)
5590           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);
5591 #endif
5592           else {
5593             if (mat->was_assembled) {
5594               if (!aij->colmap) {
5595                 ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5596               }
5597 #if defined(PETSC_USE_CTABLE)
5598               ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5599               col--;
5600 #else
5601               col = aij->colmap[in[j]] - 1;
5602 #endif
5603               if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
5604               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5605                 ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5606                 col  =  in[j];
5607                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5608                 B     = aij->B;
5609                 b     = (Mat_SeqAIJ*)B->data;
5610                 bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5611                 rp2   = bj + bi[row];
5612                 ap2   = ba + bi[row];
5613                 rmax2 = bimax[row];
5614                 nrow2 = bilen[row];
5615                 low2  = 0;
5616                 high2 = nrow2;
5617                 bm    = aij->B->rmap->n;
5618                 ba    = b->a;
5619               }
5620             } else col = in[j];
5621             MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
5622           }
5623         }
5624       } else if (!aij->donotstash) {
5625         if (roworiented) {
5626           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5627         } else {
5628           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5629         }
5630       }
5631     }
5632   }
5633   PetscFunctionReturnVoid();
5634 }
5635 
5636