xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision e489de8f4f40ef4ec69681d1270c34327e96a1d1)
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 *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       idx1[count1]    = i; /* local column index in off-diagonal part B */
3081       cmap1[count1++] = (PetscInt)PetscRealPart(cmaparray[i]);  /* column index in submat */
3082 
3083       idx[count]    = (PetscInt)PetscRealPart(xarray[i]);
3084       camp[count++] = (PetscInt)PetscRealPart(cmaparray[i]);  /* column index in submat */
3085     }
3086   }
3087   ierr = VecRestoreArray(lvec,&xarray);CHKERRQ(ierr);
3088   ierr = VecRestoreArray(lcmap,&cmaparray);CHKERRQ(ierr);
3089 
3090   ierr = PetscSortIntWithArray(count,camp,idx);CHKERRQ(ierr);
3091 
3092   ierr = ISCreateGeneral(PETSC_COMM_SELF,count1,idx1,PETSC_COPY_VALUES,iscol_o);CHKERRQ(ierr);
3093   ierr = ISCreateGeneral(PETSC_COMM_SELF,count1,cmap1,PETSC_COPY_VALUES,isgarray);CHKERRQ(ierr);
3094   ierr = ISGetBlockSize(iscol,&i);CHKERRQ(ierr);
3095   ierr = ISSetBlockSize(*iscol_o,i);CHKERRQ(ierr);
3096   ierr = PetscFree2(idx1,cmap1);CHKERRQ(ierr);
3097 
3098   ierr = PetscFree2(idx,camp);CHKERRQ(ierr);
3099   ierr = VecDestroy(&x);CHKERRQ(ierr);
3100   ierr = VecDestroy(&cmap);CHKERRQ(ierr);
3101   ierr = VecDestroy(&lcmap);CHKERRQ(ierr);
3102   PetscFunctionReturn(0);
3103 }
3104 
3105 /* Both isrow and iscol have same processor distribution as mat, output *submat is a submatrix of local mat */
3106 PetscErrorCode MatCreateSubMatrix_MPIAIJ_SameRowColDist(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *submat)
3107 {
3108   PetscErrorCode ierr;
3109   PetscInt       i,m,n,rstart,row,rend,nz,j,rbs,cbs;
3110   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)mat->data;
3111   Mat            M=NULL,B=a->B;
3112   PetscInt       *garray = a->garray,*colsub,Ncols;
3113   PetscInt       count,Bn=B->cmap->N,cstart=mat->cmap->rstart,cend=mat->cmap->rend;
3114   IS             iscol_sub,iscmap;
3115   const PetscInt *is_idx,*cmap;
3116   PetscBool      allcolumns=PETSC_FALSE;
3117   IS             iscol_local=NULL;
3118   MPI_Comm       comm;
3119   IS             iscol_d,isrow_d,iscol_o,isgarray;
3120   Mat            Asub=NULL,Bsub=NULL;
3121 
3122   PetscFunctionBegin;
3123   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3124   PetscMPIInt rank;
3125   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3126 
3127   if (call == MAT_REUSE_MATRIX) {
3128     Mat_MPIAIJ *matsub=(Mat_MPIAIJ*)(*submat)->data;
3129 
3130     ierr = PetscObjectQuery((PetscObject)*submat,"isrow_d",(PetscObject*)&isrow_d);CHKERRQ(ierr);
3131     if (!isrow_d) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"isrow_d passed in was not used before, cannot reuse");
3132 
3133     ierr = PetscObjectQuery((PetscObject)*submat,"iscol_d",(PetscObject*)&iscol_d);CHKERRQ(ierr);
3134     if (!iscol_d) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"iscol_d passed in was not used before, cannot reuse");
3135 
3136     ierr = PetscObjectQuery((PetscObject)*submat,"iscol_o",(PetscObject*)&iscol_o);CHKERRQ(ierr);
3137     if (!iscol_o) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"iscol_o passed in was not used before, cannot reuse");
3138 
3139     ierr = MatCreateSubMatrix_SeqAIJ(a->A,isrow_d,iscol_d,PETSC_DECIDE,call,&matsub->A);CHKERRQ(ierr);
3140     ierr = MatCreateSubMatrix_SeqAIJ(a->B,isrow_d,iscol_o,PETSC_DECIDE,call,&matsub->B);CHKERRQ(ierr);
3141     ierr = MatAssemblyBegin(*submat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3142     ierr = MatAssemblyEnd(*submat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3143 
3144   } else { /* call == MAT_INITIAL_MATRIX) */
3145     const PetscInt *garray1;
3146 
3147     ierr = ISGetSeqIS_SameColDist_Private(mat,isrow,iscol,&isrow_d,&iscol_d,&iscol_o,&isgarray);CHKERRQ(ierr);
3148 
3149     ierr = MatCreateSubMatrix_SeqAIJ(a->A,isrow_d,iscol_d,PETSC_DECIDE,call,&Asub);CHKERRQ(ierr);
3150     ierr = MatCreateSubMatrix_SeqAIJ(a->B,isrow_d,iscol_o,PETSC_DECIDE,call,&Bsub);CHKERRQ(ierr);
3151 
3152     PetscInt BsubN = Bsub->cmap->N;
3153     ierr = ISGetIndices(isgarray,&garray1);CHKERRQ(ierr);
3154     ierr = MatCreateMPIAIJWithSeqAIJ(comm,Asub,Bsub,garray1,&M);CHKERRQ(ierr);
3155     ierr = ISRestoreIndices(isgarray,&garray1);CHKERRQ(ierr);
3156 
3157     /* Check is Bsub == M->B? If not, compress iscol_o accordingly */
3158 
3159     a = (Mat_MPIAIJ*)M->data;
3160 #if 1
3161     if (BsubN != a->B->cmap->N) {
3162       printf("[%d] Bsub->cmap->N %d != a->B->cmap->N %d\n",rank,BsubN,a->B->cmap->N);
3163     }
3164 #endif
3165 
3166     ierr = ISDestroy(&isgarray);CHKERRQ(ierr);
3167 
3168     /* Save isrow_d, iscol_d and iscol_o used in processor for next request */
3169     ierr = PetscObjectCompose((PetscObject)M,"isrow_d",(PetscObject)isrow_d);CHKERRQ(ierr);
3170     ierr = ISDestroy(&isrow_d);CHKERRQ(ierr);
3171 
3172     ierr = PetscObjectCompose((PetscObject)M,"iscol_d",(PetscObject)iscol_d);CHKERRQ(ierr);
3173     ierr = ISDestroy(&iscol_d);CHKERRQ(ierr);
3174 
3175     ierr = PetscObjectCompose((PetscObject)M,"iscol_o",(PetscObject)iscol_o);CHKERRQ(ierr);
3176     ierr = ISDestroy(&iscol_o);CHKERRQ(ierr);
3177 
3178     *submat = M;
3179   }
3180   PetscFunctionReturn(0);
3181 }
3182 
3183 PetscErrorCode MatCreateSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3184 {
3185   PetscErrorCode ierr;
3186   IS             iscol_local,isrow_d;
3187   PetscInt       csize;
3188   PetscInt       n,i,j,start,end;
3189   PetscBool      sameRowDist=PETSC_FALSE,sameDist[2],tsameDist[2];
3190   MPI_Comm       comm;
3191 
3192   PetscFunctionBegin;
3193   /* If isrow has same processor distribution as mat,
3194      call MatCreateSubMatrix_MPIAIJ_SameRowDist() to avoid using a hash table with global size of iscol */
3195   if (call == MAT_REUSE_MATRIX) {
3196     ierr = PetscObjectQuery((PetscObject)*newmat,"isrow_d",(PetscObject*)&isrow_d);CHKERRQ(ierr);
3197     if (isrow_d) {
3198       sameRowDist  = PETSC_TRUE;
3199       tsameDist[1] = PETSC_TRUE; /* sameColDist */
3200     } else {
3201       ierr = PetscObjectQuery((PetscObject)*newmat,"SubIScol",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3202       if (iscol_local) {
3203         sameRowDist  = PETSC_TRUE;
3204         tsameDist[1] = PETSC_FALSE; /* !sameColDist */
3205       }
3206     }
3207   } else {
3208     /* Check if isrow has same processor distribution as mat */
3209     sameDist[0] = PETSC_FALSE;
3210     ierr = ISGetLocalSize(isrow,&n);CHKERRQ(ierr);
3211     if (!n) {
3212       sameDist[0] = PETSC_TRUE;
3213     } else {
3214       ierr = ISGetMinMax(isrow,&i,&j);CHKERRQ(ierr);
3215       ierr = MatGetOwnershipRange(mat,&start,&end);CHKERRQ(ierr);
3216       if (i >= start && j < end) {
3217         sameDist[0] = PETSC_TRUE;
3218       }
3219     }
3220 
3221     /* Check if iscol has same processor distribution as mat */
3222     sameDist[1] = PETSC_FALSE;
3223     ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr);
3224     if (!n) {
3225       sameDist[1] = PETSC_TRUE;
3226     } else {
3227       ierr = ISGetMinMax(iscol,&i,&j);CHKERRQ(ierr);
3228       ierr = MatGetOwnershipRangeColumn(mat,&start,&end);CHKERRQ(ierr);
3229       if (i >= start && j < end) sameDist[1] = PETSC_TRUE;
3230     }
3231 
3232     ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3233     ierr = MPIU_Allreduce(&sameDist,&tsameDist,2,MPIU_BOOL,MPI_LAND,comm);CHKERRQ(ierr);
3234     sameRowDist = tsameDist[0];
3235   }
3236 
3237   if (sameRowDist) {
3238     if (tsameDist[1]) {
3239       /* isrow and iscol have same processor distribution as mat */
3240       ierr = MatCreateSubMatrix_MPIAIJ_SameRowColDist(mat,isrow,iscol,call,newmat);CHKERRQ(ierr);
3241     } else {
3242       /* isrow has same processor distribution as mat */
3243       ierr = MatCreateSubMatrix_MPIAIJ_SameRowDist(mat,isrow,iscol,call,newmat);CHKERRQ(ierr);
3244     }
3245     PetscFunctionReturn(0);
3246   }
3247 
3248   /* General case: iscol -> iscol_local which has global size of iscol */
3249   if (call == MAT_REUSE_MATRIX) {
3250     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3251     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3252   } else {
3253     ierr = ISGetSeqIS_Private(mat,iscol,&iscol_local);CHKERRQ(ierr);
3254   }
3255 
3256   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3257   ierr = MatCreateSubMatrix_MPIAIJ_nonscalable(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
3258 
3259   if (call == MAT_INITIAL_MATRIX) {
3260     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3261     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3262   }
3263   PetscFunctionReturn(0);
3264 }
3265 
3266 /*@C
3267      MatCreateMPIAIJWithSeqAIJ - creates a MPIAIJ matrix using SeqAIJ matrices that contain the "diagonal"
3268          and "off-diagonal" part of the matrix in CSR format.
3269 
3270    Collective on MPI_Comm
3271 
3272    Input Parameters:
3273 +  comm - MPI communicator
3274 .  A - "diagonal" portion of matrix
3275 .  B - "off-diagonal" portion of matrix, destroyed by this routine
3276 -  garray - global index of B columns
3277 
3278    Output Parameter:
3279 .   mat - the matrix, with input A as its local diagonal matrix
3280    Level: advanced
3281 
3282    Notes:
3283        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix.
3284        A becomes part of output mat, B is destroyed by this routine. The user cannot use A and B anymore.
3285 
3286 .seealso: MatCreateMPIAIJWithSplitArrays()
3287 @*/
3288 PetscErrorCode MatCreateMPIAIJWithSeqAIJ(MPI_Comm comm,Mat A,Mat B,const PetscInt garray[],Mat *mat)
3289 {
3290   PetscErrorCode ierr;
3291   Mat_MPIAIJ     *maij;
3292   Mat_SeqAIJ     *b=(Mat_SeqAIJ*)B->data,*bnew;
3293   PetscInt       *oi=b->i,*oj=b->j,i,nz,col;
3294   PetscScalar    *oa=b->a;
3295   Mat            Bnew;
3296   PetscInt       m,n,N;
3297 
3298   PetscFunctionBegin;
3299   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
3300   ierr = MatGetSize(A,&m,&n);CHKERRQ(ierr);
3301   if (m != B->rmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Am %D != Bm %D",m,B->rmap->N);
3302   if (A->rmap->bs != B->rmap->bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"A row bs %D != B row bs %D",A->rmap->bs,B->rmap->bs);
3303   if (A->cmap->bs != B->cmap->bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"A column bs %D != B column bs %D",A->cmap->bs,B->cmap->bs);
3304 
3305   /* Get global columns of mat */
3306   ierr = MPIU_Allreduce(&n,&N,1,MPI_INT,MPI_SUM,comm);CHKERRQ(ierr);
3307 
3308   ierr = MatSetSizes(*mat,m,n,PETSC_DECIDE,N);CHKERRQ(ierr);
3309   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
3310   ierr = MatSetBlockSizes(*mat,A->rmap->bs,A->cmap->bs);CHKERRQ(ierr);
3311   maij = (Mat_MPIAIJ*)(*mat)->data;
3312 
3313   (*mat)->preallocated = PETSC_TRUE;
3314 
3315   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
3316   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
3317 
3318   /* Set A as diagonal portion of *mat */
3319   maij->A = A;
3320 
3321   nz = oi[m];
3322   for (i=0; i<nz; i++) {
3323     col   = oj[i];
3324     oj[i] = garray[col];
3325   }
3326 
3327    /* Set Bnew as off-diagonal portion of *mat */
3328   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,N,oi,oj,oa,&Bnew);CHKERRQ(ierr);
3329   bnew        = (Mat_SeqAIJ*)Bnew->data;
3330   bnew->maxnz = b->maxnz; /* allocated nonzeros of B */
3331   maij->B     = Bnew;
3332 
3333   PetscMPIInt rank;
3334   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3335   if (rank == -1) {
3336       printf("[%d] Bnew:\n",rank);
3337       ierr = PetscViewerPushFormat(PETSC_VIEWER_STDOUT_SELF, PETSC_VIEWER_ASCII_INFO);CHKERRQ(ierr);
3338       ierr = MatView(Bnew,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
3339       ierr = PetscViewerPopFormat(PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
3340       if (!rank) printf("--------------------\n");
3341   }
3342 
3343   // Check B == Bnew??? see src/ksp/ksp/examples/tests/runex21_2,3
3344 
3345   if (B->rmap->N != Bnew->rmap->N) SETERRQ2(PETSC_COMM_SELF,0,"BN %d != BnewN %d",B->rmap->N,Bnew->rmap->N);
3346 
3347   b->singlemalloc = PETSC_FALSE; /* B arrays are shared by Bnew */
3348   b->free_a       = PETSC_FALSE;
3349   b->free_ij      = PETSC_FALSE;
3350   ierr = MatDestroy(&B);CHKERRQ(ierr);
3351 
3352   bnew->singlemalloc = PETSC_TRUE; /* arrays will be freed by MatDestroy(&Bnew) */
3353   bnew->free_a       = PETSC_TRUE;
3354   bnew->free_ij      = PETSC_TRUE;
3355 
3356   /* condense columns of maij->B */
3357   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
3358   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3359   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3360   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_FALSE);CHKERRQ(ierr);
3361   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3362   PetscFunctionReturn(0);
3363 }
3364 
3365 extern PetscErrorCode MatCreateSubMatrices_MPIAIJ_SingleIS_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool,Mat*);
3366 
3367 PetscErrorCode MatCreateSubMatrix_MPIAIJ_SameRowDist(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3368 {
3369   PetscErrorCode ierr;
3370   PetscInt       i,m,n,rstart,row,rend,nz,j,bs,cbs;
3371   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
3372   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)mat->data;
3373   Mat            M,Msub,B=a->B,Mnew=NULL;
3374   MatScalar      *aa;
3375   Mat_SeqAIJ     *aij;
3376   PetscInt       *garray = a->garray,*colsub,Ncols;
3377   PetscInt       count,Bn=B->cmap->N,cstart=mat->cmap->rstart,cend=mat->cmap->rend;
3378   IS             iscol_sub,iscmap;
3379   const PetscInt *is_idx,*cmap;
3380   PetscBool      allcolumns=PETSC_FALSE;
3381   IS             iscol_local=NULL;
3382   MPI_Comm       comm;
3383   IS             iscol_d,isrow_d,iscol_o,isgarray;
3384   Mat            Asub=NULL,Bsub=NULL;
3385 
3386   PetscFunctionBegin;
3387   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3388   PetscMPIInt rank;
3389   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3390 
3391   if (call == MAT_REUSE_MATRIX) {
3392     ierr = PetscObjectQuery((PetscObject)*newmat,"SubIScol",(PetscObject*)&iscol_sub);CHKERRQ(ierr);
3393     if (!iscol_sub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"SubIScol passed in was not used before, cannot reuse");
3394     ierr = ISGetLocalSize(iscol_sub,&count);CHKERRQ(ierr);
3395 
3396     ierr = PetscObjectQuery((PetscObject)*newmat,"Subcmap",(PetscObject*)&iscmap);CHKERRQ(ierr);
3397     if (!iscmap) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Subcmap passed in was not used before, cannot reuse");
3398 
3399     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Msub);CHKERRQ(ierr);
3400     if (!Msub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3401 
3402     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol_sub,MAT_REUSE_MATRIX,PETSC_FALSE,&Msub);CHKERRQ(ierr);
3403 
3404   } else { /* call == MAT_INITIAL_MATRIX) */
3405     PetscBool flg;
3406 
3407     ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr);
3408     ierr = ISGetSize(iscol,&Ncols);CHKERRQ(ierr);
3409 
3410     /* (1) iscol -> nonscalable iscol_local */
3411     ierr = ISGetSeqIS_Private(mat,iscol,&iscol_local);CHKERRQ(ierr);
3412     ierr = ISGetLocalSize(iscol_local,&n);CHKERRQ(ierr); /* local size of iscol_local = global columns of newmat */
3413     if (n != Ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"n %d != Ncols %d",n,Ncols);
3414 
3415     /* Check for special case: each processor gets entire matrix columns */
3416     ierr = ISIdentity(iscol_local,&flg);CHKERRQ(ierr);
3417     if (flg && n == mat->cmap->N) allcolumns = PETSC_TRUE;
3418     if (allcolumns) {
3419       iscol_sub = iscol_local;
3420       ierr = PetscObjectReference((PetscObject)iscol_local);CHKERRQ(ierr);
3421       ierr = ISCreateStride(PETSC_COMM_SELF,n,0,1,&iscmap);CHKERRQ(ierr);
3422 
3423     } else {
3424       /* (2) iscol_local -> iscol_sub and iscmap */
3425       PetscInt *idx,*cmap1,k,cbs;
3426 
3427       /* implementation below requires iscol_local be sorted, it can have duplicate indices */
3428       ierr = ISSorted(iscol_local,&flg);CHKERRQ(ierr);
3429       if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"unsorted iscol_local is not implemented yet");
3430 
3431       ierr = PetscMalloc2(Ncols,&idx,Ncols,&cmap1);CHKERRQ(ierr);
3432       ierr = ISGetIndices(iscol_local,&is_idx);CHKERRQ(ierr);
3433       count = 0;
3434       k     = 0;
3435       for (i=0; i<Ncols; i++) {
3436         j = is_idx[i];
3437         if (j >= cstart && j < cend) {
3438           /* diagonal part of mat */
3439           idx[count]     = j;
3440           cmap1[count++] = i; /* column index in submat */
3441         } else if (Bn) {
3442           /* off-diagonal part of mat */
3443           if (j == garray[k]) {
3444             idx[count]     = j;
3445             cmap1[count++] = i;  /* column index in submat */
3446           } else if (j > garray[k]) {
3447             while (j > garray[k] && k < Bn-1) k++;
3448             if (j == garray[k]) {
3449               idx[count]     = j;
3450               cmap1[count++] = i; /* column index in submat */
3451             }
3452           }
3453         }
3454       }
3455       ierr = ISRestoreIndices(iscol_local,&is_idx);CHKERRQ(ierr);
3456 
3457       ierr = ISCreateGeneral(PETSC_COMM_SELF,count,idx,PETSC_COPY_VALUES,&iscol_sub);CHKERRQ(ierr);
3458       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
3459       ierr = ISSetBlockSize(iscol_sub,cbs);CHKERRQ(ierr);
3460 
3461       ierr = ISCreateGeneral(PetscObjectComm((PetscObject)iscol_local),count,cmap1,PETSC_COPY_VALUES,&iscmap);CHKERRQ(ierr);
3462       ierr = PetscFree2(idx,cmap1);CHKERRQ(ierr);
3463     }
3464 
3465     /* (3) Create sequential Msub */
3466     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol_sub,MAT_INITIAL_MATRIX,allcolumns,&Msub);CHKERRQ(ierr);
3467   }
3468 
3469   ierr = ISGetLocalSize(iscol_sub,&count);CHKERRQ(ierr);
3470   aij  = (Mat_SeqAIJ*)(Msub)->data;
3471   ii   = aij->i;
3472   ierr = ISGetIndices(iscmap,&cmap);CHKERRQ(ierr);
3473 
3474   /*
3475       m - number of local rows
3476       Ncols - number of columns (same on all processors)
3477       rstart - first row in new global matrix generated
3478   */
3479   ierr = MatGetSize(Msub,&m,NULL);CHKERRQ(ierr);
3480 
3481   if (call == MAT_INITIAL_MATRIX) {
3482     /* (4) Create parallel newmat */
3483     PetscMPIInt    rank,size;
3484     PetscInt       csize;
3485 
3486     ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3487     ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3488 
3489     /*
3490         Determine the number of non-zeros in the diagonal and off-diagonal
3491         portions of the matrix in order to do correct preallocation
3492     */
3493 
3494     /* first get start and end of "diagonal" columns */
3495     ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3496     if (csize == PETSC_DECIDE) {
3497       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3498       if (mglobal == Ncols) { /* square matrix */
3499         nlocal = m;
3500       } else {
3501         nlocal = Ncols/size + ((Ncols % size) > rank);
3502       }
3503     } else {
3504       nlocal = csize;
3505     }
3506     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3507     rstart = rend - nlocal;
3508     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);
3509 
3510     /* next, compute all the lengths */
3511     jj    = aij->j;
3512     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3513     olens = dlens + m;
3514     for (i=0; i<m; i++) {
3515       jend = ii[i+1] - ii[i];
3516       olen = 0;
3517       dlen = 0;
3518       for (j=0; j<jend; j++) {
3519         if (cmap[*jj] < rstart || cmap[*jj] >= rend) olen++;
3520         else dlen++;
3521         jj++;
3522       }
3523       olens[i] = olen;
3524       dlens[i] = dlen;
3525     }
3526     ierr = MatGetBlockSizes(Msub,&bs,&cbs);CHKERRQ(ierr);
3527 
3528     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3529     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,Ncols);CHKERRQ(ierr);
3530     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3531     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3532     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3533     ierr = PetscFree(dlens);CHKERRQ(ierr);
3534 
3535   } else { /* call == MAT_REUSE_MATRIX */
3536     M    = *newmat;
3537     ierr = MatGetLocalSize(M,&i,NULL);CHKERRQ(ierr);
3538     if (i != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3539     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3540     /*
3541          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3542        rather than the slower MatSetValues().
3543     */
3544     M->was_assembled = PETSC_TRUE;
3545     M->assembled     = PETSC_FALSE;
3546   }
3547 
3548   /* (5) Set values of Msub to *newmat */
3549   ierr = PetscMalloc1(count,&colsub);CHKERRQ(ierr);
3550   ierr = MatGetOwnershipRange(M,&rstart,NULL);CHKERRQ(ierr);
3551 
3552   jj   = aij->j;
3553   aa   = aij->a;
3554   for (i=0; i<m; i++) {
3555     row = rstart + i;
3556     nz  = ii[i+1] - ii[i];
3557     for (j=0; j<nz; j++) colsub[j] = cmap[jj[j]];
3558     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,colsub,aa,INSERT_VALUES);CHKERRQ(ierr);
3559     jj += nz; aa += nz;
3560   }
3561   ierr = ISRestoreIndices(iscmap,&cmap);CHKERRQ(ierr);
3562 
3563   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3564   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3565 
3566   ierr = PetscFree(colsub);CHKERRQ(ierr);
3567 
3568   /* save Msub, iscol_sub and iscmap used in processor for next request */
3569   if (call ==  MAT_INITIAL_MATRIX) {
3570     *newmat = M;
3571     ierr = PetscObjectCompose((PetscObject)(*newmat),"SubMatrix",(PetscObject)Msub);CHKERRQ(ierr);
3572     ierr = MatDestroy(&Msub);CHKERRQ(ierr);
3573 
3574     ierr = PetscObjectCompose((PetscObject)(*newmat),"SubIScol",(PetscObject)iscol_sub);CHKERRQ(ierr);
3575     ierr = ISDestroy(&iscol_sub);CHKERRQ(ierr);
3576 
3577     ierr = PetscObjectCompose((PetscObject)(*newmat),"Subcmap",(PetscObject)iscmap);CHKERRQ(ierr);
3578     ierr = ISDestroy(&iscmap);CHKERRQ(ierr);
3579 
3580     if (iscol_local) {
3581       ierr = PetscObjectCompose((PetscObject)(*newmat),"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3582       ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3583     }
3584   }
3585   PetscFunctionReturn(0);
3586 }
3587 
3588 /*
3589     Not great since it makes two copies of the submatrix, first an SeqAIJ
3590   in local and then by concatenating the local matrices the end result.
3591   Writing it directly would be much like MatCreateSubMatrices_MPIAIJ()
3592 
3593   Note: This requires a sequential iscol with all indices.
3594 */
3595 PetscErrorCode MatCreateSubMatrix_MPIAIJ_nonscalable(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3596 {
3597   PetscErrorCode ierr;
3598   PetscMPIInt    rank,size;
3599   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3600   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
3601   Mat            M,Mreuse;
3602   MatScalar      *aa,*vwork;
3603   MPI_Comm       comm;
3604   Mat_SeqAIJ     *aij;
3605   PetscBool      colflag,allcolumns=PETSC_FALSE;
3606 
3607   PetscFunctionBegin;
3608   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3609   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3610   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3611 
3612   /* Check for special case: each processor gets entire matrix columns */
3613   ierr = ISIdentity(iscol,&colflag);CHKERRQ(ierr);
3614   ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr);
3615   if (colflag && n == mat->cmap->N) allcolumns = PETSC_TRUE;
3616 
3617   if (call ==  MAT_REUSE_MATRIX) {
3618     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3619     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3620     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,allcolumns,&Mreuse);CHKERRQ(ierr);
3621   } else {
3622     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,allcolumns,&Mreuse);CHKERRQ(ierr);
3623   }
3624 
3625   /*
3626       m - number of local rows
3627       n - number of columns (same on all processors)
3628       rstart - first row in new global matrix generated
3629   */
3630   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3631   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3632   if (call == MAT_INITIAL_MATRIX) {
3633     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3634     ii  = aij->i;
3635     jj  = aij->j;
3636 
3637     /*
3638         Determine the number of non-zeros in the diagonal and off-diagonal
3639         portions of the matrix in order to do correct preallocation
3640     */
3641 
3642     /* first get start and end of "diagonal" columns */
3643     if (csize == PETSC_DECIDE) {
3644       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3645       if (mglobal == n) { /* square matrix */
3646         nlocal = m;
3647       } else {
3648         nlocal = n/size + ((n % size) > rank);
3649       }
3650     } else {
3651       nlocal = csize;
3652     }
3653     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3654     rstart = rend - nlocal;
3655     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);
3656 
3657     /* next, compute all the lengths */
3658     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3659     olens = dlens + m;
3660     for (i=0; i<m; i++) {
3661       jend = ii[i+1] - ii[i];
3662       olen = 0;
3663       dlen = 0;
3664       for (j=0; j<jend; j++) {
3665         if (*jj < rstart || *jj >= rend) olen++;
3666         else dlen++;
3667         jj++;
3668       }
3669       olens[i] = olen;
3670       dlens[i] = dlen;
3671     }
3672     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3673     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3674     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3675     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3676     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3677     ierr = PetscFree(dlens);CHKERRQ(ierr);
3678   } else {
3679     PetscInt ml,nl;
3680 
3681     M    = *newmat;
3682     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3683     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3684     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3685     /*
3686          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3687        rather than the slower MatSetValues().
3688     */
3689     M->was_assembled = PETSC_TRUE;
3690     M->assembled     = PETSC_FALSE;
3691   }
3692   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3693   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3694   ii   = aij->i;
3695   jj   = aij->j;
3696   aa   = aij->a;
3697   for (i=0; i<m; i++) {
3698     row   = rstart + i;
3699     nz    = ii[i+1] - ii[i];
3700     cwork = jj;     jj += nz;
3701     vwork = aa;     aa += nz;
3702     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3703   }
3704 
3705   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3706   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3707   *newmat = M;
3708 
3709   /* save submatrix used in processor for next request */
3710   if (call ==  MAT_INITIAL_MATRIX) {
3711     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3712     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3713   }
3714   PetscFunctionReturn(0);
3715 }
3716 
3717 PetscErrorCode MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3718 {
3719   PetscInt       m,cstart, cend,j,nnz,i,d;
3720   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3721   const PetscInt *JJ;
3722   PetscScalar    *values;
3723   PetscErrorCode ierr;
3724   PetscBool      nooffprocentries;
3725 
3726   PetscFunctionBegin;
3727   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3728 
3729   ierr   = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3730   ierr   = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3731   m      = B->rmap->n;
3732   cstart = B->cmap->rstart;
3733   cend   = B->cmap->rend;
3734   rstart = B->rmap->rstart;
3735 
3736   ierr = PetscMalloc2(m,&d_nnz,m,&o_nnz);CHKERRQ(ierr);
3737 
3738 #if defined(PETSC_USE_DEBUGGING)
3739   for (i=0; i<m; i++) {
3740     nnz = Ii[i+1]- Ii[i];
3741     JJ  = J + Ii[i];
3742     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3743     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3744     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);
3745   }
3746 #endif
3747 
3748   for (i=0; i<m; i++) {
3749     nnz     = Ii[i+1]- Ii[i];
3750     JJ      = J + Ii[i];
3751     nnz_max = PetscMax(nnz_max,nnz);
3752     d       = 0;
3753     for (j=0; j<nnz; j++) {
3754       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3755     }
3756     d_nnz[i] = d;
3757     o_nnz[i] = nnz - d;
3758   }
3759   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3760   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3761 
3762   if (v) values = (PetscScalar*)v;
3763   else {
3764     ierr = PetscCalloc1(nnz_max+1,&values);CHKERRQ(ierr);
3765   }
3766 
3767   for (i=0; i<m; i++) {
3768     ii   = i + rstart;
3769     nnz  = Ii[i+1]- Ii[i];
3770     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3771   }
3772   nooffprocentries    = B->nooffprocentries;
3773   B->nooffprocentries = PETSC_TRUE;
3774   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3775   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3776   B->nooffprocentries = nooffprocentries;
3777 
3778   if (!v) {
3779     ierr = PetscFree(values);CHKERRQ(ierr);
3780   }
3781   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3782   PetscFunctionReturn(0);
3783 }
3784 
3785 /*@
3786    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3787    (the default parallel PETSc format).
3788 
3789    Collective on MPI_Comm
3790 
3791    Input Parameters:
3792 +  B - the matrix
3793 .  i - the indices into j for the start of each local row (starts with zero)
3794 .  j - the column indices for each local row (starts with zero)
3795 -  v - optional values in the matrix
3796 
3797    Level: developer
3798 
3799    Notes:
3800        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3801      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3802      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3803 
3804        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3805 
3806        The format which is used for the sparse matrix input, is equivalent to a
3807     row-major ordering.. i.e for the following matrix, the input data expected is
3808     as shown
3809 
3810 $        1 0 0
3811 $        2 0 3     P0
3812 $       -------
3813 $        4 5 6     P1
3814 $
3815 $     Process0 [P0]: rows_owned=[0,1]
3816 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3817 $        j =  {0,0,2}  [size = 3]
3818 $        v =  {1,2,3}  [size = 3]
3819 $
3820 $     Process1 [P1]: rows_owned=[2]
3821 $        i =  {0,3}    [size = nrow+1  = 1+1]
3822 $        j =  {0,1,2}  [size = 3]
3823 $        v =  {4,5,6}  [size = 3]
3824 
3825 .keywords: matrix, aij, compressed row, sparse, parallel
3826 
3827 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MATMPIAIJ,
3828           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3829 @*/
3830 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3831 {
3832   PetscErrorCode ierr;
3833 
3834   PetscFunctionBegin;
3835   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3836   PetscFunctionReturn(0);
3837 }
3838 
3839 /*@C
3840    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3841    (the default parallel PETSc format).  For good matrix assembly performance
3842    the user should preallocate the matrix storage by setting the parameters
3843    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3844    performance can be increased by more than a factor of 50.
3845 
3846    Collective on MPI_Comm
3847 
3848    Input Parameters:
3849 +  B - the matrix
3850 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3851            (same value is used for all local rows)
3852 .  d_nnz - array containing the number of nonzeros in the various rows of the
3853            DIAGONAL portion of the local submatrix (possibly different for each row)
3854            or NULL (PETSC_NULL_INTEGER in Fortran), if d_nz is used to specify the nonzero structure.
3855            The size of this array is equal to the number of local rows, i.e 'm'.
3856            For matrices that will be factored, you must leave room for (and set)
3857            the diagonal entry even if it is zero.
3858 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3859            submatrix (same value is used for all local rows).
3860 -  o_nnz - array containing the number of nonzeros in the various rows of the
3861            OFF-DIAGONAL portion of the local submatrix (possibly different for
3862            each row) or NULL (PETSC_NULL_INTEGER in Fortran), if o_nz is used to specify the nonzero
3863            structure. The size of this array is equal to the number
3864            of local rows, i.e 'm'.
3865 
3866    If the *_nnz parameter is given then the *_nz parameter is ignored
3867 
3868    The AIJ format (also called the Yale sparse matrix format or
3869    compressed row storage (CSR)), is fully compatible with standard Fortran 77
3870    storage.  The stored row and column indices begin with zero.
3871    See Users-Manual: ch_mat for details.
3872 
3873    The parallel matrix is partitioned such that the first m0 rows belong to
3874    process 0, the next m1 rows belong to process 1, the next m2 rows belong
3875    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
3876 
3877    The DIAGONAL portion of the local submatrix of a processor can be defined
3878    as the submatrix which is obtained by extraction the part corresponding to
3879    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
3880    first row that belongs to the processor, r2 is the last row belonging to
3881    the this processor, and c1-c2 is range of indices of the local part of a
3882    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
3883    common case of a square matrix, the row and column ranges are the same and
3884    the DIAGONAL part is also square. The remaining portion of the local
3885    submatrix (mxN) constitute the OFF-DIAGONAL portion.
3886 
3887    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3888 
3889    You can call MatGetInfo() to get information on how effective the preallocation was;
3890    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3891    You can also run with the option -info and look for messages with the string
3892    malloc in them to see if additional memory allocation was needed.
3893 
3894    Example usage:
3895 
3896    Consider the following 8x8 matrix with 34 non-zero values, that is
3897    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3898    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3899    as follows:
3900 
3901 .vb
3902             1  2  0  |  0  3  0  |  0  4
3903     Proc0   0  5  6  |  7  0  0  |  8  0
3904             9  0 10  | 11  0  0  | 12  0
3905     -------------------------------------
3906            13  0 14  | 15 16 17  |  0  0
3907     Proc1   0 18  0  | 19 20 21  |  0  0
3908             0  0  0  | 22 23  0  | 24  0
3909     -------------------------------------
3910     Proc2  25 26 27  |  0  0 28  | 29  0
3911            30  0  0  | 31 32 33  |  0 34
3912 .ve
3913 
3914    This can be represented as a collection of submatrices as:
3915 
3916 .vb
3917       A B C
3918       D E F
3919       G H I
3920 .ve
3921 
3922    Where the submatrices A,B,C are owned by proc0, D,E,F are
3923    owned by proc1, G,H,I are owned by proc2.
3924 
3925    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3926    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3927    The 'M','N' parameters are 8,8, and have the same values on all procs.
3928 
3929    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3930    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3931    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3932    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3933    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3934    matrix, ans [DF] as another SeqAIJ matrix.
3935 
3936    When d_nz, o_nz parameters are specified, d_nz storage elements are
3937    allocated for every row of the local diagonal submatrix, and o_nz
3938    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3939    One way to choose d_nz and o_nz is to use the max nonzerors per local
3940    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3941    In this case, the values of d_nz,o_nz are:
3942 .vb
3943      proc0 : dnz = 2, o_nz = 2
3944      proc1 : dnz = 3, o_nz = 2
3945      proc2 : dnz = 1, o_nz = 4
3946 .ve
3947    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3948    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3949    for proc3. i.e we are using 12+15+10=37 storage locations to store
3950    34 values.
3951 
3952    When d_nnz, o_nnz parameters are specified, the storage is specified
3953    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3954    In the above case the values for d_nnz,o_nnz are:
3955 .vb
3956      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3957      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3958      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3959 .ve
3960    Here the space allocated is sum of all the above values i.e 34, and
3961    hence pre-allocation is perfect.
3962 
3963    Level: intermediate
3964 
3965 .keywords: matrix, aij, compressed row, sparse, parallel
3966 
3967 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
3968           MATMPIAIJ, MatGetInfo(), PetscSplitOwnership()
3969 @*/
3970 PetscErrorCode MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3971 {
3972   PetscErrorCode ierr;
3973 
3974   PetscFunctionBegin;
3975   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3976   PetscValidType(B,1);
3977   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
3978   PetscFunctionReturn(0);
3979 }
3980 
3981 /*@
3982      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
3983          CSR format the local rows.
3984 
3985    Collective on MPI_Comm
3986 
3987    Input Parameters:
3988 +  comm - MPI communicator
3989 .  m - number of local rows (Cannot be PETSC_DECIDE)
3990 .  n - This value should be the same as the local size used in creating the
3991        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3992        calculated if N is given) For square matrices n is almost always m.
3993 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3994 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3995 .   i - row indices
3996 .   j - column indices
3997 -   a - matrix values
3998 
3999    Output Parameter:
4000 .   mat - the matrix
4001 
4002    Level: intermediate
4003 
4004    Notes:
4005        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
4006      thus you CANNOT change the matrix entries by changing the values of a[] after you have
4007      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
4008 
4009        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
4010 
4011        The format which is used for the sparse matrix input, is equivalent to a
4012     row-major ordering.. i.e for the following matrix, the input data expected is
4013     as shown
4014 
4015 $        1 0 0
4016 $        2 0 3     P0
4017 $       -------
4018 $        4 5 6     P1
4019 $
4020 $     Process0 [P0]: rows_owned=[0,1]
4021 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
4022 $        j =  {0,0,2}  [size = 3]
4023 $        v =  {1,2,3}  [size = 3]
4024 $
4025 $     Process1 [P1]: rows_owned=[2]
4026 $        i =  {0,3}    [size = nrow+1  = 1+1]
4027 $        j =  {0,1,2}  [size = 3]
4028 $        v =  {4,5,6}  [size = 3]
4029 
4030 .keywords: matrix, aij, compressed row, sparse, parallel
4031 
4032 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
4033           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
4034 @*/
4035 PetscErrorCode MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
4036 {
4037   PetscErrorCode ierr;
4038 
4039   PetscFunctionBegin;
4040   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
4041   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
4042   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4043   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
4044   /* ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr); */
4045   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
4046   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
4047   PetscFunctionReturn(0);
4048 }
4049 
4050 /*@C
4051    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
4052    (the default parallel PETSc format).  For good matrix assembly performance
4053    the user should preallocate the matrix storage by setting the parameters
4054    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
4055    performance can be increased by more than a factor of 50.
4056 
4057    Collective on MPI_Comm
4058 
4059    Input Parameters:
4060 +  comm - MPI communicator
4061 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
4062            This value should be the same as the local size used in creating the
4063            y vector for the matrix-vector product y = Ax.
4064 .  n - This value should be the same as the local size used in creating the
4065        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
4066        calculated if N is given) For square matrices n is almost always m.
4067 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
4068 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
4069 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
4070            (same value is used for all local rows)
4071 .  d_nnz - array containing the number of nonzeros in the various rows of the
4072            DIAGONAL portion of the local submatrix (possibly different for each row)
4073            or NULL, if d_nz is used to specify the nonzero structure.
4074            The size of this array is equal to the number of local rows, i.e 'm'.
4075 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
4076            submatrix (same value is used for all local rows).
4077 -  o_nnz - array containing the number of nonzeros in the various rows of the
4078            OFF-DIAGONAL portion of the local submatrix (possibly different for
4079            each row) or NULL, if o_nz is used to specify the nonzero
4080            structure. The size of this array is equal to the number
4081            of local rows, i.e 'm'.
4082 
4083    Output Parameter:
4084 .  A - the matrix
4085 
4086    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
4087    MatXXXXSetPreallocation() paradgm instead of this routine directly.
4088    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
4089 
4090    Notes:
4091    If the *_nnz parameter is given then the *_nz parameter is ignored
4092 
4093    m,n,M,N parameters specify the size of the matrix, and its partitioning across
4094    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
4095    storage requirements for this matrix.
4096 
4097    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
4098    processor than it must be used on all processors that share the object for
4099    that argument.
4100 
4101    The user MUST specify either the local or global matrix dimensions
4102    (possibly both).
4103 
4104    The parallel matrix is partitioned across processors such that the
4105    first m0 rows belong to process 0, the next m1 rows belong to
4106    process 1, the next m2 rows belong to process 2 etc.. where
4107    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
4108    values corresponding to [m x N] submatrix.
4109 
4110    The columns are logically partitioned with the n0 columns belonging
4111    to 0th partition, the next n1 columns belonging to the next
4112    partition etc.. where n0,n1,n2... are the input parameter 'n'.
4113 
4114    The DIAGONAL portion of the local submatrix on any given processor
4115    is the submatrix corresponding to the rows and columns m,n
4116    corresponding to the given processor. i.e diagonal matrix on
4117    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
4118    etc. The remaining portion of the local submatrix [m x (N-n)]
4119    constitute the OFF-DIAGONAL portion. The example below better
4120    illustrates this concept.
4121 
4122    For a square global matrix we define each processor's diagonal portion
4123    to be its local rows and the corresponding columns (a square submatrix);
4124    each processor's off-diagonal portion encompasses the remainder of the
4125    local matrix (a rectangular submatrix).
4126 
4127    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
4128 
4129    When calling this routine with a single process communicator, a matrix of
4130    type SEQAIJ is returned.  If a matrix of type MATMPIAIJ is desired for this
4131    type of communicator, use the construction mechanism:
4132      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
4133 
4134    By default, this format uses inodes (identical nodes) when possible.
4135    We search for consecutive rows with the same nonzero structure, thereby
4136    reusing matrix information to achieve increased efficiency.
4137 
4138    Options Database Keys:
4139 +  -mat_no_inode  - Do not use inodes
4140 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
4141 -  -mat_aij_oneindex - Internally use indexing starting at 1
4142         rather than 0.  Note that when calling MatSetValues(),
4143         the user still MUST index entries starting at 0!
4144 
4145 
4146    Example usage:
4147 
4148    Consider the following 8x8 matrix with 34 non-zero values, that is
4149    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
4150    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
4151    as follows:
4152 
4153 .vb
4154             1  2  0  |  0  3  0  |  0  4
4155     Proc0   0  5  6  |  7  0  0  |  8  0
4156             9  0 10  | 11  0  0  | 12  0
4157     -------------------------------------
4158            13  0 14  | 15 16 17  |  0  0
4159     Proc1   0 18  0  | 19 20 21  |  0  0
4160             0  0  0  | 22 23  0  | 24  0
4161     -------------------------------------
4162     Proc2  25 26 27  |  0  0 28  | 29  0
4163            30  0  0  | 31 32 33  |  0 34
4164 .ve
4165 
4166    This can be represented as a collection of submatrices as:
4167 
4168 .vb
4169       A B C
4170       D E F
4171       G H I
4172 .ve
4173 
4174    Where the submatrices A,B,C are owned by proc0, D,E,F are
4175    owned by proc1, G,H,I are owned by proc2.
4176 
4177    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4178    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4179    The 'M','N' parameters are 8,8, and have the same values on all procs.
4180 
4181    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
4182    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
4183    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
4184    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
4185    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
4186    matrix, ans [DF] as another SeqAIJ matrix.
4187 
4188    When d_nz, o_nz parameters are specified, d_nz storage elements are
4189    allocated for every row of the local diagonal submatrix, and o_nz
4190    storage locations are allocated for every row of the OFF-DIAGONAL submat.
4191    One way to choose d_nz and o_nz is to use the max nonzerors per local
4192    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
4193    In this case, the values of d_nz,o_nz are:
4194 .vb
4195      proc0 : dnz = 2, o_nz = 2
4196      proc1 : dnz = 3, o_nz = 2
4197      proc2 : dnz = 1, o_nz = 4
4198 .ve
4199    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
4200    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
4201    for proc3. i.e we are using 12+15+10=37 storage locations to store
4202    34 values.
4203 
4204    When d_nnz, o_nnz parameters are specified, the storage is specified
4205    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
4206    In the above case the values for d_nnz,o_nnz are:
4207 .vb
4208      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
4209      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
4210      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
4211 .ve
4212    Here the space allocated is sum of all the above values i.e 34, and
4213    hence pre-allocation is perfect.
4214 
4215    Level: intermediate
4216 
4217 .keywords: matrix, aij, compressed row, sparse, parallel
4218 
4219 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
4220           MATMPIAIJ, MatCreateMPIAIJWithArrays()
4221 @*/
4222 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)
4223 {
4224   PetscErrorCode ierr;
4225   PetscMPIInt    size;
4226 
4227   PetscFunctionBegin;
4228   ierr = MatCreate(comm,A);CHKERRQ(ierr);
4229   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
4230   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4231   if (size > 1) {
4232     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
4233     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
4234   } else {
4235     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
4236     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
4237   }
4238   PetscFunctionReturn(0);
4239 }
4240 
4241 PetscErrorCode MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
4242 {
4243   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
4244   PetscBool      flg;
4245   PetscErrorCode ierr;
4246 
4247   PetscFunctionBegin;
4248   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&flg);CHKERRQ(ierr);
4249   if (!flg) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"This function requires a MATMPIAIJ matrix as input");
4250   if (Ad)     *Ad     = a->A;
4251   if (Ao)     *Ao     = a->B;
4252   if (colmap) *colmap = a->garray;
4253   PetscFunctionReturn(0);
4254 }
4255 
4256 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
4257 {
4258   PetscErrorCode ierr;
4259   PetscInt       m,N,i,rstart,nnz,Ii;
4260   PetscInt       *indx;
4261   PetscScalar    *values;
4262 
4263   PetscFunctionBegin;
4264   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
4265   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
4266     PetscInt       *dnz,*onz,sum,bs,cbs;
4267 
4268     if (n == PETSC_DECIDE) {
4269       ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
4270     }
4271     /* Check sum(n) = N */
4272     ierr = MPIU_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4273     if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
4274 
4275     ierr    = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4276     rstart -= m;
4277 
4278     ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4279     for (i=0; i<m; i++) {
4280       ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
4281       ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
4282       ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
4283     }
4284 
4285     ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
4286     ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4287     ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
4288     ierr = MatSetBlockSizes(*outmat,bs,cbs);CHKERRQ(ierr);
4289     ierr = MatSetType(*outmat,MATAIJ);CHKERRQ(ierr);
4290     ierr = MatSeqAIJSetPreallocation(*outmat,0,dnz);CHKERRQ(ierr);
4291     ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
4292     ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4293   }
4294 
4295   /* numeric phase */
4296   ierr = MatGetOwnershipRange(*outmat,&rstart,NULL);CHKERRQ(ierr);
4297   for (i=0; i<m; i++) {
4298     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4299     Ii   = i + rstart;
4300     ierr = MatSetValues(*outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4301     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4302   }
4303   ierr = MatAssemblyBegin(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4304   ierr = MatAssemblyEnd(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4305   PetscFunctionReturn(0);
4306 }
4307 
4308 PetscErrorCode MatFileSplit(Mat A,char *outfile)
4309 {
4310   PetscErrorCode    ierr;
4311   PetscMPIInt       rank;
4312   PetscInt          m,N,i,rstart,nnz;
4313   size_t            len;
4314   const PetscInt    *indx;
4315   PetscViewer       out;
4316   char              *name;
4317   Mat               B;
4318   const PetscScalar *values;
4319 
4320   PetscFunctionBegin;
4321   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
4322   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
4323   /* Should this be the type of the diagonal block of A? */
4324   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
4325   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
4326   ierr = MatSetBlockSizesFromMats(B,A,A);CHKERRQ(ierr);
4327   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
4328   ierr = MatSeqAIJSetPreallocation(B,0,NULL);CHKERRQ(ierr);
4329   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
4330   for (i=0; i<m; i++) {
4331     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4332     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4333     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4334   }
4335   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4336   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4337 
4338   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
4339   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
4340   ierr = PetscMalloc1(len+5,&name);CHKERRQ(ierr);
4341   sprintf(name,"%s.%d",outfile,rank);
4342   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
4343   ierr = PetscFree(name);CHKERRQ(ierr);
4344   ierr = MatView(B,out);CHKERRQ(ierr);
4345   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
4346   ierr = MatDestroy(&B);CHKERRQ(ierr);
4347   PetscFunctionReturn(0);
4348 }
4349 
4350 PetscErrorCode MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
4351 {
4352   PetscErrorCode      ierr;
4353   Mat_Merge_SeqsToMPI *merge;
4354   PetscContainer      container;
4355 
4356   PetscFunctionBegin;
4357   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4358   if (container) {
4359     ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4360     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
4361     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
4362     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
4363     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
4364     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
4365     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
4366     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
4367     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
4368     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
4369     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
4370     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
4371     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
4372     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
4373     ierr = PetscFree(merge);CHKERRQ(ierr);
4374     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
4375   }
4376   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
4377   PetscFunctionReturn(0);
4378 }
4379 
4380 #include <../src/mat/utils/freespace.h>
4381 #include <petscbt.h>
4382 
4383 PetscErrorCode MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
4384 {
4385   PetscErrorCode      ierr;
4386   MPI_Comm            comm;
4387   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
4388   PetscMPIInt         size,rank,taga,*len_s;
4389   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
4390   PetscInt            proc,m;
4391   PetscInt            **buf_ri,**buf_rj;
4392   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
4393   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
4394   MPI_Request         *s_waits,*r_waits;
4395   MPI_Status          *status;
4396   MatScalar           *aa=a->a;
4397   MatScalar           **abuf_r,*ba_i;
4398   Mat_Merge_SeqsToMPI *merge;
4399   PetscContainer      container;
4400 
4401   PetscFunctionBegin;
4402   ierr = PetscObjectGetComm((PetscObject)mpimat,&comm);CHKERRQ(ierr);
4403   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4404 
4405   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4406   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4407 
4408   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4409   ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4410 
4411   bi     = merge->bi;
4412   bj     = merge->bj;
4413   buf_ri = merge->buf_ri;
4414   buf_rj = merge->buf_rj;
4415 
4416   ierr   = PetscMalloc1(size,&status);CHKERRQ(ierr);
4417   owners = merge->rowmap->range;
4418   len_s  = merge->len_s;
4419 
4420   /* send and recv matrix values */
4421   /*-----------------------------*/
4422   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
4423   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
4424 
4425   ierr = PetscMalloc1(merge->nsend+1,&s_waits);CHKERRQ(ierr);
4426   for (proc=0,k=0; proc<size; proc++) {
4427     if (!len_s[proc]) continue;
4428     i    = owners[proc];
4429     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
4430     k++;
4431   }
4432 
4433   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
4434   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
4435   ierr = PetscFree(status);CHKERRQ(ierr);
4436 
4437   ierr = PetscFree(s_waits);CHKERRQ(ierr);
4438   ierr = PetscFree(r_waits);CHKERRQ(ierr);
4439 
4440   /* insert mat values of mpimat */
4441   /*----------------------------*/
4442   ierr = PetscMalloc1(N,&ba_i);CHKERRQ(ierr);
4443   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4444 
4445   for (k=0; k<merge->nrecv; k++) {
4446     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4447     nrows       = *(buf_ri_k[k]);
4448     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
4449     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4450   }
4451 
4452   /* set values of ba */
4453   m = merge->rowmap->n;
4454   for (i=0; i<m; i++) {
4455     arow = owners[rank] + i;
4456     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
4457     bnzi = bi[i+1] - bi[i];
4458     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
4459 
4460     /* add local non-zero vals of this proc's seqmat into ba */
4461     anzi   = ai[arow+1] - ai[arow];
4462     aj     = a->j + ai[arow];
4463     aa     = a->a + ai[arow];
4464     nextaj = 0;
4465     for (j=0; nextaj<anzi; j++) {
4466       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4467         ba_i[j] += aa[nextaj++];
4468       }
4469     }
4470 
4471     /* add received vals into ba */
4472     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4473       /* i-th row */
4474       if (i == *nextrow[k]) {
4475         anzi   = *(nextai[k]+1) - *nextai[k];
4476         aj     = buf_rj[k] + *(nextai[k]);
4477         aa     = abuf_r[k] + *(nextai[k]);
4478         nextaj = 0;
4479         for (j=0; nextaj<anzi; j++) {
4480           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4481             ba_i[j] += aa[nextaj++];
4482           }
4483         }
4484         nextrow[k]++; nextai[k]++;
4485       }
4486     }
4487     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
4488   }
4489   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4490   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4491 
4492   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
4493   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
4494   ierr = PetscFree(ba_i);CHKERRQ(ierr);
4495   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4496   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4497   PetscFunctionReturn(0);
4498 }
4499 
4500 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4501 {
4502   PetscErrorCode      ierr;
4503   Mat                 B_mpi;
4504   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
4505   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4506   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
4507   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4508   PetscInt            len,proc,*dnz,*onz,bs,cbs;
4509   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4510   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4511   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
4512   MPI_Status          *status;
4513   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
4514   PetscBT             lnkbt;
4515   Mat_Merge_SeqsToMPI *merge;
4516   PetscContainer      container;
4517 
4518   PetscFunctionBegin;
4519   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4520 
4521   /* make sure it is a PETSc comm */
4522   ierr = PetscCommDuplicate(comm,&comm,NULL);CHKERRQ(ierr);
4523   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4524   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4525 
4526   ierr = PetscNew(&merge);CHKERRQ(ierr);
4527   ierr = PetscMalloc1(size,&status);CHKERRQ(ierr);
4528 
4529   /* determine row ownership */
4530   /*---------------------------------------------------------*/
4531   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
4532   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
4533   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
4534   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
4535   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
4536   ierr = PetscMalloc1(size,&len_si);CHKERRQ(ierr);
4537   ierr = PetscMalloc1(size,&merge->len_s);CHKERRQ(ierr);
4538 
4539   m      = merge->rowmap->n;
4540   owners = merge->rowmap->range;
4541 
4542   /* determine the number of messages to send, their lengths */
4543   /*---------------------------------------------------------*/
4544   len_s = merge->len_s;
4545 
4546   len          = 0; /* length of buf_si[] */
4547   merge->nsend = 0;
4548   for (proc=0; proc<size; proc++) {
4549     len_si[proc] = 0;
4550     if (proc == rank) {
4551       len_s[proc] = 0;
4552     } else {
4553       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4554       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4555     }
4556     if (len_s[proc]) {
4557       merge->nsend++;
4558       nrows = 0;
4559       for (i=owners[proc]; i<owners[proc+1]; i++) {
4560         if (ai[i+1] > ai[i]) nrows++;
4561       }
4562       len_si[proc] = 2*(nrows+1);
4563       len         += len_si[proc];
4564     }
4565   }
4566 
4567   /* determine the number and length of messages to receive for ij-structure */
4568   /*-------------------------------------------------------------------------*/
4569   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
4570   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
4571 
4572   /* post the Irecv of j-structure */
4573   /*-------------------------------*/
4574   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
4575   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
4576 
4577   /* post the Isend of j-structure */
4578   /*--------------------------------*/
4579   ierr = PetscMalloc2(merge->nsend,&si_waits,merge->nsend,&sj_waits);CHKERRQ(ierr);
4580 
4581   for (proc=0, k=0; proc<size; proc++) {
4582     if (!len_s[proc]) continue;
4583     i    = owners[proc];
4584     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
4585     k++;
4586   }
4587 
4588   /* receives and sends of j-structure are complete */
4589   /*------------------------------------------------*/
4590   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
4591   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
4592 
4593   /* send and recv i-structure */
4594   /*---------------------------*/
4595   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
4596   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
4597 
4598   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
4599   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4600   for (proc=0,k=0; proc<size; proc++) {
4601     if (!len_s[proc]) continue;
4602     /* form outgoing message for i-structure:
4603          buf_si[0]:                 nrows to be sent
4604                [1:nrows]:           row index (global)
4605                [nrows+1:2*nrows+1]: i-structure index
4606     */
4607     /*-------------------------------------------*/
4608     nrows       = len_si[proc]/2 - 1;
4609     buf_si_i    = buf_si + nrows+1;
4610     buf_si[0]   = nrows;
4611     buf_si_i[0] = 0;
4612     nrows       = 0;
4613     for (i=owners[proc]; i<owners[proc+1]; i++) {
4614       anzi = ai[i+1] - ai[i];
4615       if (anzi) {
4616         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4617         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4618         nrows++;
4619       }
4620     }
4621     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4622     k++;
4623     buf_si += len_si[proc];
4624   }
4625 
4626   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4627   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4628 
4629   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4630   for (i=0; i<merge->nrecv; i++) {
4631     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);
4632   }
4633 
4634   ierr = PetscFree(len_si);CHKERRQ(ierr);
4635   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4636   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4637   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4638   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4639   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4640   ierr = PetscFree(status);CHKERRQ(ierr);
4641 
4642   /* compute a local seq matrix in each processor */
4643   /*----------------------------------------------*/
4644   /* allocate bi array and free space for accumulating nonzero column info */
4645   ierr  = PetscMalloc1(m+1,&bi);CHKERRQ(ierr);
4646   bi[0] = 0;
4647 
4648   /* create and initialize a linked list */
4649   nlnk = N+1;
4650   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4651 
4652   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4653   len  = ai[owners[rank+1]] - ai[owners[rank]];
4654   ierr = PetscFreeSpaceGet(PetscIntMultTruncate(2,len)+1,&free_space);CHKERRQ(ierr);
4655 
4656   current_space = free_space;
4657 
4658   /* determine symbolic info for each local row */
4659   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4660 
4661   for (k=0; k<merge->nrecv; k++) {
4662     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4663     nrows       = *buf_ri_k[k];
4664     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4665     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4666   }
4667 
4668   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4669   len  = 0;
4670   for (i=0; i<m; i++) {
4671     bnzi = 0;
4672     /* add local non-zero cols of this proc's seqmat into lnk */
4673     arow  = owners[rank] + i;
4674     anzi  = ai[arow+1] - ai[arow];
4675     aj    = a->j + ai[arow];
4676     ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4677     bnzi += nlnk;
4678     /* add received col data into lnk */
4679     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4680       if (i == *nextrow[k]) { /* i-th row */
4681         anzi  = *(nextai[k]+1) - *nextai[k];
4682         aj    = buf_rj[k] + *nextai[k];
4683         ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4684         bnzi += nlnk;
4685         nextrow[k]++; nextai[k]++;
4686       }
4687     }
4688     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4689 
4690     /* if free space is not available, make more free space */
4691     if (current_space->local_remaining<bnzi) {
4692       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(bnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
4693       nspacedouble++;
4694     }
4695     /* copy data into free space, then initialize lnk */
4696     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4697     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
4698 
4699     current_space->array           += bnzi;
4700     current_space->local_used      += bnzi;
4701     current_space->local_remaining -= bnzi;
4702 
4703     bi[i+1] = bi[i] + bnzi;
4704   }
4705 
4706   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4707 
4708   ierr = PetscMalloc1(bi[m]+1,&bj);CHKERRQ(ierr);
4709   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
4710   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4711 
4712   /* create symbolic parallel matrix B_mpi */
4713   /*---------------------------------------*/
4714   ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
4715   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
4716   if (n==PETSC_DECIDE) {
4717     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
4718   } else {
4719     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4720   }
4721   ierr = MatSetBlockSizes(B_mpi,bs,cbs);CHKERRQ(ierr);
4722   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
4723   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
4724   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4725   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
4726 
4727   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4728   B_mpi->assembled    = PETSC_FALSE;
4729   B_mpi->ops->destroy = MatDestroy_MPIAIJ_SeqsToMPI;
4730   merge->bi           = bi;
4731   merge->bj           = bj;
4732   merge->buf_ri       = buf_ri;
4733   merge->buf_rj       = buf_rj;
4734   merge->coi          = NULL;
4735   merge->coj          = NULL;
4736   merge->owners_co    = NULL;
4737 
4738   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
4739 
4740   /* attach the supporting struct to B_mpi for reuse */
4741   ierr    = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
4742   ierr    = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
4743   ierr    = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
4744   ierr    = PetscContainerDestroy(&container);CHKERRQ(ierr);
4745   *mpimat = B_mpi;
4746 
4747   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4748   PetscFunctionReturn(0);
4749 }
4750 
4751 /*@C
4752       MatCreateMPIAIJSumSeqAIJ - Creates a MATMPIAIJ matrix by adding sequential
4753                  matrices from each processor
4754 
4755     Collective on MPI_Comm
4756 
4757    Input Parameters:
4758 +    comm - the communicators the parallel matrix will live on
4759 .    seqmat - the input sequential matrices
4760 .    m - number of local rows (or PETSC_DECIDE)
4761 .    n - number of local columns (or PETSC_DECIDE)
4762 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4763 
4764    Output Parameter:
4765 .    mpimat - the parallel matrix generated
4766 
4767     Level: advanced
4768 
4769    Notes:
4770      The dimensions of the sequential matrix in each processor MUST be the same.
4771      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
4772      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
4773 @*/
4774 PetscErrorCode MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
4775 {
4776   PetscErrorCode ierr;
4777   PetscMPIInt    size;
4778 
4779   PetscFunctionBegin;
4780   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4781   if (size == 1) {
4782     ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4783     if (scall == MAT_INITIAL_MATRIX) {
4784       ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
4785     } else {
4786       ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4787     }
4788     ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4789     PetscFunctionReturn(0);
4790   }
4791   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4792   if (scall == MAT_INITIAL_MATRIX) {
4793     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
4794   }
4795   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
4796   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4797   PetscFunctionReturn(0);
4798 }
4799 
4800 /*@
4801      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MATMPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
4802           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
4803           with MatGetSize()
4804 
4805     Not Collective
4806 
4807    Input Parameters:
4808 +    A - the matrix
4809 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4810 
4811    Output Parameter:
4812 .    A_loc - the local sequential matrix generated
4813 
4814     Level: developer
4815 
4816 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
4817 
4818 @*/
4819 PetscErrorCode MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
4820 {
4821   PetscErrorCode ierr;
4822   Mat_MPIAIJ     *mpimat=(Mat_MPIAIJ*)A->data;
4823   Mat_SeqAIJ     *mat,*a,*b;
4824   PetscInt       *ai,*aj,*bi,*bj,*cmap=mpimat->garray;
4825   MatScalar      *aa,*ba,*cam;
4826   PetscScalar    *ca;
4827   PetscInt       am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
4828   PetscInt       *ci,*cj,col,ncols_d,ncols_o,jo;
4829   PetscBool      match;
4830   MPI_Comm       comm;
4831   PetscMPIInt    size;
4832 
4833   PetscFunctionBegin;
4834   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4835   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
4836   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4837   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4838   if (size == 1 && scall == MAT_REUSE_MATRIX) PetscFunctionReturn(0);
4839 
4840   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4841   a = (Mat_SeqAIJ*)(mpimat->A)->data;
4842   b = (Mat_SeqAIJ*)(mpimat->B)->data;
4843   ai = a->i; aj = a->j; bi = b->i; bj = b->j;
4844   aa = a->a; ba = b->a;
4845   if (scall == MAT_INITIAL_MATRIX) {
4846     if (size == 1) {
4847       ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ai,aj,aa,A_loc);CHKERRQ(ierr);
4848       PetscFunctionReturn(0);
4849     }
4850 
4851     ierr  = PetscMalloc1(1+am,&ci);CHKERRQ(ierr);
4852     ci[0] = 0;
4853     for (i=0; i<am; i++) {
4854       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
4855     }
4856     ierr = PetscMalloc1(1+ci[am],&cj);CHKERRQ(ierr);
4857     ierr = PetscMalloc1(1+ci[am],&ca);CHKERRQ(ierr);
4858     k    = 0;
4859     for (i=0; i<am; i++) {
4860       ncols_o = bi[i+1] - bi[i];
4861       ncols_d = ai[i+1] - ai[i];
4862       /* off-diagonal portion of A */
4863       for (jo=0; jo<ncols_o; jo++) {
4864         col = cmap[*bj];
4865         if (col >= cstart) break;
4866         cj[k]   = col; bj++;
4867         ca[k++] = *ba++;
4868       }
4869       /* diagonal portion of A */
4870       for (j=0; j<ncols_d; j++) {
4871         cj[k]   = cstart + *aj++;
4872         ca[k++] = *aa++;
4873       }
4874       /* off-diagonal portion of A */
4875       for (j=jo; j<ncols_o; j++) {
4876         cj[k]   = cmap[*bj++];
4877         ca[k++] = *ba++;
4878       }
4879     }
4880     /* put together the new matrix */
4881     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
4882     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4883     /* Since these are PETSc arrays, change flags to free them as necessary. */
4884     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
4885     mat->free_a  = PETSC_TRUE;
4886     mat->free_ij = PETSC_TRUE;
4887     mat->nonew   = 0;
4888   } else if (scall == MAT_REUSE_MATRIX) {
4889     mat=(Mat_SeqAIJ*)(*A_loc)->data;
4890     ci = mat->i; cj = mat->j; cam = mat->a;
4891     for (i=0; i<am; i++) {
4892       /* off-diagonal portion of A */
4893       ncols_o = bi[i+1] - bi[i];
4894       for (jo=0; jo<ncols_o; jo++) {
4895         col = cmap[*bj];
4896         if (col >= cstart) break;
4897         *cam++ = *ba++; bj++;
4898       }
4899       /* diagonal portion of A */
4900       ncols_d = ai[i+1] - ai[i];
4901       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
4902       /* off-diagonal portion of A */
4903       for (j=jo; j<ncols_o; j++) {
4904         *cam++ = *ba++; bj++;
4905       }
4906     }
4907   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
4908   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4909   PetscFunctionReturn(0);
4910 }
4911 
4912 /*@C
4913      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MATMPIAIJ matrix by taking all its local rows and NON-ZERO columns
4914 
4915     Not Collective
4916 
4917    Input Parameters:
4918 +    A - the matrix
4919 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4920 -    row, col - index sets of rows and columns to extract (or NULL)
4921 
4922    Output Parameter:
4923 .    A_loc - the local sequential matrix generated
4924 
4925     Level: developer
4926 
4927 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
4928 
4929 @*/
4930 PetscErrorCode MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
4931 {
4932   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4933   PetscErrorCode ierr;
4934   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
4935   IS             isrowa,iscola;
4936   Mat            *aloc;
4937   PetscBool      match;
4938 
4939   PetscFunctionBegin;
4940   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4941   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
4942   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4943   if (!row) {
4944     start = A->rmap->rstart; end = A->rmap->rend;
4945     ierr  = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
4946   } else {
4947     isrowa = *row;
4948   }
4949   if (!col) {
4950     start = A->cmap->rstart;
4951     cmap  = a->garray;
4952     nzA   = a->A->cmap->n;
4953     nzB   = a->B->cmap->n;
4954     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4955     ncols = 0;
4956     for (i=0; i<nzB; i++) {
4957       if (cmap[i] < start) idx[ncols++] = cmap[i];
4958       else break;
4959     }
4960     imark = i;
4961     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
4962     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
4963     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
4964   } else {
4965     iscola = *col;
4966   }
4967   if (scall != MAT_INITIAL_MATRIX) {
4968     ierr    = PetscMalloc1(1,&aloc);CHKERRQ(ierr);
4969     aloc[0] = *A_loc;
4970   }
4971   ierr   = MatCreateSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
4972   *A_loc = aloc[0];
4973   ierr   = PetscFree(aloc);CHKERRQ(ierr);
4974   if (!row) {
4975     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
4976   }
4977   if (!col) {
4978     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
4979   }
4980   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4981   PetscFunctionReturn(0);
4982 }
4983 
4984 /*@C
4985     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
4986 
4987     Collective on Mat
4988 
4989    Input Parameters:
4990 +    A,B - the matrices in mpiaij format
4991 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4992 -    rowb, colb - index sets of rows and columns of B to extract (or NULL)
4993 
4994    Output Parameter:
4995 +    rowb, colb - index sets of rows and columns of B to extract
4996 -    B_seq - the sequential matrix generated
4997 
4998     Level: developer
4999 
5000 @*/
5001 PetscErrorCode MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
5002 {
5003   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
5004   PetscErrorCode ierr;
5005   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
5006   IS             isrowb,iscolb;
5007   Mat            *bseq=NULL;
5008 
5009   PetscFunctionBegin;
5010   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
5011     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);
5012   }
5013   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
5014 
5015   if (scall == MAT_INITIAL_MATRIX) {
5016     start = A->cmap->rstart;
5017     cmap  = a->garray;
5018     nzA   = a->A->cmap->n;
5019     nzB   = a->B->cmap->n;
5020     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
5021     ncols = 0;
5022     for (i=0; i<nzB; i++) {  /* row < local row index */
5023       if (cmap[i] < start) idx[ncols++] = cmap[i];
5024       else break;
5025     }
5026     imark = i;
5027     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
5028     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
5029     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
5030     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
5031   } else {
5032     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
5033     isrowb  = *rowb; iscolb = *colb;
5034     ierr    = PetscMalloc1(1,&bseq);CHKERRQ(ierr);
5035     bseq[0] = *B_seq;
5036   }
5037   ierr   = MatCreateSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
5038   *B_seq = bseq[0];
5039   ierr   = PetscFree(bseq);CHKERRQ(ierr);
5040   if (!rowb) {
5041     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
5042   } else {
5043     *rowb = isrowb;
5044   }
5045   if (!colb) {
5046     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
5047   } else {
5048     *colb = iscolb;
5049   }
5050   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
5051   PetscFunctionReturn(0);
5052 }
5053 
5054 /*
5055     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
5056     of the OFF-DIAGONAL portion of local A
5057 
5058     Collective on Mat
5059 
5060    Input Parameters:
5061 +    A,B - the matrices in mpiaij format
5062 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5063 
5064    Output Parameter:
5065 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
5066 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
5067 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
5068 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
5069 
5070     Level: developer
5071 
5072 */
5073 PetscErrorCode MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
5074 {
5075   VecScatter_MPI_General *gen_to,*gen_from;
5076   PetscErrorCode         ierr;
5077   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
5078   Mat_SeqAIJ             *b_oth;
5079   VecScatter             ctx =a->Mvctx;
5080   MPI_Comm               comm;
5081   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
5082   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
5083   PetscInt               *rvalues,*svalues;
5084   MatScalar              *b_otha,*bufa,*bufA;
5085   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
5086   MPI_Request            *rwaits = NULL,*swaits = NULL;
5087   MPI_Status             *sstatus,rstatus;
5088   PetscMPIInt            jj,size;
5089   PetscInt               *cols,sbs,rbs;
5090   PetscScalar            *vals;
5091 
5092   PetscFunctionBegin;
5093   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
5094   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
5095 
5096   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
5097     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);
5098   }
5099   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5100   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
5101 
5102   if (size == 1) {
5103     startsj_s = NULL;
5104     bufa_ptr  = NULL;
5105     *B_oth    = NULL;
5106     PetscFunctionReturn(0);
5107   }
5108 
5109   gen_to   = (VecScatter_MPI_General*)ctx->todata;
5110   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
5111   nrecvs   = gen_from->n;
5112   nsends   = gen_to->n;
5113 
5114   ierr    = PetscMalloc2(nrecvs,&rwaits,nsends,&swaits);CHKERRQ(ierr);
5115   srow    = gen_to->indices;    /* local row index to be sent */
5116   sstarts = gen_to->starts;
5117   sprocs  = gen_to->procs;
5118   sstatus = gen_to->sstatus;
5119   sbs     = gen_to->bs;
5120   rstarts = gen_from->starts;
5121   rprocs  = gen_from->procs;
5122   rbs     = gen_from->bs;
5123 
5124   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
5125   if (scall == MAT_INITIAL_MATRIX) {
5126     /* i-array */
5127     /*---------*/
5128     /*  post receives */
5129     ierr = PetscMalloc1(rbs*(rstarts[nrecvs] - rstarts[0]),&rvalues);CHKERRQ(ierr);
5130     for (i=0; i<nrecvs; i++) {
5131       rowlen = rvalues + rstarts[i]*rbs;
5132       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
5133       ierr   = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5134     }
5135 
5136     /* pack the outgoing message */
5137     ierr = PetscMalloc2(nsends+1,&sstartsj,nrecvs+1,&rstartsj);CHKERRQ(ierr);
5138 
5139     sstartsj[0] = 0;
5140     rstartsj[0] = 0;
5141     len         = 0; /* total length of j or a array to be sent */
5142     k           = 0;
5143     ierr = PetscMalloc1(sbs*(sstarts[nsends] - sstarts[0]),&svalues);CHKERRQ(ierr);
5144     for (i=0; i<nsends; i++) {
5145       rowlen = svalues + sstarts[i]*sbs;
5146       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
5147       for (j=0; j<nrows; j++) {
5148         row = srow[k] + B->rmap->range[rank]; /* global row idx */
5149         for (l=0; l<sbs; l++) {
5150           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr); /* rowlength */
5151 
5152           rowlen[j*sbs+l] = ncols;
5153 
5154           len += ncols;
5155           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr);
5156         }
5157         k++;
5158       }
5159       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5160 
5161       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
5162     }
5163     /* recvs and sends of i-array are completed */
5164     i = nrecvs;
5165     while (i--) {
5166       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5167     }
5168     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5169     ierr = PetscFree(svalues);CHKERRQ(ierr);
5170 
5171     /* allocate buffers for sending j and a arrays */
5172     ierr = PetscMalloc1(len+1,&bufj);CHKERRQ(ierr);
5173     ierr = PetscMalloc1(len+1,&bufa);CHKERRQ(ierr);
5174 
5175     /* create i-array of B_oth */
5176     ierr = PetscMalloc1(aBn+2,&b_othi);CHKERRQ(ierr);
5177 
5178     b_othi[0] = 0;
5179     len       = 0; /* total length of j or a array to be received */
5180     k         = 0;
5181     for (i=0; i<nrecvs; i++) {
5182       rowlen = rvalues + rstarts[i]*rbs;
5183       nrows  = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be received */
5184       for (j=0; j<nrows; j++) {
5185         b_othi[k+1] = b_othi[k] + rowlen[j];
5186         ierr = PetscIntSumError(rowlen[j],len,&len);CHKERRQ(ierr);
5187         k++;
5188       }
5189       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
5190     }
5191     ierr = PetscFree(rvalues);CHKERRQ(ierr);
5192 
5193     /* allocate space for j and a arrrays of B_oth */
5194     ierr = PetscMalloc1(b_othi[aBn]+1,&b_othj);CHKERRQ(ierr);
5195     ierr = PetscMalloc1(b_othi[aBn]+1,&b_otha);CHKERRQ(ierr);
5196 
5197     /* j-array */
5198     /*---------*/
5199     /*  post receives of j-array */
5200     for (i=0; i<nrecvs; i++) {
5201       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5202       ierr  = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5203     }
5204 
5205     /* pack the outgoing message j-array */
5206     k = 0;
5207     for (i=0; i<nsends; i++) {
5208       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5209       bufJ  = bufj+sstartsj[i];
5210       for (j=0; j<nrows; j++) {
5211         row = srow[k++] + B->rmap->range[rank];  /* global row idx */
5212         for (ll=0; ll<sbs; ll++) {
5213           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
5214           for (l=0; l<ncols; l++) {
5215             *bufJ++ = cols[l];
5216           }
5217           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
5218         }
5219       }
5220       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5221     }
5222 
5223     /* recvs and sends of j-array are completed */
5224     i = nrecvs;
5225     while (i--) {
5226       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5227     }
5228     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5229   } else if (scall == MAT_REUSE_MATRIX) {
5230     sstartsj = *startsj_s;
5231     rstartsj = *startsj_r;
5232     bufa     = *bufa_ptr;
5233     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
5234     b_otha   = b_oth->a;
5235   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
5236 
5237   /* a-array */
5238   /*---------*/
5239   /*  post receives of a-array */
5240   for (i=0; i<nrecvs; i++) {
5241     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5242     ierr  = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5243   }
5244 
5245   /* pack the outgoing message a-array */
5246   k = 0;
5247   for (i=0; i<nsends; i++) {
5248     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5249     bufA  = bufa+sstartsj[i];
5250     for (j=0; j<nrows; j++) {
5251       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
5252       for (ll=0; ll<sbs; ll++) {
5253         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
5254         for (l=0; l<ncols; l++) {
5255           *bufA++ = vals[l];
5256         }
5257         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
5258       }
5259     }
5260     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5261   }
5262   /* recvs and sends of a-array are completed */
5263   i = nrecvs;
5264   while (i--) {
5265     ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5266   }
5267   if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5268   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
5269 
5270   if (scall == MAT_INITIAL_MATRIX) {
5271     /* put together the new matrix */
5272     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
5273 
5274     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
5275     /* Since these are PETSc arrays, change flags to free them as necessary. */
5276     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
5277     b_oth->free_a  = PETSC_TRUE;
5278     b_oth->free_ij = PETSC_TRUE;
5279     b_oth->nonew   = 0;
5280 
5281     ierr = PetscFree(bufj);CHKERRQ(ierr);
5282     if (!startsj_s || !bufa_ptr) {
5283       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
5284       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
5285     } else {
5286       *startsj_s = sstartsj;
5287       *startsj_r = rstartsj;
5288       *bufa_ptr  = bufa;
5289     }
5290   }
5291   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5292   PetscFunctionReturn(0);
5293 }
5294 
5295 /*@C
5296   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
5297 
5298   Not Collective
5299 
5300   Input Parameters:
5301 . A - The matrix in mpiaij format
5302 
5303   Output Parameter:
5304 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
5305 . colmap - A map from global column index to local index into lvec
5306 - multScatter - A scatter from the argument of a matrix-vector product to lvec
5307 
5308   Level: developer
5309 
5310 @*/
5311 #if defined(PETSC_USE_CTABLE)
5312 PetscErrorCode MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
5313 #else
5314 PetscErrorCode MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
5315 #endif
5316 {
5317   Mat_MPIAIJ *a;
5318 
5319   PetscFunctionBegin;
5320   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
5321   PetscValidPointer(lvec, 2);
5322   PetscValidPointer(colmap, 3);
5323   PetscValidPointer(multScatter, 4);
5324   a = (Mat_MPIAIJ*) A->data;
5325   if (lvec) *lvec = a->lvec;
5326   if (colmap) *colmap = a->colmap;
5327   if (multScatter) *multScatter = a->Mvctx;
5328   PetscFunctionReturn(0);
5329 }
5330 
5331 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
5332 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
5333 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
5334 #if defined(PETSC_HAVE_ELEMENTAL)
5335 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
5336 #endif
5337 #if defined(PETSC_HAVE_HYPRE)
5338 PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat,MatType,MatReuse,Mat*);
5339 PETSC_INTERN PetscErrorCode MatMatMatMult_Transpose_AIJ_AIJ(Mat,Mat,Mat,MatReuse,PetscReal,Mat*);
5340 #endif
5341 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_IS(Mat,MatType,MatReuse,Mat*);
5342 
5343 /*
5344     Computes (B'*A')' since computing B*A directly is untenable
5345 
5346                n                       p                          p
5347         (              )       (              )         (                  )
5348       m (      A       )  *  n (       B      )   =   m (         C        )
5349         (              )       (              )         (                  )
5350 
5351 */
5352 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
5353 {
5354   PetscErrorCode ierr;
5355   Mat            At,Bt,Ct;
5356 
5357   PetscFunctionBegin;
5358   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
5359   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
5360   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
5361   ierr = MatDestroy(&At);CHKERRQ(ierr);
5362   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
5363   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
5364   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
5365   PetscFunctionReturn(0);
5366 }
5367 
5368 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
5369 {
5370   PetscErrorCode ierr;
5371   PetscInt       m=A->rmap->n,n=B->cmap->n;
5372   Mat            Cmat;
5373 
5374   PetscFunctionBegin;
5375   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);
5376   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
5377   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
5378   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
5379   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
5380   ierr = MatMPIDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
5381   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5382   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5383 
5384   Cmat->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
5385 
5386   *C = Cmat;
5387   PetscFunctionReturn(0);
5388 }
5389 
5390 /* ----------------------------------------------------------------*/
5391 PETSC_INTERN PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
5392 {
5393   PetscErrorCode ierr;
5394 
5395   PetscFunctionBegin;
5396   if (scall == MAT_INITIAL_MATRIX) {
5397     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5398     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
5399     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5400   }
5401   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5402   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
5403   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5404   PetscFunctionReturn(0);
5405 }
5406 
5407 /*MC
5408    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
5409 
5410    Options Database Keys:
5411 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
5412 
5413   Level: beginner
5414 
5415 .seealso: MatCreateAIJ()
5416 M*/
5417 
5418 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
5419 {
5420   Mat_MPIAIJ     *b;
5421   PetscErrorCode ierr;
5422   PetscMPIInt    size;
5423 
5424   PetscFunctionBegin;
5425   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
5426 
5427   ierr          = PetscNewLog(B,&b);CHKERRQ(ierr);
5428   B->data       = (void*)b;
5429   ierr          = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
5430   B->assembled  = PETSC_FALSE;
5431   B->insertmode = NOT_SET_VALUES;
5432   b->size       = size;
5433 
5434   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank);CHKERRQ(ierr);
5435 
5436   /* build cache for off array entries formed */
5437   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash);CHKERRQ(ierr);
5438 
5439   b->donotstash  = PETSC_FALSE;
5440   b->colmap      = 0;
5441   b->garray      = 0;
5442   b->roworiented = PETSC_TRUE;
5443 
5444   /* stuff used for matrix vector multiply */
5445   b->lvec  = NULL;
5446   b->Mvctx = NULL;
5447 
5448   /* stuff for MatGetRow() */
5449   b->rowindices   = 0;
5450   b->rowvalues    = 0;
5451   b->getrowactive = PETSC_FALSE;
5452 
5453   /* flexible pointer used in CUSP/CUSPARSE classes */
5454   b->spptr = NULL;
5455 
5456   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetUseScalableIncreaseOverlap_C",MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ);CHKERRQ(ierr);
5457   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ);CHKERRQ(ierr);
5458   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
5459   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
5460   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
5461   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
5462   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
5463   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
5464   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
5465   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
5466 #if defined(PETSC_HAVE_ELEMENTAL)
5467   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_elemental_C",MatConvert_MPIAIJ_Elemental);CHKERRQ(ierr);
5468 #endif
5469 #if defined(PETSC_HAVE_HYPRE)
5470   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_hypre_C",MatConvert_AIJ_HYPRE);CHKERRQ(ierr);
5471 #endif
5472   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_is_C",MatConvert_MPIAIJ_IS);CHKERRQ(ierr);
5473   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
5474   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
5475   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
5476 #if defined(PETSC_HAVE_HYPRE)
5477   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMatMult_transpose_mpiaij_mpiaij_C",MatMatMatMult_Transpose_AIJ_AIJ);CHKERRQ(ierr);
5478 #endif
5479   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
5480   PetscFunctionReturn(0);
5481 }
5482 
5483 /*@C
5484      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
5485          and "off-diagonal" part of the matrix in CSR format.
5486 
5487    Collective on MPI_Comm
5488 
5489    Input Parameters:
5490 +  comm - MPI communicator
5491 .  m - number of local rows (Cannot be PETSC_DECIDE)
5492 .  n - This value should be the same as the local size used in creating the
5493        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
5494        calculated if N is given) For square matrices n is almost always m.
5495 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
5496 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
5497 .   i - row indices for "diagonal" portion of matrix
5498 .   j - column indices
5499 .   a - matrix values
5500 .   oi - row indices for "off-diagonal" portion of matrix
5501 .   oj - column indices
5502 -   oa - matrix values
5503 
5504    Output Parameter:
5505 .   mat - the matrix
5506 
5507    Level: advanced
5508 
5509    Notes:
5510        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
5511        must free the arrays once the matrix has been destroyed and not before.
5512 
5513        The i and j indices are 0 based
5514 
5515        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
5516 
5517        This sets local rows and cannot be used to set off-processor values.
5518 
5519        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
5520        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
5521        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
5522        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
5523        keep track of the underlying array. Use MatSetOption(A,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
5524        communication if it is known that only local entries will be set.
5525 
5526 .keywords: matrix, aij, compressed row, sparse, parallel
5527 
5528 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
5529           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
5530 @*/
5531 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)
5532 {
5533   PetscErrorCode ierr;
5534   Mat_MPIAIJ     *maij;
5535 
5536   PetscFunctionBegin;
5537   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
5538   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
5539   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
5540   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
5541   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
5542   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
5543   maij = (Mat_MPIAIJ*) (*mat)->data;
5544 
5545   (*mat)->preallocated = PETSC_TRUE;
5546 
5547   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
5548   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
5549 
5550   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
5551   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
5552 
5553   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5554   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5555   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5556   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5557 
5558   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
5559   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5560   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5561   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_FALSE);CHKERRQ(ierr);
5562   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
5563   PetscFunctionReturn(0);
5564 }
5565 
5566 /*
5567     Special version for direct calls from Fortran
5568 */
5569 #include <petsc/private/fortranimpl.h>
5570 
5571 /* Change these macros so can be used in void function */
5572 #undef CHKERRQ
5573 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
5574 #undef SETERRQ2
5575 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5576 #undef SETERRQ3
5577 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5578 #undef SETERRQ
5579 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
5580 
5581 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5582 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
5583 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5584 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
5585 #else
5586 #endif
5587 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)
5588 {
5589   Mat            mat  = *mmat;
5590   PetscInt       m    = *mm, n = *mn;
5591   InsertMode     addv = *maddv;
5592   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
5593   PetscScalar    value;
5594   PetscErrorCode ierr;
5595 
5596   MatCheckPreallocated(mat,1);
5597   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
5598 
5599 #if defined(PETSC_USE_DEBUG)
5600   else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
5601 #endif
5602   {
5603     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
5604     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
5605     PetscBool roworiented = aij->roworiented;
5606 
5607     /* Some Variables required in the macro */
5608     Mat        A                 = aij->A;
5609     Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
5610     PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
5611     MatScalar  *aa               = a->a;
5612     PetscBool  ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
5613     Mat        B                 = aij->B;
5614     Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
5615     PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5616     MatScalar  *ba               = b->a;
5617 
5618     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5619     PetscInt  nonew = a->nonew;
5620     MatScalar *ap1,*ap2;
5621 
5622     PetscFunctionBegin;
5623     for (i=0; i<m; i++) {
5624       if (im[i] < 0) continue;
5625 #if defined(PETSC_USE_DEBUG)
5626       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);
5627 #endif
5628       if (im[i] >= rstart && im[i] < rend) {
5629         row      = im[i] - rstart;
5630         lastcol1 = -1;
5631         rp1      = aj + ai[row];
5632         ap1      = aa + ai[row];
5633         rmax1    = aimax[row];
5634         nrow1    = ailen[row];
5635         low1     = 0;
5636         high1    = nrow1;
5637         lastcol2 = -1;
5638         rp2      = bj + bi[row];
5639         ap2      = ba + bi[row];
5640         rmax2    = bimax[row];
5641         nrow2    = bilen[row];
5642         low2     = 0;
5643         high2    = nrow2;
5644 
5645         for (j=0; j<n; j++) {
5646           if (roworiented) value = v[i*n+j];
5647           else value = v[i+j*m];
5648           if (in[j] >= cstart && in[j] < cend) {
5649             col = in[j] - cstart;
5650             if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
5651             MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
5652           } else if (in[j] < 0) continue;
5653 #if defined(PETSC_USE_DEBUG)
5654           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);
5655 #endif
5656           else {
5657             if (mat->was_assembled) {
5658               if (!aij->colmap) {
5659                 ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5660               }
5661 #if defined(PETSC_USE_CTABLE)
5662               ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5663               col--;
5664 #else
5665               col = aij->colmap[in[j]] - 1;
5666 #endif
5667               if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
5668               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5669                 ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5670                 col  =  in[j];
5671                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5672                 B     = aij->B;
5673                 b     = (Mat_SeqAIJ*)B->data;
5674                 bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5675                 rp2   = bj + bi[row];
5676                 ap2   = ba + bi[row];
5677                 rmax2 = bimax[row];
5678                 nrow2 = bilen[row];
5679                 low2  = 0;
5680                 high2 = nrow2;
5681                 bm    = aij->B->rmap->n;
5682                 ba    = b->a;
5683               }
5684             } else col = in[j];
5685             MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
5686           }
5687         }
5688       } else if (!aij->donotstash) {
5689         if (roworiented) {
5690           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5691         } else {
5692           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5693         }
5694       }
5695     }
5696   }
5697   PetscFunctionReturnVoid();
5698 }
5699 
5700