xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision 1fd43edeb478cbe4da75215f5ae558ab45665f4d)
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   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)mat->data;
3110   Mat            M=NULL;
3111   MPI_Comm       comm;
3112   IS             iscol_d,isrow_d,iscol_o,isgarray;
3113   Mat            Asub=NULL,Bsub=NULL;
3114 
3115   PetscFunctionBegin;
3116   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3117   PetscMPIInt rank;
3118   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3119 
3120   if (call == MAT_REUSE_MATRIX) {
3121     Mat_MPIAIJ *matsub=(Mat_MPIAIJ*)(*submat)->data;
3122 
3123     ierr = PetscObjectQuery((PetscObject)*submat,"isrow_d",(PetscObject*)&isrow_d);CHKERRQ(ierr);
3124     if (!isrow_d) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"isrow_d passed in was not used before, cannot reuse");
3125 
3126     ierr = PetscObjectQuery((PetscObject)*submat,"iscol_d",(PetscObject*)&iscol_d);CHKERRQ(ierr);
3127     if (!iscol_d) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"iscol_d passed in was not used before, cannot reuse");
3128 
3129     ierr = PetscObjectQuery((PetscObject)*submat,"iscol_o",(PetscObject*)&iscol_o);CHKERRQ(ierr);
3130     if (!iscol_o) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"iscol_o passed in was not used before, cannot reuse");
3131 
3132     /* Update *submat via diagonal and off-diagonal portions of submat */
3133     ierr = MatCreateSubMatrix_SeqAIJ(a->A,isrow_d,iscol_d,PETSC_DECIDE,call,&matsub->A);CHKERRQ(ierr);
3134     ierr = MatCreateSubMatrix_SeqAIJ(a->B,isrow_d,iscol_o,PETSC_DECIDE,call,&matsub->B);CHKERRQ(ierr);
3135     ierr = MatAssemblyBegin(*submat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3136     ierr = MatAssemblyEnd(*submat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3137 
3138   } else { /* call == MAT_INITIAL_MATRIX) */
3139     const PetscInt *garray1;
3140 
3141     ierr = ISGetSeqIS_SameColDist_Private(mat,isrow,iscol,&isrow_d,&iscol_d,&iscol_o,&isgarray);CHKERRQ(ierr);
3142 
3143     ierr = MatCreateSubMatrix_SeqAIJ(a->A,isrow_d,iscol_d,PETSC_DECIDE,call,&Asub);CHKERRQ(ierr);
3144     ierr = MatCreateSubMatrix_SeqAIJ(a->B,isrow_d,iscol_o,PETSC_DECIDE,call,&Bsub);CHKERRQ(ierr);
3145 
3146     PetscInt BsubN = Bsub->cmap->N;
3147     ierr = ISGetIndices(isgarray,&garray1);CHKERRQ(ierr);
3148     ierr = MatCreateMPIAIJWithSeqAIJ(comm,Asub,Bsub,garray1,&M);CHKERRQ(ierr);
3149     ierr = ISRestoreIndices(isgarray,&garray1);CHKERRQ(ierr);
3150 
3151     /* Check is Bsub == M->B? If not, compress iscol_o accordingly */
3152     //========================
3153     a = (Mat_MPIAIJ*)M->data;
3154     if (BsubN > a->B->cmap->N) {
3155       printf("[%d] Bsub->cmap->N %d != a->B->cmap->N %d\n",rank,BsubN,a->B->cmap->N);
3156     } else if (BsubN < a->B->cmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Columns of Bsub cannot be smaller than B's",BsubN,a->B->cmap->N);
3157 
3158 
3159     //======================
3160     ierr = ISDestroy(&isgarray);CHKERRQ(ierr);
3161 
3162     /* Save isrow_d, iscol_d and iscol_o used in processor for next request */
3163     ierr = PetscObjectCompose((PetscObject)M,"isrow_d",(PetscObject)isrow_d);CHKERRQ(ierr);
3164     ierr = ISDestroy(&isrow_d);CHKERRQ(ierr);
3165 
3166     ierr = PetscObjectCompose((PetscObject)M,"iscol_d",(PetscObject)iscol_d);CHKERRQ(ierr);
3167     ierr = ISDestroy(&iscol_d);CHKERRQ(ierr);
3168 
3169     ierr = PetscObjectCompose((PetscObject)M,"iscol_o",(PetscObject)iscol_o);CHKERRQ(ierr);
3170     ierr = ISDestroy(&iscol_o);CHKERRQ(ierr);
3171 
3172     *submat = M;
3173   }
3174   PetscFunctionReturn(0);
3175 }
3176 
3177 PetscErrorCode MatCreateSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3178 {
3179   PetscErrorCode ierr;
3180   IS             iscol_local,isrow_d;
3181   PetscInt       csize;
3182   PetscInt       n,i,j,start,end;
3183   PetscBool      sameRowDist=PETSC_FALSE,sameDist[2],tsameDist[2];
3184   MPI_Comm       comm;
3185 
3186   PetscFunctionBegin;
3187   /* If isrow has same processor distribution as mat,
3188      call MatCreateSubMatrix_MPIAIJ_SameRowDist() to avoid using a hash table with global size of iscol */
3189   if (call == MAT_REUSE_MATRIX) {
3190     ierr = PetscObjectQuery((PetscObject)*newmat,"isrow_d",(PetscObject*)&isrow_d);CHKERRQ(ierr);
3191     if (isrow_d) {
3192       sameRowDist  = PETSC_TRUE;
3193       tsameDist[1] = PETSC_TRUE; /* sameColDist */
3194     } else {
3195       ierr = PetscObjectQuery((PetscObject)*newmat,"SubIScol",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3196       if (iscol_local) {
3197         sameRowDist  = PETSC_TRUE;
3198         tsameDist[1] = PETSC_FALSE; /* !sameColDist */
3199       }
3200     }
3201   } else {
3202     /* Check if isrow has same processor distribution as mat */
3203     sameDist[0] = PETSC_FALSE;
3204     ierr = ISGetLocalSize(isrow,&n);CHKERRQ(ierr);
3205     if (!n) {
3206       sameDist[0] = PETSC_TRUE;
3207     } else {
3208       ierr = ISGetMinMax(isrow,&i,&j);CHKERRQ(ierr);
3209       ierr = MatGetOwnershipRange(mat,&start,&end);CHKERRQ(ierr);
3210       if (i >= start && j < end) {
3211         sameDist[0] = PETSC_TRUE;
3212       }
3213     }
3214 
3215     /* Check if iscol has same processor distribution as mat */
3216     sameDist[1] = PETSC_FALSE;
3217     ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr);
3218     if (!n) {
3219       sameDist[1] = PETSC_TRUE;
3220     } else {
3221       ierr = ISGetMinMax(iscol,&i,&j);CHKERRQ(ierr);
3222       ierr = MatGetOwnershipRangeColumn(mat,&start,&end);CHKERRQ(ierr);
3223       if (i >= start && j < end) sameDist[1] = PETSC_TRUE;
3224     }
3225 
3226     ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3227     ierr = MPIU_Allreduce(&sameDist,&tsameDist,2,MPIU_BOOL,MPI_LAND,comm);CHKERRQ(ierr);
3228     sameRowDist = tsameDist[0];
3229   }
3230 
3231   if (sameRowDist) {
3232     if (tsameDist[1]) {
3233       /* isrow and iscol have same processor distribution as mat */
3234       ierr = MatCreateSubMatrix_MPIAIJ_SameRowColDist(mat,isrow,iscol,call,newmat);CHKERRQ(ierr);
3235     } else {
3236       /* isrow has same processor distribution as mat */
3237       ierr = MatCreateSubMatrix_MPIAIJ_SameRowDist(mat,isrow,iscol,call,newmat);CHKERRQ(ierr);
3238     }
3239     PetscFunctionReturn(0);
3240   }
3241 
3242   /* General case: iscol -> iscol_local which has global size of iscol */
3243   if (call == MAT_REUSE_MATRIX) {
3244     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3245     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3246   } else {
3247     ierr = ISGetSeqIS_Private(mat,iscol,&iscol_local);CHKERRQ(ierr);
3248   }
3249 
3250   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3251   ierr = MatCreateSubMatrix_MPIAIJ_nonscalable(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
3252 
3253   if (call == MAT_INITIAL_MATRIX) {
3254     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3255     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3256   }
3257   PetscFunctionReturn(0);
3258 }
3259 
3260 /*@C
3261      MatCreateMPIAIJWithSeqAIJ - creates a MPIAIJ matrix using SeqAIJ matrices that contain the "diagonal"
3262          and "off-diagonal" part of the matrix in CSR format.
3263 
3264    Collective on MPI_Comm
3265 
3266    Input Parameters:
3267 +  comm - MPI communicator
3268 .  A - "diagonal" portion of matrix
3269 .  B - "off-diagonal" portion of matrix, destroyed by this routine
3270 -  garray - global index of B columns
3271 
3272    Output Parameter:
3273 .   mat - the matrix, with input A as its local diagonal matrix
3274    Level: advanced
3275 
3276    Notes:
3277        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix.
3278        A becomes part of output mat, B is destroyed by this routine. The user cannot use A and B anymore.
3279 
3280 .seealso: MatCreateMPIAIJWithSplitArrays()
3281 @*/
3282 PetscErrorCode MatCreateMPIAIJWithSeqAIJ(MPI_Comm comm,Mat A,Mat B,const PetscInt garray[],Mat *mat)
3283 {
3284   PetscErrorCode ierr;
3285   Mat_MPIAIJ     *maij;
3286   Mat_SeqAIJ     *b=(Mat_SeqAIJ*)B->data,*bnew;
3287   PetscInt       *oi=b->i,*oj=b->j,i,nz,col;
3288   PetscScalar    *oa=b->a;
3289   Mat            Bnew;
3290   PetscInt       m,n,N;
3291 
3292   PetscFunctionBegin;
3293   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
3294   ierr = MatGetSize(A,&m,&n);CHKERRQ(ierr);
3295   if (m != B->rmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Am %D != Bm %D",m,B->rmap->N);
3296   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);
3297   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);
3298 
3299   /* Get global columns of mat */
3300   ierr = MPIU_Allreduce(&n,&N,1,MPI_INT,MPI_SUM,comm);CHKERRQ(ierr);
3301 
3302   ierr = MatSetSizes(*mat,m,n,PETSC_DECIDE,N);CHKERRQ(ierr);
3303   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
3304   ierr = MatSetBlockSizes(*mat,A->rmap->bs,A->cmap->bs);CHKERRQ(ierr);
3305   maij = (Mat_MPIAIJ*)(*mat)->data;
3306 
3307   (*mat)->preallocated = PETSC_TRUE;
3308 
3309   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
3310   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
3311 
3312   /* Set A as diagonal portion of *mat */
3313   maij->A = A;
3314 
3315   nz = oi[m];
3316   for (i=0; i<nz; i++) {
3317     col   = oj[i];
3318     oj[i] = garray[col];
3319   }
3320 
3321    /* Set Bnew as off-diagonal portion of *mat */
3322   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,N,oi,oj,oa,&Bnew);CHKERRQ(ierr);
3323   bnew        = (Mat_SeqAIJ*)Bnew->data;
3324   bnew->maxnz = b->maxnz; /* allocated nonzeros of B */
3325   maij->B     = Bnew;
3326 
3327   PetscMPIInt rank;
3328   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3329   if (rank == -1) {
3330       printf("[%d] Bnew:\n",rank);
3331       ierr = PetscViewerPushFormat(PETSC_VIEWER_STDOUT_SELF, PETSC_VIEWER_ASCII_INFO);CHKERRQ(ierr);
3332       ierr = MatView(Bnew,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
3333       ierr = PetscViewerPopFormat(PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
3334       if (!rank) printf("--------------------\n");
3335   }
3336 
3337   // Check B == Bnew??? see src/ksp/ksp/examples/tests/runex21_2,3
3338 
3339   if (B->rmap->N != Bnew->rmap->N) SETERRQ2(PETSC_COMM_SELF,0,"BN %d != BnewN %d",B->rmap->N,Bnew->rmap->N);
3340 
3341   b->singlemalloc = PETSC_FALSE; /* B arrays are shared by Bnew */
3342   b->free_a       = PETSC_FALSE;
3343   b->free_ij      = PETSC_FALSE;
3344   ierr = MatDestroy(&B);CHKERRQ(ierr);
3345 
3346   bnew->singlemalloc = PETSC_TRUE; /* arrays will be freed by MatDestroy(&Bnew) */
3347   bnew->free_a       = PETSC_TRUE;
3348   bnew->free_ij      = PETSC_TRUE;
3349 
3350   /* condense columns of maij->B */
3351   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
3352   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3353   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3354   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_FALSE);CHKERRQ(ierr);
3355   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3356   PetscFunctionReturn(0);
3357 }
3358 
3359 extern PetscErrorCode MatCreateSubMatrices_MPIAIJ_SingleIS_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool,Mat*);
3360 
3361 PetscErrorCode MatCreateSubMatrix_MPIAIJ_SameRowDist(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3362 {
3363   PetscErrorCode ierr;
3364   PetscInt       i,m,n,rstart,row,rend,nz,j,bs,cbs;
3365   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
3366   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)mat->data;
3367   Mat            M,Msub,B=a->B;
3368   MatScalar      *aa;
3369   Mat_SeqAIJ     *aij;
3370   PetscInt       *garray = a->garray,*colsub,Ncols;
3371   PetscInt       count,Bn=B->cmap->N,cstart=mat->cmap->rstart,cend=mat->cmap->rend;
3372   IS             iscol_sub,iscmap;
3373   const PetscInt *is_idx,*cmap;
3374   PetscBool      allcolumns=PETSC_FALSE;
3375   IS             iscol_local=NULL;
3376   MPI_Comm       comm;
3377 
3378   PetscFunctionBegin;
3379   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3380   PetscMPIInt rank;
3381   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3382 
3383   if (call == MAT_REUSE_MATRIX) {
3384     ierr = PetscObjectQuery((PetscObject)*newmat,"SubIScol",(PetscObject*)&iscol_sub);CHKERRQ(ierr);
3385     if (!iscol_sub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"SubIScol passed in was not used before, cannot reuse");
3386     ierr = ISGetLocalSize(iscol_sub,&count);CHKERRQ(ierr);
3387 
3388     ierr = PetscObjectQuery((PetscObject)*newmat,"Subcmap",(PetscObject*)&iscmap);CHKERRQ(ierr);
3389     if (!iscmap) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Subcmap passed in was not used before, cannot reuse");
3390 
3391     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Msub);CHKERRQ(ierr);
3392     if (!Msub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3393 
3394     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol_sub,MAT_REUSE_MATRIX,PETSC_FALSE,&Msub);CHKERRQ(ierr);
3395 
3396   } else { /* call == MAT_INITIAL_MATRIX) */
3397     PetscBool flg;
3398 
3399     ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr);
3400     ierr = ISGetSize(iscol,&Ncols);CHKERRQ(ierr);
3401 
3402     /* (1) iscol -> nonscalable iscol_local */
3403     ierr = ISGetSeqIS_Private(mat,iscol,&iscol_local);CHKERRQ(ierr);
3404     ierr = ISGetLocalSize(iscol_local,&n);CHKERRQ(ierr); /* local size of iscol_local = global columns of newmat */
3405     if (n != Ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"n %d != Ncols %d",n,Ncols);
3406 
3407     /* Check for special case: each processor gets entire matrix columns */
3408     ierr = ISIdentity(iscol_local,&flg);CHKERRQ(ierr);
3409     if (flg && n == mat->cmap->N) allcolumns = PETSC_TRUE;
3410     if (allcolumns) {
3411       iscol_sub = iscol_local;
3412       ierr = PetscObjectReference((PetscObject)iscol_local);CHKERRQ(ierr);
3413       ierr = ISCreateStride(PETSC_COMM_SELF,n,0,1,&iscmap);CHKERRQ(ierr);
3414 
3415     } else {
3416       /* (2) iscol_local -> iscol_sub and iscmap */
3417       PetscInt *idx,*cmap1,k,cbs;
3418 
3419       /* implementation below requires iscol_local be sorted, it can have duplicate indices */
3420       ierr = ISSorted(iscol_local,&flg);CHKERRQ(ierr);
3421       if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"unsorted iscol_local is not implemented yet");
3422 
3423       ierr = PetscMalloc2(Ncols,&idx,Ncols,&cmap1);CHKERRQ(ierr);
3424       ierr = ISGetIndices(iscol_local,&is_idx);CHKERRQ(ierr);
3425       count = 0;
3426       k     = 0;
3427       for (i=0; i<Ncols; i++) {
3428         j = is_idx[i];
3429         if (j >= cstart && j < cend) {
3430           /* diagonal part of mat */
3431           idx[count]     = j;
3432           cmap1[count++] = i; /* column index in submat */
3433         } else if (Bn) {
3434           /* off-diagonal part of mat */
3435           if (j == garray[k]) {
3436             idx[count]     = j;
3437             cmap1[count++] = i;  /* column index in submat */
3438           } else if (j > garray[k]) {
3439             while (j > garray[k] && k < Bn-1) k++;
3440             if (j == garray[k]) {
3441               idx[count]     = j;
3442               cmap1[count++] = i; /* column index in submat */
3443             }
3444           }
3445         }
3446       }
3447       ierr = ISRestoreIndices(iscol_local,&is_idx);CHKERRQ(ierr);
3448 
3449       ierr = ISCreateGeneral(PETSC_COMM_SELF,count,idx,PETSC_COPY_VALUES,&iscol_sub);CHKERRQ(ierr);
3450       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
3451       ierr = ISSetBlockSize(iscol_sub,cbs);CHKERRQ(ierr);
3452 
3453       ierr = ISCreateGeneral(PetscObjectComm((PetscObject)iscol_local),count,cmap1,PETSC_COPY_VALUES,&iscmap);CHKERRQ(ierr);
3454       ierr = PetscFree2(idx,cmap1);CHKERRQ(ierr);
3455     }
3456 
3457     /* (3) Create sequential Msub */
3458     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol_sub,MAT_INITIAL_MATRIX,allcolumns,&Msub);CHKERRQ(ierr);
3459   }
3460 
3461   ierr = ISGetLocalSize(iscol_sub,&count);CHKERRQ(ierr);
3462   aij  = (Mat_SeqAIJ*)(Msub)->data;
3463   ii   = aij->i;
3464   ierr = ISGetIndices(iscmap,&cmap);CHKERRQ(ierr);
3465 
3466   /*
3467       m - number of local rows
3468       Ncols - number of columns (same on all processors)
3469       rstart - first row in new global matrix generated
3470   */
3471   ierr = MatGetSize(Msub,&m,NULL);CHKERRQ(ierr);
3472 
3473   if (call == MAT_INITIAL_MATRIX) {
3474     /* (4) Create parallel newmat */
3475     PetscMPIInt    rank,size;
3476     PetscInt       csize;
3477 
3478     ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3479     ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3480 
3481     /*
3482         Determine the number of non-zeros in the diagonal and off-diagonal
3483         portions of the matrix in order to do correct preallocation
3484     */
3485 
3486     /* first get start and end of "diagonal" columns */
3487     ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3488     if (csize == PETSC_DECIDE) {
3489       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3490       if (mglobal == Ncols) { /* square matrix */
3491         nlocal = m;
3492       } else {
3493         nlocal = Ncols/size + ((Ncols % size) > rank);
3494       }
3495     } else {
3496       nlocal = csize;
3497     }
3498     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3499     rstart = rend - nlocal;
3500     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);
3501 
3502     /* next, compute all the lengths */
3503     jj    = aij->j;
3504     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3505     olens = dlens + m;
3506     for (i=0; i<m; i++) {
3507       jend = ii[i+1] - ii[i];
3508       olen = 0;
3509       dlen = 0;
3510       for (j=0; j<jend; j++) {
3511         if (cmap[*jj] < rstart || cmap[*jj] >= rend) olen++;
3512         else dlen++;
3513         jj++;
3514       }
3515       olens[i] = olen;
3516       dlens[i] = dlen;
3517     }
3518     ierr = MatGetBlockSizes(Msub,&bs,&cbs);CHKERRQ(ierr);
3519 
3520     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3521     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,Ncols);CHKERRQ(ierr);
3522     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3523     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3524     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3525     ierr = PetscFree(dlens);CHKERRQ(ierr);
3526 
3527   } else { /* call == MAT_REUSE_MATRIX */
3528     M    = *newmat;
3529     ierr = MatGetLocalSize(M,&i,NULL);CHKERRQ(ierr);
3530     if (i != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3531     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3532     /*
3533          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3534        rather than the slower MatSetValues().
3535     */
3536     M->was_assembled = PETSC_TRUE;
3537     M->assembled     = PETSC_FALSE;
3538   }
3539 
3540   /* (5) Set values of Msub to *newmat */
3541   ierr = PetscMalloc1(count,&colsub);CHKERRQ(ierr);
3542   ierr = MatGetOwnershipRange(M,&rstart,NULL);CHKERRQ(ierr);
3543 
3544   jj   = aij->j;
3545   aa   = aij->a;
3546   for (i=0; i<m; i++) {
3547     row = rstart + i;
3548     nz  = ii[i+1] - ii[i];
3549     for (j=0; j<nz; j++) colsub[j] = cmap[jj[j]];
3550     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,colsub,aa,INSERT_VALUES);CHKERRQ(ierr);
3551     jj += nz; aa += nz;
3552   }
3553   ierr = ISRestoreIndices(iscmap,&cmap);CHKERRQ(ierr);
3554 
3555   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3556   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3557 
3558   ierr = PetscFree(colsub);CHKERRQ(ierr);
3559 
3560   /* save Msub, iscol_sub and iscmap used in processor for next request */
3561   if (call ==  MAT_INITIAL_MATRIX) {
3562     *newmat = M;
3563     ierr = PetscObjectCompose((PetscObject)(*newmat),"SubMatrix",(PetscObject)Msub);CHKERRQ(ierr);
3564     ierr = MatDestroy(&Msub);CHKERRQ(ierr);
3565 
3566     ierr = PetscObjectCompose((PetscObject)(*newmat),"SubIScol",(PetscObject)iscol_sub);CHKERRQ(ierr);
3567     ierr = ISDestroy(&iscol_sub);CHKERRQ(ierr);
3568 
3569     ierr = PetscObjectCompose((PetscObject)(*newmat),"Subcmap",(PetscObject)iscmap);CHKERRQ(ierr);
3570     ierr = ISDestroy(&iscmap);CHKERRQ(ierr);
3571 
3572     if (iscol_local) {
3573       ierr = PetscObjectCompose((PetscObject)(*newmat),"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3574       ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3575     }
3576   }
3577   PetscFunctionReturn(0);
3578 }
3579 
3580 /*
3581     Not great since it makes two copies of the submatrix, first an SeqAIJ
3582   in local and then by concatenating the local matrices the end result.
3583   Writing it directly would be much like MatCreateSubMatrices_MPIAIJ()
3584 
3585   Note: This requires a sequential iscol with all indices.
3586 */
3587 PetscErrorCode MatCreateSubMatrix_MPIAIJ_nonscalable(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3588 {
3589   PetscErrorCode ierr;
3590   PetscMPIInt    rank,size;
3591   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3592   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
3593   Mat            M,Mreuse;
3594   MatScalar      *aa,*vwork;
3595   MPI_Comm       comm;
3596   Mat_SeqAIJ     *aij;
3597   PetscBool      colflag,allcolumns=PETSC_FALSE;
3598 
3599   PetscFunctionBegin;
3600   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3601   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3602   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3603 
3604   /* Check for special case: each processor gets entire matrix columns */
3605   ierr = ISIdentity(iscol,&colflag);CHKERRQ(ierr);
3606   ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr);
3607   if (colflag && n == mat->cmap->N) allcolumns = PETSC_TRUE;
3608 
3609   if (call ==  MAT_REUSE_MATRIX) {
3610     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3611     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3612     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,allcolumns,&Mreuse);CHKERRQ(ierr);
3613   } else {
3614     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,allcolumns,&Mreuse);CHKERRQ(ierr);
3615   }
3616 
3617   /*
3618       m - number of local rows
3619       n - number of columns (same on all processors)
3620       rstart - first row in new global matrix generated
3621   */
3622   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3623   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3624   if (call == MAT_INITIAL_MATRIX) {
3625     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3626     ii  = aij->i;
3627     jj  = aij->j;
3628 
3629     /*
3630         Determine the number of non-zeros in the diagonal and off-diagonal
3631         portions of the matrix in order to do correct preallocation
3632     */
3633 
3634     /* first get start and end of "diagonal" columns */
3635     if (csize == PETSC_DECIDE) {
3636       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3637       if (mglobal == n) { /* square matrix */
3638         nlocal = m;
3639       } else {
3640         nlocal = n/size + ((n % size) > rank);
3641       }
3642     } else {
3643       nlocal = csize;
3644     }
3645     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3646     rstart = rend - nlocal;
3647     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);
3648 
3649     /* next, compute all the lengths */
3650     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3651     olens = dlens + m;
3652     for (i=0; i<m; i++) {
3653       jend = ii[i+1] - ii[i];
3654       olen = 0;
3655       dlen = 0;
3656       for (j=0; j<jend; j++) {
3657         if (*jj < rstart || *jj >= rend) olen++;
3658         else dlen++;
3659         jj++;
3660       }
3661       olens[i] = olen;
3662       dlens[i] = dlen;
3663     }
3664     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3665     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3666     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3667     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3668     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3669     ierr = PetscFree(dlens);CHKERRQ(ierr);
3670   } else {
3671     PetscInt ml,nl;
3672 
3673     M    = *newmat;
3674     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3675     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3676     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3677     /*
3678          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3679        rather than the slower MatSetValues().
3680     */
3681     M->was_assembled = PETSC_TRUE;
3682     M->assembled     = PETSC_FALSE;
3683   }
3684   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3685   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3686   ii   = aij->i;
3687   jj   = aij->j;
3688   aa   = aij->a;
3689   for (i=0; i<m; i++) {
3690     row   = rstart + i;
3691     nz    = ii[i+1] - ii[i];
3692     cwork = jj;     jj += nz;
3693     vwork = aa;     aa += nz;
3694     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3695   }
3696 
3697   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3698   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3699   *newmat = M;
3700 
3701   /* save submatrix used in processor for next request */
3702   if (call ==  MAT_INITIAL_MATRIX) {
3703     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3704     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3705   }
3706   PetscFunctionReturn(0);
3707 }
3708 
3709 PetscErrorCode MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3710 {
3711   PetscInt       m,cstart, cend,j,nnz,i,d;
3712   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3713   const PetscInt *JJ;
3714   PetscScalar    *values;
3715   PetscErrorCode ierr;
3716   PetscBool      nooffprocentries;
3717 
3718   PetscFunctionBegin;
3719   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3720 
3721   ierr   = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3722   ierr   = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3723   m      = B->rmap->n;
3724   cstart = B->cmap->rstart;
3725   cend   = B->cmap->rend;
3726   rstart = B->rmap->rstart;
3727 
3728   ierr = PetscMalloc2(m,&d_nnz,m,&o_nnz);CHKERRQ(ierr);
3729 
3730 #if defined(PETSC_USE_DEBUGGING)
3731   for (i=0; i<m; i++) {
3732     nnz = Ii[i+1]- Ii[i];
3733     JJ  = J + Ii[i];
3734     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3735     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3736     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);
3737   }
3738 #endif
3739 
3740   for (i=0; i<m; i++) {
3741     nnz     = Ii[i+1]- Ii[i];
3742     JJ      = J + Ii[i];
3743     nnz_max = PetscMax(nnz_max,nnz);
3744     d       = 0;
3745     for (j=0; j<nnz; j++) {
3746       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3747     }
3748     d_nnz[i] = d;
3749     o_nnz[i] = nnz - d;
3750   }
3751   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3752   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3753 
3754   if (v) values = (PetscScalar*)v;
3755   else {
3756     ierr = PetscCalloc1(nnz_max+1,&values);CHKERRQ(ierr);
3757   }
3758 
3759   for (i=0; i<m; i++) {
3760     ii   = i + rstart;
3761     nnz  = Ii[i+1]- Ii[i];
3762     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3763   }
3764   nooffprocentries    = B->nooffprocentries;
3765   B->nooffprocentries = PETSC_TRUE;
3766   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3767   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3768   B->nooffprocentries = nooffprocentries;
3769 
3770   if (!v) {
3771     ierr = PetscFree(values);CHKERRQ(ierr);
3772   }
3773   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3774   PetscFunctionReturn(0);
3775 }
3776 
3777 /*@
3778    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3779    (the default parallel PETSc format).
3780 
3781    Collective on MPI_Comm
3782 
3783    Input Parameters:
3784 +  B - the matrix
3785 .  i - the indices into j for the start of each local row (starts with zero)
3786 .  j - the column indices for each local row (starts with zero)
3787 -  v - optional values in the matrix
3788 
3789    Level: developer
3790 
3791    Notes:
3792        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3793      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3794      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3795 
3796        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3797 
3798        The format which is used for the sparse matrix input, is equivalent to a
3799     row-major ordering.. i.e for the following matrix, the input data expected is
3800     as shown
3801 
3802 $        1 0 0
3803 $        2 0 3     P0
3804 $       -------
3805 $        4 5 6     P1
3806 $
3807 $     Process0 [P0]: rows_owned=[0,1]
3808 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3809 $        j =  {0,0,2}  [size = 3]
3810 $        v =  {1,2,3}  [size = 3]
3811 $
3812 $     Process1 [P1]: rows_owned=[2]
3813 $        i =  {0,3}    [size = nrow+1  = 1+1]
3814 $        j =  {0,1,2}  [size = 3]
3815 $        v =  {4,5,6}  [size = 3]
3816 
3817 .keywords: matrix, aij, compressed row, sparse, parallel
3818 
3819 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MATMPIAIJ,
3820           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3821 @*/
3822 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3823 {
3824   PetscErrorCode ierr;
3825 
3826   PetscFunctionBegin;
3827   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3828   PetscFunctionReturn(0);
3829 }
3830 
3831 /*@C
3832    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3833    (the default parallel PETSc format).  For good matrix assembly performance
3834    the user should preallocate the matrix storage by setting the parameters
3835    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3836    performance can be increased by more than a factor of 50.
3837 
3838    Collective on MPI_Comm
3839 
3840    Input Parameters:
3841 +  B - the matrix
3842 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3843            (same value is used for all local rows)
3844 .  d_nnz - array containing the number of nonzeros in the various rows of the
3845            DIAGONAL portion of the local submatrix (possibly different for each row)
3846            or NULL (PETSC_NULL_INTEGER in Fortran), if d_nz is used to specify the nonzero structure.
3847            The size of this array is equal to the number of local rows, i.e 'm'.
3848            For matrices that will be factored, you must leave room for (and set)
3849            the diagonal entry even if it is zero.
3850 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3851            submatrix (same value is used for all local rows).
3852 -  o_nnz - array containing the number of nonzeros in the various rows of the
3853            OFF-DIAGONAL portion of the local submatrix (possibly different for
3854            each row) or NULL (PETSC_NULL_INTEGER in Fortran), if o_nz is used to specify the nonzero
3855            structure. The size of this array is equal to the number
3856            of local rows, i.e 'm'.
3857 
3858    If the *_nnz parameter is given then the *_nz parameter is ignored
3859 
3860    The AIJ format (also called the Yale sparse matrix format or
3861    compressed row storage (CSR)), is fully compatible with standard Fortran 77
3862    storage.  The stored row and column indices begin with zero.
3863    See Users-Manual: ch_mat for details.
3864 
3865    The parallel matrix is partitioned such that the first m0 rows belong to
3866    process 0, the next m1 rows belong to process 1, the next m2 rows belong
3867    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
3868 
3869    The DIAGONAL portion of the local submatrix of a processor can be defined
3870    as the submatrix which is obtained by extraction the part corresponding to
3871    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
3872    first row that belongs to the processor, r2 is the last row belonging to
3873    the this processor, and c1-c2 is range of indices of the local part of a
3874    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
3875    common case of a square matrix, the row and column ranges are the same and
3876    the DIAGONAL part is also square. The remaining portion of the local
3877    submatrix (mxN) constitute the OFF-DIAGONAL portion.
3878 
3879    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3880 
3881    You can call MatGetInfo() to get information on how effective the preallocation was;
3882    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3883    You can also run with the option -info and look for messages with the string
3884    malloc in them to see if additional memory allocation was needed.
3885 
3886    Example usage:
3887 
3888    Consider the following 8x8 matrix with 34 non-zero values, that is
3889    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3890    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3891    as follows:
3892 
3893 .vb
3894             1  2  0  |  0  3  0  |  0  4
3895     Proc0   0  5  6  |  7  0  0  |  8  0
3896             9  0 10  | 11  0  0  | 12  0
3897     -------------------------------------
3898            13  0 14  | 15 16 17  |  0  0
3899     Proc1   0 18  0  | 19 20 21  |  0  0
3900             0  0  0  | 22 23  0  | 24  0
3901     -------------------------------------
3902     Proc2  25 26 27  |  0  0 28  | 29  0
3903            30  0  0  | 31 32 33  |  0 34
3904 .ve
3905 
3906    This can be represented as a collection of submatrices as:
3907 
3908 .vb
3909       A B C
3910       D E F
3911       G H I
3912 .ve
3913 
3914    Where the submatrices A,B,C are owned by proc0, D,E,F are
3915    owned by proc1, G,H,I are owned by proc2.
3916 
3917    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3918    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3919    The 'M','N' parameters are 8,8, and have the same values on all procs.
3920 
3921    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3922    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3923    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3924    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3925    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3926    matrix, ans [DF] as another SeqAIJ matrix.
3927 
3928    When d_nz, o_nz parameters are specified, d_nz storage elements are
3929    allocated for every row of the local diagonal submatrix, and o_nz
3930    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3931    One way to choose d_nz and o_nz is to use the max nonzerors per local
3932    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3933    In this case, the values of d_nz,o_nz are:
3934 .vb
3935      proc0 : dnz = 2, o_nz = 2
3936      proc1 : dnz = 3, o_nz = 2
3937      proc2 : dnz = 1, o_nz = 4
3938 .ve
3939    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3940    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3941    for proc3. i.e we are using 12+15+10=37 storage locations to store
3942    34 values.
3943 
3944    When d_nnz, o_nnz parameters are specified, the storage is specified
3945    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3946    In the above case the values for d_nnz,o_nnz are:
3947 .vb
3948      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3949      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3950      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3951 .ve
3952    Here the space allocated is sum of all the above values i.e 34, and
3953    hence pre-allocation is perfect.
3954 
3955    Level: intermediate
3956 
3957 .keywords: matrix, aij, compressed row, sparse, parallel
3958 
3959 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
3960           MATMPIAIJ, MatGetInfo(), PetscSplitOwnership()
3961 @*/
3962 PetscErrorCode MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3963 {
3964   PetscErrorCode ierr;
3965 
3966   PetscFunctionBegin;
3967   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3968   PetscValidType(B,1);
3969   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
3970   PetscFunctionReturn(0);
3971 }
3972 
3973 /*@
3974      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
3975          CSR format the local rows.
3976 
3977    Collective on MPI_Comm
3978 
3979    Input Parameters:
3980 +  comm - MPI communicator
3981 .  m - number of local rows (Cannot be PETSC_DECIDE)
3982 .  n - This value should be the same as the local size used in creating the
3983        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3984        calculated if N is given) For square matrices n is almost always m.
3985 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3986 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3987 .   i - row indices
3988 .   j - column indices
3989 -   a - matrix values
3990 
3991    Output Parameter:
3992 .   mat - the matrix
3993 
3994    Level: intermediate
3995 
3996    Notes:
3997        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3998      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3999      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
4000 
4001        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
4002 
4003        The format which is used for the sparse matrix input, is equivalent to a
4004     row-major ordering.. i.e for the following matrix, the input data expected is
4005     as shown
4006 
4007 $        1 0 0
4008 $        2 0 3     P0
4009 $       -------
4010 $        4 5 6     P1
4011 $
4012 $     Process0 [P0]: rows_owned=[0,1]
4013 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
4014 $        j =  {0,0,2}  [size = 3]
4015 $        v =  {1,2,3}  [size = 3]
4016 $
4017 $     Process1 [P1]: rows_owned=[2]
4018 $        i =  {0,3}    [size = nrow+1  = 1+1]
4019 $        j =  {0,1,2}  [size = 3]
4020 $        v =  {4,5,6}  [size = 3]
4021 
4022 .keywords: matrix, aij, compressed row, sparse, parallel
4023 
4024 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
4025           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
4026 @*/
4027 PetscErrorCode MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
4028 {
4029   PetscErrorCode ierr;
4030 
4031   PetscFunctionBegin;
4032   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
4033   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
4034   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4035   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
4036   /* ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr); */
4037   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
4038   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
4039   PetscFunctionReturn(0);
4040 }
4041 
4042 /*@C
4043    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
4044    (the default parallel PETSc format).  For good matrix assembly performance
4045    the user should preallocate the matrix storage by setting the parameters
4046    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
4047    performance can be increased by more than a factor of 50.
4048 
4049    Collective on MPI_Comm
4050 
4051    Input Parameters:
4052 +  comm - MPI communicator
4053 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
4054            This value should be the same as the local size used in creating the
4055            y vector for the matrix-vector product y = Ax.
4056 .  n - This value should be the same as the local size used in creating the
4057        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
4058        calculated if N is given) For square matrices n is almost always m.
4059 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
4060 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
4061 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
4062            (same value is used for all local rows)
4063 .  d_nnz - array containing the number of nonzeros in the various rows of the
4064            DIAGONAL portion of the local submatrix (possibly different for each row)
4065            or NULL, if d_nz is used to specify the nonzero structure.
4066            The size of this array is equal to the number of local rows, i.e 'm'.
4067 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
4068            submatrix (same value is used for all local rows).
4069 -  o_nnz - array containing the number of nonzeros in the various rows of the
4070            OFF-DIAGONAL portion of the local submatrix (possibly different for
4071            each row) or NULL, if o_nz is used to specify the nonzero
4072            structure. The size of this array is equal to the number
4073            of local rows, i.e 'm'.
4074 
4075    Output Parameter:
4076 .  A - the matrix
4077 
4078    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
4079    MatXXXXSetPreallocation() paradgm instead of this routine directly.
4080    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
4081 
4082    Notes:
4083    If the *_nnz parameter is given then the *_nz parameter is ignored
4084 
4085    m,n,M,N parameters specify the size of the matrix, and its partitioning across
4086    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
4087    storage requirements for this matrix.
4088 
4089    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
4090    processor than it must be used on all processors that share the object for
4091    that argument.
4092 
4093    The user MUST specify either the local or global matrix dimensions
4094    (possibly both).
4095 
4096    The parallel matrix is partitioned across processors such that the
4097    first m0 rows belong to process 0, the next m1 rows belong to
4098    process 1, the next m2 rows belong to process 2 etc.. where
4099    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
4100    values corresponding to [m x N] submatrix.
4101 
4102    The columns are logically partitioned with the n0 columns belonging
4103    to 0th partition, the next n1 columns belonging to the next
4104    partition etc.. where n0,n1,n2... are the input parameter 'n'.
4105 
4106    The DIAGONAL portion of the local submatrix on any given processor
4107    is the submatrix corresponding to the rows and columns m,n
4108    corresponding to the given processor. i.e diagonal matrix on
4109    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
4110    etc. The remaining portion of the local submatrix [m x (N-n)]
4111    constitute the OFF-DIAGONAL portion. The example below better
4112    illustrates this concept.
4113 
4114    For a square global matrix we define each processor's diagonal portion
4115    to be its local rows and the corresponding columns (a square submatrix);
4116    each processor's off-diagonal portion encompasses the remainder of the
4117    local matrix (a rectangular submatrix).
4118 
4119    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
4120 
4121    When calling this routine with a single process communicator, a matrix of
4122    type SEQAIJ is returned.  If a matrix of type MATMPIAIJ is desired for this
4123    type of communicator, use the construction mechanism:
4124      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
4125 
4126    By default, this format uses inodes (identical nodes) when possible.
4127    We search for consecutive rows with the same nonzero structure, thereby
4128    reusing matrix information to achieve increased efficiency.
4129 
4130    Options Database Keys:
4131 +  -mat_no_inode  - Do not use inodes
4132 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
4133 -  -mat_aij_oneindex - Internally use indexing starting at 1
4134         rather than 0.  Note that when calling MatSetValues(),
4135         the user still MUST index entries starting at 0!
4136 
4137 
4138    Example usage:
4139 
4140    Consider the following 8x8 matrix with 34 non-zero values, that is
4141    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
4142    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
4143    as follows:
4144 
4145 .vb
4146             1  2  0  |  0  3  0  |  0  4
4147     Proc0   0  5  6  |  7  0  0  |  8  0
4148             9  0 10  | 11  0  0  | 12  0
4149     -------------------------------------
4150            13  0 14  | 15 16 17  |  0  0
4151     Proc1   0 18  0  | 19 20 21  |  0  0
4152             0  0  0  | 22 23  0  | 24  0
4153     -------------------------------------
4154     Proc2  25 26 27  |  0  0 28  | 29  0
4155            30  0  0  | 31 32 33  |  0 34
4156 .ve
4157 
4158    This can be represented as a collection of submatrices as:
4159 
4160 .vb
4161       A B C
4162       D E F
4163       G H I
4164 .ve
4165 
4166    Where the submatrices A,B,C are owned by proc0, D,E,F are
4167    owned by proc1, G,H,I are owned by proc2.
4168 
4169    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4170    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4171    The 'M','N' parameters are 8,8, and have the same values on all procs.
4172 
4173    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
4174    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
4175    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
4176    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
4177    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
4178    matrix, ans [DF] as another SeqAIJ matrix.
4179 
4180    When d_nz, o_nz parameters are specified, d_nz storage elements are
4181    allocated for every row of the local diagonal submatrix, and o_nz
4182    storage locations are allocated for every row of the OFF-DIAGONAL submat.
4183    One way to choose d_nz and o_nz is to use the max nonzerors per local
4184    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
4185    In this case, the values of d_nz,o_nz are:
4186 .vb
4187      proc0 : dnz = 2, o_nz = 2
4188      proc1 : dnz = 3, o_nz = 2
4189      proc2 : dnz = 1, o_nz = 4
4190 .ve
4191    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
4192    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
4193    for proc3. i.e we are using 12+15+10=37 storage locations to store
4194    34 values.
4195 
4196    When d_nnz, o_nnz parameters are specified, the storage is specified
4197    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
4198    In the above case the values for d_nnz,o_nnz are:
4199 .vb
4200      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
4201      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
4202      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
4203 .ve
4204    Here the space allocated is sum of all the above values i.e 34, and
4205    hence pre-allocation is perfect.
4206 
4207    Level: intermediate
4208 
4209 .keywords: matrix, aij, compressed row, sparse, parallel
4210 
4211 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
4212           MATMPIAIJ, MatCreateMPIAIJWithArrays()
4213 @*/
4214 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)
4215 {
4216   PetscErrorCode ierr;
4217   PetscMPIInt    size;
4218 
4219   PetscFunctionBegin;
4220   ierr = MatCreate(comm,A);CHKERRQ(ierr);
4221   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
4222   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4223   if (size > 1) {
4224     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
4225     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
4226   } else {
4227     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
4228     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
4229   }
4230   PetscFunctionReturn(0);
4231 }
4232 
4233 PetscErrorCode MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
4234 {
4235   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
4236   PetscBool      flg;
4237   PetscErrorCode ierr;
4238 
4239   PetscFunctionBegin;
4240   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&flg);CHKERRQ(ierr);
4241   if (!flg) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"This function requires a MATMPIAIJ matrix as input");
4242   if (Ad)     *Ad     = a->A;
4243   if (Ao)     *Ao     = a->B;
4244   if (colmap) *colmap = a->garray;
4245   PetscFunctionReturn(0);
4246 }
4247 
4248 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
4249 {
4250   PetscErrorCode ierr;
4251   PetscInt       m,N,i,rstart,nnz,Ii;
4252   PetscInt       *indx;
4253   PetscScalar    *values;
4254 
4255   PetscFunctionBegin;
4256   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
4257   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
4258     PetscInt       *dnz,*onz,sum,bs,cbs;
4259 
4260     if (n == PETSC_DECIDE) {
4261       ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
4262     }
4263     /* Check sum(n) = N */
4264     ierr = MPIU_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4265     if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
4266 
4267     ierr    = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4268     rstart -= m;
4269 
4270     ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4271     for (i=0; i<m; i++) {
4272       ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
4273       ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
4274       ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
4275     }
4276 
4277     ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
4278     ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4279     ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
4280     ierr = MatSetBlockSizes(*outmat,bs,cbs);CHKERRQ(ierr);
4281     ierr = MatSetType(*outmat,MATAIJ);CHKERRQ(ierr);
4282     ierr = MatSeqAIJSetPreallocation(*outmat,0,dnz);CHKERRQ(ierr);
4283     ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
4284     ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4285   }
4286 
4287   /* numeric phase */
4288   ierr = MatGetOwnershipRange(*outmat,&rstart,NULL);CHKERRQ(ierr);
4289   for (i=0; i<m; i++) {
4290     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4291     Ii   = i + rstart;
4292     ierr = MatSetValues(*outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4293     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4294   }
4295   ierr = MatAssemblyBegin(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4296   ierr = MatAssemblyEnd(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4297   PetscFunctionReturn(0);
4298 }
4299 
4300 PetscErrorCode MatFileSplit(Mat A,char *outfile)
4301 {
4302   PetscErrorCode    ierr;
4303   PetscMPIInt       rank;
4304   PetscInt          m,N,i,rstart,nnz;
4305   size_t            len;
4306   const PetscInt    *indx;
4307   PetscViewer       out;
4308   char              *name;
4309   Mat               B;
4310   const PetscScalar *values;
4311 
4312   PetscFunctionBegin;
4313   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
4314   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
4315   /* Should this be the type of the diagonal block of A? */
4316   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
4317   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
4318   ierr = MatSetBlockSizesFromMats(B,A,A);CHKERRQ(ierr);
4319   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
4320   ierr = MatSeqAIJSetPreallocation(B,0,NULL);CHKERRQ(ierr);
4321   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
4322   for (i=0; i<m; i++) {
4323     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4324     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4325     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4326   }
4327   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4328   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4329 
4330   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
4331   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
4332   ierr = PetscMalloc1(len+5,&name);CHKERRQ(ierr);
4333   sprintf(name,"%s.%d",outfile,rank);
4334   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
4335   ierr = PetscFree(name);CHKERRQ(ierr);
4336   ierr = MatView(B,out);CHKERRQ(ierr);
4337   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
4338   ierr = MatDestroy(&B);CHKERRQ(ierr);
4339   PetscFunctionReturn(0);
4340 }
4341 
4342 PetscErrorCode MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
4343 {
4344   PetscErrorCode      ierr;
4345   Mat_Merge_SeqsToMPI *merge;
4346   PetscContainer      container;
4347 
4348   PetscFunctionBegin;
4349   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4350   if (container) {
4351     ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4352     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
4353     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
4354     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
4355     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
4356     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
4357     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
4358     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
4359     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
4360     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
4361     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
4362     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
4363     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
4364     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
4365     ierr = PetscFree(merge);CHKERRQ(ierr);
4366     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
4367   }
4368   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
4369   PetscFunctionReturn(0);
4370 }
4371 
4372 #include <../src/mat/utils/freespace.h>
4373 #include <petscbt.h>
4374 
4375 PetscErrorCode MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
4376 {
4377   PetscErrorCode      ierr;
4378   MPI_Comm            comm;
4379   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
4380   PetscMPIInt         size,rank,taga,*len_s;
4381   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
4382   PetscInt            proc,m;
4383   PetscInt            **buf_ri,**buf_rj;
4384   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
4385   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
4386   MPI_Request         *s_waits,*r_waits;
4387   MPI_Status          *status;
4388   MatScalar           *aa=a->a;
4389   MatScalar           **abuf_r,*ba_i;
4390   Mat_Merge_SeqsToMPI *merge;
4391   PetscContainer      container;
4392 
4393   PetscFunctionBegin;
4394   ierr = PetscObjectGetComm((PetscObject)mpimat,&comm);CHKERRQ(ierr);
4395   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4396 
4397   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4398   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4399 
4400   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4401   ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4402 
4403   bi     = merge->bi;
4404   bj     = merge->bj;
4405   buf_ri = merge->buf_ri;
4406   buf_rj = merge->buf_rj;
4407 
4408   ierr   = PetscMalloc1(size,&status);CHKERRQ(ierr);
4409   owners = merge->rowmap->range;
4410   len_s  = merge->len_s;
4411 
4412   /* send and recv matrix values */
4413   /*-----------------------------*/
4414   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
4415   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
4416 
4417   ierr = PetscMalloc1(merge->nsend+1,&s_waits);CHKERRQ(ierr);
4418   for (proc=0,k=0; proc<size; proc++) {
4419     if (!len_s[proc]) continue;
4420     i    = owners[proc];
4421     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
4422     k++;
4423   }
4424 
4425   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
4426   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
4427   ierr = PetscFree(status);CHKERRQ(ierr);
4428 
4429   ierr = PetscFree(s_waits);CHKERRQ(ierr);
4430   ierr = PetscFree(r_waits);CHKERRQ(ierr);
4431 
4432   /* insert mat values of mpimat */
4433   /*----------------------------*/
4434   ierr = PetscMalloc1(N,&ba_i);CHKERRQ(ierr);
4435   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4436 
4437   for (k=0; k<merge->nrecv; k++) {
4438     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4439     nrows       = *(buf_ri_k[k]);
4440     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
4441     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4442   }
4443 
4444   /* set values of ba */
4445   m = merge->rowmap->n;
4446   for (i=0; i<m; i++) {
4447     arow = owners[rank] + i;
4448     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
4449     bnzi = bi[i+1] - bi[i];
4450     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
4451 
4452     /* add local non-zero vals of this proc's seqmat into ba */
4453     anzi   = ai[arow+1] - ai[arow];
4454     aj     = a->j + ai[arow];
4455     aa     = a->a + ai[arow];
4456     nextaj = 0;
4457     for (j=0; nextaj<anzi; j++) {
4458       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4459         ba_i[j] += aa[nextaj++];
4460       }
4461     }
4462 
4463     /* add received vals into ba */
4464     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4465       /* i-th row */
4466       if (i == *nextrow[k]) {
4467         anzi   = *(nextai[k]+1) - *nextai[k];
4468         aj     = buf_rj[k] + *(nextai[k]);
4469         aa     = abuf_r[k] + *(nextai[k]);
4470         nextaj = 0;
4471         for (j=0; nextaj<anzi; j++) {
4472           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4473             ba_i[j] += aa[nextaj++];
4474           }
4475         }
4476         nextrow[k]++; nextai[k]++;
4477       }
4478     }
4479     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
4480   }
4481   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4482   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4483 
4484   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
4485   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
4486   ierr = PetscFree(ba_i);CHKERRQ(ierr);
4487   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4488   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4489   PetscFunctionReturn(0);
4490 }
4491 
4492 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4493 {
4494   PetscErrorCode      ierr;
4495   Mat                 B_mpi;
4496   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
4497   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4498   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
4499   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4500   PetscInt            len,proc,*dnz,*onz,bs,cbs;
4501   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4502   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4503   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
4504   MPI_Status          *status;
4505   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
4506   PetscBT             lnkbt;
4507   Mat_Merge_SeqsToMPI *merge;
4508   PetscContainer      container;
4509 
4510   PetscFunctionBegin;
4511   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4512 
4513   /* make sure it is a PETSc comm */
4514   ierr = PetscCommDuplicate(comm,&comm,NULL);CHKERRQ(ierr);
4515   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4516   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4517 
4518   ierr = PetscNew(&merge);CHKERRQ(ierr);
4519   ierr = PetscMalloc1(size,&status);CHKERRQ(ierr);
4520 
4521   /* determine row ownership */
4522   /*---------------------------------------------------------*/
4523   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
4524   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
4525   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
4526   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
4527   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
4528   ierr = PetscMalloc1(size,&len_si);CHKERRQ(ierr);
4529   ierr = PetscMalloc1(size,&merge->len_s);CHKERRQ(ierr);
4530 
4531   m      = merge->rowmap->n;
4532   owners = merge->rowmap->range;
4533 
4534   /* determine the number of messages to send, their lengths */
4535   /*---------------------------------------------------------*/
4536   len_s = merge->len_s;
4537 
4538   len          = 0; /* length of buf_si[] */
4539   merge->nsend = 0;
4540   for (proc=0; proc<size; proc++) {
4541     len_si[proc] = 0;
4542     if (proc == rank) {
4543       len_s[proc] = 0;
4544     } else {
4545       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4546       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4547     }
4548     if (len_s[proc]) {
4549       merge->nsend++;
4550       nrows = 0;
4551       for (i=owners[proc]; i<owners[proc+1]; i++) {
4552         if (ai[i+1] > ai[i]) nrows++;
4553       }
4554       len_si[proc] = 2*(nrows+1);
4555       len         += len_si[proc];
4556     }
4557   }
4558 
4559   /* determine the number and length of messages to receive for ij-structure */
4560   /*-------------------------------------------------------------------------*/
4561   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
4562   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
4563 
4564   /* post the Irecv of j-structure */
4565   /*-------------------------------*/
4566   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
4567   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
4568 
4569   /* post the Isend of j-structure */
4570   /*--------------------------------*/
4571   ierr = PetscMalloc2(merge->nsend,&si_waits,merge->nsend,&sj_waits);CHKERRQ(ierr);
4572 
4573   for (proc=0, k=0; proc<size; proc++) {
4574     if (!len_s[proc]) continue;
4575     i    = owners[proc];
4576     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
4577     k++;
4578   }
4579 
4580   /* receives and sends of j-structure are complete */
4581   /*------------------------------------------------*/
4582   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
4583   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
4584 
4585   /* send and recv i-structure */
4586   /*---------------------------*/
4587   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
4588   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
4589 
4590   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
4591   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4592   for (proc=0,k=0; proc<size; proc++) {
4593     if (!len_s[proc]) continue;
4594     /* form outgoing message for i-structure:
4595          buf_si[0]:                 nrows to be sent
4596                [1:nrows]:           row index (global)
4597                [nrows+1:2*nrows+1]: i-structure index
4598     */
4599     /*-------------------------------------------*/
4600     nrows       = len_si[proc]/2 - 1;
4601     buf_si_i    = buf_si + nrows+1;
4602     buf_si[0]   = nrows;
4603     buf_si_i[0] = 0;
4604     nrows       = 0;
4605     for (i=owners[proc]; i<owners[proc+1]; i++) {
4606       anzi = ai[i+1] - ai[i];
4607       if (anzi) {
4608         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4609         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4610         nrows++;
4611       }
4612     }
4613     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4614     k++;
4615     buf_si += len_si[proc];
4616   }
4617 
4618   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4619   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4620 
4621   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4622   for (i=0; i<merge->nrecv; i++) {
4623     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);
4624   }
4625 
4626   ierr = PetscFree(len_si);CHKERRQ(ierr);
4627   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4628   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4629   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4630   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4631   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4632   ierr = PetscFree(status);CHKERRQ(ierr);
4633 
4634   /* compute a local seq matrix in each processor */
4635   /*----------------------------------------------*/
4636   /* allocate bi array and free space for accumulating nonzero column info */
4637   ierr  = PetscMalloc1(m+1,&bi);CHKERRQ(ierr);
4638   bi[0] = 0;
4639 
4640   /* create and initialize a linked list */
4641   nlnk = N+1;
4642   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4643 
4644   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4645   len  = ai[owners[rank+1]] - ai[owners[rank]];
4646   ierr = PetscFreeSpaceGet(PetscIntMultTruncate(2,len)+1,&free_space);CHKERRQ(ierr);
4647 
4648   current_space = free_space;
4649 
4650   /* determine symbolic info for each local row */
4651   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4652 
4653   for (k=0; k<merge->nrecv; k++) {
4654     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4655     nrows       = *buf_ri_k[k];
4656     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4657     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4658   }
4659 
4660   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4661   len  = 0;
4662   for (i=0; i<m; i++) {
4663     bnzi = 0;
4664     /* add local non-zero cols of this proc's seqmat into lnk */
4665     arow  = owners[rank] + i;
4666     anzi  = ai[arow+1] - ai[arow];
4667     aj    = a->j + ai[arow];
4668     ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4669     bnzi += nlnk;
4670     /* add received col data into lnk */
4671     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4672       if (i == *nextrow[k]) { /* i-th row */
4673         anzi  = *(nextai[k]+1) - *nextai[k];
4674         aj    = buf_rj[k] + *nextai[k];
4675         ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4676         bnzi += nlnk;
4677         nextrow[k]++; nextai[k]++;
4678       }
4679     }
4680     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4681 
4682     /* if free space is not available, make more free space */
4683     if (current_space->local_remaining<bnzi) {
4684       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(bnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
4685       nspacedouble++;
4686     }
4687     /* copy data into free space, then initialize lnk */
4688     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4689     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
4690 
4691     current_space->array           += bnzi;
4692     current_space->local_used      += bnzi;
4693     current_space->local_remaining -= bnzi;
4694 
4695     bi[i+1] = bi[i] + bnzi;
4696   }
4697 
4698   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4699 
4700   ierr = PetscMalloc1(bi[m]+1,&bj);CHKERRQ(ierr);
4701   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
4702   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4703 
4704   /* create symbolic parallel matrix B_mpi */
4705   /*---------------------------------------*/
4706   ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
4707   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
4708   if (n==PETSC_DECIDE) {
4709     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
4710   } else {
4711     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4712   }
4713   ierr = MatSetBlockSizes(B_mpi,bs,cbs);CHKERRQ(ierr);
4714   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
4715   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
4716   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4717   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
4718 
4719   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4720   B_mpi->assembled    = PETSC_FALSE;
4721   B_mpi->ops->destroy = MatDestroy_MPIAIJ_SeqsToMPI;
4722   merge->bi           = bi;
4723   merge->bj           = bj;
4724   merge->buf_ri       = buf_ri;
4725   merge->buf_rj       = buf_rj;
4726   merge->coi          = NULL;
4727   merge->coj          = NULL;
4728   merge->owners_co    = NULL;
4729 
4730   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
4731 
4732   /* attach the supporting struct to B_mpi for reuse */
4733   ierr    = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
4734   ierr    = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
4735   ierr    = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
4736   ierr    = PetscContainerDestroy(&container);CHKERRQ(ierr);
4737   *mpimat = B_mpi;
4738 
4739   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4740   PetscFunctionReturn(0);
4741 }
4742 
4743 /*@C
4744       MatCreateMPIAIJSumSeqAIJ - Creates a MATMPIAIJ matrix by adding sequential
4745                  matrices from each processor
4746 
4747     Collective on MPI_Comm
4748 
4749    Input Parameters:
4750 +    comm - the communicators the parallel matrix will live on
4751 .    seqmat - the input sequential matrices
4752 .    m - number of local rows (or PETSC_DECIDE)
4753 .    n - number of local columns (or PETSC_DECIDE)
4754 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4755 
4756    Output Parameter:
4757 .    mpimat - the parallel matrix generated
4758 
4759     Level: advanced
4760 
4761    Notes:
4762      The dimensions of the sequential matrix in each processor MUST be the same.
4763      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
4764      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
4765 @*/
4766 PetscErrorCode MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
4767 {
4768   PetscErrorCode ierr;
4769   PetscMPIInt    size;
4770 
4771   PetscFunctionBegin;
4772   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4773   if (size == 1) {
4774     ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4775     if (scall == MAT_INITIAL_MATRIX) {
4776       ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
4777     } else {
4778       ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4779     }
4780     ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4781     PetscFunctionReturn(0);
4782   }
4783   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4784   if (scall == MAT_INITIAL_MATRIX) {
4785     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
4786   }
4787   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
4788   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4789   PetscFunctionReturn(0);
4790 }
4791 
4792 /*@
4793      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MATMPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
4794           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
4795           with MatGetSize()
4796 
4797     Not Collective
4798 
4799    Input Parameters:
4800 +    A - the matrix
4801 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4802 
4803    Output Parameter:
4804 .    A_loc - the local sequential matrix generated
4805 
4806     Level: developer
4807 
4808 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
4809 
4810 @*/
4811 PetscErrorCode MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
4812 {
4813   PetscErrorCode ierr;
4814   Mat_MPIAIJ     *mpimat=(Mat_MPIAIJ*)A->data;
4815   Mat_SeqAIJ     *mat,*a,*b;
4816   PetscInt       *ai,*aj,*bi,*bj,*cmap=mpimat->garray;
4817   MatScalar      *aa,*ba,*cam;
4818   PetscScalar    *ca;
4819   PetscInt       am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
4820   PetscInt       *ci,*cj,col,ncols_d,ncols_o,jo;
4821   PetscBool      match;
4822   MPI_Comm       comm;
4823   PetscMPIInt    size;
4824 
4825   PetscFunctionBegin;
4826   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4827   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
4828   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4829   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4830   if (size == 1 && scall == MAT_REUSE_MATRIX) PetscFunctionReturn(0);
4831 
4832   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4833   a = (Mat_SeqAIJ*)(mpimat->A)->data;
4834   b = (Mat_SeqAIJ*)(mpimat->B)->data;
4835   ai = a->i; aj = a->j; bi = b->i; bj = b->j;
4836   aa = a->a; ba = b->a;
4837   if (scall == MAT_INITIAL_MATRIX) {
4838     if (size == 1) {
4839       ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ai,aj,aa,A_loc);CHKERRQ(ierr);
4840       PetscFunctionReturn(0);
4841     }
4842 
4843     ierr  = PetscMalloc1(1+am,&ci);CHKERRQ(ierr);
4844     ci[0] = 0;
4845     for (i=0; i<am; i++) {
4846       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
4847     }
4848     ierr = PetscMalloc1(1+ci[am],&cj);CHKERRQ(ierr);
4849     ierr = PetscMalloc1(1+ci[am],&ca);CHKERRQ(ierr);
4850     k    = 0;
4851     for (i=0; i<am; i++) {
4852       ncols_o = bi[i+1] - bi[i];
4853       ncols_d = ai[i+1] - ai[i];
4854       /* off-diagonal portion of A */
4855       for (jo=0; jo<ncols_o; jo++) {
4856         col = cmap[*bj];
4857         if (col >= cstart) break;
4858         cj[k]   = col; bj++;
4859         ca[k++] = *ba++;
4860       }
4861       /* diagonal portion of A */
4862       for (j=0; j<ncols_d; j++) {
4863         cj[k]   = cstart + *aj++;
4864         ca[k++] = *aa++;
4865       }
4866       /* off-diagonal portion of A */
4867       for (j=jo; j<ncols_o; j++) {
4868         cj[k]   = cmap[*bj++];
4869         ca[k++] = *ba++;
4870       }
4871     }
4872     /* put together the new matrix */
4873     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
4874     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4875     /* Since these are PETSc arrays, change flags to free them as necessary. */
4876     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
4877     mat->free_a  = PETSC_TRUE;
4878     mat->free_ij = PETSC_TRUE;
4879     mat->nonew   = 0;
4880   } else if (scall == MAT_REUSE_MATRIX) {
4881     mat=(Mat_SeqAIJ*)(*A_loc)->data;
4882     ci = mat->i; cj = mat->j; cam = mat->a;
4883     for (i=0; i<am; i++) {
4884       /* off-diagonal portion of A */
4885       ncols_o = bi[i+1] - bi[i];
4886       for (jo=0; jo<ncols_o; jo++) {
4887         col = cmap[*bj];
4888         if (col >= cstart) break;
4889         *cam++ = *ba++; bj++;
4890       }
4891       /* diagonal portion of A */
4892       ncols_d = ai[i+1] - ai[i];
4893       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
4894       /* off-diagonal portion of A */
4895       for (j=jo; j<ncols_o; j++) {
4896         *cam++ = *ba++; bj++;
4897       }
4898     }
4899   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
4900   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4901   PetscFunctionReturn(0);
4902 }
4903 
4904 /*@C
4905      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MATMPIAIJ matrix by taking all its local rows and NON-ZERO columns
4906 
4907     Not Collective
4908 
4909    Input Parameters:
4910 +    A - the matrix
4911 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4912 -    row, col - index sets of rows and columns to extract (or NULL)
4913 
4914    Output Parameter:
4915 .    A_loc - the local sequential matrix generated
4916 
4917     Level: developer
4918 
4919 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
4920 
4921 @*/
4922 PetscErrorCode MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
4923 {
4924   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4925   PetscErrorCode ierr;
4926   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
4927   IS             isrowa,iscola;
4928   Mat            *aloc;
4929   PetscBool      match;
4930 
4931   PetscFunctionBegin;
4932   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4933   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
4934   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4935   if (!row) {
4936     start = A->rmap->rstart; end = A->rmap->rend;
4937     ierr  = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
4938   } else {
4939     isrowa = *row;
4940   }
4941   if (!col) {
4942     start = A->cmap->rstart;
4943     cmap  = a->garray;
4944     nzA   = a->A->cmap->n;
4945     nzB   = a->B->cmap->n;
4946     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4947     ncols = 0;
4948     for (i=0; i<nzB; i++) {
4949       if (cmap[i] < start) idx[ncols++] = cmap[i];
4950       else break;
4951     }
4952     imark = i;
4953     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
4954     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
4955     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
4956   } else {
4957     iscola = *col;
4958   }
4959   if (scall != MAT_INITIAL_MATRIX) {
4960     ierr    = PetscMalloc1(1,&aloc);CHKERRQ(ierr);
4961     aloc[0] = *A_loc;
4962   }
4963   ierr   = MatCreateSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
4964   *A_loc = aloc[0];
4965   ierr   = PetscFree(aloc);CHKERRQ(ierr);
4966   if (!row) {
4967     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
4968   }
4969   if (!col) {
4970     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
4971   }
4972   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4973   PetscFunctionReturn(0);
4974 }
4975 
4976 /*@C
4977     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
4978 
4979     Collective on Mat
4980 
4981    Input Parameters:
4982 +    A,B - the matrices in mpiaij format
4983 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4984 -    rowb, colb - index sets of rows and columns of B to extract (or NULL)
4985 
4986    Output Parameter:
4987 +    rowb, colb - index sets of rows and columns of B to extract
4988 -    B_seq - the sequential matrix generated
4989 
4990     Level: developer
4991 
4992 @*/
4993 PetscErrorCode MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
4994 {
4995   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4996   PetscErrorCode ierr;
4997   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
4998   IS             isrowb,iscolb;
4999   Mat            *bseq=NULL;
5000 
5001   PetscFunctionBegin;
5002   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
5003     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);
5004   }
5005   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
5006 
5007   if (scall == MAT_INITIAL_MATRIX) {
5008     start = A->cmap->rstart;
5009     cmap  = a->garray;
5010     nzA   = a->A->cmap->n;
5011     nzB   = a->B->cmap->n;
5012     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
5013     ncols = 0;
5014     for (i=0; i<nzB; i++) {  /* row < local row index */
5015       if (cmap[i] < start) idx[ncols++] = cmap[i];
5016       else break;
5017     }
5018     imark = i;
5019     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
5020     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
5021     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
5022     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
5023   } else {
5024     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
5025     isrowb  = *rowb; iscolb = *colb;
5026     ierr    = PetscMalloc1(1,&bseq);CHKERRQ(ierr);
5027     bseq[0] = *B_seq;
5028   }
5029   ierr   = MatCreateSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
5030   *B_seq = bseq[0];
5031   ierr   = PetscFree(bseq);CHKERRQ(ierr);
5032   if (!rowb) {
5033     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
5034   } else {
5035     *rowb = isrowb;
5036   }
5037   if (!colb) {
5038     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
5039   } else {
5040     *colb = iscolb;
5041   }
5042   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
5043   PetscFunctionReturn(0);
5044 }
5045 
5046 /*
5047     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
5048     of the OFF-DIAGONAL portion of local A
5049 
5050     Collective on Mat
5051 
5052    Input Parameters:
5053 +    A,B - the matrices in mpiaij format
5054 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5055 
5056    Output Parameter:
5057 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
5058 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
5059 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
5060 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
5061 
5062     Level: developer
5063 
5064 */
5065 PetscErrorCode MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
5066 {
5067   VecScatter_MPI_General *gen_to,*gen_from;
5068   PetscErrorCode         ierr;
5069   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
5070   Mat_SeqAIJ             *b_oth;
5071   VecScatter             ctx =a->Mvctx;
5072   MPI_Comm               comm;
5073   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
5074   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
5075   PetscInt               *rvalues,*svalues;
5076   MatScalar              *b_otha,*bufa,*bufA;
5077   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
5078   MPI_Request            *rwaits = NULL,*swaits = NULL;
5079   MPI_Status             *sstatus,rstatus;
5080   PetscMPIInt            jj,size;
5081   PetscInt               *cols,sbs,rbs;
5082   PetscScalar            *vals;
5083 
5084   PetscFunctionBegin;
5085   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
5086   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
5087 
5088   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
5089     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);
5090   }
5091   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5092   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
5093 
5094   if (size == 1) {
5095     startsj_s = NULL;
5096     bufa_ptr  = NULL;
5097     *B_oth    = NULL;
5098     PetscFunctionReturn(0);
5099   }
5100 
5101   gen_to   = (VecScatter_MPI_General*)ctx->todata;
5102   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
5103   nrecvs   = gen_from->n;
5104   nsends   = gen_to->n;
5105 
5106   ierr    = PetscMalloc2(nrecvs,&rwaits,nsends,&swaits);CHKERRQ(ierr);
5107   srow    = gen_to->indices;    /* local row index to be sent */
5108   sstarts = gen_to->starts;
5109   sprocs  = gen_to->procs;
5110   sstatus = gen_to->sstatus;
5111   sbs     = gen_to->bs;
5112   rstarts = gen_from->starts;
5113   rprocs  = gen_from->procs;
5114   rbs     = gen_from->bs;
5115 
5116   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
5117   if (scall == MAT_INITIAL_MATRIX) {
5118     /* i-array */
5119     /*---------*/
5120     /*  post receives */
5121     ierr = PetscMalloc1(rbs*(rstarts[nrecvs] - rstarts[0]),&rvalues);CHKERRQ(ierr);
5122     for (i=0; i<nrecvs; i++) {
5123       rowlen = rvalues + rstarts[i]*rbs;
5124       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
5125       ierr   = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5126     }
5127 
5128     /* pack the outgoing message */
5129     ierr = PetscMalloc2(nsends+1,&sstartsj,nrecvs+1,&rstartsj);CHKERRQ(ierr);
5130 
5131     sstartsj[0] = 0;
5132     rstartsj[0] = 0;
5133     len         = 0; /* total length of j or a array to be sent */
5134     k           = 0;
5135     ierr = PetscMalloc1(sbs*(sstarts[nsends] - sstarts[0]),&svalues);CHKERRQ(ierr);
5136     for (i=0; i<nsends; i++) {
5137       rowlen = svalues + sstarts[i]*sbs;
5138       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
5139       for (j=0; j<nrows; j++) {
5140         row = srow[k] + B->rmap->range[rank]; /* global row idx */
5141         for (l=0; l<sbs; l++) {
5142           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr); /* rowlength */
5143 
5144           rowlen[j*sbs+l] = ncols;
5145 
5146           len += ncols;
5147           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr);
5148         }
5149         k++;
5150       }
5151       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5152 
5153       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
5154     }
5155     /* recvs and sends of i-array are completed */
5156     i = nrecvs;
5157     while (i--) {
5158       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5159     }
5160     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5161     ierr = PetscFree(svalues);CHKERRQ(ierr);
5162 
5163     /* allocate buffers for sending j and a arrays */
5164     ierr = PetscMalloc1(len+1,&bufj);CHKERRQ(ierr);
5165     ierr = PetscMalloc1(len+1,&bufa);CHKERRQ(ierr);
5166 
5167     /* create i-array of B_oth */
5168     ierr = PetscMalloc1(aBn+2,&b_othi);CHKERRQ(ierr);
5169 
5170     b_othi[0] = 0;
5171     len       = 0; /* total length of j or a array to be received */
5172     k         = 0;
5173     for (i=0; i<nrecvs; i++) {
5174       rowlen = rvalues + rstarts[i]*rbs;
5175       nrows  = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be received */
5176       for (j=0; j<nrows; j++) {
5177         b_othi[k+1] = b_othi[k] + rowlen[j];
5178         ierr = PetscIntSumError(rowlen[j],len,&len);CHKERRQ(ierr);
5179         k++;
5180       }
5181       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
5182     }
5183     ierr = PetscFree(rvalues);CHKERRQ(ierr);
5184 
5185     /* allocate space for j and a arrrays of B_oth */
5186     ierr = PetscMalloc1(b_othi[aBn]+1,&b_othj);CHKERRQ(ierr);
5187     ierr = PetscMalloc1(b_othi[aBn]+1,&b_otha);CHKERRQ(ierr);
5188 
5189     /* j-array */
5190     /*---------*/
5191     /*  post receives of j-array */
5192     for (i=0; i<nrecvs; i++) {
5193       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5194       ierr  = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5195     }
5196 
5197     /* pack the outgoing message j-array */
5198     k = 0;
5199     for (i=0; i<nsends; i++) {
5200       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5201       bufJ  = bufj+sstartsj[i];
5202       for (j=0; j<nrows; j++) {
5203         row = srow[k++] + B->rmap->range[rank];  /* global row idx */
5204         for (ll=0; ll<sbs; ll++) {
5205           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
5206           for (l=0; l<ncols; l++) {
5207             *bufJ++ = cols[l];
5208           }
5209           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
5210         }
5211       }
5212       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5213     }
5214 
5215     /* recvs and sends of j-array are completed */
5216     i = nrecvs;
5217     while (i--) {
5218       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5219     }
5220     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5221   } else if (scall == MAT_REUSE_MATRIX) {
5222     sstartsj = *startsj_s;
5223     rstartsj = *startsj_r;
5224     bufa     = *bufa_ptr;
5225     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
5226     b_otha   = b_oth->a;
5227   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
5228 
5229   /* a-array */
5230   /*---------*/
5231   /*  post receives of a-array */
5232   for (i=0; i<nrecvs; i++) {
5233     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5234     ierr  = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5235   }
5236 
5237   /* pack the outgoing message a-array */
5238   k = 0;
5239   for (i=0; i<nsends; i++) {
5240     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5241     bufA  = bufa+sstartsj[i];
5242     for (j=0; j<nrows; j++) {
5243       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
5244       for (ll=0; ll<sbs; ll++) {
5245         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
5246         for (l=0; l<ncols; l++) {
5247           *bufA++ = vals[l];
5248         }
5249         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
5250       }
5251     }
5252     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5253   }
5254   /* recvs and sends of a-array are completed */
5255   i = nrecvs;
5256   while (i--) {
5257     ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5258   }
5259   if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5260   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
5261 
5262   if (scall == MAT_INITIAL_MATRIX) {
5263     /* put together the new matrix */
5264     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
5265 
5266     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
5267     /* Since these are PETSc arrays, change flags to free them as necessary. */
5268     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
5269     b_oth->free_a  = PETSC_TRUE;
5270     b_oth->free_ij = PETSC_TRUE;
5271     b_oth->nonew   = 0;
5272 
5273     ierr = PetscFree(bufj);CHKERRQ(ierr);
5274     if (!startsj_s || !bufa_ptr) {
5275       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
5276       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
5277     } else {
5278       *startsj_s = sstartsj;
5279       *startsj_r = rstartsj;
5280       *bufa_ptr  = bufa;
5281     }
5282   }
5283   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5284   PetscFunctionReturn(0);
5285 }
5286 
5287 /*@C
5288   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
5289 
5290   Not Collective
5291 
5292   Input Parameters:
5293 . A - The matrix in mpiaij format
5294 
5295   Output Parameter:
5296 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
5297 . colmap - A map from global column index to local index into lvec
5298 - multScatter - A scatter from the argument of a matrix-vector product to lvec
5299 
5300   Level: developer
5301 
5302 @*/
5303 #if defined(PETSC_USE_CTABLE)
5304 PetscErrorCode MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
5305 #else
5306 PetscErrorCode MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
5307 #endif
5308 {
5309   Mat_MPIAIJ *a;
5310 
5311   PetscFunctionBegin;
5312   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
5313   PetscValidPointer(lvec, 2);
5314   PetscValidPointer(colmap, 3);
5315   PetscValidPointer(multScatter, 4);
5316   a = (Mat_MPIAIJ*) A->data;
5317   if (lvec) *lvec = a->lvec;
5318   if (colmap) *colmap = a->colmap;
5319   if (multScatter) *multScatter = a->Mvctx;
5320   PetscFunctionReturn(0);
5321 }
5322 
5323 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
5324 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
5325 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
5326 #if defined(PETSC_HAVE_ELEMENTAL)
5327 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
5328 #endif
5329 #if defined(PETSC_HAVE_HYPRE)
5330 PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat,MatType,MatReuse,Mat*);
5331 PETSC_INTERN PetscErrorCode MatMatMatMult_Transpose_AIJ_AIJ(Mat,Mat,Mat,MatReuse,PetscReal,Mat*);
5332 #endif
5333 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_IS(Mat,MatType,MatReuse,Mat*);
5334 
5335 /*
5336     Computes (B'*A')' since computing B*A directly is untenable
5337 
5338                n                       p                          p
5339         (              )       (              )         (                  )
5340       m (      A       )  *  n (       B      )   =   m (         C        )
5341         (              )       (              )         (                  )
5342 
5343 */
5344 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
5345 {
5346   PetscErrorCode ierr;
5347   Mat            At,Bt,Ct;
5348 
5349   PetscFunctionBegin;
5350   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
5351   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
5352   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
5353   ierr = MatDestroy(&At);CHKERRQ(ierr);
5354   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
5355   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
5356   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
5357   PetscFunctionReturn(0);
5358 }
5359 
5360 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
5361 {
5362   PetscErrorCode ierr;
5363   PetscInt       m=A->rmap->n,n=B->cmap->n;
5364   Mat            Cmat;
5365 
5366   PetscFunctionBegin;
5367   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);
5368   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
5369   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
5370   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
5371   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
5372   ierr = MatMPIDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
5373   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5374   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5375 
5376   Cmat->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
5377 
5378   *C = Cmat;
5379   PetscFunctionReturn(0);
5380 }
5381 
5382 /* ----------------------------------------------------------------*/
5383 PETSC_INTERN PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
5384 {
5385   PetscErrorCode ierr;
5386 
5387   PetscFunctionBegin;
5388   if (scall == MAT_INITIAL_MATRIX) {
5389     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5390     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
5391     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5392   }
5393   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5394   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
5395   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5396   PetscFunctionReturn(0);
5397 }
5398 
5399 /*MC
5400    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
5401 
5402    Options Database Keys:
5403 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
5404 
5405   Level: beginner
5406 
5407 .seealso: MatCreateAIJ()
5408 M*/
5409 
5410 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
5411 {
5412   Mat_MPIAIJ     *b;
5413   PetscErrorCode ierr;
5414   PetscMPIInt    size;
5415 
5416   PetscFunctionBegin;
5417   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
5418 
5419   ierr          = PetscNewLog(B,&b);CHKERRQ(ierr);
5420   B->data       = (void*)b;
5421   ierr          = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
5422   B->assembled  = PETSC_FALSE;
5423   B->insertmode = NOT_SET_VALUES;
5424   b->size       = size;
5425 
5426   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank);CHKERRQ(ierr);
5427 
5428   /* build cache for off array entries formed */
5429   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash);CHKERRQ(ierr);
5430 
5431   b->donotstash  = PETSC_FALSE;
5432   b->colmap      = 0;
5433   b->garray      = 0;
5434   b->roworiented = PETSC_TRUE;
5435 
5436   /* stuff used for matrix vector multiply */
5437   b->lvec  = NULL;
5438   b->Mvctx = NULL;
5439 
5440   /* stuff for MatGetRow() */
5441   b->rowindices   = 0;
5442   b->rowvalues    = 0;
5443   b->getrowactive = PETSC_FALSE;
5444 
5445   /* flexible pointer used in CUSP/CUSPARSE classes */
5446   b->spptr = NULL;
5447 
5448   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetUseScalableIncreaseOverlap_C",MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ);CHKERRQ(ierr);
5449   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ);CHKERRQ(ierr);
5450   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
5451   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
5452   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
5453   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
5454   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
5455   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
5456   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
5457   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
5458 #if defined(PETSC_HAVE_ELEMENTAL)
5459   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_elemental_C",MatConvert_MPIAIJ_Elemental);CHKERRQ(ierr);
5460 #endif
5461 #if defined(PETSC_HAVE_HYPRE)
5462   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_hypre_C",MatConvert_AIJ_HYPRE);CHKERRQ(ierr);
5463 #endif
5464   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_is_C",MatConvert_MPIAIJ_IS);CHKERRQ(ierr);
5465   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
5466   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
5467   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
5468 #if defined(PETSC_HAVE_HYPRE)
5469   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMatMult_transpose_mpiaij_mpiaij_C",MatMatMatMult_Transpose_AIJ_AIJ);CHKERRQ(ierr);
5470 #endif
5471   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
5472   PetscFunctionReturn(0);
5473 }
5474 
5475 /*@C
5476      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
5477          and "off-diagonal" part of the matrix in CSR format.
5478 
5479    Collective on MPI_Comm
5480 
5481    Input Parameters:
5482 +  comm - MPI communicator
5483 .  m - number of local rows (Cannot be PETSC_DECIDE)
5484 .  n - This value should be the same as the local size used in creating the
5485        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
5486        calculated if N is given) For square matrices n is almost always m.
5487 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
5488 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
5489 .   i - row indices for "diagonal" portion of matrix
5490 .   j - column indices
5491 .   a - matrix values
5492 .   oi - row indices for "off-diagonal" portion of matrix
5493 .   oj - column indices
5494 -   oa - matrix values
5495 
5496    Output Parameter:
5497 .   mat - the matrix
5498 
5499    Level: advanced
5500 
5501    Notes:
5502        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
5503        must free the arrays once the matrix has been destroyed and not before.
5504 
5505        The i and j indices are 0 based
5506 
5507        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
5508 
5509        This sets local rows and cannot be used to set off-processor values.
5510 
5511        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
5512        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
5513        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
5514        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
5515        keep track of the underlying array. Use MatSetOption(A,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
5516        communication if it is known that only local entries will be set.
5517 
5518 .keywords: matrix, aij, compressed row, sparse, parallel
5519 
5520 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
5521           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
5522 @*/
5523 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)
5524 {
5525   PetscErrorCode ierr;
5526   Mat_MPIAIJ     *maij;
5527 
5528   PetscFunctionBegin;
5529   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
5530   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
5531   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
5532   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
5533   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
5534   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
5535   maij = (Mat_MPIAIJ*) (*mat)->data;
5536 
5537   (*mat)->preallocated = PETSC_TRUE;
5538 
5539   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
5540   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
5541 
5542   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
5543   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
5544 
5545   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5546   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5547   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5548   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5549 
5550   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
5551   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5552   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5553   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_FALSE);CHKERRQ(ierr);
5554   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
5555   PetscFunctionReturn(0);
5556 }
5557 
5558 /*
5559     Special version for direct calls from Fortran
5560 */
5561 #include <petsc/private/fortranimpl.h>
5562 
5563 /* Change these macros so can be used in void function */
5564 #undef CHKERRQ
5565 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
5566 #undef SETERRQ2
5567 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5568 #undef SETERRQ3
5569 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5570 #undef SETERRQ
5571 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
5572 
5573 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5574 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
5575 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5576 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
5577 #else
5578 #endif
5579 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)
5580 {
5581   Mat            mat  = *mmat;
5582   PetscInt       m    = *mm, n = *mn;
5583   InsertMode     addv = *maddv;
5584   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
5585   PetscScalar    value;
5586   PetscErrorCode ierr;
5587 
5588   MatCheckPreallocated(mat,1);
5589   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
5590 
5591 #if defined(PETSC_USE_DEBUG)
5592   else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
5593 #endif
5594   {
5595     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
5596     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
5597     PetscBool roworiented = aij->roworiented;
5598 
5599     /* Some Variables required in the macro */
5600     Mat        A                 = aij->A;
5601     Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
5602     PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
5603     MatScalar  *aa               = a->a;
5604     PetscBool  ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
5605     Mat        B                 = aij->B;
5606     Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
5607     PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5608     MatScalar  *ba               = b->a;
5609 
5610     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5611     PetscInt  nonew = a->nonew;
5612     MatScalar *ap1,*ap2;
5613 
5614     PetscFunctionBegin;
5615     for (i=0; i<m; i++) {
5616       if (im[i] < 0) continue;
5617 #if defined(PETSC_USE_DEBUG)
5618       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);
5619 #endif
5620       if (im[i] >= rstart && im[i] < rend) {
5621         row      = im[i] - rstart;
5622         lastcol1 = -1;
5623         rp1      = aj + ai[row];
5624         ap1      = aa + ai[row];
5625         rmax1    = aimax[row];
5626         nrow1    = ailen[row];
5627         low1     = 0;
5628         high1    = nrow1;
5629         lastcol2 = -1;
5630         rp2      = bj + bi[row];
5631         ap2      = ba + bi[row];
5632         rmax2    = bimax[row];
5633         nrow2    = bilen[row];
5634         low2     = 0;
5635         high2    = nrow2;
5636 
5637         for (j=0; j<n; j++) {
5638           if (roworiented) value = v[i*n+j];
5639           else value = v[i+j*m];
5640           if (in[j] >= cstart && in[j] < cend) {
5641             col = in[j] - cstart;
5642             if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
5643             MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
5644           } else if (in[j] < 0) continue;
5645 #if defined(PETSC_USE_DEBUG)
5646           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);
5647 #endif
5648           else {
5649             if (mat->was_assembled) {
5650               if (!aij->colmap) {
5651                 ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5652               }
5653 #if defined(PETSC_USE_CTABLE)
5654               ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5655               col--;
5656 #else
5657               col = aij->colmap[in[j]] - 1;
5658 #endif
5659               if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
5660               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5661                 ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5662                 col  =  in[j];
5663                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5664                 B     = aij->B;
5665                 b     = (Mat_SeqAIJ*)B->data;
5666                 bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5667                 rp2   = bj + bi[row];
5668                 ap2   = ba + bi[row];
5669                 rmax2 = bimax[row];
5670                 nrow2 = bilen[row];
5671                 low2  = 0;
5672                 high2 = nrow2;
5673                 bm    = aij->B->rmap->n;
5674                 ba    = b->a;
5675               }
5676             } else col = in[j];
5677             MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
5678           }
5679         }
5680       } else if (!aij->donotstash) {
5681         if (roworiented) {
5682           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5683         } else {
5684           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5685         }
5686       }
5687     }
5688   }
5689   PetscFunctionReturnVoid();
5690 }
5691 
5692