xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision b20e2604dfaee60fc39a02645a44403ff61f5145)
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 /* 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,*asub;
3110   Mat            M = NULL;
3111   MPI_Comm       comm;
3112   IS             iscol_d,isrow_d,iscol_o;
3113   Mat            Asub = NULL,Bsub = NULL;
3114   PetscInt       n;
3115 
3116   PetscFunctionBegin;
3117   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3118   PetscMPIInt rank;
3119   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3120 
3121   if (call == MAT_REUSE_MATRIX) {
3122     if (!rank) printf(" _SameRowColDist reuse ...\n");
3123 
3124     /* Retrieve isrow_d, iscol_d and iscol_o from submat */
3125     ierr = PetscObjectQuery((PetscObject)*submat,"isrow_d",(PetscObject*)&isrow_d);CHKERRQ(ierr);
3126     if (!isrow_d) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"isrow_d passed in was not used before, cannot reuse");
3127 
3128     ierr = PetscObjectQuery((PetscObject)*submat,"iscol_d",(PetscObject*)&iscol_d);CHKERRQ(ierr);
3129     if (!iscol_d) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"iscol_d passed in was not used before, cannot reuse");
3130 
3131     ierr = PetscObjectQuery((PetscObject)*submat,"iscol_o",(PetscObject*)&iscol_o);CHKERRQ(ierr);
3132     if (!iscol_o) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"iscol_o passed in was not used before, cannot reuse");
3133 
3134     /* Update diagonal and off-diagonal portions of submat */
3135     asub = (Mat_MPIAIJ*)(*submat)->data;
3136     ierr = MatCreateSubMatrix_SeqAIJ(a->A,isrow_d,iscol_d,PETSC_DECIDE,MAT_REUSE_MATRIX,&asub->A);CHKERRQ(ierr);
3137     ierr = ISGetLocalSize(iscol_o,&n);CHKERRQ(ierr);
3138     if (n) {
3139       ierr = MatCreateSubMatrix_SeqAIJ(a->B,isrow_d,iscol_o,PETSC_DECIDE,MAT_REUSE_MATRIX,&asub->B);CHKERRQ(ierr);
3140     }
3141     ierr = MatAssemblyBegin(*submat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3142     ierr = MatAssemblyEnd(*submat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3143 
3144   } else { /* call == MAT_INITIAL_MATRIX) */
3145     IS             isgarray;
3146     const PetscInt *garray1;
3147     PetscInt        BsubN;
3148 
3149     /* Create isrow_d, iscol_d, iscol_o and isgarray (replace isgarray with array?) */
3150     ierr = ISGetSeqIS_SameColDist_Private(mat,isrow,iscol,&isrow_d,&iscol_d,&iscol_o,&isgarray);CHKERRQ(ierr);
3151 
3152     /* Create local submatrices Asub and Bsub */
3153     ierr = MatCreateSubMatrix_SeqAIJ(a->A,isrow_d,iscol_d,PETSC_DECIDE,MAT_INITIAL_MATRIX,&Asub);CHKERRQ(ierr);
3154     ierr = MatCreateSubMatrix_SeqAIJ(a->B,isrow_d,iscol_o,PETSC_DECIDE,MAT_INITIAL_MATRIX,&Bsub);CHKERRQ(ierr);
3155 
3156     ierr = ISGetIndices(isgarray,&garray1);CHKERRQ(ierr);
3157     ierr = MatCreateMPIAIJWithSeqAIJ(comm,Asub,Bsub,garray1,&M);CHKERRQ(ierr);
3158     ierr = ISRestoreIndices(isgarray,&garray1);CHKERRQ(ierr);
3159 
3160     /* If Bsub has empty columns, compress iscol_o such that it will retrieve condensed Bsub from a->B during reuse */
3161     asub = (Mat_MPIAIJ*)M->data;
3162 
3163     ierr = ISGetLocalSize(isgarray,&BsubN);CHKERRQ(ierr);
3164     n = asub->B->cmap->N;
3165     if (BsubN > n) {
3166       /* This case can be tested using ~petsc/src/tao/bound/examples/tutorials/runplate2_3 */
3167       const PetscInt *idx;
3168       PetscInt       i,j,*idx_new,*garray = asub->garray; //idx_new[n],
3169       printf("[%d] BsubN %d != Bn %d, update iscol_o \n",rank,BsubN,n);
3170 
3171       ierr = PetscMalloc1(n,&idx_new);CHKERRQ(ierr);
3172       j = 0;
3173       ierr = ISGetIndices(iscol_o,&idx);CHKERRQ(ierr);
3174       for (i=0; i<n; i++) {
3175         if (j >= BsubN) break;
3176         while (garray[i] > garray1[j]) j++;
3177 
3178         if (garray[i] == garray1[j]) {
3179           idx_new[i] = idx[j++];
3180         } else SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"garray[%D]=%D cannot < garray1[%D]=%D",i,garray[i],j,garray1[j]);
3181       }
3182       ierr = ISRestoreIndices(iscol_o,&idx);CHKERRQ(ierr);
3183 
3184       ierr = ISDestroy(&iscol_o);CHKERRQ(ierr);
3185       ierr = ISCreateGeneral(PETSC_COMM_SELF,n,idx_new,PETSC_OWN_POINTER,&iscol_o);CHKERRQ(ierr);
3186 
3187     } else if (BsubN < n) {
3188       SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Columns of Bsub cannot be smaller than B's",BsubN,asub->B->cmap->N);
3189     }
3190 
3191     ierr = ISDestroy(&isgarray);CHKERRQ(ierr);
3192     *submat = M;
3193 
3194     /* Save isrow_d, iscol_d and iscol_o used in processor for next request */
3195     ierr = PetscObjectCompose((PetscObject)M,"isrow_d",(PetscObject)isrow_d);CHKERRQ(ierr);
3196     ierr = ISDestroy(&isrow_d);CHKERRQ(ierr);
3197 
3198     ierr = PetscObjectCompose((PetscObject)M,"iscol_d",(PetscObject)iscol_d);CHKERRQ(ierr);
3199     ierr = ISDestroy(&iscol_d);CHKERRQ(ierr);
3200 
3201     ierr = PetscObjectCompose((PetscObject)M,"iscol_o",(PetscObject)iscol_o);CHKERRQ(ierr);
3202     ierr = ISDestroy(&iscol_o);CHKERRQ(ierr);
3203   }
3204   PetscFunctionReturn(0);
3205 }
3206 
3207 PetscErrorCode MatCreateSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3208 {
3209   PetscErrorCode ierr;
3210   IS             iscol_local,isrow_d;
3211   PetscInt       csize;
3212   PetscInt       n,i,j,start,end;
3213   PetscBool      sameRowDist=PETSC_FALSE,sameDist[2],tsameDist[2];
3214   MPI_Comm       comm;
3215 
3216   PetscFunctionBegin;
3217   /* If isrow has same processor distribution as mat,
3218      call MatCreateSubMatrix_MPIAIJ_SameRowDist() to avoid using a hash table with global size of iscol */
3219   if (call == MAT_REUSE_MATRIX) {
3220     ierr = PetscObjectQuery((PetscObject)*newmat,"isrow_d",(PetscObject*)&isrow_d);CHKERRQ(ierr);
3221     if (isrow_d) {
3222       sameRowDist  = PETSC_TRUE;
3223       tsameDist[1] = PETSC_TRUE; /* sameColDist */
3224     } else {
3225       ierr = PetscObjectQuery((PetscObject)*newmat,"SubIScol",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3226       if (iscol_local) {
3227         sameRowDist  = PETSC_TRUE;
3228         tsameDist[1] = PETSC_FALSE; /* !sameColDist */
3229       }
3230     }
3231   } else {
3232     /* Check if isrow has same processor distribution as mat */
3233     sameDist[0] = PETSC_FALSE;
3234     ierr = ISGetLocalSize(isrow,&n);CHKERRQ(ierr);
3235     if (!n) {
3236       sameDist[0] = PETSC_TRUE;
3237     } else {
3238       ierr = ISGetMinMax(isrow,&i,&j);CHKERRQ(ierr);
3239       ierr = MatGetOwnershipRange(mat,&start,&end);CHKERRQ(ierr);
3240       if (i >= start && j < end) {
3241         sameDist[0] = PETSC_TRUE;
3242       }
3243     }
3244 
3245     /* Check if iscol has same processor distribution as mat */
3246     sameDist[1] = PETSC_FALSE;
3247     ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr);
3248     if (!n) {
3249       sameDist[1] = PETSC_TRUE;
3250     } else {
3251       ierr = ISGetMinMax(iscol,&i,&j);CHKERRQ(ierr);
3252       ierr = MatGetOwnershipRangeColumn(mat,&start,&end);CHKERRQ(ierr);
3253       if (i >= start && j < end) sameDist[1] = PETSC_TRUE;
3254     }
3255 
3256     ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3257     ierr = MPIU_Allreduce(&sameDist,&tsameDist,2,MPIU_BOOL,MPI_LAND,comm);CHKERRQ(ierr);
3258     sameRowDist = tsameDist[0];
3259   }
3260 
3261   if (sameRowDist) {
3262     if (tsameDist[1]) { /* sameRowDist & sameColDist */
3263       /* isrow and iscol have same processor distribution as mat */
3264       ierr = MatCreateSubMatrix_MPIAIJ_SameRowColDist(mat,isrow,iscol,call,newmat);CHKERRQ(ierr);
3265     } else { /* sameRowDist */
3266       /* isrow has same processor distribution as mat */
3267       ierr = MatCreateSubMatrix_MPIAIJ_SameRowDist(mat,isrow,iscol,call,newmat);CHKERRQ(ierr);
3268     }
3269     PetscFunctionReturn(0);
3270   }
3271 
3272   /* General case: iscol -> iscol_local which has global size of iscol */
3273   if (call == MAT_REUSE_MATRIX) {
3274     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3275     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3276   } else {
3277     ierr = ISGetSeqIS_Private(mat,iscol,&iscol_local);CHKERRQ(ierr);
3278   }
3279 
3280   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3281   ierr = MatCreateSubMatrix_MPIAIJ_nonscalable(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
3282 
3283   if (call == MAT_INITIAL_MATRIX) {
3284     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3285     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3286   }
3287   PetscFunctionReturn(0);
3288 }
3289 
3290 /*@C
3291      MatCreateMPIAIJWithSeqAIJ - creates a MPIAIJ matrix using SeqAIJ matrices that contain the "diagonal"
3292          and "off-diagonal" part of the matrix in CSR format.
3293 
3294    Collective on MPI_Comm
3295 
3296    Input Parameters:
3297 +  comm - MPI communicator
3298 .  A - "diagonal" portion of matrix
3299 .  B - "off-diagonal" portion of matrix, may have empty columns, will be destroyed by this routine
3300 -  garray - global index of B columns
3301 
3302    Output Parameter:
3303 .   mat - the matrix, with input A as its local diagonal matrix
3304    Level: advanced
3305 
3306    Notes:
3307        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix.
3308        A becomes part of output mat, B is destroyed by this routine. The user cannot use A and B anymore.
3309 
3310 .seealso: MatCreateMPIAIJWithSplitArrays()
3311 @*/
3312 PetscErrorCode MatCreateMPIAIJWithSeqAIJ(MPI_Comm comm,Mat A,Mat B,const PetscInt garray[],Mat *mat)
3313 {
3314   PetscErrorCode ierr;
3315   Mat_MPIAIJ     *maij;
3316   Mat_SeqAIJ     *b=(Mat_SeqAIJ*)B->data,*bnew;
3317   PetscInt       *oi=b->i,*oj=b->j,i,nz,col;
3318   PetscScalar    *oa=b->a;
3319   Mat            Bnew;
3320   PetscInt       m,n,N;
3321 
3322   PetscFunctionBegin;
3323   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
3324   ierr = MatGetSize(A,&m,&n);CHKERRQ(ierr);
3325   if (m != B->rmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Am %D != Bm %D",m,B->rmap->N);
3326   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);
3327   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);
3328 
3329   /* Get global columns of mat */
3330   ierr = MPIU_Allreduce(&n,&N,1,MPI_INT,MPI_SUM,comm);CHKERRQ(ierr);
3331 
3332   ierr = MatSetSizes(*mat,m,n,PETSC_DECIDE,N);CHKERRQ(ierr);
3333   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
3334   ierr = MatSetBlockSizes(*mat,A->rmap->bs,A->cmap->bs);CHKERRQ(ierr);
3335   maij = (Mat_MPIAIJ*)(*mat)->data;
3336 
3337   (*mat)->preallocated = PETSC_TRUE;
3338 
3339   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
3340   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
3341 
3342   /* Set A as diagonal portion of *mat */
3343   maij->A = A;
3344 
3345   nz = oi[m];
3346   for (i=0; i<nz; i++) {
3347     col   = oj[i];
3348     oj[i] = garray[col];
3349   }
3350 
3351    /* Set Bnew as off-diagonal portion of *mat */
3352   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,N,oi,oj,oa,&Bnew);CHKERRQ(ierr);
3353   bnew        = (Mat_SeqAIJ*)Bnew->data;
3354   bnew->maxnz = b->maxnz; /* allocated nonzeros of B */
3355   maij->B     = Bnew;
3356 
3357   if (B->rmap->N != Bnew->rmap->N) SETERRQ2(PETSC_COMM_SELF,0,"BN %d != BnewN %d",B->rmap->N,Bnew->rmap->N);
3358 
3359   b->singlemalloc = PETSC_FALSE; /* B arrays are shared by Bnew */
3360   b->free_a       = PETSC_FALSE;
3361   b->free_ij      = PETSC_FALSE;
3362   ierr = MatDestroy(&B);CHKERRQ(ierr);
3363 
3364   bnew->singlemalloc = PETSC_TRUE; /* arrays will be freed by MatDestroy(&Bnew) */
3365   bnew->free_a       = PETSC_TRUE;
3366   bnew->free_ij      = PETSC_TRUE;
3367 
3368   /* condense columns of maij->B */
3369   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
3370   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3371   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3372   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_FALSE);CHKERRQ(ierr);
3373   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3374   PetscFunctionReturn(0);
3375 }
3376 
3377 extern PetscErrorCode MatCreateSubMatrices_MPIAIJ_SingleIS_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool,Mat*);
3378 
3379 PetscErrorCode MatCreateSubMatrix_MPIAIJ_SameRowDist(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3380 {
3381   PetscErrorCode ierr;
3382   PetscInt       i,m,n,rstart,row,rend,nz,j,bs,cbs;
3383   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
3384   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)mat->data;
3385   Mat            M,Msub,B=a->B;
3386   MatScalar      *aa;
3387   Mat_SeqAIJ     *aij;
3388   PetscInt       *garray = a->garray,*colsub,Ncols;
3389   PetscInt       count,Bn=B->cmap->N,cstart=mat->cmap->rstart,cend=mat->cmap->rend;
3390   IS             iscol_sub,iscmap;
3391   const PetscInt *is_idx,*cmap;
3392   PetscBool      allcolumns=PETSC_FALSE;
3393   IS             iscol_local=NULL;
3394   MPI_Comm       comm;
3395 
3396   PetscFunctionBegin;
3397   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3398 
3399   if (call == MAT_REUSE_MATRIX) {
3400     ierr = PetscObjectQuery((PetscObject)*newmat,"SubIScol",(PetscObject*)&iscol_sub);CHKERRQ(ierr);
3401     if (!iscol_sub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"SubIScol passed in was not used before, cannot reuse");
3402     ierr = ISGetLocalSize(iscol_sub,&count);CHKERRQ(ierr);
3403 
3404     ierr = PetscObjectQuery((PetscObject)*newmat,"Subcmap",(PetscObject*)&iscmap);CHKERRQ(ierr);
3405     if (!iscmap) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Subcmap passed in was not used before, cannot reuse");
3406 
3407     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Msub);CHKERRQ(ierr);
3408     if (!Msub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3409 
3410     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol_sub,MAT_REUSE_MATRIX,PETSC_FALSE,&Msub);CHKERRQ(ierr);
3411 
3412   } else { /* call == MAT_INITIAL_MATRIX) */
3413     PetscBool flg;
3414 
3415     ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr);
3416     ierr = ISGetSize(iscol,&Ncols);CHKERRQ(ierr);
3417 
3418     /* (1) iscol -> nonscalable iscol_local */
3419     ierr = ISGetSeqIS_Private(mat,iscol,&iscol_local);CHKERRQ(ierr);
3420     ierr = ISGetLocalSize(iscol_local,&n);CHKERRQ(ierr); /* local size of iscol_local = global columns of newmat */
3421     if (n != Ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"n %d != Ncols %d",n,Ncols);
3422 
3423     /* Check for special case: each processor gets entire matrix columns */
3424     ierr = ISIdentity(iscol_local,&flg);CHKERRQ(ierr);
3425     if (flg && n == mat->cmap->N) allcolumns = PETSC_TRUE;
3426     if (allcolumns) {
3427       iscol_sub = iscol_local;
3428       ierr = PetscObjectReference((PetscObject)iscol_local);CHKERRQ(ierr);
3429       ierr = ISCreateStride(PETSC_COMM_SELF,n,0,1,&iscmap);CHKERRQ(ierr);
3430 
3431     } else {
3432       /* (2) iscol_local -> iscol_sub and iscmap */
3433       PetscInt *idx,*cmap1,k,cbs;
3434 
3435       /* implementation below requires iscol_local be sorted, it can have duplicate indices */
3436       ierr = ISSorted(iscol_local,&flg);CHKERRQ(ierr);
3437       if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"unsorted iscol_local is not implemented yet");
3438 
3439       ierr = PetscMalloc1(Ncols,&idx);CHKERRQ(ierr);
3440       ierr = PetscMalloc1(Ncols,&cmap1);CHKERRQ(ierr);
3441       ierr = ISGetIndices(iscol_local,&is_idx);CHKERRQ(ierr);
3442       count = 0;
3443       k     = 0;
3444       for (i=0; i<Ncols; i++) {
3445         j = is_idx[i];
3446         if (j >= cstart && j < cend) {
3447           /* diagonal part of mat */
3448           idx[count]     = j;
3449           cmap1[count++] = i; /* column index in submat */
3450         } else if (Bn) {
3451           /* off-diagonal part of mat */
3452           if (j == garray[k]) {
3453             idx[count]     = j;
3454             cmap1[count++] = i;  /* column index in submat */
3455           } else if (j > garray[k]) {
3456             while (j > garray[k] && k < Bn-1) k++;
3457             if (j == garray[k]) {
3458               idx[count]     = j;
3459               cmap1[count++] = i; /* column index in submat */
3460             }
3461           }
3462         }
3463       }
3464       ierr = ISRestoreIndices(iscol_local,&is_idx);CHKERRQ(ierr);
3465 
3466       ierr = ISCreateGeneral(PETSC_COMM_SELF,count,idx,PETSC_OWN_POINTER,&iscol_sub);CHKERRQ(ierr);
3467       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
3468       ierr = ISSetBlockSize(iscol_sub,cbs);CHKERRQ(ierr);
3469 
3470       ierr = ISCreateGeneral(PetscObjectComm((PetscObject)iscol_local),count,cmap1,PETSC_OWN_POINTER,&iscmap);CHKERRQ(ierr);
3471     }
3472 
3473     /* (3) Create sequential Msub */
3474     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol_sub,MAT_INITIAL_MATRIX,allcolumns,&Msub);CHKERRQ(ierr);
3475   }
3476 
3477   ierr = ISGetLocalSize(iscol_sub,&count);CHKERRQ(ierr);
3478   aij  = (Mat_SeqAIJ*)(Msub)->data;
3479   ii   = aij->i;
3480   ierr = ISGetIndices(iscmap,&cmap);CHKERRQ(ierr);
3481 
3482   /*
3483       m - number of local rows
3484       Ncols - number of columns (same on all processors)
3485       rstart - first row in new global matrix generated
3486   */
3487   ierr = MatGetSize(Msub,&m,NULL);CHKERRQ(ierr);
3488 
3489   if (call == MAT_INITIAL_MATRIX) {
3490     /* (4) Create parallel newmat */
3491     PetscMPIInt    rank,size;
3492     PetscInt       csize;
3493 
3494     ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3495     ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3496 
3497     /*
3498         Determine the number of non-zeros in the diagonal and off-diagonal
3499         portions of the matrix in order to do correct preallocation
3500     */
3501 
3502     /* first get start and end of "diagonal" columns */
3503     ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3504     if (csize == PETSC_DECIDE) {
3505       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3506       if (mglobal == Ncols) { /* square matrix */
3507         nlocal = m;
3508       } else {
3509         nlocal = Ncols/size + ((Ncols % size) > rank);
3510       }
3511     } else {
3512       nlocal = csize;
3513     }
3514     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3515     rstart = rend - nlocal;
3516     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);
3517 
3518     /* next, compute all the lengths */
3519     jj    = aij->j;
3520     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3521     olens = dlens + m;
3522     for (i=0; i<m; i++) {
3523       jend = ii[i+1] - ii[i];
3524       olen = 0;
3525       dlen = 0;
3526       for (j=0; j<jend; j++) {
3527         if (cmap[*jj] < rstart || cmap[*jj] >= rend) olen++;
3528         else dlen++;
3529         jj++;
3530       }
3531       olens[i] = olen;
3532       dlens[i] = dlen;
3533     }
3534     ierr = MatGetBlockSizes(Msub,&bs,&cbs);CHKERRQ(ierr);
3535 
3536     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3537     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,Ncols);CHKERRQ(ierr);
3538     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3539     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3540     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3541     ierr = PetscFree(dlens);CHKERRQ(ierr);
3542 
3543   } else { /* call == MAT_REUSE_MATRIX */
3544     M    = *newmat;
3545     ierr = MatGetLocalSize(M,&i,NULL);CHKERRQ(ierr);
3546     if (i != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3547     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3548     /*
3549          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3550        rather than the slower MatSetValues().
3551     */
3552     M->was_assembled = PETSC_TRUE;
3553     M->assembled     = PETSC_FALSE;
3554   }
3555 
3556   /* (5) Set values of Msub to *newmat */
3557   ierr = PetscMalloc1(count,&colsub);CHKERRQ(ierr);
3558   ierr = MatGetOwnershipRange(M,&rstart,NULL);CHKERRQ(ierr);
3559 
3560   jj   = aij->j;
3561   aa   = aij->a;
3562   for (i=0; i<m; i++) {
3563     row = rstart + i;
3564     nz  = ii[i+1] - ii[i];
3565     for (j=0; j<nz; j++) colsub[j] = cmap[jj[j]];
3566     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,colsub,aa,INSERT_VALUES);CHKERRQ(ierr);
3567     jj += nz; aa += nz;
3568   }
3569   ierr = ISRestoreIndices(iscmap,&cmap);CHKERRQ(ierr);
3570 
3571   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3572   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3573 
3574   ierr = PetscFree(colsub);CHKERRQ(ierr);
3575 
3576   /* save Msub, iscol_sub and iscmap used in processor for next request */
3577   if (call ==  MAT_INITIAL_MATRIX) {
3578     *newmat = M;
3579     ierr = PetscObjectCompose((PetscObject)(*newmat),"SubMatrix",(PetscObject)Msub);CHKERRQ(ierr);
3580     ierr = MatDestroy(&Msub);CHKERRQ(ierr);
3581 
3582     ierr = PetscObjectCompose((PetscObject)(*newmat),"SubIScol",(PetscObject)iscol_sub);CHKERRQ(ierr);
3583     ierr = ISDestroy(&iscol_sub);CHKERRQ(ierr);
3584 
3585     ierr = PetscObjectCompose((PetscObject)(*newmat),"Subcmap",(PetscObject)iscmap);CHKERRQ(ierr);
3586     ierr = ISDestroy(&iscmap);CHKERRQ(ierr);
3587 
3588     if (iscol_local) {
3589       ierr = PetscObjectCompose((PetscObject)(*newmat),"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3590       ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3591     }
3592   }
3593   PetscFunctionReturn(0);
3594 }
3595 
3596 /*
3597     Not great since it makes two copies of the submatrix, first an SeqAIJ
3598   in local and then by concatenating the local matrices the end result.
3599   Writing it directly would be much like MatCreateSubMatrices_MPIAIJ()
3600 
3601   Note: This requires a sequential iscol with all indices.
3602 */
3603 PetscErrorCode MatCreateSubMatrix_MPIAIJ_nonscalable(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3604 {
3605   PetscErrorCode ierr;
3606   PetscMPIInt    rank,size;
3607   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3608   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
3609   Mat            M,Mreuse;
3610   MatScalar      *aa,*vwork;
3611   MPI_Comm       comm;
3612   Mat_SeqAIJ     *aij;
3613   PetscBool      colflag,allcolumns=PETSC_FALSE;
3614 
3615   PetscFunctionBegin;
3616   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3617   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3618   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3619 
3620   /* Check for special case: each processor gets entire matrix columns */
3621   ierr = ISIdentity(iscol,&colflag);CHKERRQ(ierr);
3622   ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr);
3623   if (colflag && n == mat->cmap->N) allcolumns = PETSC_TRUE;
3624 
3625   if (call ==  MAT_REUSE_MATRIX) {
3626     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3627     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3628     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,allcolumns,&Mreuse);CHKERRQ(ierr);
3629   } else {
3630     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,allcolumns,&Mreuse);CHKERRQ(ierr);
3631   }
3632 
3633   /*
3634       m - number of local rows
3635       n - number of columns (same on all processors)
3636       rstart - first row in new global matrix generated
3637   */
3638   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3639   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3640   if (call == MAT_INITIAL_MATRIX) {
3641     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3642     ii  = aij->i;
3643     jj  = aij->j;
3644 
3645     /*
3646         Determine the number of non-zeros in the diagonal and off-diagonal
3647         portions of the matrix in order to do correct preallocation
3648     */
3649 
3650     /* first get start and end of "diagonal" columns */
3651     if (csize == PETSC_DECIDE) {
3652       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3653       if (mglobal == n) { /* square matrix */
3654         nlocal = m;
3655       } else {
3656         nlocal = n/size + ((n % size) > rank);
3657       }
3658     } else {
3659       nlocal = csize;
3660     }
3661     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3662     rstart = rend - nlocal;
3663     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);
3664 
3665     /* next, compute all the lengths */
3666     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3667     olens = dlens + m;
3668     for (i=0; i<m; i++) {
3669       jend = ii[i+1] - ii[i];
3670       olen = 0;
3671       dlen = 0;
3672       for (j=0; j<jend; j++) {
3673         if (*jj < rstart || *jj >= rend) olen++;
3674         else dlen++;
3675         jj++;
3676       }
3677       olens[i] = olen;
3678       dlens[i] = dlen;
3679     }
3680     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3681     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3682     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3683     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3684     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3685     ierr = PetscFree(dlens);CHKERRQ(ierr);
3686   } else {
3687     PetscInt ml,nl;
3688 
3689     M    = *newmat;
3690     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3691     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3692     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3693     /*
3694          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3695        rather than the slower MatSetValues().
3696     */
3697     M->was_assembled = PETSC_TRUE;
3698     M->assembled     = PETSC_FALSE;
3699   }
3700   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3701   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3702   ii   = aij->i;
3703   jj   = aij->j;
3704   aa   = aij->a;
3705   for (i=0; i<m; i++) {
3706     row   = rstart + i;
3707     nz    = ii[i+1] - ii[i];
3708     cwork = jj;     jj += nz;
3709     vwork = aa;     aa += nz;
3710     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3711   }
3712 
3713   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3714   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3715   *newmat = M;
3716 
3717   /* save submatrix used in processor for next request */
3718   if (call ==  MAT_INITIAL_MATRIX) {
3719     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3720     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3721   }
3722   PetscFunctionReturn(0);
3723 }
3724 
3725 PetscErrorCode MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3726 {
3727   PetscInt       m,cstart, cend,j,nnz,i,d;
3728   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3729   const PetscInt *JJ;
3730   PetscScalar    *values;
3731   PetscErrorCode ierr;
3732   PetscBool      nooffprocentries;
3733 
3734   PetscFunctionBegin;
3735   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3736 
3737   ierr   = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3738   ierr   = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3739   m      = B->rmap->n;
3740   cstart = B->cmap->rstart;
3741   cend   = B->cmap->rend;
3742   rstart = B->rmap->rstart;
3743 
3744   ierr = PetscMalloc2(m,&d_nnz,m,&o_nnz);CHKERRQ(ierr);
3745 
3746 #if defined(PETSC_USE_DEBUGGING)
3747   for (i=0; i<m; i++) {
3748     nnz = Ii[i+1]- Ii[i];
3749     JJ  = J + Ii[i];
3750     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3751     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3752     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);
3753   }
3754 #endif
3755 
3756   for (i=0; i<m; i++) {
3757     nnz     = Ii[i+1]- Ii[i];
3758     JJ      = J + Ii[i];
3759     nnz_max = PetscMax(nnz_max,nnz);
3760     d       = 0;
3761     for (j=0; j<nnz; j++) {
3762       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3763     }
3764     d_nnz[i] = d;
3765     o_nnz[i] = nnz - d;
3766   }
3767   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3768   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3769 
3770   if (v) values = (PetscScalar*)v;
3771   else {
3772     ierr = PetscCalloc1(nnz_max+1,&values);CHKERRQ(ierr);
3773   }
3774 
3775   for (i=0; i<m; i++) {
3776     ii   = i + rstart;
3777     nnz  = Ii[i+1]- Ii[i];
3778     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3779   }
3780   nooffprocentries    = B->nooffprocentries;
3781   B->nooffprocentries = PETSC_TRUE;
3782   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3783   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3784   B->nooffprocentries = nooffprocentries;
3785 
3786   if (!v) {
3787     ierr = PetscFree(values);CHKERRQ(ierr);
3788   }
3789   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3790   PetscFunctionReturn(0);
3791 }
3792 
3793 /*@
3794    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3795    (the default parallel PETSc format).
3796 
3797    Collective on MPI_Comm
3798 
3799    Input Parameters:
3800 +  B - the matrix
3801 .  i - the indices into j for the start of each local row (starts with zero)
3802 .  j - the column indices for each local row (starts with zero)
3803 -  v - optional values in the matrix
3804 
3805    Level: developer
3806 
3807    Notes:
3808        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3809      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3810      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3811 
3812        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3813 
3814        The format which is used for the sparse matrix input, is equivalent to a
3815     row-major ordering.. i.e for the following matrix, the input data expected is
3816     as shown
3817 
3818 $        1 0 0
3819 $        2 0 3     P0
3820 $       -------
3821 $        4 5 6     P1
3822 $
3823 $     Process0 [P0]: rows_owned=[0,1]
3824 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3825 $        j =  {0,0,2}  [size = 3]
3826 $        v =  {1,2,3}  [size = 3]
3827 $
3828 $     Process1 [P1]: rows_owned=[2]
3829 $        i =  {0,3}    [size = nrow+1  = 1+1]
3830 $        j =  {0,1,2}  [size = 3]
3831 $        v =  {4,5,6}  [size = 3]
3832 
3833 .keywords: matrix, aij, compressed row, sparse, parallel
3834 
3835 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MATMPIAIJ,
3836           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3837 @*/
3838 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3839 {
3840   PetscErrorCode ierr;
3841 
3842   PetscFunctionBegin;
3843   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3844   PetscFunctionReturn(0);
3845 }
3846 
3847 /*@C
3848    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3849    (the default parallel PETSc format).  For good matrix assembly performance
3850    the user should preallocate the matrix storage by setting the parameters
3851    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3852    performance can be increased by more than a factor of 50.
3853 
3854    Collective on MPI_Comm
3855 
3856    Input Parameters:
3857 +  B - the matrix
3858 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3859            (same value is used for all local rows)
3860 .  d_nnz - array containing the number of nonzeros in the various rows of the
3861            DIAGONAL portion of the local submatrix (possibly different for each row)
3862            or NULL (PETSC_NULL_INTEGER in Fortran), if d_nz is used to specify the nonzero structure.
3863            The size of this array is equal to the number of local rows, i.e 'm'.
3864            For matrices that will be factored, you must leave room for (and set)
3865            the diagonal entry even if it is zero.
3866 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3867            submatrix (same value is used for all local rows).
3868 -  o_nnz - array containing the number of nonzeros in the various rows of the
3869            OFF-DIAGONAL portion of the local submatrix (possibly different for
3870            each row) or NULL (PETSC_NULL_INTEGER in Fortran), if o_nz is used to specify the nonzero
3871            structure. The size of this array is equal to the number
3872            of local rows, i.e 'm'.
3873 
3874    If the *_nnz parameter is given then the *_nz parameter is ignored
3875 
3876    The AIJ format (also called the Yale sparse matrix format or
3877    compressed row storage (CSR)), is fully compatible with standard Fortran 77
3878    storage.  The stored row and column indices begin with zero.
3879    See Users-Manual: ch_mat for details.
3880 
3881    The parallel matrix is partitioned such that the first m0 rows belong to
3882    process 0, the next m1 rows belong to process 1, the next m2 rows belong
3883    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
3884 
3885    The DIAGONAL portion of the local submatrix of a processor can be defined
3886    as the submatrix which is obtained by extraction the part corresponding to
3887    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
3888    first row that belongs to the processor, r2 is the last row belonging to
3889    the this processor, and c1-c2 is range of indices of the local part of a
3890    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
3891    common case of a square matrix, the row and column ranges are the same and
3892    the DIAGONAL part is also square. The remaining portion of the local
3893    submatrix (mxN) constitute the OFF-DIAGONAL portion.
3894 
3895    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3896 
3897    You can call MatGetInfo() to get information on how effective the preallocation was;
3898    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3899    You can also run with the option -info and look for messages with the string
3900    malloc in them to see if additional memory allocation was needed.
3901 
3902    Example usage:
3903 
3904    Consider the following 8x8 matrix with 34 non-zero values, that is
3905    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3906    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3907    as follows:
3908 
3909 .vb
3910             1  2  0  |  0  3  0  |  0  4
3911     Proc0   0  5  6  |  7  0  0  |  8  0
3912             9  0 10  | 11  0  0  | 12  0
3913     -------------------------------------
3914            13  0 14  | 15 16 17  |  0  0
3915     Proc1   0 18  0  | 19 20 21  |  0  0
3916             0  0  0  | 22 23  0  | 24  0
3917     -------------------------------------
3918     Proc2  25 26 27  |  0  0 28  | 29  0
3919            30  0  0  | 31 32 33  |  0 34
3920 .ve
3921 
3922    This can be represented as a collection of submatrices as:
3923 
3924 .vb
3925       A B C
3926       D E F
3927       G H I
3928 .ve
3929 
3930    Where the submatrices A,B,C are owned by proc0, D,E,F are
3931    owned by proc1, G,H,I are owned by proc2.
3932 
3933    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3934    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3935    The 'M','N' parameters are 8,8, and have the same values on all procs.
3936 
3937    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3938    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3939    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3940    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3941    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3942    matrix, ans [DF] as another SeqAIJ matrix.
3943 
3944    When d_nz, o_nz parameters are specified, d_nz storage elements are
3945    allocated for every row of the local diagonal submatrix, and o_nz
3946    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3947    One way to choose d_nz and o_nz is to use the max nonzerors per local
3948    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3949    In this case, the values of d_nz,o_nz are:
3950 .vb
3951      proc0 : dnz = 2, o_nz = 2
3952      proc1 : dnz = 3, o_nz = 2
3953      proc2 : dnz = 1, o_nz = 4
3954 .ve
3955    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3956    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3957    for proc3. i.e we are using 12+15+10=37 storage locations to store
3958    34 values.
3959 
3960    When d_nnz, o_nnz parameters are specified, the storage is specified
3961    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3962    In the above case the values for d_nnz,o_nnz are:
3963 .vb
3964      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3965      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3966      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3967 .ve
3968    Here the space allocated is sum of all the above values i.e 34, and
3969    hence pre-allocation is perfect.
3970 
3971    Level: intermediate
3972 
3973 .keywords: matrix, aij, compressed row, sparse, parallel
3974 
3975 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
3976           MATMPIAIJ, MatGetInfo(), PetscSplitOwnership()
3977 @*/
3978 PetscErrorCode MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3979 {
3980   PetscErrorCode ierr;
3981 
3982   PetscFunctionBegin;
3983   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3984   PetscValidType(B,1);
3985   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
3986   PetscFunctionReturn(0);
3987 }
3988 
3989 /*@
3990      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
3991          CSR format the local rows.
3992 
3993    Collective on MPI_Comm
3994 
3995    Input Parameters:
3996 +  comm - MPI communicator
3997 .  m - number of local rows (Cannot be PETSC_DECIDE)
3998 .  n - This value should be the same as the local size used in creating the
3999        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
4000        calculated if N is given) For square matrices n is almost always m.
4001 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
4002 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
4003 .   i - row indices
4004 .   j - column indices
4005 -   a - matrix values
4006 
4007    Output Parameter:
4008 .   mat - the matrix
4009 
4010    Level: intermediate
4011 
4012    Notes:
4013        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
4014      thus you CANNOT change the matrix entries by changing the values of a[] after you have
4015      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
4016 
4017        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
4018 
4019        The format which is used for the sparse matrix input, is equivalent to a
4020     row-major ordering.. i.e for the following matrix, the input data expected is
4021     as shown
4022 
4023 $        1 0 0
4024 $        2 0 3     P0
4025 $       -------
4026 $        4 5 6     P1
4027 $
4028 $     Process0 [P0]: rows_owned=[0,1]
4029 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
4030 $        j =  {0,0,2}  [size = 3]
4031 $        v =  {1,2,3}  [size = 3]
4032 $
4033 $     Process1 [P1]: rows_owned=[2]
4034 $        i =  {0,3}    [size = nrow+1  = 1+1]
4035 $        j =  {0,1,2}  [size = 3]
4036 $        v =  {4,5,6}  [size = 3]
4037 
4038 .keywords: matrix, aij, compressed row, sparse, parallel
4039 
4040 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
4041           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
4042 @*/
4043 PetscErrorCode MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
4044 {
4045   PetscErrorCode ierr;
4046 
4047   PetscFunctionBegin;
4048   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
4049   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
4050   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4051   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
4052   /* ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr); */
4053   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
4054   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
4055   PetscFunctionReturn(0);
4056 }
4057 
4058 /*@C
4059    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
4060    (the default parallel PETSc format).  For good matrix assembly performance
4061    the user should preallocate the matrix storage by setting the parameters
4062    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
4063    performance can be increased by more than a factor of 50.
4064 
4065    Collective on MPI_Comm
4066 
4067    Input Parameters:
4068 +  comm - MPI communicator
4069 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
4070            This value should be the same as the local size used in creating the
4071            y vector for the matrix-vector product y = Ax.
4072 .  n - This value should be the same as the local size used in creating the
4073        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
4074        calculated if N is given) For square matrices n is almost always m.
4075 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
4076 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
4077 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
4078            (same value is used for all local rows)
4079 .  d_nnz - array containing the number of nonzeros in the various rows of the
4080            DIAGONAL portion of the local submatrix (possibly different for each row)
4081            or NULL, if d_nz is used to specify the nonzero structure.
4082            The size of this array is equal to the number of local rows, i.e 'm'.
4083 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
4084            submatrix (same value is used for all local rows).
4085 -  o_nnz - array containing the number of nonzeros in the various rows of the
4086            OFF-DIAGONAL portion of the local submatrix (possibly different for
4087            each row) or NULL, if o_nz is used to specify the nonzero
4088            structure. The size of this array is equal to the number
4089            of local rows, i.e 'm'.
4090 
4091    Output Parameter:
4092 .  A - the matrix
4093 
4094    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
4095    MatXXXXSetPreallocation() paradgm instead of this routine directly.
4096    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
4097 
4098    Notes:
4099    If the *_nnz parameter is given then the *_nz parameter is ignored
4100 
4101    m,n,M,N parameters specify the size of the matrix, and its partitioning across
4102    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
4103    storage requirements for this matrix.
4104 
4105    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
4106    processor than it must be used on all processors that share the object for
4107    that argument.
4108 
4109    The user MUST specify either the local or global matrix dimensions
4110    (possibly both).
4111 
4112    The parallel matrix is partitioned across processors such that the
4113    first m0 rows belong to process 0, the next m1 rows belong to
4114    process 1, the next m2 rows belong to process 2 etc.. where
4115    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
4116    values corresponding to [m x N] submatrix.
4117 
4118    The columns are logically partitioned with the n0 columns belonging
4119    to 0th partition, the next n1 columns belonging to the next
4120    partition etc.. where n0,n1,n2... are the input parameter 'n'.
4121 
4122    The DIAGONAL portion of the local submatrix on any given processor
4123    is the submatrix corresponding to the rows and columns m,n
4124    corresponding to the given processor. i.e diagonal matrix on
4125    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
4126    etc. The remaining portion of the local submatrix [m x (N-n)]
4127    constitute the OFF-DIAGONAL portion. The example below better
4128    illustrates this concept.
4129 
4130    For a square global matrix we define each processor's diagonal portion
4131    to be its local rows and the corresponding columns (a square submatrix);
4132    each processor's off-diagonal portion encompasses the remainder of the
4133    local matrix (a rectangular submatrix).
4134 
4135    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
4136 
4137    When calling this routine with a single process communicator, a matrix of
4138    type SEQAIJ is returned.  If a matrix of type MATMPIAIJ is desired for this
4139    type of communicator, use the construction mechanism:
4140      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
4141 
4142    By default, this format uses inodes (identical nodes) when possible.
4143    We search for consecutive rows with the same nonzero structure, thereby
4144    reusing matrix information to achieve increased efficiency.
4145 
4146    Options Database Keys:
4147 +  -mat_no_inode  - Do not use inodes
4148 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
4149 -  -mat_aij_oneindex - Internally use indexing starting at 1
4150         rather than 0.  Note that when calling MatSetValues(),
4151         the user still MUST index entries starting at 0!
4152 
4153 
4154    Example usage:
4155 
4156    Consider the following 8x8 matrix with 34 non-zero values, that is
4157    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
4158    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
4159    as follows:
4160 
4161 .vb
4162             1  2  0  |  0  3  0  |  0  4
4163     Proc0   0  5  6  |  7  0  0  |  8  0
4164             9  0 10  | 11  0  0  | 12  0
4165     -------------------------------------
4166            13  0 14  | 15 16 17  |  0  0
4167     Proc1   0 18  0  | 19 20 21  |  0  0
4168             0  0  0  | 22 23  0  | 24  0
4169     -------------------------------------
4170     Proc2  25 26 27  |  0  0 28  | 29  0
4171            30  0  0  | 31 32 33  |  0 34
4172 .ve
4173 
4174    This can be represented as a collection of submatrices as:
4175 
4176 .vb
4177       A B C
4178       D E F
4179       G H I
4180 .ve
4181 
4182    Where the submatrices A,B,C are owned by proc0, D,E,F are
4183    owned by proc1, G,H,I are owned by proc2.
4184 
4185    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4186    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4187    The 'M','N' parameters are 8,8, and have the same values on all procs.
4188 
4189    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
4190    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
4191    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
4192    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
4193    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
4194    matrix, ans [DF] as another SeqAIJ matrix.
4195 
4196    When d_nz, o_nz parameters are specified, d_nz storage elements are
4197    allocated for every row of the local diagonal submatrix, and o_nz
4198    storage locations are allocated for every row of the OFF-DIAGONAL submat.
4199    One way to choose d_nz and o_nz is to use the max nonzerors per local
4200    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
4201    In this case, the values of d_nz,o_nz are:
4202 .vb
4203      proc0 : dnz = 2, o_nz = 2
4204      proc1 : dnz = 3, o_nz = 2
4205      proc2 : dnz = 1, o_nz = 4
4206 .ve
4207    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
4208    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
4209    for proc3. i.e we are using 12+15+10=37 storage locations to store
4210    34 values.
4211 
4212    When d_nnz, o_nnz parameters are specified, the storage is specified
4213    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
4214    In the above case the values for d_nnz,o_nnz are:
4215 .vb
4216      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
4217      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
4218      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
4219 .ve
4220    Here the space allocated is sum of all the above values i.e 34, and
4221    hence pre-allocation is perfect.
4222 
4223    Level: intermediate
4224 
4225 .keywords: matrix, aij, compressed row, sparse, parallel
4226 
4227 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
4228           MATMPIAIJ, MatCreateMPIAIJWithArrays()
4229 @*/
4230 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)
4231 {
4232   PetscErrorCode ierr;
4233   PetscMPIInt    size;
4234 
4235   PetscFunctionBegin;
4236   ierr = MatCreate(comm,A);CHKERRQ(ierr);
4237   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
4238   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4239   if (size > 1) {
4240     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
4241     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
4242   } else {
4243     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
4244     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
4245   }
4246   PetscFunctionReturn(0);
4247 }
4248 
4249 PetscErrorCode MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
4250 {
4251   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
4252   PetscBool      flg;
4253   PetscErrorCode ierr;
4254 
4255   PetscFunctionBegin;
4256   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&flg);CHKERRQ(ierr);
4257   if (!flg) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"This function requires a MATMPIAIJ matrix as input");
4258   if (Ad)     *Ad     = a->A;
4259   if (Ao)     *Ao     = a->B;
4260   if (colmap) *colmap = a->garray;
4261   PetscFunctionReturn(0);
4262 }
4263 
4264 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
4265 {
4266   PetscErrorCode ierr;
4267   PetscInt       m,N,i,rstart,nnz,Ii;
4268   PetscInt       *indx;
4269   PetscScalar    *values;
4270 
4271   PetscFunctionBegin;
4272   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
4273   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
4274     PetscInt       *dnz,*onz,sum,bs,cbs;
4275 
4276     if (n == PETSC_DECIDE) {
4277       ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
4278     }
4279     /* Check sum(n) = N */
4280     ierr = MPIU_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4281     if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
4282 
4283     ierr    = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4284     rstart -= m;
4285 
4286     ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4287     for (i=0; i<m; i++) {
4288       ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
4289       ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
4290       ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
4291     }
4292 
4293     ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
4294     ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4295     ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
4296     ierr = MatSetBlockSizes(*outmat,bs,cbs);CHKERRQ(ierr);
4297     ierr = MatSetType(*outmat,MATAIJ);CHKERRQ(ierr);
4298     ierr = MatSeqAIJSetPreallocation(*outmat,0,dnz);CHKERRQ(ierr);
4299     ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
4300     ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4301   }
4302 
4303   /* numeric phase */
4304   ierr = MatGetOwnershipRange(*outmat,&rstart,NULL);CHKERRQ(ierr);
4305   for (i=0; i<m; i++) {
4306     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4307     Ii   = i + rstart;
4308     ierr = MatSetValues(*outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4309     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4310   }
4311   ierr = MatAssemblyBegin(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4312   ierr = MatAssemblyEnd(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4313   PetscFunctionReturn(0);
4314 }
4315 
4316 PetscErrorCode MatFileSplit(Mat A,char *outfile)
4317 {
4318   PetscErrorCode    ierr;
4319   PetscMPIInt       rank;
4320   PetscInt          m,N,i,rstart,nnz;
4321   size_t            len;
4322   const PetscInt    *indx;
4323   PetscViewer       out;
4324   char              *name;
4325   Mat               B;
4326   const PetscScalar *values;
4327 
4328   PetscFunctionBegin;
4329   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
4330   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
4331   /* Should this be the type of the diagonal block of A? */
4332   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
4333   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
4334   ierr = MatSetBlockSizesFromMats(B,A,A);CHKERRQ(ierr);
4335   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
4336   ierr = MatSeqAIJSetPreallocation(B,0,NULL);CHKERRQ(ierr);
4337   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
4338   for (i=0; i<m; i++) {
4339     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4340     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4341     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4342   }
4343   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4344   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4345 
4346   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
4347   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
4348   ierr = PetscMalloc1(len+5,&name);CHKERRQ(ierr);
4349   sprintf(name,"%s.%d",outfile,rank);
4350   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
4351   ierr = PetscFree(name);CHKERRQ(ierr);
4352   ierr = MatView(B,out);CHKERRQ(ierr);
4353   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
4354   ierr = MatDestroy(&B);CHKERRQ(ierr);
4355   PetscFunctionReturn(0);
4356 }
4357 
4358 PetscErrorCode MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
4359 {
4360   PetscErrorCode      ierr;
4361   Mat_Merge_SeqsToMPI *merge;
4362   PetscContainer      container;
4363 
4364   PetscFunctionBegin;
4365   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4366   if (container) {
4367     ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4368     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
4369     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
4370     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
4371     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
4372     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
4373     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
4374     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
4375     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
4376     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
4377     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
4378     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
4379     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
4380     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
4381     ierr = PetscFree(merge);CHKERRQ(ierr);
4382     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
4383   }
4384   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
4385   PetscFunctionReturn(0);
4386 }
4387 
4388 #include <../src/mat/utils/freespace.h>
4389 #include <petscbt.h>
4390 
4391 PetscErrorCode MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
4392 {
4393   PetscErrorCode      ierr;
4394   MPI_Comm            comm;
4395   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
4396   PetscMPIInt         size,rank,taga,*len_s;
4397   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
4398   PetscInt            proc,m;
4399   PetscInt            **buf_ri,**buf_rj;
4400   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
4401   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
4402   MPI_Request         *s_waits,*r_waits;
4403   MPI_Status          *status;
4404   MatScalar           *aa=a->a;
4405   MatScalar           **abuf_r,*ba_i;
4406   Mat_Merge_SeqsToMPI *merge;
4407   PetscContainer      container;
4408 
4409   PetscFunctionBegin;
4410   ierr = PetscObjectGetComm((PetscObject)mpimat,&comm);CHKERRQ(ierr);
4411   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4412 
4413   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4414   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4415 
4416   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4417   ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4418 
4419   bi     = merge->bi;
4420   bj     = merge->bj;
4421   buf_ri = merge->buf_ri;
4422   buf_rj = merge->buf_rj;
4423 
4424   ierr   = PetscMalloc1(size,&status);CHKERRQ(ierr);
4425   owners = merge->rowmap->range;
4426   len_s  = merge->len_s;
4427 
4428   /* send and recv matrix values */
4429   /*-----------------------------*/
4430   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
4431   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
4432 
4433   ierr = PetscMalloc1(merge->nsend+1,&s_waits);CHKERRQ(ierr);
4434   for (proc=0,k=0; proc<size; proc++) {
4435     if (!len_s[proc]) continue;
4436     i    = owners[proc];
4437     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
4438     k++;
4439   }
4440 
4441   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
4442   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
4443   ierr = PetscFree(status);CHKERRQ(ierr);
4444 
4445   ierr = PetscFree(s_waits);CHKERRQ(ierr);
4446   ierr = PetscFree(r_waits);CHKERRQ(ierr);
4447 
4448   /* insert mat values of mpimat */
4449   /*----------------------------*/
4450   ierr = PetscMalloc1(N,&ba_i);CHKERRQ(ierr);
4451   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4452 
4453   for (k=0; k<merge->nrecv; k++) {
4454     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4455     nrows       = *(buf_ri_k[k]);
4456     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
4457     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4458   }
4459 
4460   /* set values of ba */
4461   m = merge->rowmap->n;
4462   for (i=0; i<m; i++) {
4463     arow = owners[rank] + i;
4464     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
4465     bnzi = bi[i+1] - bi[i];
4466     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
4467 
4468     /* add local non-zero vals of this proc's seqmat into ba */
4469     anzi   = ai[arow+1] - ai[arow];
4470     aj     = a->j + ai[arow];
4471     aa     = a->a + ai[arow];
4472     nextaj = 0;
4473     for (j=0; nextaj<anzi; j++) {
4474       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4475         ba_i[j] += aa[nextaj++];
4476       }
4477     }
4478 
4479     /* add received vals into ba */
4480     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4481       /* i-th row */
4482       if (i == *nextrow[k]) {
4483         anzi   = *(nextai[k]+1) - *nextai[k];
4484         aj     = buf_rj[k] + *(nextai[k]);
4485         aa     = abuf_r[k] + *(nextai[k]);
4486         nextaj = 0;
4487         for (j=0; nextaj<anzi; j++) {
4488           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4489             ba_i[j] += aa[nextaj++];
4490           }
4491         }
4492         nextrow[k]++; nextai[k]++;
4493       }
4494     }
4495     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
4496   }
4497   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4498   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4499 
4500   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
4501   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
4502   ierr = PetscFree(ba_i);CHKERRQ(ierr);
4503   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4504   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4505   PetscFunctionReturn(0);
4506 }
4507 
4508 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4509 {
4510   PetscErrorCode      ierr;
4511   Mat                 B_mpi;
4512   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
4513   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4514   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
4515   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4516   PetscInt            len,proc,*dnz,*onz,bs,cbs;
4517   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4518   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4519   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
4520   MPI_Status          *status;
4521   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
4522   PetscBT             lnkbt;
4523   Mat_Merge_SeqsToMPI *merge;
4524   PetscContainer      container;
4525 
4526   PetscFunctionBegin;
4527   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4528 
4529   /* make sure it is a PETSc comm */
4530   ierr = PetscCommDuplicate(comm,&comm,NULL);CHKERRQ(ierr);
4531   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4532   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4533 
4534   ierr = PetscNew(&merge);CHKERRQ(ierr);
4535   ierr = PetscMalloc1(size,&status);CHKERRQ(ierr);
4536 
4537   /* determine row ownership */
4538   /*---------------------------------------------------------*/
4539   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
4540   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
4541   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
4542   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
4543   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
4544   ierr = PetscMalloc1(size,&len_si);CHKERRQ(ierr);
4545   ierr = PetscMalloc1(size,&merge->len_s);CHKERRQ(ierr);
4546 
4547   m      = merge->rowmap->n;
4548   owners = merge->rowmap->range;
4549 
4550   /* determine the number of messages to send, their lengths */
4551   /*---------------------------------------------------------*/
4552   len_s = merge->len_s;
4553 
4554   len          = 0; /* length of buf_si[] */
4555   merge->nsend = 0;
4556   for (proc=0; proc<size; proc++) {
4557     len_si[proc] = 0;
4558     if (proc == rank) {
4559       len_s[proc] = 0;
4560     } else {
4561       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4562       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4563     }
4564     if (len_s[proc]) {
4565       merge->nsend++;
4566       nrows = 0;
4567       for (i=owners[proc]; i<owners[proc+1]; i++) {
4568         if (ai[i+1] > ai[i]) nrows++;
4569       }
4570       len_si[proc] = 2*(nrows+1);
4571       len         += len_si[proc];
4572     }
4573   }
4574 
4575   /* determine the number and length of messages to receive for ij-structure */
4576   /*-------------------------------------------------------------------------*/
4577   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
4578   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
4579 
4580   /* post the Irecv of j-structure */
4581   /*-------------------------------*/
4582   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
4583   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
4584 
4585   /* post the Isend of j-structure */
4586   /*--------------------------------*/
4587   ierr = PetscMalloc2(merge->nsend,&si_waits,merge->nsend,&sj_waits);CHKERRQ(ierr);
4588 
4589   for (proc=0, k=0; proc<size; proc++) {
4590     if (!len_s[proc]) continue;
4591     i    = owners[proc];
4592     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
4593     k++;
4594   }
4595 
4596   /* receives and sends of j-structure are complete */
4597   /*------------------------------------------------*/
4598   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
4599   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
4600 
4601   /* send and recv i-structure */
4602   /*---------------------------*/
4603   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
4604   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
4605 
4606   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
4607   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4608   for (proc=0,k=0; proc<size; proc++) {
4609     if (!len_s[proc]) continue;
4610     /* form outgoing message for i-structure:
4611          buf_si[0]:                 nrows to be sent
4612                [1:nrows]:           row index (global)
4613                [nrows+1:2*nrows+1]: i-structure index
4614     */
4615     /*-------------------------------------------*/
4616     nrows       = len_si[proc]/2 - 1;
4617     buf_si_i    = buf_si + nrows+1;
4618     buf_si[0]   = nrows;
4619     buf_si_i[0] = 0;
4620     nrows       = 0;
4621     for (i=owners[proc]; i<owners[proc+1]; i++) {
4622       anzi = ai[i+1] - ai[i];
4623       if (anzi) {
4624         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4625         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4626         nrows++;
4627       }
4628     }
4629     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4630     k++;
4631     buf_si += len_si[proc];
4632   }
4633 
4634   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4635   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4636 
4637   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4638   for (i=0; i<merge->nrecv; i++) {
4639     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);
4640   }
4641 
4642   ierr = PetscFree(len_si);CHKERRQ(ierr);
4643   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4644   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4645   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4646   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4647   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4648   ierr = PetscFree(status);CHKERRQ(ierr);
4649 
4650   /* compute a local seq matrix in each processor */
4651   /*----------------------------------------------*/
4652   /* allocate bi array and free space for accumulating nonzero column info */
4653   ierr  = PetscMalloc1(m+1,&bi);CHKERRQ(ierr);
4654   bi[0] = 0;
4655 
4656   /* create and initialize a linked list */
4657   nlnk = N+1;
4658   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4659 
4660   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4661   len  = ai[owners[rank+1]] - ai[owners[rank]];
4662   ierr = PetscFreeSpaceGet(PetscIntMultTruncate(2,len)+1,&free_space);CHKERRQ(ierr);
4663 
4664   current_space = free_space;
4665 
4666   /* determine symbolic info for each local row */
4667   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4668 
4669   for (k=0; k<merge->nrecv; k++) {
4670     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4671     nrows       = *buf_ri_k[k];
4672     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4673     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4674   }
4675 
4676   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4677   len  = 0;
4678   for (i=0; i<m; i++) {
4679     bnzi = 0;
4680     /* add local non-zero cols of this proc's seqmat into lnk */
4681     arow  = owners[rank] + i;
4682     anzi  = ai[arow+1] - ai[arow];
4683     aj    = a->j + ai[arow];
4684     ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4685     bnzi += nlnk;
4686     /* add received col data into lnk */
4687     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4688       if (i == *nextrow[k]) { /* i-th row */
4689         anzi  = *(nextai[k]+1) - *nextai[k];
4690         aj    = buf_rj[k] + *nextai[k];
4691         ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4692         bnzi += nlnk;
4693         nextrow[k]++; nextai[k]++;
4694       }
4695     }
4696     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4697 
4698     /* if free space is not available, make more free space */
4699     if (current_space->local_remaining<bnzi) {
4700       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(bnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
4701       nspacedouble++;
4702     }
4703     /* copy data into free space, then initialize lnk */
4704     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4705     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
4706 
4707     current_space->array           += bnzi;
4708     current_space->local_used      += bnzi;
4709     current_space->local_remaining -= bnzi;
4710 
4711     bi[i+1] = bi[i] + bnzi;
4712   }
4713 
4714   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4715 
4716   ierr = PetscMalloc1(bi[m]+1,&bj);CHKERRQ(ierr);
4717   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
4718   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4719 
4720   /* create symbolic parallel matrix B_mpi */
4721   /*---------------------------------------*/
4722   ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
4723   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
4724   if (n==PETSC_DECIDE) {
4725     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
4726   } else {
4727     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4728   }
4729   ierr = MatSetBlockSizes(B_mpi,bs,cbs);CHKERRQ(ierr);
4730   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
4731   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
4732   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4733   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
4734 
4735   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4736   B_mpi->assembled    = PETSC_FALSE;
4737   B_mpi->ops->destroy = MatDestroy_MPIAIJ_SeqsToMPI;
4738   merge->bi           = bi;
4739   merge->bj           = bj;
4740   merge->buf_ri       = buf_ri;
4741   merge->buf_rj       = buf_rj;
4742   merge->coi          = NULL;
4743   merge->coj          = NULL;
4744   merge->owners_co    = NULL;
4745 
4746   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
4747 
4748   /* attach the supporting struct to B_mpi for reuse */
4749   ierr    = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
4750   ierr    = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
4751   ierr    = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
4752   ierr    = PetscContainerDestroy(&container);CHKERRQ(ierr);
4753   *mpimat = B_mpi;
4754 
4755   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4756   PetscFunctionReturn(0);
4757 }
4758 
4759 /*@C
4760       MatCreateMPIAIJSumSeqAIJ - Creates a MATMPIAIJ matrix by adding sequential
4761                  matrices from each processor
4762 
4763     Collective on MPI_Comm
4764 
4765    Input Parameters:
4766 +    comm - the communicators the parallel matrix will live on
4767 .    seqmat - the input sequential matrices
4768 .    m - number of local rows (or PETSC_DECIDE)
4769 .    n - number of local columns (or PETSC_DECIDE)
4770 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4771 
4772    Output Parameter:
4773 .    mpimat - the parallel matrix generated
4774 
4775     Level: advanced
4776 
4777    Notes:
4778      The dimensions of the sequential matrix in each processor MUST be the same.
4779      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
4780      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
4781 @*/
4782 PetscErrorCode MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
4783 {
4784   PetscErrorCode ierr;
4785   PetscMPIInt    size;
4786 
4787   PetscFunctionBegin;
4788   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4789   if (size == 1) {
4790     ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4791     if (scall == MAT_INITIAL_MATRIX) {
4792       ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
4793     } else {
4794       ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4795     }
4796     ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4797     PetscFunctionReturn(0);
4798   }
4799   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4800   if (scall == MAT_INITIAL_MATRIX) {
4801     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
4802   }
4803   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
4804   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4805   PetscFunctionReturn(0);
4806 }
4807 
4808 /*@
4809      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MATMPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
4810           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
4811           with MatGetSize()
4812 
4813     Not Collective
4814 
4815    Input Parameters:
4816 +    A - the matrix
4817 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4818 
4819    Output Parameter:
4820 .    A_loc - the local sequential matrix generated
4821 
4822     Level: developer
4823 
4824 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
4825 
4826 @*/
4827 PetscErrorCode MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
4828 {
4829   PetscErrorCode ierr;
4830   Mat_MPIAIJ     *mpimat=(Mat_MPIAIJ*)A->data;
4831   Mat_SeqAIJ     *mat,*a,*b;
4832   PetscInt       *ai,*aj,*bi,*bj,*cmap=mpimat->garray;
4833   MatScalar      *aa,*ba,*cam;
4834   PetscScalar    *ca;
4835   PetscInt       am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
4836   PetscInt       *ci,*cj,col,ncols_d,ncols_o,jo;
4837   PetscBool      match;
4838   MPI_Comm       comm;
4839   PetscMPIInt    size;
4840 
4841   PetscFunctionBegin;
4842   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4843   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
4844   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4845   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4846   if (size == 1 && scall == MAT_REUSE_MATRIX) PetscFunctionReturn(0);
4847 
4848   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4849   a = (Mat_SeqAIJ*)(mpimat->A)->data;
4850   b = (Mat_SeqAIJ*)(mpimat->B)->data;
4851   ai = a->i; aj = a->j; bi = b->i; bj = b->j;
4852   aa = a->a; ba = b->a;
4853   if (scall == MAT_INITIAL_MATRIX) {
4854     if (size == 1) {
4855       ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ai,aj,aa,A_loc);CHKERRQ(ierr);
4856       PetscFunctionReturn(0);
4857     }
4858 
4859     ierr  = PetscMalloc1(1+am,&ci);CHKERRQ(ierr);
4860     ci[0] = 0;
4861     for (i=0; i<am; i++) {
4862       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
4863     }
4864     ierr = PetscMalloc1(1+ci[am],&cj);CHKERRQ(ierr);
4865     ierr = PetscMalloc1(1+ci[am],&ca);CHKERRQ(ierr);
4866     k    = 0;
4867     for (i=0; i<am; i++) {
4868       ncols_o = bi[i+1] - bi[i];
4869       ncols_d = ai[i+1] - ai[i];
4870       /* off-diagonal portion of A */
4871       for (jo=0; jo<ncols_o; jo++) {
4872         col = cmap[*bj];
4873         if (col >= cstart) break;
4874         cj[k]   = col; bj++;
4875         ca[k++] = *ba++;
4876       }
4877       /* diagonal portion of A */
4878       for (j=0; j<ncols_d; j++) {
4879         cj[k]   = cstart + *aj++;
4880         ca[k++] = *aa++;
4881       }
4882       /* off-diagonal portion of A */
4883       for (j=jo; j<ncols_o; j++) {
4884         cj[k]   = cmap[*bj++];
4885         ca[k++] = *ba++;
4886       }
4887     }
4888     /* put together the new matrix */
4889     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
4890     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4891     /* Since these are PETSc arrays, change flags to free them as necessary. */
4892     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
4893     mat->free_a  = PETSC_TRUE;
4894     mat->free_ij = PETSC_TRUE;
4895     mat->nonew   = 0;
4896   } else if (scall == MAT_REUSE_MATRIX) {
4897     mat=(Mat_SeqAIJ*)(*A_loc)->data;
4898     ci = mat->i; cj = mat->j; cam = mat->a;
4899     for (i=0; i<am; i++) {
4900       /* off-diagonal portion of A */
4901       ncols_o = bi[i+1] - bi[i];
4902       for (jo=0; jo<ncols_o; jo++) {
4903         col = cmap[*bj];
4904         if (col >= cstart) break;
4905         *cam++ = *ba++; bj++;
4906       }
4907       /* diagonal portion of A */
4908       ncols_d = ai[i+1] - ai[i];
4909       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
4910       /* off-diagonal portion of A */
4911       for (j=jo; j<ncols_o; j++) {
4912         *cam++ = *ba++; bj++;
4913       }
4914     }
4915   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
4916   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4917   PetscFunctionReturn(0);
4918 }
4919 
4920 /*@C
4921      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MATMPIAIJ matrix by taking all its local rows and NON-ZERO columns
4922 
4923     Not Collective
4924 
4925    Input Parameters:
4926 +    A - the matrix
4927 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4928 -    row, col - index sets of rows and columns to extract (or NULL)
4929 
4930    Output Parameter:
4931 .    A_loc - the local sequential matrix generated
4932 
4933     Level: developer
4934 
4935 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
4936 
4937 @*/
4938 PetscErrorCode MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
4939 {
4940   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4941   PetscErrorCode ierr;
4942   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
4943   IS             isrowa,iscola;
4944   Mat            *aloc;
4945   PetscBool      match;
4946 
4947   PetscFunctionBegin;
4948   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4949   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
4950   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4951   if (!row) {
4952     start = A->rmap->rstart; end = A->rmap->rend;
4953     ierr  = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
4954   } else {
4955     isrowa = *row;
4956   }
4957   if (!col) {
4958     start = A->cmap->rstart;
4959     cmap  = a->garray;
4960     nzA   = a->A->cmap->n;
4961     nzB   = a->B->cmap->n;
4962     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4963     ncols = 0;
4964     for (i=0; i<nzB; i++) {
4965       if (cmap[i] < start) idx[ncols++] = cmap[i];
4966       else break;
4967     }
4968     imark = i;
4969     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
4970     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
4971     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
4972   } else {
4973     iscola = *col;
4974   }
4975   if (scall != MAT_INITIAL_MATRIX) {
4976     ierr    = PetscMalloc1(1,&aloc);CHKERRQ(ierr);
4977     aloc[0] = *A_loc;
4978   }
4979   ierr   = MatCreateSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
4980   *A_loc = aloc[0];
4981   ierr   = PetscFree(aloc);CHKERRQ(ierr);
4982   if (!row) {
4983     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
4984   }
4985   if (!col) {
4986     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
4987   }
4988   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4989   PetscFunctionReturn(0);
4990 }
4991 
4992 /*@C
4993     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
4994 
4995     Collective on Mat
4996 
4997    Input Parameters:
4998 +    A,B - the matrices in mpiaij format
4999 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5000 -    rowb, colb - index sets of rows and columns of B to extract (or NULL)
5001 
5002    Output Parameter:
5003 +    rowb, colb - index sets of rows and columns of B to extract
5004 -    B_seq - the sequential matrix generated
5005 
5006     Level: developer
5007 
5008 @*/
5009 PetscErrorCode MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
5010 {
5011   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
5012   PetscErrorCode ierr;
5013   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
5014   IS             isrowb,iscolb;
5015   Mat            *bseq=NULL;
5016 
5017   PetscFunctionBegin;
5018   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
5019     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);
5020   }
5021   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
5022 
5023   if (scall == MAT_INITIAL_MATRIX) {
5024     start = A->cmap->rstart;
5025     cmap  = a->garray;
5026     nzA   = a->A->cmap->n;
5027     nzB   = a->B->cmap->n;
5028     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
5029     ncols = 0;
5030     for (i=0; i<nzB; i++) {  /* row < local row index */
5031       if (cmap[i] < start) idx[ncols++] = cmap[i];
5032       else break;
5033     }
5034     imark = i;
5035     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
5036     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
5037     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
5038     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
5039   } else {
5040     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
5041     isrowb  = *rowb; iscolb = *colb;
5042     ierr    = PetscMalloc1(1,&bseq);CHKERRQ(ierr);
5043     bseq[0] = *B_seq;
5044   }
5045   ierr   = MatCreateSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
5046   *B_seq = bseq[0];
5047   ierr   = PetscFree(bseq);CHKERRQ(ierr);
5048   if (!rowb) {
5049     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
5050   } else {
5051     *rowb = isrowb;
5052   }
5053   if (!colb) {
5054     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
5055   } else {
5056     *colb = iscolb;
5057   }
5058   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
5059   PetscFunctionReturn(0);
5060 }
5061 
5062 /*
5063     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
5064     of the OFF-DIAGONAL portion of local A
5065 
5066     Collective on Mat
5067 
5068    Input Parameters:
5069 +    A,B - the matrices in mpiaij format
5070 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5071 
5072    Output Parameter:
5073 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
5074 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
5075 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
5076 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
5077 
5078     Level: developer
5079 
5080 */
5081 PetscErrorCode MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
5082 {
5083   VecScatter_MPI_General *gen_to,*gen_from;
5084   PetscErrorCode         ierr;
5085   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
5086   Mat_SeqAIJ             *b_oth;
5087   VecScatter             ctx =a->Mvctx;
5088   MPI_Comm               comm;
5089   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
5090   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
5091   PetscInt               *rvalues,*svalues;
5092   MatScalar              *b_otha,*bufa,*bufA;
5093   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
5094   MPI_Request            *rwaits = NULL,*swaits = NULL;
5095   MPI_Status             *sstatus,rstatus;
5096   PetscMPIInt            jj,size;
5097   PetscInt               *cols,sbs,rbs;
5098   PetscScalar            *vals;
5099 
5100   PetscFunctionBegin;
5101   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
5102   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
5103 
5104   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
5105     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);
5106   }
5107   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5108   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
5109 
5110   if (size == 1) {
5111     startsj_s = NULL;
5112     bufa_ptr  = NULL;
5113     *B_oth    = NULL;
5114     PetscFunctionReturn(0);
5115   }
5116 
5117   gen_to   = (VecScatter_MPI_General*)ctx->todata;
5118   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
5119   nrecvs   = gen_from->n;
5120   nsends   = gen_to->n;
5121 
5122   ierr    = PetscMalloc2(nrecvs,&rwaits,nsends,&swaits);CHKERRQ(ierr);
5123   srow    = gen_to->indices;    /* local row index to be sent */
5124   sstarts = gen_to->starts;
5125   sprocs  = gen_to->procs;
5126   sstatus = gen_to->sstatus;
5127   sbs     = gen_to->bs;
5128   rstarts = gen_from->starts;
5129   rprocs  = gen_from->procs;
5130   rbs     = gen_from->bs;
5131 
5132   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
5133   if (scall == MAT_INITIAL_MATRIX) {
5134     /* i-array */
5135     /*---------*/
5136     /*  post receives */
5137     ierr = PetscMalloc1(rbs*(rstarts[nrecvs] - rstarts[0]),&rvalues);CHKERRQ(ierr);
5138     for (i=0; i<nrecvs; i++) {
5139       rowlen = rvalues + rstarts[i]*rbs;
5140       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
5141       ierr   = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5142     }
5143 
5144     /* pack the outgoing message */
5145     ierr = PetscMalloc2(nsends+1,&sstartsj,nrecvs+1,&rstartsj);CHKERRQ(ierr);
5146 
5147     sstartsj[0] = 0;
5148     rstartsj[0] = 0;
5149     len         = 0; /* total length of j or a array to be sent */
5150     k           = 0;
5151     ierr = PetscMalloc1(sbs*(sstarts[nsends] - sstarts[0]),&svalues);CHKERRQ(ierr);
5152     for (i=0; i<nsends; i++) {
5153       rowlen = svalues + sstarts[i]*sbs;
5154       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
5155       for (j=0; j<nrows; j++) {
5156         row = srow[k] + B->rmap->range[rank]; /* global row idx */
5157         for (l=0; l<sbs; l++) {
5158           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr); /* rowlength */
5159 
5160           rowlen[j*sbs+l] = ncols;
5161 
5162           len += ncols;
5163           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr);
5164         }
5165         k++;
5166       }
5167       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5168 
5169       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
5170     }
5171     /* recvs and sends of i-array are completed */
5172     i = nrecvs;
5173     while (i--) {
5174       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5175     }
5176     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5177     ierr = PetscFree(svalues);CHKERRQ(ierr);
5178 
5179     /* allocate buffers for sending j and a arrays */
5180     ierr = PetscMalloc1(len+1,&bufj);CHKERRQ(ierr);
5181     ierr = PetscMalloc1(len+1,&bufa);CHKERRQ(ierr);
5182 
5183     /* create i-array of B_oth */
5184     ierr = PetscMalloc1(aBn+2,&b_othi);CHKERRQ(ierr);
5185 
5186     b_othi[0] = 0;
5187     len       = 0; /* total length of j or a array to be received */
5188     k         = 0;
5189     for (i=0; i<nrecvs; i++) {
5190       rowlen = rvalues + rstarts[i]*rbs;
5191       nrows  = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be received */
5192       for (j=0; j<nrows; j++) {
5193         b_othi[k+1] = b_othi[k] + rowlen[j];
5194         ierr = PetscIntSumError(rowlen[j],len,&len);CHKERRQ(ierr);
5195         k++;
5196       }
5197       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
5198     }
5199     ierr = PetscFree(rvalues);CHKERRQ(ierr);
5200 
5201     /* allocate space for j and a arrrays of B_oth */
5202     ierr = PetscMalloc1(b_othi[aBn]+1,&b_othj);CHKERRQ(ierr);
5203     ierr = PetscMalloc1(b_othi[aBn]+1,&b_otha);CHKERRQ(ierr);
5204 
5205     /* j-array */
5206     /*---------*/
5207     /*  post receives of j-array */
5208     for (i=0; i<nrecvs; i++) {
5209       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5210       ierr  = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5211     }
5212 
5213     /* pack the outgoing message j-array */
5214     k = 0;
5215     for (i=0; i<nsends; i++) {
5216       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5217       bufJ  = bufj+sstartsj[i];
5218       for (j=0; j<nrows; j++) {
5219         row = srow[k++] + B->rmap->range[rank];  /* global row idx */
5220         for (ll=0; ll<sbs; ll++) {
5221           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
5222           for (l=0; l<ncols; l++) {
5223             *bufJ++ = cols[l];
5224           }
5225           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
5226         }
5227       }
5228       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5229     }
5230 
5231     /* recvs and sends of j-array are completed */
5232     i = nrecvs;
5233     while (i--) {
5234       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5235     }
5236     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5237   } else if (scall == MAT_REUSE_MATRIX) {
5238     sstartsj = *startsj_s;
5239     rstartsj = *startsj_r;
5240     bufa     = *bufa_ptr;
5241     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
5242     b_otha   = b_oth->a;
5243   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
5244 
5245   /* a-array */
5246   /*---------*/
5247   /*  post receives of a-array */
5248   for (i=0; i<nrecvs; i++) {
5249     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5250     ierr  = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5251   }
5252 
5253   /* pack the outgoing message a-array */
5254   k = 0;
5255   for (i=0; i<nsends; i++) {
5256     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5257     bufA  = bufa+sstartsj[i];
5258     for (j=0; j<nrows; j++) {
5259       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
5260       for (ll=0; ll<sbs; ll++) {
5261         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
5262         for (l=0; l<ncols; l++) {
5263           *bufA++ = vals[l];
5264         }
5265         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
5266       }
5267     }
5268     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5269   }
5270   /* recvs and sends of a-array are completed */
5271   i = nrecvs;
5272   while (i--) {
5273     ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5274   }
5275   if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5276   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
5277 
5278   if (scall == MAT_INITIAL_MATRIX) {
5279     /* put together the new matrix */
5280     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
5281 
5282     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
5283     /* Since these are PETSc arrays, change flags to free them as necessary. */
5284     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
5285     b_oth->free_a  = PETSC_TRUE;
5286     b_oth->free_ij = PETSC_TRUE;
5287     b_oth->nonew   = 0;
5288 
5289     ierr = PetscFree(bufj);CHKERRQ(ierr);
5290     if (!startsj_s || !bufa_ptr) {
5291       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
5292       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
5293     } else {
5294       *startsj_s = sstartsj;
5295       *startsj_r = rstartsj;
5296       *bufa_ptr  = bufa;
5297     }
5298   }
5299   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5300   PetscFunctionReturn(0);
5301 }
5302 
5303 /*@C
5304   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
5305 
5306   Not Collective
5307 
5308   Input Parameters:
5309 . A - The matrix in mpiaij format
5310 
5311   Output Parameter:
5312 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
5313 . colmap - A map from global column index to local index into lvec
5314 - multScatter - A scatter from the argument of a matrix-vector product to lvec
5315 
5316   Level: developer
5317 
5318 @*/
5319 #if defined(PETSC_USE_CTABLE)
5320 PetscErrorCode MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
5321 #else
5322 PetscErrorCode MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
5323 #endif
5324 {
5325   Mat_MPIAIJ *a;
5326 
5327   PetscFunctionBegin;
5328   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
5329   PetscValidPointer(lvec, 2);
5330   PetscValidPointer(colmap, 3);
5331   PetscValidPointer(multScatter, 4);
5332   a = (Mat_MPIAIJ*) A->data;
5333   if (lvec) *lvec = a->lvec;
5334   if (colmap) *colmap = a->colmap;
5335   if (multScatter) *multScatter = a->Mvctx;
5336   PetscFunctionReturn(0);
5337 }
5338 
5339 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
5340 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
5341 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
5342 #if defined(PETSC_HAVE_ELEMENTAL)
5343 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
5344 #endif
5345 #if defined(PETSC_HAVE_HYPRE)
5346 PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat,MatType,MatReuse,Mat*);
5347 PETSC_INTERN PetscErrorCode MatMatMatMult_Transpose_AIJ_AIJ(Mat,Mat,Mat,MatReuse,PetscReal,Mat*);
5348 #endif
5349 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_IS(Mat,MatType,MatReuse,Mat*);
5350 
5351 /*
5352     Computes (B'*A')' since computing B*A directly is untenable
5353 
5354                n                       p                          p
5355         (              )       (              )         (                  )
5356       m (      A       )  *  n (       B      )   =   m (         C        )
5357         (              )       (              )         (                  )
5358 
5359 */
5360 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
5361 {
5362   PetscErrorCode ierr;
5363   Mat            At,Bt,Ct;
5364 
5365   PetscFunctionBegin;
5366   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
5367   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
5368   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
5369   ierr = MatDestroy(&At);CHKERRQ(ierr);
5370   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
5371   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
5372   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
5373   PetscFunctionReturn(0);
5374 }
5375 
5376 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
5377 {
5378   PetscErrorCode ierr;
5379   PetscInt       m=A->rmap->n,n=B->cmap->n;
5380   Mat            Cmat;
5381 
5382   PetscFunctionBegin;
5383   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);
5384   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
5385   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
5386   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
5387   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
5388   ierr = MatMPIDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
5389   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5390   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5391 
5392   Cmat->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
5393 
5394   *C = Cmat;
5395   PetscFunctionReturn(0);
5396 }
5397 
5398 /* ----------------------------------------------------------------*/
5399 PETSC_INTERN PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
5400 {
5401   PetscErrorCode ierr;
5402 
5403   PetscFunctionBegin;
5404   if (scall == MAT_INITIAL_MATRIX) {
5405     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5406     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
5407     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5408   }
5409   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5410   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
5411   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5412   PetscFunctionReturn(0);
5413 }
5414 
5415 /*MC
5416    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
5417 
5418    Options Database Keys:
5419 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
5420 
5421   Level: beginner
5422 
5423 .seealso: MatCreateAIJ()
5424 M*/
5425 
5426 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
5427 {
5428   Mat_MPIAIJ     *b;
5429   PetscErrorCode ierr;
5430   PetscMPIInt    size;
5431 
5432   PetscFunctionBegin;
5433   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
5434 
5435   ierr          = PetscNewLog(B,&b);CHKERRQ(ierr);
5436   B->data       = (void*)b;
5437   ierr          = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
5438   B->assembled  = PETSC_FALSE;
5439   B->insertmode = NOT_SET_VALUES;
5440   b->size       = size;
5441 
5442   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank);CHKERRQ(ierr);
5443 
5444   /* build cache for off array entries formed */
5445   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash);CHKERRQ(ierr);
5446 
5447   b->donotstash  = PETSC_FALSE;
5448   b->colmap      = 0;
5449   b->garray      = 0;
5450   b->roworiented = PETSC_TRUE;
5451 
5452   /* stuff used for matrix vector multiply */
5453   b->lvec  = NULL;
5454   b->Mvctx = NULL;
5455 
5456   /* stuff for MatGetRow() */
5457   b->rowindices   = 0;
5458   b->rowvalues    = 0;
5459   b->getrowactive = PETSC_FALSE;
5460 
5461   /* flexible pointer used in CUSP/CUSPARSE classes */
5462   b->spptr = NULL;
5463 
5464   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetUseScalableIncreaseOverlap_C",MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ);CHKERRQ(ierr);
5465   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ);CHKERRQ(ierr);
5466   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
5467   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
5468   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
5469   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
5470   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
5471   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
5472   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
5473   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
5474 #if defined(PETSC_HAVE_ELEMENTAL)
5475   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_elemental_C",MatConvert_MPIAIJ_Elemental);CHKERRQ(ierr);
5476 #endif
5477 #if defined(PETSC_HAVE_HYPRE)
5478   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_hypre_C",MatConvert_AIJ_HYPRE);CHKERRQ(ierr);
5479 #endif
5480   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_is_C",MatConvert_MPIAIJ_IS);CHKERRQ(ierr);
5481   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
5482   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
5483   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
5484 #if defined(PETSC_HAVE_HYPRE)
5485   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMatMult_transpose_mpiaij_mpiaij_C",MatMatMatMult_Transpose_AIJ_AIJ);CHKERRQ(ierr);
5486 #endif
5487   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
5488   PetscFunctionReturn(0);
5489 }
5490 
5491 /*@C
5492      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
5493          and "off-diagonal" part of the matrix in CSR format.
5494 
5495    Collective on MPI_Comm
5496 
5497    Input Parameters:
5498 +  comm - MPI communicator
5499 .  m - number of local rows (Cannot be PETSC_DECIDE)
5500 .  n - This value should be the same as the local size used in creating the
5501        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
5502        calculated if N is given) For square matrices n is almost always m.
5503 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
5504 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
5505 .   i - row indices for "diagonal" portion of matrix
5506 .   j - column indices
5507 .   a - matrix values
5508 .   oi - row indices for "off-diagonal" portion of matrix
5509 .   oj - column indices
5510 -   oa - matrix values
5511 
5512    Output Parameter:
5513 .   mat - the matrix
5514 
5515    Level: advanced
5516 
5517    Notes:
5518        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
5519        must free the arrays once the matrix has been destroyed and not before.
5520 
5521        The i and j indices are 0 based
5522 
5523        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
5524 
5525        This sets local rows and cannot be used to set off-processor values.
5526 
5527        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
5528        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
5529        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
5530        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
5531        keep track of the underlying array. Use MatSetOption(A,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
5532        communication if it is known that only local entries will be set.
5533 
5534 .keywords: matrix, aij, compressed row, sparse, parallel
5535 
5536 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
5537           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
5538 @*/
5539 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)
5540 {
5541   PetscErrorCode ierr;
5542   Mat_MPIAIJ     *maij;
5543 
5544   PetscFunctionBegin;
5545   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
5546   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
5547   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
5548   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
5549   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
5550   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
5551   maij = (Mat_MPIAIJ*) (*mat)->data;
5552 
5553   (*mat)->preallocated = PETSC_TRUE;
5554 
5555   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
5556   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
5557 
5558   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
5559   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
5560 
5561   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5562   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5563   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5564   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5565 
5566   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
5567   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5568   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5569   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_FALSE);CHKERRQ(ierr);
5570   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
5571   PetscFunctionReturn(0);
5572 }
5573 
5574 /*
5575     Special version for direct calls from Fortran
5576 */
5577 #include <petsc/private/fortranimpl.h>
5578 
5579 /* Change these macros so can be used in void function */
5580 #undef CHKERRQ
5581 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
5582 #undef SETERRQ2
5583 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5584 #undef SETERRQ3
5585 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5586 #undef SETERRQ
5587 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
5588 
5589 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5590 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
5591 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5592 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
5593 #else
5594 #endif
5595 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)
5596 {
5597   Mat            mat  = *mmat;
5598   PetscInt       m    = *mm, n = *mn;
5599   InsertMode     addv = *maddv;
5600   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
5601   PetscScalar    value;
5602   PetscErrorCode ierr;
5603 
5604   MatCheckPreallocated(mat,1);
5605   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
5606 
5607 #if defined(PETSC_USE_DEBUG)
5608   else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
5609 #endif
5610   {
5611     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
5612     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
5613     PetscBool roworiented = aij->roworiented;
5614 
5615     /* Some Variables required in the macro */
5616     Mat        A                 = aij->A;
5617     Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
5618     PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
5619     MatScalar  *aa               = a->a;
5620     PetscBool  ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
5621     Mat        B                 = aij->B;
5622     Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
5623     PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5624     MatScalar  *ba               = b->a;
5625 
5626     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5627     PetscInt  nonew = a->nonew;
5628     MatScalar *ap1,*ap2;
5629 
5630     PetscFunctionBegin;
5631     for (i=0; i<m; i++) {
5632       if (im[i] < 0) continue;
5633 #if defined(PETSC_USE_DEBUG)
5634       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);
5635 #endif
5636       if (im[i] >= rstart && im[i] < rend) {
5637         row      = im[i] - rstart;
5638         lastcol1 = -1;
5639         rp1      = aj + ai[row];
5640         ap1      = aa + ai[row];
5641         rmax1    = aimax[row];
5642         nrow1    = ailen[row];
5643         low1     = 0;
5644         high1    = nrow1;
5645         lastcol2 = -1;
5646         rp2      = bj + bi[row];
5647         ap2      = ba + bi[row];
5648         rmax2    = bimax[row];
5649         nrow2    = bilen[row];
5650         low2     = 0;
5651         high2    = nrow2;
5652 
5653         for (j=0; j<n; j++) {
5654           if (roworiented) value = v[i*n+j];
5655           else value = v[i+j*m];
5656           if (in[j] >= cstart && in[j] < cend) {
5657             col = in[j] - cstart;
5658             if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
5659             MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
5660           } else if (in[j] < 0) continue;
5661 #if defined(PETSC_USE_DEBUG)
5662           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);
5663 #endif
5664           else {
5665             if (mat->was_assembled) {
5666               if (!aij->colmap) {
5667                 ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5668               }
5669 #if defined(PETSC_USE_CTABLE)
5670               ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5671               col--;
5672 #else
5673               col = aij->colmap[in[j]] - 1;
5674 #endif
5675               if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
5676               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5677                 ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5678                 col  =  in[j];
5679                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5680                 B     = aij->B;
5681                 b     = (Mat_SeqAIJ*)B->data;
5682                 bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5683                 rp2   = bj + bi[row];
5684                 ap2   = ba + bi[row];
5685                 rmax2 = bimax[row];
5686                 nrow2 = bilen[row];
5687                 low2  = 0;
5688                 high2 = nrow2;
5689                 bm    = aij->B->rmap->n;
5690                 ba    = b->a;
5691               }
5692             } else col = in[j];
5693             MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
5694           }
5695         }
5696       } else if (!aij->donotstash) {
5697         if (roworiented) {
5698           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5699         } else {
5700           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5701         }
5702       }
5703     }
5704   }
5705   PetscFunctionReturnVoid();
5706 }
5707 
5708