xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision b117cd09e766aba90b52b0bef2091bbb861995da)
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 by MatCreateSubMatrix_MPIAIJ_SameRowColDist() to avoid ISAllGather() and global size of iscol_local
2978  (see MatCreateSubMatrix_MPIAIJ_nonscalable)
2979 
2980  Input Parameters:
2981    mat - matrix
2982    isrow - parallel row index set; its local indices are a subset of local columns of mat,
2983            i.e., mat->rstart <= isrow[i] < mat->rend
2984    iscol - parallel column index set; its local indices are a subset of local columns of mat,
2985            i.e., mat->cstart <= iscol[i] < mat->cend
2986  Output Parameter:
2987    isrow_d,iscol_d - sequential row and column index sets for retrieving mat->A
2988    iscol_o - sequential column index set for retrieving mat->B
2989    garray - column map; garray[i] indicates global location of iscol_o[i] in iscol
2990  */
2991 PetscErrorCode ISGetSeqIS_SameColDist_Private(Mat mat,IS isrow,IS iscol,IS *isrow_d,IS *iscol_d,IS *iscol_o,const PetscInt *garray[])
2992 {
2993   PetscErrorCode ierr;
2994   Vec            x,cmap;
2995   const PetscInt *is_idx;
2996   PetscScalar    *xarray,*cmaparray;
2997   PetscInt       ncols,isstart,*idx,m,rstart,*cmap1,count;
2998   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)mat->data;
2999   Mat            B=a->B;
3000   Vec            lvec=a->lvec,lcmap;
3001   PetscInt       i,cstart,cend,Bn=B->cmap->N;
3002   MPI_Comm       comm;
3003 
3004   PetscFunctionBegin;
3005   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3006   ierr = ISGetLocalSize(iscol,&ncols);CHKERRQ(ierr);
3007 
3008   /* (1) iscol is a sub-column vector of mat, pad it with '-1.' to form a full vector x */
3009   ierr = MatCreateVecs(mat,&x,NULL);CHKERRQ(ierr);
3010   ierr = VecDuplicate(x,&cmap);CHKERRQ(ierr);
3011   ierr = VecSet(x,-1.0);CHKERRQ(ierr);
3012 
3013   /* Get start indices */
3014   ierr = MPI_Scan(&ncols,&isstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3015   isstart -= ncols;
3016   ierr = MatGetOwnershipRangeColumn(mat,&cstart,&cend);CHKERRQ(ierr);
3017 
3018   ierr = ISGetIndices(iscol,&is_idx);CHKERRQ(ierr);
3019   ierr = VecGetArray(x,&xarray);CHKERRQ(ierr);
3020   ierr = VecGetArray(cmap,&cmaparray);CHKERRQ(ierr);
3021   ierr = PetscMalloc1(ncols,&idx);CHKERRQ(ierr);
3022   for (i=0; i<ncols; i++) {
3023     xarray[is_idx[i]-cstart]    = (PetscScalar)is_idx[i];
3024     cmaparray[is_idx[i]-cstart] = i + isstart;      /* global index of iscol[i] */
3025     idx[i]                      = is_idx[i]-cstart; /* local index of iscol[i]  */
3026   }
3027   ierr = VecRestoreArray(x,&xarray);CHKERRQ(ierr);
3028   ierr = VecRestoreArray(cmap,&cmaparray);CHKERRQ(ierr);
3029   ierr = ISRestoreIndices(iscol,&is_idx);CHKERRQ(ierr);
3030 
3031   /* Get iscol_d */
3032   ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,iscol_d);CHKERRQ(ierr);
3033   ierr = ISGetBlockSize(iscol,&i);CHKERRQ(ierr);
3034   ierr = ISSetBlockSize(*iscol_d,i);CHKERRQ(ierr);
3035 
3036   /* Get isrow_d */
3037   ierr = ISGetLocalSize(isrow,&m);CHKERRQ(ierr);
3038   rstart = mat->rmap->rstart;
3039   ierr = PetscMalloc1(m,&idx);CHKERRQ(ierr);
3040   ierr = ISGetIndices(isrow,&is_idx);CHKERRQ(ierr);
3041   for (i=0; i<m; i++) idx[i] = is_idx[i]-rstart;
3042   ierr = ISRestoreIndices(isrow,&is_idx);CHKERRQ(ierr);
3043 
3044   ierr = ISCreateGeneral(PETSC_COMM_SELF,m,idx,PETSC_OWN_POINTER,isrow_d);CHKERRQ(ierr);
3045   ierr = ISGetBlockSize(isrow,&i);CHKERRQ(ierr);
3046   ierr = ISSetBlockSize(*isrow_d,i);CHKERRQ(ierr);
3047 
3048   /* (2) Scatter x and cmap using aij->Mvctx to get their off-process portions (see MatMult_MPIAIJ) */
3049   ierr = VecScatterBegin(a->Mvctx,x,lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3050 
3051   ierr = VecDuplicate(lvec,&lcmap);CHKERRQ(ierr);
3052 
3053   ierr = VecScatterEnd(a->Mvctx,x,lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3054   ierr = VecScatterBegin(a->Mvctx,cmap,lcmap,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3055   ierr = VecScatterEnd(a->Mvctx,cmap,lcmap,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3056 
3057   /* (3) create sequential iscol_o (a subset of iscol) and isgarray */
3058   /* off-process column indices */
3059   count = 0;
3060   ierr = PetscMalloc1(Bn,&idx);CHKERRQ(ierr);
3061   ierr = PetscMalloc1(Bn,&cmap1);CHKERRQ(ierr);
3062 
3063   ierr = VecGetArray(lvec,&xarray);CHKERRQ(ierr);
3064   ierr = VecGetArray(lcmap,&cmaparray);CHKERRQ(ierr);
3065   for (i=0; i<Bn; i++) {
3066     if (PetscRealPart(xarray[i]) > -1.0) {
3067       idx[count]     = i;                   /* local column index in off-diagonal part B */
3068       cmap1[count++] = (PetscInt)PetscRealPart(cmaparray[i]);  /* column index in submat */
3069     }
3070   }
3071   ierr = VecRestoreArray(lvec,&xarray);CHKERRQ(ierr);
3072   ierr = VecRestoreArray(lcmap,&cmaparray);CHKERRQ(ierr);
3073 
3074   ierr = ISCreateGeneral(PETSC_COMM_SELF,count,idx,PETSC_COPY_VALUES,iscol_o);CHKERRQ(ierr);
3075   ierr = ISGetBlockSize(iscol,&i);CHKERRQ(ierr);
3076   ierr = ISSetBlockSize(*iscol_o,i);CHKERRQ(ierr);
3077   ierr = PetscFree(idx);CHKERRQ(ierr);
3078 
3079   *garray = cmap1;
3080 
3081   ierr = VecDestroy(&x);CHKERRQ(ierr);
3082   ierr = VecDestroy(&cmap);CHKERRQ(ierr);
3083   ierr = VecDestroy(&lcmap);CHKERRQ(ierr);
3084   PetscFunctionReturn(0);
3085 }
3086 
3087 /* isrow and iscol have same processor distribution as mat, output *submat is a submatrix of local mat */
3088 PetscErrorCode MatCreateSubMatrix_MPIAIJ_SameRowColDist(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *submat)
3089 {
3090   PetscErrorCode ierr;
3091   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)mat->data,*asub;
3092   Mat            M = NULL;
3093   MPI_Comm       comm;
3094   IS             iscol_d,isrow_d,iscol_o;
3095   Mat            Asub = NULL,Bsub = NULL;
3096   PetscInt       n;
3097 
3098   PetscFunctionBegin;
3099   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3100 
3101   if (call == MAT_REUSE_MATRIX) {
3102     /* Retrieve isrow_d, iscol_d and iscol_o from submat */
3103     ierr = PetscObjectQuery((PetscObject)*submat,"isrow_d",(PetscObject*)&isrow_d);CHKERRQ(ierr);
3104     if (!isrow_d) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"isrow_d passed in was not used before, cannot reuse");
3105 
3106     ierr = PetscObjectQuery((PetscObject)*submat,"iscol_d",(PetscObject*)&iscol_d);CHKERRQ(ierr);
3107     if (!iscol_d) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"iscol_d passed in was not used before, cannot reuse");
3108 
3109     ierr = PetscObjectQuery((PetscObject)*submat,"iscol_o",(PetscObject*)&iscol_o);CHKERRQ(ierr);
3110     if (!iscol_o) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"iscol_o passed in was not used before, cannot reuse");
3111 
3112     /* Update diagonal and off-diagonal portions of submat */
3113     asub = (Mat_MPIAIJ*)(*submat)->data;
3114     ierr = MatCreateSubMatrix_SeqAIJ(a->A,isrow_d,iscol_d,PETSC_DECIDE,MAT_REUSE_MATRIX,&asub->A);CHKERRQ(ierr);
3115     ierr = ISGetLocalSize(iscol_o,&n);CHKERRQ(ierr);
3116     if (n) {
3117       ierr = MatCreateSubMatrix_SeqAIJ(a->B,isrow_d,iscol_o,PETSC_DECIDE,MAT_REUSE_MATRIX,&asub->B);CHKERRQ(ierr);
3118     }
3119     ierr = MatAssemblyBegin(*submat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3120     ierr = MatAssemblyEnd(*submat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3121 
3122   } else { /* call == MAT_INITIAL_MATRIX) */
3123     const PetscInt *garray;
3124     PetscInt        BsubN;
3125 
3126     /* Create isrow_d, iscol_d, iscol_o and isgarray (replace isgarray with array?) */
3127     ierr = ISGetSeqIS_SameColDist_Private(mat,isrow,iscol,&isrow_d,&iscol_d,&iscol_o,&garray);CHKERRQ(ierr);
3128 
3129     /* Create local submatrices Asub and Bsub */
3130     ierr = MatCreateSubMatrix_SeqAIJ(a->A,isrow_d,iscol_d,PETSC_DECIDE,MAT_INITIAL_MATRIX,&Asub);CHKERRQ(ierr);
3131     ierr = MatCreateSubMatrix_SeqAIJ(a->B,isrow_d,iscol_o,PETSC_DECIDE,MAT_INITIAL_MATRIX,&Bsub);CHKERRQ(ierr);
3132 
3133     /* Create submatrix M */
3134     ierr = MatCreateMPIAIJWithSeqAIJ(comm,Asub,Bsub,garray,&M);CHKERRQ(ierr);
3135 
3136     /* If Bsub has empty columns, compress iscol_o such that it will retrieve condensed Bsub from a->B during reuse */
3137     asub = (Mat_MPIAIJ*)M->data;
3138 
3139     ierr = ISGetLocalSize(iscol_o,&BsubN);CHKERRQ(ierr);
3140     n = asub->B->cmap->N;
3141     if (BsubN > n) {
3142       /* This case can be tested using ~petsc/src/tao/bound/examples/tutorials/runplate2_3 */
3143       const PetscInt *idx;
3144       PetscInt       i,j,*idx_new,*subgarray = asub->garray;
3145       ierr = PetscInfo2(M,"submatrix Bn %D != BsubN %D, update iscol_o\n",n,BsubN);CHKERRQ(ierr);
3146 
3147       ierr = PetscMalloc1(n,&idx_new);CHKERRQ(ierr);
3148       j = 0;
3149       ierr = ISGetIndices(iscol_o,&idx);CHKERRQ(ierr);
3150       for (i=0; i<n; i++) {
3151         if (j >= BsubN) break;
3152         while (subgarray[i] > garray[j]) j++;
3153 
3154         if (subgarray[i] == garray[j]) {
3155           idx_new[i] = idx[j++];
3156         } else SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"subgarray[%D]=%D cannot < garray[%D]=%D",i,subgarray[i],j,garray[j]);
3157       }
3158       ierr = ISRestoreIndices(iscol_o,&idx);CHKERRQ(ierr);
3159 
3160       ierr = ISDestroy(&iscol_o);CHKERRQ(ierr);
3161       ierr = ISCreateGeneral(PETSC_COMM_SELF,n,idx_new,PETSC_OWN_POINTER,&iscol_o);CHKERRQ(ierr);
3162 
3163     } else if (BsubN < n) {
3164       SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Columns of Bsub cannot be smaller than B's",BsubN,asub->B->cmap->N);
3165     }
3166 
3167     ierr = PetscFree(garray);CHKERRQ(ierr);
3168     *submat = M;
3169 
3170     /* Save isrow_d, iscol_d and iscol_o used in processor for next request */
3171     ierr = PetscObjectCompose((PetscObject)M,"isrow_d",(PetscObject)isrow_d);CHKERRQ(ierr);
3172     ierr = ISDestroy(&isrow_d);CHKERRQ(ierr);
3173 
3174     ierr = PetscObjectCompose((PetscObject)M,"iscol_d",(PetscObject)iscol_d);CHKERRQ(ierr);
3175     ierr = ISDestroy(&iscol_d);CHKERRQ(ierr);
3176 
3177     ierr = PetscObjectCompose((PetscObject)M,"iscol_o",(PetscObject)iscol_o);CHKERRQ(ierr);
3178     ierr = ISDestroy(&iscol_o);CHKERRQ(ierr);
3179   }
3180   PetscFunctionReturn(0);
3181 }
3182 
3183 PetscErrorCode MatCreateSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3184 {
3185   PetscErrorCode ierr;
3186   IS             iscol_local,isrow_d;
3187   PetscInt       csize;
3188   PetscInt       n,i,j,start,end;
3189   PetscBool      sameRowDist=PETSC_FALSE,sameDist[2],tsameDist[2];
3190   MPI_Comm       comm;
3191 
3192   PetscFunctionBegin;
3193   /* If isrow has same processor distribution as mat,
3194      call MatCreateSubMatrix_MPIAIJ_SameRowDist() to avoid using a hash table with global size of iscol */
3195   if (call == MAT_REUSE_MATRIX) {
3196     ierr = PetscObjectQuery((PetscObject)*newmat,"isrow_d",(PetscObject*)&isrow_d);CHKERRQ(ierr);
3197     if (isrow_d) {
3198       sameRowDist  = PETSC_TRUE;
3199       tsameDist[1] = PETSC_TRUE; /* sameColDist */
3200     } else {
3201       ierr = PetscObjectQuery((PetscObject)*newmat,"SubIScol",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3202       if (iscol_local) {
3203         sameRowDist  = PETSC_TRUE;
3204         tsameDist[1] = PETSC_FALSE; /* !sameColDist */
3205       }
3206     }
3207   } else {
3208     /* Check if isrow has same processor distribution as mat */
3209     sameDist[0] = PETSC_FALSE;
3210     ierr = ISGetLocalSize(isrow,&n);CHKERRQ(ierr);
3211     if (!n) {
3212       sameDist[0] = PETSC_TRUE;
3213     } else {
3214       ierr = ISGetMinMax(isrow,&i,&j);CHKERRQ(ierr);
3215       ierr = MatGetOwnershipRange(mat,&start,&end);CHKERRQ(ierr);
3216       if (i >= start && j < end) {
3217         sameDist[0] = PETSC_TRUE;
3218       }
3219     }
3220 
3221     /* Check if iscol has same processor distribution as mat */
3222     sameDist[1] = PETSC_FALSE;
3223     ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr);
3224     if (!n) {
3225       sameDist[1] = PETSC_TRUE;
3226     } else {
3227       ierr = ISGetMinMax(iscol,&i,&j);CHKERRQ(ierr);
3228       ierr = MatGetOwnershipRangeColumn(mat,&start,&end);CHKERRQ(ierr);
3229       if (i >= start && j < end) sameDist[1] = PETSC_TRUE;
3230     }
3231 
3232     ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3233     ierr = MPIU_Allreduce(&sameDist,&tsameDist,2,MPIU_BOOL,MPI_LAND,comm);CHKERRQ(ierr);
3234     sameRowDist = tsameDist[0];
3235   }
3236 
3237   if (sameRowDist) {
3238     if (tsameDist[1]) { /* sameRowDist & sameColDist */
3239       /* isrow and iscol have same processor distribution as mat */
3240       ierr = MatCreateSubMatrix_MPIAIJ_SameRowColDist(mat,isrow,iscol,call,newmat);CHKERRQ(ierr);
3241     } else { /* sameRowDist */
3242       /* isrow has same processor distribution as mat */
3243       ierr = MatCreateSubMatrix_MPIAIJ_SameRowDist(mat,isrow,iscol,call,newmat);CHKERRQ(ierr);
3244     }
3245     PetscFunctionReturn(0);
3246   }
3247 
3248   /* General case: iscol -> iscol_local which has global size of iscol */
3249   if (call == MAT_REUSE_MATRIX) {
3250     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3251     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3252   } else {
3253     ierr = ISGetSeqIS_Private(mat,iscol,&iscol_local);CHKERRQ(ierr);
3254   }
3255 
3256   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3257   ierr = MatCreateSubMatrix_MPIAIJ_nonscalable(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
3258 
3259   if (call == MAT_INITIAL_MATRIX) {
3260     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3261     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3262   }
3263   PetscFunctionReturn(0);
3264 }
3265 
3266 /*@C
3267      MatCreateMPIAIJWithSeqAIJ - creates a MPIAIJ matrix using SeqAIJ matrices that contain the "diagonal"
3268          and "off-diagonal" part of the matrix in CSR format.
3269 
3270    Collective on MPI_Comm
3271 
3272    Input Parameters:
3273 +  comm - MPI communicator
3274 .  A - "diagonal" portion of matrix
3275 .  B - "off-diagonal" portion of matrix, may have empty columns, will be destroyed by this routine
3276 -  garray - global index of B columns
3277 
3278    Output Parameter:
3279 .   mat - the matrix, with input A as its local diagonal matrix
3280    Level: advanced
3281 
3282    Notes:
3283        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix.
3284        A becomes part of output mat, B is destroyed by this routine. The user cannot use A and B anymore.
3285 
3286 .seealso: MatCreateMPIAIJWithSplitArrays()
3287 @*/
3288 PetscErrorCode MatCreateMPIAIJWithSeqAIJ(MPI_Comm comm,Mat A,Mat B,const PetscInt garray[],Mat *mat)
3289 {
3290   PetscErrorCode ierr;
3291   Mat_MPIAIJ     *maij;
3292   Mat_SeqAIJ     *b=(Mat_SeqAIJ*)B->data,*bnew;
3293   PetscInt       *oi=b->i,*oj=b->j,i,nz,col;
3294   PetscScalar    *oa=b->a;
3295   Mat            Bnew;
3296   PetscInt       m,n,N;
3297 
3298   PetscFunctionBegin;
3299   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
3300   ierr = MatGetSize(A,&m,&n);CHKERRQ(ierr);
3301   if (m != B->rmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Am %D != Bm %D",m,B->rmap->N);
3302   if (A->rmap->bs != B->rmap->bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"A row bs %D != B row bs %D",A->rmap->bs,B->rmap->bs);
3303   if (A->cmap->bs != B->cmap->bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"A column bs %D != B column bs %D",A->cmap->bs,B->cmap->bs);
3304 
3305   /* Get global columns of mat */
3306   ierr = MPIU_Allreduce(&n,&N,1,MPI_INT,MPI_SUM,comm);CHKERRQ(ierr);
3307 
3308   ierr = MatSetSizes(*mat,m,n,PETSC_DECIDE,N);CHKERRQ(ierr);
3309   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
3310   ierr = MatSetBlockSizes(*mat,A->rmap->bs,A->cmap->bs);CHKERRQ(ierr);
3311   maij = (Mat_MPIAIJ*)(*mat)->data;
3312 
3313   (*mat)->preallocated = PETSC_TRUE;
3314 
3315   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
3316   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
3317 
3318   /* Set A as diagonal portion of *mat */
3319   maij->A = A;
3320 
3321   nz = oi[m];
3322   for (i=0; i<nz; i++) {
3323     col   = oj[i];
3324     oj[i] = garray[col];
3325   }
3326 
3327    /* Set Bnew as off-diagonal portion of *mat */
3328   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,N,oi,oj,oa,&Bnew);CHKERRQ(ierr);
3329   bnew        = (Mat_SeqAIJ*)Bnew->data;
3330   bnew->maxnz = b->maxnz; /* allocated nonzeros of B */
3331   maij->B     = Bnew;
3332 
3333   if (B->rmap->N != Bnew->rmap->N) SETERRQ2(PETSC_COMM_SELF,0,"BN %d != BnewN %d",B->rmap->N,Bnew->rmap->N);
3334 
3335   b->singlemalloc = PETSC_FALSE; /* B arrays are shared by Bnew */
3336   b->free_a       = PETSC_FALSE;
3337   b->free_ij      = PETSC_FALSE;
3338   ierr = MatDestroy(&B);CHKERRQ(ierr);
3339 
3340   bnew->singlemalloc = PETSC_TRUE; /* arrays will be freed by MatDestroy(&Bnew) */
3341   bnew->free_a       = PETSC_TRUE;
3342   bnew->free_ij      = PETSC_TRUE;
3343 
3344   /* condense columns of maij->B */
3345   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
3346   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3347   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3348   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_FALSE);CHKERRQ(ierr);
3349   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3350   PetscFunctionReturn(0);
3351 }
3352 
3353 extern PetscErrorCode MatCreateSubMatrices_MPIAIJ_SingleIS_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool,Mat*);
3354 
3355 PetscErrorCode MatCreateSubMatrix_MPIAIJ_SameRowDist(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3356 {
3357   PetscErrorCode ierr;
3358   PetscInt       i,m,n,rstart,row,rend,nz,j,bs,cbs;
3359   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
3360   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)mat->data;
3361   Mat            M,Msub,B=a->B;
3362   MatScalar      *aa;
3363   Mat_SeqAIJ     *aij;
3364   PetscInt       *garray = a->garray,*colsub,Ncols;
3365   PetscInt       count,Bn=B->cmap->N,cstart=mat->cmap->rstart,cend=mat->cmap->rend;
3366   IS             iscol_sub,iscmap;
3367   const PetscInt *is_idx,*cmap;
3368   PetscBool      allcolumns=PETSC_FALSE;
3369   IS             iscol_local=NULL;
3370   MPI_Comm       comm;
3371 
3372   PetscFunctionBegin;
3373   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3374 
3375   if (call == MAT_REUSE_MATRIX) {
3376     ierr = PetscObjectQuery((PetscObject)*newmat,"SubIScol",(PetscObject*)&iscol_sub);CHKERRQ(ierr);
3377     if (!iscol_sub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"SubIScol passed in was not used before, cannot reuse");
3378     ierr = ISGetLocalSize(iscol_sub,&count);CHKERRQ(ierr);
3379 
3380     ierr = PetscObjectQuery((PetscObject)*newmat,"Subcmap",(PetscObject*)&iscmap);CHKERRQ(ierr);
3381     if (!iscmap) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Subcmap passed in was not used before, cannot reuse");
3382 
3383     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Msub);CHKERRQ(ierr);
3384     if (!Msub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3385 
3386     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol_sub,MAT_REUSE_MATRIX,PETSC_FALSE,&Msub);CHKERRQ(ierr);
3387 
3388   } else { /* call == MAT_INITIAL_MATRIX) */
3389     PetscBool flg;
3390 
3391     ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr);
3392     ierr = ISGetSize(iscol,&Ncols);CHKERRQ(ierr);
3393 
3394     /* (1) iscol -> nonscalable iscol_local */
3395     ierr = ISGetSeqIS_Private(mat,iscol,&iscol_local);CHKERRQ(ierr);
3396     ierr = ISGetLocalSize(iscol_local,&n);CHKERRQ(ierr); /* local size of iscol_local = global columns of newmat */
3397     if (n != Ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"n %d != Ncols %d",n,Ncols);
3398 
3399     /* Check for special case: each processor gets entire matrix columns */
3400     ierr = ISIdentity(iscol_local,&flg);CHKERRQ(ierr);
3401     if (flg && n == mat->cmap->N) allcolumns = PETSC_TRUE;
3402     if (allcolumns) {
3403       iscol_sub = iscol_local;
3404       ierr = PetscObjectReference((PetscObject)iscol_local);CHKERRQ(ierr);
3405       ierr = ISCreateStride(PETSC_COMM_SELF,n,0,1,&iscmap);CHKERRQ(ierr);
3406 
3407     } else {
3408       /* (2) iscol_local -> iscol_sub and iscmap */
3409       PetscInt *idx,*cmap1,k,cbs;
3410 
3411       /* implementation below requires iscol_local be sorted, it can have duplicate indices */
3412       ierr = ISSorted(iscol_local,&flg);CHKERRQ(ierr);
3413       if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"unsorted iscol_local is not implemented yet");
3414 
3415       ierr = PetscMalloc1(Ncols,&idx);CHKERRQ(ierr);
3416       ierr = PetscMalloc1(Ncols,&cmap1);CHKERRQ(ierr);
3417       ierr = ISGetIndices(iscol_local,&is_idx);CHKERRQ(ierr);
3418       count = 0;
3419       k     = 0;
3420       for (i=0; i<Ncols; i++) {
3421         j = is_idx[i];
3422         if (j >= cstart && j < cend) {
3423           /* diagonal part of mat */
3424           idx[count]     = j;
3425           cmap1[count++] = i; /* column index in submat */
3426         } else if (Bn) {
3427           /* off-diagonal part of mat */
3428           if (j == garray[k]) {
3429             idx[count]     = j;
3430             cmap1[count++] = i;  /* column index in submat */
3431           } else if (j > garray[k]) {
3432             while (j > garray[k] && k < Bn-1) k++;
3433             if (j == garray[k]) {
3434               idx[count]     = j;
3435               cmap1[count++] = i; /* column index in submat */
3436             }
3437           }
3438         }
3439       }
3440       ierr = ISRestoreIndices(iscol_local,&is_idx);CHKERRQ(ierr);
3441 
3442       ierr = ISCreateGeneral(PETSC_COMM_SELF,count,idx,PETSC_OWN_POINTER,&iscol_sub);CHKERRQ(ierr);
3443       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
3444       ierr = ISSetBlockSize(iscol_sub,cbs);CHKERRQ(ierr);
3445 
3446       ierr = ISCreateGeneral(PetscObjectComm((PetscObject)iscol_local),count,cmap1,PETSC_OWN_POINTER,&iscmap);CHKERRQ(ierr);
3447     }
3448 
3449     /* (3) Create sequential Msub */
3450     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol_sub,MAT_INITIAL_MATRIX,allcolumns,&Msub);CHKERRQ(ierr);
3451   }
3452 
3453   ierr = ISGetLocalSize(iscol_sub,&count);CHKERRQ(ierr);
3454   aij  = (Mat_SeqAIJ*)(Msub)->data;
3455   ii   = aij->i;
3456   ierr = ISGetIndices(iscmap,&cmap);CHKERRQ(ierr);
3457 
3458   /*
3459       m - number of local rows
3460       Ncols - number of columns (same on all processors)
3461       rstart - first row in new global matrix generated
3462   */
3463   ierr = MatGetSize(Msub,&m,NULL);CHKERRQ(ierr);
3464 
3465   if (call == MAT_INITIAL_MATRIX) {
3466     /* (4) Create parallel newmat */
3467     PetscMPIInt    rank,size;
3468     PetscInt       csize;
3469 
3470     ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3471     ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3472 
3473     /*
3474         Determine the number of non-zeros in the diagonal and off-diagonal
3475         portions of the matrix in order to do correct preallocation
3476     */
3477 
3478     /* first get start and end of "diagonal" columns */
3479     ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3480     if (csize == PETSC_DECIDE) {
3481       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3482       if (mglobal == Ncols) { /* square matrix */
3483         nlocal = m;
3484       } else {
3485         nlocal = Ncols/size + ((Ncols % size) > rank);
3486       }
3487     } else {
3488       nlocal = csize;
3489     }
3490     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3491     rstart = rend - nlocal;
3492     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);
3493 
3494     /* next, compute all the lengths */
3495     jj    = aij->j;
3496     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3497     olens = dlens + m;
3498     for (i=0; i<m; i++) {
3499       jend = ii[i+1] - ii[i];
3500       olen = 0;
3501       dlen = 0;
3502       for (j=0; j<jend; j++) {
3503         if (cmap[*jj] < rstart || cmap[*jj] >= rend) olen++;
3504         else dlen++;
3505         jj++;
3506       }
3507       olens[i] = olen;
3508       dlens[i] = dlen;
3509     }
3510     ierr = MatGetBlockSizes(Msub,&bs,&cbs);CHKERRQ(ierr);
3511 
3512     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3513     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,Ncols);CHKERRQ(ierr);
3514     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3515     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3516     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3517     ierr = PetscFree(dlens);CHKERRQ(ierr);
3518 
3519   } else { /* call == MAT_REUSE_MATRIX */
3520     M    = *newmat;
3521     ierr = MatGetLocalSize(M,&i,NULL);CHKERRQ(ierr);
3522     if (i != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3523     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3524     /*
3525          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3526        rather than the slower MatSetValues().
3527     */
3528     M->was_assembled = PETSC_TRUE;
3529     M->assembled     = PETSC_FALSE;
3530   }
3531 
3532   /* (5) Set values of Msub to *newmat */
3533   ierr = PetscMalloc1(count,&colsub);CHKERRQ(ierr);
3534   ierr = MatGetOwnershipRange(M,&rstart,NULL);CHKERRQ(ierr);
3535 
3536   jj   = aij->j;
3537   aa   = aij->a;
3538   for (i=0; i<m; i++) {
3539     row = rstart + i;
3540     nz  = ii[i+1] - ii[i];
3541     for (j=0; j<nz; j++) colsub[j] = cmap[jj[j]];
3542     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,colsub,aa,INSERT_VALUES);CHKERRQ(ierr);
3543     jj += nz; aa += nz;
3544   }
3545   ierr = ISRestoreIndices(iscmap,&cmap);CHKERRQ(ierr);
3546 
3547   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3548   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3549 
3550   ierr = PetscFree(colsub);CHKERRQ(ierr);
3551 
3552   /* save Msub, iscol_sub and iscmap used in processor for next request */
3553   if (call ==  MAT_INITIAL_MATRIX) {
3554     *newmat = M;
3555     ierr = PetscObjectCompose((PetscObject)(*newmat),"SubMatrix",(PetscObject)Msub);CHKERRQ(ierr);
3556     ierr = MatDestroy(&Msub);CHKERRQ(ierr);
3557 
3558     ierr = PetscObjectCompose((PetscObject)(*newmat),"SubIScol",(PetscObject)iscol_sub);CHKERRQ(ierr);
3559     ierr = ISDestroy(&iscol_sub);CHKERRQ(ierr);
3560 
3561     ierr = PetscObjectCompose((PetscObject)(*newmat),"Subcmap",(PetscObject)iscmap);CHKERRQ(ierr);
3562     ierr = ISDestroy(&iscmap);CHKERRQ(ierr);
3563 
3564     if (iscol_local) {
3565       ierr = PetscObjectCompose((PetscObject)(*newmat),"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3566       ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3567     }
3568   }
3569   PetscFunctionReturn(0);
3570 }
3571 
3572 /*
3573     Not great since it makes two copies of the submatrix, first an SeqAIJ
3574   in local and then by concatenating the local matrices the end result.
3575   Writing it directly would be much like MatCreateSubMatrices_MPIAIJ()
3576 
3577   Note: This requires a sequential iscol with all indices.
3578 */
3579 PetscErrorCode MatCreateSubMatrix_MPIAIJ_nonscalable(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3580 {
3581   PetscErrorCode ierr;
3582   PetscMPIInt    rank,size;
3583   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3584   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
3585   Mat            M,Mreuse;
3586   MatScalar      *aa,*vwork;
3587   MPI_Comm       comm;
3588   Mat_SeqAIJ     *aij;
3589   PetscBool      colflag,allcolumns=PETSC_FALSE;
3590 
3591   PetscFunctionBegin;
3592   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3593   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3594   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3595 
3596   /* Check for special case: each processor gets entire matrix columns */
3597   ierr = ISIdentity(iscol,&colflag);CHKERRQ(ierr);
3598   ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr);
3599   if (colflag && n == mat->cmap->N) allcolumns = PETSC_TRUE;
3600 
3601   if (call ==  MAT_REUSE_MATRIX) {
3602     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3603     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3604     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,allcolumns,&Mreuse);CHKERRQ(ierr);
3605   } else {
3606     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,allcolumns,&Mreuse);CHKERRQ(ierr);
3607   }
3608 
3609   /*
3610       m - number of local rows
3611       n - number of columns (same on all processors)
3612       rstart - first row in new global matrix generated
3613   */
3614   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3615   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3616   if (call == MAT_INITIAL_MATRIX) {
3617     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3618     ii  = aij->i;
3619     jj  = aij->j;
3620 
3621     /*
3622         Determine the number of non-zeros in the diagonal and off-diagonal
3623         portions of the matrix in order to do correct preallocation
3624     */
3625 
3626     /* first get start and end of "diagonal" columns */
3627     if (csize == PETSC_DECIDE) {
3628       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3629       if (mglobal == n) { /* square matrix */
3630         nlocal = m;
3631       } else {
3632         nlocal = n/size + ((n % size) > rank);
3633       }
3634     } else {
3635       nlocal = csize;
3636     }
3637     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3638     rstart = rend - nlocal;
3639     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);
3640 
3641     /* next, compute all the lengths */
3642     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3643     olens = dlens + m;
3644     for (i=0; i<m; i++) {
3645       jend = ii[i+1] - ii[i];
3646       olen = 0;
3647       dlen = 0;
3648       for (j=0; j<jend; j++) {
3649         if (*jj < rstart || *jj >= rend) olen++;
3650         else dlen++;
3651         jj++;
3652       }
3653       olens[i] = olen;
3654       dlens[i] = dlen;
3655     }
3656     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3657     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3658     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3659     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3660     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3661     ierr = PetscFree(dlens);CHKERRQ(ierr);
3662   } else {
3663     PetscInt ml,nl;
3664 
3665     M    = *newmat;
3666     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3667     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3668     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3669     /*
3670          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3671        rather than the slower MatSetValues().
3672     */
3673     M->was_assembled = PETSC_TRUE;
3674     M->assembled     = PETSC_FALSE;
3675   }
3676   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3677   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3678   ii   = aij->i;
3679   jj   = aij->j;
3680   aa   = aij->a;
3681   for (i=0; i<m; i++) {
3682     row   = rstart + i;
3683     nz    = ii[i+1] - ii[i];
3684     cwork = jj;     jj += nz;
3685     vwork = aa;     aa += nz;
3686     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3687   }
3688 
3689   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3690   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3691   *newmat = M;
3692 
3693   /* save submatrix used in processor for next request */
3694   if (call ==  MAT_INITIAL_MATRIX) {
3695     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3696     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3697   }
3698   PetscFunctionReturn(0);
3699 }
3700 
3701 PetscErrorCode MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3702 {
3703   PetscInt       m,cstart, cend,j,nnz,i,d;
3704   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3705   const PetscInt *JJ;
3706   PetscScalar    *values;
3707   PetscErrorCode ierr;
3708   PetscBool      nooffprocentries;
3709 
3710   PetscFunctionBegin;
3711   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3712 
3713   ierr   = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3714   ierr   = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3715   m      = B->rmap->n;
3716   cstart = B->cmap->rstart;
3717   cend   = B->cmap->rend;
3718   rstart = B->rmap->rstart;
3719 
3720   ierr = PetscMalloc2(m,&d_nnz,m,&o_nnz);CHKERRQ(ierr);
3721 
3722 #if defined(PETSC_USE_DEBUGGING)
3723   for (i=0; i<m; i++) {
3724     nnz = Ii[i+1]- Ii[i];
3725     JJ  = J + Ii[i];
3726     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3727     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3728     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);
3729   }
3730 #endif
3731 
3732   for (i=0; i<m; i++) {
3733     nnz     = Ii[i+1]- Ii[i];
3734     JJ      = J + Ii[i];
3735     nnz_max = PetscMax(nnz_max,nnz);
3736     d       = 0;
3737     for (j=0; j<nnz; j++) {
3738       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3739     }
3740     d_nnz[i] = d;
3741     o_nnz[i] = nnz - d;
3742   }
3743   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3744   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3745 
3746   if (v) values = (PetscScalar*)v;
3747   else {
3748     ierr = PetscCalloc1(nnz_max+1,&values);CHKERRQ(ierr);
3749   }
3750 
3751   for (i=0; i<m; i++) {
3752     ii   = i + rstart;
3753     nnz  = Ii[i+1]- Ii[i];
3754     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3755   }
3756   nooffprocentries    = B->nooffprocentries;
3757   B->nooffprocentries = PETSC_TRUE;
3758   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3759   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3760   B->nooffprocentries = nooffprocentries;
3761 
3762   if (!v) {
3763     ierr = PetscFree(values);CHKERRQ(ierr);
3764   }
3765   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3766   PetscFunctionReturn(0);
3767 }
3768 
3769 /*@
3770    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3771    (the default parallel PETSc format).
3772 
3773    Collective on MPI_Comm
3774 
3775    Input Parameters:
3776 +  B - the matrix
3777 .  i - the indices into j for the start of each local row (starts with zero)
3778 .  j - the column indices for each local row (starts with zero)
3779 -  v - optional values in the matrix
3780 
3781    Level: developer
3782 
3783    Notes:
3784        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3785      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3786      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3787 
3788        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3789 
3790        The format which is used for the sparse matrix input, is equivalent to a
3791     row-major ordering.. i.e for the following matrix, the input data expected is
3792     as shown
3793 
3794 $        1 0 0
3795 $        2 0 3     P0
3796 $       -------
3797 $        4 5 6     P1
3798 $
3799 $     Process0 [P0]: rows_owned=[0,1]
3800 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3801 $        j =  {0,0,2}  [size = 3]
3802 $        v =  {1,2,3}  [size = 3]
3803 $
3804 $     Process1 [P1]: rows_owned=[2]
3805 $        i =  {0,3}    [size = nrow+1  = 1+1]
3806 $        j =  {0,1,2}  [size = 3]
3807 $        v =  {4,5,6}  [size = 3]
3808 
3809 .keywords: matrix, aij, compressed row, sparse, parallel
3810 
3811 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MATMPIAIJ,
3812           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3813 @*/
3814 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3815 {
3816   PetscErrorCode ierr;
3817 
3818   PetscFunctionBegin;
3819   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3820   PetscFunctionReturn(0);
3821 }
3822 
3823 /*@C
3824    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3825    (the default parallel PETSc format).  For good matrix assembly performance
3826    the user should preallocate the matrix storage by setting the parameters
3827    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3828    performance can be increased by more than a factor of 50.
3829 
3830    Collective on MPI_Comm
3831 
3832    Input Parameters:
3833 +  B - the matrix
3834 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3835            (same value is used for all local rows)
3836 .  d_nnz - array containing the number of nonzeros in the various rows of the
3837            DIAGONAL portion of the local submatrix (possibly different for each row)
3838            or NULL (PETSC_NULL_INTEGER in Fortran), if d_nz is used to specify the nonzero structure.
3839            The size of this array is equal to the number of local rows, i.e 'm'.
3840            For matrices that will be factored, you must leave room for (and set)
3841            the diagonal entry even if it is zero.
3842 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3843            submatrix (same value is used for all local rows).
3844 -  o_nnz - array containing the number of nonzeros in the various rows of the
3845            OFF-DIAGONAL portion of the local submatrix (possibly different for
3846            each row) or NULL (PETSC_NULL_INTEGER in Fortran), if o_nz is used to specify the nonzero
3847            structure. The size of this array is equal to the number
3848            of local rows, i.e 'm'.
3849 
3850    If the *_nnz parameter is given then the *_nz parameter is ignored
3851 
3852    The AIJ format (also called the Yale sparse matrix format or
3853    compressed row storage (CSR)), is fully compatible with standard Fortran 77
3854    storage.  The stored row and column indices begin with zero.
3855    See Users-Manual: ch_mat for details.
3856 
3857    The parallel matrix is partitioned such that the first m0 rows belong to
3858    process 0, the next m1 rows belong to process 1, the next m2 rows belong
3859    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
3860 
3861    The DIAGONAL portion of the local submatrix of a processor can be defined
3862    as the submatrix which is obtained by extraction the part corresponding to
3863    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
3864    first row that belongs to the processor, r2 is the last row belonging to
3865    the this processor, and c1-c2 is range of indices of the local part of a
3866    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
3867    common case of a square matrix, the row and column ranges are the same and
3868    the DIAGONAL part is also square. The remaining portion of the local
3869    submatrix (mxN) constitute the OFF-DIAGONAL portion.
3870 
3871    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3872 
3873    You can call MatGetInfo() to get information on how effective the preallocation was;
3874    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3875    You can also run with the option -info and look for messages with the string
3876    malloc in them to see if additional memory allocation was needed.
3877 
3878    Example usage:
3879 
3880    Consider the following 8x8 matrix with 34 non-zero values, that is
3881    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3882    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3883    as follows:
3884 
3885 .vb
3886             1  2  0  |  0  3  0  |  0  4
3887     Proc0   0  5  6  |  7  0  0  |  8  0
3888             9  0 10  | 11  0  0  | 12  0
3889     -------------------------------------
3890            13  0 14  | 15 16 17  |  0  0
3891     Proc1   0 18  0  | 19 20 21  |  0  0
3892             0  0  0  | 22 23  0  | 24  0
3893     -------------------------------------
3894     Proc2  25 26 27  |  0  0 28  | 29  0
3895            30  0  0  | 31 32 33  |  0 34
3896 .ve
3897 
3898    This can be represented as a collection of submatrices as:
3899 
3900 .vb
3901       A B C
3902       D E F
3903       G H I
3904 .ve
3905 
3906    Where the submatrices A,B,C are owned by proc0, D,E,F are
3907    owned by proc1, G,H,I are owned by proc2.
3908 
3909    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3910    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3911    The 'M','N' parameters are 8,8, and have the same values on all procs.
3912 
3913    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3914    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3915    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3916    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3917    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3918    matrix, ans [DF] as another SeqAIJ matrix.
3919 
3920    When d_nz, o_nz parameters are specified, d_nz storage elements are
3921    allocated for every row of the local diagonal submatrix, and o_nz
3922    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3923    One way to choose d_nz and o_nz is to use the max nonzerors per local
3924    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3925    In this case, the values of d_nz,o_nz are:
3926 .vb
3927      proc0 : dnz = 2, o_nz = 2
3928      proc1 : dnz = 3, o_nz = 2
3929      proc2 : dnz = 1, o_nz = 4
3930 .ve
3931    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3932    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3933    for proc3. i.e we are using 12+15+10=37 storage locations to store
3934    34 values.
3935 
3936    When d_nnz, o_nnz parameters are specified, the storage is specified
3937    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3938    In the above case the values for d_nnz,o_nnz are:
3939 .vb
3940      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3941      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3942      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3943 .ve
3944    Here the space allocated is sum of all the above values i.e 34, and
3945    hence pre-allocation is perfect.
3946 
3947    Level: intermediate
3948 
3949 .keywords: matrix, aij, compressed row, sparse, parallel
3950 
3951 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
3952           MATMPIAIJ, MatGetInfo(), PetscSplitOwnership()
3953 @*/
3954 PetscErrorCode MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3955 {
3956   PetscErrorCode ierr;
3957 
3958   PetscFunctionBegin;
3959   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3960   PetscValidType(B,1);
3961   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
3962   PetscFunctionReturn(0);
3963 }
3964 
3965 /*@
3966      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
3967          CSR format the local rows.
3968 
3969    Collective on MPI_Comm
3970 
3971    Input Parameters:
3972 +  comm - MPI communicator
3973 .  m - number of local rows (Cannot be PETSC_DECIDE)
3974 .  n - This value should be the same as the local size used in creating the
3975        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3976        calculated if N is given) For square matrices n is almost always m.
3977 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3978 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3979 .   i - row indices
3980 .   j - column indices
3981 -   a - matrix values
3982 
3983    Output Parameter:
3984 .   mat - the matrix
3985 
3986    Level: intermediate
3987 
3988    Notes:
3989        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3990      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3991      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3992 
3993        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3994 
3995        The format which is used for the sparse matrix input, is equivalent to a
3996     row-major ordering.. i.e for the following matrix, the input data expected is
3997     as shown
3998 
3999 $        1 0 0
4000 $        2 0 3     P0
4001 $       -------
4002 $        4 5 6     P1
4003 $
4004 $     Process0 [P0]: rows_owned=[0,1]
4005 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
4006 $        j =  {0,0,2}  [size = 3]
4007 $        v =  {1,2,3}  [size = 3]
4008 $
4009 $     Process1 [P1]: rows_owned=[2]
4010 $        i =  {0,3}    [size = nrow+1  = 1+1]
4011 $        j =  {0,1,2}  [size = 3]
4012 $        v =  {4,5,6}  [size = 3]
4013 
4014 .keywords: matrix, aij, compressed row, sparse, parallel
4015 
4016 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
4017           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
4018 @*/
4019 PetscErrorCode MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
4020 {
4021   PetscErrorCode ierr;
4022 
4023   PetscFunctionBegin;
4024   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
4025   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
4026   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4027   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
4028   /* ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr); */
4029   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
4030   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
4031   PetscFunctionReturn(0);
4032 }
4033 
4034 /*@C
4035    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
4036    (the default parallel PETSc format).  For good matrix assembly performance
4037    the user should preallocate the matrix storage by setting the parameters
4038    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
4039    performance can be increased by more than a factor of 50.
4040 
4041    Collective on MPI_Comm
4042 
4043    Input Parameters:
4044 +  comm - MPI communicator
4045 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
4046            This value should be the same as the local size used in creating the
4047            y vector for the matrix-vector product y = Ax.
4048 .  n - This value should be the same as the local size used in creating the
4049        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
4050        calculated if N is given) For square matrices n is almost always m.
4051 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
4052 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
4053 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
4054            (same value is used for all local rows)
4055 .  d_nnz - array containing the number of nonzeros in the various rows of the
4056            DIAGONAL portion of the local submatrix (possibly different for each row)
4057            or NULL, if d_nz is used to specify the nonzero structure.
4058            The size of this array is equal to the number of local rows, i.e 'm'.
4059 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
4060            submatrix (same value is used for all local rows).
4061 -  o_nnz - array containing the number of nonzeros in the various rows of the
4062            OFF-DIAGONAL portion of the local submatrix (possibly different for
4063            each row) or NULL, if o_nz is used to specify the nonzero
4064            structure. The size of this array is equal to the number
4065            of local rows, i.e 'm'.
4066 
4067    Output Parameter:
4068 .  A - the matrix
4069 
4070    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
4071    MatXXXXSetPreallocation() paradgm instead of this routine directly.
4072    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
4073 
4074    Notes:
4075    If the *_nnz parameter is given then the *_nz parameter is ignored
4076 
4077    m,n,M,N parameters specify the size of the matrix, and its partitioning across
4078    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
4079    storage requirements for this matrix.
4080 
4081    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
4082    processor than it must be used on all processors that share the object for
4083    that argument.
4084 
4085    The user MUST specify either the local or global matrix dimensions
4086    (possibly both).
4087 
4088    The parallel matrix is partitioned across processors such that the
4089    first m0 rows belong to process 0, the next m1 rows belong to
4090    process 1, the next m2 rows belong to process 2 etc.. where
4091    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
4092    values corresponding to [m x N] submatrix.
4093 
4094    The columns are logically partitioned with the n0 columns belonging
4095    to 0th partition, the next n1 columns belonging to the next
4096    partition etc.. where n0,n1,n2... are the input parameter 'n'.
4097 
4098    The DIAGONAL portion of the local submatrix on any given processor
4099    is the submatrix corresponding to the rows and columns m,n
4100    corresponding to the given processor. i.e diagonal matrix on
4101    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
4102    etc. The remaining portion of the local submatrix [m x (N-n)]
4103    constitute the OFF-DIAGONAL portion. The example below better
4104    illustrates this concept.
4105 
4106    For a square global matrix we define each processor's diagonal portion
4107    to be its local rows and the corresponding columns (a square submatrix);
4108    each processor's off-diagonal portion encompasses the remainder of the
4109    local matrix (a rectangular submatrix).
4110 
4111    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
4112 
4113    When calling this routine with a single process communicator, a matrix of
4114    type SEQAIJ is returned.  If a matrix of type MATMPIAIJ is desired for this
4115    type of communicator, use the construction mechanism:
4116      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
4117 
4118    By default, this format uses inodes (identical nodes) when possible.
4119    We search for consecutive rows with the same nonzero structure, thereby
4120    reusing matrix information to achieve increased efficiency.
4121 
4122    Options Database Keys:
4123 +  -mat_no_inode  - Do not use inodes
4124 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
4125 -  -mat_aij_oneindex - Internally use indexing starting at 1
4126         rather than 0.  Note that when calling MatSetValues(),
4127         the user still MUST index entries starting at 0!
4128 
4129 
4130    Example usage:
4131 
4132    Consider the following 8x8 matrix with 34 non-zero values, that is
4133    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
4134    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
4135    as follows:
4136 
4137 .vb
4138             1  2  0  |  0  3  0  |  0  4
4139     Proc0   0  5  6  |  7  0  0  |  8  0
4140             9  0 10  | 11  0  0  | 12  0
4141     -------------------------------------
4142            13  0 14  | 15 16 17  |  0  0
4143     Proc1   0 18  0  | 19 20 21  |  0  0
4144             0  0  0  | 22 23  0  | 24  0
4145     -------------------------------------
4146     Proc2  25 26 27  |  0  0 28  | 29  0
4147            30  0  0  | 31 32 33  |  0 34
4148 .ve
4149 
4150    This can be represented as a collection of submatrices as:
4151 
4152 .vb
4153       A B C
4154       D E F
4155       G H I
4156 .ve
4157 
4158    Where the submatrices A,B,C are owned by proc0, D,E,F are
4159    owned by proc1, G,H,I are owned by proc2.
4160 
4161    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4162    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4163    The 'M','N' parameters are 8,8, and have the same values on all procs.
4164 
4165    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
4166    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
4167    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
4168    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
4169    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
4170    matrix, ans [DF] as another SeqAIJ matrix.
4171 
4172    When d_nz, o_nz parameters are specified, d_nz storage elements are
4173    allocated for every row of the local diagonal submatrix, and o_nz
4174    storage locations are allocated for every row of the OFF-DIAGONAL submat.
4175    One way to choose d_nz and o_nz is to use the max nonzerors per local
4176    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
4177    In this case, the values of d_nz,o_nz are:
4178 .vb
4179      proc0 : dnz = 2, o_nz = 2
4180      proc1 : dnz = 3, o_nz = 2
4181      proc2 : dnz = 1, o_nz = 4
4182 .ve
4183    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
4184    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
4185    for proc3. i.e we are using 12+15+10=37 storage locations to store
4186    34 values.
4187 
4188    When d_nnz, o_nnz parameters are specified, the storage is specified
4189    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
4190    In the above case the values for d_nnz,o_nnz are:
4191 .vb
4192      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
4193      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
4194      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
4195 .ve
4196    Here the space allocated is sum of all the above values i.e 34, and
4197    hence pre-allocation is perfect.
4198 
4199    Level: intermediate
4200 
4201 .keywords: matrix, aij, compressed row, sparse, parallel
4202 
4203 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
4204           MATMPIAIJ, MatCreateMPIAIJWithArrays()
4205 @*/
4206 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)
4207 {
4208   PetscErrorCode ierr;
4209   PetscMPIInt    size;
4210 
4211   PetscFunctionBegin;
4212   ierr = MatCreate(comm,A);CHKERRQ(ierr);
4213   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
4214   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4215   if (size > 1) {
4216     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
4217     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
4218   } else {
4219     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
4220     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
4221   }
4222   PetscFunctionReturn(0);
4223 }
4224 
4225 PetscErrorCode MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
4226 {
4227   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
4228   PetscBool      flg;
4229   PetscErrorCode ierr;
4230 
4231   PetscFunctionBegin;
4232   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&flg);CHKERRQ(ierr);
4233   if (!flg) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"This function requires a MATMPIAIJ matrix as input");
4234   if (Ad)     *Ad     = a->A;
4235   if (Ao)     *Ao     = a->B;
4236   if (colmap) *colmap = a->garray;
4237   PetscFunctionReturn(0);
4238 }
4239 
4240 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
4241 {
4242   PetscErrorCode ierr;
4243   PetscInt       m,N,i,rstart,nnz,Ii;
4244   PetscInt       *indx;
4245   PetscScalar    *values;
4246 
4247   PetscFunctionBegin;
4248   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
4249   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
4250     PetscInt       *dnz,*onz,sum,bs,cbs;
4251 
4252     if (n == PETSC_DECIDE) {
4253       ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
4254     }
4255     /* Check sum(n) = N */
4256     ierr = MPIU_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4257     if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
4258 
4259     ierr    = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4260     rstart -= m;
4261 
4262     ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4263     for (i=0; i<m; i++) {
4264       ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
4265       ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
4266       ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
4267     }
4268 
4269     ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
4270     ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4271     ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
4272     ierr = MatSetBlockSizes(*outmat,bs,cbs);CHKERRQ(ierr);
4273     ierr = MatSetType(*outmat,MATAIJ);CHKERRQ(ierr);
4274     ierr = MatSeqAIJSetPreallocation(*outmat,0,dnz);CHKERRQ(ierr);
4275     ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
4276     ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4277   }
4278 
4279   /* numeric phase */
4280   ierr = MatGetOwnershipRange(*outmat,&rstart,NULL);CHKERRQ(ierr);
4281   for (i=0; i<m; i++) {
4282     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4283     Ii   = i + rstart;
4284     ierr = MatSetValues(*outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4285     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4286   }
4287   ierr = MatAssemblyBegin(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4288   ierr = MatAssemblyEnd(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4289   PetscFunctionReturn(0);
4290 }
4291 
4292 PetscErrorCode MatFileSplit(Mat A,char *outfile)
4293 {
4294   PetscErrorCode    ierr;
4295   PetscMPIInt       rank;
4296   PetscInt          m,N,i,rstart,nnz;
4297   size_t            len;
4298   const PetscInt    *indx;
4299   PetscViewer       out;
4300   char              *name;
4301   Mat               B;
4302   const PetscScalar *values;
4303 
4304   PetscFunctionBegin;
4305   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
4306   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
4307   /* Should this be the type of the diagonal block of A? */
4308   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
4309   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
4310   ierr = MatSetBlockSizesFromMats(B,A,A);CHKERRQ(ierr);
4311   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
4312   ierr = MatSeqAIJSetPreallocation(B,0,NULL);CHKERRQ(ierr);
4313   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
4314   for (i=0; i<m; i++) {
4315     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4316     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4317     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4318   }
4319   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4320   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4321 
4322   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
4323   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
4324   ierr = PetscMalloc1(len+5,&name);CHKERRQ(ierr);
4325   sprintf(name,"%s.%d",outfile,rank);
4326   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
4327   ierr = PetscFree(name);CHKERRQ(ierr);
4328   ierr = MatView(B,out);CHKERRQ(ierr);
4329   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
4330   ierr = MatDestroy(&B);CHKERRQ(ierr);
4331   PetscFunctionReturn(0);
4332 }
4333 
4334 PetscErrorCode MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
4335 {
4336   PetscErrorCode      ierr;
4337   Mat_Merge_SeqsToMPI *merge;
4338   PetscContainer      container;
4339 
4340   PetscFunctionBegin;
4341   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4342   if (container) {
4343     ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4344     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
4345     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
4346     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
4347     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
4348     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
4349     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
4350     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
4351     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
4352     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
4353     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
4354     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
4355     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
4356     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
4357     ierr = PetscFree(merge);CHKERRQ(ierr);
4358     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
4359   }
4360   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
4361   PetscFunctionReturn(0);
4362 }
4363 
4364 #include <../src/mat/utils/freespace.h>
4365 #include <petscbt.h>
4366 
4367 PetscErrorCode MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
4368 {
4369   PetscErrorCode      ierr;
4370   MPI_Comm            comm;
4371   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
4372   PetscMPIInt         size,rank,taga,*len_s;
4373   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
4374   PetscInt            proc,m;
4375   PetscInt            **buf_ri,**buf_rj;
4376   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
4377   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
4378   MPI_Request         *s_waits,*r_waits;
4379   MPI_Status          *status;
4380   MatScalar           *aa=a->a;
4381   MatScalar           **abuf_r,*ba_i;
4382   Mat_Merge_SeqsToMPI *merge;
4383   PetscContainer      container;
4384 
4385   PetscFunctionBegin;
4386   ierr = PetscObjectGetComm((PetscObject)mpimat,&comm);CHKERRQ(ierr);
4387   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4388 
4389   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4390   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4391 
4392   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4393   ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4394 
4395   bi     = merge->bi;
4396   bj     = merge->bj;
4397   buf_ri = merge->buf_ri;
4398   buf_rj = merge->buf_rj;
4399 
4400   ierr   = PetscMalloc1(size,&status);CHKERRQ(ierr);
4401   owners = merge->rowmap->range;
4402   len_s  = merge->len_s;
4403 
4404   /* send and recv matrix values */
4405   /*-----------------------------*/
4406   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
4407   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
4408 
4409   ierr = PetscMalloc1(merge->nsend+1,&s_waits);CHKERRQ(ierr);
4410   for (proc=0,k=0; proc<size; proc++) {
4411     if (!len_s[proc]) continue;
4412     i    = owners[proc];
4413     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
4414     k++;
4415   }
4416 
4417   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
4418   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
4419   ierr = PetscFree(status);CHKERRQ(ierr);
4420 
4421   ierr = PetscFree(s_waits);CHKERRQ(ierr);
4422   ierr = PetscFree(r_waits);CHKERRQ(ierr);
4423 
4424   /* insert mat values of mpimat */
4425   /*----------------------------*/
4426   ierr = PetscMalloc1(N,&ba_i);CHKERRQ(ierr);
4427   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4428 
4429   for (k=0; k<merge->nrecv; k++) {
4430     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4431     nrows       = *(buf_ri_k[k]);
4432     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
4433     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4434   }
4435 
4436   /* set values of ba */
4437   m = merge->rowmap->n;
4438   for (i=0; i<m; i++) {
4439     arow = owners[rank] + i;
4440     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
4441     bnzi = bi[i+1] - bi[i];
4442     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
4443 
4444     /* add local non-zero vals of this proc's seqmat into ba */
4445     anzi   = ai[arow+1] - ai[arow];
4446     aj     = a->j + ai[arow];
4447     aa     = a->a + ai[arow];
4448     nextaj = 0;
4449     for (j=0; nextaj<anzi; j++) {
4450       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4451         ba_i[j] += aa[nextaj++];
4452       }
4453     }
4454 
4455     /* add received vals into ba */
4456     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4457       /* i-th row */
4458       if (i == *nextrow[k]) {
4459         anzi   = *(nextai[k]+1) - *nextai[k];
4460         aj     = buf_rj[k] + *(nextai[k]);
4461         aa     = abuf_r[k] + *(nextai[k]);
4462         nextaj = 0;
4463         for (j=0; nextaj<anzi; j++) {
4464           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4465             ba_i[j] += aa[nextaj++];
4466           }
4467         }
4468         nextrow[k]++; nextai[k]++;
4469       }
4470     }
4471     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
4472   }
4473   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4474   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4475 
4476   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
4477   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
4478   ierr = PetscFree(ba_i);CHKERRQ(ierr);
4479   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4480   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4481   PetscFunctionReturn(0);
4482 }
4483 
4484 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4485 {
4486   PetscErrorCode      ierr;
4487   Mat                 B_mpi;
4488   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
4489   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4490   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
4491   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4492   PetscInt            len,proc,*dnz,*onz,bs,cbs;
4493   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4494   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4495   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
4496   MPI_Status          *status;
4497   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
4498   PetscBT             lnkbt;
4499   Mat_Merge_SeqsToMPI *merge;
4500   PetscContainer      container;
4501 
4502   PetscFunctionBegin;
4503   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4504 
4505   /* make sure it is a PETSc comm */
4506   ierr = PetscCommDuplicate(comm,&comm,NULL);CHKERRQ(ierr);
4507   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4508   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4509 
4510   ierr = PetscNew(&merge);CHKERRQ(ierr);
4511   ierr = PetscMalloc1(size,&status);CHKERRQ(ierr);
4512 
4513   /* determine row ownership */
4514   /*---------------------------------------------------------*/
4515   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
4516   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
4517   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
4518   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
4519   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
4520   ierr = PetscMalloc1(size,&len_si);CHKERRQ(ierr);
4521   ierr = PetscMalloc1(size,&merge->len_s);CHKERRQ(ierr);
4522 
4523   m      = merge->rowmap->n;
4524   owners = merge->rowmap->range;
4525 
4526   /* determine the number of messages to send, their lengths */
4527   /*---------------------------------------------------------*/
4528   len_s = merge->len_s;
4529 
4530   len          = 0; /* length of buf_si[] */
4531   merge->nsend = 0;
4532   for (proc=0; proc<size; proc++) {
4533     len_si[proc] = 0;
4534     if (proc == rank) {
4535       len_s[proc] = 0;
4536     } else {
4537       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4538       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4539     }
4540     if (len_s[proc]) {
4541       merge->nsend++;
4542       nrows = 0;
4543       for (i=owners[proc]; i<owners[proc+1]; i++) {
4544         if (ai[i+1] > ai[i]) nrows++;
4545       }
4546       len_si[proc] = 2*(nrows+1);
4547       len         += len_si[proc];
4548     }
4549   }
4550 
4551   /* determine the number and length of messages to receive for ij-structure */
4552   /*-------------------------------------------------------------------------*/
4553   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
4554   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
4555 
4556   /* post the Irecv of j-structure */
4557   /*-------------------------------*/
4558   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
4559   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
4560 
4561   /* post the Isend of j-structure */
4562   /*--------------------------------*/
4563   ierr = PetscMalloc2(merge->nsend,&si_waits,merge->nsend,&sj_waits);CHKERRQ(ierr);
4564 
4565   for (proc=0, k=0; proc<size; proc++) {
4566     if (!len_s[proc]) continue;
4567     i    = owners[proc];
4568     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
4569     k++;
4570   }
4571 
4572   /* receives and sends of j-structure are complete */
4573   /*------------------------------------------------*/
4574   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
4575   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
4576 
4577   /* send and recv i-structure */
4578   /*---------------------------*/
4579   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
4580   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
4581 
4582   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
4583   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4584   for (proc=0,k=0; proc<size; proc++) {
4585     if (!len_s[proc]) continue;
4586     /* form outgoing message for i-structure:
4587          buf_si[0]:                 nrows to be sent
4588                [1:nrows]:           row index (global)
4589                [nrows+1:2*nrows+1]: i-structure index
4590     */
4591     /*-------------------------------------------*/
4592     nrows       = len_si[proc]/2 - 1;
4593     buf_si_i    = buf_si + nrows+1;
4594     buf_si[0]   = nrows;
4595     buf_si_i[0] = 0;
4596     nrows       = 0;
4597     for (i=owners[proc]; i<owners[proc+1]; i++) {
4598       anzi = ai[i+1] - ai[i];
4599       if (anzi) {
4600         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4601         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4602         nrows++;
4603       }
4604     }
4605     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4606     k++;
4607     buf_si += len_si[proc];
4608   }
4609 
4610   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4611   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4612 
4613   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4614   for (i=0; i<merge->nrecv; i++) {
4615     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);
4616   }
4617 
4618   ierr = PetscFree(len_si);CHKERRQ(ierr);
4619   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4620   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4621   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4622   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4623   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4624   ierr = PetscFree(status);CHKERRQ(ierr);
4625 
4626   /* compute a local seq matrix in each processor */
4627   /*----------------------------------------------*/
4628   /* allocate bi array and free space for accumulating nonzero column info */
4629   ierr  = PetscMalloc1(m+1,&bi);CHKERRQ(ierr);
4630   bi[0] = 0;
4631 
4632   /* create and initialize a linked list */
4633   nlnk = N+1;
4634   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4635 
4636   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4637   len  = ai[owners[rank+1]] - ai[owners[rank]];
4638   ierr = PetscFreeSpaceGet(PetscIntMultTruncate(2,len)+1,&free_space);CHKERRQ(ierr);
4639 
4640   current_space = free_space;
4641 
4642   /* determine symbolic info for each local row */
4643   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4644 
4645   for (k=0; k<merge->nrecv; k++) {
4646     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4647     nrows       = *buf_ri_k[k];
4648     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4649     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4650   }
4651 
4652   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4653   len  = 0;
4654   for (i=0; i<m; i++) {
4655     bnzi = 0;
4656     /* add local non-zero cols of this proc's seqmat into lnk */
4657     arow  = owners[rank] + i;
4658     anzi  = ai[arow+1] - ai[arow];
4659     aj    = a->j + ai[arow];
4660     ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4661     bnzi += nlnk;
4662     /* add received col data into lnk */
4663     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4664       if (i == *nextrow[k]) { /* i-th row */
4665         anzi  = *(nextai[k]+1) - *nextai[k];
4666         aj    = buf_rj[k] + *nextai[k];
4667         ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4668         bnzi += nlnk;
4669         nextrow[k]++; nextai[k]++;
4670       }
4671     }
4672     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4673 
4674     /* if free space is not available, make more free space */
4675     if (current_space->local_remaining<bnzi) {
4676       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(bnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
4677       nspacedouble++;
4678     }
4679     /* copy data into free space, then initialize lnk */
4680     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4681     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
4682 
4683     current_space->array           += bnzi;
4684     current_space->local_used      += bnzi;
4685     current_space->local_remaining -= bnzi;
4686 
4687     bi[i+1] = bi[i] + bnzi;
4688   }
4689 
4690   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4691 
4692   ierr = PetscMalloc1(bi[m]+1,&bj);CHKERRQ(ierr);
4693   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
4694   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4695 
4696   /* create symbolic parallel matrix B_mpi */
4697   /*---------------------------------------*/
4698   ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
4699   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
4700   if (n==PETSC_DECIDE) {
4701     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
4702   } else {
4703     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4704   }
4705   ierr = MatSetBlockSizes(B_mpi,bs,cbs);CHKERRQ(ierr);
4706   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
4707   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
4708   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4709   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
4710 
4711   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4712   B_mpi->assembled    = PETSC_FALSE;
4713   B_mpi->ops->destroy = MatDestroy_MPIAIJ_SeqsToMPI;
4714   merge->bi           = bi;
4715   merge->bj           = bj;
4716   merge->buf_ri       = buf_ri;
4717   merge->buf_rj       = buf_rj;
4718   merge->coi          = NULL;
4719   merge->coj          = NULL;
4720   merge->owners_co    = NULL;
4721 
4722   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
4723 
4724   /* attach the supporting struct to B_mpi for reuse */
4725   ierr    = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
4726   ierr    = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
4727   ierr    = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
4728   ierr    = PetscContainerDestroy(&container);CHKERRQ(ierr);
4729   *mpimat = B_mpi;
4730 
4731   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4732   PetscFunctionReturn(0);
4733 }
4734 
4735 /*@C
4736       MatCreateMPIAIJSumSeqAIJ - Creates a MATMPIAIJ matrix by adding sequential
4737                  matrices from each processor
4738 
4739     Collective on MPI_Comm
4740 
4741    Input Parameters:
4742 +    comm - the communicators the parallel matrix will live on
4743 .    seqmat - the input sequential matrices
4744 .    m - number of local rows (or PETSC_DECIDE)
4745 .    n - number of local columns (or PETSC_DECIDE)
4746 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4747 
4748    Output Parameter:
4749 .    mpimat - the parallel matrix generated
4750 
4751     Level: advanced
4752 
4753    Notes:
4754      The dimensions of the sequential matrix in each processor MUST be the same.
4755      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
4756      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
4757 @*/
4758 PetscErrorCode MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
4759 {
4760   PetscErrorCode ierr;
4761   PetscMPIInt    size;
4762 
4763   PetscFunctionBegin;
4764   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4765   if (size == 1) {
4766     ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4767     if (scall == MAT_INITIAL_MATRIX) {
4768       ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
4769     } else {
4770       ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4771     }
4772     ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4773     PetscFunctionReturn(0);
4774   }
4775   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4776   if (scall == MAT_INITIAL_MATRIX) {
4777     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
4778   }
4779   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
4780   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4781   PetscFunctionReturn(0);
4782 }
4783 
4784 /*@
4785      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MATMPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
4786           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
4787           with MatGetSize()
4788 
4789     Not Collective
4790 
4791    Input Parameters:
4792 +    A - the matrix
4793 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4794 
4795    Output Parameter:
4796 .    A_loc - the local sequential matrix generated
4797 
4798     Level: developer
4799 
4800 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
4801 
4802 @*/
4803 PetscErrorCode MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
4804 {
4805   PetscErrorCode ierr;
4806   Mat_MPIAIJ     *mpimat=(Mat_MPIAIJ*)A->data;
4807   Mat_SeqAIJ     *mat,*a,*b;
4808   PetscInt       *ai,*aj,*bi,*bj,*cmap=mpimat->garray;
4809   MatScalar      *aa,*ba,*cam;
4810   PetscScalar    *ca;
4811   PetscInt       am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
4812   PetscInt       *ci,*cj,col,ncols_d,ncols_o,jo;
4813   PetscBool      match;
4814   MPI_Comm       comm;
4815   PetscMPIInt    size;
4816 
4817   PetscFunctionBegin;
4818   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4819   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
4820   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4821   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4822   if (size == 1 && scall == MAT_REUSE_MATRIX) PetscFunctionReturn(0);
4823 
4824   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4825   a = (Mat_SeqAIJ*)(mpimat->A)->data;
4826   b = (Mat_SeqAIJ*)(mpimat->B)->data;
4827   ai = a->i; aj = a->j; bi = b->i; bj = b->j;
4828   aa = a->a; ba = b->a;
4829   if (scall == MAT_INITIAL_MATRIX) {
4830     if (size == 1) {
4831       ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ai,aj,aa,A_loc);CHKERRQ(ierr);
4832       PetscFunctionReturn(0);
4833     }
4834 
4835     ierr  = PetscMalloc1(1+am,&ci);CHKERRQ(ierr);
4836     ci[0] = 0;
4837     for (i=0; i<am; i++) {
4838       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
4839     }
4840     ierr = PetscMalloc1(1+ci[am],&cj);CHKERRQ(ierr);
4841     ierr = PetscMalloc1(1+ci[am],&ca);CHKERRQ(ierr);
4842     k    = 0;
4843     for (i=0; i<am; i++) {
4844       ncols_o = bi[i+1] - bi[i];
4845       ncols_d = ai[i+1] - ai[i];
4846       /* off-diagonal portion of A */
4847       for (jo=0; jo<ncols_o; jo++) {
4848         col = cmap[*bj];
4849         if (col >= cstart) break;
4850         cj[k]   = col; bj++;
4851         ca[k++] = *ba++;
4852       }
4853       /* diagonal portion of A */
4854       for (j=0; j<ncols_d; j++) {
4855         cj[k]   = cstart + *aj++;
4856         ca[k++] = *aa++;
4857       }
4858       /* off-diagonal portion of A */
4859       for (j=jo; j<ncols_o; j++) {
4860         cj[k]   = cmap[*bj++];
4861         ca[k++] = *ba++;
4862       }
4863     }
4864     /* put together the new matrix */
4865     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
4866     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4867     /* Since these are PETSc arrays, change flags to free them as necessary. */
4868     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
4869     mat->free_a  = PETSC_TRUE;
4870     mat->free_ij = PETSC_TRUE;
4871     mat->nonew   = 0;
4872   } else if (scall == MAT_REUSE_MATRIX) {
4873     mat=(Mat_SeqAIJ*)(*A_loc)->data;
4874     ci = mat->i; cj = mat->j; cam = mat->a;
4875     for (i=0; i<am; i++) {
4876       /* off-diagonal portion of A */
4877       ncols_o = bi[i+1] - bi[i];
4878       for (jo=0; jo<ncols_o; jo++) {
4879         col = cmap[*bj];
4880         if (col >= cstart) break;
4881         *cam++ = *ba++; bj++;
4882       }
4883       /* diagonal portion of A */
4884       ncols_d = ai[i+1] - ai[i];
4885       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
4886       /* off-diagonal portion of A */
4887       for (j=jo; j<ncols_o; j++) {
4888         *cam++ = *ba++; bj++;
4889       }
4890     }
4891   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
4892   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4893   PetscFunctionReturn(0);
4894 }
4895 
4896 /*@C
4897      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MATMPIAIJ matrix by taking all its local rows and NON-ZERO columns
4898 
4899     Not Collective
4900 
4901    Input Parameters:
4902 +    A - the matrix
4903 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4904 -    row, col - index sets of rows and columns to extract (or NULL)
4905 
4906    Output Parameter:
4907 .    A_loc - the local sequential matrix generated
4908 
4909     Level: developer
4910 
4911 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
4912 
4913 @*/
4914 PetscErrorCode MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
4915 {
4916   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4917   PetscErrorCode ierr;
4918   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
4919   IS             isrowa,iscola;
4920   Mat            *aloc;
4921   PetscBool      match;
4922 
4923   PetscFunctionBegin;
4924   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4925   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
4926   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4927   if (!row) {
4928     start = A->rmap->rstart; end = A->rmap->rend;
4929     ierr  = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
4930   } else {
4931     isrowa = *row;
4932   }
4933   if (!col) {
4934     start = A->cmap->rstart;
4935     cmap  = a->garray;
4936     nzA   = a->A->cmap->n;
4937     nzB   = a->B->cmap->n;
4938     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4939     ncols = 0;
4940     for (i=0; i<nzB; i++) {
4941       if (cmap[i] < start) idx[ncols++] = cmap[i];
4942       else break;
4943     }
4944     imark = i;
4945     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
4946     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
4947     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
4948   } else {
4949     iscola = *col;
4950   }
4951   if (scall != MAT_INITIAL_MATRIX) {
4952     ierr    = PetscMalloc1(1,&aloc);CHKERRQ(ierr);
4953     aloc[0] = *A_loc;
4954   }
4955   ierr   = MatCreateSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
4956   *A_loc = aloc[0];
4957   ierr   = PetscFree(aloc);CHKERRQ(ierr);
4958   if (!row) {
4959     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
4960   }
4961   if (!col) {
4962     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
4963   }
4964   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4965   PetscFunctionReturn(0);
4966 }
4967 
4968 /*@C
4969     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
4970 
4971     Collective on Mat
4972 
4973    Input Parameters:
4974 +    A,B - the matrices in mpiaij format
4975 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4976 -    rowb, colb - index sets of rows and columns of B to extract (or NULL)
4977 
4978    Output Parameter:
4979 +    rowb, colb - index sets of rows and columns of B to extract
4980 -    B_seq - the sequential matrix generated
4981 
4982     Level: developer
4983 
4984 @*/
4985 PetscErrorCode MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
4986 {
4987   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4988   PetscErrorCode ierr;
4989   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
4990   IS             isrowb,iscolb;
4991   Mat            *bseq=NULL;
4992 
4993   PetscFunctionBegin;
4994   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4995     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);
4996   }
4997   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4998 
4999   if (scall == MAT_INITIAL_MATRIX) {
5000     start = A->cmap->rstart;
5001     cmap  = a->garray;
5002     nzA   = a->A->cmap->n;
5003     nzB   = a->B->cmap->n;
5004     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
5005     ncols = 0;
5006     for (i=0; i<nzB; i++) {  /* row < local row index */
5007       if (cmap[i] < start) idx[ncols++] = cmap[i];
5008       else break;
5009     }
5010     imark = i;
5011     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
5012     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
5013     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
5014     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
5015   } else {
5016     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
5017     isrowb  = *rowb; iscolb = *colb;
5018     ierr    = PetscMalloc1(1,&bseq);CHKERRQ(ierr);
5019     bseq[0] = *B_seq;
5020   }
5021   ierr   = MatCreateSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
5022   *B_seq = bseq[0];
5023   ierr   = PetscFree(bseq);CHKERRQ(ierr);
5024   if (!rowb) {
5025     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
5026   } else {
5027     *rowb = isrowb;
5028   }
5029   if (!colb) {
5030     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
5031   } else {
5032     *colb = iscolb;
5033   }
5034   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
5035   PetscFunctionReturn(0);
5036 }
5037 
5038 /*
5039     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
5040     of the OFF-DIAGONAL portion of local A
5041 
5042     Collective on Mat
5043 
5044    Input Parameters:
5045 +    A,B - the matrices in mpiaij format
5046 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5047 
5048    Output Parameter:
5049 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
5050 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
5051 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
5052 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
5053 
5054     Level: developer
5055 
5056 */
5057 PetscErrorCode MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
5058 {
5059   VecScatter_MPI_General *gen_to,*gen_from;
5060   PetscErrorCode         ierr;
5061   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
5062   Mat_SeqAIJ             *b_oth;
5063   VecScatter             ctx =a->Mvctx;
5064   MPI_Comm               comm;
5065   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
5066   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
5067   PetscInt               *rvalues,*svalues;
5068   MatScalar              *b_otha,*bufa,*bufA;
5069   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
5070   MPI_Request            *rwaits = NULL,*swaits = NULL;
5071   MPI_Status             *sstatus,rstatus;
5072   PetscMPIInt            jj,size;
5073   PetscInt               *cols,sbs,rbs;
5074   PetscScalar            *vals;
5075 
5076   PetscFunctionBegin;
5077   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
5078   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
5079 
5080   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
5081     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);
5082   }
5083   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5084   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
5085 
5086   if (size == 1) {
5087     startsj_s = NULL;
5088     bufa_ptr  = NULL;
5089     *B_oth    = NULL;
5090     PetscFunctionReturn(0);
5091   }
5092 
5093   gen_to   = (VecScatter_MPI_General*)ctx->todata;
5094   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
5095   nrecvs   = gen_from->n;
5096   nsends   = gen_to->n;
5097 
5098   ierr    = PetscMalloc2(nrecvs,&rwaits,nsends,&swaits);CHKERRQ(ierr);
5099   srow    = gen_to->indices;    /* local row index to be sent */
5100   sstarts = gen_to->starts;
5101   sprocs  = gen_to->procs;
5102   sstatus = gen_to->sstatus;
5103   sbs     = gen_to->bs;
5104   rstarts = gen_from->starts;
5105   rprocs  = gen_from->procs;
5106   rbs     = gen_from->bs;
5107 
5108   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
5109   if (scall == MAT_INITIAL_MATRIX) {
5110     /* i-array */
5111     /*---------*/
5112     /*  post receives */
5113     ierr = PetscMalloc1(rbs*(rstarts[nrecvs] - rstarts[0]),&rvalues);CHKERRQ(ierr);
5114     for (i=0; i<nrecvs; i++) {
5115       rowlen = rvalues + rstarts[i]*rbs;
5116       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
5117       ierr   = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5118     }
5119 
5120     /* pack the outgoing message */
5121     ierr = PetscMalloc2(nsends+1,&sstartsj,nrecvs+1,&rstartsj);CHKERRQ(ierr);
5122 
5123     sstartsj[0] = 0;
5124     rstartsj[0] = 0;
5125     len         = 0; /* total length of j or a array to be sent */
5126     k           = 0;
5127     ierr = PetscMalloc1(sbs*(sstarts[nsends] - sstarts[0]),&svalues);CHKERRQ(ierr);
5128     for (i=0; i<nsends; i++) {
5129       rowlen = svalues + sstarts[i]*sbs;
5130       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
5131       for (j=0; j<nrows; j++) {
5132         row = srow[k] + B->rmap->range[rank]; /* global row idx */
5133         for (l=0; l<sbs; l++) {
5134           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr); /* rowlength */
5135 
5136           rowlen[j*sbs+l] = ncols;
5137 
5138           len += ncols;
5139           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr);
5140         }
5141         k++;
5142       }
5143       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5144 
5145       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
5146     }
5147     /* recvs and sends of i-array are completed */
5148     i = nrecvs;
5149     while (i--) {
5150       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5151     }
5152     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5153     ierr = PetscFree(svalues);CHKERRQ(ierr);
5154 
5155     /* allocate buffers for sending j and a arrays */
5156     ierr = PetscMalloc1(len+1,&bufj);CHKERRQ(ierr);
5157     ierr = PetscMalloc1(len+1,&bufa);CHKERRQ(ierr);
5158 
5159     /* create i-array of B_oth */
5160     ierr = PetscMalloc1(aBn+2,&b_othi);CHKERRQ(ierr);
5161 
5162     b_othi[0] = 0;
5163     len       = 0; /* total length of j or a array to be received */
5164     k         = 0;
5165     for (i=0; i<nrecvs; i++) {
5166       rowlen = rvalues + rstarts[i]*rbs;
5167       nrows  = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be received */
5168       for (j=0; j<nrows; j++) {
5169         b_othi[k+1] = b_othi[k] + rowlen[j];
5170         ierr = PetscIntSumError(rowlen[j],len,&len);CHKERRQ(ierr);
5171         k++;
5172       }
5173       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
5174     }
5175     ierr = PetscFree(rvalues);CHKERRQ(ierr);
5176 
5177     /* allocate space for j and a arrrays of B_oth */
5178     ierr = PetscMalloc1(b_othi[aBn]+1,&b_othj);CHKERRQ(ierr);
5179     ierr = PetscMalloc1(b_othi[aBn]+1,&b_otha);CHKERRQ(ierr);
5180 
5181     /* j-array */
5182     /*---------*/
5183     /*  post receives of j-array */
5184     for (i=0; i<nrecvs; i++) {
5185       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5186       ierr  = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5187     }
5188 
5189     /* pack the outgoing message j-array */
5190     k = 0;
5191     for (i=0; i<nsends; i++) {
5192       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5193       bufJ  = bufj+sstartsj[i];
5194       for (j=0; j<nrows; j++) {
5195         row = srow[k++] + B->rmap->range[rank];  /* global row idx */
5196         for (ll=0; ll<sbs; ll++) {
5197           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
5198           for (l=0; l<ncols; l++) {
5199             *bufJ++ = cols[l];
5200           }
5201           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
5202         }
5203       }
5204       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5205     }
5206 
5207     /* recvs and sends of j-array are completed */
5208     i = nrecvs;
5209     while (i--) {
5210       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5211     }
5212     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5213   } else if (scall == MAT_REUSE_MATRIX) {
5214     sstartsj = *startsj_s;
5215     rstartsj = *startsj_r;
5216     bufa     = *bufa_ptr;
5217     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
5218     b_otha   = b_oth->a;
5219   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
5220 
5221   /* a-array */
5222   /*---------*/
5223   /*  post receives of a-array */
5224   for (i=0; i<nrecvs; i++) {
5225     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5226     ierr  = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5227   }
5228 
5229   /* pack the outgoing message a-array */
5230   k = 0;
5231   for (i=0; i<nsends; i++) {
5232     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5233     bufA  = bufa+sstartsj[i];
5234     for (j=0; j<nrows; j++) {
5235       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
5236       for (ll=0; ll<sbs; ll++) {
5237         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
5238         for (l=0; l<ncols; l++) {
5239           *bufA++ = vals[l];
5240         }
5241         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
5242       }
5243     }
5244     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5245   }
5246   /* recvs and sends of a-array are completed */
5247   i = nrecvs;
5248   while (i--) {
5249     ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5250   }
5251   if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5252   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
5253 
5254   if (scall == MAT_INITIAL_MATRIX) {
5255     /* put together the new matrix */
5256     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
5257 
5258     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
5259     /* Since these are PETSc arrays, change flags to free them as necessary. */
5260     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
5261     b_oth->free_a  = PETSC_TRUE;
5262     b_oth->free_ij = PETSC_TRUE;
5263     b_oth->nonew   = 0;
5264 
5265     ierr = PetscFree(bufj);CHKERRQ(ierr);
5266     if (!startsj_s || !bufa_ptr) {
5267       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
5268       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
5269     } else {
5270       *startsj_s = sstartsj;
5271       *startsj_r = rstartsj;
5272       *bufa_ptr  = bufa;
5273     }
5274   }
5275   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5276   PetscFunctionReturn(0);
5277 }
5278 
5279 /*@C
5280   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
5281 
5282   Not Collective
5283 
5284   Input Parameters:
5285 . A - The matrix in mpiaij format
5286 
5287   Output Parameter:
5288 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
5289 . colmap - A map from global column index to local index into lvec
5290 - multScatter - A scatter from the argument of a matrix-vector product to lvec
5291 
5292   Level: developer
5293 
5294 @*/
5295 #if defined(PETSC_USE_CTABLE)
5296 PetscErrorCode MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
5297 #else
5298 PetscErrorCode MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
5299 #endif
5300 {
5301   Mat_MPIAIJ *a;
5302 
5303   PetscFunctionBegin;
5304   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
5305   PetscValidPointer(lvec, 2);
5306   PetscValidPointer(colmap, 3);
5307   PetscValidPointer(multScatter, 4);
5308   a = (Mat_MPIAIJ*) A->data;
5309   if (lvec) *lvec = a->lvec;
5310   if (colmap) *colmap = a->colmap;
5311   if (multScatter) *multScatter = a->Mvctx;
5312   PetscFunctionReturn(0);
5313 }
5314 
5315 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
5316 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
5317 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
5318 #if defined(PETSC_HAVE_ELEMENTAL)
5319 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
5320 #endif
5321 #if defined(PETSC_HAVE_HYPRE)
5322 PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat,MatType,MatReuse,Mat*);
5323 PETSC_INTERN PetscErrorCode MatMatMatMult_Transpose_AIJ_AIJ(Mat,Mat,Mat,MatReuse,PetscReal,Mat*);
5324 #endif
5325 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_IS(Mat,MatType,MatReuse,Mat*);
5326 
5327 /*
5328     Computes (B'*A')' since computing B*A directly is untenable
5329 
5330                n                       p                          p
5331         (              )       (              )         (                  )
5332       m (      A       )  *  n (       B      )   =   m (         C        )
5333         (              )       (              )         (                  )
5334 
5335 */
5336 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
5337 {
5338   PetscErrorCode ierr;
5339   Mat            At,Bt,Ct;
5340 
5341   PetscFunctionBegin;
5342   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
5343   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
5344   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
5345   ierr = MatDestroy(&At);CHKERRQ(ierr);
5346   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
5347   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
5348   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
5349   PetscFunctionReturn(0);
5350 }
5351 
5352 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
5353 {
5354   PetscErrorCode ierr;
5355   PetscInt       m=A->rmap->n,n=B->cmap->n;
5356   Mat            Cmat;
5357 
5358   PetscFunctionBegin;
5359   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);
5360   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
5361   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
5362   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
5363   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
5364   ierr = MatMPIDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
5365   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5366   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5367 
5368   Cmat->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
5369 
5370   *C = Cmat;
5371   PetscFunctionReturn(0);
5372 }
5373 
5374 /* ----------------------------------------------------------------*/
5375 PETSC_INTERN PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
5376 {
5377   PetscErrorCode ierr;
5378 
5379   PetscFunctionBegin;
5380   if (scall == MAT_INITIAL_MATRIX) {
5381     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5382     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
5383     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5384   }
5385   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5386   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
5387   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5388   PetscFunctionReturn(0);
5389 }
5390 
5391 /*MC
5392    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
5393 
5394    Options Database Keys:
5395 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
5396 
5397   Level: beginner
5398 
5399 .seealso: MatCreateAIJ()
5400 M*/
5401 
5402 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
5403 {
5404   Mat_MPIAIJ     *b;
5405   PetscErrorCode ierr;
5406   PetscMPIInt    size;
5407 
5408   PetscFunctionBegin;
5409   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
5410 
5411   ierr          = PetscNewLog(B,&b);CHKERRQ(ierr);
5412   B->data       = (void*)b;
5413   ierr          = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
5414   B->assembled  = PETSC_FALSE;
5415   B->insertmode = NOT_SET_VALUES;
5416   b->size       = size;
5417 
5418   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank);CHKERRQ(ierr);
5419 
5420   /* build cache for off array entries formed */
5421   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash);CHKERRQ(ierr);
5422 
5423   b->donotstash  = PETSC_FALSE;
5424   b->colmap      = 0;
5425   b->garray      = 0;
5426   b->roworiented = PETSC_TRUE;
5427 
5428   /* stuff used for matrix vector multiply */
5429   b->lvec  = NULL;
5430   b->Mvctx = NULL;
5431 
5432   /* stuff for MatGetRow() */
5433   b->rowindices   = 0;
5434   b->rowvalues    = 0;
5435   b->getrowactive = PETSC_FALSE;
5436 
5437   /* flexible pointer used in CUSP/CUSPARSE classes */
5438   b->spptr = NULL;
5439 
5440   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetUseScalableIncreaseOverlap_C",MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ);CHKERRQ(ierr);
5441   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ);CHKERRQ(ierr);
5442   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
5443   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
5444   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
5445   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
5446   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
5447   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
5448   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
5449   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
5450 #if defined(PETSC_HAVE_ELEMENTAL)
5451   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_elemental_C",MatConvert_MPIAIJ_Elemental);CHKERRQ(ierr);
5452 #endif
5453 #if defined(PETSC_HAVE_HYPRE)
5454   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_hypre_C",MatConvert_AIJ_HYPRE);CHKERRQ(ierr);
5455 #endif
5456   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_is_C",MatConvert_MPIAIJ_IS);CHKERRQ(ierr);
5457   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
5458   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
5459   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
5460 #if defined(PETSC_HAVE_HYPRE)
5461   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMatMult_transpose_mpiaij_mpiaij_C",MatMatMatMult_Transpose_AIJ_AIJ);CHKERRQ(ierr);
5462 #endif
5463   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
5464   PetscFunctionReturn(0);
5465 }
5466 
5467 /*@C
5468      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
5469          and "off-diagonal" part of the matrix in CSR format.
5470 
5471    Collective on MPI_Comm
5472 
5473    Input Parameters:
5474 +  comm - MPI communicator
5475 .  m - number of local rows (Cannot be PETSC_DECIDE)
5476 .  n - This value should be the same as the local size used in creating the
5477        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
5478        calculated if N is given) For square matrices n is almost always m.
5479 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
5480 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
5481 .   i - row indices for "diagonal" portion of matrix
5482 .   j - column indices
5483 .   a - matrix values
5484 .   oi - row indices for "off-diagonal" portion of matrix
5485 .   oj - column indices
5486 -   oa - matrix values
5487 
5488    Output Parameter:
5489 .   mat - the matrix
5490 
5491    Level: advanced
5492 
5493    Notes:
5494        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
5495        must free the arrays once the matrix has been destroyed and not before.
5496 
5497        The i and j indices are 0 based
5498 
5499        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
5500 
5501        This sets local rows and cannot be used to set off-processor values.
5502 
5503        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
5504        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
5505        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
5506        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
5507        keep track of the underlying array. Use MatSetOption(A,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
5508        communication if it is known that only local entries will be set.
5509 
5510 .keywords: matrix, aij, compressed row, sparse, parallel
5511 
5512 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
5513           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
5514 @*/
5515 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)
5516 {
5517   PetscErrorCode ierr;
5518   Mat_MPIAIJ     *maij;
5519 
5520   PetscFunctionBegin;
5521   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
5522   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
5523   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
5524   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
5525   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
5526   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
5527   maij = (Mat_MPIAIJ*) (*mat)->data;
5528 
5529   (*mat)->preallocated = PETSC_TRUE;
5530 
5531   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
5532   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
5533 
5534   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
5535   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
5536 
5537   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5538   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5539   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5540   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5541 
5542   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
5543   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5544   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5545   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_FALSE);CHKERRQ(ierr);
5546   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
5547   PetscFunctionReturn(0);
5548 }
5549 
5550 /*
5551     Special version for direct calls from Fortran
5552 */
5553 #include <petsc/private/fortranimpl.h>
5554 
5555 /* Change these macros so can be used in void function */
5556 #undef CHKERRQ
5557 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
5558 #undef SETERRQ2
5559 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5560 #undef SETERRQ3
5561 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5562 #undef SETERRQ
5563 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
5564 
5565 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5566 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
5567 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5568 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
5569 #else
5570 #endif
5571 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)
5572 {
5573   Mat            mat  = *mmat;
5574   PetscInt       m    = *mm, n = *mn;
5575   InsertMode     addv = *maddv;
5576   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
5577   PetscScalar    value;
5578   PetscErrorCode ierr;
5579 
5580   MatCheckPreallocated(mat,1);
5581   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
5582 
5583 #if defined(PETSC_USE_DEBUG)
5584   else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
5585 #endif
5586   {
5587     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
5588     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
5589     PetscBool roworiented = aij->roworiented;
5590 
5591     /* Some Variables required in the macro */
5592     Mat        A                 = aij->A;
5593     Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
5594     PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
5595     MatScalar  *aa               = a->a;
5596     PetscBool  ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
5597     Mat        B                 = aij->B;
5598     Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
5599     PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5600     MatScalar  *ba               = b->a;
5601 
5602     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5603     PetscInt  nonew = a->nonew;
5604     MatScalar *ap1,*ap2;
5605 
5606     PetscFunctionBegin;
5607     for (i=0; i<m; i++) {
5608       if (im[i] < 0) continue;
5609 #if defined(PETSC_USE_DEBUG)
5610       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);
5611 #endif
5612       if (im[i] >= rstart && im[i] < rend) {
5613         row      = im[i] - rstart;
5614         lastcol1 = -1;
5615         rp1      = aj + ai[row];
5616         ap1      = aa + ai[row];
5617         rmax1    = aimax[row];
5618         nrow1    = ailen[row];
5619         low1     = 0;
5620         high1    = nrow1;
5621         lastcol2 = -1;
5622         rp2      = bj + bi[row];
5623         ap2      = ba + bi[row];
5624         rmax2    = bimax[row];
5625         nrow2    = bilen[row];
5626         low2     = 0;
5627         high2    = nrow2;
5628 
5629         for (j=0; j<n; j++) {
5630           if (roworiented) value = v[i*n+j];
5631           else value = v[i+j*m];
5632           if (in[j] >= cstart && in[j] < cend) {
5633             col = in[j] - cstart;
5634             if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
5635             MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
5636           } else if (in[j] < 0) continue;
5637 #if defined(PETSC_USE_DEBUG)
5638           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);
5639 #endif
5640           else {
5641             if (mat->was_assembled) {
5642               if (!aij->colmap) {
5643                 ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5644               }
5645 #if defined(PETSC_USE_CTABLE)
5646               ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5647               col--;
5648 #else
5649               col = aij->colmap[in[j]] - 1;
5650 #endif
5651               if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
5652               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5653                 ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5654                 col  =  in[j];
5655                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5656                 B     = aij->B;
5657                 b     = (Mat_SeqAIJ*)B->data;
5658                 bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5659                 rp2   = bj + bi[row];
5660                 ap2   = ba + bi[row];
5661                 rmax2 = bimax[row];
5662                 nrow2 = bilen[row];
5663                 low2  = 0;
5664                 high2 = nrow2;
5665                 bm    = aij->B->rmap->n;
5666                 ba    = b->a;
5667               }
5668             } else col = in[j];
5669             MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
5670           }
5671         }
5672       } else if (!aij->donotstash) {
5673         if (roworiented) {
5674           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5675         } else {
5676           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5677         }
5678       }
5679     }
5680   }
5681   PetscFunctionReturnVoid();
5682 }
5683 
5684