xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision 9c988bcab2d9407ab30a1ddc0e1b6835062ae894)
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   PetscMPIInt rank;
3007   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3008   ierr = ISGetLocalSize(iscol,&ncols);CHKERRQ(ierr);
3009 
3010   /* (1) iscol is a sub-column vector of mat, pad it with '-1.' to form a full vector x */
3011   ierr = MatCreateVecs(mat,&x,NULL);CHKERRQ(ierr);
3012   ierr = VecDuplicate(x,&cmap);CHKERRQ(ierr);
3013   ierr = VecSet(x,-1.0);CHKERRQ(ierr);
3014 
3015   /* Get start indices */
3016   ierr = MPI_Scan(&ncols,&isstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3017   isstart -= ncols;
3018   ierr = MatGetOwnershipRangeColumn(mat,&cstart,&cend);CHKERRQ(ierr);
3019 
3020   ierr = ISGetIndices(iscol,&is_idx);CHKERRQ(ierr);
3021   ierr = VecGetArray(x,&xarray);CHKERRQ(ierr);
3022   ierr = VecGetArray(cmap,&cmaparray);CHKERRQ(ierr);
3023   ierr = PetscMalloc1(ncols,&idx);CHKERRQ(ierr);
3024   for (i=0; i<ncols; i++) {
3025     xarray[is_idx[i]-cstart]    = (PetscScalar)is_idx[i];
3026     cmaparray[is_idx[i]-cstart] = i + isstart;      /* global index of iscol[i] */
3027     idx[i]                      = is_idx[i]-cstart; /* local index of iscol[i]  */
3028   }
3029   ierr = VecRestoreArray(x,&xarray);CHKERRQ(ierr);
3030   ierr = VecRestoreArray(cmap,&cmaparray);CHKERRQ(ierr);
3031   ierr = ISRestoreIndices(iscol,&is_idx);CHKERRQ(ierr);
3032 
3033   /* Get iscol_d */
3034   ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,iscol_d);CHKERRQ(ierr);
3035   ierr = ISGetBlockSize(iscol,&i);CHKERRQ(ierr);
3036   ierr = ISSetBlockSize(*iscol_d,i);CHKERRQ(ierr);
3037 
3038   /* Get isrow_d */
3039   ierr = ISGetLocalSize(isrow,&m);CHKERRQ(ierr);
3040   rstart = mat->rmap->rstart;
3041   ierr = PetscMalloc1(m,&idx);CHKERRQ(ierr);
3042   ierr = ISGetIndices(isrow,&is_idx);CHKERRQ(ierr);
3043   for (i=0; i<m; i++) idx[i] = is_idx[i]-rstart;
3044   ierr = ISRestoreIndices(isrow,&is_idx);CHKERRQ(ierr);
3045 
3046   ierr = ISCreateGeneral(PETSC_COMM_SELF,m,idx,PETSC_OWN_POINTER,isrow_d);CHKERRQ(ierr);
3047   ierr = ISGetBlockSize(isrow,&i);CHKERRQ(ierr);
3048   ierr = ISSetBlockSize(*isrow_d,i);CHKERRQ(ierr);
3049 
3050   /* (2) Scatter x and cmap using aij->Mvctx to get their off-process portions (see MatMult_MPIAIJ) */
3051   ierr = VecScatterBegin(a->Mvctx,x,lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3052 
3053   ierr = VecDuplicate(lvec,&lcmap);CHKERRQ(ierr);
3054 
3055   ierr = VecScatterEnd(a->Mvctx,x,lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3056   ierr = VecScatterBegin(a->Mvctx,cmap,lcmap,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3057   ierr = VecScatterEnd(a->Mvctx,cmap,lcmap,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3058 
3059   /* (3) create sequential iscol_o (a subset of iscol) and isgarray */
3060   /* off-process column indices */
3061   count = 0;
3062   ierr = PetscMalloc1(Bn,&idx);CHKERRQ(ierr);
3063   ierr = PetscMalloc1(Bn,&cmap1);CHKERRQ(ierr);
3064 
3065   ierr = VecGetArray(lvec,&xarray);CHKERRQ(ierr);
3066   ierr = VecGetArray(lcmap,&cmaparray);CHKERRQ(ierr);
3067   for (i=0; i<Bn; i++) {
3068     if (PetscRealPart(xarray[i]) > -1.0) {
3069       idx[count]     = i;                   /* local column index in off-diagonal part B */
3070       cmap1[count++] = (PetscInt)PetscRealPart(cmaparray[i]);  /* column index in submat */
3071     }
3072   }
3073   ierr = VecRestoreArray(lvec,&xarray);CHKERRQ(ierr);
3074   ierr = VecRestoreArray(lcmap,&cmaparray);CHKERRQ(ierr);
3075 
3076   ierr = ISCreateGeneral(PETSC_COMM_SELF,count,idx,PETSC_COPY_VALUES,iscol_o);CHKERRQ(ierr);
3077   ierr = ISGetBlockSize(iscol,&i);CHKERRQ(ierr);
3078   ierr = ISSetBlockSize(*iscol_o,i);CHKERRQ(ierr);
3079   ierr = PetscFree(idx);CHKERRQ(ierr);
3080 
3081   *garray = cmap1;
3082 
3083   ierr = VecDestroy(&x);CHKERRQ(ierr);
3084   ierr = VecDestroy(&cmap);CHKERRQ(ierr);
3085   ierr = VecDestroy(&lcmap);CHKERRQ(ierr);
3086   PetscFunctionReturn(0);
3087 }
3088 
3089 /* isrow and iscol have same processor distribution as mat, output *submat is a submatrix of local mat */
3090 PetscErrorCode MatCreateSubMatrix_MPIAIJ_SameRowColDist(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *submat)
3091 {
3092   PetscErrorCode ierr;
3093   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)mat->data,*asub;
3094   Mat            M = NULL;
3095   MPI_Comm       comm;
3096   IS             iscol_d,isrow_d,iscol_o;
3097   Mat            Asub = NULL,Bsub = NULL;
3098   PetscInt       n;
3099 
3100   PetscFunctionBegin;
3101   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3102   PetscMPIInt rank;
3103   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3104 
3105   if (call == MAT_REUSE_MATRIX) {
3106     if (!rank) printf(" _SameRowColDist reuse ...\n");
3107 
3108     /* Retrieve isrow_d, iscol_d and iscol_o from submat */
3109     ierr = PetscObjectQuery((PetscObject)*submat,"isrow_d",(PetscObject*)&isrow_d);CHKERRQ(ierr);
3110     if (!isrow_d) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"isrow_d passed in was not used before, cannot reuse");
3111 
3112     ierr = PetscObjectQuery((PetscObject)*submat,"iscol_d",(PetscObject*)&iscol_d);CHKERRQ(ierr);
3113     if (!iscol_d) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"iscol_d passed in was not used before, cannot reuse");
3114 
3115     ierr = PetscObjectQuery((PetscObject)*submat,"iscol_o",(PetscObject*)&iscol_o);CHKERRQ(ierr);
3116     if (!iscol_o) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"iscol_o passed in was not used before, cannot reuse");
3117 
3118     /* Update diagonal and off-diagonal portions of submat */
3119     asub = (Mat_MPIAIJ*)(*submat)->data;
3120     ierr = MatCreateSubMatrix_SeqAIJ(a->A,isrow_d,iscol_d,PETSC_DECIDE,MAT_REUSE_MATRIX,&asub->A);CHKERRQ(ierr);
3121     ierr = ISGetLocalSize(iscol_o,&n);CHKERRQ(ierr);
3122     if (n) {
3123       ierr = MatCreateSubMatrix_SeqAIJ(a->B,isrow_d,iscol_o,PETSC_DECIDE,MAT_REUSE_MATRIX,&asub->B);CHKERRQ(ierr);
3124     }
3125     ierr = MatAssemblyBegin(*submat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3126     ierr = MatAssemblyEnd(*submat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3127 
3128   } else { /* call == MAT_INITIAL_MATRIX) */
3129     const PetscInt *garray;
3130     PetscInt        BsubN;
3131 
3132     /* Create isrow_d, iscol_d, iscol_o and isgarray (replace isgarray with array?) */
3133     ierr = ISGetSeqIS_SameColDist_Private(mat,isrow,iscol,&isrow_d,&iscol_d,&iscol_o,&garray);CHKERRQ(ierr);
3134 
3135     /* Create local submatrices Asub and Bsub */
3136     ierr = MatCreateSubMatrix_SeqAIJ(a->A,isrow_d,iscol_d,PETSC_DECIDE,MAT_INITIAL_MATRIX,&Asub);CHKERRQ(ierr);
3137     ierr = MatCreateSubMatrix_SeqAIJ(a->B,isrow_d,iscol_o,PETSC_DECIDE,MAT_INITIAL_MATRIX,&Bsub);CHKERRQ(ierr);
3138 
3139     /* Create submatrix M */
3140     ierr = MatCreateMPIAIJWithSeqAIJ(comm,Asub,Bsub,garray,&M);CHKERRQ(ierr);
3141 
3142     /* If Bsub has empty columns, compress iscol_o such that it will retrieve condensed Bsub from a->B during reuse */
3143     asub = (Mat_MPIAIJ*)M->data;
3144 
3145     ierr = ISGetLocalSize(iscol_o,&BsubN);CHKERRQ(ierr);
3146     n = asub->B->cmap->N;
3147     if (BsubN > n) {
3148       /* This case can be tested using ~petsc/src/tao/bound/examples/tutorials/runplate2_3 */
3149       const PetscInt *idx;
3150       PetscInt       i,j,*idx_new,*subgarray = asub->garray;
3151       ierr = PetscInfo2(M,"submatrix Bn %D != BsubN %D, update iscol_o\n",n,BsubN);CHKERRQ(ierr);
3152 
3153       ierr = PetscMalloc1(n,&idx_new);CHKERRQ(ierr);
3154       j = 0;
3155       ierr = ISGetIndices(iscol_o,&idx);CHKERRQ(ierr);
3156       for (i=0; i<n; i++) {
3157         if (j >= BsubN) break;
3158         while (subgarray[i] > garray[j]) j++;
3159 
3160         if (subgarray[i] == garray[j]) {
3161           idx_new[i] = idx[j++];
3162         } else SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"subgarray[%D]=%D cannot < garray[%D]=%D",i,subgarray[i],j,garray[j]);
3163       }
3164       ierr = ISRestoreIndices(iscol_o,&idx);CHKERRQ(ierr);
3165 
3166       ierr = ISDestroy(&iscol_o);CHKERRQ(ierr);
3167       ierr = ISCreateGeneral(PETSC_COMM_SELF,n,idx_new,PETSC_OWN_POINTER,&iscol_o);CHKERRQ(ierr);
3168 
3169     } else if (BsubN < n) {
3170       SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Columns of Bsub cannot be smaller than B's",BsubN,asub->B->cmap->N);
3171     }
3172 
3173     ierr = PetscFree(garray);CHKERRQ(ierr);
3174     *submat = M;
3175 
3176     /* Save isrow_d, iscol_d and iscol_o used in processor for next request */
3177     ierr = PetscObjectCompose((PetscObject)M,"isrow_d",(PetscObject)isrow_d);CHKERRQ(ierr);
3178     ierr = ISDestroy(&isrow_d);CHKERRQ(ierr);
3179 
3180     ierr = PetscObjectCompose((PetscObject)M,"iscol_d",(PetscObject)iscol_d);CHKERRQ(ierr);
3181     ierr = ISDestroy(&iscol_d);CHKERRQ(ierr);
3182 
3183     ierr = PetscObjectCompose((PetscObject)M,"iscol_o",(PetscObject)iscol_o);CHKERRQ(ierr);
3184     ierr = ISDestroy(&iscol_o);CHKERRQ(ierr);
3185   }
3186   PetscFunctionReturn(0);
3187 }
3188 
3189 PetscErrorCode MatCreateSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3190 {
3191   PetscErrorCode ierr;
3192   IS             iscol_local,isrow_d;
3193   PetscInt       csize;
3194   PetscInt       n,i,j,start,end;
3195   PetscBool      sameRowDist=PETSC_FALSE,sameDist[2],tsameDist[2];
3196   MPI_Comm       comm;
3197 
3198   PetscFunctionBegin;
3199   /* If isrow has same processor distribution as mat,
3200      call MatCreateSubMatrix_MPIAIJ_SameRowDist() to avoid using a hash table with global size of iscol */
3201   if (call == MAT_REUSE_MATRIX) {
3202     ierr = PetscObjectQuery((PetscObject)*newmat,"isrow_d",(PetscObject*)&isrow_d);CHKERRQ(ierr);
3203     if (isrow_d) {
3204       sameRowDist  = PETSC_TRUE;
3205       tsameDist[1] = PETSC_TRUE; /* sameColDist */
3206     } else {
3207       ierr = PetscObjectQuery((PetscObject)*newmat,"SubIScol",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3208       if (iscol_local) {
3209         sameRowDist  = PETSC_TRUE;
3210         tsameDist[1] = PETSC_FALSE; /* !sameColDist */
3211       }
3212     }
3213   } else {
3214     /* Check if isrow has same processor distribution as mat */
3215     sameDist[0] = PETSC_FALSE;
3216     ierr = ISGetLocalSize(isrow,&n);CHKERRQ(ierr);
3217     if (!n) {
3218       sameDist[0] = PETSC_TRUE;
3219     } else {
3220       ierr = ISGetMinMax(isrow,&i,&j);CHKERRQ(ierr);
3221       ierr = MatGetOwnershipRange(mat,&start,&end);CHKERRQ(ierr);
3222       if (i >= start && j < end) {
3223         sameDist[0] = PETSC_TRUE;
3224       }
3225     }
3226 
3227     /* Check if iscol has same processor distribution as mat */
3228     sameDist[1] = PETSC_FALSE;
3229     ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr);
3230     if (!n) {
3231       sameDist[1] = PETSC_TRUE;
3232     } else {
3233       ierr = ISGetMinMax(iscol,&i,&j);CHKERRQ(ierr);
3234       ierr = MatGetOwnershipRangeColumn(mat,&start,&end);CHKERRQ(ierr);
3235       if (i >= start && j < end) sameDist[1] = PETSC_TRUE;
3236     }
3237 
3238     ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3239     ierr = MPIU_Allreduce(&sameDist,&tsameDist,2,MPIU_BOOL,MPI_LAND,comm);CHKERRQ(ierr);
3240     sameRowDist = tsameDist[0];
3241   }
3242 
3243   if (sameRowDist) {
3244     if (tsameDist[1]) { /* sameRowDist & sameColDist */
3245       /* isrow and iscol have same processor distribution as mat */
3246       ierr = MatCreateSubMatrix_MPIAIJ_SameRowColDist(mat,isrow,iscol,call,newmat);CHKERRQ(ierr);
3247     } else { /* sameRowDist */
3248       /* isrow has same processor distribution as mat */
3249       ierr = MatCreateSubMatrix_MPIAIJ_SameRowDist(mat,isrow,iscol,call,newmat);CHKERRQ(ierr);
3250     }
3251     PetscFunctionReturn(0);
3252   }
3253 
3254   /* General case: iscol -> iscol_local which has global size of iscol */
3255   if (call == MAT_REUSE_MATRIX) {
3256     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3257     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3258   } else {
3259     ierr = ISGetSeqIS_Private(mat,iscol,&iscol_local);CHKERRQ(ierr);
3260   }
3261 
3262   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3263   ierr = MatCreateSubMatrix_MPIAIJ_nonscalable(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
3264 
3265   if (call == MAT_INITIAL_MATRIX) {
3266     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3267     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3268   }
3269   PetscFunctionReturn(0);
3270 }
3271 
3272 /*@C
3273      MatCreateMPIAIJWithSeqAIJ - creates a MPIAIJ matrix using SeqAIJ matrices that contain the "diagonal"
3274          and "off-diagonal" part of the matrix in CSR format.
3275 
3276    Collective on MPI_Comm
3277 
3278    Input Parameters:
3279 +  comm - MPI communicator
3280 .  A - "diagonal" portion of matrix
3281 .  B - "off-diagonal" portion of matrix, may have empty columns, will be destroyed by this routine
3282 -  garray - global index of B columns
3283 
3284    Output Parameter:
3285 .   mat - the matrix, with input A as its local diagonal matrix
3286    Level: advanced
3287 
3288    Notes:
3289        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix.
3290        A becomes part of output mat, B is destroyed by this routine. The user cannot use A and B anymore.
3291 
3292 .seealso: MatCreateMPIAIJWithSplitArrays()
3293 @*/
3294 PetscErrorCode MatCreateMPIAIJWithSeqAIJ(MPI_Comm comm,Mat A,Mat B,const PetscInt garray[],Mat *mat)
3295 {
3296   PetscErrorCode ierr;
3297   Mat_MPIAIJ     *maij;
3298   Mat_SeqAIJ     *b=(Mat_SeqAIJ*)B->data,*bnew;
3299   PetscInt       *oi=b->i,*oj=b->j,i,nz,col;
3300   PetscScalar    *oa=b->a;
3301   Mat            Bnew;
3302   PetscInt       m,n,N;
3303 
3304   PetscFunctionBegin;
3305   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
3306   ierr = MatGetSize(A,&m,&n);CHKERRQ(ierr);
3307   if (m != B->rmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Am %D != Bm %D",m,B->rmap->N);
3308   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);
3309   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);
3310 
3311   /* Get global columns of mat */
3312   ierr = MPIU_Allreduce(&n,&N,1,MPI_INT,MPI_SUM,comm);CHKERRQ(ierr);
3313 
3314   ierr = MatSetSizes(*mat,m,n,PETSC_DECIDE,N);CHKERRQ(ierr);
3315   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
3316   ierr = MatSetBlockSizes(*mat,A->rmap->bs,A->cmap->bs);CHKERRQ(ierr);
3317   maij = (Mat_MPIAIJ*)(*mat)->data;
3318 
3319   (*mat)->preallocated = PETSC_TRUE;
3320 
3321   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
3322   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
3323 
3324   /* Set A as diagonal portion of *mat */
3325   maij->A = A;
3326 
3327   nz = oi[m];
3328   for (i=0; i<nz; i++) {
3329     col   = oj[i];
3330     oj[i] = garray[col];
3331   }
3332 
3333    /* Set Bnew as off-diagonal portion of *mat */
3334   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,N,oi,oj,oa,&Bnew);CHKERRQ(ierr);
3335   bnew        = (Mat_SeqAIJ*)Bnew->data;
3336   bnew->maxnz = b->maxnz; /* allocated nonzeros of B */
3337   maij->B     = Bnew;
3338 
3339   if (B->rmap->N != Bnew->rmap->N) SETERRQ2(PETSC_COMM_SELF,0,"BN %d != BnewN %d",B->rmap->N,Bnew->rmap->N);
3340 
3341   b->singlemalloc = PETSC_FALSE; /* B arrays are shared by Bnew */
3342   b->free_a       = PETSC_FALSE;
3343   b->free_ij      = PETSC_FALSE;
3344   ierr = MatDestroy(&B);CHKERRQ(ierr);
3345 
3346   bnew->singlemalloc = PETSC_TRUE; /* arrays will be freed by MatDestroy(&Bnew) */
3347   bnew->free_a       = PETSC_TRUE;
3348   bnew->free_ij      = PETSC_TRUE;
3349 
3350   /* condense columns of maij->B */
3351   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
3352   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3353   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3354   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_FALSE);CHKERRQ(ierr);
3355   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3356   PetscFunctionReturn(0);
3357 }
3358 
3359 extern PetscErrorCode MatCreateSubMatrices_MPIAIJ_SingleIS_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool,Mat*);
3360 
3361 PetscErrorCode MatCreateSubMatrix_MPIAIJ_SameRowDist(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3362 {
3363   PetscErrorCode ierr;
3364   PetscInt       i,m,n,rstart,row,rend,nz,j,bs,cbs;
3365   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
3366   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)mat->data;
3367   Mat            M,Msub,B=a->B;
3368   MatScalar      *aa;
3369   Mat_SeqAIJ     *aij;
3370   PetscInt       *garray = a->garray,*colsub,Ncols;
3371   PetscInt       count,Bn=B->cmap->N,cstart=mat->cmap->rstart,cend=mat->cmap->rend;
3372   IS             iscol_sub,iscmap;
3373   const PetscInt *is_idx,*cmap;
3374   PetscBool      allcolumns=PETSC_FALSE;
3375   IS             iscol_local=NULL;
3376   MPI_Comm       comm;
3377 
3378   PetscFunctionBegin;
3379   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3380 
3381   if (call == MAT_REUSE_MATRIX) {
3382     ierr = PetscObjectQuery((PetscObject)*newmat,"SubIScol",(PetscObject*)&iscol_sub);CHKERRQ(ierr);
3383     if (!iscol_sub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"SubIScol passed in was not used before, cannot reuse");
3384     ierr = ISGetLocalSize(iscol_sub,&count);CHKERRQ(ierr);
3385 
3386     ierr = PetscObjectQuery((PetscObject)*newmat,"Subcmap",(PetscObject*)&iscmap);CHKERRQ(ierr);
3387     if (!iscmap) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Subcmap passed in was not used before, cannot reuse");
3388 
3389     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Msub);CHKERRQ(ierr);
3390     if (!Msub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3391 
3392     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol_sub,MAT_REUSE_MATRIX,PETSC_FALSE,&Msub);CHKERRQ(ierr);
3393 
3394   } else { /* call == MAT_INITIAL_MATRIX) */
3395     PetscBool flg;
3396 
3397     ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr);
3398     ierr = ISGetSize(iscol,&Ncols);CHKERRQ(ierr);
3399 
3400     /* (1) iscol -> nonscalable iscol_local */
3401     ierr = ISGetSeqIS_Private(mat,iscol,&iscol_local);CHKERRQ(ierr);
3402     ierr = ISGetLocalSize(iscol_local,&n);CHKERRQ(ierr); /* local size of iscol_local = global columns of newmat */
3403     if (n != Ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"n %d != Ncols %d",n,Ncols);
3404 
3405     /* Check for special case: each processor gets entire matrix columns */
3406     ierr = ISIdentity(iscol_local,&flg);CHKERRQ(ierr);
3407     if (flg && n == mat->cmap->N) allcolumns = PETSC_TRUE;
3408     if (allcolumns) {
3409       iscol_sub = iscol_local;
3410       ierr = PetscObjectReference((PetscObject)iscol_local);CHKERRQ(ierr);
3411       ierr = ISCreateStride(PETSC_COMM_SELF,n,0,1,&iscmap);CHKERRQ(ierr);
3412 
3413     } else {
3414       /* (2) iscol_local -> iscol_sub and iscmap */
3415       PetscInt *idx,*cmap1,k,cbs;
3416 
3417       /* implementation below requires iscol_local be sorted, it can have duplicate indices */
3418       ierr = ISSorted(iscol_local,&flg);CHKERRQ(ierr);
3419       if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"unsorted iscol_local is not implemented yet");
3420 
3421       ierr = PetscMalloc1(Ncols,&idx);CHKERRQ(ierr);
3422       ierr = PetscMalloc1(Ncols,&cmap1);CHKERRQ(ierr);
3423       ierr = ISGetIndices(iscol_local,&is_idx);CHKERRQ(ierr);
3424       count = 0;
3425       k     = 0;
3426       for (i=0; i<Ncols; i++) {
3427         j = is_idx[i];
3428         if (j >= cstart && j < cend) {
3429           /* diagonal part of mat */
3430           idx[count]     = j;
3431           cmap1[count++] = i; /* column index in submat */
3432         } else if (Bn) {
3433           /* off-diagonal part of mat */
3434           if (j == garray[k]) {
3435             idx[count]     = j;
3436             cmap1[count++] = i;  /* column index in submat */
3437           } else if (j > garray[k]) {
3438             while (j > garray[k] && k < Bn-1) k++;
3439             if (j == garray[k]) {
3440               idx[count]     = j;
3441               cmap1[count++] = i; /* column index in submat */
3442             }
3443           }
3444         }
3445       }
3446       ierr = ISRestoreIndices(iscol_local,&is_idx);CHKERRQ(ierr);
3447 
3448       ierr = ISCreateGeneral(PETSC_COMM_SELF,count,idx,PETSC_OWN_POINTER,&iscol_sub);CHKERRQ(ierr);
3449       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
3450       ierr = ISSetBlockSize(iscol_sub,cbs);CHKERRQ(ierr);
3451 
3452       ierr = ISCreateGeneral(PetscObjectComm((PetscObject)iscol_local),count,cmap1,PETSC_OWN_POINTER,&iscmap);CHKERRQ(ierr);
3453     }
3454 
3455     /* (3) Create sequential Msub */
3456     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol_sub,MAT_INITIAL_MATRIX,allcolumns,&Msub);CHKERRQ(ierr);
3457   }
3458 
3459   ierr = ISGetLocalSize(iscol_sub,&count);CHKERRQ(ierr);
3460   aij  = (Mat_SeqAIJ*)(Msub)->data;
3461   ii   = aij->i;
3462   ierr = ISGetIndices(iscmap,&cmap);CHKERRQ(ierr);
3463 
3464   /*
3465       m - number of local rows
3466       Ncols - number of columns (same on all processors)
3467       rstart - first row in new global matrix generated
3468   */
3469   ierr = MatGetSize(Msub,&m,NULL);CHKERRQ(ierr);
3470 
3471   if (call == MAT_INITIAL_MATRIX) {
3472     /* (4) Create parallel newmat */
3473     PetscMPIInt    rank,size;
3474     PetscInt       csize;
3475 
3476     ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3477     ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3478 
3479     /*
3480         Determine the number of non-zeros in the diagonal and off-diagonal
3481         portions of the matrix in order to do correct preallocation
3482     */
3483 
3484     /* first get start and end of "diagonal" columns */
3485     ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3486     if (csize == PETSC_DECIDE) {
3487       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3488       if (mglobal == Ncols) { /* square matrix */
3489         nlocal = m;
3490       } else {
3491         nlocal = Ncols/size + ((Ncols % size) > rank);
3492       }
3493     } else {
3494       nlocal = csize;
3495     }
3496     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3497     rstart = rend - nlocal;
3498     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);
3499 
3500     /* next, compute all the lengths */
3501     jj    = aij->j;
3502     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3503     olens = dlens + m;
3504     for (i=0; i<m; i++) {
3505       jend = ii[i+1] - ii[i];
3506       olen = 0;
3507       dlen = 0;
3508       for (j=0; j<jend; j++) {
3509         if (cmap[*jj] < rstart || cmap[*jj] >= rend) olen++;
3510         else dlen++;
3511         jj++;
3512       }
3513       olens[i] = olen;
3514       dlens[i] = dlen;
3515     }
3516     ierr = MatGetBlockSizes(Msub,&bs,&cbs);CHKERRQ(ierr);
3517 
3518     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3519     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,Ncols);CHKERRQ(ierr);
3520     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3521     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3522     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3523     ierr = PetscFree(dlens);CHKERRQ(ierr);
3524 
3525   } else { /* call == MAT_REUSE_MATRIX */
3526     M    = *newmat;
3527     ierr = MatGetLocalSize(M,&i,NULL);CHKERRQ(ierr);
3528     if (i != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3529     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3530     /*
3531          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3532        rather than the slower MatSetValues().
3533     */
3534     M->was_assembled = PETSC_TRUE;
3535     M->assembled     = PETSC_FALSE;
3536   }
3537 
3538   /* (5) Set values of Msub to *newmat */
3539   ierr = PetscMalloc1(count,&colsub);CHKERRQ(ierr);
3540   ierr = MatGetOwnershipRange(M,&rstart,NULL);CHKERRQ(ierr);
3541 
3542   jj   = aij->j;
3543   aa   = aij->a;
3544   for (i=0; i<m; i++) {
3545     row = rstart + i;
3546     nz  = ii[i+1] - ii[i];
3547     for (j=0; j<nz; j++) colsub[j] = cmap[jj[j]];
3548     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,colsub,aa,INSERT_VALUES);CHKERRQ(ierr);
3549     jj += nz; aa += nz;
3550   }
3551   ierr = ISRestoreIndices(iscmap,&cmap);CHKERRQ(ierr);
3552 
3553   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3554   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3555 
3556   ierr = PetscFree(colsub);CHKERRQ(ierr);
3557 
3558   /* save Msub, iscol_sub and iscmap used in processor for next request */
3559   if (call ==  MAT_INITIAL_MATRIX) {
3560     *newmat = M;
3561     ierr = PetscObjectCompose((PetscObject)(*newmat),"SubMatrix",(PetscObject)Msub);CHKERRQ(ierr);
3562     ierr = MatDestroy(&Msub);CHKERRQ(ierr);
3563 
3564     ierr = PetscObjectCompose((PetscObject)(*newmat),"SubIScol",(PetscObject)iscol_sub);CHKERRQ(ierr);
3565     ierr = ISDestroy(&iscol_sub);CHKERRQ(ierr);
3566 
3567     ierr = PetscObjectCompose((PetscObject)(*newmat),"Subcmap",(PetscObject)iscmap);CHKERRQ(ierr);
3568     ierr = ISDestroy(&iscmap);CHKERRQ(ierr);
3569 
3570     if (iscol_local) {
3571       ierr = PetscObjectCompose((PetscObject)(*newmat),"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3572       ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3573     }
3574   }
3575   PetscFunctionReturn(0);
3576 }
3577 
3578 /*
3579     Not great since it makes two copies of the submatrix, first an SeqAIJ
3580   in local and then by concatenating the local matrices the end result.
3581   Writing it directly would be much like MatCreateSubMatrices_MPIAIJ()
3582 
3583   Note: This requires a sequential iscol with all indices.
3584 */
3585 PetscErrorCode MatCreateSubMatrix_MPIAIJ_nonscalable(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3586 {
3587   PetscErrorCode ierr;
3588   PetscMPIInt    rank,size;
3589   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3590   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
3591   Mat            M,Mreuse;
3592   MatScalar      *aa,*vwork;
3593   MPI_Comm       comm;
3594   Mat_SeqAIJ     *aij;
3595   PetscBool      colflag,allcolumns=PETSC_FALSE;
3596 
3597   PetscFunctionBegin;
3598   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3599   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3600   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3601 
3602   /* Check for special case: each processor gets entire matrix columns */
3603   ierr = ISIdentity(iscol,&colflag);CHKERRQ(ierr);
3604   ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr);
3605   if (colflag && n == mat->cmap->N) allcolumns = PETSC_TRUE;
3606 
3607   if (call ==  MAT_REUSE_MATRIX) {
3608     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3609     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3610     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,allcolumns,&Mreuse);CHKERRQ(ierr);
3611   } else {
3612     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,allcolumns,&Mreuse);CHKERRQ(ierr);
3613   }
3614 
3615   /*
3616       m - number of local rows
3617       n - number of columns (same on all processors)
3618       rstart - first row in new global matrix generated
3619   */
3620   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3621   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3622   if (call == MAT_INITIAL_MATRIX) {
3623     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3624     ii  = aij->i;
3625     jj  = aij->j;
3626 
3627     /*
3628         Determine the number of non-zeros in the diagonal and off-diagonal
3629         portions of the matrix in order to do correct preallocation
3630     */
3631 
3632     /* first get start and end of "diagonal" columns */
3633     if (csize == PETSC_DECIDE) {
3634       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3635       if (mglobal == n) { /* square matrix */
3636         nlocal = m;
3637       } else {
3638         nlocal = n/size + ((n % size) > rank);
3639       }
3640     } else {
3641       nlocal = csize;
3642     }
3643     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3644     rstart = rend - nlocal;
3645     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);
3646 
3647     /* next, compute all the lengths */
3648     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3649     olens = dlens + m;
3650     for (i=0; i<m; i++) {
3651       jend = ii[i+1] - ii[i];
3652       olen = 0;
3653       dlen = 0;
3654       for (j=0; j<jend; j++) {
3655         if (*jj < rstart || *jj >= rend) olen++;
3656         else dlen++;
3657         jj++;
3658       }
3659       olens[i] = olen;
3660       dlens[i] = dlen;
3661     }
3662     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3663     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3664     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3665     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3666     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3667     ierr = PetscFree(dlens);CHKERRQ(ierr);
3668   } else {
3669     PetscInt ml,nl;
3670 
3671     M    = *newmat;
3672     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3673     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3674     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3675     /*
3676          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3677        rather than the slower MatSetValues().
3678     */
3679     M->was_assembled = PETSC_TRUE;
3680     M->assembled     = PETSC_FALSE;
3681   }
3682   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3683   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3684   ii   = aij->i;
3685   jj   = aij->j;
3686   aa   = aij->a;
3687   for (i=0; i<m; i++) {
3688     row   = rstart + i;
3689     nz    = ii[i+1] - ii[i];
3690     cwork = jj;     jj += nz;
3691     vwork = aa;     aa += nz;
3692     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3693   }
3694 
3695   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3696   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3697   *newmat = M;
3698 
3699   /* save submatrix used in processor for next request */
3700   if (call ==  MAT_INITIAL_MATRIX) {
3701     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3702     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3703   }
3704   PetscFunctionReturn(0);
3705 }
3706 
3707 PetscErrorCode MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3708 {
3709   PetscInt       m,cstart, cend,j,nnz,i,d;
3710   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3711   const PetscInt *JJ;
3712   PetscScalar    *values;
3713   PetscErrorCode ierr;
3714   PetscBool      nooffprocentries;
3715 
3716   PetscFunctionBegin;
3717   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3718 
3719   ierr   = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3720   ierr   = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3721   m      = B->rmap->n;
3722   cstart = B->cmap->rstart;
3723   cend   = B->cmap->rend;
3724   rstart = B->rmap->rstart;
3725 
3726   ierr = PetscMalloc2(m,&d_nnz,m,&o_nnz);CHKERRQ(ierr);
3727 
3728 #if defined(PETSC_USE_DEBUGGING)
3729   for (i=0; i<m; i++) {
3730     nnz = Ii[i+1]- Ii[i];
3731     JJ  = J + Ii[i];
3732     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3733     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3734     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);
3735   }
3736 #endif
3737 
3738   for (i=0; i<m; i++) {
3739     nnz     = Ii[i+1]- Ii[i];
3740     JJ      = J + Ii[i];
3741     nnz_max = PetscMax(nnz_max,nnz);
3742     d       = 0;
3743     for (j=0; j<nnz; j++) {
3744       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3745     }
3746     d_nnz[i] = d;
3747     o_nnz[i] = nnz - d;
3748   }
3749   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3750   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3751 
3752   if (v) values = (PetscScalar*)v;
3753   else {
3754     ierr = PetscCalloc1(nnz_max+1,&values);CHKERRQ(ierr);
3755   }
3756 
3757   for (i=0; i<m; i++) {
3758     ii   = i + rstart;
3759     nnz  = Ii[i+1]- Ii[i];
3760     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3761   }
3762   nooffprocentries    = B->nooffprocentries;
3763   B->nooffprocentries = PETSC_TRUE;
3764   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3765   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3766   B->nooffprocentries = nooffprocentries;
3767 
3768   if (!v) {
3769     ierr = PetscFree(values);CHKERRQ(ierr);
3770   }
3771   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3772   PetscFunctionReturn(0);
3773 }
3774 
3775 /*@
3776    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3777    (the default parallel PETSc format).
3778 
3779    Collective on MPI_Comm
3780 
3781    Input Parameters:
3782 +  B - the matrix
3783 .  i - the indices into j for the start of each local row (starts with zero)
3784 .  j - the column indices for each local row (starts with zero)
3785 -  v - optional values in the matrix
3786 
3787    Level: developer
3788 
3789    Notes:
3790        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3791      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3792      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3793 
3794        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3795 
3796        The format which is used for the sparse matrix input, is equivalent to a
3797     row-major ordering.. i.e for the following matrix, the input data expected is
3798     as shown
3799 
3800 $        1 0 0
3801 $        2 0 3     P0
3802 $       -------
3803 $        4 5 6     P1
3804 $
3805 $     Process0 [P0]: rows_owned=[0,1]
3806 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3807 $        j =  {0,0,2}  [size = 3]
3808 $        v =  {1,2,3}  [size = 3]
3809 $
3810 $     Process1 [P1]: rows_owned=[2]
3811 $        i =  {0,3}    [size = nrow+1  = 1+1]
3812 $        j =  {0,1,2}  [size = 3]
3813 $        v =  {4,5,6}  [size = 3]
3814 
3815 .keywords: matrix, aij, compressed row, sparse, parallel
3816 
3817 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MATMPIAIJ,
3818           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3819 @*/
3820 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3821 {
3822   PetscErrorCode ierr;
3823 
3824   PetscFunctionBegin;
3825   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3826   PetscFunctionReturn(0);
3827 }
3828 
3829 /*@C
3830    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3831    (the default parallel PETSc format).  For good matrix assembly performance
3832    the user should preallocate the matrix storage by setting the parameters
3833    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3834    performance can be increased by more than a factor of 50.
3835 
3836    Collective on MPI_Comm
3837 
3838    Input Parameters:
3839 +  B - the matrix
3840 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3841            (same value is used for all local rows)
3842 .  d_nnz - array containing the number of nonzeros in the various rows of the
3843            DIAGONAL portion of the local submatrix (possibly different for each row)
3844            or NULL (PETSC_NULL_INTEGER in Fortran), if d_nz is used to specify the nonzero structure.
3845            The size of this array is equal to the number of local rows, i.e 'm'.
3846            For matrices that will be factored, you must leave room for (and set)
3847            the diagonal entry even if it is zero.
3848 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3849            submatrix (same value is used for all local rows).
3850 -  o_nnz - array containing the number of nonzeros in the various rows of the
3851            OFF-DIAGONAL portion of the local submatrix (possibly different for
3852            each row) or NULL (PETSC_NULL_INTEGER in Fortran), if o_nz is used to specify the nonzero
3853            structure. The size of this array is equal to the number
3854            of local rows, i.e 'm'.
3855 
3856    If the *_nnz parameter is given then the *_nz parameter is ignored
3857 
3858    The AIJ format (also called the Yale sparse matrix format or
3859    compressed row storage (CSR)), is fully compatible with standard Fortran 77
3860    storage.  The stored row and column indices begin with zero.
3861    See Users-Manual: ch_mat for details.
3862 
3863    The parallel matrix is partitioned such that the first m0 rows belong to
3864    process 0, the next m1 rows belong to process 1, the next m2 rows belong
3865    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
3866 
3867    The DIAGONAL portion of the local submatrix of a processor can be defined
3868    as the submatrix which is obtained by extraction the part corresponding to
3869    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
3870    first row that belongs to the processor, r2 is the last row belonging to
3871    the this processor, and c1-c2 is range of indices of the local part of a
3872    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
3873    common case of a square matrix, the row and column ranges are the same and
3874    the DIAGONAL part is also square. The remaining portion of the local
3875    submatrix (mxN) constitute the OFF-DIAGONAL portion.
3876 
3877    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3878 
3879    You can call MatGetInfo() to get information on how effective the preallocation was;
3880    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3881    You can also run with the option -info and look for messages with the string
3882    malloc in them to see if additional memory allocation was needed.
3883 
3884    Example usage:
3885 
3886    Consider the following 8x8 matrix with 34 non-zero values, that is
3887    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3888    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3889    as follows:
3890 
3891 .vb
3892             1  2  0  |  0  3  0  |  0  4
3893     Proc0   0  5  6  |  7  0  0  |  8  0
3894             9  0 10  | 11  0  0  | 12  0
3895     -------------------------------------
3896            13  0 14  | 15 16 17  |  0  0
3897     Proc1   0 18  0  | 19 20 21  |  0  0
3898             0  0  0  | 22 23  0  | 24  0
3899     -------------------------------------
3900     Proc2  25 26 27  |  0  0 28  | 29  0
3901            30  0  0  | 31 32 33  |  0 34
3902 .ve
3903 
3904    This can be represented as a collection of submatrices as:
3905 
3906 .vb
3907       A B C
3908       D E F
3909       G H I
3910 .ve
3911 
3912    Where the submatrices A,B,C are owned by proc0, D,E,F are
3913    owned by proc1, G,H,I are owned by proc2.
3914 
3915    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3916    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3917    The 'M','N' parameters are 8,8, and have the same values on all procs.
3918 
3919    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3920    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3921    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3922    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3923    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3924    matrix, ans [DF] as another SeqAIJ matrix.
3925 
3926    When d_nz, o_nz parameters are specified, d_nz storage elements are
3927    allocated for every row of the local diagonal submatrix, and o_nz
3928    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3929    One way to choose d_nz and o_nz is to use the max nonzerors per local
3930    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3931    In this case, the values of d_nz,o_nz are:
3932 .vb
3933      proc0 : dnz = 2, o_nz = 2
3934      proc1 : dnz = 3, o_nz = 2
3935      proc2 : dnz = 1, o_nz = 4
3936 .ve
3937    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3938    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3939    for proc3. i.e we are using 12+15+10=37 storage locations to store
3940    34 values.
3941 
3942    When d_nnz, o_nnz parameters are specified, the storage is specified
3943    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3944    In the above case the values for d_nnz,o_nnz are:
3945 .vb
3946      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3947      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3948      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3949 .ve
3950    Here the space allocated is sum of all the above values i.e 34, and
3951    hence pre-allocation is perfect.
3952 
3953    Level: intermediate
3954 
3955 .keywords: matrix, aij, compressed row, sparse, parallel
3956 
3957 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
3958           MATMPIAIJ, MatGetInfo(), PetscSplitOwnership()
3959 @*/
3960 PetscErrorCode MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3961 {
3962   PetscErrorCode ierr;
3963 
3964   PetscFunctionBegin;
3965   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3966   PetscValidType(B,1);
3967   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
3968   PetscFunctionReturn(0);
3969 }
3970 
3971 /*@
3972      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
3973          CSR format the local rows.
3974 
3975    Collective on MPI_Comm
3976 
3977    Input Parameters:
3978 +  comm - MPI communicator
3979 .  m - number of local rows (Cannot be PETSC_DECIDE)
3980 .  n - This value should be the same as the local size used in creating the
3981        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3982        calculated if N is given) For square matrices n is almost always m.
3983 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3984 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3985 .   i - row indices
3986 .   j - column indices
3987 -   a - matrix values
3988 
3989    Output Parameter:
3990 .   mat - the matrix
3991 
3992    Level: intermediate
3993 
3994    Notes:
3995        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3996      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3997      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3998 
3999        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
4000 
4001        The format which is used for the sparse matrix input, is equivalent to a
4002     row-major ordering.. i.e for the following matrix, the input data expected is
4003     as shown
4004 
4005 $        1 0 0
4006 $        2 0 3     P0
4007 $       -------
4008 $        4 5 6     P1
4009 $
4010 $     Process0 [P0]: rows_owned=[0,1]
4011 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
4012 $        j =  {0,0,2}  [size = 3]
4013 $        v =  {1,2,3}  [size = 3]
4014 $
4015 $     Process1 [P1]: rows_owned=[2]
4016 $        i =  {0,3}    [size = nrow+1  = 1+1]
4017 $        j =  {0,1,2}  [size = 3]
4018 $        v =  {4,5,6}  [size = 3]
4019 
4020 .keywords: matrix, aij, compressed row, sparse, parallel
4021 
4022 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
4023           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
4024 @*/
4025 PetscErrorCode MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
4026 {
4027   PetscErrorCode ierr;
4028 
4029   PetscFunctionBegin;
4030   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
4031   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
4032   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4033   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
4034   /* ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr); */
4035   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
4036   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
4037   PetscFunctionReturn(0);
4038 }
4039 
4040 /*@C
4041    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
4042    (the default parallel PETSc format).  For good matrix assembly performance
4043    the user should preallocate the matrix storage by setting the parameters
4044    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
4045    performance can be increased by more than a factor of 50.
4046 
4047    Collective on MPI_Comm
4048 
4049    Input Parameters:
4050 +  comm - MPI communicator
4051 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
4052            This value should be the same as the local size used in creating the
4053            y vector for the matrix-vector product y = Ax.
4054 .  n - This value should be the same as the local size used in creating the
4055        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
4056        calculated if N is given) For square matrices n is almost always m.
4057 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
4058 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
4059 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
4060            (same value is used for all local rows)
4061 .  d_nnz - array containing the number of nonzeros in the various rows of the
4062            DIAGONAL portion of the local submatrix (possibly different for each row)
4063            or NULL, if d_nz is used to specify the nonzero structure.
4064            The size of this array is equal to the number of local rows, i.e 'm'.
4065 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
4066            submatrix (same value is used for all local rows).
4067 -  o_nnz - array containing the number of nonzeros in the various rows of the
4068            OFF-DIAGONAL portion of the local submatrix (possibly different for
4069            each row) or NULL, if o_nz is used to specify the nonzero
4070            structure. The size of this array is equal to the number
4071            of local rows, i.e 'm'.
4072 
4073    Output Parameter:
4074 .  A - the matrix
4075 
4076    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
4077    MatXXXXSetPreallocation() paradgm instead of this routine directly.
4078    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
4079 
4080    Notes:
4081    If the *_nnz parameter is given then the *_nz parameter is ignored
4082 
4083    m,n,M,N parameters specify the size of the matrix, and its partitioning across
4084    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
4085    storage requirements for this matrix.
4086 
4087    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
4088    processor than it must be used on all processors that share the object for
4089    that argument.
4090 
4091    The user MUST specify either the local or global matrix dimensions
4092    (possibly both).
4093 
4094    The parallel matrix is partitioned across processors such that the
4095    first m0 rows belong to process 0, the next m1 rows belong to
4096    process 1, the next m2 rows belong to process 2 etc.. where
4097    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
4098    values corresponding to [m x N] submatrix.
4099 
4100    The columns are logically partitioned with the n0 columns belonging
4101    to 0th partition, the next n1 columns belonging to the next
4102    partition etc.. where n0,n1,n2... are the input parameter 'n'.
4103 
4104    The DIAGONAL portion of the local submatrix on any given processor
4105    is the submatrix corresponding to the rows and columns m,n
4106    corresponding to the given processor. i.e diagonal matrix on
4107    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
4108    etc. The remaining portion of the local submatrix [m x (N-n)]
4109    constitute the OFF-DIAGONAL portion. The example below better
4110    illustrates this concept.
4111 
4112    For a square global matrix we define each processor's diagonal portion
4113    to be its local rows and the corresponding columns (a square submatrix);
4114    each processor's off-diagonal portion encompasses the remainder of the
4115    local matrix (a rectangular submatrix).
4116 
4117    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
4118 
4119    When calling this routine with a single process communicator, a matrix of
4120    type SEQAIJ is returned.  If a matrix of type MATMPIAIJ is desired for this
4121    type of communicator, use the construction mechanism:
4122      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
4123 
4124    By default, this format uses inodes (identical nodes) when possible.
4125    We search for consecutive rows with the same nonzero structure, thereby
4126    reusing matrix information to achieve increased efficiency.
4127 
4128    Options Database Keys:
4129 +  -mat_no_inode  - Do not use inodes
4130 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
4131 -  -mat_aij_oneindex - Internally use indexing starting at 1
4132         rather than 0.  Note that when calling MatSetValues(),
4133         the user still MUST index entries starting at 0!
4134 
4135 
4136    Example usage:
4137 
4138    Consider the following 8x8 matrix with 34 non-zero values, that is
4139    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
4140    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
4141    as follows:
4142 
4143 .vb
4144             1  2  0  |  0  3  0  |  0  4
4145     Proc0   0  5  6  |  7  0  0  |  8  0
4146             9  0 10  | 11  0  0  | 12  0
4147     -------------------------------------
4148            13  0 14  | 15 16 17  |  0  0
4149     Proc1   0 18  0  | 19 20 21  |  0  0
4150             0  0  0  | 22 23  0  | 24  0
4151     -------------------------------------
4152     Proc2  25 26 27  |  0  0 28  | 29  0
4153            30  0  0  | 31 32 33  |  0 34
4154 .ve
4155 
4156    This can be represented as a collection of submatrices as:
4157 
4158 .vb
4159       A B C
4160       D E F
4161       G H I
4162 .ve
4163 
4164    Where the submatrices A,B,C are owned by proc0, D,E,F are
4165    owned by proc1, G,H,I are owned by proc2.
4166 
4167    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4168    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4169    The 'M','N' parameters are 8,8, and have the same values on all procs.
4170 
4171    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
4172    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
4173    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
4174    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
4175    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
4176    matrix, ans [DF] as another SeqAIJ matrix.
4177 
4178    When d_nz, o_nz parameters are specified, d_nz storage elements are
4179    allocated for every row of the local diagonal submatrix, and o_nz
4180    storage locations are allocated for every row of the OFF-DIAGONAL submat.
4181    One way to choose d_nz and o_nz is to use the max nonzerors per local
4182    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
4183    In this case, the values of d_nz,o_nz are:
4184 .vb
4185      proc0 : dnz = 2, o_nz = 2
4186      proc1 : dnz = 3, o_nz = 2
4187      proc2 : dnz = 1, o_nz = 4
4188 .ve
4189    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
4190    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
4191    for proc3. i.e we are using 12+15+10=37 storage locations to store
4192    34 values.
4193 
4194    When d_nnz, o_nnz parameters are specified, the storage is specified
4195    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
4196    In the above case the values for d_nnz,o_nnz are:
4197 .vb
4198      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
4199      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
4200      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
4201 .ve
4202    Here the space allocated is sum of all the above values i.e 34, and
4203    hence pre-allocation is perfect.
4204 
4205    Level: intermediate
4206 
4207 .keywords: matrix, aij, compressed row, sparse, parallel
4208 
4209 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
4210           MATMPIAIJ, MatCreateMPIAIJWithArrays()
4211 @*/
4212 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)
4213 {
4214   PetscErrorCode ierr;
4215   PetscMPIInt    size;
4216 
4217   PetscFunctionBegin;
4218   ierr = MatCreate(comm,A);CHKERRQ(ierr);
4219   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
4220   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4221   if (size > 1) {
4222     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
4223     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
4224   } else {
4225     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
4226     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
4227   }
4228   PetscFunctionReturn(0);
4229 }
4230 
4231 PetscErrorCode MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
4232 {
4233   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
4234   PetscBool      flg;
4235   PetscErrorCode ierr;
4236 
4237   PetscFunctionBegin;
4238   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&flg);CHKERRQ(ierr);
4239   if (!flg) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"This function requires a MATMPIAIJ matrix as input");
4240   if (Ad)     *Ad     = a->A;
4241   if (Ao)     *Ao     = a->B;
4242   if (colmap) *colmap = a->garray;
4243   PetscFunctionReturn(0);
4244 }
4245 
4246 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
4247 {
4248   PetscErrorCode ierr;
4249   PetscInt       m,N,i,rstart,nnz,Ii;
4250   PetscInt       *indx;
4251   PetscScalar    *values;
4252 
4253   PetscFunctionBegin;
4254   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
4255   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
4256     PetscInt       *dnz,*onz,sum,bs,cbs;
4257 
4258     if (n == PETSC_DECIDE) {
4259       ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
4260     }
4261     /* Check sum(n) = N */
4262     ierr = MPIU_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4263     if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
4264 
4265     ierr    = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4266     rstart -= m;
4267 
4268     ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4269     for (i=0; i<m; i++) {
4270       ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
4271       ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
4272       ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
4273     }
4274 
4275     ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
4276     ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4277     ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
4278     ierr = MatSetBlockSizes(*outmat,bs,cbs);CHKERRQ(ierr);
4279     ierr = MatSetType(*outmat,MATAIJ);CHKERRQ(ierr);
4280     ierr = MatSeqAIJSetPreallocation(*outmat,0,dnz);CHKERRQ(ierr);
4281     ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
4282     ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4283   }
4284 
4285   /* numeric phase */
4286   ierr = MatGetOwnershipRange(*outmat,&rstart,NULL);CHKERRQ(ierr);
4287   for (i=0; i<m; i++) {
4288     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4289     Ii   = i + rstart;
4290     ierr = MatSetValues(*outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4291     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4292   }
4293   ierr = MatAssemblyBegin(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4294   ierr = MatAssemblyEnd(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4295   PetscFunctionReturn(0);
4296 }
4297 
4298 PetscErrorCode MatFileSplit(Mat A,char *outfile)
4299 {
4300   PetscErrorCode    ierr;
4301   PetscMPIInt       rank;
4302   PetscInt          m,N,i,rstart,nnz;
4303   size_t            len;
4304   const PetscInt    *indx;
4305   PetscViewer       out;
4306   char              *name;
4307   Mat               B;
4308   const PetscScalar *values;
4309 
4310   PetscFunctionBegin;
4311   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
4312   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
4313   /* Should this be the type of the diagonal block of A? */
4314   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
4315   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
4316   ierr = MatSetBlockSizesFromMats(B,A,A);CHKERRQ(ierr);
4317   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
4318   ierr = MatSeqAIJSetPreallocation(B,0,NULL);CHKERRQ(ierr);
4319   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
4320   for (i=0; i<m; i++) {
4321     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4322     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4323     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4324   }
4325   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4326   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4327 
4328   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
4329   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
4330   ierr = PetscMalloc1(len+5,&name);CHKERRQ(ierr);
4331   sprintf(name,"%s.%d",outfile,rank);
4332   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
4333   ierr = PetscFree(name);CHKERRQ(ierr);
4334   ierr = MatView(B,out);CHKERRQ(ierr);
4335   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
4336   ierr = MatDestroy(&B);CHKERRQ(ierr);
4337   PetscFunctionReturn(0);
4338 }
4339 
4340 PetscErrorCode MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
4341 {
4342   PetscErrorCode      ierr;
4343   Mat_Merge_SeqsToMPI *merge;
4344   PetscContainer      container;
4345 
4346   PetscFunctionBegin;
4347   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4348   if (container) {
4349     ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4350     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
4351     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
4352     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
4353     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
4354     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
4355     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
4356     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
4357     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
4358     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
4359     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
4360     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
4361     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
4362     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
4363     ierr = PetscFree(merge);CHKERRQ(ierr);
4364     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
4365   }
4366   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
4367   PetscFunctionReturn(0);
4368 }
4369 
4370 #include <../src/mat/utils/freespace.h>
4371 #include <petscbt.h>
4372 
4373 PetscErrorCode MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
4374 {
4375   PetscErrorCode      ierr;
4376   MPI_Comm            comm;
4377   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
4378   PetscMPIInt         size,rank,taga,*len_s;
4379   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
4380   PetscInt            proc,m;
4381   PetscInt            **buf_ri,**buf_rj;
4382   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
4383   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
4384   MPI_Request         *s_waits,*r_waits;
4385   MPI_Status          *status;
4386   MatScalar           *aa=a->a;
4387   MatScalar           **abuf_r,*ba_i;
4388   Mat_Merge_SeqsToMPI *merge;
4389   PetscContainer      container;
4390 
4391   PetscFunctionBegin;
4392   ierr = PetscObjectGetComm((PetscObject)mpimat,&comm);CHKERRQ(ierr);
4393   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4394 
4395   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4396   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4397 
4398   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4399   ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4400 
4401   bi     = merge->bi;
4402   bj     = merge->bj;
4403   buf_ri = merge->buf_ri;
4404   buf_rj = merge->buf_rj;
4405 
4406   ierr   = PetscMalloc1(size,&status);CHKERRQ(ierr);
4407   owners = merge->rowmap->range;
4408   len_s  = merge->len_s;
4409 
4410   /* send and recv matrix values */
4411   /*-----------------------------*/
4412   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
4413   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
4414 
4415   ierr = PetscMalloc1(merge->nsend+1,&s_waits);CHKERRQ(ierr);
4416   for (proc=0,k=0; proc<size; proc++) {
4417     if (!len_s[proc]) continue;
4418     i    = owners[proc];
4419     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
4420     k++;
4421   }
4422 
4423   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
4424   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
4425   ierr = PetscFree(status);CHKERRQ(ierr);
4426 
4427   ierr = PetscFree(s_waits);CHKERRQ(ierr);
4428   ierr = PetscFree(r_waits);CHKERRQ(ierr);
4429 
4430   /* insert mat values of mpimat */
4431   /*----------------------------*/
4432   ierr = PetscMalloc1(N,&ba_i);CHKERRQ(ierr);
4433   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4434 
4435   for (k=0; k<merge->nrecv; k++) {
4436     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4437     nrows       = *(buf_ri_k[k]);
4438     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
4439     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4440   }
4441 
4442   /* set values of ba */
4443   m = merge->rowmap->n;
4444   for (i=0; i<m; i++) {
4445     arow = owners[rank] + i;
4446     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
4447     bnzi = bi[i+1] - bi[i];
4448     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
4449 
4450     /* add local non-zero vals of this proc's seqmat into ba */
4451     anzi   = ai[arow+1] - ai[arow];
4452     aj     = a->j + ai[arow];
4453     aa     = a->a + ai[arow];
4454     nextaj = 0;
4455     for (j=0; nextaj<anzi; j++) {
4456       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4457         ba_i[j] += aa[nextaj++];
4458       }
4459     }
4460 
4461     /* add received vals into ba */
4462     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4463       /* i-th row */
4464       if (i == *nextrow[k]) {
4465         anzi   = *(nextai[k]+1) - *nextai[k];
4466         aj     = buf_rj[k] + *(nextai[k]);
4467         aa     = abuf_r[k] + *(nextai[k]);
4468         nextaj = 0;
4469         for (j=0; nextaj<anzi; j++) {
4470           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4471             ba_i[j] += aa[nextaj++];
4472           }
4473         }
4474         nextrow[k]++; nextai[k]++;
4475       }
4476     }
4477     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
4478   }
4479   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4480   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4481 
4482   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
4483   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
4484   ierr = PetscFree(ba_i);CHKERRQ(ierr);
4485   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4486   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4487   PetscFunctionReturn(0);
4488 }
4489 
4490 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4491 {
4492   PetscErrorCode      ierr;
4493   Mat                 B_mpi;
4494   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
4495   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4496   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
4497   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4498   PetscInt            len,proc,*dnz,*onz,bs,cbs;
4499   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4500   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4501   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
4502   MPI_Status          *status;
4503   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
4504   PetscBT             lnkbt;
4505   Mat_Merge_SeqsToMPI *merge;
4506   PetscContainer      container;
4507 
4508   PetscFunctionBegin;
4509   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4510 
4511   /* make sure it is a PETSc comm */
4512   ierr = PetscCommDuplicate(comm,&comm,NULL);CHKERRQ(ierr);
4513   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4514   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4515 
4516   ierr = PetscNew(&merge);CHKERRQ(ierr);
4517   ierr = PetscMalloc1(size,&status);CHKERRQ(ierr);
4518 
4519   /* determine row ownership */
4520   /*---------------------------------------------------------*/
4521   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
4522   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
4523   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
4524   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
4525   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
4526   ierr = PetscMalloc1(size,&len_si);CHKERRQ(ierr);
4527   ierr = PetscMalloc1(size,&merge->len_s);CHKERRQ(ierr);
4528 
4529   m      = merge->rowmap->n;
4530   owners = merge->rowmap->range;
4531 
4532   /* determine the number of messages to send, their lengths */
4533   /*---------------------------------------------------------*/
4534   len_s = merge->len_s;
4535 
4536   len          = 0; /* length of buf_si[] */
4537   merge->nsend = 0;
4538   for (proc=0; proc<size; proc++) {
4539     len_si[proc] = 0;
4540     if (proc == rank) {
4541       len_s[proc] = 0;
4542     } else {
4543       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4544       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4545     }
4546     if (len_s[proc]) {
4547       merge->nsend++;
4548       nrows = 0;
4549       for (i=owners[proc]; i<owners[proc+1]; i++) {
4550         if (ai[i+1] > ai[i]) nrows++;
4551       }
4552       len_si[proc] = 2*(nrows+1);
4553       len         += len_si[proc];
4554     }
4555   }
4556 
4557   /* determine the number and length of messages to receive for ij-structure */
4558   /*-------------------------------------------------------------------------*/
4559   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
4560   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
4561 
4562   /* post the Irecv of j-structure */
4563   /*-------------------------------*/
4564   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
4565   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
4566 
4567   /* post the Isend of j-structure */
4568   /*--------------------------------*/
4569   ierr = PetscMalloc2(merge->nsend,&si_waits,merge->nsend,&sj_waits);CHKERRQ(ierr);
4570 
4571   for (proc=0, k=0; proc<size; proc++) {
4572     if (!len_s[proc]) continue;
4573     i    = owners[proc];
4574     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
4575     k++;
4576   }
4577 
4578   /* receives and sends of j-structure are complete */
4579   /*------------------------------------------------*/
4580   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
4581   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
4582 
4583   /* send and recv i-structure */
4584   /*---------------------------*/
4585   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
4586   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
4587 
4588   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
4589   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4590   for (proc=0,k=0; proc<size; proc++) {
4591     if (!len_s[proc]) continue;
4592     /* form outgoing message for i-structure:
4593          buf_si[0]:                 nrows to be sent
4594                [1:nrows]:           row index (global)
4595                [nrows+1:2*nrows+1]: i-structure index
4596     */
4597     /*-------------------------------------------*/
4598     nrows       = len_si[proc]/2 - 1;
4599     buf_si_i    = buf_si + nrows+1;
4600     buf_si[0]   = nrows;
4601     buf_si_i[0] = 0;
4602     nrows       = 0;
4603     for (i=owners[proc]; i<owners[proc+1]; i++) {
4604       anzi = ai[i+1] - ai[i];
4605       if (anzi) {
4606         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4607         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4608         nrows++;
4609       }
4610     }
4611     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4612     k++;
4613     buf_si += len_si[proc];
4614   }
4615 
4616   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4617   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4618 
4619   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4620   for (i=0; i<merge->nrecv; i++) {
4621     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);
4622   }
4623 
4624   ierr = PetscFree(len_si);CHKERRQ(ierr);
4625   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4626   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4627   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4628   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4629   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4630   ierr = PetscFree(status);CHKERRQ(ierr);
4631 
4632   /* compute a local seq matrix in each processor */
4633   /*----------------------------------------------*/
4634   /* allocate bi array and free space for accumulating nonzero column info */
4635   ierr  = PetscMalloc1(m+1,&bi);CHKERRQ(ierr);
4636   bi[0] = 0;
4637 
4638   /* create and initialize a linked list */
4639   nlnk = N+1;
4640   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4641 
4642   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4643   len  = ai[owners[rank+1]] - ai[owners[rank]];
4644   ierr = PetscFreeSpaceGet(PetscIntMultTruncate(2,len)+1,&free_space);CHKERRQ(ierr);
4645 
4646   current_space = free_space;
4647 
4648   /* determine symbolic info for each local row */
4649   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4650 
4651   for (k=0; k<merge->nrecv; k++) {
4652     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4653     nrows       = *buf_ri_k[k];
4654     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4655     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4656   }
4657 
4658   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4659   len  = 0;
4660   for (i=0; i<m; i++) {
4661     bnzi = 0;
4662     /* add local non-zero cols of this proc's seqmat into lnk */
4663     arow  = owners[rank] + i;
4664     anzi  = ai[arow+1] - ai[arow];
4665     aj    = a->j + ai[arow];
4666     ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4667     bnzi += nlnk;
4668     /* add received col data into lnk */
4669     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4670       if (i == *nextrow[k]) { /* i-th row */
4671         anzi  = *(nextai[k]+1) - *nextai[k];
4672         aj    = buf_rj[k] + *nextai[k];
4673         ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4674         bnzi += nlnk;
4675         nextrow[k]++; nextai[k]++;
4676       }
4677     }
4678     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4679 
4680     /* if free space is not available, make more free space */
4681     if (current_space->local_remaining<bnzi) {
4682       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(bnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
4683       nspacedouble++;
4684     }
4685     /* copy data into free space, then initialize lnk */
4686     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4687     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
4688 
4689     current_space->array           += bnzi;
4690     current_space->local_used      += bnzi;
4691     current_space->local_remaining -= bnzi;
4692 
4693     bi[i+1] = bi[i] + bnzi;
4694   }
4695 
4696   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4697 
4698   ierr = PetscMalloc1(bi[m]+1,&bj);CHKERRQ(ierr);
4699   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
4700   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4701 
4702   /* create symbolic parallel matrix B_mpi */
4703   /*---------------------------------------*/
4704   ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
4705   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
4706   if (n==PETSC_DECIDE) {
4707     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
4708   } else {
4709     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4710   }
4711   ierr = MatSetBlockSizes(B_mpi,bs,cbs);CHKERRQ(ierr);
4712   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
4713   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
4714   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4715   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
4716 
4717   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4718   B_mpi->assembled    = PETSC_FALSE;
4719   B_mpi->ops->destroy = MatDestroy_MPIAIJ_SeqsToMPI;
4720   merge->bi           = bi;
4721   merge->bj           = bj;
4722   merge->buf_ri       = buf_ri;
4723   merge->buf_rj       = buf_rj;
4724   merge->coi          = NULL;
4725   merge->coj          = NULL;
4726   merge->owners_co    = NULL;
4727 
4728   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
4729 
4730   /* attach the supporting struct to B_mpi for reuse */
4731   ierr    = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
4732   ierr    = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
4733   ierr    = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
4734   ierr    = PetscContainerDestroy(&container);CHKERRQ(ierr);
4735   *mpimat = B_mpi;
4736 
4737   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4738   PetscFunctionReturn(0);
4739 }
4740 
4741 /*@C
4742       MatCreateMPIAIJSumSeqAIJ - Creates a MATMPIAIJ matrix by adding sequential
4743                  matrices from each processor
4744 
4745     Collective on MPI_Comm
4746 
4747    Input Parameters:
4748 +    comm - the communicators the parallel matrix will live on
4749 .    seqmat - the input sequential matrices
4750 .    m - number of local rows (or PETSC_DECIDE)
4751 .    n - number of local columns (or PETSC_DECIDE)
4752 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4753 
4754    Output Parameter:
4755 .    mpimat - the parallel matrix generated
4756 
4757     Level: advanced
4758 
4759    Notes:
4760      The dimensions of the sequential matrix in each processor MUST be the same.
4761      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
4762      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
4763 @*/
4764 PetscErrorCode MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
4765 {
4766   PetscErrorCode ierr;
4767   PetscMPIInt    size;
4768 
4769   PetscFunctionBegin;
4770   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4771   if (size == 1) {
4772     ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4773     if (scall == MAT_INITIAL_MATRIX) {
4774       ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
4775     } else {
4776       ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4777     }
4778     ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4779     PetscFunctionReturn(0);
4780   }
4781   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4782   if (scall == MAT_INITIAL_MATRIX) {
4783     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
4784   }
4785   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
4786   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4787   PetscFunctionReturn(0);
4788 }
4789 
4790 /*@
4791      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MATMPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
4792           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
4793           with MatGetSize()
4794 
4795     Not Collective
4796 
4797    Input Parameters:
4798 +    A - the matrix
4799 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4800 
4801    Output Parameter:
4802 .    A_loc - the local sequential matrix generated
4803 
4804     Level: developer
4805 
4806 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
4807 
4808 @*/
4809 PetscErrorCode MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
4810 {
4811   PetscErrorCode ierr;
4812   Mat_MPIAIJ     *mpimat=(Mat_MPIAIJ*)A->data;
4813   Mat_SeqAIJ     *mat,*a,*b;
4814   PetscInt       *ai,*aj,*bi,*bj,*cmap=mpimat->garray;
4815   MatScalar      *aa,*ba,*cam;
4816   PetscScalar    *ca;
4817   PetscInt       am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
4818   PetscInt       *ci,*cj,col,ncols_d,ncols_o,jo;
4819   PetscBool      match;
4820   MPI_Comm       comm;
4821   PetscMPIInt    size;
4822 
4823   PetscFunctionBegin;
4824   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4825   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
4826   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4827   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4828   if (size == 1 && scall == MAT_REUSE_MATRIX) PetscFunctionReturn(0);
4829 
4830   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4831   a = (Mat_SeqAIJ*)(mpimat->A)->data;
4832   b = (Mat_SeqAIJ*)(mpimat->B)->data;
4833   ai = a->i; aj = a->j; bi = b->i; bj = b->j;
4834   aa = a->a; ba = b->a;
4835   if (scall == MAT_INITIAL_MATRIX) {
4836     if (size == 1) {
4837       ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ai,aj,aa,A_loc);CHKERRQ(ierr);
4838       PetscFunctionReturn(0);
4839     }
4840 
4841     ierr  = PetscMalloc1(1+am,&ci);CHKERRQ(ierr);
4842     ci[0] = 0;
4843     for (i=0; i<am; i++) {
4844       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
4845     }
4846     ierr = PetscMalloc1(1+ci[am],&cj);CHKERRQ(ierr);
4847     ierr = PetscMalloc1(1+ci[am],&ca);CHKERRQ(ierr);
4848     k    = 0;
4849     for (i=0; i<am; i++) {
4850       ncols_o = bi[i+1] - bi[i];
4851       ncols_d = ai[i+1] - ai[i];
4852       /* off-diagonal portion of A */
4853       for (jo=0; jo<ncols_o; jo++) {
4854         col = cmap[*bj];
4855         if (col >= cstart) break;
4856         cj[k]   = col; bj++;
4857         ca[k++] = *ba++;
4858       }
4859       /* diagonal portion of A */
4860       for (j=0; j<ncols_d; j++) {
4861         cj[k]   = cstart + *aj++;
4862         ca[k++] = *aa++;
4863       }
4864       /* off-diagonal portion of A */
4865       for (j=jo; j<ncols_o; j++) {
4866         cj[k]   = cmap[*bj++];
4867         ca[k++] = *ba++;
4868       }
4869     }
4870     /* put together the new matrix */
4871     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
4872     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4873     /* Since these are PETSc arrays, change flags to free them as necessary. */
4874     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
4875     mat->free_a  = PETSC_TRUE;
4876     mat->free_ij = PETSC_TRUE;
4877     mat->nonew   = 0;
4878   } else if (scall == MAT_REUSE_MATRIX) {
4879     mat=(Mat_SeqAIJ*)(*A_loc)->data;
4880     ci = mat->i; cj = mat->j; cam = mat->a;
4881     for (i=0; i<am; i++) {
4882       /* off-diagonal portion of A */
4883       ncols_o = bi[i+1] - bi[i];
4884       for (jo=0; jo<ncols_o; jo++) {
4885         col = cmap[*bj];
4886         if (col >= cstart) break;
4887         *cam++ = *ba++; bj++;
4888       }
4889       /* diagonal portion of A */
4890       ncols_d = ai[i+1] - ai[i];
4891       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
4892       /* off-diagonal portion of A */
4893       for (j=jo; j<ncols_o; j++) {
4894         *cam++ = *ba++; bj++;
4895       }
4896     }
4897   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
4898   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4899   PetscFunctionReturn(0);
4900 }
4901 
4902 /*@C
4903      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MATMPIAIJ matrix by taking all its local rows and NON-ZERO columns
4904 
4905     Not Collective
4906 
4907    Input Parameters:
4908 +    A - the matrix
4909 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4910 -    row, col - index sets of rows and columns to extract (or NULL)
4911 
4912    Output Parameter:
4913 .    A_loc - the local sequential matrix generated
4914 
4915     Level: developer
4916 
4917 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
4918 
4919 @*/
4920 PetscErrorCode MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
4921 {
4922   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4923   PetscErrorCode ierr;
4924   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
4925   IS             isrowa,iscola;
4926   Mat            *aloc;
4927   PetscBool      match;
4928 
4929   PetscFunctionBegin;
4930   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4931   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
4932   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4933   if (!row) {
4934     start = A->rmap->rstart; end = A->rmap->rend;
4935     ierr  = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
4936   } else {
4937     isrowa = *row;
4938   }
4939   if (!col) {
4940     start = A->cmap->rstart;
4941     cmap  = a->garray;
4942     nzA   = a->A->cmap->n;
4943     nzB   = a->B->cmap->n;
4944     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4945     ncols = 0;
4946     for (i=0; i<nzB; i++) {
4947       if (cmap[i] < start) idx[ncols++] = cmap[i];
4948       else break;
4949     }
4950     imark = i;
4951     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
4952     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
4953     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
4954   } else {
4955     iscola = *col;
4956   }
4957   if (scall != MAT_INITIAL_MATRIX) {
4958     ierr    = PetscMalloc1(1,&aloc);CHKERRQ(ierr);
4959     aloc[0] = *A_loc;
4960   }
4961   ierr   = MatCreateSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
4962   *A_loc = aloc[0];
4963   ierr   = PetscFree(aloc);CHKERRQ(ierr);
4964   if (!row) {
4965     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
4966   }
4967   if (!col) {
4968     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
4969   }
4970   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4971   PetscFunctionReturn(0);
4972 }
4973 
4974 /*@C
4975     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
4976 
4977     Collective on Mat
4978 
4979    Input Parameters:
4980 +    A,B - the matrices in mpiaij format
4981 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4982 -    rowb, colb - index sets of rows and columns of B to extract (or NULL)
4983 
4984    Output Parameter:
4985 +    rowb, colb - index sets of rows and columns of B to extract
4986 -    B_seq - the sequential matrix generated
4987 
4988     Level: developer
4989 
4990 @*/
4991 PetscErrorCode MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
4992 {
4993   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4994   PetscErrorCode ierr;
4995   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
4996   IS             isrowb,iscolb;
4997   Mat            *bseq=NULL;
4998 
4999   PetscFunctionBegin;
5000   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
5001     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);
5002   }
5003   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
5004 
5005   if (scall == MAT_INITIAL_MATRIX) {
5006     start = A->cmap->rstart;
5007     cmap  = a->garray;
5008     nzA   = a->A->cmap->n;
5009     nzB   = a->B->cmap->n;
5010     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
5011     ncols = 0;
5012     for (i=0; i<nzB; i++) {  /* row < local row index */
5013       if (cmap[i] < start) idx[ncols++] = cmap[i];
5014       else break;
5015     }
5016     imark = i;
5017     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
5018     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
5019     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
5020     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
5021   } else {
5022     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
5023     isrowb  = *rowb; iscolb = *colb;
5024     ierr    = PetscMalloc1(1,&bseq);CHKERRQ(ierr);
5025     bseq[0] = *B_seq;
5026   }
5027   ierr   = MatCreateSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
5028   *B_seq = bseq[0];
5029   ierr   = PetscFree(bseq);CHKERRQ(ierr);
5030   if (!rowb) {
5031     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
5032   } else {
5033     *rowb = isrowb;
5034   }
5035   if (!colb) {
5036     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
5037   } else {
5038     *colb = iscolb;
5039   }
5040   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
5041   PetscFunctionReturn(0);
5042 }
5043 
5044 /*
5045     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
5046     of the OFF-DIAGONAL portion of local A
5047 
5048     Collective on Mat
5049 
5050    Input Parameters:
5051 +    A,B - the matrices in mpiaij format
5052 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5053 
5054    Output Parameter:
5055 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
5056 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
5057 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
5058 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
5059 
5060     Level: developer
5061 
5062 */
5063 PetscErrorCode MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
5064 {
5065   VecScatter_MPI_General *gen_to,*gen_from;
5066   PetscErrorCode         ierr;
5067   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
5068   Mat_SeqAIJ             *b_oth;
5069   VecScatter             ctx =a->Mvctx;
5070   MPI_Comm               comm;
5071   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
5072   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
5073   PetscInt               *rvalues,*svalues;
5074   MatScalar              *b_otha,*bufa,*bufA;
5075   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
5076   MPI_Request            *rwaits = NULL,*swaits = NULL;
5077   MPI_Status             *sstatus,rstatus;
5078   PetscMPIInt            jj,size;
5079   PetscInt               *cols,sbs,rbs;
5080   PetscScalar            *vals;
5081 
5082   PetscFunctionBegin;
5083   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
5084   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
5085 
5086   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
5087     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);
5088   }
5089   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5090   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
5091 
5092   if (size == 1) {
5093     startsj_s = NULL;
5094     bufa_ptr  = NULL;
5095     *B_oth    = NULL;
5096     PetscFunctionReturn(0);
5097   }
5098 
5099   gen_to   = (VecScatter_MPI_General*)ctx->todata;
5100   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
5101   nrecvs   = gen_from->n;
5102   nsends   = gen_to->n;
5103 
5104   ierr    = PetscMalloc2(nrecvs,&rwaits,nsends,&swaits);CHKERRQ(ierr);
5105   srow    = gen_to->indices;    /* local row index to be sent */
5106   sstarts = gen_to->starts;
5107   sprocs  = gen_to->procs;
5108   sstatus = gen_to->sstatus;
5109   sbs     = gen_to->bs;
5110   rstarts = gen_from->starts;
5111   rprocs  = gen_from->procs;
5112   rbs     = gen_from->bs;
5113 
5114   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
5115   if (scall == MAT_INITIAL_MATRIX) {
5116     /* i-array */
5117     /*---------*/
5118     /*  post receives */
5119     ierr = PetscMalloc1(rbs*(rstarts[nrecvs] - rstarts[0]),&rvalues);CHKERRQ(ierr);
5120     for (i=0; i<nrecvs; i++) {
5121       rowlen = rvalues + rstarts[i]*rbs;
5122       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
5123       ierr   = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5124     }
5125 
5126     /* pack the outgoing message */
5127     ierr = PetscMalloc2(nsends+1,&sstartsj,nrecvs+1,&rstartsj);CHKERRQ(ierr);
5128 
5129     sstartsj[0] = 0;
5130     rstartsj[0] = 0;
5131     len         = 0; /* total length of j or a array to be sent */
5132     k           = 0;
5133     ierr = PetscMalloc1(sbs*(sstarts[nsends] - sstarts[0]),&svalues);CHKERRQ(ierr);
5134     for (i=0; i<nsends; i++) {
5135       rowlen = svalues + sstarts[i]*sbs;
5136       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
5137       for (j=0; j<nrows; j++) {
5138         row = srow[k] + B->rmap->range[rank]; /* global row idx */
5139         for (l=0; l<sbs; l++) {
5140           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr); /* rowlength */
5141 
5142           rowlen[j*sbs+l] = ncols;
5143 
5144           len += ncols;
5145           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr);
5146         }
5147         k++;
5148       }
5149       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5150 
5151       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
5152     }
5153     /* recvs and sends of i-array are completed */
5154     i = nrecvs;
5155     while (i--) {
5156       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5157     }
5158     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5159     ierr = PetscFree(svalues);CHKERRQ(ierr);
5160 
5161     /* allocate buffers for sending j and a arrays */
5162     ierr = PetscMalloc1(len+1,&bufj);CHKERRQ(ierr);
5163     ierr = PetscMalloc1(len+1,&bufa);CHKERRQ(ierr);
5164 
5165     /* create i-array of B_oth */
5166     ierr = PetscMalloc1(aBn+2,&b_othi);CHKERRQ(ierr);
5167 
5168     b_othi[0] = 0;
5169     len       = 0; /* total length of j or a array to be received */
5170     k         = 0;
5171     for (i=0; i<nrecvs; i++) {
5172       rowlen = rvalues + rstarts[i]*rbs;
5173       nrows  = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be received */
5174       for (j=0; j<nrows; j++) {
5175         b_othi[k+1] = b_othi[k] + rowlen[j];
5176         ierr = PetscIntSumError(rowlen[j],len,&len);CHKERRQ(ierr);
5177         k++;
5178       }
5179       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
5180     }
5181     ierr = PetscFree(rvalues);CHKERRQ(ierr);
5182 
5183     /* allocate space for j and a arrrays of B_oth */
5184     ierr = PetscMalloc1(b_othi[aBn]+1,&b_othj);CHKERRQ(ierr);
5185     ierr = PetscMalloc1(b_othi[aBn]+1,&b_otha);CHKERRQ(ierr);
5186 
5187     /* j-array */
5188     /*---------*/
5189     /*  post receives of j-array */
5190     for (i=0; i<nrecvs; i++) {
5191       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5192       ierr  = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5193     }
5194 
5195     /* pack the outgoing message j-array */
5196     k = 0;
5197     for (i=0; i<nsends; i++) {
5198       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5199       bufJ  = bufj+sstartsj[i];
5200       for (j=0; j<nrows; j++) {
5201         row = srow[k++] + B->rmap->range[rank];  /* global row idx */
5202         for (ll=0; ll<sbs; ll++) {
5203           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
5204           for (l=0; l<ncols; l++) {
5205             *bufJ++ = cols[l];
5206           }
5207           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
5208         }
5209       }
5210       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5211     }
5212 
5213     /* recvs and sends of j-array are completed */
5214     i = nrecvs;
5215     while (i--) {
5216       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5217     }
5218     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5219   } else if (scall == MAT_REUSE_MATRIX) {
5220     sstartsj = *startsj_s;
5221     rstartsj = *startsj_r;
5222     bufa     = *bufa_ptr;
5223     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
5224     b_otha   = b_oth->a;
5225   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
5226 
5227   /* a-array */
5228   /*---------*/
5229   /*  post receives of a-array */
5230   for (i=0; i<nrecvs; i++) {
5231     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5232     ierr  = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5233   }
5234 
5235   /* pack the outgoing message a-array */
5236   k = 0;
5237   for (i=0; i<nsends; i++) {
5238     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5239     bufA  = bufa+sstartsj[i];
5240     for (j=0; j<nrows; j++) {
5241       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
5242       for (ll=0; ll<sbs; ll++) {
5243         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
5244         for (l=0; l<ncols; l++) {
5245           *bufA++ = vals[l];
5246         }
5247         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
5248       }
5249     }
5250     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5251   }
5252   /* recvs and sends of a-array are completed */
5253   i = nrecvs;
5254   while (i--) {
5255     ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5256   }
5257   if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5258   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
5259 
5260   if (scall == MAT_INITIAL_MATRIX) {
5261     /* put together the new matrix */
5262     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
5263 
5264     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
5265     /* Since these are PETSc arrays, change flags to free them as necessary. */
5266     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
5267     b_oth->free_a  = PETSC_TRUE;
5268     b_oth->free_ij = PETSC_TRUE;
5269     b_oth->nonew   = 0;
5270 
5271     ierr = PetscFree(bufj);CHKERRQ(ierr);
5272     if (!startsj_s || !bufa_ptr) {
5273       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
5274       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
5275     } else {
5276       *startsj_s = sstartsj;
5277       *startsj_r = rstartsj;
5278       *bufa_ptr  = bufa;
5279     }
5280   }
5281   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5282   PetscFunctionReturn(0);
5283 }
5284 
5285 /*@C
5286   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
5287 
5288   Not Collective
5289 
5290   Input Parameters:
5291 . A - The matrix in mpiaij format
5292 
5293   Output Parameter:
5294 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
5295 . colmap - A map from global column index to local index into lvec
5296 - multScatter - A scatter from the argument of a matrix-vector product to lvec
5297 
5298   Level: developer
5299 
5300 @*/
5301 #if defined(PETSC_USE_CTABLE)
5302 PetscErrorCode MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
5303 #else
5304 PetscErrorCode MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
5305 #endif
5306 {
5307   Mat_MPIAIJ *a;
5308 
5309   PetscFunctionBegin;
5310   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
5311   PetscValidPointer(lvec, 2);
5312   PetscValidPointer(colmap, 3);
5313   PetscValidPointer(multScatter, 4);
5314   a = (Mat_MPIAIJ*) A->data;
5315   if (lvec) *lvec = a->lvec;
5316   if (colmap) *colmap = a->colmap;
5317   if (multScatter) *multScatter = a->Mvctx;
5318   PetscFunctionReturn(0);
5319 }
5320 
5321 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
5322 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
5323 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
5324 #if defined(PETSC_HAVE_ELEMENTAL)
5325 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
5326 #endif
5327 #if defined(PETSC_HAVE_HYPRE)
5328 PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat,MatType,MatReuse,Mat*);
5329 PETSC_INTERN PetscErrorCode MatMatMatMult_Transpose_AIJ_AIJ(Mat,Mat,Mat,MatReuse,PetscReal,Mat*);
5330 #endif
5331 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_IS(Mat,MatType,MatReuse,Mat*);
5332 
5333 /*
5334     Computes (B'*A')' since computing B*A directly is untenable
5335 
5336                n                       p                          p
5337         (              )       (              )         (                  )
5338       m (      A       )  *  n (       B      )   =   m (         C        )
5339         (              )       (              )         (                  )
5340 
5341 */
5342 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
5343 {
5344   PetscErrorCode ierr;
5345   Mat            At,Bt,Ct;
5346 
5347   PetscFunctionBegin;
5348   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
5349   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
5350   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
5351   ierr = MatDestroy(&At);CHKERRQ(ierr);
5352   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
5353   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
5354   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
5355   PetscFunctionReturn(0);
5356 }
5357 
5358 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
5359 {
5360   PetscErrorCode ierr;
5361   PetscInt       m=A->rmap->n,n=B->cmap->n;
5362   Mat            Cmat;
5363 
5364   PetscFunctionBegin;
5365   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);
5366   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
5367   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
5368   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
5369   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
5370   ierr = MatMPIDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
5371   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5372   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5373 
5374   Cmat->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
5375 
5376   *C = Cmat;
5377   PetscFunctionReturn(0);
5378 }
5379 
5380 /* ----------------------------------------------------------------*/
5381 PETSC_INTERN PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
5382 {
5383   PetscErrorCode ierr;
5384 
5385   PetscFunctionBegin;
5386   if (scall == MAT_INITIAL_MATRIX) {
5387     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5388     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
5389     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5390   }
5391   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5392   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
5393   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5394   PetscFunctionReturn(0);
5395 }
5396 
5397 /*MC
5398    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
5399 
5400    Options Database Keys:
5401 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
5402 
5403   Level: beginner
5404 
5405 .seealso: MatCreateAIJ()
5406 M*/
5407 
5408 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
5409 {
5410   Mat_MPIAIJ     *b;
5411   PetscErrorCode ierr;
5412   PetscMPIInt    size;
5413 
5414   PetscFunctionBegin;
5415   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
5416 
5417   ierr          = PetscNewLog(B,&b);CHKERRQ(ierr);
5418   B->data       = (void*)b;
5419   ierr          = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
5420   B->assembled  = PETSC_FALSE;
5421   B->insertmode = NOT_SET_VALUES;
5422   b->size       = size;
5423 
5424   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank);CHKERRQ(ierr);
5425 
5426   /* build cache for off array entries formed */
5427   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash);CHKERRQ(ierr);
5428 
5429   b->donotstash  = PETSC_FALSE;
5430   b->colmap      = 0;
5431   b->garray      = 0;
5432   b->roworiented = PETSC_TRUE;
5433 
5434   /* stuff used for matrix vector multiply */
5435   b->lvec  = NULL;
5436   b->Mvctx = NULL;
5437 
5438   /* stuff for MatGetRow() */
5439   b->rowindices   = 0;
5440   b->rowvalues    = 0;
5441   b->getrowactive = PETSC_FALSE;
5442 
5443   /* flexible pointer used in CUSP/CUSPARSE classes */
5444   b->spptr = NULL;
5445 
5446   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetUseScalableIncreaseOverlap_C",MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ);CHKERRQ(ierr);
5447   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ);CHKERRQ(ierr);
5448   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
5449   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
5450   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
5451   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
5452   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
5453   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
5454   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
5455   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
5456 #if defined(PETSC_HAVE_ELEMENTAL)
5457   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_elemental_C",MatConvert_MPIAIJ_Elemental);CHKERRQ(ierr);
5458 #endif
5459 #if defined(PETSC_HAVE_HYPRE)
5460   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_hypre_C",MatConvert_AIJ_HYPRE);CHKERRQ(ierr);
5461 #endif
5462   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_is_C",MatConvert_MPIAIJ_IS);CHKERRQ(ierr);
5463   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
5464   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
5465   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
5466 #if defined(PETSC_HAVE_HYPRE)
5467   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMatMult_transpose_mpiaij_mpiaij_C",MatMatMatMult_Transpose_AIJ_AIJ);CHKERRQ(ierr);
5468 #endif
5469   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
5470   PetscFunctionReturn(0);
5471 }
5472 
5473 /*@C
5474      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
5475          and "off-diagonal" part of the matrix in CSR format.
5476 
5477    Collective on MPI_Comm
5478 
5479    Input Parameters:
5480 +  comm - MPI communicator
5481 .  m - number of local rows (Cannot be PETSC_DECIDE)
5482 .  n - This value should be the same as the local size used in creating the
5483        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
5484        calculated if N is given) For square matrices n is almost always m.
5485 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
5486 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
5487 .   i - row indices for "diagonal" portion of matrix
5488 .   j - column indices
5489 .   a - matrix values
5490 .   oi - row indices for "off-diagonal" portion of matrix
5491 .   oj - column indices
5492 -   oa - matrix values
5493 
5494    Output Parameter:
5495 .   mat - the matrix
5496 
5497    Level: advanced
5498 
5499    Notes:
5500        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
5501        must free the arrays once the matrix has been destroyed and not before.
5502 
5503        The i and j indices are 0 based
5504 
5505        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
5506 
5507        This sets local rows and cannot be used to set off-processor values.
5508 
5509        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
5510        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
5511        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
5512        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
5513        keep track of the underlying array. Use MatSetOption(A,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
5514        communication if it is known that only local entries will be set.
5515 
5516 .keywords: matrix, aij, compressed row, sparse, parallel
5517 
5518 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
5519           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
5520 @*/
5521 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)
5522 {
5523   PetscErrorCode ierr;
5524   Mat_MPIAIJ     *maij;
5525 
5526   PetscFunctionBegin;
5527   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
5528   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
5529   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
5530   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
5531   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
5532   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
5533   maij = (Mat_MPIAIJ*) (*mat)->data;
5534 
5535   (*mat)->preallocated = PETSC_TRUE;
5536 
5537   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
5538   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
5539 
5540   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
5541   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
5542 
5543   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5544   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5545   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5546   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5547 
5548   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
5549   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5550   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5551   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_FALSE);CHKERRQ(ierr);
5552   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
5553   PetscFunctionReturn(0);
5554 }
5555 
5556 /*
5557     Special version for direct calls from Fortran
5558 */
5559 #include <petsc/private/fortranimpl.h>
5560 
5561 /* Change these macros so can be used in void function */
5562 #undef CHKERRQ
5563 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
5564 #undef SETERRQ2
5565 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5566 #undef SETERRQ3
5567 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5568 #undef SETERRQ
5569 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
5570 
5571 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5572 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
5573 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5574 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
5575 #else
5576 #endif
5577 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)
5578 {
5579   Mat            mat  = *mmat;
5580   PetscInt       m    = *mm, n = *mn;
5581   InsertMode     addv = *maddv;
5582   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
5583   PetscScalar    value;
5584   PetscErrorCode ierr;
5585 
5586   MatCheckPreallocated(mat,1);
5587   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
5588 
5589 #if defined(PETSC_USE_DEBUG)
5590   else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
5591 #endif
5592   {
5593     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
5594     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
5595     PetscBool roworiented = aij->roworiented;
5596 
5597     /* Some Variables required in the macro */
5598     Mat        A                 = aij->A;
5599     Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
5600     PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
5601     MatScalar  *aa               = a->a;
5602     PetscBool  ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
5603     Mat        B                 = aij->B;
5604     Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
5605     PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5606     MatScalar  *ba               = b->a;
5607 
5608     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5609     PetscInt  nonew = a->nonew;
5610     MatScalar *ap1,*ap2;
5611 
5612     PetscFunctionBegin;
5613     for (i=0; i<m; i++) {
5614       if (im[i] < 0) continue;
5615 #if defined(PETSC_USE_DEBUG)
5616       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);
5617 #endif
5618       if (im[i] >= rstart && im[i] < rend) {
5619         row      = im[i] - rstart;
5620         lastcol1 = -1;
5621         rp1      = aj + ai[row];
5622         ap1      = aa + ai[row];
5623         rmax1    = aimax[row];
5624         nrow1    = ailen[row];
5625         low1     = 0;
5626         high1    = nrow1;
5627         lastcol2 = -1;
5628         rp2      = bj + bi[row];
5629         ap2      = ba + bi[row];
5630         rmax2    = bimax[row];
5631         nrow2    = bilen[row];
5632         low2     = 0;
5633         high2    = nrow2;
5634 
5635         for (j=0; j<n; j++) {
5636           if (roworiented) value = v[i*n+j];
5637           else value = v[i+j*m];
5638           if (in[j] >= cstart && in[j] < cend) {
5639             col = in[j] - cstart;
5640             if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
5641             MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
5642           } else if (in[j] < 0) continue;
5643 #if defined(PETSC_USE_DEBUG)
5644           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);
5645 #endif
5646           else {
5647             if (mat->was_assembled) {
5648               if (!aij->colmap) {
5649                 ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5650               }
5651 #if defined(PETSC_USE_CTABLE)
5652               ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5653               col--;
5654 #else
5655               col = aij->colmap[in[j]] - 1;
5656 #endif
5657               if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
5658               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5659                 ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5660                 col  =  in[j];
5661                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5662                 B     = aij->B;
5663                 b     = (Mat_SeqAIJ*)B->data;
5664                 bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5665                 rp2   = bj + bi[row];
5666                 ap2   = ba + bi[row];
5667                 rmax2 = bimax[row];
5668                 nrow2 = bilen[row];
5669                 low2  = 0;
5670                 high2 = nrow2;
5671                 bm    = aij->B->rmap->n;
5672                 ba    = b->a;
5673               }
5674             } else col = in[j];
5675             MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
5676           }
5677         }
5678       } else if (!aij->donotstash) {
5679         if (roworiented) {
5680           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5681         } else {
5682           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5683         }
5684       }
5685     }
5686   }
5687   PetscFunctionReturnVoid();
5688 }
5689 
5690