xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision f86b9fba6afbb510b5a4e5909e38406c0861ad7a)
1 
2 #include <../src/mat/impls/aij/mpi/mpiaij.h>   /*I "petscmat.h" I*/
3 #include <petsc-private/vecimpl.h>
4 #include <petscblaslapack.h>
5 #include <petscsf.h>
6 
7 /*MC
8    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.
9 
10    This matrix type is identical to MATSEQAIJ when constructed with a single process communicator,
11    and MATMPIAIJ otherwise.  As a result, for single process communicators,
12   MatSeqAIJSetPreallocation is supported, and similarly MatMPIAIJSetPreallocation is supported
13   for communicators controlling multiple processes.  It is recommended that you call both of
14   the above preallocation routines for simplicity.
15 
16    Options Database Keys:
17 . -mat_type aij - sets the matrix type to "aij" during a call to MatSetFromOptions()
18 
19   Developer Notes: Subclasses include MATAIJCUSP, MATAIJCUSPARSE, MATAIJPERM, MATAIJCRL, and also automatically switches over to use inodes when
20    enough exist.
21 
22   Level: beginner
23 
24 .seealso: MatCreateAIJ(), MatCreateSeqAIJ(), MATSEQAIJ,MATMPIAIJ
25 M*/
26 
27 /*MC
28    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.
29 
30    This matrix type is identical to MATSEQAIJCRL when constructed with a single process communicator,
31    and MATMPIAIJCRL otherwise.  As a result, for single process communicators,
32    MatSeqAIJSetPreallocation() is supported, and similarly MatMPIAIJSetPreallocation() is supported
33   for communicators controlling multiple processes.  It is recommended that you call both of
34   the above preallocation routines for simplicity.
35 
36    Options Database Keys:
37 . -mat_type aijcrl - sets the matrix type to "aijcrl" during a call to MatSetFromOptions()
38 
39   Level: beginner
40 
41 .seealso: MatCreateMPIAIJCRL,MATSEQAIJCRL,MATMPIAIJCRL, MATSEQAIJCRL, MATMPIAIJCRL
42 M*/
43 
44 #undef __FUNCT__
45 #define __FUNCT__ "MatFindNonzeroRows_MPIAIJ"
46 PetscErrorCode MatFindNonzeroRows_MPIAIJ(Mat M,IS *keptrows)
47 {
48   PetscErrorCode  ierr;
49   Mat_MPIAIJ      *mat = (Mat_MPIAIJ*)M->data;
50   Mat_SeqAIJ      *a   = (Mat_SeqAIJ*)mat->A->data;
51   Mat_SeqAIJ      *b   = (Mat_SeqAIJ*)mat->B->data;
52   const PetscInt  *ia,*ib;
53   const MatScalar *aa,*bb;
54   PetscInt        na,nb,i,j,*rows,cnt=0,n0rows;
55   PetscInt        m = M->rmap->n,rstart = M->rmap->rstart;
56 
57   PetscFunctionBegin;
58   *keptrows = 0;
59   ia        = a->i;
60   ib        = b->i;
61   for (i=0; i<m; i++) {
62     na = ia[i+1] - ia[i];
63     nb = ib[i+1] - ib[i];
64     if (!na && !nb) {
65       cnt++;
66       goto ok1;
67     }
68     aa = a->a + ia[i];
69     for (j=0; j<na; j++) {
70       if (aa[j] != 0.0) goto ok1;
71     }
72     bb = b->a + ib[i];
73     for (j=0; j <nb; j++) {
74       if (bb[j] != 0.0) goto ok1;
75     }
76     cnt++;
77 ok1:;
78   }
79   ierr = MPI_Allreduce(&cnt,&n0rows,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)M));CHKERRQ(ierr);
80   if (!n0rows) PetscFunctionReturn(0);
81   ierr = PetscMalloc((M->rmap->n-cnt)*sizeof(PetscInt),&rows);CHKERRQ(ierr);
82   cnt  = 0;
83   for (i=0; i<m; i++) {
84     na = ia[i+1] - ia[i];
85     nb = ib[i+1] - ib[i];
86     if (!na && !nb) continue;
87     aa = a->a + ia[i];
88     for (j=0; j<na;j++) {
89       if (aa[j] != 0.0) {
90         rows[cnt++] = rstart + i;
91         goto ok2;
92       }
93     }
94     bb = b->a + ib[i];
95     for (j=0; j<nb; j++) {
96       if (bb[j] != 0.0) {
97         rows[cnt++] = rstart + i;
98         goto ok2;
99       }
100     }
101 ok2:;
102   }
103   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)M),cnt,rows,PETSC_OWN_POINTER,keptrows);CHKERRQ(ierr);
104   PetscFunctionReturn(0);
105 }
106 
107 #undef __FUNCT__
108 #define __FUNCT__ "MatFindZeroDiagonals_MPIAIJ"
109 PetscErrorCode MatFindZeroDiagonals_MPIAIJ(Mat M,IS *zrows)
110 {
111   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)M->data;
112   PetscErrorCode ierr;
113   PetscInt       i,rstart,nrows,*rows;
114 
115   PetscFunctionBegin;
116   *zrows = NULL;
117   ierr   = MatFindZeroDiagonals_SeqAIJ_Private(aij->A,&nrows,&rows);CHKERRQ(ierr);
118   ierr   = MatGetOwnershipRange(M,&rstart,NULL);CHKERRQ(ierr);
119   for (i=0; i<nrows; i++) rows[i] += rstart;
120   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)M),nrows,rows,PETSC_OWN_POINTER,zrows);CHKERRQ(ierr);
121   PetscFunctionReturn(0);
122 }
123 
124 #undef __FUNCT__
125 #define __FUNCT__ "MatGetColumnNorms_MPIAIJ"
126 PetscErrorCode MatGetColumnNorms_MPIAIJ(Mat A,NormType type,PetscReal *norms)
127 {
128   PetscErrorCode ierr;
129   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)A->data;
130   PetscInt       i,n,*garray = aij->garray;
131   Mat_SeqAIJ     *a_aij = (Mat_SeqAIJ*) aij->A->data;
132   Mat_SeqAIJ     *b_aij = (Mat_SeqAIJ*) aij->B->data;
133   PetscReal      *work;
134 
135   PetscFunctionBegin;
136   ierr = MatGetSize(A,NULL,&n);CHKERRQ(ierr);
137   ierr = PetscMalloc(n*sizeof(PetscReal),&work);CHKERRQ(ierr);
138   ierr = PetscMemzero(work,n*sizeof(PetscReal));CHKERRQ(ierr);
139   if (type == NORM_2) {
140     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
141       work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i]*a_aij->a[i]);
142     }
143     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
144       work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]*b_aij->a[i]);
145     }
146   } else if (type == NORM_1) {
147     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
148       work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i]);
149     }
150     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
151       work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]);
152     }
153   } else if (type == NORM_INFINITY) {
154     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
155       work[A->cmap->rstart + a_aij->j[i]] = PetscMax(PetscAbsScalar(a_aij->a[i]), work[A->cmap->rstart + a_aij->j[i]]);
156     }
157     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
158       work[garray[b_aij->j[i]]] = PetscMax(PetscAbsScalar(b_aij->a[i]),work[garray[b_aij->j[i]]]);
159     }
160 
161   } else SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Unknown NormType");
162   if (type == NORM_INFINITY) {
163     ierr = MPI_Allreduce(work,norms,n,MPIU_REAL,MPIU_MAX,A->hdr.comm);CHKERRQ(ierr);
164   } else {
165     ierr = MPI_Allreduce(work,norms,n,MPIU_REAL,MPIU_SUM,A->hdr.comm);CHKERRQ(ierr);
166   }
167   ierr = PetscFree(work);CHKERRQ(ierr);
168   if (type == NORM_2) {
169     for (i=0; i<n; i++) norms[i] = PetscSqrtReal(norms[i]);
170   }
171   PetscFunctionReturn(0);
172 }
173 
174 #undef __FUNCT__
175 #define __FUNCT__ "MatDistribute_MPIAIJ"
176 /*
177     Distributes a SeqAIJ matrix across a set of processes. Code stolen from
178     MatLoad_MPIAIJ(). Horrible lack of reuse. Should be a routine for each matrix type.
179 
180     Only for square matrices
181 
182     Used by a preconditioner, hence PETSC_EXTERN
183 */
184 PETSC_EXTERN PetscErrorCode MatDistribute_MPIAIJ(MPI_Comm comm,Mat gmat,PetscInt m,MatReuse reuse,Mat *inmat)
185 {
186   PetscMPIInt    rank,size;
187   PetscInt       *rowners,*dlens,*olens,i,rstart,rend,j,jj,nz,*gmataj,cnt,row,*ld,bses[2];
188   PetscErrorCode ierr;
189   Mat            mat;
190   Mat_SeqAIJ     *gmata;
191   PetscMPIInt    tag;
192   MPI_Status     status;
193   PetscBool      aij;
194   MatScalar      *gmataa,*ao,*ad,*gmataarestore=0;
195 
196   PetscFunctionBegin;
197   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
198   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
199   if (!rank) {
200     ierr = PetscObjectTypeCompare((PetscObject)gmat,MATSEQAIJ,&aij);CHKERRQ(ierr);
201     if (!aij) SETERRQ1(PetscObjectComm((PetscObject)gmat),PETSC_ERR_SUP,"Currently no support for input matrix of type %s\n",((PetscObject)gmat)->type_name);
202   }
203   if (reuse == MAT_INITIAL_MATRIX) {
204     ierr = MatCreate(comm,&mat);CHKERRQ(ierr);
205     ierr = MatSetSizes(mat,m,m,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
206     if (!rank) {
207       bses[0] = gmat->rmap->bs;
208       bses[1] = gmat->cmap->bs;
209     }
210     ierr = MPI_Bcast(bses,2,MPIU_INT,0,comm);CHKERRQ(ierr);
211     ierr = MatSetBlockSizes(mat,bses[0],bses[1]);CHKERRQ(ierr);
212     ierr = MatSetType(mat,MATAIJ);CHKERRQ(ierr);
213     ierr = PetscMalloc((size+1)*sizeof(PetscInt),&rowners);CHKERRQ(ierr);
214     ierr = PetscMalloc2(m,PetscInt,&dlens,m,PetscInt,&olens);CHKERRQ(ierr);
215     ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
216 
217     rowners[0] = 0;
218     for (i=2; i<=size; i++) rowners[i] += rowners[i-1];
219     rstart = rowners[rank];
220     rend   = rowners[rank+1];
221     ierr   = PetscObjectGetNewTag((PetscObject)mat,&tag);CHKERRQ(ierr);
222     if (!rank) {
223       gmata = (Mat_SeqAIJ*) gmat->data;
224       /* send row lengths to all processors */
225       for (i=0; i<m; i++) dlens[i] = gmata->ilen[i];
226       for (i=1; i<size; i++) {
227         ierr = MPI_Send(gmata->ilen + rowners[i],rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
228       }
229       /* determine number diagonal and off-diagonal counts */
230       ierr = PetscMemzero(olens,m*sizeof(PetscInt));CHKERRQ(ierr);
231       ierr = PetscMalloc(m*sizeof(PetscInt),&ld);CHKERRQ(ierr);
232       ierr = PetscMemzero(ld,m*sizeof(PetscInt));CHKERRQ(ierr);
233       jj   = 0;
234       for (i=0; i<m; i++) {
235         for (j=0; j<dlens[i]; j++) {
236           if (gmata->j[jj] < rstart) ld[i]++;
237           if (gmata->j[jj] < rstart || gmata->j[jj] >= rend) olens[i]++;
238           jj++;
239         }
240       }
241       /* send column indices to other processes */
242       for (i=1; i<size; i++) {
243         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
244         ierr = MPI_Send(&nz,1,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
245         ierr = MPI_Send(gmata->j + gmata->i[rowners[i]],nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
246       }
247 
248       /* send numerical values to other processes */
249       for (i=1; i<size; i++) {
250         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
251         ierr = MPI_Send(gmata->a + gmata->i[rowners[i]],nz,MPIU_SCALAR,i,tag,comm);CHKERRQ(ierr);
252       }
253       gmataa = gmata->a;
254       gmataj = gmata->j;
255 
256     } else {
257       /* receive row lengths */
258       ierr = MPI_Recv(dlens,m,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
259       /* receive column indices */
260       ierr = MPI_Recv(&nz,1,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
261       ierr = PetscMalloc2(nz,PetscScalar,&gmataa,nz,PetscInt,&gmataj);CHKERRQ(ierr);
262       ierr = MPI_Recv(gmataj,nz,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
263       /* determine number diagonal and off-diagonal counts */
264       ierr = PetscMemzero(olens,m*sizeof(PetscInt));CHKERRQ(ierr);
265       ierr = PetscMalloc(m*sizeof(PetscInt),&ld);CHKERRQ(ierr);
266       ierr = PetscMemzero(ld,m*sizeof(PetscInt));CHKERRQ(ierr);
267       jj   = 0;
268       for (i=0; i<m; i++) {
269         for (j=0; j<dlens[i]; j++) {
270           if (gmataj[jj] < rstart) ld[i]++;
271           if (gmataj[jj] < rstart || gmataj[jj] >= rend) olens[i]++;
272           jj++;
273         }
274       }
275       /* receive numerical values */
276       ierr = PetscMemzero(gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr);
277       ierr = MPI_Recv(gmataa,nz,MPIU_SCALAR,0,tag,comm,&status);CHKERRQ(ierr);
278     }
279     /* set preallocation */
280     for (i=0; i<m; i++) {
281       dlens[i] -= olens[i];
282     }
283     ierr = MatSeqAIJSetPreallocation(mat,0,dlens);CHKERRQ(ierr);
284     ierr = MatMPIAIJSetPreallocation(mat,0,dlens,0,olens);CHKERRQ(ierr);
285 
286     for (i=0; i<m; i++) {
287       dlens[i] += olens[i];
288     }
289     cnt = 0;
290     for (i=0; i<m; i++) {
291       row  = rstart + i;
292       ierr = MatSetValues(mat,1,&row,dlens[i],gmataj+cnt,gmataa+cnt,INSERT_VALUES);CHKERRQ(ierr);
293       cnt += dlens[i];
294     }
295     if (rank) {
296       ierr = PetscFree2(gmataa,gmataj);CHKERRQ(ierr);
297     }
298     ierr = PetscFree2(dlens,olens);CHKERRQ(ierr);
299     ierr = PetscFree(rowners);CHKERRQ(ierr);
300 
301     ((Mat_MPIAIJ*)(mat->data))->ld = ld;
302 
303     *inmat = mat;
304   } else {   /* column indices are already set; only need to move over numerical values from process 0 */
305     Mat_SeqAIJ *Ad = (Mat_SeqAIJ*)((Mat_MPIAIJ*)((*inmat)->data))->A->data;
306     Mat_SeqAIJ *Ao = (Mat_SeqAIJ*)((Mat_MPIAIJ*)((*inmat)->data))->B->data;
307     mat  = *inmat;
308     ierr = PetscObjectGetNewTag((PetscObject)mat,&tag);CHKERRQ(ierr);
309     if (!rank) {
310       /* send numerical values to other processes */
311       gmata  = (Mat_SeqAIJ*) gmat->data;
312       ierr   = MatGetOwnershipRanges(mat,(const PetscInt**)&rowners);CHKERRQ(ierr);
313       gmataa = gmata->a;
314       for (i=1; i<size; i++) {
315         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
316         ierr = MPI_Send(gmataa + gmata->i[rowners[i]],nz,MPIU_SCALAR,i,tag,comm);CHKERRQ(ierr);
317       }
318       nz = gmata->i[rowners[1]]-gmata->i[rowners[0]];
319     } else {
320       /* receive numerical values from process 0*/
321       nz   = Ad->nz + Ao->nz;
322       ierr = PetscMalloc(nz*sizeof(PetscScalar),&gmataa);CHKERRQ(ierr); gmataarestore = gmataa;
323       ierr = MPI_Recv(gmataa,nz,MPIU_SCALAR,0,tag,comm,&status);CHKERRQ(ierr);
324     }
325     /* transfer numerical values into the diagonal A and off diagonal B parts of mat */
326     ld = ((Mat_MPIAIJ*)(mat->data))->ld;
327     ad = Ad->a;
328     ao = Ao->a;
329     if (mat->rmap->n) {
330       i  = 0;
331       nz = ld[i];                                   ierr = PetscMemcpy(ao,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ao += nz; gmataa += nz;
332       nz = Ad->i[i+1] - Ad->i[i];                   ierr = PetscMemcpy(ad,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ad += nz; gmataa += nz;
333     }
334     for (i=1; i<mat->rmap->n; i++) {
335       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;
336       nz = Ad->i[i+1] - Ad->i[i];                   ierr = PetscMemcpy(ad,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ad += nz; gmataa += nz;
337     }
338     i--;
339     if (mat->rmap->n) {
340       nz = Ao->i[i+1] - Ao->i[i] - ld[i];           ierr = PetscMemcpy(ao,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr);
341     }
342     if (rank) {
343       ierr = PetscFree(gmataarestore);CHKERRQ(ierr);
344     }
345   }
346   ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
347   ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
348   PetscFunctionReturn(0);
349 }
350 
351 /*
352   Local utility routine that creates a mapping from the global column
353 number to the local number in the off-diagonal part of the local
354 storage of the matrix.  When PETSC_USE_CTABLE is used this is scalable at
355 a slightly higher hash table cost; without it it is not scalable (each processor
356 has an order N integer array but is fast to acess.
357 */
358 #undef __FUNCT__
359 #define __FUNCT__ "MatCreateColmap_MPIAIJ_Private"
360 PetscErrorCode MatCreateColmap_MPIAIJ_Private(Mat mat)
361 {
362   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
363   PetscErrorCode ierr;
364   PetscInt       n = aij->B->cmap->n,i;
365 
366   PetscFunctionBegin;
367   if (!aij->garray) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"MPIAIJ Matrix was assembled but is missing garray");
368 #if defined(PETSC_USE_CTABLE)
369   ierr = PetscTableCreate(n,mat->cmap->N+1,&aij->colmap);CHKERRQ(ierr);
370   for (i=0; i<n; i++) {
371     ierr = PetscTableAdd(aij->colmap,aij->garray[i]+1,i+1,INSERT_VALUES);CHKERRQ(ierr);
372   }
373 #else
374   ierr = PetscMalloc((mat->cmap->N+1)*sizeof(PetscInt),&aij->colmap);CHKERRQ(ierr);
375   ierr = PetscLogObjectMemory((PetscObject)mat,mat->cmap->N*sizeof(PetscInt));CHKERRQ(ierr);
376   ierr = PetscMemzero(aij->colmap,mat->cmap->N*sizeof(PetscInt));CHKERRQ(ierr);
377   for (i=0; i<n; i++) aij->colmap[aij->garray[i]] = i+1;
378 #endif
379   PetscFunctionReturn(0);
380 }
381 
382 #define MatSetValues_SeqAIJ_A_Private(row,col,value,addv) \
383 { \
384     if (col <= lastcol1)  low1 = 0;     \
385     else                 high1 = nrow1; \
386     lastcol1 = col;\
387     while (high1-low1 > 5) { \
388       t = (low1+high1)/2; \
389       if (rp1[t] > col) high1 = t; \
390       else              low1  = t; \
391     } \
392       for (_i=low1; _i<high1; _i++) { \
393         if (rp1[_i] > col) break; \
394         if (rp1[_i] == col) { \
395           if (addv == ADD_VALUES) ap1[_i] += value;   \
396           else                    ap1[_i] = value; \
397           goto a_noinsert; \
398         } \
399       }  \
400       if (value == 0.0 && ignorezeroentries) {low1 = 0; high1 = nrow1;goto a_noinsert;} \
401       if (nonew == 1) {low1 = 0; high1 = nrow1; goto a_noinsert;}                \
402       if (nonew == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero (%D, %D) into matrix", row, col); \
403       MatSeqXAIJReallocateAIJ(A,am,1,nrow1,row,col,rmax1,aa,ai,aj,rp1,ap1,aimax,nonew,MatScalar); \
404       N = nrow1++ - 1; a->nz++; high1++; \
405       /* shift up all the later entries in this row */ \
406       for (ii=N; ii>=_i; ii--) { \
407         rp1[ii+1] = rp1[ii]; \
408         ap1[ii+1] = ap1[ii]; \
409       } \
410       rp1[_i] = col;  \
411       ap1[_i] = value;  \
412       a_noinsert: ; \
413       ailen[row] = nrow1; \
414 }
415 
416 
417 #define MatSetValues_SeqAIJ_B_Private(row,col,value,addv) \
418   { \
419     if (col <= lastcol2) low2 = 0;                        \
420     else high2 = nrow2;                                   \
421     lastcol2 = col;                                       \
422     while (high2-low2 > 5) {                              \
423       t = (low2+high2)/2;                                 \
424       if (rp2[t] > col) high2 = t;                        \
425       else             low2  = t;                         \
426     }                                                     \
427     for (_i=low2; _i<high2; _i++) {                       \
428       if (rp2[_i] > col) break;                           \
429       if (rp2[_i] == col) {                               \
430         if (addv == ADD_VALUES) ap2[_i] += value;         \
431         else                    ap2[_i] = value;          \
432         goto b_noinsert;                                  \
433       }                                                   \
434     }                                                     \
435     if (value == 0.0 && ignorezeroentries) {low2 = 0; high2 = nrow2; goto b_noinsert;} \
436     if (nonew == 1) {low2 = 0; high2 = nrow2; goto b_noinsert;}                        \
437     if (nonew == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero (%D, %D) into matrix", row, col); \
438     MatSeqXAIJReallocateAIJ(B,bm,1,nrow2,row,col,rmax2,ba,bi,bj,rp2,ap2,bimax,nonew,MatScalar); \
439     N = nrow2++ - 1; b->nz++; high2++;                    \
440     /* shift up all the later entries in this row */      \
441     for (ii=N; ii>=_i; ii--) {                            \
442       rp2[ii+1] = rp2[ii];                                \
443       ap2[ii+1] = ap2[ii];                                \
444     }                                                     \
445     rp2[_i] = col;                                        \
446     ap2[_i] = value;                                      \
447     b_noinsert: ;                                         \
448     bilen[row] = nrow2;                                   \
449   }
450 
451 #undef __FUNCT__
452 #define __FUNCT__ "MatSetValuesRow_MPIAIJ"
453 PetscErrorCode MatSetValuesRow_MPIAIJ(Mat A,PetscInt row,const PetscScalar v[])
454 {
455   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)A->data;
456   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)mat->A->data,*b = (Mat_SeqAIJ*)mat->B->data;
457   PetscErrorCode ierr;
458   PetscInt       l,*garray = mat->garray,diag;
459 
460   PetscFunctionBegin;
461   /* code only works for square matrices A */
462 
463   /* find size of row to the left of the diagonal part */
464   ierr = MatGetOwnershipRange(A,&diag,0);CHKERRQ(ierr);
465   row  = row - diag;
466   for (l=0; l<b->i[row+1]-b->i[row]; l++) {
467     if (garray[b->j[b->i[row]+l]] > diag) break;
468   }
469   ierr = PetscMemcpy(b->a+b->i[row],v,l*sizeof(PetscScalar));CHKERRQ(ierr);
470 
471   /* diagonal part */
472   ierr = PetscMemcpy(a->a+a->i[row],v+l,(a->i[row+1]-a->i[row])*sizeof(PetscScalar));CHKERRQ(ierr);
473 
474   /* right of diagonal part */
475   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);
476   PetscFunctionReturn(0);
477 }
478 
479 #undef __FUNCT__
480 #define __FUNCT__ "MatSetValues_MPIAIJ"
481 PetscErrorCode MatSetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode addv)
482 {
483   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
484   PetscScalar    value;
485   PetscErrorCode ierr;
486   PetscInt       i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
487   PetscInt       cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
488   PetscBool      roworiented = aij->roworiented;
489 
490   /* Some Variables required in the macro */
491   Mat        A                 = aij->A;
492   Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
493   PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
494   MatScalar  *aa               = a->a;
495   PetscBool  ignorezeroentries = a->ignorezeroentries;
496   Mat        B                 = aij->B;
497   Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
498   PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
499   MatScalar  *ba               = b->a;
500 
501   PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
502   PetscInt  nonew;
503   MatScalar *ap1,*ap2;
504 
505   PetscFunctionBegin;
506   if (v) PetscValidScalarPointer(v,6);
507   for (i=0; i<m; i++) {
508     if (im[i] < 0) continue;
509 #if defined(PETSC_USE_DEBUG)
510     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);
511 #endif
512     if (im[i] >= rstart && im[i] < rend) {
513       row      = im[i] - rstart;
514       lastcol1 = -1;
515       rp1      = aj + ai[row];
516       ap1      = aa + ai[row];
517       rmax1    = aimax[row];
518       nrow1    = ailen[row];
519       low1     = 0;
520       high1    = nrow1;
521       lastcol2 = -1;
522       rp2      = bj + bi[row];
523       ap2      = ba + bi[row];
524       rmax2    = bimax[row];
525       nrow2    = bilen[row];
526       low2     = 0;
527       high2    = nrow2;
528 
529       for (j=0; j<n; j++) {
530         if (v) {
531           if (roworiented) value = v[i*n+j];
532           else             value = v[i+j*m];
533         } else value = 0.0;
534         if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES)) continue;
535         if (in[j] >= cstart && in[j] < cend) {
536           col   = in[j] - cstart;
537           nonew = a->nonew;
538           MatSetValues_SeqAIJ_A_Private(row,col,value,addv);
539         } else if (in[j] < 0) continue;
540 #if defined(PETSC_USE_DEBUG)
541         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);
542 #endif
543         else {
544           if (mat->was_assembled) {
545             if (!aij->colmap) {
546               ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
547             }
548 #if defined(PETSC_USE_CTABLE)
549             ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
550             col--;
551 #else
552             col = aij->colmap[in[j]] - 1;
553 #endif
554             if (col < 0 && !((Mat_SeqAIJ*)(aij->B->data))->nonew) {
555               ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
556               col  =  in[j];
557               /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
558               B     = aij->B;
559               b     = (Mat_SeqAIJ*)B->data;
560               bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j; ba = b->a;
561               rp2   = bj + bi[row];
562               ap2   = ba + bi[row];
563               rmax2 = bimax[row];
564               nrow2 = bilen[row];
565               low2  = 0;
566               high2 = nrow2;
567               bm    = aij->B->rmap->n;
568               ba    = b->a;
569             } else if (col < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero (%D, %D) into matrix", im[i], in[j]);
570           } else col = in[j];
571           nonew = b->nonew;
572           MatSetValues_SeqAIJ_B_Private(row,col,value,addv);
573         }
574       }
575     } else {
576       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]);
577       if (!aij->donotstash) {
578         mat->assembled = PETSC_FALSE;
579         if (roworiented) {
580           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
581         } else {
582           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
583         }
584       }
585     }
586   }
587   PetscFunctionReturn(0);
588 }
589 
590 #undef __FUNCT__
591 #define __FUNCT__ "MatGetValues_MPIAIJ"
592 PetscErrorCode MatGetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],PetscScalar v[])
593 {
594   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
595   PetscErrorCode ierr;
596   PetscInt       i,j,rstart = mat->rmap->rstart,rend = mat->rmap->rend;
597   PetscInt       cstart = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
598 
599   PetscFunctionBegin;
600   for (i=0; i<m; i++) {
601     if (idxm[i] < 0) continue; /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative row: %D",idxm[i]);*/
602     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);
603     if (idxm[i] >= rstart && idxm[i] < rend) {
604       row = idxm[i] - rstart;
605       for (j=0; j<n; j++) {
606         if (idxn[j] < 0) continue; /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column: %D",idxn[j]); */
607         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);
608         if (idxn[j] >= cstart && idxn[j] < cend) {
609           col  = idxn[j] - cstart;
610           ierr = MatGetValues(aij->A,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
611         } else {
612           if (!aij->colmap) {
613             ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
614           }
615 #if defined(PETSC_USE_CTABLE)
616           ierr = PetscTableFind(aij->colmap,idxn[j]+1,&col);CHKERRQ(ierr);
617           col--;
618 #else
619           col = aij->colmap[idxn[j]] - 1;
620 #endif
621           if ((col < 0) || (aij->garray[col] != idxn[j])) *(v+i*n+j) = 0.0;
622           else {
623             ierr = MatGetValues(aij->B,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
624           }
625         }
626       }
627     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only local values currently supported");
628   }
629   PetscFunctionReturn(0);
630 }
631 
632 extern PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat,Vec,Vec);
633 
634 #undef __FUNCT__
635 #define __FUNCT__ "MatAssemblyBegin_MPIAIJ"
636 PetscErrorCode MatAssemblyBegin_MPIAIJ(Mat mat,MatAssemblyType mode)
637 {
638   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
639   PetscErrorCode ierr;
640   PetscInt       nstash,reallocs;
641   InsertMode     addv;
642 
643   PetscFunctionBegin;
644   if (aij->donotstash || mat->nooffprocentries) PetscFunctionReturn(0);
645 
646   /* make sure all processors are either in INSERTMODE or ADDMODE */
647   ierr = MPI_Allreduce((PetscEnum*)&mat->insertmode,(PetscEnum*)&addv,1,MPIU_ENUM,MPI_BOR,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
648   if (addv == (ADD_VALUES|INSERT_VALUES)) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Some processors inserted others added");
649   mat->insertmode = addv; /* in case this processor had no cache */
650 
651   ierr = MatStashScatterBegin_Private(mat,&mat->stash,mat->rmap->range);CHKERRQ(ierr);
652   ierr = MatStashGetInfo_Private(&mat->stash,&nstash,&reallocs);CHKERRQ(ierr);
653   ierr = PetscInfo2(aij->A,"Stash has %D entries, uses %D mallocs.\n",nstash,reallocs);CHKERRQ(ierr);
654   PetscFunctionReturn(0);
655 }
656 
657 #undef __FUNCT__
658 #define __FUNCT__ "MatAssemblyEnd_MPIAIJ"
659 PetscErrorCode MatAssemblyEnd_MPIAIJ(Mat mat,MatAssemblyType mode)
660 {
661   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
662   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)aij->A->data;
663   PetscErrorCode ierr;
664   PetscMPIInt    n;
665   PetscInt       i,j,rstart,ncols,flg;
666   PetscInt       *row,*col;
667   PetscBool      other_disassembled;
668   PetscScalar    *val;
669   InsertMode     addv = mat->insertmode;
670 
671   /* do not use 'b = (Mat_SeqAIJ*)aij->B->data' as B can be reset in disassembly */
672 
673   PetscFunctionBegin;
674   if (!aij->donotstash && !mat->nooffprocentries) {
675     while (1) {
676       ierr = MatStashScatterGetMesg_Private(&mat->stash,&n,&row,&col,&val,&flg);CHKERRQ(ierr);
677       if (!flg) break;
678 
679       for (i=0; i<n; ) {
680         /* Now identify the consecutive vals belonging to the same row */
681         for (j=i,rstart=row[j]; j<n; j++) {
682           if (row[j] != rstart) break;
683         }
684         if (j < n) ncols = j-i;
685         else       ncols = n-i;
686         /* Now assemble all these values with a single function call */
687         ierr = MatSetValues_MPIAIJ(mat,1,row+i,ncols,col+i,val+i,addv);CHKERRQ(ierr);
688 
689         i = j;
690       }
691     }
692     ierr = MatStashScatterEnd_Private(&mat->stash);CHKERRQ(ierr);
693   }
694   ierr = MatAssemblyBegin(aij->A,mode);CHKERRQ(ierr);
695   ierr = MatAssemblyEnd(aij->A,mode);CHKERRQ(ierr);
696 
697   /* determine if any processor has disassembled, if so we must
698      also disassemble ourselfs, in order that we may reassemble. */
699   /*
700      if nonzero structure of submatrix B cannot change then we know that
701      no processor disassembled thus we can skip this stuff
702   */
703   if (!((Mat_SeqAIJ*)aij->B->data)->nonew) {
704     ierr = MPI_Allreduce(&mat->was_assembled,&other_disassembled,1,MPIU_BOOL,MPI_PROD,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
705     if (mat->was_assembled && !other_disassembled) {
706       ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
707     }
708   }
709   if (!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) {
710     ierr = MatSetUpMultiply_MPIAIJ(mat);CHKERRQ(ierr);
711   }
712   ierr = MatSetOption(aij->B,MAT_USE_INODES,PETSC_FALSE);CHKERRQ(ierr);
713   ierr = MatSetOption(aij->B,MAT_CHECK_COMPRESSED_ROW,PETSC_FALSE);CHKERRQ(ierr);
714   ierr = MatAssemblyBegin(aij->B,mode);CHKERRQ(ierr);
715   ierr = MatAssemblyEnd(aij->B,mode);CHKERRQ(ierr);
716 
717   ierr = PetscFree2(aij->rowvalues,aij->rowindices);CHKERRQ(ierr);
718 
719   aij->rowvalues = 0;
720 
721   /* used by MatAXPY() */
722   a->xtoy = 0; ((Mat_SeqAIJ*)aij->B->data)->xtoy = 0;   /* b->xtoy = 0 */
723   a->XtoY = 0; ((Mat_SeqAIJ*)aij->B->data)->XtoY = 0;   /* b->XtoY = 0 */
724 
725   ierr = VecDestroy(&aij->diag);CHKERRQ(ierr);
726   if (a->inode.size) mat->ops->multdiagonalblock = MatMultDiagonalBlock_MPIAIJ;
727   PetscFunctionReturn(0);
728 }
729 
730 #undef __FUNCT__
731 #define __FUNCT__ "MatZeroEntries_MPIAIJ"
732 PetscErrorCode MatZeroEntries_MPIAIJ(Mat A)
733 {
734   Mat_MPIAIJ     *l = (Mat_MPIAIJ*)A->data;
735   PetscErrorCode ierr;
736 
737   PetscFunctionBegin;
738   ierr = MatZeroEntries(l->A);CHKERRQ(ierr);
739   ierr = MatZeroEntries(l->B);CHKERRQ(ierr);
740   PetscFunctionReturn(0);
741 }
742 
743 #undef __FUNCT__
744 #define __FUNCT__ "MatZeroRows_MPIAIJ"
745 PetscErrorCode MatZeroRows_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
746 {
747   Mat_MPIAIJ        *l = (Mat_MPIAIJ*)A->data;
748   PetscErrorCode    ierr;
749   PetscMPIInt       size = l->size,imdex,n,rank = l->rank,tag = ((PetscObject)A)->tag,lastidx = -1;
750   PetscInt          i,*owners = A->rmap->range;
751   PetscInt          *nprocs,j,idx,nsends,row;
752   PetscInt          nmax,*svalues,*starts,*owner,nrecvs;
753   PetscInt          *rvalues,count,base,slen,*source;
754   PetscInt          *lens,*lrows,*values,rstart=A->rmap->rstart;
755   MPI_Comm          comm;
756   MPI_Request       *send_waits,*recv_waits;
757   MPI_Status        recv_status,*send_status;
758   const PetscScalar *xx;
759   PetscScalar       *bb;
760 #if defined(PETSC_DEBUG)
761   PetscBool found = PETSC_FALSE;
762 #endif
763 
764   PetscFunctionBegin;
765   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
766   /*  first count number of contributors to each processor */
767   ierr = PetscMalloc(2*size*sizeof(PetscInt),&nprocs);CHKERRQ(ierr);
768   ierr = PetscMemzero(nprocs,2*size*sizeof(PetscInt));CHKERRQ(ierr);
769   ierr = PetscMalloc((N+1)*sizeof(PetscInt),&owner);CHKERRQ(ierr); /* see note*/
770   j    = 0;
771   for (i=0; i<N; i++) {
772     if (lastidx > (idx = rows[i])) j = 0;
773     lastidx = idx;
774     for (; j<size; j++) {
775       if (idx >= owners[j] && idx < owners[j+1]) {
776         nprocs[2*j]++;
777         nprocs[2*j+1] = 1;
778         owner[i]      = j;
779 #if defined(PETSC_DEBUG)
780         found = PETSC_TRUE;
781 #endif
782         break;
783       }
784     }
785 #if defined(PETSC_DEBUG)
786     if (!found) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Index out of range");
787     found = PETSC_FALSE;
788 #endif
789   }
790   nsends = 0;
791   for (i=0; i<size; i++) nsends += nprocs[2*i+1];
792 
793   if (A->nooffproczerorows) {
794     if (nsends > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"You called MatSetOption(,MAT_NO_OFF_PROC_ZERO_ROWS,PETSC_TRUE) but set an off process zero row");
795     nrecvs = nsends;
796     nmax   = N;
797   } else {
798     /* inform other processors of number of messages and max length*/
799     ierr = PetscMaxSum(comm,nprocs,&nmax,&nrecvs);CHKERRQ(ierr);
800   }
801 
802   /* post receives:   */
803   ierr = PetscMalloc((nrecvs+1)*(nmax+1)*sizeof(PetscInt),&rvalues);CHKERRQ(ierr);
804   ierr = PetscMalloc((nrecvs+1)*sizeof(MPI_Request),&recv_waits);CHKERRQ(ierr);
805   for (i=0; i<nrecvs; i++) {
806     ierr = MPI_Irecv(rvalues+nmax*i,nmax,MPIU_INT,MPI_ANY_SOURCE,tag,comm,recv_waits+i);CHKERRQ(ierr);
807   }
808 
809   /* do sends:
810       1) starts[i] gives the starting index in svalues for stuff going to
811          the ith processor
812   */
813   ierr = PetscMalloc((N+1)*sizeof(PetscInt),&svalues);CHKERRQ(ierr);
814   ierr = PetscMalloc((nsends+1)*sizeof(MPI_Request),&send_waits);CHKERRQ(ierr);
815   ierr = PetscMalloc((size+1)*sizeof(PetscInt),&starts);CHKERRQ(ierr);
816 
817   starts[0] = 0;
818   for (i=1; i<size; i++) starts[i] = starts[i-1] + nprocs[2*i-2];
819   for (i=0; i<N; i++) svalues[starts[owner[i]]++] = rows[i];
820 
821   starts[0] = 0;
822   for (i=1; i<size+1; i++) starts[i] = starts[i-1] + nprocs[2*i-2];
823   count = 0;
824   for (i=0; i<size; i++) {
825     if (nprocs[2*i+1]) {
826       ierr = MPI_Isend(svalues+starts[i],nprocs[2*i],MPIU_INT,i,tag,comm,send_waits+count++);CHKERRQ(ierr);
827     }
828   }
829   ierr = PetscFree(starts);CHKERRQ(ierr);
830 
831   base = owners[rank];
832 
833   /*  wait on receives */
834   ierr  = PetscMalloc2(nrecvs,PetscInt,&lens,nrecvs,PetscInt,&source);CHKERRQ(ierr);
835   count = nrecvs; slen = 0;
836   while (count) {
837     ierr = MPI_Waitany(nrecvs,recv_waits,&imdex,&recv_status);CHKERRQ(ierr);
838     /* unpack receives into our local space */
839     ierr = MPI_Get_count(&recv_status,MPIU_INT,&n);CHKERRQ(ierr);
840 
841     source[imdex] = recv_status.MPI_SOURCE;
842     lens[imdex]   = n;
843     slen         += n;
844     count--;
845   }
846   ierr = PetscFree(recv_waits);CHKERRQ(ierr);
847 
848   /* move the data into the send scatter */
849   ierr  = PetscMalloc((slen+1)*sizeof(PetscInt),&lrows);CHKERRQ(ierr);
850   count = 0;
851   for (i=0; i<nrecvs; i++) {
852     values = rvalues + i*nmax;
853     for (j=0; j<lens[i]; j++) lrows[count++] = values[j] - base;
854   }
855   ierr = PetscFree(rvalues);CHKERRQ(ierr);
856   ierr = PetscFree2(lens,source);CHKERRQ(ierr);
857   ierr = PetscFree(owner);CHKERRQ(ierr);
858   ierr = PetscFree(nprocs);CHKERRQ(ierr);
859 
860   /* fix right hand side if needed */
861   if (x && b) {
862     ierr = VecGetArrayRead(x,&xx);CHKERRQ(ierr);
863     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
864     for (i=0; i<slen; i++) bb[lrows[i]] = diag*xx[lrows[i]];
865     ierr = VecRestoreArrayRead(x,&xx);CHKERRQ(ierr);
866     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
867   }
868   /*
869         Zero the required rows. If the "diagonal block" of the matrix
870      is square and the user wishes to set the diagonal we use separate
871      code so that MatSetValues() is not called for each diagonal allocating
872      new memory, thus calling lots of mallocs and slowing things down.
873 
874   */
875   /* must zero l->B before l->A because the (diag) case below may put values into l->B*/
876   ierr = MatZeroRows(l->B,slen,lrows,0.0,0,0);CHKERRQ(ierr);
877   if ((diag != 0.0) && (l->A->rmap->N == l->A->cmap->N)) {
878     ierr = MatZeroRows(l->A,slen,lrows,diag,0,0);CHKERRQ(ierr);
879   } else if (diag != 0.0) {
880     ierr = MatZeroRows(l->A,slen,lrows,0.0,0,0);CHKERRQ(ierr);
881     if (((Mat_SeqAIJ*)l->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");
882     for (i = 0; i < slen; i++) {
883       row  = lrows[i] + rstart;
884       ierr = MatSetValues(A,1,&row,1,&row,&diag,INSERT_VALUES);CHKERRQ(ierr);
885     }
886     ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
887     ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
888   } else {
889     ierr = MatZeroRows(l->A,slen,lrows,0.0,0,0);CHKERRQ(ierr);
890   }
891   ierr = PetscFree(lrows);CHKERRQ(ierr);
892 
893   /* wait on sends */
894   if (nsends) {
895     ierr = PetscMalloc(nsends*sizeof(MPI_Status),&send_status);CHKERRQ(ierr);
896     ierr = MPI_Waitall(nsends,send_waits,send_status);CHKERRQ(ierr);
897     ierr = PetscFree(send_status);CHKERRQ(ierr);
898   }
899   ierr = PetscFree(send_waits);CHKERRQ(ierr);
900   ierr = PetscFree(svalues);CHKERRQ(ierr);
901   PetscFunctionReturn(0);
902 }
903 
904 #undef __FUNCT__
905 #define __FUNCT__ "MatZeroRowsColumns_MPIAIJ"
906 PetscErrorCode MatZeroRowsColumns_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
907 {
908   Mat_MPIAIJ        *l = (Mat_MPIAIJ*)A->data;
909   PetscErrorCode    ierr;
910   PetscMPIInt       size = l->size,imdex,n,rank = l->rank,tag = ((PetscObject)A)->tag,lastidx = -1;
911   PetscInt          i,*owners = A->rmap->range;
912   PetscInt          *nprocs,j,idx,nsends;
913   PetscInt          nmax,*svalues,*starts,*owner,nrecvs;
914   PetscInt          *rvalues,count,base,slen,*source;
915   PetscInt          *lens,*lrows,*values,m;
916   MPI_Comm          comm;
917   MPI_Request       *send_waits,*recv_waits;
918   MPI_Status        recv_status,*send_status;
919   const PetscScalar *xx;
920   PetscScalar       *bb,*mask;
921   Vec               xmask,lmask;
922   Mat_SeqAIJ        *aij = (Mat_SeqAIJ*)l->B->data;
923   const PetscInt    *aj, *ii,*ridx;
924   PetscScalar       *aa;
925 #if defined(PETSC_DEBUG)
926   PetscBool found = PETSC_FALSE;
927 #endif
928 
929   PetscFunctionBegin;
930   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
931   /*  first count number of contributors to each processor */
932   ierr = PetscMalloc(2*size*sizeof(PetscInt),&nprocs);CHKERRQ(ierr);
933   ierr = PetscMemzero(nprocs,2*size*sizeof(PetscInt));CHKERRQ(ierr);
934   ierr = PetscMalloc((N+1)*sizeof(PetscInt),&owner);CHKERRQ(ierr); /* see note*/
935   j    = 0;
936   for (i=0; i<N; i++) {
937     if (lastidx > (idx = rows[i])) j = 0;
938     lastidx = idx;
939     for (; j<size; j++) {
940       if (idx >= owners[j] && idx < owners[j+1]) {
941         nprocs[2*j]++;
942         nprocs[2*j+1] = 1;
943         owner[i]      = j;
944 #if defined(PETSC_DEBUG)
945         found = PETSC_TRUE;
946 #endif
947         break;
948       }
949     }
950 #if defined(PETSC_DEBUG)
951     if (!found) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Index out of range");
952     found = PETSC_FALSE;
953 #endif
954   }
955   nsends = 0;  for (i=0; i<size; i++) nsends += nprocs[2*i+1];
956 
957   /* inform other processors of number of messages and max length*/
958   ierr = PetscMaxSum(comm,nprocs,&nmax,&nrecvs);CHKERRQ(ierr);
959 
960   /* post receives:   */
961   ierr = PetscMalloc((nrecvs+1)*(nmax+1)*sizeof(PetscInt),&rvalues);CHKERRQ(ierr);
962   ierr = PetscMalloc((nrecvs+1)*sizeof(MPI_Request),&recv_waits);CHKERRQ(ierr);
963   for (i=0; i<nrecvs; i++) {
964     ierr = MPI_Irecv(rvalues+nmax*i,nmax,MPIU_INT,MPI_ANY_SOURCE,tag,comm,recv_waits+i);CHKERRQ(ierr);
965   }
966 
967   /* do sends:
968       1) starts[i] gives the starting index in svalues for stuff going to
969          the ith processor
970   */
971   ierr = PetscMalloc((N+1)*sizeof(PetscInt),&svalues);CHKERRQ(ierr);
972   ierr = PetscMalloc((nsends+1)*sizeof(MPI_Request),&send_waits);CHKERRQ(ierr);
973   ierr = PetscMalloc((size+1)*sizeof(PetscInt),&starts);CHKERRQ(ierr);
974 
975   starts[0] = 0;
976   for (i=1; i<size; i++) starts[i] = starts[i-1] + nprocs[2*i-2];
977   for (i=0; i<N; i++) svalues[starts[owner[i]]++] = rows[i];
978 
979   starts[0] = 0;
980   for (i=1; i<size+1; i++) starts[i] = starts[i-1] + nprocs[2*i-2];
981   count = 0;
982   for (i=0; i<size; i++) {
983     if (nprocs[2*i+1]) {
984       ierr = MPI_Isend(svalues+starts[i],nprocs[2*i],MPIU_INT,i,tag,comm,send_waits+count++);CHKERRQ(ierr);
985     }
986   }
987   ierr = PetscFree(starts);CHKERRQ(ierr);
988 
989   base = owners[rank];
990 
991   /*  wait on receives */
992   ierr  = PetscMalloc2(nrecvs,PetscInt,&lens,nrecvs,PetscInt,&source);CHKERRQ(ierr);
993   count = nrecvs; slen = 0;
994   while (count) {
995     ierr = MPI_Waitany(nrecvs,recv_waits,&imdex,&recv_status);CHKERRQ(ierr);
996     /* unpack receives into our local space */
997     ierr = MPI_Get_count(&recv_status,MPIU_INT,&n);CHKERRQ(ierr);
998 
999     source[imdex] = recv_status.MPI_SOURCE;
1000     lens[imdex]   = n;
1001     slen         += n;
1002     count--;
1003   }
1004   ierr = PetscFree(recv_waits);CHKERRQ(ierr);
1005 
1006   /* move the data into the send scatter */
1007   ierr  = PetscMalloc((slen+1)*sizeof(PetscInt),&lrows);CHKERRQ(ierr);
1008   count = 0;
1009   for (i=0; i<nrecvs; i++) {
1010     values = rvalues + i*nmax;
1011     for (j=0; j<lens[i]; j++) lrows[count++] = values[j] - base;
1012   }
1013   ierr = PetscFree(rvalues);CHKERRQ(ierr);
1014   ierr = PetscFree2(lens,source);CHKERRQ(ierr);
1015   ierr = PetscFree(owner);CHKERRQ(ierr);
1016   ierr = PetscFree(nprocs);CHKERRQ(ierr);
1017   /* lrows are the local rows to be zeroed, slen is the number of local rows */
1018 
1019   /* zero diagonal part of matrix */
1020   ierr = MatZeroRowsColumns(l->A,slen,lrows,diag,x,b);CHKERRQ(ierr);
1021 
1022   /* handle off diagonal part of matrix */
1023   ierr = MatGetVecs(A,&xmask,NULL);CHKERRQ(ierr);
1024   ierr = VecDuplicate(l->lvec,&lmask);CHKERRQ(ierr);
1025   ierr = VecGetArray(xmask,&bb);CHKERRQ(ierr);
1026   for (i=0; i<slen; i++) bb[lrows[i]] = 1;
1027   ierr = VecRestoreArray(xmask,&bb);CHKERRQ(ierr);
1028   ierr = VecScatterBegin(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1029   ierr = VecScatterEnd(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1030   ierr = VecDestroy(&xmask);CHKERRQ(ierr);
1031   if (x) {
1032     ierr = VecScatterBegin(l->Mvctx,x,l->lvec,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1033     ierr = VecScatterEnd(l->Mvctx,x,l->lvec,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1034     ierr = VecGetArrayRead(l->lvec,&xx);CHKERRQ(ierr);
1035     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
1036   }
1037   ierr = VecGetArray(lmask,&mask);CHKERRQ(ierr);
1038 
1039   /* remove zeroed rows of off diagonal matrix */
1040   ii = aij->i;
1041   for (i=0; i<slen; i++) {
1042     ierr = PetscMemzero(aij->a + ii[lrows[i]],(ii[lrows[i]+1] - ii[lrows[i]])*sizeof(PetscScalar));CHKERRQ(ierr);
1043   }
1044 
1045   /* loop over all elements of off process part of matrix zeroing removed columns*/
1046   if (aij->compressedrow.use) {
1047     m    = aij->compressedrow.nrows;
1048     ii   = aij->compressedrow.i;
1049     ridx = aij->compressedrow.rindex;
1050     for (i=0; i<m; i++) {
1051       n  = ii[i+1] - ii[i];
1052       aj = aij->j + ii[i];
1053       aa = aij->a + ii[i];
1054 
1055       for (j=0; j<n; j++) {
1056         if (PetscAbsScalar(mask[*aj])) {
1057           if (b) bb[*ridx] -= *aa*xx[*aj];
1058           *aa = 0.0;
1059         }
1060         aa++;
1061         aj++;
1062       }
1063       ridx++;
1064     }
1065   } else { /* do not use compressed row format */
1066     m = l->B->rmap->n;
1067     for (i=0; i<m; i++) {
1068       n  = ii[i+1] - ii[i];
1069       aj = aij->j + ii[i];
1070       aa = aij->a + ii[i];
1071       for (j=0; j<n; j++) {
1072         if (PetscAbsScalar(mask[*aj])) {
1073           if (b) bb[i] -= *aa*xx[*aj];
1074           *aa = 0.0;
1075         }
1076         aa++;
1077         aj++;
1078       }
1079     }
1080   }
1081   if (x) {
1082     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
1083     ierr = VecRestoreArrayRead(l->lvec,&xx);CHKERRQ(ierr);
1084   }
1085   ierr = VecRestoreArray(lmask,&mask);CHKERRQ(ierr);
1086   ierr = VecDestroy(&lmask);CHKERRQ(ierr);
1087   ierr = PetscFree(lrows);CHKERRQ(ierr);
1088 
1089   /* wait on sends */
1090   if (nsends) {
1091     ierr = PetscMalloc(nsends*sizeof(MPI_Status),&send_status);CHKERRQ(ierr);
1092     ierr = MPI_Waitall(nsends,send_waits,send_status);CHKERRQ(ierr);
1093     ierr = PetscFree(send_status);CHKERRQ(ierr);
1094   }
1095   ierr = PetscFree(send_waits);CHKERRQ(ierr);
1096   ierr = PetscFree(svalues);CHKERRQ(ierr);
1097   PetscFunctionReturn(0);
1098 }
1099 
1100 #undef __FUNCT__
1101 #define __FUNCT__ "MatMult_MPIAIJ"
1102 PetscErrorCode MatMult_MPIAIJ(Mat A,Vec xx,Vec yy)
1103 {
1104   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1105   PetscErrorCode ierr;
1106   PetscInt       nt;
1107 
1108   PetscFunctionBegin;
1109   ierr = VecGetLocalSize(xx,&nt);CHKERRQ(ierr);
1110   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);
1111   ierr = VecScatterBegin(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1112   ierr = (*a->A->ops->mult)(a->A,xx,yy);CHKERRQ(ierr);
1113   ierr = VecScatterEnd(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1114   ierr = (*a->B->ops->multadd)(a->B,a->lvec,yy,yy);CHKERRQ(ierr);
1115   PetscFunctionReturn(0);
1116 }
1117 
1118 #undef __FUNCT__
1119 #define __FUNCT__ "MatMultDiagonalBlock_MPIAIJ"
1120 PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat A,Vec bb,Vec xx)
1121 {
1122   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1123   PetscErrorCode ierr;
1124 
1125   PetscFunctionBegin;
1126   ierr = MatMultDiagonalBlock(a->A,bb,xx);CHKERRQ(ierr);
1127   PetscFunctionReturn(0);
1128 }
1129 
1130 #undef __FUNCT__
1131 #define __FUNCT__ "MatMultAdd_MPIAIJ"
1132 PetscErrorCode MatMultAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1133 {
1134   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1135   PetscErrorCode ierr;
1136 
1137   PetscFunctionBegin;
1138   ierr = VecScatterBegin(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1139   ierr = (*a->A->ops->multadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
1140   ierr = VecScatterEnd(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1141   ierr = (*a->B->ops->multadd)(a->B,a->lvec,zz,zz);CHKERRQ(ierr);
1142   PetscFunctionReturn(0);
1143 }
1144 
1145 #undef __FUNCT__
1146 #define __FUNCT__ "MatMultTranspose_MPIAIJ"
1147 PetscErrorCode MatMultTranspose_MPIAIJ(Mat A,Vec xx,Vec yy)
1148 {
1149   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1150   PetscErrorCode ierr;
1151   PetscBool      merged;
1152 
1153   PetscFunctionBegin;
1154   ierr = VecScatterGetMerged(a->Mvctx,&merged);CHKERRQ(ierr);
1155   /* do nondiagonal part */
1156   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
1157   if (!merged) {
1158     /* send it on its way */
1159     ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1160     /* do local part */
1161     ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
1162     /* receive remote parts: note this assumes the values are not actually */
1163     /* added in yy until the next line, */
1164     ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1165   } else {
1166     /* do local part */
1167     ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
1168     /* send it on its way */
1169     ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1170     /* values actually were received in the Begin() but we need to call this nop */
1171     ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1172   }
1173   PetscFunctionReturn(0);
1174 }
1175 
1176 #undef __FUNCT__
1177 #define __FUNCT__ "MatIsTranspose_MPIAIJ"
1178 PetscErrorCode  MatIsTranspose_MPIAIJ(Mat Amat,Mat Bmat,PetscReal tol,PetscBool  *f)
1179 {
1180   MPI_Comm       comm;
1181   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ*) Amat->data, *Bij;
1182   Mat            Adia = Aij->A, Bdia, Aoff,Boff,*Aoffs,*Boffs;
1183   IS             Me,Notme;
1184   PetscErrorCode ierr;
1185   PetscInt       M,N,first,last,*notme,i;
1186   PetscMPIInt    size;
1187 
1188   PetscFunctionBegin;
1189   /* Easy test: symmetric diagonal block */
1190   Bij  = (Mat_MPIAIJ*) Bmat->data; Bdia = Bij->A;
1191   ierr = MatIsTranspose(Adia,Bdia,tol,f);CHKERRQ(ierr);
1192   if (!*f) PetscFunctionReturn(0);
1193   ierr = PetscObjectGetComm((PetscObject)Amat,&comm);CHKERRQ(ierr);
1194   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1195   if (size == 1) PetscFunctionReturn(0);
1196 
1197   /* Hard test: off-diagonal block. This takes a MatGetSubMatrix. */
1198   ierr = MatGetSize(Amat,&M,&N);CHKERRQ(ierr);
1199   ierr = MatGetOwnershipRange(Amat,&first,&last);CHKERRQ(ierr);
1200   ierr = PetscMalloc((N-last+first)*sizeof(PetscInt),&notme);CHKERRQ(ierr);
1201   for (i=0; i<first; i++) notme[i] = i;
1202   for (i=last; i<M; i++) notme[i-last+first] = i;
1203   ierr = ISCreateGeneral(MPI_COMM_SELF,N-last+first,notme,PETSC_COPY_VALUES,&Notme);CHKERRQ(ierr);
1204   ierr = ISCreateStride(MPI_COMM_SELF,last-first,first,1,&Me);CHKERRQ(ierr);
1205   ierr = MatGetSubMatrices(Amat,1,&Me,&Notme,MAT_INITIAL_MATRIX,&Aoffs);CHKERRQ(ierr);
1206   Aoff = Aoffs[0];
1207   ierr = MatGetSubMatrices(Bmat,1,&Notme,&Me,MAT_INITIAL_MATRIX,&Boffs);CHKERRQ(ierr);
1208   Boff = Boffs[0];
1209   ierr = MatIsTranspose(Aoff,Boff,tol,f);CHKERRQ(ierr);
1210   ierr = MatDestroyMatrices(1,&Aoffs);CHKERRQ(ierr);
1211   ierr = MatDestroyMatrices(1,&Boffs);CHKERRQ(ierr);
1212   ierr = ISDestroy(&Me);CHKERRQ(ierr);
1213   ierr = ISDestroy(&Notme);CHKERRQ(ierr);
1214   ierr = PetscFree(notme);CHKERRQ(ierr);
1215   PetscFunctionReturn(0);
1216 }
1217 
1218 #undef __FUNCT__
1219 #define __FUNCT__ "MatMultTransposeAdd_MPIAIJ"
1220 PetscErrorCode MatMultTransposeAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1221 {
1222   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1223   PetscErrorCode ierr;
1224 
1225   PetscFunctionBegin;
1226   /* do nondiagonal part */
1227   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
1228   /* send it on its way */
1229   ierr = VecScatterBegin(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1230   /* do local part */
1231   ierr = (*a->A->ops->multtransposeadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
1232   /* receive remote parts */
1233   ierr = VecScatterEnd(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1234   PetscFunctionReturn(0);
1235 }
1236 
1237 /*
1238   This only works correctly for square matrices where the subblock A->A is the
1239    diagonal block
1240 */
1241 #undef __FUNCT__
1242 #define __FUNCT__ "MatGetDiagonal_MPIAIJ"
1243 PetscErrorCode MatGetDiagonal_MPIAIJ(Mat A,Vec v)
1244 {
1245   PetscErrorCode ierr;
1246   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1247 
1248   PetscFunctionBegin;
1249   if (A->rmap->N != A->cmap->N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Supports only square matrix where A->A is diag block");
1250   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");
1251   ierr = MatGetDiagonal(a->A,v);CHKERRQ(ierr);
1252   PetscFunctionReturn(0);
1253 }
1254 
1255 #undef __FUNCT__
1256 #define __FUNCT__ "MatScale_MPIAIJ"
1257 PetscErrorCode MatScale_MPIAIJ(Mat A,PetscScalar aa)
1258 {
1259   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1260   PetscErrorCode ierr;
1261 
1262   PetscFunctionBegin;
1263   ierr = MatScale(a->A,aa);CHKERRQ(ierr);
1264   ierr = MatScale(a->B,aa);CHKERRQ(ierr);
1265   PetscFunctionReturn(0);
1266 }
1267 
1268 #undef __FUNCT__
1269 #define __FUNCT__ "MatDestroy_MPIAIJ"
1270 PetscErrorCode MatDestroy_MPIAIJ(Mat mat)
1271 {
1272   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1273   PetscErrorCode ierr;
1274 
1275   PetscFunctionBegin;
1276 #if defined(PETSC_USE_LOG)
1277   PetscLogObjectState((PetscObject)mat,"Rows=%D, Cols=%D",mat->rmap->N,mat->cmap->N);
1278 #endif
1279   ierr = MatStashDestroy_Private(&mat->stash);CHKERRQ(ierr);
1280   ierr = VecDestroy(&aij->diag);CHKERRQ(ierr);
1281   ierr = MatDestroy(&aij->A);CHKERRQ(ierr);
1282   ierr = MatDestroy(&aij->B);CHKERRQ(ierr);
1283 #if defined(PETSC_USE_CTABLE)
1284   ierr = PetscTableDestroy(&aij->colmap);CHKERRQ(ierr);
1285 #else
1286   ierr = PetscFree(aij->colmap);CHKERRQ(ierr);
1287 #endif
1288   ierr = PetscFree(aij->garray);CHKERRQ(ierr);
1289   ierr = VecDestroy(&aij->lvec);CHKERRQ(ierr);
1290   ierr = VecScatterDestroy(&aij->Mvctx);CHKERRQ(ierr);
1291   ierr = PetscFree2(aij->rowvalues,aij->rowindices);CHKERRQ(ierr);
1292   ierr = PetscFree(aij->ld);CHKERRQ(ierr);
1293   ierr = PetscFree(mat->data);CHKERRQ(ierr);
1294 
1295   ierr = PetscObjectChangeTypeName((PetscObject)mat,0);CHKERRQ(ierr);
1296   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatStoreValues_C",NULL);CHKERRQ(ierr);
1297   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatRetrieveValues_C",NULL);CHKERRQ(ierr);
1298   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatGetDiagonalBlock_C",NULL);CHKERRQ(ierr);
1299   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatIsTranspose_C",NULL);CHKERRQ(ierr);
1300   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocation_C",NULL);CHKERRQ(ierr);
1301   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocationCSR_C",NULL);CHKERRQ(ierr);
1302   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDiagonalScaleLocal_C",NULL);CHKERRQ(ierr);
1303   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_mpisbaij_C",NULL);CHKERRQ(ierr);
1304   PetscFunctionReturn(0);
1305 }
1306 
1307 #undef __FUNCT__
1308 #define __FUNCT__ "MatView_MPIAIJ_Binary"
1309 PetscErrorCode MatView_MPIAIJ_Binary(Mat mat,PetscViewer viewer)
1310 {
1311   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1312   Mat_SeqAIJ     *A   = (Mat_SeqAIJ*)aij->A->data;
1313   Mat_SeqAIJ     *B   = (Mat_SeqAIJ*)aij->B->data;
1314   PetscErrorCode ierr;
1315   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
1316   int            fd;
1317   PetscInt       nz,header[4],*row_lengths,*range=0,rlen,i;
1318   PetscInt       nzmax,*column_indices,j,k,col,*garray = aij->garray,cnt,cstart = mat->cmap->rstart,rnz;
1319   PetscScalar    *column_values;
1320   PetscInt       message_count,flowcontrolcount;
1321   FILE           *file;
1322 
1323   PetscFunctionBegin;
1324   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
1325   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);CHKERRQ(ierr);
1326   nz   = A->nz + B->nz;
1327   if (!rank) {
1328     header[0] = MAT_FILE_CLASSID;
1329     header[1] = mat->rmap->N;
1330     header[2] = mat->cmap->N;
1331 
1332     ierr = MPI_Reduce(&nz,&header[3],1,MPIU_INT,MPI_SUM,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1333     ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
1334     ierr = PetscBinaryWrite(fd,header,4,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1335     /* get largest number of rows any processor has */
1336     rlen  = mat->rmap->n;
1337     range = mat->rmap->range;
1338     for (i=1; i<size; i++) rlen = PetscMax(rlen,range[i+1] - range[i]);
1339   } else {
1340     ierr = MPI_Reduce(&nz,0,1,MPIU_INT,MPI_SUM,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1341     rlen = mat->rmap->n;
1342   }
1343 
1344   /* load up the local row counts */
1345   ierr = PetscMalloc((rlen+1)*sizeof(PetscInt),&row_lengths);CHKERRQ(ierr);
1346   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];
1347 
1348   /* store the row lengths to the file */
1349   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1350   if (!rank) {
1351     ierr = PetscBinaryWrite(fd,row_lengths,mat->rmap->n,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1352     for (i=1; i<size; i++) {
1353       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1354       rlen = range[i+1] - range[i];
1355       ierr = MPIULong_Recv(row_lengths,rlen,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1356       ierr = PetscBinaryWrite(fd,row_lengths,rlen,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1357     }
1358     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1359   } else {
1360     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1361     ierr = MPIULong_Send(row_lengths,mat->rmap->n,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1362     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1363   }
1364   ierr = PetscFree(row_lengths);CHKERRQ(ierr);
1365 
1366   /* load up the local column indices */
1367   nzmax = nz; /* th processor needs space a largest processor needs */
1368   ierr  = MPI_Reduce(&nz,&nzmax,1,MPIU_INT,MPI_MAX,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1369   ierr  = PetscMalloc((nzmax+1)*sizeof(PetscInt),&column_indices);CHKERRQ(ierr);
1370   cnt   = 0;
1371   for (i=0; i<mat->rmap->n; i++) {
1372     for (j=B->i[i]; j<B->i[i+1]; j++) {
1373       if ((col = garray[B->j[j]]) > cstart) break;
1374       column_indices[cnt++] = col;
1375     }
1376     for (k=A->i[i]; k<A->i[i+1]; k++) column_indices[cnt++] = A->j[k] + cstart;
1377     for (; j<B->i[i+1]; j++) column_indices[cnt++] = garray[B->j[j]];
1378   }
1379   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);
1380 
1381   /* store the column indices to the file */
1382   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1383   if (!rank) {
1384     MPI_Status status;
1385     ierr = PetscBinaryWrite(fd,column_indices,nz,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1386     for (i=1; i<size; i++) {
1387       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1388       ierr = MPI_Recv(&rnz,1,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat),&status);CHKERRQ(ierr);
1389       if (rnz > nzmax) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: nz = %D nzmax = %D",nz,nzmax);
1390       ierr = MPIULong_Recv(column_indices,rnz,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1391       ierr = PetscBinaryWrite(fd,column_indices,rnz,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1392     }
1393     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1394   } else {
1395     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1396     ierr = MPI_Send(&nz,1,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1397     ierr = MPIULong_Send(column_indices,nz,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1398     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1399   }
1400   ierr = PetscFree(column_indices);CHKERRQ(ierr);
1401 
1402   /* load up the local column values */
1403   ierr = PetscMalloc((nzmax+1)*sizeof(PetscScalar),&column_values);CHKERRQ(ierr);
1404   cnt  = 0;
1405   for (i=0; i<mat->rmap->n; i++) {
1406     for (j=B->i[i]; j<B->i[i+1]; j++) {
1407       if (garray[B->j[j]] > cstart) break;
1408       column_values[cnt++] = B->a[j];
1409     }
1410     for (k=A->i[i]; k<A->i[i+1]; k++) column_values[cnt++] = A->a[k];
1411     for (; j<B->i[i+1]; j++) column_values[cnt++] = B->a[j];
1412   }
1413   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);
1414 
1415   /* store the column values to the file */
1416   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1417   if (!rank) {
1418     MPI_Status status;
1419     ierr = PetscBinaryWrite(fd,column_values,nz,PETSC_SCALAR,PETSC_TRUE);CHKERRQ(ierr);
1420     for (i=1; i<size; i++) {
1421       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1422       ierr = MPI_Recv(&rnz,1,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat),&status);CHKERRQ(ierr);
1423       if (rnz > nzmax) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: nz = %D nzmax = %D",nz,nzmax);
1424       ierr = MPIULong_Recv(column_values,rnz,MPIU_SCALAR,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1425       ierr = PetscBinaryWrite(fd,column_values,rnz,PETSC_SCALAR,PETSC_TRUE);CHKERRQ(ierr);
1426     }
1427     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1428   } else {
1429     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1430     ierr = MPI_Send(&nz,1,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1431     ierr = MPIULong_Send(column_values,nz,MPIU_SCALAR,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1432     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1433   }
1434   ierr = PetscFree(column_values);CHKERRQ(ierr);
1435 
1436   ierr = PetscViewerBinaryGetInfoPointer(viewer,&file);CHKERRQ(ierr);
1437   if (file) fprintf(file,"-matload_block_size %d\n",(int)mat->rmap->bs);
1438   PetscFunctionReturn(0);
1439 }
1440 
1441 #include <petscdraw.h>
1442 #undef __FUNCT__
1443 #define __FUNCT__ "MatView_MPIAIJ_ASCIIorDraworSocket"
1444 PetscErrorCode MatView_MPIAIJ_ASCIIorDraworSocket(Mat mat,PetscViewer viewer)
1445 {
1446   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)mat->data;
1447   PetscErrorCode    ierr;
1448   PetscMPIInt       rank = aij->rank,size = aij->size;
1449   PetscBool         isdraw,iascii,isbinary;
1450   PetscViewer       sviewer;
1451   PetscViewerFormat format;
1452 
1453   PetscFunctionBegin;
1454   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1455   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1456   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1457   if (iascii) {
1458     ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
1459     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
1460       MatInfo   info;
1461       PetscBool inodes;
1462 
1463       ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
1464       ierr = MatGetInfo(mat,MAT_LOCAL,&info);CHKERRQ(ierr);
1465       ierr = MatInodeGetInodeSizes(aij->A,NULL,(PetscInt**)&inodes,NULL);CHKERRQ(ierr);
1466       ierr = PetscViewerASCIISynchronizedAllow(viewer,PETSC_TRUE);CHKERRQ(ierr);
1467       if (!inodes) {
1468         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %D nz %D nz alloced %D mem %D, not using I-node routines\n",
1469                                                   rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
1470       } else {
1471         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %D nz %D nz alloced %D mem %D, using I-node routines\n",
1472                                                   rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
1473       }
1474       ierr = MatGetInfo(aij->A,MAT_LOCAL,&info);CHKERRQ(ierr);
1475       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] on-diagonal part: nz %D \n",rank,(PetscInt)info.nz_used);CHKERRQ(ierr);
1476       ierr = MatGetInfo(aij->B,MAT_LOCAL,&info);CHKERRQ(ierr);
1477       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] off-diagonal part: nz %D \n",rank,(PetscInt)info.nz_used);CHKERRQ(ierr);
1478       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1479       ierr = PetscViewerASCIISynchronizedAllow(viewer,PETSC_FALSE);CHKERRQ(ierr);
1480       ierr = PetscViewerASCIIPrintf(viewer,"Information on VecScatter used in matrix-vector product: \n");CHKERRQ(ierr);
1481       ierr = VecScatterView(aij->Mvctx,viewer);CHKERRQ(ierr);
1482       PetscFunctionReturn(0);
1483     } else if (format == PETSC_VIEWER_ASCII_INFO) {
1484       PetscInt inodecount,inodelimit,*inodes;
1485       ierr = MatInodeGetInodeSizes(aij->A,&inodecount,&inodes,&inodelimit);CHKERRQ(ierr);
1486       if (inodes) {
1487         ierr = PetscViewerASCIIPrintf(viewer,"using I-node (on process 0) routines: found %D nodes, limit used is %D\n",inodecount,inodelimit);CHKERRQ(ierr);
1488       } else {
1489         ierr = PetscViewerASCIIPrintf(viewer,"not using I-node (on process 0) routines\n");CHKERRQ(ierr);
1490       }
1491       PetscFunctionReturn(0);
1492     } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO) {
1493       PetscFunctionReturn(0);
1494     }
1495   } else if (isbinary) {
1496     if (size == 1) {
1497       ierr = PetscObjectSetName((PetscObject)aij->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1498       ierr = MatView(aij->A,viewer);CHKERRQ(ierr);
1499     } else {
1500       ierr = MatView_MPIAIJ_Binary(mat,viewer);CHKERRQ(ierr);
1501     }
1502     PetscFunctionReturn(0);
1503   } else if (isdraw) {
1504     PetscDraw draw;
1505     PetscBool isnull;
1506     ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
1507     ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr); if (isnull) PetscFunctionReturn(0);
1508   }
1509 
1510   if (size == 1) {
1511     ierr = PetscObjectSetName((PetscObject)aij->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1512     ierr = MatView(aij->A,viewer);CHKERRQ(ierr);
1513   } else {
1514     /* assemble the entire matrix onto first processor. */
1515     Mat        A;
1516     Mat_SeqAIJ *Aloc;
1517     PetscInt   M = mat->rmap->N,N = mat->cmap->N,m,*ai,*aj,row,*cols,i,*ct;
1518     MatScalar  *a;
1519 
1520     if (mat->rmap->N > 1024) {
1521       PetscBool flg = PETSC_FALSE;
1522 
1523       ierr = PetscOptionsGetBool(((PetscObject) mat)->prefix, "-mat_ascii_output_large", &flg,NULL);CHKERRQ(ierr);
1524       if (!flg) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_OUTOFRANGE,"ASCII matrix output not allowed for matrices with more than 1024 rows, use binary format instead.\nYou can override this restriction using -mat_ascii_output_large.");
1525     }
1526 
1527     ierr = MatCreate(PetscObjectComm((PetscObject)mat),&A);CHKERRQ(ierr);
1528     if (!rank) {
1529       ierr = MatSetSizes(A,M,N,M,N);CHKERRQ(ierr);
1530     } else {
1531       ierr = MatSetSizes(A,0,0,M,N);CHKERRQ(ierr);
1532     }
1533     /* This is just a temporary matrix, so explicitly using MATMPIAIJ is probably best */
1534     ierr = MatSetType(A,MATMPIAIJ);CHKERRQ(ierr);
1535     ierr = MatMPIAIJSetPreallocation(A,0,NULL,0,NULL);CHKERRQ(ierr);
1536     ierr = MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
1537     ierr = PetscLogObjectParent((PetscObject)mat,(PetscObject)A);CHKERRQ(ierr);
1538 
1539     /* copy over the A part */
1540     Aloc = (Mat_SeqAIJ*)aij->A->data;
1541     m    = aij->A->rmap->n; ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
1542     row  = mat->rmap->rstart;
1543     for (i=0; i<ai[m]; i++) aj[i] += mat->cmap->rstart;
1544     for (i=0; i<m; i++) {
1545       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],aj,a,INSERT_VALUES);CHKERRQ(ierr);
1546       row++;
1547       a += ai[i+1]-ai[i]; aj += ai[i+1]-ai[i];
1548     }
1549     aj = Aloc->j;
1550     for (i=0; i<ai[m]; i++) aj[i] -= mat->cmap->rstart;
1551 
1552     /* copy over the B part */
1553     Aloc = (Mat_SeqAIJ*)aij->B->data;
1554     m    = aij->B->rmap->n;  ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
1555     row  = mat->rmap->rstart;
1556     ierr = PetscMalloc((ai[m]+1)*sizeof(PetscInt),&cols);CHKERRQ(ierr);
1557     ct   = cols;
1558     for (i=0; i<ai[m]; i++) cols[i] = aij->garray[aj[i]];
1559     for (i=0; i<m; i++) {
1560       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],cols,a,INSERT_VALUES);CHKERRQ(ierr);
1561       row++;
1562       a += ai[i+1]-ai[i]; cols += ai[i+1]-ai[i];
1563     }
1564     ierr = PetscFree(ct);CHKERRQ(ierr);
1565     ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1566     ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1567     /*
1568        Everyone has to call to draw the matrix since the graphics waits are
1569        synchronized across all processors that share the PetscDraw object
1570     */
1571     ierr = PetscViewerGetSingleton(viewer,&sviewer);CHKERRQ(ierr);
1572     if (!rank) {
1573       ierr = PetscObjectSetName((PetscObject)((Mat_MPIAIJ*)(A->data))->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1574       /* Set the type name to MATMPIAIJ so that the correct type can be printed out by PetscObjectPrintClassNamePrefixType() in MatView_SeqAIJ_ASCII()*/
1575       PetscStrcpy(((PetscObject)((Mat_MPIAIJ*)(A->data))->A)->type_name,MATMPIAIJ);
1576       ierr = MatView(((Mat_MPIAIJ*)(A->data))->A,sviewer);CHKERRQ(ierr);
1577     }
1578     ierr = PetscViewerRestoreSingleton(viewer,&sviewer);CHKERRQ(ierr);
1579     ierr = MatDestroy(&A);CHKERRQ(ierr);
1580   }
1581   PetscFunctionReturn(0);
1582 }
1583 
1584 #undef __FUNCT__
1585 #define __FUNCT__ "MatView_MPIAIJ"
1586 PetscErrorCode MatView_MPIAIJ(Mat mat,PetscViewer viewer)
1587 {
1588   PetscErrorCode ierr;
1589   PetscBool      iascii,isdraw,issocket,isbinary;
1590 
1591   PetscFunctionBegin;
1592   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1593   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1594   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1595   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSOCKET,&issocket);CHKERRQ(ierr);
1596   if (iascii || isdraw || isbinary || issocket) {
1597     ierr = MatView_MPIAIJ_ASCIIorDraworSocket(mat,viewer);CHKERRQ(ierr);
1598   }
1599   PetscFunctionReturn(0);
1600 }
1601 
1602 #undef __FUNCT__
1603 #define __FUNCT__ "MatSOR_MPIAIJ"
1604 PetscErrorCode MatSOR_MPIAIJ(Mat matin,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
1605 {
1606   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1607   PetscErrorCode ierr;
1608   Vec            bb1 = 0;
1609   PetscBool      hasop;
1610 
1611   PetscFunctionBegin;
1612   if (flag == SOR_APPLY_UPPER) {
1613     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1614     PetscFunctionReturn(0);
1615   }
1616 
1617   if (its > 1 || ~flag & SOR_ZERO_INITIAL_GUESS || flag & SOR_EISENSTAT) {
1618     ierr = VecDuplicate(bb,&bb1);CHKERRQ(ierr);
1619   }
1620 
1621   if ((flag & SOR_LOCAL_SYMMETRIC_SWEEP) == SOR_LOCAL_SYMMETRIC_SWEEP) {
1622     if (flag & SOR_ZERO_INITIAL_GUESS) {
1623       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1624       its--;
1625     }
1626 
1627     while (its--) {
1628       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1629       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1630 
1631       /* update rhs: bb1 = bb - B*x */
1632       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1633       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1634 
1635       /* local sweep */
1636       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_SYMMETRIC_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1637     }
1638   } else if (flag & SOR_LOCAL_FORWARD_SWEEP) {
1639     if (flag & SOR_ZERO_INITIAL_GUESS) {
1640       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1641       its--;
1642     }
1643     while (its--) {
1644       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1645       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1646 
1647       /* update rhs: bb1 = bb - B*x */
1648       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1649       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1650 
1651       /* local sweep */
1652       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_FORWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1653     }
1654   } else if (flag & SOR_LOCAL_BACKWARD_SWEEP) {
1655     if (flag & SOR_ZERO_INITIAL_GUESS) {
1656       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1657       its--;
1658     }
1659     while (its--) {
1660       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1661       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1662 
1663       /* update rhs: bb1 = bb - B*x */
1664       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1665       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1666 
1667       /* local sweep */
1668       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_BACKWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1669     }
1670   } else if (flag & SOR_EISENSTAT) {
1671     Vec xx1;
1672 
1673     ierr = VecDuplicate(bb,&xx1);CHKERRQ(ierr);
1674     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_BACKWARD_SWEEP),fshift,lits,1,xx);CHKERRQ(ierr);
1675 
1676     ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1677     ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1678     if (!mat->diag) {
1679       ierr = MatGetVecs(matin,&mat->diag,NULL);CHKERRQ(ierr);
1680       ierr = MatGetDiagonal(matin,mat->diag);CHKERRQ(ierr);
1681     }
1682     ierr = MatHasOperation(matin,MATOP_MULT_DIAGONAL_BLOCK,&hasop);CHKERRQ(ierr);
1683     if (hasop) {
1684       ierr = MatMultDiagonalBlock(matin,xx,bb1);CHKERRQ(ierr);
1685     } else {
1686       ierr = VecPointwiseMult(bb1,mat->diag,xx);CHKERRQ(ierr);
1687     }
1688     ierr = VecAYPX(bb1,(omega-2.0)/omega,bb);CHKERRQ(ierr);
1689 
1690     ierr = MatMultAdd(mat->B,mat->lvec,bb1,bb1);CHKERRQ(ierr);
1691 
1692     /* local sweep */
1693     ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_FORWARD_SWEEP),fshift,lits,1,xx1);CHKERRQ(ierr);
1694     ierr = VecAXPY(xx,1.0,xx1);CHKERRQ(ierr);
1695     ierr = VecDestroy(&xx1);CHKERRQ(ierr);
1696   } else SETERRQ(PetscObjectComm((PetscObject)matin),PETSC_ERR_SUP,"Parallel SOR not supported");
1697 
1698   ierr = VecDestroy(&bb1);CHKERRQ(ierr);
1699   PetscFunctionReturn(0);
1700 }
1701 
1702 #undef __FUNCT__
1703 #define __FUNCT__ "MatPermute_MPIAIJ"
1704 PetscErrorCode MatPermute_MPIAIJ(Mat A,IS rowp,IS colp,Mat *B)
1705 {
1706   Mat            aA,aB,Aperm;
1707   const PetscInt *rwant,*cwant,*gcols,*ai,*bi,*aj,*bj;
1708   PetscScalar    *aa,*ba;
1709   PetscInt       i,j,m,n,ng,anz,bnz,*dnnz,*onnz,*tdnnz,*tonnz,*rdest,*cdest,*work,*gcdest;
1710   PetscSF        rowsf,sf;
1711   IS             parcolp = NULL;
1712   PetscBool      done;
1713   PetscErrorCode ierr;
1714 
1715   PetscFunctionBegin;
1716   ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
1717   ierr = ISGetIndices(rowp,&rwant);CHKERRQ(ierr);
1718   ierr = ISGetIndices(colp,&cwant);CHKERRQ(ierr);
1719   ierr = PetscMalloc3(PetscMax(m,n),PetscInt,&work,m,PetscInt,&rdest,n,PetscInt,&cdest);CHKERRQ(ierr);
1720 
1721   /* Invert row permutation to find out where my rows should go */
1722   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&rowsf);CHKERRQ(ierr);
1723   ierr = PetscSFSetGraphLayout(rowsf,A->rmap,A->rmap->n,NULL,PETSC_OWN_POINTER,rwant);CHKERRQ(ierr);
1724   ierr = PetscSFSetFromOptions(rowsf);CHKERRQ(ierr);
1725   for (i=0; i<m; i++) work[i] = A->rmap->rstart + i;
1726   ierr = PetscSFReduceBegin(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1727   ierr = PetscSFReduceEnd(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1728 
1729   /* Invert column permutation to find out where my columns should go */
1730   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1731   ierr = PetscSFSetGraphLayout(sf,A->cmap,A->cmap->n,NULL,PETSC_OWN_POINTER,cwant);CHKERRQ(ierr);
1732   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1733   for (i=0; i<n; i++) work[i] = A->cmap->rstart + i;
1734   ierr = PetscSFReduceBegin(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1735   ierr = PetscSFReduceEnd(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1736   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1737 
1738   ierr = ISRestoreIndices(rowp,&rwant);CHKERRQ(ierr);
1739   ierr = ISRestoreIndices(colp,&cwant);CHKERRQ(ierr);
1740   ierr = MatMPIAIJGetSeqAIJ(A,&aA,&aB,&gcols);CHKERRQ(ierr);
1741 
1742   /* Find out where my gcols should go */
1743   ierr = MatGetSize(aB,NULL,&ng);CHKERRQ(ierr);
1744   ierr = PetscMalloc(ng*sizeof(PetscInt),&gcdest);CHKERRQ(ierr);
1745   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1746   ierr = PetscSFSetGraphLayout(sf,A->cmap,ng,NULL,PETSC_OWN_POINTER,gcols);CHKERRQ(ierr);
1747   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1748   ierr = PetscSFBcastBegin(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1749   ierr = PetscSFBcastEnd(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1750   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1751 
1752   ierr = PetscMalloc4(m,PetscInt,&dnnz,m,PetscInt,&onnz,m,PetscInt,&tdnnz,m,PetscInt,&tonnz);CHKERRQ(ierr);
1753   ierr = PetscMemzero(dnnz,m*sizeof(PetscInt));CHKERRQ(ierr);
1754   ierr = PetscMemzero(onnz,m*sizeof(PetscInt));CHKERRQ(ierr);
1755   ierr = MatGetRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1756   ierr = MatGetRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1757   for (i=0; i<m; i++) {
1758     PetscInt row = rdest[i],rowner;
1759     ierr = PetscLayoutFindOwner(A->rmap,row,&rowner);CHKERRQ(ierr);
1760     for (j=ai[i]; j<ai[i+1]; j++) {
1761       PetscInt cowner,col = cdest[aj[j]];
1762       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr); /* Could build an index for the columns to eliminate this search */
1763       if (rowner == cowner) dnnz[i]++;
1764       else onnz[i]++;
1765     }
1766     for (j=bi[i]; j<bi[i+1]; j++) {
1767       PetscInt cowner,col = gcdest[bj[j]];
1768       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr);
1769       if (rowner == cowner) dnnz[i]++;
1770       else onnz[i]++;
1771     }
1772   }
1773   ierr = PetscMemzero(tdnnz,m*sizeof(PetscInt));CHKERRQ(ierr);
1774   ierr = PetscMemzero(tonnz,m*sizeof(PetscInt));CHKERRQ(ierr);
1775   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1776   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1777   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1778   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1779   ierr = PetscSFDestroy(&rowsf);CHKERRQ(ierr);
1780 
1781   ierr = MatCreateAIJ(PetscObjectComm((PetscObject)A),A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N,0,tdnnz,0,tonnz,&Aperm);CHKERRQ(ierr);
1782   ierr = MatSeqAIJGetArray(aA,&aa);CHKERRQ(ierr);
1783   ierr = MatSeqAIJGetArray(aB,&ba);CHKERRQ(ierr);
1784   for (i=0; i<m; i++) {
1785     PetscInt *acols = dnnz,*bcols = onnz; /* Repurpose now-unneeded arrays */
1786     PetscInt rowlen;
1787     rowlen = ai[i+1] - ai[i];
1788     for (j=0; j<rowlen; j++) acols[j] = cdest[aj[ai[i]+j]];
1789     ierr   = MatSetValues(Aperm,1,&rdest[i],rowlen,acols,aa+ai[i],INSERT_VALUES);CHKERRQ(ierr);
1790     rowlen = bi[i+1] - bi[i];
1791     for (j=0; j<rowlen; j++) bcols[j] = gcdest[bj[bi[i]+j]];
1792     ierr = MatSetValues(Aperm,1,&rdest[i],rowlen,bcols,ba+bi[i],INSERT_VALUES);CHKERRQ(ierr);
1793   }
1794   ierr = MatAssemblyBegin(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1795   ierr = MatAssemblyEnd(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1796   ierr = MatRestoreRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1797   ierr = MatRestoreRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1798   ierr = MatSeqAIJRestoreArray(aA,&aa);CHKERRQ(ierr);
1799   ierr = MatSeqAIJRestoreArray(aB,&ba);CHKERRQ(ierr);
1800   ierr = PetscFree4(dnnz,onnz,tdnnz,tonnz);CHKERRQ(ierr);
1801   ierr = PetscFree3(work,rdest,cdest);CHKERRQ(ierr);
1802   ierr = PetscFree(gcdest);CHKERRQ(ierr);
1803   if (parcolp) {ierr = ISDestroy(&colp);CHKERRQ(ierr);}
1804   *B = Aperm;
1805   PetscFunctionReturn(0);
1806 }
1807 
1808 #undef __FUNCT__
1809 #define __FUNCT__ "MatGetInfo_MPIAIJ"
1810 PetscErrorCode MatGetInfo_MPIAIJ(Mat matin,MatInfoType flag,MatInfo *info)
1811 {
1812   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1813   Mat            A    = mat->A,B = mat->B;
1814   PetscErrorCode ierr;
1815   PetscReal      isend[5],irecv[5];
1816 
1817   PetscFunctionBegin;
1818   info->block_size = 1.0;
1819   ierr             = MatGetInfo(A,MAT_LOCAL,info);CHKERRQ(ierr);
1820 
1821   isend[0] = info->nz_used; isend[1] = info->nz_allocated; isend[2] = info->nz_unneeded;
1822   isend[3] = info->memory;  isend[4] = info->mallocs;
1823 
1824   ierr = MatGetInfo(B,MAT_LOCAL,info);CHKERRQ(ierr);
1825 
1826   isend[0] += info->nz_used; isend[1] += info->nz_allocated; isend[2] += info->nz_unneeded;
1827   isend[3] += info->memory;  isend[4] += info->mallocs;
1828   if (flag == MAT_LOCAL) {
1829     info->nz_used      = isend[0];
1830     info->nz_allocated = isend[1];
1831     info->nz_unneeded  = isend[2];
1832     info->memory       = isend[3];
1833     info->mallocs      = isend[4];
1834   } else if (flag == MAT_GLOBAL_MAX) {
1835     ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1836 
1837     info->nz_used      = irecv[0];
1838     info->nz_allocated = irecv[1];
1839     info->nz_unneeded  = irecv[2];
1840     info->memory       = irecv[3];
1841     info->mallocs      = irecv[4];
1842   } else if (flag == MAT_GLOBAL_SUM) {
1843     ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1844 
1845     info->nz_used      = irecv[0];
1846     info->nz_allocated = irecv[1];
1847     info->nz_unneeded  = irecv[2];
1848     info->memory       = irecv[3];
1849     info->mallocs      = irecv[4];
1850   }
1851   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
1852   info->fill_ratio_needed = 0;
1853   info->factor_mallocs    = 0;
1854   PetscFunctionReturn(0);
1855 }
1856 
1857 #undef __FUNCT__
1858 #define __FUNCT__ "MatSetOption_MPIAIJ"
1859 PetscErrorCode MatSetOption_MPIAIJ(Mat A,MatOption op,PetscBool flg)
1860 {
1861   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1862   PetscErrorCode ierr;
1863 
1864   PetscFunctionBegin;
1865   switch (op) {
1866   case MAT_NEW_NONZERO_LOCATIONS:
1867   case MAT_NEW_NONZERO_ALLOCATION_ERR:
1868   case MAT_UNUSED_NONZERO_LOCATION_ERR:
1869   case MAT_KEEP_NONZERO_PATTERN:
1870   case MAT_NEW_NONZERO_LOCATION_ERR:
1871   case MAT_USE_INODES:
1872   case MAT_IGNORE_ZERO_ENTRIES:
1873     MatCheckPreallocated(A,1);
1874     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1875     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1876     break;
1877   case MAT_ROW_ORIENTED:
1878     a->roworiented = flg;
1879 
1880     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1881     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1882     break;
1883   case MAT_NEW_DIAGONALS:
1884     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
1885     break;
1886   case MAT_IGNORE_OFF_PROC_ENTRIES:
1887     a->donotstash = flg;
1888     break;
1889   case MAT_SPD:
1890     A->spd_set = PETSC_TRUE;
1891     A->spd     = flg;
1892     if (flg) {
1893       A->symmetric                  = PETSC_TRUE;
1894       A->structurally_symmetric     = PETSC_TRUE;
1895       A->symmetric_set              = PETSC_TRUE;
1896       A->structurally_symmetric_set = PETSC_TRUE;
1897     }
1898     break;
1899   case MAT_SYMMETRIC:
1900     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1901     break;
1902   case MAT_STRUCTURALLY_SYMMETRIC:
1903     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1904     break;
1905   case MAT_HERMITIAN:
1906     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1907     break;
1908   case MAT_SYMMETRY_ETERNAL:
1909     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1910     break;
1911   default:
1912     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %d",op);
1913   }
1914   PetscFunctionReturn(0);
1915 }
1916 
1917 #undef __FUNCT__
1918 #define __FUNCT__ "MatGetRow_MPIAIJ"
1919 PetscErrorCode MatGetRow_MPIAIJ(Mat matin,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1920 {
1921   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1922   PetscScalar    *vworkA,*vworkB,**pvA,**pvB,*v_p;
1923   PetscErrorCode ierr;
1924   PetscInt       i,*cworkA,*cworkB,**pcA,**pcB,cstart = matin->cmap->rstart;
1925   PetscInt       nztot,nzA,nzB,lrow,rstart = matin->rmap->rstart,rend = matin->rmap->rend;
1926   PetscInt       *cmap,*idx_p;
1927 
1928   PetscFunctionBegin;
1929   if (mat->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Already active");
1930   mat->getrowactive = PETSC_TRUE;
1931 
1932   if (!mat->rowvalues && (idx || v)) {
1933     /*
1934         allocate enough space to hold information from the longest row.
1935     */
1936     Mat_SeqAIJ *Aa = (Mat_SeqAIJ*)mat->A->data,*Ba = (Mat_SeqAIJ*)mat->B->data;
1937     PetscInt   max = 1,tmp;
1938     for (i=0; i<matin->rmap->n; i++) {
1939       tmp = Aa->i[i+1] - Aa->i[i] + Ba->i[i+1] - Ba->i[i];
1940       if (max < tmp) max = tmp;
1941     }
1942     ierr = PetscMalloc2(max,PetscScalar,&mat->rowvalues,max,PetscInt,&mat->rowindices);CHKERRQ(ierr);
1943   }
1944 
1945   if (row < rstart || row >= rend) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Only local rows");
1946   lrow = row - rstart;
1947 
1948   pvA = &vworkA; pcA = &cworkA; pvB = &vworkB; pcB = &cworkB;
1949   if (!v)   {pvA = 0; pvB = 0;}
1950   if (!idx) {pcA = 0; if (!v) pcB = 0;}
1951   ierr  = (*mat->A->ops->getrow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1952   ierr  = (*mat->B->ops->getrow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1953   nztot = nzA + nzB;
1954 
1955   cmap = mat->garray;
1956   if (v  || idx) {
1957     if (nztot) {
1958       /* Sort by increasing column numbers, assuming A and B already sorted */
1959       PetscInt imark = -1;
1960       if (v) {
1961         *v = v_p = mat->rowvalues;
1962         for (i=0; i<nzB; i++) {
1963           if (cmap[cworkB[i]] < cstart) v_p[i] = vworkB[i];
1964           else break;
1965         }
1966         imark = i;
1967         for (i=0; i<nzA; i++)     v_p[imark+i] = vworkA[i];
1968         for (i=imark; i<nzB; i++) v_p[nzA+i]   = vworkB[i];
1969       }
1970       if (idx) {
1971         *idx = idx_p = mat->rowindices;
1972         if (imark > -1) {
1973           for (i=0; i<imark; i++) {
1974             idx_p[i] = cmap[cworkB[i]];
1975           }
1976         } else {
1977           for (i=0; i<nzB; i++) {
1978             if (cmap[cworkB[i]] < cstart) idx_p[i] = cmap[cworkB[i]];
1979             else break;
1980           }
1981           imark = i;
1982         }
1983         for (i=0; i<nzA; i++)     idx_p[imark+i] = cstart + cworkA[i];
1984         for (i=imark; i<nzB; i++) idx_p[nzA+i]   = cmap[cworkB[i]];
1985       }
1986     } else {
1987       if (idx) *idx = 0;
1988       if (v)   *v   = 0;
1989     }
1990   }
1991   *nz  = nztot;
1992   ierr = (*mat->A->ops->restorerow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1993   ierr = (*mat->B->ops->restorerow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1994   PetscFunctionReturn(0);
1995 }
1996 
1997 #undef __FUNCT__
1998 #define __FUNCT__ "MatRestoreRow_MPIAIJ"
1999 PetscErrorCode MatRestoreRow_MPIAIJ(Mat mat,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
2000 {
2001   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
2002 
2003   PetscFunctionBegin;
2004   if (!aij->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"MatGetRow() must be called first");
2005   aij->getrowactive = PETSC_FALSE;
2006   PetscFunctionReturn(0);
2007 }
2008 
2009 #undef __FUNCT__
2010 #define __FUNCT__ "MatNorm_MPIAIJ"
2011 PetscErrorCode MatNorm_MPIAIJ(Mat mat,NormType type,PetscReal *norm)
2012 {
2013   Mat_MPIAIJ     *aij  = (Mat_MPIAIJ*)mat->data;
2014   Mat_SeqAIJ     *amat = (Mat_SeqAIJ*)aij->A->data,*bmat = (Mat_SeqAIJ*)aij->B->data;
2015   PetscErrorCode ierr;
2016   PetscInt       i,j,cstart = mat->cmap->rstart;
2017   PetscReal      sum = 0.0;
2018   MatScalar      *v;
2019 
2020   PetscFunctionBegin;
2021   if (aij->size == 1) {
2022     ierr =  MatNorm(aij->A,type,norm);CHKERRQ(ierr);
2023   } else {
2024     if (type == NORM_FROBENIUS) {
2025       v = amat->a;
2026       for (i=0; i<amat->nz; i++) {
2027         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
2028       }
2029       v = bmat->a;
2030       for (i=0; i<bmat->nz; i++) {
2031         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
2032       }
2033       ierr  = MPI_Allreduce(&sum,norm,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
2034       *norm = PetscSqrtReal(*norm);
2035     } else if (type == NORM_1) { /* max column norm */
2036       PetscReal *tmp,*tmp2;
2037       PetscInt  *jj,*garray = aij->garray;
2038       ierr  = PetscMalloc((mat->cmap->N+1)*sizeof(PetscReal),&tmp);CHKERRQ(ierr);
2039       ierr  = PetscMalloc((mat->cmap->N+1)*sizeof(PetscReal),&tmp2);CHKERRQ(ierr);
2040       ierr  = PetscMemzero(tmp,mat->cmap->N*sizeof(PetscReal));CHKERRQ(ierr);
2041       *norm = 0.0;
2042       v     = amat->a; jj = amat->j;
2043       for (j=0; j<amat->nz; j++) {
2044         tmp[cstart + *jj++] += PetscAbsScalar(*v);  v++;
2045       }
2046       v = bmat->a; jj = bmat->j;
2047       for (j=0; j<bmat->nz; j++) {
2048         tmp[garray[*jj++]] += PetscAbsScalar(*v); v++;
2049       }
2050       ierr = MPI_Allreduce(tmp,tmp2,mat->cmap->N,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
2051       for (j=0; j<mat->cmap->N; j++) {
2052         if (tmp2[j] > *norm) *norm = tmp2[j];
2053       }
2054       ierr = PetscFree(tmp);CHKERRQ(ierr);
2055       ierr = PetscFree(tmp2);CHKERRQ(ierr);
2056     } else if (type == NORM_INFINITY) { /* max row norm */
2057       PetscReal ntemp = 0.0;
2058       for (j=0; j<aij->A->rmap->n; j++) {
2059         v   = amat->a + amat->i[j];
2060         sum = 0.0;
2061         for (i=0; i<amat->i[j+1]-amat->i[j]; i++) {
2062           sum += PetscAbsScalar(*v); v++;
2063         }
2064         v = bmat->a + bmat->i[j];
2065         for (i=0; i<bmat->i[j+1]-bmat->i[j]; i++) {
2066           sum += PetscAbsScalar(*v); v++;
2067         }
2068         if (sum > ntemp) ntemp = sum;
2069       }
2070       ierr = MPI_Allreduce(&ntemp,norm,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
2071     } else SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"No support for two norm");
2072   }
2073   PetscFunctionReturn(0);
2074 }
2075 
2076 #undef __FUNCT__
2077 #define __FUNCT__ "MatTranspose_MPIAIJ"
2078 PetscErrorCode MatTranspose_MPIAIJ(Mat A,MatReuse reuse,Mat *matout)
2079 {
2080   Mat_MPIAIJ     *a   = (Mat_MPIAIJ*)A->data;
2081   Mat_SeqAIJ     *Aloc=(Mat_SeqAIJ*)a->A->data,*Bloc=(Mat_SeqAIJ*)a->B->data;
2082   PetscErrorCode ierr;
2083   PetscInt       M      = A->rmap->N,N = A->cmap->N,ma,na,mb,nb,*ai,*aj,*bi,*bj,row,*cols,*cols_tmp,i;
2084   PetscInt       cstart = A->cmap->rstart,ncol;
2085   Mat            B;
2086   MatScalar      *array;
2087 
2088   PetscFunctionBegin;
2089   if (reuse == MAT_REUSE_MATRIX && A == *matout && M != N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Square matrix only for in-place");
2090 
2091   ma = A->rmap->n; na = A->cmap->n; mb = a->B->rmap->n; nb = a->B->cmap->n;
2092   ai = Aloc->i; aj = Aloc->j;
2093   bi = Bloc->i; bj = Bloc->j;
2094   if (reuse == MAT_INITIAL_MATRIX || *matout == A) {
2095     PetscInt             *d_nnz,*g_nnz,*o_nnz;
2096     PetscSFNode          *oloc;
2097     PETSC_UNUSED PetscSF sf;
2098 
2099     ierr = PetscMalloc4(na,PetscInt,&d_nnz,na,PetscInt,&o_nnz,nb,PetscInt,&g_nnz,nb,PetscSFNode,&oloc);CHKERRQ(ierr);
2100     /* compute d_nnz for preallocation */
2101     ierr = PetscMemzero(d_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
2102     for (i=0; i<ai[ma]; i++) {
2103       d_nnz[aj[i]]++;
2104       aj[i] += cstart; /* global col index to be used by MatSetValues() */
2105     }
2106     /* compute local off-diagonal contributions */
2107     ierr = PetscMemzero(g_nnz,nb*sizeof(PetscInt));CHKERRQ(ierr);
2108     for (i=0; i<bi[ma]; i++) g_nnz[bj[i]]++;
2109     /* map those to global */
2110     ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
2111     ierr = PetscSFSetGraphLayout(sf,A->cmap,nb,NULL,PETSC_USE_POINTER,a->garray);CHKERRQ(ierr);
2112     ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
2113     ierr = PetscMemzero(o_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
2114     ierr = PetscSFReduceBegin(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
2115     ierr = PetscSFReduceEnd(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
2116     ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
2117 
2118     ierr = MatCreate(PetscObjectComm((PetscObject)A),&B);CHKERRQ(ierr);
2119     ierr = MatSetSizes(B,A->cmap->n,A->rmap->n,N,M);CHKERRQ(ierr);
2120     ierr = MatSetBlockSizes(B,A->cmap->bs,A->rmap->bs);CHKERRQ(ierr);
2121     ierr = MatSetType(B,((PetscObject)A)->type_name);CHKERRQ(ierr);
2122     ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
2123     ierr = PetscFree4(d_nnz,o_nnz,g_nnz,oloc);CHKERRQ(ierr);
2124   } else {
2125     B    = *matout;
2126     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
2127     for (i=0; i<ai[ma]; i++) aj[i] += cstart; /* global col index to be used by MatSetValues() */
2128   }
2129 
2130   /* copy over the A part */
2131   array = Aloc->a;
2132   row   = A->rmap->rstart;
2133   for (i=0; i<ma; i++) {
2134     ncol = ai[i+1]-ai[i];
2135     ierr = MatSetValues(B,ncol,aj,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
2136     row++;
2137     array += ncol; aj += ncol;
2138   }
2139   aj = Aloc->j;
2140   for (i=0; i<ai[ma]; i++) aj[i] -= cstart; /* resume local col index */
2141 
2142   /* copy over the B part */
2143   ierr  = PetscMalloc(bi[mb]*sizeof(PetscInt),&cols);CHKERRQ(ierr);
2144   ierr  = PetscMemzero(cols,bi[mb]*sizeof(PetscInt));CHKERRQ(ierr);
2145   array = Bloc->a;
2146   row   = A->rmap->rstart;
2147   for (i=0; i<bi[mb]; i++) cols[i] = a->garray[bj[i]];
2148   cols_tmp = cols;
2149   for (i=0; i<mb; i++) {
2150     ncol = bi[i+1]-bi[i];
2151     ierr = MatSetValues(B,ncol,cols_tmp,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
2152     row++;
2153     array += ncol; cols_tmp += ncol;
2154   }
2155   ierr = PetscFree(cols);CHKERRQ(ierr);
2156 
2157   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2158   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2159   if (reuse == MAT_INITIAL_MATRIX || *matout != A) {
2160     *matout = B;
2161   } else {
2162     ierr = MatHeaderMerge(A,B);CHKERRQ(ierr);
2163   }
2164   PetscFunctionReturn(0);
2165 }
2166 
2167 #undef __FUNCT__
2168 #define __FUNCT__ "MatDiagonalScale_MPIAIJ"
2169 PetscErrorCode MatDiagonalScale_MPIAIJ(Mat mat,Vec ll,Vec rr)
2170 {
2171   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2172   Mat            a    = aij->A,b = aij->B;
2173   PetscErrorCode ierr;
2174   PetscInt       s1,s2,s3;
2175 
2176   PetscFunctionBegin;
2177   ierr = MatGetLocalSize(mat,&s2,&s3);CHKERRQ(ierr);
2178   if (rr) {
2179     ierr = VecGetLocalSize(rr,&s1);CHKERRQ(ierr);
2180     if (s1!=s3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"right vector non-conforming local size");
2181     /* Overlap communication with computation. */
2182     ierr = VecScatterBegin(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2183   }
2184   if (ll) {
2185     ierr = VecGetLocalSize(ll,&s1);CHKERRQ(ierr);
2186     if (s1!=s2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"left vector non-conforming local size");
2187     ierr = (*b->ops->diagonalscale)(b,ll,0);CHKERRQ(ierr);
2188   }
2189   /* scale  the diagonal block */
2190   ierr = (*a->ops->diagonalscale)(a,ll,rr);CHKERRQ(ierr);
2191 
2192   if (rr) {
2193     /* Do a scatter end and then right scale the off-diagonal block */
2194     ierr = VecScatterEnd(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2195     ierr = (*b->ops->diagonalscale)(b,0,aij->lvec);CHKERRQ(ierr);
2196   }
2197   PetscFunctionReturn(0);
2198 }
2199 
2200 #undef __FUNCT__
2201 #define __FUNCT__ "MatSetUnfactored_MPIAIJ"
2202 PetscErrorCode MatSetUnfactored_MPIAIJ(Mat A)
2203 {
2204   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2205   PetscErrorCode ierr;
2206 
2207   PetscFunctionBegin;
2208   ierr = MatSetUnfactored(a->A);CHKERRQ(ierr);
2209   PetscFunctionReturn(0);
2210 }
2211 
2212 #undef __FUNCT__
2213 #define __FUNCT__ "MatEqual_MPIAIJ"
2214 PetscErrorCode MatEqual_MPIAIJ(Mat A,Mat B,PetscBool  *flag)
2215 {
2216   Mat_MPIAIJ     *matB = (Mat_MPIAIJ*)B->data,*matA = (Mat_MPIAIJ*)A->data;
2217   Mat            a,b,c,d;
2218   PetscBool      flg;
2219   PetscErrorCode ierr;
2220 
2221   PetscFunctionBegin;
2222   a = matA->A; b = matA->B;
2223   c = matB->A; d = matB->B;
2224 
2225   ierr = MatEqual(a,c,&flg);CHKERRQ(ierr);
2226   if (flg) {
2227     ierr = MatEqual(b,d,&flg);CHKERRQ(ierr);
2228   }
2229   ierr = MPI_Allreduce(&flg,flag,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
2230   PetscFunctionReturn(0);
2231 }
2232 
2233 #undef __FUNCT__
2234 #define __FUNCT__ "MatCopy_MPIAIJ"
2235 PetscErrorCode MatCopy_MPIAIJ(Mat A,Mat B,MatStructure str)
2236 {
2237   PetscErrorCode ierr;
2238   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2239   Mat_MPIAIJ     *b = (Mat_MPIAIJ*)B->data;
2240 
2241   PetscFunctionBegin;
2242   /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
2243   if ((str != SAME_NONZERO_PATTERN) || (A->ops->copy != B->ops->copy)) {
2244     /* because of the column compression in the off-processor part of the matrix a->B,
2245        the number of columns in a->B and b->B may be different, hence we cannot call
2246        the MatCopy() directly on the two parts. If need be, we can provide a more
2247        efficient copy than the MatCopy_Basic() by first uncompressing the a->B matrices
2248        then copying the submatrices */
2249     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
2250   } else {
2251     ierr = MatCopy(a->A,b->A,str);CHKERRQ(ierr);
2252     ierr = MatCopy(a->B,b->B,str);CHKERRQ(ierr);
2253   }
2254   PetscFunctionReturn(0);
2255 }
2256 
2257 #undef __FUNCT__
2258 #define __FUNCT__ "MatSetUp_MPIAIJ"
2259 PetscErrorCode MatSetUp_MPIAIJ(Mat A)
2260 {
2261   PetscErrorCode ierr;
2262 
2263   PetscFunctionBegin;
2264   ierr =  MatMPIAIJSetPreallocation(A,PETSC_DEFAULT,0,PETSC_DEFAULT,0);CHKERRQ(ierr);
2265   PetscFunctionReturn(0);
2266 }
2267 
2268 #undef __FUNCT__
2269 #define __FUNCT__ "MatAXPYGetPreallocation_MPIAIJ"
2270 /* This is the same as MatAXPYGetPreallocation_SeqAIJ, except that the local-to-global map is provided */
2271 static PetscErrorCode MatAXPYGetPreallocation_MPIAIJ(Mat Y,const PetscInt *yltog,Mat X,const PetscInt *xltog,PetscInt *nnz)
2272 {
2273   PetscInt       i,m=Y->rmap->N;
2274   Mat_SeqAIJ     *x  = (Mat_SeqAIJ*)X->data;
2275   Mat_SeqAIJ     *y  = (Mat_SeqAIJ*)Y->data;
2276   const PetscInt *xi = x->i,*yi = y->i;
2277 
2278   PetscFunctionBegin;
2279   /* Set the number of nonzeros in the new matrix */
2280   for (i=0; i<m; i++) {
2281     PetscInt       j,k,nzx = xi[i+1] - xi[i],nzy = yi[i+1] - yi[i];
2282     const PetscInt *xj = x->j+xi[i],*yj = y->j+yi[i];
2283     nnz[i] = 0;
2284     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2285       for (; k<nzy && yltog[yj[k]]<xltog[xj[j]]; k++) nnz[i]++; /* Catch up to X */
2286       if (k<nzy && yltog[yj[k]]==xltog[xj[j]]) k++;             /* Skip duplicate */
2287       nnz[i]++;
2288     }
2289     for (; k<nzy; k++) nnz[i]++;
2290   }
2291   PetscFunctionReturn(0);
2292 }
2293 
2294 #undef __FUNCT__
2295 #define __FUNCT__ "MatAXPY_MPIAIJ"
2296 PetscErrorCode MatAXPY_MPIAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
2297 {
2298   PetscErrorCode ierr;
2299   PetscInt       i;
2300   Mat_MPIAIJ     *xx = (Mat_MPIAIJ*)X->data,*yy = (Mat_MPIAIJ*)Y->data;
2301   PetscBLASInt   bnz,one=1;
2302   Mat_SeqAIJ     *x,*y;
2303 
2304   PetscFunctionBegin;
2305   if (str == SAME_NONZERO_PATTERN) {
2306     PetscScalar alpha = a;
2307     x    = (Mat_SeqAIJ*)xx->A->data;
2308     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2309     y    = (Mat_SeqAIJ*)yy->A->data;
2310     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2311     x    = (Mat_SeqAIJ*)xx->B->data;
2312     y    = (Mat_SeqAIJ*)yy->B->data;
2313     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2314     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2315   } else if (str == SUBSET_NONZERO_PATTERN) {
2316     ierr = MatAXPY_SeqAIJ(yy->A,a,xx->A,str);CHKERRQ(ierr);
2317 
2318     x = (Mat_SeqAIJ*)xx->B->data;
2319     y = (Mat_SeqAIJ*)yy->B->data;
2320     if (y->xtoy && y->XtoY != xx->B) {
2321       ierr = PetscFree(y->xtoy);CHKERRQ(ierr);
2322       ierr = MatDestroy(&y->XtoY);CHKERRQ(ierr);
2323     }
2324     if (!y->xtoy) { /* get xtoy */
2325       ierr    = MatAXPYGetxtoy_Private(xx->B->rmap->n,x->i,x->j,xx->garray,y->i,y->j,yy->garray,&y->xtoy);CHKERRQ(ierr);
2326       y->XtoY = xx->B;
2327       ierr    = PetscObjectReference((PetscObject)xx->B);CHKERRQ(ierr);
2328     }
2329     for (i=0; i<x->nz; i++) y->a[y->xtoy[i]] += a*(x->a[i]);
2330   } else {
2331     Mat      B;
2332     PetscInt *nnz_d,*nnz_o;
2333     ierr = PetscMalloc(yy->A->rmap->N*sizeof(PetscInt),&nnz_d);CHKERRQ(ierr);
2334     ierr = PetscMalloc(yy->B->rmap->N*sizeof(PetscInt),&nnz_o);CHKERRQ(ierr);
2335     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
2336     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
2337     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
2338     ierr = MatSetBlockSizes(B,Y->rmap->bs,Y->cmap->bs);CHKERRQ(ierr);
2339     ierr = MatSetType(B,MATMPIAIJ);CHKERRQ(ierr);
2340     ierr = MatAXPYGetPreallocation_SeqAIJ(yy->A,xx->A,nnz_d);CHKERRQ(ierr);
2341     ierr = MatAXPYGetPreallocation_MPIAIJ(yy->B,yy->garray,xx->B,xx->garray,nnz_o);CHKERRQ(ierr);
2342     ierr = MatMPIAIJSetPreallocation(B,0,nnz_d,0,nnz_o);CHKERRQ(ierr);
2343     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
2344     ierr = MatHeaderReplace(Y,B);CHKERRQ(ierr);
2345     ierr = PetscFree(nnz_d);CHKERRQ(ierr);
2346     ierr = PetscFree(nnz_o);CHKERRQ(ierr);
2347   }
2348   PetscFunctionReturn(0);
2349 }
2350 
2351 extern PetscErrorCode  MatConjugate_SeqAIJ(Mat);
2352 
2353 #undef __FUNCT__
2354 #define __FUNCT__ "MatConjugate_MPIAIJ"
2355 PetscErrorCode  MatConjugate_MPIAIJ(Mat mat)
2356 {
2357 #if defined(PETSC_USE_COMPLEX)
2358   PetscErrorCode ierr;
2359   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2360 
2361   PetscFunctionBegin;
2362   ierr = MatConjugate_SeqAIJ(aij->A);CHKERRQ(ierr);
2363   ierr = MatConjugate_SeqAIJ(aij->B);CHKERRQ(ierr);
2364 #else
2365   PetscFunctionBegin;
2366 #endif
2367   PetscFunctionReturn(0);
2368 }
2369 
2370 #undef __FUNCT__
2371 #define __FUNCT__ "MatRealPart_MPIAIJ"
2372 PetscErrorCode MatRealPart_MPIAIJ(Mat A)
2373 {
2374   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2375   PetscErrorCode ierr;
2376 
2377   PetscFunctionBegin;
2378   ierr = MatRealPart(a->A);CHKERRQ(ierr);
2379   ierr = MatRealPart(a->B);CHKERRQ(ierr);
2380   PetscFunctionReturn(0);
2381 }
2382 
2383 #undef __FUNCT__
2384 #define __FUNCT__ "MatImaginaryPart_MPIAIJ"
2385 PetscErrorCode MatImaginaryPart_MPIAIJ(Mat A)
2386 {
2387   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2388   PetscErrorCode ierr;
2389 
2390   PetscFunctionBegin;
2391   ierr = MatImaginaryPart(a->A);CHKERRQ(ierr);
2392   ierr = MatImaginaryPart(a->B);CHKERRQ(ierr);
2393   PetscFunctionReturn(0);
2394 }
2395 
2396 #if defined(PETSC_HAVE_PBGL)
2397 
2398 #include <boost/parallel/mpi/bsp_process_group.hpp>
2399 #include <boost/graph/distributed/ilu_default_graph.hpp>
2400 #include <boost/graph/distributed/ilu_0_block.hpp>
2401 #include <boost/graph/distributed/ilu_preconditioner.hpp>
2402 #include <boost/graph/distributed/petsc/interface.hpp>
2403 #include <boost/multi_array.hpp>
2404 #include <boost/parallel/distributed_property_map->hpp>
2405 
2406 #undef __FUNCT__
2407 #define __FUNCT__ "MatILUFactorSymbolic_MPIAIJ"
2408 /*
2409   This uses the parallel ILU factorization of Peter Gottschling <pgottsch@osl.iu.edu>
2410 */
2411 PetscErrorCode MatILUFactorSymbolic_MPIAIJ(Mat fact,Mat A, IS isrow, IS iscol, const MatFactorInfo *info)
2412 {
2413   namespace petsc = boost::distributed::petsc;
2414 
2415   namespace graph_dist = boost::graph::distributed;
2416   using boost::graph::distributed::ilu_default::process_group_type;
2417   using boost::graph::ilu_permuted;
2418 
2419   PetscBool      row_identity, col_identity;
2420   PetscContainer c;
2421   PetscInt       m, n, M, N;
2422   PetscErrorCode ierr;
2423 
2424   PetscFunctionBegin;
2425   if (info->levels != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only levels = 0 supported for parallel ilu");
2426   ierr = ISIdentity(isrow, &row_identity);CHKERRQ(ierr);
2427   ierr = ISIdentity(iscol, &col_identity);CHKERRQ(ierr);
2428   if (!row_identity || !col_identity) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Row and column permutations must be identity for parallel ILU");
2429 
2430   process_group_type pg;
2431   typedef graph_dist::ilu_default::ilu_level_graph_type lgraph_type;
2432   lgraph_type  *lgraph_p   = new lgraph_type(petsc::num_global_vertices(A), pg, petsc::matrix_distribution(A, pg));
2433   lgraph_type& level_graph = *lgraph_p;
2434   graph_dist::ilu_default::graph_type&            graph(level_graph.graph);
2435 
2436   petsc::read_matrix(A, graph, get(boost::edge_weight, graph));
2437   ilu_permuted(level_graph);
2438 
2439   /* put together the new matrix */
2440   ierr = MatCreate(PetscObjectComm((PetscObject)A), fact);CHKERRQ(ierr);
2441   ierr = MatGetLocalSize(A, &m, &n);CHKERRQ(ierr);
2442   ierr = MatGetSize(A, &M, &N);CHKERRQ(ierr);
2443   ierr = MatSetSizes(fact, m, n, M, N);CHKERRQ(ierr);
2444   ierr = MatSetBlockSizes(fact,A->rmap->bs,A->cmap->bs);CHKERRQ(ierr);
2445   ierr = MatSetType(fact, ((PetscObject)A)->type_name);CHKERRQ(ierr);
2446   ierr = MatAssemblyBegin(fact, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2447   ierr = MatAssemblyEnd(fact, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2448 
2449   ierr = PetscContainerCreate(PetscObjectComm((PetscObject)A), &c);
2450   ierr = PetscContainerSetPointer(c, lgraph_p);
2451   ierr = PetscObjectCompose((PetscObject) (fact), "graph", (PetscObject) c);
2452   ierr = PetscContainerDestroy(&c);
2453   PetscFunctionReturn(0);
2454 }
2455 
2456 #undef __FUNCT__
2457 #define __FUNCT__ "MatLUFactorNumeric_MPIAIJ"
2458 PetscErrorCode MatLUFactorNumeric_MPIAIJ(Mat B,Mat A, const MatFactorInfo *info)
2459 {
2460   PetscFunctionBegin;
2461   PetscFunctionReturn(0);
2462 }
2463 
2464 #undef __FUNCT__
2465 #define __FUNCT__ "MatSolve_MPIAIJ"
2466 /*
2467   This uses the parallel ILU factorization of Peter Gottschling <pgottsch@osl.iu.edu>
2468 */
2469 PetscErrorCode MatSolve_MPIAIJ(Mat A, Vec b, Vec x)
2470 {
2471   namespace graph_dist = boost::graph::distributed;
2472 
2473   typedef graph_dist::ilu_default::ilu_level_graph_type lgraph_type;
2474   lgraph_type    *lgraph_p;
2475   PetscContainer c;
2476   PetscErrorCode ierr;
2477 
2478   PetscFunctionBegin;
2479   ierr = PetscObjectQuery((PetscObject) A, "graph", (PetscObject*) &c);CHKERRQ(ierr);
2480   ierr = PetscContainerGetPointer(c, (void**) &lgraph_p);CHKERRQ(ierr);
2481   ierr = VecCopy(b, x);CHKERRQ(ierr);
2482 
2483   PetscScalar *array_x;
2484   ierr = VecGetArray(x, &array_x);CHKERRQ(ierr);
2485   PetscInt sx;
2486   ierr = VecGetSize(x, &sx);CHKERRQ(ierr);
2487 
2488   PetscScalar *array_b;
2489   ierr = VecGetArray(b, &array_b);CHKERRQ(ierr);
2490   PetscInt sb;
2491   ierr = VecGetSize(b, &sb);CHKERRQ(ierr);
2492 
2493   lgraph_type& level_graph = *lgraph_p;
2494   graph_dist::ilu_default::graph_type&            graph(level_graph.graph);
2495 
2496   typedef boost::multi_array_ref<PetscScalar, 1> array_ref_type;
2497   array_ref_type                                 ref_b(array_b, boost::extents[num_vertices(graph)]);
2498   array_ref_type                                 ref_x(array_x, boost::extents[num_vertices(graph)]);
2499 
2500   typedef boost::iterator_property_map<array_ref_type::iterator,
2501                                        boost::property_map<graph_dist::ilu_default::graph_type, boost::vertex_index_t>::type>  gvector_type;
2502   gvector_type                                   vector_b(ref_b.begin(), get(boost::vertex_index, graph));
2503   gvector_type                                   vector_x(ref_x.begin(), get(boost::vertex_index, graph));
2504 
2505   ilu_set_solve(*lgraph_p, vector_b, vector_x);
2506   PetscFunctionReturn(0);
2507 }
2508 #endif
2509 
2510 #undef __FUNCT__
2511 #define __FUNCT__ "MatDestroy_MatRedundant"
2512 PetscErrorCode MatDestroy_MatRedundant(Mat A)
2513 {
2514   PetscErrorCode ierr;
2515   Mat_Redundant  *redund;
2516   PetscInt       i;
2517   PetscMPIInt    size;
2518 
2519   PetscFunctionBegin;
2520   ierr = MPI_Comm_size(((PetscObject)A)->comm,&size);CHKERRQ(ierr);
2521   if (size == 1) {
2522     Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2523     redund = a->redundant;
2524   } else {
2525     Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
2526     redund = a->redundant;
2527   }
2528   if (redund){
2529     if (redund->matseq) { /* via MatGetSubMatrices()  */
2530       ierr = ISDestroy(&redund->isrow);CHKERRQ(ierr);
2531       ierr = ISDestroy(&redund->iscol);CHKERRQ(ierr);
2532       ierr = MatDestroy(&redund->matseq[0]);CHKERRQ(ierr);
2533       ierr = PetscFree(redund->matseq);CHKERRQ(ierr);
2534     } else {
2535       ierr = PetscFree2(redund->send_rank,redund->recv_rank);CHKERRQ(ierr);
2536       ierr = PetscFree(redund->sbuf_j);CHKERRQ(ierr);
2537       ierr = PetscFree(redund->sbuf_a);CHKERRQ(ierr);
2538       for (i=0; i<redund->nrecvs; i++) {
2539         ierr = PetscFree(redund->rbuf_j[i]);CHKERRQ(ierr);
2540         ierr = PetscFree(redund->rbuf_a[i]);CHKERRQ(ierr);
2541       }
2542       ierr = PetscFree4(redund->sbuf_nz,redund->rbuf_nz,redund->rbuf_j,redund->rbuf_a);CHKERRQ(ierr);
2543     }
2544 
2545     if (redund->psubcomm) {
2546       ierr = PetscSubcommDestroy(&redund->psubcomm);CHKERRQ(ierr);
2547     }
2548     ierr = redund->Destroy(A);CHKERRQ(ierr);
2549     ierr = PetscFree(redund);CHKERRQ(ierr);
2550   }
2551   PetscFunctionReturn(0);
2552 }
2553 
2554 #undef __FUNCT__
2555 #define __FUNCT__ "MatGetRedundantMatrix_MPIAIJ_interlaced"
2556 PetscErrorCode MatGetRedundantMatrix_MPIAIJ_interlaced(Mat mat,PetscInt nsubcomm,MPI_Comm subcomm,MatReuse reuse,Mat *matredundant)
2557 {
2558   PetscMPIInt    rank,size;
2559   MPI_Comm       comm;
2560   PetscErrorCode ierr;
2561   PetscInt       nsends=0,nrecvs=0,i,rownz_max=0,M=mat->rmap->N,N=mat->cmap->N;
2562   PetscMPIInt    *send_rank= NULL,*recv_rank=NULL,subrank,subsize;
2563   PetscInt       *rowrange = mat->rmap->range;
2564   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2565   Mat            A = aij->A,B=aij->B,C=*matredundant;
2566   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data;
2567   PetscScalar    *sbuf_a;
2568   PetscInt       nzlocal=a->nz+b->nz;
2569   PetscInt       j,cstart=mat->cmap->rstart,cend=mat->cmap->rend,row,nzA,nzB,ncols,*cworkA,*cworkB;
2570   PetscInt       rstart=mat->rmap->rstart,rend=mat->rmap->rend,*bmap=aij->garray;
2571   PetscInt       *cols,ctmp,lwrite,*rptr,l,*sbuf_j;
2572   MatScalar      *aworkA,*aworkB;
2573   PetscScalar    *vals;
2574   PetscMPIInt    tag1,tag2,tag3,imdex;
2575   MPI_Request    *s_waits1=NULL,*s_waits2=NULL,*s_waits3=NULL;
2576   MPI_Request    *r_waits1=NULL,*r_waits2=NULL,*r_waits3=NULL;
2577   MPI_Status     recv_status,*send_status;
2578   PetscInt       *sbuf_nz=NULL,*rbuf_nz=NULL,count;
2579   PetscInt       **rbuf_j=NULL;
2580   PetscScalar    **rbuf_a=NULL;
2581   Mat_Redundant  *redund =NULL;
2582 
2583   PetscFunctionBegin;
2584   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
2585   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2586   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2587   ierr = MPI_Comm_rank(subcomm,&subrank);CHKERRQ(ierr);
2588   ierr = MPI_Comm_size(subcomm,&subsize);CHKERRQ(ierr);
2589 
2590   if (reuse == MAT_REUSE_MATRIX) {
2591     if (M != mat->rmap->N || N != mat->cmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. Wrong global size");
2592     if (subsize == 1) {
2593       Mat_SeqAIJ *c = (Mat_SeqAIJ*)C->data;
2594       redund = c->redundant;
2595     } else {
2596       Mat_MPIAIJ *c = (Mat_MPIAIJ*)C->data;
2597       redund = c->redundant;
2598     }
2599     if (nzlocal != redund->nzlocal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. Wrong nzlocal");
2600 
2601     nsends    = redund->nsends;
2602     nrecvs    = redund->nrecvs;
2603     send_rank = redund->send_rank;
2604     recv_rank = redund->recv_rank;
2605     sbuf_nz   = redund->sbuf_nz;
2606     rbuf_nz   = redund->rbuf_nz;
2607     sbuf_j    = redund->sbuf_j;
2608     sbuf_a    = redund->sbuf_a;
2609     rbuf_j    = redund->rbuf_j;
2610     rbuf_a    = redund->rbuf_a;
2611   }
2612 
2613   if (reuse == MAT_INITIAL_MATRIX) {
2614     PetscInt    nleftover,np_subcomm;
2615 
2616     /* get the destination processors' id send_rank, nsends and nrecvs */
2617     ierr = PetscMalloc2(size,PetscMPIInt,&send_rank,size,PetscMPIInt,&recv_rank);CHKERRQ(ierr);
2618 
2619     np_subcomm = size/nsubcomm;
2620     nleftover  = size - nsubcomm*np_subcomm;
2621 
2622     /* block of codes below is specific for INTERLACED */
2623     /* ------------------------------------------------*/
2624     nsends = 0; nrecvs = 0;
2625     for (i=0; i<size; i++) {
2626       if (subrank == i/nsubcomm && i != rank) { /* my_subrank == other's subrank */
2627         send_rank[nsends++] = i;
2628         recv_rank[nrecvs++] = i;
2629       }
2630     }
2631     if (rank >= size - nleftover) { /* this proc is a leftover processor */
2632       i = size-nleftover-1;
2633       j = 0;
2634       while (j < nsubcomm - nleftover) {
2635         send_rank[nsends++] = i;
2636         i--; j++;
2637       }
2638     }
2639 
2640     if (nleftover && subsize == size/nsubcomm && subrank==subsize-1) { /* this proc recvs from leftover processors */
2641       for (i=0; i<nleftover; i++) {
2642         recv_rank[nrecvs++] = size-nleftover+i;
2643       }
2644     }
2645     /*----------------------------------------------*/
2646 
2647     /* allocate sbuf_j, sbuf_a */
2648     i    = nzlocal + rowrange[rank+1] - rowrange[rank] + 2;
2649     ierr = PetscMalloc(i*sizeof(PetscInt),&sbuf_j);CHKERRQ(ierr);
2650     ierr = PetscMalloc((nzlocal+1)*sizeof(PetscScalar),&sbuf_a);CHKERRQ(ierr);
2651     /*
2652     ierr = PetscSynchronizedPrintf(comm,"[%d] nsends %d, nrecvs %d\n",rank,nsends,nrecvs);CHKERRQ(ierr);
2653     ierr = PetscSynchronizedFlush(comm);CHKERRQ(ierr);
2654      */
2655   } /* endof if (reuse == MAT_INITIAL_MATRIX) */
2656 
2657   /* copy mat's local entries into the buffers */
2658   if (reuse == MAT_INITIAL_MATRIX) {
2659     rownz_max = 0;
2660     rptr      = sbuf_j;
2661     cols      = sbuf_j + rend-rstart + 1;
2662     vals      = sbuf_a;
2663     rptr[0]   = 0;
2664     for (i=0; i<rend-rstart; i++) {
2665       row    = i + rstart;
2666       nzA    = a->i[i+1] - a->i[i]; nzB = b->i[i+1] - b->i[i];
2667       ncols  = nzA + nzB;
2668       cworkA = a->j + a->i[i]; cworkB = b->j + b->i[i];
2669       aworkA = a->a + a->i[i]; aworkB = b->a + b->i[i];
2670       /* load the column indices for this row into cols */
2671       lwrite = 0;
2672       for (l=0; l<nzB; l++) {
2673         if ((ctmp = bmap[cworkB[l]]) < cstart) {
2674           vals[lwrite]   = aworkB[l];
2675           cols[lwrite++] = ctmp;
2676         }
2677       }
2678       for (l=0; l<nzA; l++) {
2679         vals[lwrite]   = aworkA[l];
2680         cols[lwrite++] = cstart + cworkA[l];
2681       }
2682       for (l=0; l<nzB; l++) {
2683         if ((ctmp = bmap[cworkB[l]]) >= cend) {
2684           vals[lwrite]   = aworkB[l];
2685           cols[lwrite++] = ctmp;
2686         }
2687       }
2688       vals     += ncols;
2689       cols     += ncols;
2690       rptr[i+1] = rptr[i] + ncols;
2691       if (rownz_max < ncols) rownz_max = ncols;
2692     }
2693     if (rptr[rend-rstart] != a->nz + b->nz) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_PLIB, "rptr[%d] %d != %d + %d",rend-rstart,rptr[rend-rstart+1],a->nz,b->nz);
2694   } else { /* only copy matrix values into sbuf_a */
2695     rptr    = sbuf_j;
2696     vals    = sbuf_a;
2697     rptr[0] = 0;
2698     for (i=0; i<rend-rstart; i++) {
2699       row    = i + rstart;
2700       nzA    = a->i[i+1] - a->i[i]; nzB = b->i[i+1] - b->i[i];
2701       ncols  = nzA + nzB;
2702       cworkB = b->j + b->i[i];
2703       aworkA = a->a + a->i[i];
2704       aworkB = b->a + b->i[i];
2705       lwrite = 0;
2706       for (l=0; l<nzB; l++) {
2707         if ((ctmp = bmap[cworkB[l]]) < cstart) vals[lwrite++] = aworkB[l];
2708       }
2709       for (l=0; l<nzA; l++) vals[lwrite++] = aworkA[l];
2710       for (l=0; l<nzB; l++) {
2711         if ((ctmp = bmap[cworkB[l]]) >= cend) vals[lwrite++] = aworkB[l];
2712       }
2713       vals     += ncols;
2714       rptr[i+1] = rptr[i] + ncols;
2715     }
2716   } /* endof if (reuse == MAT_INITIAL_MATRIX) */
2717 
2718   /* send nzlocal to others, and recv other's nzlocal */
2719   /*--------------------------------------------------*/
2720   if (reuse == MAT_INITIAL_MATRIX) {
2721     ierr = PetscMalloc2(3*(nsends + nrecvs)+1,MPI_Request,&s_waits3,nsends+1,MPI_Status,&send_status);CHKERRQ(ierr);
2722 
2723     s_waits2 = s_waits3 + nsends;
2724     s_waits1 = s_waits2 + nsends;
2725     r_waits1 = s_waits1 + nsends;
2726     r_waits2 = r_waits1 + nrecvs;
2727     r_waits3 = r_waits2 + nrecvs;
2728   } else {
2729     ierr = PetscMalloc2(nsends + nrecvs +1,MPI_Request,&s_waits3,nsends+1,MPI_Status,&send_status);CHKERRQ(ierr);
2730 
2731     r_waits3 = s_waits3 + nsends;
2732   }
2733 
2734   ierr = PetscObjectGetNewTag((PetscObject)mat,&tag3);CHKERRQ(ierr);
2735   if (reuse == MAT_INITIAL_MATRIX) {
2736     /* get new tags to keep the communication clean */
2737     ierr = PetscObjectGetNewTag((PetscObject)mat,&tag1);CHKERRQ(ierr);
2738     ierr = PetscObjectGetNewTag((PetscObject)mat,&tag2);CHKERRQ(ierr);
2739     ierr = PetscMalloc4(nsends,PetscInt,&sbuf_nz,nrecvs,PetscInt,&rbuf_nz,nrecvs,PetscInt*,&rbuf_j,nrecvs,PetscScalar*,&rbuf_a);CHKERRQ(ierr);
2740 
2741     /* post receives of other's nzlocal */
2742     for (i=0; i<nrecvs; i++) {
2743       ierr = MPI_Irecv(rbuf_nz+i,1,MPIU_INT,MPI_ANY_SOURCE,tag1,comm,r_waits1+i);CHKERRQ(ierr);
2744     }
2745     /* send nzlocal to others */
2746     for (i=0; i<nsends; i++) {
2747       sbuf_nz[i] = nzlocal;
2748       ierr       = MPI_Isend(sbuf_nz+i,1,MPIU_INT,send_rank[i],tag1,comm,s_waits1+i);CHKERRQ(ierr);
2749     }
2750     /* wait on receives of nzlocal; allocate space for rbuf_j, rbuf_a */
2751     count = nrecvs;
2752     while (count) {
2753       ierr = MPI_Waitany(nrecvs,r_waits1,&imdex,&recv_status);CHKERRQ(ierr);
2754 
2755       recv_rank[imdex] = recv_status.MPI_SOURCE;
2756       /* allocate rbuf_a and rbuf_j; then post receives of rbuf_j */
2757       ierr = PetscMalloc((rbuf_nz[imdex]+1)*sizeof(PetscScalar),&rbuf_a[imdex]);CHKERRQ(ierr);
2758 
2759       i = rowrange[recv_status.MPI_SOURCE+1] - rowrange[recv_status.MPI_SOURCE]; /* number of expected mat->i */
2760 
2761       rbuf_nz[imdex] += i + 2;
2762 
2763       ierr = PetscMalloc(rbuf_nz[imdex]*sizeof(PetscInt),&rbuf_j[imdex]);CHKERRQ(ierr);
2764       ierr = MPI_Irecv(rbuf_j[imdex],rbuf_nz[imdex],MPIU_INT,recv_status.MPI_SOURCE,tag2,comm,r_waits2+imdex);CHKERRQ(ierr);
2765       count--;
2766     }
2767     /* wait on sends of nzlocal */
2768     if (nsends) {ierr = MPI_Waitall(nsends,s_waits1,send_status);CHKERRQ(ierr);}
2769     /* send mat->i,j to others, and recv from other's */
2770     /*------------------------------------------------*/
2771     for (i=0; i<nsends; i++) {
2772       j    = nzlocal + rowrange[rank+1] - rowrange[rank] + 1;
2773       ierr = MPI_Isend(sbuf_j,j,MPIU_INT,send_rank[i],tag2,comm,s_waits2+i);CHKERRQ(ierr);
2774     }
2775     /* wait on receives of mat->i,j */
2776     /*------------------------------*/
2777     count = nrecvs;
2778     while (count) {
2779       ierr = MPI_Waitany(nrecvs,r_waits2,&imdex,&recv_status);CHKERRQ(ierr);
2780       if (recv_rank[imdex] != recv_status.MPI_SOURCE) SETERRQ2(PETSC_COMM_SELF,1, "recv_rank %d != MPI_SOURCE %d",recv_rank[imdex],recv_status.MPI_SOURCE);
2781       count--;
2782     }
2783     /* wait on sends of mat->i,j */
2784     /*---------------------------*/
2785     if (nsends) {
2786       ierr = MPI_Waitall(nsends,s_waits2,send_status);CHKERRQ(ierr);
2787     }
2788   } /* endof if (reuse == MAT_INITIAL_MATRIX) */
2789 
2790   /* post receives, send and receive mat->a */
2791   /*----------------------------------------*/
2792   for (imdex=0; imdex<nrecvs; imdex++) {
2793     ierr = MPI_Irecv(rbuf_a[imdex],rbuf_nz[imdex],MPIU_SCALAR,recv_rank[imdex],tag3,comm,r_waits3+imdex);CHKERRQ(ierr);
2794   }
2795   for (i=0; i<nsends; i++) {
2796     ierr = MPI_Isend(sbuf_a,nzlocal,MPIU_SCALAR,send_rank[i],tag3,comm,s_waits3+i);CHKERRQ(ierr);
2797   }
2798   count = nrecvs;
2799   while (count) {
2800     ierr = MPI_Waitany(nrecvs,r_waits3,&imdex,&recv_status);CHKERRQ(ierr);
2801     if (recv_rank[imdex] != recv_status.MPI_SOURCE) SETERRQ2(PETSC_COMM_SELF,1, "recv_rank %d != MPI_SOURCE %d",recv_rank[imdex],recv_status.MPI_SOURCE);
2802     count--;
2803   }
2804   if (nsends) {
2805     ierr = MPI_Waitall(nsends,s_waits3,send_status);CHKERRQ(ierr);
2806   }
2807 
2808   ierr = PetscFree2(s_waits3,send_status);CHKERRQ(ierr);
2809 
2810   /* create redundant matrix */
2811   /*-------------------------*/
2812   if (reuse == MAT_INITIAL_MATRIX) {
2813     const PetscInt *range;
2814     PetscInt       rstart_sub,rend_sub,mloc_sub;
2815 
2816     /* compute rownz_max for preallocation */
2817     for (imdex=0; imdex<nrecvs; imdex++) {
2818       j    = rowrange[recv_rank[imdex]+1] - rowrange[recv_rank[imdex]];
2819       rptr = rbuf_j[imdex];
2820       for (i=0; i<j; i++) {
2821         ncols = rptr[i+1] - rptr[i];
2822         if (rownz_max < ncols) rownz_max = ncols;
2823       }
2824     }
2825 
2826     ierr = MatCreate(subcomm,&C);CHKERRQ(ierr);
2827 
2828     /* get local size of redundant matrix
2829        - mloc_sub is chosen for PETSC_SUBCOMM_INTERLACED, works for other types, but may not efficient! */
2830     ierr = MatGetOwnershipRanges(mat,&range);CHKERRQ(ierr);
2831     rstart_sub = range[nsubcomm*subrank];
2832     if (subrank+1 < subsize) { /* not the last proc in subcomm */
2833       rend_sub = range[nsubcomm*(subrank+1)];
2834     } else {
2835       rend_sub = mat->rmap->N;
2836     }
2837     mloc_sub = rend_sub - rstart_sub;
2838 
2839     if (M == N) {
2840       ierr = MatSetSizes(C,mloc_sub,mloc_sub,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
2841     } else { /* non-square matrix */
2842       ierr = MatSetSizes(C,mloc_sub,PETSC_DECIDE,PETSC_DECIDE,mat->cmap->N);CHKERRQ(ierr);
2843     }
2844     ierr = MatSetBlockSizes(C,mat->rmap->bs,mat->cmap->bs);CHKERRQ(ierr);
2845     ierr = MatSetFromOptions(C);CHKERRQ(ierr);
2846     ierr = MatSeqAIJSetPreallocation(C,rownz_max,NULL);CHKERRQ(ierr);
2847     ierr = MatMPIAIJSetPreallocation(C,rownz_max,NULL,rownz_max,NULL);CHKERRQ(ierr);
2848   } else {
2849     C = *matredundant;
2850   }
2851 
2852   /* insert local matrix entries */
2853   rptr = sbuf_j;
2854   cols = sbuf_j + rend-rstart + 1;
2855   vals = sbuf_a;
2856   for (i=0; i<rend-rstart; i++) {
2857     row   = i + rstart;
2858     ncols = rptr[i+1] - rptr[i];
2859     ierr  = MatSetValues(C,1,&row,ncols,cols,vals,INSERT_VALUES);CHKERRQ(ierr);
2860     vals += ncols;
2861     cols += ncols;
2862   }
2863   /* insert received matrix entries */
2864   for (imdex=0; imdex<nrecvs; imdex++) {
2865     rstart = rowrange[recv_rank[imdex]];
2866     rend   = rowrange[recv_rank[imdex]+1];
2867     /* printf("[%d] insert rows %d - %d\n",rank,rstart,rend-1); */
2868     rptr   = rbuf_j[imdex];
2869     cols   = rbuf_j[imdex] + rend-rstart + 1;
2870     vals   = rbuf_a[imdex];
2871     for (i=0; i<rend-rstart; i++) {
2872       row   = i + rstart;
2873       ncols = rptr[i+1] - rptr[i];
2874       ierr  = MatSetValues(C,1,&row,ncols,cols,vals,INSERT_VALUES);CHKERRQ(ierr);
2875       vals += ncols;
2876       cols += ncols;
2877     }
2878   }
2879   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2880   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2881 
2882   if (reuse == MAT_INITIAL_MATRIX) {
2883     *matredundant = C;
2884 
2885     /* create a supporting struct and attach it to C for reuse */
2886     ierr = PetscNewLog(C,Mat_Redundant,&redund);CHKERRQ(ierr);
2887     if (subsize == 1) {
2888       Mat_SeqAIJ *c = (Mat_SeqAIJ*)C->data;
2889       c->redundant = redund;
2890     } else {
2891       Mat_MPIAIJ *c = (Mat_MPIAIJ*)C->data;
2892       c->redundant = redund;
2893     }
2894 
2895     redund->nzlocal   = nzlocal;
2896     redund->nsends    = nsends;
2897     redund->nrecvs    = nrecvs;
2898     redund->send_rank = send_rank;
2899     redund->recv_rank = recv_rank;
2900     redund->sbuf_nz   = sbuf_nz;
2901     redund->rbuf_nz   = rbuf_nz;
2902     redund->sbuf_j    = sbuf_j;
2903     redund->sbuf_a    = sbuf_a;
2904     redund->rbuf_j    = rbuf_j;
2905     redund->rbuf_a    = rbuf_a;
2906     redund->psubcomm  = NULL;
2907 
2908     redund->Destroy = C->ops->destroy;
2909     C->ops->destroy = MatDestroy_MatRedundant;
2910   }
2911   PetscFunctionReturn(0);
2912 }
2913 
2914 #undef __FUNCT__
2915 #define __FUNCT__ "MatGetRedundantMatrix_MPIAIJ"
2916 PetscErrorCode MatGetRedundantMatrix_MPIAIJ(Mat mat,PetscInt nsubcomm,MPI_Comm subcomm,MatReuse reuse,Mat *matredundant)
2917 {
2918   PetscErrorCode ierr;
2919   MPI_Comm       comm;
2920   PetscMPIInt    size,subsize;
2921   PetscInt       mloc_sub,rstart,rend,M=mat->rmap->N,N=mat->cmap->N;
2922   Mat_Redundant  *redund=NULL;
2923   PetscSubcomm   psubcomm=NULL;
2924   MPI_Comm       subcomm_in=subcomm;
2925   Mat            *matseq;
2926   IS             isrow,iscol;
2927 
2928   PetscFunctionBegin;
2929   if (subcomm_in == MPI_COMM_NULL) { /* user does not provide subcomm */
2930     if (reuse ==  MAT_INITIAL_MATRIX) {
2931       /* create psubcomm, then get subcomm */
2932       ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
2933       ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2934       if (nsubcomm < 1 || nsubcomm > size) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"nsubcomm must between 1 and %D",size);
2935 
2936       ierr = PetscSubcommCreate(comm,&psubcomm);CHKERRQ(ierr);
2937       ierr = PetscSubcommSetNumber(psubcomm,nsubcomm);CHKERRQ(ierr);
2938       ierr = PetscSubcommSetType(psubcomm,PETSC_SUBCOMM_CONTIGUOUS);CHKERRQ(ierr);
2939       ierr = PetscSubcommSetFromOptions(psubcomm);CHKERRQ(ierr);
2940       subcomm = psubcomm->comm;
2941     } else { /* retrieve psubcomm and subcomm */
2942       ierr = PetscObjectGetComm((PetscObject)(*matredundant),&subcomm);CHKERRQ(ierr);
2943       ierr = MPI_Comm_size(subcomm,&subsize);CHKERRQ(ierr);
2944       if (subsize == 1) {
2945         Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*matredundant)->data;
2946         redund = c->redundant;
2947       } else {
2948         Mat_MPIAIJ *c = (Mat_MPIAIJ*)(*matredundant)->data;
2949         redund = c->redundant;
2950       }
2951       psubcomm = redund->psubcomm;
2952     }
2953     if (psubcomm->type == PETSC_SUBCOMM_INTERLACED) {
2954       ierr = MatGetRedundantMatrix_MPIAIJ_interlaced(mat,nsubcomm,subcomm,reuse,matredundant);CHKERRQ(ierr);
2955       if (reuse ==  MAT_INITIAL_MATRIX) { /* psubcomm is created in this routine, free it in MatDestroy_MatRedundant() */
2956         ierr = MPI_Comm_size(psubcomm->comm,&subsize);CHKERRQ(ierr);
2957         if (subsize == 1) {
2958           Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*matredundant)->data;
2959           c->redundant->psubcomm = psubcomm;
2960         } else {
2961           Mat_MPIAIJ *c = (Mat_MPIAIJ*)(*matredundant)->data;
2962           c->redundant->psubcomm = psubcomm ;
2963         }
2964       }
2965       PetscFunctionReturn(0);
2966     }
2967   }
2968 
2969   /* use MPI subcomm via MatGetSubMatrices(); use subcomm_in or psubcomm->comm (psubcomm->type != INTERLACED) */
2970   ierr = MPI_Comm_size(subcomm,&subsize);CHKERRQ(ierr);
2971   if (reuse == MAT_INITIAL_MATRIX) {
2972     /* create a local sequential matrix matseq[0] */
2973     mloc_sub = PETSC_DECIDE;
2974     ierr = PetscSplitOwnership(subcomm,&mloc_sub,&M);CHKERRQ(ierr);
2975     ierr = MPI_Scan(&mloc_sub,&rend,1,MPIU_INT,MPI_SUM,subcomm);CHKERRQ(ierr);
2976     rstart = rend - mloc_sub;
2977     ierr = ISCreateStride(PETSC_COMM_SELF,mloc_sub,rstart,1,&isrow);CHKERRQ(ierr);
2978     ierr = ISCreateStride(PETSC_COMM_SELF,N,0,1,&iscol);CHKERRQ(ierr);
2979   } else { /* reuse == MAT_REUSE_MATRIX */
2980     if (subsize == 1) {
2981       Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*matredundant)->data;
2982       redund = c->redundant;
2983     } else {
2984       Mat_MPIAIJ *c = (Mat_MPIAIJ*)(*matredundant)->data;
2985       redund = c->redundant;
2986     }
2987 
2988     isrow  = redund->isrow;
2989     iscol  = redund->iscol;
2990     matseq = redund->matseq;
2991   }
2992   ierr = MatGetSubMatrices(mat,1,&isrow,&iscol,reuse,&matseq);CHKERRQ(ierr);
2993   ierr = MatCreateMPIAIJConcatenateSeqAIJ(subcomm,matseq[0],PETSC_DECIDE,reuse,matredundant);CHKERRQ(ierr);
2994 
2995   if (reuse == MAT_INITIAL_MATRIX) {
2996     /* create a supporting struct and attach it to C for reuse */
2997     ierr = PetscNewLog(*matredundant,Mat_Redundant,&redund);CHKERRQ(ierr);
2998     if (subsize == 1) {
2999       Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*matredundant)->data;
3000       c->redundant = redund;
3001     } else {
3002       Mat_MPIAIJ *c = (Mat_MPIAIJ*)(*matredundant)->data;
3003       c->redundant = redund;
3004     }
3005     redund->isrow    = isrow;
3006     redund->iscol    = iscol;
3007     redund->matseq   = matseq;
3008     redund->psubcomm = psubcomm;
3009     redund->Destroy               = (*matredundant)->ops->destroy;
3010     (*matredundant)->ops->destroy = MatDestroy_MatRedundant;
3011   }
3012   PetscFunctionReturn(0);
3013 }
3014 
3015 #undef __FUNCT__
3016 #define __FUNCT__ "MatGetRowMaxAbs_MPIAIJ"
3017 PetscErrorCode MatGetRowMaxAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
3018 {
3019   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3020   PetscErrorCode ierr;
3021   PetscInt       i,*idxb = 0;
3022   PetscScalar    *va,*vb;
3023   Vec            vtmp;
3024 
3025   PetscFunctionBegin;
3026   ierr = MatGetRowMaxAbs(a->A,v,idx);CHKERRQ(ierr);
3027   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
3028   if (idx) {
3029     for (i=0; i<A->rmap->n; i++) {
3030       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
3031     }
3032   }
3033 
3034   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
3035   if (idx) {
3036     ierr = PetscMalloc(A->rmap->n*sizeof(PetscInt),&idxb);CHKERRQ(ierr);
3037   }
3038   ierr = MatGetRowMaxAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
3039   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
3040 
3041   for (i=0; i<A->rmap->n; i++) {
3042     if (PetscAbsScalar(va[i]) < PetscAbsScalar(vb[i])) {
3043       va[i] = vb[i];
3044       if (idx) idx[i] = a->garray[idxb[i]];
3045     }
3046   }
3047 
3048   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
3049   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
3050   ierr = PetscFree(idxb);CHKERRQ(ierr);
3051   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
3052   PetscFunctionReturn(0);
3053 }
3054 
3055 #undef __FUNCT__
3056 #define __FUNCT__ "MatGetRowMinAbs_MPIAIJ"
3057 PetscErrorCode MatGetRowMinAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
3058 {
3059   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3060   PetscErrorCode ierr;
3061   PetscInt       i,*idxb = 0;
3062   PetscScalar    *va,*vb;
3063   Vec            vtmp;
3064 
3065   PetscFunctionBegin;
3066   ierr = MatGetRowMinAbs(a->A,v,idx);CHKERRQ(ierr);
3067   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
3068   if (idx) {
3069     for (i=0; i<A->cmap->n; i++) {
3070       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
3071     }
3072   }
3073 
3074   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
3075   if (idx) {
3076     ierr = PetscMalloc(A->rmap->n*sizeof(PetscInt),&idxb);CHKERRQ(ierr);
3077   }
3078   ierr = MatGetRowMinAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
3079   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
3080 
3081   for (i=0; i<A->rmap->n; i++) {
3082     if (PetscAbsScalar(va[i]) > PetscAbsScalar(vb[i])) {
3083       va[i] = vb[i];
3084       if (idx) idx[i] = a->garray[idxb[i]];
3085     }
3086   }
3087 
3088   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
3089   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
3090   ierr = PetscFree(idxb);CHKERRQ(ierr);
3091   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
3092   PetscFunctionReturn(0);
3093 }
3094 
3095 #undef __FUNCT__
3096 #define __FUNCT__ "MatGetRowMin_MPIAIJ"
3097 PetscErrorCode MatGetRowMin_MPIAIJ(Mat A, Vec v, PetscInt idx[])
3098 {
3099   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
3100   PetscInt       n      = A->rmap->n;
3101   PetscInt       cstart = A->cmap->rstart;
3102   PetscInt       *cmap  = mat->garray;
3103   PetscInt       *diagIdx, *offdiagIdx;
3104   Vec            diagV, offdiagV;
3105   PetscScalar    *a, *diagA, *offdiagA;
3106   PetscInt       r;
3107   PetscErrorCode ierr;
3108 
3109   PetscFunctionBegin;
3110   ierr = PetscMalloc2(n,PetscInt,&diagIdx,n,PetscInt,&offdiagIdx);CHKERRQ(ierr);
3111   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &diagV);CHKERRQ(ierr);
3112   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &offdiagV);CHKERRQ(ierr);
3113   ierr = MatGetRowMin(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
3114   ierr = MatGetRowMin(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
3115   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
3116   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
3117   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
3118   for (r = 0; r < n; ++r) {
3119     if (PetscAbsScalar(diagA[r]) <= PetscAbsScalar(offdiagA[r])) {
3120       a[r]   = diagA[r];
3121       idx[r] = cstart + diagIdx[r];
3122     } else {
3123       a[r]   = offdiagA[r];
3124       idx[r] = cmap[offdiagIdx[r]];
3125     }
3126   }
3127   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
3128   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
3129   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
3130   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
3131   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
3132   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
3133   PetscFunctionReturn(0);
3134 }
3135 
3136 #undef __FUNCT__
3137 #define __FUNCT__ "MatGetRowMax_MPIAIJ"
3138 PetscErrorCode MatGetRowMax_MPIAIJ(Mat A, Vec v, PetscInt idx[])
3139 {
3140   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
3141   PetscInt       n      = A->rmap->n;
3142   PetscInt       cstart = A->cmap->rstart;
3143   PetscInt       *cmap  = mat->garray;
3144   PetscInt       *diagIdx, *offdiagIdx;
3145   Vec            diagV, offdiagV;
3146   PetscScalar    *a, *diagA, *offdiagA;
3147   PetscInt       r;
3148   PetscErrorCode ierr;
3149 
3150   PetscFunctionBegin;
3151   ierr = PetscMalloc2(n,PetscInt,&diagIdx,n,PetscInt,&offdiagIdx);CHKERRQ(ierr);
3152   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &diagV);CHKERRQ(ierr);
3153   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &offdiagV);CHKERRQ(ierr);
3154   ierr = MatGetRowMax(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
3155   ierr = MatGetRowMax(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
3156   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
3157   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
3158   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
3159   for (r = 0; r < n; ++r) {
3160     if (PetscAbsScalar(diagA[r]) >= PetscAbsScalar(offdiagA[r])) {
3161       a[r]   = diagA[r];
3162       idx[r] = cstart + diagIdx[r];
3163     } else {
3164       a[r]   = offdiagA[r];
3165       idx[r] = cmap[offdiagIdx[r]];
3166     }
3167   }
3168   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
3169   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
3170   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
3171   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
3172   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
3173   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
3174   PetscFunctionReturn(0);
3175 }
3176 
3177 #undef __FUNCT__
3178 #define __FUNCT__ "MatGetSeqNonzeroStructure_MPIAIJ"
3179 PetscErrorCode MatGetSeqNonzeroStructure_MPIAIJ(Mat mat,Mat *newmat)
3180 {
3181   PetscErrorCode ierr;
3182   Mat            *dummy;
3183 
3184   PetscFunctionBegin;
3185   ierr    = MatGetSubMatrix_MPIAIJ_All(mat,MAT_DO_NOT_GET_VALUES,MAT_INITIAL_MATRIX,&dummy);CHKERRQ(ierr);
3186   *newmat = *dummy;
3187   ierr    = PetscFree(dummy);CHKERRQ(ierr);
3188   PetscFunctionReturn(0);
3189 }
3190 
3191 #undef __FUNCT__
3192 #define __FUNCT__ "MatInvertBlockDiagonal_MPIAIJ"
3193 PetscErrorCode  MatInvertBlockDiagonal_MPIAIJ(Mat A,const PetscScalar **values)
3194 {
3195   Mat_MPIAIJ     *a = (Mat_MPIAIJ*) A->data;
3196   PetscErrorCode ierr;
3197 
3198   PetscFunctionBegin;
3199   ierr = MatInvertBlockDiagonal(a->A,values);CHKERRQ(ierr);
3200   PetscFunctionReturn(0);
3201 }
3202 
3203 #undef __FUNCT__
3204 #define __FUNCT__ "MatSetRandom_MPIAIJ"
3205 static PetscErrorCode  MatSetRandom_MPIAIJ(Mat x,PetscRandom rctx)
3206 {
3207   PetscErrorCode ierr;
3208   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)x->data;
3209 
3210   PetscFunctionBegin;
3211   ierr = MatSetRandom(aij->A,rctx);CHKERRQ(ierr);
3212   ierr = MatSetRandom(aij->B,rctx);CHKERRQ(ierr);
3213   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3214   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3215   PetscFunctionReturn(0);
3216 }
3217 
3218 /* -------------------------------------------------------------------*/
3219 static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
3220                                        MatGetRow_MPIAIJ,
3221                                        MatRestoreRow_MPIAIJ,
3222                                        MatMult_MPIAIJ,
3223                                 /* 4*/ MatMultAdd_MPIAIJ,
3224                                        MatMultTranspose_MPIAIJ,
3225                                        MatMultTransposeAdd_MPIAIJ,
3226 #if defined(PETSC_HAVE_PBGL)
3227                                        MatSolve_MPIAIJ,
3228 #else
3229                                        0,
3230 #endif
3231                                        0,
3232                                        0,
3233                                 /*10*/ 0,
3234                                        0,
3235                                        0,
3236                                        MatSOR_MPIAIJ,
3237                                        MatTranspose_MPIAIJ,
3238                                 /*15*/ MatGetInfo_MPIAIJ,
3239                                        MatEqual_MPIAIJ,
3240                                        MatGetDiagonal_MPIAIJ,
3241                                        MatDiagonalScale_MPIAIJ,
3242                                        MatNorm_MPIAIJ,
3243                                 /*20*/ MatAssemblyBegin_MPIAIJ,
3244                                        MatAssemblyEnd_MPIAIJ,
3245                                        MatSetOption_MPIAIJ,
3246                                        MatZeroEntries_MPIAIJ,
3247                                 /*24*/ MatZeroRows_MPIAIJ,
3248                                        0,
3249 #if defined(PETSC_HAVE_PBGL)
3250                                        0,
3251 #else
3252                                        0,
3253 #endif
3254                                        0,
3255                                        0,
3256                                 /*29*/ MatSetUp_MPIAIJ,
3257 #if defined(PETSC_HAVE_PBGL)
3258                                        0,
3259 #else
3260                                        0,
3261 #endif
3262                                        0,
3263                                        0,
3264                                        0,
3265                                 /*34*/ MatDuplicate_MPIAIJ,
3266                                        0,
3267                                        0,
3268                                        0,
3269                                        0,
3270                                 /*39*/ MatAXPY_MPIAIJ,
3271                                        MatGetSubMatrices_MPIAIJ,
3272                                        MatIncreaseOverlap_MPIAIJ,
3273                                        MatGetValues_MPIAIJ,
3274                                        MatCopy_MPIAIJ,
3275                                 /*44*/ MatGetRowMax_MPIAIJ,
3276                                        MatScale_MPIAIJ,
3277                                        0,
3278                                        0,
3279                                        MatZeroRowsColumns_MPIAIJ,
3280                                 /*49*/ MatSetRandom_MPIAIJ,
3281                                        0,
3282                                        0,
3283                                        0,
3284                                        0,
3285                                 /*54*/ 0,
3286                                        0,
3287                                        MatSetUnfactored_MPIAIJ,
3288                                        MatPermute_MPIAIJ,
3289                                        0,
3290                                 /*59*/ MatGetSubMatrix_MPIAIJ,
3291                                        MatDestroy_MPIAIJ,
3292                                        MatView_MPIAIJ,
3293                                        0,
3294                                        MatMatMatMult_MPIAIJ_MPIAIJ_MPIAIJ,
3295                                 /*64*/ MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ,
3296                                        MatMatMatMultNumeric_MPIAIJ_MPIAIJ_MPIAIJ,
3297                                        0,
3298                                        0,
3299                                        0,
3300                                 /*69*/ MatGetRowMaxAbs_MPIAIJ,
3301                                        MatGetRowMinAbs_MPIAIJ,
3302                                        0,
3303                                        MatSetColoring_MPIAIJ,
3304                                        0,
3305                                        MatSetValuesAdifor_MPIAIJ,
3306                                 /*75*/ MatFDColoringApply_AIJ,
3307                                        0,
3308                                        0,
3309                                        0,
3310                                        MatFindZeroDiagonals_MPIAIJ,
3311                                 /*80*/ 0,
3312                                        0,
3313                                        0,
3314                                 /*83*/ MatLoad_MPIAIJ,
3315                                        0,
3316                                        0,
3317                                        0,
3318                                        0,
3319                                        0,
3320                                 /*89*/ MatMatMult_MPIAIJ_MPIAIJ,
3321                                        MatMatMultSymbolic_MPIAIJ_MPIAIJ,
3322                                        MatMatMultNumeric_MPIAIJ_MPIAIJ,
3323                                        MatPtAP_MPIAIJ_MPIAIJ,
3324                                        MatPtAPSymbolic_MPIAIJ_MPIAIJ,
3325                                 /*94*/ MatPtAPNumeric_MPIAIJ_MPIAIJ,
3326                                        0,
3327                                        0,
3328                                        0,
3329                                        0,
3330                                 /*99*/ 0,
3331                                        0,
3332                                        0,
3333                                        MatConjugate_MPIAIJ,
3334                                        0,
3335                                 /*104*/MatSetValuesRow_MPIAIJ,
3336                                        MatRealPart_MPIAIJ,
3337                                        MatImaginaryPart_MPIAIJ,
3338                                        0,
3339                                        0,
3340                                 /*109*/0,
3341                                        MatGetRedundantMatrix_MPIAIJ,
3342                                        MatGetRowMin_MPIAIJ,
3343                                        0,
3344                                        0,
3345                                 /*114*/MatGetSeqNonzeroStructure_MPIAIJ,
3346                                        0,
3347                                        0,
3348                                        0,
3349                                        0,
3350                                 /*119*/0,
3351                                        0,
3352                                        0,
3353                                        0,
3354                                        MatGetMultiProcBlock_MPIAIJ,
3355                                 /*124*/MatFindNonzeroRows_MPIAIJ,
3356                                        MatGetColumnNorms_MPIAIJ,
3357                                        MatInvertBlockDiagonal_MPIAIJ,
3358                                        0,
3359                                        MatGetSubMatricesParallel_MPIAIJ,
3360                                 /*129*/0,
3361                                        MatTransposeMatMult_MPIAIJ_MPIAIJ,
3362                                        MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ,
3363                                        MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ,
3364                                        0,
3365                                 /*134*/0,
3366                                        0,
3367                                        0,
3368                                        0,
3369                                        0,
3370                                 /*139*/0,
3371                                        0,
3372                                        MatFDColoringSetUp_MPIXAIJ
3373 };
3374 
3375 /* ----------------------------------------------------------------------------------------*/
3376 
3377 #undef __FUNCT__
3378 #define __FUNCT__ "MatStoreValues_MPIAIJ"
3379 PetscErrorCode  MatStoreValues_MPIAIJ(Mat mat)
3380 {
3381   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
3382   PetscErrorCode ierr;
3383 
3384   PetscFunctionBegin;
3385   ierr = MatStoreValues(aij->A);CHKERRQ(ierr);
3386   ierr = MatStoreValues(aij->B);CHKERRQ(ierr);
3387   PetscFunctionReturn(0);
3388 }
3389 
3390 #undef __FUNCT__
3391 #define __FUNCT__ "MatRetrieveValues_MPIAIJ"
3392 PetscErrorCode  MatRetrieveValues_MPIAIJ(Mat mat)
3393 {
3394   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
3395   PetscErrorCode ierr;
3396 
3397   PetscFunctionBegin;
3398   ierr = MatRetrieveValues(aij->A);CHKERRQ(ierr);
3399   ierr = MatRetrieveValues(aij->B);CHKERRQ(ierr);
3400   PetscFunctionReturn(0);
3401 }
3402 
3403 #undef __FUNCT__
3404 #define __FUNCT__ "MatMPIAIJSetPreallocation_MPIAIJ"
3405 PetscErrorCode  MatMPIAIJSetPreallocation_MPIAIJ(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3406 {
3407   Mat_MPIAIJ     *b;
3408   PetscErrorCode ierr;
3409 
3410   PetscFunctionBegin;
3411   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3412   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3413   b = (Mat_MPIAIJ*)B->data;
3414 
3415   if (!B->preallocated) {
3416     /* Explicitly create 2 MATSEQAIJ matrices. */
3417     ierr = MatCreate(PETSC_COMM_SELF,&b->A);CHKERRQ(ierr);
3418     ierr = MatSetSizes(b->A,B->rmap->n,B->cmap->n,B->rmap->n,B->cmap->n);CHKERRQ(ierr);
3419     ierr = MatSetBlockSizes(b->A,B->rmap->bs,B->cmap->bs);CHKERRQ(ierr);
3420     ierr = MatSetType(b->A,MATSEQAIJ);CHKERRQ(ierr);
3421     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->A);CHKERRQ(ierr);
3422     ierr = MatCreate(PETSC_COMM_SELF,&b->B);CHKERRQ(ierr);
3423     ierr = MatSetSizes(b->B,B->rmap->n,B->cmap->N,B->rmap->n,B->cmap->N);CHKERRQ(ierr);
3424     ierr = MatSetBlockSizes(b->B,B->rmap->bs,B->cmap->bs);CHKERRQ(ierr);
3425     ierr = MatSetType(b->B,MATSEQAIJ);CHKERRQ(ierr);
3426     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->B);CHKERRQ(ierr);
3427   }
3428 
3429   ierr = MatSeqAIJSetPreallocation(b->A,d_nz,d_nnz);CHKERRQ(ierr);
3430   ierr = MatSeqAIJSetPreallocation(b->B,o_nz,o_nnz);CHKERRQ(ierr);
3431   B->preallocated = PETSC_TRUE;
3432   PetscFunctionReturn(0);
3433 }
3434 
3435 #undef __FUNCT__
3436 #define __FUNCT__ "MatDuplicate_MPIAIJ"
3437 PetscErrorCode MatDuplicate_MPIAIJ(Mat matin,MatDuplicateOption cpvalues,Mat *newmat)
3438 {
3439   Mat            mat;
3440   Mat_MPIAIJ     *a,*oldmat = (Mat_MPIAIJ*)matin->data;
3441   PetscErrorCode ierr;
3442 
3443   PetscFunctionBegin;
3444   *newmat = 0;
3445   ierr    = MatCreate(PetscObjectComm((PetscObject)matin),&mat);CHKERRQ(ierr);
3446   ierr    = MatSetSizes(mat,matin->rmap->n,matin->cmap->n,matin->rmap->N,matin->cmap->N);CHKERRQ(ierr);
3447   ierr    = MatSetBlockSizes(mat,matin->rmap->bs,matin->cmap->bs);CHKERRQ(ierr);
3448   ierr    = MatSetType(mat,((PetscObject)matin)->type_name);CHKERRQ(ierr);
3449   ierr    = PetscMemcpy(mat->ops,matin->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
3450   a       = (Mat_MPIAIJ*)mat->data;
3451 
3452   mat->factortype   = matin->factortype;
3453   mat->rmap->bs     = matin->rmap->bs;
3454   mat->cmap->bs     = matin->cmap->bs;
3455   mat->assembled    = PETSC_TRUE;
3456   mat->insertmode   = NOT_SET_VALUES;
3457   mat->preallocated = PETSC_TRUE;
3458 
3459   a->size         = oldmat->size;
3460   a->rank         = oldmat->rank;
3461   a->donotstash   = oldmat->donotstash;
3462   a->roworiented  = oldmat->roworiented;
3463   a->rowindices   = 0;
3464   a->rowvalues    = 0;
3465   a->getrowactive = PETSC_FALSE;
3466 
3467   ierr = PetscLayoutReference(matin->rmap,&mat->rmap);CHKERRQ(ierr);
3468   ierr = PetscLayoutReference(matin->cmap,&mat->cmap);CHKERRQ(ierr);
3469 
3470   if (oldmat->colmap) {
3471 #if defined(PETSC_USE_CTABLE)
3472     ierr = PetscTableCreateCopy(oldmat->colmap,&a->colmap);CHKERRQ(ierr);
3473 #else
3474     ierr = PetscMalloc((mat->cmap->N)*sizeof(PetscInt),&a->colmap);CHKERRQ(ierr);
3475     ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
3476     ierr = PetscMemcpy(a->colmap,oldmat->colmap,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
3477 #endif
3478   } else a->colmap = 0;
3479   if (oldmat->garray) {
3480     PetscInt len;
3481     len  = oldmat->B->cmap->n;
3482     ierr = PetscMalloc((len+1)*sizeof(PetscInt),&a->garray);CHKERRQ(ierr);
3483     ierr = PetscLogObjectMemory((PetscObject)mat,len*sizeof(PetscInt));CHKERRQ(ierr);
3484     if (len) { ierr = PetscMemcpy(a->garray,oldmat->garray,len*sizeof(PetscInt));CHKERRQ(ierr); }
3485   } else a->garray = 0;
3486 
3487   ierr    = VecDuplicate(oldmat->lvec,&a->lvec);CHKERRQ(ierr);
3488   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->lvec);CHKERRQ(ierr);
3489   ierr    = VecScatterCopy(oldmat->Mvctx,&a->Mvctx);CHKERRQ(ierr);
3490   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->Mvctx);CHKERRQ(ierr);
3491   ierr    = MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
3492   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->A);CHKERRQ(ierr);
3493   ierr    = MatDuplicate(oldmat->B,cpvalues,&a->B);CHKERRQ(ierr);
3494   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->B);CHKERRQ(ierr);
3495   ierr    = PetscFunctionListDuplicate(((PetscObject)matin)->qlist,&((PetscObject)mat)->qlist);CHKERRQ(ierr);
3496   *newmat = mat;
3497   PetscFunctionReturn(0);
3498 }
3499 
3500 
3501 
3502 #undef __FUNCT__
3503 #define __FUNCT__ "MatLoad_MPIAIJ"
3504 PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
3505 {
3506   PetscScalar    *vals,*svals;
3507   MPI_Comm       comm;
3508   PetscErrorCode ierr;
3509   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
3510   PetscInt       i,nz,j,rstart,rend,mmax,maxnz = 0,grows,gcols;
3511   PetscInt       header[4],*rowlengths = 0,M,N,m,*cols;
3512   PetscInt       *ourlens = NULL,*procsnz = NULL,*offlens = NULL,jj,*mycols,*smycols;
3513   PetscInt       cend,cstart,n,*rowners,sizesset=1;
3514   int            fd;
3515   PetscInt       bs = 1;
3516 
3517   PetscFunctionBegin;
3518   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
3519   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3520   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3521   if (!rank) {
3522     ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
3523     ierr = PetscBinaryRead(fd,(char*)header,4,PETSC_INT);CHKERRQ(ierr);
3524     if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
3525   }
3526 
3527   ierr = PetscOptionsBegin(comm,NULL,"Options for loading SEQAIJ matrix","Mat");CHKERRQ(ierr);
3528   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
3529   ierr = PetscOptionsEnd();CHKERRQ(ierr);
3530 
3531   if (newMat->rmap->n < 0 && newMat->rmap->N < 0 && newMat->cmap->n < 0 && newMat->cmap->N < 0) sizesset = 0;
3532 
3533   ierr = MPI_Bcast(header+1,3,MPIU_INT,0,comm);CHKERRQ(ierr);
3534   M    = header[1]; N = header[2];
3535   /* If global rows/cols are set to PETSC_DECIDE, set it to the sizes given in the file */
3536   if (sizesset && newMat->rmap->N < 0) newMat->rmap->N = M;
3537   if (sizesset && newMat->cmap->N < 0) newMat->cmap->N = N;
3538 
3539   /* If global sizes are set, check if they are consistent with that given in the file */
3540   if (sizesset) {
3541     ierr = MatGetSize(newMat,&grows,&gcols);CHKERRQ(ierr);
3542   }
3543   if (sizesset && newMat->rmap->N != grows) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Inconsistent # of rows:Matrix in file has (%d) and input matrix has (%d)",M,grows);
3544   if (sizesset && newMat->cmap->N != gcols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Inconsistent # of cols:Matrix in file has (%d) and input matrix has (%d)",N,gcols);
3545 
3546   /* determine ownership of all (block) rows */
3547   if (M%bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Inconsistent # of rows (%d) and block size (%d)",M,bs);
3548   if (newMat->rmap->n < 0) m = bs*((M/bs)/size + (((M/bs) % size) > rank));    /* PETSC_DECIDE */
3549   else m = newMat->rmap->n; /* Set by user */
3550 
3551   ierr = PetscMalloc((size+1)*sizeof(PetscInt),&rowners);CHKERRQ(ierr);
3552   ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
3553 
3554   /* First process needs enough room for process with most rows */
3555   if (!rank) {
3556     mmax = rowners[1];
3557     for (i=2; i<=size; i++) {
3558       mmax = PetscMax(mmax, rowners[i]);
3559     }
3560   } else mmax = -1;             /* unused, but compilers complain */
3561 
3562   rowners[0] = 0;
3563   for (i=2; i<=size; i++) {
3564     rowners[i] += rowners[i-1];
3565   }
3566   rstart = rowners[rank];
3567   rend   = rowners[rank+1];
3568 
3569   /* distribute row lengths to all processors */
3570   ierr = PetscMalloc2(m,PetscInt,&ourlens,m,PetscInt,&offlens);CHKERRQ(ierr);
3571   if (!rank) {
3572     ierr = PetscBinaryRead(fd,ourlens,m,PETSC_INT);CHKERRQ(ierr);
3573     ierr = PetscMalloc(mmax*sizeof(PetscInt),&rowlengths);CHKERRQ(ierr);
3574     ierr = PetscMalloc(size*sizeof(PetscInt),&procsnz);CHKERRQ(ierr);
3575     ierr = PetscMemzero(procsnz,size*sizeof(PetscInt));CHKERRQ(ierr);
3576     for (j=0; j<m; j++) {
3577       procsnz[0] += ourlens[j];
3578     }
3579     for (i=1; i<size; i++) {
3580       ierr = PetscBinaryRead(fd,rowlengths,rowners[i+1]-rowners[i],PETSC_INT);CHKERRQ(ierr);
3581       /* calculate the number of nonzeros on each processor */
3582       for (j=0; j<rowners[i+1]-rowners[i]; j++) {
3583         procsnz[i] += rowlengths[j];
3584       }
3585       ierr = MPIULong_Send(rowlengths,rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
3586     }
3587     ierr = PetscFree(rowlengths);CHKERRQ(ierr);
3588   } else {
3589     ierr = MPIULong_Recv(ourlens,m,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
3590   }
3591 
3592   if (!rank) {
3593     /* determine max buffer needed and allocate it */
3594     maxnz = 0;
3595     for (i=0; i<size; i++) {
3596       maxnz = PetscMax(maxnz,procsnz[i]);
3597     }
3598     ierr = PetscMalloc(maxnz*sizeof(PetscInt),&cols);CHKERRQ(ierr);
3599 
3600     /* read in my part of the matrix column indices  */
3601     nz   = procsnz[0];
3602     ierr = PetscMalloc(nz*sizeof(PetscInt),&mycols);CHKERRQ(ierr);
3603     ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);
3604 
3605     /* read in every one elses and ship off */
3606     for (i=1; i<size; i++) {
3607       nz   = procsnz[i];
3608       ierr = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
3609       ierr = MPIULong_Send(cols,nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
3610     }
3611     ierr = PetscFree(cols);CHKERRQ(ierr);
3612   } else {
3613     /* determine buffer space needed for message */
3614     nz = 0;
3615     for (i=0; i<m; i++) {
3616       nz += ourlens[i];
3617     }
3618     ierr = PetscMalloc(nz*sizeof(PetscInt),&mycols);CHKERRQ(ierr);
3619 
3620     /* receive message of column indices*/
3621     ierr = MPIULong_Recv(mycols,nz,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
3622   }
3623 
3624   /* determine column ownership if matrix is not square */
3625   if (N != M) {
3626     if (newMat->cmap->n < 0) n = N/size + ((N % size) > rank);
3627     else n = newMat->cmap->n;
3628     ierr   = MPI_Scan(&n,&cend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3629     cstart = cend - n;
3630   } else {
3631     cstart = rstart;
3632     cend   = rend;
3633     n      = cend - cstart;
3634   }
3635 
3636   /* loop over local rows, determining number of off diagonal entries */
3637   ierr = PetscMemzero(offlens,m*sizeof(PetscInt));CHKERRQ(ierr);
3638   jj   = 0;
3639   for (i=0; i<m; i++) {
3640     for (j=0; j<ourlens[i]; j++) {
3641       if (mycols[jj] < cstart || mycols[jj] >= cend) offlens[i]++;
3642       jj++;
3643     }
3644   }
3645 
3646   for (i=0; i<m; i++) {
3647     ourlens[i] -= offlens[i];
3648   }
3649   if (!sizesset) {
3650     ierr = MatSetSizes(newMat,m,n,M,N);CHKERRQ(ierr);
3651   }
3652 
3653   if (bs > 1) {ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);}
3654 
3655   ierr = MatMPIAIJSetPreallocation(newMat,0,ourlens,0,offlens);CHKERRQ(ierr);
3656 
3657   for (i=0; i<m; i++) {
3658     ourlens[i] += offlens[i];
3659   }
3660 
3661   if (!rank) {
3662     ierr = PetscMalloc((maxnz+1)*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
3663 
3664     /* read in my part of the matrix numerical values  */
3665     nz   = procsnz[0];
3666     ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
3667 
3668     /* insert into matrix */
3669     jj      = rstart;
3670     smycols = mycols;
3671     svals   = vals;
3672     for (i=0; i<m; i++) {
3673       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
3674       smycols += ourlens[i];
3675       svals   += ourlens[i];
3676       jj++;
3677     }
3678 
3679     /* read in other processors and ship out */
3680     for (i=1; i<size; i++) {
3681       nz   = procsnz[i];
3682       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
3683       ierr = MPIULong_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
3684     }
3685     ierr = PetscFree(procsnz);CHKERRQ(ierr);
3686   } else {
3687     /* receive numeric values */
3688     ierr = PetscMalloc((nz+1)*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
3689 
3690     /* receive message of values*/
3691     ierr = MPIULong_Recv(vals,nz,MPIU_SCALAR,0,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
3692 
3693     /* insert into matrix */
3694     jj      = rstart;
3695     smycols = mycols;
3696     svals   = vals;
3697     for (i=0; i<m; i++) {
3698       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
3699       smycols += ourlens[i];
3700       svals   += ourlens[i];
3701       jj++;
3702     }
3703   }
3704   ierr = PetscFree2(ourlens,offlens);CHKERRQ(ierr);
3705   ierr = PetscFree(vals);CHKERRQ(ierr);
3706   ierr = PetscFree(mycols);CHKERRQ(ierr);
3707   ierr = PetscFree(rowners);CHKERRQ(ierr);
3708   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3709   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3710   PetscFunctionReturn(0);
3711 }
3712 
3713 #undef __FUNCT__
3714 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ"
3715 PetscErrorCode MatGetSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3716 {
3717   PetscErrorCode ierr;
3718   IS             iscol_local;
3719   PetscInt       csize;
3720 
3721   PetscFunctionBegin;
3722   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3723   if (call == MAT_REUSE_MATRIX) {
3724     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3725     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3726   } else {
3727     PetscInt cbs;
3728     ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
3729     ierr = ISAllGather(iscol,&iscol_local);CHKERRQ(ierr);
3730     ierr = ISSetBlockSize(iscol_local,cbs);CHKERRQ(ierr);
3731   }
3732   ierr = MatGetSubMatrix_MPIAIJ_Private(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
3733   if (call == MAT_INITIAL_MATRIX) {
3734     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3735     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3736   }
3737   PetscFunctionReturn(0);
3738 }
3739 
3740 extern PetscErrorCode MatGetSubMatrices_MPIAIJ_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool*,Mat*);
3741 #undef __FUNCT__
3742 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ_Private"
3743 /*
3744     Not great since it makes two copies of the submatrix, first an SeqAIJ
3745   in local and then by concatenating the local matrices the end result.
3746   Writing it directly would be much like MatGetSubMatrices_MPIAIJ()
3747 
3748   Note: This requires a sequential iscol with all indices.
3749 */
3750 PetscErrorCode MatGetSubMatrix_MPIAIJ_Private(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3751 {
3752   PetscErrorCode ierr;
3753   PetscMPIInt    rank,size;
3754   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3755   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal,ncol;
3756   PetscBool      allcolumns, colflag;
3757   Mat            M,Mreuse;
3758   MatScalar      *vwork,*aa;
3759   MPI_Comm       comm;
3760   Mat_SeqAIJ     *aij;
3761 
3762   PetscFunctionBegin;
3763   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3764   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3765   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3766 
3767   ierr = ISIdentity(iscol,&colflag);CHKERRQ(ierr);
3768   ierr = ISGetLocalSize(iscol,&ncol);CHKERRQ(ierr);
3769   if (colflag && ncol == mat->cmap->N) {
3770     allcolumns = PETSC_TRUE;
3771   } else {
3772     allcolumns = PETSC_FALSE;
3773   }
3774   if (call ==  MAT_REUSE_MATRIX) {
3775     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3776     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3777     ierr = MatGetSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,&allcolumns,&Mreuse);CHKERRQ(ierr);
3778   } else {
3779     ierr = MatGetSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&allcolumns,&Mreuse);CHKERRQ(ierr);
3780   }
3781 
3782   /*
3783       m - number of local rows
3784       n - number of columns (same on all processors)
3785       rstart - first row in new global matrix generated
3786   */
3787   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3788   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3789   if (call == MAT_INITIAL_MATRIX) {
3790     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3791     ii  = aij->i;
3792     jj  = aij->j;
3793 
3794     /*
3795         Determine the number of non-zeros in the diagonal and off-diagonal
3796         portions of the matrix in order to do correct preallocation
3797     */
3798 
3799     /* first get start and end of "diagonal" columns */
3800     if (csize == PETSC_DECIDE) {
3801       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3802       if (mglobal == n) { /* square matrix */
3803         nlocal = m;
3804       } else {
3805         nlocal = n/size + ((n % size) > rank);
3806       }
3807     } else {
3808       nlocal = csize;
3809     }
3810     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3811     rstart = rend - nlocal;
3812     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);
3813 
3814     /* next, compute all the lengths */
3815     ierr  = PetscMalloc((2*m+1)*sizeof(PetscInt),&dlens);CHKERRQ(ierr);
3816     olens = dlens + m;
3817     for (i=0; i<m; i++) {
3818       jend = ii[i+1] - ii[i];
3819       olen = 0;
3820       dlen = 0;
3821       for (j=0; j<jend; j++) {
3822         if (*jj < rstart || *jj >= rend) olen++;
3823         else dlen++;
3824         jj++;
3825       }
3826       olens[i] = olen;
3827       dlens[i] = dlen;
3828     }
3829     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3830     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3831     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3832     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3833     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3834     ierr = PetscFree(dlens);CHKERRQ(ierr);
3835   } else {
3836     PetscInt ml,nl;
3837 
3838     M    = *newmat;
3839     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3840     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3841     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3842     /*
3843          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3844        rather than the slower MatSetValues().
3845     */
3846     M->was_assembled = PETSC_TRUE;
3847     M->assembled     = PETSC_FALSE;
3848   }
3849   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3850   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3851   ii   = aij->i;
3852   jj   = aij->j;
3853   aa   = aij->a;
3854   for (i=0; i<m; i++) {
3855     row   = rstart + i;
3856     nz    = ii[i+1] - ii[i];
3857     cwork = jj;     jj += nz;
3858     vwork = aa;     aa += nz;
3859     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3860   }
3861 
3862   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3863   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3864   *newmat = M;
3865 
3866   /* save submatrix used in processor for next request */
3867   if (call ==  MAT_INITIAL_MATRIX) {
3868     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3869     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3870   }
3871   PetscFunctionReturn(0);
3872 }
3873 
3874 #undef __FUNCT__
3875 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR_MPIAIJ"
3876 PetscErrorCode  MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3877 {
3878   PetscInt       m,cstart, cend,j,nnz,i,d;
3879   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3880   const PetscInt *JJ;
3881   PetscScalar    *values;
3882   PetscErrorCode ierr;
3883 
3884   PetscFunctionBegin;
3885   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3886 
3887   ierr   = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3888   ierr   = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3889   m      = B->rmap->n;
3890   cstart = B->cmap->rstart;
3891   cend   = B->cmap->rend;
3892   rstart = B->rmap->rstart;
3893 
3894   ierr = PetscMalloc2(m,PetscInt,&d_nnz,m,PetscInt,&o_nnz);CHKERRQ(ierr);
3895 
3896 #if defined(PETSC_USE_DEBUGGING)
3897   for (i=0; i<m; i++) {
3898     nnz = Ii[i+1]- Ii[i];
3899     JJ  = J + Ii[i];
3900     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3901     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3902     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);
3903   }
3904 #endif
3905 
3906   for (i=0; i<m; i++) {
3907     nnz     = Ii[i+1]- Ii[i];
3908     JJ      = J + Ii[i];
3909     nnz_max = PetscMax(nnz_max,nnz);
3910     d       = 0;
3911     for (j=0; j<nnz; j++) {
3912       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3913     }
3914     d_nnz[i] = d;
3915     o_nnz[i] = nnz - d;
3916   }
3917   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3918   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3919 
3920   if (v) values = (PetscScalar*)v;
3921   else {
3922     ierr = PetscMalloc((nnz_max+1)*sizeof(PetscScalar),&values);CHKERRQ(ierr);
3923     ierr = PetscMemzero(values,nnz_max*sizeof(PetscScalar));CHKERRQ(ierr);
3924   }
3925 
3926   for (i=0; i<m; i++) {
3927     ii   = i + rstart;
3928     nnz  = Ii[i+1]- Ii[i];
3929     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3930   }
3931   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3932   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3933 
3934   if (!v) {
3935     ierr = PetscFree(values);CHKERRQ(ierr);
3936   }
3937   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3938   PetscFunctionReturn(0);
3939 }
3940 
3941 #undef __FUNCT__
3942 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR"
3943 /*@
3944    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3945    (the default parallel PETSc format).
3946 
3947    Collective on MPI_Comm
3948 
3949    Input Parameters:
3950 +  B - the matrix
3951 .  i - the indices into j for the start of each local row (starts with zero)
3952 .  j - the column indices for each local row (starts with zero)
3953 -  v - optional values in the matrix
3954 
3955    Level: developer
3956 
3957    Notes:
3958        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3959      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3960      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3961 
3962        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3963 
3964        The format which is used for the sparse matrix input, is equivalent to a
3965     row-major ordering.. i.e for the following matrix, the input data expected is
3966     as shown:
3967 
3968         1 0 0
3969         2 0 3     P0
3970        -------
3971         4 5 6     P1
3972 
3973      Process0 [P0]: rows_owned=[0,1]
3974         i =  {0,1,3}  [size = nrow+1  = 2+1]
3975         j =  {0,0,2}  [size = nz = 6]
3976         v =  {1,2,3}  [size = nz = 6]
3977 
3978      Process1 [P1]: rows_owned=[2]
3979         i =  {0,3}    [size = nrow+1  = 1+1]
3980         j =  {0,1,2}  [size = nz = 6]
3981         v =  {4,5,6}  [size = nz = 6]
3982 
3983 .keywords: matrix, aij, compressed row, sparse, parallel
3984 
3985 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MPIAIJ,
3986           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3987 @*/
3988 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3989 {
3990   PetscErrorCode ierr;
3991 
3992   PetscFunctionBegin;
3993   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3994   PetscFunctionReturn(0);
3995 }
3996 
3997 #undef __FUNCT__
3998 #define __FUNCT__ "MatMPIAIJSetPreallocation"
3999 /*@C
4000    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
4001    (the default parallel PETSc format).  For good matrix assembly performance
4002    the user should preallocate the matrix storage by setting the parameters
4003    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
4004    performance can be increased by more than a factor of 50.
4005 
4006    Collective on MPI_Comm
4007 
4008    Input Parameters:
4009 +  A - the matrix
4010 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
4011            (same value is used for all local rows)
4012 .  d_nnz - array containing the number of nonzeros in the various rows of the
4013            DIAGONAL portion of the local submatrix (possibly different for each row)
4014            or NULL, if d_nz is used to specify the nonzero structure.
4015            The size of this array is equal to the number of local rows, i.e 'm'.
4016            For matrices that will be factored, you must leave room for (and set)
4017            the diagonal entry even if it is zero.
4018 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
4019            submatrix (same value is used for all local rows).
4020 -  o_nnz - array containing the number of nonzeros in the various rows of the
4021            OFF-DIAGONAL portion of the local submatrix (possibly different for
4022            each row) or NULL, if o_nz is used to specify the nonzero
4023            structure. The size of this array is equal to the number
4024            of local rows, i.e 'm'.
4025 
4026    If the *_nnz parameter is given then the *_nz parameter is ignored
4027 
4028    The AIJ format (also called the Yale sparse matrix format or
4029    compressed row storage (CSR)), is fully compatible with standard Fortran 77
4030    storage.  The stored row and column indices begin with zero.
4031    See the <A href="../../docs/manual.pdf#nameddest=ch_mat">Mat chapter of the users manual</A> for details.
4032 
4033    The parallel matrix is partitioned such that the first m0 rows belong to
4034    process 0, the next m1 rows belong to process 1, the next m2 rows belong
4035    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
4036 
4037    The DIAGONAL portion of the local submatrix of a processor can be defined
4038    as the submatrix which is obtained by extraction the part corresponding to
4039    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
4040    first row that belongs to the processor, r2 is the last row belonging to
4041    the this processor, and c1-c2 is range of indices of the local part of a
4042    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
4043    common case of a square matrix, the row and column ranges are the same and
4044    the DIAGONAL part is also square. The remaining portion of the local
4045    submatrix (mxN) constitute the OFF-DIAGONAL portion.
4046 
4047    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
4048 
4049    You can call MatGetInfo() to get information on how effective the preallocation was;
4050    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
4051    You can also run with the option -info and look for messages with the string
4052    malloc in them to see if additional memory allocation was needed.
4053 
4054    Example usage:
4055 
4056    Consider the following 8x8 matrix with 34 non-zero values, that is
4057    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
4058    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
4059    as follows:
4060 
4061 .vb
4062             1  2  0  |  0  3  0  |  0  4
4063     Proc0   0  5  6  |  7  0  0  |  8  0
4064             9  0 10  | 11  0  0  | 12  0
4065     -------------------------------------
4066            13  0 14  | 15 16 17  |  0  0
4067     Proc1   0 18  0  | 19 20 21  |  0  0
4068             0  0  0  | 22 23  0  | 24  0
4069     -------------------------------------
4070     Proc2  25 26 27  |  0  0 28  | 29  0
4071            30  0  0  | 31 32 33  |  0 34
4072 .ve
4073 
4074    This can be represented as a collection of submatrices as:
4075 
4076 .vb
4077       A B C
4078       D E F
4079       G H I
4080 .ve
4081 
4082    Where the submatrices A,B,C are owned by proc0, D,E,F are
4083    owned by proc1, G,H,I are owned by proc2.
4084 
4085    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4086    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4087    The 'M','N' parameters are 8,8, and have the same values on all procs.
4088 
4089    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
4090    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
4091    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
4092    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
4093    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
4094    matrix, ans [DF] as another SeqAIJ matrix.
4095 
4096    When d_nz, o_nz parameters are specified, d_nz storage elements are
4097    allocated for every row of the local diagonal submatrix, and o_nz
4098    storage locations are allocated for every row of the OFF-DIAGONAL submat.
4099    One way to choose d_nz and o_nz is to use the max nonzerors per local
4100    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
4101    In this case, the values of d_nz,o_nz are:
4102 .vb
4103      proc0 : dnz = 2, o_nz = 2
4104      proc1 : dnz = 3, o_nz = 2
4105      proc2 : dnz = 1, o_nz = 4
4106 .ve
4107    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
4108    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
4109    for proc3. i.e we are using 12+15+10=37 storage locations to store
4110    34 values.
4111 
4112    When d_nnz, o_nnz parameters are specified, the storage is specified
4113    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
4114    In the above case the values for d_nnz,o_nnz are:
4115 .vb
4116      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
4117      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
4118      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
4119 .ve
4120    Here the space allocated is sum of all the above values i.e 34, and
4121    hence pre-allocation is perfect.
4122 
4123    Level: intermediate
4124 
4125 .keywords: matrix, aij, compressed row, sparse, parallel
4126 
4127 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
4128           MPIAIJ, MatGetInfo(), PetscSplitOwnership()
4129 @*/
4130 PetscErrorCode  MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
4131 {
4132   PetscErrorCode ierr;
4133 
4134   PetscFunctionBegin;
4135   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
4136   PetscValidType(B,1);
4137   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
4138   PetscFunctionReturn(0);
4139 }
4140 
4141 #undef __FUNCT__
4142 #define __FUNCT__ "MatCreateMPIAIJWithArrays"
4143 /*@
4144      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
4145          CSR format the local rows.
4146 
4147    Collective on MPI_Comm
4148 
4149    Input Parameters:
4150 +  comm - MPI communicator
4151 .  m - number of local rows (Cannot be PETSC_DECIDE)
4152 .  n - This value should be the same as the local size used in creating the
4153        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
4154        calculated if N is given) For square matrices n is almost always m.
4155 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
4156 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
4157 .   i - row indices
4158 .   j - column indices
4159 -   a - matrix values
4160 
4161    Output Parameter:
4162 .   mat - the matrix
4163 
4164    Level: intermediate
4165 
4166    Notes:
4167        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
4168      thus you CANNOT change the matrix entries by changing the values of a[] after you have
4169      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
4170 
4171        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
4172 
4173        The format which is used for the sparse matrix input, is equivalent to a
4174     row-major ordering.. i.e for the following matrix, the input data expected is
4175     as shown:
4176 
4177         1 0 0
4178         2 0 3     P0
4179        -------
4180         4 5 6     P1
4181 
4182      Process0 [P0]: rows_owned=[0,1]
4183         i =  {0,1,3}  [size = nrow+1  = 2+1]
4184         j =  {0,0,2}  [size = nz = 6]
4185         v =  {1,2,3}  [size = nz = 6]
4186 
4187      Process1 [P1]: rows_owned=[2]
4188         i =  {0,3}    [size = nrow+1  = 1+1]
4189         j =  {0,1,2}  [size = nz = 6]
4190         v =  {4,5,6}  [size = nz = 6]
4191 
4192 .keywords: matrix, aij, compressed row, sparse, parallel
4193 
4194 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
4195           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
4196 @*/
4197 PetscErrorCode  MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
4198 {
4199   PetscErrorCode ierr;
4200 
4201   PetscFunctionBegin;
4202   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
4203   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
4204   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4205   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
4206   /* ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr); */
4207   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
4208   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
4209   PetscFunctionReturn(0);
4210 }
4211 
4212 #undef __FUNCT__
4213 #define __FUNCT__ "MatCreateAIJ"
4214 /*@C
4215    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
4216    (the default parallel PETSc format).  For good matrix assembly performance
4217    the user should preallocate the matrix storage by setting the parameters
4218    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
4219    performance can be increased by more than a factor of 50.
4220 
4221    Collective on MPI_Comm
4222 
4223    Input Parameters:
4224 +  comm - MPI communicator
4225 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
4226            This value should be the same as the local size used in creating the
4227            y vector for the matrix-vector product y = Ax.
4228 .  n - This value should be the same as the local size used in creating the
4229        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
4230        calculated if N is given) For square matrices n is almost always m.
4231 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
4232 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
4233 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
4234            (same value is used for all local rows)
4235 .  d_nnz - array containing the number of nonzeros in the various rows of the
4236            DIAGONAL portion of the local submatrix (possibly different for each row)
4237            or NULL, if d_nz is used to specify the nonzero structure.
4238            The size of this array is equal to the number of local rows, i.e 'm'.
4239 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
4240            submatrix (same value is used for all local rows).
4241 -  o_nnz - array containing the number of nonzeros in the various rows of the
4242            OFF-DIAGONAL portion of the local submatrix (possibly different for
4243            each row) or NULL, if o_nz is used to specify the nonzero
4244            structure. The size of this array is equal to the number
4245            of local rows, i.e 'm'.
4246 
4247    Output Parameter:
4248 .  A - the matrix
4249 
4250    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
4251    MatXXXXSetPreallocation() paradgm instead of this routine directly.
4252    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
4253 
4254    Notes:
4255    If the *_nnz parameter is given then the *_nz parameter is ignored
4256 
4257    m,n,M,N parameters specify the size of the matrix, and its partitioning across
4258    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
4259    storage requirements for this matrix.
4260 
4261    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
4262    processor than it must be used on all processors that share the object for
4263    that argument.
4264 
4265    The user MUST specify either the local or global matrix dimensions
4266    (possibly both).
4267 
4268    The parallel matrix is partitioned across processors such that the
4269    first m0 rows belong to process 0, the next m1 rows belong to
4270    process 1, the next m2 rows belong to process 2 etc.. where
4271    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
4272    values corresponding to [m x N] submatrix.
4273 
4274    The columns are logically partitioned with the n0 columns belonging
4275    to 0th partition, the next n1 columns belonging to the next
4276    partition etc.. where n0,n1,n2... are the the input parameter 'n'.
4277 
4278    The DIAGONAL portion of the local submatrix on any given processor
4279    is the submatrix corresponding to the rows and columns m,n
4280    corresponding to the given processor. i.e diagonal matrix on
4281    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
4282    etc. The remaining portion of the local submatrix [m x (N-n)]
4283    constitute the OFF-DIAGONAL portion. The example below better
4284    illustrates this concept.
4285 
4286    For a square global matrix we define each processor's diagonal portion
4287    to be its local rows and the corresponding columns (a square submatrix);
4288    each processor's off-diagonal portion encompasses the remainder of the
4289    local matrix (a rectangular submatrix).
4290 
4291    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
4292 
4293    When calling this routine with a single process communicator, a matrix of
4294    type SEQAIJ is returned.  If a matrix of type MPIAIJ is desired for this
4295    type of communicator, use the construction mechanism:
4296      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
4297 
4298    By default, this format uses inodes (identical nodes) when possible.
4299    We search for consecutive rows with the same nonzero structure, thereby
4300    reusing matrix information to achieve increased efficiency.
4301 
4302    Options Database Keys:
4303 +  -mat_no_inode  - Do not use inodes
4304 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
4305 -  -mat_aij_oneindex - Internally use indexing starting at 1
4306         rather than 0.  Note that when calling MatSetValues(),
4307         the user still MUST index entries starting at 0!
4308 
4309 
4310    Example usage:
4311 
4312    Consider the following 8x8 matrix with 34 non-zero values, that is
4313    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
4314    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
4315    as follows:
4316 
4317 .vb
4318             1  2  0  |  0  3  0  |  0  4
4319     Proc0   0  5  6  |  7  0  0  |  8  0
4320             9  0 10  | 11  0  0  | 12  0
4321     -------------------------------------
4322            13  0 14  | 15 16 17  |  0  0
4323     Proc1   0 18  0  | 19 20 21  |  0  0
4324             0  0  0  | 22 23  0  | 24  0
4325     -------------------------------------
4326     Proc2  25 26 27  |  0  0 28  | 29  0
4327            30  0  0  | 31 32 33  |  0 34
4328 .ve
4329 
4330    This can be represented as a collection of submatrices as:
4331 
4332 .vb
4333       A B C
4334       D E F
4335       G H I
4336 .ve
4337 
4338    Where the submatrices A,B,C are owned by proc0, D,E,F are
4339    owned by proc1, G,H,I are owned by proc2.
4340 
4341    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4342    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4343    The 'M','N' parameters are 8,8, and have the same values on all procs.
4344 
4345    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
4346    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
4347    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
4348    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
4349    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
4350    matrix, ans [DF] as another SeqAIJ matrix.
4351 
4352    When d_nz, o_nz parameters are specified, d_nz storage elements are
4353    allocated for every row of the local diagonal submatrix, and o_nz
4354    storage locations are allocated for every row of the OFF-DIAGONAL submat.
4355    One way to choose d_nz and o_nz is to use the max nonzerors per local
4356    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
4357    In this case, the values of d_nz,o_nz are:
4358 .vb
4359      proc0 : dnz = 2, o_nz = 2
4360      proc1 : dnz = 3, o_nz = 2
4361      proc2 : dnz = 1, o_nz = 4
4362 .ve
4363    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
4364    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
4365    for proc3. i.e we are using 12+15+10=37 storage locations to store
4366    34 values.
4367 
4368    When d_nnz, o_nnz parameters are specified, the storage is specified
4369    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
4370    In the above case the values for d_nnz,o_nnz are:
4371 .vb
4372      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
4373      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
4374      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
4375 .ve
4376    Here the space allocated is sum of all the above values i.e 34, and
4377    hence pre-allocation is perfect.
4378 
4379    Level: intermediate
4380 
4381 .keywords: matrix, aij, compressed row, sparse, parallel
4382 
4383 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
4384           MPIAIJ, MatCreateMPIAIJWithArrays()
4385 @*/
4386 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)
4387 {
4388   PetscErrorCode ierr;
4389   PetscMPIInt    size;
4390 
4391   PetscFunctionBegin;
4392   ierr = MatCreate(comm,A);CHKERRQ(ierr);
4393   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
4394   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4395   if (size > 1) {
4396     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
4397     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
4398   } else {
4399     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
4400     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
4401   }
4402   PetscFunctionReturn(0);
4403 }
4404 
4405 #undef __FUNCT__
4406 #define __FUNCT__ "MatMPIAIJGetSeqAIJ"
4407 PetscErrorCode  MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
4408 {
4409   Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
4410 
4411   PetscFunctionBegin;
4412   *Ad     = a->A;
4413   *Ao     = a->B;
4414   *colmap = a->garray;
4415   PetscFunctionReturn(0);
4416 }
4417 
4418 #undef __FUNCT__
4419 #define __FUNCT__ "MatSetColoring_MPIAIJ"
4420 PetscErrorCode MatSetColoring_MPIAIJ(Mat A,ISColoring coloring)
4421 {
4422   PetscErrorCode ierr;
4423   PetscInt       i;
4424   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
4425 
4426   PetscFunctionBegin;
4427   if (coloring->ctype == IS_COLORING_GLOBAL) {
4428     ISColoringValue *allcolors,*colors;
4429     ISColoring      ocoloring;
4430 
4431     /* set coloring for diagonal portion */
4432     ierr = MatSetColoring_SeqAIJ(a->A,coloring);CHKERRQ(ierr);
4433 
4434     /* set coloring for off-diagonal portion */
4435     ierr = ISAllGatherColors(PetscObjectComm((PetscObject)A),coloring->n,coloring->colors,NULL,&allcolors);CHKERRQ(ierr);
4436     ierr = PetscMalloc((a->B->cmap->n+1)*sizeof(ISColoringValue),&colors);CHKERRQ(ierr);
4437     for (i=0; i<a->B->cmap->n; i++) {
4438       colors[i] = allcolors[a->garray[i]];
4439     }
4440     ierr = PetscFree(allcolors);CHKERRQ(ierr);
4441     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,&ocoloring);CHKERRQ(ierr);
4442     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
4443     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
4444   } else if (coloring->ctype == IS_COLORING_GHOSTED) {
4445     ISColoringValue *colors;
4446     PetscInt        *larray;
4447     ISColoring      ocoloring;
4448 
4449     /* set coloring for diagonal portion */
4450     ierr = PetscMalloc((a->A->cmap->n+1)*sizeof(PetscInt),&larray);CHKERRQ(ierr);
4451     for (i=0; i<a->A->cmap->n; i++) {
4452       larray[i] = i + A->cmap->rstart;
4453     }
4454     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->A->cmap->n,larray,NULL,larray);CHKERRQ(ierr);
4455     ierr = PetscMalloc((a->A->cmap->n+1)*sizeof(ISColoringValue),&colors);CHKERRQ(ierr);
4456     for (i=0; i<a->A->cmap->n; i++) {
4457       colors[i] = coloring->colors[larray[i]];
4458     }
4459     ierr = PetscFree(larray);CHKERRQ(ierr);
4460     ierr = ISColoringCreate(PETSC_COMM_SELF,coloring->n,a->A->cmap->n,colors,&ocoloring);CHKERRQ(ierr);
4461     ierr = MatSetColoring_SeqAIJ(a->A,ocoloring);CHKERRQ(ierr);
4462     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
4463 
4464     /* set coloring for off-diagonal portion */
4465     ierr = PetscMalloc((a->B->cmap->n+1)*sizeof(PetscInt),&larray);CHKERRQ(ierr);
4466     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->B->cmap->n,a->garray,NULL,larray);CHKERRQ(ierr);
4467     ierr = PetscMalloc((a->B->cmap->n+1)*sizeof(ISColoringValue),&colors);CHKERRQ(ierr);
4468     for (i=0; i<a->B->cmap->n; i++) {
4469       colors[i] = coloring->colors[larray[i]];
4470     }
4471     ierr = PetscFree(larray);CHKERRQ(ierr);
4472     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,&ocoloring);CHKERRQ(ierr);
4473     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
4474     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
4475   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support ISColoringType %d",(int)coloring->ctype);
4476   PetscFunctionReturn(0);
4477 }
4478 
4479 #undef __FUNCT__
4480 #define __FUNCT__ "MatSetValuesAdifor_MPIAIJ"
4481 PetscErrorCode MatSetValuesAdifor_MPIAIJ(Mat A,PetscInt nl,void *advalues)
4482 {
4483   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
4484   PetscErrorCode ierr;
4485 
4486   PetscFunctionBegin;
4487   ierr = MatSetValuesAdifor_SeqAIJ(a->A,nl,advalues);CHKERRQ(ierr);
4488   ierr = MatSetValuesAdifor_SeqAIJ(a->B,nl,advalues);CHKERRQ(ierr);
4489   PetscFunctionReturn(0);
4490 }
4491 
4492 #undef __FUNCT__
4493 #define __FUNCT__ "MatCreateMPIAIJConcatenateSeqAIJSymbolic"
4494 PetscErrorCode  MatCreateMPIAIJConcatenateSeqAIJSymbolic(MPI_Comm comm,Mat inmat,PetscInt n,Mat *outmat)
4495 {
4496   PetscErrorCode ierr;
4497   PetscInt       m,N,i,rstart,nnz,*dnz,*onz,sum,bs,cbs;
4498   PetscInt       *indx;
4499 
4500   PetscFunctionBegin;
4501   /* This routine will ONLY return MPIAIJ type matrix */
4502   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
4503   ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
4504   if (n == PETSC_DECIDE) {
4505     ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
4506   }
4507   /* Check sum(n) = N */
4508   ierr = MPI_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4509   if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
4510 
4511   ierr    = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4512   rstart -= m;
4513 
4514   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4515   for (i=0; i<m; i++) {
4516     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
4517     ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
4518     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
4519   }
4520 
4521   ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
4522   ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4523   ierr = MatSetBlockSizes(*outmat,bs,cbs);CHKERRQ(ierr);
4524   ierr = MatSetType(*outmat,MATMPIAIJ);CHKERRQ(ierr);
4525   ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
4526   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4527   PetscFunctionReturn(0);
4528 }
4529 
4530 #undef __FUNCT__
4531 #define __FUNCT__ "MatCreateMPIAIJConcatenateSeqAIJNumeric"
4532 PetscErrorCode  MatCreateMPIAIJConcatenateSeqAIJNumeric(MPI_Comm comm,Mat inmat,PetscInt n,Mat outmat)
4533 {
4534   PetscErrorCode ierr;
4535   PetscInt       m,N,i,rstart,nnz,Ii;
4536   PetscInt       *indx;
4537   PetscScalar    *values;
4538 
4539   PetscFunctionBegin;
4540   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
4541   ierr = MatGetOwnershipRange(outmat,&rstart,NULL);CHKERRQ(ierr);
4542   for (i=0; i<m; i++) {
4543     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4544     Ii   = i + rstart;
4545     ierr = MatSetValues(outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4546     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4547   }
4548   ierr = MatAssemblyBegin(outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4549   ierr = MatAssemblyEnd(outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4550   PetscFunctionReturn(0);
4551 }
4552 
4553 #undef __FUNCT__
4554 #define __FUNCT__ "MatCreateMPIAIJConcatenateSeqAIJ"
4555 /*@
4556       MatCreateMPIAIJConcatenateSeqAIJ - Creates a single large PETSc matrix by concatenating sequential
4557                  matrices from each processor
4558 
4559     Collective on MPI_Comm
4560 
4561    Input Parameters:
4562 +    comm - the communicators the parallel matrix will live on
4563 .    inmat - the input sequential matrices
4564 .    n - number of local columns (or PETSC_DECIDE)
4565 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4566 
4567    Output Parameter:
4568 .    outmat - the parallel matrix generated
4569 
4570     Level: advanced
4571 
4572    Notes: The number of columns of the matrix in EACH processor MUST be the same.
4573 
4574 @*/
4575 PetscErrorCode  MatCreateMPIAIJConcatenateSeqAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
4576 {
4577   PetscErrorCode ierr;
4578   PetscMPIInt    size;
4579 
4580   PetscFunctionBegin;
4581   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4582   ierr = PetscLogEventBegin(MAT_Merge,inmat,0,0,0);CHKERRQ(ierr);
4583   if (size == 1) {
4584     if (scall == MAT_INITIAL_MATRIX) {
4585       ierr = MatDuplicate(inmat,MAT_COPY_VALUES,outmat);CHKERRQ(ierr);
4586     } else {
4587       ierr = MatCopy(inmat,*outmat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4588     }
4589   } else {
4590     if (scall == MAT_INITIAL_MATRIX) {
4591       ierr = MatCreateMPIAIJConcatenateSeqAIJSymbolic(comm,inmat,n,outmat);CHKERRQ(ierr);
4592     }
4593     ierr = MatCreateMPIAIJConcatenateSeqAIJNumeric(comm,inmat,n,*outmat);CHKERRQ(ierr);
4594   }
4595   ierr = PetscLogEventEnd(MAT_Merge,inmat,0,0,0);CHKERRQ(ierr);
4596   PetscFunctionReturn(0);
4597 }
4598 
4599 #undef __FUNCT__
4600 #define __FUNCT__ "MatFileSplit"
4601 PetscErrorCode MatFileSplit(Mat A,char *outfile)
4602 {
4603   PetscErrorCode    ierr;
4604   PetscMPIInt       rank;
4605   PetscInt          m,N,i,rstart,nnz;
4606   size_t            len;
4607   const PetscInt    *indx;
4608   PetscViewer       out;
4609   char              *name;
4610   Mat               B;
4611   const PetscScalar *values;
4612 
4613   PetscFunctionBegin;
4614   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
4615   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
4616   /* Should this be the type of the diagonal block of A? */
4617   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
4618   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
4619   ierr = MatSetBlockSizes(B,A->rmap->bs,A->cmap->bs);CHKERRQ(ierr);
4620   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
4621   ierr = MatSeqAIJSetPreallocation(B,0,NULL);CHKERRQ(ierr);
4622   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
4623   for (i=0; i<m; i++) {
4624     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4625     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4626     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4627   }
4628   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4629   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4630 
4631   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
4632   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
4633   ierr = PetscMalloc((len+5)*sizeof(char),&name);CHKERRQ(ierr);
4634   sprintf(name,"%s.%d",outfile,rank);
4635   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
4636   ierr = PetscFree(name);CHKERRQ(ierr);
4637   ierr = MatView(B,out);CHKERRQ(ierr);
4638   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
4639   ierr = MatDestroy(&B);CHKERRQ(ierr);
4640   PetscFunctionReturn(0);
4641 }
4642 
4643 extern PetscErrorCode MatDestroy_MPIAIJ(Mat);
4644 #undef __FUNCT__
4645 #define __FUNCT__ "MatDestroy_MPIAIJ_SeqsToMPI"
4646 PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
4647 {
4648   PetscErrorCode      ierr;
4649   Mat_Merge_SeqsToMPI *merge;
4650   PetscContainer      container;
4651 
4652   PetscFunctionBegin;
4653   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4654   if (container) {
4655     ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4656     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
4657     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
4658     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
4659     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
4660     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
4661     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
4662     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
4663     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
4664     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
4665     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
4666     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
4667     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
4668     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
4669     ierr = PetscFree(merge);CHKERRQ(ierr);
4670     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
4671   }
4672   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
4673   PetscFunctionReturn(0);
4674 }
4675 
4676 #include <../src/mat/utils/freespace.h>
4677 #include <petscbt.h>
4678 
4679 #undef __FUNCT__
4680 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJNumeric"
4681 PetscErrorCode  MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
4682 {
4683   PetscErrorCode      ierr;
4684   MPI_Comm            comm;
4685   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
4686   PetscMPIInt         size,rank,taga,*len_s;
4687   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
4688   PetscInt            proc,m;
4689   PetscInt            **buf_ri,**buf_rj;
4690   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
4691   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
4692   MPI_Request         *s_waits,*r_waits;
4693   MPI_Status          *status;
4694   MatScalar           *aa=a->a;
4695   MatScalar           **abuf_r,*ba_i;
4696   Mat_Merge_SeqsToMPI *merge;
4697   PetscContainer      container;
4698 
4699   PetscFunctionBegin;
4700   ierr = PetscObjectGetComm((PetscObject)mpimat,&comm);CHKERRQ(ierr);
4701   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4702 
4703   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4704   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4705 
4706   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4707   ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4708 
4709   bi     = merge->bi;
4710   bj     = merge->bj;
4711   buf_ri = merge->buf_ri;
4712   buf_rj = merge->buf_rj;
4713 
4714   ierr   = PetscMalloc(size*sizeof(MPI_Status),&status);CHKERRQ(ierr);
4715   owners = merge->rowmap->range;
4716   len_s  = merge->len_s;
4717 
4718   /* send and recv matrix values */
4719   /*-----------------------------*/
4720   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
4721   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
4722 
4723   ierr = PetscMalloc((merge->nsend+1)*sizeof(MPI_Request),&s_waits);CHKERRQ(ierr);
4724   for (proc=0,k=0; proc<size; proc++) {
4725     if (!len_s[proc]) continue;
4726     i    = owners[proc];
4727     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
4728     k++;
4729   }
4730 
4731   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
4732   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
4733   ierr = PetscFree(status);CHKERRQ(ierr);
4734 
4735   ierr = PetscFree(s_waits);CHKERRQ(ierr);
4736   ierr = PetscFree(r_waits);CHKERRQ(ierr);
4737 
4738   /* insert mat values of mpimat */
4739   /*----------------------------*/
4740   ierr = PetscMalloc(N*sizeof(PetscScalar),&ba_i);CHKERRQ(ierr);
4741   ierr = PetscMalloc3(merge->nrecv,PetscInt*,&buf_ri_k,merge->nrecv,PetscInt*,&nextrow,merge->nrecv,PetscInt*,&nextai);CHKERRQ(ierr);
4742 
4743   for (k=0; k<merge->nrecv; k++) {
4744     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4745     nrows       = *(buf_ri_k[k]);
4746     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
4747     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4748   }
4749 
4750   /* set values of ba */
4751   m = merge->rowmap->n;
4752   for (i=0; i<m; i++) {
4753     arow = owners[rank] + i;
4754     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
4755     bnzi = bi[i+1] - bi[i];
4756     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
4757 
4758     /* add local non-zero vals of this proc's seqmat into ba */
4759     anzi   = ai[arow+1] - ai[arow];
4760     aj     = a->j + ai[arow];
4761     aa     = a->a + ai[arow];
4762     nextaj = 0;
4763     for (j=0; nextaj<anzi; j++) {
4764       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4765         ba_i[j] += aa[nextaj++];
4766       }
4767     }
4768 
4769     /* add received vals into ba */
4770     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4771       /* i-th row */
4772       if (i == *nextrow[k]) {
4773         anzi   = *(nextai[k]+1) - *nextai[k];
4774         aj     = buf_rj[k] + *(nextai[k]);
4775         aa     = abuf_r[k] + *(nextai[k]);
4776         nextaj = 0;
4777         for (j=0; nextaj<anzi; j++) {
4778           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4779             ba_i[j] += aa[nextaj++];
4780           }
4781         }
4782         nextrow[k]++; nextai[k]++;
4783       }
4784     }
4785     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
4786   }
4787   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4788   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4789 
4790   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
4791   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
4792   ierr = PetscFree(ba_i);CHKERRQ(ierr);
4793   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4794   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4795   PetscFunctionReturn(0);
4796 }
4797 
4798 extern PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat);
4799 
4800 #undef __FUNCT__
4801 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJSymbolic"
4802 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4803 {
4804   PetscErrorCode      ierr;
4805   Mat                 B_mpi;
4806   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
4807   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4808   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
4809   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4810   PetscInt            len,proc,*dnz,*onz,bs,cbs;
4811   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4812   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4813   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
4814   MPI_Status          *status;
4815   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
4816   PetscBT             lnkbt;
4817   Mat_Merge_SeqsToMPI *merge;
4818   PetscContainer      container;
4819 
4820   PetscFunctionBegin;
4821   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4822 
4823   /* make sure it is a PETSc comm */
4824   ierr = PetscCommDuplicate(comm,&comm,NULL);CHKERRQ(ierr);
4825   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4826   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4827 
4828   ierr = PetscNew(Mat_Merge_SeqsToMPI,&merge);CHKERRQ(ierr);
4829   ierr = PetscMalloc(size*sizeof(MPI_Status),&status);CHKERRQ(ierr);
4830 
4831   /* determine row ownership */
4832   /*---------------------------------------------------------*/
4833   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
4834   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
4835   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
4836   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
4837   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
4838   ierr = PetscMalloc(size*sizeof(PetscMPIInt),&len_si);CHKERRQ(ierr);
4839   ierr = PetscMalloc(size*sizeof(PetscMPIInt),&merge->len_s);CHKERRQ(ierr);
4840 
4841   m      = merge->rowmap->n;
4842   owners = merge->rowmap->range;
4843 
4844   /* determine the number of messages to send, their lengths */
4845   /*---------------------------------------------------------*/
4846   len_s = merge->len_s;
4847 
4848   len          = 0; /* length of buf_si[] */
4849   merge->nsend = 0;
4850   for (proc=0; proc<size; proc++) {
4851     len_si[proc] = 0;
4852     if (proc == rank) {
4853       len_s[proc] = 0;
4854     } else {
4855       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4856       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4857     }
4858     if (len_s[proc]) {
4859       merge->nsend++;
4860       nrows = 0;
4861       for (i=owners[proc]; i<owners[proc+1]; i++) {
4862         if (ai[i+1] > ai[i]) nrows++;
4863       }
4864       len_si[proc] = 2*(nrows+1);
4865       len         += len_si[proc];
4866     }
4867   }
4868 
4869   /* determine the number and length of messages to receive for ij-structure */
4870   /*-------------------------------------------------------------------------*/
4871   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
4872   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
4873 
4874   /* post the Irecv of j-structure */
4875   /*-------------------------------*/
4876   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
4877   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
4878 
4879   /* post the Isend of j-structure */
4880   /*--------------------------------*/
4881   ierr = PetscMalloc2(merge->nsend,MPI_Request,&si_waits,merge->nsend,MPI_Request,&sj_waits);CHKERRQ(ierr);
4882 
4883   for (proc=0, k=0; proc<size; proc++) {
4884     if (!len_s[proc]) continue;
4885     i    = owners[proc];
4886     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
4887     k++;
4888   }
4889 
4890   /* receives and sends of j-structure are complete */
4891   /*------------------------------------------------*/
4892   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
4893   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
4894 
4895   /* send and recv i-structure */
4896   /*---------------------------*/
4897   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
4898   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
4899 
4900   ierr   = PetscMalloc((len+1)*sizeof(PetscInt),&buf_s);CHKERRQ(ierr);
4901   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4902   for (proc=0,k=0; proc<size; proc++) {
4903     if (!len_s[proc]) continue;
4904     /* form outgoing message for i-structure:
4905          buf_si[0]:                 nrows to be sent
4906                [1:nrows]:           row index (global)
4907                [nrows+1:2*nrows+1]: i-structure index
4908     */
4909     /*-------------------------------------------*/
4910     nrows       = len_si[proc]/2 - 1;
4911     buf_si_i    = buf_si + nrows+1;
4912     buf_si[0]   = nrows;
4913     buf_si_i[0] = 0;
4914     nrows       = 0;
4915     for (i=owners[proc]; i<owners[proc+1]; i++) {
4916       anzi = ai[i+1] - ai[i];
4917       if (anzi) {
4918         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4919         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4920         nrows++;
4921       }
4922     }
4923     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4924     k++;
4925     buf_si += len_si[proc];
4926   }
4927 
4928   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4929   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4930 
4931   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4932   for (i=0; i<merge->nrecv; i++) {
4933     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);
4934   }
4935 
4936   ierr = PetscFree(len_si);CHKERRQ(ierr);
4937   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4938   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4939   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4940   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4941   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4942   ierr = PetscFree(status);CHKERRQ(ierr);
4943 
4944   /* compute a local seq matrix in each processor */
4945   /*----------------------------------------------*/
4946   /* allocate bi array and free space for accumulating nonzero column info */
4947   ierr  = PetscMalloc((m+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
4948   bi[0] = 0;
4949 
4950   /* create and initialize a linked list */
4951   nlnk = N+1;
4952   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4953 
4954   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4955   len  = ai[owners[rank+1]] - ai[owners[rank]];
4956   ierr = PetscFreeSpaceGet((PetscInt)(2*len+1),&free_space);CHKERRQ(ierr);
4957 
4958   current_space = free_space;
4959 
4960   /* determine symbolic info for each local row */
4961   ierr = PetscMalloc3(merge->nrecv,PetscInt*,&buf_ri_k,merge->nrecv,PetscInt*,&nextrow,merge->nrecv,PetscInt*,&nextai);CHKERRQ(ierr);
4962 
4963   for (k=0; k<merge->nrecv; k++) {
4964     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4965     nrows       = *buf_ri_k[k];
4966     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4967     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4968   }
4969 
4970   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4971   len  = 0;
4972   for (i=0; i<m; i++) {
4973     bnzi = 0;
4974     /* add local non-zero cols of this proc's seqmat into lnk */
4975     arow  = owners[rank] + i;
4976     anzi  = ai[arow+1] - ai[arow];
4977     aj    = a->j + ai[arow];
4978     ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4979     bnzi += nlnk;
4980     /* add received col data into lnk */
4981     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4982       if (i == *nextrow[k]) { /* i-th row */
4983         anzi  = *(nextai[k]+1) - *nextai[k];
4984         aj    = buf_rj[k] + *nextai[k];
4985         ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4986         bnzi += nlnk;
4987         nextrow[k]++; nextai[k]++;
4988       }
4989     }
4990     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4991 
4992     /* if free space is not available, make more free space */
4993     if (current_space->local_remaining<bnzi) {
4994       ierr = PetscFreeSpaceGet(bnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
4995       nspacedouble++;
4996     }
4997     /* copy data into free space, then initialize lnk */
4998     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4999     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
5000 
5001     current_space->array           += bnzi;
5002     current_space->local_used      += bnzi;
5003     current_space->local_remaining -= bnzi;
5004 
5005     bi[i+1] = bi[i] + bnzi;
5006   }
5007 
5008   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
5009 
5010   ierr = PetscMalloc((bi[m]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
5011   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
5012   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
5013 
5014   /* create symbolic parallel matrix B_mpi */
5015   /*---------------------------------------*/
5016   ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
5017   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
5018   if (n==PETSC_DECIDE) {
5019     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
5020   } else {
5021     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
5022   }
5023   ierr = MatSetBlockSizes(B_mpi,bs,cbs);CHKERRQ(ierr);
5024   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
5025   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
5026   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
5027   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
5028 
5029   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
5030   B_mpi->assembled    = PETSC_FALSE;
5031   B_mpi->ops->destroy = MatDestroy_MPIAIJ_SeqsToMPI;
5032   merge->bi           = bi;
5033   merge->bj           = bj;
5034   merge->buf_ri       = buf_ri;
5035   merge->buf_rj       = buf_rj;
5036   merge->coi          = NULL;
5037   merge->coj          = NULL;
5038   merge->owners_co    = NULL;
5039 
5040   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
5041 
5042   /* attach the supporting struct to B_mpi for reuse */
5043   ierr    = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
5044   ierr    = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
5045   ierr    = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
5046   ierr    = PetscContainerDestroy(&container);CHKERRQ(ierr);
5047   *mpimat = B_mpi;
5048 
5049   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
5050   PetscFunctionReturn(0);
5051 }
5052 
5053 #undef __FUNCT__
5054 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJ"
5055 /*@C
5056       MatCreateMPIAIJSumSeqAIJ - Creates a MPIAIJ matrix by adding sequential
5057                  matrices from each processor
5058 
5059     Collective on MPI_Comm
5060 
5061    Input Parameters:
5062 +    comm - the communicators the parallel matrix will live on
5063 .    seqmat - the input sequential matrices
5064 .    m - number of local rows (or PETSC_DECIDE)
5065 .    n - number of local columns (or PETSC_DECIDE)
5066 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5067 
5068    Output Parameter:
5069 .    mpimat - the parallel matrix generated
5070 
5071     Level: advanced
5072 
5073    Notes:
5074      The dimensions of the sequential matrix in each processor MUST be the same.
5075      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
5076      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
5077 @*/
5078 PetscErrorCode  MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
5079 {
5080   PetscErrorCode ierr;
5081   PetscMPIInt    size;
5082 
5083   PetscFunctionBegin;
5084   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
5085   if (size == 1) {
5086     ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
5087     if (scall == MAT_INITIAL_MATRIX) {
5088       ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
5089     } else {
5090       ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
5091     }
5092     ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
5093     PetscFunctionReturn(0);
5094   }
5095   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
5096   if (scall == MAT_INITIAL_MATRIX) {
5097     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
5098   }
5099   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
5100   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
5101   PetscFunctionReturn(0);
5102 }
5103 
5104 #undef __FUNCT__
5105 #define __FUNCT__ "MatMPIAIJGetLocalMat"
5106 /*@
5107      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
5108           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
5109           with MatGetSize()
5110 
5111     Not Collective
5112 
5113    Input Parameters:
5114 +    A - the matrix
5115 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5116 
5117    Output Parameter:
5118 .    A_loc - the local sequential matrix generated
5119 
5120     Level: developer
5121 
5122 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
5123 
5124 @*/
5125 PetscErrorCode  MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
5126 {
5127   PetscErrorCode ierr;
5128   Mat_MPIAIJ     *mpimat=(Mat_MPIAIJ*)A->data;
5129   Mat_SeqAIJ     *mat,*a=(Mat_SeqAIJ*)(mpimat->A)->data,*b=(Mat_SeqAIJ*)(mpimat->B)->data;
5130   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*cmap=mpimat->garray;
5131   MatScalar      *aa=a->a,*ba=b->a,*cam;
5132   PetscScalar    *ca;
5133   PetscInt       am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
5134   PetscInt       *ci,*cj,col,ncols_d,ncols_o,jo;
5135   PetscBool      match;
5136 
5137   PetscFunctionBegin;
5138   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
5139   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
5140   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
5141   if (scall == MAT_INITIAL_MATRIX) {
5142     ierr  = PetscMalloc((1+am)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
5143     ci[0] = 0;
5144     for (i=0; i<am; i++) {
5145       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
5146     }
5147     ierr = PetscMalloc((1+ci[am])*sizeof(PetscInt),&cj);CHKERRQ(ierr);
5148     ierr = PetscMalloc((1+ci[am])*sizeof(PetscScalar),&ca);CHKERRQ(ierr);
5149     k    = 0;
5150     for (i=0; i<am; i++) {
5151       ncols_o = bi[i+1] - bi[i];
5152       ncols_d = ai[i+1] - ai[i];
5153       /* off-diagonal portion of A */
5154       for (jo=0; jo<ncols_o; jo++) {
5155         col = cmap[*bj];
5156         if (col >= cstart) break;
5157         cj[k]   = col; bj++;
5158         ca[k++] = *ba++;
5159       }
5160       /* diagonal portion of A */
5161       for (j=0; j<ncols_d; j++) {
5162         cj[k]   = cstart + *aj++;
5163         ca[k++] = *aa++;
5164       }
5165       /* off-diagonal portion of A */
5166       for (j=jo; j<ncols_o; j++) {
5167         cj[k]   = cmap[*bj++];
5168         ca[k++] = *ba++;
5169       }
5170     }
5171     /* put together the new matrix */
5172     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
5173     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
5174     /* Since these are PETSc arrays, change flags to free them as necessary. */
5175     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
5176     mat->free_a  = PETSC_TRUE;
5177     mat->free_ij = PETSC_TRUE;
5178     mat->nonew   = 0;
5179   } else if (scall == MAT_REUSE_MATRIX) {
5180     mat=(Mat_SeqAIJ*)(*A_loc)->data;
5181     ci = mat->i; cj = mat->j; cam = mat->a;
5182     for (i=0; i<am; i++) {
5183       /* off-diagonal portion of A */
5184       ncols_o = bi[i+1] - bi[i];
5185       for (jo=0; jo<ncols_o; jo++) {
5186         col = cmap[*bj];
5187         if (col >= cstart) break;
5188         *cam++ = *ba++; bj++;
5189       }
5190       /* diagonal portion of A */
5191       ncols_d = ai[i+1] - ai[i];
5192       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
5193       /* off-diagonal portion of A */
5194       for (j=jo; j<ncols_o; j++) {
5195         *cam++ = *ba++; bj++;
5196       }
5197     }
5198   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
5199   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
5200   PetscFunctionReturn(0);
5201 }
5202 
5203 #undef __FUNCT__
5204 #define __FUNCT__ "MatMPIAIJGetLocalMatCondensed"
5205 /*@C
5206      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MPIAIJ matrix by taking all its local rows and NON-ZERO columns
5207 
5208     Not Collective
5209 
5210    Input Parameters:
5211 +    A - the matrix
5212 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5213 -    row, col - index sets of rows and columns to extract (or NULL)
5214 
5215    Output Parameter:
5216 .    A_loc - the local sequential matrix generated
5217 
5218     Level: developer
5219 
5220 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
5221 
5222 @*/
5223 PetscErrorCode  MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
5224 {
5225   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
5226   PetscErrorCode ierr;
5227   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
5228   IS             isrowa,iscola;
5229   Mat            *aloc;
5230   PetscBool      match;
5231 
5232   PetscFunctionBegin;
5233   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
5234   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
5235   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
5236   if (!row) {
5237     start = A->rmap->rstart; end = A->rmap->rend;
5238     ierr  = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
5239   } else {
5240     isrowa = *row;
5241   }
5242   if (!col) {
5243     start = A->cmap->rstart;
5244     cmap  = a->garray;
5245     nzA   = a->A->cmap->n;
5246     nzB   = a->B->cmap->n;
5247     ierr  = PetscMalloc((nzA+nzB)*sizeof(PetscInt), &idx);CHKERRQ(ierr);
5248     ncols = 0;
5249     for (i=0; i<nzB; i++) {
5250       if (cmap[i] < start) idx[ncols++] = cmap[i];
5251       else break;
5252     }
5253     imark = i;
5254     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
5255     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
5256     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
5257   } else {
5258     iscola = *col;
5259   }
5260   if (scall != MAT_INITIAL_MATRIX) {
5261     ierr    = PetscMalloc(sizeof(Mat),&aloc);CHKERRQ(ierr);
5262     aloc[0] = *A_loc;
5263   }
5264   ierr   = MatGetSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
5265   *A_loc = aloc[0];
5266   ierr   = PetscFree(aloc);CHKERRQ(ierr);
5267   if (!row) {
5268     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
5269   }
5270   if (!col) {
5271     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
5272   }
5273   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
5274   PetscFunctionReturn(0);
5275 }
5276 
5277 #undef __FUNCT__
5278 #define __FUNCT__ "MatGetBrowsOfAcols"
5279 /*@C
5280     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
5281 
5282     Collective on Mat
5283 
5284    Input Parameters:
5285 +    A,B - the matrices in mpiaij format
5286 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5287 -    rowb, colb - index sets of rows and columns of B to extract (or NULL)
5288 
5289    Output Parameter:
5290 +    rowb, colb - index sets of rows and columns of B to extract
5291 -    B_seq - the sequential matrix generated
5292 
5293     Level: developer
5294 
5295 @*/
5296 PetscErrorCode  MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
5297 {
5298   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
5299   PetscErrorCode ierr;
5300   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
5301   IS             isrowb,iscolb;
5302   Mat            *bseq=NULL;
5303 
5304   PetscFunctionBegin;
5305   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
5306     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);
5307   }
5308   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
5309 
5310   if (scall == MAT_INITIAL_MATRIX) {
5311     start = A->cmap->rstart;
5312     cmap  = a->garray;
5313     nzA   = a->A->cmap->n;
5314     nzB   = a->B->cmap->n;
5315     ierr  = PetscMalloc((nzA+nzB)*sizeof(PetscInt), &idx);CHKERRQ(ierr);
5316     ncols = 0;
5317     for (i=0; i<nzB; i++) {  /* row < local row index */
5318       if (cmap[i] < start) idx[ncols++] = cmap[i];
5319       else break;
5320     }
5321     imark = i;
5322     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
5323     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
5324     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
5325     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
5326   } else {
5327     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
5328     isrowb  = *rowb; iscolb = *colb;
5329     ierr    = PetscMalloc(sizeof(Mat),&bseq);CHKERRQ(ierr);
5330     bseq[0] = *B_seq;
5331   }
5332   ierr   = MatGetSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
5333   *B_seq = bseq[0];
5334   ierr   = PetscFree(bseq);CHKERRQ(ierr);
5335   if (!rowb) {
5336     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
5337   } else {
5338     *rowb = isrowb;
5339   }
5340   if (!colb) {
5341     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
5342   } else {
5343     *colb = iscolb;
5344   }
5345   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
5346   PetscFunctionReturn(0);
5347 }
5348 
5349 #undef __FUNCT__
5350 #define __FUNCT__ "MatGetBrowsOfAoCols_MPIAIJ"
5351 /*
5352     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
5353     of the OFF-DIAGONAL portion of local A
5354 
5355     Collective on Mat
5356 
5357    Input Parameters:
5358 +    A,B - the matrices in mpiaij format
5359 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5360 
5361    Output Parameter:
5362 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
5363 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
5364 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
5365 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
5366 
5367     Level: developer
5368 
5369 */
5370 PetscErrorCode  MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
5371 {
5372   VecScatter_MPI_General *gen_to,*gen_from;
5373   PetscErrorCode         ierr;
5374   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
5375   Mat_SeqAIJ             *b_oth;
5376   VecScatter             ctx =a->Mvctx;
5377   MPI_Comm               comm;
5378   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
5379   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
5380   PetscScalar            *rvalues,*svalues;
5381   MatScalar              *b_otha,*bufa,*bufA;
5382   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
5383   MPI_Request            *rwaits = NULL,*swaits = NULL;
5384   MPI_Status             *sstatus,rstatus;
5385   PetscMPIInt            jj;
5386   PetscInt               *cols,sbs,rbs;
5387   PetscScalar            *vals;
5388 
5389   PetscFunctionBegin;
5390   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
5391   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
5392     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);
5393   }
5394   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5395   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
5396 
5397   gen_to   = (VecScatter_MPI_General*)ctx->todata;
5398   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
5399   rvalues  = gen_from->values; /* holds the length of receiving row */
5400   svalues  = gen_to->values;   /* holds the length of sending row */
5401   nrecvs   = gen_from->n;
5402   nsends   = gen_to->n;
5403 
5404   ierr    = PetscMalloc2(nrecvs,MPI_Request,&rwaits,nsends,MPI_Request,&swaits);CHKERRQ(ierr);
5405   srow    = gen_to->indices;    /* local row index to be sent */
5406   sstarts = gen_to->starts;
5407   sprocs  = gen_to->procs;
5408   sstatus = gen_to->sstatus;
5409   sbs     = gen_to->bs;
5410   rstarts = gen_from->starts;
5411   rprocs  = gen_from->procs;
5412   rbs     = gen_from->bs;
5413 
5414   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
5415   if (scall == MAT_INITIAL_MATRIX) {
5416     /* i-array */
5417     /*---------*/
5418     /*  post receives */
5419     for (i=0; i<nrecvs; i++) {
5420       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
5421       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
5422       ierr   = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5423     }
5424 
5425     /* pack the outgoing message */
5426     ierr = PetscMalloc2(nsends+1,PetscInt,&sstartsj,nrecvs+1,PetscInt,&rstartsj);CHKERRQ(ierr);
5427 
5428     sstartsj[0] = 0;
5429     rstartsj[0] = 0;
5430     len         = 0; /* total length of j or a array to be sent */
5431     k           = 0;
5432     for (i=0; i<nsends; i++) {
5433       rowlen = (PetscInt*)svalues + sstarts[i]*sbs;
5434       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
5435       for (j=0; j<nrows; j++) {
5436         row = srow[k] + B->rmap->range[rank]; /* global row idx */
5437         for (l=0; l<sbs; l++) {
5438           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr); /* rowlength */
5439 
5440           rowlen[j*sbs+l] = ncols;
5441 
5442           len += ncols;
5443           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr);
5444         }
5445         k++;
5446       }
5447       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5448 
5449       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
5450     }
5451     /* recvs and sends of i-array are completed */
5452     i = nrecvs;
5453     while (i--) {
5454       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5455     }
5456     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5457 
5458     /* allocate buffers for sending j and a arrays */
5459     ierr = PetscMalloc((len+1)*sizeof(PetscInt),&bufj);CHKERRQ(ierr);
5460     ierr = PetscMalloc((len+1)*sizeof(PetscScalar),&bufa);CHKERRQ(ierr);
5461 
5462     /* create i-array of B_oth */
5463     ierr = PetscMalloc((aBn+2)*sizeof(PetscInt),&b_othi);CHKERRQ(ierr);
5464 
5465     b_othi[0] = 0;
5466     len       = 0; /* total length of j or a array to be received */
5467     k         = 0;
5468     for (i=0; i<nrecvs; i++) {
5469       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
5470       nrows  = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be recieved */
5471       for (j=0; j<nrows; j++) {
5472         b_othi[k+1] = b_othi[k] + rowlen[j];
5473         len        += rowlen[j]; k++;
5474       }
5475       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
5476     }
5477 
5478     /* allocate space for j and a arrrays of B_oth */
5479     ierr = PetscMalloc((b_othi[aBn]+1)*sizeof(PetscInt),&b_othj);CHKERRQ(ierr);
5480     ierr = PetscMalloc((b_othi[aBn]+1)*sizeof(MatScalar),&b_otha);CHKERRQ(ierr);
5481 
5482     /* j-array */
5483     /*---------*/
5484     /*  post receives of j-array */
5485     for (i=0; i<nrecvs; i++) {
5486       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5487       ierr  = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5488     }
5489 
5490     /* pack the outgoing message j-array */
5491     k = 0;
5492     for (i=0; i<nsends; i++) {
5493       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5494       bufJ  = bufj+sstartsj[i];
5495       for (j=0; j<nrows; j++) {
5496         row = srow[k++] + B->rmap->range[rank];  /* global row idx */
5497         for (ll=0; ll<sbs; ll++) {
5498           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
5499           for (l=0; l<ncols; l++) {
5500             *bufJ++ = cols[l];
5501           }
5502           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
5503         }
5504       }
5505       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5506     }
5507 
5508     /* recvs and sends of j-array are completed */
5509     i = nrecvs;
5510     while (i--) {
5511       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5512     }
5513     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5514   } else if (scall == MAT_REUSE_MATRIX) {
5515     sstartsj = *startsj_s;
5516     rstartsj = *startsj_r;
5517     bufa     = *bufa_ptr;
5518     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
5519     b_otha   = b_oth->a;
5520   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
5521 
5522   /* a-array */
5523   /*---------*/
5524   /*  post receives of a-array */
5525   for (i=0; i<nrecvs; i++) {
5526     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5527     ierr  = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5528   }
5529 
5530   /* pack the outgoing message a-array */
5531   k = 0;
5532   for (i=0; i<nsends; i++) {
5533     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5534     bufA  = bufa+sstartsj[i];
5535     for (j=0; j<nrows; j++) {
5536       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
5537       for (ll=0; ll<sbs; ll++) {
5538         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
5539         for (l=0; l<ncols; l++) {
5540           *bufA++ = vals[l];
5541         }
5542         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
5543       }
5544     }
5545     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5546   }
5547   /* recvs and sends of a-array are completed */
5548   i = nrecvs;
5549   while (i--) {
5550     ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5551   }
5552   if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5553   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
5554 
5555   if (scall == MAT_INITIAL_MATRIX) {
5556     /* put together the new matrix */
5557     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
5558 
5559     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
5560     /* Since these are PETSc arrays, change flags to free them as necessary. */
5561     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
5562     b_oth->free_a  = PETSC_TRUE;
5563     b_oth->free_ij = PETSC_TRUE;
5564     b_oth->nonew   = 0;
5565 
5566     ierr = PetscFree(bufj);CHKERRQ(ierr);
5567     if (!startsj_s || !bufa_ptr) {
5568       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
5569       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
5570     } else {
5571       *startsj_s = sstartsj;
5572       *startsj_r = rstartsj;
5573       *bufa_ptr  = bufa;
5574     }
5575   }
5576   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5577   PetscFunctionReturn(0);
5578 }
5579 
5580 #undef __FUNCT__
5581 #define __FUNCT__ "MatGetCommunicationStructs"
5582 /*@C
5583   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
5584 
5585   Not Collective
5586 
5587   Input Parameters:
5588 . A - The matrix in mpiaij format
5589 
5590   Output Parameter:
5591 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
5592 . colmap - A map from global column index to local index into lvec
5593 - multScatter - A scatter from the argument of a matrix-vector product to lvec
5594 
5595   Level: developer
5596 
5597 @*/
5598 #if defined(PETSC_USE_CTABLE)
5599 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
5600 #else
5601 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
5602 #endif
5603 {
5604   Mat_MPIAIJ *a;
5605 
5606   PetscFunctionBegin;
5607   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
5608   PetscValidPointer(lvec, 2);
5609   PetscValidPointer(colmap, 3);
5610   PetscValidPointer(multScatter, 4);
5611   a = (Mat_MPIAIJ*) A->data;
5612   if (lvec) *lvec = a->lvec;
5613   if (colmap) *colmap = a->colmap;
5614   if (multScatter) *multScatter = a->Mvctx;
5615   PetscFunctionReturn(0);
5616 }
5617 
5618 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
5619 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
5620 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
5621 
5622 #undef __FUNCT__
5623 #define __FUNCT__ "MatMatMultNumeric_MPIDense_MPIAIJ"
5624 /*
5625     Computes (B'*A')' since computing B*A directly is untenable
5626 
5627                n                       p                          p
5628         (              )       (              )         (                  )
5629       m (      A       )  *  n (       B      )   =   m (         C        )
5630         (              )       (              )         (                  )
5631 
5632 */
5633 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
5634 {
5635   PetscErrorCode ierr;
5636   Mat            At,Bt,Ct;
5637 
5638   PetscFunctionBegin;
5639   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
5640   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
5641   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
5642   ierr = MatDestroy(&At);CHKERRQ(ierr);
5643   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
5644   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
5645   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
5646   PetscFunctionReturn(0);
5647 }
5648 
5649 #undef __FUNCT__
5650 #define __FUNCT__ "MatMatMultSymbolic_MPIDense_MPIAIJ"
5651 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
5652 {
5653   PetscErrorCode ierr;
5654   PetscInt       m=A->rmap->n,n=B->cmap->n;
5655   Mat            Cmat;
5656 
5657   PetscFunctionBegin;
5658   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);
5659   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
5660   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
5661   ierr = MatSetBlockSizes(Cmat,A->rmap->bs,B->cmap->bs);CHKERRQ(ierr);
5662   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
5663   ierr = MatMPIDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
5664   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5665   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5666 
5667   Cmat->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
5668 
5669   *C = Cmat;
5670   PetscFunctionReturn(0);
5671 }
5672 
5673 /* ----------------------------------------------------------------*/
5674 #undef __FUNCT__
5675 #define __FUNCT__ "MatMatMult_MPIDense_MPIAIJ"
5676 PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
5677 {
5678   PetscErrorCode ierr;
5679 
5680   PetscFunctionBegin;
5681   if (scall == MAT_INITIAL_MATRIX) {
5682     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5683     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
5684     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5685   }
5686   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5687   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
5688   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5689   PetscFunctionReturn(0);
5690 }
5691 
5692 #if defined(PETSC_HAVE_MUMPS)
5693 PETSC_EXTERN PetscErrorCode MatGetFactor_aij_mumps(Mat,MatFactorType,Mat*);
5694 #endif
5695 #if defined(PETSC_HAVE_PASTIX)
5696 PETSC_EXTERN PetscErrorCode MatGetFactor_mpiaij_pastix(Mat,MatFactorType,Mat*);
5697 #endif
5698 #if defined(PETSC_HAVE_SUPERLU_DIST)
5699 PETSC_EXTERN PetscErrorCode MatGetFactor_mpiaij_superlu_dist(Mat,MatFactorType,Mat*);
5700 #endif
5701 #if defined(PETSC_HAVE_CLIQUE)
5702 PETSC_EXTERN PetscErrorCode MatGetFactor_aij_clique(Mat,MatFactorType,Mat*);
5703 #endif
5704 
5705 /*MC
5706    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
5707 
5708    Options Database Keys:
5709 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
5710 
5711   Level: beginner
5712 
5713 .seealso: MatCreateAIJ()
5714 M*/
5715 
5716 #undef __FUNCT__
5717 #define __FUNCT__ "MatCreate_MPIAIJ"
5718 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
5719 {
5720   Mat_MPIAIJ     *b;
5721   PetscErrorCode ierr;
5722   PetscMPIInt    size;
5723 
5724   PetscFunctionBegin;
5725   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
5726 
5727   ierr          = PetscNewLog(B,Mat_MPIAIJ,&b);CHKERRQ(ierr);
5728   B->data       = (void*)b;
5729   ierr          = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
5730   B->assembled  = PETSC_FALSE;
5731   B->insertmode = NOT_SET_VALUES;
5732   b->size       = size;
5733 
5734   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank);CHKERRQ(ierr);
5735 
5736   /* build cache for off array entries formed */
5737   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash);CHKERRQ(ierr);
5738 
5739   b->donotstash  = PETSC_FALSE;
5740   b->colmap      = 0;
5741   b->garray      = 0;
5742   b->roworiented = PETSC_TRUE;
5743 
5744   /* stuff used for matrix vector multiply */
5745   b->lvec  = NULL;
5746   b->Mvctx = NULL;
5747 
5748   /* stuff for MatGetRow() */
5749   b->rowindices   = 0;
5750   b->rowvalues    = 0;
5751   b->getrowactive = PETSC_FALSE;
5752 
5753   /* flexible pointer used in CUSP/CUSPARSE classes */
5754   b->spptr = NULL;
5755 
5756 #if defined(PETSC_HAVE_MUMPS)
5757   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_mumps_C",MatGetFactor_aij_mumps);CHKERRQ(ierr);
5758 #endif
5759 #if defined(PETSC_HAVE_PASTIX)
5760   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_pastix_C",MatGetFactor_mpiaij_pastix);CHKERRQ(ierr);
5761 #endif
5762 #if defined(PETSC_HAVE_SUPERLU_DIST)
5763   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_superlu_dist_C",MatGetFactor_mpiaij_superlu_dist);CHKERRQ(ierr);
5764 #endif
5765 #if defined(PETSC_HAVE_CLIQUE)
5766   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_clique_C",MatGetFactor_aij_clique);CHKERRQ(ierr);
5767 #endif
5768   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ);CHKERRQ(ierr);
5769   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
5770   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetDiagonalBlock_C",MatGetDiagonalBlock_MPIAIJ);CHKERRQ(ierr);
5771   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
5772   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
5773   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
5774   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
5775   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
5776   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
5777   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
5778   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
5779   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
5780   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
5781   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
5782   PetscFunctionReturn(0);
5783 }
5784 
5785 #undef __FUNCT__
5786 #define __FUNCT__ "MatCreateMPIAIJWithSplitArrays"
5787 /*@
5788      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
5789          and "off-diagonal" part of the matrix in CSR format.
5790 
5791    Collective on MPI_Comm
5792 
5793    Input Parameters:
5794 +  comm - MPI communicator
5795 .  m - number of local rows (Cannot be PETSC_DECIDE)
5796 .  n - This value should be the same as the local size used in creating the
5797        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
5798        calculated if N is given) For square matrices n is almost always m.
5799 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
5800 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
5801 .   i - row indices for "diagonal" portion of matrix
5802 .   j - column indices
5803 .   a - matrix values
5804 .   oi - row indices for "off-diagonal" portion of matrix
5805 .   oj - column indices
5806 -   oa - matrix values
5807 
5808    Output Parameter:
5809 .   mat - the matrix
5810 
5811    Level: advanced
5812 
5813    Notes:
5814        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
5815        must free the arrays once the matrix has been destroyed and not before.
5816 
5817        The i and j indices are 0 based
5818 
5819        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
5820 
5821        This sets local rows and cannot be used to set off-processor values.
5822 
5823        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
5824        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
5825        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
5826        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
5827        keep track of the underlying array. Use MatSetOption(A,MAT_IGNORE_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
5828        communication if it is known that only local entries will be set.
5829 
5830 .keywords: matrix, aij, compressed row, sparse, parallel
5831 
5832 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
5833           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
5834 @*/
5835 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)
5836 {
5837   PetscErrorCode ierr;
5838   Mat_MPIAIJ     *maij;
5839 
5840   PetscFunctionBegin;
5841   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
5842   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
5843   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
5844   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
5845   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
5846   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
5847   maij = (Mat_MPIAIJ*) (*mat)->data;
5848 
5849   (*mat)->preallocated = PETSC_TRUE;
5850 
5851   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
5852   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
5853 
5854   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
5855   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
5856 
5857   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5858   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5859   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5860   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5861 
5862   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5863   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5864   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
5865   PetscFunctionReturn(0);
5866 }
5867 
5868 /*
5869     Special version for direct calls from Fortran
5870 */
5871 #include <petsc-private/fortranimpl.h>
5872 
5873 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5874 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
5875 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5876 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
5877 #endif
5878 
5879 /* Change these macros so can be used in void function */
5880 #undef CHKERRQ
5881 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
5882 #undef SETERRQ2
5883 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5884 #undef SETERRQ3
5885 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5886 #undef SETERRQ
5887 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
5888 
5889 #undef __FUNCT__
5890 #define __FUNCT__ "matsetvaluesmpiaij_"
5891 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)
5892 {
5893   Mat            mat  = *mmat;
5894   PetscInt       m    = *mm, n = *mn;
5895   InsertMode     addv = *maddv;
5896   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
5897   PetscScalar    value;
5898   PetscErrorCode ierr;
5899 
5900   MatCheckPreallocated(mat,1);
5901   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
5902 
5903 #if defined(PETSC_USE_DEBUG)
5904   else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
5905 #endif
5906   {
5907     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
5908     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
5909     PetscBool roworiented = aij->roworiented;
5910 
5911     /* Some Variables required in the macro */
5912     Mat        A                 = aij->A;
5913     Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
5914     PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
5915     MatScalar  *aa               = a->a;
5916     PetscBool  ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
5917     Mat        B                 = aij->B;
5918     Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
5919     PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5920     MatScalar  *ba               = b->a;
5921 
5922     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5923     PetscInt  nonew = a->nonew;
5924     MatScalar *ap1,*ap2;
5925 
5926     PetscFunctionBegin;
5927     for (i=0; i<m; i++) {
5928       if (im[i] < 0) continue;
5929 #if defined(PETSC_USE_DEBUG)
5930       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);
5931 #endif
5932       if (im[i] >= rstart && im[i] < rend) {
5933         row      = im[i] - rstart;
5934         lastcol1 = -1;
5935         rp1      = aj + ai[row];
5936         ap1      = aa + ai[row];
5937         rmax1    = aimax[row];
5938         nrow1    = ailen[row];
5939         low1     = 0;
5940         high1    = nrow1;
5941         lastcol2 = -1;
5942         rp2      = bj + bi[row];
5943         ap2      = ba + bi[row];
5944         rmax2    = bimax[row];
5945         nrow2    = bilen[row];
5946         low2     = 0;
5947         high2    = nrow2;
5948 
5949         for (j=0; j<n; j++) {
5950           if (roworiented) value = v[i*n+j];
5951           else value = v[i+j*m];
5952           if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES)) continue;
5953           if (in[j] >= cstart && in[j] < cend) {
5954             col = in[j] - cstart;
5955             MatSetValues_SeqAIJ_A_Private(row,col,value,addv);
5956           } else if (in[j] < 0) continue;
5957 #if defined(PETSC_USE_DEBUG)
5958           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);
5959 #endif
5960           else {
5961             if (mat->was_assembled) {
5962               if (!aij->colmap) {
5963                 ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5964               }
5965 #if defined(PETSC_USE_CTABLE)
5966               ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5967               col--;
5968 #else
5969               col = aij->colmap[in[j]] - 1;
5970 #endif
5971               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5972                 ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5973                 col  =  in[j];
5974                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5975                 B     = aij->B;
5976                 b     = (Mat_SeqAIJ*)B->data;
5977                 bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5978                 rp2   = bj + bi[row];
5979                 ap2   = ba + bi[row];
5980                 rmax2 = bimax[row];
5981                 nrow2 = bilen[row];
5982                 low2  = 0;
5983                 high2 = nrow2;
5984                 bm    = aij->B->rmap->n;
5985                 ba    = b->a;
5986               }
5987             } else col = in[j];
5988             MatSetValues_SeqAIJ_B_Private(row,col,value,addv);
5989           }
5990         }
5991       } else if (!aij->donotstash) {
5992         if (roworiented) {
5993           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5994         } else {
5995           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5996         }
5997       }
5998     }
5999   }
6000   PetscFunctionReturnVoid();
6001 }
6002 
6003