xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision c5a91927a79ad9cab725a7b5de69d80e2942facd)
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(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(mat,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     ierr = PetscFree2(redund->send_rank,redund->recv_rank);CHKERRQ(ierr);
2530     ierr = PetscFree(redund->sbuf_j);CHKERRQ(ierr);
2531     ierr = PetscFree(redund->sbuf_a);CHKERRQ(ierr);
2532     for (i=0; i<redund->nrecvs; i++) {
2533       ierr = PetscFree(redund->rbuf_j[i]);CHKERRQ(ierr);
2534       ierr = PetscFree(redund->rbuf_a[i]);CHKERRQ(ierr);
2535     }
2536     ierr = PetscFree4(redund->sbuf_nz,redund->rbuf_nz,redund->rbuf_j,redund->rbuf_a);CHKERRQ(ierr);
2537 
2538     if (redund->psubcomm) {
2539       ierr = PetscSubcommDestroy(&redund->psubcomm);CHKERRQ(ierr);
2540     }
2541 
2542     ierr = redund->Destroy(A);CHKERRQ(ierr);
2543     ierr = PetscFree(redund);CHKERRQ(ierr);
2544   }
2545   PetscFunctionReturn(0);
2546 }
2547 
2548 #undef __FUNCT__
2549 #define __FUNCT__ "MatGetRedundantMatrix_MPIAIJ_psubcomm"
2550 PetscErrorCode MatGetRedundantMatrix_MPIAIJ_psubcomm(Mat mat,PetscInt nsubcomm,PetscSubcomm psubcomm,MatReuse reuse,Mat *matredundant)
2551 {
2552   PetscMPIInt    rank,size;
2553   MPI_Comm       comm,subcomm=psubcomm->comm;
2554   PetscErrorCode ierr;
2555   PetscInt       nsends=0,nrecvs=0,i,rownz_max=0,M=mat->rmap->N,N=mat->cmap->N;
2556   PetscMPIInt    *send_rank= NULL,*recv_rank=NULL,subrank,subsize;
2557   PetscInt       *rowrange = mat->rmap->range;
2558   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2559   Mat            A = aij->A,B=aij->B,C=*matredundant;
2560   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data;
2561   PetscScalar    *sbuf_a;
2562   PetscInt       nzlocal=a->nz+b->nz;
2563   PetscInt       j,cstart=mat->cmap->rstart,cend=mat->cmap->rend,row,nzA,nzB,ncols,*cworkA,*cworkB;
2564   PetscInt       rstart=mat->rmap->rstart,rend=mat->rmap->rend,*bmap=aij->garray;
2565   PetscInt       *cols,ctmp,lwrite,*rptr,l,*sbuf_j;
2566   MatScalar      *aworkA,*aworkB;
2567   PetscScalar    *vals;
2568   PetscMPIInt    tag1,tag2,tag3,imdex;
2569   MPI_Request    *s_waits1=NULL,*s_waits2=NULL,*s_waits3=NULL;
2570   MPI_Request    *r_waits1=NULL,*r_waits2=NULL,*r_waits3=NULL;
2571   MPI_Status     recv_status,*send_status;
2572   PetscInt       *sbuf_nz=NULL,*rbuf_nz=NULL,count;
2573   PetscInt       **rbuf_j=NULL;
2574   PetscScalar    **rbuf_a=NULL;
2575   Mat_Redundant  *redund =NULL;
2576 
2577   PetscFunctionBegin;
2578   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
2579   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2580   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2581   ierr = MPI_Comm_rank(subcomm,&subrank);CHKERRQ(ierr);
2582   ierr = MPI_Comm_size(subcomm,&subsize);CHKERRQ(ierr);
2583 
2584   if (reuse == MAT_REUSE_MATRIX) {
2585     if (M != mat->rmap->N || N != mat->cmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. Wrong global size");
2586     if (subsize == 1) {
2587       Mat_SeqAIJ *c = (Mat_SeqAIJ*)C->data;
2588       redund = c->redundant;
2589     } else {
2590       Mat_MPIAIJ *c = (Mat_MPIAIJ*)C->data;
2591       redund = c->redundant;
2592     }
2593     if (nzlocal != redund->nzlocal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. Wrong nzlocal");
2594 
2595     nsends    = redund->nsends;
2596     nrecvs    = redund->nrecvs;
2597     send_rank = redund->send_rank;
2598     recv_rank = redund->recv_rank;
2599     sbuf_nz   = redund->sbuf_nz;
2600     rbuf_nz   = redund->rbuf_nz;
2601     sbuf_j    = redund->sbuf_j;
2602     sbuf_a    = redund->sbuf_a;
2603     rbuf_j    = redund->rbuf_j;
2604     rbuf_a    = redund->rbuf_a;
2605   }
2606 
2607   if (reuse == MAT_INITIAL_MATRIX) {
2608     PetscInt    nleftover,np_subcomm;
2609 
2610     /* get the destination processors' id send_rank, nsends and nrecvs */
2611     ierr = PetscMalloc2(size,PetscMPIInt,&send_rank,size,PetscMPIInt,&recv_rank);CHKERRQ(ierr);
2612 
2613     np_subcomm = size/nsubcomm;
2614     nleftover  = size - nsubcomm*np_subcomm;
2615 
2616     nsends = 0; nrecvs = 0;
2617     if (psubcomm->type == PETSC_SUBCOMM_INTERLACED) {
2618       /* -------------------------------------------*/
2619       for (i=0; i<size; i++) {
2620         if (subrank == i/nsubcomm && i != rank) { /* my_subrank == other's subrank */
2621           send_rank[nsends]   = i; nsends++;
2622           recv_rank[nrecvs++] = i;
2623           /* printf("[%d] send to and recv from [%d]\n",rank,i); */
2624         }
2625       }
2626       if (rank >= size - nleftover) { /* this proc is a leftover processor */
2627         i = size-nleftover-1;
2628         j = 0;
2629         while (j < nsubcomm - nleftover) {
2630           send_rank[nsends++] = i;
2631           i--; j++;
2632           /* printf("[%d] send to [%d]\n",rank,i); */
2633         }
2634       }
2635 
2636       if (nleftover && subsize == size/nsubcomm && subrank==subsize-1) { /* this proc recvs from leftover processors */
2637         for (i=0; i<nleftover; i++) {
2638           recv_rank[nrecvs++] = size-nleftover+i;
2639           /* printf("[%d] recv from [%d]\n",rank,i); */
2640         }
2641       }
2642     } else if (psubcomm->type == PETSC_SUBCOMM_CONTIGUOUS) {
2643       /* --------------------------------------------------*/
2644       PetscInt color,subcommstart;
2645       subcommstart=0;
2646       for (color=0; color<nsubcomm; color++) {
2647         if (psubcomm->color != color) {
2648           for (i=0; i<psubcomm->subsize[color]; i++) {
2649             if (subrank == i) { /* my_subrank == other's subrank */
2650               send_rank[nsends++] = subcommstart+i;
2651               recv_rank[nrecvs++] = subcommstart+i;
2652               /* printf("[%d] send to and recv from [%d]\n",rank,subcommstart+i); */
2653             }
2654           }
2655         }
2656         subcommstart += psubcomm->subsize[color];
2657       }
2658       if (nleftover && subrank == size/nsubcomm) { /* this proc is a leftover proc, send to subcomm that does not have leftover proc */
2659         subcommstart=0;
2660         for (color=0; color<nsubcomm; color++) {
2661           subcommstart += psubcomm->subsize[color];
2662           if (psubcomm->color == color) continue;
2663           if (psubcomm->subsize[color] == size/nsubcomm) { /* subcomm does not have leftover proc */
2664             send_rank[nsends++] = subcommstart -1; /* send to the last proc of subcomm[color] */
2665             /* printf("[%d] leftover send to [%d] \n",rank,subcommstart -1); */
2666           }
2667         }
2668       }
2669 
2670       if (nleftover && subsize == size/nsubcomm && subrank==subsize-1) { /* this proc recvs from leftover processors */
2671         subcommstart=0;
2672         for (color=0; color<nsubcomm; color++) {
2673           subcommstart += psubcomm->subsize[color];
2674           if (psubcomm->subsize[color] > size/nsubcomm) { /* subcomm has leftover proc */
2675             recv_rank[nrecvs++] = subcommstart -1; /* recv from the last proc of subcomm[color] */
2676             /* printf("[%d] recv from [%d]\n",rank,subcommstart -1); */
2677           }
2678         }
2679       }
2680     } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for PetscSubcomm type %D",psubcomm->type);
2681 
2682     /* allocate sbuf_j, sbuf_a */
2683     i    = nzlocal + rowrange[rank+1] - rowrange[rank] + 2;
2684     ierr = PetscMalloc(i*sizeof(PetscInt),&sbuf_j);CHKERRQ(ierr);
2685     ierr = PetscMalloc((nzlocal+1)*sizeof(PetscScalar),&sbuf_a);CHKERRQ(ierr);
2686     /*
2687     ierr = PetscSynchronizedPrintf(comm,"[%d] nsends %d, nrecvs %d\n",rank,nsends,nrecvs);CHKERRQ(ierr);
2688     ierr = PetscSynchronizedFlush(comm);CHKERRQ(ierr);
2689      */
2690   } /* endof if (reuse == MAT_INITIAL_MATRIX) */
2691 
2692   /* copy mat's local entries into the buffers */
2693   if (reuse == MAT_INITIAL_MATRIX) {
2694     rownz_max = 0;
2695     rptr      = sbuf_j;
2696     cols      = sbuf_j + rend-rstart + 1;
2697     vals      = sbuf_a;
2698     rptr[0]   = 0;
2699     for (i=0; i<rend-rstart; i++) {
2700       row    = i + rstart;
2701       nzA    = a->i[i+1] - a->i[i]; nzB = b->i[i+1] - b->i[i];
2702       ncols  = nzA + nzB;
2703       cworkA = a->j + a->i[i]; cworkB = b->j + b->i[i];
2704       aworkA = a->a + a->i[i]; aworkB = b->a + b->i[i];
2705       /* load the column indices for this row into cols */
2706       lwrite = 0;
2707       for (l=0; l<nzB; l++) {
2708         if ((ctmp = bmap[cworkB[l]]) < cstart) {
2709           vals[lwrite]   = aworkB[l];
2710           cols[lwrite++] = ctmp;
2711         }
2712       }
2713       for (l=0; l<nzA; l++) {
2714         vals[lwrite]   = aworkA[l];
2715         cols[lwrite++] = cstart + cworkA[l];
2716       }
2717       for (l=0; l<nzB; l++) {
2718         if ((ctmp = bmap[cworkB[l]]) >= cend) {
2719           vals[lwrite]   = aworkB[l];
2720           cols[lwrite++] = ctmp;
2721         }
2722       }
2723       vals     += ncols;
2724       cols     += ncols;
2725       rptr[i+1] = rptr[i] + ncols;
2726       if (rownz_max < ncols) rownz_max = ncols;
2727     }
2728     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);
2729   } else { /* only copy matrix values into sbuf_a */
2730     rptr    = sbuf_j;
2731     vals    = sbuf_a;
2732     rptr[0] = 0;
2733     for (i=0; i<rend-rstart; i++) {
2734       row    = i + rstart;
2735       nzA    = a->i[i+1] - a->i[i]; nzB = b->i[i+1] - b->i[i];
2736       ncols  = nzA + nzB;
2737       cworkB = b->j + b->i[i];
2738       aworkA = a->a + a->i[i];
2739       aworkB = b->a + b->i[i];
2740       lwrite = 0;
2741       for (l=0; l<nzB; l++) {
2742         if ((ctmp = bmap[cworkB[l]]) < cstart) vals[lwrite++] = aworkB[l];
2743       }
2744       for (l=0; l<nzA; l++) vals[lwrite++] = aworkA[l];
2745       for (l=0; l<nzB; l++) {
2746         if ((ctmp = bmap[cworkB[l]]) >= cend) vals[lwrite++] = aworkB[l];
2747       }
2748       vals     += ncols;
2749       rptr[i+1] = rptr[i] + ncols;
2750     }
2751   } /* endof if (reuse == MAT_INITIAL_MATRIX) */
2752 
2753   /* send nzlocal to others, and recv other's nzlocal */
2754   /*--------------------------------------------------*/
2755   if (reuse == MAT_INITIAL_MATRIX) {
2756     ierr = PetscMalloc2(3*(nsends + nrecvs)+1,MPI_Request,&s_waits3,nsends+1,MPI_Status,&send_status);CHKERRQ(ierr);
2757 
2758     s_waits2 = s_waits3 + nsends;
2759     s_waits1 = s_waits2 + nsends;
2760     r_waits1 = s_waits1 + nsends;
2761     r_waits2 = r_waits1 + nrecvs;
2762     r_waits3 = r_waits2 + nrecvs;
2763   } else {
2764     ierr = PetscMalloc2(nsends + nrecvs +1,MPI_Request,&s_waits3,nsends+1,MPI_Status,&send_status);CHKERRQ(ierr);
2765 
2766     r_waits3 = s_waits3 + nsends;
2767   }
2768 
2769   ierr = PetscObjectGetNewTag((PetscObject)mat,&tag3);CHKERRQ(ierr);
2770   if (reuse == MAT_INITIAL_MATRIX) {
2771     /* get new tags to keep the communication clean */
2772     ierr = PetscObjectGetNewTag((PetscObject)mat,&tag1);CHKERRQ(ierr);
2773     ierr = PetscObjectGetNewTag((PetscObject)mat,&tag2);CHKERRQ(ierr);
2774     ierr = PetscMalloc4(nsends,PetscInt,&sbuf_nz,nrecvs,PetscInt,&rbuf_nz,nrecvs,PetscInt*,&rbuf_j,nrecvs,PetscScalar*,&rbuf_a);CHKERRQ(ierr);
2775 
2776     /* post receives of other's nzlocal */
2777     for (i=0; i<nrecvs; i++) {
2778       ierr = MPI_Irecv(rbuf_nz+i,1,MPIU_INT,MPI_ANY_SOURCE,tag1,comm,r_waits1+i);CHKERRQ(ierr);
2779     }
2780     /* send nzlocal to others */
2781     for (i=0; i<nsends; i++) {
2782       sbuf_nz[i] = nzlocal;
2783       ierr       = MPI_Isend(sbuf_nz+i,1,MPIU_INT,send_rank[i],tag1,comm,s_waits1+i);CHKERRQ(ierr);
2784     }
2785     /* wait on receives of nzlocal; allocate space for rbuf_j, rbuf_a */
2786     count = nrecvs;
2787     while (count) {
2788       ierr = MPI_Waitany(nrecvs,r_waits1,&imdex,&recv_status);CHKERRQ(ierr);
2789 
2790       recv_rank[imdex] = recv_status.MPI_SOURCE;
2791       /* allocate rbuf_a and rbuf_j; then post receives of rbuf_j */
2792       ierr = PetscMalloc((rbuf_nz[imdex]+1)*sizeof(PetscScalar),&rbuf_a[imdex]);CHKERRQ(ierr);
2793 
2794       i = rowrange[recv_status.MPI_SOURCE+1] - rowrange[recv_status.MPI_SOURCE]; /* number of expected mat->i */
2795 
2796       rbuf_nz[imdex] += i + 2;
2797 
2798       ierr = PetscMalloc(rbuf_nz[imdex]*sizeof(PetscInt),&rbuf_j[imdex]);CHKERRQ(ierr);
2799       ierr = MPI_Irecv(rbuf_j[imdex],rbuf_nz[imdex],MPIU_INT,recv_status.MPI_SOURCE,tag2,comm,r_waits2+imdex);CHKERRQ(ierr);
2800       count--;
2801     }
2802     /* wait on sends of nzlocal */
2803     if (nsends) {ierr = MPI_Waitall(nsends,s_waits1,send_status);CHKERRQ(ierr);}
2804     /* send mat->i,j to others, and recv from other's */
2805     /*------------------------------------------------*/
2806     for (i=0; i<nsends; i++) {
2807       j    = nzlocal + rowrange[rank+1] - rowrange[rank] + 1;
2808       ierr = MPI_Isend(sbuf_j,j,MPIU_INT,send_rank[i],tag2,comm,s_waits2+i);CHKERRQ(ierr);
2809     }
2810     /* wait on receives of mat->i,j */
2811     /*------------------------------*/
2812     count = nrecvs;
2813     while (count) {
2814       ierr = MPI_Waitany(nrecvs,r_waits2,&imdex,&recv_status);CHKERRQ(ierr);
2815       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);
2816       count--;
2817     }
2818     /* wait on sends of mat->i,j */
2819     /*---------------------------*/
2820     if (nsends) {
2821       ierr = MPI_Waitall(nsends,s_waits2,send_status);CHKERRQ(ierr);
2822     }
2823   } /* endof if (reuse == MAT_INITIAL_MATRIX) */
2824 
2825   /* post receives, send and receive mat->a */
2826   /*----------------------------------------*/
2827   for (imdex=0; imdex<nrecvs; imdex++) {
2828     ierr = MPI_Irecv(rbuf_a[imdex],rbuf_nz[imdex],MPIU_SCALAR,recv_rank[imdex],tag3,comm,r_waits3+imdex);CHKERRQ(ierr);
2829   }
2830   for (i=0; i<nsends; i++) {
2831     ierr = MPI_Isend(sbuf_a,nzlocal,MPIU_SCALAR,send_rank[i],tag3,comm,s_waits3+i);CHKERRQ(ierr);
2832   }
2833   count = nrecvs;
2834   while (count) {
2835     ierr = MPI_Waitany(nrecvs,r_waits3,&imdex,&recv_status);CHKERRQ(ierr);
2836     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);
2837     count--;
2838   }
2839   if (nsends) {
2840     ierr = MPI_Waitall(nsends,s_waits3,send_status);CHKERRQ(ierr);
2841   }
2842 
2843   ierr = PetscFree2(s_waits3,send_status);CHKERRQ(ierr);
2844 
2845   /* create redundant matrix */
2846   /*-------------------------*/
2847   if (reuse == MAT_INITIAL_MATRIX) {
2848     const PetscInt *range;
2849     PetscInt       rstart_sub,rend_sub,mloc_sub;
2850 
2851     /* compute rownz_max for preallocation */
2852     for (imdex=0; imdex<nrecvs; imdex++) {
2853       j    = rowrange[recv_rank[imdex]+1] - rowrange[recv_rank[imdex]];
2854       rptr = rbuf_j[imdex];
2855       for (i=0; i<j; i++) {
2856         ncols = rptr[i+1] - rptr[i];
2857         if (rownz_max < ncols) rownz_max = ncols;
2858       }
2859     }
2860 
2861     ierr = MatCreate(subcomm,&C);CHKERRQ(ierr);
2862 
2863     /* get local size of redundant matrix
2864        - mloc_sub is chosen for PETSC_SUBCOMM_INTERLACED, works for other types, but may not efficient! */
2865     ierr = MatGetOwnershipRanges(mat,&range);CHKERRQ(ierr);
2866     rstart_sub = range[nsubcomm*subrank];
2867     if (subrank+1 < subsize) { /* not the last proc in subcomm */
2868       rend_sub = range[nsubcomm*(subrank+1)];
2869     } else {
2870       rend_sub = mat->rmap->N;
2871     }
2872     mloc_sub = rend_sub - rstart_sub;
2873 
2874     if (M == N) {
2875       ierr = MatSetSizes(C,mloc_sub,mloc_sub,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
2876     } else { /* non-square matrix */
2877       ierr = MatSetSizes(C,mloc_sub,PETSC_DECIDE,PETSC_DECIDE,mat->cmap->N);CHKERRQ(ierr);
2878     }
2879     ierr = MatSetBlockSizes(C,mat->rmap->bs,mat->cmap->bs);CHKERRQ(ierr);
2880     ierr = MatSetFromOptions(C);CHKERRQ(ierr);
2881     ierr = MatSeqAIJSetPreallocation(C,rownz_max,NULL);CHKERRQ(ierr);
2882     ierr = MatMPIAIJSetPreallocation(C,rownz_max,NULL,rownz_max,NULL);CHKERRQ(ierr);
2883   } else {
2884     C = *matredundant;
2885   }
2886 
2887   /* insert local matrix entries */
2888   rptr = sbuf_j;
2889   cols = sbuf_j + rend-rstart + 1;
2890   vals = sbuf_a;
2891   for (i=0; i<rend-rstart; i++) {
2892     row   = i + rstart;
2893     ncols = rptr[i+1] - rptr[i];
2894     ierr  = MatSetValues(C,1,&row,ncols,cols,vals,INSERT_VALUES);CHKERRQ(ierr);
2895     vals += ncols;
2896     cols += ncols;
2897   }
2898   /* insert received matrix entries */
2899   for (imdex=0; imdex<nrecvs; imdex++) {
2900     rstart = rowrange[recv_rank[imdex]];
2901     rend   = rowrange[recv_rank[imdex]+1];
2902     /* printf("[%d] insert rows %d - %d\n",rank,rstart,rend-1); */
2903     rptr   = rbuf_j[imdex];
2904     cols   = rbuf_j[imdex] + rend-rstart + 1;
2905     vals   = rbuf_a[imdex];
2906     for (i=0; i<rend-rstart; i++) {
2907       row   = i + rstart;
2908       ncols = rptr[i+1] - rptr[i];
2909       ierr  = MatSetValues(C,1,&row,ncols,cols,vals,INSERT_VALUES);CHKERRQ(ierr);
2910       vals += ncols;
2911       cols += ncols;
2912     }
2913   }
2914   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2915   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2916 
2917   if (reuse == MAT_INITIAL_MATRIX) {
2918     *matredundant = C;
2919 
2920     /* create a supporting struct and attach it to C for reuse */
2921     ierr = PetscNewLog(C,Mat_Redundant,&redund);CHKERRQ(ierr);
2922     if (subsize == 1) {
2923       Mat_SeqAIJ *c = (Mat_SeqAIJ*)C->data;
2924       c->redundant = redund;
2925     } else {
2926       Mat_MPIAIJ *c = (Mat_MPIAIJ*)C->data;
2927       c->redundant = redund;
2928     }
2929 
2930     redund->nzlocal   = nzlocal;
2931     redund->nsends    = nsends;
2932     redund->nrecvs    = nrecvs;
2933     redund->send_rank = send_rank;
2934     redund->recv_rank = recv_rank;
2935     redund->sbuf_nz   = sbuf_nz;
2936     redund->rbuf_nz   = rbuf_nz;
2937     redund->sbuf_j    = sbuf_j;
2938     redund->sbuf_a    = sbuf_a;
2939     redund->rbuf_j    = rbuf_j;
2940     redund->rbuf_a    = rbuf_a;
2941     redund->psubcomm  = NULL;
2942 
2943     redund->Destroy = C->ops->destroy;
2944     C->ops->destroy = MatDestroy_MatRedundant;
2945   }
2946   PetscFunctionReturn(0);
2947 }
2948 
2949 #undef __FUNCT__
2950 #define __FUNCT__ "MatGetRedundantMatrix_MPIAIJ"
2951 PetscErrorCode MatGetRedundantMatrix_MPIAIJ(Mat mat,PetscInt nsubcomm,MPI_Comm subcomm,MatReuse reuse,Mat *matredundant)
2952 {
2953   PetscErrorCode ierr;
2954 
2955   PetscFunctionBegin;
2956   if (subcomm == MPI_COMM_NULL || subcomm == PETSC_COMM_SELF) { /* create psubcomm */
2957     MPI_Comm       comm;
2958     PetscSubcomm   psubcomm;
2959     PetscMPIInt    size,subsize;
2960 
2961     ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
2962     ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2963     ierr = PetscSubcommCreate(comm,&psubcomm);CHKERRQ(ierr);
2964     ierr = PetscSubcommSetNumber(psubcomm,nsubcomm);CHKERRQ(ierr);
2965     ierr = PetscSubcommSetType(psubcomm,PETSC_SUBCOMM_INTERLACED);CHKERRQ(ierr);
2966     ierr = PetscSubcommSetFromOptions(psubcomm);CHKERRQ(ierr);
2967 
2968     ierr = MatGetRedundantMatrix_MPIAIJ_psubcomm(mat,nsubcomm,psubcomm,reuse,matredundant);CHKERRQ(ierr);
2969 
2970     /* free psubcomm in MatDestroy_MatRedundant() */
2971     ierr = MPI_Comm_size(psubcomm->comm,&subsize);CHKERRQ(ierr);
2972     if (subsize == 1) {
2973       Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*matredundant)->data;
2974       c->redundant->psubcomm = psubcomm;
2975     } else {
2976       Mat_MPIAIJ *c = (Mat_MPIAIJ*)(*matredundant)->data;
2977       c->redundant->psubcomm = psubcomm ;
2978     }
2979   } else {
2980     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support yet");
2981   }
2982   PetscFunctionReturn(0);
2983 }
2984 
2985 #undef __FUNCT__
2986 #define __FUNCT__ "MatGetRowMaxAbs_MPIAIJ"
2987 PetscErrorCode MatGetRowMaxAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2988 {
2989   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2990   PetscErrorCode ierr;
2991   PetscInt       i,*idxb = 0;
2992   PetscScalar    *va,*vb;
2993   Vec            vtmp;
2994 
2995   PetscFunctionBegin;
2996   ierr = MatGetRowMaxAbs(a->A,v,idx);CHKERRQ(ierr);
2997   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2998   if (idx) {
2999     for (i=0; i<A->rmap->n; i++) {
3000       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
3001     }
3002   }
3003 
3004   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
3005   if (idx) {
3006     ierr = PetscMalloc(A->rmap->n*sizeof(PetscInt),&idxb);CHKERRQ(ierr);
3007   }
3008   ierr = MatGetRowMaxAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
3009   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
3010 
3011   for (i=0; i<A->rmap->n; i++) {
3012     if (PetscAbsScalar(va[i]) < PetscAbsScalar(vb[i])) {
3013       va[i] = vb[i];
3014       if (idx) idx[i] = a->garray[idxb[i]];
3015     }
3016   }
3017 
3018   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
3019   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
3020   ierr = PetscFree(idxb);CHKERRQ(ierr);
3021   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
3022   PetscFunctionReturn(0);
3023 }
3024 
3025 #undef __FUNCT__
3026 #define __FUNCT__ "MatGetRowMinAbs_MPIAIJ"
3027 PetscErrorCode MatGetRowMinAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
3028 {
3029   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3030   PetscErrorCode ierr;
3031   PetscInt       i,*idxb = 0;
3032   PetscScalar    *va,*vb;
3033   Vec            vtmp;
3034 
3035   PetscFunctionBegin;
3036   ierr = MatGetRowMinAbs(a->A,v,idx);CHKERRQ(ierr);
3037   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
3038   if (idx) {
3039     for (i=0; i<A->cmap->n; i++) {
3040       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
3041     }
3042   }
3043 
3044   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
3045   if (idx) {
3046     ierr = PetscMalloc(A->rmap->n*sizeof(PetscInt),&idxb);CHKERRQ(ierr);
3047   }
3048   ierr = MatGetRowMinAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
3049   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
3050 
3051   for (i=0; i<A->rmap->n; i++) {
3052     if (PetscAbsScalar(va[i]) > PetscAbsScalar(vb[i])) {
3053       va[i] = vb[i];
3054       if (idx) idx[i] = a->garray[idxb[i]];
3055     }
3056   }
3057 
3058   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
3059   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
3060   ierr = PetscFree(idxb);CHKERRQ(ierr);
3061   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
3062   PetscFunctionReturn(0);
3063 }
3064 
3065 #undef __FUNCT__
3066 #define __FUNCT__ "MatGetRowMin_MPIAIJ"
3067 PetscErrorCode MatGetRowMin_MPIAIJ(Mat A, Vec v, PetscInt idx[])
3068 {
3069   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
3070   PetscInt       n      = A->rmap->n;
3071   PetscInt       cstart = A->cmap->rstart;
3072   PetscInt       *cmap  = mat->garray;
3073   PetscInt       *diagIdx, *offdiagIdx;
3074   Vec            diagV, offdiagV;
3075   PetscScalar    *a, *diagA, *offdiagA;
3076   PetscInt       r;
3077   PetscErrorCode ierr;
3078 
3079   PetscFunctionBegin;
3080   ierr = PetscMalloc2(n,PetscInt,&diagIdx,n,PetscInt,&offdiagIdx);CHKERRQ(ierr);
3081   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &diagV);CHKERRQ(ierr);
3082   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &offdiagV);CHKERRQ(ierr);
3083   ierr = MatGetRowMin(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
3084   ierr = MatGetRowMin(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
3085   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
3086   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
3087   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
3088   for (r = 0; r < n; ++r) {
3089     if (PetscAbsScalar(diagA[r]) <= PetscAbsScalar(offdiagA[r])) {
3090       a[r]   = diagA[r];
3091       idx[r] = cstart + diagIdx[r];
3092     } else {
3093       a[r]   = offdiagA[r];
3094       idx[r] = cmap[offdiagIdx[r]];
3095     }
3096   }
3097   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
3098   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
3099   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
3100   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
3101   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
3102   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
3103   PetscFunctionReturn(0);
3104 }
3105 
3106 #undef __FUNCT__
3107 #define __FUNCT__ "MatGetRowMax_MPIAIJ"
3108 PetscErrorCode MatGetRowMax_MPIAIJ(Mat A, Vec v, PetscInt idx[])
3109 {
3110   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
3111   PetscInt       n      = A->rmap->n;
3112   PetscInt       cstart = A->cmap->rstart;
3113   PetscInt       *cmap  = mat->garray;
3114   PetscInt       *diagIdx, *offdiagIdx;
3115   Vec            diagV, offdiagV;
3116   PetscScalar    *a, *diagA, *offdiagA;
3117   PetscInt       r;
3118   PetscErrorCode ierr;
3119 
3120   PetscFunctionBegin;
3121   ierr = PetscMalloc2(n,PetscInt,&diagIdx,n,PetscInt,&offdiagIdx);CHKERRQ(ierr);
3122   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &diagV);CHKERRQ(ierr);
3123   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &offdiagV);CHKERRQ(ierr);
3124   ierr = MatGetRowMax(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
3125   ierr = MatGetRowMax(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
3126   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
3127   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
3128   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
3129   for (r = 0; r < n; ++r) {
3130     if (PetscAbsScalar(diagA[r]) >= PetscAbsScalar(offdiagA[r])) {
3131       a[r]   = diagA[r];
3132       idx[r] = cstart + diagIdx[r];
3133     } else {
3134       a[r]   = offdiagA[r];
3135       idx[r] = cmap[offdiagIdx[r]];
3136     }
3137   }
3138   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
3139   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
3140   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
3141   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
3142   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
3143   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
3144   PetscFunctionReturn(0);
3145 }
3146 
3147 #undef __FUNCT__
3148 #define __FUNCT__ "MatGetSeqNonzeroStructure_MPIAIJ"
3149 PetscErrorCode MatGetSeqNonzeroStructure_MPIAIJ(Mat mat,Mat *newmat)
3150 {
3151   PetscErrorCode ierr;
3152   Mat            *dummy;
3153 
3154   PetscFunctionBegin;
3155   ierr    = MatGetSubMatrix_MPIAIJ_All(mat,MAT_DO_NOT_GET_VALUES,MAT_INITIAL_MATRIX,&dummy);CHKERRQ(ierr);
3156   *newmat = *dummy;
3157   ierr    = PetscFree(dummy);CHKERRQ(ierr);
3158   PetscFunctionReturn(0);
3159 }
3160 
3161 extern PetscErrorCode  MatFDColoringApply_AIJ(Mat,MatFDColoring,Vec,MatStructure*,void*);
3162 
3163 #undef __FUNCT__
3164 #define __FUNCT__ "MatInvertBlockDiagonal_MPIAIJ"
3165 PetscErrorCode  MatInvertBlockDiagonal_MPIAIJ(Mat A,const PetscScalar **values)
3166 {
3167   Mat_MPIAIJ     *a = (Mat_MPIAIJ*) A->data;
3168   PetscErrorCode ierr;
3169 
3170   PetscFunctionBegin;
3171   ierr = MatInvertBlockDiagonal(a->A,values);CHKERRQ(ierr);
3172   PetscFunctionReturn(0);
3173 }
3174 
3175 #undef __FUNCT__
3176 #define __FUNCT__ "MatSetRandom_MPIAIJ"
3177 static PetscErrorCode  MatSetRandom_MPIAIJ(Mat x,PetscRandom rctx)
3178 {
3179   PetscErrorCode ierr;
3180   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)x->data;
3181 
3182   PetscFunctionBegin;
3183   ierr = MatSetRandom(aij->A,rctx);CHKERRQ(ierr);
3184   ierr = MatSetRandom(aij->B,rctx);CHKERRQ(ierr);
3185   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3186   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3187   PetscFunctionReturn(0);
3188 }
3189 
3190 /* -------------------------------------------------------------------*/
3191 static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
3192                                        MatGetRow_MPIAIJ,
3193                                        MatRestoreRow_MPIAIJ,
3194                                        MatMult_MPIAIJ,
3195                                 /* 4*/ MatMultAdd_MPIAIJ,
3196                                        MatMultTranspose_MPIAIJ,
3197                                        MatMultTransposeAdd_MPIAIJ,
3198 #if defined(PETSC_HAVE_PBGL)
3199                                        MatSolve_MPIAIJ,
3200 #else
3201                                        0,
3202 #endif
3203                                        0,
3204                                        0,
3205                                 /*10*/ 0,
3206                                        0,
3207                                        0,
3208                                        MatSOR_MPIAIJ,
3209                                        MatTranspose_MPIAIJ,
3210                                 /*15*/ MatGetInfo_MPIAIJ,
3211                                        MatEqual_MPIAIJ,
3212                                        MatGetDiagonal_MPIAIJ,
3213                                        MatDiagonalScale_MPIAIJ,
3214                                        MatNorm_MPIAIJ,
3215                                 /*20*/ MatAssemblyBegin_MPIAIJ,
3216                                        MatAssemblyEnd_MPIAIJ,
3217                                        MatSetOption_MPIAIJ,
3218                                        MatZeroEntries_MPIAIJ,
3219                                 /*24*/ MatZeroRows_MPIAIJ,
3220                                        0,
3221 #if defined(PETSC_HAVE_PBGL)
3222                                        0,
3223 #else
3224                                        0,
3225 #endif
3226                                        0,
3227                                        0,
3228                                 /*29*/ MatSetUp_MPIAIJ,
3229 #if defined(PETSC_HAVE_PBGL)
3230                                        0,
3231 #else
3232                                        0,
3233 #endif
3234                                        0,
3235                                        0,
3236                                        0,
3237                                 /*34*/ MatDuplicate_MPIAIJ,
3238                                        0,
3239                                        0,
3240                                        0,
3241                                        0,
3242                                 /*39*/ MatAXPY_MPIAIJ,
3243                                        MatGetSubMatrices_MPIAIJ,
3244                                        MatIncreaseOverlap_MPIAIJ,
3245                                        MatGetValues_MPIAIJ,
3246                                        MatCopy_MPIAIJ,
3247                                 /*44*/ MatGetRowMax_MPIAIJ,
3248                                        MatScale_MPIAIJ,
3249                                        0,
3250                                        0,
3251                                        MatZeroRowsColumns_MPIAIJ,
3252                                 /*49*/ MatSetRandom_MPIAIJ,
3253                                        0,
3254                                        0,
3255                                        0,
3256                                        0,
3257                                 /*54*/ MatFDColoringCreate_MPIAIJ,
3258                                        0,
3259                                        MatSetUnfactored_MPIAIJ,
3260                                        MatPermute_MPIAIJ,
3261                                        0,
3262                                 /*59*/ MatGetSubMatrix_MPIAIJ,
3263                                        MatDestroy_MPIAIJ,
3264                                        MatView_MPIAIJ,
3265                                        0,
3266                                        MatMatMatMult_MPIAIJ_MPIAIJ_MPIAIJ,
3267                                 /*64*/ MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ,
3268                                        MatMatMatMultNumeric_MPIAIJ_MPIAIJ_MPIAIJ,
3269                                        0,
3270                                        0,
3271                                        0,
3272                                 /*69*/ MatGetRowMaxAbs_MPIAIJ,
3273                                        MatGetRowMinAbs_MPIAIJ,
3274                                        0,
3275                                        MatSetColoring_MPIAIJ,
3276                                        0,
3277                                        MatSetValuesAdifor_MPIAIJ,
3278                                 /*75*/ MatFDColoringApply_AIJ,
3279                                        0,
3280                                        0,
3281                                        0,
3282                                        MatFindZeroDiagonals_MPIAIJ,
3283                                 /*80*/ 0,
3284                                        0,
3285                                        0,
3286                                 /*83*/ MatLoad_MPIAIJ,
3287                                        0,
3288                                        0,
3289                                        0,
3290                                        0,
3291                                        0,
3292                                 /*89*/ MatMatMult_MPIAIJ_MPIAIJ,
3293                                        MatMatMultSymbolic_MPIAIJ_MPIAIJ,
3294                                        MatMatMultNumeric_MPIAIJ_MPIAIJ,
3295                                        MatPtAP_MPIAIJ_MPIAIJ,
3296                                        MatPtAPSymbolic_MPIAIJ_MPIAIJ,
3297                                 /*94*/ MatPtAPNumeric_MPIAIJ_MPIAIJ,
3298                                        0,
3299                                        0,
3300                                        0,
3301                                        0,
3302                                 /*99*/ 0,
3303                                        0,
3304                                        0,
3305                                        MatConjugate_MPIAIJ,
3306                                        0,
3307                                 /*104*/MatSetValuesRow_MPIAIJ,
3308                                        MatRealPart_MPIAIJ,
3309                                        MatImaginaryPart_MPIAIJ,
3310                                        0,
3311                                        0,
3312                                 /*109*/0,
3313                                        MatGetRedundantMatrix_MPIAIJ,
3314                                        MatGetRowMin_MPIAIJ,
3315                                        0,
3316                                        0,
3317                                 /*114*/MatGetSeqNonzeroStructure_MPIAIJ,
3318                                        0,
3319                                        0,
3320                                        0,
3321                                        0,
3322                                 /*119*/0,
3323                                        0,
3324                                        0,
3325                                        0,
3326                                        MatGetMultiProcBlock_MPIAIJ,
3327                                 /*124*/MatFindNonzeroRows_MPIAIJ,
3328                                        MatGetColumnNorms_MPIAIJ,
3329                                        MatInvertBlockDiagonal_MPIAIJ,
3330                                        0,
3331                                        MatGetSubMatricesParallel_MPIAIJ,
3332                                 /*129*/0,
3333                                        MatTransposeMatMult_MPIAIJ_MPIAIJ,
3334                                        MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ,
3335                                        MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ,
3336                                        0,
3337                                 /*134*/0,
3338                                        0,
3339                                        0,
3340                                        0,
3341                                        0,
3342                                 /*139*/0,
3343                                        0
3344 };
3345 
3346 /* ----------------------------------------------------------------------------------------*/
3347 
3348 #undef __FUNCT__
3349 #define __FUNCT__ "MatStoreValues_MPIAIJ"
3350 PetscErrorCode  MatStoreValues_MPIAIJ(Mat mat)
3351 {
3352   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
3353   PetscErrorCode ierr;
3354 
3355   PetscFunctionBegin;
3356   ierr = MatStoreValues(aij->A);CHKERRQ(ierr);
3357   ierr = MatStoreValues(aij->B);CHKERRQ(ierr);
3358   PetscFunctionReturn(0);
3359 }
3360 
3361 #undef __FUNCT__
3362 #define __FUNCT__ "MatRetrieveValues_MPIAIJ"
3363 PetscErrorCode  MatRetrieveValues_MPIAIJ(Mat mat)
3364 {
3365   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
3366   PetscErrorCode ierr;
3367 
3368   PetscFunctionBegin;
3369   ierr = MatRetrieveValues(aij->A);CHKERRQ(ierr);
3370   ierr = MatRetrieveValues(aij->B);CHKERRQ(ierr);
3371   PetscFunctionReturn(0);
3372 }
3373 
3374 #undef __FUNCT__
3375 #define __FUNCT__ "MatMPIAIJSetPreallocation_MPIAIJ"
3376 PetscErrorCode  MatMPIAIJSetPreallocation_MPIAIJ(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3377 {
3378   Mat_MPIAIJ     *b;
3379   PetscErrorCode ierr;
3380 
3381   PetscFunctionBegin;
3382   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3383   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3384   b = (Mat_MPIAIJ*)B->data;
3385 
3386   if (!B->preallocated) {
3387     /* Explicitly create 2 MATSEQAIJ matrices. */
3388     ierr = MatCreate(PETSC_COMM_SELF,&b->A);CHKERRQ(ierr);
3389     ierr = MatSetSizes(b->A,B->rmap->n,B->cmap->n,B->rmap->n,B->cmap->n);CHKERRQ(ierr);
3390     ierr = MatSetBlockSizes(b->A,B->rmap->bs,B->cmap->bs);CHKERRQ(ierr);
3391     ierr = MatSetType(b->A,MATSEQAIJ);CHKERRQ(ierr);
3392     ierr = PetscLogObjectParent(B,b->A);CHKERRQ(ierr);
3393     ierr = MatCreate(PETSC_COMM_SELF,&b->B);CHKERRQ(ierr);
3394     ierr = MatSetSizes(b->B,B->rmap->n,B->cmap->N,B->rmap->n,B->cmap->N);CHKERRQ(ierr);
3395     ierr = MatSetBlockSizes(b->B,B->rmap->bs,B->cmap->bs);CHKERRQ(ierr);
3396     ierr = MatSetType(b->B,MATSEQAIJ);CHKERRQ(ierr);
3397     ierr = PetscLogObjectParent(B,b->B);CHKERRQ(ierr);
3398   }
3399 
3400   ierr = MatSeqAIJSetPreallocation(b->A,d_nz,d_nnz);CHKERRQ(ierr);
3401   ierr = MatSeqAIJSetPreallocation(b->B,o_nz,o_nnz);CHKERRQ(ierr);
3402   B->preallocated = PETSC_TRUE;
3403   PetscFunctionReturn(0);
3404 }
3405 
3406 #undef __FUNCT__
3407 #define __FUNCT__ "MatDuplicate_MPIAIJ"
3408 PetscErrorCode MatDuplicate_MPIAIJ(Mat matin,MatDuplicateOption cpvalues,Mat *newmat)
3409 {
3410   Mat            mat;
3411   Mat_MPIAIJ     *a,*oldmat = (Mat_MPIAIJ*)matin->data;
3412   PetscErrorCode ierr;
3413 
3414   PetscFunctionBegin;
3415   *newmat = 0;
3416   ierr    = MatCreate(PetscObjectComm((PetscObject)matin),&mat);CHKERRQ(ierr);
3417   ierr    = MatSetSizes(mat,matin->rmap->n,matin->cmap->n,matin->rmap->N,matin->cmap->N);CHKERRQ(ierr);
3418   ierr    = MatSetBlockSizes(mat,matin->rmap->bs,matin->cmap->bs);CHKERRQ(ierr);
3419   ierr    = MatSetType(mat,((PetscObject)matin)->type_name);CHKERRQ(ierr);
3420   ierr    = PetscMemcpy(mat->ops,matin->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
3421   a       = (Mat_MPIAIJ*)mat->data;
3422 
3423   mat->factortype   = matin->factortype;
3424   mat->rmap->bs     = matin->rmap->bs;
3425   mat->cmap->bs     = matin->cmap->bs;
3426   mat->assembled    = PETSC_TRUE;
3427   mat->insertmode   = NOT_SET_VALUES;
3428   mat->preallocated = PETSC_TRUE;
3429 
3430   a->size         = oldmat->size;
3431   a->rank         = oldmat->rank;
3432   a->donotstash   = oldmat->donotstash;
3433   a->roworiented  = oldmat->roworiented;
3434   a->rowindices   = 0;
3435   a->rowvalues    = 0;
3436   a->getrowactive = PETSC_FALSE;
3437 
3438   ierr = PetscLayoutReference(matin->rmap,&mat->rmap);CHKERRQ(ierr);
3439   ierr = PetscLayoutReference(matin->cmap,&mat->cmap);CHKERRQ(ierr);
3440 
3441   if (oldmat->colmap) {
3442 #if defined(PETSC_USE_CTABLE)
3443     ierr = PetscTableCreateCopy(oldmat->colmap,&a->colmap);CHKERRQ(ierr);
3444 #else
3445     ierr = PetscMalloc((mat->cmap->N)*sizeof(PetscInt),&a->colmap);CHKERRQ(ierr);
3446     ierr = PetscLogObjectMemory(mat,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
3447     ierr = PetscMemcpy(a->colmap,oldmat->colmap,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
3448 #endif
3449   } else a->colmap = 0;
3450   if (oldmat->garray) {
3451     PetscInt len;
3452     len  = oldmat->B->cmap->n;
3453     ierr = PetscMalloc((len+1)*sizeof(PetscInt),&a->garray);CHKERRQ(ierr);
3454     ierr = PetscLogObjectMemory(mat,len*sizeof(PetscInt));CHKERRQ(ierr);
3455     if (len) { ierr = PetscMemcpy(a->garray,oldmat->garray,len*sizeof(PetscInt));CHKERRQ(ierr); }
3456   } else a->garray = 0;
3457 
3458   ierr    = VecDuplicate(oldmat->lvec,&a->lvec);CHKERRQ(ierr);
3459   ierr    = PetscLogObjectParent(mat,a->lvec);CHKERRQ(ierr);
3460   ierr    = VecScatterCopy(oldmat->Mvctx,&a->Mvctx);CHKERRQ(ierr);
3461   ierr    = PetscLogObjectParent(mat,a->Mvctx);CHKERRQ(ierr);
3462   ierr    = MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
3463   ierr    = PetscLogObjectParent(mat,a->A);CHKERRQ(ierr);
3464   ierr    = MatDuplicate(oldmat->B,cpvalues,&a->B);CHKERRQ(ierr);
3465   ierr    = PetscLogObjectParent(mat,a->B);CHKERRQ(ierr);
3466   ierr    = PetscFunctionListDuplicate(((PetscObject)matin)->qlist,&((PetscObject)mat)->qlist);CHKERRQ(ierr);
3467   *newmat = mat;
3468   PetscFunctionReturn(0);
3469 }
3470 
3471 
3472 
3473 #undef __FUNCT__
3474 #define __FUNCT__ "MatLoad_MPIAIJ"
3475 PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
3476 {
3477   PetscScalar    *vals,*svals;
3478   MPI_Comm       comm;
3479   PetscErrorCode ierr;
3480   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
3481   PetscInt       i,nz,j,rstart,rend,mmax,maxnz = 0,grows,gcols;
3482   PetscInt       header[4],*rowlengths = 0,M,N,m,*cols;
3483   PetscInt       *ourlens = NULL,*procsnz = NULL,*offlens = NULL,jj,*mycols,*smycols;
3484   PetscInt       cend,cstart,n,*rowners,sizesset=1;
3485   int            fd;
3486   PetscInt       bs = 1;
3487 
3488   PetscFunctionBegin;
3489   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
3490   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3491   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3492   if (!rank) {
3493     ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
3494     ierr = PetscBinaryRead(fd,(char*)header,4,PETSC_INT);CHKERRQ(ierr);
3495     if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
3496   }
3497 
3498   ierr = PetscOptionsBegin(comm,NULL,"Options for loading SEQAIJ matrix","Mat");CHKERRQ(ierr);
3499   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
3500   ierr = PetscOptionsEnd();CHKERRQ(ierr);
3501 
3502   if (newMat->rmap->n < 0 && newMat->rmap->N < 0 && newMat->cmap->n < 0 && newMat->cmap->N < 0) sizesset = 0;
3503 
3504   ierr = MPI_Bcast(header+1,3,MPIU_INT,0,comm);CHKERRQ(ierr);
3505   M    = header[1]; N = header[2];
3506   /* If global rows/cols are set to PETSC_DECIDE, set it to the sizes given in the file */
3507   if (sizesset && newMat->rmap->N < 0) newMat->rmap->N = M;
3508   if (sizesset && newMat->cmap->N < 0) newMat->cmap->N = N;
3509 
3510   /* If global sizes are set, check if they are consistent with that given in the file */
3511   if (sizesset) {
3512     ierr = MatGetSize(newMat,&grows,&gcols);CHKERRQ(ierr);
3513   }
3514   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);
3515   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);
3516 
3517   /* determine ownership of all (block) rows */
3518   if (M%bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Inconsistent # of rows (%d) and block size (%d)",M,bs);
3519   if (newMat->rmap->n < 0) m = bs*((M/bs)/size + (((M/bs) % size) > rank));    /* PETSC_DECIDE */
3520   else m = newMat->rmap->n; /* Set by user */
3521 
3522   ierr = PetscMalloc((size+1)*sizeof(PetscInt),&rowners);CHKERRQ(ierr);
3523   ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
3524 
3525   /* First process needs enough room for process with most rows */
3526   if (!rank) {
3527     mmax = rowners[1];
3528     for (i=2; i<=size; i++) {
3529       mmax = PetscMax(mmax, rowners[i]);
3530     }
3531   } else mmax = -1;             /* unused, but compilers complain */
3532 
3533   rowners[0] = 0;
3534   for (i=2; i<=size; i++) {
3535     rowners[i] += rowners[i-1];
3536   }
3537   rstart = rowners[rank];
3538   rend   = rowners[rank+1];
3539 
3540   /* distribute row lengths to all processors */
3541   ierr = PetscMalloc2(m,PetscInt,&ourlens,m,PetscInt,&offlens);CHKERRQ(ierr);
3542   if (!rank) {
3543     ierr = PetscBinaryRead(fd,ourlens,m,PETSC_INT);CHKERRQ(ierr);
3544     ierr = PetscMalloc(mmax*sizeof(PetscInt),&rowlengths);CHKERRQ(ierr);
3545     ierr = PetscMalloc(size*sizeof(PetscInt),&procsnz);CHKERRQ(ierr);
3546     ierr = PetscMemzero(procsnz,size*sizeof(PetscInt));CHKERRQ(ierr);
3547     for (j=0; j<m; j++) {
3548       procsnz[0] += ourlens[j];
3549     }
3550     for (i=1; i<size; i++) {
3551       ierr = PetscBinaryRead(fd,rowlengths,rowners[i+1]-rowners[i],PETSC_INT);CHKERRQ(ierr);
3552       /* calculate the number of nonzeros on each processor */
3553       for (j=0; j<rowners[i+1]-rowners[i]; j++) {
3554         procsnz[i] += rowlengths[j];
3555       }
3556       ierr = MPIULong_Send(rowlengths,rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
3557     }
3558     ierr = PetscFree(rowlengths);CHKERRQ(ierr);
3559   } else {
3560     ierr = MPIULong_Recv(ourlens,m,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
3561   }
3562 
3563   if (!rank) {
3564     /* determine max buffer needed and allocate it */
3565     maxnz = 0;
3566     for (i=0; i<size; i++) {
3567       maxnz = PetscMax(maxnz,procsnz[i]);
3568     }
3569     ierr = PetscMalloc(maxnz*sizeof(PetscInt),&cols);CHKERRQ(ierr);
3570 
3571     /* read in my part of the matrix column indices  */
3572     nz   = procsnz[0];
3573     ierr = PetscMalloc(nz*sizeof(PetscInt),&mycols);CHKERRQ(ierr);
3574     ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);
3575 
3576     /* read in every one elses and ship off */
3577     for (i=1; i<size; i++) {
3578       nz   = procsnz[i];
3579       ierr = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
3580       ierr = MPIULong_Send(cols,nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
3581     }
3582     ierr = PetscFree(cols);CHKERRQ(ierr);
3583   } else {
3584     /* determine buffer space needed for message */
3585     nz = 0;
3586     for (i=0; i<m; i++) {
3587       nz += ourlens[i];
3588     }
3589     ierr = PetscMalloc(nz*sizeof(PetscInt),&mycols);CHKERRQ(ierr);
3590 
3591     /* receive message of column indices*/
3592     ierr = MPIULong_Recv(mycols,nz,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
3593   }
3594 
3595   /* determine column ownership if matrix is not square */
3596   if (N != M) {
3597     if (newMat->cmap->n < 0) n = N/size + ((N % size) > rank);
3598     else n = newMat->cmap->n;
3599     ierr   = MPI_Scan(&n,&cend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3600     cstart = cend - n;
3601   } else {
3602     cstart = rstart;
3603     cend   = rend;
3604     n      = cend - cstart;
3605   }
3606 
3607   /* loop over local rows, determining number of off diagonal entries */
3608   ierr = PetscMemzero(offlens,m*sizeof(PetscInt));CHKERRQ(ierr);
3609   jj   = 0;
3610   for (i=0; i<m; i++) {
3611     for (j=0; j<ourlens[i]; j++) {
3612       if (mycols[jj] < cstart || mycols[jj] >= cend) offlens[i]++;
3613       jj++;
3614     }
3615   }
3616 
3617   for (i=0; i<m; i++) {
3618     ourlens[i] -= offlens[i];
3619   }
3620   if (!sizesset) {
3621     ierr = MatSetSizes(newMat,m,n,M,N);CHKERRQ(ierr);
3622   }
3623 
3624   if (bs > 1) {ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);}
3625 
3626   ierr = MatMPIAIJSetPreallocation(newMat,0,ourlens,0,offlens);CHKERRQ(ierr);
3627 
3628   for (i=0; i<m; i++) {
3629     ourlens[i] += offlens[i];
3630   }
3631 
3632   if (!rank) {
3633     ierr = PetscMalloc((maxnz+1)*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
3634 
3635     /* read in my part of the matrix numerical values  */
3636     nz   = procsnz[0];
3637     ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
3638 
3639     /* insert into matrix */
3640     jj      = rstart;
3641     smycols = mycols;
3642     svals   = vals;
3643     for (i=0; i<m; i++) {
3644       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
3645       smycols += ourlens[i];
3646       svals   += ourlens[i];
3647       jj++;
3648     }
3649 
3650     /* read in other processors and ship out */
3651     for (i=1; i<size; i++) {
3652       nz   = procsnz[i];
3653       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
3654       ierr = MPIULong_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
3655     }
3656     ierr = PetscFree(procsnz);CHKERRQ(ierr);
3657   } else {
3658     /* receive numeric values */
3659     ierr = PetscMalloc((nz+1)*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
3660 
3661     /* receive message of values*/
3662     ierr = MPIULong_Recv(vals,nz,MPIU_SCALAR,0,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
3663 
3664     /* insert into matrix */
3665     jj      = rstart;
3666     smycols = mycols;
3667     svals   = vals;
3668     for (i=0; i<m; i++) {
3669       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
3670       smycols += ourlens[i];
3671       svals   += ourlens[i];
3672       jj++;
3673     }
3674   }
3675   ierr = PetscFree2(ourlens,offlens);CHKERRQ(ierr);
3676   ierr = PetscFree(vals);CHKERRQ(ierr);
3677   ierr = PetscFree(mycols);CHKERRQ(ierr);
3678   ierr = PetscFree(rowners);CHKERRQ(ierr);
3679   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3680   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3681   PetscFunctionReturn(0);
3682 }
3683 
3684 #undef __FUNCT__
3685 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ"
3686 PetscErrorCode MatGetSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3687 {
3688   PetscErrorCode ierr;
3689   IS             iscol_local;
3690   PetscInt       csize;
3691 
3692   PetscFunctionBegin;
3693   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3694   if (call == MAT_REUSE_MATRIX) {
3695     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3696     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3697   } else {
3698     PetscInt cbs;
3699     ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
3700     ierr = ISAllGather(iscol,&iscol_local);CHKERRQ(ierr);
3701     ierr = ISSetBlockSize(iscol_local,cbs);CHKERRQ(ierr);
3702   }
3703   ierr = MatGetSubMatrix_MPIAIJ_Private(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
3704   if (call == MAT_INITIAL_MATRIX) {
3705     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3706     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3707   }
3708   PetscFunctionReturn(0);
3709 }
3710 
3711 extern PetscErrorCode MatGetSubMatrices_MPIAIJ_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool*,Mat*);
3712 #undef __FUNCT__
3713 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ_Private"
3714 /*
3715     Not great since it makes two copies of the submatrix, first an SeqAIJ
3716   in local and then by concatenating the local matrices the end result.
3717   Writing it directly would be much like MatGetSubMatrices_MPIAIJ()
3718 
3719   Note: This requires a sequential iscol with all indices.
3720 */
3721 PetscErrorCode MatGetSubMatrix_MPIAIJ_Private(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3722 {
3723   PetscErrorCode ierr;
3724   PetscMPIInt    rank,size;
3725   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3726   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal,ncol;
3727   PetscBool      allcolumns, colflag;
3728   Mat            M,Mreuse;
3729   MatScalar      *vwork,*aa;
3730   MPI_Comm       comm;
3731   Mat_SeqAIJ     *aij;
3732 
3733   PetscFunctionBegin;
3734   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3735   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3736   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3737 
3738   ierr = ISIdentity(iscol,&colflag);CHKERRQ(ierr);
3739   ierr = ISGetLocalSize(iscol,&ncol);CHKERRQ(ierr);
3740   if (colflag && ncol == mat->cmap->N) {
3741     allcolumns = PETSC_TRUE;
3742   } else {
3743     allcolumns = PETSC_FALSE;
3744   }
3745   if (call ==  MAT_REUSE_MATRIX) {
3746     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3747     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3748     ierr = MatGetSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,&allcolumns,&Mreuse);CHKERRQ(ierr);
3749   } else {
3750     ierr = MatGetSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&allcolumns,&Mreuse);CHKERRQ(ierr);
3751   }
3752 
3753   /*
3754       m - number of local rows
3755       n - number of columns (same on all processors)
3756       rstart - first row in new global matrix generated
3757   */
3758   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3759   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3760   if (call == MAT_INITIAL_MATRIX) {
3761     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3762     ii  = aij->i;
3763     jj  = aij->j;
3764 
3765     /*
3766         Determine the number of non-zeros in the diagonal and off-diagonal
3767         portions of the matrix in order to do correct preallocation
3768     */
3769 
3770     /* first get start and end of "diagonal" columns */
3771     if (csize == PETSC_DECIDE) {
3772       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3773       if (mglobal == n) { /* square matrix */
3774         nlocal = m;
3775       } else {
3776         nlocal = n/size + ((n % size) > rank);
3777       }
3778     } else {
3779       nlocal = csize;
3780     }
3781     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3782     rstart = rend - nlocal;
3783     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);
3784 
3785     /* next, compute all the lengths */
3786     ierr  = PetscMalloc((2*m+1)*sizeof(PetscInt),&dlens);CHKERRQ(ierr);
3787     olens = dlens + m;
3788     for (i=0; i<m; i++) {
3789       jend = ii[i+1] - ii[i];
3790       olen = 0;
3791       dlen = 0;
3792       for (j=0; j<jend; j++) {
3793         if (*jj < rstart || *jj >= rend) olen++;
3794         else dlen++;
3795         jj++;
3796       }
3797       olens[i] = olen;
3798       dlens[i] = dlen;
3799     }
3800     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3801     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3802     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3803     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3804     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3805     ierr = PetscFree(dlens);CHKERRQ(ierr);
3806   } else {
3807     PetscInt ml,nl;
3808 
3809     M    = *newmat;
3810     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3811     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3812     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3813     /*
3814          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3815        rather than the slower MatSetValues().
3816     */
3817     M->was_assembled = PETSC_TRUE;
3818     M->assembled     = PETSC_FALSE;
3819   }
3820   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3821   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3822   ii   = aij->i;
3823   jj   = aij->j;
3824   aa   = aij->a;
3825   for (i=0; i<m; i++) {
3826     row   = rstart + i;
3827     nz    = ii[i+1] - ii[i];
3828     cwork = jj;     jj += nz;
3829     vwork = aa;     aa += nz;
3830     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3831   }
3832 
3833   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3834   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3835   *newmat = M;
3836 
3837   /* save submatrix used in processor for next request */
3838   if (call ==  MAT_INITIAL_MATRIX) {
3839     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3840     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3841   }
3842   PetscFunctionReturn(0);
3843 }
3844 
3845 #undef __FUNCT__
3846 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR_MPIAIJ"
3847 PetscErrorCode  MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3848 {
3849   PetscInt       m,cstart, cend,j,nnz,i,d;
3850   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3851   const PetscInt *JJ;
3852   PetscScalar    *values;
3853   PetscErrorCode ierr;
3854 
3855   PetscFunctionBegin;
3856   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3857 
3858   ierr   = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3859   ierr   = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3860   m      = B->rmap->n;
3861   cstart = B->cmap->rstart;
3862   cend   = B->cmap->rend;
3863   rstart = B->rmap->rstart;
3864 
3865   ierr = PetscMalloc2(m,PetscInt,&d_nnz,m,PetscInt,&o_nnz);CHKERRQ(ierr);
3866 
3867 #if defined(PETSC_USE_DEBUGGING)
3868   for (i=0; i<m; i++) {
3869     nnz = Ii[i+1]- Ii[i];
3870     JJ  = J + Ii[i];
3871     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3872     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3873     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);
3874   }
3875 #endif
3876 
3877   for (i=0; i<m; i++) {
3878     nnz     = Ii[i+1]- Ii[i];
3879     JJ      = J + Ii[i];
3880     nnz_max = PetscMax(nnz_max,nnz);
3881     d       = 0;
3882     for (j=0; j<nnz; j++) {
3883       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3884     }
3885     d_nnz[i] = d;
3886     o_nnz[i] = nnz - d;
3887   }
3888   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3889   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3890 
3891   if (v) values = (PetscScalar*)v;
3892   else {
3893     ierr = PetscMalloc((nnz_max+1)*sizeof(PetscScalar),&values);CHKERRQ(ierr);
3894     ierr = PetscMemzero(values,nnz_max*sizeof(PetscScalar));CHKERRQ(ierr);
3895   }
3896 
3897   for (i=0; i<m; i++) {
3898     ii   = i + rstart;
3899     nnz  = Ii[i+1]- Ii[i];
3900     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3901   }
3902   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3903   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3904 
3905   if (!v) {
3906     ierr = PetscFree(values);CHKERRQ(ierr);
3907   }
3908   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3909   PetscFunctionReturn(0);
3910 }
3911 
3912 #undef __FUNCT__
3913 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR"
3914 /*@
3915    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3916    (the default parallel PETSc format).
3917 
3918    Collective on MPI_Comm
3919 
3920    Input Parameters:
3921 +  B - the matrix
3922 .  i - the indices into j for the start of each local row (starts with zero)
3923 .  j - the column indices for each local row (starts with zero)
3924 -  v - optional values in the matrix
3925 
3926    Level: developer
3927 
3928    Notes:
3929        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3930      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3931      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3932 
3933        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3934 
3935        The format which is used for the sparse matrix input, is equivalent to a
3936     row-major ordering.. i.e for the following matrix, the input data expected is
3937     as shown:
3938 
3939         1 0 0
3940         2 0 3     P0
3941        -------
3942         4 5 6     P1
3943 
3944      Process0 [P0]: rows_owned=[0,1]
3945         i =  {0,1,3}  [size = nrow+1  = 2+1]
3946         j =  {0,0,2}  [size = nz = 6]
3947         v =  {1,2,3}  [size = nz = 6]
3948 
3949      Process1 [P1]: rows_owned=[2]
3950         i =  {0,3}    [size = nrow+1  = 1+1]
3951         j =  {0,1,2}  [size = nz = 6]
3952         v =  {4,5,6}  [size = nz = 6]
3953 
3954 .keywords: matrix, aij, compressed row, sparse, parallel
3955 
3956 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MPIAIJ,
3957           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3958 @*/
3959 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3960 {
3961   PetscErrorCode ierr;
3962 
3963   PetscFunctionBegin;
3964   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3965   PetscFunctionReturn(0);
3966 }
3967 
3968 #undef __FUNCT__
3969 #define __FUNCT__ "MatMPIAIJSetPreallocation"
3970 /*@C
3971    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3972    (the default parallel PETSc format).  For good matrix assembly performance
3973    the user should preallocate the matrix storage by setting the parameters
3974    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3975    performance can be increased by more than a factor of 50.
3976 
3977    Collective on MPI_Comm
3978 
3979    Input Parameters:
3980 +  A - the matrix
3981 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3982            (same value is used for all local rows)
3983 .  d_nnz - array containing the number of nonzeros in the various rows of the
3984            DIAGONAL portion of the local submatrix (possibly different for each row)
3985            or NULL, if d_nz is used to specify the nonzero structure.
3986            The size of this array is equal to the number of local rows, i.e 'm'.
3987            For matrices that will be factored, you must leave room for (and set)
3988            the diagonal entry even if it is zero.
3989 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3990            submatrix (same value is used for all local rows).
3991 -  o_nnz - array containing the number of nonzeros in the various rows of the
3992            OFF-DIAGONAL portion of the local submatrix (possibly different for
3993            each row) or NULL, if o_nz is used to specify the nonzero
3994            structure. The size of this array is equal to the number
3995            of local rows, i.e 'm'.
3996 
3997    If the *_nnz parameter is given then the *_nz parameter is ignored
3998 
3999    The AIJ format (also called the Yale sparse matrix format or
4000    compressed row storage (CSR)), is fully compatible with standard Fortran 77
4001    storage.  The stored row and column indices begin with zero.
4002    See the <A href="../../docs/manual.pdf#nameddest=ch_mat">Mat chapter of the users manual</A> for details.
4003 
4004    The parallel matrix is partitioned such that the first m0 rows belong to
4005    process 0, the next m1 rows belong to process 1, the next m2 rows belong
4006    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
4007 
4008    The DIAGONAL portion of the local submatrix of a processor can be defined
4009    as the submatrix which is obtained by extraction the part corresponding to
4010    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
4011    first row that belongs to the processor, r2 is the last row belonging to
4012    the this processor, and c1-c2 is range of indices of the local part of a
4013    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
4014    common case of a square matrix, the row and column ranges are the same and
4015    the DIAGONAL part is also square. The remaining portion of the local
4016    submatrix (mxN) constitute the OFF-DIAGONAL portion.
4017 
4018    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
4019 
4020    You can call MatGetInfo() to get information on how effective the preallocation was;
4021    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
4022    You can also run with the option -info and look for messages with the string
4023    malloc in them to see if additional memory allocation was needed.
4024 
4025    Example usage:
4026 
4027    Consider the following 8x8 matrix with 34 non-zero values, that is
4028    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
4029    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
4030    as follows:
4031 
4032 .vb
4033             1  2  0  |  0  3  0  |  0  4
4034     Proc0   0  5  6  |  7  0  0  |  8  0
4035             9  0 10  | 11  0  0  | 12  0
4036     -------------------------------------
4037            13  0 14  | 15 16 17  |  0  0
4038     Proc1   0 18  0  | 19 20 21  |  0  0
4039             0  0  0  | 22 23  0  | 24  0
4040     -------------------------------------
4041     Proc2  25 26 27  |  0  0 28  | 29  0
4042            30  0  0  | 31 32 33  |  0 34
4043 .ve
4044 
4045    This can be represented as a collection of submatrices as:
4046 
4047 .vb
4048       A B C
4049       D E F
4050       G H I
4051 .ve
4052 
4053    Where the submatrices A,B,C are owned by proc0, D,E,F are
4054    owned by proc1, G,H,I are owned by proc2.
4055 
4056    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4057    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4058    The 'M','N' parameters are 8,8, and have the same values on all procs.
4059 
4060    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
4061    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
4062    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
4063    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
4064    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
4065    matrix, ans [DF] as another SeqAIJ matrix.
4066 
4067    When d_nz, o_nz parameters are specified, d_nz storage elements are
4068    allocated for every row of the local diagonal submatrix, and o_nz
4069    storage locations are allocated for every row of the OFF-DIAGONAL submat.
4070    One way to choose d_nz and o_nz is to use the max nonzerors per local
4071    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
4072    In this case, the values of d_nz,o_nz are:
4073 .vb
4074      proc0 : dnz = 2, o_nz = 2
4075      proc1 : dnz = 3, o_nz = 2
4076      proc2 : dnz = 1, o_nz = 4
4077 .ve
4078    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
4079    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
4080    for proc3. i.e we are using 12+15+10=37 storage locations to store
4081    34 values.
4082 
4083    When d_nnz, o_nnz parameters are specified, the storage is specified
4084    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
4085    In the above case the values for d_nnz,o_nnz are:
4086 .vb
4087      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
4088      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
4089      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
4090 .ve
4091    Here the space allocated is sum of all the above values i.e 34, and
4092    hence pre-allocation is perfect.
4093 
4094    Level: intermediate
4095 
4096 .keywords: matrix, aij, compressed row, sparse, parallel
4097 
4098 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
4099           MPIAIJ, MatGetInfo(), PetscSplitOwnership()
4100 @*/
4101 PetscErrorCode  MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
4102 {
4103   PetscErrorCode ierr;
4104 
4105   PetscFunctionBegin;
4106   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
4107   PetscValidType(B,1);
4108   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
4109   PetscFunctionReturn(0);
4110 }
4111 
4112 #undef __FUNCT__
4113 #define __FUNCT__ "MatCreateMPIAIJWithArrays"
4114 /*@
4115      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
4116          CSR format the local rows.
4117 
4118    Collective on MPI_Comm
4119 
4120    Input Parameters:
4121 +  comm - MPI communicator
4122 .  m - number of local rows (Cannot be PETSC_DECIDE)
4123 .  n - This value should be the same as the local size used in creating the
4124        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
4125        calculated if N is given) For square matrices n is almost always m.
4126 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
4127 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
4128 .   i - row indices
4129 .   j - column indices
4130 -   a - matrix values
4131 
4132    Output Parameter:
4133 .   mat - the matrix
4134 
4135    Level: intermediate
4136 
4137    Notes:
4138        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
4139      thus you CANNOT change the matrix entries by changing the values of a[] after you have
4140      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
4141 
4142        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
4143 
4144        The format which is used for the sparse matrix input, is equivalent to a
4145     row-major ordering.. i.e for the following matrix, the input data expected is
4146     as shown:
4147 
4148         1 0 0
4149         2 0 3     P0
4150        -------
4151         4 5 6     P1
4152 
4153      Process0 [P0]: rows_owned=[0,1]
4154         i =  {0,1,3}  [size = nrow+1  = 2+1]
4155         j =  {0,0,2}  [size = nz = 6]
4156         v =  {1,2,3}  [size = nz = 6]
4157 
4158      Process1 [P1]: rows_owned=[2]
4159         i =  {0,3}    [size = nrow+1  = 1+1]
4160         j =  {0,1,2}  [size = nz = 6]
4161         v =  {4,5,6}  [size = nz = 6]
4162 
4163 .keywords: matrix, aij, compressed row, sparse, parallel
4164 
4165 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
4166           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
4167 @*/
4168 PetscErrorCode  MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
4169 {
4170   PetscErrorCode ierr;
4171 
4172   PetscFunctionBegin;
4173   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
4174   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
4175   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4176   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
4177   /* ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr); */
4178   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
4179   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
4180   PetscFunctionReturn(0);
4181 }
4182 
4183 #undef __FUNCT__
4184 #define __FUNCT__ "MatCreateAIJ"
4185 /*@C
4186    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
4187    (the default parallel PETSc format).  For good matrix assembly performance
4188    the user should preallocate the matrix storage by setting the parameters
4189    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
4190    performance can be increased by more than a factor of 50.
4191 
4192    Collective on MPI_Comm
4193 
4194    Input Parameters:
4195 +  comm - MPI communicator
4196 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
4197            This value should be the same as the local size used in creating the
4198            y vector for the matrix-vector product y = Ax.
4199 .  n - This value should be the same as the local size used in creating the
4200        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
4201        calculated if N is given) For square matrices n is almost always m.
4202 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
4203 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
4204 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
4205            (same value is used for all local rows)
4206 .  d_nnz - array containing the number of nonzeros in the various rows of the
4207            DIAGONAL portion of the local submatrix (possibly different for each row)
4208            or NULL, if d_nz is used to specify the nonzero structure.
4209            The size of this array is equal to the number of local rows, i.e 'm'.
4210 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
4211            submatrix (same value is used for all local rows).
4212 -  o_nnz - array containing the number of nonzeros in the various rows of the
4213            OFF-DIAGONAL portion of the local submatrix (possibly different for
4214            each row) or NULL, if o_nz is used to specify the nonzero
4215            structure. The size of this array is equal to the number
4216            of local rows, i.e 'm'.
4217 
4218    Output Parameter:
4219 .  A - the matrix
4220 
4221    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
4222    MatXXXXSetPreallocation() paradgm instead of this routine directly.
4223    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
4224 
4225    Notes:
4226    If the *_nnz parameter is given then the *_nz parameter is ignored
4227 
4228    m,n,M,N parameters specify the size of the matrix, and its partitioning across
4229    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
4230    storage requirements for this matrix.
4231 
4232    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
4233    processor than it must be used on all processors that share the object for
4234    that argument.
4235 
4236    The user MUST specify either the local or global matrix dimensions
4237    (possibly both).
4238 
4239    The parallel matrix is partitioned across processors such that the
4240    first m0 rows belong to process 0, the next m1 rows belong to
4241    process 1, the next m2 rows belong to process 2 etc.. where
4242    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
4243    values corresponding to [m x N] submatrix.
4244 
4245    The columns are logically partitioned with the n0 columns belonging
4246    to 0th partition, the next n1 columns belonging to the next
4247    partition etc.. where n0,n1,n2... are the the input parameter 'n'.
4248 
4249    The DIAGONAL portion of the local submatrix on any given processor
4250    is the submatrix corresponding to the rows and columns m,n
4251    corresponding to the given processor. i.e diagonal matrix on
4252    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
4253    etc. The remaining portion of the local submatrix [m x (N-n)]
4254    constitute the OFF-DIAGONAL portion. The example below better
4255    illustrates this concept.
4256 
4257    For a square global matrix we define each processor's diagonal portion
4258    to be its local rows and the corresponding columns (a square submatrix);
4259    each processor's off-diagonal portion encompasses the remainder of the
4260    local matrix (a rectangular submatrix).
4261 
4262    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
4263 
4264    When calling this routine with a single process communicator, a matrix of
4265    type SEQAIJ is returned.  If a matrix of type MPIAIJ is desired for this
4266    type of communicator, use the construction mechanism:
4267      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
4268 
4269    By default, this format uses inodes (identical nodes) when possible.
4270    We search for consecutive rows with the same nonzero structure, thereby
4271    reusing matrix information to achieve increased efficiency.
4272 
4273    Options Database Keys:
4274 +  -mat_no_inode  - Do not use inodes
4275 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
4276 -  -mat_aij_oneindex - Internally use indexing starting at 1
4277         rather than 0.  Note that when calling MatSetValues(),
4278         the user still MUST index entries starting at 0!
4279 
4280 
4281    Example usage:
4282 
4283    Consider the following 8x8 matrix with 34 non-zero values, that is
4284    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
4285    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
4286    as follows:
4287 
4288 .vb
4289             1  2  0  |  0  3  0  |  0  4
4290     Proc0   0  5  6  |  7  0  0  |  8  0
4291             9  0 10  | 11  0  0  | 12  0
4292     -------------------------------------
4293            13  0 14  | 15 16 17  |  0  0
4294     Proc1   0 18  0  | 19 20 21  |  0  0
4295             0  0  0  | 22 23  0  | 24  0
4296     -------------------------------------
4297     Proc2  25 26 27  |  0  0 28  | 29  0
4298            30  0  0  | 31 32 33  |  0 34
4299 .ve
4300 
4301    This can be represented as a collection of submatrices as:
4302 
4303 .vb
4304       A B C
4305       D E F
4306       G H I
4307 .ve
4308 
4309    Where the submatrices A,B,C are owned by proc0, D,E,F are
4310    owned by proc1, G,H,I are owned by proc2.
4311 
4312    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4313    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4314    The 'M','N' parameters are 8,8, and have the same values on all procs.
4315 
4316    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
4317    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
4318    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
4319    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
4320    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
4321    matrix, ans [DF] as another SeqAIJ matrix.
4322 
4323    When d_nz, o_nz parameters are specified, d_nz storage elements are
4324    allocated for every row of the local diagonal submatrix, and o_nz
4325    storage locations are allocated for every row of the OFF-DIAGONAL submat.
4326    One way to choose d_nz and o_nz is to use the max nonzerors per local
4327    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
4328    In this case, the values of d_nz,o_nz are:
4329 .vb
4330      proc0 : dnz = 2, o_nz = 2
4331      proc1 : dnz = 3, o_nz = 2
4332      proc2 : dnz = 1, o_nz = 4
4333 .ve
4334    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
4335    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
4336    for proc3. i.e we are using 12+15+10=37 storage locations to store
4337    34 values.
4338 
4339    When d_nnz, o_nnz parameters are specified, the storage is specified
4340    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
4341    In the above case the values for d_nnz,o_nnz are:
4342 .vb
4343      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
4344      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
4345      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
4346 .ve
4347    Here the space allocated is sum of all the above values i.e 34, and
4348    hence pre-allocation is perfect.
4349 
4350    Level: intermediate
4351 
4352 .keywords: matrix, aij, compressed row, sparse, parallel
4353 
4354 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
4355           MPIAIJ, MatCreateMPIAIJWithArrays()
4356 @*/
4357 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)
4358 {
4359   PetscErrorCode ierr;
4360   PetscMPIInt    size;
4361 
4362   PetscFunctionBegin;
4363   ierr = MatCreate(comm,A);CHKERRQ(ierr);
4364   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
4365   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4366   if (size > 1) {
4367     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
4368     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
4369   } else {
4370     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
4371     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
4372   }
4373   PetscFunctionReturn(0);
4374 }
4375 
4376 #undef __FUNCT__
4377 #define __FUNCT__ "MatMPIAIJGetSeqAIJ"
4378 PetscErrorCode  MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
4379 {
4380   Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
4381 
4382   PetscFunctionBegin;
4383   *Ad     = a->A;
4384   *Ao     = a->B;
4385   *colmap = a->garray;
4386   PetscFunctionReturn(0);
4387 }
4388 
4389 #undef __FUNCT__
4390 #define __FUNCT__ "MatSetColoring_MPIAIJ"
4391 PetscErrorCode MatSetColoring_MPIAIJ(Mat A,ISColoring coloring)
4392 {
4393   PetscErrorCode ierr;
4394   PetscInt       i;
4395   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
4396 
4397   PetscFunctionBegin;
4398   if (coloring->ctype == IS_COLORING_GLOBAL) {
4399     ISColoringValue *allcolors,*colors;
4400     ISColoring      ocoloring;
4401 
4402     /* set coloring for diagonal portion */
4403     ierr = MatSetColoring_SeqAIJ(a->A,coloring);CHKERRQ(ierr);
4404 
4405     /* set coloring for off-diagonal portion */
4406     ierr = ISAllGatherColors(PetscObjectComm((PetscObject)A),coloring->n,coloring->colors,NULL,&allcolors);CHKERRQ(ierr);
4407     ierr = PetscMalloc((a->B->cmap->n+1)*sizeof(ISColoringValue),&colors);CHKERRQ(ierr);
4408     for (i=0; i<a->B->cmap->n; i++) {
4409       colors[i] = allcolors[a->garray[i]];
4410     }
4411     ierr = PetscFree(allcolors);CHKERRQ(ierr);
4412     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,&ocoloring);CHKERRQ(ierr);
4413     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
4414     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
4415   } else if (coloring->ctype == IS_COLORING_GHOSTED) {
4416     ISColoringValue *colors;
4417     PetscInt        *larray;
4418     ISColoring      ocoloring;
4419 
4420     /* set coloring for diagonal portion */
4421     ierr = PetscMalloc((a->A->cmap->n+1)*sizeof(PetscInt),&larray);CHKERRQ(ierr);
4422     for (i=0; i<a->A->cmap->n; i++) {
4423       larray[i] = i + A->cmap->rstart;
4424     }
4425     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->A->cmap->n,larray,NULL,larray);CHKERRQ(ierr);
4426     ierr = PetscMalloc((a->A->cmap->n+1)*sizeof(ISColoringValue),&colors);CHKERRQ(ierr);
4427     for (i=0; i<a->A->cmap->n; i++) {
4428       colors[i] = coloring->colors[larray[i]];
4429     }
4430     ierr = PetscFree(larray);CHKERRQ(ierr);
4431     ierr = ISColoringCreate(PETSC_COMM_SELF,coloring->n,a->A->cmap->n,colors,&ocoloring);CHKERRQ(ierr);
4432     ierr = MatSetColoring_SeqAIJ(a->A,ocoloring);CHKERRQ(ierr);
4433     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
4434 
4435     /* set coloring for off-diagonal portion */
4436     ierr = PetscMalloc((a->B->cmap->n+1)*sizeof(PetscInt),&larray);CHKERRQ(ierr);
4437     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->B->cmap->n,a->garray,NULL,larray);CHKERRQ(ierr);
4438     ierr = PetscMalloc((a->B->cmap->n+1)*sizeof(ISColoringValue),&colors);CHKERRQ(ierr);
4439     for (i=0; i<a->B->cmap->n; i++) {
4440       colors[i] = coloring->colors[larray[i]];
4441     }
4442     ierr = PetscFree(larray);CHKERRQ(ierr);
4443     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,&ocoloring);CHKERRQ(ierr);
4444     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
4445     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
4446   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support ISColoringType %d",(int)coloring->ctype);
4447   PetscFunctionReturn(0);
4448 }
4449 
4450 #undef __FUNCT__
4451 #define __FUNCT__ "MatSetValuesAdifor_MPIAIJ"
4452 PetscErrorCode MatSetValuesAdifor_MPIAIJ(Mat A,PetscInt nl,void *advalues)
4453 {
4454   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
4455   PetscErrorCode ierr;
4456 
4457   PetscFunctionBegin;
4458   ierr = MatSetValuesAdifor_SeqAIJ(a->A,nl,advalues);CHKERRQ(ierr);
4459   ierr = MatSetValuesAdifor_SeqAIJ(a->B,nl,advalues);CHKERRQ(ierr);
4460   PetscFunctionReturn(0);
4461 }
4462 
4463 #undef __FUNCT__
4464 #define __FUNCT__ "MatCreateMPIAIJConcatenateSeqAIJSymbolic"
4465 PetscErrorCode  MatCreateMPIAIJConcatenateSeqAIJSymbolic(MPI_Comm comm,Mat inmat,PetscInt n,Mat *outmat)
4466 {
4467   PetscErrorCode ierr;
4468   PetscInt       m,N,i,rstart,nnz,*dnz,*onz,sum,bs,cbs;
4469   PetscInt       *indx;
4470 
4471   PetscFunctionBegin;
4472   /* This routine will ONLY return MPIAIJ type matrix */
4473   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
4474   ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
4475   if (n == PETSC_DECIDE) {
4476     ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
4477   }
4478   /* Check sum(n) = N */
4479   ierr = MPI_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4480   if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
4481 
4482   ierr    = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4483   rstart -= m;
4484 
4485   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4486   for (i=0; i<m; i++) {
4487     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
4488     ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
4489     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
4490   }
4491 
4492   ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
4493   ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4494   ierr = MatSetBlockSizes(*outmat,bs,cbs);CHKERRQ(ierr);
4495   ierr = MatSetType(*outmat,MATMPIAIJ);CHKERRQ(ierr);
4496   ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
4497   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4498   PetscFunctionReturn(0);
4499 }
4500 
4501 #undef __FUNCT__
4502 #define __FUNCT__ "MatCreateMPIAIJConcatenateSeqAIJNumeric"
4503 PetscErrorCode  MatCreateMPIAIJConcatenateSeqAIJNumeric(MPI_Comm comm,Mat inmat,PetscInt n,Mat outmat)
4504 {
4505   PetscErrorCode ierr;
4506   PetscInt       m,N,i,rstart,nnz,Ii;
4507   PetscInt       *indx;
4508   PetscScalar    *values;
4509 
4510   PetscFunctionBegin;
4511   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
4512   ierr = MatGetOwnershipRange(outmat,&rstart,NULL);CHKERRQ(ierr);
4513   for (i=0; i<m; i++) {
4514     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4515     Ii   = i + rstart;
4516     ierr = MatSetValues_MPIAIJ(outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4517     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4518   }
4519   ierr = MatAssemblyBegin(outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4520   ierr = MatAssemblyEnd(outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4521   PetscFunctionReturn(0);
4522 }
4523 
4524 #undef __FUNCT__
4525 #define __FUNCT__ "MatCreateMPIAIJConcatenateSeqAIJ"
4526 /*@
4527       MatCreateMPIAIJConcatenateSeqAIJ - Creates a single large PETSc matrix by concatenating sequential
4528                  matrices from each processor
4529 
4530     Collective on MPI_Comm
4531 
4532    Input Parameters:
4533 +    comm - the communicators the parallel matrix will live on
4534 .    inmat - the input sequential matrices
4535 .    n - number of local columns (or PETSC_DECIDE)
4536 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4537 
4538    Output Parameter:
4539 .    outmat - the parallel matrix generated
4540 
4541     Level: advanced
4542 
4543    Notes: The number of columns of the matrix in EACH processor MUST be the same.
4544 
4545 @*/
4546 PetscErrorCode  MatCreateMPIAIJConcatenateSeqAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
4547 {
4548   PetscErrorCode ierr;
4549 
4550   PetscFunctionBegin;
4551   ierr = PetscLogEventBegin(MAT_Merge,inmat,0,0,0);CHKERRQ(ierr);
4552   if (scall == MAT_INITIAL_MATRIX) {
4553     ierr = MatCreateMPIAIJConcatenateSeqAIJSymbolic(comm,inmat,n,outmat);CHKERRQ(ierr);
4554   }
4555   ierr = MatCreateMPIAIJConcatenateSeqAIJNumeric(comm,inmat,n,*outmat);CHKERRQ(ierr);
4556   ierr = PetscLogEventEnd(MAT_Merge,inmat,0,0,0);CHKERRQ(ierr);
4557   PetscFunctionReturn(0);
4558 }
4559 
4560 #undef __FUNCT__
4561 #define __FUNCT__ "MatFileSplit"
4562 PetscErrorCode MatFileSplit(Mat A,char *outfile)
4563 {
4564   PetscErrorCode    ierr;
4565   PetscMPIInt       rank;
4566   PetscInt          m,N,i,rstart,nnz;
4567   size_t            len;
4568   const PetscInt    *indx;
4569   PetscViewer       out;
4570   char              *name;
4571   Mat               B;
4572   const PetscScalar *values;
4573 
4574   PetscFunctionBegin;
4575   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
4576   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
4577   /* Should this be the type of the diagonal block of A? */
4578   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
4579   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
4580   ierr = MatSetBlockSizes(B,A->rmap->bs,A->cmap->bs);CHKERRQ(ierr);
4581   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
4582   ierr = MatSeqAIJSetPreallocation(B,0,NULL);CHKERRQ(ierr);
4583   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
4584   for (i=0; i<m; i++) {
4585     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4586     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4587     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4588   }
4589   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4590   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4591 
4592   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
4593   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
4594   ierr = PetscMalloc((len+5)*sizeof(char),&name);CHKERRQ(ierr);
4595   sprintf(name,"%s.%d",outfile,rank);
4596   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
4597   ierr = PetscFree(name);CHKERRQ(ierr);
4598   ierr = MatView(B,out);CHKERRQ(ierr);
4599   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
4600   ierr = MatDestroy(&B);CHKERRQ(ierr);
4601   PetscFunctionReturn(0);
4602 }
4603 
4604 extern PetscErrorCode MatDestroy_MPIAIJ(Mat);
4605 #undef __FUNCT__
4606 #define __FUNCT__ "MatDestroy_MPIAIJ_SeqsToMPI"
4607 PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
4608 {
4609   PetscErrorCode      ierr;
4610   Mat_Merge_SeqsToMPI *merge;
4611   PetscContainer      container;
4612 
4613   PetscFunctionBegin;
4614   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4615   if (container) {
4616     ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4617     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
4618     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
4619     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
4620     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
4621     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
4622     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
4623     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
4624     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
4625     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
4626     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
4627     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
4628     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
4629     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
4630     ierr = PetscFree(merge);CHKERRQ(ierr);
4631     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
4632   }
4633   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
4634   PetscFunctionReturn(0);
4635 }
4636 
4637 #include <../src/mat/utils/freespace.h>
4638 #include <petscbt.h>
4639 
4640 #undef __FUNCT__
4641 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJNumeric"
4642 PetscErrorCode  MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
4643 {
4644   PetscErrorCode      ierr;
4645   MPI_Comm            comm;
4646   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
4647   PetscMPIInt         size,rank,taga,*len_s;
4648   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
4649   PetscInt            proc,m;
4650   PetscInt            **buf_ri,**buf_rj;
4651   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
4652   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
4653   MPI_Request         *s_waits,*r_waits;
4654   MPI_Status          *status;
4655   MatScalar           *aa=a->a;
4656   MatScalar           **abuf_r,*ba_i;
4657   Mat_Merge_SeqsToMPI *merge;
4658   PetscContainer      container;
4659 
4660   PetscFunctionBegin;
4661   ierr = PetscObjectGetComm((PetscObject)mpimat,&comm);CHKERRQ(ierr);
4662   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4663 
4664   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4665   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4666 
4667   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4668   ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4669 
4670   bi     = merge->bi;
4671   bj     = merge->bj;
4672   buf_ri = merge->buf_ri;
4673   buf_rj = merge->buf_rj;
4674 
4675   ierr   = PetscMalloc(size*sizeof(MPI_Status),&status);CHKERRQ(ierr);
4676   owners = merge->rowmap->range;
4677   len_s  = merge->len_s;
4678 
4679   /* send and recv matrix values */
4680   /*-----------------------------*/
4681   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
4682   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
4683 
4684   ierr = PetscMalloc((merge->nsend+1)*sizeof(MPI_Request),&s_waits);CHKERRQ(ierr);
4685   for (proc=0,k=0; proc<size; proc++) {
4686     if (!len_s[proc]) continue;
4687     i    = owners[proc];
4688     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
4689     k++;
4690   }
4691 
4692   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
4693   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
4694   ierr = PetscFree(status);CHKERRQ(ierr);
4695 
4696   ierr = PetscFree(s_waits);CHKERRQ(ierr);
4697   ierr = PetscFree(r_waits);CHKERRQ(ierr);
4698 
4699   /* insert mat values of mpimat */
4700   /*----------------------------*/
4701   ierr = PetscMalloc(N*sizeof(PetscScalar),&ba_i);CHKERRQ(ierr);
4702   ierr = PetscMalloc3(merge->nrecv,PetscInt*,&buf_ri_k,merge->nrecv,PetscInt*,&nextrow,merge->nrecv,PetscInt*,&nextai);CHKERRQ(ierr);
4703 
4704   for (k=0; k<merge->nrecv; k++) {
4705     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4706     nrows       = *(buf_ri_k[k]);
4707     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
4708     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4709   }
4710 
4711   /* set values of ba */
4712   m = merge->rowmap->n;
4713   for (i=0; i<m; i++) {
4714     arow = owners[rank] + i;
4715     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
4716     bnzi = bi[i+1] - bi[i];
4717     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
4718 
4719     /* add local non-zero vals of this proc's seqmat into ba */
4720     anzi   = ai[arow+1] - ai[arow];
4721     aj     = a->j + ai[arow];
4722     aa     = a->a + ai[arow];
4723     nextaj = 0;
4724     for (j=0; nextaj<anzi; j++) {
4725       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4726         ba_i[j] += aa[nextaj++];
4727       }
4728     }
4729 
4730     /* add received vals into ba */
4731     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4732       /* i-th row */
4733       if (i == *nextrow[k]) {
4734         anzi   = *(nextai[k]+1) - *nextai[k];
4735         aj     = buf_rj[k] + *(nextai[k]);
4736         aa     = abuf_r[k] + *(nextai[k]);
4737         nextaj = 0;
4738         for (j=0; nextaj<anzi; j++) {
4739           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4740             ba_i[j] += aa[nextaj++];
4741           }
4742         }
4743         nextrow[k]++; nextai[k]++;
4744       }
4745     }
4746     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
4747   }
4748   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4749   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4750 
4751   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
4752   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
4753   ierr = PetscFree(ba_i);CHKERRQ(ierr);
4754   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4755   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4756   PetscFunctionReturn(0);
4757 }
4758 
4759 extern PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat);
4760 
4761 #undef __FUNCT__
4762 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJSymbolic"
4763 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4764 {
4765   PetscErrorCode      ierr;
4766   Mat                 B_mpi;
4767   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
4768   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4769   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
4770   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4771   PetscInt            len,proc,*dnz,*onz,bs,cbs;
4772   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4773   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4774   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
4775   MPI_Status          *status;
4776   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
4777   PetscBT             lnkbt;
4778   Mat_Merge_SeqsToMPI *merge;
4779   PetscContainer      container;
4780 
4781   PetscFunctionBegin;
4782   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4783 
4784   /* make sure it is a PETSc comm */
4785   ierr = PetscCommDuplicate(comm,&comm,NULL);CHKERRQ(ierr);
4786   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4787   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4788 
4789   ierr = PetscNew(Mat_Merge_SeqsToMPI,&merge);CHKERRQ(ierr);
4790   ierr = PetscMalloc(size*sizeof(MPI_Status),&status);CHKERRQ(ierr);
4791 
4792   /* determine row ownership */
4793   /*---------------------------------------------------------*/
4794   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
4795   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
4796   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
4797   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
4798   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
4799   ierr = PetscMalloc(size*sizeof(PetscMPIInt),&len_si);CHKERRQ(ierr);
4800   ierr = PetscMalloc(size*sizeof(PetscMPIInt),&merge->len_s);CHKERRQ(ierr);
4801 
4802   m      = merge->rowmap->n;
4803   owners = merge->rowmap->range;
4804 
4805   /* determine the number of messages to send, their lengths */
4806   /*---------------------------------------------------------*/
4807   len_s = merge->len_s;
4808 
4809   len          = 0; /* length of buf_si[] */
4810   merge->nsend = 0;
4811   for (proc=0; proc<size; proc++) {
4812     len_si[proc] = 0;
4813     if (proc == rank) {
4814       len_s[proc] = 0;
4815     } else {
4816       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4817       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4818     }
4819     if (len_s[proc]) {
4820       merge->nsend++;
4821       nrows = 0;
4822       for (i=owners[proc]; i<owners[proc+1]; i++) {
4823         if (ai[i+1] > ai[i]) nrows++;
4824       }
4825       len_si[proc] = 2*(nrows+1);
4826       len         += len_si[proc];
4827     }
4828   }
4829 
4830   /* determine the number and length of messages to receive for ij-structure */
4831   /*-------------------------------------------------------------------------*/
4832   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
4833   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
4834 
4835   /* post the Irecv of j-structure */
4836   /*-------------------------------*/
4837   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
4838   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
4839 
4840   /* post the Isend of j-structure */
4841   /*--------------------------------*/
4842   ierr = PetscMalloc2(merge->nsend,MPI_Request,&si_waits,merge->nsend,MPI_Request,&sj_waits);CHKERRQ(ierr);
4843 
4844   for (proc=0, k=0; proc<size; proc++) {
4845     if (!len_s[proc]) continue;
4846     i    = owners[proc];
4847     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
4848     k++;
4849   }
4850 
4851   /* receives and sends of j-structure are complete */
4852   /*------------------------------------------------*/
4853   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
4854   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
4855 
4856   /* send and recv i-structure */
4857   /*---------------------------*/
4858   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
4859   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
4860 
4861   ierr   = PetscMalloc((len+1)*sizeof(PetscInt),&buf_s);CHKERRQ(ierr);
4862   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4863   for (proc=0,k=0; proc<size; proc++) {
4864     if (!len_s[proc]) continue;
4865     /* form outgoing message for i-structure:
4866          buf_si[0]:                 nrows to be sent
4867                [1:nrows]:           row index (global)
4868                [nrows+1:2*nrows+1]: i-structure index
4869     */
4870     /*-------------------------------------------*/
4871     nrows       = len_si[proc]/2 - 1;
4872     buf_si_i    = buf_si + nrows+1;
4873     buf_si[0]   = nrows;
4874     buf_si_i[0] = 0;
4875     nrows       = 0;
4876     for (i=owners[proc]; i<owners[proc+1]; i++) {
4877       anzi = ai[i+1] - ai[i];
4878       if (anzi) {
4879         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4880         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4881         nrows++;
4882       }
4883     }
4884     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4885     k++;
4886     buf_si += len_si[proc];
4887   }
4888 
4889   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4890   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4891 
4892   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4893   for (i=0; i<merge->nrecv; i++) {
4894     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);
4895   }
4896 
4897   ierr = PetscFree(len_si);CHKERRQ(ierr);
4898   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4899   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4900   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4901   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4902   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4903   ierr = PetscFree(status);CHKERRQ(ierr);
4904 
4905   /* compute a local seq matrix in each processor */
4906   /*----------------------------------------------*/
4907   /* allocate bi array and free space for accumulating nonzero column info */
4908   ierr  = PetscMalloc((m+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
4909   bi[0] = 0;
4910 
4911   /* create and initialize a linked list */
4912   nlnk = N+1;
4913   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4914 
4915   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4916   len  = ai[owners[rank+1]] - ai[owners[rank]];
4917   ierr = PetscFreeSpaceGet((PetscInt)(2*len+1),&free_space);CHKERRQ(ierr);
4918 
4919   current_space = free_space;
4920 
4921   /* determine symbolic info for each local row */
4922   ierr = PetscMalloc3(merge->nrecv,PetscInt*,&buf_ri_k,merge->nrecv,PetscInt*,&nextrow,merge->nrecv,PetscInt*,&nextai);CHKERRQ(ierr);
4923 
4924   for (k=0; k<merge->nrecv; k++) {
4925     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4926     nrows       = *buf_ri_k[k];
4927     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4928     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4929   }
4930 
4931   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4932   len  = 0;
4933   for (i=0; i<m; i++) {
4934     bnzi = 0;
4935     /* add local non-zero cols of this proc's seqmat into lnk */
4936     arow  = owners[rank] + i;
4937     anzi  = ai[arow+1] - ai[arow];
4938     aj    = a->j + ai[arow];
4939     ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4940     bnzi += nlnk;
4941     /* add received col data into lnk */
4942     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4943       if (i == *nextrow[k]) { /* i-th row */
4944         anzi  = *(nextai[k]+1) - *nextai[k];
4945         aj    = buf_rj[k] + *nextai[k];
4946         ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4947         bnzi += nlnk;
4948         nextrow[k]++; nextai[k]++;
4949       }
4950     }
4951     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4952 
4953     /* if free space is not available, make more free space */
4954     if (current_space->local_remaining<bnzi) {
4955       ierr = PetscFreeSpaceGet(bnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
4956       nspacedouble++;
4957     }
4958     /* copy data into free space, then initialize lnk */
4959     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4960     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
4961 
4962     current_space->array           += bnzi;
4963     current_space->local_used      += bnzi;
4964     current_space->local_remaining -= bnzi;
4965 
4966     bi[i+1] = bi[i] + bnzi;
4967   }
4968 
4969   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4970 
4971   ierr = PetscMalloc((bi[m]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
4972   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
4973   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4974 
4975   /* create symbolic parallel matrix B_mpi */
4976   /*---------------------------------------*/
4977   ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
4978   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
4979   if (n==PETSC_DECIDE) {
4980     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
4981   } else {
4982     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4983   }
4984   ierr = MatSetBlockSizes(B_mpi,bs,cbs);CHKERRQ(ierr);
4985   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
4986   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
4987   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4988   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
4989 
4990   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4991   B_mpi->assembled    = PETSC_FALSE;
4992   B_mpi->ops->destroy = MatDestroy_MPIAIJ_SeqsToMPI;
4993   merge->bi           = bi;
4994   merge->bj           = bj;
4995   merge->buf_ri       = buf_ri;
4996   merge->buf_rj       = buf_rj;
4997   merge->coi          = NULL;
4998   merge->coj          = NULL;
4999   merge->owners_co    = NULL;
5000 
5001   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
5002 
5003   /* attach the supporting struct to B_mpi for reuse */
5004   ierr    = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
5005   ierr    = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
5006   ierr    = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
5007   ierr    = PetscContainerDestroy(&container);CHKERRQ(ierr);
5008   *mpimat = B_mpi;
5009 
5010   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
5011   PetscFunctionReturn(0);
5012 }
5013 
5014 #undef __FUNCT__
5015 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJ"
5016 /*@C
5017       MatCreateMPIAIJSumSeqAIJ - Creates a MPIAIJ matrix by adding sequential
5018                  matrices from each processor
5019 
5020     Collective on MPI_Comm
5021 
5022    Input Parameters:
5023 +    comm - the communicators the parallel matrix will live on
5024 .    seqmat - the input sequential matrices
5025 .    m - number of local rows (or PETSC_DECIDE)
5026 .    n - number of local columns (or PETSC_DECIDE)
5027 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5028 
5029    Output Parameter:
5030 .    mpimat - the parallel matrix generated
5031 
5032     Level: advanced
5033 
5034    Notes:
5035      The dimensions of the sequential matrix in each processor MUST be the same.
5036      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
5037      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
5038 @*/
5039 PetscErrorCode  MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
5040 {
5041   PetscErrorCode ierr;
5042   PetscMPIInt    size;
5043 
5044   PetscFunctionBegin;
5045   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
5046   if (size == 1) {
5047     ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
5048     if (scall == MAT_INITIAL_MATRIX) {
5049       ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
5050     } else {
5051       ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
5052     }
5053     ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
5054     PetscFunctionReturn(0);
5055   }
5056   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
5057   if (scall == MAT_INITIAL_MATRIX) {
5058     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
5059   }
5060   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
5061   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
5062   PetscFunctionReturn(0);
5063 }
5064 
5065 #undef __FUNCT__
5066 #define __FUNCT__ "MatMPIAIJGetLocalMat"
5067 /*@
5068      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
5069           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
5070           with MatGetSize()
5071 
5072     Not Collective
5073 
5074    Input Parameters:
5075 +    A - the matrix
5076 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5077 
5078    Output Parameter:
5079 .    A_loc - the local sequential matrix generated
5080 
5081     Level: developer
5082 
5083 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
5084 
5085 @*/
5086 PetscErrorCode  MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
5087 {
5088   PetscErrorCode ierr;
5089   Mat_MPIAIJ     *mpimat=(Mat_MPIAIJ*)A->data;
5090   Mat_SeqAIJ     *mat,*a=(Mat_SeqAIJ*)(mpimat->A)->data,*b=(Mat_SeqAIJ*)(mpimat->B)->data;
5091   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*cmap=mpimat->garray;
5092   MatScalar      *aa=a->a,*ba=b->a,*cam;
5093   PetscScalar    *ca;
5094   PetscInt       am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
5095   PetscInt       *ci,*cj,col,ncols_d,ncols_o,jo;
5096   PetscBool      match;
5097 
5098   PetscFunctionBegin;
5099   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
5100   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
5101   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
5102   if (scall == MAT_INITIAL_MATRIX) {
5103     ierr  = PetscMalloc((1+am)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
5104     ci[0] = 0;
5105     for (i=0; i<am; i++) {
5106       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
5107     }
5108     ierr = PetscMalloc((1+ci[am])*sizeof(PetscInt),&cj);CHKERRQ(ierr);
5109     ierr = PetscMalloc((1+ci[am])*sizeof(PetscScalar),&ca);CHKERRQ(ierr);
5110     k    = 0;
5111     for (i=0; i<am; i++) {
5112       ncols_o = bi[i+1] - bi[i];
5113       ncols_d = ai[i+1] - ai[i];
5114       /* off-diagonal portion of A */
5115       for (jo=0; jo<ncols_o; jo++) {
5116         col = cmap[*bj];
5117         if (col >= cstart) break;
5118         cj[k]   = col; bj++;
5119         ca[k++] = *ba++;
5120       }
5121       /* diagonal portion of A */
5122       for (j=0; j<ncols_d; j++) {
5123         cj[k]   = cstart + *aj++;
5124         ca[k++] = *aa++;
5125       }
5126       /* off-diagonal portion of A */
5127       for (j=jo; j<ncols_o; j++) {
5128         cj[k]   = cmap[*bj++];
5129         ca[k++] = *ba++;
5130       }
5131     }
5132     /* put together the new matrix */
5133     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
5134     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
5135     /* Since these are PETSc arrays, change flags to free them as necessary. */
5136     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
5137     mat->free_a  = PETSC_TRUE;
5138     mat->free_ij = PETSC_TRUE;
5139     mat->nonew   = 0;
5140   } else if (scall == MAT_REUSE_MATRIX) {
5141     mat=(Mat_SeqAIJ*)(*A_loc)->data;
5142     ci = mat->i; cj = mat->j; cam = mat->a;
5143     for (i=0; i<am; i++) {
5144       /* off-diagonal portion of A */
5145       ncols_o = bi[i+1] - bi[i];
5146       for (jo=0; jo<ncols_o; jo++) {
5147         col = cmap[*bj];
5148         if (col >= cstart) break;
5149         *cam++ = *ba++; bj++;
5150       }
5151       /* diagonal portion of A */
5152       ncols_d = ai[i+1] - ai[i];
5153       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
5154       /* off-diagonal portion of A */
5155       for (j=jo; j<ncols_o; j++) {
5156         *cam++ = *ba++; bj++;
5157       }
5158     }
5159   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
5160   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
5161   PetscFunctionReturn(0);
5162 }
5163 
5164 #undef __FUNCT__
5165 #define __FUNCT__ "MatMPIAIJGetLocalMatCondensed"
5166 /*@C
5167      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MPIAIJ matrix by taking all its local rows and NON-ZERO columns
5168 
5169     Not Collective
5170 
5171    Input Parameters:
5172 +    A - the matrix
5173 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5174 -    row, col - index sets of rows and columns to extract (or NULL)
5175 
5176    Output Parameter:
5177 .    A_loc - the local sequential matrix generated
5178 
5179     Level: developer
5180 
5181 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
5182 
5183 @*/
5184 PetscErrorCode  MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
5185 {
5186   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
5187   PetscErrorCode ierr;
5188   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
5189   IS             isrowa,iscola;
5190   Mat            *aloc;
5191   PetscBool      match;
5192 
5193   PetscFunctionBegin;
5194   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
5195   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
5196   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
5197   if (!row) {
5198     start = A->rmap->rstart; end = A->rmap->rend;
5199     ierr  = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
5200   } else {
5201     isrowa = *row;
5202   }
5203   if (!col) {
5204     start = A->cmap->rstart;
5205     cmap  = a->garray;
5206     nzA   = a->A->cmap->n;
5207     nzB   = a->B->cmap->n;
5208     ierr  = PetscMalloc((nzA+nzB)*sizeof(PetscInt), &idx);CHKERRQ(ierr);
5209     ncols = 0;
5210     for (i=0; i<nzB; i++) {
5211       if (cmap[i] < start) idx[ncols++] = cmap[i];
5212       else break;
5213     }
5214     imark = i;
5215     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
5216     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
5217     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
5218   } else {
5219     iscola = *col;
5220   }
5221   if (scall != MAT_INITIAL_MATRIX) {
5222     ierr    = PetscMalloc(sizeof(Mat),&aloc);CHKERRQ(ierr);
5223     aloc[0] = *A_loc;
5224   }
5225   ierr   = MatGetSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
5226   *A_loc = aloc[0];
5227   ierr   = PetscFree(aloc);CHKERRQ(ierr);
5228   if (!row) {
5229     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
5230   }
5231   if (!col) {
5232     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
5233   }
5234   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
5235   PetscFunctionReturn(0);
5236 }
5237 
5238 #undef __FUNCT__
5239 #define __FUNCT__ "MatGetBrowsOfAcols"
5240 /*@C
5241     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
5242 
5243     Collective on Mat
5244 
5245    Input Parameters:
5246 +    A,B - the matrices in mpiaij format
5247 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5248 -    rowb, colb - index sets of rows and columns of B to extract (or NULL)
5249 
5250    Output Parameter:
5251 +    rowb, colb - index sets of rows and columns of B to extract
5252 -    B_seq - the sequential matrix generated
5253 
5254     Level: developer
5255 
5256 @*/
5257 PetscErrorCode  MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
5258 {
5259   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
5260   PetscErrorCode ierr;
5261   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
5262   IS             isrowb,iscolb;
5263   Mat            *bseq=NULL;
5264 
5265   PetscFunctionBegin;
5266   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
5267     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);
5268   }
5269   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
5270 
5271   if (scall == MAT_INITIAL_MATRIX) {
5272     start = A->cmap->rstart;
5273     cmap  = a->garray;
5274     nzA   = a->A->cmap->n;
5275     nzB   = a->B->cmap->n;
5276     ierr  = PetscMalloc((nzA+nzB)*sizeof(PetscInt), &idx);CHKERRQ(ierr);
5277     ncols = 0;
5278     for (i=0; i<nzB; i++) {  /* row < local row index */
5279       if (cmap[i] < start) idx[ncols++] = cmap[i];
5280       else break;
5281     }
5282     imark = i;
5283     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
5284     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
5285     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
5286     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
5287   } else {
5288     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
5289     isrowb  = *rowb; iscolb = *colb;
5290     ierr    = PetscMalloc(sizeof(Mat),&bseq);CHKERRQ(ierr);
5291     bseq[0] = *B_seq;
5292   }
5293   ierr   = MatGetSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
5294   *B_seq = bseq[0];
5295   ierr   = PetscFree(bseq);CHKERRQ(ierr);
5296   if (!rowb) {
5297     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
5298   } else {
5299     *rowb = isrowb;
5300   }
5301   if (!colb) {
5302     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
5303   } else {
5304     *colb = iscolb;
5305   }
5306   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
5307   PetscFunctionReturn(0);
5308 }
5309 
5310 #undef __FUNCT__
5311 #define __FUNCT__ "MatGetBrowsOfAoCols_MPIAIJ"
5312 /*
5313     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
5314     of the OFF-DIAGONAL portion of local A
5315 
5316     Collective on Mat
5317 
5318    Input Parameters:
5319 +    A,B - the matrices in mpiaij format
5320 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5321 
5322    Output Parameter:
5323 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
5324 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
5325 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
5326 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
5327 
5328     Level: developer
5329 
5330 */
5331 PetscErrorCode  MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
5332 {
5333   VecScatter_MPI_General *gen_to,*gen_from;
5334   PetscErrorCode         ierr;
5335   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
5336   Mat_SeqAIJ             *b_oth;
5337   VecScatter             ctx =a->Mvctx;
5338   MPI_Comm               comm;
5339   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
5340   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
5341   PetscScalar            *rvalues,*svalues;
5342   MatScalar              *b_otha,*bufa,*bufA;
5343   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
5344   MPI_Request            *rwaits = NULL,*swaits = NULL;
5345   MPI_Status             *sstatus,rstatus;
5346   PetscMPIInt            jj;
5347   PetscInt               *cols,sbs,rbs;
5348   PetscScalar            *vals;
5349 
5350   PetscFunctionBegin;
5351   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
5352   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
5353     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);
5354   }
5355   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5356   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
5357 
5358   gen_to   = (VecScatter_MPI_General*)ctx->todata;
5359   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
5360   rvalues  = gen_from->values; /* holds the length of receiving row */
5361   svalues  = gen_to->values;   /* holds the length of sending row */
5362   nrecvs   = gen_from->n;
5363   nsends   = gen_to->n;
5364 
5365   ierr    = PetscMalloc2(nrecvs,MPI_Request,&rwaits,nsends,MPI_Request,&swaits);CHKERRQ(ierr);
5366   srow    = gen_to->indices;    /* local row index to be sent */
5367   sstarts = gen_to->starts;
5368   sprocs  = gen_to->procs;
5369   sstatus = gen_to->sstatus;
5370   sbs     = gen_to->bs;
5371   rstarts = gen_from->starts;
5372   rprocs  = gen_from->procs;
5373   rbs     = gen_from->bs;
5374 
5375   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
5376   if (scall == MAT_INITIAL_MATRIX) {
5377     /* i-array */
5378     /*---------*/
5379     /*  post receives */
5380     for (i=0; i<nrecvs; i++) {
5381       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
5382       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
5383       ierr   = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5384     }
5385 
5386     /* pack the outgoing message */
5387     ierr = PetscMalloc2(nsends+1,PetscInt,&sstartsj,nrecvs+1,PetscInt,&rstartsj);CHKERRQ(ierr);
5388 
5389     sstartsj[0] = 0;
5390     rstartsj[0] = 0;
5391     len         = 0; /* total length of j or a array to be sent */
5392     k           = 0;
5393     for (i=0; i<nsends; i++) {
5394       rowlen = (PetscInt*)svalues + sstarts[i]*sbs;
5395       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
5396       for (j=0; j<nrows; j++) {
5397         row = srow[k] + B->rmap->range[rank]; /* global row idx */
5398         for (l=0; l<sbs; l++) {
5399           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr); /* rowlength */
5400 
5401           rowlen[j*sbs+l] = ncols;
5402 
5403           len += ncols;
5404           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr);
5405         }
5406         k++;
5407       }
5408       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5409 
5410       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
5411     }
5412     /* recvs and sends of i-array are completed */
5413     i = nrecvs;
5414     while (i--) {
5415       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5416     }
5417     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5418 
5419     /* allocate buffers for sending j and a arrays */
5420     ierr = PetscMalloc((len+1)*sizeof(PetscInt),&bufj);CHKERRQ(ierr);
5421     ierr = PetscMalloc((len+1)*sizeof(PetscScalar),&bufa);CHKERRQ(ierr);
5422 
5423     /* create i-array of B_oth */
5424     ierr = PetscMalloc((aBn+2)*sizeof(PetscInt),&b_othi);CHKERRQ(ierr);
5425 
5426     b_othi[0] = 0;
5427     len       = 0; /* total length of j or a array to be received */
5428     k         = 0;
5429     for (i=0; i<nrecvs; i++) {
5430       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
5431       nrows  = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be recieved */
5432       for (j=0; j<nrows; j++) {
5433         b_othi[k+1] = b_othi[k] + rowlen[j];
5434         len        += rowlen[j]; k++;
5435       }
5436       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
5437     }
5438 
5439     /* allocate space for j and a arrrays of B_oth */
5440     ierr = PetscMalloc((b_othi[aBn]+1)*sizeof(PetscInt),&b_othj);CHKERRQ(ierr);
5441     ierr = PetscMalloc((b_othi[aBn]+1)*sizeof(MatScalar),&b_otha);CHKERRQ(ierr);
5442 
5443     /* j-array */
5444     /*---------*/
5445     /*  post receives of j-array */
5446     for (i=0; i<nrecvs; i++) {
5447       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5448       ierr  = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5449     }
5450 
5451     /* pack the outgoing message j-array */
5452     k = 0;
5453     for (i=0; i<nsends; i++) {
5454       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5455       bufJ  = bufj+sstartsj[i];
5456       for (j=0; j<nrows; j++) {
5457         row = srow[k++] + B->rmap->range[rank];  /* global row idx */
5458         for (ll=0; ll<sbs; ll++) {
5459           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
5460           for (l=0; l<ncols; l++) {
5461             *bufJ++ = cols[l];
5462           }
5463           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
5464         }
5465       }
5466       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5467     }
5468 
5469     /* recvs and sends of j-array are completed */
5470     i = nrecvs;
5471     while (i--) {
5472       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5473     }
5474     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5475   } else if (scall == MAT_REUSE_MATRIX) {
5476     sstartsj = *startsj_s;
5477     rstartsj = *startsj_r;
5478     bufa     = *bufa_ptr;
5479     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
5480     b_otha   = b_oth->a;
5481   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
5482 
5483   /* a-array */
5484   /*---------*/
5485   /*  post receives of a-array */
5486   for (i=0; i<nrecvs; i++) {
5487     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5488     ierr  = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5489   }
5490 
5491   /* pack the outgoing message a-array */
5492   k = 0;
5493   for (i=0; i<nsends; i++) {
5494     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5495     bufA  = bufa+sstartsj[i];
5496     for (j=0; j<nrows; j++) {
5497       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
5498       for (ll=0; ll<sbs; ll++) {
5499         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
5500         for (l=0; l<ncols; l++) {
5501           *bufA++ = vals[l];
5502         }
5503         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
5504       }
5505     }
5506     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5507   }
5508   /* recvs and sends of a-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   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
5515 
5516   if (scall == MAT_INITIAL_MATRIX) {
5517     /* put together the new matrix */
5518     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
5519 
5520     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
5521     /* Since these are PETSc arrays, change flags to free them as necessary. */
5522     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
5523     b_oth->free_a  = PETSC_TRUE;
5524     b_oth->free_ij = PETSC_TRUE;
5525     b_oth->nonew   = 0;
5526 
5527     ierr = PetscFree(bufj);CHKERRQ(ierr);
5528     if (!startsj_s || !bufa_ptr) {
5529       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
5530       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
5531     } else {
5532       *startsj_s = sstartsj;
5533       *startsj_r = rstartsj;
5534       *bufa_ptr  = bufa;
5535     }
5536   }
5537   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5538   PetscFunctionReturn(0);
5539 }
5540 
5541 #undef __FUNCT__
5542 #define __FUNCT__ "MatGetCommunicationStructs"
5543 /*@C
5544   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
5545 
5546   Not Collective
5547 
5548   Input Parameters:
5549 . A - The matrix in mpiaij format
5550 
5551   Output Parameter:
5552 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
5553 . colmap - A map from global column index to local index into lvec
5554 - multScatter - A scatter from the argument of a matrix-vector product to lvec
5555 
5556   Level: developer
5557 
5558 @*/
5559 #if defined(PETSC_USE_CTABLE)
5560 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
5561 #else
5562 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
5563 #endif
5564 {
5565   Mat_MPIAIJ *a;
5566 
5567   PetscFunctionBegin;
5568   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
5569   PetscValidPointer(lvec, 2);
5570   PetscValidPointer(colmap, 3);
5571   PetscValidPointer(multScatter, 4);
5572   a = (Mat_MPIAIJ*) A->data;
5573   if (lvec) *lvec = a->lvec;
5574   if (colmap) *colmap = a->colmap;
5575   if (multScatter) *multScatter = a->Mvctx;
5576   PetscFunctionReturn(0);
5577 }
5578 
5579 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
5580 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
5581 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
5582 
5583 #undef __FUNCT__
5584 #define __FUNCT__ "MatMatMultNumeric_MPIDense_MPIAIJ"
5585 /*
5586     Computes (B'*A')' since computing B*A directly is untenable
5587 
5588                n                       p                          p
5589         (              )       (              )         (                  )
5590       m (      A       )  *  n (       B      )   =   m (         C        )
5591         (              )       (              )         (                  )
5592 
5593 */
5594 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
5595 {
5596   PetscErrorCode ierr;
5597   Mat            At,Bt,Ct;
5598 
5599   PetscFunctionBegin;
5600   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
5601   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
5602   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
5603   ierr = MatDestroy(&At);CHKERRQ(ierr);
5604   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
5605   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
5606   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
5607   PetscFunctionReturn(0);
5608 }
5609 
5610 #undef __FUNCT__
5611 #define __FUNCT__ "MatMatMultSymbolic_MPIDense_MPIAIJ"
5612 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
5613 {
5614   PetscErrorCode ierr;
5615   PetscInt       m=A->rmap->n,n=B->cmap->n;
5616   Mat            Cmat;
5617 
5618   PetscFunctionBegin;
5619   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);
5620   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
5621   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
5622   ierr = MatSetBlockSizes(Cmat,A->rmap->bs,B->cmap->bs);CHKERRQ(ierr);
5623   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
5624   ierr = MatMPIDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
5625   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5626   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5627 
5628   Cmat->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
5629 
5630   *C = Cmat;
5631   PetscFunctionReturn(0);
5632 }
5633 
5634 /* ----------------------------------------------------------------*/
5635 #undef __FUNCT__
5636 #define __FUNCT__ "MatMatMult_MPIDense_MPIAIJ"
5637 PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
5638 {
5639   PetscErrorCode ierr;
5640 
5641   PetscFunctionBegin;
5642   if (scall == MAT_INITIAL_MATRIX) {
5643     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5644     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
5645     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5646   }
5647   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5648   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
5649   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5650   PetscFunctionReturn(0);
5651 }
5652 
5653 #if defined(PETSC_HAVE_MUMPS)
5654 PETSC_EXTERN PetscErrorCode MatGetFactor_aij_mumps(Mat,MatFactorType,Mat*);
5655 #endif
5656 #if defined(PETSC_HAVE_PASTIX)
5657 PETSC_EXTERN PetscErrorCode MatGetFactor_mpiaij_pastix(Mat,MatFactorType,Mat*);
5658 #endif
5659 #if defined(PETSC_HAVE_SUPERLU_DIST)
5660 PETSC_EXTERN PetscErrorCode MatGetFactor_mpiaij_superlu_dist(Mat,MatFactorType,Mat*);
5661 #endif
5662 #if defined(PETSC_HAVE_CLIQUE)
5663 PETSC_EXTERN PetscErrorCode MatGetFactor_aij_clique(Mat,MatFactorType,Mat*);
5664 #endif
5665 
5666 /*MC
5667    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
5668 
5669    Options Database Keys:
5670 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
5671 
5672   Level: beginner
5673 
5674 .seealso: MatCreateAIJ()
5675 M*/
5676 
5677 #undef __FUNCT__
5678 #define __FUNCT__ "MatCreate_MPIAIJ"
5679 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
5680 {
5681   Mat_MPIAIJ     *b;
5682   PetscErrorCode ierr;
5683   PetscMPIInt    size;
5684 
5685   PetscFunctionBegin;
5686   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
5687 
5688   ierr          = PetscNewLog(B,Mat_MPIAIJ,&b);CHKERRQ(ierr);
5689   B->data       = (void*)b;
5690   ierr          = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
5691   B->assembled  = PETSC_FALSE;
5692   B->insertmode = NOT_SET_VALUES;
5693   b->size       = size;
5694 
5695   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank);CHKERRQ(ierr);
5696 
5697   /* build cache for off array entries formed */
5698   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash);CHKERRQ(ierr);
5699 
5700   b->donotstash  = PETSC_FALSE;
5701   b->colmap      = 0;
5702   b->garray      = 0;
5703   b->roworiented = PETSC_TRUE;
5704 
5705   /* stuff used for matrix vector multiply */
5706   b->lvec  = NULL;
5707   b->Mvctx = NULL;
5708 
5709   /* stuff for MatGetRow() */
5710   b->rowindices   = 0;
5711   b->rowvalues    = 0;
5712   b->getrowactive = PETSC_FALSE;
5713 
5714   /* flexible pointer used in CUSP/CUSPARSE classes */
5715   b->spptr = NULL;
5716 
5717 #if defined(PETSC_HAVE_MUMPS)
5718   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_mumps_C",MatGetFactor_aij_mumps);CHKERRQ(ierr);
5719 #endif
5720 #if defined(PETSC_HAVE_PASTIX)
5721   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_pastix_C",MatGetFactor_mpiaij_pastix);CHKERRQ(ierr);
5722 #endif
5723 #if defined(PETSC_HAVE_SUPERLU_DIST)
5724   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_superlu_dist_C",MatGetFactor_mpiaij_superlu_dist);CHKERRQ(ierr);
5725 #endif
5726 #if defined(PETSC_HAVE_CLIQUE)
5727   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_clique_C",MatGetFactor_aij_clique);CHKERRQ(ierr);
5728 #endif
5729   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ);CHKERRQ(ierr);
5730   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
5731   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetDiagonalBlock_C",MatGetDiagonalBlock_MPIAIJ);CHKERRQ(ierr);
5732   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
5733   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
5734   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
5735   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
5736   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
5737   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
5738   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
5739   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
5740   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
5741   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
5742   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
5743   PetscFunctionReturn(0);
5744 }
5745 
5746 #undef __FUNCT__
5747 #define __FUNCT__ "MatCreateMPIAIJWithSplitArrays"
5748 /*@
5749      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
5750          and "off-diagonal" part of the matrix in CSR format.
5751 
5752    Collective on MPI_Comm
5753 
5754    Input Parameters:
5755 +  comm - MPI communicator
5756 .  m - number of local rows (Cannot be PETSC_DECIDE)
5757 .  n - This value should be the same as the local size used in creating the
5758        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
5759        calculated if N is given) For square matrices n is almost always m.
5760 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
5761 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
5762 .   i - row indices for "diagonal" portion of matrix
5763 .   j - column indices
5764 .   a - matrix values
5765 .   oi - row indices for "off-diagonal" portion of matrix
5766 .   oj - column indices
5767 -   oa - matrix values
5768 
5769    Output Parameter:
5770 .   mat - the matrix
5771 
5772    Level: advanced
5773 
5774    Notes:
5775        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
5776        must free the arrays once the matrix has been destroyed and not before.
5777 
5778        The i and j indices are 0 based
5779 
5780        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
5781 
5782        This sets local rows and cannot be used to set off-processor values.
5783 
5784        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
5785        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
5786        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
5787        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
5788        keep track of the underlying array. Use MatSetOption(A,MAT_IGNORE_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
5789        communication if it is known that only local entries will be set.
5790 
5791 .keywords: matrix, aij, compressed row, sparse, parallel
5792 
5793 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
5794           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
5795 @*/
5796 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)
5797 {
5798   PetscErrorCode ierr;
5799   Mat_MPIAIJ     *maij;
5800 
5801   PetscFunctionBegin;
5802   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
5803   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
5804   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
5805   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
5806   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
5807   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
5808   maij = (Mat_MPIAIJ*) (*mat)->data;
5809 
5810   (*mat)->preallocated = PETSC_TRUE;
5811 
5812   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
5813   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
5814 
5815   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
5816   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
5817 
5818   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5819   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5820   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5821   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5822 
5823   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5824   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5825   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
5826   PetscFunctionReturn(0);
5827 }
5828 
5829 /*
5830     Special version for direct calls from Fortran
5831 */
5832 #include <petsc-private/fortranimpl.h>
5833 
5834 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5835 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
5836 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5837 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
5838 #endif
5839 
5840 /* Change these macros so can be used in void function */
5841 #undef CHKERRQ
5842 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
5843 #undef SETERRQ2
5844 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5845 #undef SETERRQ3
5846 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5847 #undef SETERRQ
5848 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
5849 
5850 #undef __FUNCT__
5851 #define __FUNCT__ "matsetvaluesmpiaij_"
5852 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)
5853 {
5854   Mat            mat  = *mmat;
5855   PetscInt       m    = *mm, n = *mn;
5856   InsertMode     addv = *maddv;
5857   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
5858   PetscScalar    value;
5859   PetscErrorCode ierr;
5860 
5861   MatCheckPreallocated(mat,1);
5862   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
5863 
5864 #if defined(PETSC_USE_DEBUG)
5865   else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
5866 #endif
5867   {
5868     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
5869     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
5870     PetscBool roworiented = aij->roworiented;
5871 
5872     /* Some Variables required in the macro */
5873     Mat        A                 = aij->A;
5874     Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
5875     PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
5876     MatScalar  *aa               = a->a;
5877     PetscBool  ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
5878     Mat        B                 = aij->B;
5879     Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
5880     PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5881     MatScalar  *ba               = b->a;
5882 
5883     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5884     PetscInt  nonew = a->nonew;
5885     MatScalar *ap1,*ap2;
5886 
5887     PetscFunctionBegin;
5888     for (i=0; i<m; i++) {
5889       if (im[i] < 0) continue;
5890 #if defined(PETSC_USE_DEBUG)
5891       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);
5892 #endif
5893       if (im[i] >= rstart && im[i] < rend) {
5894         row      = im[i] - rstart;
5895         lastcol1 = -1;
5896         rp1      = aj + ai[row];
5897         ap1      = aa + ai[row];
5898         rmax1    = aimax[row];
5899         nrow1    = ailen[row];
5900         low1     = 0;
5901         high1    = nrow1;
5902         lastcol2 = -1;
5903         rp2      = bj + bi[row];
5904         ap2      = ba + bi[row];
5905         rmax2    = bimax[row];
5906         nrow2    = bilen[row];
5907         low2     = 0;
5908         high2    = nrow2;
5909 
5910         for (j=0; j<n; j++) {
5911           if (roworiented) value = v[i*n+j];
5912           else value = v[i+j*m];
5913           if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES)) continue;
5914           if (in[j] >= cstart && in[j] < cend) {
5915             col = in[j] - cstart;
5916             MatSetValues_SeqAIJ_A_Private(row,col,value,addv);
5917           } else if (in[j] < 0) continue;
5918 #if defined(PETSC_USE_DEBUG)
5919           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);
5920 #endif
5921           else {
5922             if (mat->was_assembled) {
5923               if (!aij->colmap) {
5924                 ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5925               }
5926 #if defined(PETSC_USE_CTABLE)
5927               ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5928               col--;
5929 #else
5930               col = aij->colmap[in[j]] - 1;
5931 #endif
5932               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5933                 ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5934                 col  =  in[j];
5935                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5936                 B     = aij->B;
5937                 b     = (Mat_SeqAIJ*)B->data;
5938                 bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5939                 rp2   = bj + bi[row];
5940                 ap2   = ba + bi[row];
5941                 rmax2 = bimax[row];
5942                 nrow2 = bilen[row];
5943                 low2  = 0;
5944                 high2 = nrow2;
5945                 bm    = aij->B->rmap->n;
5946                 ba    = b->a;
5947               }
5948             } else col = in[j];
5949             MatSetValues_SeqAIJ_B_Private(row,col,value,addv);
5950           }
5951         }
5952       } else if (!aij->donotstash) {
5953         if (roworiented) {
5954           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5955         } else {
5956           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5957         }
5958       }
5959     }
5960   }
5961   PetscFunctionReturnVoid();
5962 }
5963 
5964