xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision b2bf63709b6a963fd02e2640983e9e8c2a88c2e3)
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     if (redund->matseq) { /* via MatGetSubMatrices()  */
2530       ierr = ISDestroy(&redund->isrow);CHKERRQ(ierr);
2531       ierr = ISDestroy(&redund->iscol);CHKERRQ(ierr);
2532       ierr = MatDestroy(&redund->matseq[0]);CHKERRQ(ierr);
2533       ierr = PetscFree(redund->matseq);CHKERRQ(ierr);
2534     } else {
2535       ierr = PetscFree2(redund->send_rank,redund->recv_rank);CHKERRQ(ierr);
2536       ierr = PetscFree(redund->sbuf_j);CHKERRQ(ierr);
2537       ierr = PetscFree(redund->sbuf_a);CHKERRQ(ierr);
2538       for (i=0; i<redund->nrecvs; i++) {
2539         ierr = PetscFree(redund->rbuf_j[i]);CHKERRQ(ierr);
2540         ierr = PetscFree(redund->rbuf_a[i]);CHKERRQ(ierr);
2541       }
2542       ierr = PetscFree4(redund->sbuf_nz,redund->rbuf_nz,redund->rbuf_j,redund->rbuf_a);CHKERRQ(ierr);
2543     }
2544 
2545     if (redund->psubcomm) {
2546       ierr = PetscSubcommDestroy(&redund->psubcomm);CHKERRQ(ierr);
2547     }
2548     ierr = redund->Destroy(A);CHKERRQ(ierr);
2549     ierr = PetscFree(redund);CHKERRQ(ierr);
2550   }
2551   PetscFunctionReturn(0);
2552 }
2553 
2554 #undef __FUNCT__
2555 #define __FUNCT__ "MatGetRedundantMatrix_MPIAIJ_interlaced"
2556 PetscErrorCode MatGetRedundantMatrix_MPIAIJ_interlaced(Mat mat,PetscInt nsubcomm,MPI_Comm subcomm,MatReuse reuse,Mat *matredundant)
2557 {
2558   PetscMPIInt    rank,size;
2559   MPI_Comm       comm;
2560   PetscErrorCode ierr;
2561   PetscInt       nsends=0,nrecvs=0,i,rownz_max=0,M=mat->rmap->N,N=mat->cmap->N;
2562   PetscMPIInt    *send_rank= NULL,*recv_rank=NULL,subrank,subsize;
2563   PetscInt       *rowrange = mat->rmap->range;
2564   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2565   Mat            A = aij->A,B=aij->B,C=*matredundant;
2566   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data;
2567   PetscScalar    *sbuf_a;
2568   PetscInt       nzlocal=a->nz+b->nz;
2569   PetscInt       j,cstart=mat->cmap->rstart,cend=mat->cmap->rend,row,nzA,nzB,ncols,*cworkA,*cworkB;
2570   PetscInt       rstart=mat->rmap->rstart,rend=mat->rmap->rend,*bmap=aij->garray;
2571   PetscInt       *cols,ctmp,lwrite,*rptr,l,*sbuf_j;
2572   MatScalar      *aworkA,*aworkB;
2573   PetscScalar    *vals;
2574   PetscMPIInt    tag1,tag2,tag3,imdex;
2575   MPI_Request    *s_waits1=NULL,*s_waits2=NULL,*s_waits3=NULL;
2576   MPI_Request    *r_waits1=NULL,*r_waits2=NULL,*r_waits3=NULL;
2577   MPI_Status     recv_status,*send_status;
2578   PetscInt       *sbuf_nz=NULL,*rbuf_nz=NULL,count;
2579   PetscInt       **rbuf_j=NULL;
2580   PetscScalar    **rbuf_a=NULL;
2581   Mat_Redundant  *redund =NULL;
2582 
2583   PetscFunctionBegin;
2584   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
2585   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2586   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2587   ierr = MPI_Comm_rank(subcomm,&subrank);CHKERRQ(ierr);
2588   ierr = MPI_Comm_size(subcomm,&subsize);CHKERRQ(ierr);
2589 
2590   if (reuse == MAT_REUSE_MATRIX) {
2591     if (M != mat->rmap->N || N != mat->cmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. Wrong global size");
2592     if (subsize == 1) {
2593       Mat_SeqAIJ *c = (Mat_SeqAIJ*)C->data;
2594       redund = c->redundant;
2595     } else {
2596       Mat_MPIAIJ *c = (Mat_MPIAIJ*)C->data;
2597       redund = c->redundant;
2598     }
2599     if (nzlocal != redund->nzlocal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. Wrong nzlocal");
2600 
2601     nsends    = redund->nsends;
2602     nrecvs    = redund->nrecvs;
2603     send_rank = redund->send_rank;
2604     recv_rank = redund->recv_rank;
2605     sbuf_nz   = redund->sbuf_nz;
2606     rbuf_nz   = redund->rbuf_nz;
2607     sbuf_j    = redund->sbuf_j;
2608     sbuf_a    = redund->sbuf_a;
2609     rbuf_j    = redund->rbuf_j;
2610     rbuf_a    = redund->rbuf_a;
2611   }
2612 
2613   if (reuse == MAT_INITIAL_MATRIX) {
2614     PetscInt    nleftover,np_subcomm;
2615 
2616     /* get the destination processors' id send_rank, nsends and nrecvs */
2617     ierr = PetscMalloc2(size,PetscMPIInt,&send_rank,size,PetscMPIInt,&recv_rank);CHKERRQ(ierr);
2618 
2619     np_subcomm = size/nsubcomm;
2620     nleftover  = size - nsubcomm*np_subcomm;
2621 
2622     /* block of codes below is specific for INTERLACED */
2623     /* ------------------------------------------------*/
2624     nsends = 0; nrecvs = 0;
2625     for (i=0; i<size; i++) {
2626       if (subrank == i/nsubcomm && i != rank) { /* my_subrank == other's subrank */
2627         send_rank[nsends++] = i;
2628         recv_rank[nrecvs++] = i;
2629       }
2630     }
2631     if (rank >= size - nleftover) { /* this proc is a leftover processor */
2632       i = size-nleftover-1;
2633       j = 0;
2634       while (j < nsubcomm - nleftover) {
2635         send_rank[nsends++] = i;
2636         i--; j++;
2637       }
2638     }
2639 
2640     if (nleftover && subsize == size/nsubcomm && subrank==subsize-1) { /* this proc recvs from leftover processors */
2641       for (i=0; i<nleftover; i++) {
2642         recv_rank[nrecvs++] = size-nleftover+i;
2643       }
2644     }
2645     /*----------------------------------------------*/
2646 
2647     /* allocate sbuf_j, sbuf_a */
2648     i    = nzlocal + rowrange[rank+1] - rowrange[rank] + 2;
2649     ierr = PetscMalloc(i*sizeof(PetscInt),&sbuf_j);CHKERRQ(ierr);
2650     ierr = PetscMalloc((nzlocal+1)*sizeof(PetscScalar),&sbuf_a);CHKERRQ(ierr);
2651     /*
2652     ierr = PetscSynchronizedPrintf(comm,"[%d] nsends %d, nrecvs %d\n",rank,nsends,nrecvs);CHKERRQ(ierr);
2653     ierr = PetscSynchronizedFlush(comm);CHKERRQ(ierr);
2654      */
2655   } /* endof if (reuse == MAT_INITIAL_MATRIX) */
2656 
2657   /* copy mat's local entries into the buffers */
2658   if (reuse == MAT_INITIAL_MATRIX) {
2659     rownz_max = 0;
2660     rptr      = sbuf_j;
2661     cols      = sbuf_j + rend-rstart + 1;
2662     vals      = sbuf_a;
2663     rptr[0]   = 0;
2664     for (i=0; i<rend-rstart; i++) {
2665       row    = i + rstart;
2666       nzA    = a->i[i+1] - a->i[i]; nzB = b->i[i+1] - b->i[i];
2667       ncols  = nzA + nzB;
2668       cworkA = a->j + a->i[i]; cworkB = b->j + b->i[i];
2669       aworkA = a->a + a->i[i]; aworkB = b->a + b->i[i];
2670       /* load the column indices for this row into cols */
2671       lwrite = 0;
2672       for (l=0; l<nzB; l++) {
2673         if ((ctmp = bmap[cworkB[l]]) < cstart) {
2674           vals[lwrite]   = aworkB[l];
2675           cols[lwrite++] = ctmp;
2676         }
2677       }
2678       for (l=0; l<nzA; l++) {
2679         vals[lwrite]   = aworkA[l];
2680         cols[lwrite++] = cstart + cworkA[l];
2681       }
2682       for (l=0; l<nzB; l++) {
2683         if ((ctmp = bmap[cworkB[l]]) >= cend) {
2684           vals[lwrite]   = aworkB[l];
2685           cols[lwrite++] = ctmp;
2686         }
2687       }
2688       vals     += ncols;
2689       cols     += ncols;
2690       rptr[i+1] = rptr[i] + ncols;
2691       if (rownz_max < ncols) rownz_max = ncols;
2692     }
2693     if (rptr[rend-rstart] != a->nz + b->nz) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_PLIB, "rptr[%d] %d != %d + %d",rend-rstart,rptr[rend-rstart+1],a->nz,b->nz);
2694   } else { /* only copy matrix values into sbuf_a */
2695     rptr    = sbuf_j;
2696     vals    = sbuf_a;
2697     rptr[0] = 0;
2698     for (i=0; i<rend-rstart; i++) {
2699       row    = i + rstart;
2700       nzA    = a->i[i+1] - a->i[i]; nzB = b->i[i+1] - b->i[i];
2701       ncols  = nzA + nzB;
2702       cworkB = b->j + b->i[i];
2703       aworkA = a->a + a->i[i];
2704       aworkB = b->a + b->i[i];
2705       lwrite = 0;
2706       for (l=0; l<nzB; l++) {
2707         if ((ctmp = bmap[cworkB[l]]) < cstart) vals[lwrite++] = aworkB[l];
2708       }
2709       for (l=0; l<nzA; l++) vals[lwrite++] = aworkA[l];
2710       for (l=0; l<nzB; l++) {
2711         if ((ctmp = bmap[cworkB[l]]) >= cend) vals[lwrite++] = aworkB[l];
2712       }
2713       vals     += ncols;
2714       rptr[i+1] = rptr[i] + ncols;
2715     }
2716   } /* endof if (reuse == MAT_INITIAL_MATRIX) */
2717 
2718   /* send nzlocal to others, and recv other's nzlocal */
2719   /*--------------------------------------------------*/
2720   if (reuse == MAT_INITIAL_MATRIX) {
2721     ierr = PetscMalloc2(3*(nsends + nrecvs)+1,MPI_Request,&s_waits3,nsends+1,MPI_Status,&send_status);CHKERRQ(ierr);
2722 
2723     s_waits2 = s_waits3 + nsends;
2724     s_waits1 = s_waits2 + nsends;
2725     r_waits1 = s_waits1 + nsends;
2726     r_waits2 = r_waits1 + nrecvs;
2727     r_waits3 = r_waits2 + nrecvs;
2728   } else {
2729     ierr = PetscMalloc2(nsends + nrecvs +1,MPI_Request,&s_waits3,nsends+1,MPI_Status,&send_status);CHKERRQ(ierr);
2730 
2731     r_waits3 = s_waits3 + nsends;
2732   }
2733 
2734   ierr = PetscObjectGetNewTag((PetscObject)mat,&tag3);CHKERRQ(ierr);
2735   if (reuse == MAT_INITIAL_MATRIX) {
2736     /* get new tags to keep the communication clean */
2737     ierr = PetscObjectGetNewTag((PetscObject)mat,&tag1);CHKERRQ(ierr);
2738     ierr = PetscObjectGetNewTag((PetscObject)mat,&tag2);CHKERRQ(ierr);
2739     ierr = PetscMalloc4(nsends,PetscInt,&sbuf_nz,nrecvs,PetscInt,&rbuf_nz,nrecvs,PetscInt*,&rbuf_j,nrecvs,PetscScalar*,&rbuf_a);CHKERRQ(ierr);
2740 
2741     /* post receives of other's nzlocal */
2742     for (i=0; i<nrecvs; i++) {
2743       ierr = MPI_Irecv(rbuf_nz+i,1,MPIU_INT,MPI_ANY_SOURCE,tag1,comm,r_waits1+i);CHKERRQ(ierr);
2744     }
2745     /* send nzlocal to others */
2746     for (i=0; i<nsends; i++) {
2747       sbuf_nz[i] = nzlocal;
2748       ierr       = MPI_Isend(sbuf_nz+i,1,MPIU_INT,send_rank[i],tag1,comm,s_waits1+i);CHKERRQ(ierr);
2749     }
2750     /* wait on receives of nzlocal; allocate space for rbuf_j, rbuf_a */
2751     count = nrecvs;
2752     while (count) {
2753       ierr = MPI_Waitany(nrecvs,r_waits1,&imdex,&recv_status);CHKERRQ(ierr);
2754 
2755       recv_rank[imdex] = recv_status.MPI_SOURCE;
2756       /* allocate rbuf_a and rbuf_j; then post receives of rbuf_j */
2757       ierr = PetscMalloc((rbuf_nz[imdex]+1)*sizeof(PetscScalar),&rbuf_a[imdex]);CHKERRQ(ierr);
2758 
2759       i = rowrange[recv_status.MPI_SOURCE+1] - rowrange[recv_status.MPI_SOURCE]; /* number of expected mat->i */
2760 
2761       rbuf_nz[imdex] += i + 2;
2762 
2763       ierr = PetscMalloc(rbuf_nz[imdex]*sizeof(PetscInt),&rbuf_j[imdex]);CHKERRQ(ierr);
2764       ierr = MPI_Irecv(rbuf_j[imdex],rbuf_nz[imdex],MPIU_INT,recv_status.MPI_SOURCE,tag2,comm,r_waits2+imdex);CHKERRQ(ierr);
2765       count--;
2766     }
2767     /* wait on sends of nzlocal */
2768     if (nsends) {ierr = MPI_Waitall(nsends,s_waits1,send_status);CHKERRQ(ierr);}
2769     /* send mat->i,j to others, and recv from other's */
2770     /*------------------------------------------------*/
2771     for (i=0; i<nsends; i++) {
2772       j    = nzlocal + rowrange[rank+1] - rowrange[rank] + 1;
2773       ierr = MPI_Isend(sbuf_j,j,MPIU_INT,send_rank[i],tag2,comm,s_waits2+i);CHKERRQ(ierr);
2774     }
2775     /* wait on receives of mat->i,j */
2776     /*------------------------------*/
2777     count = nrecvs;
2778     while (count) {
2779       ierr = MPI_Waitany(nrecvs,r_waits2,&imdex,&recv_status);CHKERRQ(ierr);
2780       if (recv_rank[imdex] != recv_status.MPI_SOURCE) SETERRQ2(PETSC_COMM_SELF,1, "recv_rank %d != MPI_SOURCE %d",recv_rank[imdex],recv_status.MPI_SOURCE);
2781       count--;
2782     }
2783     /* wait on sends of mat->i,j */
2784     /*---------------------------*/
2785     if (nsends) {
2786       ierr = MPI_Waitall(nsends,s_waits2,send_status);CHKERRQ(ierr);
2787     }
2788   } /* endof if (reuse == MAT_INITIAL_MATRIX) */
2789 
2790   /* post receives, send and receive mat->a */
2791   /*----------------------------------------*/
2792   for (imdex=0; imdex<nrecvs; imdex++) {
2793     ierr = MPI_Irecv(rbuf_a[imdex],rbuf_nz[imdex],MPIU_SCALAR,recv_rank[imdex],tag3,comm,r_waits3+imdex);CHKERRQ(ierr);
2794   }
2795   for (i=0; i<nsends; i++) {
2796     ierr = MPI_Isend(sbuf_a,nzlocal,MPIU_SCALAR,send_rank[i],tag3,comm,s_waits3+i);CHKERRQ(ierr);
2797   }
2798   count = nrecvs;
2799   while (count) {
2800     ierr = MPI_Waitany(nrecvs,r_waits3,&imdex,&recv_status);CHKERRQ(ierr);
2801     if (recv_rank[imdex] != recv_status.MPI_SOURCE) SETERRQ2(PETSC_COMM_SELF,1, "recv_rank %d != MPI_SOURCE %d",recv_rank[imdex],recv_status.MPI_SOURCE);
2802     count--;
2803   }
2804   if (nsends) {
2805     ierr = MPI_Waitall(nsends,s_waits3,send_status);CHKERRQ(ierr);
2806   }
2807 
2808   ierr = PetscFree2(s_waits3,send_status);CHKERRQ(ierr);
2809 
2810   /* create redundant matrix */
2811   /*-------------------------*/
2812   if (reuse == MAT_INITIAL_MATRIX) {
2813     const PetscInt *range;
2814     PetscInt       rstart_sub,rend_sub,mloc_sub;
2815 
2816     /* compute rownz_max for preallocation */
2817     for (imdex=0; imdex<nrecvs; imdex++) {
2818       j    = rowrange[recv_rank[imdex]+1] - rowrange[recv_rank[imdex]];
2819       rptr = rbuf_j[imdex];
2820       for (i=0; i<j; i++) {
2821         ncols = rptr[i+1] - rptr[i];
2822         if (rownz_max < ncols) rownz_max = ncols;
2823       }
2824     }
2825 
2826     ierr = MatCreate(subcomm,&C);CHKERRQ(ierr);
2827 
2828     /* get local size of redundant matrix
2829        - mloc_sub is chosen for PETSC_SUBCOMM_INTERLACED, works for other types, but may not efficient! */
2830     ierr = MatGetOwnershipRanges(mat,&range);CHKERRQ(ierr);
2831     rstart_sub = range[nsubcomm*subrank];
2832     if (subrank+1 < subsize) { /* not the last proc in subcomm */
2833       rend_sub = range[nsubcomm*(subrank+1)];
2834     } else {
2835       rend_sub = mat->rmap->N;
2836     }
2837     mloc_sub = rend_sub - rstart_sub;
2838 
2839     if (M == N) {
2840       ierr = MatSetSizes(C,mloc_sub,mloc_sub,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
2841     } else { /* non-square matrix */
2842       ierr = MatSetSizes(C,mloc_sub,PETSC_DECIDE,PETSC_DECIDE,mat->cmap->N);CHKERRQ(ierr);
2843     }
2844     ierr = MatSetBlockSizes(C,mat->rmap->bs,mat->cmap->bs);CHKERRQ(ierr);
2845     ierr = MatSetFromOptions(C);CHKERRQ(ierr);
2846     ierr = MatSeqAIJSetPreallocation(C,rownz_max,NULL);CHKERRQ(ierr);
2847     ierr = MatMPIAIJSetPreallocation(C,rownz_max,NULL,rownz_max,NULL);CHKERRQ(ierr);
2848   } else {
2849     C = *matredundant;
2850   }
2851 
2852   /* insert local matrix entries */
2853   rptr = sbuf_j;
2854   cols = sbuf_j + rend-rstart + 1;
2855   vals = sbuf_a;
2856   for (i=0; i<rend-rstart; i++) {
2857     row   = i + rstart;
2858     ncols = rptr[i+1] - rptr[i];
2859     ierr  = MatSetValues(C,1,&row,ncols,cols,vals,INSERT_VALUES);CHKERRQ(ierr);
2860     vals += ncols;
2861     cols += ncols;
2862   }
2863   /* insert received matrix entries */
2864   for (imdex=0; imdex<nrecvs; imdex++) {
2865     rstart = rowrange[recv_rank[imdex]];
2866     rend   = rowrange[recv_rank[imdex]+1];
2867     /* printf("[%d] insert rows %d - %d\n",rank,rstart,rend-1); */
2868     rptr   = rbuf_j[imdex];
2869     cols   = rbuf_j[imdex] + rend-rstart + 1;
2870     vals   = rbuf_a[imdex];
2871     for (i=0; i<rend-rstart; i++) {
2872       row   = i + rstart;
2873       ncols = rptr[i+1] - rptr[i];
2874       ierr  = MatSetValues(C,1,&row,ncols,cols,vals,INSERT_VALUES);CHKERRQ(ierr);
2875       vals += ncols;
2876       cols += ncols;
2877     }
2878   }
2879   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2880   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2881 
2882   if (reuse == MAT_INITIAL_MATRIX) {
2883     *matredundant = C;
2884 
2885     /* create a supporting struct and attach it to C for reuse */
2886     ierr = PetscNewLog(C,Mat_Redundant,&redund);CHKERRQ(ierr);
2887     if (subsize == 1) {
2888       Mat_SeqAIJ *c = (Mat_SeqAIJ*)C->data;
2889       c->redundant = redund;
2890     } else {
2891       Mat_MPIAIJ *c = (Mat_MPIAIJ*)C->data;
2892       c->redundant = redund;
2893     }
2894 
2895     redund->nzlocal   = nzlocal;
2896     redund->nsends    = nsends;
2897     redund->nrecvs    = nrecvs;
2898     redund->send_rank = send_rank;
2899     redund->recv_rank = recv_rank;
2900     redund->sbuf_nz   = sbuf_nz;
2901     redund->rbuf_nz   = rbuf_nz;
2902     redund->sbuf_j    = sbuf_j;
2903     redund->sbuf_a    = sbuf_a;
2904     redund->rbuf_j    = rbuf_j;
2905     redund->rbuf_a    = rbuf_a;
2906     redund->psubcomm  = NULL;
2907 
2908     redund->Destroy = C->ops->destroy;
2909     C->ops->destroy = MatDestroy_MatRedundant;
2910   }
2911   PetscFunctionReturn(0);
2912 }
2913 
2914 #undef __FUNCT__
2915 #define __FUNCT__ "MatGetRedundantMatrix_MPIAIJ"
2916 PetscErrorCode MatGetRedundantMatrix_MPIAIJ(Mat mat,PetscInt nsubcomm,MPI_Comm subcomm,MatReuse reuse,Mat *matredundant)
2917 {
2918   PetscErrorCode ierr;
2919   MPI_Comm       comm;
2920   PetscMPIInt    size,subsize;
2921   PetscInt       mloc_sub,rstart,rend,M=mat->rmap->N,N=mat->cmap->N;
2922   Mat_Redundant  *redund=NULL;
2923   PetscSubcomm   psubcomm=NULL,psubcomm_in=NULL;
2924   MPI_Comm       subcomm_in=subcomm;
2925 
2926   PetscFunctionBegin;
2927   if (subcomm_in == MPI_COMM_NULL) { /* get subcomm=psubcomm->comm */
2928     if (reuse ==  MAT_INITIAL_MATRIX) {
2929       if (psubcomm_in == NULL) { /* user does not provide psubcomm, create it here */
2930         ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
2931         ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2932         if (nsubcomm < 1 || nsubcomm > size) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"nsubcomm must between 1 and %D",size);
2933 
2934         ierr = PetscSubcommCreate(comm,&psubcomm);CHKERRQ(ierr);
2935         ierr = PetscSubcommSetNumber(psubcomm,nsubcomm);CHKERRQ(ierr);
2936         ierr = PetscSubcommSetType(psubcomm,PETSC_SUBCOMM_CONTIGUOUS);CHKERRQ(ierr);
2937         ierr = PetscSubcommSetFromOptions(psubcomm);CHKERRQ(ierr);
2938       }
2939       subcomm = psubcomm->comm;
2940     } else { /* retrieve psubcomm and subcomm */
2941       ierr = PetscObjectGetComm((PetscObject)(*matredundant),&subcomm);CHKERRQ(ierr);
2942       ierr = MPI_Comm_size(subcomm,&subsize);CHKERRQ(ierr);
2943       if (subsize == 1) {
2944         Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*matredundant)->data;
2945         redund = c->redundant;
2946       } else {
2947         Mat_MPIAIJ *c = (Mat_MPIAIJ*)(*matredundant)->data;
2948         redund = c->redundant;
2949       }
2950       psubcomm = redund->psubcomm;
2951     }
2952     if (subcomm_in == MPI_COMM_NULL && psubcomm->type == PETSC_SUBCOMM_INTERLACED) {
2953       ierr = MatGetRedundantMatrix_MPIAIJ_interlaced(mat,nsubcomm,subcomm,reuse,matredundant);CHKERRQ(ierr);
2954     }
2955   }
2956 
2957   if (subcomm_in != MPI_COMM_NULL) {
2958     /* use MPI subcomm_in via MatGetSubMatrices() */
2959     Mat  *matseq;
2960     IS   isrow,iscol;
2961 
2962     ierr = MPI_Comm_size(subcomm,&subsize);CHKERRQ(ierr);
2963     if (reuse == MAT_INITIAL_MATRIX) {
2964       /* create a local sequential matrix matseq[0] */
2965       mloc_sub = PETSC_DECIDE;
2966       ierr = PetscSplitOwnership(subcomm,&mloc_sub,&M);CHKERRQ(ierr);
2967       ierr = MPI_Scan(&mloc_sub,&rend,1,MPIU_INT,MPI_SUM,subcomm);CHKERRQ(ierr);
2968       rstart = rend - mloc_sub;
2969       ierr = ISCreateStride(PETSC_COMM_SELF,mloc_sub,rstart,1,&isrow);CHKERRQ(ierr);
2970       ierr = ISCreateStride(PETSC_COMM_SELF,N,0,1,&iscol);CHKERRQ(ierr);
2971     } else { /* reuse == MAT_REUSE_MATRIX */
2972       if (subsize == 1) {
2973         Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*matredundant)->data;
2974         redund = c->redundant;
2975       } else {
2976         Mat_MPIAIJ *c = (Mat_MPIAIJ*)(*matredundant)->data;
2977         redund = c->redundant;
2978       }
2979 
2980       isrow  = redund->isrow;
2981       iscol  = redund->iscol;
2982       matseq = redund->matseq;
2983     }
2984     ierr = MatGetSubMatrices(mat,1,&isrow,&iscol,reuse,&matseq);CHKERRQ(ierr);
2985     ierr = MatCreateMPIAIJConcatenateSeqAIJ(subcomm,matseq[0],PETSC_DECIDE,reuse,matredundant);CHKERRQ(ierr);
2986 
2987     if (reuse == MAT_INITIAL_MATRIX) {
2988       /* create a supporting struct and attach it to C for reuse */
2989       ierr = PetscNewLog(*matredundant,Mat_Redundant,&redund);CHKERRQ(ierr);
2990       if (subsize == 1) {
2991         Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*matredundant)->data;
2992         c->redundant = redund;
2993       } else {
2994         Mat_MPIAIJ *c = (Mat_MPIAIJ*)(*matredundant)->data;
2995         c->redundant = redund;
2996       }
2997       redund->isrow    = isrow;
2998       redund->iscol    = iscol;
2999       redund->matseq   = matseq;
3000       redund->psubcomm = NULL;
3001       redund->Destroy               = (*matredundant)->ops->destroy;
3002       (*matredundant)->ops->destroy = MatDestroy_MatRedundant;
3003     }
3004   }
3005 
3006   if (psubcomm && reuse ==  MAT_INITIAL_MATRIX) {
3007     /* if psubcomm is created in this routine, free it in MatDestroy_MatRedundant() */
3008     ierr = MPI_Comm_size(psubcomm->comm,&subsize);CHKERRQ(ierr);
3009     if (subsize == 1) {
3010       Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*matredundant)->data;
3011       c->redundant->psubcomm = psubcomm;
3012     } else {
3013       Mat_MPIAIJ *c = (Mat_MPIAIJ*)(*matredundant)->data;
3014       c->redundant->psubcomm = psubcomm ;
3015     }
3016   }
3017   PetscFunctionReturn(0);
3018 }
3019 
3020 #undef __FUNCT__
3021 #define __FUNCT__ "MatGetRowMaxAbs_MPIAIJ"
3022 PetscErrorCode MatGetRowMaxAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
3023 {
3024   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3025   PetscErrorCode ierr;
3026   PetscInt       i,*idxb = 0;
3027   PetscScalar    *va,*vb;
3028   Vec            vtmp;
3029 
3030   PetscFunctionBegin;
3031   ierr = MatGetRowMaxAbs(a->A,v,idx);CHKERRQ(ierr);
3032   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
3033   if (idx) {
3034     for (i=0; i<A->rmap->n; i++) {
3035       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
3036     }
3037   }
3038 
3039   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
3040   if (idx) {
3041     ierr = PetscMalloc(A->rmap->n*sizeof(PetscInt),&idxb);CHKERRQ(ierr);
3042   }
3043   ierr = MatGetRowMaxAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
3044   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
3045 
3046   for (i=0; i<A->rmap->n; i++) {
3047     if (PetscAbsScalar(va[i]) < PetscAbsScalar(vb[i])) {
3048       va[i] = vb[i];
3049       if (idx) idx[i] = a->garray[idxb[i]];
3050     }
3051   }
3052 
3053   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
3054   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
3055   ierr = PetscFree(idxb);CHKERRQ(ierr);
3056   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
3057   PetscFunctionReturn(0);
3058 }
3059 
3060 #undef __FUNCT__
3061 #define __FUNCT__ "MatGetRowMinAbs_MPIAIJ"
3062 PetscErrorCode MatGetRowMinAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
3063 {
3064   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3065   PetscErrorCode ierr;
3066   PetscInt       i,*idxb = 0;
3067   PetscScalar    *va,*vb;
3068   Vec            vtmp;
3069 
3070   PetscFunctionBegin;
3071   ierr = MatGetRowMinAbs(a->A,v,idx);CHKERRQ(ierr);
3072   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
3073   if (idx) {
3074     for (i=0; i<A->cmap->n; i++) {
3075       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
3076     }
3077   }
3078 
3079   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
3080   if (idx) {
3081     ierr = PetscMalloc(A->rmap->n*sizeof(PetscInt),&idxb);CHKERRQ(ierr);
3082   }
3083   ierr = MatGetRowMinAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
3084   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
3085 
3086   for (i=0; i<A->rmap->n; i++) {
3087     if (PetscAbsScalar(va[i]) > PetscAbsScalar(vb[i])) {
3088       va[i] = vb[i];
3089       if (idx) idx[i] = a->garray[idxb[i]];
3090     }
3091   }
3092 
3093   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
3094   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
3095   ierr = PetscFree(idxb);CHKERRQ(ierr);
3096   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
3097   PetscFunctionReturn(0);
3098 }
3099 
3100 #undef __FUNCT__
3101 #define __FUNCT__ "MatGetRowMin_MPIAIJ"
3102 PetscErrorCode MatGetRowMin_MPIAIJ(Mat A, Vec v, PetscInt idx[])
3103 {
3104   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
3105   PetscInt       n      = A->rmap->n;
3106   PetscInt       cstart = A->cmap->rstart;
3107   PetscInt       *cmap  = mat->garray;
3108   PetscInt       *diagIdx, *offdiagIdx;
3109   Vec            diagV, offdiagV;
3110   PetscScalar    *a, *diagA, *offdiagA;
3111   PetscInt       r;
3112   PetscErrorCode ierr;
3113 
3114   PetscFunctionBegin;
3115   ierr = PetscMalloc2(n,PetscInt,&diagIdx,n,PetscInt,&offdiagIdx);CHKERRQ(ierr);
3116   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &diagV);CHKERRQ(ierr);
3117   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &offdiagV);CHKERRQ(ierr);
3118   ierr = MatGetRowMin(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
3119   ierr = MatGetRowMin(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
3120   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
3121   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
3122   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
3123   for (r = 0; r < n; ++r) {
3124     if (PetscAbsScalar(diagA[r]) <= PetscAbsScalar(offdiagA[r])) {
3125       a[r]   = diagA[r];
3126       idx[r] = cstart + diagIdx[r];
3127     } else {
3128       a[r]   = offdiagA[r];
3129       idx[r] = cmap[offdiagIdx[r]];
3130     }
3131   }
3132   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
3133   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
3134   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
3135   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
3136   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
3137   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
3138   PetscFunctionReturn(0);
3139 }
3140 
3141 #undef __FUNCT__
3142 #define __FUNCT__ "MatGetRowMax_MPIAIJ"
3143 PetscErrorCode MatGetRowMax_MPIAIJ(Mat A, Vec v, PetscInt idx[])
3144 {
3145   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
3146   PetscInt       n      = A->rmap->n;
3147   PetscInt       cstart = A->cmap->rstart;
3148   PetscInt       *cmap  = mat->garray;
3149   PetscInt       *diagIdx, *offdiagIdx;
3150   Vec            diagV, offdiagV;
3151   PetscScalar    *a, *diagA, *offdiagA;
3152   PetscInt       r;
3153   PetscErrorCode ierr;
3154 
3155   PetscFunctionBegin;
3156   ierr = PetscMalloc2(n,PetscInt,&diagIdx,n,PetscInt,&offdiagIdx);CHKERRQ(ierr);
3157   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &diagV);CHKERRQ(ierr);
3158   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &offdiagV);CHKERRQ(ierr);
3159   ierr = MatGetRowMax(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
3160   ierr = MatGetRowMax(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
3161   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
3162   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
3163   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
3164   for (r = 0; r < n; ++r) {
3165     if (PetscAbsScalar(diagA[r]) >= PetscAbsScalar(offdiagA[r])) {
3166       a[r]   = diagA[r];
3167       idx[r] = cstart + diagIdx[r];
3168     } else {
3169       a[r]   = offdiagA[r];
3170       idx[r] = cmap[offdiagIdx[r]];
3171     }
3172   }
3173   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
3174   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
3175   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
3176   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
3177   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
3178   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
3179   PetscFunctionReturn(0);
3180 }
3181 
3182 #undef __FUNCT__
3183 #define __FUNCT__ "MatGetSeqNonzeroStructure_MPIAIJ"
3184 PetscErrorCode MatGetSeqNonzeroStructure_MPIAIJ(Mat mat,Mat *newmat)
3185 {
3186   PetscErrorCode ierr;
3187   Mat            *dummy;
3188 
3189   PetscFunctionBegin;
3190   ierr    = MatGetSubMatrix_MPIAIJ_All(mat,MAT_DO_NOT_GET_VALUES,MAT_INITIAL_MATRIX,&dummy);CHKERRQ(ierr);
3191   *newmat = *dummy;
3192   ierr    = PetscFree(dummy);CHKERRQ(ierr);
3193   PetscFunctionReturn(0);
3194 }
3195 
3196 extern PetscErrorCode  MatFDColoringApply_AIJ(Mat,MatFDColoring,Vec,MatStructure*,void*);
3197 
3198 #undef __FUNCT__
3199 #define __FUNCT__ "MatInvertBlockDiagonal_MPIAIJ"
3200 PetscErrorCode  MatInvertBlockDiagonal_MPIAIJ(Mat A,const PetscScalar **values)
3201 {
3202   Mat_MPIAIJ     *a = (Mat_MPIAIJ*) A->data;
3203   PetscErrorCode ierr;
3204 
3205   PetscFunctionBegin;
3206   ierr = MatInvertBlockDiagonal(a->A,values);CHKERRQ(ierr);
3207   PetscFunctionReturn(0);
3208 }
3209 
3210 #undef __FUNCT__
3211 #define __FUNCT__ "MatSetRandom_MPIAIJ"
3212 static PetscErrorCode  MatSetRandom_MPIAIJ(Mat x,PetscRandom rctx)
3213 {
3214   PetscErrorCode ierr;
3215   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)x->data;
3216 
3217   PetscFunctionBegin;
3218   ierr = MatSetRandom(aij->A,rctx);CHKERRQ(ierr);
3219   ierr = MatSetRandom(aij->B,rctx);CHKERRQ(ierr);
3220   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3221   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3222   PetscFunctionReturn(0);
3223 }
3224 
3225 /* -------------------------------------------------------------------*/
3226 static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
3227                                        MatGetRow_MPIAIJ,
3228                                        MatRestoreRow_MPIAIJ,
3229                                        MatMult_MPIAIJ,
3230                                 /* 4*/ MatMultAdd_MPIAIJ,
3231                                        MatMultTranspose_MPIAIJ,
3232                                        MatMultTransposeAdd_MPIAIJ,
3233 #if defined(PETSC_HAVE_PBGL)
3234                                        MatSolve_MPIAIJ,
3235 #else
3236                                        0,
3237 #endif
3238                                        0,
3239                                        0,
3240                                 /*10*/ 0,
3241                                        0,
3242                                        0,
3243                                        MatSOR_MPIAIJ,
3244                                        MatTranspose_MPIAIJ,
3245                                 /*15*/ MatGetInfo_MPIAIJ,
3246                                        MatEqual_MPIAIJ,
3247                                        MatGetDiagonal_MPIAIJ,
3248                                        MatDiagonalScale_MPIAIJ,
3249                                        MatNorm_MPIAIJ,
3250                                 /*20*/ MatAssemblyBegin_MPIAIJ,
3251                                        MatAssemblyEnd_MPIAIJ,
3252                                        MatSetOption_MPIAIJ,
3253                                        MatZeroEntries_MPIAIJ,
3254                                 /*24*/ MatZeroRows_MPIAIJ,
3255                                        0,
3256 #if defined(PETSC_HAVE_PBGL)
3257                                        0,
3258 #else
3259                                        0,
3260 #endif
3261                                        0,
3262                                        0,
3263                                 /*29*/ MatSetUp_MPIAIJ,
3264 #if defined(PETSC_HAVE_PBGL)
3265                                        0,
3266 #else
3267                                        0,
3268 #endif
3269                                        0,
3270                                        0,
3271                                        0,
3272                                 /*34*/ MatDuplicate_MPIAIJ,
3273                                        0,
3274                                        0,
3275                                        0,
3276                                        0,
3277                                 /*39*/ MatAXPY_MPIAIJ,
3278                                        MatGetSubMatrices_MPIAIJ,
3279                                        MatIncreaseOverlap_MPIAIJ,
3280                                        MatGetValues_MPIAIJ,
3281                                        MatCopy_MPIAIJ,
3282                                 /*44*/ MatGetRowMax_MPIAIJ,
3283                                        MatScale_MPIAIJ,
3284                                        0,
3285                                        0,
3286                                        MatZeroRowsColumns_MPIAIJ,
3287                                 /*49*/ MatSetRandom_MPIAIJ,
3288                                        0,
3289                                        0,
3290                                        0,
3291                                        0,
3292                                 /*54*/ MatFDColoringCreate_MPIAIJ,
3293                                        0,
3294                                        MatSetUnfactored_MPIAIJ,
3295                                        MatPermute_MPIAIJ,
3296                                        0,
3297                                 /*59*/ MatGetSubMatrix_MPIAIJ,
3298                                        MatDestroy_MPIAIJ,
3299                                        MatView_MPIAIJ,
3300                                        0,
3301                                        MatMatMatMult_MPIAIJ_MPIAIJ_MPIAIJ,
3302                                 /*64*/ MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ,
3303                                        MatMatMatMultNumeric_MPIAIJ_MPIAIJ_MPIAIJ,
3304                                        0,
3305                                        0,
3306                                        0,
3307                                 /*69*/ MatGetRowMaxAbs_MPIAIJ,
3308                                        MatGetRowMinAbs_MPIAIJ,
3309                                        0,
3310                                        MatSetColoring_MPIAIJ,
3311                                        0,
3312                                        MatSetValuesAdifor_MPIAIJ,
3313                                 /*75*/ MatFDColoringApply_AIJ,
3314                                        0,
3315                                        0,
3316                                        0,
3317                                        MatFindZeroDiagonals_MPIAIJ,
3318                                 /*80*/ 0,
3319                                        0,
3320                                        0,
3321                                 /*83*/ MatLoad_MPIAIJ,
3322                                        0,
3323                                        0,
3324                                        0,
3325                                        0,
3326                                        0,
3327                                 /*89*/ MatMatMult_MPIAIJ_MPIAIJ,
3328                                        MatMatMultSymbolic_MPIAIJ_MPIAIJ,
3329                                        MatMatMultNumeric_MPIAIJ_MPIAIJ,
3330                                        MatPtAP_MPIAIJ_MPIAIJ,
3331                                        MatPtAPSymbolic_MPIAIJ_MPIAIJ,
3332                                 /*94*/ MatPtAPNumeric_MPIAIJ_MPIAIJ,
3333                                        0,
3334                                        0,
3335                                        0,
3336                                        0,
3337                                 /*99*/ 0,
3338                                        0,
3339                                        0,
3340                                        MatConjugate_MPIAIJ,
3341                                        0,
3342                                 /*104*/MatSetValuesRow_MPIAIJ,
3343                                        MatRealPart_MPIAIJ,
3344                                        MatImaginaryPart_MPIAIJ,
3345                                        0,
3346                                        0,
3347                                 /*109*/0,
3348                                        MatGetRedundantMatrix_MPIAIJ,
3349                                        MatGetRowMin_MPIAIJ,
3350                                        0,
3351                                        0,
3352                                 /*114*/MatGetSeqNonzeroStructure_MPIAIJ,
3353                                        0,
3354                                        0,
3355                                        0,
3356                                        0,
3357                                 /*119*/0,
3358                                        0,
3359                                        0,
3360                                        0,
3361                                        MatGetMultiProcBlock_MPIAIJ,
3362                                 /*124*/MatFindNonzeroRows_MPIAIJ,
3363                                        MatGetColumnNorms_MPIAIJ,
3364                                        MatInvertBlockDiagonal_MPIAIJ,
3365                                        0,
3366                                        MatGetSubMatricesParallel_MPIAIJ,
3367                                 /*129*/0,
3368                                        MatTransposeMatMult_MPIAIJ_MPIAIJ,
3369                                        MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ,
3370                                        MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ,
3371                                        0,
3372                                 /*134*/0,
3373                                        0,
3374                                        0,
3375                                        0,
3376                                        0,
3377                                 /*139*/0,
3378                                        0
3379 };
3380 
3381 /* ----------------------------------------------------------------------------------------*/
3382 
3383 #undef __FUNCT__
3384 #define __FUNCT__ "MatStoreValues_MPIAIJ"
3385 PetscErrorCode  MatStoreValues_MPIAIJ(Mat mat)
3386 {
3387   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
3388   PetscErrorCode ierr;
3389 
3390   PetscFunctionBegin;
3391   ierr = MatStoreValues(aij->A);CHKERRQ(ierr);
3392   ierr = MatStoreValues(aij->B);CHKERRQ(ierr);
3393   PetscFunctionReturn(0);
3394 }
3395 
3396 #undef __FUNCT__
3397 #define __FUNCT__ "MatRetrieveValues_MPIAIJ"
3398 PetscErrorCode  MatRetrieveValues_MPIAIJ(Mat mat)
3399 {
3400   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
3401   PetscErrorCode ierr;
3402 
3403   PetscFunctionBegin;
3404   ierr = MatRetrieveValues(aij->A);CHKERRQ(ierr);
3405   ierr = MatRetrieveValues(aij->B);CHKERRQ(ierr);
3406   PetscFunctionReturn(0);
3407 }
3408 
3409 #undef __FUNCT__
3410 #define __FUNCT__ "MatMPIAIJSetPreallocation_MPIAIJ"
3411 PetscErrorCode  MatMPIAIJSetPreallocation_MPIAIJ(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3412 {
3413   Mat_MPIAIJ     *b;
3414   PetscErrorCode ierr;
3415 
3416   PetscFunctionBegin;
3417   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3418   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3419   b = (Mat_MPIAIJ*)B->data;
3420 
3421   if (!B->preallocated) {
3422     /* Explicitly create 2 MATSEQAIJ matrices. */
3423     ierr = MatCreate(PETSC_COMM_SELF,&b->A);CHKERRQ(ierr);
3424     ierr = MatSetSizes(b->A,B->rmap->n,B->cmap->n,B->rmap->n,B->cmap->n);CHKERRQ(ierr);
3425     ierr = MatSetBlockSizes(b->A,B->rmap->bs,B->cmap->bs);CHKERRQ(ierr);
3426     ierr = MatSetType(b->A,MATSEQAIJ);CHKERRQ(ierr);
3427     ierr = PetscLogObjectParent(B,b->A);CHKERRQ(ierr);
3428     ierr = MatCreate(PETSC_COMM_SELF,&b->B);CHKERRQ(ierr);
3429     ierr = MatSetSizes(b->B,B->rmap->n,B->cmap->N,B->rmap->n,B->cmap->N);CHKERRQ(ierr);
3430     ierr = MatSetBlockSizes(b->B,B->rmap->bs,B->cmap->bs);CHKERRQ(ierr);
3431     ierr = MatSetType(b->B,MATSEQAIJ);CHKERRQ(ierr);
3432     ierr = PetscLogObjectParent(B,b->B);CHKERRQ(ierr);
3433   }
3434 
3435   ierr = MatSeqAIJSetPreallocation(b->A,d_nz,d_nnz);CHKERRQ(ierr);
3436   ierr = MatSeqAIJSetPreallocation(b->B,o_nz,o_nnz);CHKERRQ(ierr);
3437   B->preallocated = PETSC_TRUE;
3438   PetscFunctionReturn(0);
3439 }
3440 
3441 #undef __FUNCT__
3442 #define __FUNCT__ "MatDuplicate_MPIAIJ"
3443 PetscErrorCode MatDuplicate_MPIAIJ(Mat matin,MatDuplicateOption cpvalues,Mat *newmat)
3444 {
3445   Mat            mat;
3446   Mat_MPIAIJ     *a,*oldmat = (Mat_MPIAIJ*)matin->data;
3447   PetscErrorCode ierr;
3448 
3449   PetscFunctionBegin;
3450   *newmat = 0;
3451   ierr    = MatCreate(PetscObjectComm((PetscObject)matin),&mat);CHKERRQ(ierr);
3452   ierr    = MatSetSizes(mat,matin->rmap->n,matin->cmap->n,matin->rmap->N,matin->cmap->N);CHKERRQ(ierr);
3453   ierr    = MatSetBlockSizes(mat,matin->rmap->bs,matin->cmap->bs);CHKERRQ(ierr);
3454   ierr    = MatSetType(mat,((PetscObject)matin)->type_name);CHKERRQ(ierr);
3455   ierr    = PetscMemcpy(mat->ops,matin->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
3456   a       = (Mat_MPIAIJ*)mat->data;
3457 
3458   mat->factortype   = matin->factortype;
3459   mat->rmap->bs     = matin->rmap->bs;
3460   mat->cmap->bs     = matin->cmap->bs;
3461   mat->assembled    = PETSC_TRUE;
3462   mat->insertmode   = NOT_SET_VALUES;
3463   mat->preallocated = PETSC_TRUE;
3464 
3465   a->size         = oldmat->size;
3466   a->rank         = oldmat->rank;
3467   a->donotstash   = oldmat->donotstash;
3468   a->roworiented  = oldmat->roworiented;
3469   a->rowindices   = 0;
3470   a->rowvalues    = 0;
3471   a->getrowactive = PETSC_FALSE;
3472 
3473   ierr = PetscLayoutReference(matin->rmap,&mat->rmap);CHKERRQ(ierr);
3474   ierr = PetscLayoutReference(matin->cmap,&mat->cmap);CHKERRQ(ierr);
3475 
3476   if (oldmat->colmap) {
3477 #if defined(PETSC_USE_CTABLE)
3478     ierr = PetscTableCreateCopy(oldmat->colmap,&a->colmap);CHKERRQ(ierr);
3479 #else
3480     ierr = PetscMalloc((mat->cmap->N)*sizeof(PetscInt),&a->colmap);CHKERRQ(ierr);
3481     ierr = PetscLogObjectMemory(mat,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
3482     ierr = PetscMemcpy(a->colmap,oldmat->colmap,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
3483 #endif
3484   } else a->colmap = 0;
3485   if (oldmat->garray) {
3486     PetscInt len;
3487     len  = oldmat->B->cmap->n;
3488     ierr = PetscMalloc((len+1)*sizeof(PetscInt),&a->garray);CHKERRQ(ierr);
3489     ierr = PetscLogObjectMemory(mat,len*sizeof(PetscInt));CHKERRQ(ierr);
3490     if (len) { ierr = PetscMemcpy(a->garray,oldmat->garray,len*sizeof(PetscInt));CHKERRQ(ierr); }
3491   } else a->garray = 0;
3492 
3493   ierr    = VecDuplicate(oldmat->lvec,&a->lvec);CHKERRQ(ierr);
3494   ierr    = PetscLogObjectParent(mat,a->lvec);CHKERRQ(ierr);
3495   ierr    = VecScatterCopy(oldmat->Mvctx,&a->Mvctx);CHKERRQ(ierr);
3496   ierr    = PetscLogObjectParent(mat,a->Mvctx);CHKERRQ(ierr);
3497   ierr    = MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
3498   ierr    = PetscLogObjectParent(mat,a->A);CHKERRQ(ierr);
3499   ierr    = MatDuplicate(oldmat->B,cpvalues,&a->B);CHKERRQ(ierr);
3500   ierr    = PetscLogObjectParent(mat,a->B);CHKERRQ(ierr);
3501   ierr    = PetscFunctionListDuplicate(((PetscObject)matin)->qlist,&((PetscObject)mat)->qlist);CHKERRQ(ierr);
3502   *newmat = mat;
3503   PetscFunctionReturn(0);
3504 }
3505 
3506 
3507 
3508 #undef __FUNCT__
3509 #define __FUNCT__ "MatLoad_MPIAIJ"
3510 PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
3511 {
3512   PetscScalar    *vals,*svals;
3513   MPI_Comm       comm;
3514   PetscErrorCode ierr;
3515   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
3516   PetscInt       i,nz,j,rstart,rend,mmax,maxnz = 0,grows,gcols;
3517   PetscInt       header[4],*rowlengths = 0,M,N,m,*cols;
3518   PetscInt       *ourlens = NULL,*procsnz = NULL,*offlens = NULL,jj,*mycols,*smycols;
3519   PetscInt       cend,cstart,n,*rowners,sizesset=1;
3520   int            fd;
3521   PetscInt       bs = 1;
3522 
3523   PetscFunctionBegin;
3524   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
3525   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3526   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3527   if (!rank) {
3528     ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
3529     ierr = PetscBinaryRead(fd,(char*)header,4,PETSC_INT);CHKERRQ(ierr);
3530     if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
3531   }
3532 
3533   ierr = PetscOptionsBegin(comm,NULL,"Options for loading SEQAIJ matrix","Mat");CHKERRQ(ierr);
3534   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
3535   ierr = PetscOptionsEnd();CHKERRQ(ierr);
3536 
3537   if (newMat->rmap->n < 0 && newMat->rmap->N < 0 && newMat->cmap->n < 0 && newMat->cmap->N < 0) sizesset = 0;
3538 
3539   ierr = MPI_Bcast(header+1,3,MPIU_INT,0,comm);CHKERRQ(ierr);
3540   M    = header[1]; N = header[2];
3541   /* If global rows/cols are set to PETSC_DECIDE, set it to the sizes given in the file */
3542   if (sizesset && newMat->rmap->N < 0) newMat->rmap->N = M;
3543   if (sizesset && newMat->cmap->N < 0) newMat->cmap->N = N;
3544 
3545   /* If global sizes are set, check if they are consistent with that given in the file */
3546   if (sizesset) {
3547     ierr = MatGetSize(newMat,&grows,&gcols);CHKERRQ(ierr);
3548   }
3549   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);
3550   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);
3551 
3552   /* determine ownership of all (block) rows */
3553   if (M%bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Inconsistent # of rows (%d) and block size (%d)",M,bs);
3554   if (newMat->rmap->n < 0) m = bs*((M/bs)/size + (((M/bs) % size) > rank));    /* PETSC_DECIDE */
3555   else m = newMat->rmap->n; /* Set by user */
3556 
3557   ierr = PetscMalloc((size+1)*sizeof(PetscInt),&rowners);CHKERRQ(ierr);
3558   ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
3559 
3560   /* First process needs enough room for process with most rows */
3561   if (!rank) {
3562     mmax = rowners[1];
3563     for (i=2; i<=size; i++) {
3564       mmax = PetscMax(mmax, rowners[i]);
3565     }
3566   } else mmax = -1;             /* unused, but compilers complain */
3567 
3568   rowners[0] = 0;
3569   for (i=2; i<=size; i++) {
3570     rowners[i] += rowners[i-1];
3571   }
3572   rstart = rowners[rank];
3573   rend   = rowners[rank+1];
3574 
3575   /* distribute row lengths to all processors */
3576   ierr = PetscMalloc2(m,PetscInt,&ourlens,m,PetscInt,&offlens);CHKERRQ(ierr);
3577   if (!rank) {
3578     ierr = PetscBinaryRead(fd,ourlens,m,PETSC_INT);CHKERRQ(ierr);
3579     ierr = PetscMalloc(mmax*sizeof(PetscInt),&rowlengths);CHKERRQ(ierr);
3580     ierr = PetscMalloc(size*sizeof(PetscInt),&procsnz);CHKERRQ(ierr);
3581     ierr = PetscMemzero(procsnz,size*sizeof(PetscInt));CHKERRQ(ierr);
3582     for (j=0; j<m; j++) {
3583       procsnz[0] += ourlens[j];
3584     }
3585     for (i=1; i<size; i++) {
3586       ierr = PetscBinaryRead(fd,rowlengths,rowners[i+1]-rowners[i],PETSC_INT);CHKERRQ(ierr);
3587       /* calculate the number of nonzeros on each processor */
3588       for (j=0; j<rowners[i+1]-rowners[i]; j++) {
3589         procsnz[i] += rowlengths[j];
3590       }
3591       ierr = MPIULong_Send(rowlengths,rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
3592     }
3593     ierr = PetscFree(rowlengths);CHKERRQ(ierr);
3594   } else {
3595     ierr = MPIULong_Recv(ourlens,m,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
3596   }
3597 
3598   if (!rank) {
3599     /* determine max buffer needed and allocate it */
3600     maxnz = 0;
3601     for (i=0; i<size; i++) {
3602       maxnz = PetscMax(maxnz,procsnz[i]);
3603     }
3604     ierr = PetscMalloc(maxnz*sizeof(PetscInt),&cols);CHKERRQ(ierr);
3605 
3606     /* read in my part of the matrix column indices  */
3607     nz   = procsnz[0];
3608     ierr = PetscMalloc(nz*sizeof(PetscInt),&mycols);CHKERRQ(ierr);
3609     ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);
3610 
3611     /* read in every one elses and ship off */
3612     for (i=1; i<size; i++) {
3613       nz   = procsnz[i];
3614       ierr = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
3615       ierr = MPIULong_Send(cols,nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
3616     }
3617     ierr = PetscFree(cols);CHKERRQ(ierr);
3618   } else {
3619     /* determine buffer space needed for message */
3620     nz = 0;
3621     for (i=0; i<m; i++) {
3622       nz += ourlens[i];
3623     }
3624     ierr = PetscMalloc(nz*sizeof(PetscInt),&mycols);CHKERRQ(ierr);
3625 
3626     /* receive message of column indices*/
3627     ierr = MPIULong_Recv(mycols,nz,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
3628   }
3629 
3630   /* determine column ownership if matrix is not square */
3631   if (N != M) {
3632     if (newMat->cmap->n < 0) n = N/size + ((N % size) > rank);
3633     else n = newMat->cmap->n;
3634     ierr   = MPI_Scan(&n,&cend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3635     cstart = cend - n;
3636   } else {
3637     cstart = rstart;
3638     cend   = rend;
3639     n      = cend - cstart;
3640   }
3641 
3642   /* loop over local rows, determining number of off diagonal entries */
3643   ierr = PetscMemzero(offlens,m*sizeof(PetscInt));CHKERRQ(ierr);
3644   jj   = 0;
3645   for (i=0; i<m; i++) {
3646     for (j=0; j<ourlens[i]; j++) {
3647       if (mycols[jj] < cstart || mycols[jj] >= cend) offlens[i]++;
3648       jj++;
3649     }
3650   }
3651 
3652   for (i=0; i<m; i++) {
3653     ourlens[i] -= offlens[i];
3654   }
3655   if (!sizesset) {
3656     ierr = MatSetSizes(newMat,m,n,M,N);CHKERRQ(ierr);
3657   }
3658 
3659   if (bs > 1) {ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);}
3660 
3661   ierr = MatMPIAIJSetPreallocation(newMat,0,ourlens,0,offlens);CHKERRQ(ierr);
3662 
3663   for (i=0; i<m; i++) {
3664     ourlens[i] += offlens[i];
3665   }
3666 
3667   if (!rank) {
3668     ierr = PetscMalloc((maxnz+1)*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
3669 
3670     /* read in my part of the matrix numerical values  */
3671     nz   = procsnz[0];
3672     ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
3673 
3674     /* insert into matrix */
3675     jj      = rstart;
3676     smycols = mycols;
3677     svals   = vals;
3678     for (i=0; i<m; i++) {
3679       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
3680       smycols += ourlens[i];
3681       svals   += ourlens[i];
3682       jj++;
3683     }
3684 
3685     /* read in other processors and ship out */
3686     for (i=1; i<size; i++) {
3687       nz   = procsnz[i];
3688       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
3689       ierr = MPIULong_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
3690     }
3691     ierr = PetscFree(procsnz);CHKERRQ(ierr);
3692   } else {
3693     /* receive numeric values */
3694     ierr = PetscMalloc((nz+1)*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
3695 
3696     /* receive message of values*/
3697     ierr = MPIULong_Recv(vals,nz,MPIU_SCALAR,0,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
3698 
3699     /* insert into matrix */
3700     jj      = rstart;
3701     smycols = mycols;
3702     svals   = vals;
3703     for (i=0; i<m; i++) {
3704       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
3705       smycols += ourlens[i];
3706       svals   += ourlens[i];
3707       jj++;
3708     }
3709   }
3710   ierr = PetscFree2(ourlens,offlens);CHKERRQ(ierr);
3711   ierr = PetscFree(vals);CHKERRQ(ierr);
3712   ierr = PetscFree(mycols);CHKERRQ(ierr);
3713   ierr = PetscFree(rowners);CHKERRQ(ierr);
3714   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3715   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3716   PetscFunctionReturn(0);
3717 }
3718 
3719 #undef __FUNCT__
3720 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ"
3721 PetscErrorCode MatGetSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3722 {
3723   PetscErrorCode ierr;
3724   IS             iscol_local;
3725   PetscInt       csize;
3726 
3727   PetscFunctionBegin;
3728   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3729   if (call == MAT_REUSE_MATRIX) {
3730     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3731     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3732   } else {
3733     PetscInt cbs;
3734     ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
3735     ierr = ISAllGather(iscol,&iscol_local);CHKERRQ(ierr);
3736     ierr = ISSetBlockSize(iscol_local,cbs);CHKERRQ(ierr);
3737   }
3738   ierr = MatGetSubMatrix_MPIAIJ_Private(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
3739   if (call == MAT_INITIAL_MATRIX) {
3740     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3741     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3742   }
3743   PetscFunctionReturn(0);
3744 }
3745 
3746 extern PetscErrorCode MatGetSubMatrices_MPIAIJ_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool*,Mat*);
3747 #undef __FUNCT__
3748 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ_Private"
3749 /*
3750     Not great since it makes two copies of the submatrix, first an SeqAIJ
3751   in local and then by concatenating the local matrices the end result.
3752   Writing it directly would be much like MatGetSubMatrices_MPIAIJ()
3753 
3754   Note: This requires a sequential iscol with all indices.
3755 */
3756 PetscErrorCode MatGetSubMatrix_MPIAIJ_Private(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3757 {
3758   PetscErrorCode ierr;
3759   PetscMPIInt    rank,size;
3760   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3761   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal,ncol;
3762   PetscBool      allcolumns, colflag;
3763   Mat            M,Mreuse;
3764   MatScalar      *vwork,*aa;
3765   MPI_Comm       comm;
3766   Mat_SeqAIJ     *aij;
3767 
3768   PetscFunctionBegin;
3769   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3770   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3771   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3772 
3773   ierr = ISIdentity(iscol,&colflag);CHKERRQ(ierr);
3774   ierr = ISGetLocalSize(iscol,&ncol);CHKERRQ(ierr);
3775   if (colflag && ncol == mat->cmap->N) {
3776     allcolumns = PETSC_TRUE;
3777   } else {
3778     allcolumns = PETSC_FALSE;
3779   }
3780   if (call ==  MAT_REUSE_MATRIX) {
3781     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3782     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3783     ierr = MatGetSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,&allcolumns,&Mreuse);CHKERRQ(ierr);
3784   } else {
3785     ierr = MatGetSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&allcolumns,&Mreuse);CHKERRQ(ierr);
3786   }
3787 
3788   /*
3789       m - number of local rows
3790       n - number of columns (same on all processors)
3791       rstart - first row in new global matrix generated
3792   */
3793   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3794   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3795   if (call == MAT_INITIAL_MATRIX) {
3796     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3797     ii  = aij->i;
3798     jj  = aij->j;
3799 
3800     /*
3801         Determine the number of non-zeros in the diagonal and off-diagonal
3802         portions of the matrix in order to do correct preallocation
3803     */
3804 
3805     /* first get start and end of "diagonal" columns */
3806     if (csize == PETSC_DECIDE) {
3807       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3808       if (mglobal == n) { /* square matrix */
3809         nlocal = m;
3810       } else {
3811         nlocal = n/size + ((n % size) > rank);
3812       }
3813     } else {
3814       nlocal = csize;
3815     }
3816     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3817     rstart = rend - nlocal;
3818     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);
3819 
3820     /* next, compute all the lengths */
3821     ierr  = PetscMalloc((2*m+1)*sizeof(PetscInt),&dlens);CHKERRQ(ierr);
3822     olens = dlens + m;
3823     for (i=0; i<m; i++) {
3824       jend = ii[i+1] - ii[i];
3825       olen = 0;
3826       dlen = 0;
3827       for (j=0; j<jend; j++) {
3828         if (*jj < rstart || *jj >= rend) olen++;
3829         else dlen++;
3830         jj++;
3831       }
3832       olens[i] = olen;
3833       dlens[i] = dlen;
3834     }
3835     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3836     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3837     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3838     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3839     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3840     ierr = PetscFree(dlens);CHKERRQ(ierr);
3841   } else {
3842     PetscInt ml,nl;
3843 
3844     M    = *newmat;
3845     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3846     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3847     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3848     /*
3849          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3850        rather than the slower MatSetValues().
3851     */
3852     M->was_assembled = PETSC_TRUE;
3853     M->assembled     = PETSC_FALSE;
3854   }
3855   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3856   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3857   ii   = aij->i;
3858   jj   = aij->j;
3859   aa   = aij->a;
3860   for (i=0; i<m; i++) {
3861     row   = rstart + i;
3862     nz    = ii[i+1] - ii[i];
3863     cwork = jj;     jj += nz;
3864     vwork = aa;     aa += nz;
3865     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3866   }
3867 
3868   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3869   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3870   *newmat = M;
3871 
3872   /* save submatrix used in processor for next request */
3873   if (call ==  MAT_INITIAL_MATRIX) {
3874     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3875     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3876   }
3877   PetscFunctionReturn(0);
3878 }
3879 
3880 #undef __FUNCT__
3881 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR_MPIAIJ"
3882 PetscErrorCode  MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3883 {
3884   PetscInt       m,cstart, cend,j,nnz,i,d;
3885   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3886   const PetscInt *JJ;
3887   PetscScalar    *values;
3888   PetscErrorCode ierr;
3889 
3890   PetscFunctionBegin;
3891   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3892 
3893   ierr   = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3894   ierr   = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3895   m      = B->rmap->n;
3896   cstart = B->cmap->rstart;
3897   cend   = B->cmap->rend;
3898   rstart = B->rmap->rstart;
3899 
3900   ierr = PetscMalloc2(m,PetscInt,&d_nnz,m,PetscInt,&o_nnz);CHKERRQ(ierr);
3901 
3902 #if defined(PETSC_USE_DEBUGGING)
3903   for (i=0; i<m; i++) {
3904     nnz = Ii[i+1]- Ii[i];
3905     JJ  = J + Ii[i];
3906     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3907     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3908     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);
3909   }
3910 #endif
3911 
3912   for (i=0; i<m; i++) {
3913     nnz     = Ii[i+1]- Ii[i];
3914     JJ      = J + Ii[i];
3915     nnz_max = PetscMax(nnz_max,nnz);
3916     d       = 0;
3917     for (j=0; j<nnz; j++) {
3918       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3919     }
3920     d_nnz[i] = d;
3921     o_nnz[i] = nnz - d;
3922   }
3923   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3924   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3925 
3926   if (v) values = (PetscScalar*)v;
3927   else {
3928     ierr = PetscMalloc((nnz_max+1)*sizeof(PetscScalar),&values);CHKERRQ(ierr);
3929     ierr = PetscMemzero(values,nnz_max*sizeof(PetscScalar));CHKERRQ(ierr);
3930   }
3931 
3932   for (i=0; i<m; i++) {
3933     ii   = i + rstart;
3934     nnz  = Ii[i+1]- Ii[i];
3935     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3936   }
3937   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3938   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3939 
3940   if (!v) {
3941     ierr = PetscFree(values);CHKERRQ(ierr);
3942   }
3943   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3944   PetscFunctionReturn(0);
3945 }
3946 
3947 #undef __FUNCT__
3948 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR"
3949 /*@
3950    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3951    (the default parallel PETSc format).
3952 
3953    Collective on MPI_Comm
3954 
3955    Input Parameters:
3956 +  B - the matrix
3957 .  i - the indices into j for the start of each local row (starts with zero)
3958 .  j - the column indices for each local row (starts with zero)
3959 -  v - optional values in the matrix
3960 
3961    Level: developer
3962 
3963    Notes:
3964        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3965      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3966      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3967 
3968        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3969 
3970        The format which is used for the sparse matrix input, is equivalent to a
3971     row-major ordering.. i.e for the following matrix, the input data expected is
3972     as shown:
3973 
3974         1 0 0
3975         2 0 3     P0
3976        -------
3977         4 5 6     P1
3978 
3979      Process0 [P0]: rows_owned=[0,1]
3980         i =  {0,1,3}  [size = nrow+1  = 2+1]
3981         j =  {0,0,2}  [size = nz = 6]
3982         v =  {1,2,3}  [size = nz = 6]
3983 
3984      Process1 [P1]: rows_owned=[2]
3985         i =  {0,3}    [size = nrow+1  = 1+1]
3986         j =  {0,1,2}  [size = nz = 6]
3987         v =  {4,5,6}  [size = nz = 6]
3988 
3989 .keywords: matrix, aij, compressed row, sparse, parallel
3990 
3991 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MPIAIJ,
3992           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3993 @*/
3994 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3995 {
3996   PetscErrorCode ierr;
3997 
3998   PetscFunctionBegin;
3999   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
4000   PetscFunctionReturn(0);
4001 }
4002 
4003 #undef __FUNCT__
4004 #define __FUNCT__ "MatMPIAIJSetPreallocation"
4005 /*@C
4006    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
4007    (the default parallel PETSc format).  For good matrix assembly performance
4008    the user should preallocate the matrix storage by setting the parameters
4009    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
4010    performance can be increased by more than a factor of 50.
4011 
4012    Collective on MPI_Comm
4013 
4014    Input Parameters:
4015 +  A - the matrix
4016 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
4017            (same value is used for all local rows)
4018 .  d_nnz - array containing the number of nonzeros in the various rows of the
4019            DIAGONAL portion of the local submatrix (possibly different for each row)
4020            or NULL, if d_nz is used to specify the nonzero structure.
4021            The size of this array is equal to the number of local rows, i.e 'm'.
4022            For matrices that will be factored, you must leave room for (and set)
4023            the diagonal entry even if it is zero.
4024 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
4025            submatrix (same value is used for all local rows).
4026 -  o_nnz - array containing the number of nonzeros in the various rows of the
4027            OFF-DIAGONAL portion of the local submatrix (possibly different for
4028            each row) or NULL, if o_nz is used to specify the nonzero
4029            structure. The size of this array is equal to the number
4030            of local rows, i.e 'm'.
4031 
4032    If the *_nnz parameter is given then the *_nz parameter is ignored
4033 
4034    The AIJ format (also called the Yale sparse matrix format or
4035    compressed row storage (CSR)), is fully compatible with standard Fortran 77
4036    storage.  The stored row and column indices begin with zero.
4037    See the <A href="../../docs/manual.pdf#nameddest=ch_mat">Mat chapter of the users manual</A> for details.
4038 
4039    The parallel matrix is partitioned such that the first m0 rows belong to
4040    process 0, the next m1 rows belong to process 1, the next m2 rows belong
4041    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
4042 
4043    The DIAGONAL portion of the local submatrix of a processor can be defined
4044    as the submatrix which is obtained by extraction the part corresponding to
4045    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
4046    first row that belongs to the processor, r2 is the last row belonging to
4047    the this processor, and c1-c2 is range of indices of the local part of a
4048    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
4049    common case of a square matrix, the row and column ranges are the same and
4050    the DIAGONAL part is also square. The remaining portion of the local
4051    submatrix (mxN) constitute the OFF-DIAGONAL portion.
4052 
4053    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
4054 
4055    You can call MatGetInfo() to get information on how effective the preallocation was;
4056    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
4057    You can also run with the option -info and look for messages with the string
4058    malloc in them to see if additional memory allocation was needed.
4059 
4060    Example usage:
4061 
4062    Consider the following 8x8 matrix with 34 non-zero values, that is
4063    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
4064    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
4065    as follows:
4066 
4067 .vb
4068             1  2  0  |  0  3  0  |  0  4
4069     Proc0   0  5  6  |  7  0  0  |  8  0
4070             9  0 10  | 11  0  0  | 12  0
4071     -------------------------------------
4072            13  0 14  | 15 16 17  |  0  0
4073     Proc1   0 18  0  | 19 20 21  |  0  0
4074             0  0  0  | 22 23  0  | 24  0
4075     -------------------------------------
4076     Proc2  25 26 27  |  0  0 28  | 29  0
4077            30  0  0  | 31 32 33  |  0 34
4078 .ve
4079 
4080    This can be represented as a collection of submatrices as:
4081 
4082 .vb
4083       A B C
4084       D E F
4085       G H I
4086 .ve
4087 
4088    Where the submatrices A,B,C are owned by proc0, D,E,F are
4089    owned by proc1, G,H,I are owned by proc2.
4090 
4091    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4092    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4093    The 'M','N' parameters are 8,8, and have the same values on all procs.
4094 
4095    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
4096    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
4097    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
4098    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
4099    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
4100    matrix, ans [DF] as another SeqAIJ matrix.
4101 
4102    When d_nz, o_nz parameters are specified, d_nz storage elements are
4103    allocated for every row of the local diagonal submatrix, and o_nz
4104    storage locations are allocated for every row of the OFF-DIAGONAL submat.
4105    One way to choose d_nz and o_nz is to use the max nonzerors per local
4106    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
4107    In this case, the values of d_nz,o_nz are:
4108 .vb
4109      proc0 : dnz = 2, o_nz = 2
4110      proc1 : dnz = 3, o_nz = 2
4111      proc2 : dnz = 1, o_nz = 4
4112 .ve
4113    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
4114    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
4115    for proc3. i.e we are using 12+15+10=37 storage locations to store
4116    34 values.
4117 
4118    When d_nnz, o_nnz parameters are specified, the storage is specified
4119    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
4120    In the above case the values for d_nnz,o_nnz are:
4121 .vb
4122      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
4123      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
4124      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
4125 .ve
4126    Here the space allocated is sum of all the above values i.e 34, and
4127    hence pre-allocation is perfect.
4128 
4129    Level: intermediate
4130 
4131 .keywords: matrix, aij, compressed row, sparse, parallel
4132 
4133 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
4134           MPIAIJ, MatGetInfo(), PetscSplitOwnership()
4135 @*/
4136 PetscErrorCode  MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
4137 {
4138   PetscErrorCode ierr;
4139 
4140   PetscFunctionBegin;
4141   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
4142   PetscValidType(B,1);
4143   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
4144   PetscFunctionReturn(0);
4145 }
4146 
4147 #undef __FUNCT__
4148 #define __FUNCT__ "MatCreateMPIAIJWithArrays"
4149 /*@
4150      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
4151          CSR format the local rows.
4152 
4153    Collective on MPI_Comm
4154 
4155    Input Parameters:
4156 +  comm - MPI communicator
4157 .  m - number of local rows (Cannot be PETSC_DECIDE)
4158 .  n - This value should be the same as the local size used in creating the
4159        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
4160        calculated if N is given) For square matrices n is almost always m.
4161 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
4162 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
4163 .   i - row indices
4164 .   j - column indices
4165 -   a - matrix values
4166 
4167    Output Parameter:
4168 .   mat - the matrix
4169 
4170    Level: intermediate
4171 
4172    Notes:
4173        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
4174      thus you CANNOT change the matrix entries by changing the values of a[] after you have
4175      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
4176 
4177        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
4178 
4179        The format which is used for the sparse matrix input, is equivalent to a
4180     row-major ordering.. i.e for the following matrix, the input data expected is
4181     as shown:
4182 
4183         1 0 0
4184         2 0 3     P0
4185        -------
4186         4 5 6     P1
4187 
4188      Process0 [P0]: rows_owned=[0,1]
4189         i =  {0,1,3}  [size = nrow+1  = 2+1]
4190         j =  {0,0,2}  [size = nz = 6]
4191         v =  {1,2,3}  [size = nz = 6]
4192 
4193      Process1 [P1]: rows_owned=[2]
4194         i =  {0,3}    [size = nrow+1  = 1+1]
4195         j =  {0,1,2}  [size = nz = 6]
4196         v =  {4,5,6}  [size = nz = 6]
4197 
4198 .keywords: matrix, aij, compressed row, sparse, parallel
4199 
4200 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
4201           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
4202 @*/
4203 PetscErrorCode  MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
4204 {
4205   PetscErrorCode ierr;
4206 
4207   PetscFunctionBegin;
4208   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
4209   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
4210   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4211   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
4212   /* ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr); */
4213   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
4214   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
4215   PetscFunctionReturn(0);
4216 }
4217 
4218 #undef __FUNCT__
4219 #define __FUNCT__ "MatCreateAIJ"
4220 /*@C
4221    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
4222    (the default parallel PETSc format).  For good matrix assembly performance
4223    the user should preallocate the matrix storage by setting the parameters
4224    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
4225    performance can be increased by more than a factor of 50.
4226 
4227    Collective on MPI_Comm
4228 
4229    Input Parameters:
4230 +  comm - MPI communicator
4231 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
4232            This value should be the same as the local size used in creating the
4233            y vector for the matrix-vector product y = Ax.
4234 .  n - This value should be the same as the local size used in creating the
4235        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
4236        calculated if N is given) For square matrices n is almost always m.
4237 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
4238 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
4239 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
4240            (same value is used for all local rows)
4241 .  d_nnz - array containing the number of nonzeros in the various rows of the
4242            DIAGONAL portion of the local submatrix (possibly different for each row)
4243            or NULL, if d_nz is used to specify the nonzero structure.
4244            The size of this array is equal to the number of local rows, i.e 'm'.
4245 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
4246            submatrix (same value is used for all local rows).
4247 -  o_nnz - array containing the number of nonzeros in the various rows of the
4248            OFF-DIAGONAL portion of the local submatrix (possibly different for
4249            each row) or NULL, if o_nz is used to specify the nonzero
4250            structure. The size of this array is equal to the number
4251            of local rows, i.e 'm'.
4252 
4253    Output Parameter:
4254 .  A - the matrix
4255 
4256    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
4257    MatXXXXSetPreallocation() paradgm instead of this routine directly.
4258    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
4259 
4260    Notes:
4261    If the *_nnz parameter is given then the *_nz parameter is ignored
4262 
4263    m,n,M,N parameters specify the size of the matrix, and its partitioning across
4264    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
4265    storage requirements for this matrix.
4266 
4267    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
4268    processor than it must be used on all processors that share the object for
4269    that argument.
4270 
4271    The user MUST specify either the local or global matrix dimensions
4272    (possibly both).
4273 
4274    The parallel matrix is partitioned across processors such that the
4275    first m0 rows belong to process 0, the next m1 rows belong to
4276    process 1, the next m2 rows belong to process 2 etc.. where
4277    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
4278    values corresponding to [m x N] submatrix.
4279 
4280    The columns are logically partitioned with the n0 columns belonging
4281    to 0th partition, the next n1 columns belonging to the next
4282    partition etc.. where n0,n1,n2... are the the input parameter 'n'.
4283 
4284    The DIAGONAL portion of the local submatrix on any given processor
4285    is the submatrix corresponding to the rows and columns m,n
4286    corresponding to the given processor. i.e diagonal matrix on
4287    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
4288    etc. The remaining portion of the local submatrix [m x (N-n)]
4289    constitute the OFF-DIAGONAL portion. The example below better
4290    illustrates this concept.
4291 
4292    For a square global matrix we define each processor's diagonal portion
4293    to be its local rows and the corresponding columns (a square submatrix);
4294    each processor's off-diagonal portion encompasses the remainder of the
4295    local matrix (a rectangular submatrix).
4296 
4297    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
4298 
4299    When calling this routine with a single process communicator, a matrix of
4300    type SEQAIJ is returned.  If a matrix of type MPIAIJ is desired for this
4301    type of communicator, use the construction mechanism:
4302      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
4303 
4304    By default, this format uses inodes (identical nodes) when possible.
4305    We search for consecutive rows with the same nonzero structure, thereby
4306    reusing matrix information to achieve increased efficiency.
4307 
4308    Options Database Keys:
4309 +  -mat_no_inode  - Do not use inodes
4310 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
4311 -  -mat_aij_oneindex - Internally use indexing starting at 1
4312         rather than 0.  Note that when calling MatSetValues(),
4313         the user still MUST index entries starting at 0!
4314 
4315 
4316    Example usage:
4317 
4318    Consider the following 8x8 matrix with 34 non-zero values, that is
4319    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
4320    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
4321    as follows:
4322 
4323 .vb
4324             1  2  0  |  0  3  0  |  0  4
4325     Proc0   0  5  6  |  7  0  0  |  8  0
4326             9  0 10  | 11  0  0  | 12  0
4327     -------------------------------------
4328            13  0 14  | 15 16 17  |  0  0
4329     Proc1   0 18  0  | 19 20 21  |  0  0
4330             0  0  0  | 22 23  0  | 24  0
4331     -------------------------------------
4332     Proc2  25 26 27  |  0  0 28  | 29  0
4333            30  0  0  | 31 32 33  |  0 34
4334 .ve
4335 
4336    This can be represented as a collection of submatrices as:
4337 
4338 .vb
4339       A B C
4340       D E F
4341       G H I
4342 .ve
4343 
4344    Where the submatrices A,B,C are owned by proc0, D,E,F are
4345    owned by proc1, G,H,I are owned by proc2.
4346 
4347    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4348    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4349    The 'M','N' parameters are 8,8, and have the same values on all procs.
4350 
4351    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
4352    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
4353    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
4354    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
4355    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
4356    matrix, ans [DF] as another SeqAIJ matrix.
4357 
4358    When d_nz, o_nz parameters are specified, d_nz storage elements are
4359    allocated for every row of the local diagonal submatrix, and o_nz
4360    storage locations are allocated for every row of the OFF-DIAGONAL submat.
4361    One way to choose d_nz and o_nz is to use the max nonzerors per local
4362    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
4363    In this case, the values of d_nz,o_nz are:
4364 .vb
4365      proc0 : dnz = 2, o_nz = 2
4366      proc1 : dnz = 3, o_nz = 2
4367      proc2 : dnz = 1, o_nz = 4
4368 .ve
4369    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
4370    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
4371    for proc3. i.e we are using 12+15+10=37 storage locations to store
4372    34 values.
4373 
4374    When d_nnz, o_nnz parameters are specified, the storage is specified
4375    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
4376    In the above case the values for d_nnz,o_nnz are:
4377 .vb
4378      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
4379      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
4380      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
4381 .ve
4382    Here the space allocated is sum of all the above values i.e 34, and
4383    hence pre-allocation is perfect.
4384 
4385    Level: intermediate
4386 
4387 .keywords: matrix, aij, compressed row, sparse, parallel
4388 
4389 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
4390           MPIAIJ, MatCreateMPIAIJWithArrays()
4391 @*/
4392 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)
4393 {
4394   PetscErrorCode ierr;
4395   PetscMPIInt    size;
4396 
4397   PetscFunctionBegin;
4398   ierr = MatCreate(comm,A);CHKERRQ(ierr);
4399   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
4400   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4401   if (size > 1) {
4402     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
4403     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
4404   } else {
4405     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
4406     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
4407   }
4408   PetscFunctionReturn(0);
4409 }
4410 
4411 #undef __FUNCT__
4412 #define __FUNCT__ "MatMPIAIJGetSeqAIJ"
4413 PetscErrorCode  MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
4414 {
4415   Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
4416 
4417   PetscFunctionBegin;
4418   *Ad     = a->A;
4419   *Ao     = a->B;
4420   *colmap = a->garray;
4421   PetscFunctionReturn(0);
4422 }
4423 
4424 #undef __FUNCT__
4425 #define __FUNCT__ "MatSetColoring_MPIAIJ"
4426 PetscErrorCode MatSetColoring_MPIAIJ(Mat A,ISColoring coloring)
4427 {
4428   PetscErrorCode ierr;
4429   PetscInt       i;
4430   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
4431 
4432   PetscFunctionBegin;
4433   if (coloring->ctype == IS_COLORING_GLOBAL) {
4434     ISColoringValue *allcolors,*colors;
4435     ISColoring      ocoloring;
4436 
4437     /* set coloring for diagonal portion */
4438     ierr = MatSetColoring_SeqAIJ(a->A,coloring);CHKERRQ(ierr);
4439 
4440     /* set coloring for off-diagonal portion */
4441     ierr = ISAllGatherColors(PetscObjectComm((PetscObject)A),coloring->n,coloring->colors,NULL,&allcolors);CHKERRQ(ierr);
4442     ierr = PetscMalloc((a->B->cmap->n+1)*sizeof(ISColoringValue),&colors);CHKERRQ(ierr);
4443     for (i=0; i<a->B->cmap->n; i++) {
4444       colors[i] = allcolors[a->garray[i]];
4445     }
4446     ierr = PetscFree(allcolors);CHKERRQ(ierr);
4447     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,&ocoloring);CHKERRQ(ierr);
4448     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
4449     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
4450   } else if (coloring->ctype == IS_COLORING_GHOSTED) {
4451     ISColoringValue *colors;
4452     PetscInt        *larray;
4453     ISColoring      ocoloring;
4454 
4455     /* set coloring for diagonal portion */
4456     ierr = PetscMalloc((a->A->cmap->n+1)*sizeof(PetscInt),&larray);CHKERRQ(ierr);
4457     for (i=0; i<a->A->cmap->n; i++) {
4458       larray[i] = i + A->cmap->rstart;
4459     }
4460     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->A->cmap->n,larray,NULL,larray);CHKERRQ(ierr);
4461     ierr = PetscMalloc((a->A->cmap->n+1)*sizeof(ISColoringValue),&colors);CHKERRQ(ierr);
4462     for (i=0; i<a->A->cmap->n; i++) {
4463       colors[i] = coloring->colors[larray[i]];
4464     }
4465     ierr = PetscFree(larray);CHKERRQ(ierr);
4466     ierr = ISColoringCreate(PETSC_COMM_SELF,coloring->n,a->A->cmap->n,colors,&ocoloring);CHKERRQ(ierr);
4467     ierr = MatSetColoring_SeqAIJ(a->A,ocoloring);CHKERRQ(ierr);
4468     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
4469 
4470     /* set coloring for off-diagonal portion */
4471     ierr = PetscMalloc((a->B->cmap->n+1)*sizeof(PetscInt),&larray);CHKERRQ(ierr);
4472     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->B->cmap->n,a->garray,NULL,larray);CHKERRQ(ierr);
4473     ierr = PetscMalloc((a->B->cmap->n+1)*sizeof(ISColoringValue),&colors);CHKERRQ(ierr);
4474     for (i=0; i<a->B->cmap->n; i++) {
4475       colors[i] = coloring->colors[larray[i]];
4476     }
4477     ierr = PetscFree(larray);CHKERRQ(ierr);
4478     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,&ocoloring);CHKERRQ(ierr);
4479     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
4480     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
4481   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support ISColoringType %d",(int)coloring->ctype);
4482   PetscFunctionReturn(0);
4483 }
4484 
4485 #undef __FUNCT__
4486 #define __FUNCT__ "MatSetValuesAdifor_MPIAIJ"
4487 PetscErrorCode MatSetValuesAdifor_MPIAIJ(Mat A,PetscInt nl,void *advalues)
4488 {
4489   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
4490   PetscErrorCode ierr;
4491 
4492   PetscFunctionBegin;
4493   ierr = MatSetValuesAdifor_SeqAIJ(a->A,nl,advalues);CHKERRQ(ierr);
4494   ierr = MatSetValuesAdifor_SeqAIJ(a->B,nl,advalues);CHKERRQ(ierr);
4495   PetscFunctionReturn(0);
4496 }
4497 
4498 #undef __FUNCT__
4499 #define __FUNCT__ "MatCreateMPIAIJConcatenateSeqAIJSymbolic"
4500 PetscErrorCode  MatCreateMPIAIJConcatenateSeqAIJSymbolic(MPI_Comm comm,Mat inmat,PetscInt n,Mat *outmat)
4501 {
4502   PetscErrorCode ierr;
4503   PetscInt       m,N,i,rstart,nnz,*dnz,*onz,sum,bs,cbs;
4504   PetscInt       *indx;
4505 
4506   PetscFunctionBegin;
4507   /* This routine will ONLY return MPIAIJ type matrix */
4508   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
4509   ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
4510   if (n == PETSC_DECIDE) {
4511     ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
4512   }
4513   /* Check sum(n) = N */
4514   ierr = MPI_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4515   if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
4516 
4517   ierr    = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4518   rstart -= m;
4519 
4520   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4521   for (i=0; i<m; i++) {
4522     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
4523     ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
4524     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
4525   }
4526 
4527   ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
4528   ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4529   ierr = MatSetBlockSizes(*outmat,bs,cbs);CHKERRQ(ierr);
4530   ierr = MatSetType(*outmat,MATMPIAIJ);CHKERRQ(ierr);
4531   ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
4532   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4533   PetscFunctionReturn(0);
4534 }
4535 
4536 #undef __FUNCT__
4537 #define __FUNCT__ "MatCreateMPIAIJConcatenateSeqAIJNumeric"
4538 PetscErrorCode  MatCreateMPIAIJConcatenateSeqAIJNumeric(MPI_Comm comm,Mat inmat,PetscInt n,Mat outmat)
4539 {
4540   PetscErrorCode ierr;
4541   PetscInt       m,N,i,rstart,nnz,Ii;
4542   PetscInt       *indx;
4543   PetscScalar    *values;
4544 
4545   PetscFunctionBegin;
4546   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
4547   ierr = MatGetOwnershipRange(outmat,&rstart,NULL);CHKERRQ(ierr);
4548   for (i=0; i<m; i++) {
4549     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4550     Ii   = i + rstart;
4551     ierr = MatSetValues(outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4552     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4553   }
4554   ierr = MatAssemblyBegin(outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4555   ierr = MatAssemblyEnd(outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4556   PetscFunctionReturn(0);
4557 }
4558 
4559 #undef __FUNCT__
4560 #define __FUNCT__ "MatCreateMPIAIJConcatenateSeqAIJ"
4561 /*@
4562       MatCreateMPIAIJConcatenateSeqAIJ - Creates a single large PETSc matrix by concatenating sequential
4563                  matrices from each processor
4564 
4565     Collective on MPI_Comm
4566 
4567    Input Parameters:
4568 +    comm - the communicators the parallel matrix will live on
4569 .    inmat - the input sequential matrices
4570 .    n - number of local columns (or PETSC_DECIDE)
4571 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4572 
4573    Output Parameter:
4574 .    outmat - the parallel matrix generated
4575 
4576     Level: advanced
4577 
4578    Notes: The number of columns of the matrix in EACH processor MUST be the same.
4579 
4580 @*/
4581 PetscErrorCode  MatCreateMPIAIJConcatenateSeqAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
4582 {
4583   PetscErrorCode ierr;
4584   PetscMPIInt    size;
4585 
4586   PetscFunctionBegin;
4587   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4588   ierr = PetscLogEventBegin(MAT_Merge,inmat,0,0,0);CHKERRQ(ierr);
4589   if (size == 1) {
4590     if (scall == MAT_INITIAL_MATRIX) {
4591       ierr = MatDuplicate(inmat,MAT_COPY_VALUES,outmat);CHKERRQ(ierr);
4592     } else {
4593       ierr = MatCopy(inmat,*outmat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4594     }
4595   } else {
4596     if (scall == MAT_INITIAL_MATRIX) {
4597       ierr = MatCreateMPIAIJConcatenateSeqAIJSymbolic(comm,inmat,n,outmat);CHKERRQ(ierr);
4598     }
4599     ierr = MatCreateMPIAIJConcatenateSeqAIJNumeric(comm,inmat,n,*outmat);CHKERRQ(ierr);
4600   }
4601   ierr = PetscLogEventEnd(MAT_Merge,inmat,0,0,0);CHKERRQ(ierr);
4602   PetscFunctionReturn(0);
4603 }
4604 
4605 #undef __FUNCT__
4606 #define __FUNCT__ "MatFileSplit"
4607 PetscErrorCode MatFileSplit(Mat A,char *outfile)
4608 {
4609   PetscErrorCode    ierr;
4610   PetscMPIInt       rank;
4611   PetscInt          m,N,i,rstart,nnz;
4612   size_t            len;
4613   const PetscInt    *indx;
4614   PetscViewer       out;
4615   char              *name;
4616   Mat               B;
4617   const PetscScalar *values;
4618 
4619   PetscFunctionBegin;
4620   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
4621   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
4622   /* Should this be the type of the diagonal block of A? */
4623   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
4624   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
4625   ierr = MatSetBlockSizes(B,A->rmap->bs,A->cmap->bs);CHKERRQ(ierr);
4626   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
4627   ierr = MatSeqAIJSetPreallocation(B,0,NULL);CHKERRQ(ierr);
4628   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
4629   for (i=0; i<m; i++) {
4630     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4631     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4632     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4633   }
4634   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4635   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4636 
4637   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
4638   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
4639   ierr = PetscMalloc((len+5)*sizeof(char),&name);CHKERRQ(ierr);
4640   sprintf(name,"%s.%d",outfile,rank);
4641   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
4642   ierr = PetscFree(name);CHKERRQ(ierr);
4643   ierr = MatView(B,out);CHKERRQ(ierr);
4644   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
4645   ierr = MatDestroy(&B);CHKERRQ(ierr);
4646   PetscFunctionReturn(0);
4647 }
4648 
4649 extern PetscErrorCode MatDestroy_MPIAIJ(Mat);
4650 #undef __FUNCT__
4651 #define __FUNCT__ "MatDestroy_MPIAIJ_SeqsToMPI"
4652 PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
4653 {
4654   PetscErrorCode      ierr;
4655   Mat_Merge_SeqsToMPI *merge;
4656   PetscContainer      container;
4657 
4658   PetscFunctionBegin;
4659   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4660   if (container) {
4661     ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4662     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
4663     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
4664     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
4665     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
4666     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
4667     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
4668     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
4669     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
4670     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
4671     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
4672     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
4673     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
4674     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
4675     ierr = PetscFree(merge);CHKERRQ(ierr);
4676     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
4677   }
4678   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
4679   PetscFunctionReturn(0);
4680 }
4681 
4682 #include <../src/mat/utils/freespace.h>
4683 #include <petscbt.h>
4684 
4685 #undef __FUNCT__
4686 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJNumeric"
4687 PetscErrorCode  MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
4688 {
4689   PetscErrorCode      ierr;
4690   MPI_Comm            comm;
4691   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
4692   PetscMPIInt         size,rank,taga,*len_s;
4693   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
4694   PetscInt            proc,m;
4695   PetscInt            **buf_ri,**buf_rj;
4696   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
4697   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
4698   MPI_Request         *s_waits,*r_waits;
4699   MPI_Status          *status;
4700   MatScalar           *aa=a->a;
4701   MatScalar           **abuf_r,*ba_i;
4702   Mat_Merge_SeqsToMPI *merge;
4703   PetscContainer      container;
4704 
4705   PetscFunctionBegin;
4706   ierr = PetscObjectGetComm((PetscObject)mpimat,&comm);CHKERRQ(ierr);
4707   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4708 
4709   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4710   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4711 
4712   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4713   ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4714 
4715   bi     = merge->bi;
4716   bj     = merge->bj;
4717   buf_ri = merge->buf_ri;
4718   buf_rj = merge->buf_rj;
4719 
4720   ierr   = PetscMalloc(size*sizeof(MPI_Status),&status);CHKERRQ(ierr);
4721   owners = merge->rowmap->range;
4722   len_s  = merge->len_s;
4723 
4724   /* send and recv matrix values */
4725   /*-----------------------------*/
4726   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
4727   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
4728 
4729   ierr = PetscMalloc((merge->nsend+1)*sizeof(MPI_Request),&s_waits);CHKERRQ(ierr);
4730   for (proc=0,k=0; proc<size; proc++) {
4731     if (!len_s[proc]) continue;
4732     i    = owners[proc];
4733     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
4734     k++;
4735   }
4736 
4737   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
4738   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
4739   ierr = PetscFree(status);CHKERRQ(ierr);
4740 
4741   ierr = PetscFree(s_waits);CHKERRQ(ierr);
4742   ierr = PetscFree(r_waits);CHKERRQ(ierr);
4743 
4744   /* insert mat values of mpimat */
4745   /*----------------------------*/
4746   ierr = PetscMalloc(N*sizeof(PetscScalar),&ba_i);CHKERRQ(ierr);
4747   ierr = PetscMalloc3(merge->nrecv,PetscInt*,&buf_ri_k,merge->nrecv,PetscInt*,&nextrow,merge->nrecv,PetscInt*,&nextai);CHKERRQ(ierr);
4748 
4749   for (k=0; k<merge->nrecv; k++) {
4750     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4751     nrows       = *(buf_ri_k[k]);
4752     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
4753     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4754   }
4755 
4756   /* set values of ba */
4757   m = merge->rowmap->n;
4758   for (i=0; i<m; i++) {
4759     arow = owners[rank] + i;
4760     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
4761     bnzi = bi[i+1] - bi[i];
4762     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
4763 
4764     /* add local non-zero vals of this proc's seqmat into ba */
4765     anzi   = ai[arow+1] - ai[arow];
4766     aj     = a->j + ai[arow];
4767     aa     = a->a + ai[arow];
4768     nextaj = 0;
4769     for (j=0; nextaj<anzi; j++) {
4770       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4771         ba_i[j] += aa[nextaj++];
4772       }
4773     }
4774 
4775     /* add received vals into ba */
4776     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4777       /* i-th row */
4778       if (i == *nextrow[k]) {
4779         anzi   = *(nextai[k]+1) - *nextai[k];
4780         aj     = buf_rj[k] + *(nextai[k]);
4781         aa     = abuf_r[k] + *(nextai[k]);
4782         nextaj = 0;
4783         for (j=0; nextaj<anzi; j++) {
4784           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4785             ba_i[j] += aa[nextaj++];
4786           }
4787         }
4788         nextrow[k]++; nextai[k]++;
4789       }
4790     }
4791     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
4792   }
4793   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4794   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4795 
4796   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
4797   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
4798   ierr = PetscFree(ba_i);CHKERRQ(ierr);
4799   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4800   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4801   PetscFunctionReturn(0);
4802 }
4803 
4804 extern PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat);
4805 
4806 #undef __FUNCT__
4807 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJSymbolic"
4808 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4809 {
4810   PetscErrorCode      ierr;
4811   Mat                 B_mpi;
4812   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
4813   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4814   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
4815   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4816   PetscInt            len,proc,*dnz,*onz,bs,cbs;
4817   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4818   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4819   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
4820   MPI_Status          *status;
4821   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
4822   PetscBT             lnkbt;
4823   Mat_Merge_SeqsToMPI *merge;
4824   PetscContainer      container;
4825 
4826   PetscFunctionBegin;
4827   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4828 
4829   /* make sure it is a PETSc comm */
4830   ierr = PetscCommDuplicate(comm,&comm,NULL);CHKERRQ(ierr);
4831   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4832   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4833 
4834   ierr = PetscNew(Mat_Merge_SeqsToMPI,&merge);CHKERRQ(ierr);
4835   ierr = PetscMalloc(size*sizeof(MPI_Status),&status);CHKERRQ(ierr);
4836 
4837   /* determine row ownership */
4838   /*---------------------------------------------------------*/
4839   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
4840   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
4841   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
4842   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
4843   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
4844   ierr = PetscMalloc(size*sizeof(PetscMPIInt),&len_si);CHKERRQ(ierr);
4845   ierr = PetscMalloc(size*sizeof(PetscMPIInt),&merge->len_s);CHKERRQ(ierr);
4846 
4847   m      = merge->rowmap->n;
4848   owners = merge->rowmap->range;
4849 
4850   /* determine the number of messages to send, their lengths */
4851   /*---------------------------------------------------------*/
4852   len_s = merge->len_s;
4853 
4854   len          = 0; /* length of buf_si[] */
4855   merge->nsend = 0;
4856   for (proc=0; proc<size; proc++) {
4857     len_si[proc] = 0;
4858     if (proc == rank) {
4859       len_s[proc] = 0;
4860     } else {
4861       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4862       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4863     }
4864     if (len_s[proc]) {
4865       merge->nsend++;
4866       nrows = 0;
4867       for (i=owners[proc]; i<owners[proc+1]; i++) {
4868         if (ai[i+1] > ai[i]) nrows++;
4869       }
4870       len_si[proc] = 2*(nrows+1);
4871       len         += len_si[proc];
4872     }
4873   }
4874 
4875   /* determine the number and length of messages to receive for ij-structure */
4876   /*-------------------------------------------------------------------------*/
4877   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
4878   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
4879 
4880   /* post the Irecv of j-structure */
4881   /*-------------------------------*/
4882   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
4883   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
4884 
4885   /* post the Isend of j-structure */
4886   /*--------------------------------*/
4887   ierr = PetscMalloc2(merge->nsend,MPI_Request,&si_waits,merge->nsend,MPI_Request,&sj_waits);CHKERRQ(ierr);
4888 
4889   for (proc=0, k=0; proc<size; proc++) {
4890     if (!len_s[proc]) continue;
4891     i    = owners[proc];
4892     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
4893     k++;
4894   }
4895 
4896   /* receives and sends of j-structure are complete */
4897   /*------------------------------------------------*/
4898   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
4899   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
4900 
4901   /* send and recv i-structure */
4902   /*---------------------------*/
4903   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
4904   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
4905 
4906   ierr   = PetscMalloc((len+1)*sizeof(PetscInt),&buf_s);CHKERRQ(ierr);
4907   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4908   for (proc=0,k=0; proc<size; proc++) {
4909     if (!len_s[proc]) continue;
4910     /* form outgoing message for i-structure:
4911          buf_si[0]:                 nrows to be sent
4912                [1:nrows]:           row index (global)
4913                [nrows+1:2*nrows+1]: i-structure index
4914     */
4915     /*-------------------------------------------*/
4916     nrows       = len_si[proc]/2 - 1;
4917     buf_si_i    = buf_si + nrows+1;
4918     buf_si[0]   = nrows;
4919     buf_si_i[0] = 0;
4920     nrows       = 0;
4921     for (i=owners[proc]; i<owners[proc+1]; i++) {
4922       anzi = ai[i+1] - ai[i];
4923       if (anzi) {
4924         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4925         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4926         nrows++;
4927       }
4928     }
4929     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4930     k++;
4931     buf_si += len_si[proc];
4932   }
4933 
4934   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4935   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4936 
4937   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4938   for (i=0; i<merge->nrecv; i++) {
4939     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);
4940   }
4941 
4942   ierr = PetscFree(len_si);CHKERRQ(ierr);
4943   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4944   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4945   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4946   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4947   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4948   ierr = PetscFree(status);CHKERRQ(ierr);
4949 
4950   /* compute a local seq matrix in each processor */
4951   /*----------------------------------------------*/
4952   /* allocate bi array and free space for accumulating nonzero column info */
4953   ierr  = PetscMalloc((m+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
4954   bi[0] = 0;
4955 
4956   /* create and initialize a linked list */
4957   nlnk = N+1;
4958   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4959 
4960   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4961   len  = ai[owners[rank+1]] - ai[owners[rank]];
4962   ierr = PetscFreeSpaceGet((PetscInt)(2*len+1),&free_space);CHKERRQ(ierr);
4963 
4964   current_space = free_space;
4965 
4966   /* determine symbolic info for each local row */
4967   ierr = PetscMalloc3(merge->nrecv,PetscInt*,&buf_ri_k,merge->nrecv,PetscInt*,&nextrow,merge->nrecv,PetscInt*,&nextai);CHKERRQ(ierr);
4968 
4969   for (k=0; k<merge->nrecv; k++) {
4970     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4971     nrows       = *buf_ri_k[k];
4972     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4973     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4974   }
4975 
4976   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4977   len  = 0;
4978   for (i=0; i<m; i++) {
4979     bnzi = 0;
4980     /* add local non-zero cols of this proc's seqmat into lnk */
4981     arow  = owners[rank] + i;
4982     anzi  = ai[arow+1] - ai[arow];
4983     aj    = a->j + ai[arow];
4984     ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4985     bnzi += nlnk;
4986     /* add received col data into lnk */
4987     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4988       if (i == *nextrow[k]) { /* i-th row */
4989         anzi  = *(nextai[k]+1) - *nextai[k];
4990         aj    = buf_rj[k] + *nextai[k];
4991         ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4992         bnzi += nlnk;
4993         nextrow[k]++; nextai[k]++;
4994       }
4995     }
4996     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4997 
4998     /* if free space is not available, make more free space */
4999     if (current_space->local_remaining<bnzi) {
5000       ierr = PetscFreeSpaceGet(bnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
5001       nspacedouble++;
5002     }
5003     /* copy data into free space, then initialize lnk */
5004     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
5005     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
5006 
5007     current_space->array           += bnzi;
5008     current_space->local_used      += bnzi;
5009     current_space->local_remaining -= bnzi;
5010 
5011     bi[i+1] = bi[i] + bnzi;
5012   }
5013 
5014   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
5015 
5016   ierr = PetscMalloc((bi[m]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
5017   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
5018   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
5019 
5020   /* create symbolic parallel matrix B_mpi */
5021   /*---------------------------------------*/
5022   ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
5023   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
5024   if (n==PETSC_DECIDE) {
5025     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
5026   } else {
5027     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
5028   }
5029   ierr = MatSetBlockSizes(B_mpi,bs,cbs);CHKERRQ(ierr);
5030   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
5031   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
5032   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
5033   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
5034 
5035   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
5036   B_mpi->assembled    = PETSC_FALSE;
5037   B_mpi->ops->destroy = MatDestroy_MPIAIJ_SeqsToMPI;
5038   merge->bi           = bi;
5039   merge->bj           = bj;
5040   merge->buf_ri       = buf_ri;
5041   merge->buf_rj       = buf_rj;
5042   merge->coi          = NULL;
5043   merge->coj          = NULL;
5044   merge->owners_co    = NULL;
5045 
5046   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
5047 
5048   /* attach the supporting struct to B_mpi for reuse */
5049   ierr    = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
5050   ierr    = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
5051   ierr    = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
5052   ierr    = PetscContainerDestroy(&container);CHKERRQ(ierr);
5053   *mpimat = B_mpi;
5054 
5055   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
5056   PetscFunctionReturn(0);
5057 }
5058 
5059 #undef __FUNCT__
5060 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJ"
5061 /*@C
5062       MatCreateMPIAIJSumSeqAIJ - Creates a MPIAIJ matrix by adding sequential
5063                  matrices from each processor
5064 
5065     Collective on MPI_Comm
5066 
5067    Input Parameters:
5068 +    comm - the communicators the parallel matrix will live on
5069 .    seqmat - the input sequential matrices
5070 .    m - number of local rows (or PETSC_DECIDE)
5071 .    n - number of local columns (or PETSC_DECIDE)
5072 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5073 
5074    Output Parameter:
5075 .    mpimat - the parallel matrix generated
5076 
5077     Level: advanced
5078 
5079    Notes:
5080      The dimensions of the sequential matrix in each processor MUST be the same.
5081      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
5082      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
5083 @*/
5084 PetscErrorCode  MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
5085 {
5086   PetscErrorCode ierr;
5087   PetscMPIInt    size;
5088 
5089   PetscFunctionBegin;
5090   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
5091   if (size == 1) {
5092     ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
5093     if (scall == MAT_INITIAL_MATRIX) {
5094       ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
5095     } else {
5096       ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
5097     }
5098     ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
5099     PetscFunctionReturn(0);
5100   }
5101   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
5102   if (scall == MAT_INITIAL_MATRIX) {
5103     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
5104   }
5105   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
5106   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
5107   PetscFunctionReturn(0);
5108 }
5109 
5110 #undef __FUNCT__
5111 #define __FUNCT__ "MatMPIAIJGetLocalMat"
5112 /*@
5113      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
5114           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
5115           with MatGetSize()
5116 
5117     Not Collective
5118 
5119    Input Parameters:
5120 +    A - the matrix
5121 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5122 
5123    Output Parameter:
5124 .    A_loc - the local sequential matrix generated
5125 
5126     Level: developer
5127 
5128 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
5129 
5130 @*/
5131 PetscErrorCode  MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
5132 {
5133   PetscErrorCode ierr;
5134   Mat_MPIAIJ     *mpimat=(Mat_MPIAIJ*)A->data;
5135   Mat_SeqAIJ     *mat,*a=(Mat_SeqAIJ*)(mpimat->A)->data,*b=(Mat_SeqAIJ*)(mpimat->B)->data;
5136   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*cmap=mpimat->garray;
5137   MatScalar      *aa=a->a,*ba=b->a,*cam;
5138   PetscScalar    *ca;
5139   PetscInt       am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
5140   PetscInt       *ci,*cj,col,ncols_d,ncols_o,jo;
5141   PetscBool      match;
5142 
5143   PetscFunctionBegin;
5144   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
5145   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
5146   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
5147   if (scall == MAT_INITIAL_MATRIX) {
5148     ierr  = PetscMalloc((1+am)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
5149     ci[0] = 0;
5150     for (i=0; i<am; i++) {
5151       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
5152     }
5153     ierr = PetscMalloc((1+ci[am])*sizeof(PetscInt),&cj);CHKERRQ(ierr);
5154     ierr = PetscMalloc((1+ci[am])*sizeof(PetscScalar),&ca);CHKERRQ(ierr);
5155     k    = 0;
5156     for (i=0; i<am; i++) {
5157       ncols_o = bi[i+1] - bi[i];
5158       ncols_d = ai[i+1] - ai[i];
5159       /* off-diagonal portion of A */
5160       for (jo=0; jo<ncols_o; jo++) {
5161         col = cmap[*bj];
5162         if (col >= cstart) break;
5163         cj[k]   = col; bj++;
5164         ca[k++] = *ba++;
5165       }
5166       /* diagonal portion of A */
5167       for (j=0; j<ncols_d; j++) {
5168         cj[k]   = cstart + *aj++;
5169         ca[k++] = *aa++;
5170       }
5171       /* off-diagonal portion of A */
5172       for (j=jo; j<ncols_o; j++) {
5173         cj[k]   = cmap[*bj++];
5174         ca[k++] = *ba++;
5175       }
5176     }
5177     /* put together the new matrix */
5178     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
5179     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
5180     /* Since these are PETSc arrays, change flags to free them as necessary. */
5181     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
5182     mat->free_a  = PETSC_TRUE;
5183     mat->free_ij = PETSC_TRUE;
5184     mat->nonew   = 0;
5185   } else if (scall == MAT_REUSE_MATRIX) {
5186     mat=(Mat_SeqAIJ*)(*A_loc)->data;
5187     ci = mat->i; cj = mat->j; cam = mat->a;
5188     for (i=0; i<am; i++) {
5189       /* off-diagonal portion of A */
5190       ncols_o = bi[i+1] - bi[i];
5191       for (jo=0; jo<ncols_o; jo++) {
5192         col = cmap[*bj];
5193         if (col >= cstart) break;
5194         *cam++ = *ba++; bj++;
5195       }
5196       /* diagonal portion of A */
5197       ncols_d = ai[i+1] - ai[i];
5198       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
5199       /* off-diagonal portion of A */
5200       for (j=jo; j<ncols_o; j++) {
5201         *cam++ = *ba++; bj++;
5202       }
5203     }
5204   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
5205   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
5206   PetscFunctionReturn(0);
5207 }
5208 
5209 #undef __FUNCT__
5210 #define __FUNCT__ "MatMPIAIJGetLocalMatCondensed"
5211 /*@C
5212      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MPIAIJ matrix by taking all its local rows and NON-ZERO columns
5213 
5214     Not Collective
5215 
5216    Input Parameters:
5217 +    A - the matrix
5218 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5219 -    row, col - index sets of rows and columns to extract (or NULL)
5220 
5221    Output Parameter:
5222 .    A_loc - the local sequential matrix generated
5223 
5224     Level: developer
5225 
5226 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
5227 
5228 @*/
5229 PetscErrorCode  MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
5230 {
5231   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
5232   PetscErrorCode ierr;
5233   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
5234   IS             isrowa,iscola;
5235   Mat            *aloc;
5236   PetscBool      match;
5237 
5238   PetscFunctionBegin;
5239   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
5240   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
5241   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
5242   if (!row) {
5243     start = A->rmap->rstart; end = A->rmap->rend;
5244     ierr  = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
5245   } else {
5246     isrowa = *row;
5247   }
5248   if (!col) {
5249     start = A->cmap->rstart;
5250     cmap  = a->garray;
5251     nzA   = a->A->cmap->n;
5252     nzB   = a->B->cmap->n;
5253     ierr  = PetscMalloc((nzA+nzB)*sizeof(PetscInt), &idx);CHKERRQ(ierr);
5254     ncols = 0;
5255     for (i=0; i<nzB; i++) {
5256       if (cmap[i] < start) idx[ncols++] = cmap[i];
5257       else break;
5258     }
5259     imark = i;
5260     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
5261     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
5262     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
5263   } else {
5264     iscola = *col;
5265   }
5266   if (scall != MAT_INITIAL_MATRIX) {
5267     ierr    = PetscMalloc(sizeof(Mat),&aloc);CHKERRQ(ierr);
5268     aloc[0] = *A_loc;
5269   }
5270   ierr   = MatGetSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
5271   *A_loc = aloc[0];
5272   ierr   = PetscFree(aloc);CHKERRQ(ierr);
5273   if (!row) {
5274     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
5275   }
5276   if (!col) {
5277     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
5278   }
5279   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
5280   PetscFunctionReturn(0);
5281 }
5282 
5283 #undef __FUNCT__
5284 #define __FUNCT__ "MatGetBrowsOfAcols"
5285 /*@C
5286     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
5287 
5288     Collective on Mat
5289 
5290    Input Parameters:
5291 +    A,B - the matrices in mpiaij format
5292 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5293 -    rowb, colb - index sets of rows and columns of B to extract (or NULL)
5294 
5295    Output Parameter:
5296 +    rowb, colb - index sets of rows and columns of B to extract
5297 -    B_seq - the sequential matrix generated
5298 
5299     Level: developer
5300 
5301 @*/
5302 PetscErrorCode  MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
5303 {
5304   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
5305   PetscErrorCode ierr;
5306   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
5307   IS             isrowb,iscolb;
5308   Mat            *bseq=NULL;
5309 
5310   PetscFunctionBegin;
5311   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
5312     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);
5313   }
5314   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
5315 
5316   if (scall == MAT_INITIAL_MATRIX) {
5317     start = A->cmap->rstart;
5318     cmap  = a->garray;
5319     nzA   = a->A->cmap->n;
5320     nzB   = a->B->cmap->n;
5321     ierr  = PetscMalloc((nzA+nzB)*sizeof(PetscInt), &idx);CHKERRQ(ierr);
5322     ncols = 0;
5323     for (i=0; i<nzB; i++) {  /* row < local row index */
5324       if (cmap[i] < start) idx[ncols++] = cmap[i];
5325       else break;
5326     }
5327     imark = i;
5328     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
5329     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
5330     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
5331     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
5332   } else {
5333     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
5334     isrowb  = *rowb; iscolb = *colb;
5335     ierr    = PetscMalloc(sizeof(Mat),&bseq);CHKERRQ(ierr);
5336     bseq[0] = *B_seq;
5337   }
5338   ierr   = MatGetSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
5339   *B_seq = bseq[0];
5340   ierr   = PetscFree(bseq);CHKERRQ(ierr);
5341   if (!rowb) {
5342     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
5343   } else {
5344     *rowb = isrowb;
5345   }
5346   if (!colb) {
5347     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
5348   } else {
5349     *colb = iscolb;
5350   }
5351   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
5352   PetscFunctionReturn(0);
5353 }
5354 
5355 #undef __FUNCT__
5356 #define __FUNCT__ "MatGetBrowsOfAoCols_MPIAIJ"
5357 /*
5358     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
5359     of the OFF-DIAGONAL portion of local A
5360 
5361     Collective on Mat
5362 
5363    Input Parameters:
5364 +    A,B - the matrices in mpiaij format
5365 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5366 
5367    Output Parameter:
5368 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
5369 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
5370 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
5371 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
5372 
5373     Level: developer
5374 
5375 */
5376 PetscErrorCode  MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
5377 {
5378   VecScatter_MPI_General *gen_to,*gen_from;
5379   PetscErrorCode         ierr;
5380   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
5381   Mat_SeqAIJ             *b_oth;
5382   VecScatter             ctx =a->Mvctx;
5383   MPI_Comm               comm;
5384   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
5385   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
5386   PetscScalar            *rvalues,*svalues;
5387   MatScalar              *b_otha,*bufa,*bufA;
5388   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
5389   MPI_Request            *rwaits = NULL,*swaits = NULL;
5390   MPI_Status             *sstatus,rstatus;
5391   PetscMPIInt            jj;
5392   PetscInt               *cols,sbs,rbs;
5393   PetscScalar            *vals;
5394 
5395   PetscFunctionBegin;
5396   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
5397   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
5398     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);
5399   }
5400   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5401   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
5402 
5403   gen_to   = (VecScatter_MPI_General*)ctx->todata;
5404   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
5405   rvalues  = gen_from->values; /* holds the length of receiving row */
5406   svalues  = gen_to->values;   /* holds the length of sending row */
5407   nrecvs   = gen_from->n;
5408   nsends   = gen_to->n;
5409 
5410   ierr    = PetscMalloc2(nrecvs,MPI_Request,&rwaits,nsends,MPI_Request,&swaits);CHKERRQ(ierr);
5411   srow    = gen_to->indices;    /* local row index to be sent */
5412   sstarts = gen_to->starts;
5413   sprocs  = gen_to->procs;
5414   sstatus = gen_to->sstatus;
5415   sbs     = gen_to->bs;
5416   rstarts = gen_from->starts;
5417   rprocs  = gen_from->procs;
5418   rbs     = gen_from->bs;
5419 
5420   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
5421   if (scall == MAT_INITIAL_MATRIX) {
5422     /* i-array */
5423     /*---------*/
5424     /*  post receives */
5425     for (i=0; i<nrecvs; i++) {
5426       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
5427       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
5428       ierr   = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5429     }
5430 
5431     /* pack the outgoing message */
5432     ierr = PetscMalloc2(nsends+1,PetscInt,&sstartsj,nrecvs+1,PetscInt,&rstartsj);CHKERRQ(ierr);
5433 
5434     sstartsj[0] = 0;
5435     rstartsj[0] = 0;
5436     len         = 0; /* total length of j or a array to be sent */
5437     k           = 0;
5438     for (i=0; i<nsends; i++) {
5439       rowlen = (PetscInt*)svalues + sstarts[i]*sbs;
5440       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
5441       for (j=0; j<nrows; j++) {
5442         row = srow[k] + B->rmap->range[rank]; /* global row idx */
5443         for (l=0; l<sbs; l++) {
5444           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr); /* rowlength */
5445 
5446           rowlen[j*sbs+l] = ncols;
5447 
5448           len += ncols;
5449           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr);
5450         }
5451         k++;
5452       }
5453       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5454 
5455       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
5456     }
5457     /* recvs and sends of i-array are completed */
5458     i = nrecvs;
5459     while (i--) {
5460       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5461     }
5462     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5463 
5464     /* allocate buffers for sending j and a arrays */
5465     ierr = PetscMalloc((len+1)*sizeof(PetscInt),&bufj);CHKERRQ(ierr);
5466     ierr = PetscMalloc((len+1)*sizeof(PetscScalar),&bufa);CHKERRQ(ierr);
5467 
5468     /* create i-array of B_oth */
5469     ierr = PetscMalloc((aBn+2)*sizeof(PetscInt),&b_othi);CHKERRQ(ierr);
5470 
5471     b_othi[0] = 0;
5472     len       = 0; /* total length of j or a array to be received */
5473     k         = 0;
5474     for (i=0; i<nrecvs; i++) {
5475       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
5476       nrows  = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be recieved */
5477       for (j=0; j<nrows; j++) {
5478         b_othi[k+1] = b_othi[k] + rowlen[j];
5479         len        += rowlen[j]; k++;
5480       }
5481       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
5482     }
5483 
5484     /* allocate space for j and a arrrays of B_oth */
5485     ierr = PetscMalloc((b_othi[aBn]+1)*sizeof(PetscInt),&b_othj);CHKERRQ(ierr);
5486     ierr = PetscMalloc((b_othi[aBn]+1)*sizeof(MatScalar),&b_otha);CHKERRQ(ierr);
5487 
5488     /* j-array */
5489     /*---------*/
5490     /*  post receives of j-array */
5491     for (i=0; i<nrecvs; i++) {
5492       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5493       ierr  = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5494     }
5495 
5496     /* pack the outgoing message j-array */
5497     k = 0;
5498     for (i=0; i<nsends; i++) {
5499       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5500       bufJ  = bufj+sstartsj[i];
5501       for (j=0; j<nrows; j++) {
5502         row = srow[k++] + B->rmap->range[rank];  /* global row idx */
5503         for (ll=0; ll<sbs; ll++) {
5504           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
5505           for (l=0; l<ncols; l++) {
5506             *bufJ++ = cols[l];
5507           }
5508           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
5509         }
5510       }
5511       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5512     }
5513 
5514     /* recvs and sends of j-array are completed */
5515     i = nrecvs;
5516     while (i--) {
5517       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5518     }
5519     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5520   } else if (scall == MAT_REUSE_MATRIX) {
5521     sstartsj = *startsj_s;
5522     rstartsj = *startsj_r;
5523     bufa     = *bufa_ptr;
5524     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
5525     b_otha   = b_oth->a;
5526   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
5527 
5528   /* a-array */
5529   /*---------*/
5530   /*  post receives of a-array */
5531   for (i=0; i<nrecvs; i++) {
5532     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5533     ierr  = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5534   }
5535 
5536   /* pack the outgoing message a-array */
5537   k = 0;
5538   for (i=0; i<nsends; i++) {
5539     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5540     bufA  = bufa+sstartsj[i];
5541     for (j=0; j<nrows; j++) {
5542       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
5543       for (ll=0; ll<sbs; ll++) {
5544         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
5545         for (l=0; l<ncols; l++) {
5546           *bufA++ = vals[l];
5547         }
5548         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
5549       }
5550     }
5551     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5552   }
5553   /* recvs and sends of a-array are completed */
5554   i = nrecvs;
5555   while (i--) {
5556     ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5557   }
5558   if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5559   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
5560 
5561   if (scall == MAT_INITIAL_MATRIX) {
5562     /* put together the new matrix */
5563     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
5564 
5565     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
5566     /* Since these are PETSc arrays, change flags to free them as necessary. */
5567     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
5568     b_oth->free_a  = PETSC_TRUE;
5569     b_oth->free_ij = PETSC_TRUE;
5570     b_oth->nonew   = 0;
5571 
5572     ierr = PetscFree(bufj);CHKERRQ(ierr);
5573     if (!startsj_s || !bufa_ptr) {
5574       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
5575       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
5576     } else {
5577       *startsj_s = sstartsj;
5578       *startsj_r = rstartsj;
5579       *bufa_ptr  = bufa;
5580     }
5581   }
5582   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5583   PetscFunctionReturn(0);
5584 }
5585 
5586 #undef __FUNCT__
5587 #define __FUNCT__ "MatGetCommunicationStructs"
5588 /*@C
5589   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
5590 
5591   Not Collective
5592 
5593   Input Parameters:
5594 . A - The matrix in mpiaij format
5595 
5596   Output Parameter:
5597 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
5598 . colmap - A map from global column index to local index into lvec
5599 - multScatter - A scatter from the argument of a matrix-vector product to lvec
5600 
5601   Level: developer
5602 
5603 @*/
5604 #if defined(PETSC_USE_CTABLE)
5605 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
5606 #else
5607 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
5608 #endif
5609 {
5610   Mat_MPIAIJ *a;
5611 
5612   PetscFunctionBegin;
5613   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
5614   PetscValidPointer(lvec, 2);
5615   PetscValidPointer(colmap, 3);
5616   PetscValidPointer(multScatter, 4);
5617   a = (Mat_MPIAIJ*) A->data;
5618   if (lvec) *lvec = a->lvec;
5619   if (colmap) *colmap = a->colmap;
5620   if (multScatter) *multScatter = a->Mvctx;
5621   PetscFunctionReturn(0);
5622 }
5623 
5624 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
5625 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
5626 PETSC_EXTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
5627 
5628 #undef __FUNCT__
5629 #define __FUNCT__ "MatMatMultNumeric_MPIDense_MPIAIJ"
5630 /*
5631     Computes (B'*A')' since computing B*A directly is untenable
5632 
5633                n                       p                          p
5634         (              )       (              )         (                  )
5635       m (      A       )  *  n (       B      )   =   m (         C        )
5636         (              )       (              )         (                  )
5637 
5638 */
5639 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
5640 {
5641   PetscErrorCode ierr;
5642   Mat            At,Bt,Ct;
5643 
5644   PetscFunctionBegin;
5645   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
5646   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
5647   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
5648   ierr = MatDestroy(&At);CHKERRQ(ierr);
5649   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
5650   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
5651   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
5652   PetscFunctionReturn(0);
5653 }
5654 
5655 #undef __FUNCT__
5656 #define __FUNCT__ "MatMatMultSymbolic_MPIDense_MPIAIJ"
5657 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
5658 {
5659   PetscErrorCode ierr;
5660   PetscInt       m=A->rmap->n,n=B->cmap->n;
5661   Mat            Cmat;
5662 
5663   PetscFunctionBegin;
5664   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);
5665   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
5666   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
5667   ierr = MatSetBlockSizes(Cmat,A->rmap->bs,B->cmap->bs);CHKERRQ(ierr);
5668   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
5669   ierr = MatMPIDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
5670   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5671   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5672 
5673   Cmat->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
5674 
5675   *C = Cmat;
5676   PetscFunctionReturn(0);
5677 }
5678 
5679 /* ----------------------------------------------------------------*/
5680 #undef __FUNCT__
5681 #define __FUNCT__ "MatMatMult_MPIDense_MPIAIJ"
5682 PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
5683 {
5684   PetscErrorCode ierr;
5685 
5686   PetscFunctionBegin;
5687   if (scall == MAT_INITIAL_MATRIX) {
5688     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5689     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
5690     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5691   }
5692   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5693   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
5694   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5695   PetscFunctionReturn(0);
5696 }
5697 
5698 #if defined(PETSC_HAVE_MUMPS)
5699 PETSC_EXTERN PetscErrorCode MatGetFactor_aij_mumps(Mat,MatFactorType,Mat*);
5700 #endif
5701 #if defined(PETSC_HAVE_PASTIX)
5702 PETSC_EXTERN PetscErrorCode MatGetFactor_mpiaij_pastix(Mat,MatFactorType,Mat*);
5703 #endif
5704 #if defined(PETSC_HAVE_SUPERLU_DIST)
5705 PETSC_EXTERN PetscErrorCode MatGetFactor_mpiaij_superlu_dist(Mat,MatFactorType,Mat*);
5706 #endif
5707 #if defined(PETSC_HAVE_CLIQUE)
5708 PETSC_EXTERN PetscErrorCode MatGetFactor_aij_clique(Mat,MatFactorType,Mat*);
5709 #endif
5710 
5711 /*MC
5712    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
5713 
5714    Options Database Keys:
5715 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
5716 
5717   Level: beginner
5718 
5719 .seealso: MatCreateAIJ()
5720 M*/
5721 
5722 #undef __FUNCT__
5723 #define __FUNCT__ "MatCreate_MPIAIJ"
5724 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
5725 {
5726   Mat_MPIAIJ     *b;
5727   PetscErrorCode ierr;
5728   PetscMPIInt    size;
5729 
5730   PetscFunctionBegin;
5731   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
5732 
5733   ierr          = PetscNewLog(B,Mat_MPIAIJ,&b);CHKERRQ(ierr);
5734   B->data       = (void*)b;
5735   ierr          = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
5736   B->assembled  = PETSC_FALSE;
5737   B->insertmode = NOT_SET_VALUES;
5738   b->size       = size;
5739 
5740   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank);CHKERRQ(ierr);
5741 
5742   /* build cache for off array entries formed */
5743   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash);CHKERRQ(ierr);
5744 
5745   b->donotstash  = PETSC_FALSE;
5746   b->colmap      = 0;
5747   b->garray      = 0;
5748   b->roworiented = PETSC_TRUE;
5749 
5750   /* stuff used for matrix vector multiply */
5751   b->lvec  = NULL;
5752   b->Mvctx = NULL;
5753 
5754   /* stuff for MatGetRow() */
5755   b->rowindices   = 0;
5756   b->rowvalues    = 0;
5757   b->getrowactive = PETSC_FALSE;
5758 
5759   /* flexible pointer used in CUSP/CUSPARSE classes */
5760   b->spptr = NULL;
5761 
5762 #if defined(PETSC_HAVE_MUMPS)
5763   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_mumps_C",MatGetFactor_aij_mumps);CHKERRQ(ierr);
5764 #endif
5765 #if defined(PETSC_HAVE_PASTIX)
5766   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_pastix_C",MatGetFactor_mpiaij_pastix);CHKERRQ(ierr);
5767 #endif
5768 #if defined(PETSC_HAVE_SUPERLU_DIST)
5769   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_superlu_dist_C",MatGetFactor_mpiaij_superlu_dist);CHKERRQ(ierr);
5770 #endif
5771 #if defined(PETSC_HAVE_CLIQUE)
5772   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_clique_C",MatGetFactor_aij_clique);CHKERRQ(ierr);
5773 #endif
5774   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ);CHKERRQ(ierr);
5775   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
5776   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetDiagonalBlock_C",MatGetDiagonalBlock_MPIAIJ);CHKERRQ(ierr);
5777   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
5778   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
5779   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
5780   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
5781   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
5782   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
5783   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
5784   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
5785   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
5786   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
5787   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
5788   PetscFunctionReturn(0);
5789 }
5790 
5791 #undef __FUNCT__
5792 #define __FUNCT__ "MatCreateMPIAIJWithSplitArrays"
5793 /*@
5794      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
5795          and "off-diagonal" part of the matrix in CSR format.
5796 
5797    Collective on MPI_Comm
5798 
5799    Input Parameters:
5800 +  comm - MPI communicator
5801 .  m - number of local rows (Cannot be PETSC_DECIDE)
5802 .  n - This value should be the same as the local size used in creating the
5803        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
5804        calculated if N is given) For square matrices n is almost always m.
5805 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
5806 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
5807 .   i - row indices for "diagonal" portion of matrix
5808 .   j - column indices
5809 .   a - matrix values
5810 .   oi - row indices for "off-diagonal" portion of matrix
5811 .   oj - column indices
5812 -   oa - matrix values
5813 
5814    Output Parameter:
5815 .   mat - the matrix
5816 
5817    Level: advanced
5818 
5819    Notes:
5820        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
5821        must free the arrays once the matrix has been destroyed and not before.
5822 
5823        The i and j indices are 0 based
5824 
5825        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
5826 
5827        This sets local rows and cannot be used to set off-processor values.
5828 
5829        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
5830        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
5831        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
5832        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
5833        keep track of the underlying array. Use MatSetOption(A,MAT_IGNORE_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
5834        communication if it is known that only local entries will be set.
5835 
5836 .keywords: matrix, aij, compressed row, sparse, parallel
5837 
5838 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
5839           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
5840 @*/
5841 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)
5842 {
5843   PetscErrorCode ierr;
5844   Mat_MPIAIJ     *maij;
5845 
5846   PetscFunctionBegin;
5847   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
5848   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
5849   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
5850   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
5851   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
5852   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
5853   maij = (Mat_MPIAIJ*) (*mat)->data;
5854 
5855   (*mat)->preallocated = PETSC_TRUE;
5856 
5857   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
5858   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
5859 
5860   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
5861   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
5862 
5863   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5864   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5865   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5866   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5867 
5868   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5869   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5870   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
5871   PetscFunctionReturn(0);
5872 }
5873 
5874 /*
5875     Special version for direct calls from Fortran
5876 */
5877 #include <petsc-private/fortranimpl.h>
5878 
5879 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5880 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
5881 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5882 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
5883 #endif
5884 
5885 /* Change these macros so can be used in void function */
5886 #undef CHKERRQ
5887 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
5888 #undef SETERRQ2
5889 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5890 #undef SETERRQ3
5891 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5892 #undef SETERRQ
5893 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
5894 
5895 #undef __FUNCT__
5896 #define __FUNCT__ "matsetvaluesmpiaij_"
5897 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)
5898 {
5899   Mat            mat  = *mmat;
5900   PetscInt       m    = *mm, n = *mn;
5901   InsertMode     addv = *maddv;
5902   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
5903   PetscScalar    value;
5904   PetscErrorCode ierr;
5905 
5906   MatCheckPreallocated(mat,1);
5907   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
5908 
5909 #if defined(PETSC_USE_DEBUG)
5910   else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
5911 #endif
5912   {
5913     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
5914     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
5915     PetscBool roworiented = aij->roworiented;
5916 
5917     /* Some Variables required in the macro */
5918     Mat        A                 = aij->A;
5919     Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
5920     PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
5921     MatScalar  *aa               = a->a;
5922     PetscBool  ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
5923     Mat        B                 = aij->B;
5924     Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
5925     PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5926     MatScalar  *ba               = b->a;
5927 
5928     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5929     PetscInt  nonew = a->nonew;
5930     MatScalar *ap1,*ap2;
5931 
5932     PetscFunctionBegin;
5933     for (i=0; i<m; i++) {
5934       if (im[i] < 0) continue;
5935 #if defined(PETSC_USE_DEBUG)
5936       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);
5937 #endif
5938       if (im[i] >= rstart && im[i] < rend) {
5939         row      = im[i] - rstart;
5940         lastcol1 = -1;
5941         rp1      = aj + ai[row];
5942         ap1      = aa + ai[row];
5943         rmax1    = aimax[row];
5944         nrow1    = ailen[row];
5945         low1     = 0;
5946         high1    = nrow1;
5947         lastcol2 = -1;
5948         rp2      = bj + bi[row];
5949         ap2      = ba + bi[row];
5950         rmax2    = bimax[row];
5951         nrow2    = bilen[row];
5952         low2     = 0;
5953         high2    = nrow2;
5954 
5955         for (j=0; j<n; j++) {
5956           if (roworiented) value = v[i*n+j];
5957           else value = v[i+j*m];
5958           if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES)) continue;
5959           if (in[j] >= cstart && in[j] < cend) {
5960             col = in[j] - cstart;
5961             MatSetValues_SeqAIJ_A_Private(row,col,value,addv);
5962           } else if (in[j] < 0) continue;
5963 #if defined(PETSC_USE_DEBUG)
5964           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);
5965 #endif
5966           else {
5967             if (mat->was_assembled) {
5968               if (!aij->colmap) {
5969                 ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5970               }
5971 #if defined(PETSC_USE_CTABLE)
5972               ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5973               col--;
5974 #else
5975               col = aij->colmap[in[j]] - 1;
5976 #endif
5977               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5978                 ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5979                 col  =  in[j];
5980                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5981                 B     = aij->B;
5982                 b     = (Mat_SeqAIJ*)B->data;
5983                 bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5984                 rp2   = bj + bi[row];
5985                 ap2   = ba + bi[row];
5986                 rmax2 = bimax[row];
5987                 nrow2 = bilen[row];
5988                 low2  = 0;
5989                 high2 = nrow2;
5990                 bm    = aij->B->rmap->n;
5991                 ba    = b->a;
5992               }
5993             } else col = in[j];
5994             MatSetValues_SeqAIJ_B_Private(row,col,value,addv);
5995           }
5996         }
5997       } else if (!aij->donotstash) {
5998         if (roworiented) {
5999           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
6000         } else {
6001           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
6002         }
6003       }
6004     }
6005   }
6006   PetscFunctionReturnVoid();
6007 }
6008 
6009