xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision 5b0d26cfbf6ed9982f633be5fbebf5c618cfd10c)
1 
2 #include <../src/mat/impls/aij/mpi/mpiaij.h>   /*I "petscmat.h" I*/
3 #include <petscblaslapack.h>
4 
5 /*MC
6    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.
7 
8    This matrix type is identical to MATSEQAIJ when constructed with a single process communicator,
9    and MATMPIAIJ otherwise.  As a result, for single process communicators,
10   MatSeqAIJSetPreallocation is supported, and similarly MatMPIAIJSetPreallocation is supported
11   for communicators controlling multiple processes.  It is recommended that you call both of
12   the above preallocation routines for simplicity.
13 
14    Options Database Keys:
15 . -mat_type aij - sets the matrix type to "aij" during a call to MatSetFromOptions()
16 
17   Developer Notes: Subclasses include MATAIJCUSP, MATAIJPERM, MATAIJCRL, and also automatically switches over to use inodes when
18    enough exist.
19 
20   Level: beginner
21 
22 .seealso: MatCreateAIJ(), MatCreateSeqAIJ(), MATSEQAIJ,MATMPIAIJ
23 M*/
24 
25 /*MC
26    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.
27 
28    This matrix type is identical to MATSEQAIJCRL when constructed with a single process communicator,
29    and MATMPIAIJCRL otherwise.  As a result, for single process communicators,
30    MatSeqAIJSetPreallocation() is supported, and similarly MatMPIAIJSetPreallocation() is supported
31   for communicators controlling multiple processes.  It is recommended that you call both of
32   the above preallocation routines for simplicity.
33 
34    Options Database Keys:
35 . -mat_type aijcrl - sets the matrix type to "aijcrl" during a call to MatSetFromOptions()
36 
37   Level: beginner
38 
39 .seealso: MatCreateMPIAIJCRL,MATSEQAIJCRL,MATMPIAIJCRL, MATSEQAIJCRL, MATMPIAIJCRL
40 M*/
41 
42 #undef __FUNCT__
43 #define __FUNCT__ "MatFindNonZeroRows_MPIAIJ"
44 PetscErrorCode MatFindNonZeroRows_MPIAIJ(Mat M,IS *keptrows)
45 {
46   PetscErrorCode  ierr;
47   Mat_MPIAIJ      *mat = (Mat_MPIAIJ*)M->data;
48   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)mat->A->data;
49   Mat_SeqAIJ      *b = (Mat_SeqAIJ*)mat->B->data;
50   const PetscInt  *ia,*ib;
51   const MatScalar *aa,*bb;
52   PetscInt        na,nb,i,j,*rows,cnt=0,n0rows;
53   PetscInt        m = M->rmap->n,rstart = M->rmap->rstart;
54 
55   PetscFunctionBegin;
56   *keptrows = 0;
57   ia = a->i;
58   ib = b->i;
59   for (i=0; i<m; i++) {
60     na = ia[i+1] - ia[i];
61     nb = ib[i+1] - ib[i];
62     if (!na && !nb) {
63       cnt++;
64       goto ok1;
65     }
66     aa = a->a + ia[i];
67     for (j=0; j<na; j++) {
68       if (aa[j] != 0.0) goto ok1;
69     }
70     bb = b->a + ib[i];
71     for (j=0; j <nb; j++) {
72       if (bb[j] != 0.0) goto ok1;
73     }
74     cnt++;
75     ok1:;
76   }
77   ierr = MPI_Allreduce(&cnt,&n0rows,1,MPIU_INT,MPI_SUM,((PetscObject)M)->comm);CHKERRQ(ierr);
78   if (!n0rows) PetscFunctionReturn(0);
79   ierr = PetscMalloc((M->rmap->n-cnt)*sizeof(PetscInt),&rows);CHKERRQ(ierr);
80   cnt = 0;
81   for (i=0; i<m; i++) {
82     na = ia[i+1] - ia[i];
83     nb = ib[i+1] - ib[i];
84     if (!na && !nb) continue;
85     aa = a->a + ia[i];
86     for(j=0; j<na;j++) {
87       if (aa[j] != 0.0) {
88         rows[cnt++] = rstart + i;
89         goto ok2;
90       }
91     }
92     bb = b->a + ib[i];
93     for (j=0; j<nb; j++) {
94       if (bb[j] != 0.0) {
95         rows[cnt++] = rstart + i;
96         goto ok2;
97       }
98     }
99     ok2:;
100   }
101   ierr = ISCreateGeneral(((PetscObject)M)->comm,cnt,rows,PETSC_OWN_POINTER,keptrows);CHKERRQ(ierr);
102   PetscFunctionReturn(0);
103 }
104 
105 #undef __FUNCT__
106 #define __FUNCT__ "MatGetColumnNorms_MPIAIJ"
107 PetscErrorCode MatGetColumnNorms_MPIAIJ(Mat A,NormType type,PetscReal *norms)
108 {
109   PetscErrorCode ierr;
110   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)A->data;
111   PetscInt       i,n,*garray = aij->garray;
112   Mat_SeqAIJ     *a_aij = (Mat_SeqAIJ*) aij->A->data;
113   Mat_SeqAIJ     *b_aij = (Mat_SeqAIJ*) aij->B->data;
114   PetscReal      *work;
115 
116   PetscFunctionBegin;
117   ierr = MatGetSize(A,PETSC_NULL,&n);CHKERRQ(ierr);
118   ierr = PetscMalloc(n*sizeof(PetscReal),&work);CHKERRQ(ierr);
119   ierr = PetscMemzero(work,n*sizeof(PetscReal));CHKERRQ(ierr);
120   if (type == NORM_2) {
121     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
122       work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i]*a_aij->a[i]);
123     }
124     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
125       work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]*b_aij->a[i]);
126     }
127   } else if (type == NORM_1) {
128     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
129       work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i]);
130     }
131     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
132       work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]);
133     }
134   } else if (type == NORM_INFINITY) {
135     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
136       work[A->cmap->rstart + a_aij->j[i]] = PetscMax(PetscAbsScalar(a_aij->a[i]), work[A->cmap->rstart + a_aij->j[i]]);
137     }
138     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
139       work[garray[b_aij->j[i]]] = PetscMax(PetscAbsScalar(b_aij->a[i]),work[garray[b_aij->j[i]]]);
140     }
141 
142   } else SETERRQ(((PetscObject)A)->comm,PETSC_ERR_ARG_WRONG,"Unknown NormType");
143   if (type == NORM_INFINITY) {
144     ierr = MPI_Allreduce(work,norms,n,MPIU_REAL,MPIU_MAX,A->hdr.comm);CHKERRQ(ierr);
145   } else {
146     ierr = MPI_Allreduce(work,norms,n,MPIU_REAL,MPIU_SUM,A->hdr.comm);CHKERRQ(ierr);
147   }
148   ierr = PetscFree(work);CHKERRQ(ierr);
149   if (type == NORM_2) {
150     for (i=0; i<n; i++) norms[i] = PetscSqrtReal(norms[i]);
151   }
152   PetscFunctionReturn(0);
153 }
154 
155 #undef __FUNCT__
156 #define __FUNCT__ "MatDistribute_MPIAIJ"
157 /*
158     Distributes a SeqAIJ matrix across a set of processes. Code stolen from
159     MatLoad_MPIAIJ(). Horrible lack of reuse. Should be a routine for each matrix type.
160 
161     Only for square matrices
162 */
163 PetscErrorCode MatDistribute_MPIAIJ(MPI_Comm comm,Mat gmat,PetscInt m,MatReuse reuse,Mat *inmat)
164 {
165   PetscMPIInt    rank,size;
166   PetscInt       *rowners,*dlens,*olens,i,rstart,rend,j,jj,nz,*gmataj,cnt,row,*ld;
167   PetscErrorCode ierr;
168   Mat            mat;
169   Mat_SeqAIJ     *gmata;
170   PetscMPIInt    tag;
171   MPI_Status     status;
172   PetscBool      aij;
173   MatScalar      *gmataa,*ao,*ad,*gmataarestore=0;
174 
175   PetscFunctionBegin;
176   CHKMEMQ;
177   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
178   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
179   if (!rank) {
180     ierr = PetscObjectTypeCompare((PetscObject)gmat,MATSEQAIJ,&aij);CHKERRQ(ierr);
181     if (!aij) SETERRQ1(((PetscObject)gmat)->comm,PETSC_ERR_SUP,"Currently no support for input matrix of type %s\n",((PetscObject)gmat)->type_name);
182   }
183   if (reuse == MAT_INITIAL_MATRIX) {
184     ierr = MatCreate(comm,&mat);CHKERRQ(ierr);
185     ierr = MatSetSizes(mat,m,m,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
186     ierr = MatSetBlockSizes(mat,gmat->rmap->bs,gmat->cmap->bs);CHKERRQ(ierr);
187     ierr = MatSetType(mat,MATAIJ);CHKERRQ(ierr);
188     ierr = PetscMalloc((size+1)*sizeof(PetscInt),&rowners);CHKERRQ(ierr);
189     ierr = PetscMalloc2(m,PetscInt,&dlens,m,PetscInt,&olens);CHKERRQ(ierr);
190     ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
191     rowners[0] = 0;
192     for (i=2; i<=size; i++) {
193       rowners[i] += rowners[i-1];
194     }
195     rstart = rowners[rank];
196     rend   = rowners[rank+1];
197     ierr   = PetscObjectGetNewTag((PetscObject)mat,&tag);CHKERRQ(ierr);
198     if (!rank) {
199       gmata = (Mat_SeqAIJ*) gmat->data;
200       /* send row lengths to all processors */
201       for (i=0; i<m; i++) dlens[i] = gmata->ilen[i];
202       for (i=1; i<size; i++) {
203 	ierr = MPI_Send(gmata->ilen + rowners[i],rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
204       }
205       /* determine number diagonal and off-diagonal counts */
206       ierr = PetscMemzero(olens,m*sizeof(PetscInt));CHKERRQ(ierr);
207       ierr = PetscMalloc(m*sizeof(PetscInt),&ld);CHKERRQ(ierr);
208       ierr = PetscMemzero(ld,m*sizeof(PetscInt));CHKERRQ(ierr);
209       jj = 0;
210       for (i=0; i<m; i++) {
211 	for (j=0; j<dlens[i]; j++) {
212           if (gmata->j[jj] < rstart) ld[i]++;
213 	  if (gmata->j[jj] < rstart || gmata->j[jj] >= rend) olens[i]++;
214 	  jj++;
215 	}
216       }
217       /* send column indices to other processes */
218       for (i=1; i<size; i++) {
219 	nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
220 	ierr = MPI_Send(&nz,1,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
221 	ierr = MPI_Send(gmata->j + gmata->i[rowners[i]],nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
222       }
223 
224       /* send numerical values to other processes */
225       for (i=1; i<size; i++) {
226         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
227         ierr = MPI_Send(gmata->a + gmata->i[rowners[i]],nz,MPIU_SCALAR,i,tag,comm);CHKERRQ(ierr);
228       }
229       gmataa = gmata->a;
230       gmataj = gmata->j;
231 
232     } else {
233       /* receive row lengths */
234       ierr = MPI_Recv(dlens,m,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
235       /* receive column indices */
236       ierr = MPI_Recv(&nz,1,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
237       ierr = PetscMalloc2(nz,PetscScalar,&gmataa,nz,PetscInt,&gmataj);CHKERRQ(ierr);
238       ierr = MPI_Recv(gmataj,nz,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
239       /* determine number diagonal and off-diagonal counts */
240       ierr = PetscMemzero(olens,m*sizeof(PetscInt));CHKERRQ(ierr);
241       ierr = PetscMalloc(m*sizeof(PetscInt),&ld);CHKERRQ(ierr);
242       ierr = PetscMemzero(ld,m*sizeof(PetscInt));CHKERRQ(ierr);
243       jj = 0;
244       for (i=0; i<m; i++) {
245 	for (j=0; j<dlens[i]; j++) {
246           if (gmataj[jj] < rstart) ld[i]++;
247 	  if (gmataj[jj] < rstart || gmataj[jj] >= rend) olens[i]++;
248 	  jj++;
249 	}
250       }
251       /* receive numerical values */
252       ierr = PetscMemzero(gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr);
253       ierr = MPI_Recv(gmataa,nz,MPIU_SCALAR,0,tag,comm,&status);CHKERRQ(ierr);
254     }
255     /* set preallocation */
256     for (i=0; i<m; i++) {
257       dlens[i] -= olens[i];
258     }
259     ierr = MatSeqAIJSetPreallocation(mat,0,dlens);CHKERRQ(ierr);
260     ierr = MatMPIAIJSetPreallocation(mat,0,dlens,0,olens);CHKERRQ(ierr);
261 
262     for (i=0; i<m; i++) {
263       dlens[i] += olens[i];
264     }
265     cnt  = 0;
266     for (i=0; i<m; i++) {
267       row  = rstart + i;
268       ierr = MatSetValues(mat,1,&row,dlens[i],gmataj+cnt,gmataa+cnt,INSERT_VALUES);CHKERRQ(ierr);
269       cnt += dlens[i];
270     }
271     if (rank) {
272       ierr = PetscFree2(gmataa,gmataj);CHKERRQ(ierr);
273     }
274     ierr = PetscFree2(dlens,olens);CHKERRQ(ierr);
275     ierr = PetscFree(rowners);CHKERRQ(ierr);
276     ((Mat_MPIAIJ*)(mat->data))->ld = ld;
277     *inmat = mat;
278   } else {   /* column indices are already set; only need to move over numerical values from process 0 */
279     Mat_SeqAIJ *Ad = (Mat_SeqAIJ*)((Mat_MPIAIJ*)((*inmat)->data))->A->data;
280     Mat_SeqAIJ *Ao = (Mat_SeqAIJ*)((Mat_MPIAIJ*)((*inmat)->data))->B->data;
281     mat   = *inmat;
282     ierr  = PetscObjectGetNewTag((PetscObject)mat,&tag);CHKERRQ(ierr);
283     if (!rank) {
284       /* send numerical values to other processes */
285       gmata = (Mat_SeqAIJ*) gmat->data;
286       ierr   = MatGetOwnershipRanges(mat,(const PetscInt**)&rowners);CHKERRQ(ierr);
287       gmataa = gmata->a;
288       for (i=1; i<size; i++) {
289         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
290         ierr = MPI_Send(gmataa + gmata->i[rowners[i]],nz,MPIU_SCALAR,i,tag,comm);CHKERRQ(ierr);
291       }
292       nz   = gmata->i[rowners[1]]-gmata->i[rowners[0]];
293     } else {
294       /* receive numerical values from process 0*/
295       nz   = Ad->nz + Ao->nz;
296       ierr = PetscMalloc(nz*sizeof(PetscScalar),&gmataa);CHKERRQ(ierr); gmataarestore = gmataa;
297       ierr = MPI_Recv(gmataa,nz,MPIU_SCALAR,0,tag,comm,&status);CHKERRQ(ierr);
298     }
299     /* transfer numerical values into the diagonal A and off diagonal B parts of mat */
300     ld = ((Mat_MPIAIJ*)(mat->data))->ld;
301     ad = Ad->a;
302     ao = Ao->a;
303     if (mat->rmap->n) {
304       i  = 0;
305       nz = ld[i];                                   ierr = PetscMemcpy(ao,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ao += nz; gmataa += nz;
306       nz = Ad->i[i+1] - Ad->i[i];                   ierr = PetscMemcpy(ad,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ad += nz; gmataa += nz;
307     }
308     for (i=1; i<mat->rmap->n; i++) {
309       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;
310       nz = Ad->i[i+1] - Ad->i[i];                   ierr = PetscMemcpy(ad,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ad += nz; gmataa += nz;
311     }
312     i--;
313     if (mat->rmap->n) {
314       nz = Ao->i[i+1] - Ao->i[i] - ld[i];           ierr = PetscMemcpy(ao,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ao += nz; gmataa += nz;
315     }
316     if (rank) {
317       ierr = PetscFree(gmataarestore);CHKERRQ(ierr);
318     }
319   }
320   ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
321   ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
322   CHKMEMQ;
323   PetscFunctionReturn(0);
324 }
325 
326 /*
327   Local utility routine that creates a mapping from the global column
328 number to the local number in the off-diagonal part of the local
329 storage of the matrix.  When PETSC_USE_CTABLE is used this is scalable at
330 a slightly higher hash table cost; without it it is not scalable (each processor
331 has an order N integer array but is fast to acess.
332 */
333 #undef __FUNCT__
334 #define __FUNCT__ "MatCreateColmap_MPIAIJ_Private"
335 PetscErrorCode MatCreateColmap_MPIAIJ_Private(Mat mat)
336 {
337   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
338   PetscErrorCode ierr;
339   PetscInt       n = aij->B->cmap->n,i;
340 
341   PetscFunctionBegin;
342   if (!aij->garray) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"MPIAIJ Matrix was assembled but is missing garray");
343 #if defined (PETSC_USE_CTABLE)
344   ierr = PetscTableCreate(n,mat->cmap->N+1,&aij->colmap);CHKERRQ(ierr);
345   for (i=0; i<n; i++){
346     ierr = PetscTableAdd(aij->colmap,aij->garray[i]+1,i+1,INSERT_VALUES);CHKERRQ(ierr);
347   }
348 #else
349   ierr = PetscMalloc((mat->cmap->N+1)*sizeof(PetscInt),&aij->colmap);CHKERRQ(ierr);
350   ierr = PetscLogObjectMemory(mat,mat->cmap->N*sizeof(PetscInt));CHKERRQ(ierr);
351   ierr = PetscMemzero(aij->colmap,mat->cmap->N*sizeof(PetscInt));CHKERRQ(ierr);
352   for (i=0; i<n; i++) aij->colmap[aij->garray[i]] = i+1;
353 #endif
354   PetscFunctionReturn(0);
355 }
356 
357 #define MatSetValues_SeqAIJ_A_Private(row,col,value,addv) \
358 { \
359     if (col <= lastcol1) low1 = 0; else high1 = nrow1; \
360     lastcol1 = col;\
361     while (high1-low1 > 5) { \
362       t = (low1+high1)/2; \
363       if (rp1[t] > col) high1 = t; \
364       else             low1  = t; \
365     } \
366       for (_i=low1; _i<high1; _i++) { \
367         if (rp1[_i] > col) break; \
368         if (rp1[_i] == col) { \
369           if (addv == ADD_VALUES) ap1[_i] += value;   \
370           else                    ap1[_i] = value; \
371           goto a_noinsert; \
372         } \
373       }  \
374       if (value == 0.0 && ignorezeroentries) {low1 = 0; high1 = nrow1;goto a_noinsert;} \
375       if (nonew == 1) {low1 = 0; high1 = nrow1; goto a_noinsert;}		\
376       if (nonew == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero (%D, %D) into matrix", row, col); \
377       MatSeqXAIJReallocateAIJ(A,am,1,nrow1,row,col,rmax1,aa,ai,aj,rp1,ap1,aimax,nonew,MatScalar); \
378       N = nrow1++ - 1; a->nz++; high1++; \
379       /* shift up all the later entries in this row */ \
380       for (ii=N; ii>=_i; ii--) { \
381         rp1[ii+1] = rp1[ii]; \
382         ap1[ii+1] = ap1[ii]; \
383       } \
384       rp1[_i] = col;  \
385       ap1[_i] = value;  \
386       a_noinsert: ; \
387       ailen[row] = nrow1; \
388 }
389 
390 
391 #define MatSetValues_SeqAIJ_B_Private(row,col,value,addv) \
392 { \
393     if (col <= lastcol2) low2 = 0; else high2 = nrow2; \
394     lastcol2 = col;\
395     while (high2-low2 > 5) { \
396       t = (low2+high2)/2; \
397       if (rp2[t] > col) high2 = t; \
398       else             low2  = t; \
399     } \
400     for (_i=low2; _i<high2; _i++) {		\
401       if (rp2[_i] > col) break;			\
402       if (rp2[_i] == col) {			      \
403 	if (addv == ADD_VALUES) ap2[_i] += value;     \
404 	else                    ap2[_i] = value;      \
405 	goto b_noinsert;			      \
406       }						      \
407     }							      \
408     if (value == 0.0 && ignorezeroentries) {low2 = 0; high2 = nrow2; goto b_noinsert;} \
409     if (nonew == 1) {low2 = 0; high2 = nrow2; goto b_noinsert;}		\
410     if (nonew == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero (%D, %D) into matrix", row, col); \
411     MatSeqXAIJReallocateAIJ(B,bm,1,nrow2,row,col,rmax2,ba,bi,bj,rp2,ap2,bimax,nonew,MatScalar); \
412     N = nrow2++ - 1; b->nz++; high2++;					\
413     /* shift up all the later entries in this row */			\
414     for (ii=N; ii>=_i; ii--) {						\
415       rp2[ii+1] = rp2[ii];						\
416       ap2[ii+1] = ap2[ii];						\
417     }									\
418     rp2[_i] = col;							\
419     ap2[_i] = value;							\
420     b_noinsert: ;								\
421     bilen[row] = nrow2;							\
422 }
423 
424 #undef __FUNCT__
425 #define __FUNCT__ "MatSetValuesRow_MPIAIJ"
426 PetscErrorCode MatSetValuesRow_MPIAIJ(Mat A,PetscInt row,const PetscScalar v[])
427 {
428   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)A->data;
429   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)mat->A->data,*b = (Mat_SeqAIJ*)mat->B->data;
430   PetscErrorCode ierr;
431   PetscInt       l,*garray = mat->garray,diag;
432 
433   PetscFunctionBegin;
434   /* code only works for square matrices A */
435 
436   /* find size of row to the left of the diagonal part */
437   ierr = MatGetOwnershipRange(A,&diag,0);CHKERRQ(ierr);
438   row  = row - diag;
439   for (l=0; l<b->i[row+1]-b->i[row]; l++) {
440     if (garray[b->j[b->i[row]+l]] > diag) break;
441   }
442   ierr = PetscMemcpy(b->a+b->i[row],v,l*sizeof(PetscScalar));CHKERRQ(ierr);
443 
444   /* diagonal part */
445   ierr = PetscMemcpy(a->a+a->i[row],v+l,(a->i[row+1]-a->i[row])*sizeof(PetscScalar));CHKERRQ(ierr);
446 
447   /* right of diagonal part */
448   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);
449   PetscFunctionReturn(0);
450 }
451 
452 #undef __FUNCT__
453 #define __FUNCT__ "MatSetValues_MPIAIJ"
454 PetscErrorCode MatSetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode addv)
455 {
456   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
457   PetscScalar    value;
458   PetscErrorCode ierr;
459   PetscInt       i,j,rstart = mat->rmap->rstart,rend = mat->rmap->rend;
460   PetscInt       cstart = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
461   PetscBool      roworiented = aij->roworiented;
462 
463   /* Some Variables required in the macro */
464   Mat            A = aij->A;
465   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
466   PetscInt       *aimax = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
467   MatScalar      *aa = a->a;
468   PetscBool      ignorezeroentries = a->ignorezeroentries;
469   Mat            B = aij->B;
470   Mat_SeqAIJ     *b = (Mat_SeqAIJ*)B->data;
471   PetscInt       *bimax = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
472   MatScalar      *ba = b->a;
473 
474   PetscInt       *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
475   PetscInt       nonew;
476   MatScalar      *ap1,*ap2;
477 
478   PetscFunctionBegin;
479   if (v) PetscValidScalarPointer(v,6);
480   for (i=0; i<m; i++) {
481     if (im[i] < 0) continue;
482 #if defined(PETSC_USE_DEBUG)
483     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);
484 #endif
485     if (im[i] >= rstart && im[i] < rend) {
486       row      = im[i] - rstart;
487       lastcol1 = -1;
488       rp1      = aj + ai[row];
489       ap1      = aa + ai[row];
490       rmax1    = aimax[row];
491       nrow1    = ailen[row];
492       low1     = 0;
493       high1    = nrow1;
494       lastcol2 = -1;
495       rp2      = bj + bi[row];
496       ap2      = ba + bi[row];
497       rmax2    = bimax[row];
498       nrow2    = bilen[row];
499       low2     = 0;
500       high2    = nrow2;
501 
502       for (j=0; j<n; j++) {
503         if (v) {if (roworiented) value = v[i*n+j]; else value = v[i+j*m];} else value = 0.0;
504         if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES)) continue;
505         if (in[j] >= cstart && in[j] < cend){
506           col = in[j] - cstart;
507           nonew = a->nonew;
508           MatSetValues_SeqAIJ_A_Private(row,col,value,addv);
509         } else if (in[j] < 0) continue;
510 #if defined(PETSC_USE_DEBUG)
511         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);
512 #endif
513         else {
514           if (mat->was_assembled) {
515             if (!aij->colmap) {
516               ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
517             }
518 #if defined (PETSC_USE_CTABLE)
519             ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
520 	    col--;
521 #else
522             col = aij->colmap[in[j]] - 1;
523 #endif
524             if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
525               ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
526               col =  in[j];
527               /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
528               B = aij->B;
529               b = (Mat_SeqAIJ*)B->data;
530               bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j; ba = b->a;
531               rp2      = bj + bi[row];
532               ap2      = ba + bi[row];
533               rmax2    = bimax[row];
534               nrow2    = bilen[row];
535               low2     = 0;
536               high2    = nrow2;
537               bm       = aij->B->rmap->n;
538               ba = b->a;
539             }
540           } else col = in[j];
541           nonew = b->nonew;
542           MatSetValues_SeqAIJ_B_Private(row,col,value,addv);
543         }
544       }
545     } else {
546       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]);
547       if (!aij->donotstash) {
548         mat->assembled = PETSC_FALSE;
549         if (roworiented) {
550           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
551         } else {
552           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
553         }
554       }
555     }
556   }
557   PetscFunctionReturn(0);
558 }
559 
560 #undef __FUNCT__
561 #define __FUNCT__ "MatGetValues_MPIAIJ"
562 PetscErrorCode MatGetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],PetscScalar v[])
563 {
564   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
565   PetscErrorCode ierr;
566   PetscInt       i,j,rstart = mat->rmap->rstart,rend = mat->rmap->rend;
567   PetscInt       cstart = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
568 
569   PetscFunctionBegin;
570   for (i=0; i<m; i++) {
571     if (idxm[i] < 0) continue; /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative row: %D",idxm[i]);*/
572     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);
573     if (idxm[i] >= rstart && idxm[i] < rend) {
574       row = idxm[i] - rstart;
575       for (j=0; j<n; j++) {
576         if (idxn[j] < 0) continue; /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column: %D",idxn[j]); */
577         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);
578         if (idxn[j] >= cstart && idxn[j] < cend){
579           col = idxn[j] - cstart;
580           ierr = MatGetValues(aij->A,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
581         } else {
582           if (!aij->colmap) {
583             ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
584           }
585 #if defined (PETSC_USE_CTABLE)
586           ierr = PetscTableFind(aij->colmap,idxn[j]+1,&col);CHKERRQ(ierr);
587           col --;
588 #else
589           col = aij->colmap[idxn[j]] - 1;
590 #endif
591           if ((col < 0) || (aij->garray[col] != idxn[j])) *(v+i*n+j) = 0.0;
592           else {
593             ierr = MatGetValues(aij->B,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
594           }
595         }
596       }
597     } else {
598       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only local values currently supported");
599     }
600   }
601   PetscFunctionReturn(0);
602 }
603 
604 extern PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat,Vec,Vec);
605 
606 #undef __FUNCT__
607 #define __FUNCT__ "MatAssemblyBegin_MPIAIJ"
608 PetscErrorCode MatAssemblyBegin_MPIAIJ(Mat mat,MatAssemblyType mode)
609 {
610   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
611   PetscErrorCode ierr;
612   PetscInt       nstash,reallocs;
613   InsertMode     addv;
614 
615   PetscFunctionBegin;
616   if (aij->donotstash || mat->nooffprocentries) {
617     PetscFunctionReturn(0);
618   }
619 
620   /* make sure all processors are either in INSERTMODE or ADDMODE */
621   ierr = MPI_Allreduce(&mat->insertmode,&addv,1,MPI_INT,MPI_BOR,((PetscObject)mat)->comm);CHKERRQ(ierr);
622   if (addv == (ADD_VALUES|INSERT_VALUES)) SETERRQ(((PetscObject)mat)->comm,PETSC_ERR_ARG_WRONGSTATE,"Some processors inserted others added");
623   mat->insertmode = addv; /* in case this processor had no cache */
624 
625   ierr = MatStashScatterBegin_Private(mat,&mat->stash,mat->rmap->range);CHKERRQ(ierr);
626   ierr = MatStashGetInfo_Private(&mat->stash,&nstash,&reallocs);CHKERRQ(ierr);
627   ierr = PetscInfo2(aij->A,"Stash has %D entries, uses %D mallocs.\n",nstash,reallocs);CHKERRQ(ierr);
628   PetscFunctionReturn(0);
629 }
630 
631 #undef __FUNCT__
632 #define __FUNCT__ "MatAssemblyEnd_MPIAIJ"
633 PetscErrorCode MatAssemblyEnd_MPIAIJ(Mat mat,MatAssemblyType mode)
634 {
635   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
636   Mat_SeqAIJ     *a=(Mat_SeqAIJ *)aij->A->data;
637   PetscErrorCode ierr;
638   PetscMPIInt    n;
639   PetscInt       i,j,rstart,ncols,flg;
640   PetscInt       *row,*col;
641   PetscBool      other_disassembled;
642   PetscScalar    *val;
643   InsertMode     addv = mat->insertmode;
644 
645   /* do not use 'b = (Mat_SeqAIJ *)aij->B->data' as B can be reset in disassembly */
646   PetscFunctionBegin;
647   if (!aij->donotstash && !mat->nooffprocentries) {
648     while (1) {
649       ierr = MatStashScatterGetMesg_Private(&mat->stash,&n,&row,&col,&val,&flg);CHKERRQ(ierr);
650       if (!flg) break;
651 
652       for (i=0; i<n;) {
653         /* Now identify the consecutive vals belonging to the same row */
654         for (j=i,rstart=row[j]; j<n; j++) { if (row[j] != rstart) break; }
655         if (j < n) ncols = j-i;
656         else       ncols = n-i;
657         /* Now assemble all these values with a single function call */
658         ierr = MatSetValues_MPIAIJ(mat,1,row+i,ncols,col+i,val+i,addv);CHKERRQ(ierr);
659         i = j;
660       }
661     }
662     ierr = MatStashScatterEnd_Private(&mat->stash);CHKERRQ(ierr);
663   }
664   ierr = MatAssemblyBegin(aij->A,mode);CHKERRQ(ierr);
665   ierr = MatAssemblyEnd(aij->A,mode);CHKERRQ(ierr);
666 
667   /* determine if any processor has disassembled, if so we must
668      also disassemble ourselfs, in order that we may reassemble. */
669   /*
670      if nonzero structure of submatrix B cannot change then we know that
671      no processor disassembled thus we can skip this stuff
672   */
673   if (!((Mat_SeqAIJ*)aij->B->data)->nonew)  {
674     ierr = MPI_Allreduce(&mat->was_assembled,&other_disassembled,1,MPI_INT,MPI_PROD,((PetscObject)mat)->comm);CHKERRQ(ierr);
675     if (mat->was_assembled && !other_disassembled) {
676       ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
677     }
678   }
679   if (!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) {
680     ierr = MatSetUpMultiply_MPIAIJ(mat);CHKERRQ(ierr);
681   }
682   ierr = MatSetOption(aij->B,MAT_USE_INODES,PETSC_FALSE);CHKERRQ(ierr);
683   ierr = MatSetOption(aij->B,MAT_CHECK_COMPRESSED_ROW,PETSC_FALSE);CHKERRQ(ierr);
684   ierr = MatAssemblyBegin(aij->B,mode);CHKERRQ(ierr);
685   ierr = MatAssemblyEnd(aij->B,mode);CHKERRQ(ierr);
686 
687   ierr = PetscFree2(aij->rowvalues,aij->rowindices);CHKERRQ(ierr);
688   aij->rowvalues = 0;
689 
690   /* used by MatAXPY() */
691   a->xtoy = 0; ((Mat_SeqAIJ *)aij->B->data)->xtoy = 0;  /* b->xtoy = 0 */
692   a->XtoY = 0; ((Mat_SeqAIJ *)aij->B->data)->XtoY = 0;  /* b->XtoY = 0 */
693 
694   ierr = VecDestroy(&aij->diag);CHKERRQ(ierr);
695   if (a->inode.size) mat->ops->multdiagonalblock = MatMultDiagonalBlock_MPIAIJ;
696   PetscFunctionReturn(0);
697 }
698 
699 #undef __FUNCT__
700 #define __FUNCT__ "MatZeroEntries_MPIAIJ"
701 PetscErrorCode MatZeroEntries_MPIAIJ(Mat A)
702 {
703   Mat_MPIAIJ     *l = (Mat_MPIAIJ*)A->data;
704   PetscErrorCode ierr;
705 
706   PetscFunctionBegin;
707   ierr = MatZeroEntries(l->A);CHKERRQ(ierr);
708   ierr = MatZeroEntries(l->B);CHKERRQ(ierr);
709   PetscFunctionReturn(0);
710 }
711 
712 #undef __FUNCT__
713 #define __FUNCT__ "MatZeroRows_MPIAIJ"
714 PetscErrorCode MatZeroRows_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
715 {
716   Mat_MPIAIJ        *l = (Mat_MPIAIJ*)A->data;
717   PetscErrorCode    ierr;
718   PetscMPIInt       size = l->size,imdex,n,rank = l->rank,tag = ((PetscObject)A)->tag,lastidx = -1;
719   PetscInt          i,*owners = A->rmap->range;
720   PetscInt          *nprocs,j,idx,nsends,row;
721   PetscInt          nmax,*svalues,*starts,*owner,nrecvs;
722   PetscInt          *rvalues,count,base,slen,*source;
723   PetscInt          *lens,*lrows,*values,rstart=A->rmap->rstart;
724   MPI_Comm          comm = ((PetscObject)A)->comm;
725   MPI_Request       *send_waits,*recv_waits;
726   MPI_Status        recv_status,*send_status;
727   const PetscScalar *xx;
728   PetscScalar       *bb;
729 #if defined(PETSC_DEBUG)
730   PetscBool      found = PETSC_FALSE;
731 #endif
732 
733   PetscFunctionBegin;
734   /*  first count number of contributors to each processor */
735   ierr = PetscMalloc(2*size*sizeof(PetscInt),&nprocs);CHKERRQ(ierr);
736   ierr = PetscMemzero(nprocs,2*size*sizeof(PetscInt));CHKERRQ(ierr);
737   ierr = PetscMalloc((N+1)*sizeof(PetscInt),&owner);CHKERRQ(ierr); /* see note*/
738   j = 0;
739   for (i=0; i<N; i++) {
740     if (lastidx > (idx = rows[i])) j = 0;
741     lastidx = idx;
742     for (; j<size; j++) {
743       if (idx >= owners[j] && idx < owners[j+1]) {
744         nprocs[2*j]++;
745         nprocs[2*j+1] = 1;
746         owner[i] = j;
747 #if defined(PETSC_DEBUG)
748         found = PETSC_TRUE;
749 #endif
750         break;
751       }
752     }
753 #if defined(PETSC_DEBUG)
754     if (!found) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Index out of range");
755     found = PETSC_FALSE;
756 #endif
757   }
758   nsends = 0;  for (i=0; i<size; i++) { nsends += nprocs[2*i+1];}
759 
760   if (A->nooffproczerorows) {
761     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");
762     nrecvs = nsends;
763     nmax   = N;
764   } else {
765     /* inform other processors of number of messages and max length*/
766     ierr = PetscMaxSum(comm,nprocs,&nmax,&nrecvs);CHKERRQ(ierr);
767   }
768 
769   /* post receives:   */
770   ierr = PetscMalloc((nrecvs+1)*(nmax+1)*sizeof(PetscInt),&rvalues);CHKERRQ(ierr);
771   ierr = PetscMalloc((nrecvs+1)*sizeof(MPI_Request),&recv_waits);CHKERRQ(ierr);
772   for (i=0; i<nrecvs; i++) {
773     ierr = MPI_Irecv(rvalues+nmax*i,nmax,MPIU_INT,MPI_ANY_SOURCE,tag,comm,recv_waits+i);CHKERRQ(ierr);
774   }
775 
776   /* do sends:
777       1) starts[i] gives the starting index in svalues for stuff going to
778          the ith processor
779   */
780   ierr = PetscMalloc((N+1)*sizeof(PetscInt),&svalues);CHKERRQ(ierr);
781   ierr = PetscMalloc((nsends+1)*sizeof(MPI_Request),&send_waits);CHKERRQ(ierr);
782   ierr = PetscMalloc((size+1)*sizeof(PetscInt),&starts);CHKERRQ(ierr);
783   starts[0] = 0;
784   for (i=1; i<size; i++) { starts[i] = starts[i-1] + nprocs[2*i-2];}
785   for (i=0; i<N; i++) {
786     svalues[starts[owner[i]]++] = rows[i];
787   }
788 
789   starts[0] = 0;
790   for (i=1; i<size+1; i++) { starts[i] = starts[i-1] + nprocs[2*i-2];}
791   count = 0;
792   for (i=0; i<size; i++) {
793     if (nprocs[2*i+1]) {
794       ierr = MPI_Isend(svalues+starts[i],nprocs[2*i],MPIU_INT,i,tag,comm,send_waits+count++);CHKERRQ(ierr);
795     }
796   }
797   ierr = PetscFree(starts);CHKERRQ(ierr);
798 
799   base = owners[rank];
800 
801   /*  wait on receives */
802   ierr   = PetscMalloc2(nrecvs,PetscInt,&lens,nrecvs,PetscInt,&source);CHKERRQ(ierr);
803   count  = nrecvs; slen = 0;
804   while (count) {
805     ierr = MPI_Waitany(nrecvs,recv_waits,&imdex,&recv_status);CHKERRQ(ierr);
806     /* unpack receives into our local space */
807     ierr = MPI_Get_count(&recv_status,MPIU_INT,&n);CHKERRQ(ierr);
808     source[imdex]  = recv_status.MPI_SOURCE;
809     lens[imdex]    = n;
810     slen          += n;
811     count--;
812   }
813   ierr = PetscFree(recv_waits);CHKERRQ(ierr);
814 
815   /* move the data into the send scatter */
816   ierr = PetscMalloc((slen+1)*sizeof(PetscInt),&lrows);CHKERRQ(ierr);
817   count = 0;
818   for (i=0; i<nrecvs; i++) {
819     values = rvalues + i*nmax;
820     for (j=0; j<lens[i]; j++) {
821       lrows[count++] = values[j] - base;
822     }
823   }
824   ierr = PetscFree(rvalues);CHKERRQ(ierr);
825   ierr = PetscFree2(lens,source);CHKERRQ(ierr);
826   ierr = PetscFree(owner);CHKERRQ(ierr);
827   ierr = PetscFree(nprocs);CHKERRQ(ierr);
828 
829   /* fix right hand side if needed */
830   if (x && b) {
831     ierr = VecGetArrayRead(x,&xx);CHKERRQ(ierr);
832     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
833     for (i=0; i<slen; i++) {
834       bb[lrows[i]] = diag*xx[lrows[i]];
835     }
836     ierr = VecRestoreArrayRead(x,&xx);CHKERRQ(ierr);
837     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
838   }
839   /*
840         Zero the required rows. If the "diagonal block" of the matrix
841      is square and the user wishes to set the diagonal we use separate
842      code so that MatSetValues() is not called for each diagonal allocating
843      new memory, thus calling lots of mallocs and slowing things down.
844 
845   */
846   /* must zero l->B before l->A because the (diag) case below may put values into l->B*/
847   ierr = MatZeroRows(l->B,slen,lrows,0.0,0,0);CHKERRQ(ierr);
848   if ((diag != 0.0) && (l->A->rmap->N == l->A->cmap->N)) {
849     ierr = MatZeroRows(l->A,slen,lrows,diag,0,0);CHKERRQ(ierr);
850   } else if (diag != 0.0) {
851     ierr = MatZeroRows(l->A,slen,lrows,0.0,0,0);CHKERRQ(ierr);
852     if (((Mat_SeqAIJ*)l->A->data)->nonew) {
853       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatZeroRows() on rectangular matrices cannot be used with the Mat options\n\
854 MAT_NEW_NONZERO_LOCATIONS,MAT_NEW_NONZERO_LOCATION_ERR,MAT_NEW_NONZERO_ALLOCATION_ERR");
855     }
856     for (i = 0; i < slen; i++) {
857       row  = lrows[i] + rstart;
858       ierr = MatSetValues(A,1,&row,1,&row,&diag,INSERT_VALUES);CHKERRQ(ierr);
859     }
860     ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
861     ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
862   } else {
863     ierr = MatZeroRows(l->A,slen,lrows,0.0,0,0);CHKERRQ(ierr);
864   }
865   ierr = PetscFree(lrows);CHKERRQ(ierr);
866 
867   /* wait on sends */
868   if (nsends) {
869     ierr = PetscMalloc(nsends*sizeof(MPI_Status),&send_status);CHKERRQ(ierr);
870     ierr = MPI_Waitall(nsends,send_waits,send_status);CHKERRQ(ierr);
871     ierr = PetscFree(send_status);CHKERRQ(ierr);
872   }
873   ierr = PetscFree(send_waits);CHKERRQ(ierr);
874   ierr = PetscFree(svalues);CHKERRQ(ierr);
875   PetscFunctionReturn(0);
876 }
877 
878 #undef __FUNCT__
879 #define __FUNCT__ "MatZeroRowsColumns_MPIAIJ"
880 PetscErrorCode MatZeroRowsColumns_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
881 {
882   Mat_MPIAIJ        *l = (Mat_MPIAIJ*)A->data;
883   PetscErrorCode    ierr;
884   PetscMPIInt       size = l->size,imdex,n,rank = l->rank,tag = ((PetscObject)A)->tag,lastidx = -1;
885   PetscInt          i,*owners = A->rmap->range;
886   PetscInt          *nprocs,j,idx,nsends;
887   PetscInt          nmax,*svalues,*starts,*owner,nrecvs;
888   PetscInt          *rvalues,count,base,slen,*source;
889   PetscInt          *lens,*lrows,*values,m;
890   MPI_Comm          comm = ((PetscObject)A)->comm;
891   MPI_Request       *send_waits,*recv_waits;
892   MPI_Status        recv_status,*send_status;
893   const PetscScalar *xx;
894   PetscScalar       *bb,*mask;
895   Vec               xmask,lmask;
896   Mat_SeqAIJ        *aij = (Mat_SeqAIJ*)l->B->data;
897   const PetscInt    *aj, *ii,*ridx;
898   PetscScalar       *aa;
899 #if defined(PETSC_DEBUG)
900   PetscBool         found = PETSC_FALSE;
901 #endif
902 
903   PetscFunctionBegin;
904   /*  first count number of contributors to each processor */
905   ierr = PetscMalloc(2*size*sizeof(PetscInt),&nprocs);CHKERRQ(ierr);
906   ierr = PetscMemzero(nprocs,2*size*sizeof(PetscInt));CHKERRQ(ierr);
907   ierr = PetscMalloc((N+1)*sizeof(PetscInt),&owner);CHKERRQ(ierr); /* see note*/
908   j = 0;
909   for (i=0; i<N; i++) {
910     if (lastidx > (idx = rows[i])) j = 0;
911     lastidx = idx;
912     for (; j<size; j++) {
913       if (idx >= owners[j] && idx < owners[j+1]) {
914         nprocs[2*j]++;
915         nprocs[2*j+1] = 1;
916         owner[i] = j;
917 #if defined(PETSC_DEBUG)
918         found = PETSC_TRUE;
919 #endif
920         break;
921       }
922     }
923 #if defined(PETSC_DEBUG)
924     if (!found) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Index out of range");
925     found = PETSC_FALSE;
926 #endif
927   }
928   nsends = 0;  for (i=0; i<size; i++) { nsends += nprocs[2*i+1];}
929 
930   /* inform other processors of number of messages and max length*/
931   ierr = PetscMaxSum(comm,nprocs,&nmax,&nrecvs);CHKERRQ(ierr);
932 
933   /* post receives:   */
934   ierr = PetscMalloc((nrecvs+1)*(nmax+1)*sizeof(PetscInt),&rvalues);CHKERRQ(ierr);
935   ierr = PetscMalloc((nrecvs+1)*sizeof(MPI_Request),&recv_waits);CHKERRQ(ierr);
936   for (i=0; i<nrecvs; i++) {
937     ierr = MPI_Irecv(rvalues+nmax*i,nmax,MPIU_INT,MPI_ANY_SOURCE,tag,comm,recv_waits+i);CHKERRQ(ierr);
938   }
939 
940   /* do sends:
941       1) starts[i] gives the starting index in svalues for stuff going to
942          the ith processor
943   */
944   ierr = PetscMalloc((N+1)*sizeof(PetscInt),&svalues);CHKERRQ(ierr);
945   ierr = PetscMalloc((nsends+1)*sizeof(MPI_Request),&send_waits);CHKERRQ(ierr);
946   ierr = PetscMalloc((size+1)*sizeof(PetscInt),&starts);CHKERRQ(ierr);
947   starts[0] = 0;
948   for (i=1; i<size; i++) { starts[i] = starts[i-1] + nprocs[2*i-2];}
949   for (i=0; i<N; i++) {
950     svalues[starts[owner[i]]++] = rows[i];
951   }
952 
953   starts[0] = 0;
954   for (i=1; i<size+1; i++) { starts[i] = starts[i-1] + nprocs[2*i-2];}
955   count = 0;
956   for (i=0; i<size; i++) {
957     if (nprocs[2*i+1]) {
958       ierr = MPI_Isend(svalues+starts[i],nprocs[2*i],MPIU_INT,i,tag,comm,send_waits+count++);CHKERRQ(ierr);
959     }
960   }
961   ierr = PetscFree(starts);CHKERRQ(ierr);
962 
963   base = owners[rank];
964 
965   /*  wait on receives */
966   ierr   = PetscMalloc2(nrecvs,PetscInt,&lens,nrecvs,PetscInt,&source);CHKERRQ(ierr);
967   count  = nrecvs; slen = 0;
968   while (count) {
969     ierr = MPI_Waitany(nrecvs,recv_waits,&imdex,&recv_status);CHKERRQ(ierr);
970     /* unpack receives into our local space */
971     ierr = MPI_Get_count(&recv_status,MPIU_INT,&n);CHKERRQ(ierr);
972     source[imdex]  = recv_status.MPI_SOURCE;
973     lens[imdex]    = n;
974     slen          += n;
975     count--;
976   }
977   ierr = PetscFree(recv_waits);CHKERRQ(ierr);
978 
979   /* move the data into the send scatter */
980   ierr = PetscMalloc((slen+1)*sizeof(PetscInt),&lrows);CHKERRQ(ierr);
981   count = 0;
982   for (i=0; i<nrecvs; i++) {
983     values = rvalues + i*nmax;
984     for (j=0; j<lens[i]; j++) {
985       lrows[count++] = values[j] - base;
986     }
987   }
988   ierr = PetscFree(rvalues);CHKERRQ(ierr);
989   ierr = PetscFree2(lens,source);CHKERRQ(ierr);
990   ierr = PetscFree(owner);CHKERRQ(ierr);
991   ierr = PetscFree(nprocs);CHKERRQ(ierr);
992   /* lrows are the local rows to be zeroed, slen is the number of local rows */
993 
994   /* zero diagonal part of matrix */
995   ierr = MatZeroRowsColumns(l->A,slen,lrows,diag,x,b);CHKERRQ(ierr);
996 
997   /* handle off diagonal part of matrix */
998   ierr = MatGetVecs(A,&xmask,PETSC_NULL);CHKERRQ(ierr);
999   ierr = VecDuplicate(l->lvec,&lmask);CHKERRQ(ierr);
1000   ierr = VecGetArray(xmask,&bb);CHKERRQ(ierr);
1001   for (i=0; i<slen; i++) {
1002     bb[lrows[i]] = 1;
1003   }
1004   ierr = VecRestoreArray(xmask,&bb);CHKERRQ(ierr);
1005   ierr = VecScatterBegin(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1006   ierr = VecScatterEnd(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1007   ierr = VecDestroy(&xmask);CHKERRQ(ierr);
1008   if (x) {
1009     ierr = VecScatterBegin(l->Mvctx,x,l->lvec,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1010     ierr = VecScatterEnd(l->Mvctx,x,l->lvec,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1011     ierr = VecGetArrayRead(l->lvec,&xx);CHKERRQ(ierr);
1012     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
1013   }
1014   ierr = VecGetArray(lmask,&mask);CHKERRQ(ierr);
1015 
1016   /* remove zeroed rows of off diagonal matrix */
1017   ii = aij->i;
1018   for (i=0; i<slen; i++) {
1019     ierr = PetscMemzero(aij->a + ii[lrows[i]],(ii[lrows[i]+1] - ii[lrows[i]])*sizeof(PetscScalar));CHKERRQ(ierr);
1020   }
1021 
1022   /* loop over all elements of off process part of matrix zeroing removed columns*/
1023   if (aij->compressedrow.use){
1024     m    = aij->compressedrow.nrows;
1025     ii   = aij->compressedrow.i;
1026     ridx = aij->compressedrow.rindex;
1027     for (i=0; i<m; i++){
1028       n   = ii[i+1] - ii[i];
1029       aj  = aij->j + ii[i];
1030       aa  = aij->a + ii[i];
1031 
1032       for (j=0; j<n; j++) {
1033         if (PetscAbsScalar(mask[*aj])) {
1034           if (b) bb[*ridx] -= *aa*xx[*aj];
1035           *aa        = 0.0;
1036         }
1037         aa++;
1038         aj++;
1039       }
1040       ridx++;
1041     }
1042   } else { /* do not use compressed row format */
1043     m = l->B->rmap->n;
1044     for (i=0; i<m; i++) {
1045       n   = ii[i+1] - ii[i];
1046       aj  = aij->j + ii[i];
1047       aa  = aij->a + ii[i];
1048       for (j=0; j<n; j++) {
1049         if (PetscAbsScalar(mask[*aj])) {
1050           if (b) bb[i] -= *aa*xx[*aj];
1051           *aa    = 0.0;
1052         }
1053         aa++;
1054         aj++;
1055       }
1056     }
1057   }
1058   if (x) {
1059     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
1060     ierr = VecRestoreArrayRead(l->lvec,&xx);CHKERRQ(ierr);
1061   }
1062   ierr = VecRestoreArray(lmask,&mask);CHKERRQ(ierr);
1063   ierr = VecDestroy(&lmask);CHKERRQ(ierr);
1064   ierr = PetscFree(lrows);CHKERRQ(ierr);
1065 
1066   /* wait on sends */
1067   if (nsends) {
1068     ierr = PetscMalloc(nsends*sizeof(MPI_Status),&send_status);CHKERRQ(ierr);
1069     ierr = MPI_Waitall(nsends,send_waits,send_status);CHKERRQ(ierr);
1070     ierr = PetscFree(send_status);CHKERRQ(ierr);
1071   }
1072   ierr = PetscFree(send_waits);CHKERRQ(ierr);
1073   ierr = PetscFree(svalues);CHKERRQ(ierr);
1074 
1075   PetscFunctionReturn(0);
1076 }
1077 
1078 #undef __FUNCT__
1079 #define __FUNCT__ "MatMult_MPIAIJ"
1080 PetscErrorCode MatMult_MPIAIJ(Mat A,Vec xx,Vec yy)
1081 {
1082   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1083   PetscErrorCode ierr;
1084   PetscInt       nt;
1085 
1086   PetscFunctionBegin;
1087   ierr = VecGetLocalSize(xx,&nt);CHKERRQ(ierr);
1088   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);
1089   ierr = VecScatterBegin(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1090   ierr = (*a->A->ops->mult)(a->A,xx,yy);CHKERRQ(ierr);
1091   ierr = VecScatterEnd(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1092   ierr = (*a->B->ops->multadd)(a->B,a->lvec,yy,yy);CHKERRQ(ierr);
1093   PetscFunctionReturn(0);
1094 }
1095 
1096 #undef __FUNCT__
1097 #define __FUNCT__ "MatMultDiagonalBlock_MPIAIJ"
1098 PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat A,Vec bb,Vec xx)
1099 {
1100   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1101   PetscErrorCode ierr;
1102 
1103   PetscFunctionBegin;
1104   ierr = MatMultDiagonalBlock(a->A,bb,xx);CHKERRQ(ierr);
1105   PetscFunctionReturn(0);
1106 }
1107 
1108 #undef __FUNCT__
1109 #define __FUNCT__ "MatMultAdd_MPIAIJ"
1110 PetscErrorCode MatMultAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1111 {
1112   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1113   PetscErrorCode ierr;
1114 
1115   PetscFunctionBegin;
1116   ierr = VecScatterBegin(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1117   ierr = (*a->A->ops->multadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
1118   ierr = VecScatterEnd(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1119   ierr = (*a->B->ops->multadd)(a->B,a->lvec,zz,zz);CHKERRQ(ierr);
1120   PetscFunctionReturn(0);
1121 }
1122 
1123 #undef __FUNCT__
1124 #define __FUNCT__ "MatMultTranspose_MPIAIJ"
1125 PetscErrorCode MatMultTranspose_MPIAIJ(Mat A,Vec xx,Vec yy)
1126 {
1127   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1128   PetscErrorCode ierr;
1129   PetscBool      merged;
1130 
1131   PetscFunctionBegin;
1132   ierr = VecScatterGetMerged(a->Mvctx,&merged);CHKERRQ(ierr);
1133   /* do nondiagonal part */
1134   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
1135   if (!merged) {
1136     /* send it on its way */
1137     ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1138     /* do local part */
1139     ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
1140     /* receive remote parts: note this assumes the values are not actually */
1141     /* added in yy until the next line, */
1142     ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1143   } else {
1144     /* do local part */
1145     ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
1146     /* send it on its way */
1147     ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1148     /* values actually were received in the Begin() but we need to call this nop */
1149     ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1150   }
1151   PetscFunctionReturn(0);
1152 }
1153 
1154 EXTERN_C_BEGIN
1155 #undef __FUNCT__
1156 #define __FUNCT__ "MatIsTranspose_MPIAIJ"
1157 PetscErrorCode  MatIsTranspose_MPIAIJ(Mat Amat,Mat Bmat,PetscReal tol,PetscBool  *f)
1158 {
1159   MPI_Comm       comm;
1160   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ *) Amat->data, *Bij;
1161   Mat            Adia = Aij->A, Bdia, Aoff,Boff,*Aoffs,*Boffs;
1162   IS             Me,Notme;
1163   PetscErrorCode ierr;
1164   PetscInt       M,N,first,last,*notme,i;
1165   PetscMPIInt    size;
1166 
1167   PetscFunctionBegin;
1168 
1169   /* Easy test: symmetric diagonal block */
1170   Bij = (Mat_MPIAIJ *) Bmat->data; Bdia = Bij->A;
1171   ierr = MatIsTranspose(Adia,Bdia,tol,f);CHKERRQ(ierr);
1172   if (!*f) PetscFunctionReturn(0);
1173   ierr = PetscObjectGetComm((PetscObject)Amat,&comm);CHKERRQ(ierr);
1174   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1175   if (size == 1) PetscFunctionReturn(0);
1176 
1177   /* Hard test: off-diagonal block. This takes a MatGetSubMatrix. */
1178   ierr = MatGetSize(Amat,&M,&N);CHKERRQ(ierr);
1179   ierr = MatGetOwnershipRange(Amat,&first,&last);CHKERRQ(ierr);
1180   ierr = PetscMalloc((N-last+first)*sizeof(PetscInt),&notme);CHKERRQ(ierr);
1181   for (i=0; i<first; i++) notme[i] = i;
1182   for (i=last; i<M; i++) notme[i-last+first] = i;
1183   ierr = ISCreateGeneral(MPI_COMM_SELF,N-last+first,notme,PETSC_COPY_VALUES,&Notme);CHKERRQ(ierr);
1184   ierr = ISCreateStride(MPI_COMM_SELF,last-first,first,1,&Me);CHKERRQ(ierr);
1185   ierr = MatGetSubMatrices(Amat,1,&Me,&Notme,MAT_INITIAL_MATRIX,&Aoffs);CHKERRQ(ierr);
1186   Aoff = Aoffs[0];
1187   ierr = MatGetSubMatrices(Bmat,1,&Notme,&Me,MAT_INITIAL_MATRIX,&Boffs);CHKERRQ(ierr);
1188   Boff = Boffs[0];
1189   ierr = MatIsTranspose(Aoff,Boff,tol,f);CHKERRQ(ierr);
1190   ierr = MatDestroyMatrices(1,&Aoffs);CHKERRQ(ierr);
1191   ierr = MatDestroyMatrices(1,&Boffs);CHKERRQ(ierr);
1192   ierr = ISDestroy(&Me);CHKERRQ(ierr);
1193   ierr = ISDestroy(&Notme);CHKERRQ(ierr);
1194   ierr = PetscFree(notme);CHKERRQ(ierr);
1195    PetscFunctionReturn(0);
1196 }
1197 EXTERN_C_END
1198 
1199 #undef __FUNCT__
1200 #define __FUNCT__ "MatMultTransposeAdd_MPIAIJ"
1201 PetscErrorCode MatMultTransposeAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1202 {
1203   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1204   PetscErrorCode ierr;
1205 
1206   PetscFunctionBegin;
1207   /* do nondiagonal part */
1208   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
1209   /* send it on its way */
1210   ierr = VecScatterBegin(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1211   /* do local part */
1212   ierr = (*a->A->ops->multtransposeadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
1213   /* receive remote parts */
1214   ierr = VecScatterEnd(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1215   PetscFunctionReturn(0);
1216 }
1217 
1218 /*
1219   This only works correctly for square matrices where the subblock A->A is the
1220    diagonal block
1221 */
1222 #undef __FUNCT__
1223 #define __FUNCT__ "MatGetDiagonal_MPIAIJ"
1224 PetscErrorCode MatGetDiagonal_MPIAIJ(Mat A,Vec v)
1225 {
1226   PetscErrorCode ierr;
1227   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1228 
1229   PetscFunctionBegin;
1230   if (A->rmap->N != A->cmap->N) SETERRQ(((PetscObject)A)->comm,PETSC_ERR_SUP,"Supports only square matrix where A->A is diag block");
1231   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");
1232   ierr = MatGetDiagonal(a->A,v);CHKERRQ(ierr);
1233   PetscFunctionReturn(0);
1234 }
1235 
1236 #undef __FUNCT__
1237 #define __FUNCT__ "MatScale_MPIAIJ"
1238 PetscErrorCode MatScale_MPIAIJ(Mat A,PetscScalar aa)
1239 {
1240   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1241   PetscErrorCode ierr;
1242 
1243   PetscFunctionBegin;
1244   ierr = MatScale(a->A,aa);CHKERRQ(ierr);
1245   ierr = MatScale(a->B,aa);CHKERRQ(ierr);
1246   PetscFunctionReturn(0);
1247 }
1248 
1249 #undef __FUNCT__
1250 #define __FUNCT__ "MatDestroy_MPIAIJ"
1251 PetscErrorCode MatDestroy_MPIAIJ(Mat mat)
1252 {
1253   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1254   PetscErrorCode ierr;
1255 
1256   PetscFunctionBegin;
1257 #if defined(PETSC_USE_LOG)
1258   PetscLogObjectState((PetscObject)mat,"Rows=%D, Cols=%D",mat->rmap->N,mat->cmap->N);
1259 #endif
1260   ierr = MatStashDestroy_Private(&mat->stash);CHKERRQ(ierr);
1261   ierr = VecDestroy(&aij->diag);CHKERRQ(ierr);
1262   ierr = MatDestroy(&aij->A);CHKERRQ(ierr);
1263   ierr = MatDestroy(&aij->B);CHKERRQ(ierr);
1264 #if defined (PETSC_USE_CTABLE)
1265   ierr = PetscTableDestroy(&aij->colmap);CHKERRQ(ierr);
1266 #else
1267   ierr = PetscFree(aij->colmap);CHKERRQ(ierr);
1268 #endif
1269   ierr = PetscFree(aij->garray);CHKERRQ(ierr);
1270   ierr = VecDestroy(&aij->lvec);CHKERRQ(ierr);
1271   ierr = VecScatterDestroy(&aij->Mvctx);CHKERRQ(ierr);
1272   ierr = PetscFree2(aij->rowvalues,aij->rowindices);CHKERRQ(ierr);
1273   ierr = PetscFree(aij->ld);CHKERRQ(ierr);
1274   ierr = PetscFree(mat->data);CHKERRQ(ierr);
1275 
1276   ierr = PetscObjectChangeTypeName((PetscObject)mat,0);CHKERRQ(ierr);
1277   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatStoreValues_C","",PETSC_NULL);CHKERRQ(ierr);
1278   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatRetrieveValues_C","",PETSC_NULL);CHKERRQ(ierr);
1279   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatGetDiagonalBlock_C","",PETSC_NULL);CHKERRQ(ierr);
1280   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatIsTranspose_C","",PETSC_NULL);CHKERRQ(ierr);
1281   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocation_C","",PETSC_NULL);CHKERRQ(ierr);
1282   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocationCSR_C","",PETSC_NULL);CHKERRQ(ierr);
1283   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDiagonalScaleLocal_C","",PETSC_NULL);CHKERRQ(ierr);
1284   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_mpisbaij_C","",PETSC_NULL);CHKERRQ(ierr);
1285   PetscFunctionReturn(0);
1286 }
1287 
1288 #undef __FUNCT__
1289 #define __FUNCT__ "MatView_MPIAIJ_Binary"
1290 PetscErrorCode MatView_MPIAIJ_Binary(Mat mat,PetscViewer viewer)
1291 {
1292   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)mat->data;
1293   Mat_SeqAIJ*       A = (Mat_SeqAIJ*)aij->A->data;
1294   Mat_SeqAIJ*       B = (Mat_SeqAIJ*)aij->B->data;
1295   PetscErrorCode    ierr;
1296   PetscMPIInt       rank,size,tag = ((PetscObject)viewer)->tag;
1297   int               fd;
1298   PetscInt          nz,header[4],*row_lengths,*range=0,rlen,i;
1299   PetscInt          nzmax,*column_indices,j,k,col,*garray = aij->garray,cnt,cstart = mat->cmap->rstart,rnz;
1300   PetscScalar       *column_values;
1301   PetscInt          message_count,flowcontrolcount;
1302 
1303   PetscFunctionBegin;
1304   ierr = MPI_Comm_rank(((PetscObject)mat)->comm,&rank);CHKERRQ(ierr);
1305   ierr = MPI_Comm_size(((PetscObject)mat)->comm,&size);CHKERRQ(ierr);
1306   nz   = A->nz + B->nz;
1307   if (!rank) {
1308     header[0] = MAT_FILE_CLASSID;
1309     header[1] = mat->rmap->N;
1310     header[2] = mat->cmap->N;
1311     ierr = MPI_Reduce(&nz,&header[3],1,MPIU_INT,MPI_SUM,0,((PetscObject)mat)->comm);CHKERRQ(ierr);
1312     ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
1313     ierr = PetscBinaryWrite(fd,header,4,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1314     /* get largest number of rows any processor has */
1315     rlen = mat->rmap->n;
1316     range = mat->rmap->range;
1317     for (i=1; i<size; i++) {
1318       rlen = PetscMax(rlen,range[i+1] - range[i]);
1319     }
1320   } else {
1321     ierr = MPI_Reduce(&nz,0,1,MPIU_INT,MPI_SUM,0,((PetscObject)mat)->comm);CHKERRQ(ierr);
1322     rlen = mat->rmap->n;
1323   }
1324 
1325   /* load up the local row counts */
1326   ierr = PetscMalloc((rlen+1)*sizeof(PetscInt),&row_lengths);CHKERRQ(ierr);
1327   for (i=0; i<mat->rmap->n; i++) {
1328     row_lengths[i] = A->i[i+1] - A->i[i] + B->i[i+1] - B->i[i];
1329   }
1330 
1331   /* store the row lengths to the file */
1332   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1333   if (!rank) {
1334     ierr = PetscBinaryWrite(fd,row_lengths,mat->rmap->n,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1335     for (i=1; i<size; i++) {
1336       ierr = PetscViewerFlowControlStepMaster(viewer,i,message_count,flowcontrolcount);CHKERRQ(ierr);
1337       rlen = range[i+1] - range[i];
1338       ierr = MPIULong_Recv(row_lengths,rlen,MPIU_INT,i,tag,((PetscObject)mat)->comm);CHKERRQ(ierr);
1339       ierr = PetscBinaryWrite(fd,row_lengths,rlen,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1340     }
1341     ierr = PetscViewerFlowControlEndMaster(viewer,message_count);CHKERRQ(ierr);
1342   } else {
1343     ierr = PetscViewerFlowControlStepWorker(viewer,rank,message_count);CHKERRQ(ierr);
1344     ierr = MPIULong_Send(row_lengths,mat->rmap->n,MPIU_INT,0,tag,((PetscObject)mat)->comm);CHKERRQ(ierr);
1345     ierr = PetscViewerFlowControlEndWorker(viewer,message_count);CHKERRQ(ierr);
1346   }
1347   ierr = PetscFree(row_lengths);CHKERRQ(ierr);
1348 
1349   /* load up the local column indices */
1350   nzmax = nz; /* )th processor needs space a largest processor needs */
1351   ierr = MPI_Reduce(&nz,&nzmax,1,MPIU_INT,MPI_MAX,0,((PetscObject)mat)->comm);CHKERRQ(ierr);
1352   ierr = PetscMalloc((nzmax+1)*sizeof(PetscInt),&column_indices);CHKERRQ(ierr);
1353   cnt  = 0;
1354   for (i=0; i<mat->rmap->n; i++) {
1355     for (j=B->i[i]; j<B->i[i+1]; j++) {
1356       if ( (col = garray[B->j[j]]) > cstart) break;
1357       column_indices[cnt++] = col;
1358     }
1359     for (k=A->i[i]; k<A->i[i+1]; k++) {
1360       column_indices[cnt++] = A->j[k] + cstart;
1361     }
1362     for (; j<B->i[i+1]; j++) {
1363       column_indices[cnt++] = garray[B->j[j]];
1364     }
1365   }
1366   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);
1367 
1368   /* store the column indices to the file */
1369    ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1370   if (!rank) {
1371     MPI_Status status;
1372     ierr = PetscBinaryWrite(fd,column_indices,nz,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1373     for (i=1; i<size; i++) {
1374       ierr = PetscViewerFlowControlStepMaster(viewer,i,message_count,flowcontrolcount);CHKERRQ(ierr);
1375       ierr = MPI_Recv(&rnz,1,MPIU_INT,i,tag,((PetscObject)mat)->comm,&status);CHKERRQ(ierr);
1376       if (rnz > nzmax) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: nz = %D nzmax = %D",nz,nzmax);
1377       ierr = MPIULong_Recv(column_indices,rnz,MPIU_INT,i,tag,((PetscObject)mat)->comm);CHKERRQ(ierr);
1378       ierr = PetscBinaryWrite(fd,column_indices,rnz,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1379     }
1380      ierr = PetscViewerFlowControlEndMaster(viewer,message_count);CHKERRQ(ierr);
1381   } else {
1382     ierr = PetscViewerFlowControlStepWorker(viewer,rank,message_count);CHKERRQ(ierr);
1383     ierr = MPI_Send(&nz,1,MPIU_INT,0,tag,((PetscObject)mat)->comm);CHKERRQ(ierr);
1384     ierr = MPIULong_Send(column_indices,nz,MPIU_INT,0,tag,((PetscObject)mat)->comm);CHKERRQ(ierr);
1385     ierr = PetscViewerFlowControlEndWorker(viewer,message_count);CHKERRQ(ierr);
1386   }
1387   ierr = PetscFree(column_indices);CHKERRQ(ierr);
1388 
1389   /* load up the local column values */
1390   ierr = PetscMalloc((nzmax+1)*sizeof(PetscScalar),&column_values);CHKERRQ(ierr);
1391   cnt  = 0;
1392   for (i=0; i<mat->rmap->n; i++) {
1393     for (j=B->i[i]; j<B->i[i+1]; j++) {
1394       if ( garray[B->j[j]] > cstart) break;
1395       column_values[cnt++] = B->a[j];
1396     }
1397     for (k=A->i[i]; k<A->i[i+1]; k++) {
1398       column_values[cnt++] = A->a[k];
1399     }
1400     for (; j<B->i[i+1]; j++) {
1401       column_values[cnt++] = B->a[j];
1402     }
1403   }
1404   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);
1405 
1406   /* store the column values to the file */
1407    ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1408   if (!rank) {
1409     MPI_Status status;
1410     ierr = PetscBinaryWrite(fd,column_values,nz,PETSC_SCALAR,PETSC_TRUE);CHKERRQ(ierr);
1411     for (i=1; i<size; i++) {
1412        ierr = PetscViewerFlowControlStepMaster(viewer,i,message_count,flowcontrolcount);CHKERRQ(ierr);
1413       ierr = MPI_Recv(&rnz,1,MPIU_INT,i,tag,((PetscObject)mat)->comm,&status);CHKERRQ(ierr);
1414       if (rnz > nzmax) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: nz = %D nzmax = %D",nz,nzmax);
1415       ierr = MPIULong_Recv(column_values,rnz,MPIU_SCALAR,i,tag,((PetscObject)mat)->comm);CHKERRQ(ierr);
1416       ierr = PetscBinaryWrite(fd,column_values,rnz,PETSC_SCALAR,PETSC_TRUE);CHKERRQ(ierr);
1417     }
1418     ierr = PetscViewerFlowControlEndMaster(viewer,message_count);CHKERRQ(ierr);
1419   } else {
1420     ierr = PetscViewerFlowControlStepWorker(viewer,rank,message_count);CHKERRQ(ierr);
1421     ierr = MPI_Send(&nz,1,MPIU_INT,0,tag,((PetscObject)mat)->comm);CHKERRQ(ierr);
1422     ierr = MPIULong_Send(column_values,nz,MPIU_SCALAR,0,tag,((PetscObject)mat)->comm);CHKERRQ(ierr);
1423     ierr = PetscViewerFlowControlEndWorker(viewer,message_count);CHKERRQ(ierr);
1424   }
1425   ierr = PetscFree(column_values);CHKERRQ(ierr);
1426   PetscFunctionReturn(0);
1427 }
1428 
1429 #undef __FUNCT__
1430 #define __FUNCT__ "MatView_MPIAIJ_ASCIIorDraworSocket"
1431 PetscErrorCode MatView_MPIAIJ_ASCIIorDraworSocket(Mat mat,PetscViewer viewer)
1432 {
1433   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)mat->data;
1434   PetscErrorCode    ierr;
1435   PetscMPIInt       rank = aij->rank,size = aij->size;
1436   PetscBool         isdraw,iascii,isbinary;
1437   PetscViewer       sviewer;
1438   PetscViewerFormat format;
1439 
1440   PetscFunctionBegin;
1441   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1442   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1443   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1444   if (iascii) {
1445     ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
1446     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
1447       MatInfo    info;
1448       PetscBool  inodes;
1449 
1450       ierr = MPI_Comm_rank(((PetscObject)mat)->comm,&rank);CHKERRQ(ierr);
1451       ierr = MatGetInfo(mat,MAT_LOCAL,&info);CHKERRQ(ierr);
1452       ierr = MatInodeGetInodeSizes(aij->A,PETSC_NULL,(PetscInt **)&inodes,PETSC_NULL);CHKERRQ(ierr);
1453       ierr = PetscViewerASCIISynchronizedAllow(viewer,PETSC_TRUE);CHKERRQ(ierr);
1454       if (!inodes) {
1455         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %D nz %D nz alloced %D mem %D, not using I-node routines\n",
1456 					      rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
1457       } else {
1458         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %D nz %D nz alloced %D mem %D, using I-node routines\n",
1459 		    rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
1460       }
1461       ierr = MatGetInfo(aij->A,MAT_LOCAL,&info);CHKERRQ(ierr);
1462       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] on-diagonal part: nz %D \n",rank,(PetscInt)info.nz_used);CHKERRQ(ierr);
1463       ierr = MatGetInfo(aij->B,MAT_LOCAL,&info);CHKERRQ(ierr);
1464       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] off-diagonal part: nz %D \n",rank,(PetscInt)info.nz_used);CHKERRQ(ierr);
1465       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1466       ierr = PetscViewerASCIISynchronizedAllow(viewer,PETSC_FALSE);CHKERRQ(ierr);
1467       ierr = PetscViewerASCIIPrintf(viewer,"Information on VecScatter used in matrix-vector product: \n");CHKERRQ(ierr);
1468       ierr = VecScatterView(aij->Mvctx,viewer);CHKERRQ(ierr);
1469       PetscFunctionReturn(0);
1470     } else if (format == PETSC_VIEWER_ASCII_INFO) {
1471       PetscInt   inodecount,inodelimit,*inodes;
1472       ierr = MatInodeGetInodeSizes(aij->A,&inodecount,&inodes,&inodelimit);CHKERRQ(ierr);
1473       if (inodes) {
1474         ierr = PetscViewerASCIIPrintf(viewer,"using I-node (on process 0) routines: found %D nodes, limit used is %D\n",inodecount,inodelimit);CHKERRQ(ierr);
1475       } else {
1476         ierr = PetscViewerASCIIPrintf(viewer,"not using I-node (on process 0) routines\n");CHKERRQ(ierr);
1477       }
1478       PetscFunctionReturn(0);
1479     } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO) {
1480       PetscFunctionReturn(0);
1481     }
1482   } else if (isbinary) {
1483     if (size == 1) {
1484       ierr = PetscObjectSetName((PetscObject)aij->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1485       ierr = MatView(aij->A,viewer);CHKERRQ(ierr);
1486     } else {
1487       ierr = MatView_MPIAIJ_Binary(mat,viewer);CHKERRQ(ierr);
1488     }
1489     PetscFunctionReturn(0);
1490   } else if (isdraw) {
1491     PetscDraw  draw;
1492     PetscBool  isnull;
1493     ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
1494     ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr); if (isnull) PetscFunctionReturn(0);
1495   }
1496 
1497   if (size == 1) {
1498     ierr = PetscObjectSetName((PetscObject)aij->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1499     ierr = MatView(aij->A,viewer);CHKERRQ(ierr);
1500   } else {
1501     /* assemble the entire matrix onto first processor. */
1502     Mat         A;
1503     Mat_SeqAIJ  *Aloc;
1504     PetscInt    M = mat->rmap->N,N = mat->cmap->N,m,*ai,*aj,row,*cols,i,*ct;
1505     MatScalar   *a;
1506 
1507     if (mat->rmap->N > 1024) {
1508       PetscBool  flg = PETSC_FALSE;
1509 
1510       ierr = PetscOptionsGetBool(((PetscObject) mat)->prefix, "-mat_ascii_output_large", &flg,PETSC_NULL);CHKERRQ(ierr);
1511       if (!flg) {
1512         SETERRQ(((PetscObject)mat)->comm,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.");
1513       }
1514     }
1515 
1516     ierr = MatCreate(((PetscObject)mat)->comm,&A);CHKERRQ(ierr);
1517     if (!rank) {
1518       ierr = MatSetSizes(A,M,N,M,N);CHKERRQ(ierr);
1519     } else {
1520       ierr = MatSetSizes(A,0,0,M,N);CHKERRQ(ierr);
1521     }
1522     /* This is just a temporary matrix, so explicitly using MATMPIAIJ is probably best */
1523     ierr = MatSetType(A,MATMPIAIJ);CHKERRQ(ierr);
1524     ierr = MatMPIAIJSetPreallocation(A,0,PETSC_NULL,0,PETSC_NULL);CHKERRQ(ierr);
1525     ierr = MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
1526     ierr = PetscLogObjectParent(mat,A);CHKERRQ(ierr);
1527 
1528     /* copy over the A part */
1529     Aloc = (Mat_SeqAIJ*)aij->A->data;
1530     m = aij->A->rmap->n; ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
1531     row = mat->rmap->rstart;
1532     for (i=0; i<ai[m]; i++) {aj[i] += mat->cmap->rstart ;}
1533     for (i=0; i<m; i++) {
1534       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],aj,a,INSERT_VALUES);CHKERRQ(ierr);
1535       row++; a += ai[i+1]-ai[i]; aj += ai[i+1]-ai[i];
1536     }
1537     aj = Aloc->j;
1538     for (i=0; i<ai[m]; i++) {aj[i] -= mat->cmap->rstart;}
1539 
1540     /* copy over the B part */
1541     Aloc = (Mat_SeqAIJ*)aij->B->data;
1542     m    = aij->B->rmap->n;  ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
1543     row  = mat->rmap->rstart;
1544     ierr = PetscMalloc((ai[m]+1)*sizeof(PetscInt),&cols);CHKERRQ(ierr);
1545     ct   = cols;
1546     for (i=0; i<ai[m]; i++) {cols[i] = aij->garray[aj[i]];}
1547     for (i=0; i<m; i++) {
1548       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],cols,a,INSERT_VALUES);CHKERRQ(ierr);
1549       row++; a += ai[i+1]-ai[i]; cols += ai[i+1]-ai[i];
1550     }
1551     ierr = PetscFree(ct);CHKERRQ(ierr);
1552     ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1553     ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1554     /*
1555        Everyone has to call to draw the matrix since the graphics waits are
1556        synchronized across all processors that share the PetscDraw object
1557     */
1558     ierr = PetscViewerGetSingleton(viewer,&sviewer);CHKERRQ(ierr);
1559     if (!rank) {
1560       ierr = PetscObjectSetName((PetscObject)((Mat_MPIAIJ*)(A->data))->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1561       /* Set the type name to MATMPIAIJ so that the correct type can be printed out by PetscObjectPrintClassNamePrefixType() in MatView_SeqAIJ_ASCII()*/
1562       PetscStrcpy(((PetscObject)((Mat_MPIAIJ*)(A->data))->A)->type_name,MATMPIAIJ);
1563       ierr = MatView(((Mat_MPIAIJ*)(A->data))->A,sviewer);CHKERRQ(ierr);
1564     }
1565     ierr = PetscViewerRestoreSingleton(viewer,&sviewer);CHKERRQ(ierr);
1566     ierr = MatDestroy(&A);CHKERRQ(ierr);
1567   }
1568   PetscFunctionReturn(0);
1569 }
1570 
1571 #undef __FUNCT__
1572 #define __FUNCT__ "MatView_MPIAIJ"
1573 PetscErrorCode MatView_MPIAIJ(Mat mat,PetscViewer viewer)
1574 {
1575   PetscErrorCode ierr;
1576   PetscBool      iascii,isdraw,issocket,isbinary;
1577 
1578   PetscFunctionBegin;
1579   ierr  = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1580   ierr  = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1581   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1582   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSOCKET,&issocket);CHKERRQ(ierr);
1583   if (iascii || isdraw || isbinary || issocket) {
1584     ierr = MatView_MPIAIJ_ASCIIorDraworSocket(mat,viewer);CHKERRQ(ierr);
1585   } else {
1586     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Viewer type %s not supported by MPIAIJ matrices",((PetscObject)viewer)->type_name);
1587   }
1588   PetscFunctionReturn(0);
1589 }
1590 
1591 #undef __FUNCT__
1592 #define __FUNCT__ "MatSOR_MPIAIJ"
1593 PetscErrorCode MatSOR_MPIAIJ(Mat matin,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
1594 {
1595   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1596   PetscErrorCode ierr;
1597   Vec            bb1 = 0;
1598   PetscBool      hasop;
1599 
1600   PetscFunctionBegin;
1601   if (its > 1 || ~flag & SOR_ZERO_INITIAL_GUESS || flag & SOR_EISENSTAT) {
1602     ierr = VecDuplicate(bb,&bb1);CHKERRQ(ierr);
1603   }
1604 
1605   if (flag == SOR_APPLY_UPPER) {
1606     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1607     PetscFunctionReturn(0);
1608   }
1609 
1610   if ((flag & SOR_LOCAL_SYMMETRIC_SWEEP) == SOR_LOCAL_SYMMETRIC_SWEEP){
1611     if (flag & SOR_ZERO_INITIAL_GUESS) {
1612       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1613       its--;
1614     }
1615 
1616     while (its--) {
1617       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1618       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1619 
1620       /* update rhs: bb1 = bb - B*x */
1621       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1622       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1623 
1624       /* local sweep */
1625       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_SYMMETRIC_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1626     }
1627   } else if (flag & SOR_LOCAL_FORWARD_SWEEP){
1628     if (flag & SOR_ZERO_INITIAL_GUESS) {
1629       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1630       its--;
1631     }
1632     while (its--) {
1633       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1634       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1635 
1636       /* update rhs: bb1 = bb - B*x */
1637       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1638       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1639 
1640       /* local sweep */
1641       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_FORWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1642     }
1643   } else if (flag & SOR_LOCAL_BACKWARD_SWEEP){
1644     if (flag & SOR_ZERO_INITIAL_GUESS) {
1645       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1646       its--;
1647     }
1648     while (its--) {
1649       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1650       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1651 
1652       /* update rhs: bb1 = bb - B*x */
1653       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1654       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1655 
1656       /* local sweep */
1657       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_BACKWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1658     }
1659   }  else if (flag & SOR_EISENSTAT) {
1660     Vec         xx1;
1661 
1662     ierr = VecDuplicate(bb,&xx1);CHKERRQ(ierr);
1663     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_BACKWARD_SWEEP),fshift,lits,1,xx);CHKERRQ(ierr);
1664 
1665     ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1666     ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1667     if (!mat->diag) {
1668       ierr = MatGetVecs(matin,&mat->diag,PETSC_NULL);CHKERRQ(ierr);
1669       ierr = MatGetDiagonal(matin,mat->diag);CHKERRQ(ierr);
1670     }
1671     ierr = MatHasOperation(matin,MATOP_MULT_DIAGONAL_BLOCK,&hasop);CHKERRQ(ierr);
1672     if (hasop) {
1673       ierr = MatMultDiagonalBlock(matin,xx,bb1);CHKERRQ(ierr);
1674     } else {
1675       ierr = VecPointwiseMult(bb1,mat->diag,xx);CHKERRQ(ierr);
1676     }
1677     ierr = VecAYPX(bb1,(omega-2.0)/omega,bb);CHKERRQ(ierr);
1678 
1679     ierr = MatMultAdd(mat->B,mat->lvec,bb1,bb1);CHKERRQ(ierr);
1680 
1681     /* local sweep */
1682     ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_FORWARD_SWEEP),fshift,lits,1,xx1);CHKERRQ(ierr);
1683     ierr = VecAXPY(xx,1.0,xx1);CHKERRQ(ierr);
1684     ierr = VecDestroy(&xx1);CHKERRQ(ierr);
1685   } else SETERRQ(((PetscObject)matin)->comm,PETSC_ERR_SUP,"Parallel SOR not supported");
1686 
1687   ierr = VecDestroy(&bb1);CHKERRQ(ierr);
1688   PetscFunctionReturn(0);
1689 }
1690 
1691 #undef __FUNCT__
1692 #define __FUNCT__ "MatPermute_MPIAIJ"
1693 PetscErrorCode MatPermute_MPIAIJ(Mat A,IS rowp,IS colp,Mat *B)
1694 {
1695   MPI_Comm       comm;
1696   PetscInt       first,local_rowsize,local_colsize;
1697   const PetscInt *rows;
1698   IS             crowp,growp,irowp,lrowp,lcolp,icolp;
1699   PetscErrorCode ierr;
1700 
1701   PetscFunctionBegin;
1702   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
1703   /* make a collective version of 'rowp', this is to be tolerant of users who pass serial index sets */
1704   ierr = ISOnComm(rowp,comm,PETSC_USE_POINTER,&crowp);CHKERRQ(ierr);
1705   /* collect the global row permutation and invert it */
1706   ierr = ISAllGather(crowp,&growp);CHKERRQ(ierr);
1707   ierr = ISSetPermutation(growp);CHKERRQ(ierr);
1708   ierr = ISDestroy(&crowp);CHKERRQ(ierr);
1709   ierr = ISInvertPermutation(growp,PETSC_DECIDE,&irowp);CHKERRQ(ierr);
1710   ierr = ISDestroy(&growp);CHKERRQ(ierr);
1711   /* get the local target indices */
1712   ierr = MatGetOwnershipRange(A,&first,PETSC_NULL);CHKERRQ(ierr);
1713   ierr = MatGetLocalSize(A,&local_rowsize,&local_colsize);CHKERRQ(ierr);
1714   ierr = ISGetIndices(irowp,&rows);CHKERRQ(ierr);
1715   ierr = ISCreateGeneral(PETSC_COMM_SELF,local_rowsize,rows+first,PETSC_COPY_VALUES,&lrowp);CHKERRQ(ierr);
1716   ierr = ISRestoreIndices(irowp,&rows);CHKERRQ(ierr);
1717   ierr = ISDestroy(&irowp);CHKERRQ(ierr);
1718   /* the column permutation is so much easier;
1719      make a local version of 'colp' and invert it */
1720   ierr = ISOnComm(colp,PETSC_COMM_SELF,PETSC_USE_POINTER,&lcolp);CHKERRQ(ierr);
1721   ierr = ISSetPermutation(lcolp);CHKERRQ(ierr);
1722   ierr = ISInvertPermutation(lcolp,PETSC_DECIDE,&icolp);CHKERRQ(ierr);
1723   ierr = ISDestroy(&lcolp);CHKERRQ(ierr);
1724   /* now we just get the submatrix */
1725   ierr = MatGetSubMatrix_MPIAIJ_Private(A,lrowp,icolp,local_colsize,MAT_INITIAL_MATRIX,B);CHKERRQ(ierr);
1726   /* clean up */
1727   ierr = ISDestroy(&lrowp);CHKERRQ(ierr);
1728   ierr = ISDestroy(&icolp);CHKERRQ(ierr);
1729   PetscFunctionReturn(0);
1730 }
1731 
1732 #undef __FUNCT__
1733 #define __FUNCT__ "MatGetInfo_MPIAIJ"
1734 PetscErrorCode MatGetInfo_MPIAIJ(Mat matin,MatInfoType flag,MatInfo *info)
1735 {
1736   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1737   Mat            A = mat->A,B = mat->B;
1738   PetscErrorCode ierr;
1739   PetscReal      isend[5],irecv[5];
1740 
1741   PetscFunctionBegin;
1742   info->block_size     = 1.0;
1743   ierr = MatGetInfo(A,MAT_LOCAL,info);CHKERRQ(ierr);
1744   isend[0] = info->nz_used; isend[1] = info->nz_allocated; isend[2] = info->nz_unneeded;
1745   isend[3] = info->memory;  isend[4] = info->mallocs;
1746   ierr = MatGetInfo(B,MAT_LOCAL,info);CHKERRQ(ierr);
1747   isend[0] += info->nz_used; isend[1] += info->nz_allocated; isend[2] += info->nz_unneeded;
1748   isend[3] += info->memory;  isend[4] += info->mallocs;
1749   if (flag == MAT_LOCAL) {
1750     info->nz_used      = isend[0];
1751     info->nz_allocated = isend[1];
1752     info->nz_unneeded  = isend[2];
1753     info->memory       = isend[3];
1754     info->mallocs      = isend[4];
1755   } else if (flag == MAT_GLOBAL_MAX) {
1756     ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_MAX,((PetscObject)matin)->comm);CHKERRQ(ierr);
1757     info->nz_used      = irecv[0];
1758     info->nz_allocated = irecv[1];
1759     info->nz_unneeded  = irecv[2];
1760     info->memory       = irecv[3];
1761     info->mallocs      = irecv[4];
1762   } else if (flag == MAT_GLOBAL_SUM) {
1763     ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_SUM,((PetscObject)matin)->comm);CHKERRQ(ierr);
1764     info->nz_used      = irecv[0];
1765     info->nz_allocated = irecv[1];
1766     info->nz_unneeded  = irecv[2];
1767     info->memory       = irecv[3];
1768     info->mallocs      = irecv[4];
1769   }
1770   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
1771   info->fill_ratio_needed = 0;
1772   info->factor_mallocs    = 0;
1773 
1774   PetscFunctionReturn(0);
1775 }
1776 
1777 #undef __FUNCT__
1778 #define __FUNCT__ "MatSetOption_MPIAIJ"
1779 PetscErrorCode MatSetOption_MPIAIJ(Mat A,MatOption op,PetscBool  flg)
1780 {
1781   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1782   PetscErrorCode ierr;
1783 
1784   PetscFunctionBegin;
1785   switch (op) {
1786   case MAT_NEW_NONZERO_LOCATIONS:
1787   case MAT_NEW_NONZERO_ALLOCATION_ERR:
1788   case MAT_UNUSED_NONZERO_LOCATION_ERR:
1789   case MAT_KEEP_NONZERO_PATTERN:
1790   case MAT_NEW_NONZERO_LOCATION_ERR:
1791   case MAT_USE_INODES:
1792   case MAT_IGNORE_ZERO_ENTRIES:
1793     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1794     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1795     break;
1796   case MAT_ROW_ORIENTED:
1797     a->roworiented = flg;
1798     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1799     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1800     break;
1801   case MAT_NEW_DIAGONALS:
1802     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
1803     break;
1804   case MAT_IGNORE_OFF_PROC_ENTRIES:
1805     a->donotstash = flg;
1806     break;
1807   case MAT_SPD:
1808     A->spd_set                         = PETSC_TRUE;
1809     A->spd                             = flg;
1810     if (flg) {
1811       A->symmetric                     = PETSC_TRUE;
1812       A->structurally_symmetric        = PETSC_TRUE;
1813       A->symmetric_set                 = PETSC_TRUE;
1814       A->structurally_symmetric_set    = PETSC_TRUE;
1815     }
1816     break;
1817   case MAT_SYMMETRIC:
1818     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1819     break;
1820   case MAT_STRUCTURALLY_SYMMETRIC:
1821     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1822     break;
1823   case MAT_HERMITIAN:
1824     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1825     break;
1826   case MAT_SYMMETRY_ETERNAL:
1827     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1828     break;
1829   default:
1830     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %d",op);
1831   }
1832   PetscFunctionReturn(0);
1833 }
1834 
1835 #undef __FUNCT__
1836 #define __FUNCT__ "MatGetRow_MPIAIJ"
1837 PetscErrorCode MatGetRow_MPIAIJ(Mat matin,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1838 {
1839   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1840   PetscScalar    *vworkA,*vworkB,**pvA,**pvB,*v_p;
1841   PetscErrorCode ierr;
1842   PetscInt       i,*cworkA,*cworkB,**pcA,**pcB,cstart = matin->cmap->rstart;
1843   PetscInt       nztot,nzA,nzB,lrow,rstart = matin->rmap->rstart,rend = matin->rmap->rend;
1844   PetscInt       *cmap,*idx_p;
1845 
1846   PetscFunctionBegin;
1847   if (mat->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Already active");
1848   mat->getrowactive = PETSC_TRUE;
1849 
1850   if (!mat->rowvalues && (idx || v)) {
1851     /*
1852         allocate enough space to hold information from the longest row.
1853     */
1854     Mat_SeqAIJ *Aa = (Mat_SeqAIJ*)mat->A->data,*Ba = (Mat_SeqAIJ*)mat->B->data;
1855     PetscInt   max = 1,tmp;
1856     for (i=0; i<matin->rmap->n; i++) {
1857       tmp = Aa->i[i+1] - Aa->i[i] + Ba->i[i+1] - Ba->i[i];
1858       if (max < tmp) { max = tmp; }
1859     }
1860     ierr = PetscMalloc2(max,PetscScalar,&mat->rowvalues,max,PetscInt,&mat->rowindices);CHKERRQ(ierr);
1861   }
1862 
1863   if (row < rstart || row >= rend) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Only local rows");
1864   lrow = row - rstart;
1865 
1866   pvA = &vworkA; pcA = &cworkA; pvB = &vworkB; pcB = &cworkB;
1867   if (!v)   {pvA = 0; pvB = 0;}
1868   if (!idx) {pcA = 0; if (!v) pcB = 0;}
1869   ierr = (*mat->A->ops->getrow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1870   ierr = (*mat->B->ops->getrow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1871   nztot = nzA + nzB;
1872 
1873   cmap  = mat->garray;
1874   if (v  || idx) {
1875     if (nztot) {
1876       /* Sort by increasing column numbers, assuming A and B already sorted */
1877       PetscInt imark = -1;
1878       if (v) {
1879         *v = v_p = mat->rowvalues;
1880         for (i=0; i<nzB; i++) {
1881           if (cmap[cworkB[i]] < cstart)   v_p[i] = vworkB[i];
1882           else break;
1883         }
1884         imark = i;
1885         for (i=0; i<nzA; i++)     v_p[imark+i] = vworkA[i];
1886         for (i=imark; i<nzB; i++) v_p[nzA+i]   = vworkB[i];
1887       }
1888       if (idx) {
1889         *idx = idx_p = mat->rowindices;
1890         if (imark > -1) {
1891           for (i=0; i<imark; i++) {
1892             idx_p[i] = cmap[cworkB[i]];
1893           }
1894         } else {
1895           for (i=0; i<nzB; i++) {
1896             if (cmap[cworkB[i]] < cstart)   idx_p[i] = cmap[cworkB[i]];
1897             else break;
1898           }
1899           imark = i;
1900         }
1901         for (i=0; i<nzA; i++)     idx_p[imark+i] = cstart + cworkA[i];
1902         for (i=imark; i<nzB; i++) idx_p[nzA+i]   = cmap[cworkB[i]];
1903       }
1904     } else {
1905       if (idx) *idx = 0;
1906       if (v)   *v   = 0;
1907     }
1908   }
1909   *nz = nztot;
1910   ierr = (*mat->A->ops->restorerow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1911   ierr = (*mat->B->ops->restorerow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1912   PetscFunctionReturn(0);
1913 }
1914 
1915 #undef __FUNCT__
1916 #define __FUNCT__ "MatRestoreRow_MPIAIJ"
1917 PetscErrorCode MatRestoreRow_MPIAIJ(Mat mat,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1918 {
1919   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1920 
1921   PetscFunctionBegin;
1922   if (!aij->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"MatGetRow() must be called first");
1923   aij->getrowactive = PETSC_FALSE;
1924   PetscFunctionReturn(0);
1925 }
1926 
1927 #undef __FUNCT__
1928 #define __FUNCT__ "MatNorm_MPIAIJ"
1929 PetscErrorCode MatNorm_MPIAIJ(Mat mat,NormType type,PetscReal *norm)
1930 {
1931   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1932   Mat_SeqAIJ     *amat = (Mat_SeqAIJ*)aij->A->data,*bmat = (Mat_SeqAIJ*)aij->B->data;
1933   PetscErrorCode ierr;
1934   PetscInt       i,j,cstart = mat->cmap->rstart;
1935   PetscReal      sum = 0.0;
1936   MatScalar      *v;
1937 
1938   PetscFunctionBegin;
1939   if (aij->size == 1) {
1940     ierr =  MatNorm(aij->A,type,norm);CHKERRQ(ierr);
1941   } else {
1942     if (type == NORM_FROBENIUS) {
1943       v = amat->a;
1944       for (i=0; i<amat->nz; i++) {
1945 #if defined(PETSC_USE_COMPLEX)
1946         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1947 #else
1948         sum += (*v)*(*v); v++;
1949 #endif
1950       }
1951       v = bmat->a;
1952       for (i=0; i<bmat->nz; i++) {
1953 #if defined(PETSC_USE_COMPLEX)
1954         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1955 #else
1956         sum += (*v)*(*v); v++;
1957 #endif
1958       }
1959       ierr = MPI_Allreduce(&sum,norm,1,MPIU_REAL,MPIU_SUM,((PetscObject)mat)->comm);CHKERRQ(ierr);
1960       *norm = PetscSqrtReal(*norm);
1961     } else if (type == NORM_1) { /* max column norm */
1962       PetscReal *tmp,*tmp2;
1963       PetscInt  *jj,*garray = aij->garray;
1964       ierr = PetscMalloc((mat->cmap->N+1)*sizeof(PetscReal),&tmp);CHKERRQ(ierr);
1965       ierr = PetscMalloc((mat->cmap->N+1)*sizeof(PetscReal),&tmp2);CHKERRQ(ierr);
1966       ierr = PetscMemzero(tmp,mat->cmap->N*sizeof(PetscReal));CHKERRQ(ierr);
1967       *norm = 0.0;
1968       v = amat->a; jj = amat->j;
1969       for (j=0; j<amat->nz; j++) {
1970         tmp[cstart + *jj++ ] += PetscAbsScalar(*v);  v++;
1971       }
1972       v = bmat->a; jj = bmat->j;
1973       for (j=0; j<bmat->nz; j++) {
1974         tmp[garray[*jj++]] += PetscAbsScalar(*v); v++;
1975       }
1976       ierr = MPI_Allreduce(tmp,tmp2,mat->cmap->N,MPIU_REAL,MPIU_SUM,((PetscObject)mat)->comm);CHKERRQ(ierr);
1977       for (j=0; j<mat->cmap->N; j++) {
1978         if (tmp2[j] > *norm) *norm = tmp2[j];
1979       }
1980       ierr = PetscFree(tmp);CHKERRQ(ierr);
1981       ierr = PetscFree(tmp2);CHKERRQ(ierr);
1982     } else if (type == NORM_INFINITY) { /* max row norm */
1983       PetscReal ntemp = 0.0;
1984       for (j=0; j<aij->A->rmap->n; j++) {
1985         v = amat->a + amat->i[j];
1986         sum = 0.0;
1987         for (i=0; i<amat->i[j+1]-amat->i[j]; i++) {
1988           sum += PetscAbsScalar(*v); v++;
1989         }
1990         v = bmat->a + bmat->i[j];
1991         for (i=0; i<bmat->i[j+1]-bmat->i[j]; i++) {
1992           sum += PetscAbsScalar(*v); v++;
1993         }
1994         if (sum > ntemp) ntemp = sum;
1995       }
1996       ierr = MPI_Allreduce(&ntemp,norm,1,MPIU_REAL,MPIU_MAX,((PetscObject)mat)->comm);CHKERRQ(ierr);
1997     } else {
1998       SETERRQ(((PetscObject)mat)->comm,PETSC_ERR_SUP,"No support for two norm");
1999     }
2000   }
2001   PetscFunctionReturn(0);
2002 }
2003 
2004 #undef __FUNCT__
2005 #define __FUNCT__ "MatTranspose_MPIAIJ"
2006 PetscErrorCode MatTranspose_MPIAIJ(Mat A,MatReuse reuse,Mat *matout)
2007 {
2008   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2009   Mat_SeqAIJ     *Aloc=(Mat_SeqAIJ*)a->A->data,*Bloc=(Mat_SeqAIJ*)a->B->data;
2010   PetscErrorCode ierr;
2011   PetscInt       M = A->rmap->N,N = A->cmap->N,ma,na,mb,*ai,*aj,*bi,*bj,row,*cols,*cols_tmp,i,*d_nnz;
2012   PetscInt       cstart=A->cmap->rstart,ncol;
2013   Mat            B;
2014   MatScalar      *array;
2015 
2016   PetscFunctionBegin;
2017   if (reuse == MAT_REUSE_MATRIX && A == *matout && M != N) SETERRQ(((PetscObject)A)->comm,PETSC_ERR_ARG_SIZ,"Square matrix only for in-place");
2018 
2019   ma = A->rmap->n; na = A->cmap->n; mb = a->B->rmap->n;
2020   ai = Aloc->i; aj = Aloc->j;
2021   bi = Bloc->i; bj = Bloc->j;
2022   if (reuse == MAT_INITIAL_MATRIX || *matout == A) {
2023     /* compute d_nnz for preallocation; o_nnz is approximated by d_nnz to avoid communication */
2024     ierr = PetscMalloc((1+na)*sizeof(PetscInt),&d_nnz);CHKERRQ(ierr);
2025     ierr = PetscMemzero(d_nnz,(1+na)*sizeof(PetscInt));CHKERRQ(ierr);
2026     for (i=0; i<ai[ma]; i++){
2027       d_nnz[aj[i]] ++;
2028       aj[i] += cstart; /* global col index to be used by MatSetValues() */
2029     }
2030 
2031     ierr = MatCreate(((PetscObject)A)->comm,&B);CHKERRQ(ierr);
2032     ierr = MatSetSizes(B,A->cmap->n,A->rmap->n,N,M);CHKERRQ(ierr);
2033     ierr = MatSetBlockSizes(B,A->cmap->bs,A->rmap->bs); CHKERRQ(ierr);
2034     ierr = MatSetType(B,((PetscObject)A)->type_name);CHKERRQ(ierr);
2035     ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,d_nnz);CHKERRQ(ierr);
2036     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
2037     ierr = PetscFree(d_nnz);CHKERRQ(ierr);
2038   } else {
2039     B = *matout;
2040   }
2041 
2042   /* copy over the A part */
2043   array = Aloc->a;
2044   row = A->rmap->rstart;
2045   for (i=0; i<ma; i++) {
2046     ncol = ai[i+1]-ai[i];
2047     ierr = MatSetValues(B,ncol,aj,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
2048     row++; array += ncol; aj += ncol;
2049   }
2050   aj = Aloc->j;
2051   for (i=0; i<ai[ma]; i++) aj[i] -= cstart; /* resume local col index */
2052 
2053   /* copy over the B part */
2054   ierr = PetscMalloc(bi[mb]*sizeof(PetscInt),&cols);CHKERRQ(ierr);
2055   ierr = PetscMemzero(cols,bi[mb]*sizeof(PetscInt));CHKERRQ(ierr);
2056   array = Bloc->a;
2057   row = A->rmap->rstart;
2058   for (i=0; i<bi[mb]; i++) {cols[i] = a->garray[bj[i]];}
2059   cols_tmp = cols;
2060   for (i=0; i<mb; i++) {
2061     ncol = bi[i+1]-bi[i];
2062     ierr = MatSetValues(B,ncol,cols_tmp,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
2063     row++; array += ncol; cols_tmp += ncol;
2064   }
2065   ierr = PetscFree(cols);CHKERRQ(ierr);
2066 
2067   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2068   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2069   if (reuse == MAT_INITIAL_MATRIX || *matout != A) {
2070     *matout = B;
2071   } else {
2072     ierr = MatHeaderMerge(A,B);CHKERRQ(ierr);
2073   }
2074   PetscFunctionReturn(0);
2075 }
2076 
2077 #undef __FUNCT__
2078 #define __FUNCT__ "MatDiagonalScale_MPIAIJ"
2079 PetscErrorCode MatDiagonalScale_MPIAIJ(Mat mat,Vec ll,Vec rr)
2080 {
2081   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2082   Mat            a = aij->A,b = aij->B;
2083   PetscErrorCode ierr;
2084   PetscInt       s1,s2,s3;
2085 
2086   PetscFunctionBegin;
2087   ierr = MatGetLocalSize(mat,&s2,&s3);CHKERRQ(ierr);
2088   if (rr) {
2089     ierr = VecGetLocalSize(rr,&s1);CHKERRQ(ierr);
2090     if (s1!=s3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"right vector non-conforming local size");
2091     /* Overlap communication with computation. */
2092     ierr = VecScatterBegin(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2093   }
2094   if (ll) {
2095     ierr = VecGetLocalSize(ll,&s1);CHKERRQ(ierr);
2096     if (s1!=s2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"left vector non-conforming local size");
2097     ierr = (*b->ops->diagonalscale)(b,ll,0);CHKERRQ(ierr);
2098   }
2099   /* scale  the diagonal block */
2100   ierr = (*a->ops->diagonalscale)(a,ll,rr);CHKERRQ(ierr);
2101 
2102   if (rr) {
2103     /* Do a scatter end and then right scale the off-diagonal block */
2104     ierr = VecScatterEnd(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2105     ierr = (*b->ops->diagonalscale)(b,0,aij->lvec);CHKERRQ(ierr);
2106   }
2107 
2108   PetscFunctionReturn(0);
2109 }
2110 
2111 #undef __FUNCT__
2112 #define __FUNCT__ "MatSetUnfactored_MPIAIJ"
2113 PetscErrorCode MatSetUnfactored_MPIAIJ(Mat A)
2114 {
2115   Mat_MPIAIJ     *a   = (Mat_MPIAIJ*)A->data;
2116   PetscErrorCode ierr;
2117 
2118   PetscFunctionBegin;
2119   ierr = MatSetUnfactored(a->A);CHKERRQ(ierr);
2120   PetscFunctionReturn(0);
2121 }
2122 
2123 #undef __FUNCT__
2124 #define __FUNCT__ "MatEqual_MPIAIJ"
2125 PetscErrorCode MatEqual_MPIAIJ(Mat A,Mat B,PetscBool  *flag)
2126 {
2127   Mat_MPIAIJ     *matB = (Mat_MPIAIJ*)B->data,*matA = (Mat_MPIAIJ*)A->data;
2128   Mat            a,b,c,d;
2129   PetscBool      flg;
2130   PetscErrorCode ierr;
2131 
2132   PetscFunctionBegin;
2133   a = matA->A; b = matA->B;
2134   c = matB->A; d = matB->B;
2135 
2136   ierr = MatEqual(a,c,&flg);CHKERRQ(ierr);
2137   if (flg) {
2138     ierr = MatEqual(b,d,&flg);CHKERRQ(ierr);
2139   }
2140   ierr = MPI_Allreduce(&flg,flag,1,MPI_INT,MPI_LAND,((PetscObject)A)->comm);CHKERRQ(ierr);
2141   PetscFunctionReturn(0);
2142 }
2143 
2144 #undef __FUNCT__
2145 #define __FUNCT__ "MatCopy_MPIAIJ"
2146 PetscErrorCode MatCopy_MPIAIJ(Mat A,Mat B,MatStructure str)
2147 {
2148   PetscErrorCode ierr;
2149   Mat_MPIAIJ     *a = (Mat_MPIAIJ *)A->data;
2150   Mat_MPIAIJ     *b = (Mat_MPIAIJ *)B->data;
2151 
2152   PetscFunctionBegin;
2153   /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
2154   if ((str != SAME_NONZERO_PATTERN) || (A->ops->copy != B->ops->copy)) {
2155     /* because of the column compression in the off-processor part of the matrix a->B,
2156        the number of columns in a->B and b->B may be different, hence we cannot call
2157        the MatCopy() directly on the two parts. If need be, we can provide a more
2158        efficient copy than the MatCopy_Basic() by first uncompressing the a->B matrices
2159        then copying the submatrices */
2160     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
2161   } else {
2162     ierr = MatCopy(a->A,b->A,str);CHKERRQ(ierr);
2163     ierr = MatCopy(a->B,b->B,str);CHKERRQ(ierr);
2164   }
2165   PetscFunctionReturn(0);
2166 }
2167 
2168 #undef __FUNCT__
2169 #define __FUNCT__ "MatSetUp_MPIAIJ"
2170 PetscErrorCode MatSetUp_MPIAIJ(Mat A)
2171 {
2172   PetscErrorCode ierr;
2173 
2174   PetscFunctionBegin;
2175   ierr =  MatMPIAIJSetPreallocation(A,PETSC_DEFAULT,0,PETSC_DEFAULT,0);CHKERRQ(ierr);
2176   PetscFunctionReturn(0);
2177 }
2178 
2179 #undef __FUNCT__
2180 #define __FUNCT__ "MatAXPYGetPreallocation_MPIAIJ"
2181 /* This is the same as MatAXPYGetPreallocation_SeqAIJ, except that the local-to-global map is provided */
2182 static PetscErrorCode MatAXPYGetPreallocation_MPIAIJ(Mat Y,const PetscInt *yltog,Mat X,const PetscInt *xltog,PetscInt* nnz)
2183 {
2184   PetscInt          i,m=Y->rmap->N;
2185   Mat_SeqAIJ        *x = (Mat_SeqAIJ*)X->data;
2186   Mat_SeqAIJ        *y = (Mat_SeqAIJ*)Y->data;
2187   const PetscInt    *xi = x->i,*yi = y->i;
2188 
2189   PetscFunctionBegin;
2190   /* Set the number of nonzeros in the new matrix */
2191   for(i=0; i<m; i++) {
2192     PetscInt j,k,nzx = xi[i+1] - xi[i],nzy = yi[i+1] - yi[i];
2193     const PetscInt *xj = x->j+xi[i],*yj = y->j+yi[i];
2194     nnz[i] = 0;
2195     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2196       for (; k<nzy && yltog[yj[k]]<xltog[xj[j]]; k++) nnz[i]++; /* Catch up to X */
2197       if (k<nzy && yltog[yj[k]]==xltog[xj[j]]) k++;             /* Skip duplicate */
2198       nnz[i]++;
2199     }
2200     for (; k<nzy; k++) nnz[i]++;
2201   }
2202   PetscFunctionReturn(0);
2203 }
2204 
2205 #undef __FUNCT__
2206 #define __FUNCT__ "MatAXPY_MPIAIJ"
2207 PetscErrorCode MatAXPY_MPIAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
2208 {
2209   PetscErrorCode ierr;
2210   PetscInt       i;
2211   Mat_MPIAIJ     *xx = (Mat_MPIAIJ *)X->data,*yy = (Mat_MPIAIJ *)Y->data;
2212   PetscBLASInt   bnz,one=1;
2213   Mat_SeqAIJ     *x,*y;
2214 
2215   PetscFunctionBegin;
2216   if (str == SAME_NONZERO_PATTERN) {
2217     PetscScalar alpha = a;
2218     x = (Mat_SeqAIJ *)xx->A->data;
2219     y = (Mat_SeqAIJ *)yy->A->data;
2220     bnz = PetscBLASIntCast(x->nz);
2221     BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one);
2222     x = (Mat_SeqAIJ *)xx->B->data;
2223     y = (Mat_SeqAIJ *)yy->B->data;
2224     bnz = PetscBLASIntCast(x->nz);
2225     BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one);
2226   } else if (str == SUBSET_NONZERO_PATTERN) {
2227     ierr = MatAXPY_SeqAIJ(yy->A,a,xx->A,str);CHKERRQ(ierr);
2228 
2229     x = (Mat_SeqAIJ *)xx->B->data;
2230     y = (Mat_SeqAIJ *)yy->B->data;
2231     if (y->xtoy && y->XtoY != xx->B) {
2232       ierr = PetscFree(y->xtoy);CHKERRQ(ierr);
2233       ierr = MatDestroy(&y->XtoY);CHKERRQ(ierr);
2234     }
2235     if (!y->xtoy) { /* get xtoy */
2236       ierr = MatAXPYGetxtoy_Private(xx->B->rmap->n,x->i,x->j,xx->garray,y->i,y->j,yy->garray,&y->xtoy);CHKERRQ(ierr);
2237       y->XtoY = xx->B;
2238       ierr = PetscObjectReference((PetscObject)xx->B);CHKERRQ(ierr);
2239     }
2240     for (i=0; i<x->nz; i++) y->a[y->xtoy[i]] += a*(x->a[i]);
2241   } else {
2242     Mat B;
2243     PetscInt *nnz_d,*nnz_o;
2244     ierr = PetscMalloc(yy->A->rmap->N*sizeof(PetscInt),&nnz_d);CHKERRQ(ierr);
2245     ierr = PetscMalloc(yy->B->rmap->N*sizeof(PetscInt),&nnz_o);CHKERRQ(ierr);
2246     ierr = MatCreate(((PetscObject)Y)->comm,&B);CHKERRQ(ierr);
2247     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
2248     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
2249     ierr = MatSetBlockSizes(B,Y->rmap->bs,Y->cmap->bs);CHKERRQ(ierr);
2250     ierr = MatSetType(B,MATMPIAIJ);CHKERRQ(ierr);
2251     ierr = MatAXPYGetPreallocation_SeqAIJ(yy->A,xx->A,nnz_d);CHKERRQ(ierr);
2252     ierr = MatAXPYGetPreallocation_MPIAIJ(yy->B,yy->garray,xx->B,xx->garray,nnz_o);CHKERRQ(ierr);
2253     ierr = MatMPIAIJSetPreallocation(B,0,nnz_d,0,nnz_o);CHKERRQ(ierr);
2254     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
2255     ierr = MatHeaderReplace(Y,B);
2256     ierr = PetscFree(nnz_d);CHKERRQ(ierr);
2257     ierr = PetscFree(nnz_o);CHKERRQ(ierr);
2258   }
2259   PetscFunctionReturn(0);
2260 }
2261 
2262 extern PetscErrorCode  MatConjugate_SeqAIJ(Mat);
2263 
2264 #undef __FUNCT__
2265 #define __FUNCT__ "MatConjugate_MPIAIJ"
2266 PetscErrorCode  MatConjugate_MPIAIJ(Mat mat)
2267 {
2268 #if defined(PETSC_USE_COMPLEX)
2269   PetscErrorCode ierr;
2270   Mat_MPIAIJ     *aij = (Mat_MPIAIJ *)mat->data;
2271 
2272   PetscFunctionBegin;
2273   ierr = MatConjugate_SeqAIJ(aij->A);CHKERRQ(ierr);
2274   ierr = MatConjugate_SeqAIJ(aij->B);CHKERRQ(ierr);
2275 #else
2276   PetscFunctionBegin;
2277 #endif
2278   PetscFunctionReturn(0);
2279 }
2280 
2281 #undef __FUNCT__
2282 #define __FUNCT__ "MatRealPart_MPIAIJ"
2283 PetscErrorCode MatRealPart_MPIAIJ(Mat A)
2284 {
2285   Mat_MPIAIJ   *a = (Mat_MPIAIJ*)A->data;
2286   PetscErrorCode ierr;
2287 
2288   PetscFunctionBegin;
2289   ierr = MatRealPart(a->A);CHKERRQ(ierr);
2290   ierr = MatRealPart(a->B);CHKERRQ(ierr);
2291   PetscFunctionReturn(0);
2292 }
2293 
2294 #undef __FUNCT__
2295 #define __FUNCT__ "MatImaginaryPart_MPIAIJ"
2296 PetscErrorCode MatImaginaryPart_MPIAIJ(Mat A)
2297 {
2298   Mat_MPIAIJ   *a = (Mat_MPIAIJ*)A->data;
2299   PetscErrorCode ierr;
2300 
2301   PetscFunctionBegin;
2302   ierr = MatImaginaryPart(a->A);CHKERRQ(ierr);
2303   ierr = MatImaginaryPart(a->B);CHKERRQ(ierr);
2304   PetscFunctionReturn(0);
2305 }
2306 
2307 #ifdef PETSC_HAVE_PBGL
2308 
2309 #include <boost/parallel/mpi/bsp_process_group.hpp>
2310 #include <boost/graph/distributed/ilu_default_graph.hpp>
2311 #include <boost/graph/distributed/ilu_0_block.hpp>
2312 #include <boost/graph/distributed/ilu_preconditioner.hpp>
2313 #include <boost/graph/distributed/petsc/interface.hpp>
2314 #include <boost/multi_array.hpp>
2315 #include <boost/parallel/distributed_property_map->hpp>
2316 
2317 #undef __FUNCT__
2318 #define __FUNCT__ "MatILUFactorSymbolic_MPIAIJ"
2319 /*
2320   This uses the parallel ILU factorization of Peter Gottschling <pgottsch@osl.iu.edu>
2321 */
2322 PetscErrorCode MatILUFactorSymbolic_MPIAIJ(Mat fact,Mat A, IS isrow, IS iscol, const MatFactorInfo *info)
2323 {
2324   namespace petsc = boost::distributed::petsc;
2325 
2326   namespace graph_dist = boost::graph::distributed;
2327   using boost::graph::distributed::ilu_default::process_group_type;
2328   using boost::graph::ilu_permuted;
2329 
2330   PetscBool       row_identity, col_identity;
2331   PetscContainer  c;
2332   PetscInt        m, n, M, N;
2333   PetscErrorCode  ierr;
2334 
2335   PetscFunctionBegin;
2336   if (info->levels != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only levels = 0 supported for parallel ilu");
2337   ierr = ISIdentity(isrow, &row_identity);CHKERRQ(ierr);
2338   ierr = ISIdentity(iscol, &col_identity);CHKERRQ(ierr);
2339   if (!row_identity || !col_identity) {
2340     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Row and column permutations must be identity for parallel ILU");
2341   }
2342 
2343   process_group_type pg;
2344   typedef graph_dist::ilu_default::ilu_level_graph_type  lgraph_type;
2345   lgraph_type*   lgraph_p = new lgraph_type(petsc::num_global_vertices(A), pg, petsc::matrix_distribution(A, pg));
2346   lgraph_type&   level_graph = *lgraph_p;
2347   graph_dist::ilu_default::graph_type&            graph(level_graph.graph);
2348 
2349   petsc::read_matrix(A, graph, get(boost::edge_weight, graph));
2350   ilu_permuted(level_graph);
2351 
2352   /* put together the new matrix */
2353   ierr = MatCreate(((PetscObject)A)->comm, fact);CHKERRQ(ierr);
2354   ierr = MatGetLocalSize(A, &m, &n);CHKERRQ(ierr);
2355   ierr = MatGetSize(A, &M, &N);CHKERRQ(ierr);
2356   ierr = MatSetSizes(fact, m, n, M, N);CHKERRQ(ierr);
2357   ierr = MatSetBlockSizes(fact,A->rmap->bs,A->cmap->bs); CHKERRQ(ierr);
2358   ierr = MatSetType(fact, ((PetscObject)A)->type_name);CHKERRQ(ierr);
2359   ierr = MatAssemblyBegin(fact, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2360   ierr = MatAssemblyEnd(fact, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2361 
2362   ierr = PetscContainerCreate(((PetscObject)A)->comm, &c);
2363   ierr = PetscContainerSetPointer(c, lgraph_p);
2364   ierr = PetscObjectCompose((PetscObject) (fact), "graph", (PetscObject) c);
2365   ierr = PetscContainerDestroy(&c);
2366   PetscFunctionReturn(0);
2367 }
2368 
2369 #undef __FUNCT__
2370 #define __FUNCT__ "MatLUFactorNumeric_MPIAIJ"
2371 PetscErrorCode MatLUFactorNumeric_MPIAIJ(Mat B,Mat A, const MatFactorInfo *info)
2372 {
2373   PetscFunctionBegin;
2374   PetscFunctionReturn(0);
2375 }
2376 
2377 #undef __FUNCT__
2378 #define __FUNCT__ "MatSolve_MPIAIJ"
2379 /*
2380   This uses the parallel ILU factorization of Peter Gottschling <pgottsch@osl.iu.edu>
2381 */
2382 PetscErrorCode MatSolve_MPIAIJ(Mat A, Vec b, Vec x)
2383 {
2384   namespace graph_dist = boost::graph::distributed;
2385 
2386   typedef graph_dist::ilu_default::ilu_level_graph_type  lgraph_type;
2387   lgraph_type*   lgraph_p;
2388   PetscContainer c;
2389   PetscErrorCode ierr;
2390 
2391   PetscFunctionBegin;
2392   ierr = PetscObjectQuery((PetscObject) A, "graph", (PetscObject *) &c);CHKERRQ(ierr);
2393   ierr = PetscContainerGetPointer(c, (void **) &lgraph_p);CHKERRQ(ierr);
2394   ierr = VecCopy(b, x);CHKERRQ(ierr);
2395 
2396   PetscScalar* array_x;
2397   ierr = VecGetArray(x, &array_x);CHKERRQ(ierr);
2398   PetscInt sx;
2399   ierr = VecGetSize(x, &sx);CHKERRQ(ierr);
2400 
2401   PetscScalar* array_b;
2402   ierr = VecGetArray(b, &array_b);CHKERRQ(ierr);
2403   PetscInt sb;
2404   ierr = VecGetSize(b, &sb);CHKERRQ(ierr);
2405 
2406   lgraph_type&   level_graph = *lgraph_p;
2407   graph_dist::ilu_default::graph_type&            graph(level_graph.graph);
2408 
2409   typedef boost::multi_array_ref<PetscScalar, 1> array_ref_type;
2410   array_ref_type                                 ref_b(array_b, boost::extents[num_vertices(graph)]),
2411                                                  ref_x(array_x, boost::extents[num_vertices(graph)]);
2412 
2413   typedef boost::iterator_property_map<array_ref_type::iterator,
2414                                 boost::property_map<graph_dist::ilu_default::graph_type, boost::vertex_index_t>::type>  gvector_type;
2415   gvector_type                                   vector_b(ref_b.begin(), get(boost::vertex_index, graph)),
2416                                                  vector_x(ref_x.begin(), get(boost::vertex_index, graph));
2417 
2418   ilu_set_solve(*lgraph_p, vector_b, vector_x);
2419 
2420   PetscFunctionReturn(0);
2421 }
2422 #endif
2423 
2424 typedef struct { /* used by MatGetRedundantMatrix() for reusing matredundant */
2425   PetscInt       nzlocal,nsends,nrecvs;
2426   PetscMPIInt    *send_rank,*recv_rank;
2427   PetscInt       *sbuf_nz,*rbuf_nz,*sbuf_j,**rbuf_j;
2428   PetscScalar    *sbuf_a,**rbuf_a;
2429   PetscErrorCode (*Destroy)(Mat);
2430 } Mat_Redundant;
2431 
2432 #undef __FUNCT__
2433 #define __FUNCT__ "PetscContainerDestroy_MatRedundant"
2434 PetscErrorCode PetscContainerDestroy_MatRedundant(void *ptr)
2435 {
2436   PetscErrorCode       ierr;
2437   Mat_Redundant        *redund=(Mat_Redundant*)ptr;
2438   PetscInt             i;
2439 
2440   PetscFunctionBegin;
2441   ierr = PetscFree2(redund->send_rank,redund->recv_rank);CHKERRQ(ierr);
2442   ierr = PetscFree(redund->sbuf_j);CHKERRQ(ierr);
2443   ierr = PetscFree(redund->sbuf_a);CHKERRQ(ierr);
2444   for (i=0; i<redund->nrecvs; i++){
2445     ierr = PetscFree(redund->rbuf_j[i]);CHKERRQ(ierr);
2446     ierr = PetscFree(redund->rbuf_a[i]);CHKERRQ(ierr);
2447   }
2448   ierr = PetscFree4(redund->sbuf_nz,redund->rbuf_nz,redund->rbuf_j,redund->rbuf_a);CHKERRQ(ierr);
2449   ierr = PetscFree(redund);CHKERRQ(ierr);
2450   PetscFunctionReturn(0);
2451 }
2452 
2453 #undef __FUNCT__
2454 #define __FUNCT__ "MatDestroy_MatRedundant"
2455 PetscErrorCode MatDestroy_MatRedundant(Mat A)
2456 {
2457   PetscErrorCode  ierr;
2458   PetscContainer  container;
2459   Mat_Redundant   *redund=PETSC_NULL;
2460 
2461   PetscFunctionBegin;
2462   ierr = PetscObjectQuery((PetscObject)A,"Mat_Redundant",(PetscObject *)&container);CHKERRQ(ierr);
2463   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
2464   ierr = PetscContainerGetPointer(container,(void **)&redund);CHKERRQ(ierr);
2465   A->ops->destroy = redund->Destroy;
2466   ierr = PetscObjectCompose((PetscObject)A,"Mat_Redundant",0);CHKERRQ(ierr);
2467   if (A->ops->destroy) {
2468     ierr = (*A->ops->destroy)(A);CHKERRQ(ierr);
2469   }
2470   PetscFunctionReturn(0);
2471 }
2472 
2473 #undef __FUNCT__
2474 #define __FUNCT__ "MatGetRedundantMatrix_MPIAIJ"
2475 PetscErrorCode MatGetRedundantMatrix_MPIAIJ(Mat mat,PetscInt nsubcomm,MPI_Comm subcomm,PetscInt mlocal_sub,MatReuse reuse,Mat *matredundant)
2476 {
2477   PetscMPIInt    rank,size;
2478   MPI_Comm       comm=((PetscObject)mat)->comm;
2479   PetscErrorCode ierr;
2480   PetscInt       nsends=0,nrecvs=0,i,rownz_max=0;
2481   PetscMPIInt    *send_rank=PETSC_NULL,*recv_rank=PETSC_NULL;
2482   PetscInt       *rowrange=mat->rmap->range;
2483   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2484   Mat            A=aij->A,B=aij->B,C=*matredundant;
2485   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data;
2486   PetscScalar    *sbuf_a;
2487   PetscInt       nzlocal=a->nz+b->nz;
2488   PetscInt       j,cstart=mat->cmap->rstart,cend=mat->cmap->rend,row,nzA,nzB,ncols,*cworkA,*cworkB;
2489   PetscInt       rstart=mat->rmap->rstart,rend=mat->rmap->rend,*bmap=aij->garray,M,N;
2490   PetscInt       *cols,ctmp,lwrite,*rptr,l,*sbuf_j;
2491   MatScalar      *aworkA,*aworkB;
2492   PetscScalar    *vals;
2493   PetscMPIInt    tag1,tag2,tag3,imdex;
2494   MPI_Request    *s_waits1=PETSC_NULL,*s_waits2=PETSC_NULL,*s_waits3=PETSC_NULL,
2495                  *r_waits1=PETSC_NULL,*r_waits2=PETSC_NULL,*r_waits3=PETSC_NULL;
2496   MPI_Status     recv_status,*send_status;
2497   PetscInt       *sbuf_nz=PETSC_NULL,*rbuf_nz=PETSC_NULL,count;
2498   PetscInt       **rbuf_j=PETSC_NULL;
2499   PetscScalar    **rbuf_a=PETSC_NULL;
2500   Mat_Redundant  *redund=PETSC_NULL;
2501   PetscContainer container;
2502 
2503   PetscFunctionBegin;
2504   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2505   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2506 
2507   if (reuse == MAT_REUSE_MATRIX) {
2508     ierr = MatGetSize(C,&M,&N);CHKERRQ(ierr);
2509     if (M != N || M != mat->rmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. Wrong global size");
2510     ierr = MatGetLocalSize(C,&M,&N);CHKERRQ(ierr);
2511     if (M != N || M != mlocal_sub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. Wrong local size");
2512     ierr = PetscObjectQuery((PetscObject)C,"Mat_Redundant",(PetscObject *)&container);CHKERRQ(ierr);
2513     if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
2514     ierr = PetscContainerGetPointer(container,(void **)&redund);CHKERRQ(ierr);
2515     if (nzlocal != redund->nzlocal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. Wrong nzlocal");
2516 
2517     nsends    = redund->nsends;
2518     nrecvs    = redund->nrecvs;
2519     send_rank = redund->send_rank;
2520     recv_rank = redund->recv_rank;
2521     sbuf_nz   = redund->sbuf_nz;
2522     rbuf_nz   = redund->rbuf_nz;
2523     sbuf_j    = redund->sbuf_j;
2524     sbuf_a    = redund->sbuf_a;
2525     rbuf_j    = redund->rbuf_j;
2526     rbuf_a    = redund->rbuf_a;
2527   }
2528 
2529   if (reuse == MAT_INITIAL_MATRIX){
2530     PetscMPIInt  subrank,subsize;
2531     PetscInt     nleftover,np_subcomm;
2532     /* get the destination processors' id send_rank, nsends and nrecvs */
2533     ierr = MPI_Comm_rank(subcomm,&subrank);CHKERRQ(ierr);
2534     ierr = MPI_Comm_size(subcomm,&subsize);CHKERRQ(ierr);
2535     ierr = PetscMalloc2(size,PetscMPIInt,&send_rank,size,PetscMPIInt,&recv_rank);
2536     np_subcomm = size/nsubcomm;
2537     nleftover  = size - nsubcomm*np_subcomm;
2538     nsends = 0; nrecvs = 0;
2539     for (i=0; i<size; i++){ /* i=rank*/
2540       if (subrank == i/nsubcomm && rank != i){ /* my_subrank == other's subrank */
2541         send_rank[nsends] = i; nsends++;
2542         recv_rank[nrecvs++] = i;
2543       }
2544     }
2545     if (rank >= size - nleftover){/* this proc is a leftover processor */
2546       i = size-nleftover-1;
2547       j = 0;
2548       while (j < nsubcomm - nleftover){
2549         send_rank[nsends++] = i;
2550         i--; j++;
2551       }
2552     }
2553 
2554     if (nleftover && subsize == size/nsubcomm && subrank==subsize-1){ /* this proc recvs from leftover processors */
2555       for (i=0; i<nleftover; i++){
2556         recv_rank[nrecvs++] = size-nleftover+i;
2557       }
2558     }
2559 
2560     /* allocate sbuf_j, sbuf_a */
2561     i = nzlocal + rowrange[rank+1] - rowrange[rank] + 2;
2562     ierr = PetscMalloc(i*sizeof(PetscInt),&sbuf_j);CHKERRQ(ierr);
2563     ierr = PetscMalloc((nzlocal+1)*sizeof(PetscScalar),&sbuf_a);CHKERRQ(ierr);
2564   } /* endof if (reuse == MAT_INITIAL_MATRIX) */
2565 
2566   /* copy mat's local entries into the buffers */
2567   if (reuse == MAT_INITIAL_MATRIX){
2568     rownz_max = 0;
2569     rptr = sbuf_j;
2570     cols = sbuf_j + rend-rstart + 1;
2571     vals = sbuf_a;
2572     rptr[0] = 0;
2573     for (i=0; i<rend-rstart; i++){
2574       row = i + rstart;
2575       nzA    = a->i[i+1] - a->i[i]; nzB = b->i[i+1] - b->i[i];
2576       ncols  = nzA + nzB;
2577       cworkA = a->j + a->i[i]; cworkB = b->j + b->i[i];
2578       aworkA = a->a + a->i[i]; aworkB = b->a + b->i[i];
2579       /* load the column indices for this row into cols */
2580       lwrite = 0;
2581       for (l=0; l<nzB; l++) {
2582         if ((ctmp = bmap[cworkB[l]]) < cstart){
2583           vals[lwrite]   = aworkB[l];
2584           cols[lwrite++] = ctmp;
2585         }
2586       }
2587       for (l=0; l<nzA; l++){
2588         vals[lwrite]   = aworkA[l];
2589         cols[lwrite++] = cstart + cworkA[l];
2590       }
2591       for (l=0; l<nzB; l++) {
2592         if ((ctmp = bmap[cworkB[l]]) >= cend){
2593           vals[lwrite]   = aworkB[l];
2594           cols[lwrite++] = ctmp;
2595         }
2596       }
2597       vals += ncols;
2598       cols += ncols;
2599       rptr[i+1] = rptr[i] + ncols;
2600       if (rownz_max < ncols) rownz_max = ncols;
2601     }
2602     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);
2603   } else { /* only copy matrix values into sbuf_a */
2604     rptr = sbuf_j;
2605     vals = sbuf_a;
2606     rptr[0] = 0;
2607     for (i=0; i<rend-rstart; i++){
2608       row = i + rstart;
2609       nzA    = a->i[i+1] - a->i[i]; nzB = b->i[i+1] - b->i[i];
2610       ncols  = nzA + nzB;
2611       cworkA = a->j + a->i[i]; cworkB = b->j + b->i[i];
2612       aworkA = a->a + a->i[i]; aworkB = b->a + b->i[i];
2613       lwrite = 0;
2614       for (l=0; l<nzB; l++) {
2615         if ((ctmp = bmap[cworkB[l]]) < cstart) vals[lwrite++] = aworkB[l];
2616       }
2617       for (l=0; l<nzA; l++) vals[lwrite++] = aworkA[l];
2618       for (l=0; l<nzB; l++) {
2619         if ((ctmp = bmap[cworkB[l]]) >= cend) vals[lwrite++] = aworkB[l];
2620       }
2621       vals += ncols;
2622       rptr[i+1] = rptr[i] + ncols;
2623     }
2624   } /* endof if (reuse == MAT_INITIAL_MATRIX) */
2625 
2626   /* send nzlocal to others, and recv other's nzlocal */
2627   /*--------------------------------------------------*/
2628   if (reuse == MAT_INITIAL_MATRIX){
2629     ierr = PetscMalloc2(3*(nsends + nrecvs)+1,MPI_Request,&s_waits3,nsends+1,MPI_Status,&send_status);CHKERRQ(ierr);
2630     s_waits2 = s_waits3 + nsends;
2631     s_waits1 = s_waits2 + nsends;
2632     r_waits1 = s_waits1 + nsends;
2633     r_waits2 = r_waits1 + nrecvs;
2634     r_waits3 = r_waits2 + nrecvs;
2635   } else {
2636     ierr = PetscMalloc2(nsends + nrecvs +1,MPI_Request,&s_waits3,nsends+1,MPI_Status,&send_status);CHKERRQ(ierr);
2637     r_waits3 = s_waits3 + nsends;
2638   }
2639 
2640   ierr = PetscObjectGetNewTag((PetscObject)mat,&tag3);CHKERRQ(ierr);
2641   if (reuse == MAT_INITIAL_MATRIX){
2642     /* get new tags to keep the communication clean */
2643     ierr = PetscObjectGetNewTag((PetscObject)mat,&tag1);CHKERRQ(ierr);
2644     ierr = PetscObjectGetNewTag((PetscObject)mat,&tag2);CHKERRQ(ierr);
2645     ierr = PetscMalloc4(nsends,PetscInt,&sbuf_nz,nrecvs,PetscInt,&rbuf_nz,nrecvs,PetscInt*,&rbuf_j,nrecvs,PetscScalar*,&rbuf_a);CHKERRQ(ierr);
2646 
2647     /* post receives of other's nzlocal */
2648     for (i=0; i<nrecvs; i++){
2649       ierr = MPI_Irecv(rbuf_nz+i,1,MPIU_INT,MPI_ANY_SOURCE,tag1,comm,r_waits1+i);CHKERRQ(ierr);
2650     }
2651     /* send nzlocal to others */
2652     for (i=0; i<nsends; i++){
2653       sbuf_nz[i] = nzlocal;
2654       ierr = MPI_Isend(sbuf_nz+i,1,MPIU_INT,send_rank[i],tag1,comm,s_waits1+i);CHKERRQ(ierr);
2655     }
2656     /* wait on receives of nzlocal; allocate space for rbuf_j, rbuf_a */
2657     count = nrecvs;
2658     while (count) {
2659       ierr = MPI_Waitany(nrecvs,r_waits1,&imdex,&recv_status);CHKERRQ(ierr);
2660       recv_rank[imdex] = recv_status.MPI_SOURCE;
2661       /* allocate rbuf_a and rbuf_j; then post receives of rbuf_j */
2662       ierr = PetscMalloc((rbuf_nz[imdex]+1)*sizeof(PetscScalar),&rbuf_a[imdex]);CHKERRQ(ierr);
2663 
2664       i = rowrange[recv_status.MPI_SOURCE+1] - rowrange[recv_status.MPI_SOURCE]; /* number of expected mat->i */
2665       rbuf_nz[imdex] += i + 2;
2666       ierr = PetscMalloc(rbuf_nz[imdex]*sizeof(PetscInt),&rbuf_j[imdex]);CHKERRQ(ierr);
2667       ierr = MPI_Irecv(rbuf_j[imdex],rbuf_nz[imdex],MPIU_INT,recv_status.MPI_SOURCE,tag2,comm,r_waits2+imdex);CHKERRQ(ierr);
2668       count--;
2669     }
2670     /* wait on sends of nzlocal */
2671     if (nsends) {ierr = MPI_Waitall(nsends,s_waits1,send_status);CHKERRQ(ierr);}
2672     /* send mat->i,j to others, and recv from other's */
2673     /*------------------------------------------------*/
2674     for (i=0; i<nsends; i++){
2675       j = nzlocal + rowrange[rank+1] - rowrange[rank] + 1;
2676       ierr = MPI_Isend(sbuf_j,j,MPIU_INT,send_rank[i],tag2,comm,s_waits2+i);CHKERRQ(ierr);
2677     }
2678     /* wait on receives of mat->i,j */
2679     /*------------------------------*/
2680     count = nrecvs;
2681     while (count) {
2682       ierr = MPI_Waitany(nrecvs,r_waits2,&imdex,&recv_status);CHKERRQ(ierr);
2683       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);
2684       count--;
2685     }
2686     /* wait on sends of mat->i,j */
2687     /*---------------------------*/
2688     if (nsends) {
2689       ierr = MPI_Waitall(nsends,s_waits2,send_status);CHKERRQ(ierr);
2690     }
2691   } /* endof if (reuse == MAT_INITIAL_MATRIX) */
2692 
2693   /* post receives, send and receive mat->a */
2694   /*----------------------------------------*/
2695   for (imdex=0; imdex<nrecvs; imdex++) {
2696     ierr = MPI_Irecv(rbuf_a[imdex],rbuf_nz[imdex],MPIU_SCALAR,recv_rank[imdex],tag3,comm,r_waits3+imdex);CHKERRQ(ierr);
2697   }
2698   for (i=0; i<nsends; i++){
2699     ierr = MPI_Isend(sbuf_a,nzlocal,MPIU_SCALAR,send_rank[i],tag3,comm,s_waits3+i);CHKERRQ(ierr);
2700   }
2701   count = nrecvs;
2702   while (count) {
2703     ierr = MPI_Waitany(nrecvs,r_waits3,&imdex,&recv_status);CHKERRQ(ierr);
2704     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);
2705     count--;
2706   }
2707   if (nsends) {
2708     ierr = MPI_Waitall(nsends,s_waits3,send_status);CHKERRQ(ierr);
2709   }
2710 
2711   ierr = PetscFree2(s_waits3,send_status);CHKERRQ(ierr);
2712 
2713   /* create redundant matrix */
2714   /*-------------------------*/
2715   if (reuse == MAT_INITIAL_MATRIX){
2716     /* compute rownz_max for preallocation */
2717     for (imdex=0; imdex<nrecvs; imdex++){
2718       j = rowrange[recv_rank[imdex]+1] - rowrange[recv_rank[imdex]];
2719       rptr = rbuf_j[imdex];
2720       for (i=0; i<j; i++){
2721         ncols = rptr[i+1] - rptr[i];
2722         if (rownz_max < ncols) rownz_max = ncols;
2723       }
2724     }
2725 
2726     ierr = MatCreate(subcomm,&C);CHKERRQ(ierr);
2727     ierr = MatSetSizes(C,mlocal_sub,mlocal_sub,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
2728     ierr = MatSetBlockSizes(C,mat->rmap->bs,mat->cmap->bs); CHKERRQ(ierr);
2729     ierr = MatSetFromOptions(C);CHKERRQ(ierr);
2730     ierr = MatSeqAIJSetPreallocation(C,rownz_max,PETSC_NULL);CHKERRQ(ierr);
2731     ierr = MatMPIAIJSetPreallocation(C,rownz_max,PETSC_NULL,rownz_max,PETSC_NULL);CHKERRQ(ierr);
2732   } else {
2733     C = *matredundant;
2734   }
2735 
2736   /* insert local matrix entries */
2737   rptr = sbuf_j;
2738   cols = sbuf_j + rend-rstart + 1;
2739   vals = sbuf_a;
2740   for (i=0; i<rend-rstart; i++){
2741     row   = i + rstart;
2742     ncols = rptr[i+1] - rptr[i];
2743     ierr = MatSetValues(C,1,&row,ncols,cols,vals,INSERT_VALUES);CHKERRQ(ierr);
2744     vals += ncols;
2745     cols += ncols;
2746   }
2747   /* insert received matrix entries */
2748   for (imdex=0; imdex<nrecvs; imdex++){
2749     rstart = rowrange[recv_rank[imdex]];
2750     rend   = rowrange[recv_rank[imdex]+1];
2751     rptr = rbuf_j[imdex];
2752     cols = rbuf_j[imdex] + rend-rstart + 1;
2753     vals = rbuf_a[imdex];
2754     for (i=0; i<rend-rstart; i++){
2755       row   = i + rstart;
2756       ncols = rptr[i+1] - rptr[i];
2757       ierr = MatSetValues(C,1,&row,ncols,cols,vals,INSERT_VALUES);CHKERRQ(ierr);
2758       vals += ncols;
2759       cols += ncols;
2760     }
2761   }
2762   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2763   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2764   ierr = MatGetSize(C,&M,&N);CHKERRQ(ierr);
2765   if (M != mat->rmap->N || N != mat->cmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"redundant mat size %d != input mat size %d",M,mat->rmap->N);
2766   if (reuse == MAT_INITIAL_MATRIX) {
2767     PetscContainer container;
2768     *matredundant = C;
2769     /* create a supporting struct and attach it to C for reuse */
2770     ierr = PetscNewLog(C,Mat_Redundant,&redund);CHKERRQ(ierr);
2771     ierr = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
2772     ierr = PetscContainerSetPointer(container,redund);CHKERRQ(ierr);
2773     ierr = PetscContainerSetUserDestroy(container,PetscContainerDestroy_MatRedundant);CHKERRQ(ierr);
2774     ierr = PetscObjectCompose((PetscObject)C,"Mat_Redundant",(PetscObject)container);CHKERRQ(ierr);
2775     ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
2776 
2777     redund->nzlocal = nzlocal;
2778     redund->nsends  = nsends;
2779     redund->nrecvs  = nrecvs;
2780     redund->send_rank = send_rank;
2781     redund->recv_rank = recv_rank;
2782     redund->sbuf_nz = sbuf_nz;
2783     redund->rbuf_nz = rbuf_nz;
2784     redund->sbuf_j  = sbuf_j;
2785     redund->sbuf_a  = sbuf_a;
2786     redund->rbuf_j  = rbuf_j;
2787     redund->rbuf_a  = rbuf_a;
2788 
2789     redund->Destroy = C->ops->destroy;
2790     C->ops->destroy = MatDestroy_MatRedundant;
2791   }
2792   PetscFunctionReturn(0);
2793 }
2794 
2795 #undef __FUNCT__
2796 #define __FUNCT__ "MatGetRowMaxAbs_MPIAIJ"
2797 PetscErrorCode MatGetRowMaxAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2798 {
2799   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2800   PetscErrorCode ierr;
2801   PetscInt       i,*idxb = 0;
2802   PetscScalar    *va,*vb;
2803   Vec            vtmp;
2804 
2805   PetscFunctionBegin;
2806   ierr = MatGetRowMaxAbs(a->A,v,idx);CHKERRQ(ierr);
2807   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2808   if (idx) {
2809     for (i=0; i<A->rmap->n; i++) {
2810       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2811     }
2812   }
2813 
2814   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2815   if (idx) {
2816     ierr = PetscMalloc(A->rmap->n*sizeof(PetscInt),&idxb);CHKERRQ(ierr);
2817   }
2818   ierr = MatGetRowMaxAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2819   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2820 
2821   for (i=0; i<A->rmap->n; i++){
2822     if (PetscAbsScalar(va[i]) < PetscAbsScalar(vb[i])) {
2823       va[i] = vb[i];
2824       if (idx) idx[i] = a->garray[idxb[i]];
2825     }
2826   }
2827 
2828   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2829   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2830   ierr = PetscFree(idxb);CHKERRQ(ierr);
2831   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2832   PetscFunctionReturn(0);
2833 }
2834 
2835 #undef __FUNCT__
2836 #define __FUNCT__ "MatGetRowMinAbs_MPIAIJ"
2837 PetscErrorCode MatGetRowMinAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2838 {
2839   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2840   PetscErrorCode ierr;
2841   PetscInt       i,*idxb = 0;
2842   PetscScalar    *va,*vb;
2843   Vec            vtmp;
2844 
2845   PetscFunctionBegin;
2846   ierr = MatGetRowMinAbs(a->A,v,idx);CHKERRQ(ierr);
2847   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2848   if (idx) {
2849     for (i=0; i<A->cmap->n; i++) {
2850       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2851     }
2852   }
2853 
2854   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2855   if (idx) {
2856     ierr = PetscMalloc(A->rmap->n*sizeof(PetscInt),&idxb);CHKERRQ(ierr);
2857   }
2858   ierr = MatGetRowMinAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2859   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2860 
2861   for (i=0; i<A->rmap->n; i++){
2862     if (PetscAbsScalar(va[i]) > PetscAbsScalar(vb[i])) {
2863       va[i] = vb[i];
2864       if (idx) idx[i] = a->garray[idxb[i]];
2865     }
2866   }
2867 
2868   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2869   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2870   ierr = PetscFree(idxb);CHKERRQ(ierr);
2871   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2872   PetscFunctionReturn(0);
2873 }
2874 
2875 #undef __FUNCT__
2876 #define __FUNCT__ "MatGetRowMin_MPIAIJ"
2877 PetscErrorCode MatGetRowMin_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2878 {
2879   Mat_MPIAIJ    *mat    = (Mat_MPIAIJ *) A->data;
2880   PetscInt       n      = A->rmap->n;
2881   PetscInt       cstart = A->cmap->rstart;
2882   PetscInt      *cmap   = mat->garray;
2883   PetscInt      *diagIdx, *offdiagIdx;
2884   Vec            diagV, offdiagV;
2885   PetscScalar   *a, *diagA, *offdiagA;
2886   PetscInt       r;
2887   PetscErrorCode ierr;
2888 
2889   PetscFunctionBegin;
2890   ierr = PetscMalloc2(n,PetscInt,&diagIdx,n,PetscInt,&offdiagIdx);CHKERRQ(ierr);
2891   ierr = VecCreateSeq(((PetscObject)A)->comm, n, &diagV);CHKERRQ(ierr);
2892   ierr = VecCreateSeq(((PetscObject)A)->comm, n, &offdiagV);CHKERRQ(ierr);
2893   ierr = MatGetRowMin(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2894   ierr = MatGetRowMin(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2895   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2896   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2897   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2898   for(r = 0; r < n; ++r) {
2899     if (PetscAbsScalar(diagA[r]) <= PetscAbsScalar(offdiagA[r])) {
2900       a[r]   = diagA[r];
2901       idx[r] = cstart + diagIdx[r];
2902     } else {
2903       a[r]   = offdiagA[r];
2904       idx[r] = cmap[offdiagIdx[r]];
2905     }
2906   }
2907   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2908   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2909   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2910   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2911   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2912   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2913   PetscFunctionReturn(0);
2914 }
2915 
2916 #undef __FUNCT__
2917 #define __FUNCT__ "MatGetRowMax_MPIAIJ"
2918 PetscErrorCode MatGetRowMax_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2919 {
2920   Mat_MPIAIJ    *mat    = (Mat_MPIAIJ *) A->data;
2921   PetscInt       n      = A->rmap->n;
2922   PetscInt       cstart = A->cmap->rstart;
2923   PetscInt      *cmap   = mat->garray;
2924   PetscInt      *diagIdx, *offdiagIdx;
2925   Vec            diagV, offdiagV;
2926   PetscScalar   *a, *diagA, *offdiagA;
2927   PetscInt       r;
2928   PetscErrorCode ierr;
2929 
2930   PetscFunctionBegin;
2931   ierr = PetscMalloc2(n,PetscInt,&diagIdx,n,PetscInt,&offdiagIdx);CHKERRQ(ierr);
2932   ierr = VecCreateSeq(((PetscObject)A)->comm, n, &diagV);CHKERRQ(ierr);
2933   ierr = VecCreateSeq(((PetscObject)A)->comm, n, &offdiagV);CHKERRQ(ierr);
2934   ierr = MatGetRowMax(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2935   ierr = MatGetRowMax(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2936   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2937   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2938   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2939   for(r = 0; r < n; ++r) {
2940     if (PetscAbsScalar(diagA[r]) >= PetscAbsScalar(offdiagA[r])) {
2941       a[r]   = diagA[r];
2942       idx[r] = cstart + diagIdx[r];
2943     } else {
2944       a[r]   = offdiagA[r];
2945       idx[r] = cmap[offdiagIdx[r]];
2946     }
2947   }
2948   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2949   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2950   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2951   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2952   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2953   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2954   PetscFunctionReturn(0);
2955 }
2956 
2957 #undef __FUNCT__
2958 #define __FUNCT__ "MatGetSeqNonzeroStructure_MPIAIJ"
2959 PetscErrorCode MatGetSeqNonzeroStructure_MPIAIJ(Mat mat,Mat *newmat)
2960 {
2961   PetscErrorCode ierr;
2962   Mat            *dummy;
2963 
2964   PetscFunctionBegin;
2965   ierr = MatGetSubMatrix_MPIAIJ_All(mat,MAT_DO_NOT_GET_VALUES,MAT_INITIAL_MATRIX,&dummy);CHKERRQ(ierr);
2966   *newmat = *dummy;
2967   ierr = PetscFree(dummy);CHKERRQ(ierr);
2968   PetscFunctionReturn(0);
2969 }
2970 
2971 extern PetscErrorCode  MatFDColoringApply_AIJ(Mat,MatFDColoring,Vec,MatStructure*,void*);
2972 
2973 #undef __FUNCT__
2974 #define __FUNCT__ "MatInvertBlockDiagonal_MPIAIJ"
2975 PetscErrorCode  MatInvertBlockDiagonal_MPIAIJ(Mat A,PetscScalar **values)
2976 {
2977   Mat_MPIAIJ    *a = (Mat_MPIAIJ*) A->data;
2978   PetscErrorCode ierr;
2979 
2980   PetscFunctionBegin;
2981   ierr = MatInvertBlockDiagonal(a->A,values);CHKERRQ(ierr);
2982   PetscFunctionReturn(0);
2983 }
2984 
2985 
2986 /* -------------------------------------------------------------------*/
2987 static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
2988        MatGetRow_MPIAIJ,
2989        MatRestoreRow_MPIAIJ,
2990        MatMult_MPIAIJ,
2991 /* 4*/ MatMultAdd_MPIAIJ,
2992        MatMultTranspose_MPIAIJ,
2993        MatMultTransposeAdd_MPIAIJ,
2994 #ifdef PETSC_HAVE_PBGL
2995        MatSolve_MPIAIJ,
2996 #else
2997        0,
2998 #endif
2999        0,
3000        0,
3001 /*10*/ 0,
3002        0,
3003        0,
3004        MatSOR_MPIAIJ,
3005        MatTranspose_MPIAIJ,
3006 /*15*/ MatGetInfo_MPIAIJ,
3007        MatEqual_MPIAIJ,
3008        MatGetDiagonal_MPIAIJ,
3009        MatDiagonalScale_MPIAIJ,
3010        MatNorm_MPIAIJ,
3011 /*20*/ MatAssemblyBegin_MPIAIJ,
3012        MatAssemblyEnd_MPIAIJ,
3013        MatSetOption_MPIAIJ,
3014        MatZeroEntries_MPIAIJ,
3015 /*24*/ MatZeroRows_MPIAIJ,
3016        0,
3017 #ifdef PETSC_HAVE_PBGL
3018        0,
3019 #else
3020        0,
3021 #endif
3022        0,
3023        0,
3024 /*29*/ MatSetUp_MPIAIJ,
3025 #ifdef PETSC_HAVE_PBGL
3026        0,
3027 #else
3028        0,
3029 #endif
3030        0,
3031        0,
3032        0,
3033 /*34*/ MatDuplicate_MPIAIJ,
3034        0,
3035        0,
3036        0,
3037        0,
3038 /*39*/ MatAXPY_MPIAIJ,
3039        MatGetSubMatrices_MPIAIJ,
3040        MatIncreaseOverlap_MPIAIJ,
3041        MatGetValues_MPIAIJ,
3042        MatCopy_MPIAIJ,
3043 /*44*/ MatGetRowMax_MPIAIJ,
3044        MatScale_MPIAIJ,
3045        0,
3046        0,
3047        MatZeroRowsColumns_MPIAIJ,
3048 /*49*/ 0,
3049        0,
3050        0,
3051        0,
3052        0,
3053 /*54*/ MatFDColoringCreate_MPIAIJ,
3054        0,
3055        MatSetUnfactored_MPIAIJ,
3056        MatPermute_MPIAIJ,
3057        0,
3058 /*59*/ MatGetSubMatrix_MPIAIJ,
3059        MatDestroy_MPIAIJ,
3060        MatView_MPIAIJ,
3061        0,
3062        0,
3063 /*64*/ 0,
3064        0,
3065        0,
3066        0,
3067        0,
3068 /*69*/ MatGetRowMaxAbs_MPIAIJ,
3069        MatGetRowMinAbs_MPIAIJ,
3070        0,
3071        MatSetColoring_MPIAIJ,
3072 #if defined(PETSC_HAVE_ADIC)
3073        MatSetValuesAdic_MPIAIJ,
3074 #else
3075        0,
3076 #endif
3077        MatSetValuesAdifor_MPIAIJ,
3078 /*75*/ MatFDColoringApply_AIJ,
3079        0,
3080        0,
3081        0,
3082        0,
3083 /*80*/ 0,
3084        0,
3085        0,
3086 /*83*/ MatLoad_MPIAIJ,
3087        0,
3088        0,
3089        0,
3090        0,
3091        0,
3092 /*89*/ MatMatMult_MPIAIJ_MPIAIJ,
3093        MatMatMultSymbolic_MPIAIJ_MPIAIJ,
3094        MatMatMultNumeric_MPIAIJ_MPIAIJ,
3095        MatPtAP_Basic,
3096        MatPtAPSymbolic_MPIAIJ,
3097 /*94*/ MatPtAPNumeric_MPIAIJ,
3098        0,
3099        0,
3100        0,
3101        0,
3102 /*99*/ 0,
3103        MatPtAPSymbolic_MPIAIJ_MPIAIJ,
3104        MatPtAPNumeric_MPIAIJ_MPIAIJ,
3105        MatConjugate_MPIAIJ,
3106        0,
3107 /*104*/MatSetValuesRow_MPIAIJ,
3108        MatRealPart_MPIAIJ,
3109        MatImaginaryPart_MPIAIJ,
3110        0,
3111        0,
3112 /*109*/0,
3113        MatGetRedundantMatrix_MPIAIJ,
3114        MatGetRowMin_MPIAIJ,
3115        0,
3116        0,
3117 /*114*/MatGetSeqNonzeroStructure_MPIAIJ,
3118        0,
3119        0,
3120        0,
3121        0,
3122 /*119*/0,
3123        0,
3124        0,
3125        0,
3126        MatGetMultiProcBlock_MPIAIJ,
3127 /*124*/MatFindNonZeroRows_MPIAIJ,
3128        MatGetColumnNorms_MPIAIJ,
3129        MatInvertBlockDiagonal_MPIAIJ,
3130        0,
3131        MatGetSubMatricesParallel_MPIAIJ,
3132 /*129*/0,
3133        MatTransposeMatMult_MPIAIJ_MPIAIJ,
3134        MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ,
3135        MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ,
3136        0,
3137 /*134*/0,
3138        0,
3139        0,
3140        0,
3141        0
3142 };
3143 
3144 /* ----------------------------------------------------------------------------------------*/
3145 
3146 EXTERN_C_BEGIN
3147 #undef __FUNCT__
3148 #define __FUNCT__ "MatStoreValues_MPIAIJ"
3149 PetscErrorCode  MatStoreValues_MPIAIJ(Mat mat)
3150 {
3151   Mat_MPIAIJ     *aij = (Mat_MPIAIJ *)mat->data;
3152   PetscErrorCode ierr;
3153 
3154   PetscFunctionBegin;
3155   ierr = MatStoreValues(aij->A);CHKERRQ(ierr);
3156   ierr = MatStoreValues(aij->B);CHKERRQ(ierr);
3157   PetscFunctionReturn(0);
3158 }
3159 EXTERN_C_END
3160 
3161 EXTERN_C_BEGIN
3162 #undef __FUNCT__
3163 #define __FUNCT__ "MatRetrieveValues_MPIAIJ"
3164 PetscErrorCode  MatRetrieveValues_MPIAIJ(Mat mat)
3165 {
3166   Mat_MPIAIJ     *aij = (Mat_MPIAIJ *)mat->data;
3167   PetscErrorCode ierr;
3168 
3169   PetscFunctionBegin;
3170   ierr = MatRetrieveValues(aij->A);CHKERRQ(ierr);
3171   ierr = MatRetrieveValues(aij->B);CHKERRQ(ierr);
3172   PetscFunctionReturn(0);
3173 }
3174 EXTERN_C_END
3175 
3176 EXTERN_C_BEGIN
3177 #undef __FUNCT__
3178 #define __FUNCT__ "MatMPIAIJSetPreallocation_MPIAIJ"
3179 PetscErrorCode  MatMPIAIJSetPreallocation_MPIAIJ(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3180 {
3181   Mat_MPIAIJ     *b;
3182   PetscErrorCode ierr;
3183   PetscInt       i;
3184   PetscBool      d_realalloc = PETSC_FALSE,o_realalloc = PETSC_FALSE;
3185 
3186   PetscFunctionBegin;
3187   if (d_nz >= 0 || d_nnz) d_realalloc = PETSC_TRUE;
3188   if (o_nz >= 0 || o_nnz) o_realalloc = PETSC_TRUE;
3189   if (d_nz == PETSC_DEFAULT || d_nz == PETSC_DECIDE) d_nz = 5;
3190   if (o_nz == PETSC_DEFAULT || o_nz == PETSC_DECIDE) o_nz = 2;
3191   if (d_nz < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"d_nz cannot be less than 0: value %D",d_nz);
3192   if (o_nz < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"o_nz cannot be less than 0: value %D",o_nz);
3193 
3194   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3195   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3196   if (d_nnz) {
3197     for (i=0; i<B->rmap->n; i++) {
3198       if (d_nnz[i] < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"d_nnz cannot be less than 0: local row %D value %D",i,d_nnz[i]);
3199     }
3200   }
3201   if (o_nnz) {
3202     for (i=0; i<B->rmap->n; i++) {
3203       if (o_nnz[i] < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"o_nnz cannot be less than 0: local row %D value %D",i,o_nnz[i]);
3204     }
3205   }
3206   b = (Mat_MPIAIJ*)B->data;
3207 
3208   if (!B->preallocated) {
3209     /* Explicitly create 2 MATSEQAIJ matrices. */
3210     ierr = MatCreate(PETSC_COMM_SELF,&b->A);CHKERRQ(ierr);
3211     ierr = MatSetSizes(b->A,B->rmap->n,B->cmap->n,B->rmap->n,B->cmap->n);CHKERRQ(ierr);
3212     ierr = MatSetBlockSizes(b->A,B->rmap->bs,B->cmap->bs);CHKERRQ(ierr);
3213     ierr = MatSetType(b->A,MATSEQAIJ);CHKERRQ(ierr);
3214     ierr = PetscLogObjectParent(B,b->A);CHKERRQ(ierr);
3215     ierr = MatCreate(PETSC_COMM_SELF,&b->B);CHKERRQ(ierr);
3216     ierr = MatSetSizes(b->B,B->rmap->n,B->cmap->N,B->rmap->n,B->cmap->N);CHKERRQ(ierr);
3217     ierr = MatSetBlockSizes(b->B,B->rmap->bs,B->cmap->bs);CHKERRQ(ierr);
3218     ierr = MatSetType(b->B,MATSEQAIJ);CHKERRQ(ierr);
3219     ierr = PetscLogObjectParent(B,b->B);CHKERRQ(ierr);
3220   }
3221 
3222   ierr = MatSeqAIJSetPreallocation(b->A,d_nz,d_nnz);CHKERRQ(ierr);
3223   ierr = MatSeqAIJSetPreallocation(b->B,o_nz,o_nnz);CHKERRQ(ierr);
3224   /* Do not error if the user did not give real preallocation information. Ugly because this would overwrite a previous user call to MatSetOption(). */
3225   if (!d_realalloc) {ierr = MatSetOption(b->A,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);}
3226   if (!o_realalloc) {ierr = MatSetOption(b->B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);}
3227   B->preallocated = PETSC_TRUE;
3228   PetscFunctionReturn(0);
3229 }
3230 EXTERN_C_END
3231 
3232 #undef __FUNCT__
3233 #define __FUNCT__ "MatDuplicate_MPIAIJ"
3234 PetscErrorCode MatDuplicate_MPIAIJ(Mat matin,MatDuplicateOption cpvalues,Mat *newmat)
3235 {
3236   Mat            mat;
3237   Mat_MPIAIJ     *a,*oldmat = (Mat_MPIAIJ*)matin->data;
3238   PetscErrorCode ierr;
3239 
3240   PetscFunctionBegin;
3241   *newmat       = 0;
3242   ierr = MatCreate(((PetscObject)matin)->comm,&mat);CHKERRQ(ierr);
3243   ierr = MatSetSizes(mat,matin->rmap->n,matin->cmap->n,matin->rmap->N,matin->cmap->N);CHKERRQ(ierr);
3244   ierr = MatSetBlockSizes(mat,matin->rmap->bs,matin->cmap->bs);CHKERRQ(ierr);
3245   ierr = MatSetType(mat,((PetscObject)matin)->type_name);CHKERRQ(ierr);
3246   ierr = PetscMemcpy(mat->ops,matin->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
3247   a    = (Mat_MPIAIJ*)mat->data;
3248 
3249   mat->factortype    = matin->factortype;
3250   mat->rmap->bs      = matin->rmap->bs;
3251   mat->cmap->bs      = matin->cmap->bs;
3252   mat->assembled    = PETSC_TRUE;
3253   mat->insertmode   = NOT_SET_VALUES;
3254   mat->preallocated = PETSC_TRUE;
3255 
3256   a->size           = oldmat->size;
3257   a->rank           = oldmat->rank;
3258   a->donotstash     = oldmat->donotstash;
3259   a->roworiented    = oldmat->roworiented;
3260   a->rowindices     = 0;
3261   a->rowvalues      = 0;
3262   a->getrowactive   = PETSC_FALSE;
3263 
3264   ierr = PetscLayoutReference(matin->rmap,&mat->rmap);CHKERRQ(ierr);
3265   ierr = PetscLayoutReference(matin->cmap,&mat->cmap);CHKERRQ(ierr);
3266 
3267   if (oldmat->colmap) {
3268 #if defined (PETSC_USE_CTABLE)
3269     ierr = PetscTableCreateCopy(oldmat->colmap,&a->colmap);CHKERRQ(ierr);
3270 #else
3271     ierr = PetscMalloc((mat->cmap->N)*sizeof(PetscInt),&a->colmap);CHKERRQ(ierr);
3272     ierr = PetscLogObjectMemory(mat,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
3273     ierr = PetscMemcpy(a->colmap,oldmat->colmap,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
3274 #endif
3275   } else a->colmap = 0;
3276   if (oldmat->garray) {
3277     PetscInt len;
3278     len  = oldmat->B->cmap->n;
3279     ierr = PetscMalloc((len+1)*sizeof(PetscInt),&a->garray);CHKERRQ(ierr);
3280     ierr = PetscLogObjectMemory(mat,len*sizeof(PetscInt));CHKERRQ(ierr);
3281     if (len) { ierr = PetscMemcpy(a->garray,oldmat->garray,len*sizeof(PetscInt));CHKERRQ(ierr); }
3282   } else a->garray = 0;
3283 
3284   ierr = VecDuplicate(oldmat->lvec,&a->lvec);CHKERRQ(ierr);
3285   ierr = PetscLogObjectParent(mat,a->lvec);CHKERRQ(ierr);
3286   ierr = VecScatterCopy(oldmat->Mvctx,&a->Mvctx);CHKERRQ(ierr);
3287   ierr = PetscLogObjectParent(mat,a->Mvctx);CHKERRQ(ierr);
3288   ierr = MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
3289   ierr = PetscLogObjectParent(mat,a->A);CHKERRQ(ierr);
3290   ierr = MatDuplicate(oldmat->B,cpvalues,&a->B);CHKERRQ(ierr);
3291   ierr = PetscLogObjectParent(mat,a->B);CHKERRQ(ierr);
3292   ierr = PetscFListDuplicate(((PetscObject)matin)->qlist,&((PetscObject)mat)->qlist);CHKERRQ(ierr);
3293   *newmat = mat;
3294   PetscFunctionReturn(0);
3295 }
3296 
3297 
3298 
3299 #undef __FUNCT__
3300 #define __FUNCT__ "MatLoad_MPIAIJ"
3301 PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
3302 {
3303   PetscScalar    *vals,*svals;
3304   MPI_Comm       comm = ((PetscObject)viewer)->comm;
3305   PetscErrorCode ierr;
3306   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
3307   PetscInt       i,nz,j,rstart,rend,mmax,maxnz = 0,grows,gcols;
3308   PetscInt       header[4],*rowlengths = 0,M,N,m,*cols;
3309   PetscInt       *ourlens = PETSC_NULL,*procsnz = PETSC_NULL,*offlens = PETSC_NULL,jj,*mycols,*smycols;
3310   PetscInt       cend,cstart,n,*rowners,sizesset=1;
3311   int            fd;
3312 
3313   PetscFunctionBegin;
3314   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3315   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3316   if (!rank) {
3317     ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
3318     ierr = PetscBinaryRead(fd,(char *)header,4,PETSC_INT);CHKERRQ(ierr);
3319     if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
3320   }
3321 
3322   if (newMat->rmap->n < 0 && newMat->rmap->N < 0 && newMat->cmap->n < 0 && newMat->cmap->N < 0) sizesset = 0;
3323 
3324   ierr = MPI_Bcast(header+1,3,MPIU_INT,0,comm);CHKERRQ(ierr);
3325   M = header[1]; N = header[2];
3326   /* If global rows/cols are set to PETSC_DECIDE, set it to the sizes given in the file */
3327   if (sizesset && newMat->rmap->N < 0) newMat->rmap->N = M;
3328   if (sizesset && newMat->cmap->N < 0) newMat->cmap->N = N;
3329 
3330   /* If global sizes are set, check if they are consistent with that given in the file */
3331   if (sizesset) {
3332     ierr = MatGetSize(newMat,&grows,&gcols);CHKERRQ(ierr);
3333   }
3334   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);
3335   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);
3336 
3337   /* determine ownership of all rows */
3338   if (newMat->rmap->n < 0 ) m    = M/size + ((M % size) > rank); /* PETSC_DECIDE */
3339   else m = newMat->rmap->n; /* Set by user */
3340 
3341   ierr = PetscMalloc((size+1)*sizeof(PetscInt),&rowners);CHKERRQ(ierr);
3342   ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
3343 
3344   /* First process needs enough room for process with most rows */
3345   if (!rank) {
3346     mmax       = rowners[1];
3347     for (i=2; i<size; i++) {
3348       mmax = PetscMax(mmax,rowners[i]);
3349     }
3350   } else mmax = m;
3351 
3352   rowners[0] = 0;
3353   for (i=2; i<=size; i++) {
3354     rowners[i] += rowners[i-1];
3355   }
3356   rstart = rowners[rank];
3357   rend   = rowners[rank+1];
3358 
3359   /* distribute row lengths to all processors */
3360   ierr    = PetscMalloc2(mmax,PetscInt,&ourlens,mmax,PetscInt,&offlens);CHKERRQ(ierr);
3361   if (!rank) {
3362     ierr = PetscBinaryRead(fd,ourlens,m,PETSC_INT);CHKERRQ(ierr);
3363     ierr = PetscMalloc(m*sizeof(PetscInt),&rowlengths);CHKERRQ(ierr);
3364     ierr = PetscMalloc(size*sizeof(PetscInt),&procsnz);CHKERRQ(ierr);
3365     ierr = PetscMemzero(procsnz,size*sizeof(PetscInt));CHKERRQ(ierr);
3366     for (j=0; j<m; j++) {
3367       procsnz[0] += ourlens[j];
3368     }
3369     for (i=1; i<size; i++) {
3370       ierr = PetscBinaryRead(fd,rowlengths,rowners[i+1]-rowners[i],PETSC_INT);CHKERRQ(ierr);
3371       /* calculate the number of nonzeros on each processor */
3372       for (j=0; j<rowners[i+1]-rowners[i]; j++) {
3373         procsnz[i] += rowlengths[j];
3374       }
3375       ierr = MPIULong_Send(rowlengths,rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
3376     }
3377     ierr = PetscFree(rowlengths);CHKERRQ(ierr);
3378   } else {
3379     ierr = MPIULong_Recv(ourlens,m,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
3380   }
3381 
3382   if (!rank) {
3383     /* determine max buffer needed and allocate it */
3384     maxnz = 0;
3385     for (i=0; i<size; i++) {
3386       maxnz = PetscMax(maxnz,procsnz[i]);
3387     }
3388     ierr = PetscMalloc(maxnz*sizeof(PetscInt),&cols);CHKERRQ(ierr);
3389 
3390     /* read in my part of the matrix column indices  */
3391     nz   = procsnz[0];
3392     ierr = PetscMalloc(nz*sizeof(PetscInt),&mycols);CHKERRQ(ierr);
3393     ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);
3394 
3395     /* read in every one elses and ship off */
3396     for (i=1; i<size; i++) {
3397       nz     = procsnz[i];
3398       ierr   = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
3399       ierr   = MPIULong_Send(cols,nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
3400     }
3401     ierr = PetscFree(cols);CHKERRQ(ierr);
3402   } else {
3403     /* determine buffer space needed for message */
3404     nz = 0;
3405     for (i=0; i<m; i++) {
3406       nz += ourlens[i];
3407     }
3408     ierr = PetscMalloc(nz*sizeof(PetscInt),&mycols);CHKERRQ(ierr);
3409 
3410     /* receive message of column indices*/
3411     ierr = MPIULong_Recv(mycols,nz,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
3412   }
3413 
3414   /* determine column ownership if matrix is not square */
3415   if (N != M) {
3416     if (newMat->cmap->n < 0) n      = N/size + ((N % size) > rank);
3417     else n = newMat->cmap->n;
3418     ierr   = MPI_Scan(&n,&cend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3419     cstart = cend - n;
3420   } else {
3421     cstart = rstart;
3422     cend   = rend;
3423     n      = cend - cstart;
3424   }
3425 
3426   /* loop over local rows, determining number of off diagonal entries */
3427   ierr = PetscMemzero(offlens,m*sizeof(PetscInt));CHKERRQ(ierr);
3428   jj = 0;
3429   for (i=0; i<m; i++) {
3430     for (j=0; j<ourlens[i]; j++) {
3431       if (mycols[jj] < cstart || mycols[jj] >= cend) offlens[i]++;
3432       jj++;
3433     }
3434   }
3435 
3436   for (i=0; i<m; i++) {
3437     ourlens[i] -= offlens[i];
3438   }
3439   if (!sizesset) {
3440     ierr = MatSetSizes(newMat,m,n,M,N);CHKERRQ(ierr);
3441   }
3442   ierr = MatMPIAIJSetPreallocation(newMat,0,ourlens,0,offlens);CHKERRQ(ierr);
3443 
3444   for (i=0; i<m; i++) {
3445     ourlens[i] += offlens[i];
3446   }
3447 
3448   if (!rank) {
3449     ierr = PetscMalloc((maxnz+1)*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
3450 
3451     /* read in my part of the matrix numerical values  */
3452     nz   = procsnz[0];
3453     ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
3454 
3455     /* insert into matrix */
3456     jj      = rstart;
3457     smycols = mycols;
3458     svals   = vals;
3459     for (i=0; i<m; i++) {
3460       ierr = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
3461       smycols += ourlens[i];
3462       svals   += ourlens[i];
3463       jj++;
3464     }
3465 
3466     /* read in other processors and ship out */
3467     for (i=1; i<size; i++) {
3468       nz     = procsnz[i];
3469       ierr   = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
3470       ierr   = MPIULong_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
3471     }
3472     ierr = PetscFree(procsnz);CHKERRQ(ierr);
3473   } else {
3474     /* receive numeric values */
3475     ierr = PetscMalloc((nz+1)*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
3476 
3477     /* receive message of values*/
3478     ierr   = MPIULong_Recv(vals,nz,MPIU_SCALAR,0,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
3479 
3480     /* insert into matrix */
3481     jj      = rstart;
3482     smycols = mycols;
3483     svals   = vals;
3484     for (i=0; i<m; i++) {
3485       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
3486       smycols += ourlens[i];
3487       svals   += ourlens[i];
3488       jj++;
3489     }
3490   }
3491   ierr = PetscFree2(ourlens,offlens);CHKERRQ(ierr);
3492   ierr = PetscFree(vals);CHKERRQ(ierr);
3493   ierr = PetscFree(mycols);CHKERRQ(ierr);
3494   ierr = PetscFree(rowners);CHKERRQ(ierr);
3495 
3496   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3497   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3498   PetscFunctionReturn(0);
3499 }
3500 
3501 #undef __FUNCT__
3502 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ"
3503 PetscErrorCode MatGetSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3504 {
3505   PetscErrorCode ierr;
3506   IS             iscol_local;
3507   PetscInt       csize;
3508 
3509   PetscFunctionBegin;
3510   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3511   if (call == MAT_REUSE_MATRIX) {
3512     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3513     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3514   } else {
3515     PetscInt cbs;
3516     ierr = ISGetBlockSize(iscol,&cbs); CHKERRQ(ierr);
3517     ierr = ISAllGather(iscol,&iscol_local);CHKERRQ(ierr);
3518     ierr = ISSetBlockSize(iscol_local,cbs); CHKERRQ(ierr);
3519   }
3520   ierr = MatGetSubMatrix_MPIAIJ_Private(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
3521   if (call == MAT_INITIAL_MATRIX) {
3522     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3523     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3524   }
3525   PetscFunctionReturn(0);
3526 }
3527 
3528 #undef __FUNCT__
3529 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ_Private"
3530 /*
3531     Not great since it makes two copies of the submatrix, first an SeqAIJ
3532   in local and then by concatenating the local matrices the end result.
3533   Writing it directly would be much like MatGetSubMatrices_MPIAIJ()
3534 
3535   Note: This requires a sequential iscol with all indices.
3536 */
3537 PetscErrorCode MatGetSubMatrix_MPIAIJ_Private(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3538 {
3539   PetscErrorCode ierr;
3540   PetscMPIInt    rank,size;
3541   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3542   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
3543   Mat            *local,M,Mreuse;
3544   MatScalar      *vwork,*aa;
3545   MPI_Comm       comm = ((PetscObject)mat)->comm;
3546   Mat_SeqAIJ     *aij;
3547 
3548 
3549   PetscFunctionBegin;
3550   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3551   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3552 
3553   if (call ==  MAT_REUSE_MATRIX) {
3554     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject *)&Mreuse);CHKERRQ(ierr);
3555     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3556     local = &Mreuse;
3557     ierr  = MatGetSubMatrices(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,&local);CHKERRQ(ierr);
3558   } else {
3559     ierr   = MatGetSubMatrices(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&local);CHKERRQ(ierr);
3560     Mreuse = *local;
3561     ierr   = PetscFree(local);CHKERRQ(ierr);
3562   }
3563 
3564   /*
3565       m - number of local rows
3566       n - number of columns (same on all processors)
3567       rstart - first row in new global matrix generated
3568   */
3569   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3570   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3571   if (call == MAT_INITIAL_MATRIX) {
3572     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3573     ii  = aij->i;
3574     jj  = aij->j;
3575 
3576     /*
3577         Determine the number of non-zeros in the diagonal and off-diagonal
3578         portions of the matrix in order to do correct preallocation
3579     */
3580 
3581     /* first get start and end of "diagonal" columns */
3582     if (csize == PETSC_DECIDE) {
3583       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3584       if (mglobal == n) { /* square matrix */
3585 	nlocal = m;
3586       } else {
3587         nlocal = n/size + ((n % size) > rank);
3588       }
3589     } else {
3590       nlocal = csize;
3591     }
3592     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3593     rstart = rend - nlocal;
3594     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);
3595 
3596     /* next, compute all the lengths */
3597     ierr  = PetscMalloc((2*m+1)*sizeof(PetscInt),&dlens);CHKERRQ(ierr);
3598     olens = dlens + m;
3599     for (i=0; i<m; i++) {
3600       jend = ii[i+1] - ii[i];
3601       olen = 0;
3602       dlen = 0;
3603       for (j=0; j<jend; j++) {
3604         if (*jj < rstart || *jj >= rend) olen++;
3605         else dlen++;
3606         jj++;
3607       }
3608       olens[i] = olen;
3609       dlens[i] = dlen;
3610     }
3611     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3612     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3613     ierr = MatSetBlockSizes(M,bs,cbs); CHKERRQ(ierr);
3614     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3615     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3616     ierr = PetscFree(dlens);CHKERRQ(ierr);
3617   } else {
3618     PetscInt ml,nl;
3619 
3620     M = *newmat;
3621     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3622     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3623     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3624     /*
3625          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3626        rather than the slower MatSetValues().
3627     */
3628     M->was_assembled = PETSC_TRUE;
3629     M->assembled     = PETSC_FALSE;
3630   }
3631   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3632   aij = (Mat_SeqAIJ*)(Mreuse)->data;
3633   ii  = aij->i;
3634   jj  = aij->j;
3635   aa  = aij->a;
3636   for (i=0; i<m; i++) {
3637     row   = rstart + i;
3638     nz    = ii[i+1] - ii[i];
3639     cwork = jj;     jj += nz;
3640     vwork = aa;     aa += nz;
3641     ierr = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3642   }
3643 
3644   ierr = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3645   ierr = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3646   *newmat = M;
3647 
3648   /* save submatrix used in processor for next request */
3649   if (call ==  MAT_INITIAL_MATRIX) {
3650     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3651     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3652   }
3653 
3654   PetscFunctionReturn(0);
3655 }
3656 
3657 EXTERN_C_BEGIN
3658 #undef __FUNCT__
3659 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR_MPIAIJ"
3660 PetscErrorCode  MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3661 {
3662   PetscInt       m,cstart, cend,j,nnz,i,d;
3663   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3664   const PetscInt *JJ;
3665   PetscScalar    *values;
3666   PetscErrorCode ierr;
3667 
3668   PetscFunctionBegin;
3669   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3670 
3671   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3672   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3673   m      = B->rmap->n;
3674   cstart = B->cmap->rstart;
3675   cend   = B->cmap->rend;
3676   rstart = B->rmap->rstart;
3677 
3678   ierr  = PetscMalloc2(m,PetscInt,&d_nnz,m,PetscInt,&o_nnz);CHKERRQ(ierr);
3679 
3680 #if defined(PETSC_USE_DEBUGGING)
3681   for (i=0; i<m; i++) {
3682     nnz     = Ii[i+1]- Ii[i];
3683     JJ      = J + Ii[i];
3684     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3685     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3686     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);
3687   }
3688 #endif
3689 
3690   for (i=0; i<m; i++) {
3691     nnz     = Ii[i+1]- Ii[i];
3692     JJ      = J + Ii[i];
3693     nnz_max = PetscMax(nnz_max,nnz);
3694     d       = 0;
3695     for (j=0; j<nnz; j++) {
3696       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3697     }
3698     d_nnz[i] = d;
3699     o_nnz[i] = nnz - d;
3700   }
3701   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3702   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3703 
3704   if (v) values = (PetscScalar*)v;
3705   else {
3706     ierr = PetscMalloc((nnz_max+1)*sizeof(PetscScalar),&values);CHKERRQ(ierr);
3707     ierr = PetscMemzero(values,nnz_max*sizeof(PetscScalar));CHKERRQ(ierr);
3708   }
3709 
3710   for (i=0; i<m; i++) {
3711     ii   = i + rstart;
3712     nnz  = Ii[i+1]- Ii[i];
3713     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3714   }
3715   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3716   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3717 
3718   if (!v) {
3719     ierr = PetscFree(values);CHKERRQ(ierr);
3720   }
3721   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3722   PetscFunctionReturn(0);
3723 }
3724 EXTERN_C_END
3725 
3726 #undef __FUNCT__
3727 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR"
3728 /*@
3729    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3730    (the default parallel PETSc format).
3731 
3732    Collective on MPI_Comm
3733 
3734    Input Parameters:
3735 +  B - the matrix
3736 .  i - the indices into j for the start of each local row (starts with zero)
3737 .  j - the column indices for each local row (starts with zero)
3738 -  v - optional values in the matrix
3739 
3740    Level: developer
3741 
3742    Notes:
3743        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3744      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3745      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3746 
3747        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3748 
3749        The format which is used for the sparse matrix input, is equivalent to a
3750     row-major ordering.. i.e for the following matrix, the input data expected is
3751     as shown:
3752 
3753         1 0 0
3754         2 0 3     P0
3755        -------
3756         4 5 6     P1
3757 
3758      Process0 [P0]: rows_owned=[0,1]
3759         i =  {0,1,3}  [size = nrow+1  = 2+1]
3760         j =  {0,0,2}  [size = nz = 6]
3761         v =  {1,2,3}  [size = nz = 6]
3762 
3763      Process1 [P1]: rows_owned=[2]
3764         i =  {0,3}    [size = nrow+1  = 1+1]
3765         j =  {0,1,2}  [size = nz = 6]
3766         v =  {4,5,6}  [size = nz = 6]
3767 
3768 .keywords: matrix, aij, compressed row, sparse, parallel
3769 
3770 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MPIAIJ,
3771           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3772 @*/
3773 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3774 {
3775   PetscErrorCode ierr;
3776 
3777   PetscFunctionBegin;
3778   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3779   PetscFunctionReturn(0);
3780 }
3781 
3782 #undef __FUNCT__
3783 #define __FUNCT__ "MatMPIAIJSetPreallocation"
3784 /*@C
3785    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3786    (the default parallel PETSc format).  For good matrix assembly performance
3787    the user should preallocate the matrix storage by setting the parameters
3788    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3789    performance can be increased by more than a factor of 50.
3790 
3791    Collective on MPI_Comm
3792 
3793    Input Parameters:
3794 +  A - the matrix
3795 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3796            (same value is used for all local rows)
3797 .  d_nnz - array containing the number of nonzeros in the various rows of the
3798            DIAGONAL portion of the local submatrix (possibly different for each row)
3799            or PETSC_NULL, if d_nz is used to specify the nonzero structure.
3800            The size of this array is equal to the number of local rows, i.e 'm'.
3801            For matrices that will be factored, you must leave room for (and set)
3802            the diagonal entry even if it is zero.
3803 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3804            submatrix (same value is used for all local rows).
3805 -  o_nnz - array containing the number of nonzeros in the various rows of the
3806            OFF-DIAGONAL portion of the local submatrix (possibly different for
3807            each row) or PETSC_NULL, if o_nz is used to specify the nonzero
3808            structure. The size of this array is equal to the number
3809            of local rows, i.e 'm'.
3810 
3811    If the *_nnz parameter is given then the *_nz parameter is ignored
3812 
3813    The AIJ format (also called the Yale sparse matrix format or
3814    compressed row storage (CSR)), is fully compatible with standard Fortran 77
3815    storage.  The stored row and column indices begin with zero.
3816    See the <A href="../../docs/manual.pdf#nameddest=ch_mat">Mat chapter of the users manual</A> for details.
3817 
3818    The parallel matrix is partitioned such that the first m0 rows belong to
3819    process 0, the next m1 rows belong to process 1, the next m2 rows belong
3820    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
3821 
3822    The DIAGONAL portion of the local submatrix of a processor can be defined
3823    as the submatrix which is obtained by extraction the part corresponding to
3824    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
3825    first row that belongs to the processor, r2 is the last row belonging to
3826    the this processor, and c1-c2 is range of indices of the local part of a
3827    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
3828    common case of a square matrix, the row and column ranges are the same and
3829    the DIAGONAL part is also square. The remaining portion of the local
3830    submatrix (mxN) constitute the OFF-DIAGONAL portion.
3831 
3832    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3833 
3834    You can call MatGetInfo() to get information on how effective the preallocation was;
3835    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3836    You can also run with the option -info and look for messages with the string
3837    malloc in them to see if additional memory allocation was needed.
3838 
3839    Example usage:
3840 
3841    Consider the following 8x8 matrix with 34 non-zero values, that is
3842    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3843    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3844    as follows:
3845 
3846 .vb
3847             1  2  0  |  0  3  0  |  0  4
3848     Proc0   0  5  6  |  7  0  0  |  8  0
3849             9  0 10  | 11  0  0  | 12  0
3850     -------------------------------------
3851            13  0 14  | 15 16 17  |  0  0
3852     Proc1   0 18  0  | 19 20 21  |  0  0
3853             0  0  0  | 22 23  0  | 24  0
3854     -------------------------------------
3855     Proc2  25 26 27  |  0  0 28  | 29  0
3856            30  0  0  | 31 32 33  |  0 34
3857 .ve
3858 
3859    This can be represented as a collection of submatrices as:
3860 
3861 .vb
3862       A B C
3863       D E F
3864       G H I
3865 .ve
3866 
3867    Where the submatrices A,B,C are owned by proc0, D,E,F are
3868    owned by proc1, G,H,I are owned by proc2.
3869 
3870    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3871    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3872    The 'M','N' parameters are 8,8, and have the same values on all procs.
3873 
3874    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3875    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3876    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3877    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3878    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3879    matrix, ans [DF] as another SeqAIJ matrix.
3880 
3881    When d_nz, o_nz parameters are specified, d_nz storage elements are
3882    allocated for every row of the local diagonal submatrix, and o_nz
3883    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3884    One way to choose d_nz and o_nz is to use the max nonzerors per local
3885    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3886    In this case, the values of d_nz,o_nz are:
3887 .vb
3888      proc0 : dnz = 2, o_nz = 2
3889      proc1 : dnz = 3, o_nz = 2
3890      proc2 : dnz = 1, o_nz = 4
3891 .ve
3892    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3893    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3894    for proc3. i.e we are using 12+15+10=37 storage locations to store
3895    34 values.
3896 
3897    When d_nnz, o_nnz parameters are specified, the storage is specified
3898    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3899    In the above case the values for d_nnz,o_nnz are:
3900 .vb
3901      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3902      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3903      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3904 .ve
3905    Here the space allocated is sum of all the above values i.e 34, and
3906    hence pre-allocation is perfect.
3907 
3908    Level: intermediate
3909 
3910 .keywords: matrix, aij, compressed row, sparse, parallel
3911 
3912 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
3913           MPIAIJ, MatGetInfo()
3914 @*/
3915 PetscErrorCode  MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3916 {
3917   PetscErrorCode ierr;
3918 
3919   PetscFunctionBegin;
3920   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3921   PetscValidType(B,1);
3922   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
3923   PetscFunctionReturn(0);
3924 }
3925 
3926 #undef __FUNCT__
3927 #define __FUNCT__ "MatCreateMPIAIJWithArrays"
3928 /*@
3929      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
3930          CSR format the local rows.
3931 
3932    Collective on MPI_Comm
3933 
3934    Input Parameters:
3935 +  comm - MPI communicator
3936 .  m - number of local rows (Cannot be PETSC_DECIDE)
3937 .  n - This value should be the same as the local size used in creating the
3938        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3939        calculated if N is given) For square matrices n is almost always m.
3940 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3941 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3942 .   i - row indices
3943 .   j - column indices
3944 -   a - matrix values
3945 
3946    Output Parameter:
3947 .   mat - the matrix
3948 
3949    Level: intermediate
3950 
3951    Notes:
3952        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3953      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3954      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3955 
3956        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3957 
3958        The format which is used for the sparse matrix input, is equivalent to a
3959     row-major ordering.. i.e for the following matrix, the input data expected is
3960     as shown:
3961 
3962         1 0 0
3963         2 0 3     P0
3964        -------
3965         4 5 6     P1
3966 
3967      Process0 [P0]: rows_owned=[0,1]
3968         i =  {0,1,3}  [size = nrow+1  = 2+1]
3969         j =  {0,0,2}  [size = nz = 6]
3970         v =  {1,2,3}  [size = nz = 6]
3971 
3972      Process1 [P1]: rows_owned=[2]
3973         i =  {0,3}    [size = nrow+1  = 1+1]
3974         j =  {0,1,2}  [size = nz = 6]
3975         v =  {4,5,6}  [size = nz = 6]
3976 
3977 .keywords: matrix, aij, compressed row, sparse, parallel
3978 
3979 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3980           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
3981 @*/
3982 PetscErrorCode  MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
3983 {
3984   PetscErrorCode ierr;
3985 
3986   PetscFunctionBegin;
3987   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
3988   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
3989   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
3990   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
3991   /* ierr = MatSetBlockSizes(M,bs,cbs); CHKERRQ(ierr); */
3992   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
3993   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
3994   PetscFunctionReturn(0);
3995 }
3996 
3997 #undef __FUNCT__
3998 #define __FUNCT__ "MatCreateAIJ"
3999 /*@C
4000    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
4001    (the default parallel PETSc format).  For good matrix assembly performance
4002    the user should preallocate the matrix storage by setting the parameters
4003    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
4004    performance can be increased by more than a factor of 50.
4005 
4006    Collective on MPI_Comm
4007 
4008    Input Parameters:
4009 +  comm - MPI communicator
4010 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
4011            This value should be the same as the local size used in creating the
4012            y vector for the matrix-vector product y = Ax.
4013 .  n - This value should be the same as the local size used in creating the
4014        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
4015        calculated if N is given) For square matrices n is almost always m.
4016 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
4017 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
4018 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
4019            (same value is used for all local rows)
4020 .  d_nnz - array containing the number of nonzeros in the various rows of the
4021            DIAGONAL portion of the local submatrix (possibly different for each row)
4022            or PETSC_NULL, if d_nz is used to specify the nonzero structure.
4023            The size of this array is equal to the number of local rows, i.e 'm'.
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 PETSC_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    Output Parameter:
4033 .  A - the matrix
4034 
4035    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
4036    MatXXXXSetPreallocation() paradgm instead of this routine directly.
4037    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
4038 
4039    Notes:
4040    If the *_nnz parameter is given then the *_nz parameter is ignored
4041 
4042    m,n,M,N parameters specify the size of the matrix, and its partitioning across
4043    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
4044    storage requirements for this matrix.
4045 
4046    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
4047    processor than it must be used on all processors that share the object for
4048    that argument.
4049 
4050    The user MUST specify either the local or global matrix dimensions
4051    (possibly both).
4052 
4053    The parallel matrix is partitioned across processors such that the
4054    first m0 rows belong to process 0, the next m1 rows belong to
4055    process 1, the next m2 rows belong to process 2 etc.. where
4056    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
4057    values corresponding to [m x N] submatrix.
4058 
4059    The columns are logically partitioned with the n0 columns belonging
4060    to 0th partition, the next n1 columns belonging to the next
4061    partition etc.. where n0,n1,n2... are the the input parameter 'n'.
4062 
4063    The DIAGONAL portion of the local submatrix on any given processor
4064    is the submatrix corresponding to the rows and columns m,n
4065    corresponding to the given processor. i.e diagonal matrix on
4066    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
4067    etc. The remaining portion of the local submatrix [m x (N-n)]
4068    constitute the OFF-DIAGONAL portion. The example below better
4069    illustrates this concept.
4070 
4071    For a square global matrix we define each processor's diagonal portion
4072    to be its local rows and the corresponding columns (a square submatrix);
4073    each processor's off-diagonal portion encompasses the remainder of the
4074    local matrix (a rectangular submatrix).
4075 
4076    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
4077 
4078    When calling this routine with a single process communicator, a matrix of
4079    type SEQAIJ is returned.  If a matrix of type MPIAIJ is desired for this
4080    type of communicator, use the construction mechanism:
4081      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
4082 
4083    By default, this format uses inodes (identical nodes) when possible.
4084    We search for consecutive rows with the same nonzero structure, thereby
4085    reusing matrix information to achieve increased efficiency.
4086 
4087    Options Database Keys:
4088 +  -mat_no_inode  - Do not use inodes
4089 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
4090 -  -mat_aij_oneindex - Internally use indexing starting at 1
4091         rather than 0.  Note that when calling MatSetValues(),
4092         the user still MUST index entries starting at 0!
4093 
4094 
4095    Example usage:
4096 
4097    Consider the following 8x8 matrix with 34 non-zero values, that is
4098    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
4099    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
4100    as follows:
4101 
4102 .vb
4103             1  2  0  |  0  3  0  |  0  4
4104     Proc0   0  5  6  |  7  0  0  |  8  0
4105             9  0 10  | 11  0  0  | 12  0
4106     -------------------------------------
4107            13  0 14  | 15 16 17  |  0  0
4108     Proc1   0 18  0  | 19 20 21  |  0  0
4109             0  0  0  | 22 23  0  | 24  0
4110     -------------------------------------
4111     Proc2  25 26 27  |  0  0 28  | 29  0
4112            30  0  0  | 31 32 33  |  0 34
4113 .ve
4114 
4115    This can be represented as a collection of submatrices as:
4116 
4117 .vb
4118       A B C
4119       D E F
4120       G H I
4121 .ve
4122 
4123    Where the submatrices A,B,C are owned by proc0, D,E,F are
4124    owned by proc1, G,H,I are owned by proc2.
4125 
4126    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4127    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4128    The 'M','N' parameters are 8,8, and have the same values on all procs.
4129 
4130    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
4131    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
4132    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
4133    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
4134    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
4135    matrix, ans [DF] as another SeqAIJ matrix.
4136 
4137    When d_nz, o_nz parameters are specified, d_nz storage elements are
4138    allocated for every row of the local diagonal submatrix, and o_nz
4139    storage locations are allocated for every row of the OFF-DIAGONAL submat.
4140    One way to choose d_nz and o_nz is to use the max nonzerors per local
4141    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
4142    In this case, the values of d_nz,o_nz are:
4143 .vb
4144      proc0 : dnz = 2, o_nz = 2
4145      proc1 : dnz = 3, o_nz = 2
4146      proc2 : dnz = 1, o_nz = 4
4147 .ve
4148    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
4149    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
4150    for proc3. i.e we are using 12+15+10=37 storage locations to store
4151    34 values.
4152 
4153    When d_nnz, o_nnz parameters are specified, the storage is specified
4154    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
4155    In the above case the values for d_nnz,o_nnz are:
4156 .vb
4157      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
4158      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
4159      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
4160 .ve
4161    Here the space allocated is sum of all the above values i.e 34, and
4162    hence pre-allocation is perfect.
4163 
4164    Level: intermediate
4165 
4166 .keywords: matrix, aij, compressed row, sparse, parallel
4167 
4168 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
4169           MPIAIJ, MatCreateMPIAIJWithArrays()
4170 @*/
4171 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)
4172 {
4173   PetscErrorCode ierr;
4174   PetscMPIInt    size;
4175 
4176   PetscFunctionBegin;
4177   ierr = MatCreate(comm,A);CHKERRQ(ierr);
4178   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
4179   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4180   if (size > 1) {
4181     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
4182     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
4183   } else {
4184     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
4185     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
4186   }
4187   PetscFunctionReturn(0);
4188 }
4189 
4190 #undef __FUNCT__
4191 #define __FUNCT__ "MatMPIAIJGetSeqAIJ"
4192 PetscErrorCode  MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,PetscInt *colmap[])
4193 {
4194   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
4195 
4196   PetscFunctionBegin;
4197   *Ad     = a->A;
4198   *Ao     = a->B;
4199   *colmap = a->garray;
4200   PetscFunctionReturn(0);
4201 }
4202 
4203 #undef __FUNCT__
4204 #define __FUNCT__ "MatSetColoring_MPIAIJ"
4205 PetscErrorCode MatSetColoring_MPIAIJ(Mat A,ISColoring coloring)
4206 {
4207   PetscErrorCode ierr;
4208   PetscInt       i;
4209   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
4210 
4211   PetscFunctionBegin;
4212   if (coloring->ctype == IS_COLORING_GLOBAL) {
4213     ISColoringValue *allcolors,*colors;
4214     ISColoring      ocoloring;
4215 
4216     /* set coloring for diagonal portion */
4217     ierr = MatSetColoring_SeqAIJ(a->A,coloring);CHKERRQ(ierr);
4218 
4219     /* set coloring for off-diagonal portion */
4220     ierr = ISAllGatherColors(((PetscObject)A)->comm,coloring->n,coloring->colors,PETSC_NULL,&allcolors);CHKERRQ(ierr);
4221     ierr = PetscMalloc((a->B->cmap->n+1)*sizeof(ISColoringValue),&colors);CHKERRQ(ierr);
4222     for (i=0; i<a->B->cmap->n; i++) {
4223       colors[i] = allcolors[a->garray[i]];
4224     }
4225     ierr = PetscFree(allcolors);CHKERRQ(ierr);
4226     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,&ocoloring);CHKERRQ(ierr);
4227     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
4228     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
4229   } else if (coloring->ctype == IS_COLORING_GHOSTED) {
4230     ISColoringValue *colors;
4231     PetscInt        *larray;
4232     ISColoring      ocoloring;
4233 
4234     /* set coloring for diagonal portion */
4235     ierr = PetscMalloc((a->A->cmap->n+1)*sizeof(PetscInt),&larray);CHKERRQ(ierr);
4236     for (i=0; i<a->A->cmap->n; i++) {
4237       larray[i] = i + A->cmap->rstart;
4238     }
4239     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->A->cmap->n,larray,PETSC_NULL,larray);CHKERRQ(ierr);
4240     ierr = PetscMalloc((a->A->cmap->n+1)*sizeof(ISColoringValue),&colors);CHKERRQ(ierr);
4241     for (i=0; i<a->A->cmap->n; i++) {
4242       colors[i] = coloring->colors[larray[i]];
4243     }
4244     ierr = PetscFree(larray);CHKERRQ(ierr);
4245     ierr = ISColoringCreate(PETSC_COMM_SELF,coloring->n,a->A->cmap->n,colors,&ocoloring);CHKERRQ(ierr);
4246     ierr = MatSetColoring_SeqAIJ(a->A,ocoloring);CHKERRQ(ierr);
4247     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
4248 
4249     /* set coloring for off-diagonal portion */
4250     ierr = PetscMalloc((a->B->cmap->n+1)*sizeof(PetscInt),&larray);CHKERRQ(ierr);
4251     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->B->cmap->n,a->garray,PETSC_NULL,larray);CHKERRQ(ierr);
4252     ierr = PetscMalloc((a->B->cmap->n+1)*sizeof(ISColoringValue),&colors);CHKERRQ(ierr);
4253     for (i=0; i<a->B->cmap->n; i++) {
4254       colors[i] = coloring->colors[larray[i]];
4255     }
4256     ierr = PetscFree(larray);CHKERRQ(ierr);
4257     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,&ocoloring);CHKERRQ(ierr);
4258     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
4259     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
4260   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support ISColoringType %d",(int)coloring->ctype);
4261 
4262   PetscFunctionReturn(0);
4263 }
4264 
4265 #if defined(PETSC_HAVE_ADIC)
4266 #undef __FUNCT__
4267 #define __FUNCT__ "MatSetValuesAdic_MPIAIJ"
4268 PetscErrorCode MatSetValuesAdic_MPIAIJ(Mat A,void *advalues)
4269 {
4270   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
4271   PetscErrorCode ierr;
4272 
4273   PetscFunctionBegin;
4274   ierr = MatSetValuesAdic_SeqAIJ(a->A,advalues);CHKERRQ(ierr);
4275   ierr = MatSetValuesAdic_SeqAIJ(a->B,advalues);CHKERRQ(ierr);
4276   PetscFunctionReturn(0);
4277 }
4278 #endif
4279 
4280 #undef __FUNCT__
4281 #define __FUNCT__ "MatSetValuesAdifor_MPIAIJ"
4282 PetscErrorCode MatSetValuesAdifor_MPIAIJ(Mat A,PetscInt nl,void *advalues)
4283 {
4284   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
4285   PetscErrorCode ierr;
4286 
4287   PetscFunctionBegin;
4288   ierr = MatSetValuesAdifor_SeqAIJ(a->A,nl,advalues);CHKERRQ(ierr);
4289   ierr = MatSetValuesAdifor_SeqAIJ(a->B,nl,advalues);CHKERRQ(ierr);
4290   PetscFunctionReturn(0);
4291 }
4292 
4293 #undef __FUNCT__
4294 #define __FUNCT__ "MatCreateMPIAIJConcatenateSeqAIJSymbolic"
4295 PetscErrorCode  MatCreateMPIAIJConcatenateSeqAIJSymbolic(MPI_Comm comm,Mat inmat,PetscInt n,Mat *outmat)
4296 {
4297   PetscErrorCode ierr;
4298   PetscInt       m,N,i,rstart,nnz,*dnz,*onz,sum,bs,cbs;
4299   PetscInt       *indx;
4300 
4301   PetscFunctionBegin;
4302   /* This routine will ONLY return MPIAIJ type matrix */
4303   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
4304   ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
4305   if (n == PETSC_DECIDE){
4306     ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
4307   }
4308   /* Check sum(n) = N */
4309   ierr = MPI_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4310   if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
4311 
4312   ierr = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4313   rstart -= m;
4314 
4315   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4316   for (i=0;i<m;i++) {
4317     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,PETSC_NULL);CHKERRQ(ierr);
4318     ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
4319     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,PETSC_NULL);CHKERRQ(ierr);
4320   }
4321 
4322   ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
4323   ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE); CHKERRQ(ierr);
4324   ierr = MatSetBlockSizes(*outmat,bs,cbs); CHKERRQ(ierr);
4325   ierr = MatSetType(*outmat,MATMPIAIJ);  CHKERRQ(ierr);
4326   ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
4327   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4328   PetscFunctionReturn(0);
4329 }
4330 
4331 #undef __FUNCT__
4332 #define __FUNCT__ "MatCreateMPIAIJConcatenateSeqAIJNumeric"
4333 PetscErrorCode  MatCreateMPIAIJConcatenateSeqAIJNumeric(MPI_Comm comm,Mat inmat,PetscInt n,Mat outmat)
4334 {
4335   PetscErrorCode ierr;
4336   PetscInt       m,N,i,rstart,nnz,Ii;
4337   PetscInt       *indx;
4338   PetscScalar    *values;
4339 
4340   PetscFunctionBegin;
4341   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
4342   ierr = MatGetOwnershipRange(outmat,&rstart,PETSC_NULL);CHKERRQ(ierr);
4343   for (i=0;i<m;i++) {
4344     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4345     Ii    = i + rstart;
4346     ierr = MatSetValues_MPIAIJ(outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4347     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4348   }
4349   ierr = MatAssemblyBegin(outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4350   ierr = MatAssemblyEnd(outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4351   PetscFunctionReturn(0);
4352 }
4353 
4354 #undef __FUNCT__
4355 #define __FUNCT__ "MatCreateMPIAIJConcatenateSeqAIJ"
4356 /*@
4357       MatCreateMPIAIJConcatenateSeqAIJ - Creates a single large PETSc matrix by concatenating sequential
4358                  matrices from each processor
4359 
4360     Collective on MPI_Comm
4361 
4362    Input Parameters:
4363 +    comm - the communicators the parallel matrix will live on
4364 .    inmat - the input sequential matrices
4365 .    n - number of local columns (or PETSC_DECIDE)
4366 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4367 
4368    Output Parameter:
4369 .    outmat - the parallel matrix generated
4370 
4371     Level: advanced
4372 
4373    Notes: The number of columns of the matrix in EACH processor MUST be the same.
4374 
4375 @*/
4376 PetscErrorCode  MatCreateMPIAIJConcatenateSeqAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
4377 {
4378   PetscErrorCode ierr;
4379 
4380   PetscFunctionBegin;
4381   ierr = PetscLogEventBegin(MAT_Merge,inmat,0,0,0);CHKERRQ(ierr);
4382   if (scall == MAT_INITIAL_MATRIX){
4383     ierr = MatCreateMPIAIJConcatenateSeqAIJSymbolic(comm,inmat,n,outmat);CHKERRQ(ierr);
4384   }
4385   ierr = MatCreateMPIAIJConcatenateSeqAIJNumeric(comm,inmat,n,*outmat);CHKERRQ(ierr);
4386   ierr = PetscLogEventEnd(MAT_Merge,inmat,0,0,0);CHKERRQ(ierr);
4387   PetscFunctionReturn(0);
4388 }
4389 
4390 #undef __FUNCT__
4391 #define __FUNCT__ "MatFileSplit"
4392 PetscErrorCode MatFileSplit(Mat A,char *outfile)
4393 {
4394   PetscErrorCode    ierr;
4395   PetscMPIInt       rank;
4396   PetscInt          m,N,i,rstart,nnz;
4397   size_t            len;
4398   const PetscInt    *indx;
4399   PetscViewer       out;
4400   char              *name;
4401   Mat               B;
4402   const PetscScalar *values;
4403 
4404   PetscFunctionBegin;
4405   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
4406   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
4407   /* Should this be the type of the diagonal block of A? */
4408   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
4409   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
4410   ierr = MatSetBlockSizes(B,A->rmap->bs,A->cmap->bs);CHKERRQ(ierr);
4411   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
4412   ierr = MatSeqAIJSetPreallocation(B,0,PETSC_NULL);CHKERRQ(ierr);
4413   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
4414   for (i=0;i<m;i++) {
4415     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4416     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4417     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4418   }
4419   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4420   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4421 
4422   ierr = MPI_Comm_rank(((PetscObject)A)->comm,&rank);CHKERRQ(ierr);
4423   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
4424   ierr = PetscMalloc((len+5)*sizeof(char),&name);CHKERRQ(ierr);
4425   sprintf(name,"%s.%d",outfile,rank);
4426   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
4427   ierr = PetscFree(name);
4428   ierr = MatView(B,out);CHKERRQ(ierr);
4429   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
4430   ierr = MatDestroy(&B);CHKERRQ(ierr);
4431   PetscFunctionReturn(0);
4432 }
4433 
4434 extern PetscErrorCode MatDestroy_MPIAIJ(Mat);
4435 #undef __FUNCT__
4436 #define __FUNCT__ "MatDestroy_MPIAIJ_SeqsToMPI"
4437 PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
4438 {
4439   PetscErrorCode       ierr;
4440   Mat_Merge_SeqsToMPI  *merge;
4441   PetscContainer       container;
4442 
4443   PetscFunctionBegin;
4444   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject *)&container);CHKERRQ(ierr);
4445   if (container) {
4446     ierr = PetscContainerGetPointer(container,(void **)&merge);CHKERRQ(ierr);
4447     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
4448     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
4449     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
4450     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
4451     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
4452     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
4453     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
4454     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
4455     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
4456     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
4457     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
4458     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
4459     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
4460     ierr = PetscFree(merge);CHKERRQ(ierr);
4461     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
4462   }
4463   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
4464   PetscFunctionReturn(0);
4465 }
4466 
4467 #include <../src/mat/utils/freespace.h>
4468 #include <petscbt.h>
4469 
4470 #undef __FUNCT__
4471 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJNumeric"
4472 PetscErrorCode  MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
4473 {
4474   PetscErrorCode       ierr;
4475   MPI_Comm             comm=((PetscObject)mpimat)->comm;
4476   Mat_SeqAIJ           *a=(Mat_SeqAIJ*)seqmat->data;
4477   PetscMPIInt          size,rank,taga,*len_s;
4478   PetscInt             N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj=a->j;
4479   PetscInt             proc,m;
4480   PetscInt             **buf_ri,**buf_rj;
4481   PetscInt             k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
4482   PetscInt             nrows,**buf_ri_k,**nextrow,**nextai;
4483   MPI_Request          *s_waits,*r_waits;
4484   MPI_Status           *status;
4485   MatScalar            *aa=a->a;
4486   MatScalar            **abuf_r,*ba_i;
4487   Mat_Merge_SeqsToMPI  *merge;
4488   PetscContainer       container;
4489 
4490   PetscFunctionBegin;
4491   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4492 
4493   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4494   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4495 
4496   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject *)&container);CHKERRQ(ierr);
4497   ierr  = PetscContainerGetPointer(container,(void **)&merge);CHKERRQ(ierr);
4498 
4499   bi     = merge->bi;
4500   bj     = merge->bj;
4501   buf_ri = merge->buf_ri;
4502   buf_rj = merge->buf_rj;
4503 
4504   ierr   = PetscMalloc(size*sizeof(MPI_Status),&status);CHKERRQ(ierr);
4505   owners = merge->rowmap->range;
4506   len_s  = merge->len_s;
4507 
4508   /* send and recv matrix values */
4509   /*-----------------------------*/
4510   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
4511   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
4512 
4513   ierr = PetscMalloc((merge->nsend+1)*sizeof(MPI_Request),&s_waits);CHKERRQ(ierr);
4514   for (proc=0,k=0; proc<size; proc++){
4515     if (!len_s[proc]) continue;
4516     i = owners[proc];
4517     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
4518     k++;
4519   }
4520 
4521   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
4522   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
4523   ierr = PetscFree(status);CHKERRQ(ierr);
4524 
4525   ierr = PetscFree(s_waits);CHKERRQ(ierr);
4526   ierr = PetscFree(r_waits);CHKERRQ(ierr);
4527 
4528   /* insert mat values of mpimat */
4529   /*----------------------------*/
4530   ierr = PetscMalloc(N*sizeof(PetscScalar),&ba_i);CHKERRQ(ierr);
4531   ierr = PetscMalloc3(merge->nrecv,PetscInt*,&buf_ri_k,merge->nrecv,PetscInt*,&nextrow,merge->nrecv,PetscInt*,&nextai);CHKERRQ(ierr);
4532 
4533   for (k=0; k<merge->nrecv; k++){
4534     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4535     nrows = *(buf_ri_k[k]);
4536     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
4537     nextai[k]   = buf_ri_k[k] + (nrows + 1);/* poins to the next i-structure of k-th recved i-structure  */
4538   }
4539 
4540   /* set values of ba */
4541   m = merge->rowmap->n;
4542   for (i=0; i<m; i++) {
4543     arow = owners[rank] + i;
4544     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
4545     bnzi = bi[i+1] - bi[i];
4546     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
4547 
4548     /* add local non-zero vals of this proc's seqmat into ba */
4549     anzi = ai[arow+1] - ai[arow];
4550     aj   = a->j + ai[arow];
4551     aa   = a->a + ai[arow];
4552     nextaj = 0;
4553     for (j=0; nextaj<anzi; j++){
4554       if (*(bj_i + j) == aj[nextaj]){ /* bcol == acol */
4555         ba_i[j] += aa[nextaj++];
4556       }
4557     }
4558 
4559     /* add received vals into ba */
4560     for (k=0; k<merge->nrecv; k++){ /* k-th received message */
4561       /* i-th row */
4562       if (i == *nextrow[k]) {
4563         anzi = *(nextai[k]+1) - *nextai[k];
4564         aj   = buf_rj[k] + *(nextai[k]);
4565         aa   = abuf_r[k] + *(nextai[k]);
4566         nextaj = 0;
4567         for (j=0; nextaj<anzi; j++){
4568           if (*(bj_i + j) == aj[nextaj]){ /* bcol == acol */
4569             ba_i[j] += aa[nextaj++];
4570           }
4571         }
4572         nextrow[k]++; nextai[k]++;
4573       }
4574     }
4575     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
4576   }
4577   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4578   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4579 
4580   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
4581   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
4582   ierr = PetscFree(ba_i);CHKERRQ(ierr);
4583   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4584   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4585   PetscFunctionReturn(0);
4586 }
4587 
4588 extern PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat);
4589 
4590 #undef __FUNCT__
4591 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJSymbolic"
4592 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4593 {
4594   PetscErrorCode       ierr;
4595   Mat                  B_mpi;
4596   Mat_SeqAIJ           *a=(Mat_SeqAIJ*)seqmat->data;
4597   PetscMPIInt          size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4598   PetscInt             **buf_rj,**buf_ri,**buf_ri_k;
4599   PetscInt             M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4600   PetscInt             len,proc,*dnz,*onz,bs,cbs;
4601   PetscInt             k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4602   PetscInt             nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4603   MPI_Request          *si_waits,*sj_waits,*ri_waits,*rj_waits;
4604   MPI_Status           *status;
4605   PetscFreeSpaceList   free_space=PETSC_NULL,current_space=PETSC_NULL;
4606   PetscBT              lnkbt;
4607   Mat_Merge_SeqsToMPI  *merge;
4608   PetscContainer       container;
4609 
4610   PetscFunctionBegin;
4611   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4612 
4613   /* make sure it is a PETSc comm */
4614   ierr = PetscCommDuplicate(comm,&comm,PETSC_NULL);CHKERRQ(ierr);
4615   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4616   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4617 
4618   ierr = PetscNew(Mat_Merge_SeqsToMPI,&merge);CHKERRQ(ierr);
4619   ierr = PetscMalloc(size*sizeof(MPI_Status),&status);CHKERRQ(ierr);
4620 
4621   /* determine row ownership */
4622   /*---------------------------------------------------------*/
4623   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
4624   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
4625   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
4626   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
4627   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
4628   ierr = PetscMalloc(size*sizeof(PetscMPIInt),&len_si);CHKERRQ(ierr);
4629   ierr = PetscMalloc(size*sizeof(PetscMPIInt),&merge->len_s);CHKERRQ(ierr);
4630 
4631   m      = merge->rowmap->n;
4632   M      = merge->rowmap->N;
4633   owners = merge->rowmap->range;
4634 
4635   /* determine the number of messages to send, their lengths */
4636   /*---------------------------------------------------------*/
4637   len_s  = merge->len_s;
4638 
4639   len = 0;  /* length of buf_si[] */
4640   merge->nsend = 0;
4641   for (proc=0; proc<size; proc++){
4642     len_si[proc] = 0;
4643     if (proc == rank){
4644       len_s[proc] = 0;
4645     } else {
4646       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4647       len_s[proc] = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4648     }
4649     if (len_s[proc]) {
4650       merge->nsend++;
4651       nrows = 0;
4652       for (i=owners[proc]; i<owners[proc+1]; i++){
4653         if (ai[i+1] > ai[i]) nrows++;
4654       }
4655       len_si[proc] = 2*(nrows+1);
4656       len += len_si[proc];
4657     }
4658   }
4659 
4660   /* determine the number and length of messages to receive for ij-structure */
4661   /*-------------------------------------------------------------------------*/
4662   ierr = PetscGatherNumberOfMessages(comm,PETSC_NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
4663   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
4664 
4665   /* post the Irecv of j-structure */
4666   /*-------------------------------*/
4667   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
4668   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
4669 
4670   /* post the Isend of j-structure */
4671   /*--------------------------------*/
4672   ierr = PetscMalloc2(merge->nsend,MPI_Request,&si_waits,merge->nsend,MPI_Request,&sj_waits);CHKERRQ(ierr);
4673 
4674   for (proc=0, k=0; proc<size; proc++){
4675     if (!len_s[proc]) continue;
4676     i = owners[proc];
4677     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
4678     k++;
4679   }
4680 
4681   /* receives and sends of j-structure are complete */
4682   /*------------------------------------------------*/
4683   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
4684   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
4685 
4686   /* send and recv i-structure */
4687   /*---------------------------*/
4688   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
4689   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
4690 
4691   ierr = PetscMalloc((len+1)*sizeof(PetscInt),&buf_s);CHKERRQ(ierr);
4692   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4693   for (proc=0,k=0; proc<size; proc++){
4694     if (!len_s[proc]) continue;
4695     /* form outgoing message for i-structure:
4696          buf_si[0]:                 nrows to be sent
4697                [1:nrows]:           row index (global)
4698                [nrows+1:2*nrows+1]: i-structure index
4699     */
4700     /*-------------------------------------------*/
4701     nrows = len_si[proc]/2 - 1;
4702     buf_si_i    = buf_si + nrows+1;
4703     buf_si[0]   = nrows;
4704     buf_si_i[0] = 0;
4705     nrows = 0;
4706     for (i=owners[proc]; i<owners[proc+1]; i++){
4707       anzi = ai[i+1] - ai[i];
4708       if (anzi) {
4709         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4710         buf_si[nrows+1] = i-owners[proc]; /* local row index */
4711         nrows++;
4712       }
4713     }
4714     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4715     k++;
4716     buf_si += len_si[proc];
4717   }
4718 
4719   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4720   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4721 
4722   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4723   for (i=0; i<merge->nrecv; i++){
4724     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);
4725   }
4726 
4727   ierr = PetscFree(len_si);CHKERRQ(ierr);
4728   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4729   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4730   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4731   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4732   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4733   ierr = PetscFree(status);CHKERRQ(ierr);
4734 
4735   /* compute a local seq matrix in each processor */
4736   /*----------------------------------------------*/
4737   /* allocate bi array and free space for accumulating nonzero column info */
4738   ierr = PetscMalloc((m+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
4739   bi[0] = 0;
4740 
4741   /* create and initialize a linked list */
4742   nlnk = N+1;
4743   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4744 
4745   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4746   len = 0;
4747   len  = ai[owners[rank+1]] - ai[owners[rank]];
4748   ierr = PetscFreeSpaceGet((PetscInt)(2*len+1),&free_space);CHKERRQ(ierr);
4749   current_space = free_space;
4750 
4751   /* determine symbolic info for each local row */
4752   ierr = PetscMalloc3(merge->nrecv,PetscInt*,&buf_ri_k,merge->nrecv,PetscInt*,&nextrow,merge->nrecv,PetscInt*,&nextai);CHKERRQ(ierr);
4753 
4754   for (k=0; k<merge->nrecv; k++){
4755     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4756     nrows = *buf_ri_k[k];
4757     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4758     nextai[k]   = buf_ri_k[k] + (nrows + 1);/* poins to the next i-structure of k-th recved i-structure  */
4759   }
4760 
4761   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4762   len = 0;
4763   for (i=0;i<m;i++) {
4764     bnzi   = 0;
4765     /* add local non-zero cols of this proc's seqmat into lnk */
4766     arow   = owners[rank] + i;
4767     anzi   = ai[arow+1] - ai[arow];
4768     aj     = a->j + ai[arow];
4769     ierr = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4770     bnzi += nlnk;
4771     /* add received col data into lnk */
4772     for (k=0; k<merge->nrecv; k++){ /* k-th received message */
4773       if (i == *nextrow[k]) { /* i-th row */
4774         anzi = *(nextai[k]+1) - *nextai[k];
4775         aj   = buf_rj[k] + *nextai[k];
4776         ierr = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4777         bnzi += nlnk;
4778         nextrow[k]++; nextai[k]++;
4779       }
4780     }
4781     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4782 
4783     /* if free space is not available, make more free space */
4784     if (current_space->local_remaining<bnzi) {
4785       ierr = PetscFreeSpaceGet(bnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
4786       nspacedouble++;
4787     }
4788     /* copy data into free space, then initialize lnk */
4789     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4790     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
4791 
4792     current_space->array           += bnzi;
4793     current_space->local_used      += bnzi;
4794     current_space->local_remaining -= bnzi;
4795 
4796     bi[i+1] = bi[i] + bnzi;
4797   }
4798 
4799   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4800 
4801   ierr = PetscMalloc((bi[m]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
4802   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
4803   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4804 
4805   /* create symbolic parallel matrix B_mpi */
4806   /*---------------------------------------*/
4807     ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
4808   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
4809   if (n==PETSC_DECIDE) {
4810     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
4811   } else {
4812     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4813   }
4814   ierr = MatSetBlockSizes(B_mpi,bs,cbs); CHKERRQ(ierr);
4815   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
4816   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
4817   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4818   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
4819 
4820   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4821   B_mpi->assembled     = PETSC_FALSE;
4822   B_mpi->ops->destroy  = MatDestroy_MPIAIJ_SeqsToMPI;
4823   merge->bi            = bi;
4824   merge->bj            = bj;
4825   merge->buf_ri        = buf_ri;
4826   merge->buf_rj        = buf_rj;
4827   merge->coi           = PETSC_NULL;
4828   merge->coj           = PETSC_NULL;
4829   merge->owners_co     = PETSC_NULL;
4830 
4831   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
4832 
4833   /* attach the supporting struct to B_mpi for reuse */
4834   ierr = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
4835   ierr = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
4836   ierr = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
4837   ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
4838   *mpimat = B_mpi;
4839 
4840   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4841   PetscFunctionReturn(0);
4842 }
4843 
4844 #undef __FUNCT__
4845 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJ"
4846 /*@C
4847       MatCreateMPIAIJSumSeqAIJ - Creates a MPIAIJ matrix by adding sequential
4848                  matrices from each processor
4849 
4850     Collective on MPI_Comm
4851 
4852    Input Parameters:
4853 +    comm - the communicators the parallel matrix will live on
4854 .    seqmat - the input sequential matrices
4855 .    m - number of local rows (or PETSC_DECIDE)
4856 .    n - number of local columns (or PETSC_DECIDE)
4857 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4858 
4859    Output Parameter:
4860 .    mpimat - the parallel matrix generated
4861 
4862     Level: advanced
4863 
4864    Notes:
4865      The dimensions of the sequential matrix in each processor MUST be the same.
4866      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
4867      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
4868 @*/
4869 PetscErrorCode  MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
4870 {
4871   PetscErrorCode   ierr;
4872   PetscMPIInt     size;
4873 
4874   PetscFunctionBegin;
4875   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4876   if (size == 1){
4877      ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4878      if (scall == MAT_INITIAL_MATRIX){
4879        ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
4880      } else {
4881        ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4882      }
4883      ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4884      PetscFunctionReturn(0);
4885   }
4886   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4887   if (scall == MAT_INITIAL_MATRIX){
4888     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
4889   }
4890   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
4891   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4892   PetscFunctionReturn(0);
4893 }
4894 
4895 #undef __FUNCT__
4896 #define __FUNCT__ "MatMPIAIJGetLocalMat"
4897 /*@
4898      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
4899           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
4900           with MatGetSize()
4901 
4902     Not Collective
4903 
4904    Input Parameters:
4905 +    A - the matrix
4906 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4907 
4908    Output Parameter:
4909 .    A_loc - the local sequential matrix generated
4910 
4911     Level: developer
4912 
4913 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
4914 
4915 @*/
4916 PetscErrorCode  MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
4917 {
4918   PetscErrorCode  ierr;
4919   Mat_MPIAIJ      *mpimat=(Mat_MPIAIJ*)A->data;
4920   Mat_SeqAIJ      *mat,*a=(Mat_SeqAIJ*)(mpimat->A)->data,*b=(Mat_SeqAIJ*)(mpimat->B)->data;
4921   PetscInt        *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*cmap=mpimat->garray;
4922   MatScalar       *aa=a->a,*ba=b->a,*cam;
4923   PetscScalar     *ca;
4924   PetscInt        am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
4925   PetscInt        *ci,*cj,col,ncols_d,ncols_o,jo;
4926   PetscBool       match;
4927 
4928   PetscFunctionBegin;
4929   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4930   if (!match) SETERRQ(((PetscObject)A)->comm, PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
4931   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4932   if (scall == MAT_INITIAL_MATRIX){
4933     ierr = PetscMalloc((1+am)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
4934     ci[0] = 0;
4935     for (i=0; i<am; i++){
4936       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
4937     }
4938     ierr = PetscMalloc((1+ci[am])*sizeof(PetscInt),&cj);CHKERRQ(ierr);
4939     ierr = PetscMalloc((1+ci[am])*sizeof(PetscScalar),&ca);CHKERRQ(ierr);
4940     k = 0;
4941     for (i=0; i<am; i++) {
4942       ncols_o = bi[i+1] - bi[i];
4943       ncols_d = ai[i+1] - ai[i];
4944       /* off-diagonal portion of A */
4945       for (jo=0; jo<ncols_o; jo++) {
4946         col = cmap[*bj];
4947         if (col >= cstart) break;
4948         cj[k]   = col; bj++;
4949         ca[k++] = *ba++;
4950       }
4951       /* diagonal portion of A */
4952       for (j=0; j<ncols_d; j++) {
4953         cj[k]   = cstart + *aj++;
4954         ca[k++] = *aa++;
4955       }
4956       /* off-diagonal portion of A */
4957       for (j=jo; j<ncols_o; j++) {
4958         cj[k]   = cmap[*bj++];
4959         ca[k++] = *ba++;
4960       }
4961     }
4962     /* put together the new matrix */
4963     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
4964     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4965     /* Since these are PETSc arrays, change flags to free them as necessary. */
4966     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
4967     mat->free_a  = PETSC_TRUE;
4968     mat->free_ij = PETSC_TRUE;
4969     mat->nonew   = 0;
4970   } else if (scall == MAT_REUSE_MATRIX){
4971     mat=(Mat_SeqAIJ*)(*A_loc)->data;
4972     ci = mat->i; cj = mat->j; cam = mat->a;
4973     for (i=0; i<am; i++) {
4974       /* off-diagonal portion of A */
4975       ncols_o = bi[i+1] - bi[i];
4976       for (jo=0; jo<ncols_o; jo++) {
4977         col = cmap[*bj];
4978         if (col >= cstart) break;
4979         *cam++ = *ba++; bj++;
4980       }
4981       /* diagonal portion of A */
4982       ncols_d = ai[i+1] - ai[i];
4983       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
4984       /* off-diagonal portion of A */
4985       for (j=jo; j<ncols_o; j++) {
4986         *cam++ = *ba++; bj++;
4987       }
4988     }
4989   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
4990   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4991   PetscFunctionReturn(0);
4992 }
4993 
4994 #undef __FUNCT__
4995 #define __FUNCT__ "MatMPIAIJGetLocalMatCondensed"
4996 /*@C
4997      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MPIAIJ matrix by taking all its local rows and NON-ZERO columns
4998 
4999     Not Collective
5000 
5001    Input Parameters:
5002 +    A - the matrix
5003 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5004 -    row, col - index sets of rows and columns to extract (or PETSC_NULL)
5005 
5006    Output Parameter:
5007 .    A_loc - the local sequential matrix generated
5008 
5009     Level: developer
5010 
5011 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
5012 
5013 @*/
5014 PetscErrorCode  MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
5015 {
5016   Mat_MPIAIJ        *a=(Mat_MPIAIJ*)A->data;
5017   PetscErrorCode    ierr;
5018   PetscInt          i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
5019   IS                isrowa,iscola;
5020   Mat               *aloc;
5021   PetscBool       match;
5022 
5023   PetscFunctionBegin;
5024   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
5025   if (!match) SETERRQ(((PetscObject)A)->comm, PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
5026   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
5027   if (!row){
5028     start = A->rmap->rstart; end = A->rmap->rend;
5029     ierr = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
5030   } else {
5031     isrowa = *row;
5032   }
5033   if (!col){
5034     start = A->cmap->rstart;
5035     cmap  = a->garray;
5036     nzA   = a->A->cmap->n;
5037     nzB   = a->B->cmap->n;
5038     ierr  = PetscMalloc((nzA+nzB)*sizeof(PetscInt), &idx);CHKERRQ(ierr);
5039     ncols = 0;
5040     for (i=0; i<nzB; i++) {
5041       if (cmap[i] < start) idx[ncols++] = cmap[i];
5042       else break;
5043     }
5044     imark = i;
5045     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
5046     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
5047     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
5048   } else {
5049     iscola = *col;
5050   }
5051   if (scall != MAT_INITIAL_MATRIX){
5052     ierr = PetscMalloc(sizeof(Mat),&aloc);CHKERRQ(ierr);
5053     aloc[0] = *A_loc;
5054   }
5055   ierr = MatGetSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
5056   *A_loc = aloc[0];
5057   ierr = PetscFree(aloc);CHKERRQ(ierr);
5058   if (!row){
5059     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
5060   }
5061   if (!col){
5062     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
5063   }
5064   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
5065   PetscFunctionReturn(0);
5066 }
5067 
5068 #undef __FUNCT__
5069 #define __FUNCT__ "MatGetBrowsOfAcols"
5070 /*@C
5071     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
5072 
5073     Collective on Mat
5074 
5075    Input Parameters:
5076 +    A,B - the matrices in mpiaij format
5077 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5078 -    rowb, colb - index sets of rows and columns of B to extract (or PETSC_NULL)
5079 
5080    Output Parameter:
5081 +    rowb, colb - index sets of rows and columns of B to extract
5082 -    B_seq - the sequential matrix generated
5083 
5084     Level: developer
5085 
5086 @*/
5087 PetscErrorCode  MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
5088 {
5089   Mat_MPIAIJ        *a=(Mat_MPIAIJ*)A->data;
5090   PetscErrorCode    ierr;
5091   PetscInt          *idx,i,start,ncols,nzA,nzB,*cmap,imark;
5092   IS                isrowb,iscolb;
5093   Mat               *bseq=PETSC_NULL;
5094 
5095   PetscFunctionBegin;
5096   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend){
5097     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);
5098   }
5099   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
5100 
5101   if (scall == MAT_INITIAL_MATRIX){
5102     start = A->cmap->rstart;
5103     cmap  = a->garray;
5104     nzA   = a->A->cmap->n;
5105     nzB   = a->B->cmap->n;
5106     ierr  = PetscMalloc((nzA+nzB)*sizeof(PetscInt), &idx);CHKERRQ(ierr);
5107     ncols = 0;
5108     for (i=0; i<nzB; i++) {  /* row < local row index */
5109       if (cmap[i] < start) idx[ncols++] = cmap[i];
5110       else break;
5111     }
5112     imark = i;
5113     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
5114     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
5115     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
5116     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
5117   } else {
5118     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
5119     isrowb = *rowb; iscolb = *colb;
5120     ierr = PetscMalloc(sizeof(Mat),&bseq);CHKERRQ(ierr);
5121     bseq[0] = *B_seq;
5122   }
5123   ierr = MatGetSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
5124   *B_seq = bseq[0];
5125   ierr = PetscFree(bseq);CHKERRQ(ierr);
5126   if (!rowb){
5127     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
5128   } else {
5129     *rowb = isrowb;
5130   }
5131   if (!colb){
5132     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
5133   } else {
5134     *colb = iscolb;
5135   }
5136   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
5137   PetscFunctionReturn(0);
5138 }
5139 
5140 #undef __FUNCT__
5141 #define __FUNCT__ "MatGetBrowsOfAoCols_MPIAIJ"
5142 /*
5143     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
5144     of the OFF-DIAGONAL portion of local A
5145 
5146     Collective on Mat
5147 
5148    Input Parameters:
5149 +    A,B - the matrices in mpiaij format
5150 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5151 
5152    Output Parameter:
5153 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or PETSC_NULL)
5154 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or PETSC_NULL)
5155 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or PETSC_NULL)
5156 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
5157 
5158     Level: developer
5159 
5160 */
5161 PetscErrorCode  MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
5162 {
5163   VecScatter_MPI_General *gen_to,*gen_from;
5164   PetscErrorCode         ierr;
5165   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
5166   Mat_SeqAIJ             *b_oth;
5167   VecScatter             ctx=a->Mvctx;
5168   MPI_Comm               comm=((PetscObject)ctx)->comm;
5169   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
5170   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
5171   PetscScalar            *rvalues,*svalues;
5172   MatScalar              *b_otha,*bufa,*bufA;
5173   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
5174   MPI_Request            *rwaits = PETSC_NULL,*swaits = PETSC_NULL;
5175   MPI_Status             *sstatus,rstatus;
5176   PetscMPIInt            jj;
5177   PetscInt               *cols,sbs,rbs;
5178   PetscScalar            *vals;
5179 
5180   PetscFunctionBegin;
5181   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend){
5182     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);
5183   }
5184   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5185   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
5186 
5187   gen_to   = (VecScatter_MPI_General*)ctx->todata;
5188   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
5189   rvalues  = gen_from->values; /* holds the length of receiving row */
5190   svalues  = gen_to->values;   /* holds the length of sending row */
5191   nrecvs   = gen_from->n;
5192   nsends   = gen_to->n;
5193 
5194   ierr = PetscMalloc2(nrecvs,MPI_Request,&rwaits,nsends,MPI_Request,&swaits);CHKERRQ(ierr);
5195   srow     = gen_to->indices;   /* local row index to be sent */
5196   sstarts  = gen_to->starts;
5197   sprocs   = gen_to->procs;
5198   sstatus  = gen_to->sstatus;
5199   sbs      = gen_to->bs;
5200   rstarts  = gen_from->starts;
5201   rprocs   = gen_from->procs;
5202   rbs      = gen_from->bs;
5203 
5204   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
5205   if (scall == MAT_INITIAL_MATRIX){
5206     /* i-array */
5207     /*---------*/
5208     /*  post receives */
5209     for (i=0; i<nrecvs; i++){
5210       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
5211       nrows = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
5212       ierr = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5213     }
5214 
5215     /* pack the outgoing message */
5216     ierr = PetscMalloc2(nsends+1,PetscInt,&sstartsj,nrecvs+1,PetscInt,&rstartsj);CHKERRQ(ierr);
5217     sstartsj[0] = 0;  rstartsj[0] = 0;
5218     len = 0; /* total length of j or a array to be sent */
5219     k = 0;
5220     for (i=0; i<nsends; i++){
5221       rowlen = (PetscInt*)svalues + sstarts[i]*sbs;
5222       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5223       for (j=0; j<nrows; j++) {
5224         row = srow[k] + B->rmap->range[rank]; /* global row idx */
5225         for (l=0; l<sbs; l++){
5226           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr); /* rowlength */
5227           rowlen[j*sbs+l] = ncols;
5228           len += ncols;
5229           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
5230         }
5231         k++;
5232       }
5233       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5234       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
5235     }
5236     /* recvs and sends of i-array are completed */
5237     i = nrecvs;
5238     while (i--) {
5239       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5240     }
5241     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5242 
5243     /* allocate buffers for sending j and a arrays */
5244     ierr = PetscMalloc((len+1)*sizeof(PetscInt),&bufj);CHKERRQ(ierr);
5245     ierr = PetscMalloc((len+1)*sizeof(PetscScalar),&bufa);CHKERRQ(ierr);
5246 
5247     /* create i-array of B_oth */
5248     ierr = PetscMalloc((aBn+2)*sizeof(PetscInt),&b_othi);CHKERRQ(ierr);
5249     b_othi[0] = 0;
5250     len = 0; /* total length of j or a array to be received */
5251     k = 0;
5252     for (i=0; i<nrecvs; i++){
5253       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
5254       nrows = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be recieved */
5255       for (j=0; j<nrows; j++) {
5256         b_othi[k+1] = b_othi[k] + rowlen[j];
5257         len += rowlen[j]; k++;
5258       }
5259       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
5260     }
5261 
5262     /* allocate space for j and a arrrays of B_oth */
5263     ierr = PetscMalloc((b_othi[aBn]+1)*sizeof(PetscInt),&b_othj);CHKERRQ(ierr);
5264     ierr = PetscMalloc((b_othi[aBn]+1)*sizeof(MatScalar),&b_otha);CHKERRQ(ierr);
5265 
5266     /* j-array */
5267     /*---------*/
5268     /*  post receives of j-array */
5269     for (i=0; i<nrecvs; i++){
5270       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5271       ierr = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5272     }
5273 
5274     /* pack the outgoing message j-array */
5275     k = 0;
5276     for (i=0; i<nsends; i++){
5277       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5278       bufJ = bufj+sstartsj[i];
5279       for (j=0; j<nrows; j++) {
5280         row  = srow[k++] + B->rmap->range[rank]; /* global row idx */
5281         for (ll=0; ll<sbs; ll++){
5282           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,PETSC_NULL);CHKERRQ(ierr);
5283           for (l=0; l<ncols; l++){
5284             *bufJ++ = cols[l];
5285           }
5286           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,PETSC_NULL);CHKERRQ(ierr);
5287         }
5288       }
5289       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5290     }
5291 
5292     /* recvs and sends of j-array are completed */
5293     i = nrecvs;
5294     while (i--) {
5295       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5296     }
5297     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5298   } else if (scall == MAT_REUSE_MATRIX){
5299     sstartsj = *startsj_s;
5300     rstartsj = *startsj_r;
5301     bufa     = *bufa_ptr;
5302     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
5303     b_otha   = b_oth->a;
5304   } else {
5305     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
5306   }
5307 
5308   /* a-array */
5309   /*---------*/
5310   /*  post receives of a-array */
5311   for (i=0; i<nrecvs; i++){
5312     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5313     ierr = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5314   }
5315 
5316   /* pack the outgoing message a-array */
5317   k = 0;
5318   for (i=0; i<nsends; i++){
5319     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5320     bufA = bufa+sstartsj[i];
5321     for (j=0; j<nrows; j++) {
5322       row  = srow[k++] + B->rmap->range[rank]; /* global row idx */
5323       for (ll=0; ll<sbs; ll++){
5324         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,PETSC_NULL,&vals);CHKERRQ(ierr);
5325         for (l=0; l<ncols; l++){
5326           *bufA++ = vals[l];
5327         }
5328         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,PETSC_NULL,&vals);CHKERRQ(ierr);
5329       }
5330     }
5331     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5332   }
5333   /* recvs and sends of a-array are completed */
5334   i = nrecvs;
5335   while (i--) {
5336     ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5337   }
5338   if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5339   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
5340 
5341   if (scall == MAT_INITIAL_MATRIX){
5342     /* put together the new matrix */
5343     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
5344 
5345     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
5346     /* Since these are PETSc arrays, change flags to free them as necessary. */
5347     b_oth          = (Mat_SeqAIJ *)(*B_oth)->data;
5348     b_oth->free_a  = PETSC_TRUE;
5349     b_oth->free_ij = PETSC_TRUE;
5350     b_oth->nonew   = 0;
5351 
5352     ierr = PetscFree(bufj);CHKERRQ(ierr);
5353     if (!startsj_s || !bufa_ptr){
5354       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
5355       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
5356     } else {
5357       *startsj_s = sstartsj;
5358       *startsj_r = rstartsj;
5359       *bufa_ptr  = bufa;
5360     }
5361   }
5362   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5363   PetscFunctionReturn(0);
5364 }
5365 
5366 #undef __FUNCT__
5367 #define __FUNCT__ "MatGetCommunicationStructs"
5368 /*@C
5369   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
5370 
5371   Not Collective
5372 
5373   Input Parameters:
5374 . A - The matrix in mpiaij format
5375 
5376   Output Parameter:
5377 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
5378 . colmap - A map from global column index to local index into lvec
5379 - multScatter - A scatter from the argument of a matrix-vector product to lvec
5380 
5381   Level: developer
5382 
5383 @*/
5384 #if defined (PETSC_USE_CTABLE)
5385 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
5386 #else
5387 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
5388 #endif
5389 {
5390   Mat_MPIAIJ *a;
5391 
5392   PetscFunctionBegin;
5393   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
5394   PetscValidPointer(lvec, 2);
5395   PetscValidPointer(colmap, 3);
5396   PetscValidPointer(multScatter, 4);
5397   a = (Mat_MPIAIJ *) A->data;
5398   if (lvec) *lvec = a->lvec;
5399   if (colmap) *colmap = a->colmap;
5400   if (multScatter) *multScatter = a->Mvctx;
5401   PetscFunctionReturn(0);
5402 }
5403 
5404 EXTERN_C_BEGIN
5405 extern PetscErrorCode  MatConvert_MPIAIJ_MPIAIJCRL(Mat,const MatType,MatReuse,Mat*);
5406 extern PetscErrorCode  MatConvert_MPIAIJ_MPIAIJPERM(Mat,const MatType,MatReuse,Mat*);
5407 extern PetscErrorCode  MatConvert_MPIAIJ_MPISBAIJ(Mat,const MatType,MatReuse,Mat*);
5408 EXTERN_C_END
5409 
5410 #undef __FUNCT__
5411 #define __FUNCT__ "MatMatMultNumeric_MPIDense_MPIAIJ"
5412 /*
5413     Computes (B'*A')' since computing B*A directly is untenable
5414 
5415                n                       p                          p
5416         (              )       (              )         (                  )
5417       m (      A       )  *  n (       B      )   =   m (         C        )
5418         (              )       (              )         (                  )
5419 
5420 */
5421 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
5422 {
5423   PetscErrorCode     ierr;
5424   Mat                At,Bt,Ct;
5425 
5426   PetscFunctionBegin;
5427   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
5428   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
5429   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
5430   ierr = MatDestroy(&At);CHKERRQ(ierr);
5431   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
5432   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
5433   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
5434   PetscFunctionReturn(0);
5435 }
5436 
5437 #undef __FUNCT__
5438 #define __FUNCT__ "MatMatMultSymbolic_MPIDense_MPIAIJ"
5439 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
5440 {
5441   PetscErrorCode ierr;
5442   PetscInt       m=A->rmap->n,n=B->cmap->n;
5443   Mat            Cmat;
5444 
5445   PetscFunctionBegin;
5446   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);
5447   ierr = MatCreate(((PetscObject)A)->comm,&Cmat);CHKERRQ(ierr);
5448   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
5449   ierr = MatSetBlockSizes(Cmat,A->rmap->bs,B->cmap->bs);CHKERRQ(ierr);
5450   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
5451   ierr = MatMPIDenseSetPreallocation(Cmat,PETSC_NULL);CHKERRQ(ierr);
5452   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5453   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5454   *C   = Cmat;
5455   (*C)->ops->matmult = MatMatMult_MPIDense_MPIAIJ;
5456   PetscFunctionReturn(0);
5457 }
5458 
5459 /* ----------------------------------------------------------------*/
5460 #undef __FUNCT__
5461 #define __FUNCT__ "MatMatMult_MPIDense_MPIAIJ"
5462 PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
5463 {
5464   PetscErrorCode ierr;
5465 
5466   PetscFunctionBegin;
5467   if (scall == MAT_INITIAL_MATRIX){
5468     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
5469   }
5470   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
5471   PetscFunctionReturn(0);
5472 }
5473 
5474 EXTERN_C_BEGIN
5475 #if defined(PETSC_HAVE_MUMPS)
5476 extern PetscErrorCode MatGetFactor_aij_mumps(Mat,MatFactorType,Mat*);
5477 #endif
5478 #if defined(PETSC_HAVE_PASTIX)
5479 extern PetscErrorCode MatGetFactor_mpiaij_pastix(Mat,MatFactorType,Mat*);
5480 #endif
5481 #if defined(PETSC_HAVE_SUPERLU_DIST)
5482 extern PetscErrorCode MatGetFactor_mpiaij_superlu_dist(Mat,MatFactorType,Mat*);
5483 #endif
5484 #if defined(PETSC_HAVE_SPOOLES)
5485 extern PetscErrorCode MatGetFactor_mpiaij_spooles(Mat,MatFactorType,Mat*);
5486 #endif
5487 EXTERN_C_END
5488 
5489 /*MC
5490    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
5491 
5492    Options Database Keys:
5493 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
5494 
5495   Level: beginner
5496 
5497 .seealso: MatCreateAIJ()
5498 M*/
5499 
5500 EXTERN_C_BEGIN
5501 #undef __FUNCT__
5502 #define __FUNCT__ "MatCreate_MPIAIJ"
5503 PetscErrorCode  MatCreate_MPIAIJ(Mat B)
5504 {
5505   Mat_MPIAIJ     *b;
5506   PetscErrorCode ierr;
5507   PetscMPIInt    size;
5508 
5509   PetscFunctionBegin;
5510   ierr = MPI_Comm_size(((PetscObject)B)->comm,&size);CHKERRQ(ierr);
5511 
5512   ierr            = PetscNewLog(B,Mat_MPIAIJ,&b);CHKERRQ(ierr);
5513   B->data         = (void*)b;
5514   ierr            = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
5515   B->assembled    = PETSC_FALSE;
5516 
5517   B->insertmode   = NOT_SET_VALUES;
5518   b->size         = size;
5519   ierr = MPI_Comm_rank(((PetscObject)B)->comm,&b->rank);CHKERRQ(ierr);
5520 
5521   /* build cache for off array entries formed */
5522   ierr = MatStashCreate_Private(((PetscObject)B)->comm,1,&B->stash);CHKERRQ(ierr);
5523   b->donotstash  = PETSC_FALSE;
5524   b->colmap      = 0;
5525   b->garray      = 0;
5526   b->roworiented = PETSC_TRUE;
5527 
5528   /* stuff used for matrix vector multiply */
5529   b->lvec      = PETSC_NULL;
5530   b->Mvctx     = PETSC_NULL;
5531 
5532   /* stuff for MatGetRow() */
5533   b->rowindices   = 0;
5534   b->rowvalues    = 0;
5535   b->getrowactive = PETSC_FALSE;
5536 
5537 #if defined(PETSC_HAVE_SPOOLES)
5538   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatGetFactor_spooles_C",
5539                                      "MatGetFactor_mpiaij_spooles",
5540                                      MatGetFactor_mpiaij_spooles);CHKERRQ(ierr);
5541 #endif
5542 #if defined(PETSC_HAVE_MUMPS)
5543   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatGetFactor_mumps_C",
5544                                      "MatGetFactor_aij_mumps",
5545                                      MatGetFactor_aij_mumps);CHKERRQ(ierr);
5546 #endif
5547 #if defined(PETSC_HAVE_PASTIX)
5548   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatGetFactor_pastix_C",
5549 					   "MatGetFactor_mpiaij_pastix",
5550 					   MatGetFactor_mpiaij_pastix);CHKERRQ(ierr);
5551 #endif
5552 #if defined(PETSC_HAVE_SUPERLU_DIST)
5553   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatGetFactor_superlu_dist_C",
5554                                      "MatGetFactor_mpiaij_superlu_dist",
5555                                      MatGetFactor_mpiaij_superlu_dist);CHKERRQ(ierr);
5556 #endif
5557   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatStoreValues_C",
5558                                      "MatStoreValues_MPIAIJ",
5559                                      MatStoreValues_MPIAIJ);CHKERRQ(ierr);
5560   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatRetrieveValues_C",
5561                                      "MatRetrieveValues_MPIAIJ",
5562                                      MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
5563   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatGetDiagonalBlock_C",
5564 				     "MatGetDiagonalBlock_MPIAIJ",
5565                                      MatGetDiagonalBlock_MPIAIJ);CHKERRQ(ierr);
5566   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatIsTranspose_C",
5567 				     "MatIsTranspose_MPIAIJ",
5568 				     MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
5569   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatMPIAIJSetPreallocation_C",
5570 				     "MatMPIAIJSetPreallocation_MPIAIJ",
5571 				     MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
5572   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",
5573 				     "MatMPIAIJSetPreallocationCSR_MPIAIJ",
5574 				     MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
5575   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatDiagonalScaleLocal_C",
5576 				     "MatDiagonalScaleLocal_MPIAIJ",
5577 				     MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
5578   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",
5579                                      "MatConvert_MPIAIJ_MPIAIJPERM",
5580                                       MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
5581   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",
5582                                      "MatConvert_MPIAIJ_MPIAIJCRL",
5583                                       MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
5584   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",
5585                                      "MatConvert_MPIAIJ_MPISBAIJ",
5586                                       MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
5587   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",
5588                                      "MatMatMult_MPIDense_MPIAIJ",
5589                                       MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
5590   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",
5591                                      "MatMatMultSymbolic_MPIDense_MPIAIJ",
5592                                      MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
5593   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",
5594                                      "MatMatMultNumeric_MPIDense_MPIAIJ",
5595                                       MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
5596   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
5597   PetscFunctionReturn(0);
5598 }
5599 EXTERN_C_END
5600 
5601 #undef __FUNCT__
5602 #define __FUNCT__ "MatCreateMPIAIJWithSplitArrays"
5603 /*@
5604      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
5605          and "off-diagonal" part of the matrix in CSR format.
5606 
5607    Collective on MPI_Comm
5608 
5609    Input Parameters:
5610 +  comm - MPI communicator
5611 .  m - number of local rows (Cannot be PETSC_DECIDE)
5612 .  n - This value should be the same as the local size used in creating the
5613        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
5614        calculated if N is given) For square matrices n is almost always m.
5615 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
5616 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
5617 .   i - row indices for "diagonal" portion of matrix
5618 .   j - column indices
5619 .   a - matrix values
5620 .   oi - row indices for "off-diagonal" portion of matrix
5621 .   oj - column indices
5622 -   oa - matrix values
5623 
5624    Output Parameter:
5625 .   mat - the matrix
5626 
5627    Level: advanced
5628 
5629    Notes:
5630        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
5631        must free the arrays once the matrix has been destroyed and not before.
5632 
5633        The i and j indices are 0 based
5634 
5635        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
5636 
5637        This sets local rows and cannot be used to set off-processor values.
5638 
5639        You cannot later use MatSetValues() to change values in this matrix.
5640 
5641 .keywords: matrix, aij, compressed row, sparse, parallel
5642 
5643 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
5644           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
5645 @*/
5646 PetscErrorCode  MatCreateMPIAIJWithSplitArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,PetscInt i[],PetscInt j[],PetscScalar a[],
5647 								PetscInt oi[], PetscInt oj[],PetscScalar oa[],Mat *mat)
5648 {
5649   PetscErrorCode ierr;
5650   Mat_MPIAIJ     *maij;
5651 
5652  PetscFunctionBegin;
5653   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
5654   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
5655   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
5656   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
5657   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
5658   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
5659   maij = (Mat_MPIAIJ*) (*mat)->data;
5660   maij->donotstash     = PETSC_TRUE;
5661   (*mat)->preallocated = PETSC_TRUE;
5662 
5663   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
5664   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
5665 
5666   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
5667   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
5668 
5669   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5670   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5671   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5672   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5673 
5674   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5675   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5676   PetscFunctionReturn(0);
5677 }
5678 
5679 /*
5680     Special version for direct calls from Fortran
5681 */
5682 #include <petsc-private/fortranimpl.h>
5683 
5684 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5685 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
5686 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5687 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
5688 #endif
5689 
5690 /* Change these macros so can be used in void function */
5691 #undef CHKERRQ
5692 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
5693 #undef SETERRQ2
5694 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5695 #undef SETERRQ3
5696 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5697 #undef SETERRQ
5698 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
5699 
5700 EXTERN_C_BEGIN
5701 #undef __FUNCT__
5702 #define __FUNCT__ "matsetvaluesmpiaij_"
5703 void PETSC_STDCALL matsetvaluesmpiaij_(Mat *mmat,PetscInt *mm,const PetscInt im[],PetscInt *mn,const PetscInt in[],const PetscScalar v[],InsertMode *maddv,PetscErrorCode *_ierr)
5704 {
5705   Mat             mat = *mmat;
5706   PetscInt        m = *mm, n = *mn;
5707   InsertMode      addv = *maddv;
5708   Mat_MPIAIJ      *aij = (Mat_MPIAIJ*)mat->data;
5709   PetscScalar     value;
5710   PetscErrorCode  ierr;
5711 
5712   MatCheckPreallocated(mat,1);
5713   if (mat->insertmode == NOT_SET_VALUES) {
5714     mat->insertmode = addv;
5715   }
5716 #if defined(PETSC_USE_DEBUG)
5717   else if (mat->insertmode != addv) {
5718     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
5719   }
5720 #endif
5721   {
5722   PetscInt        i,j,rstart = mat->rmap->rstart,rend = mat->rmap->rend;
5723   PetscInt        cstart = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
5724   PetscBool       roworiented = aij->roworiented;
5725 
5726   /* Some Variables required in the macro */
5727   Mat             A = aij->A;
5728   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
5729   PetscInt        *aimax = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
5730   MatScalar       *aa = a->a;
5731   PetscBool       ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES))?PETSC_TRUE:PETSC_FALSE);
5732   Mat             B = aij->B;
5733   Mat_SeqAIJ      *b = (Mat_SeqAIJ*)B->data;
5734   PetscInt        *bimax = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5735   MatScalar       *ba = b->a;
5736 
5737   PetscInt        *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5738   PetscInt        nonew = a->nonew;
5739   MatScalar       *ap1,*ap2;
5740 
5741   PetscFunctionBegin;
5742   for (i=0; i<m; i++) {
5743     if (im[i] < 0) continue;
5744 #if defined(PETSC_USE_DEBUG)
5745     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);
5746 #endif
5747     if (im[i] >= rstart && im[i] < rend) {
5748       row      = im[i] - rstart;
5749       lastcol1 = -1;
5750       rp1      = aj + ai[row];
5751       ap1      = aa + ai[row];
5752       rmax1    = aimax[row];
5753       nrow1    = ailen[row];
5754       low1     = 0;
5755       high1    = nrow1;
5756       lastcol2 = -1;
5757       rp2      = bj + bi[row];
5758       ap2      = ba + bi[row];
5759       rmax2    = bimax[row];
5760       nrow2    = bilen[row];
5761       low2     = 0;
5762       high2    = nrow2;
5763 
5764       for (j=0; j<n; j++) {
5765         if (roworiented) value = v[i*n+j]; else value = v[i+j*m];
5766         if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES)) continue;
5767         if (in[j] >= cstart && in[j] < cend){
5768           col = in[j] - cstart;
5769           MatSetValues_SeqAIJ_A_Private(row,col,value,addv);
5770         } else if (in[j] < 0) continue;
5771 #if defined(PETSC_USE_DEBUG)
5772         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);
5773 #endif
5774         else {
5775           if (mat->was_assembled) {
5776             if (!aij->colmap) {
5777               ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5778             }
5779 #if defined (PETSC_USE_CTABLE)
5780             ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5781 	    col--;
5782 #else
5783             col = aij->colmap[in[j]] - 1;
5784 #endif
5785             if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5786               ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5787               col =  in[j];
5788               /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5789               B = aij->B;
5790               b = (Mat_SeqAIJ*)B->data;
5791               bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5792               rp2      = bj + bi[row];
5793               ap2      = ba + bi[row];
5794               rmax2    = bimax[row];
5795               nrow2    = bilen[row];
5796               low2     = 0;
5797               high2    = nrow2;
5798               bm       = aij->B->rmap->n;
5799               ba = b->a;
5800             }
5801           } else col = in[j];
5802           MatSetValues_SeqAIJ_B_Private(row,col,value,addv);
5803         }
5804       }
5805     } else {
5806       if (!aij->donotstash) {
5807         if (roworiented) {
5808           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5809         } else {
5810           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5811         }
5812       }
5813     }
5814   }}
5815   PetscFunctionReturnVoid();
5816 }
5817 EXTERN_C_END
5818 
5819