xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision e03ab78ff9ef084a9c929f4b48dbd51953cbd2bc)
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 = MatSetType(b->A,MATSEQAIJ);CHKERRQ(ierr);
3213     ierr = PetscLogObjectParent(B,b->A);CHKERRQ(ierr);
3214     ierr = MatCreate(PETSC_COMM_SELF,&b->B);CHKERRQ(ierr);
3215     ierr = MatSetSizes(b->B,B->rmap->n,B->cmap->N,B->rmap->n,B->cmap->N);CHKERRQ(ierr);
3216     ierr = MatSetType(b->B,MATSEQAIJ);CHKERRQ(ierr);
3217     ierr = PetscLogObjectParent(B,b->B);CHKERRQ(ierr);
3218   }
3219 
3220   ierr = MatSeqAIJSetPreallocation(b->A,d_nz,d_nnz);CHKERRQ(ierr);
3221   ierr = MatSeqAIJSetPreallocation(b->B,o_nz,o_nnz);CHKERRQ(ierr);
3222   /* Do not error if the user did not give real preallocation information. Ugly because this would overwrite a previous user call to MatSetOption(). */
3223   if (!d_realalloc) {ierr = MatSetOption(b->A,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);}
3224   if (!o_realalloc) {ierr = MatSetOption(b->B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);}
3225   B->preallocated = PETSC_TRUE;
3226   PetscFunctionReturn(0);
3227 }
3228 EXTERN_C_END
3229 
3230 #undef __FUNCT__
3231 #define __FUNCT__ "MatDuplicate_MPIAIJ"
3232 PetscErrorCode MatDuplicate_MPIAIJ(Mat matin,MatDuplicateOption cpvalues,Mat *newmat)
3233 {
3234   Mat            mat;
3235   Mat_MPIAIJ     *a,*oldmat = (Mat_MPIAIJ*)matin->data;
3236   PetscErrorCode ierr;
3237 
3238   PetscFunctionBegin;
3239   *newmat       = 0;
3240   ierr = MatCreate(((PetscObject)matin)->comm,&mat);CHKERRQ(ierr);
3241   ierr = MatSetSizes(mat,matin->rmap->n,matin->cmap->n,matin->rmap->N,matin->cmap->N);CHKERRQ(ierr);
3242   ierr = MatSetBlockSizes(mat,matin->rmap->bs,matin->cmap->bs);CHKERRQ(ierr);
3243   ierr = MatSetType(mat,((PetscObject)matin)->type_name);CHKERRQ(ierr);
3244   ierr = PetscMemcpy(mat->ops,matin->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
3245   a    = (Mat_MPIAIJ*)mat->data;
3246 
3247   mat->factortype    = matin->factortype;
3248   mat->rmap->bs      = matin->rmap->bs;
3249   mat->cmap->bs      = matin->cmap->bs;
3250   mat->assembled    = PETSC_TRUE;
3251   mat->insertmode   = NOT_SET_VALUES;
3252   mat->preallocated = PETSC_TRUE;
3253 
3254   a->size           = oldmat->size;
3255   a->rank           = oldmat->rank;
3256   a->donotstash     = oldmat->donotstash;
3257   a->roworiented    = oldmat->roworiented;
3258   a->rowindices     = 0;
3259   a->rowvalues      = 0;
3260   a->getrowactive   = PETSC_FALSE;
3261 
3262   ierr = PetscLayoutReference(matin->rmap,&mat->rmap);CHKERRQ(ierr);
3263   ierr = PetscLayoutReference(matin->cmap,&mat->cmap);CHKERRQ(ierr);
3264 
3265   if (oldmat->colmap) {
3266 #if defined (PETSC_USE_CTABLE)
3267     ierr = PetscTableCreateCopy(oldmat->colmap,&a->colmap);CHKERRQ(ierr);
3268 #else
3269     ierr = PetscMalloc((mat->cmap->N)*sizeof(PetscInt),&a->colmap);CHKERRQ(ierr);
3270     ierr = PetscLogObjectMemory(mat,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
3271     ierr = PetscMemcpy(a->colmap,oldmat->colmap,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
3272 #endif
3273   } else a->colmap = 0;
3274   if (oldmat->garray) {
3275     PetscInt len;
3276     len  = oldmat->B->cmap->n;
3277     ierr = PetscMalloc((len+1)*sizeof(PetscInt),&a->garray);CHKERRQ(ierr);
3278     ierr = PetscLogObjectMemory(mat,len*sizeof(PetscInt));CHKERRQ(ierr);
3279     if (len) { ierr = PetscMemcpy(a->garray,oldmat->garray,len*sizeof(PetscInt));CHKERRQ(ierr); }
3280   } else a->garray = 0;
3281 
3282   ierr = VecDuplicate(oldmat->lvec,&a->lvec);CHKERRQ(ierr);
3283   ierr = PetscLogObjectParent(mat,a->lvec);CHKERRQ(ierr);
3284   ierr = VecScatterCopy(oldmat->Mvctx,&a->Mvctx);CHKERRQ(ierr);
3285   ierr = PetscLogObjectParent(mat,a->Mvctx);CHKERRQ(ierr);
3286   ierr = MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
3287   ierr = PetscLogObjectParent(mat,a->A);CHKERRQ(ierr);
3288   ierr = MatDuplicate(oldmat->B,cpvalues,&a->B);CHKERRQ(ierr);
3289   ierr = PetscLogObjectParent(mat,a->B);CHKERRQ(ierr);
3290   ierr = PetscFListDuplicate(((PetscObject)matin)->qlist,&((PetscObject)mat)->qlist);CHKERRQ(ierr);
3291   *newmat = mat;
3292   PetscFunctionReturn(0);
3293 }
3294 
3295 
3296 
3297 #undef __FUNCT__
3298 #define __FUNCT__ "MatLoad_MPIAIJ"
3299 PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
3300 {
3301   PetscScalar    *vals,*svals;
3302   MPI_Comm       comm = ((PetscObject)viewer)->comm;
3303   PetscErrorCode ierr;
3304   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
3305   PetscInt       i,nz,j,rstart,rend,mmax,maxnz = 0,grows,gcols;
3306   PetscInt       header[4],*rowlengths = 0,M,N,m,*cols;
3307   PetscInt       *ourlens = PETSC_NULL,*procsnz = PETSC_NULL,*offlens = PETSC_NULL,jj,*mycols,*smycols;
3308   PetscInt       cend,cstart,n,*rowners,sizesset=1;
3309   int            fd;
3310 
3311   PetscFunctionBegin;
3312   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3313   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3314   if (!rank) {
3315     ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
3316     ierr = PetscBinaryRead(fd,(char *)header,4,PETSC_INT);CHKERRQ(ierr);
3317     if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
3318   }
3319 
3320   if (newMat->rmap->n < 0 && newMat->rmap->N < 0 && newMat->cmap->n < 0 && newMat->cmap->N < 0) sizesset = 0;
3321 
3322   ierr = MPI_Bcast(header+1,3,MPIU_INT,0,comm);CHKERRQ(ierr);
3323   M = header[1]; N = header[2];
3324   /* If global rows/cols are set to PETSC_DECIDE, set it to the sizes given in the file */
3325   if (sizesset && newMat->rmap->N < 0) newMat->rmap->N = M;
3326   if (sizesset && newMat->cmap->N < 0) newMat->cmap->N = N;
3327 
3328   /* If global sizes are set, check if they are consistent with that given in the file */
3329   if (sizesset) {
3330     ierr = MatGetSize(newMat,&grows,&gcols);CHKERRQ(ierr);
3331   }
3332   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);
3333   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);
3334 
3335   /* determine ownership of all rows */
3336   if (newMat->rmap->n < 0 ) m    = M/size + ((M % size) > rank); /* PETSC_DECIDE */
3337   else m = newMat->rmap->n; /* Set by user */
3338 
3339   ierr = PetscMalloc((size+1)*sizeof(PetscInt),&rowners);CHKERRQ(ierr);
3340   ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
3341 
3342   /* First process needs enough room for process with most rows */
3343   if (!rank) {
3344     mmax       = rowners[1];
3345     for (i=2; i<size; i++) {
3346       mmax = PetscMax(mmax,rowners[i]);
3347     }
3348   } else mmax = m;
3349 
3350   rowners[0] = 0;
3351   for (i=2; i<=size; i++) {
3352     rowners[i] += rowners[i-1];
3353   }
3354   rstart = rowners[rank];
3355   rend   = rowners[rank+1];
3356 
3357   /* distribute row lengths to all processors */
3358   ierr    = PetscMalloc2(mmax,PetscInt,&ourlens,mmax,PetscInt,&offlens);CHKERRQ(ierr);
3359   if (!rank) {
3360     ierr = PetscBinaryRead(fd,ourlens,m,PETSC_INT);CHKERRQ(ierr);
3361     ierr = PetscMalloc(m*sizeof(PetscInt),&rowlengths);CHKERRQ(ierr);
3362     ierr = PetscMalloc(size*sizeof(PetscInt),&procsnz);CHKERRQ(ierr);
3363     ierr = PetscMemzero(procsnz,size*sizeof(PetscInt));CHKERRQ(ierr);
3364     for (j=0; j<m; j++) {
3365       procsnz[0] += ourlens[j];
3366     }
3367     for (i=1; i<size; i++) {
3368       ierr = PetscBinaryRead(fd,rowlengths,rowners[i+1]-rowners[i],PETSC_INT);CHKERRQ(ierr);
3369       /* calculate the number of nonzeros on each processor */
3370       for (j=0; j<rowners[i+1]-rowners[i]; j++) {
3371         procsnz[i] += rowlengths[j];
3372       }
3373       ierr = MPIULong_Send(rowlengths,rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
3374     }
3375     ierr = PetscFree(rowlengths);CHKERRQ(ierr);
3376   } else {
3377     ierr = MPIULong_Recv(ourlens,m,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
3378   }
3379 
3380   if (!rank) {
3381     /* determine max buffer needed and allocate it */
3382     maxnz = 0;
3383     for (i=0; i<size; i++) {
3384       maxnz = PetscMax(maxnz,procsnz[i]);
3385     }
3386     ierr = PetscMalloc(maxnz*sizeof(PetscInt),&cols);CHKERRQ(ierr);
3387 
3388     /* read in my part of the matrix column indices  */
3389     nz   = procsnz[0];
3390     ierr = PetscMalloc(nz*sizeof(PetscInt),&mycols);CHKERRQ(ierr);
3391     ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);
3392 
3393     /* read in every one elses and ship off */
3394     for (i=1; i<size; i++) {
3395       nz     = procsnz[i];
3396       ierr   = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
3397       ierr   = MPIULong_Send(cols,nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
3398     }
3399     ierr = PetscFree(cols);CHKERRQ(ierr);
3400   } else {
3401     /* determine buffer space needed for message */
3402     nz = 0;
3403     for (i=0; i<m; i++) {
3404       nz += ourlens[i];
3405     }
3406     ierr = PetscMalloc(nz*sizeof(PetscInt),&mycols);CHKERRQ(ierr);
3407 
3408     /* receive message of column indices*/
3409     ierr = MPIULong_Recv(mycols,nz,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
3410   }
3411 
3412   /* determine column ownership if matrix is not square */
3413   if (N != M) {
3414     if (newMat->cmap->n < 0) n      = N/size + ((N % size) > rank);
3415     else n = newMat->cmap->n;
3416     ierr   = MPI_Scan(&n,&cend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3417     cstart = cend - n;
3418   } else {
3419     cstart = rstart;
3420     cend   = rend;
3421     n      = cend - cstart;
3422   }
3423 
3424   /* loop over local rows, determining number of off diagonal entries */
3425   ierr = PetscMemzero(offlens,m*sizeof(PetscInt));CHKERRQ(ierr);
3426   jj = 0;
3427   for (i=0; i<m; i++) {
3428     for (j=0; j<ourlens[i]; j++) {
3429       if (mycols[jj] < cstart || mycols[jj] >= cend) offlens[i]++;
3430       jj++;
3431     }
3432   }
3433 
3434   for (i=0; i<m; i++) {
3435     ourlens[i] -= offlens[i];
3436   }
3437   if (!sizesset) {
3438     ierr = MatSetSizes(newMat,m,n,M,N);CHKERRQ(ierr);
3439   }
3440   ierr = MatMPIAIJSetPreallocation(newMat,0,ourlens,0,offlens);CHKERRQ(ierr);
3441 
3442   for (i=0; i<m; i++) {
3443     ourlens[i] += offlens[i];
3444   }
3445 
3446   if (!rank) {
3447     ierr = PetscMalloc((maxnz+1)*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
3448 
3449     /* read in my part of the matrix numerical values  */
3450     nz   = procsnz[0];
3451     ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
3452 
3453     /* insert into matrix */
3454     jj      = rstart;
3455     smycols = mycols;
3456     svals   = vals;
3457     for (i=0; i<m; i++) {
3458       ierr = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
3459       smycols += ourlens[i];
3460       svals   += ourlens[i];
3461       jj++;
3462     }
3463 
3464     /* read in other processors and ship out */
3465     for (i=1; i<size; i++) {
3466       nz     = procsnz[i];
3467       ierr   = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
3468       ierr   = MPIULong_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
3469     }
3470     ierr = PetscFree(procsnz);CHKERRQ(ierr);
3471   } else {
3472     /* receive numeric values */
3473     ierr = PetscMalloc((nz+1)*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
3474 
3475     /* receive message of values*/
3476     ierr   = MPIULong_Recv(vals,nz,MPIU_SCALAR,0,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
3477 
3478     /* insert into matrix */
3479     jj      = rstart;
3480     smycols = mycols;
3481     svals   = vals;
3482     for (i=0; i<m; i++) {
3483       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
3484       smycols += ourlens[i];
3485       svals   += ourlens[i];
3486       jj++;
3487     }
3488   }
3489   ierr = PetscFree2(ourlens,offlens);CHKERRQ(ierr);
3490   ierr = PetscFree(vals);CHKERRQ(ierr);
3491   ierr = PetscFree(mycols);CHKERRQ(ierr);
3492   ierr = PetscFree(rowners);CHKERRQ(ierr);
3493 
3494   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3495   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3496   PetscFunctionReturn(0);
3497 }
3498 
3499 #undef __FUNCT__
3500 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ"
3501 PetscErrorCode MatGetSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
3502 {
3503   PetscErrorCode ierr;
3504   IS             iscol_local;
3505   PetscInt       csize;
3506 
3507   PetscFunctionBegin;
3508   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
3509   if (call == MAT_REUSE_MATRIX) {
3510     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
3511     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3512   } else {
3513     PetscInt cbs;
3514     ierr = ISGetBlockSize(iscol,&cbs); CHKERRQ(ierr);
3515     ierr = ISAllGather(iscol,&iscol_local);CHKERRQ(ierr);
3516     ierr = ISSetBlockSize(iscol_local,cbs); CHKERRQ(ierr);
3517   }
3518   ierr = MatGetSubMatrix_MPIAIJ_Private(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
3519   if (call == MAT_INITIAL_MATRIX) {
3520     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
3521     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
3522   }
3523   PetscFunctionReturn(0);
3524 }
3525 
3526 #undef __FUNCT__
3527 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ_Private"
3528 /*
3529     Not great since it makes two copies of the submatrix, first an SeqAIJ
3530   in local and then by concatenating the local matrices the end result.
3531   Writing it directly would be much like MatGetSubMatrices_MPIAIJ()
3532 
3533   Note: This requires a sequential iscol with all indices.
3534 */
3535 PetscErrorCode MatGetSubMatrix_MPIAIJ_Private(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3536 {
3537   PetscErrorCode ierr;
3538   PetscMPIInt    rank,size;
3539   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3540   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
3541   Mat            *local,M,Mreuse;
3542   MatScalar      *vwork,*aa;
3543   MPI_Comm       comm = ((PetscObject)mat)->comm;
3544   Mat_SeqAIJ     *aij;
3545 
3546 
3547   PetscFunctionBegin;
3548   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3549   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3550 
3551   if (call ==  MAT_REUSE_MATRIX) {
3552     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject *)&Mreuse);CHKERRQ(ierr);
3553     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3554     local = &Mreuse;
3555     ierr  = MatGetSubMatrices(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,&local);CHKERRQ(ierr);
3556   } else {
3557     ierr   = MatGetSubMatrices(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&local);CHKERRQ(ierr);
3558     Mreuse = *local;
3559     ierr   = PetscFree(local);CHKERRQ(ierr);
3560   }
3561 
3562   /*
3563       m - number of local rows
3564       n - number of columns (same on all processors)
3565       rstart - first row in new global matrix generated
3566   */
3567   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3568   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3569   if (call == MAT_INITIAL_MATRIX) {
3570     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3571     ii  = aij->i;
3572     jj  = aij->j;
3573 
3574     /*
3575         Determine the number of non-zeros in the diagonal and off-diagonal
3576         portions of the matrix in order to do correct preallocation
3577     */
3578 
3579     /* first get start and end of "diagonal" columns */
3580     if (csize == PETSC_DECIDE) {
3581       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3582       if (mglobal == n) { /* square matrix */
3583 	nlocal = m;
3584       } else {
3585         nlocal = n/size + ((n % size) > rank);
3586       }
3587     } else {
3588       nlocal = csize;
3589     }
3590     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3591     rstart = rend - nlocal;
3592     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);
3593 
3594     /* next, compute all the lengths */
3595     ierr  = PetscMalloc((2*m+1)*sizeof(PetscInt),&dlens);CHKERRQ(ierr);
3596     olens = dlens + m;
3597     for (i=0; i<m; i++) {
3598       jend = ii[i+1] - ii[i];
3599       olen = 0;
3600       dlen = 0;
3601       for (j=0; j<jend; j++) {
3602         if (*jj < rstart || *jj >= rend) olen++;
3603         else dlen++;
3604         jj++;
3605       }
3606       olens[i] = olen;
3607       dlens[i] = dlen;
3608     }
3609     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3610     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3611     ierr = MatSetBlockSizes(M,bs,cbs); CHKERRQ(ierr);
3612     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3613     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3614     ierr = PetscFree(dlens);CHKERRQ(ierr);
3615   } else {
3616     PetscInt ml,nl;
3617 
3618     M = *newmat;
3619     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3620     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3621     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3622     /*
3623          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3624        rather than the slower MatSetValues().
3625     */
3626     M->was_assembled = PETSC_TRUE;
3627     M->assembled     = PETSC_FALSE;
3628   }
3629   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3630   aij = (Mat_SeqAIJ*)(Mreuse)->data;
3631   ii  = aij->i;
3632   jj  = aij->j;
3633   aa  = aij->a;
3634   for (i=0; i<m; i++) {
3635     row   = rstart + i;
3636     nz    = ii[i+1] - ii[i];
3637     cwork = jj;     jj += nz;
3638     vwork = aa;     aa += nz;
3639     ierr = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3640   }
3641 
3642   ierr = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3643   ierr = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3644   *newmat = M;
3645 
3646   /* save submatrix used in processor for next request */
3647   if (call ==  MAT_INITIAL_MATRIX) {
3648     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3649     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3650   }
3651 
3652   PetscFunctionReturn(0);
3653 }
3654 
3655 EXTERN_C_BEGIN
3656 #undef __FUNCT__
3657 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR_MPIAIJ"
3658 PetscErrorCode  MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3659 {
3660   PetscInt       m,cstart, cend,j,nnz,i,d;
3661   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3662   const PetscInt *JJ;
3663   PetscScalar    *values;
3664   PetscErrorCode ierr;
3665 
3666   PetscFunctionBegin;
3667   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3668 
3669   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3670   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3671   m      = B->rmap->n;
3672   cstart = B->cmap->rstart;
3673   cend   = B->cmap->rend;
3674   rstart = B->rmap->rstart;
3675 
3676   ierr  = PetscMalloc2(m,PetscInt,&d_nnz,m,PetscInt,&o_nnz);CHKERRQ(ierr);
3677 
3678 #if defined(PETSC_USE_DEBUGGING)
3679   for (i=0; i<m; i++) {
3680     nnz     = Ii[i+1]- Ii[i];
3681     JJ      = J + Ii[i];
3682     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3683     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3684     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);
3685   }
3686 #endif
3687 
3688   for (i=0; i<m; i++) {
3689     nnz     = Ii[i+1]- Ii[i];
3690     JJ      = J + Ii[i];
3691     nnz_max = PetscMax(nnz_max,nnz);
3692     d       = 0;
3693     for (j=0; j<nnz; j++) {
3694       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3695     }
3696     d_nnz[i] = d;
3697     o_nnz[i] = nnz - d;
3698   }
3699   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3700   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3701 
3702   if (v) values = (PetscScalar*)v;
3703   else {
3704     ierr = PetscMalloc((nnz_max+1)*sizeof(PetscScalar),&values);CHKERRQ(ierr);
3705     ierr = PetscMemzero(values,nnz_max*sizeof(PetscScalar));CHKERRQ(ierr);
3706   }
3707 
3708   for (i=0; i<m; i++) {
3709     ii   = i + rstart;
3710     nnz  = Ii[i+1]- Ii[i];
3711     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3712   }
3713   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3714   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3715 
3716   if (!v) {
3717     ierr = PetscFree(values);CHKERRQ(ierr);
3718   }
3719   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3720   PetscFunctionReturn(0);
3721 }
3722 EXTERN_C_END
3723 
3724 #undef __FUNCT__
3725 #define __FUNCT__ "MatMPIAIJSetPreallocationCSR"
3726 /*@
3727    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3728    (the default parallel PETSc format).
3729 
3730    Collective on MPI_Comm
3731 
3732    Input Parameters:
3733 +  B - the matrix
3734 .  i - the indices into j for the start of each local row (starts with zero)
3735 .  j - the column indices for each local row (starts with zero)
3736 -  v - optional values in the matrix
3737 
3738    Level: developer
3739 
3740    Notes:
3741        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3742      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3743      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3744 
3745        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3746 
3747        The format which is used for the sparse matrix input, is equivalent to a
3748     row-major ordering.. i.e for the following matrix, the input data expected is
3749     as shown:
3750 
3751         1 0 0
3752         2 0 3     P0
3753        -------
3754         4 5 6     P1
3755 
3756      Process0 [P0]: rows_owned=[0,1]
3757         i =  {0,1,3}  [size = nrow+1  = 2+1]
3758         j =  {0,0,2}  [size = nz = 6]
3759         v =  {1,2,3}  [size = nz = 6]
3760 
3761      Process1 [P1]: rows_owned=[2]
3762         i =  {0,3}    [size = nrow+1  = 1+1]
3763         j =  {0,1,2}  [size = nz = 6]
3764         v =  {4,5,6}  [size = nz = 6]
3765 
3766 .keywords: matrix, aij, compressed row, sparse, parallel
3767 
3768 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MPIAIJ,
3769           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3770 @*/
3771 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3772 {
3773   PetscErrorCode ierr;
3774 
3775   PetscFunctionBegin;
3776   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3777   PetscFunctionReturn(0);
3778 }
3779 
3780 #undef __FUNCT__
3781 #define __FUNCT__ "MatMPIAIJSetPreallocation"
3782 /*@C
3783    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3784    (the default parallel PETSc format).  For good matrix assembly performance
3785    the user should preallocate the matrix storage by setting the parameters
3786    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3787    performance can be increased by more than a factor of 50.
3788 
3789    Collective on MPI_Comm
3790 
3791    Input Parameters:
3792 +  A - the matrix
3793 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3794            (same value is used for all local rows)
3795 .  d_nnz - array containing the number of nonzeros in the various rows of the
3796            DIAGONAL portion of the local submatrix (possibly different for each row)
3797            or PETSC_NULL, if d_nz is used to specify the nonzero structure.
3798            The size of this array is equal to the number of local rows, i.e 'm'.
3799            For matrices that will be factored, you must leave room for (and set)
3800            the diagonal entry even if it is zero.
3801 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3802            submatrix (same value is used for all local rows).
3803 -  o_nnz - array containing the number of nonzeros in the various rows of the
3804            OFF-DIAGONAL portion of the local submatrix (possibly different for
3805            each row) or PETSC_NULL, if o_nz is used to specify the nonzero
3806            structure. The size of this array is equal to the number
3807            of local rows, i.e 'm'.
3808 
3809    If the *_nnz parameter is given then the *_nz parameter is ignored
3810 
3811    The AIJ format (also called the Yale sparse matrix format or
3812    compressed row storage (CSR)), is fully compatible with standard Fortran 77
3813    storage.  The stored row and column indices begin with zero.
3814    See the <A href="../../docs/manual.pdf#nameddest=ch_mat">Mat chapter of the users manual</A> for details.
3815 
3816    The parallel matrix is partitioned such that the first m0 rows belong to
3817    process 0, the next m1 rows belong to process 1, the next m2 rows belong
3818    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
3819 
3820    The DIAGONAL portion of the local submatrix of a processor can be defined
3821    as the submatrix which is obtained by extraction the part corresponding to
3822    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
3823    first row that belongs to the processor, r2 is the last row belonging to
3824    the this processor, and c1-c2 is range of indices of the local part of a
3825    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
3826    common case of a square matrix, the row and column ranges are the same and
3827    the DIAGONAL part is also square. The remaining portion of the local
3828    submatrix (mxN) constitute the OFF-DIAGONAL portion.
3829 
3830    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3831 
3832    You can call MatGetInfo() to get information on how effective the preallocation was;
3833    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3834    You can also run with the option -info and look for messages with the string
3835    malloc in them to see if additional memory allocation was needed.
3836 
3837    Example usage:
3838 
3839    Consider the following 8x8 matrix with 34 non-zero values, that is
3840    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3841    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3842    as follows:
3843 
3844 .vb
3845             1  2  0  |  0  3  0  |  0  4
3846     Proc0   0  5  6  |  7  0  0  |  8  0
3847             9  0 10  | 11  0  0  | 12  0
3848     -------------------------------------
3849            13  0 14  | 15 16 17  |  0  0
3850     Proc1   0 18  0  | 19 20 21  |  0  0
3851             0  0  0  | 22 23  0  | 24  0
3852     -------------------------------------
3853     Proc2  25 26 27  |  0  0 28  | 29  0
3854            30  0  0  | 31 32 33  |  0 34
3855 .ve
3856 
3857    This can be represented as a collection of submatrices as:
3858 
3859 .vb
3860       A B C
3861       D E F
3862       G H I
3863 .ve
3864 
3865    Where the submatrices A,B,C are owned by proc0, D,E,F are
3866    owned by proc1, G,H,I are owned by proc2.
3867 
3868    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3869    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3870    The 'M','N' parameters are 8,8, and have the same values on all procs.
3871 
3872    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3873    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3874    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3875    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3876    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3877    matrix, ans [DF] as another SeqAIJ matrix.
3878 
3879    When d_nz, o_nz parameters are specified, d_nz storage elements are
3880    allocated for every row of the local diagonal submatrix, and o_nz
3881    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3882    One way to choose d_nz and o_nz is to use the max nonzerors per local
3883    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3884    In this case, the values of d_nz,o_nz are:
3885 .vb
3886      proc0 : dnz = 2, o_nz = 2
3887      proc1 : dnz = 3, o_nz = 2
3888      proc2 : dnz = 1, o_nz = 4
3889 .ve
3890    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3891    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3892    for proc3. i.e we are using 12+15+10=37 storage locations to store
3893    34 values.
3894 
3895    When d_nnz, o_nnz parameters are specified, the storage is specified
3896    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3897    In the above case the values for d_nnz,o_nnz are:
3898 .vb
3899      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3900      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3901      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3902 .ve
3903    Here the space allocated is sum of all the above values i.e 34, and
3904    hence pre-allocation is perfect.
3905 
3906    Level: intermediate
3907 
3908 .keywords: matrix, aij, compressed row, sparse, parallel
3909 
3910 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
3911           MPIAIJ, MatGetInfo()
3912 @*/
3913 PetscErrorCode  MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3914 {
3915   PetscErrorCode ierr;
3916 
3917   PetscFunctionBegin;
3918   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3919   PetscValidType(B,1);
3920   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
3921   PetscFunctionReturn(0);
3922 }
3923 
3924 #undef __FUNCT__
3925 #define __FUNCT__ "MatCreateMPIAIJWithArrays"
3926 /*@
3927      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
3928          CSR format the local rows.
3929 
3930    Collective on MPI_Comm
3931 
3932    Input Parameters:
3933 +  comm - MPI communicator
3934 .  m - number of local rows (Cannot be PETSC_DECIDE)
3935 .  n - This value should be the same as the local size used in creating the
3936        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3937        calculated if N is given) For square matrices n is almost always m.
3938 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3939 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3940 .   i - row indices
3941 .   j - column indices
3942 -   a - matrix values
3943 
3944    Output Parameter:
3945 .   mat - the matrix
3946 
3947    Level: intermediate
3948 
3949    Notes:
3950        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3951      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3952      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3953 
3954        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3955 
3956        The format which is used for the sparse matrix input, is equivalent to a
3957     row-major ordering.. i.e for the following matrix, the input data expected is
3958     as shown:
3959 
3960         1 0 0
3961         2 0 3     P0
3962        -------
3963         4 5 6     P1
3964 
3965      Process0 [P0]: rows_owned=[0,1]
3966         i =  {0,1,3}  [size = nrow+1  = 2+1]
3967         j =  {0,0,2}  [size = nz = 6]
3968         v =  {1,2,3}  [size = nz = 6]
3969 
3970      Process1 [P1]: rows_owned=[2]
3971         i =  {0,3}    [size = nrow+1  = 1+1]
3972         j =  {0,1,2}  [size = nz = 6]
3973         v =  {4,5,6}  [size = nz = 6]
3974 
3975 .keywords: matrix, aij, compressed row, sparse, parallel
3976 
3977 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3978           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
3979 @*/
3980 PetscErrorCode  MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
3981 {
3982   PetscErrorCode ierr;
3983 
3984   PetscFunctionBegin;
3985   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
3986   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
3987   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
3988   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
3989   /* ierr = MatSetBlockSizes(M,bs,cbs); CHKERRQ(ierr); */
3990   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
3991   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
3992   PetscFunctionReturn(0);
3993 }
3994 
3995 #undef __FUNCT__
3996 #define __FUNCT__ "MatCreateAIJ"
3997 /*@C
3998    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
3999    (the default parallel PETSc format).  For good matrix assembly performance
4000    the user should preallocate the matrix storage by setting the parameters
4001    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
4002    performance can be increased by more than a factor of 50.
4003 
4004    Collective on MPI_Comm
4005 
4006    Input Parameters:
4007 +  comm - MPI communicator
4008 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
4009            This value should be the same as the local size used in creating the
4010            y vector for the matrix-vector product y = Ax.
4011 .  n - This value should be the same as the local size used in creating the
4012        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
4013        calculated if N is given) For square matrices n is almost always m.
4014 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
4015 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
4016 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
4017            (same value is used for all local rows)
4018 .  d_nnz - array containing the number of nonzeros in the various rows of the
4019            DIAGONAL portion of the local submatrix (possibly different for each row)
4020            or PETSC_NULL, if d_nz is used to specify the nonzero structure.
4021            The size of this array is equal to the number of local rows, i.e 'm'.
4022 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
4023            submatrix (same value is used for all local rows).
4024 -  o_nnz - array containing the number of nonzeros in the various rows of the
4025            OFF-DIAGONAL portion of the local submatrix (possibly different for
4026            each row) or PETSC_NULL, if o_nz is used to specify the nonzero
4027            structure. The size of this array is equal to the number
4028            of local rows, i.e 'm'.
4029 
4030    Output Parameter:
4031 .  A - the matrix
4032 
4033    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
4034    MatXXXXSetPreallocation() paradgm instead of this routine directly.
4035    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
4036 
4037    Notes:
4038    If the *_nnz parameter is given then the *_nz parameter is ignored
4039 
4040    m,n,M,N parameters specify the size of the matrix, and its partitioning across
4041    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
4042    storage requirements for this matrix.
4043 
4044    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
4045    processor than it must be used on all processors that share the object for
4046    that argument.
4047 
4048    The user MUST specify either the local or global matrix dimensions
4049    (possibly both).
4050 
4051    The parallel matrix is partitioned across processors such that the
4052    first m0 rows belong to process 0, the next m1 rows belong to
4053    process 1, the next m2 rows belong to process 2 etc.. where
4054    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
4055    values corresponding to [m x N] submatrix.
4056 
4057    The columns are logically partitioned with the n0 columns belonging
4058    to 0th partition, the next n1 columns belonging to the next
4059    partition etc.. where n0,n1,n2... are the the input parameter 'n'.
4060 
4061    The DIAGONAL portion of the local submatrix on any given processor
4062    is the submatrix corresponding to the rows and columns m,n
4063    corresponding to the given processor. i.e diagonal matrix on
4064    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
4065    etc. The remaining portion of the local submatrix [m x (N-n)]
4066    constitute the OFF-DIAGONAL portion. The example below better
4067    illustrates this concept.
4068 
4069    For a square global matrix we define each processor's diagonal portion
4070    to be its local rows and the corresponding columns (a square submatrix);
4071    each processor's off-diagonal portion encompasses the remainder of the
4072    local matrix (a rectangular submatrix).
4073 
4074    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
4075 
4076    When calling this routine with a single process communicator, a matrix of
4077    type SEQAIJ is returned.  If a matrix of type MPIAIJ is desired for this
4078    type of communicator, use the construction mechanism:
4079      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
4080 
4081    By default, this format uses inodes (identical nodes) when possible.
4082    We search for consecutive rows with the same nonzero structure, thereby
4083    reusing matrix information to achieve increased efficiency.
4084 
4085    Options Database Keys:
4086 +  -mat_no_inode  - Do not use inodes
4087 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
4088 -  -mat_aij_oneindex - Internally use indexing starting at 1
4089         rather than 0.  Note that when calling MatSetValues(),
4090         the user still MUST index entries starting at 0!
4091 
4092 
4093    Example usage:
4094 
4095    Consider the following 8x8 matrix with 34 non-zero values, that is
4096    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
4097    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
4098    as follows:
4099 
4100 .vb
4101             1  2  0  |  0  3  0  |  0  4
4102     Proc0   0  5  6  |  7  0  0  |  8  0
4103             9  0 10  | 11  0  0  | 12  0
4104     -------------------------------------
4105            13  0 14  | 15 16 17  |  0  0
4106     Proc1   0 18  0  | 19 20 21  |  0  0
4107             0  0  0  | 22 23  0  | 24  0
4108     -------------------------------------
4109     Proc2  25 26 27  |  0  0 28  | 29  0
4110            30  0  0  | 31 32 33  |  0 34
4111 .ve
4112 
4113    This can be represented as a collection of submatrices as:
4114 
4115 .vb
4116       A B C
4117       D E F
4118       G H I
4119 .ve
4120 
4121    Where the submatrices A,B,C are owned by proc0, D,E,F are
4122    owned by proc1, G,H,I are owned by proc2.
4123 
4124    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4125    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4126    The 'M','N' parameters are 8,8, and have the same values on all procs.
4127 
4128    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
4129    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
4130    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
4131    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
4132    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
4133    matrix, ans [DF] as another SeqAIJ matrix.
4134 
4135    When d_nz, o_nz parameters are specified, d_nz storage elements are
4136    allocated for every row of the local diagonal submatrix, and o_nz
4137    storage locations are allocated for every row of the OFF-DIAGONAL submat.
4138    One way to choose d_nz and o_nz is to use the max nonzerors per local
4139    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
4140    In this case, the values of d_nz,o_nz are:
4141 .vb
4142      proc0 : dnz = 2, o_nz = 2
4143      proc1 : dnz = 3, o_nz = 2
4144      proc2 : dnz = 1, o_nz = 4
4145 .ve
4146    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
4147    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
4148    for proc3. i.e we are using 12+15+10=37 storage locations to store
4149    34 values.
4150 
4151    When d_nnz, o_nnz parameters are specified, the storage is specified
4152    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
4153    In the above case the values for d_nnz,o_nnz are:
4154 .vb
4155      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
4156      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
4157      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
4158 .ve
4159    Here the space allocated is sum of all the above values i.e 34, and
4160    hence pre-allocation is perfect.
4161 
4162    Level: intermediate
4163 
4164 .keywords: matrix, aij, compressed row, sparse, parallel
4165 
4166 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
4167           MPIAIJ, MatCreateMPIAIJWithArrays()
4168 @*/
4169 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)
4170 {
4171   PetscErrorCode ierr;
4172   PetscMPIInt    size;
4173 
4174   PetscFunctionBegin;
4175   ierr = MatCreate(comm,A);CHKERRQ(ierr);
4176   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
4177   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4178   if (size > 1) {
4179     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
4180     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
4181   } else {
4182     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
4183     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
4184   }
4185   PetscFunctionReturn(0);
4186 }
4187 
4188 #undef __FUNCT__
4189 #define __FUNCT__ "MatMPIAIJGetSeqAIJ"
4190 PetscErrorCode  MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,PetscInt *colmap[])
4191 {
4192   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
4193 
4194   PetscFunctionBegin;
4195   *Ad     = a->A;
4196   *Ao     = a->B;
4197   *colmap = a->garray;
4198   PetscFunctionReturn(0);
4199 }
4200 
4201 #undef __FUNCT__
4202 #define __FUNCT__ "MatSetColoring_MPIAIJ"
4203 PetscErrorCode MatSetColoring_MPIAIJ(Mat A,ISColoring coloring)
4204 {
4205   PetscErrorCode ierr;
4206   PetscInt       i;
4207   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
4208 
4209   PetscFunctionBegin;
4210   if (coloring->ctype == IS_COLORING_GLOBAL) {
4211     ISColoringValue *allcolors,*colors;
4212     ISColoring      ocoloring;
4213 
4214     /* set coloring for diagonal portion */
4215     ierr = MatSetColoring_SeqAIJ(a->A,coloring);CHKERRQ(ierr);
4216 
4217     /* set coloring for off-diagonal portion */
4218     ierr = ISAllGatherColors(((PetscObject)A)->comm,coloring->n,coloring->colors,PETSC_NULL,&allcolors);CHKERRQ(ierr);
4219     ierr = PetscMalloc((a->B->cmap->n+1)*sizeof(ISColoringValue),&colors);CHKERRQ(ierr);
4220     for (i=0; i<a->B->cmap->n; i++) {
4221       colors[i] = allcolors[a->garray[i]];
4222     }
4223     ierr = PetscFree(allcolors);CHKERRQ(ierr);
4224     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,&ocoloring);CHKERRQ(ierr);
4225     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
4226     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
4227   } else if (coloring->ctype == IS_COLORING_GHOSTED) {
4228     ISColoringValue *colors;
4229     PetscInt        *larray;
4230     ISColoring      ocoloring;
4231 
4232     /* set coloring for diagonal portion */
4233     ierr = PetscMalloc((a->A->cmap->n+1)*sizeof(PetscInt),&larray);CHKERRQ(ierr);
4234     for (i=0; i<a->A->cmap->n; i++) {
4235       larray[i] = i + A->cmap->rstart;
4236     }
4237     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->A->cmap->n,larray,PETSC_NULL,larray);CHKERRQ(ierr);
4238     ierr = PetscMalloc((a->A->cmap->n+1)*sizeof(ISColoringValue),&colors);CHKERRQ(ierr);
4239     for (i=0; i<a->A->cmap->n; i++) {
4240       colors[i] = coloring->colors[larray[i]];
4241     }
4242     ierr = PetscFree(larray);CHKERRQ(ierr);
4243     ierr = ISColoringCreate(PETSC_COMM_SELF,coloring->n,a->A->cmap->n,colors,&ocoloring);CHKERRQ(ierr);
4244     ierr = MatSetColoring_SeqAIJ(a->A,ocoloring);CHKERRQ(ierr);
4245     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
4246 
4247     /* set coloring for off-diagonal portion */
4248     ierr = PetscMalloc((a->B->cmap->n+1)*sizeof(PetscInt),&larray);CHKERRQ(ierr);
4249     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,a->B->cmap->n,a->garray,PETSC_NULL,larray);CHKERRQ(ierr);
4250     ierr = PetscMalloc((a->B->cmap->n+1)*sizeof(ISColoringValue),&colors);CHKERRQ(ierr);
4251     for (i=0; i<a->B->cmap->n; i++) {
4252       colors[i] = coloring->colors[larray[i]];
4253     }
4254     ierr = PetscFree(larray);CHKERRQ(ierr);
4255     ierr = ISColoringCreate(MPI_COMM_SELF,coloring->n,a->B->cmap->n,colors,&ocoloring);CHKERRQ(ierr);
4256     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
4257     ierr = ISColoringDestroy(&ocoloring);CHKERRQ(ierr);
4258   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support ISColoringType %d",(int)coloring->ctype);
4259 
4260   PetscFunctionReturn(0);
4261 }
4262 
4263 #if defined(PETSC_HAVE_ADIC)
4264 #undef __FUNCT__
4265 #define __FUNCT__ "MatSetValuesAdic_MPIAIJ"
4266 PetscErrorCode MatSetValuesAdic_MPIAIJ(Mat A,void *advalues)
4267 {
4268   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
4269   PetscErrorCode ierr;
4270 
4271   PetscFunctionBegin;
4272   ierr = MatSetValuesAdic_SeqAIJ(a->A,advalues);CHKERRQ(ierr);
4273   ierr = MatSetValuesAdic_SeqAIJ(a->B,advalues);CHKERRQ(ierr);
4274   PetscFunctionReturn(0);
4275 }
4276 #endif
4277 
4278 #undef __FUNCT__
4279 #define __FUNCT__ "MatSetValuesAdifor_MPIAIJ"
4280 PetscErrorCode MatSetValuesAdifor_MPIAIJ(Mat A,PetscInt nl,void *advalues)
4281 {
4282   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
4283   PetscErrorCode ierr;
4284 
4285   PetscFunctionBegin;
4286   ierr = MatSetValuesAdifor_SeqAIJ(a->A,nl,advalues);CHKERRQ(ierr);
4287   ierr = MatSetValuesAdifor_SeqAIJ(a->B,nl,advalues);CHKERRQ(ierr);
4288   PetscFunctionReturn(0);
4289 }
4290 
4291 #undef __FUNCT__
4292 #define __FUNCT__ "MatCreateMPIAIJConcatenateSeqAIJSymbolic"
4293 PetscErrorCode  MatCreateMPIAIJConcatenateSeqAIJSymbolic(MPI_Comm comm,Mat inmat,PetscInt n,Mat *outmat)
4294 {
4295   PetscErrorCode ierr;
4296   PetscInt       m,N,i,rstart,nnz,*dnz,*onz,sum,bs,cbs;
4297   PetscInt       *indx;
4298 
4299   PetscFunctionBegin;
4300   /* This routine will ONLY return MPIAIJ type matrix */
4301   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
4302   ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
4303   if (n == PETSC_DECIDE){
4304     ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
4305   }
4306   /* Check sum(n) = N */
4307   ierr = MPI_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4308   if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
4309 
4310   ierr = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
4311   rstart -= m;
4312 
4313   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4314   for (i=0;i<m;i++) {
4315     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,PETSC_NULL);CHKERRQ(ierr);
4316     ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
4317     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,PETSC_NULL);CHKERRQ(ierr);
4318   }
4319 
4320   ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
4321   ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE); CHKERRQ(ierr);
4322   ierr = MatSetBlockSizes(*outmat,bs,cbs); CHKERRQ(ierr);
4323   ierr = MatSetType(*outmat,MATMPIAIJ);  CHKERRQ(ierr);
4324   ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
4325   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4326   PetscFunctionReturn(0);
4327 }
4328 
4329 #undef __FUNCT__
4330 #define __FUNCT__ "MatCreateMPIAIJConcatenateSeqAIJNumeric"
4331 PetscErrorCode  MatCreateMPIAIJConcatenateSeqAIJNumeric(MPI_Comm comm,Mat inmat,PetscInt n,Mat outmat)
4332 {
4333   PetscErrorCode ierr;
4334   PetscInt       m,N,i,rstart,nnz,Ii;
4335   PetscInt       *indx;
4336   PetscScalar    *values;
4337 
4338   PetscFunctionBegin;
4339   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
4340   ierr = MatGetOwnershipRange(outmat,&rstart,PETSC_NULL);CHKERRQ(ierr);
4341   for (i=0;i<m;i++) {
4342     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4343     Ii    = i + rstart;
4344     ierr = MatSetValues_MPIAIJ(outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4345     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
4346   }
4347   ierr = MatAssemblyBegin(outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4348   ierr = MatAssemblyEnd(outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4349   PetscFunctionReturn(0);
4350 }
4351 
4352 #undef __FUNCT__
4353 #define __FUNCT__ "MatCreateMPIAIJConcatenateSeqAIJ"
4354 /*@
4355       MatCreateMPIAIJConcatenateSeqAIJ - Creates a single large PETSc matrix by concatenating sequential
4356                  matrices from each processor
4357 
4358     Collective on MPI_Comm
4359 
4360    Input Parameters:
4361 +    comm - the communicators the parallel matrix will live on
4362 .    inmat - the input sequential matrices
4363 .    n - number of local columns (or PETSC_DECIDE)
4364 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4365 
4366    Output Parameter:
4367 .    outmat - the parallel matrix generated
4368 
4369     Level: advanced
4370 
4371    Notes: The number of columns of the matrix in EACH processor MUST be the same.
4372 
4373 @*/
4374 PetscErrorCode  MatCreateMPIAIJConcatenateSeqAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
4375 {
4376   PetscErrorCode ierr;
4377 
4378   PetscFunctionBegin;
4379   ierr = PetscLogEventBegin(MAT_Merge,inmat,0,0,0);CHKERRQ(ierr);
4380   if (scall == MAT_INITIAL_MATRIX){
4381     ierr = MatCreateMPIAIJConcatenateSeqAIJSymbolic(comm,inmat,n,outmat);CHKERRQ(ierr);
4382   }
4383   ierr = MatCreateMPIAIJConcatenateSeqAIJNumeric(comm,inmat,n,*outmat);CHKERRQ(ierr);
4384   ierr = PetscLogEventEnd(MAT_Merge,inmat,0,0,0);CHKERRQ(ierr);
4385   PetscFunctionReturn(0);
4386 }
4387 
4388 #undef __FUNCT__
4389 #define __FUNCT__ "MatFileSplit"
4390 PetscErrorCode MatFileSplit(Mat A,char *outfile)
4391 {
4392   PetscErrorCode    ierr;
4393   PetscMPIInt       rank;
4394   PetscInt          m,N,i,rstart,nnz;
4395   size_t            len;
4396   const PetscInt    *indx;
4397   PetscViewer       out;
4398   char              *name;
4399   Mat               B;
4400   const PetscScalar *values;
4401 
4402   PetscFunctionBegin;
4403   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
4404   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
4405   /* Should this be the type of the diagonal block of A? */
4406   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
4407   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
4408   ierr = MatSetBlockSizes(B,A->rmap->bs,A->cmap->bs);CHKERRQ(ierr);
4409   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
4410   ierr = MatSeqAIJSetPreallocation(B,0,PETSC_NULL);CHKERRQ(ierr);
4411   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
4412   for (i=0;i<m;i++) {
4413     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4414     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
4415     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
4416   }
4417   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4418   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4419 
4420   ierr = MPI_Comm_rank(((PetscObject)A)->comm,&rank);CHKERRQ(ierr);
4421   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
4422   ierr = PetscMalloc((len+5)*sizeof(char),&name);CHKERRQ(ierr);
4423   sprintf(name,"%s.%d",outfile,rank);
4424   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
4425   ierr = PetscFree(name);
4426   ierr = MatView(B,out);CHKERRQ(ierr);
4427   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
4428   ierr = MatDestroy(&B);CHKERRQ(ierr);
4429   PetscFunctionReturn(0);
4430 }
4431 
4432 extern PetscErrorCode MatDestroy_MPIAIJ(Mat);
4433 #undef __FUNCT__
4434 #define __FUNCT__ "MatDestroy_MPIAIJ_SeqsToMPI"
4435 PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
4436 {
4437   PetscErrorCode       ierr;
4438   Mat_Merge_SeqsToMPI  *merge;
4439   PetscContainer       container;
4440 
4441   PetscFunctionBegin;
4442   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject *)&container);CHKERRQ(ierr);
4443   if (container) {
4444     ierr = PetscContainerGetPointer(container,(void **)&merge);CHKERRQ(ierr);
4445     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
4446     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
4447     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
4448     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
4449     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
4450     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
4451     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
4452     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
4453     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
4454     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
4455     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
4456     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
4457     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
4458     ierr = PetscFree(merge);CHKERRQ(ierr);
4459     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
4460   }
4461   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
4462   PetscFunctionReturn(0);
4463 }
4464 
4465 #include <../src/mat/utils/freespace.h>
4466 #include <petscbt.h>
4467 
4468 #undef __FUNCT__
4469 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJNumeric"
4470 PetscErrorCode  MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
4471 {
4472   PetscErrorCode       ierr;
4473   MPI_Comm             comm=((PetscObject)mpimat)->comm;
4474   Mat_SeqAIJ           *a=(Mat_SeqAIJ*)seqmat->data;
4475   PetscMPIInt          size,rank,taga,*len_s;
4476   PetscInt             N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj=a->j;
4477   PetscInt             proc,m;
4478   PetscInt             **buf_ri,**buf_rj;
4479   PetscInt             k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
4480   PetscInt             nrows,**buf_ri_k,**nextrow,**nextai;
4481   MPI_Request          *s_waits,*r_waits;
4482   MPI_Status           *status;
4483   MatScalar            *aa=a->a;
4484   MatScalar            **abuf_r,*ba_i;
4485   Mat_Merge_SeqsToMPI  *merge;
4486   PetscContainer       container;
4487 
4488   PetscFunctionBegin;
4489   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4490 
4491   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4492   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4493 
4494   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject *)&container);CHKERRQ(ierr);
4495   ierr  = PetscContainerGetPointer(container,(void **)&merge);CHKERRQ(ierr);
4496 
4497   bi     = merge->bi;
4498   bj     = merge->bj;
4499   buf_ri = merge->buf_ri;
4500   buf_rj = merge->buf_rj;
4501 
4502   ierr   = PetscMalloc(size*sizeof(MPI_Status),&status);CHKERRQ(ierr);
4503   owners = merge->rowmap->range;
4504   len_s  = merge->len_s;
4505 
4506   /* send and recv matrix values */
4507   /*-----------------------------*/
4508   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
4509   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
4510 
4511   ierr = PetscMalloc((merge->nsend+1)*sizeof(MPI_Request),&s_waits);CHKERRQ(ierr);
4512   for (proc=0,k=0; proc<size; proc++){
4513     if (!len_s[proc]) continue;
4514     i = owners[proc];
4515     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
4516     k++;
4517   }
4518 
4519   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
4520   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
4521   ierr = PetscFree(status);CHKERRQ(ierr);
4522 
4523   ierr = PetscFree(s_waits);CHKERRQ(ierr);
4524   ierr = PetscFree(r_waits);CHKERRQ(ierr);
4525 
4526   /* insert mat values of mpimat */
4527   /*----------------------------*/
4528   ierr = PetscMalloc(N*sizeof(PetscScalar),&ba_i);CHKERRQ(ierr);
4529   ierr = PetscMalloc3(merge->nrecv,PetscInt*,&buf_ri_k,merge->nrecv,PetscInt*,&nextrow,merge->nrecv,PetscInt*,&nextai);CHKERRQ(ierr);
4530 
4531   for (k=0; k<merge->nrecv; k++){
4532     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4533     nrows = *(buf_ri_k[k]);
4534     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
4535     nextai[k]   = buf_ri_k[k] + (nrows + 1);/* poins to the next i-structure of k-th recved i-structure  */
4536   }
4537 
4538   /* set values of ba */
4539   m = merge->rowmap->n;
4540   for (i=0; i<m; i++) {
4541     arow = owners[rank] + i;
4542     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
4543     bnzi = bi[i+1] - bi[i];
4544     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
4545 
4546     /* add local non-zero vals of this proc's seqmat into ba */
4547     anzi = ai[arow+1] - ai[arow];
4548     aj   = a->j + ai[arow];
4549     aa   = a->a + ai[arow];
4550     nextaj = 0;
4551     for (j=0; nextaj<anzi; j++){
4552       if (*(bj_i + j) == aj[nextaj]){ /* bcol == acol */
4553         ba_i[j] += aa[nextaj++];
4554       }
4555     }
4556 
4557     /* add received vals into ba */
4558     for (k=0; k<merge->nrecv; k++){ /* k-th received message */
4559       /* i-th row */
4560       if (i == *nextrow[k]) {
4561         anzi = *(nextai[k]+1) - *nextai[k];
4562         aj   = buf_rj[k] + *(nextai[k]);
4563         aa   = abuf_r[k] + *(nextai[k]);
4564         nextaj = 0;
4565         for (j=0; nextaj<anzi; j++){
4566           if (*(bj_i + j) == aj[nextaj]){ /* bcol == acol */
4567             ba_i[j] += aa[nextaj++];
4568           }
4569         }
4570         nextrow[k]++; nextai[k]++;
4571       }
4572     }
4573     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
4574   }
4575   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4576   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4577 
4578   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
4579   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
4580   ierr = PetscFree(ba_i);CHKERRQ(ierr);
4581   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4582   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4583   PetscFunctionReturn(0);
4584 }
4585 
4586 extern PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat);
4587 
4588 #undef __FUNCT__
4589 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJSymbolic"
4590 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4591 {
4592   PetscErrorCode       ierr;
4593   Mat                  B_mpi;
4594   Mat_SeqAIJ           *a=(Mat_SeqAIJ*)seqmat->data;
4595   PetscMPIInt          size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4596   PetscInt             **buf_rj,**buf_ri,**buf_ri_k;
4597   PetscInt             M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4598   PetscInt             len,proc,*dnz,*onz,bs,cbs;
4599   PetscInt             k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4600   PetscInt             nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4601   MPI_Request          *si_waits,*sj_waits,*ri_waits,*rj_waits;
4602   MPI_Status           *status;
4603   PetscFreeSpaceList   free_space=PETSC_NULL,current_space=PETSC_NULL;
4604   PetscBT              lnkbt;
4605   Mat_Merge_SeqsToMPI  *merge;
4606   PetscContainer       container;
4607 
4608   PetscFunctionBegin;
4609   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4610 
4611   /* make sure it is a PETSc comm */
4612   ierr = PetscCommDuplicate(comm,&comm,PETSC_NULL);CHKERRQ(ierr);
4613   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4614   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4615 
4616   ierr = PetscNew(Mat_Merge_SeqsToMPI,&merge);CHKERRQ(ierr);
4617   ierr = PetscMalloc(size*sizeof(MPI_Status),&status);CHKERRQ(ierr);
4618 
4619   /* determine row ownership */
4620   /*---------------------------------------------------------*/
4621   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
4622   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
4623   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
4624   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
4625   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
4626   ierr = PetscMalloc(size*sizeof(PetscMPIInt),&len_si);CHKERRQ(ierr);
4627   ierr = PetscMalloc(size*sizeof(PetscMPIInt),&merge->len_s);CHKERRQ(ierr);
4628 
4629   m      = merge->rowmap->n;
4630   M      = merge->rowmap->N;
4631   owners = merge->rowmap->range;
4632 
4633   /* determine the number of messages to send, their lengths */
4634   /*---------------------------------------------------------*/
4635   len_s  = merge->len_s;
4636 
4637   len = 0;  /* length of buf_si[] */
4638   merge->nsend = 0;
4639   for (proc=0; proc<size; proc++){
4640     len_si[proc] = 0;
4641     if (proc == rank){
4642       len_s[proc] = 0;
4643     } else {
4644       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4645       len_s[proc] = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4646     }
4647     if (len_s[proc]) {
4648       merge->nsend++;
4649       nrows = 0;
4650       for (i=owners[proc]; i<owners[proc+1]; i++){
4651         if (ai[i+1] > ai[i]) nrows++;
4652       }
4653       len_si[proc] = 2*(nrows+1);
4654       len += len_si[proc];
4655     }
4656   }
4657 
4658   /* determine the number and length of messages to receive for ij-structure */
4659   /*-------------------------------------------------------------------------*/
4660   ierr = PetscGatherNumberOfMessages(comm,PETSC_NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
4661   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
4662 
4663   /* post the Irecv of j-structure */
4664   /*-------------------------------*/
4665   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
4666   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
4667 
4668   /* post the Isend of j-structure */
4669   /*--------------------------------*/
4670   ierr = PetscMalloc2(merge->nsend,MPI_Request,&si_waits,merge->nsend,MPI_Request,&sj_waits);CHKERRQ(ierr);
4671 
4672   for (proc=0, k=0; proc<size; proc++){
4673     if (!len_s[proc]) continue;
4674     i = owners[proc];
4675     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
4676     k++;
4677   }
4678 
4679   /* receives and sends of j-structure are complete */
4680   /*------------------------------------------------*/
4681   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
4682   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
4683 
4684   /* send and recv i-structure */
4685   /*---------------------------*/
4686   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
4687   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
4688 
4689   ierr = PetscMalloc((len+1)*sizeof(PetscInt),&buf_s);CHKERRQ(ierr);
4690   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4691   for (proc=0,k=0; proc<size; proc++){
4692     if (!len_s[proc]) continue;
4693     /* form outgoing message for i-structure:
4694          buf_si[0]:                 nrows to be sent
4695                [1:nrows]:           row index (global)
4696                [nrows+1:2*nrows+1]: i-structure index
4697     */
4698     /*-------------------------------------------*/
4699     nrows = len_si[proc]/2 - 1;
4700     buf_si_i    = buf_si + nrows+1;
4701     buf_si[0]   = nrows;
4702     buf_si_i[0] = 0;
4703     nrows = 0;
4704     for (i=owners[proc]; i<owners[proc+1]; i++){
4705       anzi = ai[i+1] - ai[i];
4706       if (anzi) {
4707         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4708         buf_si[nrows+1] = i-owners[proc]; /* local row index */
4709         nrows++;
4710       }
4711     }
4712     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4713     k++;
4714     buf_si += len_si[proc];
4715   }
4716 
4717   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4718   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4719 
4720   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4721   for (i=0; i<merge->nrecv; i++){
4722     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);
4723   }
4724 
4725   ierr = PetscFree(len_si);CHKERRQ(ierr);
4726   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4727   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4728   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4729   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4730   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4731   ierr = PetscFree(status);CHKERRQ(ierr);
4732 
4733   /* compute a local seq matrix in each processor */
4734   /*----------------------------------------------*/
4735   /* allocate bi array and free space for accumulating nonzero column info */
4736   ierr = PetscMalloc((m+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
4737   bi[0] = 0;
4738 
4739   /* create and initialize a linked list */
4740   nlnk = N+1;
4741   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4742 
4743   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4744   len = 0;
4745   len  = ai[owners[rank+1]] - ai[owners[rank]];
4746   ierr = PetscFreeSpaceGet((PetscInt)(2*len+1),&free_space);CHKERRQ(ierr);
4747   current_space = free_space;
4748 
4749   /* determine symbolic info for each local row */
4750   ierr = PetscMalloc3(merge->nrecv,PetscInt*,&buf_ri_k,merge->nrecv,PetscInt*,&nextrow,merge->nrecv,PetscInt*,&nextai);CHKERRQ(ierr);
4751 
4752   for (k=0; k<merge->nrecv; k++){
4753     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4754     nrows = *buf_ri_k[k];
4755     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4756     nextai[k]   = buf_ri_k[k] + (nrows + 1);/* poins to the next i-structure of k-th recved i-structure  */
4757   }
4758 
4759   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4760   len = 0;
4761   for (i=0;i<m;i++) {
4762     bnzi   = 0;
4763     /* add local non-zero cols of this proc's seqmat into lnk */
4764     arow   = owners[rank] + i;
4765     anzi   = ai[arow+1] - ai[arow];
4766     aj     = a->j + ai[arow];
4767     ierr = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4768     bnzi += nlnk;
4769     /* add received col data into lnk */
4770     for (k=0; k<merge->nrecv; k++){ /* k-th received message */
4771       if (i == *nextrow[k]) { /* i-th row */
4772         anzi = *(nextai[k]+1) - *nextai[k];
4773         aj   = buf_rj[k] + *nextai[k];
4774         ierr = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4775         bnzi += nlnk;
4776         nextrow[k]++; nextai[k]++;
4777       }
4778     }
4779     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4780 
4781     /* if free space is not available, make more free space */
4782     if (current_space->local_remaining<bnzi) {
4783       ierr = PetscFreeSpaceGet(bnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
4784       nspacedouble++;
4785     }
4786     /* copy data into free space, then initialize lnk */
4787     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4788     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
4789 
4790     current_space->array           += bnzi;
4791     current_space->local_used      += bnzi;
4792     current_space->local_remaining -= bnzi;
4793 
4794     bi[i+1] = bi[i] + bnzi;
4795   }
4796 
4797   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4798 
4799   ierr = PetscMalloc((bi[m]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
4800   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
4801   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4802 
4803   /* create symbolic parallel matrix B_mpi */
4804   /*---------------------------------------*/
4805     ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
4806   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
4807   if (n==PETSC_DECIDE) {
4808     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
4809   } else {
4810     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4811   }
4812   ierr = MatSetBlockSizes(B_mpi,bs,cbs); CHKERRQ(ierr);
4813   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
4814   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
4815   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4816   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
4817 
4818   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4819   B_mpi->assembled     = PETSC_FALSE;
4820   B_mpi->ops->destroy  = MatDestroy_MPIAIJ_SeqsToMPI;
4821   merge->bi            = bi;
4822   merge->bj            = bj;
4823   merge->buf_ri        = buf_ri;
4824   merge->buf_rj        = buf_rj;
4825   merge->coi           = PETSC_NULL;
4826   merge->coj           = PETSC_NULL;
4827   merge->owners_co     = PETSC_NULL;
4828 
4829   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
4830 
4831   /* attach the supporting struct to B_mpi for reuse */
4832   ierr = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
4833   ierr = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
4834   ierr = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
4835   ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
4836   *mpimat = B_mpi;
4837 
4838   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4839   PetscFunctionReturn(0);
4840 }
4841 
4842 #undef __FUNCT__
4843 #define __FUNCT__ "MatCreateMPIAIJSumSeqAIJ"
4844 /*@C
4845       MatCreateMPIAIJSumSeqAIJ - Creates a MPIAIJ matrix by adding sequential
4846                  matrices from each processor
4847 
4848     Collective on MPI_Comm
4849 
4850    Input Parameters:
4851 +    comm - the communicators the parallel matrix will live on
4852 .    seqmat - the input sequential matrices
4853 .    m - number of local rows (or PETSC_DECIDE)
4854 .    n - number of local columns (or PETSC_DECIDE)
4855 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4856 
4857    Output Parameter:
4858 .    mpimat - the parallel matrix generated
4859 
4860     Level: advanced
4861 
4862    Notes:
4863      The dimensions of the sequential matrix in each processor MUST be the same.
4864      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
4865      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
4866 @*/
4867 PetscErrorCode  MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
4868 {
4869   PetscErrorCode   ierr;
4870   PetscMPIInt     size;
4871 
4872   PetscFunctionBegin;
4873   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4874   if (size == 1){
4875      ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4876      if (scall == MAT_INITIAL_MATRIX){
4877        ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
4878      } else {
4879        ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4880      }
4881      ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4882      PetscFunctionReturn(0);
4883   }
4884   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4885   if (scall == MAT_INITIAL_MATRIX){
4886     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
4887   }
4888   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
4889   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4890   PetscFunctionReturn(0);
4891 }
4892 
4893 #undef __FUNCT__
4894 #define __FUNCT__ "MatMPIAIJGetLocalMat"
4895 /*@
4896      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
4897           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
4898           with MatGetSize()
4899 
4900     Not Collective
4901 
4902    Input Parameters:
4903 +    A - the matrix
4904 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4905 
4906    Output Parameter:
4907 .    A_loc - the local sequential matrix generated
4908 
4909     Level: developer
4910 
4911 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
4912 
4913 @*/
4914 PetscErrorCode  MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
4915 {
4916   PetscErrorCode  ierr;
4917   Mat_MPIAIJ      *mpimat=(Mat_MPIAIJ*)A->data;
4918   Mat_SeqAIJ      *mat,*a=(Mat_SeqAIJ*)(mpimat->A)->data,*b=(Mat_SeqAIJ*)(mpimat->B)->data;
4919   PetscInt        *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*cmap=mpimat->garray;
4920   MatScalar       *aa=a->a,*ba=b->a,*cam;
4921   PetscScalar     *ca;
4922   PetscInt        am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
4923   PetscInt        *ci,*cj,col,ncols_d,ncols_o,jo;
4924   PetscBool       match;
4925 
4926   PetscFunctionBegin;
4927   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4928   if (!match) SETERRQ(((PetscObject)A)->comm, PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
4929   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4930   if (scall == MAT_INITIAL_MATRIX){
4931     ierr = PetscMalloc((1+am)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
4932     ci[0] = 0;
4933     for (i=0; i<am; i++){
4934       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
4935     }
4936     ierr = PetscMalloc((1+ci[am])*sizeof(PetscInt),&cj);CHKERRQ(ierr);
4937     ierr = PetscMalloc((1+ci[am])*sizeof(PetscScalar),&ca);CHKERRQ(ierr);
4938     k = 0;
4939     for (i=0; i<am; i++) {
4940       ncols_o = bi[i+1] - bi[i];
4941       ncols_d = ai[i+1] - ai[i];
4942       /* off-diagonal portion of A */
4943       for (jo=0; jo<ncols_o; jo++) {
4944         col = cmap[*bj];
4945         if (col >= cstart) break;
4946         cj[k]   = col; bj++;
4947         ca[k++] = *ba++;
4948       }
4949       /* diagonal portion of A */
4950       for (j=0; j<ncols_d; j++) {
4951         cj[k]   = cstart + *aj++;
4952         ca[k++] = *aa++;
4953       }
4954       /* off-diagonal portion of A */
4955       for (j=jo; j<ncols_o; j++) {
4956         cj[k]   = cmap[*bj++];
4957         ca[k++] = *ba++;
4958       }
4959     }
4960     /* put together the new matrix */
4961     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
4962     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4963     /* Since these are PETSc arrays, change flags to free them as necessary. */
4964     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
4965     mat->free_a  = PETSC_TRUE;
4966     mat->free_ij = PETSC_TRUE;
4967     mat->nonew   = 0;
4968   } else if (scall == MAT_REUSE_MATRIX){
4969     mat=(Mat_SeqAIJ*)(*A_loc)->data;
4970     ci = mat->i; cj = mat->j; cam = mat->a;
4971     for (i=0; i<am; i++) {
4972       /* off-diagonal portion of A */
4973       ncols_o = bi[i+1] - bi[i];
4974       for (jo=0; jo<ncols_o; jo++) {
4975         col = cmap[*bj];
4976         if (col >= cstart) break;
4977         *cam++ = *ba++; bj++;
4978       }
4979       /* diagonal portion of A */
4980       ncols_d = ai[i+1] - ai[i];
4981       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
4982       /* off-diagonal portion of A */
4983       for (j=jo; j<ncols_o; j++) {
4984         *cam++ = *ba++; bj++;
4985       }
4986     }
4987   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
4988   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4989   PetscFunctionReturn(0);
4990 }
4991 
4992 #undef __FUNCT__
4993 #define __FUNCT__ "MatMPIAIJGetLocalMatCondensed"
4994 /*@C
4995      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MPIAIJ matrix by taking all its local rows and NON-ZERO columns
4996 
4997     Not Collective
4998 
4999    Input Parameters:
5000 +    A - the matrix
5001 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5002 -    row, col - index sets of rows and columns to extract (or PETSC_NULL)
5003 
5004    Output Parameter:
5005 .    A_loc - the local sequential matrix generated
5006 
5007     Level: developer
5008 
5009 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
5010 
5011 @*/
5012 PetscErrorCode  MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
5013 {
5014   Mat_MPIAIJ        *a=(Mat_MPIAIJ*)A->data;
5015   PetscErrorCode    ierr;
5016   PetscInt          i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
5017   IS                isrowa,iscola;
5018   Mat               *aloc;
5019   PetscBool       match;
5020 
5021   PetscFunctionBegin;
5022   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
5023   if (!match) SETERRQ(((PetscObject)A)->comm, PETSC_ERR_SUP,"Requires MPIAIJ matrix as input");
5024   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
5025   if (!row){
5026     start = A->rmap->rstart; end = A->rmap->rend;
5027     ierr = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
5028   } else {
5029     isrowa = *row;
5030   }
5031   if (!col){
5032     start = A->cmap->rstart;
5033     cmap  = a->garray;
5034     nzA   = a->A->cmap->n;
5035     nzB   = a->B->cmap->n;
5036     ierr  = PetscMalloc((nzA+nzB)*sizeof(PetscInt), &idx);CHKERRQ(ierr);
5037     ncols = 0;
5038     for (i=0; i<nzB; i++) {
5039       if (cmap[i] < start) idx[ncols++] = cmap[i];
5040       else break;
5041     }
5042     imark = i;
5043     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
5044     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
5045     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
5046   } else {
5047     iscola = *col;
5048   }
5049   if (scall != MAT_INITIAL_MATRIX){
5050     ierr = PetscMalloc(sizeof(Mat),&aloc);CHKERRQ(ierr);
5051     aloc[0] = *A_loc;
5052   }
5053   ierr = MatGetSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
5054   *A_loc = aloc[0];
5055   ierr = PetscFree(aloc);CHKERRQ(ierr);
5056   if (!row){
5057     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
5058   }
5059   if (!col){
5060     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
5061   }
5062   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
5063   PetscFunctionReturn(0);
5064 }
5065 
5066 #undef __FUNCT__
5067 #define __FUNCT__ "MatGetBrowsOfAcols"
5068 /*@C
5069     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
5070 
5071     Collective on Mat
5072 
5073    Input Parameters:
5074 +    A,B - the matrices in mpiaij format
5075 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5076 -    rowb, colb - index sets of rows and columns of B to extract (or PETSC_NULL)
5077 
5078    Output Parameter:
5079 +    rowb, colb - index sets of rows and columns of B to extract
5080 -    B_seq - the sequential matrix generated
5081 
5082     Level: developer
5083 
5084 @*/
5085 PetscErrorCode  MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
5086 {
5087   Mat_MPIAIJ        *a=(Mat_MPIAIJ*)A->data;
5088   PetscErrorCode    ierr;
5089   PetscInt          *idx,i,start,ncols,nzA,nzB,*cmap,imark;
5090   IS                isrowb,iscolb;
5091   Mat               *bseq=PETSC_NULL;
5092 
5093   PetscFunctionBegin;
5094   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend){
5095     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);
5096   }
5097   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
5098 
5099   if (scall == MAT_INITIAL_MATRIX){
5100     start = A->cmap->rstart;
5101     cmap  = a->garray;
5102     nzA   = a->A->cmap->n;
5103     nzB   = a->B->cmap->n;
5104     ierr  = PetscMalloc((nzA+nzB)*sizeof(PetscInt), &idx);CHKERRQ(ierr);
5105     ncols = 0;
5106     for (i=0; i<nzB; i++) {  /* row < local row index */
5107       if (cmap[i] < start) idx[ncols++] = cmap[i];
5108       else break;
5109     }
5110     imark = i;
5111     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
5112     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
5113     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
5114     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
5115   } else {
5116     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
5117     isrowb = *rowb; iscolb = *colb;
5118     ierr = PetscMalloc(sizeof(Mat),&bseq);CHKERRQ(ierr);
5119     bseq[0] = *B_seq;
5120   }
5121   ierr = MatGetSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
5122   *B_seq = bseq[0];
5123   ierr = PetscFree(bseq);CHKERRQ(ierr);
5124   if (!rowb){
5125     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
5126   } else {
5127     *rowb = isrowb;
5128   }
5129   if (!colb){
5130     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
5131   } else {
5132     *colb = iscolb;
5133   }
5134   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
5135   PetscFunctionReturn(0);
5136 }
5137 
5138 #undef __FUNCT__
5139 #define __FUNCT__ "MatGetBrowsOfAoCols_MPIAIJ"
5140 /*
5141     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
5142     of the OFF-DIAGONAL portion of local A
5143 
5144     Collective on Mat
5145 
5146    Input Parameters:
5147 +    A,B - the matrices in mpiaij format
5148 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
5149 
5150    Output Parameter:
5151 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or PETSC_NULL)
5152 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or PETSC_NULL)
5153 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or PETSC_NULL)
5154 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
5155 
5156     Level: developer
5157 
5158 */
5159 PetscErrorCode  MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
5160 {
5161   VecScatter_MPI_General *gen_to,*gen_from;
5162   PetscErrorCode         ierr;
5163   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
5164   Mat_SeqAIJ             *b_oth;
5165   VecScatter             ctx=a->Mvctx;
5166   MPI_Comm               comm=((PetscObject)ctx)->comm;
5167   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
5168   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
5169   PetscScalar            *rvalues,*svalues;
5170   MatScalar              *b_otha,*bufa,*bufA;
5171   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
5172   MPI_Request            *rwaits = PETSC_NULL,*swaits = PETSC_NULL;
5173   MPI_Status             *sstatus,rstatus;
5174   PetscMPIInt            jj;
5175   PetscInt               *cols,sbs,rbs;
5176   PetscScalar            *vals;
5177 
5178   PetscFunctionBegin;
5179   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend){
5180     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);
5181   }
5182   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5183   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
5184 
5185   gen_to   = (VecScatter_MPI_General*)ctx->todata;
5186   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
5187   rvalues  = gen_from->values; /* holds the length of receiving row */
5188   svalues  = gen_to->values;   /* holds the length of sending row */
5189   nrecvs   = gen_from->n;
5190   nsends   = gen_to->n;
5191 
5192   ierr = PetscMalloc2(nrecvs,MPI_Request,&rwaits,nsends,MPI_Request,&swaits);CHKERRQ(ierr);
5193   srow     = gen_to->indices;   /* local row index to be sent */
5194   sstarts  = gen_to->starts;
5195   sprocs   = gen_to->procs;
5196   sstatus  = gen_to->sstatus;
5197   sbs      = gen_to->bs;
5198   rstarts  = gen_from->starts;
5199   rprocs   = gen_from->procs;
5200   rbs      = gen_from->bs;
5201 
5202   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
5203   if (scall == MAT_INITIAL_MATRIX){
5204     /* i-array */
5205     /*---------*/
5206     /*  post receives */
5207     for (i=0; i<nrecvs; i++){
5208       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
5209       nrows = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
5210       ierr = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5211     }
5212 
5213     /* pack the outgoing message */
5214     ierr = PetscMalloc2(nsends+1,PetscInt,&sstartsj,nrecvs+1,PetscInt,&rstartsj);CHKERRQ(ierr);
5215     sstartsj[0] = 0;  rstartsj[0] = 0;
5216     len = 0; /* total length of j or a array to be sent */
5217     k = 0;
5218     for (i=0; i<nsends; i++){
5219       rowlen = (PetscInt*)svalues + sstarts[i]*sbs;
5220       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5221       for (j=0; j<nrows; j++) {
5222         row = srow[k] + B->rmap->range[rank]; /* global row idx */
5223         for (l=0; l<sbs; l++){
5224           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr); /* rowlength */
5225           rowlen[j*sbs+l] = ncols;
5226           len += ncols;
5227           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
5228         }
5229         k++;
5230       }
5231       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5232       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
5233     }
5234     /* recvs and sends of i-array are completed */
5235     i = nrecvs;
5236     while (i--) {
5237       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5238     }
5239     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5240 
5241     /* allocate buffers for sending j and a arrays */
5242     ierr = PetscMalloc((len+1)*sizeof(PetscInt),&bufj);CHKERRQ(ierr);
5243     ierr = PetscMalloc((len+1)*sizeof(PetscScalar),&bufa);CHKERRQ(ierr);
5244 
5245     /* create i-array of B_oth */
5246     ierr = PetscMalloc((aBn+2)*sizeof(PetscInt),&b_othi);CHKERRQ(ierr);
5247     b_othi[0] = 0;
5248     len = 0; /* total length of j or a array to be received */
5249     k = 0;
5250     for (i=0; i<nrecvs; i++){
5251       rowlen = (PetscInt*)rvalues + rstarts[i]*rbs;
5252       nrows = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be recieved */
5253       for (j=0; j<nrows; j++) {
5254         b_othi[k+1] = b_othi[k] + rowlen[j];
5255         len += rowlen[j]; k++;
5256       }
5257       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
5258     }
5259 
5260     /* allocate space for j and a arrrays of B_oth */
5261     ierr = PetscMalloc((b_othi[aBn]+1)*sizeof(PetscInt),&b_othj);CHKERRQ(ierr);
5262     ierr = PetscMalloc((b_othi[aBn]+1)*sizeof(MatScalar),&b_otha);CHKERRQ(ierr);
5263 
5264     /* j-array */
5265     /*---------*/
5266     /*  post receives of j-array */
5267     for (i=0; i<nrecvs; i++){
5268       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5269       ierr = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5270     }
5271 
5272     /* pack the outgoing message j-array */
5273     k = 0;
5274     for (i=0; i<nsends; i++){
5275       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5276       bufJ = bufj+sstartsj[i];
5277       for (j=0; j<nrows; j++) {
5278         row  = srow[k++] + B->rmap->range[rank]; /* global row idx */
5279         for (ll=0; ll<sbs; ll++){
5280           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,PETSC_NULL);CHKERRQ(ierr);
5281           for (l=0; l<ncols; l++){
5282             *bufJ++ = cols[l];
5283           }
5284           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,PETSC_NULL);CHKERRQ(ierr);
5285         }
5286       }
5287       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5288     }
5289 
5290     /* recvs and sends of j-array are completed */
5291     i = nrecvs;
5292     while (i--) {
5293       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5294     }
5295     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5296   } else if (scall == MAT_REUSE_MATRIX){
5297     sstartsj = *startsj_s;
5298     rstartsj = *startsj_r;
5299     bufa     = *bufa_ptr;
5300     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
5301     b_otha   = b_oth->a;
5302   } else {
5303     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
5304   }
5305 
5306   /* a-array */
5307   /*---------*/
5308   /*  post receives of a-array */
5309   for (i=0; i<nrecvs; i++){
5310     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
5311     ierr = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
5312   }
5313 
5314   /* pack the outgoing message a-array */
5315   k = 0;
5316   for (i=0; i<nsends; i++){
5317     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
5318     bufA = bufa+sstartsj[i];
5319     for (j=0; j<nrows; j++) {
5320       row  = srow[k++] + B->rmap->range[rank]; /* global row idx */
5321       for (ll=0; ll<sbs; ll++){
5322         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,PETSC_NULL,&vals);CHKERRQ(ierr);
5323         for (l=0; l<ncols; l++){
5324           *bufA++ = vals[l];
5325         }
5326         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,PETSC_NULL,&vals);CHKERRQ(ierr);
5327       }
5328     }
5329     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
5330   }
5331   /* recvs and sends of a-array are completed */
5332   i = nrecvs;
5333   while (i--) {
5334     ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
5335   }
5336   if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
5337   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
5338 
5339   if (scall == MAT_INITIAL_MATRIX){
5340     /* put together the new matrix */
5341     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
5342 
5343     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
5344     /* Since these are PETSc arrays, change flags to free them as necessary. */
5345     b_oth          = (Mat_SeqAIJ *)(*B_oth)->data;
5346     b_oth->free_a  = PETSC_TRUE;
5347     b_oth->free_ij = PETSC_TRUE;
5348     b_oth->nonew   = 0;
5349 
5350     ierr = PetscFree(bufj);CHKERRQ(ierr);
5351     if (!startsj_s || !bufa_ptr){
5352       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
5353       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
5354     } else {
5355       *startsj_s = sstartsj;
5356       *startsj_r = rstartsj;
5357       *bufa_ptr  = bufa;
5358     }
5359   }
5360   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
5361   PetscFunctionReturn(0);
5362 }
5363 
5364 #undef __FUNCT__
5365 #define __FUNCT__ "MatGetCommunicationStructs"
5366 /*@C
5367   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
5368 
5369   Not Collective
5370 
5371   Input Parameters:
5372 . A - The matrix in mpiaij format
5373 
5374   Output Parameter:
5375 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
5376 . colmap - A map from global column index to local index into lvec
5377 - multScatter - A scatter from the argument of a matrix-vector product to lvec
5378 
5379   Level: developer
5380 
5381 @*/
5382 #if defined (PETSC_USE_CTABLE)
5383 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
5384 #else
5385 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
5386 #endif
5387 {
5388   Mat_MPIAIJ *a;
5389 
5390   PetscFunctionBegin;
5391   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
5392   PetscValidPointer(lvec, 2);
5393   PetscValidPointer(colmap, 3);
5394   PetscValidPointer(multScatter, 4);
5395   a = (Mat_MPIAIJ *) A->data;
5396   if (lvec) *lvec = a->lvec;
5397   if (colmap) *colmap = a->colmap;
5398   if (multScatter) *multScatter = a->Mvctx;
5399   PetscFunctionReturn(0);
5400 }
5401 
5402 EXTERN_C_BEGIN
5403 extern PetscErrorCode  MatConvert_MPIAIJ_MPIAIJCRL(Mat,const MatType,MatReuse,Mat*);
5404 extern PetscErrorCode  MatConvert_MPIAIJ_MPIAIJPERM(Mat,const MatType,MatReuse,Mat*);
5405 extern PetscErrorCode  MatConvert_MPIAIJ_MPISBAIJ(Mat,const MatType,MatReuse,Mat*);
5406 EXTERN_C_END
5407 
5408 #undef __FUNCT__
5409 #define __FUNCT__ "MatMatMultNumeric_MPIDense_MPIAIJ"
5410 /*
5411     Computes (B'*A')' since computing B*A directly is untenable
5412 
5413                n                       p                          p
5414         (              )       (              )         (                  )
5415       m (      A       )  *  n (       B      )   =   m (         C        )
5416         (              )       (              )         (                  )
5417 
5418 */
5419 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
5420 {
5421   PetscErrorCode     ierr;
5422   Mat                At,Bt,Ct;
5423 
5424   PetscFunctionBegin;
5425   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
5426   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
5427   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
5428   ierr = MatDestroy(&At);CHKERRQ(ierr);
5429   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
5430   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
5431   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
5432   PetscFunctionReturn(0);
5433 }
5434 
5435 #undef __FUNCT__
5436 #define __FUNCT__ "MatMatMultSymbolic_MPIDense_MPIAIJ"
5437 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
5438 {
5439   PetscErrorCode ierr;
5440   PetscInt       m=A->rmap->n,n=B->cmap->n;
5441   Mat            Cmat;
5442 
5443   PetscFunctionBegin;
5444   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);
5445   ierr = MatCreate(((PetscObject)A)->comm,&Cmat);CHKERRQ(ierr);
5446   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
5447   ierr = MatSetBlockSizes(Cmat,A->rmap->bs,B->cmap->bs);CHKERRQ(ierr);
5448   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
5449   ierr = MatMPIDenseSetPreallocation(Cmat,PETSC_NULL);CHKERRQ(ierr);
5450   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5451   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5452   *C   = Cmat;
5453   (*C)->ops->matmult = MatMatMult_MPIDense_MPIAIJ;
5454   PetscFunctionReturn(0);
5455 }
5456 
5457 /* ----------------------------------------------------------------*/
5458 #undef __FUNCT__
5459 #define __FUNCT__ "MatMatMult_MPIDense_MPIAIJ"
5460 PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
5461 {
5462   PetscErrorCode ierr;
5463 
5464   PetscFunctionBegin;
5465   if (scall == MAT_INITIAL_MATRIX){
5466     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
5467   }
5468   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
5469   PetscFunctionReturn(0);
5470 }
5471 
5472 EXTERN_C_BEGIN
5473 #if defined(PETSC_HAVE_MUMPS)
5474 extern PetscErrorCode MatGetFactor_aij_mumps(Mat,MatFactorType,Mat*);
5475 #endif
5476 #if defined(PETSC_HAVE_PASTIX)
5477 extern PetscErrorCode MatGetFactor_mpiaij_pastix(Mat,MatFactorType,Mat*);
5478 #endif
5479 #if defined(PETSC_HAVE_SUPERLU_DIST)
5480 extern PetscErrorCode MatGetFactor_mpiaij_superlu_dist(Mat,MatFactorType,Mat*);
5481 #endif
5482 #if defined(PETSC_HAVE_SPOOLES)
5483 extern PetscErrorCode MatGetFactor_mpiaij_spooles(Mat,MatFactorType,Mat*);
5484 #endif
5485 EXTERN_C_END
5486 
5487 /*MC
5488    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
5489 
5490    Options Database Keys:
5491 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
5492 
5493   Level: beginner
5494 
5495 .seealso: MatCreateAIJ()
5496 M*/
5497 
5498 EXTERN_C_BEGIN
5499 #undef __FUNCT__
5500 #define __FUNCT__ "MatCreate_MPIAIJ"
5501 PetscErrorCode  MatCreate_MPIAIJ(Mat B)
5502 {
5503   Mat_MPIAIJ     *b;
5504   PetscErrorCode ierr;
5505   PetscMPIInt    size;
5506 
5507   PetscFunctionBegin;
5508   ierr = MPI_Comm_size(((PetscObject)B)->comm,&size);CHKERRQ(ierr);
5509 
5510   ierr            = PetscNewLog(B,Mat_MPIAIJ,&b);CHKERRQ(ierr);
5511   B->data         = (void*)b;
5512   ierr            = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
5513   B->assembled    = PETSC_FALSE;
5514 
5515   B->insertmode   = NOT_SET_VALUES;
5516   b->size         = size;
5517   ierr = MPI_Comm_rank(((PetscObject)B)->comm,&b->rank);CHKERRQ(ierr);
5518 
5519   /* build cache for off array entries formed */
5520   ierr = MatStashCreate_Private(((PetscObject)B)->comm,1,&B->stash);CHKERRQ(ierr);
5521   b->donotstash  = PETSC_FALSE;
5522   b->colmap      = 0;
5523   b->garray      = 0;
5524   b->roworiented = PETSC_TRUE;
5525 
5526   /* stuff used for matrix vector multiply */
5527   b->lvec      = PETSC_NULL;
5528   b->Mvctx     = PETSC_NULL;
5529 
5530   /* stuff for MatGetRow() */
5531   b->rowindices   = 0;
5532   b->rowvalues    = 0;
5533   b->getrowactive = PETSC_FALSE;
5534 
5535 #if defined(PETSC_HAVE_SPOOLES)
5536   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatGetFactor_spooles_C",
5537                                      "MatGetFactor_mpiaij_spooles",
5538                                      MatGetFactor_mpiaij_spooles);CHKERRQ(ierr);
5539 #endif
5540 #if defined(PETSC_HAVE_MUMPS)
5541   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatGetFactor_mumps_C",
5542                                      "MatGetFactor_aij_mumps",
5543                                      MatGetFactor_aij_mumps);CHKERRQ(ierr);
5544 #endif
5545 #if defined(PETSC_HAVE_PASTIX)
5546   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatGetFactor_pastix_C",
5547 					   "MatGetFactor_mpiaij_pastix",
5548 					   MatGetFactor_mpiaij_pastix);CHKERRQ(ierr);
5549 #endif
5550 #if defined(PETSC_HAVE_SUPERLU_DIST)
5551   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatGetFactor_superlu_dist_C",
5552                                      "MatGetFactor_mpiaij_superlu_dist",
5553                                      MatGetFactor_mpiaij_superlu_dist);CHKERRQ(ierr);
5554 #endif
5555   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatStoreValues_C",
5556                                      "MatStoreValues_MPIAIJ",
5557                                      MatStoreValues_MPIAIJ);CHKERRQ(ierr);
5558   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatRetrieveValues_C",
5559                                      "MatRetrieveValues_MPIAIJ",
5560                                      MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
5561   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatGetDiagonalBlock_C",
5562 				     "MatGetDiagonalBlock_MPIAIJ",
5563                                      MatGetDiagonalBlock_MPIAIJ);CHKERRQ(ierr);
5564   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatIsTranspose_C",
5565 				     "MatIsTranspose_MPIAIJ",
5566 				     MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
5567   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatMPIAIJSetPreallocation_C",
5568 				     "MatMPIAIJSetPreallocation_MPIAIJ",
5569 				     MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
5570   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",
5571 				     "MatMPIAIJSetPreallocationCSR_MPIAIJ",
5572 				     MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
5573   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatDiagonalScaleLocal_C",
5574 				     "MatDiagonalScaleLocal_MPIAIJ",
5575 				     MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
5576   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",
5577                                      "MatConvert_MPIAIJ_MPIAIJPERM",
5578                                       MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
5579   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",
5580                                      "MatConvert_MPIAIJ_MPIAIJCRL",
5581                                       MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
5582   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",
5583                                      "MatConvert_MPIAIJ_MPISBAIJ",
5584                                       MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
5585   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",
5586                                      "MatMatMult_MPIDense_MPIAIJ",
5587                                       MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
5588   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",
5589                                      "MatMatMultSymbolic_MPIDense_MPIAIJ",
5590                                      MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
5591   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",
5592                                      "MatMatMultNumeric_MPIDense_MPIAIJ",
5593                                       MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
5594   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
5595   PetscFunctionReturn(0);
5596 }
5597 EXTERN_C_END
5598 
5599 #undef __FUNCT__
5600 #define __FUNCT__ "MatCreateMPIAIJWithSplitArrays"
5601 /*@
5602      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
5603          and "off-diagonal" part of the matrix in CSR format.
5604 
5605    Collective on MPI_Comm
5606 
5607    Input Parameters:
5608 +  comm - MPI communicator
5609 .  m - number of local rows (Cannot be PETSC_DECIDE)
5610 .  n - This value should be the same as the local size used in creating the
5611        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
5612        calculated if N is given) For square matrices n is almost always m.
5613 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
5614 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
5615 .   i - row indices for "diagonal" portion of matrix
5616 .   j - column indices
5617 .   a - matrix values
5618 .   oi - row indices for "off-diagonal" portion of matrix
5619 .   oj - column indices
5620 -   oa - matrix values
5621 
5622    Output Parameter:
5623 .   mat - the matrix
5624 
5625    Level: advanced
5626 
5627    Notes:
5628        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
5629        must free the arrays once the matrix has been destroyed and not before.
5630 
5631        The i and j indices are 0 based
5632 
5633        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
5634 
5635        This sets local rows and cannot be used to set off-processor values.
5636 
5637        You cannot later use MatSetValues() to change values in this matrix.
5638 
5639 .keywords: matrix, aij, compressed row, sparse, parallel
5640 
5641 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
5642           MPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
5643 @*/
5644 PetscErrorCode  MatCreateMPIAIJWithSplitArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,PetscInt i[],PetscInt j[],PetscScalar a[],
5645 								PetscInt oi[], PetscInt oj[],PetscScalar oa[],Mat *mat)
5646 {
5647   PetscErrorCode ierr;
5648   Mat_MPIAIJ     *maij;
5649 
5650  PetscFunctionBegin;
5651   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
5652   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
5653   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
5654   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
5655   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
5656   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
5657   maij = (Mat_MPIAIJ*) (*mat)->data;
5658   maij->donotstash     = PETSC_TRUE;
5659   (*mat)->preallocated = PETSC_TRUE;
5660 
5661   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
5662   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
5663 
5664   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
5665   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
5666 
5667   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5668   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5669   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5670   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5671 
5672   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5673   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5674   PetscFunctionReturn(0);
5675 }
5676 
5677 /*
5678     Special version for direct calls from Fortran
5679 */
5680 #include <petsc-private/fortranimpl.h>
5681 
5682 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5683 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
5684 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5685 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
5686 #endif
5687 
5688 /* Change these macros so can be used in void function */
5689 #undef CHKERRQ
5690 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
5691 #undef SETERRQ2
5692 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5693 #undef SETERRQ3
5694 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5695 #undef SETERRQ
5696 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
5697 
5698 EXTERN_C_BEGIN
5699 #undef __FUNCT__
5700 #define __FUNCT__ "matsetvaluesmpiaij_"
5701 void PETSC_STDCALL matsetvaluesmpiaij_(Mat *mmat,PetscInt *mm,const PetscInt im[],PetscInt *mn,const PetscInt in[],const PetscScalar v[],InsertMode *maddv,PetscErrorCode *_ierr)
5702 {
5703   Mat             mat = *mmat;
5704   PetscInt        m = *mm, n = *mn;
5705   InsertMode      addv = *maddv;
5706   Mat_MPIAIJ      *aij = (Mat_MPIAIJ*)mat->data;
5707   PetscScalar     value;
5708   PetscErrorCode  ierr;
5709 
5710   MatCheckPreallocated(mat,1);
5711   if (mat->insertmode == NOT_SET_VALUES) {
5712     mat->insertmode = addv;
5713   }
5714 #if defined(PETSC_USE_DEBUG)
5715   else if (mat->insertmode != addv) {
5716     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
5717   }
5718 #endif
5719   {
5720   PetscInt        i,j,rstart = mat->rmap->rstart,rend = mat->rmap->rend;
5721   PetscInt        cstart = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
5722   PetscBool       roworiented = aij->roworiented;
5723 
5724   /* Some Variables required in the macro */
5725   Mat             A = aij->A;
5726   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
5727   PetscInt        *aimax = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
5728   MatScalar       *aa = a->a;
5729   PetscBool       ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES))?PETSC_TRUE:PETSC_FALSE);
5730   Mat             B = aij->B;
5731   Mat_SeqAIJ      *b = (Mat_SeqAIJ*)B->data;
5732   PetscInt        *bimax = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5733   MatScalar       *ba = b->a;
5734 
5735   PetscInt        *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5736   PetscInt        nonew = a->nonew;
5737   MatScalar       *ap1,*ap2;
5738 
5739   PetscFunctionBegin;
5740   for (i=0; i<m; i++) {
5741     if (im[i] < 0) continue;
5742 #if defined(PETSC_USE_DEBUG)
5743     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);
5744 #endif
5745     if (im[i] >= rstart && im[i] < rend) {
5746       row      = im[i] - rstart;
5747       lastcol1 = -1;
5748       rp1      = aj + ai[row];
5749       ap1      = aa + ai[row];
5750       rmax1    = aimax[row];
5751       nrow1    = ailen[row];
5752       low1     = 0;
5753       high1    = nrow1;
5754       lastcol2 = -1;
5755       rp2      = bj + bi[row];
5756       ap2      = ba + bi[row];
5757       rmax2    = bimax[row];
5758       nrow2    = bilen[row];
5759       low2     = 0;
5760       high2    = nrow2;
5761 
5762       for (j=0; j<n; j++) {
5763         if (roworiented) value = v[i*n+j]; else value = v[i+j*m];
5764         if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES)) continue;
5765         if (in[j] >= cstart && in[j] < cend){
5766           col = in[j] - cstart;
5767           MatSetValues_SeqAIJ_A_Private(row,col,value,addv);
5768         } else if (in[j] < 0) continue;
5769 #if defined(PETSC_USE_DEBUG)
5770         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);
5771 #endif
5772         else {
5773           if (mat->was_assembled) {
5774             if (!aij->colmap) {
5775               ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5776             }
5777 #if defined (PETSC_USE_CTABLE)
5778             ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5779 	    col--;
5780 #else
5781             col = aij->colmap[in[j]] - 1;
5782 #endif
5783             if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5784               ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5785               col =  in[j];
5786               /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5787               B = aij->B;
5788               b = (Mat_SeqAIJ*)B->data;
5789               bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5790               rp2      = bj + bi[row];
5791               ap2      = ba + bi[row];
5792               rmax2    = bimax[row];
5793               nrow2    = bilen[row];
5794               low2     = 0;
5795               high2    = nrow2;
5796               bm       = aij->B->rmap->n;
5797               ba = b->a;
5798             }
5799           } else col = in[j];
5800           MatSetValues_SeqAIJ_B_Private(row,col,value,addv);
5801         }
5802       }
5803     } else {
5804       if (!aij->donotstash) {
5805         if (roworiented) {
5806           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5807         } else {
5808           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5809         }
5810       }
5811     }
5812   }}
5813   PetscFunctionReturnVoid();
5814 }
5815 EXTERN_C_END
5816 
5817