xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision 7065c759d0a7fd6c2c2ae4a3ee955377ccdbd953)
1 
2 #include "src/mat/impls/aij/mpi/mpiaij.h"
3 #include "src/inline/spops.h"
4 
5 /*
6   Local utility routine that creates a mapping from the global column
7 number to the local number in the off-diagonal part of the local
8 storage of the matrix.  When PETSC_USE_CTABLE is used this is scalable at
9 a slightly higher hash table cost; without it it is not scalable (each processor
10 has an order N integer array but is fast to acess.
11 */
12 #undef __FUNCT__
13 #define __FUNCT__ "CreateColmap_MPIAIJ_Private"
14 PetscErrorCode CreateColmap_MPIAIJ_Private(Mat mat)
15 {
16   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
17   PetscErrorCode ierr;
18   PetscInt       n = aij->B->n,i;
19 
20   PetscFunctionBegin;
21 #if defined (PETSC_USE_CTABLE)
22   ierr = PetscTableCreate(n,&aij->colmap);CHKERRQ(ierr);
23   for (i=0; i<n; i++){
24     ierr = PetscTableAdd(aij->colmap,aij->garray[i]+1,i+1);CHKERRQ(ierr);
25   }
26 #else
27   ierr = PetscMalloc((mat->N+1)*sizeof(PetscInt),&aij->colmap);CHKERRQ(ierr);
28   PetscLogObjectMemory(mat,mat->N*sizeof(PetscInt));
29   ierr = PetscMemzero(aij->colmap,mat->N*sizeof(PetscInt));CHKERRQ(ierr);
30   for (i=0; i<n; i++) aij->colmap[aij->garray[i]] = i+1;
31 #endif
32   PetscFunctionReturn(0);
33 }
34 
35 #define CHUNKSIZE   15
36 #define MatSetValues_SeqAIJ_A_Private(row,col,value,addv) \
37 { \
38  \
39     rp   = aj + ai[row] + shift; ap = aa + ai[row] + shift; \
40     rmax = aimax[row]; nrow = ailen[row];  \
41     col1 = col - shift; \
42      \
43     low = 0; high = nrow; \
44     while (high-low > 5) { \
45       t = (low+high)/2; \
46       if (rp[t] > col) high = t; \
47       else             low  = t; \
48     } \
49       for (_i=low; _i<high; _i++) { \
50         if (rp[_i] > col1) break; \
51         if (rp[_i] == col1) { \
52           if (addv == ADD_VALUES) ap[_i] += value;   \
53           else                  ap[_i] = value; \
54           goto a_noinsert; \
55         } \
56       }  \
57       if (nonew == 1) goto a_noinsert; \
58       else if (nonew == -1) SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero (%d, %d) into matrix", row, col); \
59       if (nrow >= rmax) { \
60         /* there is no extra room in row, therefore enlarge */ \
61         PetscInt    new_nz = ai[am] + CHUNKSIZE,len,*new_i,*new_j; \
62         PetscScalar *new_a; \
63  \
64         if (nonew == -2) SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero (%d, %d) in the matrix", row, col); \
65  \
66         /* malloc new storage space */ \
67         len     = new_nz*(sizeof(PetscInt)+sizeof(PetscScalar))+(am+1)*sizeof(PetscInt); \
68         ierr    = PetscMalloc(len,&new_a);CHKERRQ(ierr); \
69         new_j   = (PetscInt*)(new_a + new_nz); \
70         new_i   = new_j + new_nz; \
71  \
72         /* copy over old data into new slots */ \
73         for (ii=0; ii<row+1; ii++) {new_i[ii] = ai[ii];} \
74         for (ii=row+1; ii<am+1; ii++) {new_i[ii] = ai[ii]+CHUNKSIZE;} \
75         ierr = PetscMemcpy(new_j,aj,(ai[row]+nrow+shift)*sizeof(PetscInt));CHKERRQ(ierr); \
76         len = (new_nz - CHUNKSIZE - ai[row] - nrow - shift); \
77         ierr = PetscMemcpy(new_j+ai[row]+shift+nrow+CHUNKSIZE,aj+ai[row]+shift+nrow, \
78                                                            len*sizeof(PetscInt));CHKERRQ(ierr); \
79         ierr = PetscMemcpy(new_a,aa,(ai[row]+nrow+shift)*sizeof(PetscScalar));CHKERRQ(ierr); \
80         ierr = PetscMemcpy(new_a+ai[row]+shift+nrow+CHUNKSIZE,aa+ai[row]+shift+nrow, \
81                                                            len*sizeof(PetscScalar));CHKERRQ(ierr);  \
82         /* free up old matrix storage */ \
83  \
84         ierr = PetscFree(a->a);CHKERRQ(ierr);  \
85         if (!a->singlemalloc) { \
86            ierr = PetscFree(a->i);CHKERRQ(ierr); \
87            ierr = PetscFree(a->j);CHKERRQ(ierr); \
88         } \
89         aa = a->a = new_a; ai = a->i = new_i; aj = a->j = new_j;  \
90         a->singlemalloc = PETSC_TRUE; \
91  \
92         rp   = aj + ai[row] + shift; ap = aa + ai[row] + shift; \
93         rmax = aimax[row] = aimax[row] + CHUNKSIZE; \
94         PetscLogObjectMemory(A,CHUNKSIZE*(sizeof(PetscInt) + sizeof(PetscScalar))); \
95         a->maxnz += CHUNKSIZE; \
96         a->reallocs++; \
97       } \
98       N = nrow++ - 1; a->nz++; \
99       /* shift up all the later entries in this row */ \
100       for (ii=N; ii>=_i; ii--) { \
101         rp[ii+1] = rp[ii]; \
102         ap[ii+1] = ap[ii]; \
103       } \
104       rp[_i] = col1;  \
105       ap[_i] = value;  \
106       a_noinsert: ; \
107       ailen[row] = nrow; \
108 }
109 
110 #define MatSetValues_SeqAIJ_B_Private(row,col,value,addv) \
111 { \
112  \
113     rp   = bj + bi[row] + shift; ap = ba + bi[row] + shift; \
114     rmax = bimax[row]; nrow = bilen[row];  \
115     col1 = col - shift; \
116      \
117     low = 0; high = nrow; \
118     while (high-low > 5) { \
119       t = (low+high)/2; \
120       if (rp[t] > col) high = t; \
121       else             low  = t; \
122     } \
123        for (_i=low; _i<high; _i++) { \
124         if (rp[_i] > col1) break; \
125         if (rp[_i] == col1) { \
126           if (addv == ADD_VALUES) ap[_i] += value;   \
127           else                  ap[_i] = value; \
128           goto b_noinsert; \
129         } \
130       }  \
131       if (nonew == 1) goto b_noinsert; \
132       else if (nonew == -1) SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero (%d, %d) into matrix", row, col); \
133       if (nrow >= rmax) { \
134         /* there is no extra room in row, therefore enlarge */ \
135         PetscInt    new_nz = bi[bm] + CHUNKSIZE,len,*new_i,*new_j; \
136         PetscScalar *new_a; \
137  \
138         if (nonew == -2) SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero (%d, %d) in the matrix", row, col); \
139  \
140         /* malloc new storage space */ \
141         len     = new_nz*(sizeof(PetscInt)+sizeof(PetscScalar))+(bm+1)*sizeof(PetscInt); \
142         ierr    = PetscMalloc(len,&new_a);CHKERRQ(ierr); \
143         new_j   = (PetscInt*)(new_a + new_nz); \
144         new_i   = new_j + new_nz; \
145  \
146         /* copy over old data into new slots */ \
147         for (ii=0; ii<row+1; ii++) {new_i[ii] = bi[ii];} \
148         for (ii=row+1; ii<bm+1; ii++) {new_i[ii] = bi[ii]+CHUNKSIZE;} \
149         ierr = PetscMemcpy(new_j,bj,(bi[row]+nrow+shift)*sizeof(PetscInt));CHKERRQ(ierr); \
150         len = (new_nz - CHUNKSIZE - bi[row] - nrow - shift); \
151         ierr = PetscMemcpy(new_j+bi[row]+shift+nrow+CHUNKSIZE,bj+bi[row]+shift+nrow, \
152                                                            len*sizeof(PetscInt));CHKERRQ(ierr); \
153         ierr = PetscMemcpy(new_a,ba,(bi[row]+nrow+shift)*sizeof(PetscScalar));CHKERRQ(ierr); \
154         ierr = PetscMemcpy(new_a+bi[row]+shift+nrow+CHUNKSIZE,ba+bi[row]+shift+nrow, \
155                                                            len*sizeof(PetscScalar));CHKERRQ(ierr);  \
156         /* free up old matrix storage */ \
157  \
158         ierr = PetscFree(b->a);CHKERRQ(ierr);  \
159         if (!b->singlemalloc) { \
160           ierr = PetscFree(b->i);CHKERRQ(ierr); \
161           ierr = PetscFree(b->j);CHKERRQ(ierr); \
162         } \
163         ba = b->a = new_a; bi = b->i = new_i; bj = b->j = new_j;  \
164         b->singlemalloc = PETSC_TRUE; \
165  \
166         rp   = bj + bi[row] + shift; ap = ba + bi[row] + shift; \
167         rmax = bimax[row] = bimax[row] + CHUNKSIZE; \
168         PetscLogObjectMemory(B,CHUNKSIZE*(sizeof(PetscInt) + sizeof(PetscScalar))); \
169         b->maxnz += CHUNKSIZE; \
170         b->reallocs++; \
171       } \
172       N = nrow++ - 1; b->nz++; \
173       /* shift up all the later entries in this row */ \
174       for (ii=N; ii>=_i; ii--) { \
175         rp[ii+1] = rp[ii]; \
176         ap[ii+1] = ap[ii]; \
177       } \
178       rp[_i] = col1;  \
179       ap[_i] = value;  \
180       b_noinsert: ; \
181       bilen[row] = nrow; \
182 }
183 
184 #undef __FUNCT__
185 #define __FUNCT__ "MatSetValues_MPIAIJ"
186 PetscErrorCode MatSetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode addv)
187 {
188   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
189   PetscScalar    value;
190   PetscErrorCode ierr;
191   PetscInt       i,j,rstart = aij->rstart,rend = aij->rend;
192   PetscInt       cstart = aij->cstart,cend = aij->cend,row,col;
193   PetscTruth     roworiented = aij->roworiented;
194 
195   /* Some Variables required in the macro */
196   Mat            A = aij->A;
197   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
198   PetscInt       *aimax = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
199   PetscScalar    *aa = a->a;
200   PetscTruth     ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES))?PETSC_TRUE:PETSC_FALSE);
201   Mat            B = aij->B;
202   Mat_SeqAIJ     *b = (Mat_SeqAIJ*)B->data;
203   PetscInt       *bimax = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->m,am = aij->A->m;
204   PetscScalar    *ba = b->a;
205 
206   PetscInt       *rp,ii,nrow,_i,rmax,N,col1,low,high,t;
207   PetscInt       nonew = a->nonew,shift=0;
208   PetscScalar    *ap;
209 
210   PetscFunctionBegin;
211   for (i=0; i<m; i++) {
212     if (im[i] < 0) continue;
213 #if defined(PETSC_USE_BOPT_g)
214     if (im[i] >= mat->M) SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %d max %d",im[i],mat->M-1);
215 #endif
216     if (im[i] >= rstart && im[i] < rend) {
217       row = im[i] - rstart;
218       for (j=0; j<n; j++) {
219         if (in[j] >= cstart && in[j] < cend){
220           col = in[j] - cstart;
221           if (roworiented) value = v[i*n+j]; else value = v[i+j*m];
222           if (ignorezeroentries && value == 0.0) continue;
223           MatSetValues_SeqAIJ_A_Private(row,col,value,addv);
224           /* ierr = MatSetValues_SeqAIJ(aij->A,1,&row,1,&col,&value,addv);CHKERRQ(ierr); */
225         } else if (in[j] < 0) continue;
226 #if defined(PETSC_USE_BOPT_g)
227         else if (in[j] >= mat->N) {SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %d max %d",in[j],mat->N-1);}
228 #endif
229         else {
230           if (mat->was_assembled) {
231             if (!aij->colmap) {
232               ierr = CreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
233             }
234 #if defined (PETSC_USE_CTABLE)
235             ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
236 	    col--;
237 #else
238             col = aij->colmap[in[j]] - 1;
239 #endif
240             if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
241               ierr = DisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
242               col =  in[j];
243               /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
244               B = aij->B;
245               b = (Mat_SeqAIJ*)B->data;
246               bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
247               ba = b->a;
248             }
249           } else col = in[j];
250           if (roworiented) value = v[i*n+j]; else value = v[i+j*m];
251           if (ignorezeroentries && value == 0.0) continue;
252           MatSetValues_SeqAIJ_B_Private(row,col,value,addv);
253           /* ierr = MatSetValues_SeqAIJ(aij->B,1,&row,1,&col,&value,addv);CHKERRQ(ierr); */
254         }
255       }
256     } else {
257       if (!aij->donotstash) {
258         if (roworiented) {
259           if (ignorezeroentries && v[i*n] == 0.0) continue;
260           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n);CHKERRQ(ierr);
261         } else {
262           if (ignorezeroentries && v[i] == 0.0) continue;
263           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m);CHKERRQ(ierr);
264         }
265       }
266     }
267   }
268   PetscFunctionReturn(0);
269 }
270 
271 #undef __FUNCT__
272 #define __FUNCT__ "MatGetValues_MPIAIJ"
273 PetscErrorCode MatGetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],PetscScalar v[])
274 {
275   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
276   PetscErrorCode ierr;
277   PetscInt       i,j,rstart = aij->rstart,rend = aij->rend;
278   PetscInt       cstart = aij->cstart,cend = aij->cend,row,col;
279 
280   PetscFunctionBegin;
281   for (i=0; i<m; i++) {
282     if (idxm[i] < 0) SETERRQ1(PETSC_ERR_ARG_OUTOFRANGE,"Negative row: %d",idxm[i]);
283     if (idxm[i] >= mat->M) SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %d max %d",idxm[i],mat->M-1);
284     if (idxm[i] >= rstart && idxm[i] < rend) {
285       row = idxm[i] - rstart;
286       for (j=0; j<n; j++) {
287         if (idxn[j] < 0) SETERRQ1(PETSC_ERR_ARG_OUTOFRANGE,"Negative column: %d",idxn[j]);
288         if (idxn[j] >= mat->N) SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %d max %d",idxn[j],mat->N-1);
289         if (idxn[j] >= cstart && idxn[j] < cend){
290           col = idxn[j] - cstart;
291           ierr = MatGetValues(aij->A,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
292         } else {
293           if (!aij->colmap) {
294             ierr = CreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
295           }
296 #if defined (PETSC_USE_CTABLE)
297           ierr = PetscTableFind(aij->colmap,idxn[j]+1,&col);CHKERRQ(ierr);
298           col --;
299 #else
300           col = aij->colmap[idxn[j]] - 1;
301 #endif
302           if ((col < 0) || (aij->garray[col] != idxn[j])) *(v+i*n+j) = 0.0;
303           else {
304             ierr = MatGetValues(aij->B,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
305           }
306         }
307       }
308     } else {
309       SETERRQ(PETSC_ERR_SUP,"Only local values currently supported");
310     }
311   }
312   PetscFunctionReturn(0);
313 }
314 
315 #undef __FUNCT__
316 #define __FUNCT__ "MatAssemblyBegin_MPIAIJ"
317 PetscErrorCode MatAssemblyBegin_MPIAIJ(Mat mat,MatAssemblyType mode)
318 {
319   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
320   PetscErrorCode ierr;
321   PetscInt       nstash,reallocs;
322   InsertMode     addv;
323 
324   PetscFunctionBegin;
325   if (aij->donotstash) {
326     PetscFunctionReturn(0);
327   }
328 
329   /* make sure all processors are either in INSERTMODE or ADDMODE */
330   ierr = MPI_Allreduce(&mat->insertmode,&addv,1,MPI_INT,MPI_BOR,mat->comm);CHKERRQ(ierr);
331   if (addv == (ADD_VALUES|INSERT_VALUES)) {
332     SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Some processors inserted others added");
333   }
334   mat->insertmode = addv; /* in case this processor had no cache */
335 
336   ierr = MatStashScatterBegin_Private(&mat->stash,aij->rowners);CHKERRQ(ierr);
337   ierr = MatStashGetInfo_Private(&mat->stash,&nstash,&reallocs);CHKERRQ(ierr);
338   PetscLogInfo(aij->A,"MatAssemblyBegin_MPIAIJ:Stash has %d entries, uses %d mallocs.\n",nstash,reallocs);
339   PetscFunctionReturn(0);
340 }
341 
342 
343 #undef __FUNCT__
344 #define __FUNCT__ "MatAssemblyEnd_MPIAIJ"
345 PetscErrorCode MatAssemblyEnd_MPIAIJ(Mat mat,MatAssemblyType mode)
346 {
347   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
348   Mat_SeqAIJ     *a=(Mat_SeqAIJ *)aij->A->data,*b= (Mat_SeqAIJ *)aij->B->data;
349   PetscErrorCode ierr;
350   PetscMPIInt    n;
351   PetscInt       i,j,rstart,ncols,flg;
352   PetscInt       *row,*col,other_disassembled;
353   PetscScalar    *val;
354   InsertMode     addv = mat->insertmode;
355 
356   PetscFunctionBegin;
357   if (!aij->donotstash) {
358     while (1) {
359       ierr = MatStashScatterGetMesg_Private(&mat->stash,&n,&row,&col,&val,&flg);CHKERRQ(ierr);
360       if (!flg) break;
361 
362       for (i=0; i<n;) {
363         /* Now identify the consecutive vals belonging to the same row */
364         for (j=i,rstart=row[j]; j<n; j++) { if (row[j] != rstart) break; }
365         if (j < n) ncols = j-i;
366         else       ncols = n-i;
367         /* Now assemble all these values with a single function call */
368         ierr = MatSetValues_MPIAIJ(mat,1,row+i,ncols,col+i,val+i,addv);CHKERRQ(ierr);
369         i = j;
370       }
371     }
372     ierr = MatStashScatterEnd_Private(&mat->stash);CHKERRQ(ierr);
373   }
374 
375   ierr = MatAssemblyBegin(aij->A,mode);CHKERRQ(ierr);
376   ierr = MatAssemblyEnd(aij->A,mode);CHKERRQ(ierr);
377 
378   /* determine if any processor has disassembled, if so we must
379      also disassemble ourselfs, in order that we may reassemble. */
380   /*
381      if nonzero structure of submatrix B cannot change then we know that
382      no processor disassembled thus we can skip this stuff
383   */
384   if (!((Mat_SeqAIJ*)aij->B->data)->nonew)  {
385     ierr = MPI_Allreduce(&mat->was_assembled,&other_disassembled,1,MPI_INT,MPI_PROD,mat->comm);CHKERRQ(ierr);
386     if (mat->was_assembled && !other_disassembled) {
387       ierr = DisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
388       /* reaccess the b because aij->B was changed */
389       b    = (Mat_SeqAIJ *)aij->B->data;
390     }
391   }
392 
393   if (!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) {
394     ierr = MatSetUpMultiply_MPIAIJ(mat);CHKERRQ(ierr);
395   }
396   ierr = MatAssemblyBegin(aij->B,mode);CHKERRQ(ierr);
397   ierr = MatAssemblyEnd(aij->B,mode);CHKERRQ(ierr);
398 
399   if (aij->rowvalues) {
400     ierr = PetscFree(aij->rowvalues);CHKERRQ(ierr);
401     aij->rowvalues = 0;
402   }
403 
404   /* used by MatAXPY() */
405   a->xtoy = 0; b->xtoy = 0;
406   a->XtoY = 0; b->XtoY = 0;
407 
408   PetscFunctionReturn(0);
409 }
410 
411 #undef __FUNCT__
412 #define __FUNCT__ "MatZeroEntries_MPIAIJ"
413 PetscErrorCode MatZeroEntries_MPIAIJ(Mat A)
414 {
415   Mat_MPIAIJ     *l = (Mat_MPIAIJ*)A->data;
416   PetscErrorCode ierr;
417 
418   PetscFunctionBegin;
419   ierr = MatZeroEntries(l->A);CHKERRQ(ierr);
420   ierr = MatZeroEntries(l->B);CHKERRQ(ierr);
421   PetscFunctionReturn(0);
422 }
423 
424 #undef __FUNCT__
425 #define __FUNCT__ "MatZeroRows_MPIAIJ"
426 PetscErrorCode MatZeroRows_MPIAIJ(Mat A,IS is,const PetscScalar *diag)
427 {
428   Mat_MPIAIJ     *l = (Mat_MPIAIJ*)A->data;
429   PetscErrorCode ierr;
430   PetscMPIInt    size = l->size,imdex,n,rank = l->rank,tag = A->tag;
431   PetscInt       i,N,*rows,*owners = l->rowners;
432   PetscInt       *nprocs,j,idx,nsends,row;
433   PetscInt       nmax,*svalues,*starts,*owner,nrecvs;
434   PetscInt       *rvalues,count,base,slen,*source;
435   PetscInt       *lens,*lrows,*values,rstart=l->rstart;
436   MPI_Comm       comm = A->comm;
437   MPI_Request    *send_waits,*recv_waits;
438   MPI_Status     recv_status,*send_status;
439   IS             istmp;
440   PetscTruth     found;
441 
442   PetscFunctionBegin;
443   ierr = ISGetLocalSize(is,&N);CHKERRQ(ierr);
444   ierr = ISGetIndices(is,&rows);CHKERRQ(ierr);
445 
446   /*  first count number of contributors to each processor */
447   ierr = PetscMalloc(2*size*sizeof(PetscInt),&nprocs);CHKERRQ(ierr);
448   ierr   = PetscMemzero(nprocs,2*size*sizeof(PetscInt));CHKERRQ(ierr);
449   ierr = PetscMalloc((N+1)*sizeof(PetscInt),&owner);CHKERRQ(ierr); /* see note*/
450   for (i=0; i<N; i++) {
451     idx = rows[i];
452     found = PETSC_FALSE;
453     for (j=0; j<size; j++) {
454       if (idx >= owners[j] && idx < owners[j+1]) {
455         nprocs[2*j]++; nprocs[2*j+1] = 1; owner[i] = j; found = PETSC_TRUE; break;
456       }
457     }
458     if (!found) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Index out of range");
459   }
460   nsends = 0;  for (i=0; i<size; i++) { nsends += nprocs[2*i+1];}
461 
462   /* inform other processors of number of messages and max length*/
463   ierr = PetscMaxSum(comm,nprocs,&nmax,&nrecvs);CHKERRQ(ierr);
464 
465   /* post receives:   */
466   ierr = PetscMalloc((nrecvs+1)*(nmax+1)*sizeof(PetscInt),&rvalues);CHKERRQ(ierr);
467   ierr = PetscMalloc((nrecvs+1)*sizeof(MPI_Request),&recv_waits);CHKERRQ(ierr);
468   for (i=0; i<nrecvs; i++) {
469     ierr = MPI_Irecv(rvalues+nmax*i,nmax,MPIU_INT,MPI_ANY_SOURCE,tag,comm,recv_waits+i);CHKERRQ(ierr);
470   }
471 
472   /* do sends:
473       1) starts[i] gives the starting index in svalues for stuff going to
474          the ith processor
475   */
476   ierr = PetscMalloc((N+1)*sizeof(PetscInt),&svalues);CHKERRQ(ierr);
477   ierr = PetscMalloc((nsends+1)*sizeof(MPI_Request),&send_waits);CHKERRQ(ierr);
478   ierr = PetscMalloc((size+1)*sizeof(PetscInt),&starts);CHKERRQ(ierr);
479   starts[0] = 0;
480   for (i=1; i<size; i++) { starts[i] = starts[i-1] + nprocs[2*i-2];}
481   for (i=0; i<N; i++) {
482     svalues[starts[owner[i]]++] = rows[i];
483   }
484   ierr = ISRestoreIndices(is,&rows);CHKERRQ(ierr);
485 
486   starts[0] = 0;
487   for (i=1; i<size+1; i++) { starts[i] = starts[i-1] + nprocs[2*i-2];}
488   count = 0;
489   for (i=0; i<size; i++) {
490     if (nprocs[2*i+1]) {
491       ierr = MPI_Isend(svalues+starts[i],nprocs[2*i],MPIU_INT,i,tag,comm,send_waits+count++);CHKERRQ(ierr);
492     }
493   }
494   ierr = PetscFree(starts);CHKERRQ(ierr);
495 
496   base = owners[rank];
497 
498   /*  wait on receives */
499   ierr   = PetscMalloc(2*(nrecvs+1)*sizeof(PetscInt),&lens);CHKERRQ(ierr);
500   source = lens + nrecvs;
501   count  = nrecvs; slen = 0;
502   while (count) {
503     ierr = MPI_Waitany(nrecvs,recv_waits,&imdex,&recv_status);CHKERRQ(ierr);
504     /* unpack receives into our local space */
505     ierr = MPI_Get_count(&recv_status,MPIU_INT,&n);CHKERRQ(ierr);
506     source[imdex]  = recv_status.MPI_SOURCE;
507     lens[imdex]    = n;
508     slen          += n;
509     count--;
510   }
511   ierr = PetscFree(recv_waits);CHKERRQ(ierr);
512 
513   /* move the data into the send scatter */
514   ierr = PetscMalloc((slen+1)*sizeof(PetscInt),&lrows);CHKERRQ(ierr);
515   count = 0;
516   for (i=0; i<nrecvs; i++) {
517     values = rvalues + i*nmax;
518     for (j=0; j<lens[i]; j++) {
519       lrows[count++] = values[j] - base;
520     }
521   }
522   ierr = PetscFree(rvalues);CHKERRQ(ierr);
523   ierr = PetscFree(lens);CHKERRQ(ierr);
524   ierr = PetscFree(owner);CHKERRQ(ierr);
525   ierr = PetscFree(nprocs);CHKERRQ(ierr);
526 
527   /* actually zap the local rows */
528   ierr = ISCreateGeneral(PETSC_COMM_SELF,slen,lrows,&istmp);CHKERRQ(ierr);
529   PetscLogObjectParent(A,istmp);
530 
531   /*
532         Zero the required rows. If the "diagonal block" of the matrix
533      is square and the user wishes to set the diagonal we use seperate
534      code so that MatSetValues() is not called for each diagonal allocating
535      new memory, thus calling lots of mallocs and slowing things down.
536 
537        Contributed by: Mathew Knepley
538   */
539   /* must zero l->B before l->A because the (diag) case below may put values into l->B*/
540   ierr = MatZeroRows(l->B,istmp,0);CHKERRQ(ierr);
541   if (diag && (l->A->M == l->A->N)) {
542     ierr      = MatZeroRows(l->A,istmp,diag);CHKERRQ(ierr);
543   } else if (diag) {
544     ierr = MatZeroRows(l->A,istmp,0);CHKERRQ(ierr);
545     if (((Mat_SeqAIJ*)l->A->data)->nonew) {
546       SETERRQ(PETSC_ERR_SUP,"MatZeroRows() on rectangular matrices cannot be used with the Mat options\n\
547 MAT_NO_NEW_NONZERO_LOCATIONS,MAT_NEW_NONZERO_LOCATION_ERR,MAT_NEW_NONZERO_ALLOCATION_ERR");
548     }
549     for (i = 0; i < slen; i++) {
550       row  = lrows[i] + rstart;
551       ierr = MatSetValues(A,1,&row,1,&row,diag,INSERT_VALUES);CHKERRQ(ierr);
552     }
553     ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
554     ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
555   } else {
556     ierr = MatZeroRows(l->A,istmp,0);CHKERRQ(ierr);
557   }
558   ierr = ISDestroy(istmp);CHKERRQ(ierr);
559   ierr = PetscFree(lrows);CHKERRQ(ierr);
560 
561   /* wait on sends */
562   if (nsends) {
563     ierr = PetscMalloc(nsends*sizeof(MPI_Status),&send_status);CHKERRQ(ierr);
564     ierr = MPI_Waitall(nsends,send_waits,send_status);CHKERRQ(ierr);
565     ierr = PetscFree(send_status);CHKERRQ(ierr);
566   }
567   ierr = PetscFree(send_waits);CHKERRQ(ierr);
568   ierr = PetscFree(svalues);CHKERRQ(ierr);
569 
570   PetscFunctionReturn(0);
571 }
572 
573 #undef __FUNCT__
574 #define __FUNCT__ "MatMult_MPIAIJ"
575 PetscErrorCode MatMult_MPIAIJ(Mat A,Vec xx,Vec yy)
576 {
577   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
578   PetscErrorCode ierr;
579   PetscInt       nt;
580 
581   PetscFunctionBegin;
582   ierr = VecGetLocalSize(xx,&nt);CHKERRQ(ierr);
583   if (nt != A->n) {
584     SETERRQ2(PETSC_ERR_ARG_SIZ,"Incompatible partition of A (%d) and xx (%d)",A->n,nt);
585   }
586   ierr = VecScatterBegin(xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD,a->Mvctx);CHKERRQ(ierr);
587   ierr = (*a->A->ops->mult)(a->A,xx,yy);CHKERRQ(ierr);
588   ierr = VecScatterEnd(xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD,a->Mvctx);CHKERRQ(ierr);
589   ierr = (*a->B->ops->multadd)(a->B,a->lvec,yy,yy);CHKERRQ(ierr);
590   PetscFunctionReturn(0);
591 }
592 
593 #undef __FUNCT__
594 #define __FUNCT__ "MatMultAdd_MPIAIJ"
595 PetscErrorCode MatMultAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
596 {
597   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
598   PetscErrorCode ierr;
599 
600   PetscFunctionBegin;
601   ierr = VecScatterBegin(xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD,a->Mvctx);CHKERRQ(ierr);
602   ierr = (*a->A->ops->multadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
603   ierr = VecScatterEnd(xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD,a->Mvctx);CHKERRQ(ierr);
604   ierr = (*a->B->ops->multadd)(a->B,a->lvec,zz,zz);CHKERRQ(ierr);
605   PetscFunctionReturn(0);
606 }
607 
608 #undef __FUNCT__
609 #define __FUNCT__ "MatMultTranspose_MPIAIJ"
610 PetscErrorCode MatMultTranspose_MPIAIJ(Mat A,Vec xx,Vec yy)
611 {
612   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
613   PetscErrorCode ierr;
614 
615   PetscFunctionBegin;
616   /* do nondiagonal part */
617   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
618   /* send it on its way */
619   ierr = VecScatterBegin(a->lvec,yy,ADD_VALUES,SCATTER_REVERSE,a->Mvctx);CHKERRQ(ierr);
620   /* do local part */
621   ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
622   /* receive remote parts: note this assumes the values are not actually */
623   /* inserted in yy until the next line, which is true for my implementation*/
624   /* but is not perhaps always true. */
625   ierr = VecScatterEnd(a->lvec,yy,ADD_VALUES,SCATTER_REVERSE,a->Mvctx);CHKERRQ(ierr);
626   PetscFunctionReturn(0);
627 }
628 
629 EXTERN_C_BEGIN
630 #undef __FUNCT__
631 #define __FUNCT__ "MatIsTranspose_MPIAIJ"
632 PetscErrorCode MatIsTranspose_MPIAIJ(Mat Amat,Mat Bmat,PetscTruth tol,PetscTruth *f)
633 {
634   MPI_Comm       comm;
635   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ *) Amat->data, *Bij;
636   Mat            Adia = Aij->A, Bdia, Aoff,Boff,*Aoffs,*Boffs;
637   IS             Me,Notme;
638   PetscErrorCode ierr;
639   PetscInt       M,N,first,last,*notme,i;
640   PetscMPIInt    size;
641 
642   PetscFunctionBegin;
643 
644   /* Easy test: symmetric diagonal block */
645   Bij = (Mat_MPIAIJ *) Bmat->data; Bdia = Bij->A;
646   ierr = MatIsTranspose(Adia,Bdia,tol,f);CHKERRQ(ierr);
647   if (!*f) PetscFunctionReturn(0);
648   ierr = PetscObjectGetComm((PetscObject)Amat,&comm);CHKERRQ(ierr);
649   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
650   if (size == 1) PetscFunctionReturn(0);
651 
652   /* Hard test: off-diagonal block. This takes a MatGetSubMatrix. */
653   ierr = MatGetSize(Amat,&M,&N);CHKERRQ(ierr);
654   ierr = MatGetOwnershipRange(Amat,&first,&last);CHKERRQ(ierr);
655   ierr = PetscMalloc((N-last+first)*sizeof(PetscInt),&notme);CHKERRQ(ierr);
656   for (i=0; i<first; i++) notme[i] = i;
657   for (i=last; i<M; i++) notme[i-last+first] = i;
658   ierr = ISCreateGeneral(MPI_COMM_SELF,N-last+first,notme,&Notme);CHKERRQ(ierr);
659   ierr = ISCreateStride(MPI_COMM_SELF,last-first,first,1,&Me);CHKERRQ(ierr);
660   ierr = MatGetSubMatrices(Amat,1,&Me,&Notme,MAT_INITIAL_MATRIX,&Aoffs);CHKERRQ(ierr);
661   Aoff = Aoffs[0];
662   ierr = MatGetSubMatrices(Bmat,1,&Notme,&Me,MAT_INITIAL_MATRIX,&Boffs);CHKERRQ(ierr);
663   Boff = Boffs[0];
664   ierr = MatIsTranspose(Aoff,Boff,tol,f);CHKERRQ(ierr);
665   ierr = MatDestroyMatrices(1,&Aoffs);CHKERRQ(ierr);
666   ierr = MatDestroyMatrices(1,&Boffs);CHKERRQ(ierr);
667   ierr = ISDestroy(Me);CHKERRQ(ierr);
668   ierr = ISDestroy(Notme);CHKERRQ(ierr);
669 
670   PetscFunctionReturn(0);
671 }
672 EXTERN_C_END
673 
674 #undef __FUNCT__
675 #define __FUNCT__ "MatMultTransposeAdd_MPIAIJ"
676 PetscErrorCode MatMultTransposeAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
677 {
678   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
679   PetscErrorCode ierr;
680 
681   PetscFunctionBegin;
682   /* do nondiagonal part */
683   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
684   /* send it on its way */
685   ierr = VecScatterBegin(a->lvec,zz,ADD_VALUES,SCATTER_REVERSE,a->Mvctx);CHKERRQ(ierr);
686   /* do local part */
687   ierr = (*a->A->ops->multtransposeadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
688   /* receive remote parts: note this assumes the values are not actually */
689   /* inserted in yy until the next line, which is true for my implementation*/
690   /* but is not perhaps always true. */
691   ierr = VecScatterEnd(a->lvec,zz,ADD_VALUES,SCATTER_REVERSE,a->Mvctx);CHKERRQ(ierr);
692   PetscFunctionReturn(0);
693 }
694 
695 /*
696   This only works correctly for square matrices where the subblock A->A is the
697    diagonal block
698 */
699 #undef __FUNCT__
700 #define __FUNCT__ "MatGetDiagonal_MPIAIJ"
701 PetscErrorCode MatGetDiagonal_MPIAIJ(Mat A,Vec v)
702 {
703   PetscErrorCode ierr;
704   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
705 
706   PetscFunctionBegin;
707   if (A->M != A->N) SETERRQ(PETSC_ERR_SUP,"Supports only square matrix where A->A is diag block");
708   if (a->rstart != a->cstart || a->rend != a->cend) {
709     SETERRQ(PETSC_ERR_ARG_SIZ,"row partition must equal col partition");
710   }
711   ierr = MatGetDiagonal(a->A,v);CHKERRQ(ierr);
712   PetscFunctionReturn(0);
713 }
714 
715 #undef __FUNCT__
716 #define __FUNCT__ "MatScale_MPIAIJ"
717 PetscErrorCode MatScale_MPIAIJ(const PetscScalar aa[],Mat A)
718 {
719   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
720   PetscErrorCode ierr;
721 
722   PetscFunctionBegin;
723   ierr = MatScale(aa,a->A);CHKERRQ(ierr);
724   ierr = MatScale(aa,a->B);CHKERRQ(ierr);
725   PetscFunctionReturn(0);
726 }
727 
728 #undef __FUNCT__
729 #define __FUNCT__ "MatDestroy_MPIAIJ"
730 PetscErrorCode MatDestroy_MPIAIJ(Mat mat)
731 {
732   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
733   PetscErrorCode ierr;
734 
735   PetscFunctionBegin;
736 #if defined(PETSC_USE_LOG)
737   PetscLogObjectState((PetscObject)mat,"Rows=%d, Cols=%d",mat->M,mat->N);
738 #endif
739   ierr = MatStashDestroy_Private(&mat->stash);CHKERRQ(ierr);
740   ierr = PetscFree(aij->rowners);CHKERRQ(ierr);
741   ierr = MatDestroy(aij->A);CHKERRQ(ierr);
742   ierr = MatDestroy(aij->B);CHKERRQ(ierr);
743 #if defined (PETSC_USE_CTABLE)
744   if (aij->colmap) {ierr = PetscTableDelete(aij->colmap);CHKERRQ(ierr);}
745 #else
746   if (aij->colmap) {ierr = PetscFree(aij->colmap);CHKERRQ(ierr);}
747 #endif
748   if (aij->garray) {ierr = PetscFree(aij->garray);CHKERRQ(ierr);}
749   if (aij->lvec)   {ierr = VecDestroy(aij->lvec);CHKERRQ(ierr);}
750   if (aij->Mvctx)  {ierr = VecScatterDestroy(aij->Mvctx);CHKERRQ(ierr);}
751   if (aij->rowvalues) {ierr = PetscFree(aij->rowvalues);CHKERRQ(ierr);}
752   ierr = PetscFree(aij);CHKERRQ(ierr);
753 
754   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatStoreValues_C","",PETSC_NULL);CHKERRQ(ierr);
755   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatRetrieveValues_C","",PETSC_NULL);CHKERRQ(ierr);
756   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatGetDiagonalBlock_C","",PETSC_NULL);CHKERRQ(ierr);
757   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatIsTranspose_C","",PETSC_NULL);CHKERRQ(ierr);
758   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocation_C","",PETSC_NULL);CHKERRQ(ierr);
759   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDiagonalScaleLocal_C","",PETSC_NULL);CHKERRQ(ierr);
760   PetscFunctionReturn(0);
761 }
762 
763 #undef __FUNCT__
764 #define __FUNCT__ "MatView_MPIAIJ_Binary"
765 PetscErrorCode MatView_MPIAIJ_Binary(Mat mat,PetscViewer viewer)
766 {
767   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)mat->data;
768   Mat_SeqAIJ*       A = (Mat_SeqAIJ*)aij->A->data;
769   Mat_SeqAIJ*       B = (Mat_SeqAIJ*)aij->B->data;
770   PetscErrorCode    ierr;
771   PetscMPIInt       rank,size,tag = ((PetscObject)viewer)->tag;
772   int               fd;
773   PetscInt          nz,header[4],*row_lengths,*range,rlen,i;
774   PetscInt          nzmax,*column_indices,j,k,col,*garray = aij->garray,cnt,cstart = aij->cstart,rnz;
775   PetscScalar       *column_values;
776 
777   PetscFunctionBegin;
778   ierr = MPI_Comm_rank(mat->comm,&rank);CHKERRQ(ierr);
779   ierr = MPI_Comm_size(mat->comm,&size);CHKERRQ(ierr);
780   nz   = A->nz + B->nz;
781   if (!rank) {
782     header[0] = MAT_FILE_COOKIE;
783     header[1] = mat->M;
784     header[2] = mat->N;
785     ierr = MPI_Reduce(&nz,&header[3],1,MPIU_INT,MPI_SUM,0,mat->comm);CHKERRQ(ierr);
786     ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
787     ierr = PetscBinaryWrite(fd,header,4,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
788     /* get largest number of rows any processor has */
789     rlen = mat->m;
790     ierr = PetscMapGetGlobalRange(mat->rmap,&range);CHKERRQ(ierr);
791     for (i=1; i<size; i++) {
792       rlen = PetscMax(rlen,range[i+1] - range[i]);
793     }
794   } else {
795     ierr = MPI_Reduce(&nz,0,1,MPIU_INT,MPI_SUM,0,mat->comm);CHKERRQ(ierr);
796     rlen = mat->m;
797   }
798 
799   /* load up the local row counts */
800   ierr = PetscMalloc((rlen+1)*sizeof(PetscInt),&row_lengths);CHKERRQ(ierr);
801   for (i=0; i<mat->m; i++) {
802     row_lengths[i] = A->i[i+1] - A->i[i] + B->i[i+1] - B->i[i];
803   }
804 
805   /* store the row lengths to the file */
806   if (!rank) {
807     MPI_Status status;
808     ierr = PetscBinaryWrite(fd,row_lengths,mat->m,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
809     for (i=1; i<size; i++) {
810       rlen = range[i+1] - range[i];
811       ierr = MPI_Recv(row_lengths,rlen,MPIU_INT,i,tag,mat->comm,&status);CHKERRQ(ierr);
812       ierr = PetscBinaryWrite(fd,row_lengths,rlen,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
813     }
814   } else {
815     ierr = MPI_Send(row_lengths,mat->m,MPIU_INT,0,tag,mat->comm);CHKERRQ(ierr);
816   }
817   ierr = PetscFree(row_lengths);CHKERRQ(ierr);
818 
819   /* load up the local column indices */
820   nzmax = nz; /* )th processor needs space a largest processor needs */
821   ierr = MPI_Reduce(&nz,&nzmax,1,MPIU_INT,MPI_MAX,0,mat->comm);CHKERRQ(ierr);
822   ierr = PetscMalloc((nzmax+1)*sizeof(PetscInt),&column_indices);CHKERRQ(ierr);
823   cnt  = 0;
824   for (i=0; i<mat->m; i++) {
825     for (j=B->i[i]; j<B->i[i+1]; j++) {
826       if ( (col = garray[B->j[j]]) > cstart) break;
827       column_indices[cnt++] = col;
828     }
829     for (k=A->i[i]; k<A->i[i+1]; k++) {
830       column_indices[cnt++] = A->j[k] + cstart;
831     }
832     for (; j<B->i[i+1]; j++) {
833       column_indices[cnt++] = garray[B->j[j]];
834     }
835   }
836   if (cnt != A->nz + B->nz) SETERRQ2(PETSC_ERR_LIB,"Internal PETSc error: cnt = %d nz = %d",cnt,A->nz+B->nz);
837 
838   /* store the column indices to the file */
839   if (!rank) {
840     MPI_Status status;
841     ierr = PetscBinaryWrite(fd,column_indices,nz,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
842     for (i=1; i<size; i++) {
843       ierr = MPI_Recv(&rnz,1,MPIU_INT,i,tag,mat->comm,&status);CHKERRQ(ierr);
844       if (rnz > nzmax) SETERRQ2(PETSC_ERR_LIB,"Internal PETSc error: nz = %d nzmax = %d",nz,nzmax);
845       ierr = MPI_Recv(column_indices,rnz,MPIU_INT,i,tag,mat->comm,&status);CHKERRQ(ierr);
846       ierr = PetscBinaryWrite(fd,column_indices,rnz,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
847     }
848   } else {
849     ierr = MPI_Send(&nz,1,MPIU_INT,0,tag,mat->comm);CHKERRQ(ierr);
850     ierr = MPI_Send(column_indices,nz,MPIU_INT,0,tag,mat->comm);CHKERRQ(ierr);
851   }
852   ierr = PetscFree(column_indices);CHKERRQ(ierr);
853 
854   /* load up the local column values */
855   ierr = PetscMalloc((nzmax+1)*sizeof(PetscScalar),&column_values);CHKERRQ(ierr);
856   cnt  = 0;
857   for (i=0; i<mat->m; i++) {
858     for (j=B->i[i]; j<B->i[i+1]; j++) {
859       if ( garray[B->j[j]] > cstart) break;
860       column_values[cnt++] = B->a[j];
861     }
862     for (k=A->i[i]; k<A->i[i+1]; k++) {
863       column_values[cnt++] = A->a[k];
864     }
865     for (; j<B->i[i+1]; j++) {
866       column_values[cnt++] = B->a[j];
867     }
868   }
869   if (cnt != A->nz + B->nz) SETERRQ2(1,"Internal PETSc error: cnt = %d nz = %d",cnt,A->nz+B->nz);
870 
871   /* store the column values to the file */
872   if (!rank) {
873     MPI_Status status;
874     ierr = PetscBinaryWrite(fd,column_values,nz,PETSC_SCALAR,PETSC_TRUE);CHKERRQ(ierr);
875     for (i=1; i<size; i++) {
876       ierr = MPI_Recv(&rnz,1,MPIU_INT,i,tag,mat->comm,&status);CHKERRQ(ierr);
877       if (rnz > nzmax) SETERRQ2(PETSC_ERR_LIB,"Internal PETSc error: nz = %d nzmax = %d",nz,nzmax);
878       ierr = MPI_Recv(column_values,rnz,MPIU_SCALAR,i,tag,mat->comm,&status);CHKERRQ(ierr);
879       ierr = PetscBinaryWrite(fd,column_values,rnz,PETSC_SCALAR,PETSC_TRUE);CHKERRQ(ierr);
880     }
881   } else {
882     ierr = MPI_Send(&nz,1,MPIU_INT,0,tag,mat->comm);CHKERRQ(ierr);
883     ierr = MPI_Send(column_values,nz,MPIU_SCALAR,0,tag,mat->comm);CHKERRQ(ierr);
884   }
885   ierr = PetscFree(column_values);CHKERRQ(ierr);
886   PetscFunctionReturn(0);
887 }
888 
889 #undef __FUNCT__
890 #define __FUNCT__ "MatView_MPIAIJ_ASCIIorDraworSocket"
891 PetscErrorCode MatView_MPIAIJ_ASCIIorDraworSocket(Mat mat,PetscViewer viewer)
892 {
893   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)mat->data;
894   PetscErrorCode    ierr;
895   PetscMPIInt       rank = aij->rank,size = aij->size;
896   PetscTruth        isdraw,iascii,flg,isbinary;
897   PetscViewer       sviewer;
898   PetscViewerFormat format;
899 
900   PetscFunctionBegin;
901   ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_DRAW,&isdraw);CHKERRQ(ierr);
902   ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&iascii);CHKERRQ(ierr);
903   ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_BINARY,&isbinary);CHKERRQ(ierr);
904   if (iascii) {
905     ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
906     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
907       MatInfo info;
908       ierr = MPI_Comm_rank(mat->comm,&rank);CHKERRQ(ierr);
909       ierr = MatGetInfo(mat,MAT_LOCAL,&info);CHKERRQ(ierr);
910       ierr = PetscOptionsHasName(PETSC_NULL,"-mat_aij_no_inode",&flg);CHKERRQ(ierr);
911       if (flg) {
912         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %d nz %d nz alloced %d mem %d, not using I-node routines\n",
913 					      rank,mat->m,(int)info.nz_used,(int)info.nz_allocated,(int)info.memory);CHKERRQ(ierr);
914       } else {
915         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %d nz %d nz alloced %d mem %d, using I-node routines\n",
916 		    rank,mat->m,(int)info.nz_used,(int)info.nz_allocated,(int)info.memory);CHKERRQ(ierr);
917       }
918       ierr = MatGetInfo(aij->A,MAT_LOCAL,&info);CHKERRQ(ierr);
919       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] on-diagonal part: nz %d \n",rank,(int)info.nz_used);CHKERRQ(ierr);
920       ierr = MatGetInfo(aij->B,MAT_LOCAL,&info);CHKERRQ(ierr);
921       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] off-diagonal part: nz %d \n",rank,(int)info.nz_used);CHKERRQ(ierr);
922       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
923       ierr = VecScatterView(aij->Mvctx,viewer);CHKERRQ(ierr);
924       PetscFunctionReturn(0);
925     } else if (format == PETSC_VIEWER_ASCII_INFO) {
926       PetscFunctionReturn(0);
927     } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO) {
928       PetscFunctionReturn(0);
929     }
930   } else if (isbinary) {
931     if (size == 1) {
932       ierr = PetscObjectSetName((PetscObject)aij->A,mat->name);CHKERRQ(ierr);
933       ierr = MatView(aij->A,viewer);CHKERRQ(ierr);
934     } else {
935       ierr = MatView_MPIAIJ_Binary(mat,viewer);CHKERRQ(ierr);
936     }
937     PetscFunctionReturn(0);
938   } else if (isdraw) {
939     PetscDraw  draw;
940     PetscTruth isnull;
941     ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
942     ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr); if (isnull) PetscFunctionReturn(0);
943   }
944 
945   if (size == 1) {
946     ierr = PetscObjectSetName((PetscObject)aij->A,mat->name);CHKERRQ(ierr);
947     ierr = MatView(aij->A,viewer);CHKERRQ(ierr);
948   } else {
949     /* assemble the entire matrix onto first processor. */
950     Mat         A;
951     Mat_SeqAIJ *Aloc;
952     PetscInt         M = mat->M,N = mat->N,m,*ai,*aj,row,*cols,i,*ct;
953     PetscScalar *a;
954 
955     if (!rank) {
956       ierr = MatCreate(mat->comm,M,N,M,N,&A);CHKERRQ(ierr);
957     } else {
958       ierr = MatCreate(mat->comm,0,0,M,N,&A);CHKERRQ(ierr);
959     }
960     /* This is just a temporary matrix, so explicitly using MATMPIAIJ is probably best */
961     ierr = MatSetType(A,MATMPIAIJ);CHKERRQ(ierr);
962     ierr = MatMPIAIJSetPreallocation(A,0,PETSC_NULL,0,PETSC_NULL);CHKERRQ(ierr);
963     PetscLogObjectParent(mat,A);
964 
965     /* copy over the A part */
966     Aloc = (Mat_SeqAIJ*)aij->A->data;
967     m = aij->A->m; ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
968     row = aij->rstart;
969     for (i=0; i<ai[m]; i++) {aj[i] += aij->cstart ;}
970     for (i=0; i<m; i++) {
971       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],aj,a,INSERT_VALUES);CHKERRQ(ierr);
972       row++; a += ai[i+1]-ai[i]; aj += ai[i+1]-ai[i];
973     }
974     aj = Aloc->j;
975     for (i=0; i<ai[m]; i++) {aj[i] -= aij->cstart;}
976 
977     /* copy over the B part */
978     Aloc = (Mat_SeqAIJ*)aij->B->data;
979     m    = aij->B->m;  ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
980     row  = aij->rstart;
981     ierr = PetscMalloc((ai[m]+1)*sizeof(PetscInt),&cols);CHKERRQ(ierr);
982     ct   = cols;
983     for (i=0; i<ai[m]; i++) {cols[i] = aij->garray[aj[i]];}
984     for (i=0; i<m; i++) {
985       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],cols,a,INSERT_VALUES);CHKERRQ(ierr);
986       row++; a += ai[i+1]-ai[i]; cols += ai[i+1]-ai[i];
987     }
988     ierr = PetscFree(ct);CHKERRQ(ierr);
989     ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
990     ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
991     /*
992        Everyone has to call to draw the matrix since the graphics waits are
993        synchronized across all processors that share the PetscDraw object
994     */
995     ierr = PetscViewerGetSingleton(viewer,&sviewer);CHKERRQ(ierr);
996     if (!rank) {
997       ierr = PetscObjectSetName((PetscObject)((Mat_MPIAIJ*)(A->data))->A,mat->name);CHKERRQ(ierr);
998       ierr = MatView(((Mat_MPIAIJ*)(A->data))->A,sviewer);CHKERRQ(ierr);
999     }
1000     ierr = PetscViewerRestoreSingleton(viewer,&sviewer);CHKERRQ(ierr);
1001     ierr = MatDestroy(A);CHKERRQ(ierr);
1002   }
1003   PetscFunctionReturn(0);
1004 }
1005 
1006 #undef __FUNCT__
1007 #define __FUNCT__ "MatView_MPIAIJ"
1008 PetscErrorCode MatView_MPIAIJ(Mat mat,PetscViewer viewer)
1009 {
1010   PetscErrorCode ierr;
1011   PetscTruth     iascii,isdraw,issocket,isbinary;
1012 
1013   PetscFunctionBegin;
1014   ierr  = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&iascii);CHKERRQ(ierr);
1015   ierr  = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_DRAW,&isdraw);CHKERRQ(ierr);
1016   ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_BINARY,&isbinary);CHKERRQ(ierr);
1017   ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_SOCKET,&issocket);CHKERRQ(ierr);
1018   if (iascii || isdraw || isbinary || issocket) {
1019     ierr = MatView_MPIAIJ_ASCIIorDraworSocket(mat,viewer);CHKERRQ(ierr);
1020   } else {
1021     SETERRQ1(1,"Viewer type %s not supported by MPIAIJ matrices",((PetscObject)viewer)->type_name);
1022   }
1023   PetscFunctionReturn(0);
1024 }
1025 
1026 
1027 
1028 #undef __FUNCT__
1029 #define __FUNCT__ "MatRelax_MPIAIJ"
1030 PetscErrorCode MatRelax_MPIAIJ(Mat matin,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
1031 {
1032   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1033   PetscErrorCode ierr;
1034   Vec            bb1;
1035   PetscScalar    mone=-1.0;
1036 
1037   PetscFunctionBegin;
1038   if (its <= 0 || lits <= 0) SETERRQ2(PETSC_ERR_ARG_WRONG,"Relaxation requires global its %d and local its %d both positive",its,lits);
1039 
1040   ierr = VecDuplicate(bb,&bb1);CHKERRQ(ierr);
1041 
1042   if ((flag & SOR_LOCAL_SYMMETRIC_SWEEP) == SOR_LOCAL_SYMMETRIC_SWEEP){
1043     if (flag & SOR_ZERO_INITIAL_GUESS) {
1044       ierr = (*mat->A->ops->relax)(mat->A,bb,omega,flag,fshift,lits,lits,xx);CHKERRQ(ierr);
1045       its--;
1046     }
1047 
1048     while (its--) {
1049       ierr = VecScatterBegin(xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD,mat->Mvctx);CHKERRQ(ierr);
1050       ierr = VecScatterEnd(xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD,mat->Mvctx);CHKERRQ(ierr);
1051 
1052       /* update rhs: bb1 = bb - B*x */
1053       ierr = VecScale(&mone,mat->lvec);CHKERRQ(ierr);
1054       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1055 
1056       /* local sweep */
1057       ierr = (*mat->A->ops->relax)(mat->A,bb1,omega,SOR_SYMMETRIC_SWEEP,fshift,lits,lits,xx);
1058       CHKERRQ(ierr);
1059     }
1060   } else if (flag & SOR_LOCAL_FORWARD_SWEEP){
1061     if (flag & SOR_ZERO_INITIAL_GUESS) {
1062       ierr = (*mat->A->ops->relax)(mat->A,bb,omega,flag,fshift,lits,PETSC_NULL,xx);CHKERRQ(ierr);
1063       its--;
1064     }
1065     while (its--) {
1066       ierr = VecScatterBegin(xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD,mat->Mvctx);CHKERRQ(ierr);
1067       ierr = VecScatterEnd(xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD,mat->Mvctx);CHKERRQ(ierr);
1068 
1069       /* update rhs: bb1 = bb - B*x */
1070       ierr = VecScale(&mone,mat->lvec);CHKERRQ(ierr);
1071       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1072 
1073       /* local sweep */
1074       ierr = (*mat->A->ops->relax)(mat->A,bb1,omega,SOR_FORWARD_SWEEP,fshift,lits,PETSC_NULL,xx);
1075       CHKERRQ(ierr);
1076     }
1077   } else if (flag & SOR_LOCAL_BACKWARD_SWEEP){
1078     if (flag & SOR_ZERO_INITIAL_GUESS) {
1079       ierr = (*mat->A->ops->relax)(mat->A,bb,omega,flag,fshift,lits,PETSC_NULL,xx);CHKERRQ(ierr);
1080       its--;
1081     }
1082     while (its--) {
1083       ierr = VecScatterBegin(xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD,mat->Mvctx);CHKERRQ(ierr);
1084       ierr = VecScatterEnd(xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD,mat->Mvctx);CHKERRQ(ierr);
1085 
1086       /* update rhs: bb1 = bb - B*x */
1087       ierr = VecScale(&mone,mat->lvec);CHKERRQ(ierr);
1088       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1089 
1090       /* local sweep */
1091       ierr = (*mat->A->ops->relax)(mat->A,bb1,omega,SOR_BACKWARD_SWEEP,fshift,lits,PETSC_NULL,xx);
1092       CHKERRQ(ierr);
1093     }
1094   } else {
1095     SETERRQ(PETSC_ERR_SUP,"Parallel SOR not supported");
1096   }
1097 
1098   ierr = VecDestroy(bb1);CHKERRQ(ierr);
1099   PetscFunctionReturn(0);
1100 }
1101 
1102 #undef __FUNCT__
1103 #define __FUNCT__ "MatGetInfo_MPIAIJ"
1104 PetscErrorCode MatGetInfo_MPIAIJ(Mat matin,MatInfoType flag,MatInfo *info)
1105 {
1106   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1107   Mat            A = mat->A,B = mat->B;
1108   PetscErrorCode ierr;
1109   PetscReal      isend[5],irecv[5];
1110 
1111   PetscFunctionBegin;
1112   info->block_size     = 1.0;
1113   ierr = MatGetInfo(A,MAT_LOCAL,info);CHKERRQ(ierr);
1114   isend[0] = info->nz_used; isend[1] = info->nz_allocated; isend[2] = info->nz_unneeded;
1115   isend[3] = info->memory;  isend[4] = info->mallocs;
1116   ierr = MatGetInfo(B,MAT_LOCAL,info);CHKERRQ(ierr);
1117   isend[0] += info->nz_used; isend[1] += info->nz_allocated; isend[2] += info->nz_unneeded;
1118   isend[3] += info->memory;  isend[4] += info->mallocs;
1119   if (flag == MAT_LOCAL) {
1120     info->nz_used      = isend[0];
1121     info->nz_allocated = isend[1];
1122     info->nz_unneeded  = isend[2];
1123     info->memory       = isend[3];
1124     info->mallocs      = isend[4];
1125   } else if (flag == MAT_GLOBAL_MAX) {
1126     ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPI_MAX,matin->comm);CHKERRQ(ierr);
1127     info->nz_used      = irecv[0];
1128     info->nz_allocated = irecv[1];
1129     info->nz_unneeded  = irecv[2];
1130     info->memory       = irecv[3];
1131     info->mallocs      = irecv[4];
1132   } else if (flag == MAT_GLOBAL_SUM) {
1133     ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPI_SUM,matin->comm);CHKERRQ(ierr);
1134     info->nz_used      = irecv[0];
1135     info->nz_allocated = irecv[1];
1136     info->nz_unneeded  = irecv[2];
1137     info->memory       = irecv[3];
1138     info->mallocs      = irecv[4];
1139   }
1140   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
1141   info->fill_ratio_needed = 0;
1142   info->factor_mallocs    = 0;
1143   info->rows_global       = (double)matin->M;
1144   info->columns_global    = (double)matin->N;
1145   info->rows_local        = (double)matin->m;
1146   info->columns_local     = (double)matin->N;
1147 
1148   PetscFunctionReturn(0);
1149 }
1150 
1151 #undef __FUNCT__
1152 #define __FUNCT__ "MatSetOption_MPIAIJ"
1153 PetscErrorCode MatSetOption_MPIAIJ(Mat A,MatOption op)
1154 {
1155   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1156   PetscErrorCode ierr;
1157 
1158   PetscFunctionBegin;
1159   switch (op) {
1160   case MAT_NO_NEW_NONZERO_LOCATIONS:
1161   case MAT_YES_NEW_NONZERO_LOCATIONS:
1162   case MAT_COLUMNS_UNSORTED:
1163   case MAT_COLUMNS_SORTED:
1164   case MAT_NEW_NONZERO_ALLOCATION_ERR:
1165   case MAT_KEEP_ZEROED_ROWS:
1166   case MAT_NEW_NONZERO_LOCATION_ERR:
1167   case MAT_USE_INODES:
1168   case MAT_DO_NOT_USE_INODES:
1169   case MAT_IGNORE_ZERO_ENTRIES:
1170     ierr = MatSetOption(a->A,op);CHKERRQ(ierr);
1171     ierr = MatSetOption(a->B,op);CHKERRQ(ierr);
1172     break;
1173   case MAT_ROW_ORIENTED:
1174     a->roworiented = PETSC_TRUE;
1175     ierr = MatSetOption(a->A,op);CHKERRQ(ierr);
1176     ierr = MatSetOption(a->B,op);CHKERRQ(ierr);
1177     break;
1178   case MAT_ROWS_SORTED:
1179   case MAT_ROWS_UNSORTED:
1180   case MAT_YES_NEW_DIAGONALS:
1181     PetscLogInfo(A,"MatSetOption_MPIAIJ:Option ignored\n");
1182     break;
1183   case MAT_COLUMN_ORIENTED:
1184     a->roworiented = PETSC_FALSE;
1185     ierr = MatSetOption(a->A,op);CHKERRQ(ierr);
1186     ierr = MatSetOption(a->B,op);CHKERRQ(ierr);
1187     break;
1188   case MAT_IGNORE_OFF_PROC_ENTRIES:
1189     a->donotstash = PETSC_TRUE;
1190     break;
1191   case MAT_NO_NEW_DIAGONALS:
1192     SETERRQ(PETSC_ERR_SUP,"MAT_NO_NEW_DIAGONALS");
1193   case MAT_SYMMETRIC:
1194   case MAT_STRUCTURALLY_SYMMETRIC:
1195   case MAT_HERMITIAN:
1196   case MAT_SYMMETRY_ETERNAL:
1197     ierr = MatSetOption(a->A,op);CHKERRQ(ierr);
1198     break;
1199   case MAT_NOT_SYMMETRIC:
1200   case MAT_NOT_STRUCTURALLY_SYMMETRIC:
1201   case MAT_NOT_HERMITIAN:
1202   case MAT_NOT_SYMMETRY_ETERNAL:
1203     break;
1204   default:
1205     SETERRQ(PETSC_ERR_SUP,"unknown option");
1206   }
1207   PetscFunctionReturn(0);
1208 }
1209 
1210 #undef __FUNCT__
1211 #define __FUNCT__ "MatGetRow_MPIAIJ"
1212 PetscErrorCode MatGetRow_MPIAIJ(Mat matin,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1213 {
1214   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1215   PetscScalar    *vworkA,*vworkB,**pvA,**pvB,*v_p;
1216   PetscErrorCode ierr;
1217   PetscInt       i,*cworkA,*cworkB,**pcA,**pcB,cstart = mat->cstart;
1218   PetscInt       nztot,nzA,nzB,lrow,rstart = mat->rstart,rend = mat->rend;
1219   PetscInt       *cmap,*idx_p;
1220 
1221   PetscFunctionBegin;
1222   if (mat->getrowactive == PETSC_TRUE) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Already active");
1223   mat->getrowactive = PETSC_TRUE;
1224 
1225   if (!mat->rowvalues && (idx || v)) {
1226     /*
1227         allocate enough space to hold information from the longest row.
1228     */
1229     Mat_SeqAIJ *Aa = (Mat_SeqAIJ*)mat->A->data,*Ba = (Mat_SeqAIJ*)mat->B->data;
1230     PetscInt     max = 1,tmp;
1231     for (i=0; i<matin->m; i++) {
1232       tmp = Aa->i[i+1] - Aa->i[i] + Ba->i[i+1] - Ba->i[i];
1233       if (max < tmp) { max = tmp; }
1234     }
1235     ierr = PetscMalloc(max*(sizeof(PetscInt)+sizeof(PetscScalar)),&mat->rowvalues);CHKERRQ(ierr);
1236     mat->rowindices = (PetscInt*)(mat->rowvalues + max);
1237   }
1238 
1239   if (row < rstart || row >= rend) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Only local rows")
1240   lrow = row - rstart;
1241 
1242   pvA = &vworkA; pcA = &cworkA; pvB = &vworkB; pcB = &cworkB;
1243   if (!v)   {pvA = 0; pvB = 0;}
1244   if (!idx) {pcA = 0; if (!v) pcB = 0;}
1245   ierr = (*mat->A->ops->getrow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1246   ierr = (*mat->B->ops->getrow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1247   nztot = nzA + nzB;
1248 
1249   cmap  = mat->garray;
1250   if (v  || idx) {
1251     if (nztot) {
1252       /* Sort by increasing column numbers, assuming A and B already sorted */
1253       PetscInt imark = -1;
1254       if (v) {
1255         *v = v_p = mat->rowvalues;
1256         for (i=0; i<nzB; i++) {
1257           if (cmap[cworkB[i]] < cstart)   v_p[i] = vworkB[i];
1258           else break;
1259         }
1260         imark = i;
1261         for (i=0; i<nzA; i++)     v_p[imark+i] = vworkA[i];
1262         for (i=imark; i<nzB; i++) v_p[nzA+i]   = vworkB[i];
1263       }
1264       if (idx) {
1265         *idx = idx_p = mat->rowindices;
1266         if (imark > -1) {
1267           for (i=0; i<imark; i++) {
1268             idx_p[i] = cmap[cworkB[i]];
1269           }
1270         } else {
1271           for (i=0; i<nzB; i++) {
1272             if (cmap[cworkB[i]] < cstart)   idx_p[i] = cmap[cworkB[i]];
1273             else break;
1274           }
1275           imark = i;
1276         }
1277         for (i=0; i<nzA; i++)     idx_p[imark+i] = cstart + cworkA[i];
1278         for (i=imark; i<nzB; i++) idx_p[nzA+i]   = cmap[cworkB[i]];
1279       }
1280     } else {
1281       if (idx) *idx = 0;
1282       if (v)   *v   = 0;
1283     }
1284   }
1285   *nz = nztot;
1286   ierr = (*mat->A->ops->restorerow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1287   ierr = (*mat->B->ops->restorerow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1288   PetscFunctionReturn(0);
1289 }
1290 
1291 #undef __FUNCT__
1292 #define __FUNCT__ "MatRestoreRow_MPIAIJ"
1293 PetscErrorCode MatRestoreRow_MPIAIJ(Mat mat,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1294 {
1295   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1296 
1297   PetscFunctionBegin;
1298   if (aij->getrowactive == PETSC_FALSE) {
1299     SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"MatGetRow not called");
1300   }
1301   aij->getrowactive = PETSC_FALSE;
1302   PetscFunctionReturn(0);
1303 }
1304 
1305 #undef __FUNCT__
1306 #define __FUNCT__ "MatNorm_MPIAIJ"
1307 PetscErrorCode MatNorm_MPIAIJ(Mat mat,NormType type,PetscReal *norm)
1308 {
1309   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1310   Mat_SeqAIJ     *amat = (Mat_SeqAIJ*)aij->A->data,*bmat = (Mat_SeqAIJ*)aij->B->data;
1311   PetscErrorCode ierr;
1312   PetscInt       i,j,cstart = aij->cstart;
1313   PetscReal      sum = 0.0;
1314   PetscScalar    *v;
1315 
1316   PetscFunctionBegin;
1317   if (aij->size == 1) {
1318     ierr =  MatNorm(aij->A,type,norm);CHKERRQ(ierr);
1319   } else {
1320     if (type == NORM_FROBENIUS) {
1321       v = amat->a;
1322       for (i=0; i<amat->nz; i++) {
1323 #if defined(PETSC_USE_COMPLEX)
1324         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1325 #else
1326         sum += (*v)*(*v); v++;
1327 #endif
1328       }
1329       v = bmat->a;
1330       for (i=0; i<bmat->nz; i++) {
1331 #if defined(PETSC_USE_COMPLEX)
1332         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1333 #else
1334         sum += (*v)*(*v); v++;
1335 #endif
1336       }
1337       ierr = MPI_Allreduce(&sum,norm,1,MPIU_REAL,MPI_SUM,mat->comm);CHKERRQ(ierr);
1338       *norm = sqrt(*norm);
1339     } else if (type == NORM_1) { /* max column norm */
1340       PetscReal *tmp,*tmp2;
1341       PetscInt    *jj,*garray = aij->garray;
1342       ierr = PetscMalloc((mat->N+1)*sizeof(PetscReal),&tmp);CHKERRQ(ierr);
1343       ierr = PetscMalloc((mat->N+1)*sizeof(PetscReal),&tmp2);CHKERRQ(ierr);
1344       ierr = PetscMemzero(tmp,mat->N*sizeof(PetscReal));CHKERRQ(ierr);
1345       *norm = 0.0;
1346       v = amat->a; jj = amat->j;
1347       for (j=0; j<amat->nz; j++) {
1348         tmp[cstart + *jj++ ] += PetscAbsScalar(*v);  v++;
1349       }
1350       v = bmat->a; jj = bmat->j;
1351       for (j=0; j<bmat->nz; j++) {
1352         tmp[garray[*jj++]] += PetscAbsScalar(*v); v++;
1353       }
1354       ierr = MPI_Allreduce(tmp,tmp2,mat->N,MPIU_REAL,MPI_SUM,mat->comm);CHKERRQ(ierr);
1355       for (j=0; j<mat->N; j++) {
1356         if (tmp2[j] > *norm) *norm = tmp2[j];
1357       }
1358       ierr = PetscFree(tmp);CHKERRQ(ierr);
1359       ierr = PetscFree(tmp2);CHKERRQ(ierr);
1360     } else if (type == NORM_INFINITY) { /* max row norm */
1361       PetscReal ntemp = 0.0;
1362       for (j=0; j<aij->A->m; j++) {
1363         v = amat->a + amat->i[j];
1364         sum = 0.0;
1365         for (i=0; i<amat->i[j+1]-amat->i[j]; i++) {
1366           sum += PetscAbsScalar(*v); v++;
1367         }
1368         v = bmat->a + bmat->i[j];
1369         for (i=0; i<bmat->i[j+1]-bmat->i[j]; i++) {
1370           sum += PetscAbsScalar(*v); v++;
1371         }
1372         if (sum > ntemp) ntemp = sum;
1373       }
1374       ierr = MPI_Allreduce(&ntemp,norm,1,MPIU_REAL,MPI_MAX,mat->comm);CHKERRQ(ierr);
1375     } else {
1376       SETERRQ(PETSC_ERR_SUP,"No support for two norm");
1377     }
1378   }
1379   PetscFunctionReturn(0);
1380 }
1381 
1382 #undef __FUNCT__
1383 #define __FUNCT__ "MatTranspose_MPIAIJ"
1384 PetscErrorCode MatTranspose_MPIAIJ(Mat A,Mat *matout)
1385 {
1386   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1387   Mat_SeqAIJ     *Aloc = (Mat_SeqAIJ*)a->A->data;
1388   PetscErrorCode ierr;
1389   PetscInt       M = A->M,N = A->N,m,*ai,*aj,row,*cols,i,*ct;
1390   Mat            B;
1391   PetscScalar    *array;
1392 
1393   PetscFunctionBegin;
1394   if (!matout && M != N) {
1395     SETERRQ(PETSC_ERR_ARG_SIZ,"Square matrix only for in-place");
1396   }
1397 
1398   ierr = MatCreate(A->comm,A->n,A->m,N,M,&B);CHKERRQ(ierr);
1399   ierr = MatSetType(B,A->type_name);CHKERRQ(ierr);
1400   ierr = MatMPIAIJSetPreallocation(B,0,PETSC_NULL,0,PETSC_NULL);CHKERRQ(ierr);
1401 
1402   /* copy over the A part */
1403   Aloc = (Mat_SeqAIJ*)a->A->data;
1404   m = a->A->m; ai = Aloc->i; aj = Aloc->j; array = Aloc->a;
1405   row = a->rstart;
1406   for (i=0; i<ai[m]; i++) {aj[i] += a->cstart ;}
1407   for (i=0; i<m; i++) {
1408     ierr = MatSetValues(B,ai[i+1]-ai[i],aj,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
1409     row++; array += ai[i+1]-ai[i]; aj += ai[i+1]-ai[i];
1410   }
1411   aj = Aloc->j;
1412   for (i=0; i<ai[m]; i++) {aj[i] -= a->cstart ;}
1413 
1414   /* copy over the B part */
1415   Aloc = (Mat_SeqAIJ*)a->B->data;
1416   m = a->B->m;  ai = Aloc->i; aj = Aloc->j; array = Aloc->a;
1417   row  = a->rstart;
1418   ierr = PetscMalloc((1+ai[m])*sizeof(PetscInt),&cols);CHKERRQ(ierr);
1419   ct   = cols;
1420   for (i=0; i<ai[m]; i++) {cols[i] = a->garray[aj[i]];}
1421   for (i=0; i<m; i++) {
1422     ierr = MatSetValues(B,ai[i+1]-ai[i],cols,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
1423     row++; array += ai[i+1]-ai[i]; cols += ai[i+1]-ai[i];
1424   }
1425   ierr = PetscFree(ct);CHKERRQ(ierr);
1426   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1427   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1428   if (matout) {
1429     *matout = B;
1430   } else {
1431     ierr = MatHeaderCopy(A,B);CHKERRQ(ierr);
1432   }
1433   PetscFunctionReturn(0);
1434 }
1435 
1436 #undef __FUNCT__
1437 #define __FUNCT__ "MatDiagonalScale_MPIAIJ"
1438 PetscErrorCode MatDiagonalScale_MPIAIJ(Mat mat,Vec ll,Vec rr)
1439 {
1440   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1441   Mat            a = aij->A,b = aij->B;
1442   PetscErrorCode ierr;
1443   PetscInt       s1,s2,s3;
1444 
1445   PetscFunctionBegin;
1446   ierr = MatGetLocalSize(mat,&s2,&s3);CHKERRQ(ierr);
1447   if (rr) {
1448     ierr = VecGetLocalSize(rr,&s1);CHKERRQ(ierr);
1449     if (s1!=s3) SETERRQ(PETSC_ERR_ARG_SIZ,"right vector non-conforming local size");
1450     /* Overlap communication with computation. */
1451     ierr = VecScatterBegin(rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD,aij->Mvctx);CHKERRQ(ierr);
1452   }
1453   if (ll) {
1454     ierr = VecGetLocalSize(ll,&s1);CHKERRQ(ierr);
1455     if (s1!=s2) SETERRQ(PETSC_ERR_ARG_SIZ,"left vector non-conforming local size");
1456     ierr = (*b->ops->diagonalscale)(b,ll,0);CHKERRQ(ierr);
1457   }
1458   /* scale  the diagonal block */
1459   ierr = (*a->ops->diagonalscale)(a,ll,rr);CHKERRQ(ierr);
1460 
1461   if (rr) {
1462     /* Do a scatter end and then right scale the off-diagonal block */
1463     ierr = VecScatterEnd(rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD,aij->Mvctx);CHKERRQ(ierr);
1464     ierr = (*b->ops->diagonalscale)(b,0,aij->lvec);CHKERRQ(ierr);
1465   }
1466 
1467   PetscFunctionReturn(0);
1468 }
1469 
1470 
1471 #undef __FUNCT__
1472 #define __FUNCT__ "MatPrintHelp_MPIAIJ"
1473 PetscErrorCode MatPrintHelp_MPIAIJ(Mat A)
1474 {
1475   Mat_MPIAIJ     *a   = (Mat_MPIAIJ*)A->data;
1476   PetscErrorCode ierr;
1477 
1478   PetscFunctionBegin;
1479   if (!a->rank) {
1480     ierr = MatPrintHelp_SeqAIJ(a->A);CHKERRQ(ierr);
1481   }
1482   PetscFunctionReturn(0);
1483 }
1484 
1485 #undef __FUNCT__
1486 #define __FUNCT__ "MatGetBlockSize_MPIAIJ"
1487 PetscErrorCode MatGetBlockSize_MPIAIJ(Mat A,PetscInt *bs)
1488 {
1489   PetscFunctionBegin;
1490   *bs = 1;
1491   PetscFunctionReturn(0);
1492 }
1493 #undef __FUNCT__
1494 #define __FUNCT__ "MatSetUnfactored_MPIAIJ"
1495 PetscErrorCode MatSetUnfactored_MPIAIJ(Mat A)
1496 {
1497   Mat_MPIAIJ     *a   = (Mat_MPIAIJ*)A->data;
1498   PetscErrorCode ierr;
1499 
1500   PetscFunctionBegin;
1501   ierr = MatSetUnfactored(a->A);CHKERRQ(ierr);
1502   PetscFunctionReturn(0);
1503 }
1504 
1505 #undef __FUNCT__
1506 #define __FUNCT__ "MatEqual_MPIAIJ"
1507 PetscErrorCode MatEqual_MPIAIJ(Mat A,Mat B,PetscTruth *flag)
1508 {
1509   Mat_MPIAIJ     *matB = (Mat_MPIAIJ*)B->data,*matA = (Mat_MPIAIJ*)A->data;
1510   Mat            a,b,c,d;
1511   PetscTruth     flg;
1512   PetscErrorCode ierr;
1513 
1514   PetscFunctionBegin;
1515   a = matA->A; b = matA->B;
1516   c = matB->A; d = matB->B;
1517 
1518   ierr = MatEqual(a,c,&flg);CHKERRQ(ierr);
1519   if (flg == PETSC_TRUE) {
1520     ierr = MatEqual(b,d,&flg);CHKERRQ(ierr);
1521   }
1522   ierr = MPI_Allreduce(&flg,flag,1,MPI_INT,MPI_LAND,A->comm);CHKERRQ(ierr);
1523   PetscFunctionReturn(0);
1524 }
1525 
1526 #undef __FUNCT__
1527 #define __FUNCT__ "MatCopy_MPIAIJ"
1528 PetscErrorCode MatCopy_MPIAIJ(Mat A,Mat B,MatStructure str)
1529 {
1530   PetscErrorCode ierr;
1531   Mat_MPIAIJ     *a = (Mat_MPIAIJ *)A->data;
1532   Mat_MPIAIJ     *b = (Mat_MPIAIJ *)B->data;
1533 
1534   PetscFunctionBegin;
1535   /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
1536   if ((str != SAME_NONZERO_PATTERN) || (A->ops->copy != B->ops->copy)) {
1537     /* because of the column compression in the off-processor part of the matrix a->B,
1538        the number of columns in a->B and b->B may be different, hence we cannot call
1539        the MatCopy() directly on the two parts. If need be, we can provide a more
1540        efficient copy than the MatCopy_Basic() by first uncompressing the a->B matrices
1541        then copying the submatrices */
1542     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
1543   } else {
1544     ierr = MatCopy(a->A,b->A,str);CHKERRQ(ierr);
1545     ierr = MatCopy(a->B,b->B,str);CHKERRQ(ierr);
1546   }
1547   PetscFunctionReturn(0);
1548 }
1549 
1550 #undef __FUNCT__
1551 #define __FUNCT__ "MatSetUpPreallocation_MPIAIJ"
1552 PetscErrorCode MatSetUpPreallocation_MPIAIJ(Mat A)
1553 {
1554   PetscErrorCode ierr;
1555 
1556   PetscFunctionBegin;
1557   ierr =  MatMPIAIJSetPreallocation(A,PETSC_DEFAULT,0,PETSC_DEFAULT,0);CHKERRQ(ierr);
1558   PetscFunctionReturn(0);
1559 }
1560 
1561 #include "petscblaslapack.h"
1562 #undef __FUNCT__
1563 #define __FUNCT__ "MatAXPY_MPIAIJ"
1564 PetscErrorCode MatAXPY_MPIAIJ(const PetscScalar a[],Mat X,Mat Y,MatStructure str)
1565 {
1566   PetscErrorCode ierr;
1567   PetscInt       i;
1568   Mat_MPIAIJ     *xx = (Mat_MPIAIJ *)X->data,*yy = (Mat_MPIAIJ *)Y->data;
1569   PetscBLASInt   bnz,one=1;
1570   Mat_SeqAIJ     *x,*y;
1571 
1572   PetscFunctionBegin;
1573   if (str == SAME_NONZERO_PATTERN) {
1574     x = (Mat_SeqAIJ *)xx->A->data;
1575     y = (Mat_SeqAIJ *)yy->A->data;
1576     bnz = (PetscBLASInt)x->nz;
1577     BLaxpy_(&bnz,(PetscScalar*)a,x->a,&one,y->a,&one);
1578     x = (Mat_SeqAIJ *)xx->B->data;
1579     y = (Mat_SeqAIJ *)yy->B->data;
1580     bnz = (PetscBLASInt)x->nz;
1581     BLaxpy_(&bnz,(PetscScalar*)a,x->a,&one,y->a,&one);
1582   } else if (str == SUBSET_NONZERO_PATTERN) {
1583     ierr = MatAXPY_SeqAIJ(a,xx->A,yy->A,str);CHKERRQ(ierr);
1584 
1585     x = (Mat_SeqAIJ *)xx->B->data;
1586     y = (Mat_SeqAIJ *)yy->B->data;
1587     if (y->xtoy && y->XtoY != xx->B) {
1588       ierr = PetscFree(y->xtoy);CHKERRQ(ierr);
1589       ierr = MatDestroy(y->XtoY);CHKERRQ(ierr);
1590     }
1591     if (!y->xtoy) { /* get xtoy */
1592       ierr = MatAXPYGetxtoy_Private(xx->B->m,x->i,x->j,xx->garray,y->i,y->j,yy->garray,&y->xtoy);CHKERRQ(ierr);
1593       y->XtoY = xx->B;
1594     }
1595     for (i=0; i<x->nz; i++) y->a[y->xtoy[i]] += (*a)*(x->a[i]);
1596   } else {
1597     ierr = MatAXPY_Basic(a,X,Y,str);CHKERRQ(ierr);
1598   }
1599   PetscFunctionReturn(0);
1600 }
1601 
1602 /* -------------------------------------------------------------------*/
1603 static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
1604        MatGetRow_MPIAIJ,
1605        MatRestoreRow_MPIAIJ,
1606        MatMult_MPIAIJ,
1607 /* 4*/ MatMultAdd_MPIAIJ,
1608        MatMultTranspose_MPIAIJ,
1609        MatMultTransposeAdd_MPIAIJ,
1610        0,
1611        0,
1612        0,
1613 /*10*/ 0,
1614        0,
1615        0,
1616        MatRelax_MPIAIJ,
1617        MatTranspose_MPIAIJ,
1618 /*15*/ MatGetInfo_MPIAIJ,
1619        MatEqual_MPIAIJ,
1620        MatGetDiagonal_MPIAIJ,
1621        MatDiagonalScale_MPIAIJ,
1622        MatNorm_MPIAIJ,
1623 /*20*/ MatAssemblyBegin_MPIAIJ,
1624        MatAssemblyEnd_MPIAIJ,
1625        0,
1626        MatSetOption_MPIAIJ,
1627        MatZeroEntries_MPIAIJ,
1628 /*25*/ MatZeroRows_MPIAIJ,
1629 #if !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_SINGLE)
1630        MatLUFactorSymbolic_MPIAIJ_TFS,
1631 #else
1632        0,
1633 #endif
1634        0,
1635        0,
1636        0,
1637 /*30*/ MatSetUpPreallocation_MPIAIJ,
1638        0,
1639        0,
1640        0,
1641        0,
1642 /*35*/ MatDuplicate_MPIAIJ,
1643        0,
1644        0,
1645        0,
1646        0,
1647 /*40*/ MatAXPY_MPIAIJ,
1648        MatGetSubMatrices_MPIAIJ,
1649        MatIncreaseOverlap_MPIAIJ,
1650        MatGetValues_MPIAIJ,
1651        MatCopy_MPIAIJ,
1652 /*45*/ MatPrintHelp_MPIAIJ,
1653        MatScale_MPIAIJ,
1654        0,
1655        0,
1656        0,
1657 /*50*/ MatGetBlockSize_MPIAIJ,
1658        0,
1659        0,
1660        0,
1661        0,
1662 /*55*/ MatFDColoringCreate_MPIAIJ,
1663        0,
1664        MatSetUnfactored_MPIAIJ,
1665        0,
1666        0,
1667 /*60*/ MatGetSubMatrix_MPIAIJ,
1668        MatDestroy_MPIAIJ,
1669        MatView_MPIAIJ,
1670        MatGetPetscMaps_Petsc,
1671        0,
1672 /*65*/ 0,
1673        0,
1674        0,
1675        0,
1676        0,
1677 /*70*/ 0,
1678        0,
1679        MatSetColoring_MPIAIJ,
1680        MatSetValuesAdic_MPIAIJ,
1681        MatSetValuesAdifor_MPIAIJ,
1682 /*75*/ 0,
1683        0,
1684        0,
1685        0,
1686        0,
1687 /*80*/ 0,
1688        0,
1689        0,
1690        0,
1691 /*84*/ MatLoad_MPIAIJ,
1692        0,
1693        0,
1694        0,
1695        0,
1696        0,
1697 /*90*/ MatMatMult_MPIAIJ_MPIAIJ,
1698        MatMatMultSymbolic_MPIAIJ_MPIAIJ,
1699        MatMatMultNumeric_MPIAIJ_MPIAIJ,
1700        MatPtAP_MPIAIJ_MPIAIJ,
1701        MatPtAPSymbolic_MPIAIJ_MPIAIJ,
1702 /*95*/ MatPtAPNumeric_MPIAIJ_MPIAIJ,
1703        0,
1704        0,
1705        0};
1706 
1707 /* ----------------------------------------------------------------------------------------*/
1708 
1709 EXTERN_C_BEGIN
1710 #undef __FUNCT__
1711 #define __FUNCT__ "MatStoreValues_MPIAIJ"
1712 PetscErrorCode MatStoreValues_MPIAIJ(Mat mat)
1713 {
1714   Mat_MPIAIJ     *aij = (Mat_MPIAIJ *)mat->data;
1715   PetscErrorCode ierr;
1716 
1717   PetscFunctionBegin;
1718   ierr = MatStoreValues(aij->A);CHKERRQ(ierr);
1719   ierr = MatStoreValues(aij->B);CHKERRQ(ierr);
1720   PetscFunctionReturn(0);
1721 }
1722 EXTERN_C_END
1723 
1724 EXTERN_C_BEGIN
1725 #undef __FUNCT__
1726 #define __FUNCT__ "MatRetrieveValues_MPIAIJ"
1727 PetscErrorCode MatRetrieveValues_MPIAIJ(Mat mat)
1728 {
1729   Mat_MPIAIJ     *aij = (Mat_MPIAIJ *)mat->data;
1730   PetscErrorCode ierr;
1731 
1732   PetscFunctionBegin;
1733   ierr = MatRetrieveValues(aij->A);CHKERRQ(ierr);
1734   ierr = MatRetrieveValues(aij->B);CHKERRQ(ierr);
1735   PetscFunctionReturn(0);
1736 }
1737 EXTERN_C_END
1738 
1739 #include "petscpc.h"
1740 EXTERN_C_BEGIN
1741 #undef __FUNCT__
1742 #define __FUNCT__ "MatMPIAIJSetPreallocation_MPIAIJ"
1743 PetscErrorCode MatMPIAIJSetPreallocation_MPIAIJ(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
1744 {
1745   Mat_MPIAIJ     *b;
1746   PetscErrorCode ierr;
1747   PetscInt       i;
1748 
1749   PetscFunctionBegin;
1750   B->preallocated = PETSC_TRUE;
1751   if (d_nz == PETSC_DEFAULT || d_nz == PETSC_DECIDE) d_nz = 5;
1752   if (o_nz == PETSC_DEFAULT || o_nz == PETSC_DECIDE) o_nz = 2;
1753   if (d_nz < 0) SETERRQ1(PETSC_ERR_ARG_OUTOFRANGE,"d_nz cannot be less than 0: value %d",d_nz);
1754   if (o_nz < 0) SETERRQ1(PETSC_ERR_ARG_OUTOFRANGE,"o_nz cannot be less than 0: value %d",o_nz);
1755   if (d_nnz) {
1756     for (i=0; i<B->m; i++) {
1757       if (d_nnz[i] < 0) SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"d_nnz cannot be less than 0: local row %d value %d",i,d_nnz[i]);
1758     }
1759   }
1760   if (o_nnz) {
1761     for (i=0; i<B->m; i++) {
1762       if (o_nnz[i] < 0) SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"o_nnz cannot be less than 0: local row %d value %d",i,o_nnz[i]);
1763     }
1764   }
1765   b = (Mat_MPIAIJ*)B->data;
1766   ierr = MatSeqAIJSetPreallocation(b->A,d_nz,d_nnz);CHKERRQ(ierr);
1767   ierr = MatSeqAIJSetPreallocation(b->B,o_nz,o_nnz);CHKERRQ(ierr);
1768 
1769   PetscFunctionReturn(0);
1770 }
1771 EXTERN_C_END
1772 
1773 /*MC
1774    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
1775 
1776    Options Database Keys:
1777 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
1778 
1779   Level: beginner
1780 
1781 .seealso: MatCreateMPIAIJ
1782 M*/
1783 
1784 EXTERN_C_BEGIN
1785 #undef __FUNCT__
1786 #define __FUNCT__ "MatCreate_MPIAIJ"
1787 PetscErrorCode MatCreate_MPIAIJ(Mat B)
1788 {
1789   Mat_MPIAIJ     *b;
1790   PetscErrorCode ierr;
1791   PetscInt       i;
1792   PetscMPIInt    size;
1793 
1794   PetscFunctionBegin;
1795   ierr = MPI_Comm_size(B->comm,&size);CHKERRQ(ierr);
1796 
1797   ierr            = PetscNew(Mat_MPIAIJ,&b);CHKERRQ(ierr);
1798   B->data         = (void*)b;
1799   ierr            = PetscMemzero(b,sizeof(Mat_MPIAIJ));CHKERRQ(ierr);
1800   ierr            = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
1801   B->factor       = 0;
1802   B->assembled    = PETSC_FALSE;
1803   B->mapping      = 0;
1804 
1805   B->insertmode      = NOT_SET_VALUES;
1806   b->size            = size;
1807   ierr = MPI_Comm_rank(B->comm,&b->rank);CHKERRQ(ierr);
1808 
1809   ierr = PetscSplitOwnership(B->comm,&B->m,&B->M);CHKERRQ(ierr);
1810   ierr = PetscSplitOwnership(B->comm,&B->n,&B->N);CHKERRQ(ierr);
1811 
1812   /* the information in the maps duplicates the information computed below, eventually
1813      we should remove the duplicate information that is not contained in the maps */
1814   ierr = PetscMapCreateMPI(B->comm,B->m,B->M,&B->rmap);CHKERRQ(ierr);
1815   ierr = PetscMapCreateMPI(B->comm,B->n,B->N,&B->cmap);CHKERRQ(ierr);
1816 
1817   /* build local table of row and column ownerships */
1818   ierr = PetscMalloc(2*(b->size+2)*sizeof(PetscInt),&b->rowners);CHKERRQ(ierr);
1819   PetscLogObjectMemory(B,2*(b->size+2)*sizeof(PetscInt)+sizeof(struct _p_Mat)+sizeof(Mat_MPIAIJ));
1820   b->cowners = b->rowners + b->size + 2;
1821   ierr = MPI_Allgather(&B->m,1,MPIU_INT,b->rowners+1,1,MPIU_INT,B->comm);CHKERRQ(ierr);
1822   b->rowners[0] = 0;
1823   for (i=2; i<=b->size; i++) {
1824     b->rowners[i] += b->rowners[i-1];
1825   }
1826   b->rstart = b->rowners[b->rank];
1827   b->rend   = b->rowners[b->rank+1];
1828   ierr = MPI_Allgather(&B->n,1,MPIU_INT,b->cowners+1,1,MPIU_INT,B->comm);CHKERRQ(ierr);
1829   b->cowners[0] = 0;
1830   for (i=2; i<=b->size; i++) {
1831     b->cowners[i] += b->cowners[i-1];
1832   }
1833   b->cstart = b->cowners[b->rank];
1834   b->cend   = b->cowners[b->rank+1];
1835 
1836   /* build cache for off array entries formed */
1837   ierr = MatStashCreate_Private(B->comm,1,&B->stash);CHKERRQ(ierr);
1838   b->donotstash  = PETSC_FALSE;
1839   b->colmap      = 0;
1840   b->garray      = 0;
1841   b->roworiented = PETSC_TRUE;
1842 
1843   /* stuff used for matrix vector multiply */
1844   b->lvec      = PETSC_NULL;
1845   b->Mvctx     = PETSC_NULL;
1846 
1847   /* stuff for MatGetRow() */
1848   b->rowindices   = 0;
1849   b->rowvalues    = 0;
1850   b->getrowactive = PETSC_FALSE;
1851 
1852   /* Explicitly create 2 MATSEQAIJ matrices. */
1853   ierr = MatCreate(PETSC_COMM_SELF,B->m,B->n,B->m,B->n,&b->A);CHKERRQ(ierr);
1854   ierr = MatSetType(b->A,MATSEQAIJ);CHKERRQ(ierr);
1855   PetscLogObjectParent(B,b->A);
1856   ierr = MatCreate(PETSC_COMM_SELF,B->m,B->N,B->m,B->N,&b->B);CHKERRQ(ierr);
1857   ierr = MatSetType(b->B,MATSEQAIJ);CHKERRQ(ierr);
1858   PetscLogObjectParent(B,b->B);
1859 
1860   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatStoreValues_C",
1861                                      "MatStoreValues_MPIAIJ",
1862                                      MatStoreValues_MPIAIJ);CHKERRQ(ierr);
1863   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatRetrieveValues_C",
1864                                      "MatRetrieveValues_MPIAIJ",
1865                                      MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
1866   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatGetDiagonalBlock_C",
1867 				     "MatGetDiagonalBlock_MPIAIJ",
1868                                      MatGetDiagonalBlock_MPIAIJ);CHKERRQ(ierr);
1869   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatIsTranspose_C",
1870 				     "MatIsTranspose_MPIAIJ",
1871 				     MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
1872   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatMPIAIJSetPreallocation_C",
1873 				     "MatMPIAIJSetPreallocation_MPIAIJ",
1874 				     MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
1875   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatDiagonalScaleLocal_C",
1876 				     "MatDiagonalScaleLocal_MPIAIJ",
1877 				     MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
1878   PetscFunctionReturn(0);
1879 }
1880 EXTERN_C_END
1881 
1882 /*MC
1883    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.
1884 
1885    This matrix type is identical to MATSEQAIJ when constructed with a single process communicator,
1886    and MATMPIAIJ otherwise.  As a result, for single process communicators,
1887   MatSeqAIJSetPreallocation is supported, and similarly MatMPIAIJSetPreallocation is supported
1888   for communicators controlling multiple processes.  It is recommended that you call both of
1889   the above preallocation routines for simplicity.
1890 
1891    Options Database Keys:
1892 . -mat_type aij - sets the matrix type to "aij" during a call to MatSetFromOptions()
1893 
1894   Level: beginner
1895 
1896 .seealso: MatCreateMPIAIJ,MATSEQAIJ,MATMPIAIJ
1897 M*/
1898 
1899 EXTERN_C_BEGIN
1900 #undef __FUNCT__
1901 #define __FUNCT__ "MatCreate_AIJ"
1902 PetscErrorCode MatCreate_AIJ(Mat A)
1903 {
1904   PetscErrorCode ierr;
1905   PetscMPIInt    size;
1906 
1907   PetscFunctionBegin;
1908   ierr = PetscObjectChangeTypeName((PetscObject)A,MATAIJ);CHKERRQ(ierr);
1909   ierr = MPI_Comm_size(A->comm,&size);CHKERRQ(ierr);
1910   if (size == 1) {
1911     ierr = MatSetType(A,MATSEQAIJ);CHKERRQ(ierr);
1912   } else {
1913     ierr = MatSetType(A,MATMPIAIJ);CHKERRQ(ierr);
1914   }
1915   PetscFunctionReturn(0);
1916 }
1917 EXTERN_C_END
1918 
1919 #undef __FUNCT__
1920 #define __FUNCT__ "MatDuplicate_MPIAIJ"
1921 PetscErrorCode MatDuplicate_MPIAIJ(Mat matin,MatDuplicateOption cpvalues,Mat *newmat)
1922 {
1923   Mat            mat;
1924   Mat_MPIAIJ     *a,*oldmat = (Mat_MPIAIJ*)matin->data;
1925   PetscErrorCode ierr;
1926 
1927   PetscFunctionBegin;
1928   *newmat       = 0;
1929   ierr = MatCreate(matin->comm,matin->m,matin->n,matin->M,matin->N,&mat);CHKERRQ(ierr);
1930   ierr = MatSetType(mat,matin->type_name);CHKERRQ(ierr);
1931   ierr = PetscMemcpy(mat->ops,matin->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
1932   a    = (Mat_MPIAIJ*)mat->data;
1933 
1934   mat->factor       = matin->factor;
1935   mat->assembled    = PETSC_TRUE;
1936   mat->insertmode   = NOT_SET_VALUES;
1937   mat->preallocated = PETSC_TRUE;
1938 
1939   a->rstart       = oldmat->rstart;
1940   a->rend         = oldmat->rend;
1941   a->cstart       = oldmat->cstart;
1942   a->cend         = oldmat->cend;
1943   a->size         = oldmat->size;
1944   a->rank         = oldmat->rank;
1945   a->donotstash   = oldmat->donotstash;
1946   a->roworiented  = oldmat->roworiented;
1947   a->rowindices   = 0;
1948   a->rowvalues    = 0;
1949   a->getrowactive = PETSC_FALSE;
1950 
1951   ierr       = PetscMemcpy(a->rowners,oldmat->rowners,2*(a->size+2)*sizeof(PetscInt));CHKERRQ(ierr);
1952   ierr       = MatStashCreate_Private(matin->comm,1,&mat->stash);CHKERRQ(ierr);
1953   if (oldmat->colmap) {
1954 #if defined (PETSC_USE_CTABLE)
1955     ierr = PetscTableCreateCopy(oldmat->colmap,&a->colmap);CHKERRQ(ierr);
1956 #else
1957     ierr = PetscMalloc((mat->N)*sizeof(PetscInt),&a->colmap);CHKERRQ(ierr);
1958     PetscLogObjectMemory(mat,(mat->N)*sizeof(PetscInt));
1959     ierr      = PetscMemcpy(a->colmap,oldmat->colmap,(mat->N)*sizeof(PetscInt));CHKERRQ(ierr);
1960 #endif
1961   } else a->colmap = 0;
1962   if (oldmat->garray) {
1963     PetscInt len;
1964     len  = oldmat->B->n;
1965     ierr = PetscMalloc((len+1)*sizeof(PetscInt),&a->garray);CHKERRQ(ierr);
1966     PetscLogObjectMemory(mat,len*sizeof(PetscInt));
1967     if (len) { ierr = PetscMemcpy(a->garray,oldmat->garray,len*sizeof(PetscInt));CHKERRQ(ierr); }
1968   } else a->garray = 0;
1969 
1970   ierr =  VecDuplicate(oldmat->lvec,&a->lvec);CHKERRQ(ierr);
1971   PetscLogObjectParent(mat,a->lvec);
1972   ierr =  VecScatterCopy(oldmat->Mvctx,&a->Mvctx);CHKERRQ(ierr);
1973   PetscLogObjectParent(mat,a->Mvctx);
1974   ierr =  MatDestroy(a->A);CHKERRQ(ierr);
1975   ierr =  MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
1976   PetscLogObjectParent(mat,a->A);
1977   ierr =  MatDestroy(a->B);CHKERRQ(ierr);
1978   ierr =  MatDuplicate(oldmat->B,cpvalues,&a->B);CHKERRQ(ierr);
1979   PetscLogObjectParent(mat,a->B);
1980   ierr = PetscFListDuplicate(matin->qlist,&mat->qlist);CHKERRQ(ierr);
1981   *newmat = mat;
1982   PetscFunctionReturn(0);
1983 }
1984 
1985 #include "petscsys.h"
1986 
1987 #undef __FUNCT__
1988 #define __FUNCT__ "MatLoad_MPIAIJ"
1989 PetscErrorCode MatLoad_MPIAIJ(PetscViewer viewer,const MatType type,Mat *newmat)
1990 {
1991   Mat            A;
1992   PetscScalar    *vals,*svals;
1993   MPI_Comm       comm = ((PetscObject)viewer)->comm;
1994   MPI_Status     status;
1995   PetscErrorCode ierr;
1996   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag,*sndcounts = 0,*rowners,maxnz;
1997   PetscInt       i,nz,j,rstart,rend;
1998   PetscInt       header[4],*rowlengths = 0,M,N,m,*cols;
1999   PetscInt       *ourlens,*procsnz = 0,*offlens,jj,*mycols,*smycols;
2000   PetscInt       cend,cstart,n;
2001   int            fd;
2002 
2003   PetscFunctionBegin;
2004   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2005   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2006   if (!rank) {
2007     ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
2008     ierr = PetscBinaryRead(fd,(char *)header,4,PETSC_INT);CHKERRQ(ierr);
2009     if (header[0] != MAT_FILE_COOKIE) SETERRQ(PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
2010     if (header[3] < 0) {
2011       SETERRQ(PETSC_ERR_FILE_UNEXPECTED,"Matrix in special format on disk, cannot load as MPIAIJ");
2012     }
2013   }
2014 
2015   ierr = MPI_Bcast(header+1,3,MPIU_INT,0,comm);CHKERRQ(ierr);
2016   M = header[1]; N = header[2];
2017   /* determine ownership of all rows */
2018   m = M/size + ((M % size) > rank);
2019   ierr = PetscMalloc((size+2)*sizeof(PetscInt),&rowners);CHKERRQ(ierr);
2020   ierr = MPI_Allgather(&m,1,MPI_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
2021   rowners[0] = 0;
2022   for (i=2; i<=size; i++) {
2023     rowners[i] += rowners[i-1];
2024   }
2025   rstart = rowners[rank];
2026   rend   = rowners[rank+1];
2027 
2028   /* distribute row lengths to all processors */
2029   ierr    = PetscMalloc(2*(rend-rstart+1)*sizeof(PetscInt),&ourlens);CHKERRQ(ierr);
2030   offlens = ourlens + (rend-rstart);
2031   if (!rank) {
2032     ierr = PetscMalloc(M*sizeof(PetscInt),&rowlengths);CHKERRQ(ierr);
2033     ierr = PetscBinaryRead(fd,rowlengths,M,PETSC_INT);CHKERRQ(ierr);
2034     ierr = PetscMalloc(size*sizeof(PetscMPIInt),&sndcounts);CHKERRQ(ierr);
2035     for (i=0; i<size; i++) sndcounts[i] = rowners[i+1] - rowners[i];
2036     ierr = MPI_Scatterv(rowlengths,sndcounts,rowners,MPIU_INT,ourlens,rend-rstart,MPIU_INT,0,comm);CHKERRQ(ierr);
2037     ierr = PetscFree(sndcounts);CHKERRQ(ierr);
2038   } else {
2039     ierr = MPI_Scatterv(0,0,0,MPIU_INT,ourlens,rend-rstart,MPIU_INT,0,comm);CHKERRQ(ierr);
2040   }
2041 
2042   if (!rank) {
2043     /* calculate the number of nonzeros on each processor */
2044     ierr = PetscMalloc(size*sizeof(PetscInt),&procsnz);CHKERRQ(ierr);
2045     ierr = PetscMemzero(procsnz,size*sizeof(PetscInt));CHKERRQ(ierr);
2046     for (i=0; i<size; i++) {
2047       for (j=rowners[i]; j< rowners[i+1]; j++) {
2048         procsnz[i] += rowlengths[j];
2049       }
2050     }
2051     ierr = PetscFree(rowlengths);CHKERRQ(ierr);
2052 
2053     /* determine max buffer needed and allocate it */
2054     maxnz = 0;
2055     for (i=0; i<size; i++) {
2056       maxnz = PetscMax(maxnz,procsnz[i]);
2057     }
2058     ierr = PetscMalloc(maxnz*sizeof(PetscInt),&cols);CHKERRQ(ierr);
2059 
2060     /* read in my part of the matrix column indices  */
2061     nz   = procsnz[0];
2062     ierr = PetscMalloc(nz*sizeof(PetscInt),&mycols);CHKERRQ(ierr);
2063     ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);
2064 
2065     /* read in every one elses and ship off */
2066     for (i=1; i<size; i++) {
2067       nz   = procsnz[i];
2068       ierr = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
2069       ierr = MPI_Send(cols,nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2070     }
2071     ierr = PetscFree(cols);CHKERRQ(ierr);
2072   } else {
2073     /* determine buffer space needed for message */
2074     nz = 0;
2075     for (i=0; i<m; i++) {
2076       nz += ourlens[i];
2077     }
2078     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&mycols);CHKERRQ(ierr);
2079 
2080     /* receive message of column indices*/
2081     ierr = MPI_Recv(mycols,nz,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
2082     ierr = MPI_Get_count(&status,MPIU_INT,&maxnz);CHKERRQ(ierr);
2083     if (maxnz != nz) SETERRQ(PETSC_ERR_FILE_UNEXPECTED,"something is wrong with file");
2084   }
2085 
2086   /* determine column ownership if matrix is not square */
2087   if (N != M) {
2088     n      = N/size + ((N % size) > rank);
2089     ierr   = MPI_Scan(&n,&cend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
2090     cstart = cend - n;
2091   } else {
2092     cstart = rstart;
2093     cend   = rend;
2094     n      = cend - cstart;
2095   }
2096 
2097   /* loop over local rows, determining number of off diagonal entries */
2098   ierr = PetscMemzero(offlens,m*sizeof(PetscInt));CHKERRQ(ierr);
2099   jj = 0;
2100   for (i=0; i<m; i++) {
2101     for (j=0; j<ourlens[i]; j++) {
2102       if (mycols[jj] < cstart || mycols[jj] >= cend) offlens[i]++;
2103       jj++;
2104     }
2105   }
2106 
2107   /* create our matrix */
2108   for (i=0; i<m; i++) {
2109     ourlens[i] -= offlens[i];
2110   }
2111   ierr = MatCreate(comm,m,n,M,N,&A);CHKERRQ(ierr);
2112   ierr = MatSetType(A,type);CHKERRQ(ierr);
2113   ierr = MatMPIAIJSetPreallocation(A,0,ourlens,0,offlens);CHKERRQ(ierr);
2114 
2115   ierr = MatSetOption(A,MAT_COLUMNS_SORTED);CHKERRQ(ierr);
2116   for (i=0; i<m; i++) {
2117     ourlens[i] += offlens[i];
2118   }
2119 
2120   if (!rank) {
2121     ierr = PetscMalloc(maxnz*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
2122 
2123     /* read in my part of the matrix numerical values  */
2124     nz   = procsnz[0];
2125     ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
2126 
2127     /* insert into matrix */
2128     jj      = rstart;
2129     smycols = mycols;
2130     svals   = vals;
2131     for (i=0; i<m; i++) {
2132       ierr = MatSetValues(A,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
2133       smycols += ourlens[i];
2134       svals   += ourlens[i];
2135       jj++;
2136     }
2137 
2138     /* read in other processors and ship out */
2139     for (i=1; i<size; i++) {
2140       nz   = procsnz[i];
2141       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
2142       ierr = MPI_Send(vals,nz,MPIU_SCALAR,i,A->tag,comm);CHKERRQ(ierr);
2143     }
2144     ierr = PetscFree(procsnz);CHKERRQ(ierr);
2145   } else {
2146     /* receive numeric values */
2147     ierr = PetscMalloc((nz+1)*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
2148 
2149     /* receive message of values*/
2150     ierr = MPI_Recv(vals,nz,MPIU_SCALAR,0,A->tag,comm,&status);CHKERRQ(ierr);
2151     ierr = MPI_Get_count(&status,MPIU_SCALAR,&maxnz);CHKERRQ(ierr);
2152     if (maxnz != nz) SETERRQ(PETSC_ERR_FILE_UNEXPECTED,"something is wrong with file");
2153 
2154     /* insert into matrix */
2155     jj      = rstart;
2156     smycols = mycols;
2157     svals   = vals;
2158     for (i=0; i<m; i++) {
2159       ierr     = MatSetValues(A,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
2160       smycols += ourlens[i];
2161       svals   += ourlens[i];
2162       jj++;
2163     }
2164   }
2165   ierr = PetscFree(ourlens);CHKERRQ(ierr);
2166   ierr = PetscFree(vals);CHKERRQ(ierr);
2167   ierr = PetscFree(mycols);CHKERRQ(ierr);
2168   ierr = PetscFree(rowners);CHKERRQ(ierr);
2169 
2170   ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2171   ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2172   *newmat = A;
2173   PetscFunctionReturn(0);
2174 }
2175 
2176 #undef __FUNCT__
2177 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ"
2178 /*
2179     Not great since it makes two copies of the submatrix, first an SeqAIJ
2180   in local and then by concatenating the local matrices the end result.
2181   Writing it directly would be much like MatGetSubMatrices_MPIAIJ()
2182 */
2183 PetscErrorCode MatGetSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
2184 {
2185   PetscErrorCode ierr;
2186   PetscMPIInt    rank,size;
2187   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j;
2188   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
2189   Mat            *local,M,Mreuse;
2190   PetscScalar    *vwork,*aa;
2191   MPI_Comm       comm = mat->comm;
2192   Mat_SeqAIJ     *aij;
2193 
2194 
2195   PetscFunctionBegin;
2196   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2197   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2198 
2199   if (call ==  MAT_REUSE_MATRIX) {
2200     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject *)&Mreuse);CHKERRQ(ierr);
2201     if (!Mreuse) SETERRQ(1,"Submatrix passed in was not used before, cannot reuse");
2202     local = &Mreuse;
2203     ierr  = MatGetSubMatrices(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,&local);CHKERRQ(ierr);
2204   } else {
2205     ierr   = MatGetSubMatrices(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&local);CHKERRQ(ierr);
2206     Mreuse = *local;
2207     ierr   = PetscFree(local);CHKERRQ(ierr);
2208   }
2209 
2210   /*
2211       m - number of local rows
2212       n - number of columns (same on all processors)
2213       rstart - first row in new global matrix generated
2214   */
2215   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
2216   if (call == MAT_INITIAL_MATRIX) {
2217     aij = (Mat_SeqAIJ*)(Mreuse)->data;
2218     ii  = aij->i;
2219     jj  = aij->j;
2220 
2221     /*
2222         Determine the number of non-zeros in the diagonal and off-diagonal
2223         portions of the matrix in order to do correct preallocation
2224     */
2225 
2226     /* first get start and end of "diagonal" columns */
2227     if (csize == PETSC_DECIDE) {
2228       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
2229       if (mglobal == n) { /* square matrix */
2230 	nlocal = m;
2231       } else {
2232         nlocal = n/size + ((n % size) > rank);
2233       }
2234     } else {
2235       nlocal = csize;
2236     }
2237     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
2238     rstart = rend - nlocal;
2239     if (rank == size - 1 && rend != n) {
2240       SETERRQ2(1,"Local column sizes %d do not add up to total number of columns %d",rend,n);
2241     }
2242 
2243     /* next, compute all the lengths */
2244     ierr  = PetscMalloc((2*m+1)*sizeof(PetscInt),&dlens);CHKERRQ(ierr);
2245     olens = dlens + m;
2246     for (i=0; i<m; i++) {
2247       jend = ii[i+1] - ii[i];
2248       olen = 0;
2249       dlen = 0;
2250       for (j=0; j<jend; j++) {
2251         if (*jj < rstart || *jj >= rend) olen++;
2252         else dlen++;
2253         jj++;
2254       }
2255       olens[i] = olen;
2256       dlens[i] = dlen;
2257     }
2258     ierr = MatCreate(comm,m,nlocal,PETSC_DECIDE,n,&M);CHKERRQ(ierr);
2259     ierr = MatSetType(M,mat->type_name);CHKERRQ(ierr);
2260     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
2261     ierr = PetscFree(dlens);CHKERRQ(ierr);
2262   } else {
2263     PetscInt ml,nl;
2264 
2265     M = *newmat;
2266     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
2267     if (ml != m) SETERRQ(PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
2268     ierr = MatZeroEntries(M);CHKERRQ(ierr);
2269     /*
2270          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
2271        rather than the slower MatSetValues().
2272     */
2273     M->was_assembled = PETSC_TRUE;
2274     M->assembled     = PETSC_FALSE;
2275   }
2276   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
2277   aij = (Mat_SeqAIJ*)(Mreuse)->data;
2278   ii  = aij->i;
2279   jj  = aij->j;
2280   aa  = aij->a;
2281   for (i=0; i<m; i++) {
2282     row   = rstart + i;
2283     nz    = ii[i+1] - ii[i];
2284     cwork = jj;     jj += nz;
2285     vwork = aa;     aa += nz;
2286     ierr = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
2287   }
2288 
2289   ierr = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2290   ierr = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2291   *newmat = M;
2292 
2293   /* save submatrix used in processor for next request */
2294   if (call ==  MAT_INITIAL_MATRIX) {
2295     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
2296     ierr = PetscObjectDereference((PetscObject)Mreuse);CHKERRQ(ierr);
2297   }
2298 
2299   PetscFunctionReturn(0);
2300 }
2301 
2302 #undef __FUNCT__
2303 #define __FUNCT__ "MatMPIAIJSetPreallocation"
2304 /*@C
2305    MatMPIAIJSetPreallocation - Creates a sparse parallel matrix in AIJ format
2306    (the default parallel PETSc format).  For good matrix assembly performance
2307    the user should preallocate the matrix storage by setting the parameters
2308    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
2309    performance can be increased by more than a factor of 50.
2310 
2311    Collective on MPI_Comm
2312 
2313    Input Parameters:
2314 +  A - the matrix
2315 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
2316            (same value is used for all local rows)
2317 .  d_nnz - array containing the number of nonzeros in the various rows of the
2318            DIAGONAL portion of the local submatrix (possibly different for each row)
2319            or PETSC_NULL, if d_nz is used to specify the nonzero structure.
2320            The size of this array is equal to the number of local rows, i.e 'm'.
2321            You must leave room for the diagonal entry even if it is zero.
2322 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
2323            submatrix (same value is used for all local rows).
2324 -  o_nnz - array containing the number of nonzeros in the various rows of the
2325            OFF-DIAGONAL portion of the local submatrix (possibly different for
2326            each row) or PETSC_NULL, if o_nz is used to specify the nonzero
2327            structure. The size of this array is equal to the number
2328            of local rows, i.e 'm'.
2329 
2330    The AIJ format (also called the Yale sparse matrix format or
2331    compressed row storage), is fully compatible with standard Fortran 77
2332    storage.  That is, the stored row and column indices can begin at
2333    either one (as in Fortran) or zero.  See the users manual for details.
2334 
2335    The user MUST specify either the local or global matrix dimensions
2336    (possibly both).
2337 
2338    The parallel matrix is partitioned such that the first m0 rows belong to
2339    process 0, the next m1 rows belong to process 1, the next m2 rows belong
2340    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
2341 
2342    The DIAGONAL portion of the local submatrix of a processor can be defined
2343    as the submatrix which is obtained by extraction the part corresponding
2344    to the rows r1-r2 and columns r1-r2 of the global matrix, where r1 is the
2345    first row that belongs to the processor, and r2 is the last row belonging
2346    to the this processor. This is a square mxm matrix. The remaining portion
2347    of the local submatrix (mxN) constitute the OFF-DIAGONAL portion.
2348 
2349    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
2350 
2351    By default, this format uses inodes (identical nodes) when possible.
2352    We search for consecutive rows with the same nonzero structure, thereby
2353    reusing matrix information to achieve increased efficiency.
2354 
2355    Options Database Keys:
2356 +  -mat_aij_no_inode  - Do not use inodes
2357 .  -mat_aij_inode_limit <limit> - Sets inode limit (max limit=5)
2358 -  -mat_aij_oneindex - Internally use indexing starting at 1
2359         rather than 0.  Note that when calling MatSetValues(),
2360         the user still MUST index entries starting at 0!
2361 
2362    Example usage:
2363 
2364    Consider the following 8x8 matrix with 34 non-zero values, that is
2365    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
2366    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
2367    as follows:
2368 
2369 .vb
2370             1  2  0  |  0  3  0  |  0  4
2371     Proc0   0  5  6  |  7  0  0  |  8  0
2372             9  0 10  | 11  0  0  | 12  0
2373     -------------------------------------
2374            13  0 14  | 15 16 17  |  0  0
2375     Proc1   0 18  0  | 19 20 21  |  0  0
2376             0  0  0  | 22 23  0  | 24  0
2377     -------------------------------------
2378     Proc2  25 26 27  |  0  0 28  | 29  0
2379            30  0  0  | 31 32 33  |  0 34
2380 .ve
2381 
2382    This can be represented as a collection of submatrices as:
2383 
2384 .vb
2385       A B C
2386       D E F
2387       G H I
2388 .ve
2389 
2390    Where the submatrices A,B,C are owned by proc0, D,E,F are
2391    owned by proc1, G,H,I are owned by proc2.
2392 
2393    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
2394    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
2395    The 'M','N' parameters are 8,8, and have the same values on all procs.
2396 
2397    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
2398    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
2399    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
2400    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
2401    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
2402    matrix, ans [DF] as another SeqAIJ matrix.
2403 
2404    When d_nz, o_nz parameters are specified, d_nz storage elements are
2405    allocated for every row of the local diagonal submatrix, and o_nz
2406    storage locations are allocated for every row of the OFF-DIAGONAL submat.
2407    One way to choose d_nz and o_nz is to use the max nonzerors per local
2408    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
2409    In this case, the values of d_nz,o_nz are:
2410 .vb
2411      proc0 : dnz = 2, o_nz = 2
2412      proc1 : dnz = 3, o_nz = 2
2413      proc2 : dnz = 1, o_nz = 4
2414 .ve
2415    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
2416    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
2417    for proc3. i.e we are using 12+15+10=37 storage locations to store
2418    34 values.
2419 
2420    When d_nnz, o_nnz parameters are specified, the storage is specified
2421    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
2422    In the above case the values for d_nnz,o_nnz are:
2423 .vb
2424      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
2425      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
2426      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
2427 .ve
2428    Here the space allocated is sum of all the above values i.e 34, and
2429    hence pre-allocation is perfect.
2430 
2431    Level: intermediate
2432 
2433 .keywords: matrix, aij, compressed row, sparse, parallel
2434 
2435 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues()
2436 @*/
2437 PetscErrorCode MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
2438 {
2439   PetscErrorCode ierr,(*f)(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]);
2440 
2441   PetscFunctionBegin;
2442   ierr = PetscObjectQueryFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",(void (**)(void))&f);CHKERRQ(ierr);
2443   if (f) {
2444     ierr = (*f)(B,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
2445   }
2446   PetscFunctionReturn(0);
2447 }
2448 
2449 #undef __FUNCT__
2450 #define __FUNCT__ "MatCreateMPIAIJ"
2451 /*@C
2452    MatCreateMPIAIJ - Creates a sparse parallel matrix in AIJ format
2453    (the default parallel PETSc format).  For good matrix assembly performance
2454    the user should preallocate the matrix storage by setting the parameters
2455    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
2456    performance can be increased by more than a factor of 50.
2457 
2458    Collective on MPI_Comm
2459 
2460    Input Parameters:
2461 +  comm - MPI communicator
2462 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
2463            This value should be the same as the local size used in creating the
2464            y vector for the matrix-vector product y = Ax.
2465 .  n - This value should be the same as the local size used in creating the
2466        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
2467        calculated if N is given) For square matrices n is almost always m.
2468 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
2469 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
2470 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
2471            (same value is used for all local rows)
2472 .  d_nnz - array containing the number of nonzeros in the various rows of the
2473            DIAGONAL portion of the local submatrix (possibly different for each row)
2474            or PETSC_NULL, if d_nz is used to specify the nonzero structure.
2475            The size of this array is equal to the number of local rows, i.e 'm'.
2476            You must leave room for the diagonal entry even if it is zero.
2477 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
2478            submatrix (same value is used for all local rows).
2479 -  o_nnz - array containing the number of nonzeros in the various rows of the
2480            OFF-DIAGONAL portion of the local submatrix (possibly different for
2481            each row) or PETSC_NULL, if o_nz is used to specify the nonzero
2482            structure. The size of this array is equal to the number
2483            of local rows, i.e 'm'.
2484 
2485    Output Parameter:
2486 .  A - the matrix
2487 
2488    Notes:
2489    m,n,M,N parameters specify the size of the matrix, and its partitioning across
2490    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
2491    storage requirements for this matrix.
2492 
2493    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
2494    processor than it must be used on all processors that share the object for
2495    that argument.
2496 
2497    The AIJ format (also called the Yale sparse matrix format or
2498    compressed row storage), is fully compatible with standard Fortran 77
2499    storage.  That is, the stored row and column indices can begin at
2500    either one (as in Fortran) or zero.  See the users manual for details.
2501 
2502    The user MUST specify either the local or global matrix dimensions
2503    (possibly both).
2504 
2505    The parallel matrix is partitioned such that the first m0 rows belong to
2506    process 0, the next m1 rows belong to process 1, the next m2 rows belong
2507    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
2508 
2509    The DIAGONAL portion of the local submatrix of a processor can be defined
2510    as the submatrix which is obtained by extraction the part corresponding
2511    to the rows r1-r2 and columns r1-r2 of the global matrix, where r1 is the
2512    first row that belongs to the processor, and r2 is the last row belonging
2513    to the this processor. This is a square mxm matrix. The remaining portion
2514    of the local submatrix (mxN) constitute the OFF-DIAGONAL portion.
2515 
2516    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
2517 
2518    When calling this routine with a single process communicator, a matrix of
2519    type SEQAIJ is returned.  If a matrix of type MPIAIJ is desired for this
2520    type of communicator, use the construction mechanism:
2521      MatCreate(...,&A); MatSetType(A,MPIAIJ); MatMPIAIJSetPreallocation(A,...);
2522 
2523    By default, this format uses inodes (identical nodes) when possible.
2524    We search for consecutive rows with the same nonzero structure, thereby
2525    reusing matrix information to achieve increased efficiency.
2526 
2527    Options Database Keys:
2528 +  -mat_aij_no_inode  - Do not use inodes
2529 .  -mat_aij_inode_limit <limit> - Sets inode limit (max limit=5)
2530 -  -mat_aij_oneindex - Internally use indexing starting at 1
2531         rather than 0.  Note that when calling MatSetValues(),
2532         the user still MUST index entries starting at 0!
2533 
2534 
2535    Example usage:
2536 
2537    Consider the following 8x8 matrix with 34 non-zero values, that is
2538    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
2539    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
2540    as follows:
2541 
2542 .vb
2543             1  2  0  |  0  3  0  |  0  4
2544     Proc0   0  5  6  |  7  0  0  |  8  0
2545             9  0 10  | 11  0  0  | 12  0
2546     -------------------------------------
2547            13  0 14  | 15 16 17  |  0  0
2548     Proc1   0 18  0  | 19 20 21  |  0  0
2549             0  0  0  | 22 23  0  | 24  0
2550     -------------------------------------
2551     Proc2  25 26 27  |  0  0 28  | 29  0
2552            30  0  0  | 31 32 33  |  0 34
2553 .ve
2554 
2555    This can be represented as a collection of submatrices as:
2556 
2557 .vb
2558       A B C
2559       D E F
2560       G H I
2561 .ve
2562 
2563    Where the submatrices A,B,C are owned by proc0, D,E,F are
2564    owned by proc1, G,H,I are owned by proc2.
2565 
2566    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
2567    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
2568    The 'M','N' parameters are 8,8, and have the same values on all procs.
2569 
2570    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
2571    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
2572    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
2573    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
2574    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
2575    matrix, ans [DF] as another SeqAIJ matrix.
2576 
2577    When d_nz, o_nz parameters are specified, d_nz storage elements are
2578    allocated for every row of the local diagonal submatrix, and o_nz
2579    storage locations are allocated for every row of the OFF-DIAGONAL submat.
2580    One way to choose d_nz and o_nz is to use the max nonzerors per local
2581    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
2582    In this case, the values of d_nz,o_nz are:
2583 .vb
2584      proc0 : dnz = 2, o_nz = 2
2585      proc1 : dnz = 3, o_nz = 2
2586      proc2 : dnz = 1, o_nz = 4
2587 .ve
2588    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
2589    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
2590    for proc3. i.e we are using 12+15+10=37 storage locations to store
2591    34 values.
2592 
2593    When d_nnz, o_nnz parameters are specified, the storage is specified
2594    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
2595    In the above case the values for d_nnz,o_nnz are:
2596 .vb
2597      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
2598      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
2599      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
2600 .ve
2601    Here the space allocated is sum of all the above values i.e 34, and
2602    hence pre-allocation is perfect.
2603 
2604    Level: intermediate
2605 
2606 .keywords: matrix, aij, compressed row, sparse, parallel
2607 
2608 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues()
2609 @*/
2610 PetscErrorCode MatCreateMPIAIJ(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)
2611 {
2612   PetscErrorCode ierr;
2613   PetscMPIInt    size;
2614 
2615   PetscFunctionBegin;
2616   ierr = MatCreate(comm,m,n,M,N,A);CHKERRQ(ierr);
2617   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2618   if (size > 1) {
2619     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
2620     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
2621   } else {
2622     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
2623     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
2624   }
2625   PetscFunctionReturn(0);
2626 }
2627 
2628 #undef __FUNCT__
2629 #define __FUNCT__ "MatMPIAIJGetSeqAIJ"
2630 PetscErrorCode MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,PetscInt *colmap[])
2631 {
2632   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
2633 
2634   PetscFunctionBegin;
2635   *Ad     = a->A;
2636   *Ao     = a->B;
2637   *colmap = a->garray;
2638   PetscFunctionReturn(0);
2639 }
2640 
2641 #undef __FUNCT__
2642 #define __FUNCT__ "MatSetColoring_MPIAIJ"
2643 PetscErrorCode MatSetColoring_MPIAIJ(Mat A,ISColoring coloring)
2644 {
2645   PetscErrorCode ierr;
2646   PetscInt       i;
2647   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2648 
2649   PetscFunctionBegin;
2650   if (coloring->ctype == IS_COLORING_LOCAL) {
2651     ISColoringValue *allcolors,*colors;
2652     ISColoring      ocoloring;
2653 
2654     /* set coloring for diagonal portion */
2655     ierr = MatSetColoring_SeqAIJ(a->A,coloring);CHKERRQ(ierr);
2656 
2657     /* set coloring for off-diagonal portion */
2658     ierr = ISAllGatherColors(A->comm,coloring->n,coloring->colors,PETSC_NULL,&allcolors);CHKERRQ(ierr);
2659     ierr = PetscMalloc((a->B->n+1)*sizeof(ISColoringValue),&colors);CHKERRQ(ierr);
2660     for (i=0; i<a->B->n; i++) {
2661       colors[i] = allcolors[a->garray[i]];
2662     }
2663     ierr = PetscFree(allcolors);CHKERRQ(ierr);
2664     ierr = ISColoringCreate(MPI_COMM_SELF,a->B->n,colors,&ocoloring);CHKERRQ(ierr);
2665     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
2666     ierr = ISColoringDestroy(ocoloring);CHKERRQ(ierr);
2667   } else if (coloring->ctype == IS_COLORING_GHOSTED) {
2668     ISColoringValue *colors;
2669     PetscInt             *larray;
2670     ISColoring      ocoloring;
2671 
2672     /* set coloring for diagonal portion */
2673     ierr = PetscMalloc((a->A->n+1)*sizeof(PetscInt),&larray);CHKERRQ(ierr);
2674     for (i=0; i<a->A->n; i++) {
2675       larray[i] = i + a->cstart;
2676     }
2677     ierr = ISGlobalToLocalMappingApply(A->mapping,IS_GTOLM_MASK,a->A->n,larray,PETSC_NULL,larray);CHKERRQ(ierr);
2678     ierr = PetscMalloc((a->A->n+1)*sizeof(ISColoringValue),&colors);CHKERRQ(ierr);
2679     for (i=0; i<a->A->n; i++) {
2680       colors[i] = coloring->colors[larray[i]];
2681     }
2682     ierr = PetscFree(larray);CHKERRQ(ierr);
2683     ierr = ISColoringCreate(PETSC_COMM_SELF,a->A->n,colors,&ocoloring);CHKERRQ(ierr);
2684     ierr = MatSetColoring_SeqAIJ(a->A,ocoloring);CHKERRQ(ierr);
2685     ierr = ISColoringDestroy(ocoloring);CHKERRQ(ierr);
2686 
2687     /* set coloring for off-diagonal portion */
2688     ierr = PetscMalloc((a->B->n+1)*sizeof(PetscInt),&larray);CHKERRQ(ierr);
2689     ierr = ISGlobalToLocalMappingApply(A->mapping,IS_GTOLM_MASK,a->B->n,a->garray,PETSC_NULL,larray);CHKERRQ(ierr);
2690     ierr = PetscMalloc((a->B->n+1)*sizeof(ISColoringValue),&colors);CHKERRQ(ierr);
2691     for (i=0; i<a->B->n; i++) {
2692       colors[i] = coloring->colors[larray[i]];
2693     }
2694     ierr = PetscFree(larray);CHKERRQ(ierr);
2695     ierr = ISColoringCreate(MPI_COMM_SELF,a->B->n,colors,&ocoloring);CHKERRQ(ierr);
2696     ierr = MatSetColoring_SeqAIJ(a->B,ocoloring);CHKERRQ(ierr);
2697     ierr = ISColoringDestroy(ocoloring);CHKERRQ(ierr);
2698   } else {
2699     SETERRQ1(1,"No support ISColoringType %d",coloring->ctype);
2700   }
2701 
2702   PetscFunctionReturn(0);
2703 }
2704 
2705 #undef __FUNCT__
2706 #define __FUNCT__ "MatSetValuesAdic_MPIAIJ"
2707 PetscErrorCode MatSetValuesAdic_MPIAIJ(Mat A,void *advalues)
2708 {
2709   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2710   PetscErrorCode ierr;
2711 
2712   PetscFunctionBegin;
2713   ierr = MatSetValuesAdic_SeqAIJ(a->A,advalues);CHKERRQ(ierr);
2714   ierr = MatSetValuesAdic_SeqAIJ(a->B,advalues);CHKERRQ(ierr);
2715   PetscFunctionReturn(0);
2716 }
2717 
2718 #undef __FUNCT__
2719 #define __FUNCT__ "MatSetValuesAdifor_MPIAIJ"
2720 PetscErrorCode MatSetValuesAdifor_MPIAIJ(Mat A,PetscInt nl,void *advalues)
2721 {
2722   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2723   PetscErrorCode ierr;
2724 
2725   PetscFunctionBegin;
2726   ierr = MatSetValuesAdifor_SeqAIJ(a->A,nl,advalues);CHKERRQ(ierr);
2727   ierr = MatSetValuesAdifor_SeqAIJ(a->B,nl,advalues);CHKERRQ(ierr);
2728   PetscFunctionReturn(0);
2729 }
2730 
2731 #undef __FUNCT__
2732 #define __FUNCT__ "MatMerge"
2733 /*@C
2734       MatMerge - Creates a single large PETSc matrix by concatinating sequential
2735                  matrices from each processor
2736 
2737     Collective on MPI_Comm
2738 
2739    Input Parameters:
2740 +    comm - the communicators the parallel matrix will live on
2741 .    inmat - the input sequential matrices
2742 .    n - number of local columns (or PETSC_DECIDE)
2743 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
2744 
2745    Output Parameter:
2746 .    outmat - the parallel matrix generated
2747 
2748     Level: advanced
2749 
2750    Notes: The number of columns of the matrix in EACH processor MUST be the same.
2751 
2752 @*/
2753 PetscErrorCode MatMerge(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
2754 {
2755   PetscErrorCode    ierr;
2756   PetscInt          m,N,i,rstart,nnz,I,*dnz,*onz;
2757   const PetscInt    *indx;
2758   const PetscScalar *values;
2759   PetscMap          columnmap,rowmap;
2760 
2761   PetscFunctionBegin;
2762     ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
2763   /*
2764   PetscMPIInt       rank;
2765   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2766   ierr = PetscPrintf(PETSC_COMM_SELF," [%d] inmat m=%d, n=%d, N=%d\n",rank,m,n,N);
2767   */
2768   if (scall == MAT_INITIAL_MATRIX){
2769     /* count nonzeros in each row, for diagonal and off diagonal portion of matrix */
2770     if (n == PETSC_DECIDE){
2771       ierr = PetscMapCreate(comm,&columnmap);CHKERRQ(ierr);
2772       ierr = PetscMapSetSize(columnmap,N);CHKERRQ(ierr);
2773       ierr = PetscMapSetType(columnmap,MAP_MPI);CHKERRQ(ierr);
2774       ierr = PetscMapGetLocalSize(columnmap,&n);CHKERRQ(ierr);
2775       ierr = PetscMapDestroy(columnmap);CHKERRQ(ierr);
2776     }
2777 
2778     ierr = PetscMapCreate(comm,&rowmap);CHKERRQ(ierr);
2779     ierr = PetscMapSetLocalSize(rowmap,m);CHKERRQ(ierr);
2780     ierr = PetscMapSetType(rowmap,MAP_MPI);CHKERRQ(ierr);
2781     ierr = PetscMapGetLocalRange(rowmap,&rstart,0);CHKERRQ(ierr);
2782     ierr = PetscMapDestroy(rowmap);CHKERRQ(ierr);
2783 
2784     ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
2785     for (i=0;i<m;i++) {
2786       ierr = MatGetRow(inmat,i,&nnz,&indx,PETSC_NULL);CHKERRQ(ierr);
2787       ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
2788       ierr = MatRestoreRow(inmat,i,&nnz,&indx,PETSC_NULL);CHKERRQ(ierr);
2789     }
2790     /* This routine will ONLY return MPIAIJ type matrix */
2791     ierr = MatCreate(comm,m,n,PETSC_DETERMINE,PETSC_DETERMINE,outmat);CHKERRQ(ierr);
2792     ierr = MatSetType(*outmat,MATMPIAIJ);CHKERRQ(ierr);
2793     ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
2794     ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
2795 
2796   } else if (scall == MAT_REUSE_MATRIX){
2797     ierr = MatGetOwnershipRange(*outmat,&rstart,PETSC_NULL);CHKERRQ(ierr);
2798   } else {
2799     SETERRQ1(PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",scall);
2800   }
2801 
2802   for (i=0;i<m;i++) {
2803     ierr = MatGetRow(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
2804     I    = i + rstart;
2805     ierr = MatSetValues(*outmat,1,&I,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
2806     ierr = MatRestoreRow(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
2807   }
2808   ierr = MatDestroy(inmat);CHKERRQ(ierr);
2809   ierr = MatAssemblyBegin(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2810   ierr = MatAssemblyEnd(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2811 
2812   PetscFunctionReturn(0);
2813 }
2814 
2815 #undef __FUNCT__
2816 #define __FUNCT__ "MatFileSplit"
2817 PetscErrorCode MatFileSplit(Mat A,char *outfile)
2818 {
2819   PetscErrorCode    ierr;
2820   PetscMPIInt       rank;
2821   PetscInt          m,N,i,rstart,nnz;
2822   size_t            len;
2823   const PetscInt    *indx;
2824   PetscViewer       out;
2825   char              *name;
2826   Mat               B;
2827   const PetscScalar *values;
2828 
2829   PetscFunctionBegin;
2830   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
2831   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
2832   /* Should this be the type of the diagonal block of A? */
2833   ierr = MatCreate(PETSC_COMM_SELF,m,N,m,N,&B);CHKERRQ(ierr);
2834   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
2835   ierr = MatSeqAIJSetPreallocation(B,0,PETSC_NULL);CHKERRQ(ierr);
2836   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
2837   for (i=0;i<m;i++) {
2838     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
2839     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
2840     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
2841   }
2842   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2843   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2844 
2845   ierr = MPI_Comm_rank(A->comm,&rank);CHKERRQ(ierr);
2846   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
2847   ierr = PetscMalloc((len+5)*sizeof(char),&name);CHKERRQ(ierr);
2848   sprintf(name,"%s.%d",outfile,rank);
2849   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,PETSC_FILE_CREATE,&out);CHKERRQ(ierr);
2850   ierr = PetscFree(name);
2851   ierr = MatView(B,out);CHKERRQ(ierr);
2852   ierr = PetscViewerDestroy(out);CHKERRQ(ierr);
2853   ierr = MatDestroy(B);CHKERRQ(ierr);
2854   PetscFunctionReturn(0);
2855 }
2856 
2857 EXTERN PetscErrorCode MatDestroy_MPIAIJ(Mat);
2858 #undef __FUNCT__
2859 #define __FUNCT__ "MatDestroy_MPIAIJ_SeqsToMPI"
2860 PetscErrorCode MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
2861 {
2862   PetscErrorCode       ierr;
2863   Mat_Merge_SeqsToMPI  *merge;
2864   PetscObjectContainer container;
2865 
2866   PetscFunctionBegin;
2867   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject *)&container);CHKERRQ(ierr);
2868   if (container) {
2869     ierr  = PetscObjectContainerGetPointer(container,(void **)&merge);CHKERRQ(ierr);
2870     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
2871     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
2872     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
2873     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
2874     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
2875     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
2876     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
2877     ierr = PetscMapDestroy(merge->rowmap);CHKERRQ(ierr);
2878     ierr = MatDestroy(merge->C_seq);CHKERRQ(ierr);
2879 
2880     ierr = PetscObjectContainerDestroy(container);CHKERRQ(ierr);
2881     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
2882   }
2883   ierr = PetscFree(merge);CHKERRQ(ierr);
2884 
2885   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
2886   PetscFunctionReturn(0);
2887 }
2888 
2889 #include "src/mat/utils/freespace.h"
2890 #include "petscbt.h"
2891 #undef __FUNCT__
2892 #define __FUNCT__ "MatMerge_SeqsToMPI"
2893 /*@C
2894       MatMerge_SeqsToMPI - Creates a MPIAIJ matrix by adding sequential
2895                  matrices from each processor
2896 
2897     Collective on MPI_Comm
2898 
2899    Input Parameters:
2900 +    comm - the communicators the parallel matrix will live on
2901 .    seqmat - the input sequential matrices
2902 .    m - number of local rows (or PETSC_DECIDE)
2903 .    n - number of local columns (or PETSC_DECIDE)
2904 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
2905 
2906    Output Parameter:
2907 .    mpimat - the parallel matrix generated
2908 
2909     Level: advanced
2910 
2911    Notes:
2912      The dimensions of the sequential matrix in each processor MUST be the same.
2913      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
2914      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
2915 @*/
2916 PetscErrorCode MatMerge_SeqsToMPINumeric(Mat seqmat,Mat mpimat)
2917 {
2918   PetscErrorCode       ierr;
2919   MPI_Comm             comm=mpimat->comm;
2920   Mat_SeqAIJ           *a=(Mat_SeqAIJ*)seqmat->data;
2921   PetscMPIInt          size,rank,taga,*len_s;
2922   PetscInt             N=mpimat->N,i,j,*owners,*ai=a->i,*aj=a->j;
2923   PetscInt             proc,m;
2924   PetscInt             **buf_ri,**buf_rj;
2925   PetscInt             k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
2926   PetscInt             nrows,**buf_ri_k,**nextrow,**nextai;
2927   MPI_Request          *s_waits,*r_waits;
2928   MPI_Status           *status;
2929   MatScalar            *aa=a->a,**abuf_r,*ba_i;
2930   Mat_Merge_SeqsToMPI  *merge;
2931   PetscObjectContainer container;
2932 
2933   PetscFunctionBegin;
2934   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2935   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2936 
2937   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject *)&container);CHKERRQ(ierr);
2938   if (container) {
2939     ierr  = PetscObjectContainerGetPointer(container,(void **)&merge);CHKERRQ(ierr);
2940   }
2941   bi     = merge->bi;
2942   bj     = merge->bj;
2943   buf_ri = merge->buf_ri;
2944   buf_rj = merge->buf_rj;
2945 
2946   ierr   = PetscMalloc(size*sizeof(MPI_Status),&status);CHKERRQ(ierr);
2947   ierr   = PetscMapGetGlobalRange(merge->rowmap,&owners);CHKERRQ(ierr);
2948   len_s  = merge->len_s;
2949 
2950   /* send and recv matrix values */
2951   /*-----------------------------*/
2952   ierr = PetscObjectGetNewTag((PetscObject)merge->rowmap,&taga);CHKERRQ(ierr);
2953   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
2954 
2955   ierr = PetscMalloc((merge->nsend+1)*sizeof(MPI_Request),&s_waits);CHKERRQ(ierr);
2956   for (proc=0,k=0; proc<size; proc++){
2957     if (!len_s[proc]) continue;
2958     i = owners[proc];
2959     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
2960     k++;
2961   }
2962 
2963   ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);
2964   ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);
2965   ierr = PetscFree(status);CHKERRQ(ierr);
2966 
2967   ierr = PetscFree(s_waits);CHKERRQ(ierr);
2968   ierr = PetscFree(r_waits);CHKERRQ(ierr);
2969 
2970   /* insert mat values of mpimat */
2971   /*----------------------------*/
2972   ierr = PetscMalloc(N*sizeof(MatScalar),&ba_i);CHKERRQ(ierr);
2973   ierr = PetscMalloc((3*merge->nrecv+1)*sizeof(PetscInt**),&buf_ri_k);CHKERRQ(ierr);
2974   nextrow = buf_ri_k + merge->nrecv;
2975   nextai  = nextrow + merge->nrecv;
2976 
2977   for (k=0; k<merge->nrecv; k++){
2978     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
2979     nrows = *(buf_ri_k[k]);
2980     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
2981     nextai[k]   = buf_ri_k[k] + (nrows + 1);/* poins to the next i-structure of k-th recved i-structure  */
2982   }
2983 
2984   /* set values of ba */
2985   ierr = PetscMapGetLocalSize(merge->rowmap,&m);CHKERRQ(ierr);
2986   for (i=0; i<m; i++) {
2987     arow = owners[rank] + i;
2988     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
2989     bnzi = bi[i+1] - bi[i];
2990     ierr = PetscMemzero(ba_i,bnzi*sizeof(MatScalar));CHKERRQ(ierr);
2991 
2992     /* add local non-zero vals of this proc's seqmat into ba */
2993     anzi = ai[arow+1] - ai[arow];
2994     aj   = a->j + ai[arow];
2995     aa   = a->a + ai[arow];
2996     nextaj = 0;
2997     for (j=0; nextaj<anzi; j++){
2998       if (*(bj_i + j) == aj[nextaj]){ /* bcol == acol */
2999         ba_i[j] += aa[nextaj++];
3000       }
3001     }
3002 
3003     /* add received vals into ba */
3004     for (k=0; k<merge->nrecv; k++){ /* k-th received message */
3005       /* i-th row */
3006       if (i == *nextrow[k]) {
3007         anzi = *(nextai[k]+1) - *nextai[k];
3008         aj   = buf_rj[k] + *(nextai[k]);
3009         aa   = abuf_r[k] + *(nextai[k]);
3010         nextaj = 0;
3011         for (j=0; nextaj<anzi; j++){
3012           if (*(bj_i + j) == aj[nextaj]){ /* bcol == acol */
3013             ba_i[j] += aa[nextaj++];
3014           }
3015         }
3016         nextrow[k]++; nextai[k]++;
3017       }
3018     }
3019     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
3020   }
3021   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3022   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3023 
3024   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
3025   ierr = PetscFree(ba_i);CHKERRQ(ierr);
3026   ierr = PetscFree(buf_ri_k);CHKERRQ(ierr);
3027 
3028   PetscFunctionReturn(0);
3029 }
3030 
3031 PetscErrorCode MatMerge_SeqsToMPISymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
3032 {
3033   Mat               B_mpi;
3034   PetscErrorCode       ierr;
3035   Mat                  B_mpi;
3036   Mat_SeqAIJ           *a=(Mat_SeqAIJ*)seqmat->data;
3037   PetscMPIInt          size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
3038   PetscInt             **buf_rj,**buf_ri,**buf_ri_k;
3039   PetscInt             M=seqmat->m,N=seqmat->n,i,*owners,*ai=a->i,*aj=a->j;
3040   PetscInt             len,proc,*dnz,*onz;
3041   PetscInt             k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
3042   PetscInt             nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
3043   MPI_Request          *si_waits,*sj_waits,*ri_waits,*rj_waits;
3044   MPI_Status           *status;
3045   MatScalar            *ba;
3046   FreeSpaceList        free_space=PETSC_NULL,current_space=PETSC_NULL;
3047   PetscBT              lnkbt;
3048   Mat_Merge_SeqsToMPI  *merge;
3049   PetscObjectContainer container;
3050 
3051   PetscFunctionBegin;
3052   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3053   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3054 
3055   ierr = PetscNew(Mat_Merge_SeqsToMPI,&merge);CHKERRQ(ierr);
3056   ierr = PetscMalloc(size*sizeof(MPI_Status),&status);CHKERRQ(ierr);
3057 
3058   /* determine the number of messages to send, their lengths */
3059   /*---------------------------------------------------------*/
3060   ierr = PetscMapCreate(comm,&merge->rowmap);CHKERRQ(ierr);
3061   if (m == PETSC_DECIDE) {
3062     ierr = PetscMapSetSize(merge->rowmap,M);CHKERRQ(ierr);
3063   } else {
3064     ierr = PetscMapSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
3065   }
3066   ierr = PetscMapSetType(merge->rowmap,MAP_MPI);CHKERRQ(ierr);
3067   ierr = PetscMalloc(size*sizeof(PetscMPIInt),&len_si);CHKERRQ(ierr);
3068   ierr = PetscMalloc(size*sizeof(PetscMPIInt),&merge->len_s);CHKERRQ(ierr);
3069 
3070   if (m == PETSC_DECIDE) {ierr = PetscMapGetLocalSize(merge->rowmap,&m);CHKERRQ(ierr); }
3071   ierr = PetscMapGetGlobalRange(merge->rowmap,&owners);CHKERRQ(ierr);
3072   len_s  = merge->len_s;
3073 
3074   len = 0;  /* length of buf_si[] */
3075   merge->nsend = 0;
3076   for (proc=0; proc<size; proc++){
3077     len_si[proc] = 0;
3078     if (proc == rank){
3079       len_si[proc] = len_s[proc] = 0;
3080     } else {
3081       len_si[proc] = owners[proc+1] - owners[proc] + 1;
3082       len_s[proc] = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
3083     }
3084     if (len_s[proc]) {
3085       merge->nsend++;
3086       nrows = 0;
3087       for (i=owners[proc]; i<owners[proc+1]; i++){
3088         if (ai[i+1] > ai[i]) nrows++;
3089       }
3090       len_si[proc] = 2*(nrows+1);
3091       len += len_si[proc];
3092     }
3093   }
3094 
3095   /* determine the number and length of messages to receive for ij-structure */
3096   /*-------------------------------------------------------------------------*/
3097   ierr = PetscGatherNumberOfMessages(comm,PETSC_NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
3098   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
3099 
3100   /* post the Irecv of j-structure */
3101   /*-------------------------------*/
3102   ierr = PetscObjectGetNewTag((PetscObject)merge->rowmap,&tagj);CHKERRQ(ierr);
3103   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
3104 
3105   /* post the Isend of j-structure */
3106   /*--------------------------------*/
3107   ierr = PetscMalloc((2*merge->nsend+1)*sizeof(MPI_Request),&si_waits);CHKERRQ(ierr);
3108   sj_waits = si_waits + merge->nsend;
3109 
3110   for (proc=0, k=0; proc<size; proc++){
3111     if (!len_s[proc]) continue;
3112     i = owners[proc];
3113     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
3114     k++;
3115   }
3116 
3117   /* receives and sends of j-structure are complete */
3118   /*------------------------------------------------*/
3119   ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);
3120   ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);
3121 
3122   /* send and recv i-structure */
3123   /*---------------------------*/
3124   ierr = PetscObjectGetNewTag((PetscObject)merge->rowmap,&tagi);CHKERRQ(ierr);
3125   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
3126 
3127   ierr = PetscMalloc((len+1)*sizeof(PetscInt),&buf_s);CHKERRQ(ierr);
3128   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
3129   for (proc=0,k=0; proc<size; proc++){
3130     if (!len_s[proc]) continue;
3131     /* form outgoing message for i-structure:
3132          buf_si[0]:                 nrows to be sent
3133                [1:nrows]:           row index (global)
3134                [nrows+1:2*nrows+1]: i-structure index
3135     */
3136     /*-------------------------------------------*/
3137     nrows = len_si[proc]/2 - 1;
3138     buf_si_i    = buf_si + nrows+1;
3139     buf_si[0]   = nrows;
3140     buf_si_i[0] = 0;
3141     nrows = 0;
3142     for (i=owners[proc]; i<owners[proc+1]; i++){
3143       anzi = ai[i+1] - ai[i];
3144       if (anzi) {
3145         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
3146         buf_si[nrows+1] = i-owners[proc]; /* local row index */
3147         nrows++;
3148       }
3149     }
3150     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
3151     k++;
3152     buf_si += len_si[proc];
3153   }
3154 
3155   ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);
3156   ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);
3157 
3158   ierr = PetscLogInfo((PetscObject)(seqmat),"MatMerge_SeqsToMPI: nsend: %d, nrecv: %d\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
3159   for (i=0; i<merge->nrecv; i++){
3160     ierr = PetscLogInfo((PetscObject)(seqmat),"MatMerge_SeqsToMPI:   recv len_ri=%d, len_rj=%d from [%d]\n",len_ri[i],merge->len_r[i],merge->id_r[i]);CHKERRQ(ierr);
3161   }
3162 
3163   ierr = PetscFree(len_si);CHKERRQ(ierr);
3164   ierr = PetscFree(len_ri);CHKERRQ(ierr);
3165   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
3166   ierr = PetscFree(si_waits);CHKERRQ(ierr);
3167   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
3168   ierr = PetscFree(buf_s);CHKERRQ(ierr);
3169   ierr = PetscFree(status);CHKERRQ(ierr);
3170 
3171   /* compute a local seq matrix in each processor */
3172   /*----------------------------------------------*/
3173   /* allocate bi array and free space for accumulating nonzero column info */
3174   ierr = PetscMalloc((m+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
3175   bi[0] = 0;
3176 
3177   /* create and initialize a linked list */
3178   nlnk = N+1;
3179   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3180 
3181   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
3182   len = 0;
3183   len  = ai[owners[rank+1]] - ai[owners[rank]];
3184   ierr = GetMoreSpace((PetscInt)(2*len+1),&free_space);CHKERRQ(ierr);
3185   current_space = free_space;
3186 
3187   /* determine symbolic info for each local row */
3188   ierr = PetscMalloc((3*merge->nrecv+1)*sizeof(PetscInt**),&buf_ri_k);CHKERRQ(ierr);
3189   nextrow = buf_ri_k + merge->nrecv;
3190   nextai  = nextrow + merge->nrecv;
3191   for (k=0; k<merge->nrecv; k++){
3192     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
3193     nrows = *buf_ri_k[k];
3194     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
3195     nextai[k]   = buf_ri_k[k] + (nrows + 1);/* poins to the next i-structure of k-th recved i-structure  */
3196   }
3197 
3198   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
3199   len = 0;
3200   for (i=0;i<m;i++) {
3201     bnzi   = 0;
3202     /* add local non-zero cols of this proc's seqmat into lnk */
3203     arow   = owners[rank] + i;
3204     anzi   = ai[arow+1] - ai[arow];
3205     aj     = a->j + ai[arow];
3206     ierr = PetscLLAdd(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3207     bnzi += nlnk;
3208     /* add received col data into lnk */
3209     for (k=0; k<merge->nrecv; k++){ /* k-th received message */
3210       if (i == *nextrow[k]) { /* i-th row */
3211         anzi = *(nextai[k]+1) - *nextai[k];
3212         aj   = buf_rj[k] + *nextai[k];
3213         ierr = PetscLLAdd(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
3214         bnzi += nlnk;
3215         nextrow[k]++; nextai[k]++;
3216       }
3217     }
3218     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
3219 
3220     /* if free space is not available, make more free space */
3221     if (current_space->local_remaining<bnzi) {
3222       ierr = GetMoreSpace(current_space->total_array_size,&current_space);CHKERRQ(ierr);
3223       nspacedouble++;
3224     }
3225     /* copy data into free space, then initialize lnk */
3226     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
3227     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
3228 
3229     current_space->array           += bnzi;
3230     current_space->local_used      += bnzi;
3231     current_space->local_remaining -= bnzi;
3232 
3233     bi[i+1] = bi[i] + bnzi;
3234   }
3235 
3236   ierr = PetscFree(buf_ri_k);CHKERRQ(ierr);
3237 
3238   ierr = PetscMalloc((bi[m]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
3239   ierr = MakeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
3240   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
3241 
3242   /* create symbolic parallel matrix B_mpi */
3243   /*---------------------------------------*/
3244   ierr = MatCreate(comm,m,n,PETSC_DETERMINE,PETSC_DETERMINE,&B_mpi);CHKERRQ(ierr);
3245   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
3246   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
3247   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
3248 
3249   ierr = PetscMalloc((len+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr);
3250   ierr = PetscMemzero(ba,(len+1)*sizeof(MatScalar));CHKERRQ(ierr);
3251   for (i=0;i<m;i++) {
3252     k = i + +owners[rank];
3253     bnzi = bi[i+1] - bi[i];
3254     ierr = MatSetValues(B_mpi,1,&k,bnzi,bj+bi[i],ba,INSERT_VALUES);CHKERRQ(ierr);
3255   }
3256   ierr = MatAssemblyBegin(B_mpi,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3257   ierr = MatAssemblyEnd(B_mpi,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3258   ierr = PetscFree(ba);CHKERRQ(ierr);
3259 
3260   B_mpi->ops->destroy  = MatDestroy_MPIAIJ_SeqsToMPI;
3261   merge->bi            = bi;
3262   merge->bj            = bj;
3263   merge->buf_ri        = buf_ri;
3264   merge->buf_rj        = buf_rj;
3265   merge->C_seq         = seqmat;
3266 
3267   /* attach the supporting struct to B_mpi for reuse */
3268   ierr = PetscObjectContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
3269   ierr = PetscObjectContainerSetPointer(container,merge);CHKERRQ(ierr);
3270   ierr = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
3271   *mpimat = B_mpi;
3272 
3273   PetscFunctionReturn(0);
3274 }
3275 
3276 PetscErrorCode MatMerge_SeqsToMPI(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
3277 {
3278   PetscErrorCode   ierr;
3279   int              SeqsToMPI = 0;
3280 
3281   PetscFunctionBegin;
3282   ierr = PetscLogEventRegister(&SeqsToMPI,"MatMerge_SeqsToMPI",MAT_COOKIE);
3283   ierr = PetscLogEventBegin(SeqsToMPI,seqmat,0,0,0);CHKERRQ(ierr);
3284   if (scall == MAT_INITIAL_MATRIX){
3285     ierr = MatMerge_SeqsToMPISymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
3286   }
3287   ierr = MatMerge_SeqsToMPINumeric(seqmat,*mpimat);CHKERRQ(ierr);
3288   ierr = PetscLogEventEnd(SeqsToMPI,seqmat,0,0,0);CHKERRQ(ierr);
3289   PetscFunctionReturn(0);
3290 }
3291 
3292 #undef __FUNCT__
3293 #define __FUNCT__ "MatGetLocalMat"
3294 /*@C
3295      MatGetLocalMat - Creates a SeqAIJ matrix by taking all its local rows
3296 
3297     Collective on Mat
3298 
3299    Input Parameters:
3300 +    A - the matrix
3301 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
3302 -    row, col - index sets of rows and columns to extract (or PETSC_NULL)
3303 
3304    Output Parameter:
3305 .    A_loc - the local sequential matrix generated
3306 
3307     Level: developer
3308 
3309 @*/
3310 PetscErrorCode MatGetLocalMat(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
3311 {
3312   Mat_MPIAIJ        *a=(Mat_MPIAIJ*)A->data;
3313   PetscErrorCode    ierr;
3314 i,start,end,ncols,nzA,nzB,*cmap,imark;
3315   IS                isrowa,iscola;
3316   Mat               *aloc;
3317 
3318   PetscFunctionBegin;
3319   ierr = PetscLogEventRegister(&GetLocalMat,"MatGetLocalMat",MAT_COOKIE);
3320   ierr = PetscLogEventBegin(GetLocalMat,A,0,0,0);CHKERRQ(ierr);
3321   if (!row){
3322     start = a->rstart; end = a->rend;
3323     ierr = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
3324   } else {
3325     isrowa = *row;
3326   }
3327   if (!col){
3328     start = a->cstart;
3329     cmap  = a->garray;
3330     nzA   = a->A->n;
3331     nzB   = a->B->n;
3332     ierr  = PetscMalloc((nzA+nzB)*sizeof(PetscInt), &idx);CHKERRQ(ierr);
3333     ncols = 0;
3334     for (i=0; i<nzB; i++) {
3335       if (cmap[i] < start) idx[ncols++] = cmap[i];
3336       else break;
3337     }
3338     imark = i;
3339     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
3340     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
3341     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,&iscola);CHKERRQ(ierr);
3342     ierr = PetscFree(idx);CHKERRQ(ierr);
3343   } else {
3344     iscola = *col;
3345   }
3346   if (scall != MAT_INITIAL_MATRIX){
3347     ierr = PetscMalloc(sizeof(Mat),&aloc);CHKERRQ(ierr);
3348     aloc[0] = *A_loc;
3349   }
3350   ierr = MatGetSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
3351   *A_loc = aloc[0];
3352   ierr = PetscFree(aloc);CHKERRQ(ierr);
3353   if (!row){
3354     ierr = ISDestroy(isrowa);CHKERRQ(ierr);
3355   }
3356   if (!col){
3357     ierr = ISDestroy(iscola);CHKERRQ(ierr);
3358   }
3359   ierr = PetscLogEventEnd(GetLocalMat,A,0,0,0);CHKERRQ(ierr);
3360   PetscFunctionReturn(0);
3361 }
3362 
3363 #undef __FUNCT__
3364 #define __FUNCT__ "MatGetBrowsOfAcols"
3365 /*@C
3366      MatGetLocalMat - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero col of A
3367 
3368     Collective on Mat
3369 
3370    Input Parameters:
3371 +    A,B - the matrices
3372 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
3373 -    rowb, colb - index sets of rows and columns of B to extract (or PETSC_NULL)
3374 
3375    Output Parameter:
3376 +    rowb, colb - index sets of rows and columns of B to extract
3377 .    brstart - row index of B_seq from which next B->m rows are taken from B's local rows
3378 -    B_seq - the sequential matrix generated
3379 
3380     Level: developer
3381 
3382 @*/
3383 PetscErrorCode MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,PetscInt *brstart,Mat *B_seq)
3384 {
3385   Mat_MPIAIJ        *a=(Mat_MPIAIJ*)A->data,*b=(Mat_MPIAIJ*)B->data;
3386   PetscErrorCode    ierr;
3387   PetscInt          *idx,i,start,ncols,nzA,nzB,*cmap,imark;
3388   IS                isrowb,iscolb;
3389   Mat               *bseq;
3390   int               GetBrowsOfAcols=0;
3391 
3392   PetscFunctionBegin;
3393   if (a->cstart != b->rstart || a->cend != b->rend){
3394     SETERRQ4(PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%d, %d) != (%d,%d)",a->cstart,a->cend,b->rstart,b->rend);
3395   }
3396   ierr = PetscLogEventRegister(&GetBrowsOfAcols,"MatGetBrowsOfAcols",MAT_COOKIE);
3397   ierr = PetscLogEventBegin(GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
3398 
3399   if (scall == MAT_INITIAL_MATRIX){
3400     start = a->cstart;
3401     cmap  = a->garray;
3402     nzA   = a->A->n;
3403     nzB   = a->B->n;
3404     ierr  = PetscMalloc((nzA+nzB)*sizeof(PetscInt), &idx);CHKERRQ(ierr);
3405     ncols = 0;
3406     for (i=0; i<nzB; i++) {
3407       if (cmap[i] < start) idx[ncols++] = cmap[i];
3408       else break;
3409     }
3410     imark = i;
3411     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
3412     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
3413     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,&isrowb);CHKERRQ(ierr);
3414     ierr = PetscFree(idx);CHKERRQ(ierr);
3415     *brstart = imark;
3416     ierr = ISCreateStride(PETSC_COMM_SELF,B->N,0,1,&iscolb);CHKERRQ(ierr);
3417   } else {
3418     if (!rowb || !colb) SETERRQ(PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
3419     isrowb = *rowb; iscolb = *colb;
3420     ierr = PetscMalloc(sizeof(Mat),&bseq);CHKERRQ(ierr);
3421     bseq[0] = *B_seq;
3422   }
3423   ierr = MatGetSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
3424   *B_seq = bseq[0];
3425   ierr = PetscFree(bseq);CHKERRQ(ierr);
3426   if (!rowb){
3427     ierr = ISDestroy(isrowb);CHKERRQ(ierr);
3428   } else {
3429     *rowb = isrowb;
3430   }
3431   if (!colb){
3432     ierr = ISDestroy(iscolb);CHKERRQ(ierr);
3433   } else {
3434     *colb = iscolb;
3435   }
3436   ierr = PetscLogEventEnd(GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
3437   PetscFunctionReturn(0);
3438 }
3439